{"article_id":"1607.02202","section_id":"i","document":"in pulsar magnetosphere , particles are significantly accelerated at the given regions , and emit electromagnetic radiation from radio to @xmath0-ray wavelength . observations by _ fermi gamma - ray space telescope _ have shown that the differential spectra above 200 mev are well described by the power - law functions with an exponential cut - off , and that the cutoff shapes sharper than the simple exponential cutoff are rejected with high significance ( e.g. , * ? ? ? this rules out the near - surface emission proposed in the polar cap cascade model @xcite , which would exhibit a much sharper spectral cut - off due to the attenuation of the magnetic pair - creation . hence , the detected @xmath0-ray pulse emission should originate from the outer region of the magnetosphere , as considered in the outer gap model ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as the current sheet model ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ) .    on the other hand , the region just above the neutron star surface ( nss ) has been considered as the site of the radio pulsed emission ( e.g. , * ? ? the mechanism of pulsar radio emission is established as a coherent process , so that the plasma dynamics near the nss would be strongly related to the emission mechanism ( e.g. , * ? ? ? the two - stream instability is a promising process to create the plasma bunches ( e.g. , * ? ? ? the curvature radiation from the bunches is usually discussed as the mechanism of the coherent radio emission ( e.g. , * ? ? ? in order to investigate the possible instabilities near the nss , we should take into account the non - stationary effects in the plasma flows . the dynamics of the plasma and the electromagnetic field near the nss highly depends on the ratio of the current density parameter along the magnetic field , @xmath2 , to the goldreich - julian ( gj ) value , @xmath3 @xcite , which is characterized by the gj charge density @xmath4 @xcite , where @xmath5 is the stellar angular velocity vector and @xmath6 is the local magnetic field vector . the parameter @xmath2 is regulated by the twist of the magnetic field ( @xmath7 ) imposed by the global stress balance of the pulsar magnetosphere ( e.g. , * ? ? ? * ) . in the polar cap region near the nss , an accelerating electric field spontaneously develops to adjust the current and charge densities to the current density parameter @xmath2 and the gj charge density @xmath8 . in the cases @xmath9 and @xmath10 , outflowing particles from the nss alone can not adjust the current and charge densities to @xmath2 and @xmath8 simultaneously ( e.g. , * ? ? ? in such cases , a significant accelerating electric field develops and causes the copious pair creation . the newly created pairs would screen the accelerating electric field for a temporary period of time ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the back - flowing particles from the outer acceleration region ( oar ) modify the above description of the dynamics near the nss . as a result of discharge at the oar in the magnetosphere ( e.g. , outer gap or current sheet ) , some fraction of charged particles would come back to the nss . such back - flowing particles are actually seen in numerical studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the existence of the back - flow is favorable to explain the observed pulse profiles in the non - thermal soft @xmath0-ray , x - ray and optical wavelengths , whose peaks are not aligned with the gev @xmath0-ray one @xcite . the back - flowing particles have been also considered to heat the nss around the magnetic pole , whose signature is observed as the thermal pulsed emission in soft x - ray band ( e.g. , * ? ? ? the threshold of the occurrence of pair cascade near the nss depends on the contribution of the back - flowing particles to the current and the charge densities @xcite . the outflow from the nss would also affect the dynamics in the oar . the outgoing particles from the nss contribute to the particle injection rate from the inner boundary of the oar ( e.g. , * ? ? ? if an outflow from the nss affects the accelerating electric field in the oar , the current and number densities of the back - flowing particles change , and the resulting particle outflow from the nss may be also modified . through such non - linear interplay between the nss and oar , the global magnetosphere is expected to reach the steady or quasi - steady state ( e.g. , periodic behavior ) . @xcite and @xcite suggest that a non - stationary outer gap model is favored to reproduce sub - exponential cut - off feature in the gev @xmath0-ray spectrum observed with _ fermi_. in order to understand the global behavior of the magnetosphere , we need to link the dynamics of the region above the nss and the oar .    in the first step , we focus on the dynamics of only the restricted region just above the nss for given back - flowing particles . if a steady electric field just above the nss exists , copious electron  positron pairs are produced via electromagnetic cascade . such pairs flow into the oar , and may screen out the electric field in the oar . therefore , the electric field just above the nss should be almost screened out to activate the oar . the local simulations have been performed to investigate the particle acceleration and the pair creation processes near the nss @xcite . since the present global simulations are difficult to include the realistic pair - creation process with the actual mass - to - charge ratio @xcite , the local simulations are complementary . in order to link the local region above the nss to the global magnetospheric structures , it is useful to model the properties of the outflowing particles from the nss for arbitrary ratio @xmath11 and the back - flow from the oar . @xcite , @xcite and @xcite performed the local particle simulations to investigate the pair cascade near the nss . in their regimes , a large number density of pairs are supplied to the oar , so that the electric field in the oar is screened by the copious pairs . then , the back - flow from the oar would be suppressed . in this context , the effect of the back - flowing particle has not been investigated in the local particle simulations so far . however , the oar as a source of the back - flowing particles should exist if the pair cascade near the nss fails to supply enough pairs .    in this paper , we study the screening of the accelerating electric field above the nss taking into account the effect of the back - flowing particles from the oar . as we have mentioned above , we consider that the screening of the electric field near the nss is a necessary condition to activate the oar , because too much pair supply from the inner magnetosphere via a strong electric field would choke the oar . the local condition of electric field screening near the nss in the absence of the pair cascade is investigated for a given ratio , @xmath11 , which is imposed in the global magnetospheric structure . in section [ model ] , we introduce our model with a particle outflow from the nss , where the number density and momentum distribution of the back - flowing particles are given as model parameters . in section [ analytic ] , we analytically show the screening condition for the velocity of the plasma flow from the nss in the case where the back - flowing particles are ultra - relativistic ( @xmath1 ) . we see that the development of the accelerating electric field can not be avoided for some combinations of the total current density and the contribution of the back - flowing particles . in section [ numerical ] , we introduce additional components of back - flowing particles , electron  positron pairs with a mildly relativistic temperature . particle - in - cell simulations are performed to investigate the screening conditions near the nss . implications of our results for the pulsar radio emission is discussed in section [ radio ] . we summarize our work in section [ summary ] .","summary":"recent-ray observations suggest that the particle acceleration occurs at the outer region of the pulsar magnetosphere . the magnetic field lines in the outer acceleration region ( oar ) are connected to the neutron star surface ( nss ) . if copious electron  positron pairs are produced near the nss , such pairs flow into the oar and screen the electric field there . to activate the oar , the electromagnetic cascade due to the electric field near the nss should be suppressed . however , since a return current is expected along the field lines through the oar , the outflow extracted from the nss alone can not screen the electric field just above the nss . in this paper , we analytically and numerically study the electric - field screening at the nss taking into account the effects of the back - flowing particles from the oar . in certain limited cases , the electric field is screened without significant pair cascade if only ultrarelativistic particles ( ) flow back to the nss . on the other hand , if electron  positron pairs with a significant number density and mildly relativistic temperature , expected to distribute in a wide region of the magnetosphere , flow back to the nss , these particles adjust the current and charge densities , so that the electric field can be screened without pair cascade . we obtain the condition for the number density of particles to screen the electric field at the nss .","abstract":"recent-ray observations suggest that the particle acceleration occurs at the outer region of the pulsar magnetosphere . the magnetic field lines in the outer acceleration region ( oar ) are connected to the neutron star surface ( nss ) . if copious electron  positron pairs are produced near the nss , such pairs flow into the oar and screen the electric field there . to activate the oar , the electromagnetic cascade due to the electric field near the nss should be suppressed . however , since a return current is expected along the field lines through the oar , the outflow extracted from the nss alone can not screen the electric field just above the nss . in this paper , we analytically and numerically study the electric - field screening at the nss taking into account the effects of the back - flowing particles from the oar . in certain limited cases , the electric field is screened without significant pair cascade if only ultrarelativistic particles ( ) flow back to the nss . on the other hand , if electron  positron pairs with a significant number density and mildly relativistic temperature , expected to distribute in a wide region of the magnetosphere , flow back to the nss , these particles adjust the current and charge densities , so that the electric field can be screened without pair cascade . we obtain the condition for the number density of particles to screen the electric field at the nss . we also find that in ion - extracted case from the nss , bunches of particles are ejected to the outer region quasi - periodically , which is a possible mechanism of observed radio emission ."}
{"article_id":"1507.03789","section_id":"i","document":"let @xmath2 be a smooth function defined in a convex body @xmath3 . let @xmath4 in @xmath5 . a classical steepest descent curve of @xmath2 is a rectifiable curve @xmath6 solution to @xmath7 classical steepest descent curves are the integral curves of a unit field normal to the sublevel sets of the given function @xmath2 . we are interested in steepest descent curves that are integral curves to a unit field normal to the family @xmath8 of the sublevel sets for a quasi convex function @xmath2 ( see definition [ defstratifications ] ) ; @xmath9 will be called a quasi convex family as in @xcite . sharp bounds about the length of the steepest descent curves for a quasi convex family , have been proved in @xcite,@xcite,@xcite . the geometry of these curves , equivalent definitions , related questions and generalizations have been studied in @xcite , @xcite , @xcite , @xcite , @xcite .    in the above works , it has beeen proved that _ steepest descent curves for a quasi convex family _ ( sdc ) can be characterized as bounded oriented rectifiable curves @xmath10 , with a locally lipschitz continuous parameterization @xmath11 satisfying @xmath12 @xmath13 is the scalar product in @xmath14 . let an ordering @xmath15 be chosen on @xmath16 , according to the orientation ; let us denote @xmath17 the curves @xmath16 satisfying are sdc for the related quasi convex family @xmath18 , where @xmath19 denotes the convex hull of the set @xmath20 . the sdc could also be chacterized in an equivalent way as _ self - distancing curves _ , namely oriented ( @xmath21 ) continuous curves with the property that the distance of @xmath22 to an arbitrarily fixed previous point @xmath23 is not decreasing : @xmath24 in @xcite self - distancing curves are called self - expanding curves . with the opposite orientation these curves have been also introduced , studied and called self - approaching curves ( see @xcite ) , or self - contracting curves ( see @xcite ) . an important property that will be used later is the property of distancing from a set @xmath20 :    [ defseca ] given a set @xmath20 , an absolutely continuous curve @xmath16 , @xmath11 has the distancing from @xmath20 property if it satisfies @xmath25    steepest descent curves ( or self - distancing curves ) @xmath16 that also satisfy the above property with respect to a convex set @xmath0 will be called @xmath26 . of course if @xmath16 is a sdc and @xmath27 then @xmath28 is a @xmath29 .    in the present work we are interested on the behaviour and properties of a * plane * sdc @xmath16 beyond its final point @xmath30 . the principal goal of the paper is to show that conditions or imply constraints for possible extensions of the curve @xmath16 beyond @xmath30 ; these constraints are written as bounding regions for the possible extensions of @xmath31 . let us outline the content of our work . in  2 introductory definitions are given and covering maps for the boundary of a plane convex set , needed for later use , are introduced . in  3 the involutes of the boundary of a plane convex body are introduced and some of their properties are proved .    in  4 plane regions depending on the convex body @xmath32 have been defined ; these regions fence in or fence out the possible extensions of @xmath31 . the boundary of these sets consists of arcs of involutes of convex bodies , constructed in  3 . as an application , in  4.1 the following problem has been studied : given a convex set @xmath0 , @xmath33 , @xmath34 is it possible to construct a @xmath26 joining @xmath35 to @xmath23 ? minimal properties of this connection have been introduced and studied . in  5 sets of points more general than sdc are studied . a set @xmath36 ( not necessarily a curve ) of ordered points satisfying will be called _ self - distancing set _ , see also definition [ defselfexpandinglinearly ] ; with the opposite order , @xmath37 was called self - contracting in @xcite and many properties of these sets , as only subsets of self contracting curves , were there obtained . a natural question arises : does it exist a steepest descent curve @xmath38 ? examples , necessary and/or sufficient conditions are given when @xmath37 consists of a finite or countable number of points @xmath39 and/or steepest descent curves @xmath40 . in the present work the two dimensional case is studied . similar results for the @xmath41 dimensional case are an open problem stated at the end of the work .","summary":"it is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on . the involutes of the boundary of an arbitrary plane convex body are defined and written by their support function . self contracting sets ( with opposite orientation ) are considered , necessary and/or sufficients conditions for them to be subsets of a sdc are proved .    bounding regions to plane steepest descent curves of quasi convex families","abstract":"two dimensional steepest descent curves ( sdc ) for a quasi convex family are considered ; the problem of their extensions ( with constraints ) outside of a convex body is studied . it is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on . these regions are bounded by arcs of involutes of and satisfy many inclusions properties . the involutes of the boundary of an arbitrary plane convex body are defined and written by their support function . extensions sdc of minimal length are constructed . self contracting sets ( with opposite orientation ) are considered , necessary and/or sufficients conditions for them to be subsets of a sdc are proved .    bounding regions to plane steepest descent curves of quasi convex families"}
{"article_id":"1108.4734","section_id":"i","document":"tremendous progress has been made in recent years in the quest to reveal the structure of the nucleon at its deepest levels . traditionally deep - inelastic scattering ( dis ) of leptons has been the primary tool used to study nucleon structure at large values of the four - momentum transfer squared , @xmath3 , where the nucleon s quark and gluon ( or parton ) constituents can be cleanly resolved . here the theoretical tools are well developed , and the nucleon s structure can be conveniently parametrized in terms of universal longitudinal momentum distribution functions of individual quarks and gluons . global analyses of dis and other hard processes have been highly successful in correlating data over a wide range of kinematics , producing fits of parton distribution functions ( pdfs ) to next - to - leading order ( in the strong coupling parameter @xmath4 ) accuracy and beyond @xcite . while the perturbative domain of large @xmath3 and small parton momentum fraction @xmath5 has received considerable attention both experimentally and theoretically , the region of large @xmath5 and low @xmath3 ( @xmath6  gev@xmath7 ) , where nonperturbative effects play a greater role , has been relatively poorly explored . this is perhaps not too surprising given the difficulty in reliably computing the various corrections that are needed to describe data in this region . examples of nonperturbative effects that are relevant here include target mass corrections ( tmcs ) associated with finite values of @xmath8 , where @xmath9 is the nucleon mass , higher twist terms arising from long - range nonperturbative multi - parton correlations , and nuclear corrections in experiments involving deuterium or heavier nuclei , which are important at large @xmath5 for any @xmath3 . the large-@xmath5 region has been particularly difficult to access experimentally , especially in high - energy colliders , due to the rapidly falling cross sections as @xmath10 . the most extensive data set available that covers this region has been from experiments at slac @xcite . more recently , progress on this front has been made with dis structure function measurements at jefferson lab , utilizing the high luminosities and duty factors available with the cebaf accelerator . indeed , an impressive body of very high - precision data has now been accumulated over the last decade on various structure functions , including accurate longitudinal  transverse separations needed for model - independent determinations of the @xmath1 and @xmath11 structure functions of protons and nuclei @xcite . future plans at the energy upgraded jefferson lab involve extending the dis measurements to even larger @xmath5 ( @xmath12 ) with planned experiments @xcite to measure the ratio of @xmath13 to @xmath14 quark distributions , as well as search for effects such as charge symmetry violation in pdfs and tests of the standard model in parity - violating dis asymmetries . the new data have the potential to provide strong constraints on pdfs at large @xmath5 , where currently uncertainties remain significant . several recent analyses @xcite have in fact attempted to utilize data at low values of @xmath3 and invariant final state hadron masses @xmath15 . stable fits of leading twist pdfs could be obtained @xcite for @xmath16 down to @xmath17  gev and @xmath18  gev@xmath7 , as long as tmc and higher twist corrections were accounted for . aside from its intrinsic value , better knowledge of pdfs at large @xmath5 may also be important for searches of new physics signals in collider experiments such as at the tevatron or the lhc at large rapidities or for heavy mass particles @xcite , as well as at more central rapidities where uncertainties in large-@xmath5 pdfs at low @xmath3 can , through @xmath3 evolution , affect cross sections at small @xmath5 and large @xmath3 @xcite . the increased kinematic reach of the future high - precision dis measurements calls for a careful evaluation of the relevant nonperturbative corrections in order to unambiguously extract information on leading twist pdfs or new physics signals . the effects that are most amenable to direct computation , in principle , are the tmcs . as discussed by nachtmann @xcite , these effects are in fact associated with leading twist operators ( hence contain no additional information on the nonperturbative parton correlations ) , even though they give rise to @xmath19 corrections , where @xmath20 is the energy transfer . nachtmann further showed that one could generalize the standard operator product expansion ( ope ) of structure function moments to finite @xmath3 such that only operators of a specific twist would appear at a given order in @xmath21 . the resulting target mass corrected structure functions can then be derived through an inverse mellin transformation , as shown by georgi and politzer @xcite ( for a review of tmcs in the ope approach see ref . @xcite ) . later an alternative formulation in terms of collinear factorization ( cf ) was used by ellis , furmanski and petronzio @xcite to derive tmcs including the effects of off - shell partons and parton transverse motion . while the ope and cf formulations yield identical results for leading twist pdfs , they differ in the details of how the target mass corrections are manifested at finite @xmath3 . other versions of tmcs were subsequently derived @xcite within the cf formalism using various assumptions about the intrinsic properties of partons and higher twist contributions , leading to rather large differences in some cases @xcite . some of the phenomenological implications of the different tmc prescriptions were discussed in refs . @xcite , including differences between leading order and next - to - leading order ( nlo ) results ; however , the effects on observables have not been systematically investigated . we do so in this paper .    in sec . [ sec : tmc ] we summarize the main results for tmcs in the ope and various cf formulations for the @xmath22 , @xmath1 , @xmath23 and @xmath11 structure functions at nlo , and illustrate the differences numerically . implications for various observables are discussed in sec . [ sec : obs ] , including the ratio of neutron to proton @xmath1 structure functions , which constrain the @xmath24 pdf ratio at large @xmath5 , longitudinal to transverse cross section ratios @xmath25 , and parity - violating ( pv ) dis asymmetries on the proton and deuteron which are sensitive to @xmath2 interference structure functions . we also quantify the effects of perturbative nlo corrections on the @xmath26 ratio for the @xmath2 interference , about which nothing is known empirically , and of nuclear effects on the deuteron pv asymmetries . some finite-@xmath3 effects on pv asymmetries were investigated previously in ref . @xcite , and higher - twists in deuteron pv asymmetries in refs . @xcite . finally , in sec . [ sec : conc ] we draw some conclusions and outline possible extensions of this work .","summary":"we assess the impact of each of these on a number of observables , such as the neutron to proton structure function ratio , and parity - violating electron scattering asymmetries for protons and deuterons which are sensitive to interference effects . the corrections from higher order radiative and nuclear effects on the parity - violating deuteron asymmetry are also quantified .","abstract":"we perform a comprehensive analysis of target mass corrections ( tmcs ) to spin - averaged structure functions and asymmetries at next - to - leading order . several different prescriptions for tmcs are considered , including the operator product expansion , and various approximations to it , collinear factorization , and-scaling . we assess the impact of each of these on a number of observables , such as the neutron to proton structure function ratio , and parity - violating electron scattering asymmetries for protons and deuterons which are sensitive to interference effects . the corrections from higher order radiative and nuclear effects on the parity - violating deuteron asymmetry are also quantified ."}
{"article_id":"1108.4734","section_id":"c","document":"with the increased precision and kinematic reach of new experiments planned in the next few years , particularly at jefferson lab with its 12  gev upgrade , the need for reliable theoretical tools with which to analyze the data is becoming ever more pertinent . this is especially true for data that will be taken at large values of @xmath5 , where a number of different subleading effects come to the fore . in this work we have performed a comprehensive analysis of one class of such corrections , namely those associated with finite values of @xmath223 , or target mass corrections . we have detailed several approaches to tmcs , including the standard ope method , as well as prescriptions based on collinear factorization , and have compared their effects on various spin - averaged structure functions at next - to - leading order .    for the tmcs computed via the ope , we find that the @xmath21 and @xmath67 approximations to the full results are accurate only up to @xmath224 , beyond which the series displays rather slow convergence . such an expansion has been proposed to avoid the threshold problem at @xmath54 ; our findings suggest , however , that a low order expansion may not be applicable as @xmath10 . numerically , we find that tmcs in the ope approach are very similar to those computed via the efp implementation of collinear factorization , especially for the vector structure functions @xmath22 ( or @xmath11 ) and @xmath1 . this can be demonstrated analytically , through the equality to order @xmath21 of the prefactors associated with the leading terms . the comparative phenomenology of these prescriptions has not previously been addressed in the literature . similarly , the @xmath0-scaling and aq prescriptions , which are derived from different approximations within the collinear factorization framework , yield corrected structure functions that closely track each other over much of the @xmath5 range accessible experimentally . in all cases the magnitude of the tmcs , and in particular their model dependence is , not surprisingly , significantly more important at low @xmath3 values ( @xmath225  gev@xmath7 ) . target mass corrections are suppressed with increasing @xmath3 , although even at @xmath193  gev@xmath7 they are not negligible for some observables at very large @xmath5 . the greatest model dependence of tmcs arises for the longitudinal structure function , where because of the mixing between the @xmath11 and @xmath1 structure functions the effects for the ope and efp prescriptions are significantly larger than for the aq and @xmath0-scaling approaches , where no mixing occurs . in addition to quantifying the impact of tmcs on structure functions , we further discussed the limitations these place on unambiguously extracting information on pdfs ( such as the @xmath24 ratio or charge symmetry violation ) from observables . for the ratio @xmath132 of neutron to proton @xmath1 structure functions we make the interesting observation that at low @xmath3 not only is one subject to greater tmc uncertainties than at large @xmath3 , but the @xmath148 rescaling due to tmcs effectively also decreases the sensitivity to the @xmath24 ratio at large @xmath5 that measurements of @xmath132 attempt to constrain .    for parity - violating dis from the proton , the effects of tmcs and perturbative nlo radiative corrections are similar in both the electromagnetic and @xmath2 interference lt ratios @xmath153 and @xmath26 , with @xmath156 differences for @xmath101  gev@xmath7 at intermediate and larger @xmath5 . for the deuteron the differences between @xmath153 and @xmath26 are smaller in the valence quark dominated region , with negligible dependence on the tmc prescription , but become larger at very small @xmath5 ( @xmath226 and 4% at @xmath101 and 10  gev@xmath7 , respectively ) through gluonic contributions at nlo . the magnitude of tmcs in the @xmath26 ratio itself , however , is significant at large @xmath5 , especially for the ope and efp prescriptions . we also considered the effects of nuclear corrections in the deuteron on the @xmath2 lt ratio , which become important for @xmath227 ; however , the similarity of these with the effects on the electromagnetic lt ratio leads to nuclear corrections largely canceling in the pvdis asymmetry . the effects of tmcs on the parity - violating asymmetries themselves are generally rather small , especially at higher @xmath3 values , @xmath193  gev@xmath7 , although at lower @xmath3 some residual tmc dependence is evident in the case of the proton asymmetry . measurements of the proton pvdis asymmetry are planned to provide a unique combination of pdfs in order to constrain the @xmath24 ratio at large @xmath5 @xcite . for the deuteron , the size of tmcs is about an order of magnitude smaller than the expected csv effects in pdfs , which are estimated to be at the @xmath228 level . on the other hand , while the corrections to the lt ratios and asymmetries computed here have been perturbative , nonperturbative effects such as those associated with nonzero parton transverse momentum in the nucleon can produce additional strength in the longitudinal structure functions @xcite . this may be particularly relevant for the ratio @xmath26 , whose phenomenology is essentially unknown at low @xmath3 . estimates of nonperturbative contributions to @xmath26 would therefore be necessary before making more definitive conclusions about its role in pvdis .    in the future , additional effects not discussed here may need to be considered at large @xmath5 , principal among which are dynamical higher twist corrections associated with nonperturbative multi - parton correlations . these are very difficult to compute from first principles , and only rudimentary model estimates have been available to date . further insight into the relation between tmcs and higher twists may also shed light on the threshold problem , whereby the target mass corrected structure functions remain finite at the nucleon elastic scattering point , @xmath54 , as well as on the difference between the various tmc prescriptions . other corrections that may affect future analysis of large-@xmath5 data are threshold resummations , which involve formally summing , to all orders in @xmath4 , terms containing logarithms of @xmath229 that become large as @xmath10 . the results on the phenomenology of the target mass corrections contained in the present work should provide a benchmark for future theoretical and experimental investigations of these additional corrections . this analysis can also be extended to the spin - dependent sector @xcite , where the phenomenology of the collinear factorization framework in particular has not been as fully developed .","summary":"we perform a comprehensive analysis of target mass corrections ( tmcs ) to spin - averaged structure functions and asymmetries at next - to - leading order .","abstract":"we perform a comprehensive analysis of target mass corrections ( tmcs ) to spin - averaged structure functions and asymmetries at next - to - leading order . several different prescriptions for tmcs are considered , including the operator product expansion , and various approximations to it , collinear factorization , and-scaling . we assess the impact of each of these on a number of observables , such as the neutron to proton structure function ratio , and parity - violating electron scattering asymmetries for protons and deuterons which are sensitive to interference effects . the corrections from higher order radiative and nuclear effects on the parity - violating deuteron asymmetry are also quantified ."}
{"article_id":"astro-ph0205210","section_id":"c","document":"with our new approach to describe line driven stellar winds at extremely low metallicity we were able to make first predictions of stellar wind properties , ionizing fluxes and synthetic spectra of a possible population of very massive stars in this range of metallicity @xmath1 . we have demonstrated that the normal scaling laws , which predict stellar - mass loss rates and wind momenta to decrease as a power law with @xmath1 break down at a certain threshold and we have replaced the power - law by a different fit - formula . we were able to disentangle the effects of line - blocking and line - blanketing on the ionizing fluxes and found that while the number of photons able to ionize hydrogen and neutral helium is barely affected by metallicity ( and stellar luminosity ) , there is a significant increase of the photons which can ionize oii , neii , ciii , with decreasing metallicity , the effect being strongest for those ionic species with ionization edges closest to the heii absorption edge . the heii ionizing photons are very strongly affected by metallicity ( and luminosity ) through the strengths of stellar winds . we also calculated synthetic spectra and were able to present for the first time predictions of uv spectra of very massive stars at extremely low metallicities . from these calculations we learned that the presence of stellar winds leads to observable broad spectral line features , which might be used for spectral diagnostics , should such an extreme stellar population be detected at high redshift . we find these first steps very encouraging to proceed with our calculations towards a number of improvements and extensions in the future . so far , our stellar parameters have been chosen from simple scaling relations and not from consistent stellar interior and evolution calculations . while this was certainly sufficient at the beginning to find out what the basic effects are , we need to remove this deficiency in a next step to become more quantitative . we also have to increase the range of effective temperatures , since the zero age main sequences of very massive stars are shifted beyond 60000k for metallicities as low as in this paper ( @xcite , @xcite , @xcite , @xcite ) . in this way , we will be able to make improved predictions about the influence of stellar winds on the evolution of very massive stars and on the evolution of galaxies through deposition of matter , radiation , momentum and energy . these improved calculations should also take into account the effects of changes in the chemical abundance pattern of metals . so far , we have adopted relative abundances as in the solar system and have only scaled the total metallicity . however , it is very likely that an early generation of very massive stars will have an abundance pattern substantially different from the sun , in particular with regard to the ratio of @xmath5 to iron group elements . as has been shown by @xcite and @xcite in the case of normal o - stars , this can have a significant influence on the stellar wind properties .    * acknowledgments *    it is a pleasure to thank my former munich university observatory colleagues adi pauldrach , joachim puls and uwe springmann for their active support during the time , when this work was started . volker bromm and avi loeb directed my attention to the important role of very massive stars in the early universe and motivated much of the work done here . special thanks go to fabio bresolin and roberto mendez for careful reading of the manuscript and critical remarks . the detailed and very constructive comments of the referee are gratefully acknowledged .","summary":"the calculations yield mass - loss rates , wind velocities , wind momenta and wind energies as a function of metallicity and can be used to discuss the influence of stellar winds on the evolution of very massive stars in the early universe and on the interstellar medium in the early phases of galaxy formation . it is shown that the normal scaling laws , which predict stellar mass - loss rates and wind momenta to decrease as a power law with metal abundance break down at a certain threshold . the new wind models are therefore also applied to calculate ionizing fluxes and observable spectra of very massive stars as a function of metallicity using the new hydrodynamic , non - lte line - blanketed flux constant model atmosphere code developed by .","abstract":"wind models of very massive stars with metallicities in a range from to 1.0 solar are calculated using a new treatment of radiation driven winds with depth dependent radiative force multipliers and a comprehensive list of more than two million of spectral lines in nlte . the models are tested by a comparison with observed stellar wind properties of o stars in the galaxy and the smc . satisfying agreement is found . the calculations yield mass - loss rates , wind velocities , wind momenta and wind energies as a function of metallicity and can be used to discuss the influence of stellar winds on the evolution of very massive stars in the early universe and on the interstellar medium in the early phases of galaxy formation . it is shown that the normal scaling laws , which predict stellar mass - loss rates and wind momenta to decrease as a power law with metal abundance break down at a certain threshold . analytical fit formulae for mass - loss rates are provided as a function of stellar parameters and metallicity .    ionizing fluxes of hot stars depend crucially on the strengths of their stellar winds , which modify the absorption edges of hydrogen and helium ( neutral and ionized ) and the line blocking in the far uv . the new wind models are therefore also applied to calculate ionizing fluxes and observable spectra of very massive stars as a function of metallicity using the new hydrodynamic , non - lte line - blanketed flux constant model atmosphere code developed by . numbers of ionizing photons for the crucial ionization stages are given . for a fixed effective temperature the he ii ionizing emergent flux depends very strongly on metallicity but also on stellar luminosity . a strong dependence on metallicity is also found for the c iii , ne ii and o ii ionizing photons , whereas the h i and he i ionizing flux is almost independent of metallicity . we also calculate uv spectra for all the models and discuss the behaviour of significant line features as a function of metallicity ."}
{"article_id":"0807.1466","section_id":"i","document":"superconductivity in multiband metals was first investigated theoretically shortly after the bcs theory@xcite . a resurgence of interest in multiband superconductivity has been mostly related to experimental discovery of mgb@xmath1@xcite , and observation of the two s - wave gaps by various techniques@xcite . recent discovery of iron oxypnictides@xcite , a new family of quasi-2d high temperature superconductors , has also attracted enormous theoretical interest to the problem of multiband superconductivity . first principles numerical band structure calculations@xcite show that several bands cross the fermi level in these materials . while the pairing mechanism in iron oxypnictides is not yet clear , several bands are involved in the determination of both normal and superconducting properties@xcite . the existence of multiband energy spectrum@xcite and associated several energy gaps@xcite was also verified experimentally in an older , quasi-2d s - wave superconductor nbse@xmath1 . bcs investigations of multiband superconductivity were restarted@xcite , but were mostly centered around the new physics that arises due to the presence of two separate gaps . the multiband energy spectrum is also present in most unconventional heavy fermion superconductors due to extreme complexity of the band structure of these materials , as indicated by de haas van alfven measurements . for example , gapless superconductivity of abrikosov - gorkov type@xcite was recently observed in thermal conductivity data for la - doped cecoin@xmath2@xcite , as indicated by unusual wiedeman - franz @xmath3 behavior of thermal conductivity at small concentration of la , @xmath4 . the unusual behavior was attributed to the multiband structure@xcite of this material , a d - wave superconductor . theoretical study of multiband superconductivity has not only been motivated by the above compounds . a somewhat modified multiband model is applicable to other new materials@xcite , where a single fermi surface gets spin - split into two pieces with different fermi momenta due to interactions , such as superconductors without center of inversion ( ci)@xcite ( for example , cept@xmath5si@xcite ) , or ferromagnetic superconductors ( uge@xmath1@xcite , zrzn@xmath1@xcite , or urhge@xcite ) . a particular case of ci - symmetry breaking is two - dimensional surface superconductivity@xcite , where two fermi surfaces arise as a result of spin - orbit interaction of rashba form@xcite . the fermi surface will also get spin - split in exchange field , an external magnetic field without orbital effects . theoretically , paramagnetic pair - breaking by exchange field corresponds to the old problem of unbalanced pairing , first studied in the early 60-s@xcite , when the @xmath0 phase diagram for three - dimensional materials in exchange field has first been obtained . orbital effects are almost always present in three dimensions , and even in very anisotropic quasi two - dimensional ( 2d ) materials , unless @xmath6 in magnetic fields parallel to the 2d plane close to clogston paramagnetic limit@xcite . this is , perhaps , the reason why the consequences of the theory have not studied in detail experimentally . a study of thin films in magnetic fields parallel to the surface remains , perhaps , the most promising experimental setup for the observation of unbalanced pairing in superconductors@xcite . a possible observation of the larkin - ovchinnikov - fulde - ferrel ( loff)@xcite has also been reported in some quasi 2d superconductors , such as those based on charge - transfer organic salts of bedt - ttf or et - ion@xcite and the 1 - 1 - 5 family heavy fermion materials@xcite .    while most theoretical studies of superconductivity in multiband compounds concentrated on the mechanism of superconductivity and the effects of several energy gaps on superconducting properties , some recent studies@xcite found that a new class of superfluids could potentially arise in these materials , one that features coexistence of fully gapped and gapless states . for the most part , this class of states was proposed in bose - einstein condensation for different non - identical fermions condensed by an optical trap@xcite , or in high - energy physics@xcite , where the `` breached '' superfluid state appears as a result of pairing between different quarks@xcite in the asymptotically free limit . gapless solutions of this type were previously known , but in most cases were found to be energetically unstable . the first example corresponds to the second unstable solution in the unbalanced pairing problem , and is commonly referred to as sarma state@xcite . the second solution of the gap equation for a superconductor placed in an exchange field was first obtained by green s functions method by baltensperger@xcite and gorkov and rusinov@xcite , where it was found to be energetically unstable . the exact nature of this unstable state , and the existence of unpaired electron- and hole- fermi surfaces was later clarified within bcs theory by sarma and takada@xcite ) . the second example is pairing in a doped ( unbalanced ) excitonic gas , leading to an excitonic condensate@xcite , which is actually the same two - band unbalanced pairing problem as one considered by liu and wilczek@xcite . the solution previously found for this problem takes the form of a magnetically ( ferromagnetically or antiferromagnetically ) polarized gapless state@xcite , and is different from `` interior gap superfluid '' of liu and wilczek . similar to sarma state , this solution is usually unstable with respect to formation of loff state or domains@xcite , although the stability of this magnetic solution has not been fully investigated as a function of masses involved . the third example is the sarma gapless state , which appears in the problem of s - wave pairing in ferromagnetic superconductors@xcite . while it has been claimed@xcite that sarma state is stabilized by the presence of ferromagnetic order , this claim has been debated later@xcite . according to recent work of liu and wilczek , a large difference in effective masses on two fermi surfaces tends to stabilize the `` breached '' superfluid state already within the unbalanced pairing problem@xcite . the main motivation for this paper is a detailed theoretical study of possible new gapless states in multiband superconductors in the presence of exchange magnetic field@xcite , or the multiband unbalanced pairing problem . while certain similarity does exist , the multiband problem is really different@xcite from the unbalanced pairing problem considered in the above cases ; pairing between two different species of fermions ( two different bands ) is usually not a relevant mechanism in multiband superconductors , since the energy difference for the two bands , @xmath7 is much greater than @xmath8 . nevertheless , for a superconductor placed in an external `` exchange '' field the unbalanced pairing problem is recovered . surprisingly , as it was shown in ref.@xcite , the multiband structure often leads to a a stabilization of unusual sarma state on the second band in exchange fields @xmath9 , where @xmath10 is the energy band on the second fermi surface . thus , in quasi-2d superconductors where several bands cross the fermi surface , such as cecoin@xmath2 of 2h - nb@xmath11 , the peculiarities of the @xmath0 phase diagram may not limited to high magnetic fields , where the loff - related phenomena are observed . new singularities and gapless states associated with the gaps on secondary fermi surfaces must arise in _ low _ magnetic fields as well@xcite . they correspond to the appearance of sarma state@xcite on the fermi surface with smaller gap , one that becomes energetically stable due to the presence of the superconducting gap on the other fermi surface . this state is characterized@xcite by the presence of unpaired spin - polarized electrons near the fermi surface of the second band , two open electron- and hole- fermi surfaces , a paramagnetic magnetic moment , and a first - order phase transition that always accompanies the appearance of this unusual state in s - wave multiband superconductors in low magnetic fields@xcite . the paper is organized as follows . in section ii we introduce the multiband model and generalize its known solution in the s - wave case to include effects of gap anisotropy and non s - wave pairing symmetry . we demonstrate that the effective coupling constants can be eliminated in favor of the measurable parameters for multiband superconductors , such as the superconducting transition temperature , @xmath12 , and the ratio of the gap amplitudes and the densities of states on different fermi surfaces . in particular , thermodynamics of multiband superconductors is additive ; the thermodynamic potential @xmath13 is a simple bcs sum over different bands . in section iii we consider the problem of paramagnetic pair - breaking in multiband superconductors and show that a new gapless state is energetically stable in low magnetic fields in some region of model parameters . we investigate the stability and the magnetic properties of this new gapless state in an s - wave two - band superconductor analytically at @xmath14 , and provide the details for the @xmath0 phase diagram and the low temperature critical point that separates the new partially gapless state from fully gapped state . in section iv we present our conclusions .","summary":"we investigate theoretically the properties of s - wave multiband superconductors in the weak coupling ( bcs ) limit in the presence of pair - breaking effects of magnetic field . s - wave multiband superconductors the order of the zero - temperature metamagnetic transition depends on model parameters , and it may take the form of a smooth crossover .","abstract":"we investigate theoretically the properties of s - wave multiband superconductors in the weak coupling ( bcs ) limit in the presence of pair - breaking effects of magnetic field . it is shown that a qualitatively new gapless superconducting state must appear in quasi-2d superconductors in magnetic fields parallel to the plane , corresponding to a sarma state induced on one of the fermi surfaces . the emergence of the new state in s - wave multiband superconductors in the absence of anisotropy or spin - orbit interaction is usually accompanied by a zero - temperature first - order metamagnetic phase transition . for anisotropic or non s - wave multiband superconductors the order of the zero - temperature metamagnetic transition depends on model parameters , and it may take the form of a smooth crossover . the details of the temperature - magnetic field phase diagram for multiband superconductors are investigated analytically at zero temperature and numerically at a finite temperature . it is shown the zero - temperatures first - order phase transition gives rise to a critical region on the phase diagram . we suggest possible experiments to detect the new gapless state ."}
{"article_id":"0807.1466","section_id":"c","document":"let us now briefly summarize our main results . we have performed a detailed calculation of energetically stable homogeneous superconducting states in the unbalanced pairing problem for s - wave multiband superconductors . our analysis shows that this problem differs from one for single - band superconductors , and that qualitatively new partially gapless states may be present in the low temperature region of the @xmath0 phase diagram . the new states are characterized by a gapless fermi spectrum , open fermi surfaces , and a finite paramagnetic magnetic moment . the phase transition between fully gapped and gapless superconducting states in magnetic field at @xmath14 is a metamagnetic first order phase transition , which corresponds to a sharp jump in magnetization on one of the fermi surfaces that becomes gapless . the superconducting order is present on both fermi surfaces , as shown in fig . [ sarmafig ] . at finite low temperatures the metamagnetic first transition results a first order line on the @xmath0 phase diagram that ends in a critical point , as shown in fig.[fig2 ] . the presence of the gapless superconductivity also modifies the high - field clogston limit . while the new state is analogous to the one studied in ref.@xcite , it is not the same . unlike the situation encountered in bose condensation or high energy physics , unbalanced pairing of different species of fermions in superconductors is energetically unfavorable because of the large difference of the corresponding fermi surfaces . pairing in multiband superconductors is associated with each fermi surface separately , although the gaps on different fermi surfaces are related by the interaction . in the weak coupling logarithmic scheme that ratio is temperature- and field - independent . nevertheless , we found that , similar to ref.@xcite , the gapless state is most visible when the superconducting gap on the heavier band is driven by the superconducting transition on the lighter band . strong anisotropy of the @xmath0 diagram , which indicates a quasi-2d nature of 2h - nbse@xmath1 , and its multi - gap superconductivity@xcite makes a case for a possible first order phase transition to a ground state of this type in low magnetic fields parallel to the plane in this material@xcite . an unusual first order phase transition has been indeed observed in this material@xcite for thermal conductivity measurements in low magnetic field @xmath199 parallel to the basal plane . this first order phase transition is inconsistent with explanations involving vortex lattice melting@xcite . the magnetic field at which this transition occurs is consistent with the value of the small energy gap @xmath200 observed in the photoemission experiments@xcite . the low - field first - order phase transition in nbse@xmath1 was found to be strongly anisotropic , and the hysteretic behavior of thermal conductivity disappears for certain field directions@xcite , a behavior not expected in a simple multiband model considered above , where a first order phase transition occurs for all field directions in the basal plane . however , in the presence of cdw the ci symmetry is broken@xcite , which itself has been shown to lead to a strong in - plane anisotropy of the @xmath0 phase diagram@xcite . similar effects must be present for the low - field metamagnetic phase transition as well . gap anisotropy , g - factor anisotropy , and spin - orbit coupling tend to wipe out the first order line on the @xmath0 phase diagram , and turn it in a smooth crossover@xcite . we have recently found that the order of the phase transition in the presence of spin orbit interaction may , too , be dependent on direction . as a result of two different terms in the spin orbit interaction , the first order phase transition becomes very anisotropic . it is present for some field directions and turns into a smooth crossover for other field directions@xcite .    experimental observation of the new gapless state is subject to the usual difficulties associated with the observation of paramagnetic pair breaking and the loff state in superconductors . namely , the orbital effects leading to @xmath6 are almost always present , even in strongly quasi-2d materials in magnetic fields parallel to the 2d planes . perhaps , an ideal realization of this state would be surface superconductivity or superconductivity in thin films in fields parallel to the surface . we note , however , that unlike the loff state , which is difficult to observe , since it quickly disappears in the presence of impurities or orbital effects , the new homogeneous partially gapless state is more robust , and will appear in many multiband strongly quasi-2d s - wave superconductors in the mixed state as well , provided that the upper critical field is close enough to the clogston limit . the details of such first order transition in the mixed state will be similar to the physics considered above . measurements of the specific heat in applied field are the most direct way to observe the low - field first order phase transition in s - wave multiband superconductors , such as 2h - nbse@xmath1@xcite .","summary":"it is shown that a qualitatively new gapless superconducting state must appear in quasi-2d superconductors in magnetic fields parallel to the plane , corresponding to a sarma state induced on one of the fermi surfaces . we suggest possible experiments to detect the new gapless state .","abstract":"we investigate theoretically the properties of s - wave multiband superconductors in the weak coupling ( bcs ) limit in the presence of pair - breaking effects of magnetic field . it is shown that a qualitatively new gapless superconducting state must appear in quasi-2d superconductors in magnetic fields parallel to the plane , corresponding to a sarma state induced on one of the fermi surfaces . the emergence of the new state in s - wave multiband superconductors in the absence of anisotropy or spin - orbit interaction is usually accompanied by a zero - temperature first - order metamagnetic phase transition . for anisotropic or non s - wave multiband superconductors the order of the zero - temperature metamagnetic transition depends on model parameters , and it may take the form of a smooth crossover . the details of the temperature - magnetic field phase diagram for multiband superconductors are investigated analytically at zero temperature and numerically at a finite temperature . it is shown the zero - temperatures first - order phase transition gives rise to a critical region on the phase diagram . we suggest possible experiments to detect the new gapless state ."}
{"article_id":"1502.07533","section_id":"i","document":"the problem we consider here is to compute the exponential of an upper block - triangular , block - toeplitz matrix , that is , a matrix of the kind @xmath0,\\ ] ] where @xmath1 , @xmath2 , are @xmath3 matrices . our interest stems from the analysis in dendievel and latouche  @xcite of the erlangization method for markovian fluid models , but the story goes further back in time . the erlangian approximation method was introduced in asmussen _ @xcite in the context of risk processes ; it was picked up in stanford _ @xcite where a connection is established with fluid queues . other relevant references are stanford _ @xcite where the focus is on modelling the spread of forest fires , and ramaswami _ et al . _ @xcite where some basic algorithms are developed . markovian fluid models are two - dimensional processes @xmath4 where @xmath5 is a markov process with infinitesimal generator @xmath6 on the state space @xmath7 ; to each state @xmath8 is associated a rate of growth @xmath9 and @xmath10 is controlled by @xmath11 through the equation @xmath12 performance measures of interest include the distributions of @xmath10 and of various first passage times . usually , @xmath11 is called the phase of the process at time @xmath13 and @xmath10 its level , and the phase space @xmath14 is partitioned into three subsets @xmath15 , @xmath16 and @xmath17 such that @xmath18 , @xmath19 or @xmath20 if @xmath8 is in @xmath15 , @xmath16 or @xmath17 , respectively . to simplify our presentation without missing any important feature , we assume below that @xmath17 is empty . the first return probabilities of @xmath10 to its initial level @xmath21 play a central role in the analysis of fluid queues . it is customary to define two matrices @xmath22 and @xmath23 of first return probabilities : @xmath24 ,    \\qquad \\mbox{$i \\in { \\mathcal{s}}_+$ , $ j \\in { \\mathcal{s}}_-$,}\\ ] ] and @xmath25 ,    \\qquad \\mbox{$i \\in { \\mathcal{s}}_-$ , $ j \\in { \\mathcal{s}}_+$,}\\ ] ] where @xmath26 is the first passage time to level 0 . thus , the entries of @xmath22 and @xmath27 are the probability of returning to the initial level after having started in the upward , and the downward directions , respectively . if the process starts from some level @xmath28 , then @xmath29   = ( \\begin{bmatrix } i \\\\ \\psi \\end{bmatrix } e^{hx})_{ij } \\qquad \\mbox{$i \\in \\{1 , \\ldots , m\\}$ , $ j \\in { \\mathcal{s}}_-$;}\\ ] ] here , @xmath30 is a square matrix on @xmath31 and is given by @xmath32 where @xmath33 and @xmath34 are submatrices of the generator @xmath6 , indexed by @xmath31 and @xmath35 , respectively , and @xmath36 is a diagonal matrix with @xmath37 on the diagonal . a similar equation holds for @xmath38 . the matrices @xmath22 and @xmath23 are solutions of algebraic riccati equations and their resolution has been the object of much attention . very efficient algorithms are available , and we refer to bini _ et al . _ @xcite and bean _ et al . _ @xcite . the erlangian approximation method is introduced in @xcite to determine the detailed distribution of @xmath39 . the idea is that , to compute the probability @xmath40 , \\qquad \\mbox{$x>0 $ , $ i \\in \\{1 , \\ldots , m\\}$}\\ ] ] for a fixed value @xmath41 , it is convenient to replace @xmath41 by a random variable @xmath42 with an erlang distribution , with parameters @xmath43 for some positive integer @xmath44 . the random variable @xmath42 has expectation @xmath41 and variance @xmath45 , so that @xmath46 is a good approximation of @xmath47 if @xmath44 is large enough . from a computational point of view , the advantage is that one replaces systems of integro - differential equations by linear equations . the long and the short of it is that the original system is replaced by the process @xmath48 with a two - dimensional phase @xmath49 on the state space @xmath50 and with the generator @xmath51 where @xmath52 . the physical interpretation is that the absorbing state 0 is entered at the random time @xmath42 , and the component @xmath53 of the phase marks the progress of time towards @xmath42 . some authors ( for instance @xcite ) report that good approximations may be obtained with small values of @xmath44 .    because of the toeplitz - like structure of @xmath54 , the matrices @xmath22 and @xmath30 are both upper block - triangular block - toeplitz and it is interesting to use the toeplitz structure in order to reduce the cost when @xmath44 is large . this is done in @xcite for the matrix @xmath22 . here we address the question of efficiently computing the exponential matrix @xmath55 for a given value of @xmath56 , where @xmath30 has the structure of . we shall assume without loss of generality that @xmath57 . we recall that the exponential function can be extended to a matrix variable by defining @xmath58 for more details on the matrix exponential and more generally on matrix functions we refer the reader to higham  @xcite . the matrix @xmath59 defined in is of order @xmath60 and it may be huge , since a larger @xmath44 leads to a better erlangian approximation , while the size @xmath61 of the blocks is generally small . the matrix @xmath59 is a subgenerator , i.e. , it has negative diagonal entries , nonnegative off - diagonal entries , and the sum of the entries on each row is nonpositive .    since block - triangular block - toeplitz matrices are closed under matrix multiplication , it follows from that the matrix exponential @xmath62 is also an upper block triangular , block - toeplitz matrix ; in particular , the diagonal blocks of @xmath62 coincide with @xmath63 . moreover , it is known that the matrix @xmath62 is nonnegative and substochastic . the problem of the computation of the exponential of a generator has been considered in xue and ye  @xcite and by shao et al . @xcite , where the authors propose component - wise accurate algorithms for the computation . these algorithms are efficient for matrices of small size . for the erlangian approximation problem , these algorithms are useless for the large size of the matrices involved . recently , some attention has been given to the computation of the exponential of general toeplitz matrices by using arnoldi method ( lee _ et al . _ @xcite , pang and sun  @xcite ) .    in our framework , toeplitz matrices are block - triangular so that they form a matrix algebra . this property is particularly effective for the design of efficient algorithms and we propose some numerical methods that exploit the block - triangular block - toeplitz structure and the generator properties . unlike the general methods , our algorithms allow one to deal with matrices @xmath59 of very large size . two methods rely on spectral and computational properties of block - circulant and block @xmath64-circulant matrices ( bini  @xcite , bini _ et al . _ @xcite ) and on the use of fast fourier transforms ( fft ) . recall that block @xmath64-circulant matrices have the form @xmath65,\\ ] ] and that a block - circulant matrix is a block @xmath64-circulant matrix with @xmath66 . for simplicity , we denote by @xmath67 the block @xmath68-circulant matrix @xmath69 . since block @xmath64-circulant matrices can be block - diagonalized by fft @xcite , the computation of the exponential of an @xmath70 block @xmath64-circulant matrix with @xmath3 blocks can be reduced to the computation of @xmath44 exponentials of @xmath3 matrices . these latter exponentials are independent from each other and can be computed simultaneously with a multi - core architecture at the cost of a single exponential . the idea of the first method is to approximate @xmath62 by @xmath71 where @xmath72 and @xmath73 is sufficiently small . we analyse the error and are thereby able to choose the value of @xmath64 which gives a good balance between the roundoff error and the approximation error . in fact , the approximation error grows as @xmath74 while the roundoff error is @xmath75 , where @xmath76 is the machine precision . this leads to an overall error which is @xmath77 . by using the fact that the solution is real , by choosing @xmath64 a pure imaginary number we get an approximation error @xmath78 which leads to an overall error @xmath79 . since the approximation error is a power series in @xmath64 , we devise a further technique which consists in averaging the solutions computed with @xmath80 different values of @xmath64 . this way , we are able to cancel out the components of the error of degree less than @xmath81 . this leads to a substantial improvement of the precision . moreover , since the different computations are independent from each other , the computational cost in a multicore architecture is independent of @xmath80 .    in our second approach , the matrix @xmath59 is embedded into a @xmath82 block - circulant matrix @xmath83 , where @xmath84 is sufficiently large , and an approximation of @xmath85 is obtained from a suitable submatrix of @xmath86 . the computation of @xmath86 is reduced to the computation of @xmath84 exponentials of @xmath3 matrices , and our error analysis allows one to choose the value of @xmath84 so as to guarantee a given error bound in the computed approximation . the third numerical method consists in specializing the shifting and taylor series method of @xcite . the block - triangular toeplitz structure is exploited in the fft - based matrix multiplications involved in the algorithm , leading to a reduction of the computational cost . the algorithm obtained in this case does not seem well suited for an implementation in a multicore architecture . we compare the three numerical methods , from a theoretical as well as from a numerical point of view . from our analysis , we conclude that the method based on @xmath64-circulant matrices is the fastest and provides a reasonable approximation to the solution . moreover , by applying the averaging technique we can dramatically improve the accuracy . the method based on embedding and the one based on power series perform an accurate computation but are slightly more expensive . it must be emphasised that the use of fft makes the algorithms norm - wise stable but that component - wise stability is not guaranteed . in consequence , the matrix elements with values of modulus below the machine precision may not be well approximated in terms of relative error . the paper is organised as follows . in sections [ sec : der ] and [ sec : fastcomp ] , we recall properties of the exponential of a subgenerator and of its derivatives , and some basic properties of block - toeplitz and block - circulant matrices which are used in our algorithms . in section [ sec : expcirc ] , we show how to compute the exponential of a block @xmath64-circulant matrix by using fast arithmetic based on fft and we perform an error analysis . we present in section [ sec : exptt ] the algorithms to compute the exponential of @xmath59 : first we analyse the decay of off - diagonal entries of the matrix exponential , next we describe the new methods and perform an error analysis . we conclude with numerical experiments in section [ sec : exper ] .","summary":"the erlangian approximation of markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block - triangular , block - toeplitz structure . to this end , we propose some algorithms which exploit the toeplitz structure and the properties of generators .","abstract":"the erlangian approximation of markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block - triangular , block - toeplitz structure . to this end , we propose some algorithms which exploit the toeplitz structure and the properties of generators . such algorithms allow to compute the exponential of very large matrices , which would otherwise be untreatable with standard methods . we also prove interesting decay properties of the exponential of a generator having a block - triangular , block - toeplitz structure .    * keyword * matrix exponential , toeplitz matrix , circulant matrix , markov generator , fluid queue , erlang approximation ."}
{"article_id":"1001.0135","section_id":"i","document":"_ stellar stratification _ is a characteristic phenomenon of star clusters , which has been well documented for more than 50 years . it is directly linked to the dynamical evolution of star clusters @xcite , and specifically to the central concentration of the massive stars as the cluster relaxes dynamically , a phenomenon known as _ mass segregation _ ( for detailed reviews see * ? ? ? * ; * ? ? ? this behavior in massive galactic globular clusters ( ggcs ) is well understood and the observed mass segregation is explained as a result of their dynamical relaxation in a timescale , @xmath1 , much longer than their ages , @xmath2 , as derived from stellar evolutionary models . this _ dynamical _ mass segregation , thus , forces more massive stars to sink inwards to the center of a cluster through weak two - body interactions . however , segregation of massive stars is observed also in young star clusters , such as the @xmath3  30  myr - old cluster ngc  330 in the small magellanic cloud @xcite , or even the @xmath3  1  myr - old galactic starburst ngc  3603 @xcite . such systems , supposedly not sufficiently old to be dynamically relaxed , can not be included in the `` traditional '' picture of dynamical mass segregation as it occurs in ggcs . for these cases the phenomenon has been  rather tentatively  characterized as _ primordial _ mass segregation , based on the suggestion that this stellar stratification is due to the formation of the stars in , or near , the central part of the clusters rather than being dynamically driven    mass segregation at early stages of clustered star formation is indeed predicted by theoretical studies , which suggest that the positions of massive stars for rich young clusters of @xmath4 can not be the result of dynamical evolution @xcite . moreover , the appearance of gas in such clusters reduces further the efficiency of any dynamically driven mass segregation . according to theory , massive protostars can be formed _ at the central part _ of the protocluster through cohesive collisions and dissipative merging of cloudlets , which lead to extensive mass segregation and energy equipartition among them @xcite , or through accretion from a distributed gaseous component in the cluster , which leads to mass segregation since stars located near the gravitational center of the cluster benefit from the attraction of the full potential and accrete at higher rates than other stars @xcite . both of the aforementioned massive star formation mechanisms predict primordial mass segregation through early dynamical processes at the central part of the protocluster . the significant difference of these processes from the subsequent energy equipartition of the stars in the formed cluster is that the latter , and consequently dynamical mass segregation , is independent of the initial cluster conditions , while the former , and therefore primordial mass segregation , is directly connected to these conditions . in order to achieve a complete understanding of the phenomenon of primordial mass segregation , many related studies are focused on clusters at very early stages of their formation , including a variety of types of stellar systems from loose stellar associations and open clusters to compact massive starbursts .    the magellanic clouds ( mcs ) , being extremely rich in young star clusters ( e.g. , * ? ? ? * ; * ? ? ? * ) , offer an outstanding sample of intermediate type of stellar systems , specifically compact young star clusters , which are not available in the galaxy . in such clusters primordial mass segregation can be sufficiently observed from ground - based observations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and they are also suitable for more detailed studies of this phenomenon from space with the high - resolving efficiency of the _ hubble space telescope _ ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? such studies contribute significantly to the debate about the phenomenon of primordial mass segregation and its origin which which is still ongoing ( see , e.g. , * ? ? ? it is interesting to note that while the existence of the phenomenon itself is being questioned @xcite , new methods are still being designed for its comprehensive identification and quantification ( e.g. , * ? ? ? * ) .    in the first part of our study of stellar stratification we developed and tested a new robust diagnostic method aimed at establishing the presence ( or not ) of this phenomenon in a cluster ( * ? * from here on paper  i ) . this method is based on the calculation of the mean - square radius , the so - called _ effective radius _ , of the stars in a cluster for different magnitude ranges , and the investigation of the dependence of the effective radii of each stellar species on magnitude as indication of stellar stratification in the cluster .    , scaledwidth=45.0% ]      stellar stratification affects the presently observable physical properties of the star cluster , and thus diagnostic tools for the identification of the phenomenon are based on the detection of mass- or brightness - dependent changes of such properties . previously established methods involve ( i ) the study of the projected stellar density distribution of stars of different magnitudes ; here , the differences in the exponents of the slopes fitted are seen as proof of mass segregation ( e.g. , * ? ? ? * ) , ( ii ) the radial dependence of the luminosity or mass function ( lf , mf ) slope ; a gradient of this slope outwards from the center of the cluster indicates stratification ( e.g. , * ? ? ? * ) , and ( iii ) the variance of the core radius of the cluster as estimated for stars in specific magnitude ( or mass ) groups ; a trend of this variance with brightness ( or mass ) signifies stratification ( e.g. , * ? ? ? while these methods can provide useful information about the segregation in a cluster , all of them are sensitive to model assumptions , since they strongly depend on data fitting for parametrizing stellar stratification ; i.e. , functional expressions for the surface density profiles , or the mfs and lfs are required for the derivation of their slopes and core radii . our method , developed in paper  i for assessment of stellar stratification in star clusters , is based on the notion of the dynamically stable _ spitzer radius _ of a star cluster , defined as the mean - square distance of the stars from the center of the cluster ( e.g. , * ? ? ? the observable counterpart of this radius , the effective radius , is given by the expression : @xmath5 where @xmath6 is the projected radial distance of the @xmath7th stellar member of the cluster in a specific brightness range and @xmath8 the corresponding total number of stars in the same brightness range . different calculations of the effective radius are performed , each for stars in different brightness ranges that cover the whole observed stellar luminosity function of the cluster . the simple application of this method can yield direct information about the spatial extent ( radial distribution ) of stellar groups in different magnitude ( mass ) ranges . in a star cluster , where stratification occurs , the segregated brighter stars are expected to be more centrally concentrated and the corresponding effective radius should be shorter than that of the non - segregated fainter stars . as a consequence , stellar stratification can be observed from the dependence of the effective radius of stars in specific magnitude ( mass ) ranges on the corresponding mean magnitude ( mass ) . this method is sufficiently described and tested in paper  i , where we show that it performs efficiently in the detection of stellar stratification , provided that the incompleteness of the photometry has been accurately measured and the contamination by the field population has been thoroughly removed . our diagnosis method is also independent of any model or theoretical prediction , in contrast to those used thus far for the detection of mass segregation . ccccccc [ t : obs ] ngc  1983 & 05@xmath927@xmath104492 & @xmath116859070 & f555w & j8ne68req & 20 & october 7 , 2003 + & & & f814w & j8ne68riq & 20 & october 7 , 2003 + ngc  2002 & 05@xmath930@xmath102080 & @xmath116655023 & f555w & j8ne70b5q & 20 & august 23 , 2003 + & & & f814w & j8ne70b7s & 20 & august 23 , 2003 + ngc  2010 & 05@xmath930@xmath103489 & @xmath117049083 & f555w & j8ne71r5q & 20 & october 7 , 2003 + & & & f814w & j8ne71r9q & 20 & october 7 , 2003 +    in this second part of our study of stellar stratification we apply the effective radius method on deep imaging data obtained with the wide - field channel ( wfc ) of the _ advanced camera for surveys _ ( acs ) onboard the hubble space telescope ( hst ) of three young star clusters in the large magellanic cloud ( lmc ) for the investigation of primordial mass segregation in them . young clusters in the magellanic clouds are quite different to each other , so that their study requires the detailed treatment of each cluster individually ( see , e.g. ,   [ s : dynamics ] , [ s : starcont ] ) , and therefore a statistical investigation of the phenomenon of mass segregation in a large sample of such clusters is not yet meaningful . the purpose of the present study is the detailed investigation with the use of a consistent method of individual selected clusters , in order to establish a comprehensive comparative framework for the assessment of mass segregation in young lmc clusters . the objects of interest , clusters ngc  1983 , ngc  2002 and ngc  2010 , are selected among others also observed with acs due to their youthfulness and the variety in their characteristics . this selection is made in order to include in this comparative study clusters , which are very different from each other . in  [ s : clussampl ] we describe the considered sample of lmc clusters and the corresponding data sets , as well as their reduction and photometry . we study the dynamical status of the clusters and discuss their structural parameters in  [ s : dynamics ] , and in   [ s : starcont ] we present the observed stellar populations , the decontamination of the stellar samples from the contribution of the local background field of the lmc and the stellar content of the clusters . the application of the diagnostic method is performed for all three clusters in   [ s : methappl ] , where we also develop a comparative scheme for the quantification of stellar stratification among different clusters , and we discuss our results . we conclude on them in   [ s : concl ] .    , scaledwidth=45.0% ]","summary":"we present a comprehensive study of stellar stratification in young star clusters in the large magellanic cloud ( lmc ) . we apply our recently developed _ effective radius method _ for the assessment of stellar stratification on imaging data obtained with the advanced camera for surveys of three young lmc clusters to characterize the phenomenon and develop a comparative scheme for its assessment in such clusters . our photometry is complete for magnitudes down to  mag , allowing the calculation of the structural parameters of the clusters , the estimation of their ages and the determination of their stellar content . our study shows that each cluster in our sample demonstrates stellar stratification in a quite different manner and at different degree from the others . our method on ngc  2002 provides evidence of _ strong _ stellar stratification for both bright and faint stars ; the cluster demonstrates the phenomenon with the highest degree in the sample .","abstract":"we present a comprehensive study of stellar stratification in young star clusters in the large magellanic cloud ( lmc ) . we apply our recently developed _ effective radius method _ for the assessment of stellar stratification on imaging data obtained with the advanced camera for surveys of three young lmc clusters to characterize the phenomenon and develop a comparative scheme for its assessment in such clusters . the clusters of our sample , ngc  1983 , ngc  2002 and ngc  2010 , are selected on the basis of their youthfulness , and their variety in appearance , structure , stellar content , and surrounding stellar ambient . our photometry is complete for magnitudes down to  mag , allowing the calculation of the structural parameters of the clusters , the estimation of their ages and the determination of their stellar content . our study shows that each cluster in our sample demonstrates stellar stratification in a quite different manner and at different degree from the others . specifically , ngc  1983 shows to be _ partially _ segregated with the effective radius increasing with fainter magnitudes only for the faintest stars of the cluster . our method on ngc  2002 provides evidence of _ strong _ stellar stratification for both bright and faint stars ; the cluster demonstrates the phenomenon with the highest degree in the sample . finally , ngc  2010 is _ not segregated _ , as its bright stellar content is not centrally concentrated , the relation of effective radius to magnitude for stars of intermediate brightness is rather flat , and we find no evidence of stratification for its faintest stars . for the parameterization of the phenomenon of stellar stratification and its quantitative comparison among these clusters , we propose the slope derived from the change in the effective radius over the corresponding magnitude range as indicative parameter of the _ degree of stratification _ in the clusters . a positive value of this slope indicates mass segregation in the cluster , while a negative or zero value signifies the lack of the phenomenon ."}
{"article_id":"1001.0135","section_id":"c","document":"we present a coherent comparative investigation of stellar stratification in three young lmc clusters with the application of a robust method for the assessment of this phenomenon on deep hst imaging . in a cluster where stellar stratification occurs , the segregated brighter stars are expected to be more centrally concentrated than the non - segregated fainter stars . stellar stratification can , thus , be investigated from the dependence of the radial extent of stars in specific magnitude ( mass ) ranges on the corresponding mean magnitude ( mass ) . according to this notion , in paper  i @xcite we developed and verified the efficiency of a robust method for the assessment of stellar stratification in star clusters . this method is based on the calculation of the mean - square radius , the _ effective radius _ @xmath110 , of stars in different magnitude ranges , and the investigation of its dependence on magnitude as indication of stellar stratification in the cluster .    in the present study we apply the _ effective radius method _ for the detection and quantification of stellar stratification in young star clusters in the lmc . we select three clusters observed with the high resolving efficiency of hst / acs , specifically ngc  1983 , ngc  2002 and ngc  2010 , on the basis of the differences in their appearance , structure , stellar content , and surrounding stellar field . our photometry delivered complete stellar catalogs down to @xmath147  -  23  mag for all three observed fields (   [ ss : phot ] ) . the stellar surface density maps of the observed regions , constructed from star counts on the photometric catalogs , demonstrate that all three clusters are morphologically quite different from each other . ngc  1983 appears to be a centrally concentrated , rather elliptical compact cluster , ngc  2002 a compact , spherical stellar concentration , and ngc  2010 a large , loose and rather amorphous cluster (   [ ss : contmap ] ) . the application of both eff @xcite and king s @xcite models on the stellar surface density profiles of the clusters allowed us the measurement of the background stellar field density of the regions , and the estimation of the core radii , @xmath46 , of the clusters . while these clusters do not seem to be tidally truncated , a tidal radius , @xmath47 is estimated , indicative of the limiting radius of each cluster (   [ s : dynamics ] ) . the latter is essential for the successful application of a random field subtraction technique for the decontamination of the stellar samples of the clusters from their surrounding young stellar ambient and the general lmc field (   [ ss : fldsub ] ) . we derive the ages of the clusters from the stellar populations comprised within the @xmath46 of the clusters and we find ages of @xmath89  28  myr , 18  myr and 159  myr for ngc  1983 , ngc  2002 , and ngc  2010 respectively (   [ ss : clusage ] ) . we finally apply the _ effective radius method _ for assessing stellar stratification in the clusters and for its quantitative study (   [ s : methappl ] ) . we bin the stars according to their magnitudes in the f814w filter , and we estimate the corresponding effective radii , @xmath110 , for every cluster in our sample . we then plot the derived radii versus the corresponding mean magnitude and we investigate the functional relation , @xmath112 , between these parameters . with our method it is shown that stellar stratification behaves differently in every cluster . ngc  1983 appears to be _ partially segregated _ , since its brightest stellar content does not appear to be centrally concentrated , while its fainter stars show a mild dependency of @xmath110 towards lower values for fainter magnitudes . the results on the bright stars of ngc  2010 show evidence of lack of stratification , since the brightest stars are located quite far away from its center . as far as the faint stars are concerned they show a rather flat @xmath112 relation , with no evidence of segregation in this relation for the faintest stars . consequently , this cluster is characterized as _ not segregated_. finally , ngc  2002 is found to be well segregated for both its brighter and fainter stars . it is a clear case of proof of stellar stratification with the effective radius method . we propose the _ slope _ @xmath140/@xmath141 , measured for stars in selected magnitude ranges , as well as in the whole magnitude range , as the most appropriate parameter for the quantification of the _ degree of stratification _ , and we use it to characterize the phenomenon as it is observed in the clusters . from the derived values of @xmath138 (   [ ss : stratdeg ] ) we find that ngc  2002 is the most strongly segregated cluster in the sample with a degree of stratification @xmath148 , ngc  1983 is a partially segregated cluster with @xmath149 for the faintest stars with @xmath118  -2.truept  15.5  mag , and ngc  2010 is not segregated with indicative @xmath150 (   [ ss : results ] ) . finally , it should be noted that the extension of this study to a larger sample of lmc clusters observed with hst will provide a more complete picture of the phenomenon of stellar stratification . naturally , the development of such a comparative scheme , which will include star clusters in the whole extent of the evolutionary sequence , requires a comprehensive set of acs and , in the near future , wfc3 observations . d. a. g. kindly acknowledges the support of the german research foundation ( deutsche forschungsgemeinschaft , dfg ) through grant go  1659/1 - 2 , and the german aerospace center ( deutsche zentrum fr luft- und raumfahrt , dlr ) through grant 50  or  0908 . sincere acknowledgements go also to m. kontizas and e. kontizas the collaboration with whom originally planted the seed of the idea for the effective radius method . based on observations made with the nasa / esa _ hubble space telescope _ , obtained from the data archive at the space telescope science institute . stsci is operated by the association of universities for research in astronomy , inc . under nasa contract nas 5 - 26555 . markwardt , c. b. 2008 , in astronomical data analysis software and systems xviii , asp conference series , eds . d. bohlender , p. dowler & d. durand ( astronomical society of the pacific : san francisco ) , in press ( arxiv:0902.2850v1 )","summary":"the clusters of our sample , ngc  1983 , ngc  2002 and ngc  2010 , are selected on the basis of their youthfulness , and their variety in appearance , structure , stellar content , and surrounding stellar ambient . we propose the slope derived from the change in the effective radius over the corresponding magnitude range as indicative parameter of the _ degree of stratification _ in the clusters . a positive value of this slope indicates mass segregation in the cluster , while a negative or zero value signifies the lack of the phenomenon .","abstract":"we present a comprehensive study of stellar stratification in young star clusters in the large magellanic cloud ( lmc ) . we apply our recently developed _ effective radius method _ for the assessment of stellar stratification on imaging data obtained with the advanced camera for surveys of three young lmc clusters to characterize the phenomenon and develop a comparative scheme for its assessment in such clusters . the clusters of our sample , ngc  1983 , ngc  2002 and ngc  2010 , are selected on the basis of their youthfulness , and their variety in appearance , structure , stellar content , and surrounding stellar ambient . our photometry is complete for magnitudes down to  mag , allowing the calculation of the structural parameters of the clusters , the estimation of their ages and the determination of their stellar content . our study shows that each cluster in our sample demonstrates stellar stratification in a quite different manner and at different degree from the others . specifically , ngc  1983 shows to be _ partially _ segregated with the effective radius increasing with fainter magnitudes only for the faintest stars of the cluster . our method on ngc  2002 provides evidence of _ strong _ stellar stratification for both bright and faint stars ; the cluster demonstrates the phenomenon with the highest degree in the sample . finally , ngc  2010 is _ not segregated _ , as its bright stellar content is not centrally concentrated , the relation of effective radius to magnitude for stars of intermediate brightness is rather flat , and we find no evidence of stratification for its faintest stars . for the parameterization of the phenomenon of stellar stratification and its quantitative comparison among these clusters , we propose the slope derived from the change in the effective radius over the corresponding magnitude range as indicative parameter of the _ degree of stratification _ in the clusters . a positive value of this slope indicates mass segregation in the cluster , while a negative or zero value signifies the lack of the phenomenon ."}
{"article_id":"1507.01007","section_id":"i","document":"the growth of planets out of km - sized planetesimals remains an attractive scenario for both terrestrial planet formation and , in the core accretion model , also as a necessary step in the creation of gas giant planets . nevertheless - regardless of whether these planetesimals form by direct gravitational collapse or agglomerative growth - there are a number of problems associated with the formation and retention of planetesimals in protoplanetary discs ( for a recent review of the subject see @xcite ) . for example , although there is observational evidence at mm and cm wavelengths for rather rapid grain growth @xcite , agglomerative growth beyond @xmath3 cm - sizes is inefficient , since collisions tend to result in fragmentation or bouncing rather than sticking and grain growth . particles in this size range are said to be ` critically coupled ' to the disc gas , having values of the stokes number ( st : the ratio of the timescale for gas drag to the dynamical time ) of around unity . drag causes such particles to lose angular momentum to the gas ( which orbits at slightly sub - keplerian velocity on account of being partially supported by outwardly directed pressure gradients ) and to drift towards the star on time - scales of 100 to 1000 orbits @xcite . once the drifting particles reach the snow - line they will sublimate , enhancing the local density in vapour form @xcite , removing most of the solids from the outer disc within @xmath4 @xcite .    the loss of solids by radial drift can potentially be overcome if pressure does not increase monotonically with decreasing radius in the disc and if instead some process can create and sustain local pressure maxima . in this case solid material can be trapped at the maximum ( since regions of outwardly increasing pressure drive outward migration of solids by the same argument ) . for example , the pressure maxima at the outer edge of gaps formed by massive planets have been proposed as an effective dust trap @xcite , and this has been invoked to explain the asymmetric dust around oph irs 48 @xcite . during the early phase of protoplanetary disc evolution , while the disc is still massive enough that gas self - gravity is important , spiral structures may likewise slow or halt the radial drift of dust grains , concentrating dust in the pressure maxima associated with spiral arms @xcite . if this focusing of dust into the spiral arms can raise its density by two orders of magnitude then it becomes the dominant mass component locally and direct gravitational collapse in the dust layer - creating km scale planetesimals - may ensue . if planetesimals do form in self - gravitating discs , then the spiral structure will drive eccentricities to @xmath5 . the high velocity dispersion ( and hence suppression of gravitational focussing ) renders collisions negligible and hence planetesimals should survive the self - gravitating phase @xcite . planetesimal formation is most likely to occur at radii greater than @xmath6 , where the relatively short cooling time is linked to a larger amplitude of spiral structure @xcite . the direct conversion of grains that are critically coupled ( with size 1  10@xmath7 in this region of a self - gravitating disc ) into planetesimals offers the attractive prospect of by - passing the problems of agglomerative growth over intermediate size scales .    since the mechanism requires a significant fraction of the dust to be in large grains that have a stokes number , @xmath8 , the success of this model depends on their survival during the self - gravitating phase . their survival is sensitive to relative velocity of collisions between particles , since collisions with velocities greater than 1  10@xmath9 result in fragmentation @xcite . since @xcite found velocity dispersions of order the sound speed , which is approximately @xmath10 at @xmath11 , collisions may destroy the grains before a sufficient density has been built up for collapse to occur . the results of competing grain growth and fragmentation processes require detailed knowledge of the velocity distributions of the dust grains during the self - gravitating phase , and this remains uncertain . in particular , early simulations of self - gravitating discs were studied using smoothed particle hydrodynamics ( sph ) , which had problems related to the need to reduce artificial viscosity in order to avoid a situation where the heating by the gravitational instability is exceeded by the action of artificial viscosity on keplerian shear @xcite . the amount of artificial viscosity in sph is typically controlled by two parameters , @xmath12 and @xmath13 , which govern artificial viscosity terms that are linear and quadratic in the relative velocity , respectively . to reduce the viscosity often @xmath12 was reduced by an order of magnitude from the typical values of @xmath14 and sometimes @xmath13 was also reduced @xcite . subsequently it has been shown that such a choice fails to generate enough entropy in shocks and results in considerable noise in the gas velocities ( @xcite ; see also @xcite and @xcite who suggest @xmath15 , even for weak shocks ) . the velocity noise is likely to be transmitted to the dust component via drag forces and this means it is not entirely clear that the velocity dispersion measured in a simulation is physical . recent shearing - box simulations go some way towards addressing the issue @xcite and also find a velocity dispersion of dust particles over the entire box of @xmath16 . however , the collision velocities are sensitive to the correlation structure in the velocity distribution , a quantity that has not been derived from these simulations .    with recent developments in computational techniques , accurate simulations of the dynamics of gas - dust mixtures are within reach @xcite . however , while there have been significant efforts to verify codes involving the simulations of turbulence and the streaming instability ( e.g. * ? ? ? * ) , there have been few ways to verify that codes capture the velocity distribution of solids in the context of self - gravitating discs .    in this work we conduct a series of tests that can be used to assess code performance in this respect . while some of these ( e.g. the dustybox and dustyshock tests described in @xcite ) have previously been used in this way , we also introduce two tests that have not previously been examined with respect to the modelling of coupled dust . these two tests involve shocks in 2d : the implosion test of @xcite and the modelling of a rigidly rotating spiral mode in an isothermal gas disc @xcite . the latter in particular was chosen because it bears some resemblance to the problem of interest ( since it involves centrifugally supported gas interacting with a pattern of spiral shocks ) but - unlike the _ self-_gravitating disc problem - is amenable to an analytic solution for the gas that is steady in the co - rotating frame . for each test we quantify the velocity structure in the dust and how this is affected by a range of numerical choices . finally , we summarise our conclusions in terms of a set of recommendations and requirements for the simulation of dust in self - gravitating protoplanetary discs .","summary":"we apply novel tests to verify its accuracy and limitations , including multi - dimensional tests that have not been previously applied to the drag - coupled dust problem and which are particularly relevant to self - gravitating protoplanetary discs . our tests demonstrate several key requirements for accurate simulations of gas - dust mixtures . [ firstpage ]    hydrodynamics  methods : numerical  protoplanetary discs  planets and satellites : formation  dust , extinction","abstract":"we present a ` two - fluid ' implementation of dust in smoothed particle hydrodynamics ( sph ) in the test particle limit . the scheme is able to handle both short and long stopping times and reproduces the short friction time limit , which is not properly handled in other implementations . we apply novel tests to verify its accuracy and limitations , including multi - dimensional tests that have not been previously applied to the drag - coupled dust problem and which are particularly relevant to self - gravitating protoplanetary discs . our tests demonstrate several key requirements for accurate simulations of gas - dust mixtures . firstly , in standard sph particle jitter can degrade the dust solution , even when the gas density is well reproduced . the use of integral gradients , a wendland kernel and a large number of neighbours can control this , albeit at a greater computational cost . secondly , when it is necessary to limit the artificial viscosity we recommend using the switch , since the alternative , using , can generate a large velocity noise up to in the dust particles . thirdly , we find that an accurate dust density estimate requires neighbours , since , unlike the gas , the dust particles do not feel regularization forces . this density noise applies to all particle - based two - fluid implementations of dust , irrespective of the hydro solver and could lead to numerically induced fragmentation . although our tests show accurate dusty gas simulations are possible , care must be taken to minimize the contribution from numerical noise .    [ firstpage ]    hydrodynamics  methods : numerical  protoplanetary discs  planets and satellites : formation  dust , extinction"}
{"article_id":"1507.01007","section_id":"c","document":"for a over a decade sph has been relied on to provide insights into the dynamics of gas and dust in self - gravitating discs . indeed to date , most of the global 3d simulations of self - gravitating discs and been performed with sph ( although @xcite investigated enrichment of solids in gas giants that are formed by gravitational instability using a 3d eulerian code ) . it is therefore necessary to take a critical look at the fidelity of the method . while many code comparisons exist in the case of purely gaseous discs @xcite , the dust implementation has been hitherto untested in this context ( although , for studies of dust in general see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? a key question in the case of self - gravitating discs concerns the velocity dispersion of solid material in the disc , since this controls the prospects for gravitational collapse in the dust phase as well as for particle growth or destruction . previous simulations @xcite found a large velocity dispersion in the dust ( of order a sound speed ) , which is unfavourable to either grain growth or gravitational collapse . it is therefore important to test whether this result is likely to be a numerical artefact .    in order to test the reliability of such codes , we have implemented dust particles into the sph code gadget-2 . we have used a two fluid approach and limited the study in the test particle limit where the feedback from the dust onto the gas can be neglected , allowing a direct comparison between simulations and analytical models . the code has been designed to accelerate the time - step using analytical solutions for the drag forces , in order to cope with particles that have stokes number @xmath80 . the chosen method has the advantage that it captures the full phase - space information of the dust , which is essential for evaluating the growth and survival of dust grains in protoplanetary discs . the code can handle the full range of stokes numbers and produces the correct terminal velocity for @xmath81 . we have focussed on extensively testing the code and its ability to tackle the questions in the dynamics of gas and dust in self - gravitating discs . in many of the tests presented we have focussed on the dynamically interesting cases in which the stopping time is comparable , or slightly smaller than the dynamical time scale . the result is that our time - stepping scheme only really saves computational time for the shortest stopping times . however , demonstrating that the time - stepping scheme can handle both situations readily is important for realistic physical problems , such as protoplanetary discs in which both short and long stopping times are present . the code performs well in the standard dustybox and dustyshock test problems , in which the high symmetry means that the orderly distribution of the particles is maintained by the symmetry in the problems . we also find good agreement in dustywave test , and have shown that our method is able to correctly reproduce the velocity of particles in a settling test , even at low resolutions and in strong drag regimes . we also run the two dimensional shock - tube or implosion problem @xcite , which involves interacting shock waves and is a much more severe test of a code s robustness . we have shown that correct modelling of the dust requires accurate modelling of the gas dynamics ; fig . [ fig : shock2d ] contains a striking demonstration that a correct modelling of the gas density distribution does _ not _ guarantee that the gas dynamics ( and the density distribution in the dust ) is well represented since the dust is quite sensitive to noise in the gas velocity . in agreement with the results of @xcite in the case of the gresho - chan vortex test , we find that using a wendland kernel ( which allows the number of neighbours to be increased beyond the traditional limit imposed by the pairing instability ) makes a huge difference to the accuracy of the velocity field , as does using integral based derivatives . since grid codes compare much more favourably in the two - dimensional shock tube problem , grid - based implementations of gas - dust mixtures will not show the same poor performance that standard sph does in this problem . however , it would be interesting to see how one - fluid sph codes perform in the presence of interacting shocks . we also tested the code on a problem that includes spiral shocks in a shearing environment , which is applicable to shocks in self - gravitating discs , or structures that form from planet - disc interactions . we find that the code is able to reproduce accurately the motion of the dust particles , giving the expected solutions . however , in general this is less true for dust density . while the gas density in sph calculations is accurate to the 1 per cent level for roughly 50 neighbours , we have found that even with 400 neighbours 10 per cent accuracy in the dust density is not achieved . the difference arises because the sph particle distribution is continually regularized by pressure forces , but the dust distribution is not . once the disc has evolved for a sufficient length of time that the initial structure of the disc has been sheared away , the dust particles then randomly sample the density distribution . this means the density error , @xmath288 , for the dust particles while @xmath289 for the gas . our results agree with the findings of @xcite , who find that roughly 1000 neighbours are required to calculate the density with an accuracy of 10 per cent when particles are placed randomly in a volume . the reason this density noise is not seen in the shock tube problems is that the turbulence has not sufficiently deteriorated the initial particle distribution . since the dust density does not enter the equations of motion within the test particle limit , the error does not affect the ability of the code to calculate the motion of dust particles . the low velocity dispersion of the dust in the steady disc problem @xmath290 verifies this . the good performance of the code in the static disc test problem is promising , producing much lower velocity dispersion than seen hitherto in simulations of self - gravitating discs . however , there are some caveats . firstly , using a low viscosity parameter , @xmath199 , fails to generate enough thermal energy at shocks , which results in post - shock oscillations in the gas when an adiabatic equation of state is used . as the static disc test case is isothermal the energy generation requirements do not apply , which may help to reduce the noise generated . however , in all our test cases the amplitude of the velocity dispersion is smaller than the velocity jump across the shock @xmath291 , setting a natural limit on the amount of noise introduced by shocks . it remains to be seen how the dusts dynamical state will be affected by these various code choices in the self - gravitating case and we leave this exploration ( which will help to distinguish between physical and numerical effects ) to a future paper . furthermore , when the dust is sufficiently dense to affect the dynamics of the gas , reducing the density error , which can be of order unity , will be important for producing reliable results . this is one area in which using a single - fluid approach would help , since the dust properties are evaluated at the location of the sph particles and the @xmath292 noise does not apply . however , in the presence of velocity noise the solution obtained by one - fluid approaches may also be deteriorated . furthermore , in problems where the full phase space information is required , using a two - fluid approach with a large number of dust particle neighbours may be necessary to ensure an accurate force estimate . indeed , similar results were reported by @xcite , who find significant noise in the dust density in a protoplanetary disc simulation , which led to artificial clumping . they found that using the gas smoothing length partially resolves the issue , since the gas has lower density and a larger smoothing length . we suspect that both error in the dust density and requirement that the gas is resolved on length scales present in the dust distribution are important for resolving the issue @xcite . reducing the noise in the dust density distribution is even more important when dust self - gravity is important , since spurious over - dense clumps may collapse and feed back on the gas phase fragmentation . when self - gravity is important it is likely to be essential that a large softening length is used . therefore , care must be taken in simulations of fragmentation in the dust layers of self - gravitating discs to avoid numerical artefacts . this is likely to apply to all particle based implementations of dust , independent of whether the gas is calculated using sph or with a grid code .","summary":"we present a ` two - fluid ' implementation of dust in smoothed particle hydrodynamics ( sph ) in the test particle limit . thirdly , we find that an accurate dust density estimate requires neighbours , since , unlike the gas , the dust particles do not feel regularization forces . this density noise applies to all particle - based two - fluid implementations of dust , irrespective of the hydro solver and could lead to numerically induced fragmentation .","abstract":"we present a ` two - fluid ' implementation of dust in smoothed particle hydrodynamics ( sph ) in the test particle limit . the scheme is able to handle both short and long stopping times and reproduces the short friction time limit , which is not properly handled in other implementations . we apply novel tests to verify its accuracy and limitations , including multi - dimensional tests that have not been previously applied to the drag - coupled dust problem and which are particularly relevant to self - gravitating protoplanetary discs . our tests demonstrate several key requirements for accurate simulations of gas - dust mixtures . firstly , in standard sph particle jitter can degrade the dust solution , even when the gas density is well reproduced . the use of integral gradients , a wendland kernel and a large number of neighbours can control this , albeit at a greater computational cost . secondly , when it is necessary to limit the artificial viscosity we recommend using the switch , since the alternative , using , can generate a large velocity noise up to in the dust particles . thirdly , we find that an accurate dust density estimate requires neighbours , since , unlike the gas , the dust particles do not feel regularization forces . this density noise applies to all particle - based two - fluid implementations of dust , irrespective of the hydro solver and could lead to numerically induced fragmentation . although our tests show accurate dusty gas simulations are possible , care must be taken to minimize the contribution from numerical noise .    [ firstpage ]    hydrodynamics  methods : numerical  protoplanetary discs  planets and satellites : formation  dust , extinction"}
{"article_id":"1507.01007","section_id":"c","document":"we have implemented dust particles in the smoothed particle hydrodynamics code gadget-2 . similarly to @xcite we avoid the need for small time - steps when the dust and gas are tightly coupled . however , unlike previous methods , our time stepping scheme produces the correct terminal velocity even when the time - step is much greater than the stopping time . we have applied a number of simple test problems that verify the code produces the expected results . the tests show the importance of producing an accurate velocity structure for capturing the dust dynamics , since a noisy velocity field introduces noise into the dust density that persists for the duration of the simulation .    we have used a rigidly rotating potential to test the dynamics of dust in spiral discs , and find that as long as the gas is well resolved numerical noise contributes a velocity dispersion @xmath293 to @xmath294 , below the levels found in simulations of _ self - gravitating _ protoplanetary discs . we find the dust density in disc problems is more difficult to estimate as shear destroys the high accuracy present in the initial density field . this means that the dust density is subject to monte - carlo noise and more than 400 neighbours are required for an accurate density estimate . while errors in the dust density do not affect the tests presented here , which are calculated in the test particle limit , when the dust density is high enough to be dynamically important , either through drag forces or self - gravity , care must be taken to ensure accurate results .    from these numerical experiments we have shown that for simulations in which the length scales in the gas are well resolved , @xmath295 , the dynamics of dust can be accurately modelled . these tests have been conducted in the test particle limit and in relation to sph , but we expect them to hold more generally with the caveat that if the dust reaches high enough densities to affect the gas dynamics then a large number of neighbours is needed to ensure robust results . as long as care is taken to ensure the density noise is controlled , then simulations should be able to tackle some of the key questions related to the physics of dusty gasses .","summary":"although our tests show accurate dusty gas simulations are possible , care must be taken to minimize the contribution from numerical noise .   ","abstract":"we present a ` two - fluid ' implementation of dust in smoothed particle hydrodynamics ( sph ) in the test particle limit . the scheme is able to handle both short and long stopping times and reproduces the short friction time limit , which is not properly handled in other implementations . we apply novel tests to verify its accuracy and limitations , including multi - dimensional tests that have not been previously applied to the drag - coupled dust problem and which are particularly relevant to self - gravitating protoplanetary discs . our tests demonstrate several key requirements for accurate simulations of gas - dust mixtures . firstly , in standard sph particle jitter can degrade the dust solution , even when the gas density is well reproduced . the use of integral gradients , a wendland kernel and a large number of neighbours can control this , albeit at a greater computational cost . secondly , when it is necessary to limit the artificial viscosity we recommend using the switch , since the alternative , using , can generate a large velocity noise up to in the dust particles . thirdly , we find that an accurate dust density estimate requires neighbours , since , unlike the gas , the dust particles do not feel regularization forces . this density noise applies to all particle - based two - fluid implementations of dust , irrespective of the hydro solver and could lead to numerically induced fragmentation . although our tests show accurate dusty gas simulations are possible , care must be taken to minimize the contribution from numerical noise .    [ firstpage ]    hydrodynamics  methods : numerical  protoplanetary discs  planets and satellites : formation  dust , extinction"}
{"article_id":"1207.6944","section_id":"i","document":"this work is a sequel to the stacs paper @xcite and its journal version @xcite . however , we try to keep it self - contained by reiterating everything of importance from the two preceeding papers . we extend their results to a more general version of power circuits . as a consequence , we can apply them to larger classes of groups . the group @xmath10 was introduced by higman in 1951 and served to provide the first known example of a finitely generated infinite simple group @xcite . it belongs to a family @xmath11 ( @xmath12 ) of groups with @xmath13 generators and @xmath13 relators : @xmath14    for @xmath15 these groups are trivial , which is easy to see for @xmath16 , but suprisingly hard for @xmath17 . the latter case was proven by hirsch @xcite , see also  23 in @xcite and @xcite . if @xmath6 , then @xmath11 is infinite , see @xcite , section 1.4 . since @xmath11 has no non - trivial normal subgroups of finite index , taking a minimal non - trivial quotient results in a finitely generated infinite simple group .    until recently , higman s group @xmath10 was a candidate for a `` natural '' group with non - elementary word problem . this was suggested by the huge compression that this group allows . in fact , there are words of length @xmath18 over the generators @xmath19 and their inverses , which in the group are equal to @xmath20 , where @xmath21 is the tower function ( also called `` tetration '' ) defined by @xmath22 and @xmath23 . however , in @xcite it was shown that the word problem of @xmath10 is decidable in @xmath24 time and @xcite improved this bound to @xmath8 . both results rely on a data structure called `` power circuit '' which was introduced by miasnikov , ushakov , and won in @xcite . power circuits had already proven useful in algorithmic group theory . in fact , their invention was entailed by the wish to efficiently solve the word problem in the baumslag - gersten group @xmath25 ( see @xcite and section [ sec : bg ] ) which shares with @xmath10 the property of huge compression . ( in @xcite the group @xmath25 is called `` baumslag group '' . we use the equally common name `` baumslag - gersten group '' to avoid confusion with the baumslag - solitar group . ) for @xmath2 , power circuits have been implemented @xcite and there is a computer program solving the word problem in @xmath25 . this paper builds on the work of diekert , ushakov , and the author conducted in @xcite and @xcite . its contributions are twofold : in section [ sec : pc ] , we extend power circuits to allow arbitrary bases @xmath0 . this necessitates changes in the reduction procedure , the core component of power circuits . in section [ sec : higman ] , we generalize higman s group @xmath10 by replacing the underlying group @xmath4 by @xmath26 . power circuits with base @xmath1 are naturally suited for computations in this group . furthermore , with the help of rewriting systems , we give a constructive method of treating any group @xmath11 ( @xmath6 ) rather that just @xmath10 . combining this with base @xmath1 power circuits leads to an algorithm for the word problem in generalized higman groups @xmath7 which retains the @xmath8 time bound proved in @xcite for @xmath2 and @xmath27 . [ [ sec : notation ] ] notation and preliminaries + + + + + + + + + + + + + + + + + + + + + + + + + +    algorithms and decision problems are classified by their time complexity on a random - access machine ( ram ) . we use the notion of amortized analysis with respect to a potential function , see section 17.3 in @xcite .    with regard to group theory , we use standard notation and facts that can be found in any textbook on the subject , e.g. @xcite . in particular , we apply the technique of britton reductions for solving the word problem in hnn extensions and amalgamated products .    rewriting systems are of particular importance for this work . we assume that the reader is familiar with the basic notions of ( local ) confluence and termination . see for example the textbook @xcite for a quick introduction .","summary":"this paper continues the 2012 stacs contribution by diekert , ushakov , and the author . this generalization is non - trivial and additional techniques are required to preserve the time bounds of arithmetic operations that were shown for the case .    , we allow arbitrary numbers of copies of , leading to an even more generalized notion of higman groups .","abstract":"this paper continues the 2012 stacs contribution by diekert , ushakov , and the author . we extend the results published in the proceedings in two ways .    first , we show that the data structure of power circuits can be generalized to work with arbitrary bases . this results in a data structure that can hold huge integers , arising by iteratively forming powers of . we show that the properties of power circuits known for translate to the general case . this generalization is non - trivial and additional techniques are required to preserve the time bounds of arithmetic operations that were shown for the case .    the extended power circuit model permits us to conduct operations in the baumslag - solitar group as efficiently as in . this allows us to solve the word problem in the generalization of higman s group , which is an amalgamated product of four copies of the baumslag - solitar group rather than in the original form .    as a second result , we allow arbitrary numbers of copies of , leading to an even more generalized notion of higman groups . we prove that the word problem of the latter can still be solved within the time bound that was shown for .    keywords : data structures ; compression ; algorithmic group theory ; word problem ."}
{"article_id":"1207.6944","section_id":"c","document":"we have shown that the word problem for the generalized higman groups @xmath366 is solvable in polynomial time . an important ingredient for this result was the extension of the power circuit data structure to arbitrary bases @xmath0 . from an algorithmic point of view , this is an interesting result in itself and may provide a useful tool in group theory as well as other areas . the techniques used in this paper do not apply to the even more general groups @xmath474 and @xmath475 , where the underlying baumslag - solitar group @xmath3 is replaced by @xmath476 for some @xmath477 . this is because @xmath478 is not a semi - direct product when @xmath479 . the word problem for these groups is open . note that even for @xmath15 the group @xmath474 can be non - trivial if @xmath479 .","summary":"the extended power circuit model permits us to conduct operations in the baumslag - solitar group as efficiently as in . keywords : data structures ; compression ; algorithmic group theory ; word problem .","abstract":"this paper continues the 2012 stacs contribution by diekert , ushakov , and the author . we extend the results published in the proceedings in two ways .    first , we show that the data structure of power circuits can be generalized to work with arbitrary bases . this results in a data structure that can hold huge integers , arising by iteratively forming powers of . we show that the properties of power circuits known for translate to the general case . this generalization is non - trivial and additional techniques are required to preserve the time bounds of arithmetic operations that were shown for the case .    the extended power circuit model permits us to conduct operations in the baumslag - solitar group as efficiently as in . this allows us to solve the word problem in the generalization of higman s group , which is an amalgamated product of four copies of the baumslag - solitar group rather than in the original form .    as a second result , we allow arbitrary numbers of copies of , leading to an even more generalized notion of higman groups . we prove that the word problem of the latter can still be solved within the time bound that was shown for .    keywords : data structures ; compression ; algorithmic group theory ; word problem ."}
{"article_id":"1608.02313","section_id":"i","document":"one of the important properties of the galaxy population is the distribution of galaxies in space ( e .. g . * ? ? ? * ; * ? ? ? this distribution can be used to infer the large scale mass distribution in the universe , thereby constraining cosmological models ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? furthermore , the spatial clustering of galaxies is also one of the key pieces of observational data to establish the relation between galaxies and dark matter ( halos ) statistically(e.g . * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and to understand how galaxies form and evolve in the cosmic density field . one of the main goals of large redshift surveys of galaxies , such as the 2 degree field galaxy redshift survey ( 2dfgrs ; * ? ? ? * ) and the sloan digital sky survey ( sdss ; * ? ? ? * ) is , therefore , to provide a data base to study the three dimensional distribution of galaxies as accurately possible . however , a key problem this endeavor is that redshifts of galaxies are not exact measures of distances due to the peculiar motions of galaxies . the spatial distribution and clustering of galaxies observed in redshift space are thus distorted with respect to the real - space distribution and clustering ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? take the two - point correlation function ( 2pcf ) of galaxies as an example . the 2pcf in the 2-dimensional space , with 1 dimension along the line - of - sight and the other in the perpendicular direction , appears elongated on small scales and squashed on large scales along the line - of - sight direction , in contrast to an isotropic pattern expected from a statistically homogeneous and isotropic distribution in real space . such anisotropies are clearly produced by redshift distortions and need to be corrected in order to get the true distribution of galaxies in space . theoretically , models of the pairwise peculiar velocities of galaxies have been used to model the effects of redshift distortions on the measured 2pcf in redshift space ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? alternatively , one simply measures the projected 2pcf and uses it to infer the three - dimensional 2pcf ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) .    in the gravitational instability scenario of structure formation , the redshift distortion is not just a contamination one has to correct in order to get the real clustering of galaxies , it in fact contains useful information about cosmology as well as the mass distribution in the universe . on large scales , the infall motions of galaxies , which produce the squashing in the 2d redshift - space 2pcf ( the kaiser effect , * ) , is linearly proportional to the amplitudes of the mass density fluctuations on large - scales . in this case , one can compute the quadrupole - to - monopole ratio of the 2d 2pcf to get @xmath7 , where @xmath8 is the density parameter of mass , and @xmath9 is the effective linear bias of the galaxies in question ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . when the measurement is combined with weak gravitational lensing results , it can also be used as a sensitive probe of ( modified ) gravitation theories on cosmology scales @xcite . on smaller scales , the modeling of redshift space distortion ( the finger of god effect ) is complicated by the nonlinear mapping between real - space and redshift - space . great efforts have been made not only to understand its impacts on galaxy clustering ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but also to extract useful cosmological information ( mo , jing & boerner 1993 ; jing , mo & boerner 1998 ; yang et al . 2004 ; li et al . 2012 ) . the approaches adopted earlier to deal with redshift distortions in galaxy clustering have been hampered by the fact that the large - scale kaiser effect and the small - scale finger of god effect are interwoven , and models based on a simple pairwise peculiar velocity distribution can only be served as an approximation . the situation is complicated even more by the fact that the effect bias in galaxy distribution may be nonlinear and its form is not known _ a priori_. models based on the projected correlation function has its own problem , because the projection mixes clustering on different scales so that the conversion from the projected function to the three dimensional function can be uncertain . thus , in order to make full use of galaxy redshift surveys to study the large - scale structure of the universe , a change of tactics is needed . one possible way is first to make corrections of redshift distortions for individual galaxies , and then use the ` pseudo ' real space distribution of galaxies to derive statistical measures of galaxy clustering in real space . as mentioned above , redshift distortions are of two different kinds . one is the kaiser effect produced by the coherent flow due to the gravitational action of large - scale structure @xcite , the other is the finger of god ( fog ) effect generated by the random motions of galaxies within virialized halos on small scales . to deal with the fog effect , @xcite used an friends - of - friends method to link galaxies and suppressed the over - density of the pairs along the line of sight by a factor of 10 . they applied this fog suppression to the 2dfgrs @xcite and sdss @xcite in their estimates of the power spectra of galaxy distribution . in a paper aimed at reconstructing the cosmic web from 2dfgrs , @xcite attempted to dealt with the fog effect by compressing 25 fingers seen in redshift space using groups identified by @xcite . for the kaiser effect , @xcite used a bias model to get the density field from the galaxy distribution and iteratively corrected the infall motions of galaxies . along the same line , a number of approaches have been taken to recover / correct the infall motions on the basis of galaxy distribution ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in particular , @xcite used galaxy groups as proxies of dark matter halos to reconstruct the density field , which in turn was used to obtain the velocity field .    so far there has been no real attempt to correct for both the large scale velocities and small scale random motions of galaxies in a systematic way . the main purpose of the present paper is to carry out such an investigation , using galaxies observed in the sdss dr7 , which is still among the best redshift surveys available . based on this galaxy catalog , ( * ? ? ? * hereafter y07 ) have constructed a galaxy group catalog using an adaptive halo - based group finder ( see also * ? ? ? . detailed tests with mock galaxy catalogues have shown that the group finder is very successful in associating galaxies according to their common dark matter halos . in particular , the group finder performs reliably not only for rich systems , but also for poor systems , including isolated central galaxies in low mass halos . the reliable memberships of galaxies in groups provide a unique opportunity to correct for the fog effects for individual galaxy systems . in addition , as shown in ( * ? ? ? * hereafter w12 ) , the group catalog can also be used to reconstruct the mass density , tidal and velocity ( mtv ) fields in the sdss dr7 volume , using the halo - domain method developed in @xcite . since the relation between halo and mass distributions is better understood than that between galaxies and mass , the mass and velocity fields constructed are much more accurate than those constructed directly from the galaxy distribution . the redshift distortions on large scales can , therefore , also be modeled accurately for individual galaxies . with all these , we can obtain a catalog of galaxies in quasi - real space . we can then not only examine in detail various types of redshift distortions , but also measure the real space clustering of galaxies . this paper is organized as follow . in section 2 we present the galaxy and group catalogs used in this paper . section 3 introduces the methods to correct for the redshift distortions and to characterize the galaxy clustering . in section 4 we use mock galaxy catalogs to test the reliability of our correction model . the application to the sdss dr7 and the results are presented in section 5 . finally , we summarize our main findings in section 6 . throughout this paper , unless stated otherwise , physical quantities are quoted using the wmap9 cosmological parameters @xcite : @xmath10 , @xmath11 , @xmath12 , @xmath13 , @xmath14 and @xmath15 .","summary":"we use an ensemble of mock catalogs to demonstrate the reliability of our method . over the range , the","abstract":"using a method to correct redshift space distortion ( rsd ) for individual galaxies , we present the measurements of real space two - point correlation functions ( 2pcfs ) of galaxies in the sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . galaxy groups selected from the sdss are used as proxies of dark matter halos to correct the virial motions of galaxies in dark matter halos , and to reconstruct the large - scale velocity field . we use an ensemble of mock catalogs to demonstrate the reliability of our method . over the range , the 2pcf measured directly in reconstructed real space is better than the measurement error due to cosmic variance , if the reconstruction uses the correct cosmology . applying the method to the sdss dr7 , we construct a real space version of the main galaxy catalog , which contains 396,068 galaxies in the north galactic cap with redshifts in the range . the sloan great wall , the largest known structure in the nearby universe , is not as dominant an over - dense structure as appears to be in redshift space . we measure the 2pcfs in reconstructed real space for galaxies of different luminosities and colors . all of them show clear deviations from single power - law forms , and reveal clear transitions from 1-halo to 2-halo terms . a comparison with the corresponding 2pcfs in redshift space nicely demonstrates how rsds boost the clustering power on large scales ( by about at scales ) and suppress it on small scales ( by about at a scale of ) . we also investigate the dependence of the bias factor on luminosity and color using the reconstructed real - space , and show how our method gives more accurate results than the traditional method based the projected 2pcf . we briefly discuss some applications of our reconstruction method , including how it can be used to constrain cosmological parameters ."}
{"article_id":"1608.02313","section_id":"i","document":"we have presented a method to correct redshift space distortions in redshift surveys of galaxies . adopting the method introduced in w12 , we use galaxy groups identified with the y05 halo - based group finder to reconstruct the large scale velocity field , which in turn is used to correct the observed redshifts for the kaiser effect . the same galaxy groups are also used to correct the finger - of - god ( fog ) effect produced by the virial motions of galaxies within their host dark matter halos . our fog correction is based on the assumption that satellite galaxies are an unbiased tracer of the mass profile and velocity structure of the host halo .    to test the method , we have constructed 10 mock sdss dr7 galaxy catalogs , in four different spaces : redshift space ( equivalent to the observational space ) , kaiser space ( space in which the fog effect is absent ) , fog space ( space in which kaiser effect if absent ) , and real space ( space in which redshift distortions are absent ) . we test the various components of our reconstruction method by comparing the two - point clustering statistics in these different spaces . the contours of the two - dimensional 2pcfs @xmath117 calculated in different spaces show that the clustering in our reconstructed space is in good agreement with that in the corresponding true space given directly by numerical simulations . on small transverse scales @xmath87 , residual fog effects are apparent , which arise mainly from the uncertainties in the group finder , including errors in group membership determinations , designations of centrals and satellites , and halo mass assignments . we have shown , though , that the one - dimensional 2pcf , @xmath6 , inferred directly from the reconstructed real space is not significantly affected , with deviations typically being smaller than the uncertainties arising from cosmic variance ( at least for a sdss - like survey ) . in fact , over the range of scales @xmath236 , the average error on the reconstructed real space 2pcf is less than two percent . hence , our method is capable of correcting redshift distortions in redshift surveys to a level that allows for an accurate , unbiased measurement of the real - space correlation function . we have applied our reconstruction method to the sdss dr7 , giving a real space version of the main galaxy catalog which contains 396,068 galaxies in the ngc with redshifts in the range @xmath237 . this real space galaxy catalog is publicly available at link : url[http://gax.shao.ac.cn / data / data1/sdss7_real.tar ] . we emphasize that the fog correction is only statistical in nature , and that the line - of - sight position of satellite galaxies in the catalog have been assigned at random , in accordance with our assumption that satellite galaxies are an unbiased tracer of the mass distribution of their host halo .    using the reconstructed real space data we have shown that the sloan great wall , the largest known structure in the universe , is not as dominant an over - dense structure as it appears in redshift space , but that its apparent over - density is strongly enhanced by the kaiser effect . we have measured the 2pcfs in reconstructed real space in different absolute magnitude bins . they all deviate clearly from a simple power - law , revealing a clear 1-halo to 2-halo transition . a comparison with the corresponding 2pcfs in redshift space nicely demonstrates how redshift space distortions boost the correlation on large scales ( by about @xmath2 at a scale of @xmath219 ) , while suppressing it on small scales ( by about @xmath4 at a scale of @xmath238 ) . we have also measured the real - space autocorrelation functions of blue and red galaxies , and their across - correlations . using the real - space ( color - dependent ) @xmath6 , we have investigated how the bias factor depends on galaxy luminosity and color , and how our method provides more reliable measurements of galaxy bias factors than the traditional method that uses the projected 2pcf , @xmath168 . the present paper , the first paper in a series , is focused on the methodology . in a forthcoming paper we will use our reconstructed , real - space sdss galaxy catalog to study in more detail how the real space clustering of galaxies depends on their intrinsic properties , such as luminosity , stellar mass , color and star formation rate . we will also use our reconstruction method to put constraints on cosmological parameters as well as halo occupation models . as briefly mentioned in  [ sec : clusan ] , the actual reconstruction is cosmology dependent , as the bias parameter @xmath63 , the halo masses assigned to galaxy groups , and the distance - redshift relation are all cosmology dependent . consequently , assuming an incorrect cosmology can result in systematic errors in our reconstruction , and distortions in the correlation functions . we can then model such distortions and constrain cosmological parameters by searching for the model that gives the best reconstructed real space , so that @xmath110 is isotropic ( i.e. , quadrupole - to - monopole ratio is close to zero ) .","summary":"using a method to correct redshift space distortion ( rsd ) for individual galaxies , we present the measurements of real space two - point correlation functions ( 2pcfs ) of galaxies in the sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . galaxy groups selected from the sdss are used as proxies of dark matter halos to correct the virial motions of galaxies in dark matter halos , and to reconstruct the large - scale velocity field . 2pcf measured directly in reconstructed real space is better than the measurement error due to cosmic variance , if the reconstruction uses the correct cosmology . applying the method to the sdss dr7 , we construct a real space version of the main galaxy catalog , which contains 396,068 galaxies in the north galactic cap with redshifts in the range . the sloan great wall , the largest known structure in the nearby universe , is not as dominant an over - dense structure as appears to be in redshift space . we measure the 2pcfs in reconstructed real space for galaxies of different luminosities and colors . a comparison with the corresponding 2pcfs in redshift space nicely demonstrates how rsds boost the clustering power on large scales ( by about at scales ) and suppress it on small scales ( by about at a scale of ) . we also investigate the dependence of the bias factor on luminosity and color using the reconstructed real - space , and show how our method gives more accurate results than the traditional method based the projected 2pcf . we briefly discuss some applications of our reconstruction method , including how it can be used to constrain cosmological parameters .","abstract":"using a method to correct redshift space distortion ( rsd ) for individual galaxies , we present the measurements of real space two - point correlation functions ( 2pcfs ) of galaxies in the sloan digital sky survey ( sdss ) data release 7 ( dr7 ) . galaxy groups selected from the sdss are used as proxies of dark matter halos to correct the virial motions of galaxies in dark matter halos , and to reconstruct the large - scale velocity field . we use an ensemble of mock catalogs to demonstrate the reliability of our method . over the range , the 2pcf measured directly in reconstructed real space is better than the measurement error due to cosmic variance , if the reconstruction uses the correct cosmology . applying the method to the sdss dr7 , we construct a real space version of the main galaxy catalog , which contains 396,068 galaxies in the north galactic cap with redshifts in the range . the sloan great wall , the largest known structure in the nearby universe , is not as dominant an over - dense structure as appears to be in redshift space . we measure the 2pcfs in reconstructed real space for galaxies of different luminosities and colors . all of them show clear deviations from single power - law forms , and reveal clear transitions from 1-halo to 2-halo terms . a comparison with the corresponding 2pcfs in redshift space nicely demonstrates how rsds boost the clustering power on large scales ( by about at scales ) and suppress it on small scales ( by about at a scale of ) . we also investigate the dependence of the bias factor on luminosity and color using the reconstructed real - space , and show how our method gives more accurate results than the traditional method based the projected 2pcf . we briefly discuss some applications of our reconstruction method , including how it can be used to constrain cosmological parameters ."}
{"article_id":"1404.6697","section_id":"i","document":"in one - dimensional ( 1d ) strongly correlated systems , the emergence of fractional quantum numbers is a generic consequence of collective behaviors @xcite . in the exactly solvable critical @xmath0 antiferromagnetic ( afm ) spin chain , the fundamental excitations are soliton - like quasiparticles ( kinks and anti - kinks ) , called _ spinons _ , which carry spin @xmath5 @xcite . similar objects exist also in the valence - bond - solid ( vbs ) state stabilized by frustrated interactions @xcite . a bound state of spinons can be induced in the heisenberg chain by an external magnetic field @xcite . in higher dimensions , in systems with long - range afm order , the fundamental excitations are magnons with spin @xmath6 , as explained successfully by spin - wave theory @xcite . spinon excitations are associated with spin - liquid ground states , which have no broken symmetries described by conventional local order parameters ( but do have non - local , topological order ) @xcite . in two - dimensional ( 2d ) afm systems , deconfined spinons should emerge when a transition into a vbs state is approached , according to the theory of `` deconfined '' quantum - critical points @xcite . the search for spinons has been a quest in experimental and theoretical condensed matter physics for decades , primarily because the fractionalization of excitations is a characteristic of exotic collective quantum many - body states , such as the spin liquids @xcite . moreover , in some cases the mechanism of confinement of spinons is a condensed - matter analog of the confinement of quarks in quantum chromodynamics . in this paper , building on a previous brief presentation @xcite , we will explore systems where confinement and deconfinement of spinons can be detected and characterized using large - scale quantum monte carlo ( qmc ) simulations in the valence - bond ( vb ) basis . we here focus on a range of different 1d systems but note that the same ideas have also already been applied to 2d systems in the context of deconfined quantum - criticality @xcite . the starting point of our studies is the @xmath0 afm heisenberg chain , defined by the hamiltonian @xmath7 where the nearest - neighbor coupling @xmath8 , @xmath9 is the total number of spins , and we apply periodic boundary conditions . we will add other interactions to this model later , in order to bring the system to the different types of ground states mentioned above . the ground state of the plain heisenberg model ( [ eq : heisenberg ] ) can in principle be solved exactly by the bethe - ansatz approach @xcite , but in practice many of its salient features , such as the power - law decaying spin - spin correlations , were found using the bosonization method @xcite . reflecting the deconfined spinons , the lowest excited states of the heisenberg model form bands of degenerate singlets and triplets @xcite with the energy @xmath10 as a function of the total momentum @xmath11 of the state being @xmath12 , which was first calculated by des cloiseaux and pearson using the bethe ansatz.@xcite forming all possible combinations of two spinons propagating independently with fixed momenta , @xmath13 and @xmath14 with @xmath15 gives a continuum above the lower bound and an upper bound given by @xmath16 . a large spectral weight between these bounds ( concentrated close to the lower bound because of matrix elements  @xcite ) , which is detectable in inelastic neutron scattering experiments @xcite , is considered a good indicator of spinons in one dimension . the continuum spectrum of spinons has been observed in weakly coupled - chain compounds such as copper pyrazine dinitrate and kcuf@xmath17 at zero magnetic field @xcite , while in none - zero magnetic fields incommensurate modes have been observed @xcite . in another chain compound , cucl@xmath18(dimethylsulfoxide ) , there is an effective internal staggered magnetic field present , and spinon bound states have been observed @xcite . in addition , in the spin ladder system ( c@xmath19h@xmath20n)@xmath21cubr@xmath22 , it was reported that the magnon could be fractionalized into spinons by tuning the external magnetic field @xcite . the above experimental results can be modeled using the heisenberg hamiltonian ( [ eq : heisenberg ] ) including the other effects mentioned above ( external fields , inter - chain couplings ) . in addition to neutron scattering , other experimental signals of spinons have also been proposed @xcite . so far , however , all the experimental probes give indirect information on the existence of spinons , and not much information on the properties of spinons other than their dispersion and excitation continuum . motivated by the on - going interest in the quantum physics of fractionalization , in this paper we are interested in exploring other aspects of spinons and their confinement - deconfinement transitions . using the qmc approach introduced in refs .   and used in ref .   to study 2d systems , we here explore a wider range of 1d systems where confinement and deconfinement can be studied systematically under various conditions . the method operates in a basis of vbs ( two - spin singlets ) and unpaired spins and allows us to compute quantities defining the size of an isolated spinon as well as the size of an @xmath23 bound state . we also show that the same length scales appear in standard spin correlation functions , but are harder to access there in practice because the signal only appears in the differences between correlations in different spin sectors ( and is therefore very noisy in qmc calculations of large systems ) . the structure of the rest of the paper is as follows : in sec . [ sec : method ] , we introduce the projector qmc method and calculate observables used to characterize spinons . in sec . [ sec:1d ] , we present results for the @xmath24-@xmath25 chain model @xcite , which undergoes a quantum phase transition from the heisenberg critical phase to a spontaneously symmetry - broken valence - bond solid ( vbs ) . this system has deconfined spinon excitation in the entire range of the ratio @xmath26 of the heisenberg exchange @xmath24 and a multi - spin coupling @xmath25 . to achieve confinement , in sec . [ sec : j1j2q3 ] we introduce a staggered pattern of @xmath24-interactions , as recently done also in an investigation of spinons binding to a static impurity @xcite . in sec . [ sec : ladder ] we study spinon confinement when two heisenberg chains are coupled to form a ladder . in sec . [ sec : crr ] , we discuss the fact that the same length scales that appear in our vb - based definition of spinons can also be identified in the fine - structure of the spin - spin correlations in the higher - spin states , thus confirming that these length scales are not basis dependent and can be investigated using other methods as well . we summarize our work and discuss future prospects in sec . [ sec : conclusion ] .","summary":"observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many - body physics . rev .  an individual spinon can be small when the confinement length is large ; this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence - bond - solid ( where the spinons are deconfined ) .","abstract":"observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many - body physics . here we further explore a computational scheme [ y. tang and a. w. sandvik , phys .  rev .  lett .  * 107 * , 157201 ( 2011 ) ] based on valence - bond quantum monte carlo simulations of quantum spin systems . using several different one - dimensional models , we characterize spinon excitations using the intrinsic spinon size and confinement length ( the size of a bound state ) . the spinons have finite size in valence - bond - solid states , infinite size in the critical region ( with overlaps characterized by power laws ) , and become ill defined ( completely unlocalizable ) in the nel state ( which we stabilize in one dimension by introducing long - range interactions ) . we also verify that pairs of spinons are deconfined in uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths ( dimerization ) or coupling two chains ( forming a ladder ) . in the dimerized system , an individual spinon can be small when the confinement length is large ; this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence - bond - solid ( where the spinons are deconfined ) . based on our numerical results , we argue that a system with is associated with weak repulsive short - range spinon - spinon interactions . in principle , both the length scales and can still be individually tuned from small to infinite ( with ) by varying model parameters . in contrast , in the ladder system the two lengths are always similar , and this is the case also in the weakly dimerized systems when the corresponding uniform chain is in the critical phase . in these systems , the effective spinon - spinon interactions are purely attractive and there is only a single large length scale close to criticality , which is reflected in the standard spin correlations as well as in the spinon characteristics ."}
{"article_id":"1404.6697","section_id":"m","document":"we use vb projector qmc ( vbpqmc ) algorithm , which has been described in detail in refs .  . here we first briefly review the essential ideas underlying simulations of spin systems with this algorithm , and then focus on the definitions of spinon quantities and how to evaluate them . searching for the ground state of a hamiltonian @xmath27 , we start with a `` trial '' wave function and write it as the linear superposition of all eigenstates of @xmath27 as latexmath:[\\[\\label{eq : trial }    @xmath27 a number @xmath29 times on this trial state to project out the ground state @xmath30 ; @xmath31,\\ ] ] where , since normally @xmath32 , we have added a minus sign in front of @xmath27 . provided that @xmath33 for all @xmath34 , which can always be accomplished by adding some negative constant to @xmath27 , the ground state is projected out when @xmath35 .    while the ground - state projection approach formulated above is completely general , the use of the vb basis has distinct advantages @xcite , as the spin of the trial state can be chosen to match that of the ground state under investigation . for the bipartite spin models we are interested in here , if the number of spins @xmath9 is even , then the ground state is a singlet and a vb basis state can be written as @xmath36 is the @xmath37th vb ( singlet ) , @xmath38 and @xmath39 sites on sublattices @xmath40 and @xmath41 , respectively . the trial state can be expanded in these vb basis states as @xmath42 where the coefficients @xmath43 , reflecting marshall s sign rule for the ground state of a bipartite system @xcite . it should be noted that the vb basis is overcomplete and , therefore , the expansion coefficients @xmath44 are in principle not unique , which , however , is not explicitly of importance in the work discussed here . what is important is that the basis is non - orthogonal , with the overlap between two states given by @xcite @xmath45 where @xmath46 is the number of loops in the _ transition graph _ formed when superimposing the bond configurations of @xmath47 and @xmath48 . an example with @xmath49 is shown in fig . [ fig : loop](a ) . expectation values of interest can normally also be expressed using transition graphs , e.g. , for studying the spin - spin correlation operator @xmath50 we need matrix elements of the form , @xmath51 where the @xmath52 and @xmath53 sign in front of @xmath54 applies for sites on the same and different sublattices , respectively . other examples of transition - graph estimators , e.g. , dimer - dimer correlations of the form @xmath55 have been discussed in refs .   and . state on an even number of sites . in ( b ) the number of sites is odd and there is an unpaired spin in both the bra and the ket states . part ( c ) shows an @xmath23 configuration , where there are two unpaired spins . in vbpqmc simulations , the distance distribution of the unpaired spins in ( b ) gives information on the size of an individual spinon , while the size of an @xmath23 bound state of two spinons is reflected in the distance distribution of unpaired spins on different sublattices in ( c).,width=245 ]    in the `` double projection '' version of the vbpqmc method @xcite that we use here , bra and ket vb states are generated stochastically by operating on the bra and ket versions of the trial state with strings of @xmath29 hamiltonian terms ( operators defined on bonds or groups of bonds for @xmath24 and @xmath25 interactions , respectively ) . the probability of the bra @xmath56 and ket @xmath57 appearing together is given by @xmath58 where the unknown coefficients are such that @xmath59 approaches the ground state of @xmath27 when @xmath60 and expectation values in this ground state are obtained using the stochastically generated transition graphs @xmath61 . for details of the computational procedures , which make use of very efficient loop updates , we refer to ref .  . for the trial state , we normally choose an amplitude - product state @xcite , where the coefficients @xmath44 in ( [ psitfa ] ) are simple products of amplitudes @xmath62 corresponding to bond - lengths @xmath63 ; @xmath64 where @xmath65 is the number of bonds of length @xmath63 in vb configuration @xmath66 . these amplitudes can in principle be determined variationally @xcite to optimize the trial state , but in practice such optimization is not crucial and the simulations converge well regardless of the details of the trial states . we typically choose a power - law form , e.g. , @xmath67 . the bonds configurations of the trial state are sampled stochastically as well @xcite . our vbpqmc calculation projects out the lowest state with given total spin , @xmath68 as discussed above or higher spins , as will be discussed further in the following . with periodic systems , the momentum is also a good quantum number and is determined by the trial state . with the simple amplitude - product trial states we are using , the momentum can be obtained very easily by translating the bonds by one lattice spacing . if the number of bonds is odd , i.e. , the number of sites is of the form @xmath69 for some integer @xmath70 , this results in a negative phase , and , thus , the momentum @xmath71 . otherwise , for @xmath72 , there is no phase and @xmath73 . these are exactly the momenta of the ground states of bipartite spin chains . in addition to the use of the vb basis for singlet ground states , extensions of the vb basis with unpaired spins also provide a natural and convenient way to describe excitations with higher spin @xcite . in our study of spinons , we will study systems with one or two unpaired spins . in the former case , the total number of sites @xmath9 is odd , and a generalized vb state can be written as latexmath:[\\[\\label{eq : shalf }    where the notation explicitly indicates the location @xmath63 in the chain of the unpaired spin and @xmath66 labels the possible @xmath76-bond configurations with this site excluded . for system with even @xmath9 and two unpaired spins , analogously an extended vb basis state is written as @xmath77 singlet pairs and two unpaired spins on different sublattices . these extended vb bases are also overcomplete and non - orthogonal in their respective total - spin sectors @xmath78 , and , if we choose ( as we do here ) the unpaired spins to have @xmath79 , the @xmath80-projection of the total spin is @xmath81 .    the transition graphs shown in figs . [ fig : loop](b ) and [ fig : loop](c ) have open strings [ with an open string of length zero being a special case corresponding to a bra and ket spinon residing on the same site , an example of which is seen in fig.[fig : loop ] ( c ) ] in addition to loops . if we fix the spin-@xmath80 orientation of the unpaired spins , as we do here , the strings do not contribute to the weight ( since they only have one allowed state , in contrast to the two allowed states of each loop ) and the overlap of two states is still given by eq . ( [ overlap ] ) . note , in particular , that the unpaired spins can be at different lattice locations and the states still always have non - zero overlap . the strings do contribute to expectation values . it should be pointed out that , in periodic chains of odd size @xmath9 , which we use here to study a single unpaired spin in @xmath0 states , there is magnetic frustration caused by the boundary condition and the lattice is no longer strictly bipartite . thus , maintaining the updating rules in the simulations @xcite the vb singlets here can some times be formed between sites on the same sublattices if we continue to label the sites as alternating a and b , except for one instance of adjacent aa or bb sites . ( in the simulation we do not explicitly label the sites and there is no breaking of translational symmetry as we just use the same updating rules for the bonds and unpaired spins as for the even-@xmath9 chains ) . the distance between the unpaired spin in the bra and ket can then be an odd number of lattice spacings ( while it is always even in a true bipartite chain ) . in many cases ( which we will discuss in detail in sec . [ sec:1d ] ) the system is completely dominated by short bonds and the distance between the bra and ket spinon is then always even in practice . the trial states used for @xmath74 calculations are simple generalizations of the amplitude - product states discussed in sec . [ sec : vbqmc0 ] , with the wave - function coefficient given by eq . ( [ apcoeff ] ) with no dependence on the unpaired spins . in principle one could improve the trial states by factors depending on the unpaired spins and spin - bond correlations as well ( as recently investigated in detail in ref .  ) , but this is not necessary here . following the reasoning in sec . [ sec : vbqmc0 ] , for @xmath23 , @xmath71 for @xmath72 and @xmath73 for @xmath69 , i.e. , the momentum difference with respect to the @xmath68 ground state is @xmath82 in both cases , as it should be for the lowest triplet excitation . for the @xmath0 states , if we strictly label the sites with sublattice labels @xmath40 and @xmath41 , there is a defect in the odd-@xmath9 system , as discussed above . however , in the simulations there are no explicit references to sublattices and in effect the system is then translationally invariant . then , under the further assumption that no bonds with length as large as @xmath83 are present ( such configurations having ill - defined signs ) @xcite , the momentum is @xmath73 or @xmath82 , for @xmath9 of the forms @xmath84 and @xmath85 , respectively .      in order to study spinon sizes and confinement lengths , we consider overlaps written in the form @xmath86 generalizing eq . ( [ pab ] ) to @xmath0 ( single - spinon ) systems and written explicitly using sums of terms with all possible locations of the unpaired spins . we have an analogous form @xmath87 for @xmath23 ( spinon - pair ) systems . the overlaps are not computed explicitly in the simulations but serve as normalization factors and weights in the sampling procedures , such that the different contributions to the above sums appear according to their relative weights . the practical simulation procedures for @xmath74 are relatively straight - forward generalizations of the method with loop updates for @xmath68 . we refer to refs .   for technical details . in the following , we discuss distribution functions used to characterize spinons . we will here make us of the unpaired spins , although in principle one can also define spinon quantities using the entire strings , of which the unpaired spins are the end points .      as discussed above , in the vbpqmc method the bra and ket states are generated stochastically , and for @xmath0 we can use eq . ( [ eq : overlapshalf ] ) to define a distribution of the separation of the unpaired spins in the bra and ket states . restricting ourselves to a translationally invariant system we have the probability of separation @xmath88 ( up to an irrelevant normalization factor which is easily computed at the end ) : @xmath89 where the subscript @xmath90 serves to indicate that the unpaired spins should be on the same sublattice ( because there is an excess of one site on one of the sublattices , which is the sublattice with the unpaired spin ) , which we can take as the @xmath40 sublattice . thus , @xmath91 should vanish when the separation @xmath63 is an odd number of lattice spacings . our basic assertion is that , if spinons are well - defined quasiparticles of the system , then we expect @xmath92 to reflect the size and shape of an _ intrinsic _ `` wave packet '' within which the net magnetization @xmath93 carried by the spinon is concentrated . we will show in the following that 1d vbs states are characterized by an exponentially decaying overlap , @xmath94 , and it is then natural to take @xmath1 as a definition of the intrinsic spinon size . we should here note again that , for a periodic system with an odd number of sites , there is , strictly speaking , no absolute distinction between the sublattices ( i.e. , the system is strictly speaking not bipartite ) . however , when the system size @xmath95 we in general expect the role of the boundary condition to diminish and @xmath91 to tend to zero for any given odd @xmath63 . in sec . [ sec:1d ] , we will discuss in detail how this limit is approached , and we will also see an example ( one where spinons are not well - defined quasi - particles ) where the boundaries continue to play a role even for infinite size .      in the case of @xmath23 states ( two spinons ) , we can define several different distributions . here , we will focus on the separation of spinons on _ different _ sublattices in the bra and ket ; @xmath96 in the case where a single spinon is a well - defined quasi - particle , i.e. , @xmath97 , we expect this quantity to give us information on the confinement or deconfinement of two spinons . in the former case , we will see that asymptotically @xmath98 and , thus , we consider @xmath2 as a definition of the confinement length - scale ( i.e. , the size of the @xmath23 spinon bound state ) . we will see that deconfined spinons give rise to characteristic broad distributions . we could also have defined the above distance distribution with the two unpaired spins both in the bra or in the ket , and we have also investigated it . this distribution typically does not differ significantly from the one defined in eq . ( [ pabdef ] ) . we will also study the analog of the @xmath0 quantity @xmath91 [ eq .  ( [ paadef1 ] ) ] in the triplet state , defined as @xmath99    where we use the @xmath100 superscript to distinguish this distribution from the single - spinon distribution ( [ paadef1 ] ) . we can define @xmath101 in the same way , and use @xmath102 to improve the statistics . we will see that , under certain conditions , @xmath103 of the triplet state contains the same information for the spinon size @xmath1 as the @xmath0 quantity @xmath92 , and we can use this property of the @xmath23 state to characterize the intrinsic spinon size also in cases where the @xmath0 state breaks translational invariance and is not appropriate for use with our calculations presuming translational invariance ( the @xmath104-leg ladder system being such an example , which will be studied below in sec . [ sec : ladder ] ) .","summary":"using several different one - dimensional models , we characterize spinon excitations using the intrinsic spinon size and confinement length ( the size of a bound state ) . the spinons have finite size in valence - bond - solid states , infinite size in the critical region ( with overlaps characterized by power laws ) , and become ill defined ( completely unlocalizable ) in the nel state ( which we stabilize in one dimension by introducing long - range interactions ) . we also verify that pairs of spinons are deconfined in uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths ( dimerization ) or coupling two chains ( forming a ladder ) . in the dimerized system ,","abstract":"observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many - body physics . here we further explore a computational scheme [ y. tang and a. w. sandvik , phys .  rev .  lett .  * 107 * , 157201 ( 2011 ) ] based on valence - bond quantum monte carlo simulations of quantum spin systems . using several different one - dimensional models , we characterize spinon excitations using the intrinsic spinon size and confinement length ( the size of a bound state ) . the spinons have finite size in valence - bond - solid states , infinite size in the critical region ( with overlaps characterized by power laws ) , and become ill defined ( completely unlocalizable ) in the nel state ( which we stabilize in one dimension by introducing long - range interactions ) . we also verify that pairs of spinons are deconfined in uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths ( dimerization ) or coupling two chains ( forming a ladder ) . in the dimerized system , an individual spinon can be small when the confinement length is large ; this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence - bond - solid ( where the spinons are deconfined ) . based on our numerical results , we argue that a system with is associated with weak repulsive short - range spinon - spinon interactions . in principle , both the length scales and can still be individually tuned from small to infinite ( with ) by varying model parameters . in contrast , in the ladder system the two lengths are always similar , and this is the case also in the weakly dimerized systems when the corresponding uniform chain is in the critical phase . in these systems , the effective spinon - spinon interactions are purely attractive and there is only a single large length scale close to criticality , which is reflected in the standard spin correlations as well as in the spinon characteristics ."}
{"article_id":"1404.6697","section_id":"i","document":"we have used a computational technique based on valence - bond projector qmc simulations to study the spinon size @xmath1 and the confinement length @xmath2 in 1d spin systems . we found that when a system has only one unpaired spinon , the overlap between valence - bond states with unpaired @xmath93 moment residing at distance @xmath63 away from each other decays as @xmath234 in a gapped vbs , where we interpret @xmath1 as characterizing the intrinsic spinon size . in a critical state , the overlap instead decays as @xmath131 , which we interpret as spinons that are only marginal particles , on the verge of losing their identities as quasi - particles . when the system has two spinons , the distribution s function for the distance between them decays as @xmath235 if the spinons are confined ( which we have studied using a modulated pattern of weak and strong coupling constants , which leads to a linear spinon - binding potential ) , with @xmath2 characterizing the size of the bound state . for deconfined spinons ( which we have studied in vbs states and critical states ) , we found that the distribution function instead exhibits a broad peak at the largest separation , demonstrating a weak repulsive potential between the spinons . we studied the heisenberg two - leg ladder system . by tuning the rung coupling , the system can be driven from a deconfining phase ( two decoupled chains ) to a confining phase . in this case the spinon size is always similar to the size of the bound state .    in the bethe - ansatz solution of the heisenberg chain , spinons are non - interacting particles ( kinks and anti - kinks ) , but it should be noted that these particles are obtained from the original spin degrees of freedom using a highly non - local transformation . what we have probed here is instead more direct measures of the spatial `` concentration '' , @xmath91 , of the total magnetization of a single spinon , and the correlations between ( essentially ) the center of mass of two such distributions , @xmath151 . since our calculation projects out the lowest state with given total spin , in the case of @xmath23 the total momentum @xmath71 ( in the case of a chain with @xmath72 sites ) therefore , the spinons here are not propagating , having individual spin @xmath232 and @xmath82 ( these giving the lowest possible energies in light of the des clauseaux - pearson dispersion ) . in principle our calculations can also handle total momentum away from @xmath71 , but in practice , due to phase problems in the monte carlo sampling , we are restricted to momenta close to @xmath232 and @xmath82 . in the future , it would be interesting to more exhaustively characterize all the length scales of the system ( including @xmath1 , @xmath2 , as well as the spin and vbs correlation lengths ) and their divergences under the various conditions afforded by the models we have performed initial studies on here .","summary":"lett .  * 107 * , 157201 ( 2011 ) ] based on valence - bond quantum monte carlo simulations of quantum spin systems .","abstract":"observing constituent particles with fractional quantum numbers in confined and deconfined states is an interesting and challenging problem in quantum many - body physics . here we further explore a computational scheme [ y. tang and a. w. sandvik , phys .  rev .  lett .  * 107 * , 157201 ( 2011 ) ] based on valence - bond quantum monte carlo simulations of quantum spin systems . using several different one - dimensional models , we characterize spinon excitations using the intrinsic spinon size and confinement length ( the size of a bound state ) . the spinons have finite size in valence - bond - solid states , infinite size in the critical region ( with overlaps characterized by power laws ) , and become ill defined ( completely unlocalizable ) in the nel state ( which we stabilize in one dimension by introducing long - range interactions ) . we also verify that pairs of spinons are deconfined in uniform spin chains but become confined upon introducing a pattern of alternating coupling strengths ( dimerization ) or coupling two chains ( forming a ladder ) . in the dimerized system , an individual spinon can be small when the confinement length is large ; this is the case when the imposed dimerization is weak but the ground state of the corresponding uniform chain is a spontaneously formed valence - bond - solid ( where the spinons are deconfined ) . based on our numerical results , we argue that a system with is associated with weak repulsive short - range spinon - spinon interactions . in principle , both the length scales and can still be individually tuned from small to infinite ( with ) by varying model parameters . in contrast , in the ladder system the two lengths are always similar , and this is the case also in the weakly dimerized systems when the corresponding uniform chain is in the critical phase . in these systems , the effective spinon - spinon interactions are purely attractive and there is only a single large length scale close to criticality , which is reflected in the standard spin correlations as well as in the spinon characteristics ."}
{"article_id":"1102.4589","section_id":"i","document":"to understand a group @xmath0 , it is often useful to decompose it as an amalgamated free product or an hnn extension over a subgroup that belongs to a well - understood class of groups , such as trivial groups , finite groups or cyclic groups . more generally , consider all possible factorizations of @xmath0 as a graph of groups with edge stabilizers in some single class of groups . it is often possible to show the existence of a single graph of groups decomposition , from which all of these factorizations can be obtained . this is called a _ jsj decomposition _ of @xmath0 ( over subgroups in the given class ) , although the notion is imprecise on how the other factorizations of @xmath0 are to be obtained from the jsj decomposition . an example is grushko s theorem , which gives all the maximal decompositions of a finitely generated group over the class of trivial groups ( i.e. the free factorizations ) . the letters jsj stand for jaco , shalen and johannson . their results in @xcite and @xcite can be interpreted as the existence of a jsj decomposition for @xmath1-manifold groups over subgroups isomorphic to @xmath2 . it was these works that motivated the study of jsj decompositions over non - trivial subgroups ( i.e. aside form the grushko decomposition ) . various existence theorems were obtained by kropholler @xcite , rips and sela @xcite , @xcite , bowditch @xcite , dunwoody and sageev @xcite , fujiwara and papasoglu @xcite , dunwoody and swenson @xcite and scott and swarup @xcite . in @xcite and @xcite guirardel and levitt propose a precise definition of jsj decomposition , which is verified by the graphs of groups constructed in most of the mentioned works . the constructions in @xcite and @xcite constitute other notions of jsj decomposition , as does the compatibility jsj decomposition in @xcite .    in this paper we will focus on the jsj decomposition due to rips and sela @xcite , for finitely presented one - ended groups , with infinite cyclic edge stabilizers ( stated here as theorem [ rips - sela ] ) . it is not always clear how to recognize whether a given graph of groups is a jsj decomposition of its fundamental group . in @xcite , forester studied the _ generalized baumslag solitar ( gbs ) groups _ , which are defined by graphs of groups whose vertex and edge stabilizers are infinite cyclic . he showed that the defining graph of a gbs group is a jsj decomposition , under mild hypotheses .    in this paper we introduce the _ quadratic baumslag solitar ( qbs ) groups_. they are defined by graphs of groups whose edge groups are infinite cyclic , and whose vertex groups can be either infinite cylic or _ quadratically hanging _ surface groups . ( for the meaning of quadratically hanging see definition [ qh ] ) . it is clear that the gbs groups are a subclass of the qbs groups . we extend forester result to the class of qbs groups . i.e. we show that the defining graph of a qbs group is a jsj decomposition , under some conditions . specifically , the main theorem in this paper is the following . [ jsj ] let @xmath3 be a qbs graph , @xmath4 . suppose that @xmath3 is reduced and satisfies the following conditions :    1 . each edge @xmath5 of @xmath3 has labels @xmath6 . each gbs component @xmath7 of @xmath3 is reduced , and @xmath8 is not a point or a line . then @xmath3 is a rips - sela jsj decomposition for @xmath0    a _ qbs graph _ is the defining graph of a qbs group . see section [ jsjintro : elem ] for the definition of a reduced graph of groups . for the edge labels , see definition [ labs ] . and the gbs components of a qbs graph are defined at the begining of section [ s - qbs ] . the paper is organized as follows : in section [ jsjintro ] we review the basics of the rips - sela jsj decomposition . there we discuss _ universality _ and _ unfoldedness _ , the two main conditions for a graph of groups ( with cyclic edge groups ) to be a jsj decomposition ( in the sense of rips and sela ) . in section [ gbs - section ] we recall the results of forester about gbs groups , which we will need when dealing with qbs groups . in section [ s - unf ] we prove a general criterion for unfoldedness , theorem [ unf - univ ] , in the same fashion of proposition 2.17 in @xcite . section [ s - univ ] is devoted to theorem [ univ - new ] . this theorem applies to general graphs of groups with cyclic edge stabilizers , and it allows us to show the universality of the whole graph from the universality of certain subgraphs . finally , in section [ s - qbs ] we introduce the qbs groups , and prove they are one - ended with the exception of @xmath9 ( proposition [ one - end ] ) . we also give the proof of theorem [ jsj ] . in this proof we combine theorem [ univ - new ] with the results of forester ( section [ gbs - section ] ) to show universality , and we use theorem [ unf - univ ] to prove unfoldedness .","summary":"generalized baumslag - solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups . forester proved that in most cases the defining graphs are cyclic jsj decompositions , in the sense of rips and sela . here we extend forester s results to graphs of groups with vertex groups that can be either infinite cyclic or quadratically hanging surface groups .","abstract":"generalized baumslag - solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups . forester proved that in most cases the defining graphs are cyclic jsj decompositions , in the sense of rips and sela . here we extend forester s results to graphs of groups with vertex groups that can be either infinite cyclic or quadratically hanging surface groups ."}
{"article_id":"1310.6354","section_id":"i","document":"as the canonical example of topological order , the fractional quantum hall ( fqh ) effect was originally discovered in two - dimensional electron gas subject to a strong perpendicular magnetic field . @xcite recently , several groups demonstrated numerically that these strongly - correlated phases also exist in a topological flat band characterized by a non - zero chern number @xmath0 , even in the absence of a magnetic field . @xcite this discovery of the so - called fractional chern insulators ( fci ) generated enormous interest . @xcite subsequent numerical studies  @xcite quickly confirmed the presence of more intricate single - component fqh states in lattice models  @xcite , such as the read - rezayi series  @xcite and the composite - fermion states  @xcite . powerful techniques from the study of fqh , including density algebra ,  @xcite entanglement spectrum ,  @xcite parton construction ,  @xcite and the hamiltonian theory of composite fermions ,  @xcite were introduced to understand the topological ground state of fci and the nature of its excitations . @xcite possible experimental realizations have also been proposed . @xcite    most of the above progress dealt with a topological band with chern number @xmath1 , which is essentially the same  @xcite as the continuum fqh in a periodic potential  @xcite . the strongly - correlated physics in a @xmath2 chern band  @xcite turned out much richer than the conventional fqh , due to the interplay between topological order and lattice structure . @xcite barkeshli and qi  @xcite mapped a @xmath2 chern band to a @xmath0-component lowest landau level ( lll ) using hybrid wannier states  @xcite , and suggested the possibility to realize multicomponent fqh states in a single chern band . numerical studies  @xcite indeed found clear signature of such states , including the color @xmath3 version of the halperin  @xcite and the non - abelian spin - singlet states  @xcite ( nass ) , but also identified qualitative deviations from these states ,  @xcite which implies a more complex structure than proposed in ref .  . in a previous paper ,  @xcite we proposed to understand these new features as the consequences of a special set of boundary conditions associated with the lll mapping . in the simplest case , this alternative boundary condition can be understood as a color - dependent magnetic flux insertion . we demonstrated that the multicomponent lll in a new bloch basis can be seen as a single manifold with constant berry curvature and chern number @xmath0 . using pseudopotential hamiltonians , we constructed model states for fci with an arbitrary chern number , and found high overlaps with the exact ground states . crucially , our model states correctly capture the anomalous features in the particle entanglement spectrum of the @xmath2 fci that make our states distinct from the conventional multicomponent fqh states .    in this paper we provide details of the mapping between a chern band and a multicomponent lll , and demonstrate the distinctive features of our pseudopotential hamiltonian due to the new boundary conditions . we construct , in a @xmath0-component lll , a momentum - space bloch basis and a hybrid wannier basis that mimic the lattice counterparts . both bases entangle the real space and the internal color space . using the explicit one - body wave functions for the bases , we derive the representation of the projected density operators in both bases . we define model states as the exact zero modes of the pseudopotential hamiltonian built from the projected density operators . as we demonstrated in our previous paper  @xcite , the bloch basis is useful for numerical studies as it preserves the full lattice symmetry . the hybrid wannier basis , on the other hand , facilitates the analysis of the pseudopotential hamiltonian . we give a detailed analysis of the simplest bosonic pseudopotential hamiltonian for the halperin color - entangled states . we show that the pseudopotential hamiltonian reduces to _ almost _ classical electrostatics in the hybrid wannier basis , when we take the so - called thin - torus limit  @xcite and carry out truncations motivated by previous numerical results . @xcite this enables us to write down the form of its zero modes in this limit . however , in contrast to most well - known fqh states such as laughlin and read - rezayi , a purely classical thin - torus description is not possible . we pinpoint the key difference from the conventional multicomponent fqh due to a subtle twist in the hybrid wannier states , and detail the procedure to compute the total bloch momentum of each zero mode . the resulting algorithm correctly predicts the degeneracy of the fci quasiholes in each lattice momentum sector , without resorting to numerical diagonalization , and can be seen as the extension of the generalized pauli principle  @xcite to the color - entangled states .","summary":"we first construct pseudopotential hamiltonians for fractional chern insulators . we achieve this by mapping the lattice problem to the lowest landau level of a multicomponent continuum quantum hall system with specially engineered boundary conditions .","abstract":"in this paper we provide analytical counting rules for the ground states and the quasiholes of fractional chern insulators with an arbitrary chern number . we first construct pseudopotential hamiltonians for fractional chern insulators . we achieve this by mapping the lattice problem to the lowest landau level of a multicomponent continuum quantum hall system with specially engineered boundary conditions . we then analyze the thin - torus limit of the pseudopotential hamiltonians , and extract counting rules ( generalized pauli principles , or haldane statistics ) for the degeneracy of its zero modes in each bloch momentum sector ."}
{"article_id":"1205.3573","section_id":"i","document":"dans ce texte , nous poursuivons notre investigation de la conjecture de manin sur le comportement asymptotique du nombre de courbes de degr born sur les hypersurfaces intrinsques linaires , cest -  - dire les varits do nt lanneau total de coordonnes sidentifie  lanneau dune hypersurface affine do nt lquation vrifie en outre une certaine proprit de linarit . nous renvoyons  la section [ sec : cox ] pour plus de prcisions sur la terminologie . signalons dores et dj que la classification de derenthal des surfaces de del pezzo gnralises de degr @xmath1 do nt lanneau total de coordonnes na quune quation ( _ cf . _ @xcite ) montre que les 21 surfaces quil obtient tombent toutes dans la classe considre , sauf une ( lune des deux surfaces cubiques avec singularit @xmath2 ) . ces surfaces ont t intensment tudies dans le cadre de la conjecture de manin arithmtique ( valuation asymptotique du nombre de points rationnels de hauteur borne lorsque le corps de base est le corps des rationnels ) , _ cf . _   @xcite    le rsultat principal obtenu dans cet article est le suivant . nous lnonons dans cette introduction sous une forme volontairement simplifie . soit @xmath3 un corps parfait et @xmath4 une @xmath3-courbe projective , lisse et gomtriquement intgre de genre @xmath5 . soit @xmath0 une surface projective , lisse et gomtriquement intgre dfinie sur @xmath3 qui est une hypersurface intrinsque linaire , et qui vrifie en outre lhypothse [ hyp : noninter ] ci - dessous . alors @xmath0 satisfait une version partielle des conjectures de manin gomtriques . le rsultat est donn sous sa forme prcise par le thorme [ thm : main ] . nous nous contentons ici de quelques commentaires . tout dabord , dans cet article , lappellation conjectures de manin gomtriques recouvrira dune part un cadre o le corps @xmath3 est suppos fini et o on sintresse  la problmatique du comptage asympotique de courbes de degr born , et dautre part un cadre o le corps @xmath3 peut tre a priori quelconque , et o on tudie la dimension et le nombre de composantes des espaces de modules de morphismes de courbes de degr donn . la section [ sec : conj ] contient plus de dtails sur la forme prcise des conjectures tudies dans ce texte . ensuite , la partialit voque dans lnonc ci - dessus est explicitement quantifiable  : le thorme dit en gros que pour les cas considrs , la conjecture de manin vaut sur une certaine partie explicite du dual @xmath6 du cne effectif de @xmath0 . par exemple le rsultat dit que sur cette partie , lespace de modules de morphismes est irrductible et a la dimension attendue . pour deux surfaces de la liste de derenthal ( en fait pour trois , mais pour la troisime le rsultat tait dj connu daprs nos travaux prcdents ) on obtient les conjectures de manin compltes , cest -  - dire que les conjectures valent sur @xmath6 , et pour cinq autres on obtient une version complte  la limite  de ces conjectures ( on peut trouver des parties en fait des runions de cnes sur lesquelles les conjectures valent et do nt le volume est aussi proche que lon veut de celui de @xmath6 ) , _ cf . _   le corollaire [ cor : manin : delpezzo ] . pour toutes les autres , on peut calculer explicitement la proportion de @xmath6 sur laquelle notre mthode montre que les conjectures valent , _ cf . _   la table [ tab : results ] . en particulier , les rsultats de @xcite ( qui concernaient le cadre de ltude de la dimension des espaces de modules ) sont amliors . nous renvoyons  la section [ sec : res : main ] pour plus de prcisions . enfin , il faut souligner que le thorme [ thm : main ] isole le terme principal attendu et identifie explicitement le terme derreur  qui est la cause de la partialit dans lnonc ci - dessus . il montre en que les conjectures compltes sont vrifies si et seulement si ce dernier terme peut tre contrl de manire ad hoc . la mthode employe dans ce texte ne nous permet dobtenir ce contrle que sur certaines rgions du dual du cne effectif , celles o les coefficients de lquation de lanneau de coordonnes total de @xmath0 sont de degr suffisamment grand . si cette dernire condition nest pas vrifie , il faut tenir compte des syzygies en bas degr , ce qui semble dlicat ( mais peut - tre pas insurmontable ) . le schma gnral de la stratgie employe dans cet article est le mme que pour @xcite  : relvement du problme de comptage en termes de lanneau total de coordonnes de @xmath0 , inversion de mbius , comptage de sections globales vrifiant certaines quations linaires  laide de riemann - roch et dalgbre linaire lmentaire et tude des sries gnratrices en dcoulant . cependant , dans le prsent travail , lutilisation dune inversion de mbius partielle  et non plus totale jointe  une tude plus fine des sries gnratrices intervenant permettent daffaiblir et de simplifier de manire significative les hypothses qui taient ncessaires dans @xcite , do nt certaines exigeaient des calculs lourds et peu clairants pour leur ventuelle vrification , et ntaient dailleurs pas vrifies pour toutes les surfaces de la liste de derenthal . la seule hypothse ncessaire est ici lhypothse [ hyp : noninter ] , qui est trs simple  vrifier pour peu quon ait une description explicite de lanneau de coordones total de la varit considre . on voit ainsi aussitt quelle est satisfaite par les 20 surfaces de la liste de derenthal . peut - tre pourrait - t - on dailleurs se risquer  esprer quelle est satisfaite pour toutes les hypersurfaces intrinsques linaires . on montre notamment sous cette seule hypothse que le terme principal de la fonction zta des hauteurs correspond bien  celui prdit par peyre ( _ cf . _   la relation ) . dans @xcite , cette proprit ncessitait a priori une vrification calculatoire au cas par cas ( _ cf . _   la remarque 11 de _ op.cit._ ) .    il est  noter que le rsultat final est dmontr pour les surfaces , mais que beaucoup darguments , notamment ceux utiliss pour le calcul du terme principal , sont valables en toute dimension , et sont donns dans ce cadre . il est sans doute possible , au prix de complications techniques , dtendre les rsultats obtenus en dimension suprieure . il faut remarquer que peu dexemples explicites dhypersurfaces intrinsques linaires en dimension suprieure semblent connus .","summary":"soit une surface do nt lanneau de cox a une seule relation , laquelle vrifie en outre une certaine proprit de linarit . nous montrons , sous une hypothse simple , que les conjectures de manin gomtriques valent pour certains degrs du cne effectif dual de ( notamment pour ces degrs lespace de modules de morphismes a la dimension attendue ) . le rsultat sapplique  une classe de surfaces de del pezzo gnralises qui a t intensment tudie dans le cadre de la conjecture de manin arithmtique .       * * msc * : 11g50 , 14j26 , 14c20 , 14d22 , 14h10","abstract":"soit une surface do nt lanneau de cox a une seule relation , laquelle vrifie en outre une certaine proprit de linarit . nous montrons , sous une hypothse simple , que les conjectures de manin gomtriques valent pour certains degrs du cne effectif dual de ( notamment pour ces degrs lespace de modules de morphismes a la dimension attendue ) . le rsultat sapplique  une classe de surfaces de del pezzo gnralises qui a t intensment tudie dans le cadre de la conjecture de manin arithmtique .       * _ some examples of curves countings on surfaces . _ * let be a surface whose cox ring has a single relation satisfying moreover a kind of linearity property . under a simple assumption , we show that the geometric manin s conjectures hold for some degrees lying in the dual of the effective cone of ( in particular , for those degrees the moduli space of morphisms has the expected dimension ) . the result applies to a class of generalized del pezzo surfaces which has been intensively studied in the context of the arithmetic manin s conjecture .    * msc * : 11g50 , 14j26 , 14c20 , 14d22 , 14h10"}
{"article_id":"astro-ph9603040","section_id":"i","document":"the apm galaxy survey ( maddox  1990a , b ) includes about two million galaxies down to magnitude @xmath1 over 4300 square degrees of the southern sky . it was the first machine - generated galaxy survey to cover an area of sky significantly larger than one schmidt plate , and has proved an important survey for measuring galaxy number - magnitude counts over a wide magnitude range ( ) and particularly for the most reliable measurement to - date of the angular correlation function of galaxies on large scales ( ) . this latter measurement was one of the first results to rule out the standard cold dark matter model of galaxy formation ( eg . ) . unfortunately , the apm galaxy survey , while complete to a faint magnitude limit of @xmath1 , is not very reliable for galaxies brighter than @xmath2 . there are several reasons for this . firstly , the surface density of galaxies brighter than @xmath2 is only about @xmath3 of the surface density of stars at the same magnitude limit even at the galactic poles . therefore the selection of an uncontaminated bright galaxy sample requires an exceptionally reliable method of rejecting stars and merged images . secondly , photographic emulsions have a limited dynamic range , and in order to detect images as faint as @xmath1 , the brighter images are necessarily saturated . thirdly , bright stars have diffraction spikes and ` ghost ' images ( ) and large galaxies contain sub - structure . all of these factors prevent the standard apm image parameters , which were designed to classify small , faint images , from selecting a sufficiently reliable bright galaxy catalogue . this paper describes the construction of a bright galaxy catalogue , complete to @xmath4 , using the same apm scans used for the faint survey . we developed a semi - automated method of star - galaxy separation , whereby most stellar images were rejected ( losing only about 3% of galaxies ) and the remaining images inspected by eye on a film copy of the photographic plate . the distinction is emphasized between a survey _ constructed _ by eye , for example the catalogue or the lick ( ) survey , where the observer has to locate each image and _ then _ decide whether it should be included in the catalogue , and a semi - automated survey like the present one where the observer is given the position of each image satisfying a magnitude limit , and then classifies it as a galaxy or star . it is much easier for the eye to distinguish a galaxy from a star than it is to select a complete magnitude or diameter limited sample , and so the semi - automated survey should be much more reliable . the apm bright galaxy catalogue ( apm - bgc ) covers almost the same area as the faint apm galaxy survey of maddox  ( 1990a , b ) , including 180 out of the 185 fields of the fainter survey , an area of approximately 4,180 square degrees . figure  [ fig : fields ] shows the distribution of the 180 survey fields in an equal area projection on the sky . the construction of the present catalogue was first described by loveday ( 1989 ) . a similar survey has been carried out by raychaudhury ( 1989 ) in the region towards the ` great attractor ' , and there is an ongoing effort ( raychaudhury  1994 ) to map out the galaxy distribution near the equator . the layout of the paper is as follows . the construction of the bright galaxy catalogue , including star - galaxy separation and plate matching , is described in  [ sec : constr ] . internal tests for uniformity , completeness and consistency are described in  [ sec : int_tests ] and comparison with other catalogues is made in  [ sec : other_cats ] .  [ sec : photometry ] describes the ccd calibrations used to check the apm to @xmath0 magnitude conversion , as a further test of photometric uniformity in the survey , and to define a second - order correction for photographic saturation . in  [ sec : catalogue ] we describe the catalogue data and present plots of the galaxy distribution . we compare the angular and spatial correlation functions of early and late type galaxies in the apm - bgc in  [ sec : clust ] . finally , the properties of the catalogue are summarized in  [ sec : summary ] .","summary":"remaining images are inspected by eye on film copies of the survey material and classed as stellar , multiple stellar , galaxy , merger or noise . * key words : * catalogues  galaxies : fundamental parameters  galaxies : general  galaxies : photometry .","abstract":"the apm bright galaxy catalogue lists positions , magnitudes , shapes and morphological types for 14,681 galaxies brighter than magnitude 16.44 over a 4,180 square degree area of the southern sky . galaxy and stellar images have been located from glass copy plates of the united kingdom schmidt telescope ( ukst ) iiiaj sky survey using the automated photographic measuring ( apm ) facility in cambridge , england . the majority of stellar images are rejected by the regularity of their image surface brightness profiles . remaining images are inspected by eye on film copies of the survey material and classed as stellar , multiple stellar , galaxy , merger or noise . galaxies are further classified as elliptical , lenticular , spiral , irregular or uncertain . the 180 survey fields are put onto a uniform photometric system by comparing the magnitudes of galaxies in the overlap regions between neighbouring plates . the magnitude zero - point , photometric uniformity and photographic saturation are checked with ccd photometry . finally , the completeness and reliability of the catalogue is assessed using various internal tests and by comparing with several independently constructed galaxy catalogues .    * key words : * catalogues  galaxies : fundamental parameters  galaxies : general  galaxies : photometry ."}
{"article_id":"astro-ph9603040","section_id":"i","document":"we have described the construction of a catalogue of 14,681 galaxies brighter than @xmath4 over a large fraction of the southern sky . the images were detected and parameterized by scanning 180 united kingdom schmidt telescope plates with the automated plate measuring system . preliminary star - galaxy separation was carried out automatically using image profiles . all galaxy candidates were inspected by eye and assigned a morphological classification . a completeness of 97% was aimed for . by comparing image classifications in overlaps between plates (  [ sec : ovlps ] ) , we infer an actual completeness of 96.3% . as an external check on completeness , we correlated the eso galaxy catalogue with the apm - bgc . we found that about 1.5% of eso galaxies are too large to be detected by the apm machine ( these galaxies are listed in table  [ tab : esobig ] ) and a further 3% of eso galaxies were detected by the apm machine but not classified as a galaxy in the apm - bgc . overall , we estimate that the apm - bgc is at least 95% complete . most of the incompleteness is due either to high surface brightness galaxies with star - like profiles ( fig . [ fig : eso_sb](d ) ) or low surface brightness galaxies which fall below our detection threshold . we plan to study surface - brightness selection effects in apm galaxy data in a future paper . the reliability of the morphological classification in the apm - bgc was checked both internally using plate overlaps and externally by comparison with other catalogues . we conclude that the apm - bgc does not reliably distinguish between elliptical and lenticular galaxies ; these classes should be combined in any statistical analysis . time - dependent classification effects may produce an error in the type - dependent angular correlation function of @xmath89 . we classify fewer galaxies as late type at fainter magnitudes . the photometry of the survey has been checked using ccd photometry of 259 galaxies . we fit a polynomial to the ccd versus apm magnitudes to correct for saturation and to define the magnitude zero - point . we find a scatter of 0.31 mag about this relation for individual galaxies . comparison of the angular correlation functions calculated using intra- and inter - plate pairs of galaxies (  [ sec : field - effects ] ) shows no evidence for significant plate - to - plate errors in photometry . the ccd@xmath105apm magnitude residuals are uncorrelated with each other and the plate zero - points , confirming the absence of large scale gradients in calibration . the apm bright galaxy catalogue is a reliable , new catalogue of bright galaxies which complements the fainter apm galaxy survey and the diameter - selected eso survey . the catalogue is about 96% complete and has essentially zero contamination since every galaxy has been inspected by eye . it has proved to be a valuable source catalogue for the stromlo - apm redshift survey ( loveday  1992 ) and we hope that it will be useful for other followup work .      the major part of this work was carried out while the author was a graduate student at the university of cambridge , and i thank the institute of astronomy and jesus college , cambridge , for their support . it is a great pleasure to thank the apm team ( mick bridgeland , pete bunclark , mike irwin and ed kibblewhite ) for making the apm galaxy surveys possible . thanks also to bruce peterson who obtained some of the ccd photometry , to somak raychaudhury for helpful comments and to bob nichol for generating some finding charts . i am indebted to george efstathiou and steve maddox for invaluable guidance , help and discussion throughout this project . * references *","summary":"the apm bright galaxy catalogue lists positions , magnitudes , shapes and morphological types for 14,681 galaxies brighter than magnitude 16.44 over a 4,180 square degree area of the southern sky . galaxy and stellar images have been located from glass copy plates of the united kingdom schmidt telescope ( ukst ) iiiaj sky survey using the automated photographic measuring ( apm ) facility in cambridge , england . finally , the completeness and reliability of the catalogue is assessed using various internal tests and by comparing with several independently constructed galaxy catalogues .   ","abstract":"the apm bright galaxy catalogue lists positions , magnitudes , shapes and morphological types for 14,681 galaxies brighter than magnitude 16.44 over a 4,180 square degree area of the southern sky . galaxy and stellar images have been located from glass copy plates of the united kingdom schmidt telescope ( ukst ) iiiaj sky survey using the automated photographic measuring ( apm ) facility in cambridge , england . the majority of stellar images are rejected by the regularity of their image surface brightness profiles . remaining images are inspected by eye on film copies of the survey material and classed as stellar , multiple stellar , galaxy , merger or noise . galaxies are further classified as elliptical , lenticular , spiral , irregular or uncertain . the 180 survey fields are put onto a uniform photometric system by comparing the magnitudes of galaxies in the overlap regions between neighbouring plates . the magnitude zero - point , photometric uniformity and photographic saturation are checked with ccd photometry . finally , the completeness and reliability of the catalogue is assessed using various internal tests and by comparing with several independently constructed galaxy catalogues .    * key words : * catalogues  galaxies : fundamental parameters  galaxies : general  galaxies : photometry ."}
{"article_id":"0711.2021","section_id":"i","document":"the fundamental understanding of dynamically arrested states is a major challenge of contemporary statistical physics and materials science @xcite . model experimental colloidal suspensions , whose dynamics has been the subject of study on its own right @xcite , have played an essential role in the study of dynamic arrest phenomena , providing experimental realizations in finely - controlled systems and conditions @xcite . thus , it is an experimental fact that by changing a macroscopic control parameter such as the volume fraction , or by tuning the effective inter - particle interactions , one may drive the system from the region of equilibrium ( ergodic ) states to the region of dynamically arrested ( non - ergodic ) states . first - principles models and theories that predict and describe these transitions thus constitute an essential aspect of the fundamental understanding of these phenomena . the mode coupling theory ( mct ) of the ideal glass transition @xcite is perhaps the most comprehensive theory of this sort , some of whose predictions have found beautiful experimental confirmation @xcite . many issues , however , still remain to be understood , and this has prompted the proposal of extended versions of this theory @xcite , or the development of alternative approaches @xcite .    in this context , in recent work a new first - principles theory of dynamic arrest has been proposed @xcite which is essentially the application of the self - consistent generalized langevin equation ( scgle ) theory of colloid dynamics @xcite to the analysis of dynamic arrest phenomena in colloidal systems . the scgle theory was originally devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate - times regimes . its self - consistent character , however , introduces a non - linear dynamic feedback , leading to the prediction of dynamic arrest in these systems , similar to that exhibited by the mode coupling ( mc ) theory of the ideal glass transition . the resulting theory of dynamic arrest in colloidal dispersions was applied in recent work to describe the glass transition in three mono - disperse experimental systems with specific ( hard - sphere , screened electrostatic , and depletion ) inter - particle effective forces @xcite , with the same quantitative predictive power as conventional mct , but with a smaller degree of difficulty in its application @xcite . the present paper introduces the multi - component extension of the scgle theory of colloid dynamics @xcite as a new alternative first - principles theory of dynamic arrest in colloidal mixtures . colloidal mixtures offer a richer variety of possible dynamic arrest scenarios @xcite . these include , for example , the possibility that the particles of one species become arrested , while the particles of the other species continue to diffuse through the disordered matrix of the arrested particles . in fact , an important prediction of the multi - component extension of mct @xcite was precisely the existence of these mixed states @xcite . later studies of dynamic arrest in mixtures @xcite have been based on mct not because it is the ultimate and definitive theory , but because it was virtually the only first - principles theory of dynamic arrest available that had a high level of predictive capability . however , relevant issues remain that have not been resolved by its application . for example , although the one - component version of mct predicts the existence of repulsive glasses in a hard - sphere system , and its melting upon the addition of a small amount of smaller particles ( depletion forces ) , followed by the reentrance to a new kind of ( attractive ) glass @xcite , no reentrance seems to be predicted by the two - component version of mct @xcite . issues like this merit the development of alternative approaches to the description of dynamic arrest phenomena in mixtures , particularly if they are independent from conventional mct . although the scgle theory presented here has several features in common with mct , such as its use of exact memory function expressions for the concentration - concentration time - correlation functions , in the scgle theory the derivations , approximations and argumentation are conceived and based on a totally different fundamental and conceptual framework @xcite . besides presenting the scgle theory of dynamic arrest in colloid mixtures , in the present paper we illustrate the scenarios predicted by this theory in the simplest conditions , namely , in its application to model binary mixtures . for two such systems , a repulsive yukawa mixture and a hard - sphere mixture , we numerically solve the full self consistent system of dynamic equations for the so - called propagators ( or green s functions ) of the self and collective intermediate scattering functions . we illustrate in this manner the two possible dynamic arrest patterns possible in a binary colloidal mixture , namely , the simultaneous and the sequential arrest of the two species . in the latter case , we discuss the hybrid or partially - arrested states in which one species is dynamically arrested while the other species remains ergodic .    determining the location of the ergodic  non - ergodic transitions and calculating the non - ergodic parameters may be done by solving the self - consistent system of equation or , more simply , by finding the long - time asymptotic stationary (  fixed - point \" ) solutions of the self - consistent system of equations . here we also address this issue , and report the derivation of a strikingly simple and general result which takes the form of a system of coupled equations for the localization length of the particles of each species . solving this system of equations leads to the unambiguous identification of which species is arrested ( finite localization length ) and which species remains ergodic ( infinite localization length ) . as a result , we are able to draw the entire ergodic  non - ergodic phase diagram of the binary hard - sphere mixture , which is one of the main specific contributions of this work . the present paper starts with a brief summary of the scgle theory of the dynamics of colloidal mixtures . this theory was developed in ref . @xcite and tested there through its comparison with the short- and intermediate - time results of brownian dynamics computer simulations for a model colloidal mixture interacting through screened coulomb pair interactions . that original version of the scgle theory required as an input not only the partial static structure factors , but also other equilibrium static structural information associated with the exact short - time conditions that this initial version of the theory aimed at incorporating . as it has been shown more recently @xcite , however , a simplified version of the scgle theory , in which this exact short - time information is neglected , happens to be equally accurate , particularly in the long - time regime and with respect to the predicted dynamic arrest scenarios . thus , we shall refer to this simplified version simply as the scgle theory , which we review in the following section . although our main interest here is in the description of dynamic arrest phenomena , in section iii we start our discussion by reviewing the predictive capability of this simplified theory in the short- and intermediate - time regimes of the model binary yukawa mixture studied in ref . @xcite in one of the fully ergodic states considered in that work . we then proceed to illustrate the dynamic arrest scenarios predicted by this theory , by taking as the initial reference the same repulsive yukawa mixture , and increase the intensity of the repulsion parameter ( a process that amounts to effectively lowering the temperature ) , until reaching a transition to a dynamically arrested state . this turns out to be a transition from a fully ergodic to a fully arrested state in which both species are simultaneously arrested . in the second of our illustrative examples , in section iv we consider a hard - sphere model colloidal mixture , whose state parameters are the size disparity and the concentration of the two species . here we present an example of a transition to a partially arrested state , in which the large particles become arrested and the smaller particles continue to diffuse in the disordered matrix formed by the arrested species . in section v we derive the equations for the non - ergodic parameters of the system , and illustrate its use in the context of the hard - sphere binary mixture by determining its entire dynamic - arrest phase diagram . the main conclusions of this paper are finally summarized in section vi .","summary":"we present a new first - principles theory of dynamic arrest in colloidal mixtures based on the multi - component self - consistent generalized langevin equation ( scgle ) theory of colloid dynamics [ phys . the latter case gives rise to mixed states in which one species is arrested while the other species remains mobile . we also derive the (  fixed point \" ) equations for the non - ergodic parameters of the system , which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species . the solution of this system of equations indicates unambiguously which species is arrested ( finite localization length ) and which species remains ergodic ( infinite localization length ) . as a result , we are able to draw the entire ergodic  non - ergodic phase diagram of the binary hard - sphere mixture .","abstract":"we present a new first - principles theory of dynamic arrest in colloidal mixtures based on the multi - component self - consistent generalized langevin equation ( scgle ) theory of colloid dynamics [ phys . rev . e * 72 * , 031107 ( 2005 ) ; ibid * 76 * , 039902 ( 2007 ) ] . we illustrate its application with the description of dynamic arrest in two simple model colloidal mixtures , namely , the hard - sphere and the repulsive yukawa binary mixtures . our results include the observation of the two patterns of dynamic arrest , one in which both species become simultaneously arrested , and the other involving the sequential arrest of the two species . the latter case gives rise to mixed states in which one species is arrested while the other species remains mobile . we also derive the (  fixed point \" ) equations for the non - ergodic parameters of the system , which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species . the solution of this system of equations indicates unambiguously which species is arrested ( finite localization length ) and which species remains ergodic ( infinite localization length ) . as a result , we are able to draw the entire ergodic  non - ergodic phase diagram of the binary hard - sphere mixture ."}
{"article_id":"0711.2021","section_id":"c","document":"in this paper we have introduced the self - consistent generalized langevin equation theory of dynamic arrest in colloidal mixtures , and we have applied it to the description of dynamic arrest phenomena in two simple model systems , namely , a repulsive yukawa and a hard - sphere mixtures , for which we illustrated the scenarios predicted by this theory through the full numerical solution of the coupled system of dynamic equations for the propagators @xmath245 and @xmath50 of the self and collective intermediate scattering functions . in this manner we identified and illustrated the two possible patterns of dynamic arrest in a binary colloidal mixture , namely , the simultaneous and the sequential arrest of the two species . the former corresponds to the transition from the region of fully ergodic states , characterized by infinite values of the order parameters @xmath210 and @xmath211 , to the region of fully non - ergodic states , characterized by finite values of these two parameters . this transition is characterized by a discontinuous jump of both order parameters . this is the only dynamic arrest transition possible for moderate size asymmetry in a binary hard - sphere mixture , as illustrated in fig . [ fig.2 ] . it is also the only transition possible for large asymmetries in the case of hard spheres provided the system is in the limit of a few large particles dispersed in a sea of small particles ( the dynamic arrest of  chancaquilla \" limit ) .    the second pattern of dynamic arrest is only observed for large enough size disparities starting in the regime in which the small particles are a minority . as illustrated in fig . [ fig.3 ] , here the system may be driven from the region of fully ergodic states ( @xmath246 ) to the region of mixed states ( finite @xmath211 and @xmath247 ) in which the large particles are arrested and the small ones diffuse through the voids left by the large species . in this transition @xmath211 jumps discontinuously from its infinite value in the fully non - ergodic region to a finite value in the region of mixed states , whereas @xmath210 retains its infinite value . finally , there is a transition from this region of mixed states to the region of fully ergodic states in which also the small particles are localized ( finite values of both , @xmath210 and @xmath211 ) . this latter transition is characterized by a continuous change in the values of both order parameters @xmath210 and @xmath211 , although the latter changes continuously from its infinite value inside the region of mixed states and right at the transition , to finite values inside the fully non - ergodic region .    locating the transitions just described may be done by numerically solving the full self - consistent system of equation , as done in figs . [ fig.2 ] and [ fig.3 ] , or by directly determining the non - ergodic parameters , which play the role of order parameters of the transition . the latter can be done more economically through the solution of the  fixed - point \" equations . in section iv we derived a strikingly simple and general result for the non - ergodic parameters @xmath210 and @xmath211 , whose use was illustrated with the construction of the phase diagram of the hard - sphere binary mixture . we must say that some of the features of the scgle results thus determined were in fact discovered and discussed in the pioneering work of refs . @xcite based on the multi - component version of mct . our aim here has been to document what is the scenario offered by the scgle theory for the same conditions previously studied , and to extend the description to new aspects not yet discussed with mct or with other theoretical approaches . in this regard , the main contribution of the present work is the proposal of a new theoretical approach that allows the determination of the entire dynamic phase diagram of simple model colloidal mixtures . thus , the second important contribution involves the simplest of such models , namely , the hard - sphere binary mixture , for which we outlined the entire dynamic arrest phase diagram . in this context we discussed the regime of mild size asymmetries , in which we reported the first apparent difference with the results of mct , namely , the fact that the scgle theory does not predict the s - shaped transitions predicted by gtze and voigtmann @xcite on the basis of mct . for more severe size disparities we also illustrated the main features of the scgle predictions , including the precise location of the region of mixed states , and its emergence for size disparities beyond a threshold asymmetry @xmath248 . these results do not have yet a mct counterpart to compare with . in this paper we also discussed the fact that other properties besides @xmath210 and @xmath211 could be employed as order parameters to classify the various dynamic phases in a mixture . for example , one can use the diagonal elements of the non - ergodic parameters associated with the self or the collective propagator matrices , which also determine unambiguously the various possible states . although not central to the main subject of this paper , we also explained that the use as order parameters of collective _ correlators _ , defined as the partial intermediate scattering functions divided by their initial value , may lead to a confusing description of the hybrid states in which one species is arrested and the other remains ergodic .    in summary , we have presented a theory for dynamic arrest phenomena in colloidal mixtures that offers some advantages over the extension to mixtures of conventional mct . first , it derives from a simpler conceptual formalism , which might allow possible generalizations and extensions . second , the resulting equations are much simpler to solve in practice than the corresponding equations of mct . in fact , the determination of ( ergodic  non - ergodic ) phase diagrams , such as that discussed in the previous section , is considerably simplified in the present case through the use of the results for the non - ergodic parameters @xmath201 in eq . ( [ nep5pp ] ) . thus , many important issues regarding the dynamics and the ( ergodic  non - ergodic ) phase behavior of colloidal mixtures may be discussed with the assistance of the scgle theory just presented . the implications of the results presented here in the context of specific physical phenomena and experimental conditions will , however , be the subject of separate reports .","summary":"we illustrate its application with the description of dynamic arrest in two simple model colloidal mixtures , namely , the hard - sphere and the repulsive yukawa binary mixtures . our results include the observation of the two patterns of dynamic arrest , one in which both species become simultaneously arrested , and the other involving the sequential arrest of the two species .","abstract":"we present a new first - principles theory of dynamic arrest in colloidal mixtures based on the multi - component self - consistent generalized langevin equation ( scgle ) theory of colloid dynamics [ phys . rev . e * 72 * , 031107 ( 2005 ) ; ibid * 76 * , 039902 ( 2007 ) ] . we illustrate its application with the description of dynamic arrest in two simple model colloidal mixtures , namely , the hard - sphere and the repulsive yukawa binary mixtures . our results include the observation of the two patterns of dynamic arrest , one in which both species become simultaneously arrested , and the other involving the sequential arrest of the two species . the latter case gives rise to mixed states in which one species is arrested while the other species remains mobile . we also derive the (  fixed point \" ) equations for the non - ergodic parameters of the system , which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species . the solution of this system of equations indicates unambiguously which species is arrested ( finite localization length ) and which species remains ergodic ( infinite localization length ) . as a result , we are able to draw the entire ergodic  non - ergodic phase diagram of the binary hard - sphere mixture ."}
{"article_id":"astro-ph0305348","section_id":"i","document":"the main aim of this paper is to make a new determination of the chemical abundances of ngc  5307 including the following improvements over previous determinations : the consideration of the temperature structure that affects the helium and heavy elements abundance determinations , the derivation of the o and c abundances from recombination line intensities , the consideration of the collisional excitation of the triplet lines from the @xmath4s level by determining the electron density from many line intensity ratios , and the study of the @xmath4s level optical depth effects on the intensity of the triplet lines by observing a large number of singlet and triplet lines of . to determine the temperature structure it is also important to discuss if the and the [ ] lines originate in the same regions under the same physical conditions . to this effect we will study the relative line intensities of the multiplet 1 in this object and other gaseous nebulae , moreover for the same reason we will also consider the wavelengths and line widths of the and [ ] lines in ngc  5307 .    in sections 2 and 3 the observations and the reduction procedure are described . in section 4 temperatures and densities are derived from five and four different intensity ratios respectively ; also in this section , the mean square temperature fluctuation , @xmath5 , is determined from the / [ ] line intensity ratios . in section 5 ionic abundances are determined based on recombination lines that are almost independent of the temperature structure , and ionic abundances based on ratios of collisionally excited lines to recombination lines that do depend on the temperature structure of the nebula . in section 6 the total abundances are determined and compared with other determinations for the same object . in sections 7 and 8 we present the discussion and the conclusions .","summary":"the data consists of vlt uves observations in the 3100 to 10360   range . electron temperatures and densities have been determined using different line intensity ratios . we determine the h , he , c , and o abundances based on recombination lines , these abundances are almost independent of the temperature structure of the nebula . we also determine the n , o , ne , s , cl , and ar abundances based on collisionally excited lines , the ratios of these abundances relative to that of h depend strongly on the temperature structure of the nebula . from the / [ ] ratios we find a . the chemical composition of ngc  5307 is compared with those of the sun and the orion nebula . from the study of the relative intensities of the recombination lines of multiplet 1 in this and other nebulae diagram we find a critical electron density of 1325 for collisional redistribution of the lines of multiplet 1 . also based on this diagram we argue that the and the [ ] lines originate in the same regions . we also find that the radial velocities and the fwhm of the and [ ] lines in ngc  5307 are similar supporting the previous result .","abstract":"echelle spectrophotometry of the planetary nebula ngc  5307 is presented . the data consists of vlt uves observations in the 3100 to 10360   range . electron temperatures and densities have been determined using different line intensity ratios . we determine the h , he , c , and o abundances based on recombination lines , these abundances are almost independent of the temperature structure of the nebula . we also determine the n , o , ne , s , cl , and ar abundances based on collisionally excited lines , the ratios of these abundances relative to that of h depend strongly on the temperature structure of the nebula . from the / [ ] ratios we find a . the chemical composition of ngc  5307 is compared with those of the sun and the orion nebula . from the study of the relative intensities of the recombination lines of multiplet 1 in this and other nebulae it is found that for electron densities smaller than about 5000 collisional redistribution is not complete , this effect has to be taken into account to derive the o abundances for those cases in which not all the lines of the multiplet are observed . from the 4649 versus ( ) diagram we find a critical electron density of 1325 for collisional redistribution of the lines of multiplet 1 . also based on this diagram we argue that the and the [ ] lines originate in the same regions . we also find that the radial velocities and the fwhm of the and [ ] lines in ngc  5307 are similar supporting the previous result . these two results imply that for ngc 5307 and probably for many other gaseous nebulae chemical inhomogeneities are not responsible for the large temperature fluctuations observed ."}
{"article_id":"astro-ph0305348","section_id":"c","document":"the relative intensity ratios of the recombination lines of multiplet 1 do not agree with the lte computation predictions , this deviation was noted before for other objects by @xcite ; @xcite ; @xcite ; and @xcite . in particular @xcite discuss this problem extensively .    to explain this deviation , we propose that the electron density is smaller than that needed to produce an lte collisional redistribution of the fine structure energy levels . to test our proposal we produced figure  [ fovsden ] that is based on the best observations in the literature , those presented in table  [ toii ] . we decided to plot @xmath11(4649 ) over the sum of the intensities of all the lines of the multiplet @xmath11(sum ) , versus the density derived from optical forbidden line ratios , mainly the [ ] lines that originate in the same regions where o is twice ionized .    from figure  [ fovsden ] we find an excellent correlation between @xmath11(4649)/@xmath11(sum ) and the forbidden line electron density , @xmath3(fl ) . we propose to adjust the data with a curve given by @xmath88_{obs } =   \\left [ \\frac{i(4649)}{i({\\rm sum } ) } \\right]_{cas } +   \\frac { \\left [ \\frac{i(4649)}{i({\\rm sum } ) } \\right]_{lte } -          \\left [ \\frac{i(4649)}{i({\\rm sum } ) } \\right]_{cas } }       { \\left [ 1 + \\frac{n_e({\\rm crit})}{n_e({\\rm fl } ) } \\right ] } , \\label{ecurve1}\\ ] ] where @xmath89_{cas}$ ] is the value produced by recombination and cascade without collisional redistribution , @xmath89_{lte}$ ] amounts to 0.397 @xcite the value predicted by collisional redistribution assuming that the populations of the upper energy levels of multiplet 1 are given by the statistical weights multiplied by the einstein a values , and @xmath3(crit ) is the critical density defined by equation  ( [ ecurve1 ] ) . from figure  [ fovsden ] we find @xmath90 @xmath1 , and @xmath91(sum)]@xmath92 , therefore equation  ( [ ecurve1 ] ) can be written as : @xmath88_{obs } =   0.105 + \\frac{0.292 } { \\left [ 1 + 1325/n_e({\\rm fl } ) \\right ] } . \\label{ecurve2}\\ ] ] it is beyond the scope of this paper to check this equation based on an atomic physics computation . equation  [ ecurve1 ] has the following applications : a ) when @xmath93 is known it is possible to use this equation to obtain @xmath11(sum ) from the observed @xmath94 and from @xmath11(sum ) to obtain the o@xmath29 abundance since @xmath11(sum ) is independent the density , from @xmath94 alone it is not possible to determine an accurate o@xmath29 abundance since this line is density dependent ; b ) from an observed @xmath11(4649)/@xmath11(sum ) it is possible to determine @xmath3 in the o@xmath29 zone ; c ) if the forbidden line density of a nebula does not fall close to the value predicted with this equation it could mean that there are extreme inhomogeneities in density or chemical composition in this object , for example an object with high - density oxygen - rich knots embedded in a low density medium would fall to the left of the curve .    from table [ toii ] it can be seen that the intensity of the lines that originate in the 3p  @xmath95d@xmath96 and 3p @xmath95d@xmath97 energy levels decreases with increasing local density , while the intensity of those lines that originate in the 3p  @xmath95d@xmath98 increases with increasing density . this is due to the effect of collisional redistribution that increases the population of the high statistical weight levels at the expense of the low statistical weight ones . note that the intensity of the lines that originate from the 3p  @xmath95d@xmath99 energy level are almost independent of the electron density . the results derived from figure  [ fovsden ] imply that in these objects the [ ] @xmath20 4363 , 4959 , and 5007 lines and the recombination lines of multiplet 1 originate in regions of similar density , this is particularly the case for those objects with @xmath3(fl ) @xmath100 3000 @xmath1 . in other words : we can not assume the presence of high density knots to explain the difference between the o@xmath29 abundances derived from the [ ] lines and the lines . consequently we propose to drop the constant temperature assumption , and to explain the apparent difference in abundances as being due to the presence of temperature fluctuations .    in general to reconcile the abundances derived from collisionally excited lines and recombination lines it is necessary to assume the presence of large temperature variations . the presence of temperature variations in gaseous nebulae has been amply reviewed in the recent literature ( e.g. * ? ? ? * ; * ? ? ? even more recent results in favor of large temperature variations in the orion nebula , the 30 doradus nebula , and other planetary nebulae have been presented by @xcite . @xcite , by comparing the line intensities of multiplets 1 , 2 , and 10 for for the planetary nebula ngc  6572 , have concluded that the lines are produced by recombination , and that the contribution of resonance fluorescence to the line intensities is not important . a similar conclusion was reached @xcite for the orion nebula . the difference between the o(cel ) abundance and the o(rl ) abundance indicates the presence of large temperature variations . there are two possible scenarios for these temperature variations : a ) that the abundances are homogeneous along the line of sight and temperature fluctuations of @xmath101 are present , an explanation for these large temperature variations has to be sought ( e.g. * ? ? ? * and references therein ) , or b ) that the abundances are not homogeneous along the line of sight and that there are high density knots with excess heavy element abundances embedded in a medium with lower heavy element abundances and higher electron temperature ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the second possibility is based on the idea that the central stars , of at least some planetary nebulae , firstly eject an envelope at relatively low velocity with almost normal heavy element abundances , and later on eject knots or clumps of material at higher velocities with an excess of heavy element abundances . in abell  58 @xcite studied a hydrogen deficient high velocity knot blueshifted relative to the main body of the nebula by 120 km s@xmath18 . while @xcite studied three knots in abell  30 , where knot j1 is redshifted relative to knot j3 by about 45 km s@xmath18 and knot j3 is redshifted relative to knot j4 by about 100 km s@xmath18 .    by assuming that chemical inhomogeneities are responsible for the temperature variations in ngc  5307 we would expect most of the flux of the [ ] lines to originate in the lower density medium that expands at lower velocity , and a considerable fraction of the flux of the lines to originate from knots or clumps that move at higher velocities . therefore if this were the case the radial velocity derived from the central wavelength of the [ ] lines could be different from that derived from the lines ; furthermore the full width at half maximum , fwhm , of the [ ] lines would be smaller than that of the lines .    for ngc  5307 the heliocentric velocity of the @xmath20 4363 , 4959 , 5007 [ ] lines is 30.1 @xmath102 km s@xmath18 , while that of the lines of multiplet 1 is 33.1 @xmath103 km s@xmath18 . the fwhm of the @xmath20 4363 , 4959 , 5007 [ ] lines is 48.4 @xmath104 km s@xmath18 , while that of the @xmath2 4649 line , the best observed line of multiplet 1 , is 44.3 @xmath105 km s@xmath18 . these results imply that there is no evidence in favor of high velocity o - rich clumps in our observations of ngc  5307 . table  [ tabund ] presents a comparison between the abundance determinations of this paper and those by other authors . a discussion of the uncertainties in the determinations by other authors is beyond the scope of this paper , the errors of this work are presented in tables [ tcl ] and  [ tta ] . the average @xmath46(he)/@xmath46(h ) value derived by the other four groups amounts to -1.02 dex in excellent agreement with our value of -1.01 dex . the c abundance derived by us is based on the @xmath2 4267 recombination line , while those derived by other authors are based on uv lines , we consider our determination to be more accurate because it is almost independent of the adopted temperature while the abundance derived from the uv collisionally excited lines depends strongly on the adopted electron temperature ( although the recombination abundances are still regarded as controversial by other authors ) . the n / h value has been already amply discussed and most of the difference among the various groups depends on the use of @xmath34 or @xmath76 lines to determine the n abundance . most of the difference among the o and ne abundances is due to the adopted @xmath5 value .    to discuss the effect of stellar evolution on the observed abundances in ngc  5307 we present in table  [ tta ] the orion nebula and solar abundances as representative of the present day interstellar medium and of the interstellar medium at the time the sun was formed . table  [ tta ] presents the solar photospheric values for c , n , o , ne , and ar , and the solar abundances derived from meteoritic data for s , cl , and fe . for the solar initial helium abundance the @xmath106 by @xcite was adopted , and not the photospheric one because , apparently , it has been affected by settling . notice that the solar oxygen abundance used in this paper is the average value of the recent results by @xcite and @xcite that indicate an o / h value of 8.71 dex , a value lower than that derived by @xcite . we are also using the c / h value by @xcite , the n / h and ne / h solar abundances were taken from @xcite , while the s / h , cl / h , and ar / h come from @xcite , the first two from the meteoritic data , while the last one from the photospheric data . the relative abundances of h , he , c , n , and o imply that ngc 5307 is a pn of type ii with a main sequence progenitor star in the 1.2 to 2.4 solar mass range @xcite .    in table [ tta ] we present the abundances of ngc 5307 , the orion nebula ( representative of the interstellar medium today ) , and the sun ( expected to be similar to the interstellar abundances when the parental star of ngc 5307 was formed ) . by comparing these abundances we reach the following conclusions : a ) the he abundance has not been significantly enriched by stellar evolution , b ) the c abundance has decreased by about a factor of three , and c ) the n abundance has increased by about a factor of three . these three results taken together indicate that the nebular material has only gone through part of the cno cycle , converting c into n , but without producing significant amounts of helium . evolutionary models of intermediate mass stars predict the n increase and the c decrease in their outer layers while the o and he abundances are almost unaffected ( e. g. * ? ? ? * ) ; n increases at the expense of c because the c / n ratio in the interstellar medium and in the sun is considerably larger than the equilibrium value produced by the cno cycle ( e. g. * ? ? ? objects that show o - rich knots , like a30 and a58 , show he / h excesses that are not present in ngc 5307 @xcite . consequently the chemical composition of ngc 5307 is also against the presence of o - rich knots in this object","summary":"echelle spectrophotometry of the planetary nebula ngc  5307 is presented . it is found that for electron densities smaller than about 5000 collisional redistribution is not complete , this effect has to be taken into account to derive the o abundances for those cases in which not all the lines of the multiplet are observed . from the 4649 versus ( ) these two results imply that for ngc 5307 and probably for many other gaseous nebulae chemical inhomogeneities are not responsible for the large temperature fluctuations observed .","abstract":"echelle spectrophotometry of the planetary nebula ngc  5307 is presented . the data consists of vlt uves observations in the 3100 to 10360   range . electron temperatures and densities have been determined using different line intensity ratios . we determine the h , he , c , and o abundances based on recombination lines , these abundances are almost independent of the temperature structure of the nebula . we also determine the n , o , ne , s , cl , and ar abundances based on collisionally excited lines , the ratios of these abundances relative to that of h depend strongly on the temperature structure of the nebula . from the / [ ] ratios we find a . the chemical composition of ngc  5307 is compared with those of the sun and the orion nebula . from the study of the relative intensities of the recombination lines of multiplet 1 in this and other nebulae it is found that for electron densities smaller than about 5000 collisional redistribution is not complete , this effect has to be taken into account to derive the o abundances for those cases in which not all the lines of the multiplet are observed . from the 4649 versus ( ) diagram we find a critical electron density of 1325 for collisional redistribution of the lines of multiplet 1 . also based on this diagram we argue that the and the [ ] lines originate in the same regions . we also find that the radial velocities and the fwhm of the and [ ] lines in ngc  5307 are similar supporting the previous result . these two results imply that for ngc 5307 and probably for many other gaseous nebulae chemical inhomogeneities are not responsible for the large temperature fluctuations observed ."}
{"article_id":"astro-ph9901176","section_id":"i","document":"the synchrotron jet hosted by the giant elliptical galaxy m87 is perhaps the most intensely studied feature of any active galaxy ( agn ) . due to its brightness and proximity ( distance 16 mpc ; tonry 1991 ) , it represents an ideal testing ground for jet models . its large - scale radio structure ( biretta 1993 , bhringer et al . 1995 ) is typical of low - power fr 1 radio galaxies ( fanaroff and riley 1974 ) : the radio lobes are edge - dimmed , and a prominent , apparently one - sided jet emerges from the nucleus . no counterjet has been seen in any optical or radio image of the jet ; however , there is strong evidence for its presence in the form of optical synchrotron emission at the location of a radio hotspot in the southeast lobe ( sparks et al . 1992 , stiavelli et al . 1992 ) .    while the gross morphology of the m87 jet is remarkably constant from the radio through the optical ( boksenberg et al . 1992 ) , small but significant differences have been found at the highest resolutions by pre- and post - costar _ observations ( sparks , biretta & macchetto 1996 , hereafter sbm96 ) . in particular , the optical jet is considerably more compact than the radio jet , and the knots are more centrally concentrated . these trends appear to continue from the optical into the uv . recent x - ray images suggest that more differences may be present in the rosat band ( neumann et al . the jet is highly polarized ( baade 1956 , warren - smith et al . 1984 , schltelburg et al . 1988 , fraix - burnet et al . 1989 ) , with some regions approaching the maximum possible for optically thin synchrotron radiation ( @xmath2 ) both in radio ( owen , hardee & cornwell 1989 , hereafter ohc89 ) and optical / uv ( this paper , capetti et al . 1997 , thomson et al . 1995 ) images . such high polarization suggests the presence of highly ordered magnetic fields in the jet . recent vla observations suggest that the kpc - scale lobes are also highly polarized ( zhou 1998 ) . high - resolution radio observations with the vla ( biretta , zhou & owen 1995 ; hereafter b95 ) have detected superluminal motions within the jet of m87 at distances @xmath3 200 pc from the nucleus , and speeds @xmath4 up to 1200 pc from the nucleus . at smaller scales , post - refurbishment _ hst _ + foc observations in the near - uv have detected a number of new superluminal components ( biretta et al . 1998 , 1999 ; hereafter b98 , b99 ) , with speeds ranging from 2 - 6@xmath5 . it is therefore interesting that vlbi observations have yet to discover any evidence of superluminal motions on parsec scales ( biretta & junor 1995 , reid et al . this may be due either to insufficient temporal sampling , or to differences between the radio and optical structure of the jet . a vlbi monitoring campaign with rapid sampling is now underway to study this issue . here we present the results of hst / wfpc-2 optical , and vla radio , polarimetry of the m87 jet . both datasets were obtained during 1994 - 1995 , and have resolution @xmath0 , translating to 15 pc linear resolution at a distance of 16 mpc . the optical data we present are much higher signal - to - noise than pre - costar foc and wfpc-1 polarimetry data ( thomson et al . 1995 , capetti et al . 1997 ) , and therefore are particularly useful in revealing many new details regarding the magnetic field structure of the inner jet which were only hinted at in earlier data . they also do not suffer from the spherically aberrated psf of pre - costar observations . they are , however , somewhat lower spatial resolution , due to the instrumental configuration used . another difference between this study and previous works ( thomson et al . 1995 , capetti et al . 1997 ) is that the radio map to which we compare our results was taken within 15 months of the optical observations . this helps to resolve some of the ambiguities noted in those papers .    in  2 , we will discuss the observational setup and data reduction procedures . our results will be presented in   3 and 4 , and the physical implications discussed in  5 . in  6 , we conclude with remarks centering on the possible impact of future observations .","summary":"we discuss optical ( hst / wfpc2 f555w ) and radio ( 15 ghz vla ) polarimetry observations of the m87 jet taken during 1994 - 1995 . many knot regions are very highly polarized ( , approaching the theoretical maximum for optically thin synchrotron radiation ) , suggesting highly ordered magnetic fields .","abstract":"we discuss optical ( hst / wfpc2 f555w ) and radio ( 15 ghz vla ) polarimetry observations of the m87 jet taken during 1994 - 1995 . the angular resolution of both of these observations is , which at the distance of m87 corresponds to 15 pc . many knot regions are very highly polarized ( , approaching the theoretical maximum for optically thin synchrotron radiation ) , suggesting highly ordered magnetic fields . high degrees of polarization are also observed in interknot regions . the optical and radio polarization maps share many similarities , and in both , the magnetic field is largely parallel to the jet , except in the `` shock - like '' knot regions ( parts of hst-1 , a , and c ) , where it becomes perpendicular to the jet .    we do observe significant differences between the radio and optical polarized structures , particularly for bright knots in the inner jet , giving us important insight into the radial structure of the jet . unlike in the radio , the optical magnetic field position angle becomes perpendicular to the jet at the upstream ends of knots hst-1 , d , e and f. moreover , the optical polarization appears to decrease markedly at the position of the flux maxima in these knots . in contrast , the magnetic field position angle observed in the radio remains parallel to the jet in most of these regions , and the decreases in radio polarization are smaller . more minor differences are seen in other jet regions . many of the differences between optical and radio polarimetry results can be explained in terms of a model whereby shocks occur in the jet interior , where higher - energy electrons are concentrated and dominate both polarized and unpolarized emissions in the optical , while the radio maps show strong contributions from lower - energy electrons in regions with * b * parallel , near the jet surface .    [ = 1 = 0.7 truecm ]"}
{"article_id":"0706.3836","section_id":"i","document":"the hypernucleus is a strongly - interacting multibaryonic system with hyperon(s ) and its lifetime is as long as the typical order of the @xmath0 weak - interaction decay ( @xmath5 sec ) . thus a variety of hypernuclear phenomena provide us with new knowledge of baryon - baryon interactions and novel behaviors of many - body structures . among these systems the @xmath0-hypernuclei have been relatively well produced mainly through the @xmath6 and @xmath7 reactions . however , as these experiments have more or less limitation due to their own kinematics , more variety of hypernuclear production processes should be challenged in order to get information on detailed properties of hyperon - nucleon interactions . in this paper we like to demonstrate a new and wide possibility of the photo- and electro - production of hypernuclei , by taking the actual experimental facilities into account , and will show a novel aspect of the reaction spectroscopy . historically , the stopped k@xmath8 absorption reaction was utilized to produce @xmath0-hypernuclei of which decays were identified in bubble chamber and nuclear emulsion . next , the in - flight reaction @xmath9 with the kaon beam momenta @xmath10 had a unique role of getting particular hypernuclear excited states taking an advantage of the recoilless condition ( @xmath11 ) with very weak spin - flip transition . then a new stage of hypernuclear production was realized by employing the @xmath12 reaction mostly at @xmath13 . this @xmath14 reaction on nuclear targets played a great role of producing a series of all @xmath0 single - particle states inside the nucleus , since the process with recoil momentum @xmath15 preferentially excites hypernuclear high - spin stretched configurations with natural parity mainly due to the spin - non - flip component of the elementary amplitudes . more details can be found in the review papers  @xcite . in general , hypernuclear states consist of multiplets which are based on the nuclear core angular momentum @xmath16 coupled with that of a hyperon @xmath17 , so that low - lying doublets with a @xmath18-state @xmath0 have spin partners : @xmath19 . the @xmath6 reaction with spin - non - flip nature leads to excitation of one of the doublet member with natural parity . although the @xmath7 spin - flip component is sizable enough to produce appreciable polarization in the final hypernuclear states  @xcite , actually the favored states with large cross section are solely restricted to the natural parity states and their unnatural parity partners get very small cross section  @xcite . in addition the typical energy resolution achieved in the @xmath7 reaction spectroscopy is 1.45 mev at best  @xcite , which is much larger than the characteristic spin - doublet splittings of the order of a few tens kev . therefore , only the energy of natural parity member of the doublets can be accessible within the restriction of such energy resolution . the coincidence @xmath20-ray measurement proved to be a nice tool to know the detailed hypernuclear level energies with a remarkably good resolution of several kev  @xcite . in contrast to the production processes mentioned above , which convert a neutron into @xmath0 , here we focus our attention on k@xmath21 photo- and electro - production process . these reactions convert a proton in nuclear targets into @xmath0 , so that new variety of hypernuclei can be produced . indeed much larger amount of spectroscopic data for other hypernuclei with various excited states are quite necessary to draw some clear conclusion about the nature of hyperon - nucleon interaction for which the elementary scattering experiments are not available . over 10 years ago , three of the present authors predicted the photo - production cross sections for @xmath22li , @xmath23b , @xmath24c , and @xmath25o targets  @xcite . among others the @xmath24c case has been remarkably well confirmed by the first experiment on the nuclear target at the thomas jefferson national laboratory ( jlab )  @xcite . these factors explain the reasons why recently the photo- and electro - production of both hyperons and hypernuclei has attracted much attention in strangeness nuclear physics . in addition the following facts encourage us to extend the theoretical estimates to wider possibilities of precise reaction spectroscopy :    * the quality of cebaf beam ( high intensity and energy resolution ) at jlab makes it possible to identify various hypernuclear energy levels with appreciable cross sections together with a resolution of about 400 kev  @xcite . * the photo- and electro - production reactions , ( @xmath26 ) and ( e , ek@xmath21 ) , are characterized by the large momentum transfer ( @xmath27 350 mev/@xmath28 ) and the strong spin - flip terms . this means especially that photons ( real or virtual ) have unique characteristics of exciting unnatural parity high - spin hypernuclear states preferentially including states with deeply - bound @xmath0 hyperon  @xcite . * in contrast to @xmath29 or ( @xmath30 ) reactions , the electro - magnetic production of k@xmath31 pair on the proton makes it possible to study some `` proton - deficient '' hypernuclear species , such as @xmath32he , @xmath33li and @xmath34b , which are not available otherwise . such ability opens a new possibility of producing neutron - rich hypernuclei with large excess of neutral baryons . the same hypernuclei may be produced in @xmath35 reaction  @xcite , but due to the weak spin - flip interaction in the latter the two reactions will afford complementary information on hypernuclear spectroscopy . the possibility to use the electro - production of strange particles as a tool for study of hypernuclei was first mentioned in a pioneering work by fetisov _ et al . _ @xcite . in 1980 s , early works on photo- and electro - production of hypernuclei have been done based on simplified models   @xcite . the production cross section and polarization of produced hypernuclei in photo - production process was examined in refs . @xcite for schematic as well as for very realistic shell - model wave functions and with full inclusion of distortion effects . electro - production of @xmath36-shell hypernuclei was investigated carefully in refs . @xcite with close link to the jlab experimental program  @xcite . the aim of this paper is , first , to demonstrate the characteristic and selective nature of the photo - production reaction in exciting hypernuclear states . for this purpose we adopt a typical medium - mass target of @xmath1si and discuss the general and novel rules based on the properties of the elementary amplitudes . we also make clear the effect of kaon distortion and the different hypernuclear wave functions . second , we examine the properties of the recent models of elementary kaon electro - magnetic production . third , by choosing medium - heavy nuclear targets such as @xmath37 , @xmath38 and @xmath39 , we present theoretical predictions of excitation spectra corresponding to the hypernuclear programs at the jlab facility  @xcite . this paper is organized as follows : section 2 briefly describes the minimum framework of calculation of the hypernuclear production cross section . in order to demonstrate the successful prediction done 10 years ago , the updated excitation spectrum for @xmath24c(e , ek@xmath21)@xmath34b is shown . in section 3 the basic properties of modern elementary amplitudes of kaon electro - magnetic production are discussed . section 4 summarizes the excitation spectra predicted for the @xmath40 reaction on @xmath41 . in order to show the novel and general selectivity found for the @xmath40 reaction , the simple configuration estimates are presented in subsection 4.1 , while sophisticated wave functions are employed in subsection 4.2 for the realistic predictions . in section 5 , the calculation is further applied to heavier hypernuclear production by choosing the @xmath38 and @xmath39 targets . conclusions and summary are given in section 6 .","summary":"the characteristic and selective nature of the electro - magnetic production of-hypernuclei in exciting states is demonstrated assuming the medium - mass targetssi ,ca , andcr . in the analysis ,","abstract":"the characteristic and selective nature of the electro - magnetic production of-hypernuclei in exciting states is demonstrated assuming the medium - mass targetssi ,ca , andcr . in the analysis , formalism of dwia is used adopting the saclay - lyon , kaon - maid , adelseck - saghai , and williams - ji - cotanch models for the elementary production process and various nuclear and hypernuclear wave functions . the elementary amplitudes are discussed in detail presenting their basic properties and comparison with data . the unique features of the electro - magnetic production of-hypernuclei shown on the examples are the selective excitation of unnatural parity highest - spin states ( natural parity ones for the-closed targets ) and a possibility to investigate the single - particle energies including a spin - orbit splitting using variety of medium - mass targets ."}
{"article_id":"0706.3836","section_id":"c","document":"the first ( e , ek@xmath21 ) experiment on the nuclear target ( @xmath24c ) was reported recently from the jefferson lab , proving it to be a nice tool for spectroscopic study of @xmath0 hypernuclei . as our theoretical prediction has been confirmed remarkably by this experiment , we applied its framework to typical heavier targets with careful consideration of modern elementary amplitudes for hyperon photo - production . in this paper we presented the ( @xmath20,@xmath226 ) excitation spectra for producing medium - mass @xmath0-hypernuclei , where we focused our attention to the novel and characteristic features of the reaction process . we started with discussions on the basic properties of modern elementary amplitudes of kaon photo - production process . among many theoretical attempts , the isobaric models for the @xmath227 process based on the feynman diagram technique are of interest and successful in the kinematical region assumed here , @xmath228 gev . four elementary amplitudes of the models are adopted in this paper , i.e. , those denoted as kaon - maid ( kmaid ) , adelseck - saghai ( as1 ) , williams - ji - cotanch ( c4 ) and saclay - lyon a ( sla ) models . the models differ in their own choices of nucleon and hyperon resonances . detailed comparison of the models has been done for the differential cross sections and polarizations for the elementary @xmath229 and their results are compared with the available experimental data . some variances of agreement between the models exist at higher energies @xmath230 gev . however , all the four models are acceptable at @xmath231 gev which is concerned in the present hypernuclear calculations . the unique and interesting feature of the @xmath232 amplitudes lies in that the spin - flip amplitudes are much larger in magnitude than the spin - non - flip one even at the forward angles at @xmath233 and @xmath234 and at energy @xmath235 gev . this feature of the amplitude together with the large momentum transfer ( @xmath236 mev/@xmath28 ) yields the novel and selective features of the excitation spectra in the medium - heavy @xmath0-hypernuclei . here we choose @xmath41 , @xmath38 and @xmath237 as the typical medium - mass target nuclei for the spectroscopic study of the @xmath0-hypernuclei in the @xmath238 reactions . first the excitation spectra of @xmath239 are discussed for two model calculations of @xmath41 . when the simple @xmath240-closed configuration is assumed for @xmath41 as a demonstrative model , the characteristic and unique excitation function is clearly seen . the result emphasized first is the selective excitation of the highest - spin state within each 1h-1p multiplet such as @xmath241_{4 ^ -}$ ] , @xmath242_{3 ^ -}$ ] , @xmath243_{5^+}$ ] and @xmath244_{4^+}$ ] . this is due to the large momentum transfer for the reaction process . second , such a novel fact is revealed that the selectively excited states with @xmath245_j$ ] are strongly populated and have unnatural parities with maximum spins of @xmath246 . this is attributed to the spin - flip transition dominance in the elementary hyperon photo - production reaction . this kind of selectivity is not seen in other hypernuclear production processes such as @xmath6 and @xmath7 reactions . the calculation has been extended to the @xmath159 full space model to describe @xmath41 . excitation function for the @xmath247 is presented , taking the empirical particle - hole width into account tentatively so as to make the comparison with the future experiment possible . the major doublets and peaks obtained with the simplified model well persist also in the extended estimates . the energy splitting of the two peaks with structures , such as @xmath241_{4 ^ -}$ ] and @xmath242_{3 ^ -}$ ] , and @xmath243_{5^+}$ ] and @xmath244_{4^+}$ ] corresponding to the proton hole in @xmath248 and @xmath0 in @xmath249 and @xmath250 , if observed experimentally , might give us information on the spin - orbit splitting of the @xmath0 @xmath49- and @xmath180-states , respectively . the photo - production reactions with @xmath38 and @xmath237 targets are discussed as other interesting cases . the former nucleus is @xmath4-closed up to @xmath251 shell orbit , so that the highest spin in the @xmath252_j$ ] multiplet is @xmath253 with a natural parity and such a state is strongly excited . however , the states of @xmath254_j\\,$]-type with @xmath255 have weak strengths in the excitation function . the @xmath256-closed shell nuclear target presents the dominant peaks of natural parity , i.e. , @xmath257 and @xmath201 as seen in @xmath258 . the present case seems to be a nice example of getting the @xmath0 single - particle energies in this mass region which has not been explored with good energy resolution . the @xmath39 target contains four protons in an active @xmath214 shell orbit . the dominant peak series in the @xmath238 reaction consists of unnatural parity states of @xmath259_j\\,$]-type with @xmath260 and @xmath261 , @xmath262 and 2 , respectively , while the @xmath0 spin - orbit partner states @xmath263_{j = l_{\\rm max}}$ ] have reduced strength as about 60% of the biggest peak within each multiplet . conclusively , the @xmath40 photo - production reactions on the medium - mass nuclear targets will provide us with novel and unique features in the @xmath0-hypernuclear spectroscopy through the selective excitation of unnatural parity highest - spin states ( natural parity high - spin states for the @xmath4-closed targets ) . a possibility is also pointed out that we might have a chance to investigate @xmath0 single - particle energies over whole periodic table including the spin - orbit splitting for @xmath49- , @xmath180- , and @xmath215-orbits . it is also notable that the reaction on various nuclear targets produces proton - deficient hypernuclear species otherwise unaccessible . thus the photo- and electro - production of @xmath0-hypernuclei will offer a nice opportunity to get knowledge on the dynamical behavior of hyperon - nucleus coupling and on the baryon behavior deeply inside the nucleus . this work has been done as a part of the japan - czech joint research project on `` electromagnetic production and weak decays of hypernuclei '' which was supported for two years by japan society for the promotion of science . the work was also supported in part by grant - in - aid for scientific research ( specially promoted research 12002001 and creative scientific research 16gs0201 and the 21st century coe program `` exploring new science by bridging particle - matter hierarchy '' by mext , japan ) . p.b . and m.s . acknowledge support by the grant agency of the czech republic , grant no . 202/05/2142 and the institutional research plan avoz10480505 .","summary":"the unique features of the electro - magnetic production of-hypernuclei shown on the examples are the selective excitation of unnatural parity highest - spin states ( natural parity ones for the-closed targets ) and a possibility to investigate the single - particle energies including a spin - orbit splitting using variety of medium - mass targets .","abstract":"the characteristic and selective nature of the electro - magnetic production of-hypernuclei in exciting states is demonstrated assuming the medium - mass targetssi ,ca , andcr . in the analysis , formalism of dwia is used adopting the saclay - lyon , kaon - maid , adelseck - saghai , and williams - ji - cotanch models for the elementary production process and various nuclear and hypernuclear wave functions . the elementary amplitudes are discussed in detail presenting their basic properties and comparison with data . the unique features of the electro - magnetic production of-hypernuclei shown on the examples are the selective excitation of unnatural parity highest - spin states ( natural parity ones for the-closed targets ) and a possibility to investigate the single - particle energies including a spin - orbit splitting using variety of medium - mass targets ."}
{"article_id":"0708.2328","section_id":"i","document":"neutrino conversions from one flavor to another combined with the change of the particle helicity , e.g. @xmath0 , are usually called neutrino spin - flavor oscillations ( see ref . this neutrino oscillations scenario is important since it could be the explanation of the time variability of the solar neutrino flux ( see , e.g. , ref . massive flavor neutrinos are known to mix and can have non - zero magnetic moments . the influence of the strong magnetic field with the realistic profile could lead to the spin - flavor oscillations of solar neutrinos ( see , e.g. , ref . moreover , studying neutrino spin - flavor oscillations happening inside the sun , one will be able to discriminate between different solar models  @xcite . however it was found out in ref . @xcite that neutrino spin - flavor oscillations in solar magnetic fields give a sub - dominant contribution to the total conversion of solar neutrinos .    in this paper we study neutrino spin and spin - flavor oscillations in matter and in an external magnetic field . we suppose that a neutrino is a dirac particle with a non - zero magnetic moment . it should be mentioned that in spite of the recent claims of the experimental confirmation that neutrinos are majorana particles  @xcite , the question about the nature of neutrinos is still open  @xcite . the possibility to distinguish between dirac and majorana particles in the partially polarized solar neutrino flux , due to the spin - flavor precession , was examined in ref . @xcite .    to describe the evolution of the neutrino system we apply the technique based on the relativistic quantum mechanics . we start from the exact solution to the dirac equation in an external field and then derive the neutrino wave functions satisfying the given initial condition . we used this method to describe neutrino flavor oscillations in vacuum  @xcite , in background matter  @xcite and spin - flavor oscillations in an external magnetic field  @xcite . note that neutrino spin - flavor oscillations in electromagnetic fields of various configurations were examined in refs . @xcite using the standard quantum mechanical approach .    in sec . [ so ] we find the solution to the dirac equation for a neutrino propagating in background matter and interacting with the twisting magnetic field . then we formulate the initial condition problem and receive the transition probability for spin oscillations in the given external fields . the standard quantum mechanical transition probability formula is re - derived and the conditions of its validity are analyzed . in sec . [ sfo ] we apply the obtained dirac equation solutions to the description of neutrino spin - flavor oscillations in the twisting magnetic field . first we discuss magnetic moment matrices of neutrinos in flavor and mass eigenstates bases . then we solve the initial condition problem in two different cases of the magnetic moments matrix in the mass eigenstates basis with ( i ) great diagonal elements and ( ii ) great non - diagonal elements . note that the analogous magnetic moments matrices were discussed in ref . we get neutrinos wave functions and calculate transition probabilities for processes like @xmath1 . the consistency of the dirac - pauli equation approach with the standard quantum mechanical treatment of spin - flavor oscillations , based on the schrdinger evolution equation , is considered in sec .  [ qm ] . then in sec . [ appl ] we present some applications and finally we summarize our results in sec .  [ concl ] .","summary":"we find the solution to the dirac equation for a massive neutrino with a magnetic moment propagating in background matter and interacting with the twisting magnetic field . in frames of the relativistic quantum mechanics approach to the description of neutrino evolution we use the obtained solution to derive neutrino wave functions satisfying the given initial condition . we again formulate the initial condition problem , derive neutrinos wave functions and calculate the transition probabilities for different magnetic moments matrices . the consistency of the obtained results with the quantum mechanical treatment of spin - flavor oscillations is discussed . we also consider several applications to astrophysical and cosmological neutrinos .","abstract":"we find the solution to the dirac equation for a massive neutrino with a magnetic moment propagating in background matter and interacting with the twisting magnetic field . in frames of the relativistic quantum mechanics approach to the description of neutrino evolution we use the obtained solution to derive neutrino wave functions satisfying the given initial condition . we apply the results to the analysis of neutrino spin oscillations in matter under the influence of the twisting magnetic field . then on the basis of the yielded results we describe spin - flavor oscillations of dirac neutrinos that mix and have non - vanishing matrix of magnetic moments . we again formulate the initial condition problem , derive neutrinos wave functions and calculate the transition probabilities for different magnetic moments matrices . the consistency of the obtained results with the quantum mechanical treatment of spin - flavor oscillations is discussed . we also consider several applications to astrophysical and cosmological neutrinos ."}
{"article_id":"0708.2328","section_id":"i","document":"we have described the evolution of dirac neutrinos in matter and in a twisting magnetic field . we have applied the recently developed approach ( see refs . @xcite ) which is based on the exact solutions to the dirac equation in an external field with the given initial condition .    first ( sec . [ so ] ) we have found the solution to the dirac equation for a neutral @xmath340-spin particle weakly interacting with background matter , that is equivalent to an external axial - vector field , and non - minimally coupled to an external electromagnetic field due to the possible presence of an anomalous magnetic moment . we have discussed the situation when a neutrino interacts with the twisting magnetic field . the energy spectrum and basis spinors have been obtained . we have applied these results to derive the transition probability of spin oscillations in matter under the influence of the twisting magnetic field . the scope of the standard quantum mechanical approach to the description of neutrino spin oscillations has been analyzed . then ( sec . [ sfo ] ) we have used the obtained solution to the dirac equation for the description of neutrino spin - flavor oscillations in a twisting magnetic field . we supposed that two dirac neutrinos could mix and have non - vanishing matrix of magnetic moments . moreover the mass and magnetic moments matrices in the flavor eigenstates basis are generally independent , i.e. the diagonalization of the mass matrix , that means the transition to the mass eigenstates basis , does not lead to the diagonalization of the magnetic moments matrix . we have discussed two possibilities .    in sec . [ dmm ] we have assumed that magnetic moments matrix in the mass eigenstates basis has great diagonal elements compared to the non - diagonal ones . in this case one can analyze neutrino spin - flavor oscillations perturbatively . note that the perturbative approach allows one to discuss neutrinos with an arbitrary initial condition . for instance , the evolution of particles with small initial momenta can be accounted for . the appearance of non - perturbative phenomena like resonances is analyzed with an example of active - to - sterile neutrinos oscillations . we have discussed the opposite situation in sec . [ mmm ] , i.e. the magnetic moment matrix with the great non - diagonal elements . in this case one had to treat the evolution of the system non - perturbatively . we have demonstrated that this situation is analogous to beatings resulting from the superposition of two oscillations . in both cases we have obtained neutrino wave functions , consistent with the initial conditions , and the transition probabilities . note that all the results are in agreement with our previous work  @xcite if we set @xmath65 , i.e. discuss a constant transversal magnetic field . we have also examined some limiting cases and compared our results with the previous studies . it has been shown in sec .  [ qm ] that one can derive the analog of the major results obtained in secs . [ dmm ] and  [ mmm ] using the schrdinger evolution equation approach for the description of spin - flavor oscillations of dirac neutrinos . the correspondence between these two approaches has been considered .    in sec . [ appl ] we have discussed magnetic moments matrices in various theoretical models which predict neutrinos magnetic moments . the validity of our approach for these situations has been considered . the applications of our results to the studying of cosmological neutrinos in laboratory conditions have been examined . in particular we have suggested that artificial crystalline undulators could be useful for such a research . the results obtained in the present work are valid for arbitrary magnetic field strength . the general case of spin - flavor oscillations of dirac neutrinos in a twisting magnetic field with an arbitrary magnetic moment matrix has not been studied analytically earlier . both experimental and theoretical information about magnetic moments of dirac neutrinos is known to be very limited ( see , e.g. refs . therefore our results can be helpful since they enable one to describe phenomenologically spin - flavor oscillations of dirac neutrinos under the influence of the magnetic field in question provided neutrinos possess non - vanishing matrix of magnetic moments . although we consider neutrinos , it is possible to straightforwardly apply our formalism to the description of any @xmath340-spin particles .    the work has been supported by the academy of finland under the contract no . the author is thankful to the russian science support foundation for a grant as well as to efrain ferrer ( western illinois university ) and kimmo kainulainen ( university of jyvskyl ) for useful comments . the referees remarks are also appreciated . j. schechter and j.  w.  f. valle , phys . d * 24 * , 1883 ( 1981 ) ; m.  b. voloshin , m.  i. vysotski , and l.  b. okun , jetp * 64 * , 446 ( 1986 ) ; sov . 44 * , 440 ( 1986 ) ; e. akhmedov , phys . b * 213 * , 64 ( 1988 ) ; c .- s . lim and w.  j. marciano , phys . d * 37 * , 1368 ( 1988 ) . m. dvornikov , phys . b * 610 * , 262 ( 2005 ) , hep - ph/0411101 ; in _ proceedings of the ipm school and conference on lepton and hadron physics , tehran , 2006 _ , ed . by y. farzan , econf  c0605151 ( 2007 ) , hep - ph/0609139 ; hep - ph/0610047 . m.  dvornikov and j.  maalampi , phys . b * 657 * , 217 ( 2007 ) , hep - ph/0701209 ; m.  dvornikov , to be published in proceedings of the @xmath341 international baksan school `` particles and cosmology '' , 0708.3572 [ hep - ph ] . m.  s. dvornikov and a.  i. studenikin , phys . at . * 64 * , 1624 ( 2001 ) ; _ ibid_. * 67 * , 719 ( 2004 ) ; e.  kh . akhmedov and m.  yu . khlopov , sov . . phys . * 47 * , 689 ( 1988 ) ; a.  egorov , a.  lobanov , and a.  studenikin , phys . b * 491 * , 137 ( 2000 ) , hep - ph/9910476 . a.  yu .  smirnov , phys . b * 260 * , 161 ( 1991 ) ; e.  kh . akhmedov , p.  i. krastev , and a.  yu .  smirnov , z. phys . c * 48 * , 701 ( 1991 ) ; e.  kh . akhmedov , s.  t. petcov , and a.  yu . smirnov , phys . d * 48 * , 2167 ( 1993 ) , hep - ph/9301211 .","summary":"we apply the results to the analysis of neutrino spin oscillations in matter under the influence of the twisting magnetic field . then on the basis of the yielded results we describe spin - flavor oscillations of dirac neutrinos that mix and have non - vanishing matrix of magnetic moments .","abstract":"we find the solution to the dirac equation for a massive neutrino with a magnetic moment propagating in background matter and interacting with the twisting magnetic field . in frames of the relativistic quantum mechanics approach to the description of neutrino evolution we use the obtained solution to derive neutrino wave functions satisfying the given initial condition . we apply the results to the analysis of neutrino spin oscillations in matter under the influence of the twisting magnetic field . then on the basis of the yielded results we describe spin - flavor oscillations of dirac neutrinos that mix and have non - vanishing matrix of magnetic moments . we again formulate the initial condition problem , derive neutrinos wave functions and calculate the transition probabilities for different magnetic moments matrices . the consistency of the obtained results with the quantum mechanical treatment of spin - flavor oscillations is discussed . we also consider several applications to astrophysical and cosmological neutrinos ."}
{"article_id":"1004.3957","section_id":"i","document":"the family of layered ruthenates is in the focus of interest since the discovery of superconductivity in sr@xmath11ruo@xmath2@xcite whose unconventional nature is still under debate . the series ca@xmath0sr@xmath1ruo@xmath2  which arises from sr@xmath11ruo@xmath2by substitution of sr by ca exhibits a variety of exciting phenomena on its own . though the replacement of sr by ca does not change the number of charge carriers , the electronic and magnetic behavior is closely coupled to slight structural changes and varies considerably as function of the sr - content x @xcite . ca@xmath11ruo@xmath2is a mott insulator and antiferromagnetically ordered below 110  k @xcite , while for x@xmath120.18 , the ground state is metallic . the strongly enhanced values of the magnetic susceptibility indicate that the system is close to a ferromagnetic instability around x=0.5 @xcite . ca@xmath0sr@xmath1ruo@xmath2-samples with x@xmath130.5 exhibit a remarkably large value of the sommerfeld coefficient of the specific heat in the range of heavy - fermion compounds . moreover , for 0.2@xmath14x@xmath140.5 a metamagnetic transition from a state with low susceptibility , reminiscent of antiferromagnetic correlations , to a state with high magnetic polarization is observed @xcite . the metamagnetic transition is also observed in the closely related bilayer ruthenate sr@xmath15ru@xmath11o@xmath16  @xcite , where the discussion about quantum - critical behavior has generated further interest . the high concentration dependence of the ground state in ca@xmath0sr@xmath1ruo@xmath2  points to a complex interplay of distinct magnetic correlations . a precise characterization of the magnetic excitations in the layered ruthenates seems interesting due to several reasons : first , ferromagnetic fluctuations are considered to play an important role in the superconducting pairing in sr@xmath11ruo@xmath2 . as ferromagnetic fluctuations are difficult to study in this material , insight can be more easily gained from the ca@xmath0sr@xmath1ruo@xmath2  compounds . in addition , the complex magnetism in ca@xmath0sr@xmath1ruo@xmath2  arrises from the interplay between structural and orbital degrees of freedom , which is relevant in many transition - metal oxides . an orbital - selective mott transition has been proposed to explain the fascinating magnetism in ca@xmath0sr@xmath1ruo@xmath2@xcite . before we discuss the experimental findings , we briefly introduce the general concepts to describe magnetic fluctuations in itinerant magnets and we summarize previous studies on magnetic correlations in layered ruthenates introducing the magnetic contributions to the magnetic scattering in ca@xmath0sr@xmath1ruo@xmath2  by the aid of an intensity map measured for x=0.2 . we then discuss in separate sections the three antiferromagnetic and the ferromagnetic components of the excitation spectrum in ca@xmath0sr@xmath1ruo@xmath2  with @xmath3 , and finally we analyze the effect of magnetic fields on these correlations .","summary":"these components constitute the measured response as function of the sr - concentration x , of the magnetic field and of the temperature .","abstract":"by inelastic neutron scattering , we have analyzed the magnetic correlations in the paramagnetic metallic region of the series casrruo , . we find different contributions that correspond to 2d ferromagnetic fluctuations and to fluctuations at incommensurate wave vectors q=(0.11,0,0 ) , q=(0.26,0,0 ) and q=(0.3,0.3,0 ) . these components constitute the measured response as function of the sr - concentration x , of the magnetic field and of the temperature . a generic model is applicable to metallic casrruo  close to the mott transition , in spite of their strongly varying physical properties . the amplitude , characteristic energy and width of the incommensurate components vary only little as function of x , but the ferromagnetic component depends sensitively on concentration , temperature and magnetic field . while ferromagnetic fluctuations are very strong in casrruo  with a low characteristic energy of 0.2  mev at t=1.5  k , they are strongly suppressed in casrruo , but reappear upon the application of a magnetic field and form a magnon mode above the metamagnetic transition . the inelastic neutron scattering results document how the competition between ferromagnetic and incommensurate antiferromagnetic instabilities governs the physics of this system .    by 2 cm"}
{"article_id":"1004.3957","section_id":"c","document":"the comprehensive ins studies provide a detailed description of the magnetic correlations in ca@xmath0sr@xmath1ruo@xmath2 . different types of magnetic fluctuations are identified : we can separate a ferromagnetic signal and different features at incommensurate q - vectors : one on the diagonal of the brillouin zone at q@xmath6=(0.3,0.3,0 ) and a broader and stronger contribution on the @xmath48/@xmath49axis . this latter one has an internal structure that can be well described by assuming two overlapping contributions from q@xmath4=(0.11,0,0 ) and q@xmath5=(0.26,0,0 ) and equivalent positions . within the accuracy of the measurement  limited primarily by the large overlap of the signals  there is no significant difference in the q - positions of these contributions for the different values of the sr - concentration x=0.2 and x=0.62 . the signal at q@xmath6  can be associated with the incommensurate signal in sr@xmath11ruo@xmath2  @xcite . as its origin is well understood arising from nesting of the @xmath55 and @xmath56 fermi surface , the presence of this signal at the same position indicates that these sheets of the fermi surface , and thus also the occupation of the ruthenium d@xmath57 and d@xmath58 orbitals are only little changed in ca@xmath0sr@xmath1ruo@xmath2  ( x=0.2/0.62 ) with respect to sr@xmath11ruo@xmath2@xcite . the origin , i.  e.the relevant sections of the fermi surface , of the signals at q@xmath4/q@xmath5  is not yet precisely identified , but for several reasons they are most likely related to the @xmath62 sheet of the fermi surface . arpes measurements and band - structure calculations clearly identify the @xmath62 band as the highly renormalized one associated with the heavy - mass electronic behavior and with the high susceptibility , but the detailed structure of the @xmath62 sheet awaits for further studies . there seems to be no significant change of the different incommensurate components for x@xmath1420.2 and x@xmath1420.62 , which is thus presumably the case for the whole range 0.18@xmath143x@xmath1431.5 . though the temperature dependence of @xmath89 and @xmath75 of these fluctuations@xcite indicates that the system approaches a magnetic instability at incommensurate ordering vectors , the system can obviously be considered as still sufficiently far away and not directly in the critical region . the structural and other variations in this range of x do not very sensitively couple to this part of the magnetic correlations . the rotational structural distortion , however , is apparently very important and causes the significant difference to sr@xmath11ruo@xmath2 , where no excitations are observed at q@xmath4  or q@xmath5 . it is remarkable that in the bilayer material sr@xmath15ru@xmath11o@xmath16  very similar excitations as at q@xmath4  and q@xmath5  have been observed@xcite . in view of the similar sr@xmath15ru@xmath11o@xmath16  crystal structure , which also exhibits the rotational distortion@xcite , this appears consistent . these two layered ruthenates and their metamagnetic transitions appear to be very similar to each other . the incommensurate fluctuations at q@xmath4/q@xmath5  have a characteristic energy of about 2.7  mev , while the characteristic energy of the excitations at the zone center is only 0.4  mev at t=10  k in ca@xmath9sr@xmath10ruo@xmath2 . in ca@xmath7sr@xmath8ruo@xmath2  this latter value further decreases to 0.2  mev at t=1.5  k and the amplitude increases , consistent with the picture of ca@xmath7sr@xmath8ruo@xmath2  approaching a ferromagnetic instability , though not reaching it at finite temperatures . in ca@xmath9sr@xmath10ruo@xmath2 , the ferromagnetic part of the response is strongly suppressed at low temperature . the values of the susceptibility related to the ferromagnetic signal are , concerning their absolute values as well as their variations with temperature and magnetic field , in perfect agreement with the macroscopically determined susceptibilities , proving that this ins signal reflects the magnetic correlations that determine the macroscopic physical properties . the application of an external magnetic field at low temperature suppresses the incommensurate part of the response . in ca@xmath9sr@xmath10ruo@xmath2 , a substantial ferromagnetic component reappears , reflecting the metamagnetic transition . at high field , the spectral weight of the ferromagnetic response is shifted towards higher energy for x=0.2 and 0.62 , opening a gap that roughly corresponds to the zeeman energy of an electron in the magnetic field . in ca@xmath9sr@xmath10ruo@xmath2  a dispersive excitation mode , corresponding to a magnon in a ferromagnet , is observed , which is well defined near the zone center and low energies , and which significantly broadens at energies above 3  mev . although only two concentrations have been studied here , x=0.2 and 0.62 , the results are most likely of relevance for the whole range 0.2@xmath143x@xmath1431.5 of the series ca@xmath0sr@xmath1ruo@xmath2 . in this region of the phase diagram , the materials are paramagnetic and metallic at all temperatures . the samples with x=0.2 and 0.62 have , though , to be regarded as quite different concerning their physical properties , as there is a second - order structural phase transition ( associated with ruo@xmath52  octahedra tilting ) at x=0.5 ; ca@xmath0sr@xmath1ruo@xmath2  seems approaches the ferromagnetic instability for x decreasing towards 0.5 , while a strongly reduced susceptibility and the metamagnetic transition are observed at x@xmath140.5 . it is thus important to realize that the measured magnetic correlations can be well described in a common model in which the change of only few parameters leads to the large differences between the nearly ferro- and nearly antiferromagnetic compounds . the ferromagnetic correlations in ca@xmath0sr@xmath1ruo@xmath2  depend sensitively on the sr - concentration x and seem to tune the different magnetic properties with the doping . the ferromagnetic instability in general arises from the high density of states close to the fermi surface of the @xmath62 sheet , which has been reveals in several arpes studies@xcite . due to this high density of states the system becomes very sensitive upon structural changes , as it is best documented in the thermal expansion anomalies @xcite .    in conclusion , the comprehensive ins experiments clearly reveal the image of competing magnetic instabilities in ca@xmath0sr@xmath1ruo@xmath2 . the whole spectrum of magnetic correlations is well described in the presented phenomenological model with ferromagnetic and incommensurate antiferromagnetic contributions . in this competition , it is mainly the variation of the ferromagnetic component as function of sr - concentration x , temperature and magnetic field , that governs the physical properties . m. kriener , p. steffens , j. baier , o. schumann , t. zabel , t. lorenz , o. friedt , r. mller , a. gukasov , p.g . radaelli , p. reutler , a. revcolevschi , s. nakatsuji , y. maeno , and m. braden , phys . * 95 * , 267403 ( 2005 ) . j. baier , p. steffens , o. schumann , m. kriener , s. stark , h. hartmann , o. friedt , a. revcolevschi , p. g. radaelli , s. nakatsuji , y. maeno , j. a. mydosh , t. lorenz , and m. braden , j. low temp . phys . * 147 * , 405 ( 2007 ) .","summary":"a generic model is applicable to metallic casrruo  close to the mott transition , in spite of their strongly varying physical properties . the amplitude , characteristic energy and width of the incommensurate components vary only little as function of x , but the ferromagnetic component depends sensitively on concentration , temperature and magnetic field . while ferromagnetic fluctuations are very strong in casrruo  with a low characteristic energy of 0.2  mev at t=1.5  k , they are strongly suppressed in casrruo , but reappear upon the application of a magnetic field and form a magnon mode above the metamagnetic transition . the inelastic neutron scattering results document how the competition between ferromagnetic and incommensurate antiferromagnetic instabilities governs the physics of this system .    by 2 cm","abstract":"by inelastic neutron scattering , we have analyzed the magnetic correlations in the paramagnetic metallic region of the series casrruo , . we find different contributions that correspond to 2d ferromagnetic fluctuations and to fluctuations at incommensurate wave vectors q=(0.11,0,0 ) , q=(0.26,0,0 ) and q=(0.3,0.3,0 ) . these components constitute the measured response as function of the sr - concentration x , of the magnetic field and of the temperature . a generic model is applicable to metallic casrruo  close to the mott transition , in spite of their strongly varying physical properties . the amplitude , characteristic energy and width of the incommensurate components vary only little as function of x , but the ferromagnetic component depends sensitively on concentration , temperature and magnetic field . while ferromagnetic fluctuations are very strong in casrruo  with a low characteristic energy of 0.2  mev at t=1.5  k , they are strongly suppressed in casrruo , but reappear upon the application of a magnetic field and form a magnon mode above the metamagnetic transition . the inelastic neutron scattering results document how the competition between ferromagnetic and incommensurate antiferromagnetic instabilities governs the physics of this system .    by 2 cm"}
{"article_id":"1401.6827","section_id":"i","document":"the main results of this study are :    1 . we confirm known facts about binary statistics of solar - type stars . periods of all binaries ( regardless of their hierarchy ) are distributed log - normally with a median @xmath180 ( @xmath26100yr ) and dispersion 2.4 . the mass ratio is distributed uniformly and is independent ( or almost independent ) of the period , except such details as short - period twins . the multiplicity fraction is @xmath181 . the fraction of hierarchical systems is 0.13@xmath770.01 , of which 0.10 have sub - system(s ) related to the primary component , 0.07 have sub - systems in the secondary component , and 0.04 have both ( figure  [ fig : stat ] ) . the presence of sub - systems in both components of wide ( outer ) binaries is correlated . 3 .   there remain about 150 undiscovered secondary ( l12 ) sub - systems . about 60% of those pairs reside in 2 + 2 hierarchies , because of the above correlation . the lack of outer systems with periods shorter than @xmath261000d is real ( not a selection effect ) . the statistics of hierarchical systems can be reproduced by recursive random selection of outer and inner binaries from the same generating period distribution with parameters @xmath182 , @xmath183 , and uniform mass ratio , @xmath184 ( @xmath151 for the secondary sub - systems ) . the amplitude of this distribution is variable ( e.g. @xmath185 $ ] with equal probability ) . only dynamically stable combinations are kept , with the dynamical cutoff in @xmath186 uniformly distributed between 0.7 and 1.7 . the frequency of secondary sub - systems is enhanced by their correlation with the primary sub - systems , while binaries with periods shorter than 1000d do not produce sub - systems . the period distribution in the inner sub - systems can be explained by dynamical truncation . however , there is an excess of tight inner binaries with @xmath177d compared to the smooth gaussian distribution , presumably caused by tidal evolution . the mass ratios in the inner and outer systems of triple stars are uncorrelated , except 2 + 2 hierarchies where the mass ratios are larger than average in both of their inner sub - systems . in triple stars , the system mass ratio of the outer binary does not depend on its period and has a median value of 0.39 , meaning that the masses of tertiary components are comparable to the masses of stars in the inner binary . the above results are not free from biases , approximations , and errors . some were mentioned above and in paper  i. we re - capitulate the most relevant _ weaknesses _ below , in order of decreasing importance .    1 .   _ missing information . _ unknown periods and mass ratios of many spectroscopic and astrometric binaries ( 32% of all binaries with @xmath187yr ) increase the uncertainty of the results . missing information is accounted for in the ml analysis and in the simulations . however , we can not reliably study the distribution of periods and mass ratios of close binaries until they are resolved or get spectroscopic orbits . _ approximate knowledge of detection probability . _ despite the effort to collect relevant data and to model the detection limits , there remains some uncertainty . for example , all binaries with separation of @xmath188 and @xmath189 are assumed to be resolved by _ hipparcos _ , but this is not actually the case . the detection of sub - systems in the secondary components is most critical , as it entails a larger correction for incompleteness . 3 .   _ uncertain data and subjective decisions . _ some binaries accepted as real may in fact be spurious or optical . conversely , we may have rejected or missed some real pairs ( see   3.10 of paper  i ) . the percentage of such cases is certainly much less than 10% of all binaries , but we do not know how much less . biases against multiple stars . _ secondary components that are themselves binary can be partially resolved and , for this reason , be missed by the point - source catalogs . their proper motion may differ substantially from that of the main target . the _ hipparcos _ parallaxes of unrecognized binaries are often biased by their orbital motion , relegating some of them beyond the 67pc distance limit . such nearby multiples as @xmath190  cnc and @xmath191  uma are missed here because they are not included in the _ hipparcos _ catalog . white dwarfs . _ the fraction of sirius - like binaries harbouring a wd companion is estimated as @xmath262% . known sirius - like systems are removed from the analysis , but the reduction of the sample size associated with the removal of wds is uncertain . most likely , the assumed sample size @xmath192 should be reduced further , the estimated @xmath5 will then increase slightly . .   _ approximations _ made in the data analysis : relation between mass and absolute magnitude in various photometric bands , evaluation of period from projected separations , evaluation of the mass ratio from photometry or from the minimum mass of single - lined spectroscopic binaries , distribution of periods and mass ratios approximated by analytical functions . it is clear that the results of this study are affected by these biases and that the formal errors quoted above underestimate the actual , larger uncertainties . future work will revise some of the parameters derived here . however , these anticipated changes will no longer be dramatic ; the fraction of hierarchical systems derived here should not be revised by more than 1 - 2% .","summary":"periods of the outer and inner binaries are selected recursively from the same log - normal distribution , subject to the stability constraint and accounting for the correlation between inner sub - systems .","abstract":"statistics of hierarchical multiplicity among solar - type dwarfs are studied using the distance - limited sample of 4847 targets presented in the accompanying paper  i. known facts about binaries ( multiplicity fraction 0.46 , log - normal period distribution with median period 100yr and logarithmic dispersion 2.4 , and nearly uniform mass - ratio distribution independent of the period ) are confirmed with a high statistical significance . the fraction of hierarchies with three or more components is , the fractions of targets with components are 54:33:8:4:1 . sub - systems in the secondary components are almost as frequent as in the primary components , but in half of such cases both inner pairs are present . the high frequency of those 2 + 2 hierarchies ( 4% ) suggests that both inner pairs were formed by a common process . the statistics of hierarchies can be reproduced by simulations , assuming that the field is a mixture coming from binary - rich and binary - poor environments . periods of the outer and inner binaries are selected recursively from the same log - normal distribution , subject to the stability constraint and accounting for the correlation between inner sub - systems . the simulator can be used to evaluate the frequency of multiple systems with specified parameters . however , it does not reproduce the observed excess of inner periods shorter than 10d , caused by tidal evolution ."}
{"article_id":"1401.6827","section_id":"c","document":"the large sample of solar - type binaries with known detection limits confirms and strengthens known facts about their statistics @xcite . the parameters of the log - normal period distribution determined here ( @xmath193 ) match well the results of r10 ( @xmath194 , @xmath195 ) . the triangular function ( [ eq : tri ] ) fits the distribution of @xmath196 even better than a gaussian . however , the period distribution of the inner sub - systems is not log - normal , it has an excess at @xmath177d . we find a nearly flat distribution of the mass ratio with the power index @xmath152 and show that it does not depend on the orbital period ( with a caveat related to partially missing binary parameters ) . @xcite fitted @xmath197 to the data of r10 , but found that @xmath198 for periods shorter than @xmath199d . considering the sensitivity of derived @xmath46 to the treatment of selection effects ( see   [ sec : beta - p ] ) , we believe that this claim is premature . @xcite derive @xmath200 for the two combined samples of dwarf binaries and argue for the independence of @xmath46 on period and primary mass . the flat @xmath201 was found by @xcite for the pre - main - sequence stars in taurus more massive than @xmath202 . this study gives the first look at unbiased statistics of hierarchical systems with three or more components . multiples are frequent ( one in eight stars ) . the 13% frequency of hierarchies estimated here is essentially the same as 12% found by @xcite in the 25-pc sample . however , they focused on companions to the primary stars and missed some secondary pairs . a few of those secondary sub - systems are recovered here , more are yet to be discovered . on the other hand , these authors may have over - estimated the number of high - order multiples . they list three multiples with five or more components ( their fig . 24 ) , while we found only 5 such systems in a sample 10@xmath156 bigger . this discrepancy is explained by the better companion census of nearby stars , by the inclusion of uncertain sub - systems ( such as hd  186858 aa , ab ) in the 25-pc sample , and by the small - number statistics . note that among the 11 quadruples in the 25-pc sample , 9 ( or 82% ) have the 2 + 2 hierarchy and only two have the 3 + 1 hierarchy . the last column of table  [ tab : comp ] predicts a 74% fraction of 2 + 2 quadruples , in agreement with the small statistics within 25pc . @xcite gives estimates of @xmath5 and @xmath75 among f - type stars within 25pc that agree well with our results . he claims that both fractions rise sharply with increasing primary mass ( however , with a low significance limited by the sample size ) . we do not confirm this trend : the observed ( not selection - corrected ) multiplicity fraction of 845 stars with @xmath203 within 67pc is @xmath204% , not significantly different from 36% in the full fg-67 sample . the statistics of hierarchical multiples are well modeled by independent selection of sub - systems from some generating distribution of periods , provided that the binary frequency is variable . this hints that the field stars were formed in different environments , binary - rich and binary - poor . indeed , the binary frequency differs between star - forming regions @xcite . moreover , some fraction of single stars come from disintegrated multiples and merged binaries , so the _ intrinsic _ frequency of the formation process @xmath55 is always larger than the multiplicity of a mature field population . variable multiplicity naturally leads to the enhanced probability of finding sub - systems in wide binaries , in comparison to all targets . this tendency was noted by @xcite . the simulations faithfully reproduce the fraction of close binaries belonging to higher - order systems for the inner periods longer than 10d ( figure  [ fig : multfrac ] ) ; at shorter inner periods , the observed fraction is much higher than predicted , because of tidal evolution . @xcite already tried to model hierarchical multiplicity in a monte - carlo simulation by producing inner sub - systems with the generating period distribution and applying the stability cutoff . similar approach was taken by @xcite in their modeling of hierarchical multiples for evaluation of false positives in exo - planet detection . the multiplicity simulator developed here is anchored to the data and can be used in such studies with confidence . correlated presence of sub - systems in both components of a wide binary is the new fact found in the course of this project @xcite . to reproduce this correlation by simulation , the frequency of secondary sub - systems is enhanced in presence of the primary sub - system and decreased otherwise . as a result , the majority of quadruple systems have the 2 + 2 hierarchy ( 67% observed , 74% predicted after correction of observational selection , 82% in the 25-pc sample ) . the fraction of quadruple stars is then larger than predicted by the independent multiplicity , and comparable to the fraction of triples ( 4% and 8% , respectively ) . the multiplicity fractions @xmath9 do not decrease in geometric progression of @xmath8 , as suggested in the early works @xcite and repeated by @xcite . poor detection of sub - systems in secondary components was not fully appreciated until recently . the relatively large fraction of 2 + 2 systems suggests that they were formed by some special process . other properties of 2 + 2 quadruples such as similarity of component s masses and inner periods point in this direction , too @xcite . both inner sub - systems in the 2 + 2 hierarchies differ from the rest of inner sub - systems by their larger mass ratios (   [ sec : q ] ) . on the other hand , when only _ one _ inner sub - system is present , it is preferentially associated with the most massive star , and its mass ratio is distributed uniformly , as in normal binaries . therefore , there must be another , dominant formation channel which produces most binary and triple stars and , by extension , 3 + 1 quadruples . statistical work on multiple stars , including this one , is motivated by the desire to understand their formation . what have we learned from this study ? hydrodynamical simulations @xcite reveal a complex process of binary formation and early evolution that shapes the multiplicity statistics . stellar pairs form by fragmentation with initial separations larger than 10 - 100au ( so - called opacity limit ) and small masses . the components grow by accreting gas and , at the same time , migrate to smaller separations . the depletion of long periods ( the right side of the `` gaussian '' ) by dynamical interactions with the environment , combined with migration , shape the observed period distribution @xcite . if the fragmentation generates periods @xmath196 longer than , say , @xmath205 ( a step function in @xmath28 ) and the period decay @xmath206 is a random function ( e.g. uniformly distributed ) , the convolution of those two distributions results in the linear decrease of binary frequency at @xmath129 , as actually observed ( figure  [ fig : phist ] ) . the approximately linear decrease of the period distribution at @xmath129 is produced under a wide range of assumptions , provided only that the initial period distribution has a lower cutoff and that the migration is random . migration is essential in understanding the origin of tight hierarchical systems where 3 or 4 stars are packed in a small volume . if all inner binaries formed with initial periods @xmath207 , the initial outer periods must be even longer , whereas the present - day outer periods can be as short as @xmath208 ( figure  [ fig : plps ] ) . migration occurs therefore at all hierarchical levels . the inner binaries must migrate faster or form earlier than the outer binaries , otherwise the multiple system becomes dynamically unstable and decays . most hierarchies seem to be assembled `` from inside - out '' , by bringing together pre - fabricated inner pairs ( or stars ) to make the outer system . the success of modeling the observed statistics by independent multiplicity strongly supports this view . the mass ratios of inner and outer systems do not correlate , the masses of outer ( tertiary ) components are comparable to the masses of the inner components . the inner and outer periods are selected independently from the same distribution and are mutually related only by the dynamical stability ( taking aside the tidal evolution ) . if hierarchies formed `` from outside - in '' by successive fragmentation of outer binaries , as envisioned e.g. by @xcite , it would be difficult to explain the independent multiplicity . considering that many hierarchies are close to the stability limit , dynamical decay of multiple systems must occur sometimes . it can happen when the outer binary migrates faster than the inner one or when other stars in the cluster disrupt the multiple or exchange components with it . however , multiple systems produced by @xmath144-body dynamical interactions ( or surviving them ) have characteristics that do not match real hierarchies : high eccentricities , low masses of distant components , and moderate ratios @xmath98 . the observed multiplicity statistics indicates that dynamical processes play only a secondary role . most hierarchical stellar systems in the field are not the surviving remnants of primordial clusters . the 2 + 2 hierarchies could be formed in a special way , e.g. by inelastic collision of two cores that prompts their fragmentation into sub - systems and , at the same time , keeps these two pairs together on a common wide orbit by dissipating the energy . such impulsively - triggered multiple - star formation was envisioned by @xcite , see his figure  2 . further evolution will depend on the relative orientation of the inner and outer orbits . if they are not aligned , the inner binaries will accrete gas with a misaligned angular momentum , which will accelerate their migration to short periods . in the opposite case of co - aligned orbits , the accretion will keep the inner binaries wide , and a quadruple with a moderate @xmath98 ratio and nearly co - planar orbits , resembling @xmath209  lyr , can be formed . another striking aspect of this prototypical 2 + 2 quadruple  similar masses of all 4 stars  matches the tendency to equal component masses in both inner sub - systems of 2 + 2 hierarchies , emerging from this study .    on the other hand , the majority of the inner sub - systems have @xmath210 , like all binaries , while their tertiary components are single . their formation process should therefore be different from the formation of 2 + 2 hierarchies . the tertiary component could have formed around the initial binary ( or joined it ) at a later stage . the cascade can continue further by adding yet another star in a 3 + 1 hierarchy . the 2 + 2 formation channel probably produced more quadruples than actually observed because some sub - systems merged , leaving triples and binaries , while some quadruples decayed dynamically . a certain fraction of binaries and triples in the field could be born as 2 + 2 systems . also , merging of the inner binaries ( natural extension of migration ) can possibly help in understanding why the outer periods in triple stars are longer than @xmath99d . it should be stressed that not _ all _ close binaries belong to multiple stars . this is true only for pairs with @xmath167d which could not be produced without tidal migration during their main - sequence life . at longer periods @xmath211d , the frequency of wide tertiary companions is comparable to the frequency of such companions in the full sample @xcite . figure  [ fig : form ] illustrates the formation channels and the fractions of different hierarchies in the field . the fragmentation produces single and binary stars . cascade `` inside - out '' fragmentation generates 2 + 1 triples and 3 + 1 quadruples . unstable hierarchies decay dynamically into single and binary stars , some close binaries merge . the alternative 2 + 2 process creates quadruple stars with components of similar mass . merging of inner pairs in the 2 + 2 quadruples contributes to the populations of triples and binaries . about 1% of targets with more than 4 components could be produced by the combination of these elementary processes . there are various ways to improve and continue the present study . the determination of unknown periods and mass ratios of close binaries is one obvious project to pursue . the prediction of the large number of undiscovered sub - systems in the secondary components should be tested observationally . it will be interesting to study relative motions in resolved triple and quadruple systems to get a better idea of the relative orbit orientation . the data used in this work are acknowledged in paper  i. i thank bo  reipurth and m.  bate for comments on the draft of this paper , p.  eggleton for discussions of multiplicity statistics and white dwarfs .","summary":"the high frequency of those 2 + 2 hierarchies ( 4% ) suggests that both inner pairs were formed by a common process . however , it does not reproduce the observed excess of inner periods shorter than 10d , caused by tidal evolution .","abstract":"statistics of hierarchical multiplicity among solar - type dwarfs are studied using the distance - limited sample of 4847 targets presented in the accompanying paper  i. known facts about binaries ( multiplicity fraction 0.46 , log - normal period distribution with median period 100yr and logarithmic dispersion 2.4 , and nearly uniform mass - ratio distribution independent of the period ) are confirmed with a high statistical significance . the fraction of hierarchies with three or more components is , the fractions of targets with components are 54:33:8:4:1 . sub - systems in the secondary components are almost as frequent as in the primary components , but in half of such cases both inner pairs are present . the high frequency of those 2 + 2 hierarchies ( 4% ) suggests that both inner pairs were formed by a common process . the statistics of hierarchies can be reproduced by simulations , assuming that the field is a mixture coming from binary - rich and binary - poor environments . periods of the outer and inner binaries are selected recursively from the same log - normal distribution , subject to the stability constraint and accounting for the correlation between inner sub - systems . the simulator can be used to evaluate the frequency of multiple systems with specified parameters . however , it does not reproduce the observed excess of inner periods shorter than 10d , caused by tidal evolution ."}
{"article_id":"0805.3845","section_id":"i","document":"let @xmath13 and @xmath14 be two closed manifolds . the manifold @xmath13 is said to _ dominate _ @xmath14 if there is a continuous map @xmath15 of degree one . an @xmath2-dimensional hyperbolic manifold @xmath14 has the smallest volume among the set of all riemannian manifolds @xmath16 such that @xmath13 dominates @xmath14 and the metric @xmath10 has ricci curvature @xmath17 . in dimension @xmath18 this is a consequence of the gauss - bonnet formula and in dimension @xmath19 this follows from the    [ minvol]@xcite let @xmath8 be an @xmath2-dimensional closed hyperbolic manifold and @xmath13 a closed manifold which dominates @xmath14 . then , for any metric @xmath10 on @xmath13 such that @xmath20 , one has @xmath21 , and equality happens if and only if @xmath16 and @xmath8 are isometric . the minimal volume of a closed manifold @xmath13 is defined as @xmath22 where @xmath23 is the sectional curvature of the riemannian metric @xmath10 . an @xmath2-dimensional hyperbolic manifold @xmath14 is characterized by its minimal volume among the set of all riemannian manifolds @xmath13 such that @xmath13 is homotopy equivalent to @xmath14 . namely ,    [ bminvol]@xcite let @xmath14 be an @xmath2-dimensional closed hyperbolic manifold and @xmath13 a closed manifold which dominates @xmath14 . then , @xmath24 if and only if @xmath14 and @xmath13 are diffeomorphic . the aim of this paper is to show the following gap result . it improves the above theorem [ bminvol ] since we now require a lower bound on the ricci curvature instead of a pinching of the sectional curvature ; moreover , under the hypothesis , we prove that if the volume of @xmath13 is close to the volume of @xmath14 then these two manifolds are diffeomorphic . more precisely ,    [ main - theorem ] given any integer @xmath19 and @xmath25 , there exists @xmath26 such that the following holds . suppose that @xmath8 is an @xmath2-dimensional closed hyperbolic manifold with diameter @xmath27 and that @xmath13 is a closed manifold which dominates @xmath14 . then @xmath13 has a metric @xmath10 such that @xmath28 if and only if @xmath29 is homotopic to a diffeomorphism .    in @xcite the authors prove the existence of closed n - dimensional manifolds @xmath13 which are homeomorphic to a closed n - dimensional hyperbolic manifold @xmath1 but not diffeomorphic to it . an immediate corollary of the above theorem is the following .    with the above notations , there exists @xmath30 depending on @xmath2 and on the diameter of @xmath14 with the property that for any such @xmath13 and any riemannian metric @xmath10 on @xmath13 whose ricci curvature is bounded below by @xmath31 one has , @xmath32    to be more precise in @xcite the manifold @xmath13 is obtained as follows : @xmath33 where @xmath34 is an exotic sphere . not every closed hyperbolic manifold @xmath14 gives rise to such a @xmath13 that is ( obviously ) homeomorphic but not diffeomorphic to @xmath14 . indeed , we may have to take a finite cover of @xmath14 . but when we get one construction that works , it does on any finite cover @xmath35 of @xmath14 as well . the authors also prove that by taking covers of arbitrary large degree we can put on @xmath13 a metric whose sectional curvature is arbitrarily pinched around , say @xmath36 . the stronger the pinching , the larger the degree . now assume that @xmath37 could be taken independent of the diameter of @xmath14 ; applying the results of @xcite one could show that the volumes of the two manifold are very close when the pinching on @xmath13 is very sharp ( close to @xmath36 ) . the volume of @xmath13 endowed with this pinched metric could then be taken smaller than @xmath38 , by choosing a covering of large degree ; the manifolds though are not diffeomorphic . this gives a contradiction and shows that `` size '' of @xmath14 has to be involved in the statement of the theorem , for example its diameter . we argue by contradiction . suppose that there is a sequence @xmath39 of closed hyperbolic manifolds with diameter @xmath27 and a sequence of closed manifolds @xmath40 , of degree one continuous maps @xmath41 and metrics @xmath42 on @xmath40 satisfying the hypothesis ( [ e0.1 ] ) and ( [ e0.2 ] ) for some @xmath43 going to zero . since @xmath44 is of degree one and @xmath45 is hyperbolic , it is equivalent to say ( thanks to mostow s rigidity theorem ) that @xmath44 is homotopic to a diffeomorphism or simply that @xmath45 and @xmath40 are diffeomorphic . we thus assume that @xmath40 and @xmath45 are not diffeomorphic . one then shows that up to a subsequence , for large @xmath46 , @xmath40 is diffeomorphic to a closed manifold @xmath13 , @xmath45 is diffeomorphic to a closed manifold @xmath14 , and @xmath14 and @xmath13 are diffeomorphic . one argues as follows : by the classical finiteness results we get the sub - convergence of the sequence @xmath47 . indeed , the curvature is @xmath36 , the diameter is bounded by hypothesis , and there is a universal lower bound for the volume of any closed hyperbolic manifold of a given dimension , thanks to margulis lemma ( see @xcite ) . finiteness theorem then applies . moreover , on a closed manifold of dimension @xmath48 , there is at most one hyperbolic metric , up to isometry . we can therefore suppose that @xmath49 is a fixed hyperbolic manifold . the inequality proved in theorem [ minvol ] provides a lower bound for the volume of @xmath40 as it is explained below . we have no a priori bounds on the diameter of @xmath50 , but we can use cheeger - colding s theory to obtain sub - convergence in the pointed gromov - hausdorff topology to a complete metric space @xmath51 with small singular set . to obtain more geometric control , the idea is to use the natural maps between @xmath40 and @xmath14 ( see @xcite ) . one can show that they sub - convergence to a limit map between @xmath52 and @xmath14 , which is an isometry . then @xmath14 is an @xmath2-dimensional smooth closed riemannian manifold which is the gromov - hausdorff limit of the sequence @xmath50 of riemannian manifold of dimension @xmath2 satisfying the lower bound ( [ e0.1 ] ) on ricci curvature , therefore @xmath14 and @xmath40 are diffeomorphic for large @xmath46 by a theorem of j. cheeger and t. colding . the paper is organised as follows . the construction and the properties of the natural maps are given in section 2 . in section 3 , we construct the limit space @xmath52 and the limit map @xmath53 . in section 4 , we prove that @xmath54 is an isometry and conclude .      for two closed manifolds @xmath13 and @xmath14 we said above that @xmath13 dominates @xmath14 if there exists a map of degree one from @xmath13 onto @xmath14 . we could have required that there exists a map @xmath55 of non - zero degree . the main theorem of @xcite was stated and proved in this set up . more precisely , the following statement holds    @xcite let @xmath8 be an @xmath2-dimensional closed hyperbolic manifold and @xmath13 a closed manifold such that there exists a map @xmath56 with non - zero degree denoted deg(f ) . then , for any metric @xmath10 on @xmath13 such that @xmath20 , one has @xmath57 , and equality happens if and only if @xmath29 is homotopic to a riemannian covering ( _ i.e. _ locally isometric ) of degree |deg(f)| from @xmath16 onto @xmath8 .    with the technique developed in this article , the following result can be proved    [ degree ] given any integer @xmath19 and @xmath25 , there exists @xmath26 such that the following holds . suppose that @xmath8 is an @xmath2-dimensional closed hyperbolic manifold with diameter @xmath27 and that @xmath13 is a closed manifold such that there exists a map @xmath56 with non - zero degree . then @xmath13 has a metric @xmath10 such that @xmath58 if and only if @xmath29 is homotopic to a covering of degree @xmath59 . the proof is essentially the one described above ; it uses the technique described below and the treatment of an arbitrary degree given in @xcite . the fact that the degree can be , in absolute value , greater than one yields extra technicalities . for the sake of clarity we shall omit this proof in the present article and leave it to the reader . a corollary is ,    let @xmath1 be a closed @xmath2-dimensional hyperbolic manifold , then there exists @xmath30 , such that , for any metric @xmath10 on the connected sum @xmath60 satisfying that its ricci curvature of @xmath10 is not smaller than @xmath31 , @xmath61    we may now ask whether such a result could be true with a lower bound on the scalar curvature instead of a lower bound on the ricci curvature . the situation in dimension @xmath62 , completely clarified by perelman s work , shows that the answer to this question is negative . more precisely , if @xmath8 is a @xmath62-dimensional closed hyperbolic manifolds , a consequence of ( * ? ? ? * inequality 2.10 ) is that , @xmath63 in dimension greater or equal to @xmath64 , it follows from @xcite and the solution to the yamabe problem that , @xmath65","summary":"in this article we prove a differentiable rigidity result . we show that there exists a number such that if the ricci curvature of the metric is bounded below by and its volume satisfies then the manifolds are diffeomorphic . the proof relies on cheeger - colding s theory of limits of riemannian manifolds under lower ricci curvature bound .","abstract":"in this article we prove a differentiable rigidity result . let and be two closed-dimensional riemannian manifolds ( ) and be a continuous map of degree . we furthermore assume that the metric is real hyperbolic and denote by the diameter of . we show that there exists a number such that if the ricci curvature of the metric is bounded below by and its volume satisfies then the manifolds are diffeomorphic . the proof relies on cheeger - colding s theory of limits of riemannian manifolds under lower ricci curvature bound ."}
{"article_id":"astro-ph0506249","section_id":"i","document":"the higher order statistics of galaxy clustering encode fundamental information about two key dynamical aspects of the large scale structure of the universe : the growth mechanism of fluctuations and the connection between the galaxy distribution and the underlying mass ( for a review , see bernardeau et  al . an accurate measurement of the three - point correlation function of galaxies has the potential to test the gravitational instability paradigm of structure formation and , on scales that are evolving in the weakly non - linear regime , to separate the effects of gravity from the contributions arising from galaxy bias ( fry & gaztaaga 1993 ; frieman & gaztaaga 1994 ) . the measurement of the three - point function and other higher order statistics from galaxy catalogues has a rich history ( peebles & groth 1975 ; groth & peebles 1977 ; fry & peebles 1978 ; baumgart & fry 1991 ; gaztaaga 1992 ; bouchet et  al . 1993 ; fry & gaztaaga 1994 ) . in the past decade , three - point statistics have supported the basic premise of gravitational instability from gaussian initial conditions ( frieman & gaztaaga 1994 ; jing & brner 1998 ; frieman & gaztaaga 1999 ; hoyle , szapudi & baugh 2000 ; feldman et  al . the impact of these measurements on theoretical models has , however , not been as great as it could have been for two reasons . first , the traditional theoretical predictions rely upon the application of perturbation theory , which limits the comparison with data to relatively large scales on which the fluctuations are evolving in a linear or weakly non - linear fashion . second , previous generations of galaxy surveys simply covered too little volume to permit accurate measurements of the higher order correlation functions on the scales that could strongly constrain the simple theoretical models . recent theoretical and observational advancess have been such that we are now in a position to realize the full potential of higher order statistics . theoretical models of galaxy formation have progressed sufficiently to make predictions for the number of galaxies that reside in dark matter haloes of different mass ( benson et  al . 2000 ; peacock & smith 2000 ; scoccimarro et  al . 2001b ; berlind et  al . this allows the prediction to be extended to scales for which perturbation theory is not valid , and provides a framework for testing the physics of galaxy formation directly against clustering measurements . observationally , two recent surveys have revolutionized our view of the local universe : the two - degree field galaxy redshift survey ( hereafter 2dfgrs ; colless et  al . 2001 ) and the sloan digital sky survey ( sdss ; york et  al . the ten - fold increase in survey size achieved by these projects means that precision measurements of higher order statistics are now be possible across a range of scales ( matarrese , verde & heavens 1997 ; colombi , szapudi & szalay 1998 ; szapudi , colombi & bernardeau 1999 ; scoccimarro , sefusatti & zaldarriaga 2004 ; sefusatti & scoccimarro 2005 ) . the higher order clustering measurements that are possible with these surveys have the potential to tighten the accepted values of basic cosmological parameters and to constrain the physics of galaxy formation that govern how galaxies are clustered . there have have been several analyses of the distribution of counts - in - cells using the final 2dfgrs catalogue . baugh  ( 2004 ) demonstrated that the higher order correlation functions display a hierarchical scaling , @xmath10 , where @xmath11 is the @xmath12-point , volume averaged correlation function ; this behaviour is expected if gravity plays a dominant role in shaping the distribution of galaxies . croton  ( 2004b ) found that the scaling of the hierarchical co - efficients show a weak ( if any ) dependence on galaxy luminosity . in the case of the three point volume averaged correlation function , both authors found that the skewness , @xmath13 . this value was found to be independent of cell size , though both baugh  and croton  noted that two large superstructures in the 2dfgrs volume broke this scale invariance in catalogues characterised by  galaxies . the result for the skewness of galaxies , @xmath14 , is at odds with the expectation for a  cosmology , in which @xmath15 . we note that conway  ( 2005 ) and wild  ( 2005 ) have also looked at the constraints that the distribution of counts - in - cells in the 2dfgrs provide on galaxy bias . all results from the 2dfgrs are in line with most previous measurements of the skewness and 3-point statistics , which are generally lower than the   predictions ( for a review , see  8 in bernardeau  2002 ) . this posses a puzzle , because the corresponding measurements for the variance and the 2-point function seem to follow the unbiased   predictions closely on large scales . in this paper , we present the first general results for the three - point correlation function measured from the final 2dfgrs catalogue . preliminary measurements of three - point statistics were made using early releases of the 2dfgrs and sdss datasets by verde et al . ( 2002 ) , jing & brner ( 2004 ) , wang et al . ( 2004 ) and kayo et  al . pan & szapudi ( 2005 ) measured the monopole moment of the three point function in the completed 2dfgrs . our analysis has the advantage over that of pan & szapudi in that it includes information about the shapes of the triangles of galaxies . a further improvement over previous approaches is a proper treatment of the correlation between data points . we follow the methodology introduced by gaztaaga & scoccimarro ( 2005 , hereafter gs05 ) to obtain constraints on bias parameters from measurements of the reduced three - point correlation function . this paper is organized as follows . in section  [ sec:3pt ] , we review some basic definitions involving the three - point function , as well as the methodology used for its estimation . in section  [ sec:2dfdata ] , we present the 2dfgrs catalogues and the associated mocks . our results are presented in section  [ sec : q3 ] . this is quite a long section that is divided into many subsections ; a detailed route map is provided at the start of this section . our results are compared with previous analyses of the 2dfgrs in section  5 . finally , our conclusions are presented in section  6 .","summary":"we present new results for the 3-point correlation function , , measured as a function of scale , luminosity and colour from the final version of the two - degree field galaxy redshift survey ( 2dfgrs ) . galaxies : statistics , cosmology : theory , large - scale structure .","abstract":"we present new results for the 3-point correlation function , , measured as a function of scale , luminosity and colour from the final version of the two - degree field galaxy redshift survey ( 2dfgrs ) . the reduced three point correlation function , , is estimated for different triangle shapes and sizes , employing a full covariance analysis . the form of is consistent with the expectations for the-cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on gaussian primordial fluctuations . however , we find a clear offset in amplitude between for galaxies and the predictions for the dark matter . we are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- level . on weakly non - linear scales , we can interpret our results in terms of galaxy bias parameters . we find a linear bias term that is consistent with unity , and a quadratic bias . this is the first significant detection of a non - zero quadratic bias , indicating a small but important non - gravitational contribution to the three point function . our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dfgrs galaxies to constrain the amplitude of matter fluctuations . we find that the _ rms _ linear theory variance in spheres of radiusmpc is , providing an independent confirmation of values derived from other techniques . on non - linear scales , where , we find that has a strong dependence on scale , colour and luminosity .    galaxies : statistics , cosmology : theory , large - scale structure ."}
{"article_id":"astro-ph0506249","section_id":"i","document":"in this section , we first give some basic definitions (  2.1 ) , before discussing the expected form of the three point correlation function (  2.2 ) . we then explain how our results can be related to the predictions for the three point function of dark matter (  2.3 ) . for a comprehensive discussion of this material , we refer the reader to the review by bernardeau et  al . the method for estimating the three point function for the 2dfgrs is set out in  [ ssec : est ] . finally , in   [ ssec : svd ] , we give an outline of how our measurement of the three point correlation function can be used to place constraints on models of bias ( for a complete discussion see gs05 ) . gs05 discuss the merits of various conventions for defining triangle shapes and scales . we adopt their preferred scheme in which a triangle is defined by the ratio of the lengths of two of the sides of the triangle , @xmath16 and the angle between them , @xmath17 : ( ) = r_12 . r_23 . the angle @xmath17 can vary between @xmath18 degrees ; for @xmath19 , the third side of the triangle is given by @xmath20 and for @xmath21 degrees , @xmath22 ( fig . [ fig:3pt ] ) . -5.5 cm      the connected two and three point correlation functions are defined as : ( r_12 ) & = & < ( r_1 ) ( r_2 ) > + ( r_12,r_23,r_13 ) & = & < ( r_1 ) ( r_2 ) ( r_3 ) > where @xmath23 is the local density fluctuation around the mean @xmath24 and the expectation value is taken over different realizations of the model or physical process . in practice , the expectation value is constructed by averaging over different spatial locations in the universe , which are assumed to form a fair sample ( peebles 1980 ) . the two and three point correlation functions change rapidly in amplitude as a function of separation . in order to study the relationship between the correlation functions in more detail , it is useful to define the reduced three point function , @xmath2 , ( groth & peebles 1977 ) : @xmath25 here we have introduced a ` hierarchical ' form for the three point function , @xmath26 . this quantity is built up from the products of two - point functions generated from cyclic permutations of the pair separations which make up the sides of the triangle . when @xmath2 is constant the dependence of the three point correlation function on triangle shape and scale is fully accounted for by the corresponding changes in @xmath26 ; in this case @xmath2 is said to have no configuration dependence . previously , @xmath2 was thought to be approximately constant as a function of triangle size or shape ( ie see groth & peebles 1977 ) , a phenomenon that is usually referred to as hierarchical scaling @xcite . however , gs05 showed that with sufficiently accurate theoretical predictions or for carefully constructed measurements , @xmath2 is not in fact constant in _ any _ clustering regime . nevertheless , the variation in @xmath2 with scale is small when compared to the corresponding changes in @xmath27 or @xmath26 . on small scales ( @xmath28 ) , and for galaxies in redshift space ( i.e. as measured by galaxy redshift surveys ) , gs05 showed that @xmath29 displays a characteristic u - shape anisotropy moving from collapsed or elongated ( @xmath30 ) to more open ( @xmath31 ) triangles . this effect is driven by the velocity dispersion of galaxies inside virialized structures . gs05 demonstrated that this u - shape is universal , being only very weakly dependent on scale , the primordial spectral index , or the values of the cosmological parameters . gs05 further demonstrated that this feature should be detectable in current galaxy surveys , even if the measurements are affected by shot - noise or if galaxies are biased tracers of the mass . on larger scales , the impact of velocity dispersion on the form of @xmath2 is reduced , with the consequence that the u - shape tends towards more of a v - shape and approaches the ( real space ) perturbation theory prediction ( see fig .  2 in gs05 ) . in order to interpret our measurements of @xmath2 for galaxies , we will compare them with theoretical predictions for dark matter in a @xmath3cdm universe . we first explain the form expected for the three point function of dark matter (  2.3.1 ) , before introducing a notation to quantify the differences found between galaxy and dark matter @xmath2 measurements (  2.3.2 ) . we shall denote the value of @xmath2 for the dark matter by @xmath32 . the theoretical predictions for @xmath33 are relatively insensitive to the precise values of the cosmological parameters , but have a strong dependence on the local spectral index , @xmath34 , of the linear perturbation theory power spectrum , @xmath35 , where @xmath36 ( eg . see fig .  9 and fig . 10 in bernardeau et  al . this is also the case in redshift space ( see fig .  4 of gs05 ) , but where the dependence is however weaker . on the scales of interest to the present work , a change in the local spectral index of @xmath37 translates roughly to a change in the mean amplitude of @xmath33 by @xmath38 ( see juszkiewicz , bouchet & colombi 1993 ) . as an illustration , the difference in the shape of the power spectrum between cdm models with density parameters of @xmath39 and @xmath40 is approximately @xmath41 on the scales of interest here , and so the change in @xmath33 between these models is small , @xmath42 ( in good agreement with fig .  4 of gs05 ) . the relative insensitivity of @xmath33 to changes in the cdm power spectrum is important as it strengthens any conclusions we reach about differences between the value of @xmath2 measured for galaxies and the predictions for the dark matter . the current levels of uncertainty on the matter density parameter , @xmath43 and the primordial spectral index @xmath44 are around the 10% level or better , and so the predicted value of @xmath33 is tightly constrained ( e.g. percival et  al . 2002 ; tegmark et  al . 2004 ; sanchez et  al . 2005 , in prep . ) . it is also possible to use an empirical approach to estimate @xmath45 , without appealing directly to the @xmath3cdm model . if we assume that the two - point function of galaxy clustering has the same shape as that of the underlying mass , then the measured correlation function or power spectrum of galaxies can be used to infer the spectral index of the dark matter . the two - point correlation function and the power spectrum of galaxy clustering have both been measured for the 2dfgrs on large scales ( percival et  al . 2001 ; hawkins et  al . 2003 ; cole et  al . it turns out that the shapes of these clustering statistics are compatible with the predictions of the @xmath3cdm model . the uncertainties in @xmath34 are small ( @xmath46 ) compared to the sampling errors in the measurements of @xmath2 for the 2dfgrs ( gs05 ) . we will therefore assume the concordance @xmath3cdm model , specified by @xmath47 , @xmath48 and @xmath49 , to generate predictions for @xmath33 , and neglect the impact of any uncertainty in these parameters . the @xmath2 value measured for galaxies may be different from the theoretical predictions for the dark matter , @xmath33 . we adopt a particularly simple scheme to quantify any such differences : q_3  ( q_3^dm+ c ) . [ eq : q3 g ] two numbers specify the difference between the measured and predicted @xmath2 : a shift or offset , @xmath50 , and a scaling , @xmath51 . the simple ansatz given in eq . [ eq : q3 g ] is general and can , in principle , be applied on any scale . however , the interpretation of the numbers @xmath51 and @xmath50 does depend upon the scale under consideration . furthermore , we should caution that this model may not necessarily always provide a good description of the transition from the clustering of the dark matter to galaxies . the form we have chosen is motivated by perturbation theory , which applies on scales for which the correlations are small , i.e. @xmath52 . fry & gaztaaga ( 1993 ) modelled fluctuations in the density of galaxies , @xmath53 , as a local , non - linear expansion of fluctuations in the mass distribution , @xmath54 : _ g = f [ ] _ k  b_k  ^k . [ eq : bk ] this formalism can be used to derive a relation between the three point function of galaxies and mass ( see fry & gaztaaga 1993 ; frieman & gaztaaga 1994 ) . on the weakly non - linear scales for which this transformation is a reasonable approximation , @xmath55 and @xmath56 : q_3  ( q_3^dm+ c_2 ) . [ eq : q3gbk ] in this case , the shift by @xmath50 can be interpreted as a non - gravitational contribution to @xmath57 and @xmath51 is a simple linear bias scaling . these effects can become degenerate if @xmath2 is approximately constant or when the measurement errors become large . nevertheless , it is possible , in principle , to compare the shape of @xmath2 measured for galaxies to that predicted for the dark matter , and so constrain @xmath51 and @xmath50 separately . norberg et  al . ( 2005 ; paper i , in prep . ) use the two point correlation function to obtain a working definition of the scale marking the approximate boundary between the non - linear and weakly non - linear regimes ; they propose that weakly non - linear scales ( @xmath58 ) correspond to pair separations of @xmath59 , whereas the non - linear regime ( @xmath60 ) is reached when @xmath61 .    from its definition in eq . [ fourtheq ] , @xmath2 is independent of the amplitude of fluctuations on large scales . we can therefore use the value of @xmath51 to constrain the amplitude of fluctuations in the dark matter . in this approach , we take the two - point correlation function measured for galaxies and divide this by @xmath62 to obtain an empherical two - point function estimate of the dark matter . then , after measuring the _ actual _ shape of the two - point function of the dark matter distribution from simulations , we can constrain the _ rms _ linear variance in spheres of radius @xmath63mpc , @xmath64 by equating our empirical dark matter estimate to the actual value . this method for constraining @xmath64 relies upon several approximations and assumptions that we have tested successfully using n - body simulations ( see norberg  2005 , paper i , in prep , for a full description of the method ) . similar approaches have already been attempted using the skewness of the distribution of galaxy counts - in - cells , @xmath65 ( fry & gaztaaga 1993 ; gaztaaga 1994 ; gaztaaga & frieman 1994 ) , the bispectrum ( eg frieman & gaztaaga 1994 ; fry 1994 ; scoccimarro 1998 ; verde et  al . 2002 ) and the angular 3-point function ( frieman & gaztaaga 1999 ) . to estimate the three point correlation function efficiently for the 2dfgrs , we use the fast grid based algorithm introduced by barriga & gaztaaga ( 2002 ) . gs05 presented further tests of this algorithm using a wide range of numerical simulations and mock catalogues . these authors demonstrated that special attention should be paid to the grid dimension employed in order to obtain robust estimates of the three point function in redshift space . for practical reasons , we use a somewhat lower than ideal pixel resolution in the estimation of the three point function from the 2dfgrs . this results in some smoothing of the u - shape in @xmath29 for collapsed configurations ( compare fig .  5 of gs05 with our fig .  5 ) . as we use the same pixelization in the analysis of the mocks and dark matter theory , this loss of resolution does not affect our conclusions , although it could result in slightly less than optimal constraints on @xmath51 and @xmath50 . the final 2dfgrs catalogue contains some incompleteness which is quantified by the spectroscopic completeness mask ( norberg et al . the spectroscopic completeness of the final 2dfgrs is much more uniform than that of the 100k release or the samples used in earlier clustering analyses by the 2dfgrs team ( e.g. verde et al . 2002 ) , as shown by fig . 3 of cole et al . we reject pixels on the sky for which the spectroscopic completeness is less than @xmath66 . we account for the remaining incompleteness by applying a weight to the galaxy cell density . further details about the 2dfgrs catalogue are given in section  3.1 . the values of @xmath2 measured for different opening angles are correlated . this needs to be taken into account when using measurements of @xmath2 to place constraints on model parameters , such as the values of @xmath51 and @xmath50 defined by eq . [ eq : q3 g ] . gs05 introduced an eigenmode approach to parameter fitting with @xmath2 , and used this to demonstrate the level of the constraints on @xmath51 and @xmath50 that could be expected from the 2dfgrs . gs05 estimated the covariance matrix for @xmath29 using the mock 2dfgrs catalogues that we describe in section  [ mock ] . they then obtained the inverse of the covariance matrix using the singular value decomposition method . in this approach , eigenmodes that fall below some specified signal - to - noise ( s / n ) threshold are discarded . the likelihood contours in the @xmath67 plane are specified by @xmath68 computed using the eigenvectors above the s / n threshold . the s / n values that we estimate are not quite optimal , because we use a finite number of mock catalogues . our errors are therefore conservative estimates . the s / n values indicate the significance of the measurement of @xmath2 ( i.e. the number of standard deviations that the signal is above the noise ) . however , the s / n ratio does not translate directly into the size of the likelihood contours in the @xmath67 plane , because the degeneracy between these parameters also depends on how far the measured @xmath2 deviates from a constant as a function of angle . even in the case of an infinite s / n , @xmath51 and @xmath50 will be degenerate if @xmath2 is independent of angle ( i.e. see eq . [ eq : q3 g ] ) .","summary":"the reduced three point correlation function , , is estimated for different triangle shapes and sizes , employing a full covariance analysis . the form of is consistent with the expectations for the-cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on gaussian primordial fluctuations . we are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- level . on weakly non - linear scales , this is the first significant detection of a non - zero quadratic bias , indicating a small but important non - gravitational contribution to the three point function .","abstract":"we present new results for the 3-point correlation function , , measured as a function of scale , luminosity and colour from the final version of the two - degree field galaxy redshift survey ( 2dfgrs ) . the reduced three point correlation function , , is estimated for different triangle shapes and sizes , employing a full covariance analysis . the form of is consistent with the expectations for the-cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on gaussian primordial fluctuations . however , we find a clear offset in amplitude between for galaxies and the predictions for the dark matter . we are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- level . on weakly non - linear scales , we can interpret our results in terms of galaxy bias parameters . we find a linear bias term that is consistent with unity , and a quadratic bias . this is the first significant detection of a non - zero quadratic bias , indicating a small but important non - gravitational contribution to the three point function . our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dfgrs galaxies to constrain the amplitude of matter fluctuations . we find that the _ rms _ linear theory variance in spheres of radiusmpc is , providing an independent confirmation of values derived from other techniques . on non - linear scales , where , we find that has a strong dependence on scale , colour and luminosity .    galaxies : statistics , cosmology : theory , large - scale structure ."}
{"article_id":"astro-ph0506249","section_id":"r","document":"as mentioned in the introduction , baugh et  al . ( 2004 ) and croton et  al . ( 2004 ) found the puzzling result that @xmath105 for 2dfgrs galaxies in contrast to the theoretical value of @xmath106 expected in on large ( weakly non - linear ) scales . this apparent inconsistencey can now be resolved using the bias parameters we have measured here , i.e. @xmath107 and @xmath108 gives @xmath109 , in good agreement with the above mesurements on large scales . in their fig . 10 , croton et  al . ( 2004 ) found a weak dependence of @xmath65 on galaxy luminosity , with a slope @xmath110 detected with @xmath111-@xmath4 confidence level . we note that this is in very good agreement with our nearly @xmath112-@xmath4 detection of @xmath113 , as quoted in table  3 . since @xmath114 , we would expect @xmath115 , as found in croton et  al . ( 2004 ) , but with a higher significance . measurements of three - point statistics from early 2dfgrs data releases were made by verde et  al . ( 2002 ) and jing & brner ( 2004 ) . these authors used compilations comprising 127k and 100k galaxies respectively . here , as remarked earlier , we use the final dataset which contains double the number of galaxies and double the volume that were available for analysis in these preliminary studies . recently , pan & szapudi ( 2005 ) have also analysed the final 2dfgrs dataset , estimating the monopole moment of the three - point function , averaging over the shape dependence of triangles . in this section , we compare our results with those obtained by these authors and also with the measurement of the projected @xmath2 for the apm survey , the parent catalogue of the 2dfgrs , made by frieman & gaztaaga ( 1999 ) . verde et  al . ( 2002 ) found , using a three - point function analysis in fourier space , that 2dfgrs galaxies are essentially unbiased tracers of the mass , recovering a linear bias factor consistent with unity , @xmath116 , and a second order bias that is effectively zero , @xmath117 . we note that lahav et  al . ( 2002 ) also reached a similar conclusion applying a different approach to the same 2dfgrs dataset , arguing that @xmath118 . there is good agreement between our best value for @xmath89 and that obtained by verde et  al , which is encouraging in view of the possible reasons for discrepancies between the results of the two studies set out below . however , our results for the quadratic bias are quite different from those of verde et  al . our optimum measurement gives a 3-@xmath4 detection of a non - zero value for the quadratic bias , whereas verde et  al . found a value consistent with zero . the discrepancy between our results and those of verde et  al . corresponds to @xmath119 for 2 degrees of freedom . this implies a 9-@xmath4 discrepancy ( recalling that the errorboxes are not square , but elongated ) . the discrepancy in the claimed values of @xmath120 is only 3 - 4 -@xmath4 if we take the nominal errors on the measurement of @xmath120 by verde et  al . and assume square errorboxes . what are the reasons behind this disagreement ? we have identified some aspects in which our analysis differs from that of verde et  al . , which will contribute to the discrepancy at different levels , over and above the fact that we used different versions of the 2dfgrs data . first , we have considered the full 2dfgrs in configuration space , thus avoiding the need to compensate for the impact of the complicated 2dfgrs angular mask on measurements carried out in fourier space . verde et  al . do not correct for the convolution of the underlying bispectrum with the angular survey window function , arguing that , for the range of wavenumbers they consider , this effect is unimportant . this conclusion is based upon tests carried out for the _ power spectrum _ by percival et  al . the impact of the window function on the bispectrum could be more extensive than in the case of the power spectrum , introducing anisotropies into the recovered bispectrum , and has not been tested explicitly . second , the range of galaxy luminosities considered is different in the two studies . we have analysed volume limited samples drawn from the 2dfgrs , whereas verde et  al . used the flux limited survey ( however our best measurement comes from galaxies with luminosities between 1.3 and 2.5  , and their sample corresponds to @xmath121  ) . third , the scales used to constrain the parameters of the bias model are also different . we use triangles that probe pair separations from 9 to @xmath122 ; verde et  al . consider 13 to @xmath123 , although most of their signal comes from the smaller scales , as shown by their fig .  4 . fourth , verde et  al . neglect the covariance between measurements of the bispectrum at different wavenumbers , which is a poor approximation even in fourier space , as shown by scoccimarro et  al . ( 2001a ) and feldman et al ( 2001 ) . neglecting the covariance will artificially suppress the errors on @xmath89 and @xmath124 by a considerable factor , corresponding roughly to the actual number of bins used divided by the number of dominant eigenmodes of the reduced three - point function , which in this case could be up to a factor of 4 . this could to some extent explain why our relative errors are larger than those quoted by verde et  al . , in spite of the more homogeneous 2dfgrs dataset used in our analysis . verde et  al use mock catalogues to estimate the errors on the recovered values of @xmath89 and @xmath124 . the true , underlying value of @xmath124 for the mocks is not known , so it is not possible to assess whether or not their method introduces any systematic biases in the recovered value of @xmath124 . a bias on @xmath124 introduced by the convolution with the angular mask and the covariance in the bispectrum measurements could affect the estimated values of both the mean and the errors . in fact , the mocks used by verde et al . are very similar to the ones used here as they were produced using the same prescription for galaxy biasing . as shown by the dashed lines in our figs .  2 ,  3 and 5 there is a systematic shift of @xmath2 in the mocks with respect to the dark matter simulations , indicating that @xmath124 is in fact non zero ( and negative ) in the mocks , in contrast to fig.2 of verde et  al . our results are in somewhat better agreement with those of jing & brner ( 2004 ) and wang et al . ( 2004 ) , who analysed the 2dfgrs 100k release ( colless et  al . 2001 ) . they found that @xmath2 measured for the 2dfgrs is smaller than the @xmath3cdm predictions , particularly for galaxies brighter than . this agrees with our result ( compare the measurements for galaxies shown by symbols in the top rows of figs .  [ fig : q3_210_wnl ] and  [ fig : q3_l_wnl ] with the dark matter predictions plotted using thick lines ) and is also at odds with the verde  result . our results for equilateral configurations in fig.[fig : q3_l_colour ] are also in good agreement with fig .  10 in wang et al . however , the comparison with these results is not straightforward for a number of reasons : ( i ) the authors used less than half the data that we have analysed . ( ii ) they used a different parametrization and binning for their measurements of @xmath2 . ( iii ) they neglected covariance between bins and used approximate bootstrap errors . jing & brner interpreted the lower values of @xmath2 that they found as a consequence of a larger linear bias , @xmath125 , in contrast to our conclusion that most of the bias comes from the quadratic term @xmath108 , with a linear bias consistent with unity . this difference has a dramatic consequence for the implied value of @xmath126 . for galaxies fainter than , jing & brner get unbiased results , which disagrees with our findings . this , however , could be a result of the smaller volume probed by jing & brner , which gives larger errors on their measurement . jing & brner also seem to find less configuration dependence for @xmath2 , i.e. as function of the triangle shape specified by @xmath17 . as pointed out in gs05 , this could partly be due to the use of too large a bin in the @xmath17 angle that parameterises triangular shape in addition to the smaller volume used . most recently , as this paper was about to be submitted , pan & szapudi ( 2005 ) presented new results on the monopole moment of the three - point function measured from the full 2dfgrs . they find @xmath127 and @xmath128 . both the technique and assumptions employed by pan & szapudi are conceptually very different from ours . the monopole contribution to the normalized three point function merely yields a constant value that is independent of triangle opening angle . it is approximately equivalent to the first eigenmode in our singular value decomposition of the covariance matrix of @xmath2 , and therefore contains much less information than we use to place constraints on the bias parameters . as a consequence , the monopole alone _ can not _ be used to separate @xmath89 from @xmath124 ; only the higher multipoles of @xmath2 can break this degeneracy . pan & szapudi instead use a simultaneous fit to the amplitudes of the two ( @xmath27 ) and three - point ( @xmath0 ) functions ( as a function of scale ) to place separate constraints on the values of @xmath89 and @xmath124 ; recall that our analysis only requires a fit to the ratio @xmath129 . both the modelling and the systematics involved in the fit used by pan & szapudi are therefore quite different from ours . our analysis is less sensitive to possible systematics in the amplitude of @xmath0 . in particular , we do not need to model the impact of redshift distortions on the amplitudes of the 2 and 3-point functions as pan & szapudi must . another important difference is the implicit assumption used by pan & szapudi that the biasing parameters , @xmath130 , are constant over the whole range of scales considered , i.e. from @xmath131 . in our case , we allow @xmath130 to change for each combination of fixed scales @xmath132 and @xmath133 . given these differences , there is surprisingly good agreement in the values obtained for @xmath89 by the two methods . however , their @xmath124 value is significantly different . this is not unexpected given the systematic uncertainties in modelling redshift distortions through the @xmath134 term in eqn . [ 6 ] of their paper . as shown in the right - hand panel of our fig . [ fig : q3_scale ] and in table  [ tab : q3_wnl ] , we find a weak trend for the bias parameters to increase as the triangle scale is reduced . this could also help to explain the slightly larger biasing parameters they find . perhaps more puzzling is their fig .  7 , which shows how @xmath89 increases for the brightest galaxies , in contrast to our fig .  7 ( which only applies to the smallest scales considered by pan & szapudi ) . our findings are compatible with the values of the projected @xmath2 measured in the apm survey , which is the parent catalogue of the 2dfgrs . frieman & gaztaaga ( 1999 ) also found values of @xmath2 that lay below the @xmath3cdm predictions . however , they did not perform a proper s / n analysis with the covariance matrix to separate @xmath89 from @xmath124 . measured in fourier space from the iras point source redshift catalogue ( pscz , saunders et  al . 2000 ) by scoccimarro  ( 2001a ) and feldman  ( 2001 ) . ] our results are also in qualitative agreement with the values of the angular skewness , @xmath135 , measured in the apm galaxy survey ( gaztaaga 1994 ) . the mean over large angular scales ( corresponding to @xmath136 ) was estimated to be @xmath137 , with an error ( dominated by sampling covariance ) of the order @xmath138 . the theoretical predictions for the projected moments using perturbation theory ( bernardeau 1995 ) and dark matter simulations ( gaztaaga & bernardeau 1998 ) yield a mean value @xmath139 over the same scales .. this was first noted by bernardeau ( 1995 ) and later confirmed with simulations by gaztaaga & bernardeau ( 1998 ) . see also comments relating to figs . 47 and 54 in bernardeau et  al . ( 2002 ) for further details . ] the skewness measured from the apm survey is thus also below the the  prediction . this agrees well with our estimates of the bias parameters @xmath107 and @xmath108 , which give @xmath140 , in excellent agreement with the observed apm values . note that the apm results correspond to configuration space , in contrast to our results which are in redshift space . thus , our simple quadratic bias model ( in redshift space ) can account simultaneously for observations of real - space ( projected ) and redshift - space results for 3-point statistics ( both skewness and 3-point function ) . our new result solves the long standing observational puzzle regarding how the measured and predicted values of @xmath65 and @xmath2 can be reconciled .","summary":"we find a linear bias term that is consistent with unity , and a quadratic bias .","abstract":"we present new results for the 3-point correlation function , , measured as a function of scale , luminosity and colour from the final version of the two - degree field galaxy redshift survey ( 2dfgrs ) . the reduced three point correlation function , , is estimated for different triangle shapes and sizes , employing a full covariance analysis . the form of is consistent with the expectations for the-cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on gaussian primordial fluctuations . however , we find a clear offset in amplitude between for galaxies and the predictions for the dark matter . we are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- level . on weakly non - linear scales , we can interpret our results in terms of galaxy bias parameters . we find a linear bias term that is consistent with unity , and a quadratic bias . this is the first significant detection of a non - zero quadratic bias , indicating a small but important non - gravitational contribution to the three point function . our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dfgrs galaxies to constrain the amplitude of matter fluctuations . we find that the _ rms _ linear theory variance in spheres of radiusmpc is , providing an independent confirmation of values derived from other techniques . on non - linear scales , where , we find that has a strong dependence on scale , colour and luminosity .    galaxies : statistics , cosmology : theory , large - scale structure ."}
{"article_id":"astro-ph0506249","section_id":"c","document":"we have measured the reduced 3-point function @xmath141 ( as defined in eq .  [ fiftheq ] ) in the final 2dfgrs catalogue , using triangles of different scales and opening angles . we have utilized a range of volume limited samples in our analysis , which allows us to look for clustering trends as a function of galaxy luminosity . the inclusion of @xmath142-band photometry in the final 2dfgrs data release also allows us to look for a dependence of the three point function on galaxy colour . another novel aspect of our analysis is that we employ an eigenmode decomposition to deal with correlations between data - points and to assess the signal - to - noise of our measurements ; our results typically have a signal - to - noise @xmath143 . there are two primary motivations for measuring the reduced three point function . the first is to test the gravitational instability paradigm for the formation of large - scale structure in the universe . there are clear predictions for the form of the three - point function in the case of an initially gaussian distribution of density fluctuations that have evolved under gravity ( see bernardeau et  al . the second motivation is to provide new constraints on models of galaxy formation , by establishing how the three - point function of galaxies differs from that of the underlying dark matter . it turns out that the predictions for the dark matter are insensitive to the amplitude of density fluctuations and to the detailed shape of the power spectrum . we have divided our analysis into two clustering regimes : weakly non - linear clustering ( i.e. @xmath144mpc or @xmath145 ) and non - linear clustering ( @xmath146mpc or @xmath147 ) . on weakly non - linear scales , there is a striking similarity between the _ shape _ of @xmath2 measured for galaxies and the predictions for the dark matter . this supports the idea that the basic phenomenon behind the clustering pattern of galaxies is gravitational instability , which confirms our previous conclusions reached from the analysis of the distribution of counts - in - cells for the 2dfgrs ( baugh et  al . 2004 ; croton et  al . 2004b ) . there are , however , significant differences , between @xmath2 measured for galaxies and the expectations for a  universe . we have modelled this discrepancy in terms of a shift and a scaling applied to the dark matter predictions . for scales on which the fluctuations are weakly nonlinear , the scaling can be identified with the linear bias , @xmath89 and the offset with the quadratic bias , @xmath148 . our best measurement of these bias parameters gives a linear bias consistent with unity , but a significant detection of a non - zero quadratic bias , @xmath149 . this is the first time that the signature of a quadratic bias has been seen so convincingly ; our measurements are 9-@xmath4 away from the case in which galaxies faithfully trace the mass ( @xmath150 and @xmath151 ) . our results disagree with some of the previous analyses of the three point function in the 2dfgrs ; a detailed discussion of the possible reasons for this is given in section 5 . we note that feldman et  al . ( 2001 ) also found a negative quadratic bias term when analysing the three point function of galaxies in the iras point source catalogue redshift survey , albeit at a less significant level than our detection . the discrepancy between @xmath2 for galaxies and the dark matter increases as the scale of the triangles is reduced ( while remaining in the weakly non - linear regime ) , which translates into a slight increase in the best - fitting values of the bias parameters ( see table  [ tab : q3_wnl ] ) . we find no significance evidence for luminosity segregation on these weakly non - linear scales .    on smaller scales we are able to detect a significant dependence of @xmath2 on scale , color and luminosity . these trends appear at first sight to be at odds with the preliminary results obtained by kayo et al . ( 2004 ) using the sdss , although the errors on the measurements presented by these authors are much larger than ours . in all cases , the measurements for the various samples of galaxies are clearly below the predictions for the dark matter . our detailed measurements , presented in fig.6 - 8 and table 3 , should provide important new constraints on models of galaxy formation ( see scoccimarro  2001b ; wang et al . 2004 ) . our strong detection of a quadratic bias offers a new explanation of the long standing puzzle of why redshift surveys have tended to measure a different skewness ( @xmath152 ; see croton et  al . 2004b for the 2dfgrs and table 19 of bernardeau et  al . 2002 for a summary of other observational results ) from that predicted for the  cosmology ( @xmath153 ) . if we take the non - linear bias relation derived by fry & gaztaaga ( 1993 ) , @xmath154 and insert our best - fitting values for the bias parameters ( @xmath155 and @xmath156 ) , then we obtain @xmath157 , just as required by the observations . the value of @xmath2 is independent of the overall amplitude of fluctuations . this means that our measurement of the linear bias , @xmath89 , is fully independent of the normalization of the fluctuations in the dark matter , as specified by @xmath64 . furthermore , the predictions for @xmath2 for dark matter are relatively insensitive to the shape of the power spectrum , making this estimate of the bias robust to minor changes in the parameters of the  model . we can therefore combine our estimate of @xmath89 with the amplitude of fluctuations measured from the galaxy distribution , @xmath158 , to derive an estimate of the amplitude of fluctuations in the dark matter , @xmath64 . cole et  al . ( 2005 ) measured the power spectrum of galaxy clustering in the 2dfgrs and found @xmath159 . the equation relating fluctuations in the galaxies to those in the dark matter involves two other terms : _ 8^g = b_1   d(z )  k ( )  _ 8  . here @xmath160 is the growth factor at the mean depth of the survey ( @xmath161 ) relative to the growth factor at @xmath162 and @xmath163 is the linear kaiser ( 1987 ) redshift space distortion factor : @xmath164 for @xmath165 . both factors depend on the cosmological density parameters for matter and vacuum energy , which we have set to their concordance model values ( @xmath166 , @xmath48 and @xmath49 ) . this allows us to estimate @xmath126 : _ 8 0.88^+0.12_-0.10  . here we have assumed that the errors are dominated by the errors in @xmath89 . this explains the good agreement found between the large scale variance in 2dfgrs galaxies and the variance of the dark matter for @xmath167 , as shown in fig .  2 of baugh  ( 2004 ) . a more detailed presentation of our result for @xmath126 will be deferred to a later paper .    * note added on submission : * on the day before our paper was submitted , hikage et  al . astro - ph/0506194 ) posted a paper on the three - point function of sdss galaxies , in which they perform a fourier phase analysis . their main result is that @xmath168 if @xmath169 , in apparent contradiction with our principal finding . however , hikage et  al . consider scales in excess of @xmath170mpc and restrict their attention to triangles with large opening angles . their analysis is therefore similar to the special case we present in fig .  9 for elongated and equilateral triangles . as we explained in  4.3 , in this case , due to the reduced number of triangles considered , the errors on the bias parameters are large . as shown in the upper right panel of our fig .  2 , the error bars become quite large for @xmath171 on large scales . furthermore , there is actually no reason to expect the bias parameters extracted by hikage et  al . to agree closely with ours , as sdss galaxies are red","summary":"however , we find a clear offset in amplitude between for galaxies and the predictions for the dark matter . our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dfgrs galaxies to constrain the amplitude of matter fluctuations . we find that the _ rms _ linear theory variance in spheres of radiusmpc is , providing an independent confirmation of values derived from other techniques . on non - linear scales , where , we find that has a strong dependence on scale , colour and luminosity .   ","abstract":"we present new results for the 3-point correlation function , , measured as a function of scale , luminosity and colour from the final version of the two - degree field galaxy redshift survey ( 2dfgrs ) . the reduced three point correlation function , , is estimated for different triangle shapes and sizes , employing a full covariance analysis . the form of is consistent with the expectations for the-cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on gaussian primordial fluctuations . however , we find a clear offset in amplitude between for galaxies and the predictions for the dark matter . we are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- level . on weakly non - linear scales , we can interpret our results in terms of galaxy bias parameters . we find a linear bias term that is consistent with unity , and a quadratic bias . this is the first significant detection of a non - zero quadratic bias , indicating a small but important non - gravitational contribution to the three point function . our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dfgrs galaxies to constrain the amplitude of matter fluctuations . we find that the _ rms _ linear theory variance in spheres of radiusmpc is , providing an independent confirmation of values derived from other techniques . on non - linear scales , where , we find that has a strong dependence on scale , colour and luminosity .    galaxies : statistics , cosmology : theory , large - scale structure ."}
{"article_id":"hep-ph0506226","section_id":"i","document":"many exclusive @xmath0-decay amplitudes in the framework of scet contain @xmath0-meson distribution amplitudes  @xcite . the amplitude of the decay @xmath1 at large photon energies is given , up to power corrections , by a convolution of a hard part ( perturbatively calculable ) and the @xmath0-meson distribution amplitude  @xcite . amplitudes of some decays , e.g. , @xmath2 at large pion energies , contain both factorizable and non - factorizable contributions  @xcite . factorizable parts of decay amplitudes contain light - cone distribution amplitudes of the initial @xmath0-meson and final hadron(s ) . they describe large - distance ( soft ) structure of these hadrons , and can not be calculated in perturbation theory . the theory of hadronic distribution amplitudes in qcd is reviewed in  @xcite . quark  antiquark distribution amplitudes of @xmath0-meson in hqet were introduced and investigated in  @xcite . they are defined as fourier transforms of matrix elements of some gauge - invariant bilocal operators between @xmath0-meson and vacuum . renormalization of these operators was calculated in one - loop approximation . however , an unusual term @xmath3 in the one - loop renormalization constants was erroneously omitted in  @xcite . the correct evolution equation for the leading - twist distribution amplitude was derived in  @xcite at one loop . the evolution kernel contains , in addition to terms obtained earlier  @xcite , an unusual term @xmath4 . the method of solution of the evolution equation is also discussed in  @xcite in detail . quark  antiquark  gluon distribution amplitudes of @xmath0-meson and their relations to quark  antiquark ones ( based on equations of motion ) are discussed in  @xcite . sum rules for the quark  antiquark distribution amplitudes were obtained in  @xcite . a simple model of these distribution amplitudes at a low normalization scale ( of order of hadronic scale ) was proposed . radiative corrections to the perturbative term and the quark - condensate term were later calculated  @xcite .    in these lectures , we first briefly discuss what is hqet ( sect . [ s : hqet ] ) . a much more detailed presentation can be found in the textbooks  @xcite . after a short discussion of @xmath5 ( sect  [ s : fb ] ) , quark  antiquark distribution amplitudes are introduced ( sect . [ s : qq ] ) . quark  antiquark  gluon distribution amplitudes and their relations to two - particle ones are discussed in sect . [ s : qqg ] . [ s : evol ] is the central ( and longest ) one . here renormalization of light - cone bilocal quark operators in hqet is considered in one - loop approximation . a detailed derivation of the evolution kernel is presented , based on the methods of  @xcite . finally , sum rules for the distribution amplitudes are briefly discussed in sect . [ s : sr ] .","summary":"is derived in one - loop approximation . qcd sum rules for distribution amplitudes are discussed .","abstract":"-meson light - cone distribution amplitudes are discussed in these lectures in the framework of hqet . the evolution equation for the leading - twist distribution amplitude is derived in one - loop approximation . qcd sum rules for distribution amplitudes are discussed ."}
{"article_id":"1510.04244","section_id":"i","document":"a stationary random graph is a random rooted graph whose distribution is invariant under re - rooting by a simple random walk . this notion was made explicit by benjamini and curien in @xcite motivated by several examples , including the uniform infinite planar triangulation / quadrangulation ( uipt / q ) , and previously defined notions such as unimodular random graphs . in said work they develop the basic entropy theory for stationary random graphs , analogous to the well known theory for random walks on finitely generated groups , see @xcite . in particular , they define an entropy and prove that if it is zero then the random graph almost surely satisfies the liouville property ( i.e. bounded harmonic functions are constant ) . the converse implication , that positive entropy implies the existence of non - constant bounded harmonic functions , was posed as a question , see ( * ? ? ? * remark 3.7 ) .    in this work we answer this question in the afirmative under an additional condition on the stationary random graph . the hypothesis is the following ( see lemma [ speedlemma ] ) :     ( ) +    our main result is the following ( see theorem [ entropytheorem ] ) . [ maintheorem ] an ergodic stationary random graph satisfying condition ( [ condition ] ) above , has zero entropy if and only if it satisfies the liouville property almost surely . furthermore , if such a graph has positive entropy , then almost surely it admits an infinite dimensional space of bounded harmonic functions . recent work of benjamini , paquette , and pfeffer implies that the space of bounded harmonic functions on a stationary random graph must be either infinite or one dimensional ( see @xcite ) . this yields an alternate proof of the second part of the above theorem ( using the first part ) .    from the direct implication , which was already proved in their paper , benjamini and curien proved that the uniform infinite planar quadrangulation almost surely satisfies the liouville property . with the extension given by our result above , it is possible to deduce that certain stationary random graphs admit many bounded harmonic functions . we will discuss in section [ applications ] a few such examples , like the @xmath0-markovian infinite planar triangulations , introduced recently by curien in @xcite , and the hyperbolic poisson - delaunay graph . an important difficulty in applying the above theorem is the lack of general criteria for establishing that a stationary random graph has at most exponential volume growth , even when the distribution of the degree of the root is known to be well behaved . in most cases where the growth of a stationary graph is known ( e.g. the uniform infinite planar quadrangulation , or the hyperbolic poisson - delaunay graph ) it seems to have been established by ad - hoc , and some times very intricate , arguments . thus , the authors consider the following question to be important :    given a stationary random graph such that the degree of the root is well behaved . under what conditions can one deduce that the graph has at most exponential volume growth ?    to the best of the author s knowledge there is no widely applicable answer to the above question available in the literature . we discuss two relevant partial results in section [ canopysection ] . first , we give an example , due to asaf nachmias , of a stationary random graph with super - exponential growth such that the degree of the root has finite mean , and in fact is comparable to a poisson variable . the example also has the special property that the degree of the root determines the entire graph up to rooted isomorphism . second , we prove that for unimodular graphs whose root has finite expectation , if the number of elements at distance @xmath1 from the root is asymptotically independent from the degree of the root , then the graph has at most exponential growth ( see lemma [ growthlemma ] ) . our proof of the main theorem involves derriennic s zero - two law , a sharp criterion for equivalence of the tail and invariant events of a markov chain ( see corollary [ zerotwocorollary ] ) , and a `` looping '' argument which allows us to avoid parity problems ( see figure [ figuralazos ] ) . in order to show that our results are valid for graphs with unbounded degree , we improve the inequalities between the linear drift and entropy from ( * ? ? ? * proposition 3.6 ) with essentially the same proof ( see lemma [ speedlemma ] ) . to show that positive entropy implies that the space of bounded harmonic functions is infinite dimensional , we relate the dimension of this space to the mutual information between the first @xmath2 steps of a random walk and its tail behavior ( see lemma [ informationandharmoniclemma ] ) . this occupies the first few sections of the paper . in section [ applications ] we discuss examples and applications of the main theorem to several examples , many of which were already known .","summary":"we prove that any stationary random graph satisfying a growth condition and having positive entropy almost surely admits an infinite dimensional space of bounded harmonics functions . applications to random infinite planar triangulations and delaunay graphs are given .","abstract":"we prove that any stationary random graph satisfying a growth condition and having positive entropy almost surely admits an infinite dimensional space of bounded harmonics functions . applications to random infinite planar triangulations and delaunay graphs are given ."}
{"article_id":"0908.2717","section_id":"i","document":"reaction - diffusion equations can be used to model phase separation and boundary evolutions in various physical contexts . typically behavior of boundaries or geometric evolution laws are studied with the help of such equations . often in such models one includes an extra noise term . this may happen for various reasons  the noise may be a simplified model for effect of additional degrees of freedom that are not reflected in the reaction - diffusion equation . from a numerical point of view noise may improve stability in the simulations . in some systems there is even a justification for an extra noise term from a scaling limit of microscopic particle systems . 3ex    _ 1 . setup and first main result _    1ex    the system considered here is the case of a symmetric bistable potential with two wells of equal depths . to be more precise , for a small parameter @xmath0 we are interested in the equation @xmath1 here @xmath2 is supposed to be a smooth ( at least @xmath3 ) symmetric double - well potential i.e. we assume that @xmath2 satisfies the following properties : @xmath4 a typical example is @xmath5 . the expression @xmath6 is a formal expression denoting space - time white noise . such equation can be given rigorous sense in various ways , for example in the sense of mild solutions ( @xcite ) or using dirichlet forms @xcite . we are interested in the behavior of the system in the sharp interface limit @xmath7 . the parameter @xmath8 is a scaling factor . our result will be valid for @xmath9 . 3ex    we study the behavior of the invariant measure of ( [ sace ] ) . this measure can be described quite explicitly as follows ( @xcite ) : let @xmath10 be the law of a rescaled brownian bridge on @xmath11 $ ] with boundary points @xmath12 . more precisely @xmath10 is the law of a gaussian process @xmath13)$ ] with expectations @xmath14=s \\quad \\forall s \\in [ -1,1]$ ] and covariance @xmath15 . another equivalent way to characterize @xmath10 is to say that it is a gaussian measure on @xmath16 $ ] with expectation function @xmath17 and covariance operator @xmath18 where @xmath19 denotes the one - dimensional dirichlet laplacian . even another equivalent way is to say that @xmath20 is the solution to the stochastic differential equation ( sde ) @xmath21 with some brownian motion @xmath22 conditionned on @xmath23 . then the invariant measure @xmath24 of ( [ sace ] ) is absolutely continuous with respect to @xmath10 and is given as @xmath25 here @xmath26 is the appropriate normalization constant . the first main result of this work is the following :    [ thm1 ] assume @xmath27 . then the measures @xmath28 converge weakly for @xmath7 as measures on @xmath16 $ ] towards a limit measure @xmath29 . this measure @xmath29 can be described as follows : if @xmath30 is a random function distributed according to @xmath29 , then @xmath31 can almost surely be written as @xmath32},\\ ] ] where @xmath33 is random , uniformly distributed in @xmath11 $ ] .    } $ ] .,title=\"fig:\",height=226][shif ]    note that by schilder s theorem together with an exponential tilting argument ( such as @xcite theorem iii.17 on page 34 ) , in the case where @xmath34 the measures @xmath35 concentrate exponentially fast around the unique minimizer of @xmath36 \\ , \\mathrm{ds},\\ ] ] under the appropriate boundary conditions . in particular the weak limit is a dirac measure on this minimizer . furthermore the minimizer is not a step function . 3ex    one can remark that by an application of girsanov s theorem also the measure @xmath24 can be considered as distribution of the solution of a sde which is conditioned on the right boundary values ( see @xcite chapter viii 3 and also @xcite ) . it could be possible to obtain similar results by studying this sde with help of large deviation theory ( see for example @xcite ) . we do not follow such an approach but conclude from theorem [ thm2 ] which is obtained essentially by a discretization argument . 3ex    the reader might consider it unusual to work with @xmath24 as measure on @xmath16 $ ] instead of @xmath37 $ ] or the space of cdlg functions @xmath38 $ ] . but all the estimates are given in the hilbert - space setting . also the class of _ continuous _ processes is closed under weak convergence of measures on @xmath38 $ ] . so certainly no similar result can be expected on this space . 3ex    _ 2 . feynman heuristic and second main result _ 1ex    often important intuition on a measure on path space can be gained from considering feynman s heuristic interpretation . in our context this heuristic interpretation states that @xmath39 is proportional to a measure @xmath40 where @xmath41 is a flat reference measure on path space . of course this picture is non - rigorous : such a measure @xmath41 does not exist and the quantity @xmath42 is almost surely not finite under @xmath39 . nontheless it is rigorous on the level of finite dimensional distributions , and various classical statements about brownian motion such as schilder s theorem or girsanov theorem have an interpretation in terms of this heuristic picture . the measure @xmath43 can then be interpreted as proportional to @xmath44 as one wants to observe an effect which results from the interaction of the _ potential term _ @xmath45 and the _ kinetic energy type term _ @xmath46 it seems reasonable to transform the system in a way that guarantees that these terms scale with the same power of @xmath47 . this transformation is given by stretching the random functions onto a growing interval @xmath48 $ ] . more precisely consider the operators @xmath49 \\rightarrow l^2[-\\varepsilon^{-\\gamma},\\varepsilon^{-\\gamma } ] \\qquad t^\\varepsilon \\tilde{u } ( s)= \\tilde{u } ( \\varepsilon^{\\gamma}s ) . \\end{split}\\ ] ] then consider the pushforward measures @xmath50 . these measures are again absolutely continuous with respect to gaussian measures : @xmath51 is the gaussian measure on @xmath52 $ ] with expectation function @xmath53 and covariance operator @xmath54 . the other equivalent characterizations for @xmath10 can be adapted with the right powers of @xmath47 . the measure @xmath35 is then given as @xmath55 note that the normalization constant @xmath56 is the same as above . in the feynman picture this suggests that @xmath57 is proportional to @xmath58   \\ , \\mathrm{ds } \\bigr ) \\mathrm{d}u.\\ ] ]    3ex    this motivates to study the energy functional appearing in the exponent : for functions @xmath59 defined on the whole line with boundary conditions @xmath60 consider the energy functional @xmath61 \\ , \\mathrm{ds}-c_*.\\ ] ] here @xmath62 is a constant chosen in a way to guarantee that the minimizers of @xmath63 with the right boundary conditions verify @xmath64 . this is the one - dimensional version of the well known real ginzburg - landau energy functional . there is a unique minimizer @xmath65 of @xmath63 subject to the condition @xmath66 and all the other minimizers are obtains via translation of @xmath65 . more details on the energy functional and the minimizers can be found in section [ sec2 ] . denote by @xmath67 the set of all these minimizers and by @xmath68 and @xmath69 the spaces of functions with the right boundary values . note that every random function distributed according to @xmath57 can be considered as function in @xmath70 by trivial extension with @xmath12 outside of @xmath71 $ ] . in this way @xmath57 can be interpreted as measure on @xmath70 . we can now state the second main result of this work :    [ thm2 ] assume @xmath27 . then there exist positive constants @xmath72 and @xmath73 such that for every @xmath74 one has @xmath75 in particular the measures @xmath76 concentrate around the set of minimizers exponentially fast . the crucial step in the proof is to find a lower bound on the exponential decay of the normalization constant @xmath56 . this lower bound can be found in section [ sec4 ] . 3ex    the same result also holds using the @xmath77-norm :    [ thm3 ] assume @xmath27 . then there exist positive constants @xmath78 and @xmath79 such that for every @xmath80 one has @xmath81    .,title=\"fig:\",height=226][standingwave ]    3ex    _ 3 . motivation and related works _    1ex    the allen - cahn equation without noise has been introduced in @xcite to model the dynamics of interfaces between different domains of different lattice structure in crystals and has been studied since in various contexts . in the one - dimensional case the dynamics of the deterministic equation are well - understood @xcite and can be described as follows : if one starts with arbitrary initial data , solutions will quickly tend to configurations which are locally constant close to @xmath12 possibly with many transition layers that roughly look like the instanton shapes @xmath65 introduced above . then these interfaces move extremely slowly until eventually some two transition layers meet and annihilate each other . after that the dynamics continue very slowly with less interfaces . 3ex    in the higher dimensional case no such metastable behavior occurs . also here solutions tend very quickly towards configurations which are locally constant with interfaces of width @xmath47 . then on a slower scale these interfaces evolve according to motion by mean curvature ( see @xcite and the references therein ) . 3ex    stochastic systems which are very similar to ( [ sace ] ) have been studied in the ninetees by funaki @xcite and brasecco , de masi , presutti @xcite . they study the one - dimensional equation in the case where the initial data is close to the instanton shape and show that in an appropriate scaling the solution will stay close to such a shape . then due to the random perturbation a dynamic along the one - parameter family of such shapes can be observed on a much faster time scale than in the deterministic case . our result theorem [ thm1 ] says that one can also pass to the sharp interface limit on the level of invariant measures . 3ex    if the process does not start in a configuration with a single interface , it is believed that these different interfaces also follow a random induced dynamic which is much quicker than in the deterministic case . different interfaces should annihilate when they meet @xcite . more recently there were also investigations of the same system on a much bigger space interval where due to entropic effects noise induced nucleation should occur . this phenomenon has been studied on the level of invariant measures @xcite . the limiting process should be related to the brownian web which has recently been investigated e.g. in @xcite . 3ex    from a point of view of statistical physics theorem [ thm2 ] can be interpreted as quite natural . in fact the feynman picture suggests to view @xmath35 as a gibbs measure with energy @xmath63 and decreasing temperature @xmath47 . on a fixed interval the result of theorem [ thm2 ] would therefore simply state that with decreasing temperature the gibbs measure concentrates around the energy minimizers exponentially fast . on a rigorous level such results follow from standard large deviation theory ( see e.g. @xcite ) . our result states that the entropic effects which originate from considering growing intervals do not change this picture . in fact also this is not very suprising - analysis of similar spin systems suggests that even on intervals that grow exponentially in @xmath82 one should not observe more than one jump . but it is not clear if one can say anything about the shape of the interface in this settings . our approach is limited to intervals growing like @xmath83 due to the @xmath84-hilbert space structure employed . 3ex    _ 4 . structure of the paper _ 1ex    in section [ sec2 ] results about the energy landscape of the ginzburg - landau energy functional are summarized . in particular we discuss in some detail the minimizers of @xmath63 and introduce tubular coordinates close to the curve of minimizers . the energy landscape is studied in terms of these tubular coordinates . in section [ sec3 ] some necessary gaussian concentration inequalities are discussed . in particular the discretization of the measure @xmath85 is given and some error bounds are proved . the proof of theorem [ thm2 ] can then be found in section [ sec4 ] . finally the proof of theorem [ thm1 ] is finished in section [ sec5 ] . we will follow the convention that @xmath86 denotes a generic constant which may change from line to line . constants that appear several times will be numbered @xmath87 .","summary":"the invariant measure of a one - dimensional allen - cahn equation with an additive space - time white noise is studied . this measure is absolutely continuous with respect to a brownian bridge with a density which can be interpreted as a potential energy term . scaling this corresponds to a gibbs type measure on a growing interval with decreasing temperature . scaling the limit measure is concentrated on configurations with precisely one jump . this jump is distributed uniformly .    3ex    _ keywords : _ stochastic reaction - diffusion equation , invariant measure , large deviations .   ","abstract":"the invariant measure of a one - dimensional allen - cahn equation with an additive space - time white noise is studied . this measure is absolutely continuous with respect to a brownian bridge with a density which can be interpreted as a potential energy term . we consider the sharp interface limit in this setup . in the right scaling this corresponds to a gibbs type measure on a growing interval with decreasing temperature . our main result is that in the limit we still see exponential convergence towards a curve of minimizers of the energy if the interval does not grow too fast . in the original scaling the limit measure is concentrated on configurations with precisely one jump . this jump is distributed uniformly .    3ex    _ keywords : _ stochastic reaction - diffusion equation , invariant measure , large deviations .   "}
{"article_id":"1602.01731","section_id":"c","document":"we have proposed a dynamic multi - objective optimization framework for ofdma based cellular systems to identify the set of active sectors and ran parameters which are required to serve a given traffic demand with minimum area power consumption while maintaining a suitable trade - offs between other metrics like network coverage , area spectral efficiency , and overlap . a genetic algorithm based solution approach is proposed to obtain the pareto optimal solution for the considered multi - objective optimization . it is seen that the maximum energy saving is achieved when the solution ( i.e. set of active sectors and ran parameters ) are selected with the objective of minimizing area power consumption . however , it is associated with a reduced area spectral efficiency and also affects the coverage performance . on the other hand , if the solution is selected with the objective of minimizing overlap then the area spectral efficiency and coverage performance improves significantly even though the energy saving is not as high as the former case . it is further seen that when the ran parameters are optimized along with the optimized active sector set , the transmit power optimization provides more es compared to tilt and height optimization . by selecting the solutions based on different objectives , at @xmath102 , @xmath3 , and @xmath198 network traffic load , it is possible to achieve es between @xmath103 to @xmath199 , @xmath1 to @xmath103 , and @xmath2 to @xmath200 , respectively . the results show that the proposed framework can be used in practical networks in a centralized manner to adaptively change the network configuration at a faster convergence rate and minimal computational complexity . the mgf of sum of binary weighted @xmath201 independent rvs can be written as the product of mgf of individual rvs as @xmath202.\\ ] ]    using the definition of mgf i.e. @xmath203 the mgf of a log - normal - gamma rvs @xmath204 can be written as @xmath205    by letting @xmath206 , the above expression can be rewritten as @xmath207}e^{-t^2}}{e^{m(\\sqrt{2}\\sigma_y t+\\mu_{\\hat{\\chi}_{ig } } ) } } dx dt.\\end{aligned}\\ ] ]    by letting @xmath208 and rearranging the terms we get @xmath209\\frac { e^{-t^2}}{e^{m(\\sqrt{2}\\sigma_{\\hat{\\chi}_{ig } } t+\\mu_{\\hat{\\chi}_{ig}})}}\\ dt.\\end{aligned}\\ ] ]    by applying the property of gamma function i.e @xmath210 , the above integral can be written as @xmath211^m}\\ dt \\nonumber \\\\   & = \\frac{1}{\\sqrt{\\pi } } \\int_0^\\infty \\bigg(1+\\frac{se^{(\\sqrt{2}\\sigma_{\\hat{\\chi}_{ig}}t+\\mu_{\\hat{\\chi}_{ig}})}}{m}\\bigg)^{-m}e^{-t^2}\\ dt . \\nonumber\\end{aligned}\\ ] ]    the above integral can be rewritten using gauss - hermite series as @xmath212 where @xmath213 is the order of the hermite integration , @xmath214 is reminder term . the weights , @xmath215 and abscissas , @xmath216 for @xmath213 are given in ( * ? ? ? 25.10 ) . the mean and variance of @xmath217 can be obtained by solving the following two equations    @xmath218\\nonumber \\\\&= \\prod_{g=1}^{n_{\\mathcal{b}_{\\mathrm{on}}}-1}\\ ! \\bigg[\\!\\beta_g\\sum_{n=1}^{n_h } \\frac{w_n}{\\sqrt{\\pi}}\\bigg(1+\\frac{s_ie^{(\\sqrt{2}\\sigma_{\\hat{\\chi}_{ig}}t_n+\\mu_{\\hat{\\chi}_{ig}})}}{m}\\bigg)^{-m}\\!+\\!(1-\\beta_g)\\!\\bigg].\\end{aligned}\\ ] ]    the values of @xmath219 and @xmath220 can be easily obtained by numerically solving the above non - linear equations at different real and positive values of @xmath126 , namely @xmath221 and @xmath222 . @xmath223p_{p_{r , ij}}(p_r)\\ dp_r \\nonumber \\end{aligned}\\ ] ]    @xmath224    where @xmath225 .    by applying chernoff bound to the @xmath226-function ( i.e. @xmath227 ) , can be approximated as @xmath228    after some manipulations @xmath229 where @xmath230 @xmath231 @xmath232 and @xmath233    the integral in the second term is a @xmath226-function . by applying chernoff bound to it the coverage probability can be obtained as @xmath234      let @xmath235 be the random variable represents the number of class-@xmath236 objects in the queue at time @xmath237 . let @xmath238 be the state of the queue at time @xmath237 and @xmath239 be the corresponding stationary stochastic process . let @xmath240 be the probability that the queue is in state @xmath241 in equilibrium . in the long run , all the users in the system generates traffic demand belongs to different classes ( @xmath242 ) . the traffic demand generated by the users belongs to @xmath236-th class can be written as @xmath243 then the equilibrium distribution of number of users is given as ( * ? ? ? * theorem : 2.1 ) @xmath244    the blocking probability of calls is obtained using kaufman - roberts algorithm ( kra ) @xcite . let @xmath245 be the set of states for which exactly @xmath246 number of sub - channels are occupied . let @xmath247 be the probability that there are @xmath248 number of sub - channels are occupied i.e. @xmath249 the occupancy probabilities satisfy the following recursive equations @xcite    @xmath250    the blocking probability of @xmath236-th class in cell @xmath66 can be obtained by @xmath251 the average blocking probability in @xmath66-th cell is obtained as the weighted sum of all class - wise blocking probabilities i.e. @xmath252 hence eqn . . since there is no closed form expression available for sum of interference components in case of log - normal fading , we prove the lemma considering a single interferer . the fraction of users belong to @xmath236-th class attached to sector @xmath66 is obtained as @xmath253 @xmath254p_{p_{r , ij}}(p_r)\\ dp_r \\nonumber \\\\ & + \\beta_2\\int_{p_{r,\\mathrm{min}}}^{\\infty } \\bigg[q\\bigg(\\frac{\\ln(p_{r}/\\gamma_{l+1})-\\mu_{p_{i_i}}}{\\sigma_{p_{i_i}}}\\bigg)\\nonumber \\\\ & \\hspace{3cm}-q\\bigg(\\frac{\\ln(p_{r}/\\gamma_{l})-\\mu_{p_{i_i}}}{\\sigma_{p_{i_i}}}\\bigg)\\bigg]p_{p_{r , ij}}(p_r)\\ dp_r \\nonumber\\end{aligned}\\ ] ] @xmath255p_{p_{r , ij}}(p_r)\\ dp_r . \\end{aligned}\\ ] ]    after applying chernoff bound , @xmath256      \\end{aligned}\\ ] ] here @xmath257 and @xmath258    by letting @xmath259 and @xmath260 eqn . is rewritten as @xmath261.\\ ] ]    consider a simple scenario where @xmath262 . then from eqn . @xmath263    after expanding the terms we get @xmath264}{[1+\\frac{1}{2}(w_j(1)+w_j(2))]}\\ ] ]    after substituting @xmath265 $ ] , @xmath266 $ ] we get @xmath267}{2+\\beta_2[x(\\gamma_{\\mathrm{max}})-x(\\gamma_1)]}\\ ] ]    after taking derivative of @xmath39 with respect to @xmath268 we get @xmath269}{\\big(2+\\beta_2[x(\\gamma_{\\mathrm{max}})-x(\\gamma_1)]\\big)^2}\\ ] ]    let @xmath270 . then , @xmath271 and @xmath272    it can be seen that @xmath273 is increasing function of @xmath274 . since @xmath275 , @xmath276 .    after taking second derivative we get @xmath277 ^ 2}{\\big(2+\\beta_2[x(\\gamma_{\\mathrm{max}})-x(\\gamma_1)]\\big)^3},\\ ] ] where @xmath278 , \\beta_2 \\in [ 0,1]$ ] . therefore @xmath279 and hence the denominator term is always positive for @xmath280 $ ] . then it follows that @xmath281 . therefore , it can be concluded that @xmath39 is concave downward on @xmath268 .","summary":"green communications , ofdma , base station , sleep mode , coverage , overlap , area spectral efficiency , area power consumption , multi - objective optimization .","abstract":"green communications , ofdma , base station , sleep mode , coverage , overlap , area spectral efficiency , area power consumption , multi - objective optimization ."}
{"article_id":"1607.04190","section_id":"i","document":"optical microscopy is a convenient tool to study biological processes , but its resolution is fundamentally limited by abbe s diffraction . the image of a point source is a pattern whose size is comparable to the optical wave - length ( @xmath3 ) , hence source points separated by a distance smaller than a wavelength are hardly distinguishable @xcite . electron microscopy provides a higher spatial resolution ( @xmath4 ) but at the cost of a more complex sample preparation which is incompatible with _ in vivo_-imaging @xcite . the recently developed super - resolution imaging techniques aim at combining the best of these two worlds . using these techniques , spatial resolution as low as @xmath5 have been achieved for imaging biological cell structures . however , their applicability to the study of dynamical biological processes is limited by their long acquisition times @xcite .    though relying on different optical probes , the super - resolution techniques known as palm ( photoactivation localization microscopy ) or storm ( stochastic optical reconstruction microscopy ) rely on a common principle : sources that lie within the same diffraction - limited volume are separated by a sequential activation process , which introduces a temporal separation between source points @xcite . within each frame , a small and random fraction of probes is activated by illumination . this sparse subset of randomly activated probes is imaged to produce a frame . then , finding the centroid of each diffraction patterns leads to a set of coordinates , having a nanometer - level precision @xcite . merging all the single - molecule positions obtained on successive frames produces the final image . since only a small fraction of probes is imaged per frame , a certain number of frames is required in order to obtain a reliable image . multiplying this number by the typical acquisition time of frames ( typically in the @xmath6 range ) , we obtain the minimal time , denoted @xmath7 , to obtain an image at a nanometer - scale resolution . a typical reported value is @xmath8 for a whole cell imaging at a @xmath9 resolution @xcite . this value is too large to study many dynamical processes that occur in living cells , such as the contraction of acto - myosin units @xcite , reorganization of focal adhesion complexes @xcite or protein cluster formation within the plasma membrane @xcite . efforts to reduce the acquisition time are hindered by the risk that the collected set of observations is incomplete .    in this article , we are interested in the risk of _ stochastic aberration _ in the final reconstructed image , whereby an incomplete observation would incorrectly suggest the presence of gaps within the structure . an illustrative example is the case of 1d structures , such as dna segments @xcite or actin filaments @xcite ( see fig . [ fig1 ] ) . suppose that the reconstructed super - resolved image contains a hole : how can we reliably discriminate whether this hole is a genuine gap in the structure rather than an aberration due to a lack of observations ? this question illustrates the interest of our model , which provides an estimate for the minimal number of observation frames required to minimize the risk of stochastic aberrations . it also highlights a major difference between stochastic and deterministic imaging techniques . with raster - scan - based techniques , e.g. stimulated emission depletion ( sted ) , the resolution is exempt of stochastic aberration but the acquisition time @xmath10 increases linearly with the size of the field of view @xcite . with widefield stochastic techniques such as palm , the imaging time is thought to be independent of the size of the field of view . the density of the observed points , and concomitantly the final image resolution , increase with the acquisition time @xmath10 . image size , density and total acquisition time are therefore essential parameters to assess the relevance and performance of widefield stochatic techniques . we briefly outline a simple reasoning that leads to the incorrect conclusion that the image completion time should be independent of the size of the field of view . we first suppose that fluorescent events are distributed according to a homogeneous poisson process , such that the probability density @xmath11 that an event occurs in an infinitesimal space of volume @xmath12 reads @xmath13 @xcite . we now consider a regular domain of volume @xmath14 within a @xmath15 dimensional space , in which we assume a constant density of fluorophore @xmath16 . furthermore , we assume that at each frame , only a fraction @xmath17 of fluorophores are detected . the number of detected fluorescence events after one frame , denoted @xmath18 , is a poisson process of density @xmath19 ; hence @xmath20 = \\exp(- \\rho { s } ) ( \\rho { s})^{n}/n!$ ] . if @xmath21 refers to the volume of the abel diffraction pattern , the mean number of fluorescence events per frame @xmath22 should be lower than @xmath0 in order to limit the risk of overlapping point spread functions . @xcite , hence @xmath24 . in the case of membrane ( @xmath25 ) with fluorophore density @xmath26 , the corresponding maximal fraction of activated fluorophores should be @xmath27 . then , after a number @xmath7 of frames , the total number of collected events is distributed according to a poisson distribution , with @xmath28 = \\exp(- \\rho { s}t ) ( \\rho { s}t)^{n}/n!$ ] . this number of collected events determines the resolution of the reconstructed image , due to the nyquist criterion , which states that the mean distance between sampling points must be at least two - fold smaller than the desired resolution @xcite . therefore , to attain a resolution of @xmath29 , a minimal requirement is to collect at least @xmath30 evenly spaced observations per resolution volume @xmath31 , or , equivalently , to have at least @xmath0 observation per volume @xmath32 . as the density of detected fluorophores up to the time @xmath7 reads @xmath33 , the nyquist criterion leads to the identity @xmath34 , in order to guarantee that , on average , there has one observation per elementary volume @xmath35 . with @xmath32 and @xmath36 , this leads to a minimal number of frames @xmath37 . in 2d and with a typical frame rate of @xmath38 , the corresponding acquisition time would be of the order of a few minutes , independently of the size of the image . the relation @xmath39 also illustrates how recent imaging techniques achieved live - cell imaging at the cost of a lower spatial resolution @xcite . however , the condition @xmath34 does not imply that every elementary volumes have collected their one observation : some elementary volume may have collected several observations while most others none .    in this paper , we argue that , due to the randomness in the localization of events in stochastic widefield microscopy , the imaging time should not be considered independent of the size of the image . the uneven spatial distribution of events leads to a correction term @xmath40 in the expression of the imaging time . hence the main result of our article lies in the following relation : @xmath41 which means that the trade - off between the spatial ( @xmath35 ) and temporal ( @xmath7 ) resolutions is not only regulated by the density of activated fluorophores per frame @xmath42 , but also by the ratio of the size of the field of view @xmath14 by the desired spatial resolution , and by an additional parameter @xmath43 which characterizes the reliability of the final image . in many situations of interest , the prefactor @xmath40 can not be assumed to be close to @xmath0 . for example , a cell of extension @xmath44 contains @xmath45 squares of area @xmath46 ( ie . a typical size for an abel diffraction pattern ) . this corresponds to the ratio @xmath47 . any specific choice for the value of @xmath48 only increases the value of the acquisition time . hence our result predicts that the image completion time should be one order of magnitude longer than what would be expected from the arguments leading to expression in the left hand side of eq . ( [ eq : main_message ] ) . the paper is organized as follows . we first present the experimental setup that we use to test the validity of our theoretical expressions , in which we measure the light scattered by brownian nano - particles at the surface of a two - dimensional sample ( method  experiments ) . we then define two image rendering schemes ( method  image rendering ) . we then prove the relation eq . ( [ eq : main_message ] ) , and we show its connexion to the coupon - collector problem @xcite . therefore , we refer to the result of eq . ( [ eq : main_message ] ) as the _ coupon - collector scaling_.    we then consider the robustness of the coupon - collector scaling for several requirement on the image completion . we first consider the effect of correlations between successive frames . this case is particularly motivated by our experimental setup , in which the escapes and returns of the brownian particles within the detection zone leads to temporally correlated scattering events between successive frames . we point out that there is a close analogy between our experiments and palm techniques in which the fluorophores blinking statistics exhibit time - correlations @xcite . we recall that bleaching refers to an irreversible transition of a probe to an inactive state , which can occurr following a fluorescence event @xcite . the analogy holds between blinking events , identified to light - scattering events from brownian particles , and bleaching events , identified to the escape events far from the illuminated region and with no ulterior return . we show that the coupon - collector scaling does not hold when a large number of coverage is required . we then compare our theoretical predictions to our experimental results . we conclude our article by presenting a procedure to estimate the risk of stochastic aberration , in real - time during the acquisition ( ie . at each frames during the image acquisition process ) .","summary":"we justify that the redundancy in the localization of detected events imposes a specific limit on the temporal resolution . based on a theoretical model , we derive analytical predictions for the minimal time required to obtain a reliable image at a given spatial resolution , called image completion time .","abstract":"widefield stochastic microscopy techniques , such as palm or storm , rely on the progressive accumulation of a large number of frames , each containing a scarce number of super - resolved point images . we justify that the redundancy in the localization of detected events imposes a specific limit on the temporal resolution . based on a theoretical model , we derive analytical predictions for the minimal time required to obtain a reliable image at a given spatial resolution , called image completion time . in contrast to standard assumptions , we find that the image completion time scales logarithmically with the ratio of the image size by the spatial resolution volume . we justify that this non - linear relation is the hallmark of a random coverage problem . we propose a method to estimate the risk that the image reconstruction is not complete , which we apply to an experimental data set . our results provide a theoretical framework to quantify the pattern detection efficiency and to optimize the trade - off between image coverage and acquisition time , with applications to , or dimension structural imaging ."}
{"article_id":"1607.04190","section_id":"m","document":"we briefly present the experimental data that we will use to test our predictions on the coverage time . in our recent work @xcite , we present a new stochastic imaging technique to map an electromagnetic field with a nano - scale resolution using light - scattering brownian particles as local probes of the intensity field . the brownian motion of the scatterers eventually lead to a full coverage of the imaged field . following @xcite , we consider the imaging problem of an evanescent wave created by a total internal reflection microscopy setup . in this setup , we consider that the optical intensity field can be modelled as @xmath49 where @xmath50 is the penetration length of the field , and @xmath51 is proportional to the optical intensity of the field at the surface  with a proportionality constant related to the scattering cross section of the particles . in principle , in most situations , both quantities @xmath50 and @xmath51 can vary with the location @xmath52 on the surface . in this context , the term image acquisition refers to the determination of the fields @xmath51 and @xmath50 . however , as a first test of the method , we have considered in @xcite a situation in which @xmath51 and @xmath50 can be considered as homogeneous within the field of view . we detail a procedure that leads to the determination of @xmath51 and @xmath50 in the si , [ sec : app : justification ] . super - resolution techniques rely on the localization of the center of diffraction spots , which provides a set of points . however , a spatial extention needs to be attributed to each point to obtain an image that is readable to the human eye . in the following , we will be interested in the two following image rendering methods : ( i ) the bfm ( bfm ) , which is adapted to a density image representation @xcite and ( ii ) the patch method ( pm ) , which is associated to a pointillist representation @xcite . the bfm considers the structure of interest as tessellated into @xmath53 square pixels of equal area , which can therefore be expressed as the ratio of the total volume by the resolution volume : @xmath54 . each new event falls within a specific pixel , thereby increasing by one the cumulative number of observations of this pixel . this method is naturally adapted to measure the densities . though we employ the term pixel in the following , our method also applies to 3d imaging problems in which @xmath53 refers to the number of voxels within the structure of interest @xcite .    in the other hand , the pm associates to each event a surrounding extension , characterized by the quantity @xmath35 , which is either a length ( 1d ) , an area ( 2d ) or a volume ( 3d ) . generally , the spatial extension is chosen to correspond to the spatial uncertainty associated to the localization procedure ( e.g. a few nanometers , @xcite ) . the image completion time is related to the minimal number of patches required to cover the structure of interest .      as discussed in the introduction , we consider that the number of events occurring on each frame follows a poisson statistics , with a mean @xmath55 , where @xmath14 is the volume of the region of interest , and @xmath42 is the density of events per frame . we consider that the density of events @xmath42 ( i ) is homogeneous within the volume of the structure of interest ( ii ) is time - independent .    concerning the homogeneous assumption , we point out that , in most cases of interest , the field of view can not be considered as homogeneous . indeed , the field of view generally contains regions where no events should occurr . for example , consider the localization problem of actin filaments within a biological cell by palm . points which are located outside of the actin filaments should not yield any observation . we assume that there is a one to one correspondence between pixels which contain fluorophores and pixels within the structure . this amounts to neglecting the background noise , ie . spurious detection events in regions where fluorophores should not be present . hence , we are interested in the imaging process of a subset of the field of view , which we call the structure of interest . similarly , in the context of the experimental application of our method with brownian nanoparticles , we expect that only a subset of the field of view is relevant , as characterized by significantly higher intensity fields . this corresponds to the experimentally relevant cases of either structured @xcite or rough @xcite metallic surfaces , which can exhibit local hotspots whereby the incident light is concentrated on the nanometre scale to produce an intense electromagnetic field . this is particularly justified as we expect the probability to observe a particle to be a function of both @xmath50 and @xmath51 . in both experimental contexts , we assume that the event probability follows a homogeneous poisson process within the volume of the structure of interest    in palm , the time - independent assumption can be questionned due to bleaching events @xcite . however , these bleaching events have no effect on the image completion time neither in the pm representation , nor in the bfm configuration with @xmath56 . in the bfm with @xmath57 , the time - independent assumption is justified if the number of the remaining unbleached fluorophores per pixel is sufficiently large . we emphasize that , in most situations , the volume of the structure is unknown _ a priori_. within the bfm , we show in the si [ sec : app : festimator ] that the maximum likelihood estimator of the number of relevant pixels @xmath53 corresponds to the quantity : @xmath58 where @xmath59 is the cumulative number of measures of the pixel @xmath60 , e.g. @xmath61 if the pixel @xmath60 has never collected any event up to time @xmath10 and @xmath62 if the pixel has been observed at least once up to time @xmath10 ( see fig . [ fig1 ] ) . similarly , within the patch - method framework , the maximum likelihood estimator of the structure volume consists in the covered volume at the time @xmath10 . these two estimators are biased , as they tend to underestimate the structure volume . that is proportional to the uncertainty of the super - localization procedure ( blue disk ) . ( b ) patches accumulate with the acquisition time , eventually covering the whole structure of interest ( patches are represented by different colors patches for separate frames ) . ( c  f ) box - filling representation , which leads to a density map in terms of a number of accumulated events per pixel . ( c ) the field of view is divided into @xmath63 pixels among which @xmath64 pixels contain probes . ( d ) a sequence of frames ( blue circle : size of the abel pattern ) . ( e ) target image . ( f ) map of the cumulative number of observations @xmath59 , for each @xmath60 and for each frame @xmath10 . complete image completion ( with @xmath65 ) is obtained after @xmath66 frames . at @xmath67 , all pixels have been observed at least @xmath68 times . , height=302 ]      we call _ image completion time _ the minimal number of frames required to obtain a _ complete _ image of the structure of interest . the term complete refers to the condition that every pixel or point ( among those that should be observed ) has been covered at least a certain number of times , denoted @xmath69 . more precisely , the image completion time @xmath7 is the random variable ( called stopping time ) that corresponds to the minimal time @xmath10 such that @xmath70 ; where @xmath71 $ ] in the bfm framework , or @xmath60 refers to any point within the volume of interest in the pm framework . we will be mainly interested in the centile of @xmath7 , denoted @xmath72 and defined as : @xmath73 = \\mathbb{p}\\left[\\min_{j}\\left(m^{(t_\\theta)}_j\\right ) \\geq r \\right ] = 1-\\theta,\\end{aligned}\\ ] ] where @xmath48 is the tolerated risk tolerance level . to summarize , the quantity @xmath74 refers to the minimal number of frames that guarantees , with @xmath75 probability , that the image is complete . both in the bfm and pm frameworks , the volume of the structure of interest is tessellated into a grid of elementary squares . in the bfm , each events covers a single elementary square ; while in the pm , each patches @xmath35 covers a square matrix of elementary squares . in both frameworks , we generate a large sample of coverage events , and analyse the distribution of coverage times using matlab s _ prctile _ function .","summary":"widefield stochastic microscopy techniques , such as palm or storm , rely on the progressive accumulation of a large number of frames , each containing a scarce number of super - resolved point images .","abstract":"widefield stochastic microscopy techniques , such as palm or storm , rely on the progressive accumulation of a large number of frames , each containing a scarce number of super - resolved point images . we justify that the redundancy in the localization of detected events imposes a specific limit on the temporal resolution . based on a theoretical model , we derive analytical predictions for the minimal time required to obtain a reliable image at a given spatial resolution , called image completion time . in contrast to standard assumptions , we find that the image completion time scales logarithmically with the ratio of the image size by the spatial resolution volume . we justify that this non - linear relation is the hallmark of a random coverage problem . we propose a method to estimate the risk that the image reconstruction is not complete , which we apply to an experimental data set . our results provide a theoretical framework to quantify the pattern detection efficiency and to optimize the trade - off between image coverage and acquisition time , with applications to , or dimension structural imaging ."}
{"article_id":"1607.04190","section_id":"m","document":"we now consider that the image results form the accumulation of circular patches , whose radius @xmath35 corresponds to the spatial resolution . the patch centers are distributed according to a homogeneous poisson distribution is called a boolean process ( see @xcite ) . ] within the structure of interest , of volume @xmath14 . the study of coverage problem has a long history @xcite . however , analytical results concerning coverage problems in two dimensions are rather recent @xcite . these studies were motivated by the study of the wifi coverage resulting from randomly located routers . we will make use of results concerning the expression of the centile @xmath102 of the number of patches required to cover a circle @xcite or a square @xcite by circular patches .    here , we seek an expression of the centile time @xmath72 , i.e. a time expressed in terms of a number of frames @xmath10 , rather than the centile time expressed in terms of the number of patches @xmath103 . we expect that @xmath104 where @xmath105 is the number of events per frame . indeed , in the small patch limit @xmath106 , full coverage events occur when the number of events is large ( @xmath107 ) in which case the number of events is simply proportional to the number of frames @xmath10 . this approximation is further justified in the si . therefore , following refs . @xcite and @xcite , we expect the centile time @xmath72 to obtain a @xmath100-fold coverage of a @xmath15-dimensional volume @xmath14 by circular patches of volume @xmath35 to read : @xmath108 \\right\\rbrace,\\end{aligned}\\ ] ] where @xmath109 in 1d @xcite and @xmath110 in 2d @xcite . it appears that no analytical expression exist concerning the 3d coverage problem . our simulations for the coverage problem by squares ( defined in method  simulations ) agree with the scaling defined eq . ( [ eq : tcc2_continuous ] ) and with the value of the constants @xmath111 ( see si , fig . [ fig_si_1 ] ) . in 3d , we find that @xmath112 . remarkably , eq . ( [ eq : tcc2_continuous ] ) takes a similar form as the coupon - collector problem from eq . ( [ eq : tcc2 ] ) . this similarity suggests that in the limit @xmath106 , regularly spaced patches of size @xmath113 behave as if they were independent . mind , however , that the expression from eq . ( [ eq : tcc2 ] ) corresponds to a value @xmath114 for any space dimension . the origin of this discrepancy at second order in the ratio @xmath106 is discussed in ref . @xcite .    in conclusion , we have shown that both the path and box - filling image rendering methods lead to similar expressions for the image completion time , which are characterized by a logarithmic dependence in terms of the ratio of the image volume by the spatial resolution volume . mind that , in the bfm , the latter ratio is equal to the number of pixels . last , we point out that both eqs . [ eq : tcc2 ] and [ eq : tcc2_continuous ] hold provided that @xmath115 .","summary":"in contrast to standard assumptions , we find that the image completion time scales logarithmically with the ratio of the image size by the spatial resolution volume .","abstract":"widefield stochastic microscopy techniques , such as palm or storm , rely on the progressive accumulation of a large number of frames , each containing a scarce number of super - resolved point images . we justify that the redundancy in the localization of detected events imposes a specific limit on the temporal resolution . based on a theoretical model , we derive analytical predictions for the minimal time required to obtain a reliable image at a given spatial resolution , called image completion time . in contrast to standard assumptions , we find that the image completion time scales logarithmically with the ratio of the image size by the spatial resolution volume . we justify that this non - linear relation is the hallmark of a random coverage problem . we propose a method to estimate the risk that the image reconstruction is not complete , which we apply to an experimental data set . our results provide a theoretical framework to quantify the pattern detection efficiency and to optimize the trade - off between image coverage and acquisition time , with applications to , or dimension structural imaging ."}
{"article_id":"0912.1288","section_id":"i","document":"the smoothed boundary method @xcite and other similar approaches @xcite have recently been demonstrated as powerful tools for solving various partial differential equations with boundary conditions imposed within the computational domain . the method s origin can be traced to the embedded boundary method and the immersed boundary method ( for an overview , see ref . this method has been successfully employed in simulating diffusion processes @xcite and wave propagation @xcite constrained within geometries described by a continuously transitioning domain indicator function ( hereafter , the domain parameter ) with a no - flux boundary condition imposed on the diffuse interface ( as defined by the narrow transitioning region of the domain parameter ) . while those works demonstrated the potential for this type of numerical methods that circumvents the difficulties with constructing the finite element mesh ( e.g. , meshing the surface and then building a volumetric mesh based on the surface mesh or by combining regular subdomains that can be easily meshed ) , which is particularly useful when dealing with complex structures . however , the method was only applicable to no - flux boundary conditions , and no approaches to extend the method to other types of equations or boundary conditions were available . recently , a different formulation , based on asymptotic analyses , to solve partial differential equations in a similar manner was proposed @xcite , providing a justification of the method as well as increasing the applicability of the approach .    in this paper , we provide a mathematically consistent smoothed boundary method and provide a precise derivation for the equations . the specific equations that we consider are : ( 1 ) the diffusion equation with neumann and/or dirichlet boundary conditions , ( 2 ) the bulk diffusion equation coupled with surface diffusion , ( 3 ) the mechanical equilibrium equation for linear elasticity , and ( 4 ) allen - cahn or cahn - hilliard equations with contact angles as boundary conditions . the method is especially useful for three - dimensional image - based simulations .","summary":"in this article , we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries . a function that has a prescribed value on the domain in which a differential equation is valid and smoothly but rapidly varying values on the boundary where boundary conditions are imposed is used to modify the original differential equations . the mathematical derivations are straight forward , and generically applicable to a wide variety of partial differential equations . to demonstrate the general applicability of the approach , we provide four examples : ( 1 ) the diffusion equation with both neumann and dirichlet boundary conditions , ( 2 ) the diffusion equation with surface diffusion , ( 3 ) the mechanical equilibrium equation , and ( 4 ) the equation for phase transformation with additional boundaries . the potential of the approach is demonstrated with five applications : surface - reaction diffusion kinetics with a complex geometry , kirkendall - effect - induced deformation , thermal stress in a complex geometry , phase transformations affected by substrate surfaces , and a self - propelling droplet .","abstract":"in this article , we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries . a function that has a prescribed value on the domain in which a differential equation is valid and smoothly but rapidly varying values on the boundary where boundary conditions are imposed is used to modify the original differential equations . the mathematical derivations are straight forward , and generically applicable to a wide variety of partial differential equations . to demonstrate the general applicability of the approach , we provide four examples : ( 1 ) the diffusion equation with both neumann and dirichlet boundary conditions , ( 2 ) the diffusion equation with surface diffusion , ( 3 ) the mechanical equilibrium equation , and ( 4 ) the equation for phase transformation with additional boundaries . the solutions for a few of these cases are validated against corresponding analytical and semi - analytical solutions . the potential of the approach is demonstrated with five applications : surface - reaction diffusion kinetics with a complex geometry , kirkendall - effect - induced deformation , thermal stress in a complex geometry , phase transformations affected by substrate surfaces , and a self - propelling droplet ."}
{"article_id":"1107.1517","section_id":"i","document":"the temporal properties of the radio wavelength sky are poorly understood . much of what is known results from follow - up of events discovered at optical , x - ray , or @xmath3-ray wavelengths such as supernovae , gamma - ray burst , and x - ray binaries . an important exception is the sub - second domain , which has been systematically , if incompletely , explored , leading to the discovery of pulsars @xcite , rotating radio transients @xcite , and other unexplained phenomena @xcite . longer - time scale searches , which tend to be sensitive to synchrotron sources , are rarer and the sky coverage is less complete .    systematic searches on long timescales for radio transients ( rts ) are undergoing a renaissance that is defining the available parameter space . these searches are motivated by the specific promise of orphan gamma - ray burst afterglows @xcite , radio supernovae , tidally - disrupted stars around massive black holes @xcite , intrinsic agn activity such as found in iii zw 2 @xcite , extreme scattering events @xcite , stellar events @xcite , and counterparts to gravity - wave events @xcite . additionally , these searches are motivated by the desire to fully characterize the radio sky and discover the unexpected and unpredicted . archival searches have proven fruitful in this search , uncovering a number of transients that are not easily explained with known source classes @xcite . these archival surveys have been powerful for the volume probed but the absence of the opportunity for real - time follow - up has significantly limited their value in characterizing the source population . synoptic transit surveys have also been carried out @xcite . in particular , a number of new variable and transient sources without deep radio or optical counterparts have been found . @xcite argue that these may be bursts from galactic neutron stars ; other evidence suggests that they could be strong bursts from low - mass flare stars . the success of archival surveys has lead to a growing number of unbiased surveys including those carried out by the allen telescope array ( ata ; * ? ? ? the atats survey places limits on rare , high flux density transients and variables @xcite . a recent vla / evla survey @xcite has now provided strong limits on the radio transient and variable population at 5 ghz . these authors also summarize existing rt surveys at frequencies @xmath4 ghz . long wavelength transients were searched for with the long wavelength array @xcite . these archival and unbiased surveys join targeted surveys of specific source classes in characterizing the radio transient sky . for example , the masiv survey @xcite and the university of michigan monitoring program @xcite provide characterization of bright , flat - spectrum radio sources , which are known to have the strongest variability amplitudes . the pi ghz sky survey ( pigss ) is a key project of the ata . in @xcite , hereafter paper i , we presented the survey description , methods in observation , data reduction , and source identification , and initial results on transient statistics . briefly , pigss is a 3.1 ghz survey of a large area of high galactic latitude sky conducted synoptically with 100  resolution and milli - jansky sensitivity . the pigss emphasis is on two surveys jointly conducted : 1 ) @xmath5 deg@xmath6 of the sky with @xmath7 ; and 2 ) individual @xmath8 deg@xmath6 fields that are observed repeatedly . paper i presented results from integrated results for a 11-deg@xmath6 field in the botes  constellation associated with the noao deep wide field survey ( ndwfs ; * ? ? ? * ; * ? ? ? * ) . numerous sensitive , large area surveys have been carried out for the botes  field , providing an important baseline for comparison with pigss results . we found no new radio sources that we could convincingly identify as rts . this sets an upper limit on the rt surface density at the millijansky flux limit .    in this paper , we present daily results from the botes  field . these consist of 78 individual epochs over five months . these observations provide a very sensitive probe of transient statistics . they also provide one of the first unbiased searches for variability in a sample of mjy brightness sources . in  [ sec : obs ] , we briefly review the observations and data analysis and present the full catalog of light curves . in  [ sec : transients ] , we present results on transient sources . in  [ sec : var ] , we characterize the variability of individual sources . in  [ sec : conc ] , we summarize our results .","summary":"these results are part of a systematic and unbiased campaign to characterize variable and transient sources in the radio sky . . we also produce light curves for 425 sources and explore the variability properties of these sources .","abstract":"we present results from daily radio continuum observations of the botes  field as part of the pi ghz sky survey ( pigss ) . these results are part of a systematic and unbiased campaign to characterize variable and transient sources in the radio sky . the observations include 78 individual epochs distributed over 5 months at a radio frequency of 3.1 ghz with a median rms image noise in each epoch of 2.8 mjy . we produce 5 monthly images with a median rms of 0.6 mjy . no transient radio sources are detected in the daily or monthly images . at 15 mjy , we set an upper limit ( ) to the surface density of 1-day radio transients at 0.025 deg . at 5 mjy , we set an upper limit ( ) to the surface density of 1-month radio transients at 0.18 deg . we also produce light curves for 425 sources and explore the variability properties of these sources . approximately 20% of the sources exhibit some variability on daily and monthly time scales . the maximum rms fractional modulations on the 1 day and 1 month time scales for sources brighter than 10 mjy are 2 and 0.5 , respectively . the probability of a daily fluctuation for all sources and all epochs by a factor of 10 is less than . we compare the radio to mid - infrared variability for sources in the field and find no correlation . finally , we apply the statistics of transient and variable populations to constrain models for a variety of source classes ."}
{"article_id":"1107.1517","section_id":"r","document":"pigss observations of the botes  field were conducted between 2009 may 20 and 2009 september 29 . typical observations consisted of three 3-minute snapshots distributed over an observing epoch , which was between 4 and 12 hours in duration . the botes  observations were interleaved with those of a larger field . multiple hour angles were necessary to achieve good @xmath9-coverage for these complex fields . the botes  field consists of 7 individual pointings arranged in a close - packed hexagonal configuration with the central pointing located at @xmath10 and @xmath11 ( j2000 ) . pointings are separated by @xmath12 , the voltage full width half maximum at 3.14 ghz , which provides nearly uniform sensitivity in the central region of the field . observations were obtained in two separate frequency bands of 100-mhz width centered at 3.04 and 3.14 ghz . the digital correlator provided 1024 channels for each frequency band with all correlations between parallel- and cross - hand terms . the bright calibrator 3c 286 was observed hourly . data reduction was performed with standard techniques including flagging of bad data due to radio frequency interference , amplitude and phase calibration using 3c 286 , and imaging using the 2d fft . most analysis was performed with the miriad package @xcite . the clean images are convolved with a synthesized beam of @xmath13 . the majority of the reduction was performed with pipeline software @xcite although some of it required human intervention . individual pointings were stitched together into images using linear - mosaicking techniques . we refer the reader to paper i for further details of the reduction technique . we show a single - epoch image in fig . [ fig : image ] . the rms flux density in images from individual epochs has a minimum of 1.4 mjy , median of 2.8 mjy , and maximum of 4.7 mjy . 90% of all images have an rms below 3.7 mjy ( fig . [ fig : rms ] ) . these rms statistics differ from those presented in paper i due to a change in how we performed the clean on the images . we used a larger number of iterations ( 3000 ) for daily images in paper i , which reduced the image rms below theoretical expectations and lead to a systematic reduction of source flux densities ( by as much as a factor of 3 at flux densities around 10 mjy ) . in this paper , we stopped clean when the first negative component is reached . this typically occurred at fewer than 100 iterations . as we show below , the agreement between daily and deep flux densities is good . there is a bias of @xmath14 in the daily flux densities relative to the deep flux densities , which we think is an effect of @xmath9-coverage . we do not correct for that effect in these data because we are primarily interested in transient detections and light curve variability , which are insensitive to the absolute flux density . the median number of sources detected at a @xmath15 threshold per individual epoch is 30 and ranges from 17 to 69 . systematic variations in the rms with time are real and are due to changing performance of the array , small variations in the number of observations per epoch , and the variable interference environment . we also create monthly images of the field that are integrated over all epochs in the five - month span of these observations ( 2009 may through september ) . these images have a significant improvement in imaging quality due to the complete @xmath9-coverage . the rms for the monthly images from june to september ranges from 0.52 to 0.67 mjy ; the variation is representative of the range of daily epochs per month . the rms for the may epochs is 1.0 mjy due to the smaller number of epochs in this month ( 7 ) . the noise statistics from the monthly images are consistent with averaging of the daily data . the number of @xmath15 sources detected per month ranged from 83 to 171 . a table of 425 sources made from the deep image was presented in paper i. source finding in each epoch image was carried out using the miriad task sfind @xcite . we search for point sources down to a threshold of @xmath16 ; a higher threshold is employed for identifying transient sources as described below . additionally , light curves for sources from the deep image were generated by fitting 2d gaussians at the fixed positions of the sources from the deep images . errors are the rms background in the residual following removal of the best - fit 2d gaussian model . we plot mean flux densities for all sources from daily and monthly data against the deep image flux density ( fig . [ fig : fluxflux ] ) . the plot demonstrates agreement between these three different measures of source flux density at the 10% level for most sources . in some sources , larger differences may be due to confusion in regions of complex sources . we extensively explored completeness of the deep pigss catalog in paper i. deviations from previous catalogs such as nvss and gb6 were explored for indication of transient sources ; the absence of these sources is a measure of the completeness at the threshold we explored . in this paper , we primarily compare individual epochs to the deep pigss field . as discussed below , the absence of transient candidates at our detection threshold indicates that the daily images are complete at the @xmath15 threshold .","summary":"the observations include 78 individual epochs distributed over 5 months at a radio frequency of 3.1 ghz with a median rms image noise in each epoch of 2.8 mjy . we produce 5 monthly images with a median rms of 0.6 mjy . the probability of a daily fluctuation for all sources and all epochs by a factor of 10 is less than . finally , we apply the statistics of transient and variable populations to constrain models for a variety of source classes .","abstract":"we present results from daily radio continuum observations of the botes  field as part of the pi ghz sky survey ( pigss ) . these results are part of a systematic and unbiased campaign to characterize variable and transient sources in the radio sky . the observations include 78 individual epochs distributed over 5 months at a radio frequency of 3.1 ghz with a median rms image noise in each epoch of 2.8 mjy . we produce 5 monthly images with a median rms of 0.6 mjy . no transient radio sources are detected in the daily or monthly images . at 15 mjy , we set an upper limit ( ) to the surface density of 1-day radio transients at 0.025 deg . at 5 mjy , we set an upper limit ( ) to the surface density of 1-month radio transients at 0.18 deg . we also produce light curves for 425 sources and explore the variability properties of these sources . approximately 20% of the sources exhibit some variability on daily and monthly time scales . the maximum rms fractional modulations on the 1 day and 1 month time scales for sources brighter than 10 mjy are 2 and 0.5 , respectively . the probability of a daily fluctuation for all sources and all epochs by a factor of 10 is less than . we compare the radio to mid - infrared variability for sources in the field and find no correlation . finally , we apply the statistics of transient and variable populations to constrain models for a variety of source classes ."}
{"article_id":"1107.1517","section_id":"c","document":"we report on daily observations of an 11-deg@xmath6 region in the botes  constellation with the ata at 3.1 ghz as part of the pigss project . the 78 epochs of observation provide a systematic look at daily and monthly variations in the radio sky . we find no radio transients . there is a single event that was detected in the deep image without a counterpart in pre - existing surveys such as nvss that , if real , has a duration @xmath119 months . we place a new constraint on the surface density of 1-day duration transients with @xmath120 mjy of 0.025 deg@xmath1 and monthly duration transients with @xmath121 mjy of 0.18 deg@xmath1 . these limits are consistent with previous efforts with the ata and with other instruments . we also explored variability of the 425 radio sources in the deep field through a variety of statistics . largely , these sources show weak or no variability with rms fractional modulations less than 1 for sources brighter than 10 mjy . 20% of the sources have statistically significant variability . the combination of 425 sources and 78 epochs provides over @xmath122 flux density samples from which we can place limits on rare , large amplitude fluctuations . the largest amplitude fluctuations ( @xmath123 ) occur fewer than 1 in @xmath5 source - days . evla characterization of a subset of these sources is important for determining the effect of systematic errors in some of the larger variations reported here . while these statistics are of the most use for broadly characterizing the population , certain classes of objects are better identified with matched filtering techniques . for instance , extreme scattering events and radio supernovae have reasonably well - defined and parametrizable light curves which could be used to explore these data sets in greater depth . future explorations of data of this kind should include matched filter analysis . the pigss results in the botes  field represent approximately 20% of the data from the pigss project and were obtained in the early phases of routine telescope operations . subsequent analysis of higher quality daily observations in the lockman hole , elais , and the coma cluster will probe significantly deeper into the radio transient and variable population . pigss observations will also characterize variability on time scales of 1 year for @xmath124 radio sources in the north galactic cap . the limits we have placed are useful constraints on the population of active high energy objects in the universe . these limits explore the populations of tidal disruption events , radio supernovae , orphan gamma - ray burst afterglows , radio counterparts to gw sources , extreme scattering events , intra - day variable sources , and flare stars . the authors would like to acknowledge the generous support of the paul g. allen family foundation , who have provided major support for design , construction , and operations of the ata . contributions from nathan myhrvold , xilinx corporation , sun microsystems , and other private donors have been instrumental in supporting the ata . the ata has been supported by contributions from the us naval observatory in addition to national science foundation grants ast-050690 , ast-0838268 , and ast-0909245 .      , m.  l.  n. , stern , d. , brodwin , m. , griffith , r. , eisenhardt , p. , kozowski , s. , kochanek , c.  s. , bock , j.  j. , borys , c. , brand , k. , brown , m.  j.  i. , cool , r. , cooray , a. , croft , s. , dey , a. , eisenstein , d. , gonzalez , a.  h. , gorjian , v. , grogin , n.  a. , ivison , r.  j. , jacob , j. , jannuzi , b.  t. , mainzer , a. , moustakas , l.  a. , rttgering , h.  j.  a. , seymour , n. , smith , h.  a. , stanford , s.  a. , stauffer , j.  r. , sullivan , i. , van breugel , w. , willner , s.  p. , & wright , e.  l. 2009 , , 701 , 428                , j.  s. , giannios , d. , metzger , b.  d. , cenko , s.  b. , perley , d.  a. , butler , 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g. , helfer , t. , hull , c. , jordan , j. , jorgensen , s. , keating , g. , kilsdonk , t. , law , c. , van leeuwen , j. , lugten , j. , macmahon , d. , mcmahon , p. , milgrome , o. , pierson , t. , randall , k. , ross , j. , shostak , s. , siemion , a. , smolek , k. , tarter , j. , thornton , d. , urry , l. , vitouchkine , a. , wadefalk , n. , welch , j. , werthimer , d. , whysong , d. , williams , p.  k.  g. , & wright , m. 2010 , , 719 , 45                                , b.  t. , dey , a. , brown , m.  j.  i. , ford , a. , hogan , e. , miller , m. , ryan , e. , tiede , g.  p. , valdes , f. , & ndwfs . 2004 , in bulletin of the american astronomical society , vol . 36 , bulletin of the american astronomical society , 1478+      , g.  k. , barott , w.  c. , & wright , m. 2010 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 7740 , society of photo - optical instrumentation engineers ( spie ) conference series      , a. , murray , s.  s. , forman , w.  r. , jones , c. , green , p. , kochanek , c.  s. , vikhlinin , a. , fabricant , d. , fazio , g. , brand , k. , brown , m.  j.  i. , dey , a. , jannuzi , b.  t. , najita , j. , mcnamara , b. , shields , j. , & rieke , m. 2005 , , 161 , 9      , s. , kochanek , c.  s. , stern , d. , ashby , m.  l.  n. , assef , r.  j. , bock , j.  j. , borys , c. , brand , k. , brodwin , m. , brown , m.  j.  i. , cool , r. , cooray , a. , croft , s. , dey , a. , eisenhardt , p.  r. , gonzalez , a. , gorjian , v. , griffith , r. , grogin , n. , ivison , r. , jacob , j. , jannuzi , b.  t. , mainzer , a. , moustakas , l. , rttgering , h. , seymour , n. , smith , h.  a. , stanford , s.  a. , stauffer , j.  r. , sullivan , i.  s. , van breugel , w. , willner , s.  p. , & wright , e.  l. 2010 , , 716 , 530        , t.  j.  w. , clarke , t.  e. , lane , w.  m. , gross , c. , kassim , n.  e. , ray , p.  s. , wood , d. , york , j.  a. , kerkhoff , a. , hicks , b. , polisensky , e. , stewart , k. , 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starling , r.  l.  c. , strom , r.  g. , wheatley , p.  j. , wijers , r.  a.  m.  j. , winters , j.  m. , wold , t. , & xu , d. 2011 , arxiv e - prints                                                          , j. , backer , d. , blitz , l. , bock , d. , bower , g.  c. , cheng , c. , croft , s. , dexter , m. , engargiola , g. , fields , e. , forster , j. , gutierrez - kraybill , c. , heiles , c. , helfer , t. , jorgensen , s. , keating , g. , lugten , j. , macmahon , d. , milgrome , o. , thornton , d. , urry , l. , van leeuwen , j. , werthimer , d. , williams , p.  h. , wright , m. , tarter , j. , ackermann , r. , atkinson , s. , backus , p. , barott , w. , bradford , t. , davis , m. , deboer , d. , dreher , j. , harp , g. , jordan , j. , kilsdonk , t. , pierson , t. , randall , k. , ross , j. , shostak , s. , fleming , m. , cork , c. , vitouchkine , a. , wadefalk , n. , & weinreb , s. 2009 , ieee proceedings , 97 , 1438    lrrrrrrrrrr j142318 + 344210 & @xmath125 & 15.14 & 1.69 & 4.62 & 9.04 & 1.31 & -6.97 & 6.81 & -2.91 & 1.15 + j142402 + 344518 & @xmath126 & 8.82 & 1.43 & 1.03 & 4.03 & 0.57 & -5.56 & 4.38 & -0.93 & 0.57 + j142421 + 343857 & @xmath127 & 5.70 & 1.49 & 8.99 & 1.60 & 0.95 & -8.17 & 11.54 & -1.51 & 1.83 + j142426 + 343602 & @xmath128 & 5.01 & 0.94 & 1.68 & 0.54 & 0.16 & -1.16 & 0.86 & -0.23 & 0.20 + j142430 + 341914 & @xmath129 & 3.85 & 1.83 & 0.82 & 5.76 & 0.63 & -12.92 & 12.39 & -1.28 & 0.78 + j142440 + 343757 & @xmath130 & 4.47 & 1.25 & 1.14 & 1.75 & 0.47 & -3.81 & 2.60 & -0.73 & 0.77 + j142445 + 341832 & @xmath131 & 3.21 & 0.72 & 0.76 & 0.29 & 0.06 & -0.84 & 0.49 & -0.07 & 0.10 + j142447 + 345317 & @xmath132 & 6.40 & 1.31 & 3.33 & 36.67 & 0.26 & -7.50 & 7.29 & -0.31 & 0.52 + j142448 + 340957 & @xmath133 & 3.19 & 1.21 & 1.27 & 1.93 & 0.48 & -4.13 & 4.71 & -0.75 & 0.55 + j142458 + 342527 & @xmath134 & 2.92 & 1.80 & 1.02 & 11.58 & 0.61 & -4.93 & 4.12 & -0.46 & 1.06 + j142503 + 334405 & @xmath135 & 4.68 & 1.37 & 3.29 & -16.59 & 1.32 & -7.45 & 8.84 & -0.33 & 7.03 + j142516 + 345310 & @xmath136 & 4.56 & 0.75 & 2.45 & 0.44 & 0.11 & -1.65 & 0.51 & -0.21 & 0.11 + j142517 + 341606 & @xmath137 & 2.32 & 0.99 & 2.39 & 0.94 & 0.27 & -2.34 & 2.23 & -0.48 & 0.20 + j142523 + 340944 & @xmath138 & 2.23 & 1.56 & 0.46 & 1.57 & 0.23 & -4.25 & 1.50 & -0.18 & 0.48 + j142536 + 331215 & @xmath139 & 10.13 & 1.45 & 0.87 & 2.89 & 0.51 & -6.13 & 4.93 & -1.18 & 0.76 + j142541 + 345848 & @xmath140 & 4.19 & 1.11 & 3.35 & 0.20 & 0.16 & -0.56 & 0.21 & -0.23 & 0.19 + j142543 + 335544 & @xmath141 & 2.33 & 1.08 & 0.84 & 0.12 & 0.03 & -0.26 & 0.50 & -0.04 & 0.08 + j142558 + 351311 & @xmath142 & 5.33 & 1.32 & 1.68 & 2.23 & 1.01 & -6.15 & 6.75 & -1.21 & 1.50 + j142601 + 343129 & @xmath143 & 1.79 & 1.26 & 0.97 & 2.31 & 0.35 & -5.80 & 7.47 & -0.59 & 0.52 + j142607 + 340433 & @xmath144 & 1.66 & 0.82 & 5.05 & 0.24 & 0.06 & -0.60 & 0.50 & -0.10 & 0.06 +    rrrrrrrrrr +   + 1 & 10 & 0.0001 & 0.0428 & 0.2355 & 0.4851 & 0.2887 & 0.1587 & 0.0354 & 0.0001 + 10 & 100 & @xmath145 & 0.0059 & 0.0669 & 0.3456 & 0.1227 & 0.0416 & 0.0084 & 0.0002 + 100 & 1000 & @xmath146 & @xmath146 & @xmath146 & @xmath146 & 0.0036 & @xmath146 & @xmath146 & @xmath146 +   +   + 1 & 10 & @xmath147 & @xmath147 & 0.0439 & 0.2346 & 0.1661 & 0.0213 & 0.0013 & @xmath147 + 10 & 100 & @xmath148 & @xmath148 & 0.0189 & 0.0615 & 0.0284 & 0.0047 & @xmath148 & @xmath148 + 100 & 1000 & @xmath149 & @xmath149 & @xmath149 & @xmath149 & @xmath149 & @xmath149 & @xmath149 & @xmath149 +","summary":"we present results from daily radio continuum observations of the botes  field as part of the pi ghz sky survey ( pigss ) . no transient radio sources are detected in the daily or monthly images . at 15 mjy , we set an upper limit ( ) to the surface density of 1-day radio transients at 0.025 deg . at 5 mjy , we set an upper limit ( ) to the surface density of 1-month radio transients at 0.18 deg","abstract":"we present results from daily radio continuum observations of the botes  field as part of the pi ghz sky survey ( pigss ) . these results are part of a systematic and unbiased campaign to characterize variable and transient sources in the radio sky . the observations include 78 individual epochs distributed over 5 months at a radio frequency of 3.1 ghz with a median rms image noise in each epoch of 2.8 mjy . we produce 5 monthly images with a median rms of 0.6 mjy . no transient radio sources are detected in the daily or monthly images . at 15 mjy , we set an upper limit ( ) to the surface density of 1-day radio transients at 0.025 deg . at 5 mjy , we set an upper limit ( ) to the surface density of 1-month radio transients at 0.18 deg . we also produce light curves for 425 sources and explore the variability properties of these sources . approximately 20% of the sources exhibit some variability on daily and monthly time scales . the maximum rms fractional modulations on the 1 day and 1 month time scales for sources brighter than 10 mjy are 2 and 0.5 , respectively . the probability of a daily fluctuation for all sources and all epochs by a factor of 10 is less than . we compare the radio to mid - infrared variability for sources in the field and find no correlation . finally , we apply the statistics of transient and variable populations to constrain models for a variety of source classes ."}
{"article_id":"1010.4827","section_id":"i","document":"from isotopic studies of meteorites it is known that the solar nebula contained at least a dozen different short - lived radionuclides , or slrs ( see reviews by * ? ? ? * ; * ? ? ? * ; * ? ? ? identification of the sources of these slrs could greatly constrain the sun s birth environment and processes acting during star formation . the half - lives of some of these isotopes are shorter than the timescales @xmath1 typically associated with star formation , so they must have been produced near the time and place of the sun s formation . the slrs @xmath0 , @xmath2 and @xmath3 , in particular , can not have been inherited from the sun s molecular cloud in abundances consistent with ongoing galactic nucleosynthesis , and must have been late additions @xcite . a leading candidate for the source of these and other slrs is one or more core - collapse supernovae in the sun s birth environment , contaminating either its molecular cloud @xcite , or its protoplanetary disk @xcite . another leading candidate is production of slrs by irradiation ( by solar cosmic rays , essentially ) , within the solar nebula @xcite . because this latter mechanism by itself is inadequate to explain the abundance of @xmath3 in the early solar system @xcite , it is generally accepted that the source of @xmath3 is core - collapse supernovae ( e.g. * ? ? ? * ) , although it is not clear whether the source of @xmath3 is a single , nearby supernova , or many ( possibly distant ) supernovae ( as in * ? the origins of the other slrs are also debated . a correlation between @xmath0 and @xmath2 has been observed in meteorites , demanding a common source for these two isotopes _ after _ the formation of the solar nebula , as in the so called  late - injection \" hypothesis of @xcite . it is not yet clear whether these two slrs are correlated with @xmath3 . if evidence for a corelation could be found , this would strongly suggest that @xmath0 and @xmath2 were injected by the same supernova or supernovae that injected @xmath3 . the lack of such evidence , though , leaves open the possibility that @xmath0 and @xmath2 were created by irradiation within the solar nebula while @xmath3 was injected separately by one or more supernovae , into the sun s molecular cloud or protoplanetary disk . the abundances of the slrs alone have not yet enabled a discrimination between these possibilities , but ( * ? ? ? * hereafter gm07 ) have proposed that the oxygen isotopic ratios of early solar system materials may be used to rule out certain hypotheses . specifically , they argue that if @xmath0 and @xmath2 were injected by a nearby supernova into the sun s protoplanetary disk , sufficient to produce the observed meteoritic ratio @xmath4 @xcite , then the oxygen isotopic ratio of the solar nebula would be considerably altered : solar nebula materials formed before the injection would have oxygen isotopic ratios _ significantly _ different from later - formed materials . gm07 calculated the shifts in oxygen isotopic ratios accompanying injection of supernova @xmath0 into the sun s protoplanetary disk , using the isotopic yields in bulk supernova ejecta calculated by @xcite . a robust prediction of the gm07 models is that @xmath5 of pre - injection materials should be significantly higher , by several percent , than post - injection materials . examples of pre - injection materials may exist in meteorites , or especially in the solar wind sample returned by the @xmath6 mission @xcite . since preliminary results from _ genesis _ suggest the sun is _ not _ isotopically heavy in oxygen @xcite , and because no such @xmath7-rich ( or @xmath8-poor ) components have been discovered in meteorites , gm07 rule out a supernova origin for the @xmath0 and @xmath2 in meteorites . the purpose of this paper is to reproduce and refine the method pioneered by gm07 , and to test the conclusion that @xmath0 can not have a supernova origin . gm07 originally considered only bulk ejecta of spherically symmetric supernova explosions . we begin our analysis with this case , but make necessary refinements to the method , and use our current nucleosynthesis models to predict the isotopic yields . we then expand on the analysis of gm07 , calculating the isotopic yields by allowing the disk to intercept ejecta from different parts of the supernova explosion rather than a uniformly mixed total yield , and by examining anisotropic explosions . we also simultaneously consider the injection of @xmath9 into the disk . the paper is organized as follows . in  2 , we outline the method used to calculate shifts in oxygen isotopic composition due to supernova injection of @xmath0 and @xmath2 , including updates to the method of gm07 . in  3 we describe the results of nucleosynthesis simulations we have carried out , to determine the isotopic yields in supernova ejecta under various explosion scenarios . we determine the inputs needed to compute the shifts in solar nebula oxygen isotopic composition . these shifts in oxygen isotope before and after injection are presented in  4 , and in  5 we draw conclusions .","summary":"injection of material from a core - collapse supernova into the solar system s already - formed disk is one proposed mechanism for producing the short - lived radionuclides , such as and , inferred from isotopic studies of meteorites to have existed in the solar nebula . we calculate again the shifts in oxygen isotopes due to injection of supernova material in the solar nebula , using a variety of nucleosynthetic conditions of our own progenitor explosions . conversely , we argue that the existence of viable counterexamples demonstrates that it is premature to use oxygen isotopes to rule out injection of and   into the solar nebula protoplanetary disk by a nearby supernova .","abstract":"injection of material from a core - collapse supernova into the solar system s already - formed disk is one proposed mechanism for producing the short - lived radionuclides , such as and , inferred from isotopic studies of meteorites to have existed in the solar nebula . this hypothesis has recently been challenged on the basis that the injection of enough supernova material to match the meteoritic abundances of and   would produce large , measureable , and unobserved collateral effects on oxygen isotopes . here we calculate again the shifts in oxygen isotopes due to injection of supernova material in the solar nebula , using a variety of nucleosynthetic conditions of our own progenitor explosions . unlike previous studies of this type , we also consider the effect of non - homogeneity in abundance distribution of the nucleosynthesis products after the explosion . we calculate the shifts in oxygen isotopes due to injection of sufficient supernova material to produce the meteoritic abundances of and , and analyze the predicted shifts in detail for compatibility with meteoritic data . we find that the range in possible isotopic shifts is considerable and sensitive to parameters such as progenitor mass and anisotropy of the explosion ; however , a small number of compatible scenarios do exist . because of the wide range of outcomes and the sensitivity of isotopic yields to assumed conditions , it is difficult to constrain the supernova that may have led to injection of in the solar nebula . conversely , we argue that the existence of viable counterexamples demonstrates that it is premature to use oxygen isotopes to rule out injection of and   into the solar nebula protoplanetary disk by a nearby supernova ."}
{"article_id":"1010.4827","section_id":"m","document":"the method of gm07 is fairly straightforward . they assume that meteoritic components that sample the solar nebula s starting composition , _ before _ the acquisition of @xmath10 , can be identified and measured . likewise , they assume samples _ after _ the acquisition of @xmath10 can be identified and measured . any difference in the oxygen isotopic content between samples of those two groups would then constitute a shift in oxygen isotopes brought about by the injection of supernova material . the preditced shift in oxygen isotopes due to injection of supernova material into the protoplanetary disk can then be compared to the actual difference in oxygen isotopes before and after . in practice , because the vast majority of meteoritic components sample the solar nebula after injection , gm07 assumed a  final \" value for the solar nebula oxygen isotopes , and used the isotopic yields in supernova ejecta to predict the initial composition . testing the supernova injection hypothesis thus amounts to finding meteoritic inclusions with this initial oxygen isotopic composition . such inclusions should have evidence for no live @xmath10 at the time of their formation , and should be among the oldest meteoritic inclusions . the earliest - formed solids in the solar system are widely accepted to be the calcium - rich , aluminum - rich inclusions ( cais ) , both because they contain minerals that are the first solids expected to condense in a cooling solar nebula @xcite , and because their pb - pb ages are the oldest measured , at 4568.6 myr @xcite . it is worth noting that because many of the minerals in cais are condensates , their isotopic composition should reflect that of the solar nebula gas . the vast majority of cais have inferred initial ratios @xmath4 or appear to have been isotopically reset at a later date @xcite . only in a handful of cais known as  fun \" cais ( fractionation with unknown nuclear effects ) has it been possible to set firm upper limits on the initial @xmath11 ratio and show these cais did not contain live @xmath0 when they formed @xcite . thus , cais overall reflect the composition of the solar nebula at an early time , and fun cais possibly record the oxygen isotopic abundance before the solar nebula acquired @xmath0 .    to make more precise statements , it is necessary to quantify the oxygen isotopic composition of the nebula and various components . the molar fraction of oxygen in gas and rock can vary , so the relevant quantities are the ratios of the stable oxygen isotopes , @xmath12 and @xmath13 . in the field of cosmochemistry , these ratios are commonly expressed as deviations from a standard , in this case standard mean ocean water ( smow ) , which has @xmath14 and @xmath15 @xcite . the fractional deviations of the isotopic ratios from these standard values are @xmath16 and @xmath17 , and are measured in parts per thousand , or  permil \" ( @xmath18 ) . [ that is , @xmath19 . ] it is also standard to report the quantity @xmath20 , because this quantity is conserved during almost all chemical fractionation processes . [ more precisely , @xmath21 @xcite . ] it is clear that the final oxygen isotopic composition of the nebula , @xmath22 , will depend on its starting composition @xmath23 , the composition of the supernova material , @xmath24 , and the mass of supernova material injected ( relative to the mass of the disk ) . it is straightforward to show that @xmath25 where @xmath26 is the isotopic ratio of the supernova material injected into the disk , and @xmath27 measures the mass of injected oxygen relative to the oxygen present in the disk ( with a similar formula applying to @xmath28 ) . in terms of the masses involved , @xmath29 most of these terms are defineable . first , @xmath30 , where @xmath31 is the time delay between supernova injection and isotopic closure of the meteoritic materials , and @xmath32 is the mean lifetime of @xmath0 . by definition , @xmath33 @xmath34 , because sufficient @xmath0 must be injected to yield the meteoritic ratio . finally , the isotopic abundances in the solar nebula are known ( the ratio @xmath35 is taken from @xcite ) , so we derive @xmath36_{\\rm sn } } \\ , \\exp ( + \\delta t / \\tau).\\ ] ] note that @xmath37 is independent of the mass of the disk , but it increases with @xmath31 , since larger values of @xmath31 imply that more supernova material had to be injected to yield the same @xmath11 ratio , thereby implying larger isotopic shifts in oxygen associated with this injection .    besides the time delay @xmath31 , the major inputs needed to infer @xmath23 are the isotopic composition @xmath24 and ratio of @xmath8 to @xmath10 in the supernova ejecta , and the oxygen isotopic composition of the post - injection solar nebula . gm07 used bulk abundances of supernova ejecta calculated by @xcite for the first set of quantities . they also assumed that the oxygen isotopic ratios of the post - injection solar nebula matched the smow values of the present - day earth : @xmath38 . this assumption is the main reason why they concluded that the pre - injection solar nebula had to be @xmath7-rich , as we now demonstrate . rearranging equation  [ eq : shift ] yields @xmath39 supernova ejecta tend to be @xmath8-rich ; in the extreme limit , @xmath40 . if @xmath41 also , then @xmath42 . that is , @xmath43 is inferred to have been positive and potentially quite large if @xmath44 . the isotopic yields of the supernova ejecta computed by @xcite were consistent with such large values of @xmath37 and @xmath45 , leading gm07 to conclude that generally @xmath46 . indeed , for progenitor masses @xmath47 , gm07 inferred @xmath48 to @xmath49 . since there are no early - formed meteoritic components with @xmath50 this high , and because the oxygen isotopic composition of the sun appears to be consistent with @xmath51 @xcite , gm07 ruled out supernova injection of @xmath0 and @xmath2 . this conclusion depends on a few key assumptions that we update below . we consider the starting composition of the solar nebula , and take into account the non - homogeneity of supernova ejecta . oxygen isotopic ratios potentially can test or rule out the supernova injection hypothesis , but several caveats must be applied to the method of gm07 . the first and most important correction involves the oxygen isotopic composition of the solar nebula immediately before and after the injection of supernova material . gm07 assumed the post - injection composition was equal to smow ; however , smow is widely understood _ not _ to reflect the oxygen isotopic ratios of the solar nebula immediately after injection . on a three - isotope diagram of @xmath16 versus @xmath17 , the oxygen isotopes of planetary and meteoritic materials are arrayed along a mixing line called the carbonaceous chondrite anhydrous mineral ( ccam ) line discovered by @xcite . after correcting for isotopic fractionation by thermal and chemical processes , @xcite inferred a mixing line with slope 1.0 in the three - isotope diagram , and so we will refer to this mixing line as the  slope-1 \" line . today the oxygen isotopic composition of the earth ( smow ) is widely recognized to reflect a mixture of an isotopically lighter rocky component ( to which cais belong ) , and an isotopically heavy reservoir ( e.g. * ? ? ? * ; * ? ? ? it is very likely that this component is isotopically heavy water , with @xmath52 @xcite . the existence of isotopically heavy water is supported by the discovery ( in the primitive carbonaceous chondrite acfer 094 ) of a poorly characterized product of aqueous alteration , with @xmath53 @xcite . quite possibly this heavy water is the result of a mass - dependent photodissociation of co in the outer solar nebula by an external ultraviolet source @xcite . the photodissociation can be isotopically selective because the different isotopologues of co molecules can self - shield ; @xmath54 and @xmath55 are optically thin and dissociate more completely , releasing @xmath7 and @xmath56 atoms that react with @xmath57 to form isotopically heavy water , while the abundant molecule @xmath58 is more optically thick and does not as completely dissociate . the light co molecule is eventually lost with the nebular gas . whatever the source of the isotopically heavy component , smow only represents a late stage in nebular evolution , and does not represent the state of the nebula immediately after injection of supernova material . applying the same reasoning , it is likely that the starting composition of the solar nebula was lower ( more @xmath8-enriched ) on the slope-1 line than most cais . the majority of cais tend to cluster near @xmath59 @xmath60 , i.e. , @xmath61 ( see * ? ? ? * and references therein ) ; but many of the most primitive and unaltered cais cluster near @xmath62 @xmath63 , or @xmath64 @xcite . likewise , @xcite report @xmath65 for  mineralogically pristine \" cais . cais also contain grains of hibonite , spinel , and corundum , which are among the first minerals expected to condense from a cooling gas of solar composition @xcite , and which are presumably even more primitive than cais themselves . @xcite report that hibonite grains are also found to cluster near @xmath66 , or @xmath67 , while @xcite observed 4 hibonite grains from allende and semarkona to have oxygen isotopes in the range @xmath68 to @xmath69 . they also found that spinel grains from the cv chondrite allende had @xmath70 , and that corundum grains from the cm chondrite semarkona clustered strongly in the range @xmath71 . @xcite likewise report @xmath71 for primitive cais and amoeboid olivine aggregates , which are also believed to have condensed from solar nebula gas . from these results we infer that @xmath72 in the solar nebula immediately after the injection of supernova material . meteoritic and other samples also constrain the initial ( pre - injection ) oxygen isotopic composition of the solar nebula , and find it to be very similar . as described above , very firm and low upper limits to initial @xmath11 exist for fun cais that mark them as having formed before the injection of @xmath0 and @xmath2 @xcite . @xcite have identified a fractionation line associated with the fun cais with @xmath73 that passes through @xmath74 . presumably the original isotopic composition of the nebula matched that of the sun , which might therefore be measured by _ mission @xcite . preliminary measurements can be interpreted as clustering on a fractionation line with @xmath75 @xcite , which would intersect the slope-1 line at @xmath76 , and other analyses suggest @xmath77 [ @xmath78 errors ] @xcite .    from these results it seems likely that the original solar nebula oxygen isotopic composition was near the _ genesis _ preliminary result of @xmath79 , or possibly much lower along the slope-1 line . subsequent reaction of rock with a @xmath8-depleted reservoir then moved material along the slope-1 line to @xmath59 @xmath60 , where most cais are found ( * ? ? ? * and references therein ) . fun cais appear to represent an intermediate stage in this process , only partially evolved along the slope-1 line . to fix values , we will simply assume the solar system protoplanetary disk isotopic ratios started as @xmath80 . the above discussion changes the criterion by which one can reject the supernova injection hypothesis . because gm07 assumed an initial solar nebula composition near smow , they concluded that pre - injection samples necessarily would have had @xmath81 , and the lack of such samples in meteorites ruled out the hypothesis . but we assert that the supernova injection hypothesis can be ruled out only if injection of supernova material necessarily shift the oxygen isotopic composition of the solar nebula from a composition near @xmath82 to one far off the slope-1 line , or one on the slope-1 line but with @xmath83 . in this way , the gm07 method of using oxygen isotopic constraints might still allow a test of the supernova injection hypothesis . there are at least three scenarios wherein the shift in oxygen isotopes following injection of supernova material can be consistent with the above constraints . from equation  [ eq : shift ] , it is seen that even if the supernova ejecta and the protoplanetary disk differ in oxygen isotopic composition by hundreds of permil , the shift in oxygen isotopes may be small ( @xmath84 permil ) if the injected mass is small , so that @xmath85 . more precisely , if @xmath0 and the other slrs are injected by a supernova into the solar nebula disk , then the magnitude of the shift in oxygen isotopes will depend on the fraction of ejecta oxygen that accompanies al . in this first scenario , o and al may be significantly fractionated during delivery of the ejecta to the solar nebula . for example , @xcite find that effectively only material condensed from the supernova ejecta into large ( @xmath86 radius ) grains can be injected directly into a protoplanetary disk . in the extreme event that the only grains that entered the protoplanetary disk were corundum ( @xmath87 ) grains , the isotopic shifts in oxygen would be negligible ( @xmath88 ) . or , if only 10% of the oxygen in the ejecta condensed into grains , and 90% remained in gas that was excluded from the disk , then the isotopic shifts in oxygen isotope ( for a given amount of injected @xmath0 ) would be 10 times smaller than predicted by gm07 . it is therefore not possible to determine the shifts in oxygen isotopes following injection into a disk without quantifying the degree to which o and al are fractionated between gas and solids . in what follows , we assume no fractionation , as such a calculation is beyond the scope of the present investigation ; but we consider dust condensation in supernova ejecta to be a very important effect , one that potentially could significantly reduce the predicted isotopic shifts .    in the second scenario , the shifts in oxygen isotopes could also remain small if the injected material was simply higher than expected in @xmath0 ( or lower in o ) , so that again @xmath85 . the calculations of gm07 relied on the _ bulk _ abundances calculated by @xcite . that is , gm07 assumed that the injected material uniformly sampled the entirety of the supernova ejecta . such a uniform sampling is unlikely , as supernovae often do explode in a clumpy fashion and asymmetrically . it has long been understood that asymmetries or hydrodynamic instabilities may disrupt the stratification of the progenitor star , but they do not result in large scale compositional mixing ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the x - ray elemental maps of the cassiopeia a supernova remnant @xcite dramatically demonstrate that massive stars are likely to explode as thousands of clumps of material , each sampling different burning zones within the progenitor . @xcite have argued that this may be a near - universal feature of core - collapse supernovae ; at the very least , observations do not rule out this possibility . so it is more than possible that the solar nebula received materials from only limited regions within the ejecta in which the @xmath89 ratio could have varied considerably from the average value for the ejecta . the non - uniformity of the @xmath89 ratio may be magnified if the star explodes asymmetrically , allowing explosive nucleosynthesis to proceed differently even in parcels of gas in the same burning zone . finally , in the third scenario by which isotopic shifts may conform to measurements , @xmath37 need not be small , and the isotopic shifts may approach @xmath90 in magnitude , so long as the injection moved the composition _ up _ the slope-1 line by @xmath91 ( i.e. , the change in @xmath16 equalled the change in @xmath17 , both being @xmath92 ) , or _ down _ the slope-1 line by a comparable or even larger amount . a shift from an initial composition @xmath93 , consistent with @xmath6 measurements of the sun s composition , to @xmath94 , consistent with primitive meteoritic components , would not conflict with the data . alternatively , a shift from an initial composition @xmath93 , to @xmath95 , or even @xmath96 , followed by mixing with the @xmath8-poor reservoir that moves solar nebula solids up the slope-1 line , would also conform to the data .    in the next section we compute the isotopic yields in core - collapse supernovae of various progenitor masses , both in spherically symmetric explosions ( as considered by * ? ? ? * ) and asymmetric explosions . these calculations allow us to predict the oxygen isotopic composition @xmath24 and the ratio @xmath37 of the supernova material at various locations within the explosion , to assess the range of possible isotopic shifts under the second and third scenarios . a supernova injection scenario would be ruled out , _ unless _ either the injection of material results in small overall shifts ( i.e. the injected material contains a high   abundance relative to oxygen , or vice versa , a low oxygen abundance relative to al ) , or the oxygen isotopes are shifted along the slope-1 line , in which case shifts of up to @xmath9710 permil in either direction are allowed .","summary":"this hypothesis has recently been challenged on the basis that the injection of enough supernova material to match the meteoritic abundances of and   would produce large , measureable , and unobserved collateral effects on oxygen isotopes . here we find that the range in possible isotopic shifts is considerable and sensitive to parameters such as progenitor mass and anisotropy of the explosion ; however , a small number of compatible scenarios do exist . because of the wide range of outcomes and the sensitivity of isotopic yields to assumed conditions , it is difficult to constrain the supernova that may have led to injection of in the solar nebula .","abstract":"injection of material from a core - collapse supernova into the solar system s already - formed disk is one proposed mechanism for producing the short - lived radionuclides , such as and , inferred from isotopic studies of meteorites to have existed in the solar nebula . this hypothesis has recently been challenged on the basis that the injection of enough supernova material to match the meteoritic abundances of and   would produce large , measureable , and unobserved collateral effects on oxygen isotopes . here we calculate again the shifts in oxygen isotopes due to injection of supernova material in the solar nebula , using a variety of nucleosynthetic conditions of our own progenitor explosions . unlike previous studies of this type , we also consider the effect of non - homogeneity in abundance distribution of the nucleosynthesis products after the explosion . we calculate the shifts in oxygen isotopes due to injection of sufficient supernova material to produce the meteoritic abundances of and , and analyze the predicted shifts in detail for compatibility with meteoritic data . we find that the range in possible isotopic shifts is considerable and sensitive to parameters such as progenitor mass and anisotropy of the explosion ; however , a small number of compatible scenarios do exist . because of the wide range of outcomes and the sensitivity of isotopic yields to assumed conditions , it is difficult to constrain the supernova that may have led to injection of in the solar nebula . conversely , we argue that the existence of viable counterexamples demonstrates that it is premature to use oxygen isotopes to rule out injection of and   into the solar nebula protoplanetary disk by a nearby supernova ."}
{"article_id":"1010.4827","section_id":"c","document":"as @xcite strongly advocated , injection of supernova ejecta can produce measurable  collateral damage \" to stable isotope systems in protoplanetary disks . gm07 in particular point to the role of oxygen isotopes in constraining this process . the point of that paper was that the injection of @xmath0 ( and @xmath2 ) from a single nearby supernova necessarily would have brought in significant levels of oxygen isotopically distinct from the pre - injection solar nebula . the solar nebula after injection , they argued , would differ in its oxygen isotopes by several tens of permil from the pre - injection values , which they robustly predicted would be more @xmath7-rich than the solar nebula . they cited the _ measurements of solar wind oxygen as those most likely to sample the pre - injection solar nebula . since preliminary results from _ genesis _ @xcite(mckeegan et al . 2009 , 2010 ) are revealing the sun to be @xmath8-rich , gm07 would rule out injection of @xmath0 and @xmath2 from a single supernova .    in this paper , we attempted to reproduce the calculations of gm07 , to apply their method of using oxygen isotopes to test the supernvoa injection hypothesis . we made necessary corrections to their method , mostly in regard to the presumed oxygen isotopic composition of the ( post - injection ) solar nebula . gm07 assumed this was identical to smow , meaning the pre - injection solar nebula had to be more @xmath280-rich than almost any known inclusions . we presented considerable evidence that the post - injection composition was in fact much more @xmath8-rich than that , closer to @xmath352 . we carried out stellar nucleosynthesis calculations , to calculate the isotopic yields of @xmath0 , @xmath2 and oxygen isotopes in a variety of supernova explosion scenarios , including the 1d ( spherically symmetric ) cases as well as 3d ( asymmetric ) explosions . because @xmath0 and @xmath2 are observed to be correlated @xcite , we also simultaneously considered injection of @xmath2 into the solar nebula . we then computed the shifts in oxygen isotopes and the final @xmath290 ratio in the solar nebula following injection of sufficient supernova material to produce the meteoritic ratio @xmath353 . our 1d simulations largely confirm the results of gm07 , that isotopic shifts are likely to be tens of permil and to make the solar nebula more @xmath8-rich than before the injection . we found that injection of material from either the bulk or the explosive c / ne burning and sub - explosive c burning regions of supernovae moved the composition of the solar nebula down the slope 1 line . our @xmath283 progenitors led to isotopic shifts in oxygen which moved the composition of the solar nebula down the slope-1 line , with the less energetic explosions producing larger shifts and time delays . the 23 m progenitors , which were the most energetic of the @xmath283 cases and especially effective in producing @xmath0 , generated shifts that amounted to only @xmath354 , including a time delay of 0.7 myr for @xmath2 to decay to its meteoritic value . this scenario , at least , is consistent with all the applied meteoritic constraints . if less than 100% of the oxygen penetrated the solar nebula material due to , for example , dust condensation , all but one of the 1d cases are consistent with the evidence from the early solar system . we note that this conclusion differs from what gm07 infer for injection of bulk ejecta from 21 and @xmath355 progenitors . gm07 likewise found isotopic shifts downward along the slope-1 line , but with a magnitude of 40 to 50 permil . it is worth noting that had gm07 assumed the same starting composition for the solar nebula , @xmath352 , that we do , then they would have found the solar nebula oxygen isotopic composition to be @xmath356 after injection of supernova material from an @xmath355 progenitor , and @xmath357 after injection of supernova material from an @xmath358 progenitor . although these shifts are moderately large , they are _ down _ the slope-1 line . as we established in  [ magofshifts ] , this would not have been _ in_compatible with the meteoritic constraints , as some very @xmath8-rich meteoritic samples in this range are known , including cais in isheyevo , at @xmath359 @xcite , and a ferromagnesian cryptocrystalline chondrule in the ch chondrite acfer 214 , at @xmath360 @xcite . subsequently the mass - independent fractionation process would have shifted the nebula upward along the slope-1 line , erasing this isotopic shift and eventually producing the composition @xmath361 common to most cais ( e.g. * ? ? ? we conclude that the supernova injection hypothesis can not be rejected based on 1d models . our investigation of other parameters suggest that it is even more difficult to be conclusive about supernova injection . we have considered a small number of progenitor masses undergoing spherically symmetric collapse ; in a few cases we varied other parameters , such as varying the explosion energy , or allowing for loss of a hydrogen envelope in a binary scenario , or allowing an asymmetrical explosion . in most of these cases the isotopic shifts in oxygen were large . among the cases considered here , the final @xmath16 values in the solar nebula varied from @xmath228 to @xmath362 , and the final @xmath17 values varied from @xmath228 to @xmath363 . as gm07 found , most of the cases where meteoritic abundances of are injected lead to large ( @xmath364 ) shifts in oxygen isotopes . we also considered the yields in a 3d anisotropic explosion of a @xmath291 progenitor , in the bulk ejecta and two @xmath0-rich zones analogous to those in the 1d explosions . we find that a wide range of outcomes is possible , with oxygen isotopic shifts as large as hundreds of permil , or as low as @xmath289 . the fact that @xmath139 can decay to @xmath365 instead of @xmath56 at high temperatures makes the yield of @xmath56 especially sensitive to the thermodynamic trajectory of the ejecta , which partially accounts for the spread in the @xmath102 yields . on the one hand , the wide range of possible outcomes makes it nearly impossible to state conclusively that all supernova injection scenarios can be ruled out . on the other hand , the wide range of possible outcomes seems to imply a degree of fine tuning so that the oxygen isotopic shifts in the solar nebula were not large , especially for the 3d case . we conclude that the hypothesis , that the @xmath0 in the solar nebula was due to supernova material injected into the sun s protoplanetary disk , can still be made compatible with meteoritic constraints , under two scenarios . the first is that the injected supernova material came from either the bulk ejecta , or from a region in a supernova that experienced thermodynamic conditions like the subexplosive c burning zone . the latter is more physically likely . with a @xmath366 myr time delay , the injection would have moved the solar nebula oxygen isotopic composition from @xmath82 to a more @xmath287-rich value along the slope one line . all but one of our explosions produce movement along the slope 1 line . we produce shifts as small as @xmath367 , which would have produced an accompanying meteoritic ratio @xmath292 . subsequent mixing of rocky material with a @xmath8-depleted reservoir would have then moved the composition of meteoritic inclusions up the slope-1 line to values @xmath66 , consistent with primitive cais , and further up the slope-1 line with time . the second scenario is one in which only dust grains are injected in to the protoplanetary disk , and very little of the supernova oxygen condenses into dust grains . if only the most refractory grains such as corundum were injected , then potentially @xmath368 , and the isotopic shifts would be negligible ( @xmath369 ) , for nearly all the cases considered here . it is worth noting that ca is equally refractory to al and is likely to condense from supernova ejecta under the same conditions that al condenses , so the meteoritic abundance of @xmath2 could still be matched following injection of @xmath0 . @xcite have calculated that only @xmath370 of gas - phase ejecta are injected into a disk . if almost all of the ca and al in the ejecta are locked up in large grains ( radii @xmath371 ) that are efficiently injected @xcite , but less than a few percent of the oxygen is , then potentially all of the isotopic shifts in oxygen calculated here should be reduced by a factor of about 100 . essentially all of the 1d cases considered here would then conform with the meteoritic constraints , and even some of the 3d cases as well . to summarize , we agree with gm07 that oxygen isotopes can be a powerful constraint on supernova injection models . our calculations of oxygen isotopic shifts following injection from the bulk ejecta of 1d supernovae broadly match the results of gm07 . had gm07 assumed the same starting composition of the solar nebula that we did , and considered a smaller time delay between injection and isotopic closure , they would have found isotopic shifts for @xmath372 progenitors that would not be inconsistent with meteoritic constraints . our own calculations of the same case predict shifts that are similar , although smaller in magnitude , and which are also consistent with meteoritic constraints . the existence of an example that is consistent with the oxygen isotopic composition and the @xmath290 ratio of the solar nebula means that the supernova injection hypothesis can not be ruled out . because the nucleosynthesis of oxygen differs in asymmetric explosions , a much wider range of oxygen isotopes is possible in 3d explosions . because of the contingent nature of the injection it becomes difficult to make any statement about the possibility that the solar nebula acquired @xmath0 from such an asymmetric explosion . finally , all oxygen isotopic shifts are reduced if only large grains are injected into the protoplanetary disk , and only a small fraction of oxygen condenses into large grains . quantifying the fractionation of al and o during injection into a protoplanetary disk is the focus of ongoing work by this research group . if only a few percent of the total oxygen is injected , then nearly all the 1d explosions considered here could be consistent with the meteoritic constraints on oxygen isotopes and @xmath2 abundances . we therefore conclude it is premature to rule out the supernova injection hypothesis based on oxygen isotopes .","summary":"we calculate the shifts in oxygen isotopes due to injection of sufficient supernova material to produce the meteoritic abundances of and , and analyze the predicted shifts in detail for compatibility with meteoritic data .","abstract":"injection of material from a core - collapse supernova into the solar system s already - formed disk is one proposed mechanism for producing the short - lived radionuclides , such as and , inferred from isotopic studies of meteorites to have existed in the solar nebula . this hypothesis has recently been challenged on the basis that the injection of enough supernova material to match the meteoritic abundances of and   would produce large , measureable , and unobserved collateral effects on oxygen isotopes . here we calculate again the shifts in oxygen isotopes due to injection of supernova material in the solar nebula , using a variety of nucleosynthetic conditions of our own progenitor explosions . unlike previous studies of this type , we also consider the effect of non - homogeneity in abundance distribution of the nucleosynthesis products after the explosion . we calculate the shifts in oxygen isotopes due to injection of sufficient supernova material to produce the meteoritic abundances of and , and analyze the predicted shifts in detail for compatibility with meteoritic data . we find that the range in possible isotopic shifts is considerable and sensitive to parameters such as progenitor mass and anisotropy of the explosion ; however , a small number of compatible scenarios do exist . because of the wide range of outcomes and the sensitivity of isotopic yields to assumed conditions , it is difficult to constrain the supernova that may have led to injection of in the solar nebula . conversely , we argue that the existence of viable counterexamples demonstrates that it is premature to use oxygen isotopes to rule out injection of and   into the solar nebula protoplanetary disk by a nearby supernova ."}
{"article_id":"1108.1680","section_id":"i","document":"the determination of conditional independence relationships through graphical models is a key component of the statistical analysis of observational studies . a pertinent example we will focus on in this paper is a functional disability data set extracted from the `` analytic '' data file for the national long term care survey ( nltcs ) created by the center of demographic studies at duke university . each observed variable is binary and corresponds to a measure of disability defined by an activity of daily living . this contingency table cross - classifies information on elderly aged @xmath0 and above pooled across four survey waves , 1982 , 1984 , 1989 and 1994see @xcite for more details . the @xmath1 dimensions of this table correspond to six activities of daily living ( adls ) and ten instrumental activities of daily living ( iadls ) . specifically , the adls relate to hygiene and personal care : eating ( adl1 ) , getting in / out of bed ( adl2 ) , getting around inside ( adl3 ) , dressing ( adl4 ) , bathing ( adl5 ) and getting to the bathroom or using a toilet ( adl6 ) . the iadls relate to activities needed to live without dedicated professional care : doing heavy house work ( iadl1 ) , doing light house work ( iadl2 ) , doing laundry ( iadl3 ) , cooking ( iadl4 ) , grocery shopping ( iadl5 ) , getting about outside ( iadl6 ) , travelling ( iadl7 ) , managing money ( iadl8 ) , taking medicine ( iadl9 ) and telephoning ( iadl10 ) . for each adl / iadl measure , subjects were classified as being either healthy ( level 1 ) or disabled ( level 2 ) on that measure . the methodology we develop in this paper allows us to determine the complex pattern of conditional associations that exist among the @xmath1 daily living activities . this represents a critical issue that was left unexplored in previous analyses of this data set [ @xcite ; @xcite ] . in fact , the domain of applicability of our methods is not restricted to contingency tables . since multivariate data sets arising from social science or economics typically contain variables of many types , our goal is to develop an approach to graphical model determination that is broad enough to be applicable to any study that involves a mixture of binary , ordinal and continuous variables . most of the research efforts in the graphical models literature have been focused on multivariate normal models or on log - linear models  see , for example , the monographs of @xcite and @xcite . these models relate to data sets that contain exclusively continuous or categorical variables . cg distributions [ @xcite ] constitute the basis of a class of graphical models for mixed variables , but they impose an overly restrictive assumption : the conditional distribution of the continuous variables given the discrete variables must be multivariate normal . as such , the three main classes of graphical models are too restrictive to be widely applicable to social science or economics studies .    copulas [ @xcite ] provide the theoretical framework in which multivariate associations can be modeled separately from the univariate distributions of the observed variables . @xcite advocate the use of copulas when modeling multivariate distributions involving discrete variables . in this paper we employ the gaussian copula and further require conditional independence constraints on the inverse of its correlation matrix . the resulting models are called copula gaussian graphical models ( cggms ) because they only impose a multivariate normal assumption for a  set of latent variables which are in a one - to - one correspondence with the set of observed variables . a related approach for inference in gaussian copulas has been developed by @xcite . their framework involves parametric models for gaussian copulas and the univariate marginal distributions of the observed variables.we treat these marginal distributions as nuisance parameters and focus on the determination of graphical models . the structure of the paper is as follows . in section [ sec : bayeslearn ] we formally introduce gaussian graphical models ( ggms ) and describe a bayesian framework for inference in this class of models . in section [ sec : ordcar ] we discuss modeling aspects related to binary and ordinal variables . in section [ sec : copulaggm ] we show how to extend ggms to represent conditional independence associations in a latent variables space . we also present a bayesian model averaging approach for graph identification and estimation in cggms . in section [ sec : examples ] we analyze the nltcs functional disability data together with another six - dimensional contingency table using cggms . we discuss our proposed methodology in section [ sec : discussion ] .","summary":"we propose a comprehensive bayesian approach for graphical model determination in observational studies that can accommodate binary , ordinal or continuous variables simultaneously . our new models are called copula gaussian graphical models ( cggms ) and embed graphical model selection inside a semiparametric gaussian copula . the domain of applicability of our methods is very broad and encompasses many studies from social science and economics .","abstract":"we propose a comprehensive bayesian approach for graphical model determination in observational studies that can accommodate binary , ordinal or continuous variables simultaneously . our new models are called copula gaussian graphical models ( cggms ) and embed graphical model selection inside a semiparametric gaussian copula . the domain of applicability of our methods is very broad and encompasses many studies from social science and economics . we illustrate the use of the copula gaussian graphical models in the analysis of a  16-dimensional functional disability contingency table .    ."}
{"article_id":"physics0404025","section_id":"i","document":"the recent developments in the cooling and trapping techniques of neutral atoms have opened the way to the realization of fermionic atomic samples at temperatures well below the degeneracy temperature  @xcite . this suggests that atomic gases are ideal candidates for the study of the physics of degenerate many - fermion systems . with respect to solid state ones , atomic systems offer in fact a better isolation from external disturbances such as material defects , a better knowledge of the microscopic details of the systems , as well as a wider range of tunability of the parameters , in particular the interparticle interactions . by tuning the external magnetic field around a feshbach resonance , the atom - atom scattering length @xmath0 can be varied from @xmath1 to @xmath2 ( @xmath3 being the fermi momentum ) opening the way towards a comprehensive study of the pairing transition both in the regime @xmath4 in which a bose - condensate ( bec ) of tightly - bound molecules is present , and in the regime @xmath5 ( bcs ) in which a condensate of cooper pairs is formed . diatomic molecules have been created and observed by several experimental groups  @xcite . bose - einstein condensation of tightly bound diatomic molecules has been recently reported  @xcite . the crossover region between bec and bcs is currently under experimental investigation  @xcite and first evidences of pairing in the crossover region have been reported in  @xcite . from the theoretical point of view , a large effort is currently made to establish the main features of the pairing for high values of the scattering length @xmath6 , regime in which the atomic gas shows strong correlations  @xcite . in particular , the dependance of the transition temperature on the interaction strength in this crossover region is still an open problem . the present paper reports a numerical study of the condensation of pairs in a regime of relatively strong interactions , so to characterize the consequences of the transition on the different observables of the system and identify specific features which may represent unambiguous signatures of the onset of condensation of pairs . the calculations have been performed by applying the quantum monte carlo ( qmc ) method developed in  @xcite to a one - dimensional lattice model of fermions with attractive on - site interactions . a short description of the model under examination is given in sec . [ sec : model ] , while the numerical algorithm used for the calculations is presented in sec . [ sec : qmc ] . numerical results are presented in sec . [ sec : results ] and then extensively compared to the predictions of a perturbative expansion in the interaction coupling constant ( sec . [ sec : pert ] ) , and of existing approximate approaches ( sec.[sec : exist ] ) , such as the bcs theory  @xcite , two versions of the random phase approximation ( rpa )  @xcite as well as the nozires schmitt - rink theory  @xcite . several among the most relevant correlation functions of the fermi gas have been considered here , in particular the opposite - spin density - density correlation function @xmath7 , the first - order pair coherence function @xmath8 and the second - order momentum space correlation function @xmath9 . the density - density correlation function has been already the object of several papers studying the experimental signatures of the bcs transition in atomic fermi systems , e.g.  @xcite , while the first - order pair coherence function is the counterpart , in a non - symmetry - breaking approach , of the order parameter of the phase transition in a landau - ginzburg theory  @xcite .","summary":"the possibility of revealing the onset of the transition with other observables such as the density - density correlations or the second - order momentum space correlations is discussed .","abstract":"a recently developed quantum monte carlo algorithm based on the stochastic evolution of hartree - fock states has been applied to compute the static correlation functions of a one - dimensional model of attractively interacting two component fermions . the numerical results have been extensively compared to existing approximate approaches . the crossover to a condensate of pairs can be identified as the first - order pair coherence extending throughout the whole size of the system . the possibility of revealing the onset of the transition with other observables such as the density - density correlations or the second - order momentum space correlations is discussed ."}
{"article_id":"physics0404025","section_id":"r","document":"a monte carlo code based on the stochastic approach described in the previous section has been used to numerically compute the expectation values of some one- and two - body correlation functions for a one - dimensional fermi gas with attractive binary interactions as described by the hamiltonian ( [ eq : hamilt ] ) with @xmath75 . the results of analogous calculations performed with a very similar monte carlo algorithm have been reported recently in  @xcite . other quantum monte carlo schemes have also been applied to the numerical study of the fermionic hubbard model with attractive interactions at finite temperature . in particular , the determinantal qmc algorithm  @xcite has been used to study the correlation functions in 2d  @xcite and the transition temperature to a pair condensate state in 2d  @xcite and in 3d  @xcite .    for our simulations , a lattice of @xmath76 points was taken , with a total number of @xmath77 atoms . a number @xmath63 of imaginary - time steps comprised between @xmath78 and @xmath79 has been used . as already mentioned , the ensemble in which observables are calculated is the canonical one ; note that the number of particles in each of the spin state can fluctuate , only the total number of particles is fixed . as the two spin components are equivalent , the mean densities in each of the spin components are equal : @xmath80 the state of the gas in the absence of interactions and at @xmath81 is depicted in fig . [ fig : schema ] : in a given spin component , the 5 lowest - lying single particle energy levels are totally filled , whereas the two degenerate states of wavevectors @xmath82 and @xmath83 are half - filled . more precisely , 10 atoms are frozen in the states of @xmath84 , and the two remaining atoms are distributed among the 4 degenerate states , @xmath85 , which can be done in @xmath86 different ways . in presence of attractive interactions , this degeneracy will obviously be lifted and the configurations with one atom @xmath87 and one atom @xmath88 with opposite momenta in the degenerate multiplicity are favorable to the formation of a cooper pair .     atoms and @xmath76 grid points . each mode is a plane wave with a wavevector @xmath89 and an energy @xmath90 , where the integer @xmath91 ranges from @xmath92 to @xmath93 . the modes with @xmath94 are totally filled , whereas the modes with @xmath95 are half - filled , the higher energy modes being empty . @xmath96 is the fermi energy . the energies are here in units of @xmath97 . [ fig : schema],width=377 ]       for different values of the temperature @xmath98 ( circles , squares , diamonds ) . @xmath77 atoms on a @xmath76 points lattice . coupling constant @xmath99 . [ fig : g1uumc],width=377 ]    the simplest observable to compute is the one - body correlation function in a single spin state @xmath55 ( normalized to the density @xmath100 ) : @xmath101 the monte carlo prediction is plotted in fig.[fig : g1uumc ] for different values of the temperature : as expected , this correlation function is short - ranged , coherence extending only on a length of the order of the fermi length @xmath102 for @xmath103 . this correlation function is indeed the fourier transform of the momentum distribution of the gas . as the interactions affect the momentum distribution only in a thin region around the fermi surface ( the fermi points in our one - dimensional geometry ) , they do not significantly modify its shape as compared to the ideal fermi distribution . because of the rotational symmetry of the density operator in the spin space , the one - body correlation function in different spin states : @xmath104 is instead always identically vanishing . density - density correlation functions are another observable of interest . both the single - spin density - density correlation function : @xmath105 and the opposite - spin one : @xmath106 with @xmath107 , have been calculated by monte carlo and plotted as a function of @xmath11 respectively in fig.[fig : g2mc]a and in fig.[fig : g2mc]b . in fig.[fig : g2udc_t ] , we have plotted @xmath108 as a function of temperature . the magnitude of actual density correlations is quantified by the difference @xmath109 .     and @xmath110 for different values of the temperature @xmath98 ( circles , squares , diamonds ) . same system parameters as in fig.[fig : g1uumc ] . [ fig : g2mc],title=\"fig:\",width=302 ]   and @xmath110 for different values of the temperature @xmath98 ( circles , squares , diamonds ) . same system parameters as in fig.[fig : g1uumc ] . [ fig : g2mc],title=\"fig:\",width=302 ]    : @xmath111 as a function of the temperature @xmath28 in the canonical ensemble . circles : monte carlo results . dotted , short dashed , long dashed , solid lines : perturbative results upto order respectively 0 , 1 , 2 , and 3 . same system parameters as in fig.[fig : g1uumc ] . the vertical line is the somewhat arbitrary lower bound on the temperature range where perturbation theory converges rapidly . [ fig : g2udc_t],width=377 ]    on one hand , the density correlations in a single spin state described by @xmath112 show a short - range hole ( pauli hole ) of width similar to the bump of the one - body correlation function @xmath113 and are weakly affected by the interactions and by the temperature variations ( fig.[fig : g2mc]a ) . on the other hand , the density correlations between opposite spins described by @xmath114 show an interesting temperature dependence in the presence of attractive interactions . the lower is the temperature , the most effective are in fact the interactions and therefore the stronger the bunching of opposite spin particles on a given lattice site . in fig.[fig : g2mc]b we have plotted the spatial profile of @xmath115 for different values of the temperature : for the lowest value of @xmath116 , notice not only the increase of @xmath117 , but also the appearance of oscillations as a function of @xmath11 . as we shall see in the next subsection , at this temperature a condensate of pairs is present . the oscillations then result from the contribution of two distinct effects : the friedel oscillations in the correlation functions of the normal phase which follow from the sharpness of the fermi surface  @xcite , and the oscillations shown by the cooper pair wavefunction described within the bcs theory by the pairing function @xmath118 . in fig.[fig : g2udc_t ] we have summarized the values of @xmath108 as a function of the temperature . notice that @xmath119 is appreciable already at the highest temperature considered in fig.[fig : g2udc_t ] , which , as we shall see in the next subsection , is much higher than the critical temperature @xmath120 for the appearance of long - range order . it is believed in statistical physics that the superfluid transition in two - component fermi systems with attractive binary interactions is related to the appearance of long - range order in the so - called _ anomalous _ averages  @xcite . in symmetry breaking theories such as the bcs one , this feature corresponds to a non - vanishing value for the gap function defined as : @xmath121 which plays the role of the order parameter of the phase transition in a ginzburg - landau approach . in number conserving approaches , quantities like ( [ eq : anomalous ] ) are zero . the phase transition however still appears in the long - range behaviour of correlation functions of the form : @xmath122 a similar criterion was used in  @xcite to determine the transition temperature . a simple physical interpretation of @xmath123 can be provided as the first order correlation function of pairs : the operator @xmath124 annihilates in fact a pair of particles in opposite spin states at the spatial position @xmath125 and the operator @xmath126 creates them back at @xmath11 . this correlation function is therefore formally equivalent to the first order coherence function of a composite boson formed by a pair of fermions with opposite spins . from this point of view , the non - vanishing long - range limit of @xmath127 is a signature of a quantum condensation of pairs .     for two different temperatures @xmath128 ( left panel ) and @xmath129 ( right panel ) in the canonical ensemble . circles : monte carlo results . dotted , dashed , solid lines in left panel : perturbative results upto order respectively 0 , 1 and 2 ( orders 1 and 2 are undistinguishable ) . dotted , short dashed , long dashed , solid lines in right panel : perturbative results upto order respectively 0 , 1 , 2 , and 3 . same system parameters as in fig.[fig : g1uumc ] . [ fig : g1pairmc],title=\"fig:\",width=302 ]   for two different temperatures @xmath128 ( left panel ) and @xmath129 ( right panel ) in the canonical ensemble . circles : monte carlo results . dotted , dashed , solid lines in left panel : perturbative results upto order respectively 0 , 1 and 2 ( orders 1 and 2 are undistinguishable ) . dotted , short dashed , long dashed , solid lines in right panel : perturbative results upto order respectively 0 , 1 , 2 , and 3 . same system parameters as in fig.[fig : g1uumc ] . [ fig : g1pairmc],title=\"fig:\",width=302 ]     pair coherence function @xmath130 as a function of the temperature @xmath28 . circles : monte carlo results in the canonical ensemble . solid line : bcs theory . same system parameters as in fig.[fig : g1uumc].,width=377 ]    monte carlo simulations for this quantity are shown in fig.[fig : g1pairmc ] . at low temperatures , @xmath127 has a finite value also for @xmath131 , i.e. at the largest distance from @xmath125 allowed by the finite size of the box . on the other hand , at higher temperatures , but still much lower than the fermi temperature , @xmath130 becomes very small and the long - range order is destroyed . to make this cross - over more apparent , we have plotted in fig . [ fig : g1pairc_t ] the value of @xmath130 as a function of the temperature : a sudden rise of this quantity appears at low temperatures . this behavior qualitatively corresponds to the one expected for a bcs transition : although a bcs transition can not occur in one dimension in the thermodynamical limit because of long wavelength fluctuations destroying the long range order @xcite , it can however be observed in our simulations because of the finite size of the system . as the system is finite , the transition temperature @xmath120 is not precisely defined and the long - range order has an analytic dependance on temperature . notice that the opposite spin density - density correlation described by @xmath108 are already important at @xmath132 and for @xmath133 they only get slightly reinforced . another observable that has been recently proposed as a possible way of detecting the transition to a pair condensate state is the second - order momentum space correlation function  @xcite : @xmath134 where the operator @xmath135 gives the occupation of the plane wave @xmath21 with spin component @xmath55 .    as discussed in  @xcite , bcs theory predicts that correlations should be absent above @xmath136 , that is @xmath137 , while the transition to a condensate state should be observable as the appearance of a non - vanishing value of @xmath138 , sharply peaked around @xmath139 . second - order momentum space correlation function @xmath140 for different values of the temperature . empty circles , squares , diamonds : monte carlo results for @xmath141 . filled circles and squares at @xmath142 : perturbative expansion up to order 3 for @xmath143 respectively . for @xmath144 a perturbative expansion to an order higher than 3 would be required to observe convergence . , width=377 ]     second - order momentum space correlation function at @xmath139 : @xmath145 as a function of the temperature @xmath28 . circles : monte carlo results in the canonical ensemble . solid line : bcs theory in the grand canonical ensemble . dashed line : ideal gas in the canonical ensemble . same system parameters as in fig.[fig : g1uumc].,width=377 ]    in fig.[fig : g2kkmc ] , we have plotted monte carlo results for @xmath138 as a function of @xmath21 for different values of the temperature . at all temperatures , the quantity is indeed strongly peaked at @xmath139 , and nearly vanishes at the other values . a summary of the temperature - dependence of @xmath145 is plotted in fig.[fig : g2kkc_t ] . at temperatures above the transition temperature @xmath120 , correlations are negative and increase as the temperature is lowered . the negative correlation simply follows from the fact that we are working in the canonical ensemble , that is at a fixed total number of particles ( see the ideal fermi gas result in fig.[fig : g2kkc_t ] ) . as the temperature drops below @xmath120 , the correlations change sign becoming large and positive . this is a signature of pairing : because of the attractive interactions , the states with a filled fermi sphere plus two particles in states of opposite momenta and spins are in fact energetically favoured . in this state , the fluctuations of the occupation numbers of the @xmath146 and @xmath147 states are positively correlated .","summary":"a recently developed quantum monte carlo algorithm based on the stochastic evolution of hartree - fock states has been applied to compute the static correlation functions of a one - dimensional model of attractively interacting two component fermions . the crossover to a condensate of pairs can be identified as the first - order pair coherence extending throughout the whole size of the system .","abstract":"a recently developed quantum monte carlo algorithm based on the stochastic evolution of hartree - fock states has been applied to compute the static correlation functions of a one - dimensional model of attractively interacting two component fermions . the numerical results have been extensively compared to existing approximate approaches . the crossover to a condensate of pairs can be identified as the first - order pair coherence extending throughout the whole size of the system . the possibility of revealing the onset of the transition with other observables such as the density - density correlations or the second - order momentum space correlations is discussed ."}
{"article_id":"physics0404025","section_id":"c","document":"in the present paper , we have presented the result of extensive quantum monte carlo simulations for the static correlation functions of a one - dimensional lattice model of attractively interacting two component fermions . the numerical results obtained by qmc have been compared to existing approximate theories . excellent agreement with the predictions of a perturbative expansion in the interaction constant has been found , as well as with the ones of the random phase approximation . although long - range order is destroyed by phase fluctuations in one - dimensional systems in the thermodynamical limit , the finite size of the system under consideration still allows for the identification of a crossover to a condensed state at the temperature @xmath120 at which the first order coherence length of the pairs becomes larger than the system size . we have found that a significant degree of opposite spin density - density correlations already exists at temperatures well above @xmath120 and is only slightly enhanced as the temperature goes below @xmath120 . this means that a measurement of the density - density correlation function @xmath114 can not provide an unambiguous signature of the onset of a condensed state in the gas . on the other hand , this could be provided by a measurement of the second - order momentum space correlation function as suggested in  @xcite , or , even more directly , of the long - range behaviour of the first - order pair coherence function @xmath372 . a non - vanishing limit of @xmath127 for large @xmath11 corresponds in fact to the presence of a finite condensate fraction in both weak- ( bcs ) and strong- ( bec ) interaction regimes . a possible experimental scheme to measure @xmath123 in atomic fermi systems by means of matter - wave interferometric techniques will be the subject of a forthcoming publication . laboratoire kastler brossel is a unit de recherche de lcole normale suprieure et de luniversit paris 6 , associe au cnrs . we acknowledge discussions with ph . chomaz , j. dalibard , b. derrida , t. jolicur , o. juillet , a. montina , c. mora , a. recati .","summary":"the numerical results have been extensively compared to existing approximate approaches .","abstract":"a recently developed quantum monte carlo algorithm based on the stochastic evolution of hartree - fock states has been applied to compute the static correlation functions of a one - dimensional model of attractively interacting two component fermions . the numerical results have been extensively compared to existing approximate approaches . the crossover to a condensate of pairs can be identified as the first - order pair coherence extending throughout the whole size of the system . the possibility of revealing the onset of the transition with other observables such as the density - density correlations or the second - order momentum space correlations is discussed ."}
{"article_id":"1303.2099","section_id":"i","document":"correlated electronic systems display some of the most fascinating phenomena in solid state physics . one of their typical characteristics is a strong sensitivity to small changes of external control parameters . hence , a precise understanding of the underlying physics and of the pivotal parameters controlling the observed phenomenology represents a crucial goal in contemporary condensed matter research , also in light of possible applications beyond the purely academic context . the intrinsic complexity of many - body physics prevents an exact ab - initio theoretical description of correlated materials . in fact , even one of the most basic models for electronic correlations , i.e. the hubbard model@xcite where only the local part of the coulomb interaction is retained , can not be exactly solved in the relevant cases of two or three dimensions . however , a great step forward in the theoretical analysis of electronic correlation in condensed matter was achieved in the last decades by means of dynamical mean - field theory ( dmft)@xcite , and , for realistic material calculations , by its merger with ab - initio density functional approaches ( lda+dmft)@xcite .    from the theoretical point of view , dmft - based methods can be viewed as a quantum extension of the classical mean - field approaches . hence , the application of dmft implies neglecting all non - local spatial correlations albeit allowing for a very accurate ( and non - perturbative ) treatment of the most relevant part of the electronic correlations stemming from the ( single or multi - orbital ) hubbard interaction i.e. , their purely local part . the ability of dmft to capture these local quantum fluctuations is one of the keys behind its success in addressing many open questions in the physics of strongly correlated materials . among those , we recall the pioneering dmft description of the mott@xcite metal - insulator transition ( mit ) in v@xmath2o@xmath3@xcite , of the @xmath4 phase of pu@xcite , of the correlation effects@xcite in fe and ni , of the volume collapse in ce@xcite , of the unconventional pairing mechanism of superconductivity in fullerenes@xcite ; most recently dmft has been also successfully applied to the analysis of the occurrence of kinks in the self - energy@xcite and in the specific heat@xcite of particular vanadates , such as srvo@xmath3 , and liv@xmath2o@xmath5 , as well as of the spectral and magnetic properties@xcite of fe - based superconductors . furthermore , it should also be recalled here , that dmft is a very flexible scheme , whose application is possible also beyond the standard case of bulk correlated systems . in fact , dmft - based methods have been recently used to study correlated nanoscopic@xcite and hetero - structures@xcite . for the latter case , we want to focus here , in particular , on the theoretical predictions for the fermi - surface properties of layered ni - based heterostructures . the application of lda+dmft to this problem , and more specifically , to the case of a @xmath6 layered lanio@xmath3/laalo@xmath3 heterostructure has raised a considerable interest , as the dmft results of refs . clearly prospect the possibility to drive the fermi surface `` topology '' of these materials very close to the one of the high - temperature superconducting cuprates . in fact , the electronic structure in the bulk nickelates , such as r@xmath7sr@xmath8nio@xmath5 , is typically characterized by _ two _ bands crossing the fermi level@xcite , which arise from the two @xmath9-orbitals of ni ( the `` planar '' @xmath10 and `` axial '' @xmath11-orbital ) . however , by growing heterostructures with planes of lanio@xmath3 intercalated with insulating planes of laalo@xmath3 and on substrates providing an epitaxial strain , such as srtio@xmath3 or prsco@xmath3 , the energetic configuration of the @xmath11 will be correspondingly disfavored@xcite , which corresponds to a ( by our definition positive ) crystal field splitting @xmath12 among the two ni @xmath13-orbitals . in this situation , lda+dmft calculations have shown that the inclusion of the correlation effects will always increase the original ( lda ) crystal field splitting between the two @xmath9-orbitals@xcite , leading , eventually , to a significant change of the `` topology '' of the fermi surface , i.e. to a situation in which only _ one _ band , with predominant @xmath14-character crosses the fermi level . hence , according to these lda+dmft calculations , in ni - based heterostructures it would be possible to `` artificially '' realize the electronic configuration of the high - temperature superconducting cuprates ( i.e. , single , almost half - filled orbital with @xmath14 symmetry close the fermi level ) , e.g. by modulating the strain through changing the substrate or the insulating layer . as the control of the low - fermi surface properties represents an essential ingredient for novel , alternative , realizations of high - temperature superconductivity , the importance of having highly accurate lda+dmft predictions becomes a crucial factor for engineering new materials . in contrast to these impressive applications of dmft - based methods , one important aspect should be stressed here : the lda+dmft procedure requires as an important step a downfolding to a chosen energy window around the fermi energy @xmath15 . for most of the above mentioned studies , this window included only a few bands around @xmath15 of dominant 3d character . in such basis for the transition metal oxides the hybridization of 3d states and oxygen ligand 2p states is included _ implicitely _ in the effective bands . in the recent past , however , it has become customary to include the oxygen 2p states _ explicitely _ , i.e. to downfold to a larger energy window . in most of the cases , these additional ( @xmath0- ) orbitals were way more extended than the correlated ones ( e.g. @xmath1 ) , and , hence , the local coulomb interaction between electrons occupying these additional orbitals ( @xmath16 ) and between electrons on different manifolds ( @xmath17 ) was either completely neglected , or , in some exceptional cases , treated at the hartree level@xcite . despite this approximation , it is quite intuitive to expect that the validity of lda+dmft calculations performed in an enlarged ( say : @xmath18 ) basis - set is more general than the corresponding one in the restricted @xmath1 manifold . in fact , quite generally : ( i ) performing a renormalization ( wannier@xcite projection , nmto@xcite downfolding , etc . ) on an enlarged basis - set allows for a better localization of the orbitals of the correlated manifold ( as the @xmath18-hopping processes are now explicitly included in the model ) ; and ( ii ) the possibility of describing explicitly charge - transfer processes between the @xmath1 and @xmath0-orbitals makes the theoretical modeling evidently closer to the actual material physics@xcite . notwithstanding these quite general arguments , the improvement of lda+dmft calculations on enlarged @xmath18 basis - sets w.r.t . the ones restricted to effective @xmath1-only basis , is not always apparent . in fact , there are cases for which a treatment on a larger basis set renders the comparison with experiment to be worse ! without attempting to give a complete review here , we recall that lda+dmft calculations including @xmath0-orbitals have improved the descriptions of the insulating behavior of nio@xcite and of the mit in nis@xmath2@xcite w.r.t . @xmath1-only calculations@xcite . also quite accurate results have been obtained for one- and two - particle properties of cobaltates ( such as srcoo@xmath3@xcite and lacoo@xmath3 @xcite ) and in several studies@xcite of the well - known class of iron - pnictides and calchogenides . in contrast to the aforementioned successful applications of @xmath18 calculations , in other , equally important , cases the @xmath18 lda+dmft results are in partial or total contradiction with the @xmath1-only calculations , and/or with the experimental findings : no mit in v@xmath2o@xmath3 was found up to unrealistically large values of the coulomb interaction if the oxygen @xmath0-orbitals are included in lda+dmft calculations @xcite . more recently also the mott - hubbard insulating phase of la@xmath2cuo@xmath5 and lanio@xmath3 was reported to be missing in the @xmath18 framework@xcite , while these materials are found to be insulating in @xmath1-only calculations for plausible values of the @xmath19 interaction . these discrepancies between @xmath1-only and @xmath18 calculations regarding the mott - hubbard mit have already raised a discussion in the recent literature . in ref . , non - local correlations to be included beyond dmft@xcite have been considered as a cause of the discrepancy . in fact , a major role of spatial correlations in determining the onset of insulating phases is quite likely , especially in the case of two - dimensional cuprates .    however , there are also other discrepancies , whose discussion will be the object of the present work , which can be hardly attributed to the effects of non - local correlations . these discrepancies are observed for systems of more than one correlated @xmath1-orbital and in broad parameter regimes ( including high temperatures ) , where effects beyond dmft should not play a crucial role . in particular , a striking disagreement between @xmath1-only and @xmath18 calculations was reported for the above - mentioned case of ni - based heterostructures . in fact , lda+dmft calculations performed including also the oxygen @xmath0-orbitals have shown@xcite exactly the opposite trend w.r.t . the previous ones : even in presence of a favorable crystal field splitting @xmath20 at the starting ( lda ) level , the net effect of the hubbard interaction was _ always _ to reduce the orbital polarization by filling back the @xmath11-orbital , which would prohibit _ de facto _ any possibility of realizing the cuprate conditions for the onset of an unconventional superconductivity . this second kind of discrepancies between lda+dmft performed with different ( @xmath1-only vs. @xmath18 ) basis - sets well illustrated by the contradicting results for the ni - based heterostructures , raises a quite general question about the proper use and interpretation of the growing number of lda+dmft calculations on extended basis sets . the correct determination of the orbital polarization and fermi surface properties is of great importance for future calculations of increasingly complex materials . in this paper we aim at understanding the relations between the results of existing lda+dmft calculations on different basis - sets for the fermi surface properties of multi - orbital systems and , ultimately , the origin of the qualitative discrepancies observed by following the standard implementation of the algorithms in different basis - sets . for this purpose , it is of primary importance to disentangle the main , qualitative , trends from the specific features of a selected case . hence , we will study model hamiltonians for different crsytal field splittings starting from a dp - basis ( 4 bands ) . subsequently , we perform a downfolding to an effective d - only basis and compare dmft ressults of both cases . this procedure will capture the above - mentioned discrepancy in the prediction of fermi surfaces of correlated multi - orbital systems and allow for a systematic study of this problem in the context of ni - based materials . the scheme of the paper is the following : in sec . ii we introduce the models . in sec . iii , we analyze the disagreement in the calculation of the orbital occupations and the shape of the fermi surfaces between @xmath1-only and @xmath18 model for a fixed set of interaction parameters . at the end of sec . iii , we also provide an analysis of the role of hund s exchange @xmath21 . in sec . iv we study the origin of the observed inconsistencies by analyzing the dependence on the @xmath1-electron - density , and we discuss its possible relation with the crossover@xcite from high - spin ( hund s regime ) to low - spin ( cf regime ) . finally , in sec . v we summarize our results .","summary":"the effective crystal field in multi - orbital correlated materials can be either enhanced or reduced by electronic correlations with crucial consequences for the topology of the fermi surface and , hence , on the physical properties of these systems . in this respect , recent local density approximation ( lda ) plus dynamical mean - field theory ( dmft ) studies of ni - based heterostructure have shown contradicting results , depending on whether the less correlated-orbitals are included or not . we investigate the origin of this problem and identify the key parameters controlling the fermi surface properties of these systems . without the-orbitals this implies that the local hund s exchange , while rather unimportant for the former case , can play a predominant role in controlling the orbital polarization for the extended basis - set by favoring the formation of a larger local magnetic moment .","abstract":"the effective crystal field in multi - orbital correlated materials can be either enhanced or reduced by electronic correlations with crucial consequences for the topology of the fermi surface and , hence , on the physical properties of these systems . in this respect , recent local density approximation ( lda ) plus dynamical mean - field theory ( dmft ) studies of ni - based heterostructure have shown contradicting results , depending on whether the less correlated-orbitals are included or not . we investigate the origin of this problem and identify the key parameters controlling the fermi surface properties of these systems . without the-orbitals the model is quarter filled , while the manifold moves rapidly towards half - filling when the-orbitals are included . this implies that the local hund s exchange , while rather unimportant for the former case , can play a predominant role in controlling the orbital polarization for the extended basis - set by favoring the formation of a larger local magnetic moment ."}
{"article_id":"1303.2099","section_id":"r","document":"in this section , we compare our dmft results obtained in the two different basis - sets . following the chronological order of appearence of realistic lda+dmft calculations for these systems , we present data for the @xmath1-only ( downfolded ) basis - set first and then the corresponding ones for the original @xmath18 hamiltonian . we mention that our model study can be qualitatively related , depending on the initial value of the energy splitting between the correlated orbitals ( @xmath68 ) , to the physics of bulk nickelates@xcite and of ni - bases heterostructures@xcite . in fact , ( i ) the nominal charge of these systems corresponds also to one electron in the outer two ni - bands and ( ii ) the bulk nickelates are typically characterized by negative values of @xmath30 , due to the tetragonal distortion along the @xmath69-axis . in the ni - based heterostructures instead , the localization effects in the @xmath69 direction , as well as the epitaxial strain due to the substrate , induce positive values for @xmath30 . orbital occupation of the @xmath1-only model with @xmath70ev , @xmath71ev ( @xmath72ev ) , @xmath73ev@xmath74 at quarter - filling ( @xmath39 ) as a function of the initial crystal field splitting @xmath30 . the dmft data ( solid symbols ) are compared with the corresponding non - interacting results ( empty symbols ) . the arrows indicate the effect of the interaction which is essentially opposite for negative and positive @xmath30 . the shaded region on the left indicates the onset of the mott - hubbard insulating phase.,scaledwidth=50.0% ]     difference of the real part of the dmft self - energies for the two orbitals of the @xmath1-only model with @xmath75ev , @xmath71ev ( @xmath72ev ) , @xmath73ev@xmath74 at quarter - filling ( @xmath39 ) extrapolated to @xmath76 ( solid symbols ) and @xmath77 ( empty symbol , hartree contribution to the self - energy ) as a function of the initial energy splitting @xmath30 . the huge enhancement of the difference between the self - energy at @xmath76 , and the consequent huge energy shift of the first orbital , marks the onset of the mott - hubbard insulating phase ( shaded region on the left).,scaledwidth=50.0% ]    in this subsection , we analyze the results for our @xmath1-only two - orbital model at quarter - filling ( @xmath39 ) , as a function of the initial energy splitting between the two downfolded @xmath9-orbitals ( @xmath30 ) : the corresponding results for the orbital occupation without interaction ( which would correspond to the lda ones , in a realistic calculation ) and with the interaction ( computed with dmft ) are shown in fig . [ fig2_dp ] . as mentioned in sec . ii , the interaction values have been chosen in consideration of typical values for transition metal oxides systems : for the @xmath1-only model , we adopted a value of @xmath78 ev , with @xmath71ev ( @xmath72ev ) . we start by briefly commenting the set of non - interacting data shown in fig . [ fig2_dp ] : they display a clear - cut dependence on the initial value of the energy splitting of the @xmath9-orbitals : the orbital occupation of the @xmath14 monotonously increases upon increasing values of @xmath30 , whereas the occupation of the @xmath11-orbital decreases . we note , however , that , since the hopping terms ( and , hence , the bandwidth ) for the two orbitals are not equal , the orbital occupation curves are not symmetric w.r.t . to @xmath30 . this also implies that the situation where the two orbitals are equally occupied ( i.e. no orbital polarization ) does not occur at @xmath79 but , for the non - interacting case , only for @xmath80ev . we discuss now the effects of the hubbard interaction on the orbital occupations , as described by our dmft(ct - qmc ) calculations . while the occupation curves remain obviously asymmetric also in presence of the interactions , from the data of fig . [ fig2_dp ] we note that , for each orbital , the deviations w.r.t . to the non - interacting values are strongly dependent on @xmath30 : the sign of the change in the orbital occupations appears closely connected with the sign of @xmath30 . specifically , for @xmath81 we observe generally an enhancement ( reduction ) of the occupation of the first(second ) , @xmath14- ( @xmath11- ) orbital , while for @xmath82 the trend is the opposite . this is reflected in an analogous trend of the change to the orbital polarization @xmath83 , formally defined as in refs . @xmath84 as well as in the fermi surfaces , shown in fig . [ fig6_dp ] . for the latter ones , which will be discussed more extensively in the next - subsection , our dmft results show that , depending on the sign of the initial orbital spliting @xmath85 , the character ( as well as the typical shape ) of the fermi surface corresponding to the lower - energy orbital gets increased by the electronic interaction .    in fact , such trends explain the qualitatively different lda+dmft results previously obtained for the shape of the fermi surface via specific @xmath1-only calculations for bulk nickelates@xcite and ni - based heterostructures@xcite , respectively : the difference in the results essentially reflects the different sign of the initial crystal field splitting ( @xmath30 ) , as estimated by the ab - initio calculations , whose final size ( @xmath86 ) gets significantly magnified by the electronic interaction . the last statement can be formalized more quantitatively through the analysis of the corresponding self - energies presented in fig . [ fig3_dp ] : here we show the differences between the real parts of the dmft self - energy of the two orbitals , i.e. @xmath87 , evaluated in the limit frequency @xmath88 and @xmath89 , respectively . we recall that in the latter limit only the hartree contributions to the electronic self - energy remain . hence , the difference between the self - energies can be also explicitly written in terms of the electronic density as : @xmath90 here , the last equality only holds at quarter - filling where @xmath91 . such a dependence on the ( final ) electronic density appears evidently in the corresponding data of fig . [ fig3_dp ] . the hartree contribution , evaluated in dmft , changes sign @xcite precisely where the orbital occupations become equal ( @xmath92 ) , i.e. for the negative values of @xmath93ev , see fig . [ fig2_dp ] . by comparing this to the previous results , it appears that the high - frequency values of the self - energy do not represent the `` crucial '' parameter . instead , the trends in the orbital polarization and , therefore , the predicted physics are controlled by the low - frequency behavior of the self - energy : up to the mit the shape of the fermi surface is determined by the `` effective '' cf splitting given by @xmath94 i.e. as the original crystal field corrected by the difference of the real self - energies for @xmath76 . this makes the interpretation of the second set of data shown in fig . [ fig3_dp ] very transparent : the sign of @xmath95 follows that of the original crystal field @xmath30 , and confirms , from the microscopic point of view , the picture of interaction effects _ always _ magnifying the size of the original crystal field . of course such enhancement will depend quantitatively on many factors : for instance , it will be bigger when the system is more correlated . a dramatic enhancement , in particular , is found when the mott metal - insulator transition is approached , i.e. when @xmath30 approaches the shaded area in fig . [ fig3_dp ] . here the low energy physics correspond to an empty ( broader ) @xmath14-orbital and a half - filled ( narrower ) @xmath11-orbital . however , as we will now discuss , these results are contradicted by corresponding calculations performed in larger basis - sets , which include also the most relevant @xmath0 degrees of freedom , as it will be shown explicitly in the next subsection . orbital occupation of the @xmath1-orbitals as a function of the initial crystal field splitting for the four - band @xmath18 model with @xmath96ev , @xmath97ev ( @xmath98ev ) , @xmath73ev@xmath74 and @xmath99 . the dmft data ( solid symbols ) are compared with the corresponding non - interacting results ( empty symbols).,scaledwidth=50.0% ]     difference of the real part of the dmft self - energies for the two @xmath1-orbitals of the four - band @xmath18 model with @xmath96ev , @xmath100ev ( @xmath98ev ) , @xmath73ev@xmath74 and the filling is @xmath99 . shown is the low and high frequency asymptotes , i.e. the extrapolation to @xmath101 ( solid symbols ) and @xmath77 ( empty symbol , hartree contribution to the self - energy).,scaledwidth=50.0% ]        for the 4 band @xmath18 model the total occupation is @xmath102 . because of the stronger localization of the @xmath1-orbitals in the @xmath18 case , larger values for @xmath46 , @xmath48 and @xmath21 have been considered : we have doubled the value of @xmath48 w.r.t . the calculation discussed in the previous section , i.e. @xmath96ev @xcite . because of the smaller screening effects on the hund s exchange constant , we have considered a reduced enhancement of @xmath21 , which has been fixed to @xmath103ev . as before , the relation @xmath104 holds .    in fig . [ fig4_dp ] we consider first the occupation of the two @xmath1-orbitals as a function of the initial crystal field splitting , starting from the non - interacting case . let us recall here that , because of the downfolding procedure , the numerical values of the energy splitting between the @xmath9-orbitals in the one - particle hamiltonian are evidently different in the @xmath18 and in the @xmath1-only basis - set . they have been labelled , respectively , with @xmath29 , see eq . [ eq : dpmodel ] , and @xmath30 . note that the latter includes , as _ ligand _ field , the effects of @xmath18 hybridization . to allow for a direct comparison to the effective d - only results we have used the relation between @xmath29 and @xmath30 and plot the dp - results as a function of @xmath30 .    by analyzing the orbital occupation shown in fig . [ fig4_dp ] , the qualitative behavior as a function of @xmath30 appears similar as in the @xmath1-only case . however , an important difference should be noted : in spite of the relatively large separation ( @xmath105ev ) between @xmath1- and @xmath0-bands , the total occupation of the @xmath1-orbitals is now much larger than before ( @xmath106 ) due to the @xmath18 hybridization . quite remarkably , according to our dmft results of fig . [ fig4_dp ] , such an enhanced occupation of the `` correlated '' @xmath1-orbitals essentially survives also upon switching on the local interaction . this fact has an obvious impact on the final results for the orbital polarization @xmath83 , as now the sign of its change w.r.t . the non - interacting case is no longer related to @xmath30 : fig . [ fig4_dp ] shows that independently on the sign @xmath30 , one _ always _ observes a reduction of the value of @xmath83 , i.e. a net enhancement ( reduction ) of the occupation of the @xmath11- ( @xmath14- ) orbital driven by the electronic interaction . the analysis of the corresponding self - energies provides a further confirmation : fig . [ fig5_dp ] shows the plot of the zero frequency extrapolation of the real part of the self - energy ( compare to [ fig3_dp ] ) . in contrast to the @xmath1-only results now the interaction correction always reduces the initial crystal field , in agreement with the systematic depletion of the @xmath14-orbital ( reduction of @xmath83 ) observed in the whole parameter range considered .    on the basis of these results , it is interesting to examine the consequences for the shape of the fermi surfaces ( fs ) in the different cases . in fig . [ fig6_dp ] we show the fermi surfaces for two different values of @xmath30 for both the @xmath1-only and the @xmath18 basis - sets . in the upper row we show the non - interacting result and in the lower row the dmft one . in particular , the two values of @xmath30 have been chosen to present the extreme cases within our data range ( provided that the solution is metallic and has a fs ) . as for the analysis of fig . [ fig6_dp ] , we start by considering the non - interacting fs of the upper row for the two different basis - sets : as a consequence of the lwdin downfolding , the shape of non - interacting fs corresponding to the same values of @xmath30 coincide , while the orbital character encoded by the colors differs in that the @xmath0 contribution is explicitly present in the @xmath18 case . additionally , for each case considered , the contribution to the fs of the @xmath11-orbital ( encoded by the red color and responsible for the formation of the `` cylindric''-shaped fs sheet around the @xmath107-point ) is stronger for negative values of @xmath30 than for positive .    by looking at the dmft data ( lower row ) for the @xmath18 4-band model , we see that the overall negative correction to @xmath86 reported in fig . [ fig5_dp ] gives a definite trend for the fermi surfaces : in the @xmath18 case , the interaction , _ independently _ of the sign of @xmath30 always enhances the @xmath11 contribution . this is reflected both in the orbital composition ( the interacting fs contain more red ) and in the shape ( enlargement of the central fs sheet ) . at the same time , our dmft data unveil quite different trends for the interacting fs of the @xmath1-only model : the @xmath11 contribution is enhanced _ only _ for @xmath82 , i.e. , only if the @xmath11 was from the beginning the lowest lying of the @xmath9-orbitals . in fact , coherently with the behavior of @xmath86 ( see fig .  [ fig3_dp ] ) , for positive values of @xmath30 , the interaction further reduces the @xmath11 contribution to the fs , which becomes progressively `` darker '' colored and more `` @xmath108''-shaped . let us note that , depending on the details of the dispersion of the specific @xmath1-only problem , there are cases in which , for @xmath109 the non - interacting fs still presents two - sheets , but the reduction of the @xmath11-character predicted by dmft , determines a transition to a single sheet fs in the interacting case , analogous to the one calculated in ref . .    summarizing the main outcome of the comparsion of our dmft calculations in different basis - sets for orbital occupations , crystal field corrections and fermi surface evolution , an evident _ qualitative _ disagreement is observed , at least in the region of positive values of the initial crystal field @xmath30 . it is worth noticing that for positive values of @xmath30 , the trend we found in the @xmath18-basis - set is consistent with the results of the @xmath18 calculations for the ni - based heterostructures of ref . : there , it was shown , that even when starting from a relatively significant orbital polarization for the @xmath14-orbital at the lda level , the polarization was always strongly reduced by the interaction , which obviously has bad implications on the possibility of actually manipulating the fermi surfaces of the ni - based heterostructures in the `` desired '' cuprate - like way @xcite . as a matter of fact , this discrepancy between @xmath1-only and @xmath18 results has been found here by also including the su(2 ) symmetry of the local interaction on the @xmath9-bands in both dmft calculations . this confirms the hypothesis of ref . that such a discrepancy in the theoretical predictions does not originate from a different treatment of the interactions between the calculations of refs . and @xcite , but rather from some more intrinsic difference in the calculations . the most evident systematic difference is the filling @xmath110 of the two @xmath9-orbitals , which , due to the @xmath18 hybridization is strongly increased w.r.t . the quarter - filling level of the @xmath1-only model . while this is rather obvious at the lda level , we note that the occupation of the @xmath1 manifold does not change much even in presence of the interaction , for typical choices of the double - counting term for the dmft ( see sec . ii , for details , and also ref . ) . quite interestingly , the possible role of an enhanced @xmath1-orbital occupation in @xmath18 calculations has been also recently addressed , for the different problem of the occurrence of the mit@xcite . the point we make here is that the hund s exchange @xmath21 has a strikingly different effect in the @xmath1-only and in the @xmath18 models , due to the fact that , close to half - filling , @xmath21 drives the system very effectively towards the hund s rule high - spin ground state @xcite . for the orbital polarization this means that @xmath21 does not play a decisive role for the quarter - filled @xmath1-only model while it becomes extremely important in the @xmath18 model , where @xmath106 . the @xmath1 and @xmath18 results can indeed be reconciled qualitatively if the hund s coupling @xmath21 for the @xmath18 model is equal to @xmath111ev or smaller . this is shown in fig . [ fig7_dp ] , in which the @xmath18 calculations have been performed reducing the value of @xmath21 from @xmath112ev to @xmath113ev , and @xmath114ev ( @xmath115ev is kept fixed , instead ) .    the combined analysis of the orbital occupation and of the self - energy ( at @xmath76 ) results shows that the @xmath18 results of fig [ fig4_dp ] and [ fig5_dp ] change qualitatively already for the case @xmath113ev : the overall trend of strong reduction of occupation of the first @xmath14-orbital disappears for a large region of values of the initial crystal field @xmath30 . in fact , the results already at @xmath21=0.5ev would lead to a physical situation which is qualitatively similar to that predicted by the @xmath1-only model . as one can expect , the change with respect to the previous @xmath18 results becomes even larger when setting @xmath114ev , as both trends of orbital occupation and effective crystal field become exactly opposite , with the @xmath14-orbital occupation always increased by the interaction irrespectively of the value of the initial @xmath30 . the sensitivity of the final @xmath18 results on the hund s coupling is very illustrative and shows the crucial role of the hund s exchange in this situation@xcite .","summary":"the model is quarter filled , while the manifold moves rapidly towards half - filling when the-orbitals are included .","abstract":"the effective crystal field in multi - orbital correlated materials can be either enhanced or reduced by electronic correlations with crucial consequences for the topology of the fermi surface and , hence , on the physical properties of these systems . in this respect , recent local density approximation ( lda ) plus dynamical mean - field theory ( dmft ) studies of ni - based heterostructure have shown contradicting results , depending on whether the less correlated-orbitals are included or not . we investigate the origin of this problem and identify the key parameters controlling the fermi surface properties of these systems . without the-orbitals the model is quarter filled , while the manifold moves rapidly towards half - filling when the-orbitals are included . this implies that the local hund s exchange , while rather unimportant for the former case , can play a predominant role in controlling the orbital polarization for the extended basis - set by favoring the formation of a larger local magnetic moment ."}
{"article_id":"astro-ph0407352","section_id":"i","document":"in its first year , the _ hubble space telescope _ ( hst ) discovered that a majority of all baryons in the current universe are not in galaxies , but instead remain in the intergalactic medium ( igm ) . in subsequent years , the uv spectrographs aboard hst and the _ far ultraviolet spectroscopic explorer _ ( fuse ) have continued these investigations of the multiphase igm , using sensitive uv tracers of diffuse gas : the lyman series of h  i (  at 1215.67   ,  at 1025.72   , etc ) and the o  vi doublet ( 1031.926 , 1037.617   ) . these hst and fuse studies have led to a preliminary `` baryon census '' of the `` warm '' ( photoionized ) and `` warm - hot '' ( collisionally ionized ) igm . with spectrographs aboard the _ chandra _ and _ xmm / newton _ x - ray telescopes , astronomers are beginning to search for even more highly ionized gas through resonance absorption lines of o  vii , o  viii , n  vii , and ne  ix .    unlike virtually all other astronomical objects , the ly@xmath16 absorption systems were first discovered at great distances ( @xmath17 ) owing to their cosmological redshifts and the near - uv atmospheric cutoff . only with the advent of hst have nearby examples been found . the first low-@xmath15  absorbers were seen in the spectrum of 3c  273 at @xmath18 ( bahcall et  al . 1991 ; morris et  al . while the number of absorbers was significantly less than the line density at high-@xmath15 , the `` local  forest '' contains far more absorbers than expected from extrapolating the ground - based data ( bahcall 1993 and subsequent qso absorption - line key project papers by jannuzi 1998 and weymann 1998 ) . although the  absorbers at @xmath17 are sufficiently abundant to account for nearly all the baryons ( rauch 1997 ; schaye 2001 ) , their substantial numbers at @xmath3 imply that @xmath230% of all baryons remain in these photoionized clouds locally ( penton , stocke , & shull 2000a , penton , shull , & stocke 2000b , 2004 , hereafter denoted papers i , ii , and iv ) .    numerical simulations ( fig .  1 ) of the evolving igm ( cen & ostriker 1999 ; dav et  al . 1999 , 2001 ) explain not only the general features of the   number density evolution , but also many detailed properties , including distributions in column density ( ) and doppler @xmath19-value ( papers ii and iv ; dav & tripp 2001 ; ricotti , gnedin , & shull 2000 ) , and their relationship to galaxies ( dav 1999 ; impey , petry , & flint 1999 ; penton , stocke , & shull 2002 , hereafter denoted paper iii ) . any accounting of the present - day distribution of baryons must include an accurate census of these absorbers and the associated mass , inferred from their ionized fractions , column densities , and physical extents . moderate - resolution uv spectroscopy of bright quasars , qsos , blazars , and seyfert galaxies has provided a substantial database of low-@xmath15   absorbers . at the same time , several ground - based galaxy surveys ( morris 1993 ; lanzetta 1995 ; chen 1998 ; tripp , lu , & savage 1998 ; rao & turnshek 1998 , 2000 ; impey , petry , & flint 1999 ; nestor 2002 ; bowen 2002 ; paper iii ; bowen & pettini 2003 ; stocke 2005 , hereafter denoted paper  v ) have probed the relationship between  absorbers and galaxies , filaments of galaxies , and voids . using nearby examples of the  phenomenon , these authors sought to identify the galaxy types responsible for the absorption and thus assist in interpreting the wealth of information ( number densities , metallicities , ionization states , line widths ) of  absorption systems at high-@xmath15 . these efforts have been somewhat successful , although the results in most column - density regimes remain controversial ( see conference proceedings edited by mulchaey & stocke 2002 ) .    in this review , we describe the various hst qso absorption line surveys that have been undertaken (   2 ) , review our present knowledge of the baryon content of the igm (   3 ) , and describe the emerging , but still controversial , evidence for the relationship between the various column densities of  absorbers and galaxies (   4 ) . the last information has come largely from studying low-@xmath15 absorbers discovered with hst . we conclude (   5 ) with a brief prospectus on low-@xmath15 igm studies facilitated by the _ cosmic origins spectrograph _ ( cos ) , a new instrument that may be installed on hst in the coming years .","summary":"the observed line density of  absorbers , for 2 , is dominated by low-  systems that exhibit slower redshift evolution than those with  2 . we also review the relationship between the various types of   absorbers and galaxies . at the highest column densities ,   , the damped  ( dla ) systems , hst can play a crucial role in a precise accounting of the local baryons and the distribution of heavy elements in the igm .","abstract":"in this review , we describe our surveys of low column density ( ) absorbers (  ) , which show that the warm photoionized igm contains% of all baryons at . this fraction is consistent with cosmological hydrodynamical simulations , which also predict that an additional 2040% of the baryons reside in much hotter 10  k gas , the warm - hot igm ( whim ) . the observed line density of  absorbers , for 2 , is dominated by low-  systems that exhibit slower redshift evolution than those with  2 . hst / fuse surveys of o  vi absorbers , together with recent detections of o  vii with _ chandra _ and _ xmm / newton _ , suggest that anywhere from 2070% ( with large errors ) of the baryons could reside in the whim , for an assumed abundance o / h 10% solar . we also review the relationship between the various types of   absorbers and galaxies . at the highest column densities ,   , the damped  ( dla ) systems are often identified with gas - rich disks of galaxies over a large range in luminosities ( 0.031  ) and morphologies . lyman - limit systems (  ) appear to be associated with bound bright ( 0.10.3 ) galaxy halos . the  absorbers with  are associated with filaments of large - scale structure in the galaxy distribution , although some may arise in unbound winds from dwarf galaxies . our discovery that% of low-  absorbers reside in galaxy voids suggests that a substantial fraction of baryons may be entirely unrelated to galaxies . in the future , hst can play a crucial role in a precise accounting of the local baryons and the distribution of heavy elements in the igm . these studies will be especially effective if nasa finds a way to install the _ cosmic origins spectrograph _ ( cos ) on _ hubble _ , allowing an order - of - magnitude improvement in throughput and a comparable increase in our ability to study the igm .   "}
{"article_id":"0809.5023","section_id":"i","document":"random multiple access protocols have played a crucial role in the development of both wired and wireless local area networks ( lans ) , and yet the performance of even the simplest of these protocols , such as slotted - aloha @xcite , is still not clearly understood . these protocols have generated a lot of research interest in the last thirty years , especially recently in attempts to use multi - hop wireless networks ( mesh and adhoc networks ) to provide low - cost high - speed access to the internet . random multiple access protocols allow users to share a resource ( e.g. a radio channel in wireless lans ) in a distributed manner without exchanging any signaling messages . a crucial question is to determine whether these protocols are efficient and fair , or whether they require significant improvements .    in this paper , we consider non - adaptive protocols , where the transmission probability of a given transmitter is basically fixed . more specifically we analyze the behavior the slotted - aloha protocol in a buffered system with a fixed number of users receiving packets from independent markovian processes of pre - defined intensities . we aim at characterizing the stability region of the system . this question has been open since the first stability analysis of aloha systems in 1979 by tsybakov and mikhailov @xcite , and we will shortly explain why it is so challenging to solve . we propose an approximate stability region and prove that it is exact when the number of users grows large . to accomplish this , we characterize the mean field regime of the system when the number of users is large , explore the stability of this limiting regime , and finally explain how the stability of the mean field regime relates to the ergodicity of systems with a finite number of users . we also show , using both theoretical arguments and numerical results , that our approximate is extremely accurate even for small systems , e.g. with three users ( the approximate is actually exact for two users ) . our approach can be generalized to other types of non - adaptive random multi - access protocols ( e.g. , csma , carrier sense multiple access ) . we present this extension at the end of the paper . consider a communication system where @xmath0 users share a common resource in a distributed manner using the slotted - aloha protocol . specifically , time is slotted , and at the beginning of each slot , should a given user @xmath1 have a packet to transmit , it attempts to use the resource with probability @xmath3 . let @xmath4 represent the vector of fixed transmission probabilities . when two users decide to transmit a packet simultaneously , a collision occurs and the packets of both users have to be retransmitted . each user is equipped with an infinite buffer , where it stores the packets in a fifo manner before there are successfully transmitted . packets arrive into user @xmath1 s buffer according to a stationary ergodic process of intensity @xmath2 . the arrival processes are independent across users , and are markov modulated . more precisely , the packet arrivals for user @xmath1 can be represented by an ergodic markov chain @xmath5 with stationary probability @xmath6 of being in state @xmath7 , and with transition kernel @xmath8 . the markov chains @xmath9 are independent across users and take values in a finite space @xmath10 . if at time slot @xmath11 @xmath12 , a new packet arrives into the buffer of user @xmath1 with probability @xmath13 , where the @xmath14 s are positive real numbers such that @xmath15 . the average arrival rate of packets per slot at user @xmath1 is then @xmath2 . we use these chains to represent various classes of packet inter - arrival times . the simplest example is that of bernoulli arrivals , i.e. , when the inter - arrivals are geometrically distributed with mean @xmath16 : this can be represented by the markov chain @xmath9 with one state . we could also represent inter - arrivals that are sums ( or random weighted sums ) of geometric random variables . in the following we denote by @xmath17 the proportion of traffic generated by user @xmath1 . denote by @xmath18 the number of packets in the buffer of user @xmath1 at the beginning of slot @xmath11 . the state of the system is given by @xmath19 at time slot @xmath11 . @xmath20 is a discrete - time markov chain . the stability region @xmath21 is defined as the set of vectors @xmath22 such that the system is stable , i.e. @xmath23 is ergodic , for packet arrival rates @xmath24 . it is important to remark that , a priori , @xmath21 depends on the transmission probabilities @xmath25 , but also on the types of arrival processes defined by the transition kernels @xmath26 and the parameters @xmath27 . but to keep the notation simple , we use @xmath21 to denote the stability region .      the problem of characterizing the stability region @xmath21 has received a lot of attention in the literature in the three last decades . first of all note that when the system is _ homogeneous _ in the sense that @xmath28 $ ] does not depend on @xmath1 , then one can show as in @xcite that the stability condition is : @xmath29 for all @xmath1 regardless of the nature of the arrival process ( in this very specific case , all buffers saturate simultaneously at the stability limit ) . for nonhomogeneous systems an exact characterization has been provided in @xcite under general traffic assumptions but only for @xmath30 users . for two users , the stability region @xmath31 is defined by : @xmath32 if and only if : @xmath33 @xmath34 the first ( resp . second ) condition is obtained assuming that at the stability limit , buffer 2 ( resp . buffer 1 ) is saturated . when the number of users is greater than two , the stability region depends not only on the mean arrival rates @xmath2 , but also on the other detailed statistical properties of the arrival processes . for example , when @xmath35 , this is due to the fact that the stability condition for a particular buffer depends on the probability that the two other buffers are empty separately or simultaneously . these probabilities actually depend on the detailed characteristics of the arrival processes , see e.g. @xcite . for @xmath35 and bernoulli arrivals , the stability region can be characterized @xcite . when the arrivals are not bernoulli , the system stability region is unknown . when the number of users @xmath0 exceeds 3 , it becomes impossible to derive explicit stability conditions . for bernoulli arrivals , as was shown in @xcite , the stability region @xmath21 can be recursively described as a function of the various stability regions of systems with @xmath36 users , @xmath37 , and of the probabilities that in these systems , some buffers are simultaneously empty . these probabilities are unknown in general , and so is the stability region . the results of @xcite have been recently generalized to more general systems of interacting queues @xcite . the only previous explicit stability condition for arbitrary @xmath0 is given in @xcite ; unfortunately , to obtain this condition , the author has to assume that the arrival processes of the different users are correlated , which is unrealistic in practice . some other authors have proposed bounds on the stability region , see e.g. @xcite . the basic idea behind most of the proposed bounds is to build systems that stochastically dominate ( or that are stochastically dominated by ) the initial system . for example , a system where one of the buffers is assumed to be always non - empty stochastically dominates the initial system , and hence has a smaller stability region . in @xcite the reader will find an interesting discussion on the existing techniques to derive bounds of the stability region . it is worth remarking that often in the literature , researchers have been interested in deriving what we refer to as the _ capacity region _ of aloha systems . it is defined as the set of vector @xmath24 such that there exists a vector @xmath25 of transmission probabilities such that the resulting system is stable . in this paper , we fix the transmission probabilities and investigate the stability region , i.e. the set of @xmath24 such that the system is stable . in particular , if we succeed in characterizing the stability region for any vector @xmath25 , then we may easily deduce the capacity region . the main contribution of this work is to propose a simple explicit approximate expression of the stability region @xmath21 . this approximate stability region @xmath38 enjoys the following properties :    * when the number @xmath0 of users grows large , the gap between @xmath38 and the actual stability region @xmath21 vanishes . * even for small systems , @xmath38 proves to be very accurate . for @xmath30 , one actually has @xmath39 ; for @xmath35 and any other number of users , the approximate region is very accurate . in fact , for any values of @xmath0 , there exists an infinite number of points where the boundaries of @xmath21 and of @xmath38 coincide , which explains the accuracy . * @xmath38 is insensitive , i.e. , it depends on the arrival processes through their intensities @xmath2 s only .    to prove that @xmath38 becomes exact when @xmath0 grows large , we use a mean field analysis of the system , and we show that the stability of the finite system of queues and that of the mean field limiting regime are related ( in fact equivalent when @xmath0 grows large ) . to our knowledge , this is the first time mean field asymptotics are used to provide stability conditions of the finite systems . the paper is organized as follows . in section ii , the approximate stability region is proposed and the main result , i.e. the fact that @xmath38 tends to @xmath21 when @xmath0 is large , is stated in theorem 1 . in section iii , we present theoretical arguments and numerical experiments to illustrate the accuracy of @xmath38 . sections iv and v are devoted to the proof of theorem 1 : in section iv , we present a mean field analysis of the system , and in section v , we investigate the stability of the system in the limiting mean field regime , and explain why the stability condition obtained provides an ergodicity condition of the finite system of queues . we generalize our results to non - adaptive csma protocols in section vi , and conclude in section vii .","summary":"we analyze the stability of standard , buffered , slotted - aloha systems . specifically , we consider a set of users , each equipped with an infinite buffer . packets arrive into user s buffer according to some stationary ergodic markovian process of intensity . at the beginning of each slot , if user has packets in its buffer , it attempts to transmit a packet with fixed probability over a shared resource / channel . the stability of such systems has been open since their very first analysis in 1979 by tsybakov and mikhailov . in this paper , we propose an approximate stability condition , that is provably exact when the number of users grows large . we provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users ( even two or three ) . random multiple access , aloha , stability , mean field asymptotics .","abstract":"we analyze the stability of standard , buffered , slotted - aloha systems . specifically , we consider a set of users , each equipped with an infinite buffer . packets arrive into user s buffer according to some stationary ergodic markovian process of intensity . at the beginning of each slot , if user has packets in its buffer , it attempts to transmit a packet with fixed probability over a shared resource / channel . the transmission is successful only when no other user attempts to use the channel . the stability of such systems has been open since their very first analysis in 1979 by tsybakov and mikhailov . in this paper , we propose an approximate stability condition , that is provably exact when the number of users grows large . we provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users ( even two or three ) . we finally extend the results to the case of more efficient csma systems .    random multiple access , aloha , stability , mean field asymptotics ."}
{"article_id":"0809.5023","section_id":"i","document":"the results of the previous sections can be extended to the case of more efficient random multiple access methods . for example , in csma systems , a user senses the channel before transmitting . if the channel is busy , the user remains silent , and when the channel is idle , the user can attempt to transmit packets . this allows users to transmit for a large number of consecutive slots without being interrupted , and thus significantly increases the system efficiency . for example , in the case of slotted - aloha , it can be easily seen that when the channel is shared by @xmath0 users with similar characteristics , i.e. , same arrival rate @xmath480 and same transmission probability , then the maximum amount of traffic @xmath24 that the system can support is @xmath481 . with csma , this amount can be made arbitrarily close to 1 ( as we would obtain using a perfect centralized multi - access scheme ) just letting the channel holding time grow large . the model is similar than the one used for slotted - aloha , except that when a user attempts to use the channel , it keeps transmitting during @xmath108 consecutive slots . in the current ieee802.11 g standard @xcite , for data packets , we have roughly @xmath482 slots . there are @xmath0 users sharing the resource , and at the beginning of each slot , user @xmath1 transmits with probability @xmath3 if it senses the channel idle . packets whose transmission take @xmath108 slots arrive according to a stationary ergodic markovian process of intensity @xmath2 in the buffer of user @xmath1 . the analysis can be generalized to the case where users transmit at different rates , i.e. , when user @xmath1 keeps the channel for @xmath483 slots . to keep the formulas simple we just assume that all users transmit packets of the same sizes and at the same rate , for all @xmath1 , @xmath484 . another possible generalization is to allow the collision to be shorter than the packet successful transmissions . this can be useful when one wants to model rts / cts signaling scheme in ieee802.11-based systems .      in csma systems , users are synchronized in the sense that they observe the same periods where the channel is busy . the analysis of these systems can then be conducted as that of slotted - aloha : it suffices to analyze the system at the instants corresponding to the beginning of idle slots or to the beginning of transmissions . the approximate stability region is then constructed as follows .    for @xmath485 , define @xmath486 : @xmath487 where @xmath488 the approximate stability region @xmath489 is the set of points lying below one of the boundaries @xmath490 defined by : @xmath491^n , \\forall i ,   \\lambda_i=\\gamma_i(\\rho,\\sigma)\\bigg\\}.\\ ] ]    under the assumptions of theorem [ th : stab1 ] ( see the paragraph above theorem [ th : stab1 ] ) , we can show that @xmath489 tends to the actual stability region when @xmath0 grows large . as in the case of unit packet duration , we can show using theoretical arguments and numerical experiments that the approximation is extremely accurate . for example , the notion of @xmath105-homogenous directions can be easily extended , and @xmath492 is exact in those directions .","summary":"the transmission is successful only when no other user attempts to use the channel . we finally extend the results to the case of more efficient csma systems .   ","abstract":"we analyze the stability of standard , buffered , slotted - aloha systems . specifically , we consider a set of users , each equipped with an infinite buffer . packets arrive into user s buffer according to some stationary ergodic markovian process of intensity . at the beginning of each slot , if user has packets in its buffer , it attempts to transmit a packet with fixed probability over a shared resource / channel . the transmission is successful only when no other user attempts to use the channel . the stability of such systems has been open since their very first analysis in 1979 by tsybakov and mikhailov . in this paper , we propose an approximate stability condition , that is provably exact when the number of users grows large . we provide theoretical evidence and numerical experiments to explain why the proposed approximate stability condition is extremely accurate even for systems with a restricted number of users ( even two or three ) . we finally extend the results to the case of more efficient csma systems .    random multiple access , aloha , stability , mean field asymptotics ."}
{"article_id":"1602.06624","section_id":"i","document":"low - frequency observations are very important for the study of the statistical signatures of extragalactic sources , in particular source counts in the low - frequency sky , which until recently have been only characterized at the very highest end of the flux scale . the number of steep - spectrum sources increases rapidly as the sample selection frequency is lowered @xcite , because these sources become too faint to be detected at high frequencies leading to an expectation that low - frequency sky surveys will uncover this population in greater numbers than current cm - wavelength studies . as it is not trivial to infer the low - frequency ( @xmath5 300 mhz ) sky from higher frequency data , deep source counts at the same frequency as eor observations are required for accurate foreground modeling and subtraction . better understanding of the statistical properties and behavior of radio sources is required and motivated by a number of science goals , such as the foreground modeling and subtraction in the detection of the eor .    over the last 30 years , a large and ever increasing number of surveys and targeted observations have been performed at low frequencies commencing with the 6th cambridge ( 6c ) survey of radio sources @xcite , which covered the entire northern sky above 30 degrees at 151 mhz . since then a number of other surveys have been completed such as the 7th and 8th cambridge survey of radio sources ( 7c , and 8c : @xcite ) , the targeted survey on the culgoora circular array @xcite in which the flux densities of 1800 high - frequency - selected radio sources were measured at 80 and 160 mhz , the 74 mhz vla low - frequency sky survey ( vlss : @xcite ) above -30 degrees , the murchison widefield array commissioning survey ( mwacs : @xcite ) covering 6,100 @xmath6 between 104 and 196 mhz , and the precision array for probing the epoch of reionization ( paper ; @xcite ) low resolution survey of the southern sky at 145 mhz . current low frequency radio interferometers , such as lofar @xcite , gmrt @xcite , lwa @xcite , mwa @xcite and paper @xcite have made a considerable advance in our understanding of the population of extragalactic radio sources at frequencies below 300 mhz with all - sky low frequency surveys(@xcite ) . the upcoming square kilometre array ( ska ) is expected to continue to push the boundaries of low - frequency astronomy , observing the radio sky at much higher sensitivity and resolution . recently , @xcite determined the 154mhz source counts with mwa observation of the so - called eor0 field ( which is centered at j2000 @xmath7 ) and compared these with the 7c counts at 151mhz @xcite , as well as the gmrt source counts at 153mhz @xcite finding good agreement to a limiting flux density of @xmath840 mjy . using lofar , @xcite examined source counts at 34 , 46 and 62 mhz , a wavelength regime not explored since the 8c observations at 38 mhz 25 years earlier . the lofar observations are the deepest images ever obtained at these frequencies and reach noise levels of the order of a few mjy , being nearly 2 orders of magnitude deeper than the 8c survey . @xcite confirmed the previously known result that the average spectral index of radio galaxies flattens towards lower frequencies , as is expected from synchrotron losses @xcite . in addition to understanding the properties of the low frequency radio population to study the population itself , it is of great importance to properly characterize the population if we are to fully exploit these instruments to detect the eor as a precise sky model is vital for subtracting foreground sources @xcite . thus , source count studies of the low frequency sky are strongly motivated by a number of complementary science goals . the north celestial pole ( ncp ) region is covered at low - frequencies by the wsrt @xcite and lofar @xcite , it is also the sky region targeted by the 21 centimeter array ( 21cma ) . the key science goal for the 21cma is to statistically measure the redshifted 21 cm signal of neutral hydrogen from the eor . determining the radio source counts and understanding the spectral properties of the radio sources are important for removing the foreground sources and extracting the faint eor signal . in this paper , we present targeted observations centered on the ncp and extending 5 degrees in radius using the 21cma . we determine the source counts using eight sub - band images between 75 mhz and 175 mhz with flux densities down to @xmath9 jy . we also investigate the spectral properties of catalog sources and compare our source counts with the recent surveys . the outline of the paper is as follows . section 2 describes the 21cma telescope , the observation and data reduction pipeline . section 3 presents the source extraction process and resultant source catalog and properties including number counts , spectral indices , completeness and errors . discussion and concluding remarks are given in section 4 .","summary":"we present a catalog of 624 radio sources detected around the north celestial pole ( ncp ) with the 21 centimeter array ( 21cma ) , a radio interferometer dedicated to the statistical measurement of the epoch of reionization ( eor ) . the data are taken from a 12 h observation made on 2013 april 13 , with a frequency coverage from 75 to 175 mhz and an angular resolution of . the catalog includes flux densities at eight sub - bands across the 21cma bandwidth and provides the in - band spectral indices for the detected sources . to reduce the complexity of interferometric imaging from the so - called `` w '' term and ionospheric effects , the present analysis the 624 radio sources are found within 5 degrees around the ncp down to jy .","abstract":"we present a catalog of 624 radio sources detected around the north celestial pole ( ncp ) with the 21 centimeter array ( 21cma ) , a radio interferometer dedicated to the statistical measurement of the epoch of reionization ( eor ) . the data are taken from a 12 h observation made on 2013 april 13 , with a frequency coverage from 75 to 175 mhz and an angular resolution of . the catalog includes flux densities at eight sub - bands across the 21cma bandwidth and provides the in - band spectral indices for the detected sources . to reduce the complexity of interferometric imaging from the so - called `` w '' term and ionospheric effects , the present analysis are restricted to the east - west baselines within 1500 m only . the 624 radio sources are found within 5 degrees around the ncp down to jy . our source counts are compared , and also exhibit a good agreement , with deep low - frequency observations made recently with the gmrt and mwa . in particular , for fainter radio sources below jy , we find a flattening trend of source counts towards lower frequencies . while the thermal noise ( mjy ) is well controlled to below the confusion limit , the dynamical range ( ) and sensitivity of current 21cma imaging is largely limited by calibration and deconvolution errors , especially the grating lobes of very bright sources , such as 3c061.1 , in the ncp field which result from the regular spacings of the 21cma . we note that particular attention should be paid to the extended sources , and their modeling and removals may constitute a large technical challenge for current eor experiments . our analysis may serve as a useful guide to design of next generation low - frequency interferometers like the square kilometre array ."}
{"article_id":"1602.06624","section_id":"c","document":"we have analyzed 12 hours of data taken from the 21cma observations centered on the ncp . to reduce the complexity of interferometric image processing and the influence of ionospheric perturbation , we have used all 40 pods along the east - west arm but restricted our analysis to within a maximum baseline of 1500 m. we have calibrated the gain and primary beam of our telescope using the bright radio sources in the ncp field . following conventional self - calibration and deconvolution methods , we have detected a total of 624 radio sources over the central field within @xmath57 in frequency range of 75 - 175 mhz and the outer annulus of @xmath54 in the 75 - 125 mhz bands . by performing a monte - carlo simulation we have estimated a completeness of @xmath11 at @xmath184 jy . we have compared our source counts with the deep low - frequency observations made recently with gmrt and mwa , and the completeness - corrected source counts show a good agreement with these recent surveys at the corresponding frequency bands . while we are able to detect the fainter sources down to 10 mjy , the detection fraction has dropped to @xmath31 , making a ultra deep observation rather difficult and even impossible with current imaging algorithms . this is primarily caused by errors in sidelobes , calibration , and deconvolution as well as the confusion limit of the array . spacings between the 21cma pods are the integral multiples of 20 m. the original design of such configuration is for the purpose of redundant calibration and statistical measurement of the eor power spectrum ( e.g. @xcite ) . however , this layout also generates the grating lobes evident in our images ( @xcite ) . these equally spaced rings around the bright sources in the field have their brightness almost comparable to the central sources , and therefore should be accurately removed in the deconvolution processing otherwise , their residuals may be the major sources of contaminations for our imaging . indeed , our image quality is largely limited by the presence of imperfectly subtracted grating lobes of the brightest source in the ncp field , 3c061.1 . although this arises partially from the inaccurate calibration , the main reason is the poor modeling of 3c061.1 in our self - calibration processing . 3c061.1 is marginally resolved with 21cma , and its modeling should take the structured components with different surface brightness and spectral index into account ( e.g. @xcite ) . our next step is to improve our sky model by using a sophisticated model for 3c061.1 and even for very bright , far field sources such as cas a and cygnus a. finally , the theoretically expected thermal noise ( @xmath3 mjy ) is well below the confusion limit due to the unresolved , fainter sources , indicating that the dominated factor of influencing the sensitivity for low - frequency interferometric imaging is no longer the system noise but the cosmic sources in the sky .    several methods to improve our imaging algorithm including an accurate calibration ( e.g. sky modeling and redundant calibration ) , application of the w - term correction , and `` peeling '' sources @xcite are currently under investigation , with our ultimate goal towards detecting the eor power spectrum . our experience with the 21cma operation and data analysis may provide a useful guide to the design of next generation low - frequency radio array such as the ska . indeed , employment of numerous redundant baselines helps to improve the precision of calibration . however , it brings about very prominent grating lobes from bright sources both in - beam and in the far - field . this not only requires a more careful and accurate calibration of visibilities but also adds an extra difficulty to deconvolution processing . in particular , the grating lobes of the bright , structured sources like giant radio galaxies with jets are hard to model and thus subtract . in this sense , both random antenna element and station layouts should preferentially be chosen for low - frequency radio interferometers to suppress the grating lobes and sidelobes of bright sources . we note that an extensive study on this topic has recently been carried out by @xcite .    to summarize , with current layout of the 21cma and conventional imaging algorithm , we have reached a sensitivity of a few mjy and a dynamical range of @xmath185 . we may have to improve our imaging quality by an order of magnitude in order to see statistically the eor signature .","summary":"are restricted to the east - west baselines within 1500 m only . our source counts are compared , and also exhibit a good agreement , with deep low - frequency observations made recently with the gmrt and mwa . in particular , for fainter radio sources below jy , we find a flattening trend of source counts towards lower frequencies . while the thermal noise ( mjy ) is well controlled to below the confusion limit , the dynamical range ( ) and sensitivity of current 21cma imaging is largely limited by calibration and deconvolution errors , especially the grating lobes of very bright sources , such as 3c061.1 , in the ncp field which result from the regular spacings of the 21cma . we note that particular attention should be paid to the extended sources , and their modeling and removals may constitute a large technical challenge for current eor experiments . our analysis may serve as a useful guide to design of next generation low - frequency interferometers like the square kilometre array .","abstract":"we present a catalog of 624 radio sources detected around the north celestial pole ( ncp ) with the 21 centimeter array ( 21cma ) , a radio interferometer dedicated to the statistical measurement of the epoch of reionization ( eor ) . the data are taken from a 12 h observation made on 2013 april 13 , with a frequency coverage from 75 to 175 mhz and an angular resolution of . the catalog includes flux densities at eight sub - bands across the 21cma bandwidth and provides the in - band spectral indices for the detected sources . to reduce the complexity of interferometric imaging from the so - called `` w '' term and ionospheric effects , the present analysis are restricted to the east - west baselines within 1500 m only . the 624 radio sources are found within 5 degrees around the ncp down to jy . our source counts are compared , and also exhibit a good agreement , with deep low - frequency observations made recently with the gmrt and mwa . in particular , for fainter radio sources below jy , we find a flattening trend of source counts towards lower frequencies . while the thermal noise ( mjy ) is well controlled to below the confusion limit , the dynamical range ( ) and sensitivity of current 21cma imaging is largely limited by calibration and deconvolution errors , especially the grating lobes of very bright sources , such as 3c061.1 , in the ncp field which result from the regular spacings of the 21cma . we note that particular attention should be paid to the extended sources , and their modeling and removals may constitute a large technical challenge for current eor experiments . our analysis may serve as a useful guide to design of next generation low - frequency interferometers like the square kilometre array ."}
{"article_id":"nucl-th9906012","section_id":"i","document":"the purpose of this paper is to derive the light - front formalism necessary to compute the properties of finite nuclei . nuclear properties are very well handled within the existing conventional nuclear theory , so it behooves us to explain why we are embarking on this project . our motivation is that understanding experiments involving high energy nuclear reactions seems to require that light - front dynamics and light cone variables be used . consider the emc experiment @xcite , which showed that there is a significant difference between the parton distributions of free nucleons and nucleons in a nucleus . this difference can interpreted as a shift in the momentum distribution of valence quarks towards smaller values of the bjorken variable @xmath8 . the bjorken variable is a ratio of the plus - momentum @xmath9 of a quark to that of the target . thus light cone variables are relevant . if one uses @xmath10 as a momentum variable the corresponding canonical spatial variable is @xmath11 and the time variable is @xmath12 . it is important to realize that the use of light - front dynamics is not limited to quarks within the nucleon  it also applies to nucleons within the nucleus . this formalism is useful whenever the momentum of initial or final state nucleons is large compared to their mass @xcite . in particular , it can be used for @xmath13 and @xmath14 reactions . if one uses light - front variables for nucleons in a nucleus , it is also necessary to maintain consistency with the information derived previously using conventional nuclear dynamics . this provides the technical challenge which we address in the present manuscript . the conventional equal - time approach to nuclear structure physics provides an excellent framework , so it is worthwhile to introduce the light - front variables and describe the expected advantages in a general way . the use of the light - cone variables can be obtained using a simple argument based on kinematics @xcite . suppose the virtual photon that is absorbed by a fermion at a space - time point ( @xmath15 , @xmath16 ) . the fermion then starts to move at high momentum and nearly the speed of light and emits the photon at another space time point ( @xmath17 , @xmath18 ) . in between the two times , the wave function of the entire system has undergone a time evolution given by the complicated operator @xmath19 . but we have @xmath20 , if the @xmath21axis is opposite to the direction of the virtual photon . the two scattering events occur at different times , but at the same value of @xmath22 . thus if we use @xmath23 as a time variable , no time evolution factor appears . the net result is that the cross section involves light - like correlation functions which involve field operators evaluated at the same light - front time : @xmath24 ( see for example the reviews @xcite ) . thus it is a specific and general feature of the light - front wave approach that knowing only the ground state wave function is sufficient for computing the distribution functions . let us review the salient features of the basic idea that using the light - front approach leads to a simplified treatment . to be specific , consider high energy electron scattering from nucleons in nuclei . the key ingredient in the light - front simplification is to realize the main difference between the two formalisms . in the equal - time formalism , sums over intermediate states are taken over eigenstates of the hamiltonian , @xmath25 . the usual three momentum is conserved , but energy is not conserved in intermediate states . in the light - front approach one sums over eigenstates of the minus component of the total momentum operator . the value of @xmath1 is not conserved in intermediate state sums , and the values of @xmath0 and @xmath26 are conserved . this is especially convenient for high energy reactions , in which the plus - component is the largest component of the momentum for each projectile or ejectile .    the advantage of using @xmath1 as an `` energy '' variable can be easily described . let the four - momentum @xmath27 of the exchanged virtual photon be given by @xmath28 , with @xmath29 , and @xmath30 and @xmath31 are both very large but @xmath32 is finite ( the bjorken limit ) . in this case it is worthwhile to use the light - cone variables @xmath33 in which @xmath34 , @xmath35 , so that @xmath36 . here @xmath37 is the mass of a nucleon and @xmath38 is the bjorken variable . we shall neglect @xmath39 in comparison to @xmath40 , noting that corrections to this can be handled in a systematic fashion . then the schematic form of the scattering cross section for @xmath41 , where @xmath42 represents the final nuclear eigenstate of @xmath1 , and @xmath43 the four - momentum of the final proton , is given by @xmath44 here the operator @xmath45 is a schematic representation of the electromagnetic current . performing the four - dimensional integral over @xmath43 leads to the expression @xmath46 the argument of the delta function @xmath47 . thus we see that @xmath48 does not appear in the argument of the delta function , or anywhere else , so that we can replace the sum over intermediate states by unity . in the usual equal - time representation , one finds the argument of the delta function to be @xmath49 . the energy of the final state appears , and one can not do the sum .    to proceed further in this schematic approach we take @xmath50 where @xmath51 is a nucleon destruction operator and @xmath52 . it is useful to define @xmath53 because @xmath54 as demanded by the delta function . then one can re - express eq . ( [ int ] ) as @xmath55 where @xmath56 is the probability for a nucleon in the ground state to have a momentum @xmath57 . integration in eq . ( [ ds2 ] ) leads to @xmath58 with @xmath59 as the probability for a nucleon in the ground state to have a plus momentum of @xmath60 .    the quantity @xmath59 has been a widely used prescription up for handling the light - front in a simple way . the variable @xmath60 is replaced by @xmath61 , in which the label @xmath62 denotes a shell - model orbital @xmath63 of binding energy @xmath64 . then @xmath65 in which @xmath66 is an occupation probability . the validity of this prescription , which rests on a reasonable assumption , is rather suspect because the variable @xmath67 is a kinematic variable , unrelated to discrete eigenvalues of a wave equation . one of the main purposes of the present paper is to see if anything like this prescription emerges from our calculations . we shall see that eq . ( [ up ] ) is not obtained , if a vector potential is a significant part of the nuclear mean field . it is useful to discuss the relation with @xmath68-scaling @xcite . the arguments that the cross section depends on a plus - momentum distribution are well known when used for quarks in a nucleon , but they also apply to nucleons in a nucleus @xcite . ji and filippone @xcite showed that the @xmath68 scaling function @xmath69 extracted in quasi - elastic electron scattering on nuclei is actually the light cone plus - momentum distribution function for nucleons in the nucleus . it is useful to use a relativistic form of the variable @xmath68 @xcite in which @xmath70 as both @xmath71 and @xmath72 are large in magnitude , and @xmath73 is the single nucleon separation energy . but @xmath74 , so that @xmath75 here @xmath76 is a new y - scaling variable . this means that according to eq . ( [ one ] ) @xmath77 so that a measurement of @xmath78 determines the probability that the struck nucleon has a plus - momentum of @xmath79 . this probability also enters in convolution model calculations of nuclear deep inelastic scattering . the use of light - front dynamics to compute nuclear wave functions should allow us to compute @xmath69 from first principles . furthermore , we claim that using light - front dynamics incorporates the experimentally relevant kinematics from the beginning , and therefore is the most efficient way to compute the cross sections for nuclear deep inelastic scattering and nuclear quasi - elastic scattering . it is worthwhile to review some of the features of the emc effect @xcite . the key experimental result is the suppression of the structure function for @xmath80 . this means that the valence quarks of bound nucleons carry less plus - momentum than those of free nucleons . one way to understand this result is to postulate that mesons carry a larger fraction of the plus - momentum in the nucleus than in free space . while such a model explains the shift in the valence distribution , one obtains at the same time a meson ( i.e. anti - quark ) distribution in the nucleus , which is strongly enhanced compared to free nucleons and which should be observable in drell - yan experiments @xcite . however , no such enhancement has been observed experimentally @xcite , and the implications are analyzed in ref . @xcite . the use of light - front dynamics allows us to compute the necessary nuclear meson distribution functions using variables which are experimentally relevant . the need for a computation of such functions in a manner consistent with generally known properties of nuclei led one of us to attempt to construct a light front treatment of nuclear physics @xcite . these calculations , using a lagrangian in which dirac nucleons are coupled to massive scalar and vector mesons @xcite , treated the example of infinite nuclear matter within the mean field approximation . in this case , the meson fields are constants in both space and time and the momentum distribution has support only at @xmath81 . such a distribution would not be accessible experimentally , so that the suppression of the plus - momentum of valence quarks would not imply the existence of a corresponding testable enhancement of anti - quarks . however , it is necessary to ask if the result is only a artifact of the infinite nuclear size and of the mean field approximation . the present paper is an attempt to handle finite - sized nuclei using light - front dynamics . it is worthwhile to discuss , in a general way , how it is that we are able to find spectra which have the correct number of degenerate states . let us imagine that we try to determine eigenstates of a lf hamiltonian by means of a variational calculation . simply minimizing the lf energy obviously leads to nonsensical results since the lf energy scales like the inverse of the lf momentum . even if one has only a poor ansatz for the intrinsic wave function , one can easily reach zero energy by letting the overall momentum scale to infinity ! however , this problem is avoided by performing a constrained variation , in which the total lf momentum is fixed by including a lagrange multiplier term proportional to the total momentum in the lf hamiltonian . note that this is not a problem if one is able to use a fock space basis in which the total plus and @xmath82 momentum of each component are fixed . in calculations involving many particles , the fock state approach can not be used in practical calculations  instead one uses a mean field in which each particle moves in an `` external '' potential . in this case the total momentum is not fixed , and a lagrange multiplier term needs to be included in order to avoid solutions with infinite lf momentum .    in order to fix this potential problem with `` runaway solutions '' ( @xmath83 ) to variational calculations for lf hamiltonians , any term proportional to @xmath0 would suffice . however , by setting the coefficient for the term proportional to @xmath0 equal to one , _ i.e. _ minimizing @xmath2 , one automatically guarantees that @xmath84 ( or @xmath85 ) . the reason is that , using covariance , @xmath1 has eigenvalues of the form @xmath86 , _ i.e. _ it scales like @xmath87 . therefore , when one minimizes @xmath88 with respect to @xmath0 , the minimum occurs for @xmath89 , which yields @xmath90 as well . this `` equipartition '' between @xmath0 and @xmath1 thus arises since the two operators scale in exactly opposite ways under longitudinal boosts . note that this is quite analogous to the nonrelativistic harmonic oscillator where , under scale transformations , potential and kinetic energy scale in opposite ways , resulting in the equipartition between potential and kinetic energy . the net result is that we minimize the sum of @xmath91 . the need to include the plus - momentum can also be seen in a simple example . consider a nucleus of @xmath7 nucleons of momentum @xmath92 , @xmath93 , which consists of a nucleon of momentum @xmath94 , and a residual @xmath95 nucleon system which must have momentum @xmath96 . the kinetic energy @xmath97 is given by the expression @xmath98 in the second expression , one is tempted to neglect the term @xmath5 in comparison with @xmath99 . this would be a mistake . instead make the expansion @xmath100 because for large @xmath7 , @xmath101 . for free particles , of ordinary three momentum @xmath102 one has @xmath103 and @xmath104 , so that @xmath105 we see that @xmath97 depends only on the magnitude of a three - momentum and rotational invariance is restored . the physical mechanism of this restoration is the inclusion of the recoil kinetic energy of the residual nucleus . the organization of the paper is as follows . the light - front quantization for our chosen lagrangian is is presented in sec . this quantization is applied , along with a constrained minimization of the expectation value of @xmath1 , to derive a light - front version of mean field theory in sec . we obtain a new light version of the equation that defines the single nucleon modes . the solutions of this equation are approximately a non - trivial phase factor times the solutions of the usual equal - time et dirac equation . the consequences of this phase factor are discussed . the meson fields are treated as expectation values of operators . the equations for these expectation values are closely related to the meson field equations appearing in the usual treatment of the walecka model . however , the mesonic fock space is accessible in our formalism . our nucleon mode equation is simplified by the use of a two - component spinor formalism @xcite , and by an angular momentum reduction in sec . the numerical aspects are discussed in app . the binding energies , nucleon and meson distributions for @xmath3o and @xmath4ca are presented in sec .  v. a concluding discussion appears in sec . numerical details of how we evaluate the momentum distributions are given in app . [ appb ] . a brief discussion of some of the results can be found in ref . . a related set of solutions of some toy model problems and a heuristic derivation of our nucleon mode equation will appear in a separate paper @xcite .","summary":"a light - front treatment for finite nuclei is developed from a relativistic effective lagrangian ( qhd1 ) involving nucleons , scalar mesons and vector mesons . we obtain a new light - front version of the equation that defines the single nucleon modes . the solutions of this equation are approximately a non - trivial phase factor times certain solutions of the usual equal - time dirac equation . the ground state wave function is treated as a meson - nucleon fock state , and the meson fields are treated as expectation values of field operators in that ground state . the resulting equations for these expectation values are shown to be closely related to the usual meson field equations . . the nucleon plus momentum distribution ( probability for a nucleon to have a given value of ) is obtained , and peaks for values of about seventy percent of the nucleon mass .","abstract":"a light - front treatment for finite nuclei is developed from a relativistic effective lagrangian ( qhd1 ) involving nucleons , scalar mesons and vector mesons . we show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator to be the same as that for . this is the same as minimizing the sum of the total momentum operators : . we obtain a new light - front version of the equation that defines the single nucleon modes . the solutions of this equation are approximately a non - trivial phase factor times certain solutions of the usual equal - time dirac equation . the ground state wave function is treated as a meson - nucleon fock state , and the meson fields are treated as expectation values of field operators in that ground state . the resulting equations for these expectation values are shown to be closely related to the usual meson field equations . a new numerical technique to solve the self - consistent field equations is introduced and applied too andca . the computed binding energies are essentially the same as for the usual equal - time theory . the nucleon plus momentum distribution ( probability for a nucleon to have a given value of ) is obtained , and peaks for values of about seventy percent of the nucleon mass . the mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions , with a result that the vector mesons carry about thirty percent of the nuclear plus - momentum . the vector meson momentum distribution becomes more concentrated at as increases ."}
{"article_id":"nucl-th9906012","section_id":"i","document":"the previous sections present a derivation of a light - front version of mean field theory . the necessary technique is to minimize expectation value of the sum @xmath2 . this leads to a new set of coupled equations ( [ nplus ] ) and ( [ nminus ] ) for the single nucleon modes . these depend on the meson fields of eqs . ( [ phieq ] ) and ( [ veq ] ) . the most qualitatively startling feature emerging from the derivation is that the meson field equations ( [ phieq ] ) and ( [ veq ] ) are the same as that of the usual theory , except that @xmath302 of the equal - time theory translates to @xmath399 of the light - front version . this can be understood in a simple manner by noting that light - front quantization occurs at @xmath24 . if one then sets @xmath400 , then @xmath401 . however , this simple argument is not really justified , because using @xmath402 precludes the use of @xmath302 and @xmath403 . a general argument , using the feature that a static source in the usual coordinates corresponds to a source moving with a constant velocity in light front coordinates , will be presented in a separate paper @xcite . that paper also contains a number of solutions of toy models .    even though the meson field equations of the light - front and equal - time theories are the same , there are substantial and significant differences between the two theories . in our treatment , the mesonic fields are treated as quantum field operators . the mean field approximation is developed by replacing these operators by their expectation values in the complete ground state nuclear wave function . this means that the ground state wave function contains fock terms with mesonic degrees of freedom . we can therefore compute expectation values other than that of the field . in particular , we are able to obtain the mesonic momentum distributions ( sec . this feature has been absent in standard approaches . we obtain an approximate solution ( [ emcv ] ) of our nucleon mode equation . our nucleon mode functions are approximately a phase factor times the usual equal - time mode functions ( evaluated at @xmath404 ) . this shows that the energy eigenvalues of the two theories should have very similar values . but the wave functions are different the presence of the phase factor explicitly shows that the nucleons give up substantial amounts of plus momentum to the vector mesons .    a new numerical technique , discussed in sec . iv and app .  [ appa ] , is introduced to solve the coupled nucleon and meson field equations . our results display the expected @xmath405 degeneracy of the single nucleons levels , and the resulting binding energies are essentially the same as for the usual equal - time formulation . this indicates that the approximation ( [ emcv ] ) is valid .    as discussed in sec . vi - d , the present results related to lepton - nucleus deep inelastic scattering experiments and @xmath398 reactions are not consistent with experimental findings . this is because , in @xmath4ca for example , the nucleons carry only 72% of the plus momentum . this is a result of the quantity @xmath397 , which acts as a nucleon effective mass , is very small , about 670 mev . the use of a small effective mass and a large vector potential enables a simple reproduction of the nuclear spin orbit force @xcite . however , effects beyond the mean field may lead to a significant effective tensor coupling of the isoscalar vector meson @xcite and to an increased value of the effective mass . such effects are incorporated in bruckner theory @xcite which , for infinite nuclear matter , results in nucleons having about 80 - 85% of the nuclear plus - momentum . a light - front version @xcite should be applied to finite nuclei with better success in reproducing the data . another approach could be to use different lagrangians , with non - linear couplings between scalar mesons and the nucleons @xcite , or ones in which the coupling is of derivative form @xcite : @xmath406 . these models are known to have significantly smaller magnitudes of the scalar and vector potentials . in particular , in nuclear matter vector mesons carry only about 10 - 15% of the nuclear - plus momentum . another interesting possibility would be to obtain a light - front version of the quark - meson coupling model @xcite , in which confined quarks interact by exchanging mesons with quarks in other nucleons . this model , also has smaller magnitudes of the scalar and vector potentials .    in any case , these kinds of nuclear physics calculations can be done in a manner in which modern nuclear dynamics is respected , boost invariance in the @xmath302-direction is preserved , and in which the rotational invariance so necessary to understanding the basic features of nuclei is maintained . p.g.b . was supported in part by the natural sciences and engineering research council of canada .","summary":"the computed binding energies are essentially the same as for the usual equal - time theory the mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions , with a result that the vector mesons carry about thirty percent of the nuclear plus - momentum .","abstract":"a light - front treatment for finite nuclei is developed from a relativistic effective lagrangian ( qhd1 ) involving nucleons , scalar mesons and vector mesons . we show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator to be the same as that for . this is the same as minimizing the sum of the total momentum operators : . we obtain a new light - front version of the equation that defines the single nucleon modes . the solutions of this equation are approximately a non - trivial phase factor times certain solutions of the usual equal - time dirac equation . the ground state wave function is treated as a meson - nucleon fock state , and the meson fields are treated as expectation values of field operators in that ground state . the resulting equations for these expectation values are shown to be closely related to the usual meson field equations . a new numerical technique to solve the self - consistent field equations is introduced and applied too andca . the computed binding energies are essentially the same as for the usual equal - time theory . the nucleon plus momentum distribution ( probability for a nucleon to have a given value of ) is obtained , and peaks for values of about seventy percent of the nucleon mass . the mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions , with a result that the vector mesons carry about thirty percent of the nuclear plus - momentum . the vector meson momentum distribution becomes more concentrated at as increases ."}
{"article_id":"astro-ph0105123","section_id":"i","document":"angular momentum is clearly one of the key physical ingredients in the process of galaxy formation . the total angular momentum , and its distribution , must have a crucial role in determining the galaxy history and final type . it has therefore been a subject for classical investigations , pioneered by hoyle ( 1949 ) , and then analysed qualitatively by peebles ( 1969 ) . this led to the ` standard ' theory for the origin of angular momentum in the framework of hierarchical cosmological structure formation , the tidal - torque theory ( ttt ) due to doroshkevich ( 1970 ) and white ( 1984 ) . special interest in the subject has been revived recently because of a  spin crisis \" , arising from cosmological simulations of galaxy formation which use hydrodynamical gravitational codes to follow the gas dynamics inside dark - matter haloes , and semi - analytical recipes for star formation and feedback . these simulations seem to yield luminous galaxies that are significantly smaller , and of much less angular momentum than observed disc galaxies ( navarro , frenk & white 1995 ; navarro & steinmetz 1997 , 2000 ) . the discovery of massive black holes in galactic centers ( kormendy & richstone 1995 ; magorrian 1998 ; gebhardt 2000a , b ) provides another motivation for understanding the detailed distribution of angular momentum within galaxies . a general need for a detailed recipe for the build - up of angular momentum in galaxies comes from the developing semi - analytic models , which have been proven very useful in the study of galaxy formation ( e.g. white & frenk 1991 ; kauffmann , white & guiderdoni 1993 ; cole et al . 1994 ; somerville & primack 1999 ) . another current motivation comes from weak lensing studies . our ability to reconstruct maps of the cosmic mass distribution from weak gravitational lensing measurements ( bacon , refregier & ellis 2000 ; kaiser , wilson & luppino 2000 ; van waerbeke 2000 , 2001 ; wittman 2000 ) is hampered by the unknown intrinsic distribution and alignment of galaxy shapes . as a first guess , one crudely assumes that the shapes and orientations of background galaxies are uncorrelated in space , and that the detected correlations of galaxy ellipticities are solely due to the lensing by the foreground mass distribution . however , a series of observations ( brown 2000 ; pen , lee & seljak 2000 ) and numerical simulations ( croft & metzler 2000 ; heavens , refregier & heymans 2000 ; dekel 2000 ) evidenced that both the intrinsic galaxy shapes and their spins are spatially correlated . theoretical models for the alignment of disc galaxies orientations tend to assume that they are induced by spin correlations ( catelan , kamionkowski & blandford 2001 ; crittenden 2001 ) . these issues add a timely aspect to the motivation for revisiting the classical problem of angular momentum , in an attempt to sharpen our understanding of its various components . this includes the first step of angular - momentum acquisition by dark haloes , which might be particularly assumed to be fairly well understood . the basic idea of ttt is that most of the angular momentum is being gained gradually by proto - haloes in the linear regime of density fluctuations growth , due to tidal torques from neighboring fluctuations , and that this process continues until the proto - halo reaches its maximum extent . the further assumption is that only little angular momentum is being exchanged between haloes later on in the non - linear regime , after the proto - haloes have decoupled from the expanding background and collapsed to virialized systems . it is commonly assumed that the baryonic material , which in general follows the dark - matter distribution inside each proto - halo , gains a similar specific angular momentum and carries it along when it contracts to form a luminous galaxy at the halo centre . this should allow us to predict galactic spins using the approximate but powerful analytic tools of quasi - linear theory of gravitational instability .    in a series of papers , we evaluate the performance of the ttt approximation , and trace the roles of its various ingredients , using a cosmological @xmath0-body simulation with thousands of well - resolved haloes . as we do so , we find to our surprise that some of the basic ingredients of ttt , which are commonly assumed to be of ` text - book ' status , involve certain unjustified assumptions and confused understandings , which may lead to poor approximations . these papers represent attempts to clarify some of these controversial issues . we address the ttt at different levels . in this paper ( paper i ) , we evaluate how well does the approximation predict the final angular momentum of a halo , given full knowledge of the corresponding initial proto - halo and the cosmological realization . in paper ii ( porciani , dekel & hoffman 2001 ) , we attempt a deeper level of understanding of the origin of halo angular momentum , by investigating the relation between the different components of ttt . this study connects to the fundamental open question of how to identify a proto - halo in a given realization of initial conditions . in paper iii ( porciani & dekel in preparation ) , we revise the standard scaling relation of ttt , based on the fact that the shear tensor is only weakly correlated with the density contrast of the proto - halo ( the density and shear being the trace and traceless parts of the same , deformation tensor ) . this scaling relation is used to predict the typical angular - momentum profile of haloes ( dekel 2001 ; bullock 2001b ) , and to provide a simple way to incorporate angular momentum in semi - analytic models of galaxy formation ( maller , dekel & somerville 2002 ) .    given the initial conditions of a proto - halo and its environment , ttt predicts the final halo angular momentum based on four specific assumptions as follows : ( a ) the flow is laminar , with a one - to - one correspondence of eulerian and lagrangian positions , or the velocity field is properly smoothed such that laminarity prevails in practice . ( b ) the velocities obey the zeldovich approximation . ( c ) the potential at every point within the proto - halo can be approximated by its taylor expansion to second order ( with respect to spatial separation ) about the centre of mass . ( d ) there is little contribution to the halo angular momentum from non - linear effects . in the current paper , we set to evaluate the global success of ttt in this task , and try to address the validity of each of the above assumptions . the role of non - linear effects , in particular , turns out to be the key issue . this will be an attempt to follow and improve on earlier work by white ( 1984 ) , hoffman ( 1986 , 1988 ) , barnes & efstathiou ( 1987 ) , catelan & theuns ( 1996 ) , lee & pen ( 2000 ) and sugerman , summers & kamionkowski ( 2000 ) . the outline of this paper is as follows : in we summarize the basics of linear tidal - torque theory . in we describe the simulation and the halo finder . in we describe the implementation of ttt to proto - haloes . in we evaluate the success of ttt in predicting the amplitudes of halo spins . in we assess the success of ttt in predicting the directions of halo spins . in we address the spatial coherence of spin directions , which is directly relevant to intrinsic alignments in the context of gravitational lensing . in we discuss our results and conclude .","summary":"( [ eq:#1 ] ) # 1#1    cosmology : dark  matter  cosmology : large - scale structure of universe  cosmology : theory  galaxies : formation  galaxies : haloes  galaxies : structure","abstract":"we evaluate the success of linear tidal - torque theory ( ttt ) in predicting galactic - halo spin using a cosmological-body simulation with thousands of well - resolved haloes . the proto - haloes are identified by tracing today s haloes back to the initial conditions . the ttt predictions for the proto - haloes match , on average , the spin amplitudes of today s virialized haloes if linear growth is assumed until , or 55 - 70 per cent of the halo effective turn - around time . this makes it a useful qualitative tool for understanding certain average properties of galaxies , such as total spin and angular - momentum distribution within haloes , but with a random scatter of the order of the signal itself . non - linear changes in spin direction cause a mean error of in the ttt prediction at , such that the linear spatial correlations of spins on scales are significantly weakened by non - linear effects . this questions the usefulness of ttt for predicting intrinsic alignments in the context of gravitational lensing . we find that the standard approximations made in ttt , including a second order expansion of the zeldovich potential and a smoothing of the tidal field , provide close - to - optimal results .    # 1[sec:#1 ] # 1fig .  [ fig:#1 ] # 1eq .  ( [ eq:#1 ] ) # 1#1    cosmology : dark  matter  cosmology : large - scale structure of universe  cosmology : theory  galaxies : formation  galaxies : haloes  galaxies : structure"}
{"article_id":"astro-ph0105123","section_id":"c","document":"we have evaluated the performance of linear tidal - torque theory in predicting the spin of galactic haloes using @xmath80 well - resolved virialized dark - matter clumps extracted from a cosmological @xmath0-body simulation . we defined haloes in today s density field using the standard friends - of - friends algorithm , but it would be useful for future work to check robustness to alternative halo finders as well as to different cosmological scenarios . we found that , for a given proto - halo at the initial conditions , ttt provides a successful order - of - magnitude estimate of the final halo spin amplitude . the ttt prediction matches on average the spin amplitude of today s virialized haloes if linear ttt growth is assumed until about @xmath242 , or about 5/9 of the turn - around time for each halo . the random error , from halo to halo , is about a factor of two . this makes ttt useful for studying certain aspects of galaxy formation , such as the origin of a universal spin profile in haloes ( bullock 2001b ; dekel 2001 ) , but only at the level of average properties . non - linear evolution causes significant variations in spin direction , which limit the accuracy of the ttt predictions to a mean error of @xmath2 . furthermore , spatial correlations of spins on scales @xmath4 are strongly weakened by non - linear effects . this limits the usefulness of ttt in predicting intrinsic galaxy alignments in the context of weak gravitational lensing ( catelan 2001 ; crittenden 2001 ) . this situation may improve if the orientations of today s discs were determined by the halo spins at a very high redshift , which are better described by ttt . on the other hand , we know this only for the haloes selected at @xmath74 , and not necessarily for the subhaloes which host disc formation at higher redshifts . a detailed study of this effect would require a high - resolution simulation in which a detailed galaxy formation scheme is incorporated . a preliminary analysis performed by using dark matter haloes selected at @xmath213 showed that , also in this case , non - linear effects decrease linear spin - spin correlations by a factor of a few .    for practitioners of ttt , we found that the standard approximations made in ttt , such as the second order expansion of the zeldovich potential , and the smoothing of the shear tensor on the proto - halo scale , are hard to improve upon . the inaccuracies in the ttt predictions are dominated by real non - linear effects rather than the above approximations .    in order to deepen our understanding of how ttt actually works , we investigate in paper ii the cross - talk between the proto - halo inertia tensor and the external shear tensor . we find to our surprise that they are strongly correlated , in the sense that their minor , major and medium principal axes tend to be aligned , in this order . this means that the angular momentum , which plays such a crucial role in the formation of disc galaxies , is only a residual which arises from the little , @xmath243 per cent deviations from perfect alignment of @xmath244 and @xmath245 . we find there that the @xmath246 correlation induces a weak tendency of the proto - halo spin to be perpendicular to the major axis of @xmath244 , but non - linear changes in spin direction erase almost any memory of the initial shear tensor , and therefore observed spin directions can not serve as very useful indicators for the initial shear tensor ( cf . lee & pen 2000 ) . on the other hand , the strong @xmath246 correlation investigated in paper ii provides a promising hint for how to solve a long - standing problem in galaxy formation theory , of identifying the boundaries of proto - haloes in cosmological initial conditions ( porciani , dekel & hoffman , in preparation ) .    in our studies of the cross - talk between the different components of ttt , we have also realized another surprise that leads to a revision in the standard scaling relation of ttt ( while 1984 ) . we find in paper iii ( porciani & dekel in preparation ) that the off - diagonal , tidal terms of the deformation tensor , which drive the torque , are weakly correlated with the diagonal terms , which determine the overdensity at the proto - halo centre . the latter enters the ttt scaling relation via the expected collapse time of the proto - halo , and the weak correlation with the torque leads to a modification in the scaling relation . the revised scaling relation can be applied shell by shell , together with an extended press - schechter recipe for merger history , in order to explain the origin of the universal angular - momentum profile of haloes ( bullock 2001b ; dekel 2001 ) . it can also be very useful in incorporating spin in semi - analytic models of galaxy formation ( maller , dekel & somerville 2002 ) . = 8 cm = 8 cm","summary":"we evaluate the success of linear tidal - torque theory ( ttt ) in predicting galactic - halo spin using a cosmological-body simulation with thousands of well - resolved haloes . the ttt predictions for the proto - haloes match , on average , the spin amplitudes of today s virialized haloes if linear growth is assumed until , or 55 - 70 per cent of the halo effective turn - around time . this makes it a useful qualitative tool for understanding certain average properties of galaxies , such as total spin and angular - momentum distribution within haloes , but with a random scatter of the order of the signal itself . non - linear changes in spin direction cause a mean error of in the ttt prediction at , such that the linear spatial correlations of spins on scales are significantly weakened by non - linear effects . this questions the usefulness of ttt for predicting intrinsic alignments in the context of gravitational lensing . we find that the standard approximations made in ttt , including a second order expansion of the zeldovich potential and a smoothing of the tidal field , provide close - to - optimal results .   ","abstract":"we evaluate the success of linear tidal - torque theory ( ttt ) in predicting galactic - halo spin using a cosmological-body simulation with thousands of well - resolved haloes . the proto - haloes are identified by tracing today s haloes back to the initial conditions . the ttt predictions for the proto - haloes match , on average , the spin amplitudes of today s virialized haloes if linear growth is assumed until , or 55 - 70 per cent of the halo effective turn - around time . this makes it a useful qualitative tool for understanding certain average properties of galaxies , such as total spin and angular - momentum distribution within haloes , but with a random scatter of the order of the signal itself . non - linear changes in spin direction cause a mean error of in the ttt prediction at , such that the linear spatial correlations of spins on scales are significantly weakened by non - linear effects . this questions the usefulness of ttt for predicting intrinsic alignments in the context of gravitational lensing . we find that the standard approximations made in ttt , including a second order expansion of the zeldovich potential and a smoothing of the tidal field , provide close - to - optimal results .    # 1[sec:#1 ] # 1fig .  [ fig:#1 ] # 1eq .  ( [ eq:#1 ] ) # 1#1    cosmology : dark  matter  cosmology : large - scale structure of universe  cosmology : theory  galaxies : formation  galaxies : haloes  galaxies : structure"}
{"article_id":"1309.4967","section_id":"r","document":"figure [ img : field ] shows the three - color composite image ( _ v _ : blue , _ r _ : green , _ i _ : red ) of the mcneil s nebula field ( fov @xmath25 arcmin@xmath26 ) obtained from igo on 2010 february 13 . secondary standard stars used for flux calibration are marked as a , b , c and d. the outburst source v1647 ori , illuminating the nebula , is marked at the center . the region c , possibly unrelated to herbig - haro object , hh 22a , which is illuminated by v1647 ori is also marked . v1647 ori had already reached its peak outburst phase before our first optical observation in september 2008 . its light curve steadily continued in peak outburst flux ( high plateau ) phase even until our last observation taken in march 2013 . however , our long - term continuous monitoring from 2008 september 14 to 2013 march 11 shows a slow but steady linear declining trend in the brightness of the source and nebula @xcite . the linear slopes and the error in estimates of slopes were obtained by simple linear regression by ordinary least square fitting . _ v _ , _ r _ and _ i _ magnitudes of v1647 ori and of region c , which is illuminated by the v1647 ori from its face - on angle of the disc , are listed in table [ table : mags ] . only a portion of the table is provided here . the complete table is available in electronic form as part of the online material . light curves of v1647 ori in _ i _ and _ r_-bands clearly show a steady dimming ( see figure [ img : v1647lightcurve ] ) . during the last four and a half years of its second outburst , the brightness in _ i _ and _ r _ bands have decreased by @xmath40 mag . the rate of decline in magnitude of v1647 ori is 0.036@xmath41 mag yr@xmath2 in _ i_-band and 0.038@xmath41 mag yr@xmath2 in _ r_-band . we do not see any statistically significant decline in _ v_-band magnitude of v1647 ori . this could be due to higher fraction of contamination of nebula over v1647 ori s aperture and slightly higher error in magnitudes due to faintness of source in _ v_-band . these flux changes are along our direct line of sight at an angle of @xmath42 to the plane of disc @xcite . however , the flux measured along the cavity in perpendicular direction to the disc , which is reflected from region c , shows a dimming trend of 0.059@xmath43 mag yr@xmath2 in _ i_-band , 0.051@xmath43 mag yr@xmath2 in _ r_-band and 0.060@xmath43 mag yr@xmath2 in _ v_-band ( see figure [ img : hh22lightcurve ] ) . hence , the region c , seems to be dimming faster than v1647 ori . this could be either due to material inflow into cavity between region c and v1647 ori as the outburst is progressing or due to a change in extinction along the cavity induced by slow dimming of v1647 ori s brightness . during the first outburst in 2003 , the linear dimming rate during the plateau stage was 0.24 mag yr@xmath2 in _ r_-band @xcite , which was @xmath44 times faster in magnitude scale than the present dimming rate in second outburst . just like in other t - tauri stars , we also see a lot of short time scale random variations in the source magnitude ( peak - to - peak @xmath45 mag , @xmath46 mag and @xmath47 mag ) , which could be due to density fluctuations in the infalling gas on to the star . our lightcurve of v1647 ori does not show any 56 day periodicity which was reported by @xcite during the first 2003 outburst . based on the correlated reddening of flux during the minima of light curve , they proposed that periodicity was due to occultation of a dense clump in accretion disc at a distance of 0.25 au from the star . the peak - to - peak amplitude in _ i_-band was @xmath5 0.3 mag in 2003 . we have not detected this variability in 2008 outburst which implies the dense clump might have got dissipated between 2003 and 2008 outburst events . our lomb - scargle periodogram analysis of magnitudes did not show any other statistically significant periodicity . the optical magnitudes during the second outburst are almost similar to that of the first outburst in 2003 . in fact the first known outburst of v1647 ori in 1966 ( @xmath5 38 years prior to 2003 ) , reported by @xcite , also had similar magnitude to the present one , however , all these three outbursts have different timescales . implications of this fact on outburst model will be discussed in section [ modelsndiscuss ] .    our nir _ j _ , _ h _ and _ k _ magnitudes are listed in table [ table : jhkmags ] . similar to optical light curve , there is a faint dimming trend in nir also . @xcite , with more nir data points , estimated the fading rate in _ j_-band to be 0.08 @xmath48 mag yr@xmath2 . the @xmath49 color - color ( cc ) diagram ( figure [ img : jhk_ccdia ] ) shows the movement of v1647 ori from 2007 data point taken in quiescent phase to outburst state . it is similar to what was seen in 2003 outburst . from the quiescent phase position in cc diagram , v1647 ori has moved towards the classical t - tauri ( ctt ) locus along the redenning vector and presently occupies the same position as in 2003 outburst . the position of v1647 ori in cc diagram is consistent with similar cc diagram published by @xcite . this implies that the decrease in line of sight extinction during the outburst is same as that seen during the 2003 outburst . since our line of sight is through the envelope , it must be likely due to a reversible mechanism like dust sublimation in the inner region of envelope during each outburst @xcite . since the star is deeply embedded , we have reflections and dust emission effects also affecting the position of v1647 ori in the cc diagram . so the extinction estimated from cc diagram is not very reliable . otherwise , we can see that the second outburst has cleared out circumstellar matter of @xmath50 mag . this is also consistent with the estimate of extinction change during first outburst by @xcite , @xmath51 mag ( see also @xcite ) .      between 2003 and 2008 outbursts , the mcneil s nebula does not have any significant morphological changes , however the intensity distribution of the nebula has changed between the outbursts . figure [ img : r11-r04 ] shows the difference in _ r_-band flux along the nebula between 2011 and 2004 . images of similar atmospheric conditions were taken and scaled to match the brightness of v1647 ori before subtracting 2004 image from that of 2011 . brighter shade implies that region is brighter in 2011 than 2004 . we can see that the region c is brighter in second outburst than it was in 2004 . this could be due to dust clearing up between the last two outbursts along the cavity seen in nir in region c direction @xcite . our photometric results show region c is dimming faster than v1647 ori and one of the explanations for that could be material inflow into cavity during the outburst . however , region c is relatively brighter in 2008 outburst than in 2004 for the same brightness of v1647 ori . this implies that the matter inflow to cavity was not occurring during the quiescent phase between 2006 and 2008 . this is also based on the implicit assumption that the extinction along the line of sight direction to v1647 ori is same between 2003 and 2008 outbursts . the other significant change is in illumination of the south - western knot ( region b ) of the nebula ; its illumination seems to have shifted slightly towards west . these illumination changes in nebula imply a structural change in the circumstellar matter above the disc and cavity . a similar pattern and conclusion were also reported between 1966 , 2003 and 2008 outbursts by @xcite . similar analysis of image pairs taken between 2008 and 2012 did not show any significant morphological changes . our image pairs had a seeing of 1.6 . hence , to check whether any change in illumination of nebula is undergoing during the present outburst , we need images with seeing less than 1.6 .      v1647 ori optical spectra show strong h@xmath12 ( 6563 @xmath0 ) emission and ca ii ir triplet at 8498 , 8542 and 8662 @xmath0 in emission . other weak lines seen are na d ( 5890 + 5896 @xmath0 ) and oi ( 7773 @xmath0 ) in absorption , and [ o i ] ( 6300 @xmath0 ) , o i ( 8446 @xmath0 ) , [ fe ii ] ( 7155 @xmath0 ) and fe i ( 8388 , 8514 @xmath0 ) in emission ( see figure [ img : v1647spectra ] ) . the equivalent widths of h@xmath12 , ca ii ir triplet lines and oi ( 7773 @xmath0 ) are listed in table [ table : eqws ] . strong @xmath29 line in v1647 ori shows a clear p - cygni profile as well as substantial variations . figure [ img : halphaplots ] shows the variations of @xmath29 profiles during our four and a half years of observations . p - cygni profiles were more prominent in early part of the outburst in 2008 . to see the absorption component clearly , a gaussian is fitted to the right wing of the profile in red color and the difference of the fit to actual spectra is plotted in green color . figure [ img : pcygnivelocity ] shows the outflow velocity and associated error bar of expanding wind from the blue - shifted absorption minima in @xmath29 profile . these blue - shifted absorption components were present in 2003 outburst also and disappeared during the fading stage of the outburst @xcite . figure [ img : halpha : eqw ] shows the variation in equivalent width ( @xmath52 in @xmath0 ) of @xmath29 emission . the calculation of @xmath52 was very sensitive to the weak continuum flux around @xmath30 @xmath0 , and the error estimate for each data point is @xmath53 @xmath0 . the @xmath52 of 2008 outburst is in similar range of that during first outburst in 2003 . since @xmath29 emission comes from the innermost accretion powered hot zone , we can expect its strength to be proportional to the accretion rate . the optical photometric magnitude in second outburst is similar to that of first outburst , which implies the continuum flux is almost of the same value . hence from the fact that @xmath52 is of similar value as of first outburst , we can deduce that the accretion rate is also of the same order in both the outbursts during its high plateaustage . the plots of equivalent widths of ca ii ir triplet lines ( 8498 , 8542 and 8662 @xmath0 ) are shown in figure [ img : caiiewq ] . we have much lesser error bars ( @xmath54 ) for the @xmath52 due to the higher continuum flux in these wavelengths . the ca ii ir triplet emission lines are seen to be in the ratio @xmath55 : @xmath56 : @xmath57 . this nearly equal ratio is due to optically thick gas with the collision decay rates larger than the effective radiative decay rates of upper states of ca ii lines . such environment is typically seen in many t - tauri stars . optical thickness along with the non - detection of forbidden [ ca ii ] lines above noise , implies number density of electrons to be @xmath58 @xmath59 @xcite . for comparison with figure 8 of @xcite , figure [ img : caiieqwratios ] shows the scatter plot between the ratios of equivalent widths , @xmath60/@xmath61 and @xmath62/@xmath61 , of our data as well as previously published data from literature . the error bar in our new data ( black squares ) is @xmath63 . from the position of 2007 data point ( red diamond ) taken during quiescent phase @xcite in this scatter plot , @xcite had concluded that the optical density of the region emitting ca ii ir triplet lines changed significantly between outburst and quiescent phases . but since there is only one data point from quiescent phase and it is lying within the scatter of points from ongoing outburst , it might be difficult to conclude that the change in ratios observed was actually due to v1647 ori moving from quiescent phase to outburst phase . we could see strong correlation between the equivalent widths ( @xmath52 ) of ca ii ir triplet lines ( see figure [ img : correlation : caii ] ) . the pearson correlation coefficient ( pcc ) between both @xmath62 and @xmath60 , and @xmath61 and @xmath60 is 0.88 with a 2-tailed p value @xmath64 . this implies that the fluctuations in @xmath52 are not random statistical error . it could be due to fluctuations of continuum flux around @xmath65 . peak - to - peak fluctuations of @xmath52 is @xmath66 , which means if the flux from these lines is assumed to be constant then the continuum flux has fluctuated by a factor of @xmath67 , which in terms of the log scale of magnitude is @xmath68 . this indeed matches with peak - to - peak fluctuation in _ i_-band magnitude during the entire period . we do not see any strong correlation between @xmath52 of @xmath29 line and ca ii ir triplets . however , it should be noted that the error bars in @xmath52 of @xmath29 are much higher than that of ca ii ir lines due to low continuum flux around @xmath69 .    in 2008 october 29 spectrum , we could clearly detect p - cygni profile in ca ii ir triplet lines ( figure [ img : caii20081029 ] ) . the strengths of absorption trough of the three lines were in the same pattern as that of t - tauri star wl 22 @xcite , i.e. the pattern with strongest absorption in @xmath70 , then @xmath71 and very weak in @xmath72 . the ratio of @xmath52 of the blue - shifted absorption between @xmath70 and @xmath71 is 0.76 : 0.45 = 1.69 : 1 . this ratio is consistent within error bars to the 1.8 : 1 ratio of intensity from atomic transition strength of these lines . hence , unlike the region producing emission lines , this absorption regions are optically thin . so by using optically thin assumption , we can estimate the column density of ca ii by the formula @xcite : + @xmath73 @xmath74 , + where the oscillator strength @xmath75 for the lines 8542 and 8662 @xmath0 are 0.39355 and 0.21478 respectively , taken from @xcite . substituting the @xmath52 , wavelength and oscillator strength for both the lines , we get the column density ( @xmath76 ) as @xmath77 @xmath74 and @xmath78 @xmath74 respectively . this is the column density of ca ii atoms in this small duration of outflow wind . assuming reasonable estimates of temperature t= 2600k ( disc temperature estimated by @xcite ) and pressure p=1 pascal ( typical pressure in solar winds ) , we get the fraction of ionisation using saha s formula to be @xmath79 . hence , dividing by this fraction we obtain the column density of ca atoms in gas blob to be @xmath80 @xmath74 . assuming solar metalicity , we obtained column density of hydrogen ( h ) in outflowing gas blob as @xmath81 @xmath74 . from the doppler shift of the absorption minima , we also obtained the wind velocity to be @xmath82 km s@xmath2 ( in @xmath70 line ) and @xmath83 km s@xmath2 ( in @xmath71 line ) . we also detected a faint p - cygni profile in @xmath70 line on 2008 december 30 , with a blue - shifted velocity of @xmath84 km s@xmath2 . apart from these two episodic events , none of our other spectra show any detectable p - cygni profile . the episodic nature of these two winds implies they are magnetic reconnection driven winds rather than pressure driven steady winds .    even though our medium resolution spectra can not be used to study line widths , since the ca ii ir triplets are near by , we could do relative comparison of the widths of the ca ii ir triplet lines , where width is taken to be the full width half maximum ( fwhm ) of gaussian fit of the continuum normalised profile . since this quantity is the fwhm of gaussian profile that we get after the convolution of instrument response on the actual line , it is not the fwhm of the line . however , since the lines are very close and the instrumental convolution is common , the wider line will give a wider fwhm after convolution . figure [ img : widthratio ] shows a scatter plot of the ratio of the widths of @xmath31 @xmath0 and @xmath32 @xmath0 versus equivalent width of the line @xmath32 @xmath0 . most of the points lie below 1.0 in the ratio axis . using the test statistic for mean with 34 data points , we could reject null hypothesis _ @xmath85 : the mean of the ratio is 1 , with 6 sigma confidence . _ this shows that the @xmath72 line is slightly narrower than @xmath70 line . similar trend is seen in most of the t - tauri stars @xcite . apart from showing this skewness , since our spectra are of only medium resolution , we can not quantify the narrowness of the line . this narrowness of optically thinner line @xmath72 could be explained by either substantial opacity broadening in @xmath70 ( since 1:9 is the ratio of atomic line strength ) or by lower dispersion velocity in the inner part of the region of ca ii ir emission @xcite . our period search in the equivalent width ( @xmath52 ) of ca ii ir triplet lines found six faint periodicities in all three lines in the range of 1 - 100 days with @xmath5 2 sigma confidence level in amplitude . the possible periodicities and confidence were estimated by lomb - scargle periodogram along with monte carlo simulation . the possible periods are 3.39 , 8.09 , 27.94 , 30.8 , 40.77 and 45.81 day . since the amplitudes are only of 2 sigma confidence level , they can be confirmed only with more observations . figure set [ img : foldedcaiieqw ] shows the folded data of the entire four and a half year observations and the statistical significance of the amplitudes . the amplitude of the least square fitted cosine function is @xmath86 . if this periodicity is due to change in the continuum flux , the corresponding amplitude of magnitude change we expect in logarithmatic _ i_-band magnitude is @xmath87 . this is not much above our error in magnitude estimate , so the fact that we do not see similar periodicity in _ i_-band magnitude does not rule out the cause of change in @xmath52 as change in continuum flux . we also do not see any corresponding significant periodicity in @xmath52 of h@xmath12 . @xcite took the spectrum of v1647 ori during the quiescent phase in february 2007 . the @xmath52 of both ca ii ir triplet lines and h@xmath12 were @xmath88 times the present value . @xcite had used ratio of @xmath52 of h@xmath12 between 2003 outburst and quiescent phase to estimate change in accretion rate . similarly , since the continuum flux changed by a factor of @xmath89 between the quiescent and 2008 outburst phase , we can estimate that the change in the line flux of both set of lines is by a factor of @xmath90 . this agrees with the change in accretion rate . thus the origin of ca ii ir triplet lines are directly connected to the accretion rate just like h@xmath12 . this is in agreement with finding of tight correlation between ca ii ir line flux and accretion rate in t - tauri stars by @xcite , which suggests the origin of these lines to be in the magnetospheric infall zone . the similar value of @xmath52 of ca ii ir lines with that of 2003 also strengthens the claim that the accretion rate on to the star from inner disc was same during both the outbursts . the most prominent oxygen line is oi 7773 @xmath0 in absorption , however , weak oi 8446 @xmath0 line is also detected in emission . we should be careful in interpreting the @xmath52 of oi @xmath91 @xmath0 absorption line because the profile shape of the line seems to be a combination of red - shifted emission component and more stronger blue - shifted absorption component ( see figure [ img : v1647spectra ] ) . a weak anti - correlation is seen between h@xmath12 and oi @xmath92 ( see figure [ img : corr_havsoi7774 ] ) . correlation had pcc = 0.54 , with a 2 tailed p value of 0.001 . this anti - correlation in @xmath93 of oi 7773 @xmath0 and h@xmath12 could be due to positive correlation between emission component of oi @xmath92 filling in the absorption dip and h@xmath12 . since oi @xmath92 can not be formed in photosphere of cool stars , the absorption component is due to warm gas in the envelope or hot photosphere above disc , while the emission component might be due to the hot gas region from which h@xmath12 is also being emitted . @xcite reported a decreasing trend in the @xmath52 of oi @xmath92 from the beginning till end of the 2003 outburst which was interpreted to be possible decrease in turbulence in outer envelope during the outburst period . we do not see such a trend in 2008 outburst , but the values of @xmath52 in 2008 outburst remain same as that during the second half of the 2003 outburst . a slight decrease of @xmath52 in the later part of 2003 outburst observed on 2005 september 8 , as reported by @xcite , in contrast to the increase of @xmath52 of other lines , could be due to increase in the @xmath52 of oi @xmath92 emission component . we detected [ o i ] ( @xmath94 ) and [ fe ii ] ( @xmath95 ) forbidden line emissions in v1647 ori s spectra . the presence of [ o i ] @xmath96 and [ fe ii ] @xmath97 implies shock regions probably originating from jets . this combined with non - detection of [ s ii ] ( @xmath98 ) line above our noise level implies the shock region has temperature @xmath99 and electron number density @xmath100 @xmath59 @xcite . we see significant variations in the strengths of the forbidden lines [ o i ] and [ fe ii ] , however , the lines are too faint in our individual spectra to quantify statistically . during the fading stage of 2003 outburst in 2006 january , when the bright continuum flux decreased , @xcite were also able to detect various strong forbidden line emissions , namely [ o i ] @xmath101 , [ s ii ] @xmath102 and [ fe ii ] @xmath103 .","summary":"forbidden [ o i ] 6300 and [ fe ii ] 7155 lines were also detected implying shock regions probably from jets .","abstract":"we present a detailed study of mcneil s nebula ( v1647 ori ) in its ongoing outburst phase starting from september 2008 to march 2013 . our 124 nights of photometric observations were carried out in optical _ v _ , _ r _ , _ i _ and near - infrared ( nir ) _ j _ , _ h _ , _ k _ bands , and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 wavelength range . all observations were carried out with 2-m himalayan _ chandra _ telescope ( hct ) and 2-m iucaa girawali telescope . our observations show that over last four and a half years , v1647 ori and the region c near herbig - haro object , hh 22a , have been undergoing a slow dimming at a rate of mag yr and mag yr respectively in _ r_-band , which is 6 times slower than the rate during similar stage of v1647 ori in 2003 outburst . we detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts . apart from steady wind of velocity km s we detected two episodic magnetic reconnection driven winds . forbidden [ o i ] 6300 and [ fe ii ] 7155 lines were also detected implying shock regions probably from jets . we tried to explain the outburst timescales of v1647 ori using the standard models of fuors kind of outburst and found that pure thermal instability models like can not explain the variations in timescales . in the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 november was due to a low density region or gap in the inner region ( 1 au ) of the disc ."}
{"article_id":"1309.4967","section_id":"c","document":"we have carried out four and a half years of continuous monitoring of v1647 ori in its second outburst phase starting from 2008 . following are our main conclusions :    1 . v1647 ori is still in outburst  stage , at similar magnitude to 2003 outburst in optical and nir bands . it is undergoing a slow dimming at a rate of 0.04 mag yr@xmath2 , which is 6 times slower than the rate during 2003 outburst . the magnitude shows significant short timescale ( @xmath5 1 day ) variations . 2 . morphological studies on illumination of nebula show a consistent change in the circumstellar gas distribution between 2008 , 2003 and 1966 outbursts . p - cygni profiles in h@xmath12 emission lines show outflowing wind velocities of @xmath5 350 km s@xmath2 . apart from the continuous wind we also detected twice short duration episodic winds driven by magnetic reconnection events , with h column density @xmath81 @xmath74 from p - cygni profiles in ca ii ir triplet lines in 2008 october and december . from ca ii ir triplet and h@xmath12 line strengths , the accretion rate was found to be same as that during the 2003 outburst and is @xmath5 10 times more than quiescent phase . 4 .   we could not detect the 56 day periodicity seen in 2003 outburst . detection of the forbidden [ oi ] @xmath158 and [ fe ii ] @xmath157 lines implies shock regions of @xmath99 and @xmath159 @xmath59 , probably originating from jets . timescales of outburst history of v1647 ori can not be explained by a simple thermal instability model by @xcite alone . to explain the large change in accretion rate from outer to inner disc between last two outbursts we require more comprehensive models which includes contribution from mri , gi and planetary perturbations . from the framework of instability models we conclude that the sudden ending of 2003 outburst could be due to a gap or low density region in inner ( @xmath5 1 au ) disc . we thank the anonymous referee for giving us invaluable comments and suggestions that improved the content of the paper . the authors thank the staff of hct , operated by indian institute of astrophysics , bangalore and igo at girawali , operated by inter - university centre for astronomy and astrophysics , pune for their assistance and support during observations . it is a pleasure to thank j. s. joshi and all the members of the infrared astronomy group of tifr for their support during the tircam2 campaign . all the plots were generated using the 2d graphics environment _ matplotlib _ @xcite . brahm , p. , mosoni , l. , henning , t. , et al . 2006 , a&a , 449 , 13 acosta - pulido , j. a. , kun , m. , brahm , p. , et al . 2007 , aj , 133 , 2020 andrews , s. m. , rothberg , b. & simon , t. 2004 , apjl , 610 , l45 aspin , c. , barbieri , c. , boschi , f. , et al . 2006 , aj , 132 , 1298 aspin , c. , beck , t. l. & reipurth , b. 2008 , aj , 135 , 423 - 440 aspin , c. & reipurth , b. 2009 , aj , 138 , 1137 aspin , c. , reipurth , b. , beck , t. l. , et al . 2009 , apjl , 692 , l67 aspin , c. 2011 , aj , 142 , 135 bell , k.r . & lin , d.n.c . 1994 , apj , 427 , 987 bessell , m. s. & brett , j. m. 1988 , pasp , 100 , 1134 bonnell , i. & bastien , p. 1992 , apj , 401 , 654 briceo , c. , vivas , a. k. , hernndez , j. , et al . 2004 , apj , 606 , l123 evans ii , n. j. , dunham , m. m. , jrgensen , j. k. , et al . 2009 , apjs , 181 , 321 fedele , d. , van den ancker , m. e. , petr - 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pollatou , a. 2004 , aj , 128 , 1872 zhu , z. , hartmann , l. , gammie , c. & mckinney , j. c. 2009 , apj , 701 , 620 - 634 zhu , z. , hartmann , l. , gammie , c. f. , et al . 2010 , apj , 713 , 1134 - 1142         arcmin@xmath160 . north is up and east is to the left - hand side . stars marked as a , b , c and d are the secondary standard stars used for magnitude calibration . the location of v1647 ori is marked at the center by two perpendicular lines . region c , overlapping herbig - haro object hh 22a , is marked together . a knot in south - western section ( region b ) of nebula is also marked . at 400 pc distance , the scale 1 corresponds to 24000 au.,scaledwidth=100.0% ]         cc diagram from the quiescent phase in 2007 to the second outburst phase . the solid curve shows the locus of field dwarfs and the dashed - dotted curve shows the locus of giants @xcite . the dotted line represents the locus of ctt stars @xcite . the diagonal straight dashed lines show the reddening vectors @xcite , with crosses denoting an @xmath165 difference of 5 mag.,scaledwidth=100.0% ]           profiles during our four and a half year observations . p - cygni profiles were more prominent in the early part of the outburst in 2008 . a gaussian is fitted to the right wing of the profile in red color and the difference of that gaussian fit to actual spectra is plotted in green color to see the absorption component clearly . _ _ figure [ img : halphaplots ] with 70 other plots of remaining nights are available in the online version of the journal.__,scaledwidth=100.0% ]     p - cygni profile . the filled circles are from hct , and grey filled squares are from igo measurements . the error bar on the bottom right corner shows the typical @xmath167 39 km / sec error estimated for data points.,scaledwidth=100.0% ]     emission . the filled circles are from hct , and filled grey squares are from igo measurements . each data point has an error bar of @xmath168 . this error bar is shown at the right bottom corner.,scaledwidth=100.0% ]      ) during the outburst period 2008 september to 2013 march . all data points are from hct measurement and each point has an error bar of @xmath169 . this error bar is shown at the right bottom corner.,scaledwidth=100.0% ]      /@xmath61 versus @xmath62/@xmath61 , of our data as well as previously published data from literature . 2003 outburst points are shown as circles @xcite , 2008 outburst points are shown as squares ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * and this work ) and 2007 quiescent phase point is shown as diamond @xcite . the typical error bar on our new data ( black squares ) is @xmath170 . , scaledwidth=100.0% ]           versus equivalent width of the line @xmath171 . most of the points lie below 1.0 in y - axis . box and whisker plot of the distribution is also ploted on the right side . this shows that the @xmath172 line is slightly narrower than @xmath171 line.,scaledwidth=100.0% ]     of ca ii ir triplet lines @xmath1668498 , @xmath1668542 and @xmath1668662 ( in @xmath0 ) , and _ i_-band magnitude . the folding is done over the entire four and a half years of data . the red , black , green , pink and blue circles correspond to data of 2008 , 2009 , 2010 , 2011 , and 2012 winter observations respectively . the amplitudes ( in @xmath0 ) of the three lines in each folded plot are as follows . for a period of 3.39 days:- 1.26 @xmath167 0.69 , 1.22 @xmath167 0.75 , 1.03 @xmath167 0.67 ; for a period of 8.09 days:- 1.13 @xmath167 0.70 , 1.33 @xmath167 0.71 , 1.17 @xmath167 0.65 ; for a period of 27.94 days:- 1.13 @xmath167 0.72 , 1.11 @xmath167 0.79 , 1.14 @xmath167 0.67 ; for a period of 30.8 days:- 1.26 @xmath167 0.61 , 1.25 @xmath167 0.63 , 0.98 @xmath167 0.58 ; for a period of 40.77 days:- 1.26 @xmath167 0.65 , 1.42 @xmath167 0.58 , 1.18 @xmath167 0.59 ; for a period of 45.81 days:- 0.95 @xmath167 0.76 , 1.29 @xmath167 0.74 , 1.10 @xmath167 0.68 . _ figures [ img : foldedcaiieqw].2 - [ img : foldedcaiieqw].6 are available in the online version of the journal . _ , scaledwidth=100.0% ]     and oi @xmath92 . typical error bar is given at the right bottom corner . pcc is 0.54 with a 2-tailed p value of 0.001 . the weak anti - correlation could be due to a positive correlation between the h@xmath12 and red - shifted emission component which is filling the absorption component in oi @xmath92 profile . bootstrap analysis gave 95% confidence range of pcc to be [ 0.29 , 0.72].,scaledwidth=100.0% ]     disc is shown above . _ r _ is the radial distance from the star and _ h _ is the thickness of the disc , which flares up as the radius _ r _ increases . @xmath143 is the radius upto which the outburst extends . we are looking into the system at @xmath173 along the dashed line drawn in the figure . in @xmath12 disc model , the viscosity is due to large turbulent eddies . the speed of eddies is upperbounded by the velocity of sound ( @xmath107 ) because any supersonic flow will get dissipated by shock . the size of eddies is also upper bounded by the thickness ( _ h _ ) of disc . thus taking @xmath12 to be a free parameter @xmath110 we get the viscosity in the disc as @xmath106 . the orbital velocity is taken to be keplarian in our problem.,scaledwidth=100.0% ]        lcccc 2008 sep 14 & 2454724 & 1.9 & @xmath174 & 300 , 480 , 240 , 2400 + 2008 sep 15 & 2454724 & 1.6 & @xmath175 & 2400 + 2008 sep 16 & 2454726 & 1.5 & @xmath176 & 600 , 720 , 240 + 2008 sep 28 & 2454738 & 1.1 & @xmath176 & 240 , 240 , 180 + 2008 oct 01 & 2454741 & 1.2 & @xmath176 & 120 , 120 , 90 + 2008 oct 02 & 2454742 & 1.2 & @xmath177 & 240 , 240 , 180 , 2400 + 2008 oct 03 & 2454743 & 1.5 & @xmath175 & 2400 +      2454724 & 19.08 & 17.06 & 14.98 & & 15.59 & 14.99 & 14.36 + 2454726 & 19.11 & 17.11 & 15.04 & & 15.57 & 14.98 & 14.36 + 2454738 & 19.00 & 17.04 & 14.99 & & 15.59 & 15.06 & 14.36 + 2454741 & 19.04 & 17.05 & 15.02 & & 15.59 & 14.98 & 14.33 + 2454742 & 19.09 & 17.09 & 15.04 & & 15.55 & 15.02 & 14.39 + 2454745 & 19.12 & & 15.02 & & 15.60 & & 14.30 + 2454751 & 19.26 & 17.08 & 15.02 & & 15.50 & 15.02 & 14.20 +      28-oct-07 & 14.12 & 11.43 & 9.36 & nircam + 19-oct-08 & 10.64 & 9.01 & 7.63 & nircam + 12-jan-09 & 10.59 & 8.76 & 7.62 & nircam + 12-feb-09 & 11.04 & 9.01 & 7.51 & nircam + 18-feb-09 & 10.87 & 9.16 & 7.68 & nircam + 23-oct-09 & 10.71 & 8.89 & 7.40 & nircam + 24-oct-09 & 10.71 & 8.88 & 7.44 & nircam + 20-feb-10 & 10.75 & 8.96 & 7.43 & nircam + 23-mar-10 & 10.73 & 9.14 & & nircam + 18-nov-11 & 10.75 & 8.90 & 7.58 & nircam + 03-dec-11 & 10.94 & 9.28 & 7.41 & tircam2 + 04-dec-11 & 10.97 & 9.19 & 7.42 & tircam2 + 06-dec-11 & 10.84 & 9.10 & 7.47 & tircam2 + 07-nov-12 & 10.73 & 9.01 & 7.46 & nircam +      2454724 & -36.35 & -8.601 & -8.758 & -8.125 & 2.483 + 2454725 & -35.1 & -8.686 & -9.1 & -7.678 & 1.754 + 2454743 & -36.52 & -12.97 & -13.35 & -12.19 & 1.491 + 2454744 & -28.62 & -10.75 & -10.86 & -10.12 & 2.407 + 2454755 & -32.84 & -7.61 & -7.621 & -7.819 & 1.839 +","summary":"we present a detailed study of mcneil s nebula ( v1647 ori ) in its ongoing outburst phase starting from september 2008 to march 2013 . our observations show that over last four and a half years , v1647 ori and the region c near herbig - haro object , hh 22a , have been undergoing a slow dimming at a rate of mag yr and mag yr respectively in _ r_-band , which is 6 times slower than the rate during similar stage of v1647 ori in 2003 outburst . we detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts . apart from steady wind of velocity km s we detected two episodic magnetic reconnection driven winds . we conclude that one possible reason for sudden ending of 2003 outburst in 2005 november was due to a low density region or gap in the inner region ( 1 au ) of the disc .","abstract":"we present a detailed study of mcneil s nebula ( v1647 ori ) in its ongoing outburst phase starting from september 2008 to march 2013 . our 124 nights of photometric observations were carried out in optical _ v _ , _ r _ , _ i _ and near - infrared ( nir ) _ j _ , _ h _ , _ k _ bands , and 59 nights of medium resolution spectroscopic observations were done in 5200 - 9000 wavelength range . all observations were carried out with 2-m himalayan _ chandra _ telescope ( hct ) and 2-m iucaa girawali telescope . our observations show that over last four and a half years , v1647 ori and the region c near herbig - haro object , hh 22a , have been undergoing a slow dimming at a rate of mag yr and mag yr respectively in _ r_-band , which is 6 times slower than the rate during similar stage of v1647 ori in 2003 outburst . we detected change in flux distribution over the reflection nebula implying changes in circumstellar matter distribution between 2003 and 2008 outbursts . apart from steady wind of velocity km s we detected two episodic magnetic reconnection driven winds . forbidden [ o i ] 6300 and [ fe ii ] 7155 lines were also detected implying shock regions probably from jets . we tried to explain the outburst timescales of v1647 ori using the standard models of fuors kind of outburst and found that pure thermal instability models like can not explain the variations in timescales . in the framework of various instability models we conclude that one possible reason for sudden ending of 2003 outburst in 2005 november was due to a low density region or gap in the inner region ( 1 au ) of the disc ."}
{"article_id":"1105.2099","section_id":"i","document":"extremely metal - poor ( emp , @xmath2}<-2.5 $ ] in this paper ) stars are stars formed in the early universe in terms of chemical evolution . they are thought to have been formed at high redshift but are still shining with the glow of nuclear burning in the local group . recent large - scaled surveys have identified hundreds of the emp stars in the milky way halo ( hk survey , beers et al .  1992 : hamburg / eso [ he s ] survey , christlieb et al .  2003 , 2008 : sloan extension for galactic understanding and exploration [ segue ] , yanny et al . element abundances of these stars are revealed by follow - up spectroscopic observations . they provide a means of probing the earliest phases of the evolution of the milky way and supernovae ( sne ) in the early universe .    in this paper , we refer to stars with @xmath2}\\leq -2.5 $ ] as emp stars , although `` emp star '' is usually used for @xmath2 } < -3 $ ] @xcite . as shown in our previous study ( * hereafter paper i ) , stars with @xmath2}\\lesssim-2.5 $ ] show some observational and theoretical peculiarities distinguishing them from more metal rich population  ii stars ( see section 2.1 of paper i ) . especially , in previous studies @xcite , we show that the initial mass function ( imf ) of stars with @xmath2}\\leq -2.5 $ ] should differ from metal rich stars . typical mass of the emp stars is @xmath4 and present emp stars in the milky way halo are the low mass minorities . we refer to the mother stellar population with @xmath2}\\leq -2.5 $ ] as emp population and low mass survivors with nuclear burning now as emp survivors . stars with @xmath2}<-5 $ ] are referred to as hyper metal - poor ( hmp ) stars . 2 hmp stars detected in the milky way halo are the most metal deficient objects observed yet ( he1327 - 2326 , frebel et al .  2005 : he0107 - 5240 , christlieb et al . formation environment of the emp population stars are thought to differ from present galaxies . emp stars are formed in the process of galaxy formation in the early universe . in the @xmath5 cold dark matter ( cdm ) universe , large galaxies like the milky way are formed through merger of smaller galaxies as building blocks . according to the hierarchical structure formation scenario , a stellar halo is an aggregation of stars formed in the many small galaxies @xcite . earlier theoretical studies show that the first stars are formed in very low mass halos with @xmath6 @xcite and host galaxies of the second generation of stars are also small @xcite . chemical abundances of these building blocks can differ from each other . unlike metal rich stars , metals in emp stars are synthesized by only one or a few precursory sn(e ) . element abundances of the emp stars can reflect individual characteristics of the precursory sn(e ) and their host galaxies . a semi - analytic hierarchical approach can provide a framework within which to study the earliest phases of the chemical evolution and the formation history of the emp stars . one important point at issue for the earliest phases of chemical evolution is a possible difference in the imf of emp stars ( e.g. * ? ? ? * ; * ? ? ? * ) . theoretically , typical mass of stars is large in extremely metal - poor environment and/or in the early universe . numerical simulations show that population  iii stars without metal are very massive ( e.g. * ? ? ? * ; * ? ? ? * ) . for emp stars with a little metal , the imf can be different from nearby stars , too @xcite . existence of the low mass emp survivors in the galactic halo proves that some low mass emp stars can be formed , but typical mass of the emp population stars can be more massive than population  i stars . @xcite give constraints on the imf of emp stars from statistics of observed emp survivors . it is known that large fraction ( @xmath7 ) of the emp survivors comprise carbon enhanced stars referred to as carbon enhanced metal - poor ( cemp ) stars . more than half of them show large _ s_-process element enhancement . abundance anomalies of the _ s_-process element enhanced cemp stars ( cemp-@xmath8  stars ) are due to binary mass transfer . intermediate massive emp stars with @xmath9 synthesize carbon and _ s_-process elements in the asymptotic giant branch ( agb ) phase , and pollute their companions to make them cemp-@xmath8  stars . we propose that cemp stars without _ s_-process enhancement ( cemp - no@xmath8  stars ) are also formed through binary mass transfer but from more massive primaries with @xmath10 . from observational statistics of the cemp-@xmath8  and cemp - no@xmath8  stars , we give constraints on mass distribution of primary stars of emp binaries and conclude that typical mass of emp stars is large @xcite . @xcite discuss the constraints of the imf from cemp stars again in detail and give an additional constraint from the total number of emp survivors . the number of emp survivors in the galactic halo is very small and it indicates that the fraction of low mass survivors among the emp population is small . as a result , a lognormal imf with medium mass , @xmath11 , and dispersion , @xmath12 , can satisfy all the constraints . @xcite also give a constraint on the imf of emp stars from statistics of cemp-@xmath8  stars and argue that the typical mass of emp stars is slightly higher than more metal rich stars . however , because they do not take account of cemp - no@xmath8  stars and assume a stellar evolution model different from ours , they conclude lower typical mass , @xmath13 .    in paper i , we build a merger tree of the galaxy and compute the enrichment history of iron abundance along the tree . the high mass imf with @xmath14 @xcite is adopted in the computations . we also discussed origin of hmp stars considering the effect of surface pollution by accretion of metal enriched interstellar matter . in this paper , we investigate chemical evolution of several elements with detailed theoretical nucleosynthetic yields of metal deficient massive stars . model results with high and low mass imfs are compared with compiled observational data . to deal with individual characteristics of the emp stars , all the individual emp population stars are registered in our computations . we discuss not only averaged abundances but also dispersion of them . @xcite presents a semianalytic hierarchical model for the galactic halo . @xcite also calculate a hierarchical model with gas blowout from halos by bursty star formation taken into account , but they do not deal with individual stars and do not investigate diversity of the element abundances . these previous studies assume the salpeter imf for emp stars . additionally , these previous studies with hierarchical models investigate only iron abundance . we calculate formation and evolution of stellar halo with different imfs and compare the predicted metallicity distribution functions ( mdfs ) and abundance ratio distributions . we use four different sets of core - collapse sn yields calculated for metal - poor stars . @xcite and @xcite investigate element abundances of emp stars using inhomogeneous chemical evolution models . however , they do not take account of the merging history of the galaxy and stars are assumed to be formed randomly in space . they also do not investigate the imf dependence . this paper is organized as follows . computation method and assumptions appear in the next section . especially , assumptions about imfs and sn yields are described in sections [ imfs ] and [ yields ] , respectively . in section [ obss ] , observational sample for comparison is described . we give results in section  [ results ] and conclude the paper in section  [ concs ] .","summary":"early phases of the chemical evolution and formation history of extremely metal poor ( emp ) stars are investigated using hierarchical galaxy formation models . we build a merger tree of the galaxy according to the extended press - schechter theory . we follow the chemical evolution along the tree , and compare the model results to the metallicity distribution function ( mdf ) and abundance ratio distribution of the milky way halo .","abstract":"early phases of the chemical evolution and formation history of extremely metal poor ( emp ) stars are investigated using hierarchical galaxy formation models . we build a merger tree of the galaxy according to the extended press - schechter theory . we follow the chemical evolution along the tree , and compare the model results to the metallicity distribution function ( mdf ) and abundance ratio distribution of the milky way halo . we adopt three different initial mass functions ( imfs ) . in a previous studies , we argue that typical mass of emp stars should be high - mass( ) based on studies of binary origin carbon - rich emp stars . in this study , we show that only the high - mass imf can explain a observed small number of emp stars . for relative element abundances , the high - mass imf and the salpeter imf predict similar distributions . we also investigate dependence on nucleosynthetic yields of supernovae ( sne ) . the theoretical sn yields by kobayashi et al.(2006 ) and chieffi & limonge ( 2004 ) show reasonable agreement with observations for-elements . our model predicts significant scatter of element abundances at}<-3 $ ] . best fit yields for one zone chemical evolution model by francois et al.(2004 ) well reproduces the trend of the typical abundances of emp stars but our model with their yield predicts much larger scatter of abundances than the observations . the model with hypernovae predicts zn abundance in agreement with observations but other models predict lower . ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances ."}
{"article_id":"1105.2099","section_id":"r","document":"figure  [ imfmdf ] shows resultant metallicity distribution functions ( mdfs ) for three models using different imfs . solid red , dashed green and dotted blue lines denote models kk , lk , and ck , respectively . all three models predict similar patterns of the mdfs but quite different total number of emp survivors . this is because fractions of low - mass stars are different . as seen in fig . [ imfmdf ] , model kk with the high mass imf is consistent with observations but other models with the lower mass imfs predict many more emp survivors . we may overestimate the efficiency of the identification of emp survivors by the he s survey , because we assume homogeneity of the galactic stellar halo and the he s survey reaches the outer end of the galactic halo . however , as seen in fig . [ imfmdf ] , the predicted number of emp survivors for models lk and ck is @xmath72 times larger than observations and this large discrepancy can not be explained by spatial inhomogeneity of the stellar halo and/or insufficiency of the survey . this indicates that typical mass of emp population stars is significantly higher than nearby pop . i stars , as shown in our earlier studies . figure  [ yieldmdf ] shows dependence on the sn yields . solid red , long - dashed green , short - dashed blue and dotted magenta lines denote results of models kk , kw , kf , and kc , respectively . all model results are similar in the total number of emp survivors .    at @xmath2}\\lesssim -3 $ ] , the patterns of the mdf differ . these extremely metal deficient stars are very early generations of stars formed with metal ejected by only one or a few sn progenitor(s ) in their host halos . a mdf at @xmath2}\\lesssim-3 $ ] is sensitive to individual sn yields . the mdf of model kk has a hump at @xmath2}\\sim -3.6 $ ] . this is because iron yields of normal sne  ii are tuned to @xmath41 in @xcite and metallicity of a primordial mini - halo with typical mass becomes @xmath2}\\sim-3.6 $ ] by a single sn . we see a smaller hump at @xmath2}=-4 $ ] to @xmath73 in other models , too . in model kk , since energetic hypernovae blow out gas from mini - halos , the predicted number of stars with @xmath2}\\sim -3 $ ] to @xmath74 is smaller than other models . model kc shows better consistency with observations than other models . the mdf of @xcite shows a steep drop around @xmath2}= -3.6 $ ] . in model kc , since iron yield and explosion energy are assumed to be the same for all the sne  ii , all the second and later generations of stars are distributed above @xmath2}\\sim -3.6 $ ] . however , theoretical iron yield strongly depend on the sn model parameters and it is difficult to distinguish which theoretical yield is the best one only from comparison with observed the mdf . additionally , at such a low metallicity , the observational sample is very small and the pattern of the mdf has not yet been well revealed . the predicted number of stars with @xmath2}\\lesssim-4.5 $ ] is very small and mdfs are bumpy because of numerical fluctuation . the number of observed hmp stars is comparable to the model results .    for more metal rich stars , a mdf depends on an averaged yield but is almost independent of characteristics of individual massive stars . at @xmath2}\\gtrsim -2 $ ] , the observed mdf overwhelms the predicted number of stars by the high mass imf models . one possible explanation of this excess is a changeover of the imf . the imf of metal rich stars is peaks at low mass . @xcite indicate that an imf can be a changeover from high mass to low mass at @xmath2}=-2.2 $ ] based on statistics of stellar abundance of zn and co. if typical mass becomes lower , the number of stars surviving increases . at this metallicity , some thick disk stars are thought to contaminate in the sample . it also increases the number of stars . formation of the thick disk and the imf of these more metal rich stars will be investigated in our future works .      in figure  [ kk ] , we show predicted and observed abundance ratio distributions for six elements for model kk . the predicted typical abundance ratio and their trend against metallicity are similar to the result of the chemical evolution model by @xcite . but since abundance ratio differs from mini - halo to mini - halo in our model , abundance distributions show significant dispersion . the predicted scatters of abundances are prominent at @xmath2}<-3 $ ] . at larger metallicity , element abundances are averaged by mixing of ejecta from many sne and the scatters decrease . as shown in paper  i , metals of stars with @xmath2}=-2.5 $ ] originate in @xmath75 precursory sne in their host mini - halos . most stars with @xmath2}<-4 $ ] are local first stars without any precursory sn exploded in their host mini - halos . metals in these stars are originate in mixtures of matter ejected to igm by sne which had exploded in other mini - halos prior to the formation of the host mini - halos of these stars . scatter of the abundances of these stars is smaller than the stars with @xmath76}\\gtrsim-4 $ ] . observed hmp stars show abundance anomalies of c , n , o and na but these are thought to be due to the surface pollution by binary mass transfer @xcite .      for mg and si , typical abundance ratio is consistent with observations . observed distribution of @xmath77 is almost flat against @xmath2}$ ] at @xmath2}<-1 $ ] and the dispersion is small . the predicted dispersion of the @xmath1-element abundances is comparable to or smaller than the dispersion of the observational sample . observationally , @xmath78 of emp stars shows a slight increasing trend as metallicity decreases but predicted abundances do not . typical o abundance of the first stars sample is @xmath79 dex higher than the predicted value . as seen in fig . [ yield ] , a larger amount of o is yielded in a more massive progenitor . if this increasing trend is real , stars more massive than @xmath80 thought to be the dominant source of metal in emp stars . however , mg and si abundances show no such a trend although a larger amount of these elements is yielded in a more massive progenitor , too . another possible additional source of oxygen for emp stars is intermediate massive agb stars . but agb stars eject both o and c , o abundances of stars other than cemp stars should not strongly affected by agb stars . we note that observational determination of the oxygen abundance is difficult and there is large uncertainty on observational data . @xcite argue that , when 3d effects are taken into account , @xmath78 decreases in the metal poor stars and the increasing trend diminishes . for some emp stars with low @xmath78 , oxygen is undetectable . the sample from the first stars project shows very small scatter for mg and si . this is consistent with the result of model kk . as seen in the following , model kk with hypernovae predicts the smallest scatters among the computations in this paper . it is because @xmath78 in the hypernovae ejecta is tuned to be constant and large energy of the hypernovae efficiently mix the ism . the observed small scatter of the first stars sample indicates that gas in the early universe is mixed with large mass . however , the subsamples by other authors show larger scatter ( @xmath71 dex ) . further observations are required to understand the gas dynamics in the early universe . for mg , the first stars sample are distributed at a slightly lower @xmath81 than the model results but other samples are consistent . @xcite argue that , when non - lte effects are taken into account , the mean value of @xmath81 increases and become similar to the mean value of @xmath78 . this will improve the consistency between model and observed data . observationally , it is known that @xmath82 decreases as @xmath2}$ ] increases at @xmath2}>-1 $ ] for stars in the milky way . in the many chemical evolution studies , this decreasing trend has been explained by the contribution of sne  ia ( * ? ? ? * and references therein ) . sne  ia eject large amounts of iron after long delay time and decrease @xmath82 at large metallicity . under the high mass imf , the contribution from sne ia is relatively weak because the number of intermediate massive stars relative to high mass stars is small . in model kk , @xmath82 decreases at @xmath2}>-1 $ ] but the rate of the decline is smaller than observations . although the imf is assumed to be the same for the whole metallicity range for simplicity in this study , our high mass imf is derived from the statistics of the emp survivors and the imf should be different at higher metallicity . [ [ na ] ] na ^^    for na , observational sample of emp stars show quite large scatter . all the subsamples shows large scatter and it is thought to be intrinsic . observed stars with lower @xmath83 have abundance similar to the model result but some other stars show larger @xmath83 . this indicates that there are additional sources of na . internal mixing may modify the surface na abundance of some evolved emp survivors @xcite . as discussed in @xcite , in intermediate massive emp stars at agb stage , na can be synthesized and dredged - up by the he - flash driven deep - mixing , which is a mixing mechanism peculiar to the emp stars . stars with high @xmath83 can be influenced by matter ejected from these agb stars . at @xmath2}>-2 $ ] , predicted typical abundance and their increasing trend are consistent with observations . we note that , when non - lte effect taken into account , na abundance of some stars for which high @xmath83 value is reported decreases to @xmath84 @xcite . [ [ cr ] ] cr ^^    @xmath85 shows a decreasing trend as decreasing metallicity . the predicted relative abundance is not consistent with the observations of emp stars , as pointed out by @xcite . we note that the sample of @xcite is distributed around @xmath86 and consistent with model results . however , the first stars sample and aoki s sample show clear decreasing trend with small scatter . [ [ zn ] ] zn ^^    in the models in this paper , zn is mainly produced by o - ne - mg sne since @xcite predict a large zn yield for o - ne - mg sne . hypernovae are also important sources of zn , especially at very low metallicity . for emp stars , all observational subsamples show similar abundance distribution and they are consistent with the model result . observations show an increasing trend of @xmath3 as decreasing metallicity . both subsamples by the first stars group and aoki et al . also show a clear increasing trend with small scatter . the model result shows flat distribution and predicts lower @xmath3 at @xmath2}\\gtrsim-2 $ ] . recentry , @xcite shows that a decrease in @xmath3 above @xmath2}>-2.2 $ ] may be due to changeover of the imf from high mass to low mass . the imf changeover lowers the frequency of hypernova and lowers the @xmath3 . the contribution from hypernovae is discussed again with results of the model without hypernovae in section [ hypers ] .    at @xmath2}=-2 $ ] to @xmath87 , the model predict higher @xmath3 than observations . zn thought to be overproduced by o - be - mg sne . criterion to be o - ne - mg sne is not yet revealed @xcite and the number of o - ne - mg sne can be smaller .    predicted scatter of zn is larger than other elements . this is because hypernovae and o - ne - mg sne eject matter with high @xmath3 but normal sne with mass @xmath44 eject a small amount of zn . figures  [ ck ] and [ lk ] show predicted abundance ratio distributions by models using different imfs . model ck predicts similar typical abundance ratio to model kk . o , mg and si , are mainly provided by stars with mass heavier than @xmath80 and iron is ejected by all sne  ii and sne  ia . for emp stars , @xmath82 depends on a fraction of stars with @xmath88 among sne  ii and it depends on the imf . for models kk and ck , typical mass of stars is quite different but the slope of the imfs at mass range to be sne  ii ( @xmath40 ) is similar , as seen in fig . [ imfs ] . relative frequency of heavier ( @xmath88 ) and lighter ( @xmath89 ) sne  ii are similar for both imfs and typical @xmath82 are also similar . however , model ck predicts that some stars with low oxygen abundance ( @xmath90 ) are distributed at very low metallicity range ( @xmath2}\\lesssim-3.5 $ ] ) . these stars are born in mini halos formed at low redshift . in this model , many sne  ia yield iron at lower redshift , and iron ejected from mini halos lower the @xmath78 of igm . metallicity of the igm is still low because ejected matter is diluted in large mass . mini halos formed with the igm polluted by sne  ia have low @xmath78 but low metallicity . observationally , these stars are not detected . if ejected matter is mixed in smaller mass , iron and oxygen abundance of polluted igm become larger and these o - poor stars dissipate . we note that , oxygen abundance of these stars can be lower than the detection limit of o. some stars without detection of o possibly have such an abundance feature .    for model lk , @xmath78 is obviously lower than models kk and ck in the whole metallicity range , as seen in fig . this is because a slope of the imf is steeper at mass range of stars to be sne  ii . the relative frequency of heavier sne  ii ( @xmath91 ) is smaller and a smaller amount of @xmath1-elements is ejected . the predicted distribution of @xmath78 is much lower than the observations for emp stars . at @xmath2}\\sim -2 $ ] , the abundances of mg , si and na relative to iron are also lower than the observations .    at @xmath2}\\gtrsim-1 $ ] , we can see clear decreasing trends for the @xmath1-element abundances as increasing metallicity for model ck and lk . relative numbers of sne  ia are larger for these models and they lower the @xmath82 at higher metallicity .      figures  [ kw ] , [ kf ] , and [ kc ] show abundance ratio distributions for models kw , kf , and kc using sn yields by @xcite , @xcite , and @xcite , respectively .    for model kw , as @xcite pointed out , predicted @xmath1-element abundances do not agree with observations . predicted abundances of the o , mg , and na relative to iron are 0.5dex or more lower than the observational sample .    for model kf , since @xcite modify the nucleosynthetic yields to match observational data , predicted typical abundances of emp stars show good agreement with observations for elements other than na . the decreasing trend of @xmath85 at low metallicity is also reproduced . they assume that a sn with larger initial mass ejects a smaller amount of cr ( see fig  [ yield ] ) . since a star with larger mass have shorter lifetime , @xmath85 increases as metallicity increases with time . however , all other studies with nucleosynthesis computations predict that a more massive star yields a larger amount of cr .    while model kf well reproduces the typical abundances , it predicts larger dispersion of the element abundances than the observations . especially , @xmath78 distributes from @xmath92 to @xmath93 at @xmath2}<-3 $ ] . this model also predicts some stars with @xmath94 . the predicted scatter is much larger than the observations and it indicates that a one - zone model is inadequate to understand earliest phases of the chemical evolution and metal yields of very metal poor sne .    model kc predicts typical abundances in agreement with observational sample , for mg and si . lower o abundance than observations is predicted but observed o abundances can be lower when non - lte and 3d effect taken into account , as mentioned above . this model predict some stars with very low @xmath78 and @xmath81 at @xmath2}<-3 $ ] . such abundance patterns are produced from sne at low - mass end of the mass range to be sne  ii . as seen in figure  2 , stars with @xmath95 yield small amount of o and mg . lower mass limit to be sne  ii is assumed to be @xmath54 in this paper but fate of the stars with @xmath0 is not well revealed . some stars with @xmath96 thought to become `` super - agb '' stars @xcite and evolve to o - ne - mg white dwarfs or electron capture supernovae @xcite with very little iron yield . absence of the very @xmath1-poor stars possibly indicate that the lower mass limit to be sne  ii is larger than @xmath54 at very low metallicity . @xcite argue that stars with @xmath97 become `` faint supernovae '' with low iron yield . although @xcite have assumed iron yield is @xmath50 for all sne , observations indicate that some sne yield lower amounts of iron . na is overproduced at higher metallicity ( @xmath2}>-2 $ ] ) . cr abundance at solar metallicity is consistent with the observations but the increasing trend is not reproduced . very large scatter of zn is predicted because they argue that a large amount of zn is yielded in a sn  ii with @xmath98 but a very little amount of zn is yielded in a sn with @xmath99 . when low mass limit to be sne  ii is larger as discussed above , stars with very high @xmath3 is not formed . a yield of zn is sensitive to entropy during explosive si - burning at sn explosion . as discussed later , energetic hypernovae thought to be required to explain zn abundance of emp stars and their trend . figures  [ mdfn ] and [ kkn ] show a result of model kkn without hypernovae contribution . the mdf of model kkn is similar to model kk . for the abundance ratio distributions , the most plausible difference from model kk is lower @xmath3 . since hypernovae synthesize a much larger amount of zn than normal sne , zn abundance of model kkn is lower than model kk and lower than observations for emp stars . @xmath1-element abundances predicted by model kkn are slightly higher than model kk and @xmath78 shows better agreement with observations than model kk . but for mg and cr , model kkn predicts slightly higher relative abundances than the observations . this is because a normal sn yields a smaller amount of iron than a hypernova . large explosion energy of hypernovae affects also gas dynamics . many mini - halos are blown up by their large explosion energy and ejected metal is mixed in a large mass . since it averages element abundances , the scatter of the predicted abundance of model kk is smaller than other models . the observed small scatter of @xmath82 suggest that there were many hypernovae in the early phases of the chemical evolution . we note that , however , @xcite have tuned parameters in their computations to get @xmath100 for all hypernovae and the scatter of the @xmath1-element abundances is decreased artificially .","summary":"the theoretical sn yields by kobayashi et al.(2006 ) and chieffi & limonge ( 2004 ) show reasonable agreement with observations for-elements . our model predicts significant scatter of element abundances at}<-3 $ ] . best fit yields for one zone chemical evolution model by francois et al.(2004 ) well reproduces the trend of the typical abundances of emp stars but our model with their yield predicts much larger scatter of abundances than the observations . the model with hypernovae predicts zn abundance in agreement with observations but other models predict lower . ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances .","abstract":"early phases of the chemical evolution and formation history of extremely metal poor ( emp ) stars are investigated using hierarchical galaxy formation models . we build a merger tree of the galaxy according to the extended press - schechter theory . we follow the chemical evolution along the tree , and compare the model results to the metallicity distribution function ( mdf ) and abundance ratio distribution of the milky way halo . we adopt three different initial mass functions ( imfs ) . in a previous studies , we argue that typical mass of emp stars should be high - mass( ) based on studies of binary origin carbon - rich emp stars . in this study , we show that only the high - mass imf can explain a observed small number of emp stars . for relative element abundances , the high - mass imf and the salpeter imf predict similar distributions . we also investigate dependence on nucleosynthetic yields of supernovae ( sne ) . the theoretical sn yields by kobayashi et al.(2006 ) and chieffi & limonge ( 2004 ) show reasonable agreement with observations for-elements . our model predicts significant scatter of element abundances at}<-3 $ ] . best fit yields for one zone chemical evolution model by francois et al.(2004 ) well reproduces the trend of the typical abundances of emp stars but our model with their yield predicts much larger scatter of abundances than the observations . the model with hypernovae predicts zn abundance in agreement with observations but other models predict lower . ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances ."}
{"article_id":"1105.2099","section_id":"c","document":"we compute formation history of emp stars with a hierarchical chemical evolution model and present mdfs and abundance ratio distributions . we adopt various imfs and sn yields and compare the results . as for imfs , we adopt the high mass imf given in our earlier studies@xcite , the imf by @xcite , and the standard low mass imf by @xcite . the pattern of the mdfs is similar for these three models but the predicted numbers of emp survivors are quite different . the high mass imf model predicts a comparable number of emp survivors to observations but other two imfs predict many more emp stars in our scenario . our hierarchical model reproduce a steep decline of the mdf below @xmath2}=-3.6 $ ] and a tail below @xmath2}<-4 $ ] . abundance ratio distributions predicted by the high mass imf are similar to the salpeter imf and the predicted @xmath1-element abundances are consistent with observations . typical value of @xmath82 depends on the slope of the imf at a mass range in which stars explode as sne  ii and the high mass imf with @xmath14 and @xmath101 has a slope similar to the salpeter imf . the imf by @xcite which has a steeper slope at @xmath40 predicts lower @xmath82 . we investigate not only the averaged abundance and their trend against metallicity but also the scatter of the abundances using our hierarchical models . abundance distributions strongly depend on the adopted sne nucleosynthesis models . for typical abundances of @xmath1-elements , yields by @xcite , @xcite , and @xcite show reasonable agreement with the observational sample . the sample from the first stars project shows very small scatter for @xmath81 and @xmath102 . this indicates that abundance ratio ejected by various sne is homogeneous or inter stellar matter is well mixed in large mass . the result with yields by @xcite is consistent with this very small scatter . however , stars analysed by other authors show larger scatter . although the sn yields by @xcite are the best fit yields as far as averaged abundances , their yields predict much larger scatter than all the observational sample for o and si . absence of stars with low @xmath78 and low @xmath81 possibly indicate that iron yields of stars with mass around @xmath54 are lower than normal sne ii . observed decreasing trend of @xmath85 as metallicity decreases can not be explained by the adopted yields by the theoretical sn nucleosynthesis computations . for na , intermediate massive agb stars or internal mixing affect surface abundances of some emp stars with na enhancement . for o , mg and na , correction of 3d and/or non - lte effect thought to decrease the scatter of observed abundances and improve the consistency to the model result . hypernovae are the plausible dominant source of zn for emp stars . models without hypernovae predict lower @xmath3 than in observations . observed increasing trend of @xmath3 as metallicity decreases is not reproduced in our hierarchical models . results in this paper are depend on the models of sn nucleosynthesis and accuracy of the abundance determination from spectroscopic observational data . uncertainty of the theoretical sn yields is still large . observational subsamples by different authors show different abundance distributions for some elements . recent studies with 3d / non - lte effects taken into account show that averaged abundances shift significantly by these effects and dispersion of abundances become smaller for some elements . further theoretical and observational studies are required to reveal the origin of metals in the emp stars and nature of the metal poor sne .","summary":"we adopt three different initial mass functions ( imfs ) . in a previous studies , we argue that typical mass of emp stars should be high - mass( ) based on studies of binary origin carbon - rich emp stars . in this study , we show that only the high - mass imf can explain a observed small number of emp stars . for relative element abundances , the high - mass imf and the salpeter imf predict similar distributions . we also investigate dependence on nucleosynthetic yields of supernovae ( sne ) .","abstract":"early phases of the chemical evolution and formation history of extremely metal poor ( emp ) stars are investigated using hierarchical galaxy formation models . we build a merger tree of the galaxy according to the extended press - schechter theory . we follow the chemical evolution along the tree , and compare the model results to the metallicity distribution function ( mdf ) and abundance ratio distribution of the milky way halo . we adopt three different initial mass functions ( imfs ) . in a previous studies , we argue that typical mass of emp stars should be high - mass( ) based on studies of binary origin carbon - rich emp stars . in this study , we show that only the high - mass imf can explain a observed small number of emp stars . for relative element abundances , the high - mass imf and the salpeter imf predict similar distributions . we also investigate dependence on nucleosynthetic yields of supernovae ( sne ) . the theoretical sn yields by kobayashi et al.(2006 ) and chieffi & limonge ( 2004 ) show reasonable agreement with observations for-elements . our model predicts significant scatter of element abundances at}<-3 $ ] . best fit yields for one zone chemical evolution model by francois et al.(2004 ) well reproduces the trend of the typical abundances of emp stars but our model with their yield predicts much larger scatter of abundances than the observations . the model with hypernovae predicts zn abundance in agreement with observations but other models predict lower . ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances ."}
{"article_id":"1210.2597","section_id":"i","document":"the ising model is one of the simplest model proposed by statistical mechanics to investigate ferromagnetic properties of metals . it is based on the following simplification of reality : we assume that a ferromagnetic material is composed of macroscopic magnet that live on a lattice and can assume only two orientation , up ( or @xmath8 ) and down ( or @xmath6 ) called spins ; the way orientation of the micromagnet are determined follows two rules : neighboring magnets like to have the same orientation , and all spins like to align with the external magnetic fields if there is one . the ising model is a probabilistic model ( i.e.  a probability law on the set of possible spin orientation ) following these rules and is defined using a boltzman - gibbs formalism , which is detailed in the next section . it describes the equilibrium state of a ferromagnet . the stochastic ising model also called glauber dynamics or heat - bath dynamics for ising model , is a markov chain on the set of spin configuration that describes the evolution of a magnet out of equilibrium ( e.g.  after a brutal change of temperature or of external magnetic fields ) . this is the object we study in this paper . our aim is to understand the time needed and the pattern used for a magnetic material to reach its equilibrium state after a change of external conditions . in order to bring a more complete answer to these questions , we consider them in a simplified but still non - trivial setup that is the zero - temperature limit . this brings heuristic intuition for what should happen in the whole low temperature regime . set @xmath9 consider the square @xmath10 ^ 2\\cap ( { { \\ensuremath{\\mathbb z } } } ^*)^2.\\ ] ] we define the set of spin configuration on @xmath11 to be @xmath12 . a generic spin configuration is denoted by @xmath13 and @xmath14 is called the spin at site @xmath15 . define the external boundary of @xmath16 as @xmath17    the ising model at inverse temperature @xmath18 , with external magnetic fields @xmath19 and boundary condition @xmath20 is a measure on the set of spin configurations defined by    @xmath21    where @xmath22 and the convention is taken that @xmath23 when @xmath24 . note that the first term in the exponential makes the spins of neighboring sites more likely to agree whereas the second term underlines that configuration with spins aligned with the magnetic fields are favored . the heat - bath dynamic for the ising model ( at inverse temperature @xmath18 , with external magnetic fields @xmath19 and boundary condition @xmath25 ) is a markov chain on the set of spin configuration @xmath26 . we denote the trajectory of the markov chain by @xmath27 . one starts from a given configuration @xmath28 and the rules for the evolution are the following :    * sites @xmath29 are equipped with independent rate one poisson process : @xmath30 where @xmath31 , i.e.  the increments @xmath32 are iid exponential variables . * the spin at site @xmath15 may change its value only when the clock at @xmath15 rings , i.e.  at time @xmath33 , @xmath34 , and its value stays constant on the intervals @xmath35 , @xmath36 . * when a clock rings , the spin at @xmath15 is updated according to the following law independently of the past history of the process : * * @xmath37 with probability @xmath38 * * @xmath39 with probability @xmath40    when @xmath15 has a neighbor @xmath41 in @xmath42 , the value @xmath43 appearing in the equations - is fixed ( by convention ) to be equal to @xmath44 for all time , where @xmath25 is the boundary condition . the update of the spin corresponds to sampling a spin configuration according to the measure @xmath45 .    as a consequence to this last remark , @xmath46 is the unique invariant measure for the dynamics , so that the law of @xmath47 converges to the equilibrium measure @xmath46 . the main questions in the study of dynamics is how much time is needed to reach equilibrium and what is the pattern used by the chain to reach it when we consider the dynamics on a very large domain @xmath16 . the answer to this question should of course depend on the temperature @xmath18 , the magnetic fields @xmath19 , the boundary condition @xmath25 the and the initial condition @xmath28 . in what follows , we denote often by @xmath8 resp .  @xmath6 the spin configuration or boundary condition where all spins are @xmath8 resp . @xmath6 . let us review shortly what is known and conjectured for these kind of dynamics when @xmath48 and @xmath49 . the property of the dynamics depends crucially on the equilibrium property of the system . recall that the two dimensional ising model undertakes a phase transition at @xmath50 ( see the seminal work of onsager @xcite ) which has the following form :    * when @xmath51 , correlation between spin at different sites decay exponentially , and for this reason what happens in the center of @xmath11 becomes independent of the boundary condition when @xmath7 tends to infinity . this is called the high temperature phase . * when @xmath52 , on the contrary , long - range correlation are present between spins , and boundary condition plays a crucial role . in particular the measure @xmath53 and @xmath54 corresponding to @xmath8 and @xmath6 boundary condition are very different . this is called the low temperature phase .    in the high temperature phase , the rapid decay of correlation between distant sites makes the evolution of the system in two distant zones of the box @xmath11 almost independent . schematically , the box of @xmath11 can be separated in @xmath55 zones of finite size that come to equilibrium independently . this requires a time of order @xmath56 . this prediction has been made rigorous by lubetzky and sly , who proved that in that case , the mixing time ( i.e.  the time to reach equilibrium ) for the dynamic in @xmath11 is equal to @xmath57 where @xmath58 is the relaxation time for the infinite volume dynamics ( see @xcite ) . for a formal definition of mixing time and relaxation time and an introduction to the modern theory of markov chain , we refer to @xcite .    in the low temperature phase the behavior of the dynamics depends on the boundary condition and for the sake of simplicity we restrict to the case of @xmath8 boundary condition . in that case , the equilibrium state is biased towards plus , and even spins in the center have a larger probability to be @xmath8 than minus . in a sense , one can say that , at equilibrium , the center of the box `` knows '' what the boundary condition is . thus , if one starts e.g.  from full @xmath6 initial condition ( @xmath59 for all @xmath29 ) , information must travel from the boundary to the center of the box in order to reach equilibrium . for this reason the mixing time is much longer than in the high temperature phase .    in @xcite , lifshitz described a conjectural pattern used by the system with @xmath8 boundary condition to reach equilibrium that can be described as follows : starting from @xmath6 initial condition the system should rapidly reach a state of local equilibrium that looks like the equilibrium measure with @xmath6 boundary condition , ( we call this the @xmath6 phase ) ; then on the time - scale @xmath60 , something looking like the true equilibrium measure with @xmath8 boundary condition , the @xmath8 phase , should start to appear in the neighborhood of the cubes boundary . the interface between the @xmath8 and the @xmath6 phase should move on the diffusive time - scale @xmath60 , having a drift in time proportional to its local curvature . as a consequence the system should reach equilibrium when the bubble formed by the @xmath6 phase disappears macroscopically , _ i.e. _ in a time @xmath55 .    for finite @xmath52 this conjecture is far from being on rigorous mathematical ground , but lifshitz ideas have been used to get bounds on the mixing time . the best to date being by lubetzky _ @xcite saying that the system reaches equilibrium in a time @xmath61 , still far from the conjecture @xmath60 . this gap between the lifshitz conjecture and the rigorous mathematical result has been one of the incentives to study the simpler zero - temperature version of the model . dynamics with different boundary condition or non - zero magnetic fields at low temperature also exhibits interesting behavior like low - temperature induced metastability ( see e.g.  @xcite ) that we choose not to expose here . note also that results are available at the critical temperature @xmath62 @xcite , where the equilibrium state of the system is somehow harder to describe .","summary":"we consider the continuous time , zero - temperature heat - bath dynamics for the nearest - neighbor ising model on with positive magnetic field . for a system of size , we start with initial condition such that if ^ 2 $ ] and and investigate the scaling limit of the set of spins when both time and space are rescaled by .","abstract":"we consider the continuous time , zero - temperature heat - bath dynamics for the nearest - neighbor ising model on with positive magnetic field . for a system of size , we start with initial condition such that if ^ 2 $ ] and and investigate the scaling limit of the set of spins when both time and space are rescaled by . we compare the obtained result and its proof with the case of zero - magnetic fields , for which a scaling result was proved in . in that case , the time - scaling is diffusive and the scaling limit is given by anisotropic motion by curvature ."}
{"article_id":"astro-ph0512116","section_id":"i","document":"damped lyman - alpha absorption lines in quasar spectra are believed to arise from intervening galaxies and intergalactic matter at various cosmological epochs . the damped lyman - alpha absorbers ( hereafter dlas ) are classically defined as quasar absorbers with @xmath6(h  i)@xmath7 while absorbers with @xmath8(h  i)@xmath9 are conventionally classified as sub - dlas . this distinction is based on the observational constraints of an early spectroscopic study @xcite . since the ly-@xmath10 line shows damping wings even at @xmath6(h  i)@xmath11 in this paper we will refer to both the sub - dla and dlas as dla systems .    at high redshifts the dlas are believed to contain a large fraction of the co - moving density of neutral hydrogen in galaxies and possibly account for all of the stars visible today ( e.g. * ? ? ? * ; * ? ? ? the evolution of metallicities in these absorbers provide important probes of the chemical enrichment and star formation history of the universe @xcite . unfortunately the connection between dlas and galaxies has not been clearly established . to shed more light on this connection , it is necessary to complement the wealth of spectroscopic data on these absorbers with information on their morphologies , luminosities , colors , and image structure from direct imaging . it has proven hard to obtain this information for most dlas . the imaging of high-@xmath12 dlas has been very difficult and a large fraction of the attempts to detect the ly-@xmath10 emission from high - redshift intervening ( @xmath13 ) dlas have produced either non - detections or weak detections ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? imaging studies of low-@xmath12 dlas have been more encouraging . although not always spectroscopically confirmed to be the absorbers , galaxies in images of low - redshift absorber fields often show a variety of morphologies : spirals , irregulars , low surface brightness ( lsb ) galaxies ( e.g. , steidel et al . 1994 , 1995 ; lebrun et al . 1997 ; bowen et al . 2001 ; cohen 2001 ; turnshek et al . most of these previous searches had limiting flux sensitivity thresholds of @xmath14 and thus could not rule out lsbs , while all of the near - ir searches lacked adequate angular resolution to rule out dwarf galaxies close to the line of sight . it is not clear which of the several competing scenarios for dlas are valid : large , bright , rotating proto - spirals ( wolfe et al . 1986 ; wolfe & prochaska 1998 ; prochaska & wolfe 1997b , 1998 ) , gas - rich dwarf galaxies ( york et al . 1986 ; matteucci et al . 1997 ) , merging proto - galactic fragments with cold dark matter ( e.g. , haehnelt , steinmetz , & rauch 1998 ; maller et al . 2001 ) , collapsing halos with merging clouds ( e.g. , mcdonald & miralda - escud 1999 ) , or low - surface brightness galaxies ( jimenez , bowen , & matteucci 1999 ) .    here we present the first adaptive optics observations of low - redshift dlas . we have obtained near infrared images of seven absorbers at @xmath15 with the university of hawaii hokupaa adaptive optics system and near - infrared camera quirc on the gemini - north telescope . we discuss the observations and data reductions in section 2 . the analysis of the data are presented in section 3 and the results from individual fields are discussed in section 4 . finally , in section 5 we characterize our sample of low - redshift dlas based on our measurements of the sizes , impact parameters , and image structure . throughout this paper we assume @xmath16 , @xmath17 , and @xmath18 .","summary":"we have carried out a high angular resolution near - infrared imaging study of the fields of 6 quasars with 7 strong absorption line systems at , using the hokupaa adaptive optics system and the quirc near - infrared camera on the gemini - north telescope . these absorption systems include 4 classical damped lyman - alpha absorbers ( dlas ) , 2 sub - dlas , and one lyman - limit system .","abstract":"we have carried out a high angular resolution near - infrared imaging study of the fields of 6 quasars with 7 strong absorption line systems at , using the hokupaa adaptive optics system and the quirc near - infrared camera on the gemini - north telescope . these absorption systems include 4 classical damped lyman - alpha absorbers ( dlas ) , 2 sub - dlas , and one lyman - limit system . images were obtained in the h or k filters with fwhm between with the goal of detecting the absorbing galaxies and identifying their morphologies . features are seen at projected separations of from the quasars and all of the fields show features at less than 2separation . we find candidate absorbers in all of the seven systems . with the assumption that some of these are associated with the absorbers , the absorbers are low luminosity or ; we do not find any large bright candidate absorbers in any of our fields . some fields show compact features that are too faint for quantitative morphology , but could arise in dwarf galaxies ."}
{"article_id":"astro-ph0512116","section_id":"r","document":"below we present the astrometric , photometric , and morphological results derived for the features in each field . table 5 summarizes the morphologies , impact parameters , luminosities , and scale lengths for the candidate objects , assuming that they are at the redshifts of the absorbers . the morphology is not listed for the objects that are too faint or too close to another object , since the profile fits for these objects are not robust . the scale lengths of the profiles are not listed for the point sources and for the sources where the profiles could not be fit . for candidate absorbers , we converted fluxes to luminosities using @xmath73 where @xmath74 is the luminosity distance of the dla candidate . these luminosities are express units of @xmath75 where we have adopted @xmath76 erg @xmath77 ( @xcite ) and @xmath78 erg @xmath77 ( @xcite ) . q0054 + 144 is a radio - quiet x - ray - bright qso at a redshift of @xmath79 . this object was imaged with hst wfpc2 ( bahcall et al . 1996 ; mclure et al . these hst data indicate that the host galaxy is well described by an early - type galaxy . a dla candidate absorber at @xmath80 with a neutral hydrogen column density of @xmath6(h  i ) = 20.1 was suggested by lanzetta et al . ( 1995 ) using iue data . however , higher resolution hst ghrs spectra showed that no dla absorption is present at @xmath80 ( bechtold et al . 2001 ) and no x - ray absorption was detected in chandra observations of bechtold et al . a low - ionization metal absorption line system is present at @xmath81 , but the ly-@xmath10 line is not damped , with @xmath6(h  i)@xmath82 ( turnshek & rao 2002 ) . thus this is a lyman - limit system . figure [ fig:0054 + 145 ] shows our h - band image of the field , the quasar - subtracted image of the central portion of the field , and the hst / wfpc2 f606w image . our h - band image is @xmath83 which corresponds to @xmath84 kpc@xmath85 at @xmath80 . we detect an object approximately 08 sw of the quasar only after the kl qso subtraction . it is too close and too faint to measure its magnitude or structural parameters . it is in the same direction and approximately the same location as the object identified in @xcite ( see their figure a11 ) but is considerably less extended . this smaller extent may be due to the smaller region over which the quasar subtraction was applied with the kl technique . in addition , a number of faint objects are seen around this elliptical galaxy in both our image and the hst image . they are all small objects and could be companions to the host galaxy . an additional object lies approximately @xmath86 south of the quasar just at the edge of our field of view and appears to correspond to an object in the hst image of mclure et al . this object was excluded from our analysis due to its close proximity to the edge of our field . q0235 + 164 ( ao 0235 + 164 ) is a radio - loud , optically violently variable , x - ray and @xmath87-ray emitting blazar . roberts et al . ( 1976 ) measured a complex 21-cm absorption profile in the radio spectrum of ao centered at z = 0.524 . based on a uv spectrum of the qso obtained with hst / stis , cohen et al . ( 1999 ) confirmed that the absorber is a dla with @xmath88 @xmath89 . junkkarinen et al . ( 2004 ) have detected the 2175  feature and diffuse interstellar bands at the redshift of this absorber . two faint objects with [ oii ] 3727 emission , have been detected within 2   from ao , and have been suggested as possible sites for the z = 0.524 absorption system ( smith et al , 1977 ; yanny et al , 1989 ) . burbidge et al . ( 1996 ) using hst / wfpc2 and hst / fos resolved these two objects more clearly . the nearest one ( @xcite s a1 ) might contribute to the complex h i 21-cm absorption , while the object 2   south of ao ( @xcite s a ) is an agn surrounded by faint nebulosity which can be classified as a balqso . in the optical and infrared imaging observations of the qso , chen & lanzetta ( 2003 ) concluded that there is a group of galaxies at the redshift of the known dla several of which likely contribute to the dla system . they find that the photometric redshift for the object @xmath90 south of the qso is consistent with the spectroscopic redshift of the known dla . @xcite found [ o  ii ] emission from both the a1 and a objects . figure [ fig:0235 + 164 ] shows our h - band image of the field before and after subtraction of the quasar image as well as the archival hst / wfpc2 f702w image . the full images are @xmath83 corresponding to @xmath91 kpc@xmath85 at @xmath92 . we identify six objects . the angular distances of these objects to the qso range from @xmath93 to @xmath94 corresponding to @xmath95 to @xmath96 kpc . objects other than object -4.93 - 7.47 have already been reported in the literature . it is unlikely to be the absorber since at the redshift of the absorber it would have an impact parameter of more than 50 kpc and its profile scale length is close to the fwhm of the quasar . object -7.15 - 7.21 appears to be a point - source in the hst images but shows a linear extension in both our h - band image and the hst image . object + 0.15 - 1.91 is the balqso object found by burbidge et al . its morphology in the nir is extended and disk dominated . an object is detected by sextractor in the psf subtracted image at a separation of 0.5   from the quasar centroid ( -0.3 - 0.4 ) . we have disregarded this object since it falls within the region where psf residuals are seen in psf subtractions of stellar images . we regard + 1.11 - 0.01 ( object a1 in burbidge et al . ( 1996 ) ) as the likely absorber . its photometric redshift is consistent with it being at the absorber redshift @xcite and its profile is consistent with a combination exponential disk and @xmath60 . absolute photometry was not possible from our data for this field because of the observations were made under nonphotometric conditions . sextractor identifies another object 25 ne of the quasar . this object was not reported in previous studies . while sextractor identifies this and object + 1.11 - 0.01 as separate objects , a 1-d cut across these two objects is well fit by a bulge+disk profile . if these are the same object , then it could be a spiral galaxy slightly inclined to our line of sight . at the redshift of the absorber , it would have an impact parameter of about 6 - 7 kpc . we note that if the object + 2.40 + 0.93 is an extension of object + 1.11 - 0.01 , then the extension is in the ne direction . this is perpendicular to the orientation suggested by @xcite . q0738 + 313 ( oi 363 ) is a core - dominated slightly variable quasar at @xmath97 . rao et al . ( 1998 ) reported the discovery of two dla systems toward the quasar at @xmath98 and @xmath99 with @xmath100 and @xmath101 @xmath89 , respectively . they concluded that a galaxy at @xmath102 from the qso line of sight is the only reasonable candidate at either absorption redshift . @xcite reported galaxies at @xmath103 and @xmath104 , @xmath105 and @xmath106 away from the quasar line of sight , respectively . she suggested that the @xmath107 galaxy may be a member of a cluster that causes the absorption at @xmath108 . the morphology of this galaxy was classified as early - type by rao et al . optical and infrared imaging observations of the qso made by turnshek et al . ( 2001 ) indicate that the dla galaxy at @xmath99 is a `` faint neutral colored galaxy with dwarf galaxy - like k and b - band luminosities . '' its spectrum is that of an early - type galaxy . turnshek et al . ( 2001 ) also suggested that the putative @xmath98 dla galaxy is likely to be all or part of the resolved light surrounding the quasar with armlike and jetlike - features . they suggested that the dla is a low surface brightness dwarf galaxy , possibly an irregular or interacting system . six objects are detected in our image . five have previously been identified . object + 1.90 - 5.38 , the dwarf galaxy at @xmath103 and designated `` g1 '' by others @xcite is a disk - dominated galaxy with a bulge - to - total ratio of 0.34 . this is consistent with an e / s0 galaxy suggested by @xcite . the object + 2.02 + 1.54 , designated `` s1 '' by @xcite , is still unresolved in our images , and gim2d identifies the object as a point - source . the faint arm and jet - like features discussed by @xcite are not apparent in our unbinned image . while our image has an angular resolution of about @xmath109 , our @xmath36 per pixel limiting surface brightness is 18.9 mag / arcsec@xmath38 . the arm and jet like features discussed by @xcite are about two magnitudes fainter . in order to achieve this sensitivity , we smoothed the image with a gaussian with a fwhm equal to the fwhm of the quasar image , subtracted an azimuthally - averaged psf , and rebinned the image to @xmath109 pixels . the resulting image is shown in the lower - right panel of figure [ fig:0738 + 313 ] . in this image we used an azimuthally averaged psf to subtract the light from the quasar because the kl analysis could not be performed over this large a field due to its computational requirements . the quasar contribution at the separation of the jet and arm are small so this subtraction should be adequate . this image was then analyszed by sextractor . the feature + 5.40 - 0.11 east of the quasar is aligned with the bright knot in the @xcite `` arm '' but the linear feature wsw of the quasar is found to be slightly rotated from the position shown in figure 1 of @xcite . in our image the linear feature extends along a line intersecting the quasar whereas in @xcite the feature appears aligned east - west . the jet clearly shows a highly mottled linear morphology . a new feature , + 0.71 + 01.63 , can be seen in the smoothed and binned image ( figure [ fig:0738 + 313 ] ) . it is also seen in the kl psf subtracted image when it is similarly smoothed and rebinned . this feature is previously unidentified . it appears to have a core with faint emission extending several arcseconds to the nnw . it is not clear whether this emission is some component of a larger object encompassing all the faint nebulosity but given its close proximity to the quasar line of sight ( b=3 or 6 kpc ) , it is likely to be associated with one of the absorption line systems . the feature seen less than @xmath110 sw of the quasar line of sight in the kl psf - subtracted image is a possible source but it is well within the region where psf subtraction artifacts are large for stellar sources so it is difficult to rule out that it is a psf subtraction artifact . this radio - quiet qso has an associated absorption system at @xmath111 . in an imaging and spectroscopic survey of faint galaxies , lanzetta et al . ( 1995 ) reported a strong ly-@xmath10 absorption system and a possible indication of weak c iv absorption at @xmath112 . they also obtained an unambiguous redshift of @xmath113 for a galaxy relatively close to the quasar sightline . the subsequent ultraviolet spectroscopic survey of lanzetta et al . ( 1997 ) showed that the ly-@xmath10 absorption system at @xmath111 has @xmath6(h  i ) = 19.8 . they concluded that this system is associated with a moderate - luminosity early - type galaxy , although it may actually arise in one of several very faint galaxies close to the qso line of sight seen in their hst / wfpc2 images . these conclusions are supported by chen et al . ( 2001 ) who confirmed the dla system and the associated galaxy . their photometric redshifts show that other galaxies in this field do not have the same redshift as the dla system . four objects are identified in our h - band images . object -9.04 + 1.53 is the galaxy designated as `` g1 '' @xcite . we find it is a disk - like galaxy with a bulge - to - disk ratio of @xmath114 and scale lengths of @xmath115 kpc and @xmath116 kpc . object -0.20 - 3.49 is the object designated `` s1 '' @xcite . it is a point source in our images as well as the hst images of @xcite . object + 1.28 + 2.55 is a diffuse arm - like feature that can be see in our h - band image as well as the hst images . the nir emission appears to extend towards the quasar . we find an apparent h magnitude of 24.7 for this diffuse emission while @xcite find an apparent ab magnitude of @xmath117 mag . the f702w - h color of -2.2 is extremely blue . object + 0.56 + 0.32 is close to the line of sight to the quasar ( 0.64 ) but we believe it to be real since we do not see a similar extension in the psf subtracted stellar image ( see figure [ fig : psfsubtraction ] ) . in fact we see extended emission to the east of the quasar in each of the four techniques used to remove the quasar light contribution . in addition , the emission at + 1.28 + 2.55 and at + 0.56 + 0.32 appears to be continuous ( figure 5 ) . we interpret the two emission features to be a single object with object + 1.28 + 2.55 being an extension of the emission . we regard it as the likely absorber . if this is the correct interpretation , then the dla is sampling a region very close @xmath1182 kpc from the center of a very blue galaxy . in addition , object -2.56 + 2.01 , while identified as a seperate object , is also very blue and could be part of this same emission . object -2.56 + 2.01 is unresolved . we do not detect the object -00023 + 00043 identified in @xcite . pks b1127 - 145 is a compact , gigahertz - peaked radio source at @xmath119 = 1.187 with a jet seen in radio and x - ray images , and variability at radio wavelengths . bergeron et al . ( 1991 ) identified mg ii , fe ii and mg i absorption in the spectrum of the quasar at z = 0.313 . they spectroscopically confirmed two late - type galaxies at the redshift of the absorber separated from the quasar by 96 and 177 and identified the closer one as the mg ii absorber . lane et al . ( 1998 ) in a survey of h i 21-cm absorption in mg ii - selected systems using wsrt , discovered 21-cm absorption at z = 0.3127 . hst / uv spectra show a damped lyman-@xmath10 profile with n(h  i ) = @xmath120 @xmath89 ( lane et al , 1998 ; rao & turnshek , 2000 ) . lane et al . ( 1998 ) concluded that the galaxy which bergeron et al . ( 1991 ) identified as the absorber , is unlikely to be the dla system since its column density is unlikely to arise at the projected impact parameter ( @xmath121 kpc ) . instead they suggested that the absorption comes from another galaxy with a separation 39 from the quasar , or from tidal debris associated with a group of galaxies . bechtold et al ( 2001 ) detected x - ray absorption with chandra / acis , and suggested that the absorbing gas of the dla has metallicity of 23@xmath122 solar . rao et al . ( 2003 ) identified the dla galaxy as a patchy / irregular lsb structure which encompasses four objects . they suggest that the dla system is more likely associated with the faintest object in the group found at the absorber redshift . chen & lanzetta ( 2003 ) also found that a group of at least four galaxies are at the redshift of the dla and they concluded that because of the proximity of these galaxies to the qso line of sight , it is difficult to separate the contribution of either of the galaxies to the dla . six objects are identified in our image of this field . the angular distances of these objects to the qso range from @xmath123 to @xmath124 corresponding to b@xmath125 = 2.5 to 70 kpc . object + 8.86 + 3.98 corresponds to the object `` g1 '' in bergeron et al . ( 1991 ) at @xmath126 . morphologically g1 appears to have both a disk and a bulge with a bulge - to - total ratio of @xmath127 . tidal warping at the edge of this galaxy can be seen both in our h - band image and the hst f814w image . our object -3.57 + 0.17 corresponds to the object identified as the likely absorber by @xcite . our image adds to the already crowded field of q1127 - 145 . we regard the object -0.13 + 0.57 , appearing after psf subtraction at an angular distance @xmath123 , as another candidate absorber simply due to its close proximity to the quasar line of sight . this object has not be indentified previously though the hst image has a shows a similar feature when the psf is removed . we do not discount that the faint diffuse emission seen around the field could also contribute to the absorbing system but this close object would have an impact parameter of only @xmath118 2.5 kpc . it has not been reported previously but appears to extend at least one arcsecond away from the quasar . we do not detect all of the faint nebulosity seen in the immediate vicinity of the quasar in the hst images but have detected very diffuse emission extending nw @xmath128 from the quasar . this radio - quiet qso ( @xmath129 ) was observed by sargent et al . ( 1988 ) , who identified four distinct absorption redshifts in its spectrum . in a spectral survey of c iv absorption systems , they found a weak mg ii doublet at @xmath130 . the iue spectrum of this object shows a low - redshift candidate dla system at @xmath131 with log @xmath132 @xcite . hst / uv spectroscopy did not confirm the presence of this system ( turnshek et al . 2002 ) however subsequent hst spectra did reveal a dla at the redshift ( @xmath133 ) of another mg ii system ( bechtold et al . based on the equivalent width of the ly@xmath10 line at @xmath134 , the dla system has a log @xmath135 = 19.7 . there are additional metal - line systems at @xmath136 ( c iv+mg ii ) , and @xmath137 ( c iv ) . five objects are identified in our image of this field . the angular distances of these objects to the qso range from @xmath138 to @xmath139 corresponding to @xmath140 to @xmath141 kpc at @xmath142 . there is no previous report of detection of these objects in the literature . @xcite detected a faint object ( @xmath143 ) with an angular distance of @xmath144 from the qso line of sight , which could be object 1.81 + 2.04 . object -1.81 + 2.04 is evident in the hst f702w image . all objects are compact and faint . objects -4.23 + 3.04 and + 2.11 - 0.94 appear slightly extended ; however , they would have impact parameters in excess of 20 kpc if they give rise to the absorption . we regard the likely absorber as the faint emission 07 south of the quasar . this object is evident in both our nir image and in the hst image though we do not have the resolution or the signal - to - noise to determine its morphology .","summary":"some fields show compact features that are too faint for quantitative morphology , but could arise in dwarf galaxies .","abstract":"we have carried out a high angular resolution near - infrared imaging study of the fields of 6 quasars with 7 strong absorption line systems at , using the hokupaa adaptive optics system and the quirc near - infrared camera on the gemini - north telescope . these absorption systems include 4 classical damped lyman - alpha absorbers ( dlas ) , 2 sub - dlas , and one lyman - limit system . images were obtained in the h or k filters with fwhm between with the goal of detecting the absorbing galaxies and identifying their morphologies . features are seen at projected separations of from the quasars and all of the fields show features at less than 2separation . we find candidate absorbers in all of the seven systems . with the assumption that some of these are associated with the absorbers , the absorbers are low luminosity or ; we do not find any large bright candidate absorbers in any of our fields . some fields show compact features that are too faint for quantitative morphology , but could arise in dwarf galaxies ."}
{"article_id":"astro-ph0512116","section_id":"i","document":"we present the first adaptive optics observations of low - redshift dlas . the images have revealed several objects at close angular separations to the quasar in each field . the adaptive optics images are comparable to the hst images in resolution and several close features are seen in common with hst and with these adaptive optics images . in addition , we report the detection of two previously unidentified objects in the fields of q0738 + 313 , where there are no hst images , and q1127 - 145 , where the hst detection is marginal .    the objects found around in these quasar absorption fields would be less than @xmath145 if they are at the absorber redshift and most of the brighter objects appear to have disks . the census of the brighter objects in these six absorber fields is 6 disk - dominated galaxies , 3 disk+bulge galaxies , 2 bulge - dominated galaxies , 3 point sources , and 5 unconstrained objects . in addition , five of the six fields show objects between 05 and 10 to the line of sight to the quasar .    our census has found likely candidates for all of the dla systems . the kl subtraction reveals a candidate object just offset from the quasar line of sight in q0054 + 144 though the hst field appears to have several faint objects distributed about the field . the dla in q0235 + 164 appears to be the object previously identified 1east of the quasar @xcite . in q0738 + 313 we find a new object to which we attribute the lower - redshift dla . this object would have an impact parameter of @xmath1183 kpc . it appears to have emission extending several arcseconds to the nw . this emission could be associated with the jet and arm features identified by @xcite though this emission is fainter than the new object detected here . the dla at @xmath146 in this field has been previously identified . in q0850 + 440 @xcite find a dwarf galaxy 9   from the quasar ( @xmath147 kpc ) . we identify another object very close to the quasar line of sight as a candidate absorber . it appears only after subtraction of the quasar but if the absorption arises from this object , then the dla arises close to the core of a very blue galaxy ( @xmath148 kpc ) . for q1127 - 145 we find a faint diffuse object close to the line of sight of the quasar and extending nnw several arcseconds . the absorber in q1329 + 412 is identified as arising from an object 07 south of the quasar . this object is also clearly seen in both our h - band image and an hst f702w image of the field . all candidate absorbers are faint , with luminosities less than 0.1 @xmath149 or @xmath150 . assuming that at least some of these objects are at the same redshift as the absorbers , we conclude that the absorbers in our fields are associated with relatively low luminosity galaxies . morphological analysis reveals that most of the brighter objects have a disk component . their sizes , inferred from the surface brightness profiles , range from small to typical scale lengths for local disk galaxies . for reference , our galaxy has a disk scale length of @xmath151  kpc measured in the @xmath152-band @xcite and m31 has a scale length of @xmath153  kpc in the @xmath152-band , and @xmath154  kpc in the @xmath155-band @xcite . table 5 summarizes object morphologies and the derived linear impact parameter , luminosity , and scale lengths assuming the objects are at the redshift of the absorber . @xcite have suggested that the dlas at @xmath156 are dominated by dwarf or low surface brightness galaxies . however , @xcite , with more photometric redshifts , have suggested that the luminosity function of @xmath156 dlas could be much broader . our observations , at higher resolution than both of these studies , have found all of the candidate absorbers to be faint , with significant disk components for the majority of the objects . this suggests that a considerable fraction of low-@xmath12 dlas may be faint , low surface brightness galaxies . such a conclusion would appear to be consistent with the low metallicities found in low-@xmath12 dlas ( e.g. , @xcite ; @xcite ; and references therein ) . however , it would be necessary to obtain redshift confirmations for our candidates and to obtain similar high - resolution images of other low-@xmath12 dlas to reach more definitive conclusions on the luminosity function of the absorber galaxies . our observations have demonstrated the use of adaptive optics for direct high - resolution imaging of the galaxies giving rise to quasar absorbers . deeper observations of the same fields in the future with higher order ao systems would help to improve the signal - to - noise ratios in the fainter objects . furthermore , adaptive optics systems with laser guide stars are not constrained by the need to have a bright guide star in the quasar field , and would thus be able to reach higher redshift absorbers .    it is crucial to also obtain spectroscopy ( or at least narrow - band imaging ) of all the fields to better constrain the redshifts of the detected candidate absorbers . with spectroscopic psf subtraction procedures ( such as those followed by @xcite ) it may be feasible to even verify the redshifts of the objects located very close to the line of sight of the quasar . it is essential to expand the sample of high - resolution broad - band images , followed with spectroscopic confirmations , for quasar absorbers at low and high redshifts . such a combination of high - resolution imaging and spectroscopic observations of quasar absorbers can give direct information on their luminosities , sizes , and star formation rates and thus the nature of these galaxies . performing such observations on different types of quasar absorbers ( e.g. , dlas , weak mg ii systems , c iv systems ) may help to understand any trends between the absorption line strengths and galaxy properties such as the luminosities and impact parameters . finally , a comparison of these properties of quasar absorbers at low and high redshifts will allow us to study the evolution of the absorbing galaxies with cosmological time and the connection between the absorbers and the present - day galaxies . this paper is based on observations obtained at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the national science foundation ( united states ) , the particle physics and astronomy research council ( united kingdom ) , the national research council ( canada ) , conicyt ( chile ) , the australian research council ( australia ) , cnpq ( brazil ) and conicet ( argentina ) . this paper is based on observations obtained with the adaptive optics system hokupaa / quirc , developed and operated by the university of hawaii adaptive optics group , with support from the national science foundation . we thank the gemini - north observatory staff for assistance during our observations , hsiao - wen chen for providing details of the published photometric data for q1127 - 145 , and b. stobie of the university of arizona for providing and assisting with the idp-3 package . we also thank the referee of the paper for making a number of positive suggestions on the paper . vpk and sg gratefully acknowledge partial support from the national science foundation grant ast-0206197 and from the university of south carolina research foundation . mt acknowledges support from national science foundation grant ast-0205960 .                                                                                                                                                                               4   region centered on the quasar . the axes are marked with 0.5   intervals . each column shows one of the techniques applied to the quasar ( top ) and a star ( bottom ) in the field of q0850 + 400 . the left most column shows the residual in the quasar / star images when the psf is constructed from the psf calibration observations . the second column shows the residuals when the psf is constructed from the star within the field . the field star residual image is by definition zero . the third column shows the residuals when the psf is constructed from the azimuthal average of the quasar image . the last column shows the residual when the psf is modeled as a fit of the first 30 modes of the karhunen - loeve ( kl ) basis calculated from the sequence of individual quasar exposures in the observation . residuals in the kl psf stellar image subtraction extend to a radius of about 05 . in all cases , the psf was scaled and translated to minimize the variance within the @xmath35 images . all images are displayed with the maximum and minimum intensities scaled to the sky @xmath157 of the peak intensity in the unsubtracted images . the residual images have been smoothed by a guassian with fwhm=3 pixels . [ fig : psfsubtraction],scaledwidth=100.0% ]       lllllll q0054 + 144 & 16.1 & 0.171 & 0.103 & @xmath158 & lyman - limit & 1 , 2 + q0235 + 164 & 15.5 - 19 & 0.940 & 0.524 & @xmath159 & dla & 3 + q0738 + 313 & 16.1 & 0.635 & 0.0912 & @xmath160 & dla & 4 , 5 + q0738 + 313 & 16.1 & 0.635 & 0.2212 & @xmath161 & dla & 4 , 6 + q0850 + 440 & 16.4 & 0.5139 & 0.1638 & @xmath162 & sub - dla & 7 + q1127 - 145 & 16.9 & 1.184 & 0.3127 & @xmath163 & dla & 3 + q1329 + 412 & 16.3 & 1.9300 & 1.282 & @xmath164 & sub - dla & 8 +    ccccccc q0054 + 144 & h & @xmath165 & 0.46 & 0.75 & 19.6 & 21.9 + q0235 + 164 & h & @xmath166 & 0.50 & 0.82 & 19.9 & 22.2 + q0738 + 313 & k@xmath1 & @xmath167 & 0.19 & 0.28 & 18.9 & 21.2 + q0850 + 440 & h & @xmath168 & 0.23 & 0.38 & 20.0 & 22.3 + q1127 - 145 & h & @xmath169 & 0.33 & 0.54 & 20.0 & 22.3 + q1329 + 412 & h & @xmath170 & 0.29 & 0.47 & 20.1 & 22.4 +    llll q0054 + 145 & qso & 0 & @xmath171 + & -0.29 - 0.74 & 0.79 & 21.5 + & & & + q0235 + 164 & qso & 0 & @xmath172 + & -0.33 - 0.45 & 0.56 & 23.9 + & + 1.11 - 0.01 & 1.11 & 21.9 + & + 0.15 - 1.91 & 1.92 & 20.2 + & + 2.40 + 0.93 & 2.57 & 24.9 + & -5.85 - 2.69 & 6.44 & 20.3 + & -4.93 - 7.47 & 8.95 & 24.3 + & -7.15 - 7.21 & 10.15 & 20.6 + & & & + q0738 + 313 & qso & 0 & @xmath173 + & + 0.71 + 1.63 & 1.78 & 22.6 + & + 2.02 + 1.54 & 2.54 & 21.3 + & + 5.40 - 0.11 & 5.40 & 23.0 + & + 1.90 - 5.38 & 5.71 & 19.8 + & -6.58 - 1.64 & 6.78 & 22.4 + & -7.96 + 5.02 & 9.41 & 21.4 + & & & + q0850 + 440 & qso & 0 & @xmath174 + & + 0.56 + 0.32 & 0.64 & ... + & + 1.28 + 2.55 & 2.85 & 24.7 + & -2.56 + 2.01 & 3.25 & 25.8 + & -0.20 - 3.49 & 3.50 & 17.6 + & -9.04 + 1.53 & 9.17 & 17.8 + & & & + q1127 - 145 & qso & 0 & @xmath175 + & -0.13 + 0.57 & 0.58 & ... + & -3.57 + 0.17 & 3.57 & 24.6 + & + 5.42 - 1.40 & 5.60 & 22.6 + & + 7.92 + 1.82 & 8.13 & 23.8 + & + 8.86 + 3.98 & 9.71 & 18.5 + & + 14.49 - 6.76 & 16.0 & 19.9 + & & & + q1329 + 412 & qso & 0 & @xmath176 + & + 0.20 - 0.69 & 0.72 & ... + & + 2.11 - 0.94 & 2.31 & 22.5 + & -1.81 + 2.04 & 2.73 & 25.7 + & -4.23 + 3.04 & 5.21 & 24.6 + & + 5.23 - 3.76 & 6.44 & 24.9 +    llllllll q0235 + 164 & & & & & & & + & @xmath177 & @xmath178 & @xmath179 & @xmath180 & @xmath181 + & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 + & @xmath187 & @xmath188 & @xmath189 & @xmath190 & @xmath191 + & @xmath192 & @xmath193 & @xmath194 & @xmath195 & @xmath196 + & @xmath197 & @xmath198 & @xmath199 & @xmath200 & @xmath201 + q0738 + 313 & & & & & & & + & @xmath202 & @xmath203 & @xmath184 & @xmath204 & @xmath205 + & @xmath206 & @xmath207 & @xmath208 & @xmath209 & @xmath210 + & @xmath211 & @xmath212 & @xmath179 & @xmath179 & @xmath213 + q0850 + 440 & & & & & & & + & @xmath214 & @xmath215 & @xmath216 & @xmath217 & @xmath218 + & @xmath219 & @xmath184 & @xmath220 & @xmath184 & @xmath221 + & @xmath222 & @xmath223 & @xmath223 & @xmath224 & @xmath225 + q1127 - 145 & & & & & & & + & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 + & @xmath231 & @xmath232 & @xmath233 & @xmath234 & @xmath235 + & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath240 + & @xmath241 & @xmath242 & @xmath243 & @xmath244 & @xmath245 + q1329 + 412 & & & & & & & + & @xmath246 & @xmath247 & @xmath248 & @xmath249 & @xmath250 + & @xmath251 & @xmath252 & @xmath184 & @xmath253 & @xmath254 + & @xmath255 & @xmath256 & @xmath257 & @xmath258 & @xmath259 + & @xmath260 & @xmath261 & @xmath262 & @xmath263 & @xmath264 +    lllllllll q0054 + 145 & -0.29 - 0.74 & 1.40 & & & & + & & & & & + q0235 + 164 & -0.33 - 0.45 & 3.36 & & & & + & + 1.11 - 0.01 & 6.66 & & & 0.0 & 0.3 + & + 0.15 - 1.91 & 11.53 & & b+d & 0.0 & 1.3 + & + 2.40 + 0.93 & 15.43 & & & & + & -5.85 - 2.69 & 38.66 & & dd & 0.1 & 1.2 + & -4.93 - 7.47 & 53.73 & & & 0.5 & 0.6 + & -7.15 - 7.21 & 60.93 & & b & 2.0 & 2.0 + & & & & & + q0738 + 313 & + 0.71 + 1.63 & 2.90 6.09 & -2.32 -1.48 & & & + & + 2.02 + 1.54 & 4.14 8.69 & -1.80 -0.96 & p & 0.0 0.0 & 0.0 0.0 + & + 5.40 - 0.11 & 8.80 18.48 & -2.48 -1.64 & & & + & + 1.90 - 5.38 & 9.31 19.54 & -1.20 -0.36 & d+b & 0.1 0.1 & 0.2 0.5 + & -6.58 - 1.64 & 11.05 23.21 & -2.24 -1.40 & & & + & -7.96 + 5.02 & 15.34 32.21 & -1.84 -1.00 & p & 0.0 0.0 & 0.0 0.0 + & & & & & + q0850 + 440 & + 0.56 + 0.32 & 1.77 & & & & + & + 1.28 + 2.55 & 7.69 & -4.09 & & & + & -2.56 + 2.01 & 8.77 & -4.53 & d & 0.0 & 0.6 + & -0.20 - 3.49 & 9.44 & -1.25 & p & 0.3 & 0.0 + & -9.04 + 1.53 & 24.74 & -1.33 & d & 0.7 & 1.1 + & & & & & + q1127 - 145 & -0.13 + 0.57 & 2.55 & & & & + & -3.57 + 0.17 & 15.70 & -3.42 & & & + & + 5.42 - 1.40 & 24.63 & -2.62 & & 0.5 & 0.0 + & + 7.92 + 1.82 & 35.75 & -3.10 & & 0.5 & 1.4 + & + 8.86 + 3.98 & 42.70 & -0.98 & & 1.0 & 3.9 + & + 14.49 - 6.76 & 70.32 & & & 0.1 & 1.0 + & & & & & + q1329 + 412 & + 0.20 - 0.69 & 4.30 & & & & + & + 2.11 - 0.94 & 13.80 & -2.06 & d & 10 . & 21 . + & -1.81 + 2.04 & 16.31 & -3.34 & & 0.0 & 1.6 + & -4.23 + 3.04 & 31.13 & -2.90 & & 0.4 & 1.8 + & + 5.23 - 3.76 & 38.48 & -3.02 & & 0.1 & 1.0 +","summary":"we find candidate absorbers in all of the seven systems . with the assumption that some of these are associated with the absorbers , the absorbers are low luminosity or ; we do not find any large bright candidate absorbers in any of our fields .","abstract":"we have carried out a high angular resolution near - infrared imaging study of the fields of 6 quasars with 7 strong absorption line systems at , using the hokupaa adaptive optics system and the quirc near - infrared camera on the gemini - north telescope . these absorption systems include 4 classical damped lyman - alpha absorbers ( dlas ) , 2 sub - dlas , and one lyman - limit system . images were obtained in the h or k filters with fwhm between with the goal of detecting the absorbing galaxies and identifying their morphologies . features are seen at projected separations of from the quasars and all of the fields show features at less than 2separation . we find candidate absorbers in all of the seven systems . with the assumption that some of these are associated with the absorbers , the absorbers are low luminosity or ; we do not find any large bright candidate absorbers in any of our fields . some fields show compact features that are too faint for quantitative morphology , but could arise in dwarf galaxies ."}
{"article_id":"1001.2916","section_id":"i","document":"the goal of this article is to study weak convergence results for the tail empirical process associated with some long memory sequences . besides of theoretical interests on its own , the results are applicable in different statistical procedures based on several extremes . a similar problem was studied in case of independent , identically distributed random variables in @xcite , or for weakly dependent sequences in @xcite , @xcite , @xcite , @xcite . our set - up is as follows . assume that @xmath0 , is a stationary gaussian process with unit variance and covariance @xmath1 where @xmath2 is the hurst exponent and @xmath3 is a slowly varying function at infinity , i.e. @xmath4 for all @xmath5 . the sequence in this case is referred to as an _ lrd _ gaussian sequence . we also consider weakly dependent gaussian sequences , i.e. such that @xmath6 . we shall consider a stochastic volatility process defined as @xmath7 where @xmath8 is a nonnegative , deterministic function and that @xmath9 , @xmath10 , is a sequence of i.i.d . random variables , independent of the process @xmath11 . we note , in particular , that if @xmath12<\\infty$ ] and @xmath13=0 $ ] , then the @xmath14s are uncorrelated , no matter the assumptions on dependence structure of the underlying gaussian sequence . stochastic volatility models have become popular in financial time series modeling . in particular , if @xmath2 , these models are believed to capture two standardized features of financial data : long memory of squares or absolute values , and conditional heteroscedascity . if @xmath15 , then the model is referred to in the econometrics literature as _ long memory in stochastic volatility _ ( lmsv ) and was introduced in @xcite . for an overview of stochastic volatility models with long memory we refer to @xcite . let @xmath16 , @xmath17 , be the marginal distribution of @xmath14 . we want to consider the case where @xmath18 belongs to the domain of attraction of an extreme value distribution with positive index @xmath19 , i.e. there exist sequences @xmath20 , @xmath21 , @xmath22 , and @xmath23 , @xmath21 , such that the associated conditional tail distribution function @xmath24 satisfies @xmath25 for the stochastic volatility model , this will be obtained through a further specification . let @xmath26 be the marginal distribution of the noise sequence . we will assume that for some @xmath27 , @xmath28 where @xmath29 is again a slowly varying function . assuming ( [ eq : pareto - assumption ] ) and @xmath30<\\infty$ ] for some @xmath31 , we conclude by breiman s lemma @xcite ( see also ( * ? ? ? * proposition 7.5 ) ) that @xmath32 { { \\mathbb p}}(z_1>x ) \\ ; , \\ \\mbox { as } x\\to\\infty.\\ ] ] consequently , @xmath33 satisfies ( [ eq : cond - tail ] ) with @xmath34 and @xmath35 . similarly to @xcite , we define the tail empirical distribution function and the tail empirical process , respectively , as @xmath36 and @xmath37 from @xcite we conclude that under appropriate mixing and other conditions on a stationary sequence @xmath14 , @xmath17 , the tail empirical process converges weakly and the limiting covariance is affected by dependence . in our case , the results @xcite do not seem applicable . in fact , it will be shown that we have two different modes of convergence . if @xmath20 is _ large _ , then @xmath38 is the proper scaling factor and the limiting process is gaussian with the same covariance structure as in case of i.i.d . random variables @xmath14 . otherwise , if @xmath20 is _ small _ , then the limit is affected by long memory of the gaussian sequence . the scaling is different and the limit may be non - normal . these results are presented in section [ sec : general ] . note that a similar dichotomous phenomenon was observed in the context of sums of extreme values associated with long memory moving averages , see @xcite for more details . on the other hand , this dichotomous behaviour is in contrast with the convergence of point processes based on stochastic volatility models with regularly varying innovations , where ( long range ) dependence does not affect the limit ( see @xcite ) . the process @xmath39 is unobservable in practice , since the parameter @xmath20 depends on the unknown distribution @xmath18 . also , @xmath20 being _ large _ or _ small _ depends on a delicate balance between the tail index @xmath40 and the hurst parameter @xmath41 . in order to overcome this , we consider as in @xcite a process with random levels . there , we set @xmath42 and replace the deterministic level @xmath20 by @xmath43 , where @xmath44 are the increasing order statistics of the sample @xmath45 . the number @xmath46 can be thought as the number of extremes used in a construction of the tail empirical process . it turns out that if the number of extremes is _ small _ ( which corresponds to a _ large _ @xmath20 above ) , then the limiting process changes as compared to the one associated with @xmath39 , but the speed of convergence remains the same . this has been already noticed in @xcite in the weakly dependent case . on the other hand , if @xmath46 is _ large _ , then the scaling from @xmath39 is no longer correct ( see corollary [ cor : practical ] ) . in fact , the process with random levels has a faster rate of convergence and we claim in theorem [ thm : practical-1 ] that the rate of convergence and the limiting process are not affected at all by long memory , provided that a technical second order regular variation condition is fulfilled . the reader is referred to section [ sec : random - levels ] . on the other hand , it should be pointed out that our results are for _ the _ long memory stochastic volatility models . it is not clear for us whether such phenomena will be valid for example for subordinated long memory gaussian sequences with infinite variance .    the results for the tail empirical process @xmath39 allow us to obtain asymptotic normality and non - normality of intermediate quantiles , as described in corollary [ coro : intermediate ] . on the other hand , the tail empirical process with random levels allows the study of the hill estimator of the tail index @xmath40 ( section [ sec : hill ] ) . consequently , as shown in corollary [ cor : hill ] , long memory does not have influence on its asymptotic behaviour . these theoretical observations are justified by simulations in section [ sec : numstudies ] . last but not least , we have some contribution to the theory of regular variation . to establish our results in the random level case , we need to work under a second order regular variation condition . consequently , one has to establish in a breimans - type lemma that such a condition is transferable from @xmath47 to @xmath48 . this is done in section [ sec : s - o - c ] .","summary":"this paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models . the tail empirical process with random levels never suffers from long memory .","abstract":"this paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models . we show that such a process has dichotomous behaviour , according to an interplay between the hurst parameter and the tail index . on the other hand , the tail empirical process with random levels never suffers from long memory . this is very desirable from a practical point of view , since such a process may be used to construct the hill estimator of the tail index . to prove our results we need to establish new results for regularly varying distributions , which may be of independent interest"}
{"article_id":"1001.2916","section_id":"r","document":"let us define a function @xmath49 on @xmath50 by @xmath51 by breiman s lemma and the regular variation of @xmath47 , we conclude that for each @xmath52 $ ] , this function converges pointwise to @xmath53 , where @xmath54 . a stronger convergence can actually be proved ( see section [ sec : proof - s - o - c ] for a proof ) . [ lem : convergence - uniforme - hermite ] if  ( [ eq : pareto - assumption ] ) holds and @xmath55<\\infty$ ] for some @xmath31 , then @xmath56 = 0 \\ ;    \\end{aligned}\\ ] ] for all @xmath57 such that @xmath58 .    in order to introduce our assumptions , we need to define the hermite rank of a function . recall that the hermite polynomials @xmath59 , @xmath60 , form an orthonormal basis of the set of functions @xmath61 such that @xmath62<\\infty$ ] , where @xmath63 denotes a generic standard gaussian random variable ( independent of all other random variables considered here ) , and have the following properties : @xmath64 = 0 \\ ; , \\ m\\geq 1 \\ ; , \\ { { \\mathrm { cov}}}(h_j(x),h_k(x ) ) =    \\delta_{j , k } k ! \\;\\end{aligned}\\ ] ] where @xmath65 is kronecker s delta , equal to 1 if @xmath66 and zero otherwise . then @xmath61 can be expanded as @xmath67 with @xmath68 $ ] and the series is convergent in the mean square . the smallest index @xmath69 such that @xmath70 is called the hermite rank of @xmath61 . note that with this definition , the hermite rank is always at least equal to one and the hermite rank of a function @xmath61 is the same as that of @xmath71 $ ] . let @xmath72 denote the hermite coefficients of the function @xmath73 . since @xmath74<\\infty$ ] for all @xmath75 , lemma  [ lem : convergence - uniforme - hermite ] implies that the hermite coefficients @xmath72 converge to @xmath76 , where @xmath77 is the @xmath78-th hermite coefficient of @xmath79 , uniformly with respect to @xmath80 . this implies that for large @xmath81 , the hermite rank of @xmath82 is not bigger than the hermite rank of @xmath79 . in order to simplify the proof of our results , we will use the following assumption , which is not very restrictive . [ [ assumption - h ] ] assumption ( h ) + + + + + + + + + + + + + +    denote by @xmath83 , @xmath84 , the hermite coefficients of @xmath82 and let @xmath85 be the hermite rank of @xmath82 . define @xmath86 the hermite rank of the class of functions @xmath87 . in other words , the number @xmath88 is the smallest @xmath78 such that @xmath89 for at least one @xmath90 . furthermore , let @xmath91 be the hermite rank of @xmath79 . we assume that @xmath92 for @xmath81 large enough .    _ remark_.  since for large enough @xmath81 it holds that @xmath93 for all @xmath90 , the assumption is fulfilled , for example , when @xmath79 has hermite rank 1 ( as is the case for the function @xmath94 ) , or if the function @xmath95 is even with the hermite rank  2 . the result for the general tail empirical process is as follows . [ thm : general ] assume ( h ) with @xmath96 ,  ( [ eq : lrd ] ) , ( [ eq : pareto - assumption ] ) , @xmath97 and that there exists @xmath31 such that @xmath98<\\infty \\ ; . \\end{aligned}\\ ] ]    a.   [ item : big - u ] if @xmath99 as @xmath100 or if @xmath101 is weakly dependent , then @xmath102 converges weakly in @xmath103 to the gaussian process @xmath104 , where @xmath105 is the standard brownian motion . b.   [ item : small - u ] if @xmath106 as @xmath100 then @xmath107 converges weakly in @xmath103 to the process @xmath108)^{-1 } j(q ) t l_q$ ] , where the random variable @xmath109 is defined in  ( [ eq : def - l_q ] ) .      1 . we rule out the borderline case @xmath110 for the sake of brevity and simplicity of exposition . it can be easily shown that if @xmath110 , then @xmath111 converges to @xmath112 provided @xmath113 tends to infinity faster than a certain slowly varying function ( e.g. if @xmath114 for some @xmath115 ) , even though it may hold in this case that @xmath116 . the reason is that the variance of the partial sums of @xmath117 is of order @xmath81 times a slowly varying function which dominates @xmath118 . @xmath119 is endowed with skorohod s @xmath120 topology , and tightness is checked by applying ( * ? ? ? * theorem 15.6 ) . since the limiting processes have almost surely continuous paths , this convergence implies uniform convergence on compact sets of @xmath121 . see also @xcite . the meaning of the above result is that for @xmath20 _ large _ , long memory does not play any role . however , if @xmath20 is _ small _ , long memory comes into play and the limit is degenerate . furthermore , in the case of theorem [ thm : general ] , _ small _ and _ large _ depend on the relative behaviour of the tail of @xmath122 and the memory parameter . note that the condition @xmath123 implies that @xmath124 , in which case the partial sums of the subordinate process @xmath125 weakly converge to the hermite process of order @xmath91 ( see section  [ sec : lrd - gaussian ] ) . the cases ( [ item : big - u ] ) and ( [ item : small - u ] ) will be referred to as the limits _ in the i.i.d . zone _ and _ in the lrd zone _ , respectively . condition @xmath30<\\infty$ ] is standard when one deals with regularly varying tails . however , we need the condition @xmath126<\\infty$ ] in order to obtain the limiting distributions in the i.i.d . and lrd zones . see section  [ sec : fidi ] . the result should be extendable to general , not necessary gaussian , long memory linear sequences . instead of the limit theorems and covariance bounds of section [ sec : lrd - gaussian ] , one can use limit theorems from @xcite , and the covariance bounds of ( * ? ? ? * lemma 3 ) . 6 . rootzen @xcite obtained asymptotic the behaviour of the tail empirical process of a general stationary sequence @xmath127 under , in particular , the following conditions ( see ( * ? ? ? * section 4 ) ) : * @xmath128 , @xmath129 ; * @xmath130\\le \\infty$ ] , where @xmath131 and @xmath132 is the point process of exceedances ; * @xmath133 , where @xmath134 is the @xmath135-mixing coefficient w.r.t . sigma field generated by the random variables @xmath136 ; * @xmath137 for some function @xmath138 . + assume that @xmath139 , @xmath129 . for the sequence @xmath140 under consideration here , it can be computed ( see section [ sec : heuristic ] ) @xmath141q!(1 - 2q(1-h ) ) } \\ ; . \\ ] ] now , using ( [ eq : lrd ] ) , @xmath142 . since @xmath129 , then the second part converges 0 under the condition @xmath143 . consequently , case ( [ item : big - u ] ) guarantees that the condition ( c3 ) is fulfilled . as for the mixing property ( c2 ) , it is usually established by proving the standard @xmath135-mixing , i.e. the one defined in terms of random variables @xmath144 , not @xmath145 . now , if @xmath101 is @xmath135-mixing ( in the latter sense ) with rate @xmath146 , then the same holds for @xmath140 . in our case , the sequence @xmath101 has long memory , and thus it can not be @xmath135-mixing . therefore , it is very doubtful that ( c2 ) can be verified . + note also that in the case latexmath:[$\\sum_{j=1}^\\infty    memory case , the conclusion of part   of theorem holds without any additional ( mixing ) assumption on the gaussian process @xmath101 . + moreover , results in the lrd zone can not be obtain by applying rootzen s or any other results for weakly dependent sequences . similarly to @xcite , we consider the case of random levels . let @xmath148 denote weak convergence in @xmath103 . define the increasing function @xmath149 on @xmath150 by @xmath151 , where @xmath152 is the left - continuous inverse of @xmath18 . let @xmath46 denote a sequence of integers depending on @xmath81 , where the dependence in @xmath81 is omitted from the notation as customary , and such that @xmath153 such a sequence is usually called an intermediate sequence . define @xmath154 . if @xmath18 is continuous , then @xmath155 , otherwise , since @xmath156 is regularly varying , it holds that @xmath157 . thus , we will assume without loss of generality that @xmath42 holds . then the statements of theorem [ thm : general ] may be written respectively as @xmath158 } \\ ; t \\cdot l_q \\ ; . \\label{eq : lrd - zone - k}\\end{gathered}\\ ] ] let us rewrite the statements of ( [ eq : iid - zone - k ] ) , ( [ eq : lrd - zone - k ] ) as @xmath159 where @xmath160 and @xmath161 if  ( [ eq : small - k ] ) holds ( i.i.d . zone ) and @xmath162)^{-1 } j(q ) t l_q$ ] if  ( [ eq : big - k ] ) holds ( lrd zone ) . we now want to center the tail empirical process at @xmath163 instead of @xmath164 . to this aim , we introduce an unprimitive second order condition . @xmath165 where @xmath166 the following result is a straightforward corollary of theorem  [ thm : general ] . [ coro : centre ] under the assumptions of theorem  [ thm : general ] , if moreover  ( [ eq : second - ordre - unprimitive ] ) holds , then @xmath167 converges weakly in @xmath103 to the process @xmath168 . let @xmath169 be the increasing order statistics of @xmath170 . the former result and verwaat s lemma ( * ? ? ? * proposition 3.3 ) yield the convergence of the intermediate quantiles . [ coro : intermediate ] under the assumptions of corollary  [ coro : centre ] , @xmath171 converges weakly to @xmath172 . define @xmath173 in this section we consider the _ practical _ process @xmath174 for the process @xmath175 , the previous results yield the following corollary . [ cor : practical ] assume ( h ) , ( [ eq : lrd ] ) , ( [ eq : pareto - assumption ] ) , ( [ eq : moment-2alpha+epsilon ] ) and ( [ eq : second - ordre - unprimitive ] ) . then @xmath176 converges weakly in @xmath103 to @xmath177 , i.e.    * if @xmath178 or @xmath101 is weakly dependent , then @xmath179 where @xmath180 is the brownian bridge . * if @xmath181 , then @xmath182    the convergence of @xmath183 to @xmath184 is standard . the surprising result is that in the lrd zone the limiting process is 0 , because the limiting process of @xmath185 has a degenerate form , i.e. the limit is the random @xmath109 , multiplied by the deterministic function @xmath186 . in fact , as we will see below , there is no dichotomy for the process with random levels , and the rate of convergence of @xmath187 is the same as in the i.i.d . case . to proceed , we need to introduce a more precise second order conditions on the distribution function @xmath26 of @xmath188 . several types of second order assumptions have been proposed in the literature . we follow here @xcite . [ [ assumption - so ] ] assumption ( so ) + + + + + + + + + + + + + + +    there exists a bounded non increasing function @xmath189 on @xmath121 , regularly varying at infinity with index @xmath190 for some @xmath191 , and such that @xmath192 and there exists a measurable function @xmath193 such that for @xmath194 , @xmath195 if  ( [ eq : representation ] ) and ( [ eq : borne - eta ] ) hold , we will say that @xmath47 is second order regularly varying with index @xmath196 and rate function @xmath189 , in shorthand @xmath197 . [ thm : practical-1 ] assume ( h ) , ( [ eq : lrd ] ) , ( [ eq : pareto - assumption ] ) , ( so ) with rate function @xmath189 regularly varying at infinity with index @xmath190 and there exists @xmath198 such  that @xmath199<\\infty \\ ; .\\ ] ] if @xmath200 then @xmath201 converges weakly in @xmath103 to @xmath202 , where @xmath180 is the brownian bridge ( regardless of the behaviour of @xmath203 ) . _ remark_. the additional moment condition ( [ eq : additional - moment ] ) ensures that the distribution of @xmath204 satisfies a second order condition . see section [ sec : s - o - c ] for more details . it is also used in a proof of tightness argument ( see ( [ eq : uniform - conv ] ) below ) . the behaviour described in theorem [ thm : practical-1 ] is quite unexpected , since the process with _ estimated _ levels @xmath43 has a faster rate of convergence than the one with the deterministic levels @xmath20 . a similar phenomenon was observed in the context of lrd based empirical processes with estimated parameters . we refer to @xcite for more details .      a natural application of the asymptotic result for the tail empirical process @xmath187 is the asymptotic normality of the hill estimator of the extreme value index @xmath19 defined by @xmath205 since @xmath206 , we have @xmath207 thus we can apply theorem  [ thm : practical-1 ] to obtain the asymptotic distribution of the hill estimator . [ cor : hill ] under the assumptions of theorem  [ thm : practical-1 ] , @xmath208 converges weakly to the centered gaussian distribution with variance @xmath209 . it is known that the above result gives the best possible rate of convergence for the hill estimator ( see @xcite ) . the surprising result is that it is possible to achieve the i.i.d . rates regardless of @xmath41 . whereas the transfer of the tail index of @xmath188 to @xmath204 is well known , the transfer of the second order property seems to have been less investigated . we state this in the next proposition , as well as the rate of convergence of @xmath164 to @xmath163 and @xmath49 to @xmath210 . [ prop : transfert - second - ordre ] if @xmath211 , where @xmath189 is regularly varying at infinity with index @xmath190 , for some @xmath191 , and if @xmath212 < \\infty \\ ; ,     \\end{aligned}\\ ] ] for some @xmath31 , then @xmath213 , and @xmath214 moreover , for any @xmath215 such that @xmath216 , @xmath217 = o(\\eta^*(u_n)^p ) \\ ; . \\label{eq : rate - g_n }       \\end{gathered}\\ ] ]    [ [ examples ] ] examples + + + + + + + +    the most commonly used second order assumption is that @xmath218 for some @xmath219 . then @xmath220 for some constant @xmath221 . then , @xmath222 , and the second order condition  ( [ eq : second - ordre - unprimitive ] ) becomes @xmath223 and @xmath224 condition  ( [ eq : negligibility-1 ] ) holds if both @xmath225 and @xmath226 . the central limit theorem with rate @xmath227 holds if @xmath228 with @xmath229 condition  ( [ eq : negligibility-2 ] ) holds if @xmath230 . this may happen only if @xmath231 or equivalently @xmath232 as @xmath233 , only for very long memory processes ( i.e. @xmath41 close to 1 ) will the lrd zone be possible . the extreme case is the case @xmath234 , i.e. @xmath189 slowly varying . for instance , if @xmath235 ( for @xmath236 large ) , then the tail @xmath237 belongs to @xmath238 and @xmath239 . the second order condition  ( [ eq : second - ordre - unprimitive ] ) holds if @xmath240 if this condition holds , then @xmath241 for any @xmath242 and the lrd zone never arises , because the lrd term in the decomposition  ( [ eq : decomposition - sv ] ) is always dominated by the bias .","summary":"this is very desirable from a practical point of view , since such a process may be used to construct the hill estimator of the tail index . to prove our results we need to establish new results for regularly varying distributions , which may be of independent interest","abstract":"this paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models . we show that such a process has dichotomous behaviour , according to an interplay between the hurst parameter and the tail index . on the other hand , the tail empirical process with random levels never suffers from long memory . this is very desirable from a practical point of view , since such a process may be used to construct the hill estimator of the tail index . to prove our results we need to establish new results for regularly varying distributions , which may be of independent interest"}
{"article_id":"1001.2916","section_id":"r","document":"we conducted some simulation experiments to illustrate our results . we used r functions hillmse ( ) and hillplot available on the authors webpages .    our first experiment deals with the mean squared error .    1 .   using r - fracdiff package we simulated fractional gaussian noises sequences @xmath243 with parameters @xmath244 . here , @xmath245 , so that @xmath246 corresponds to the case of an i.i.d . sequence . we simulated @xmath247 i.i.d . pareto random variables @xmath248 with parameters @xmath249 and @xmath250 . we set @xmath251 . hill estimator was constructed for different number of extremes . this procedure was repeated 10000 times . the results are displayed on figure [ fig:1 ] , for @xmath249 and @xmath252 , respectively . on each plot , we visualise mean square error ( with the true centering ) w.r.t . the number of extremes . solid lines represent different lrd parameters : black for @xmath246 , blue for @xmath253 , red for @xmath254 and green for @xmath255 . ( left panel ) , @xmath252 ( right panel ) ; color codes : black - @xmath246 , blue - @xmath253 , red - @xmath254 , green - @xmath255,title=\"fig:\",scaledwidth=45.0% ]   ( left panel ) , @xmath252 ( right panel ) ; color codes : black - @xmath246 , blue - @xmath253 , red - @xmath254 , green - @xmath255,title=\"fig:\",scaledwidth=45.0% ]    we note that for @xmath249 , when a small number of extreme order statistics @xmath46 is used to build the hill estimator , there is not much influence of the lrd parameter , and in particular the mse is minimal for more or less the same values of @xmath46 through all the range of values of @xmath256 . this is in accordance with our theoretical results . for @xmath252 , the influence of the memory parameter is more significant . these two features can be interpreted . first , it seems natural that the long memory effect appears when a greater number of extreme order statistics is used , since our result is of an asymptotic nature . for a small number of extremes the i.i.d . type of behaviour dominates ( see @xmath257 in ( [ eq : decomposition - sv ] ) ) , so the asymptotic result is seen ; for a larger number of extremes , the long memory term @xmath258 in ( [ eq : decomposition - sv ] ) starts to dominate . for an extremely large number of order statistics ( i.e. @xmath259 ) , the bias dominates . the influence of @xmath40 on the quality of the estimation is twofold . on one hand , the asymptotic variance of the hill estimator is @xmath260 , so that the mse increases with @xmath40 . also , for very small values of @xmath40 , the peaks observed are extremely high and completely overshadow the effect of long memory . next , we show hill plots for several models , since in practice one usually deals with just a single realization .    1 . we consider the model @xmath261 , where @xmath11 is as above a fractional gaussian noise and @xmath262 or @xmath250 . we simulated @xmath247 i.i.d . pareto random variables @xmath248 with parameter @xmath252 . 3 .   we simulated fractional gaussian noise sequences @xmath11 with parameters @xmath246 ( i.i.d . case ) , 0.2 , 0.4 , @xmath255 . the estimators are plotted on figures [ fig:2 ] and [ fig:3 ] . the left panel corresponds to the hill estimator for iid pareto random variables @xmath263 , and the right one for the long memory stochastic volatility process @xmath264 . recall that the @xmath14 are dependent asympotically pareto random variables , so that there are two sources of bias for the hill estimator .     and pareto iid ( left panel ) , @xmath262 ( right panel ) ; color codes : black - @xmath246 , blue - @xmath253 , red - @xmath254 , green - @xmath255,scaledwidth=100.0% ]     and pareto iid ( left panel ) , @xmath265 ( right panel ) ; color codes : black - @xmath246 , blue - @xmath253 , red - @xmath254 , green - @xmath255,scaledwidth=100.0% ]    we may observe that for a small volatility parameter @xmath266 there is not too much difference between the two plots . however , if @xmath266 becomes bigger , the estimation with a large number of extremes is completely inappropriate if @xmath267 , though without much influence of the strength of the dependence ( i.e. increase of @xmath256 ) on this degradation . the reason is that the second order condition satisfied by the stochastic volatility model yields the same rate of convergence as in the i.i.d . case , but an increase in the variance of the gaussian process @xmath268 entails a bigger bias in finite sample .","summary":"we show that such a process has dichotomous behaviour , according to an interplay between the hurst parameter and the tail index . on the other hand ,","abstract":"this paper describes the limiting behaviour of tail empirical processes associated with long memory stochastic volatility models . we show that such a process has dichotomous behaviour , according to an interplay between the hurst parameter and the tail index . on the other hand , the tail empirical process with random levels never suffers from long memory . this is very desirable from a practical point of view , since such a process may be used to construct the hill estimator of the tail index . to prove our results we need to establish new results for regularly varying distributions , which may be of independent interest"}
{"article_id":"1306.6741","section_id":"i","document":"ricci curvature is a fundamental concept in riemannian geometry , which provides a way of measuring the degree to which the geometry determined by a given riemannian metric might differ from that of @xmath3 . ricci curvature plays an important role in general relativity , where it is the key term in the einstein field equations , and in the celebrated ricci flow equation , where a time - dependent riemannian metric is deformed in the direction of negative its ricci curvature . bakry and mery @xcite attempted to define ricci - curvature through the heat semigroup on a metric measure space . in the recent years , there has been several work on defining a synthetic ricci curvature on general metric measure spaces by sturm @xcite , lott and villani @xcite , and ohta @xcite .    in the context of graphs , chung and yau @xcite developed the notion of ricci - flat graphs , while proving log - sobolev inequalities . later , lin and yau @xcite generalized the notion of bakry and mery to the framework of graphs . finally , ollivier @xcite introduced a notion of coarse ricci - curvature that extends to any markov chains on metric spaces . this was used to generalize a series of classical theorems in positive ricci - curvature , such as spectral gap estimates , concentration of measure or log - sobolev inequalities @xcite . joulin and ollivier @xcite proved nonasymptotic estimates for the rate of convergence of empirical means of markov chains , together with a gaussian or exponential control on the deviations of empirical means , under the assumption of positive curvature of the underlying space . this assumption reduces to the well - known contraction under path coupling when the underlying space is a finite graph , which has been used extensively to prove fast mixing of several discrete markov chains ( refer to chapter 14 of levin et al . @xcite for details on path coupling and its application to fast mixing and approximate counting of proper @xmath4-colorings of a graph ) . recently , ollivier s ricci - curvature has been studied in the context of graph by jost and liu @xcite , paeng @xcite , and cho and paeng @xcite . lin et al . @xcite considered a modified definition of ricci - curvature of graphs , and proved several analogous results . in this paper we study ollivier s ricci - curvature on graphs using the markov kernel of the simple random walk on the graph . we obtain exact formulas for ricci - curvature for bipartite graphs and for the graphs with girth at least 5 . previously , an exact formula was only known for graphs with girth at least 6 @xcite . our formulas extend these results and provide , for the first time , exact expressions for the ricci - curvature for a large class of graphs . using these results we characterize ricci - flat graphs of girth at least 5 . we also prove several other bounds on the ricci - curvature , involving different graph parameters . the most interesting among them is the derivation of a general lower bound in terms of the size of the maximum matching in an appropriate neighborhood subgraph . using this we a first necessary and sufficient condition on the structure of ricci - flat regular graphs of girth 4 . finally , using some results from approximate matching in random graphs , we study the asymptotic behavior of ricci - curvature of random bipartite graphs @xmath0 and random graphs @xmath1 , in various regimes of @xmath2 .      in this section we recall some basic facts about ollivier s ricci curvature on graphs and introduce other relevant definitions and notations .    for two probability measures @xmath5 on a metric space @xmath6 , the _ transportation distance _ ( or the _ wasserstein distance _ ) between them is defined as @xmath7 where @xmath8 is the collection of probability measures on @xmath9 with marginals @xmath10 and @xmath11 . another useful representation of the transportation distance is through the celebrated kantorovich duality ( theorem 1.14 , villiani @xcite ) , which states that @xmath12 where the supremum is taken over all functions @xmath13 which satisfy @xmath14 , for all @xmath15 . the transportation distance between probability measure is used to define the ricci - curvature of metric measure spaces . a metric measure space @xmath16 is a metric space @xmath6 , and a collection of probability measures @xmath17 indexed by the points of @xmath18 . the coarse ricci curvature of a metric measure space is defined as follows :    on any metric measure space @xmath19 , for any two distinct points @xmath15 , the _ coarse ricci curvature _ of @xmath19 of @xmath20 is defined as @xmath21 . [ def : ollivierdef ]    hereafter , we shall refer to ollivier s coarse ricci curvature simply as ricci curvature and we shall study it for locally finite graphs . consider a locally finite unweighted graph @xmath22 , equipped with the standard shortest path graph distance @xmath23 , that is , @xmath24 for @xmath25 , is the length of the shortest path in @xmath26 connecting @xmath27 and @xmath28 . for @xmath29 denote by @xmath30 and @xmath31 the degree of @xmath27 and the set of neighbors of @xmath27 , respectively for each @xmath32 define a probability measure @xmath33 note that these are just the transition probabilities of a simple random walk on the vertices of @xmath26 . if @xmath34 , then considering the metric measure space @xmath35 , we can define the ricci curvature for any edge @xmath36 as @xmath37 . applying equation ( [ eq : wd ] ) for @xmath38 we get @xmath39 where @xmath40 denotes the set of all @xmath41 matrices with entries indexed by @xmath42 such that @xmath43 , @xmath44 , and @xmath45 , for all @xmath46 and @xmath47 . by the kantorovich duality in equation ( [ eq : wdduality ] ) we can also write @xmath48    henceforth , we denote by @xmath49 the set of all 1-lipschitz functions on @xmath26 , that is , the set of all functions @xmath50 such that @xmath51 , for @xmath25 . for any @xmath32 and any function @xmath52 , define @xmath53 . with these notations , equation ( [ rcdef ] ) now becomes @xmath54}. hereafter , the subscript and superscript @xmath26 from @xmath55 , @xmath56 , and @xmath23 will be often omitted when the graph is clear from the context . recently , there has been a series of papers on coarse ricci - curvature when the metric space is a graph @xmath26 . jost and liu proved the following general bounds :    [ th : jost ] for any graph @xmath26 , with @xmath36 , @xmath57 where @xmath58 is the number of triangles supported on @xmath20 . they also show that the above lower bound is tight for trees . in fact , it is clear from their proof that the lower bound is an equality whenever there are no 3 , 4 , or 5 cycles supported on @xmath20 . in particular , the lower bound is tight whenever @xmath59 , where @xmath60 is the girth of the graph @xmath26 . recently , cho and paeng @xcite proved this independently , and also showed that the girth condition and the tree formula , obtained by putting @xmath61 in the lower bound in ( [ eq : jlcp ] ) , are equivalent in the following sense : the tree formula holds for all @xmath36 , if and only if @xmath59 . cho and paeng @xcite also proved other ricci - curvature bounds involving girth . in particular , they showed that if @xmath62 , then @xmath63 , where @xmath64 is the minimum degree in @xmath26 , and @xmath36 . they also obtained interesting lower bounds on the clique number and chromatic number of a graph with the ricci curvature . paeng @xcite used ollivier s ricci curvature to obtain upper bounds of diameter and volume for finite graphs . lin et al . @xcite introduced a different notion of ricci - curvature on graphs by modifying ollivier s definition . it is defined as the differential limit of a lazy random random walk on the graph , and we shall refer to it as the modified ricci - curvature to distinguish it from ollivier s coarse ricci - curvature . the modified definition has some properties which are similar to the original definition , however , in several contexts they are very different . using the modified definition , they proved a theorem on the modified ricci curvature of the cartesian product of graphs . they established upper bounds for diameters and the number of vertices for graphs with positive curvatures , and also proved some asymptotic properties of modified ricci - curvature for random graphs . recently , lin et al . @xcite characterized the set of all modified ricci - flat graphs with girth at least 5 , where a graph is called modified ricci - flat whenever it has modified ricci - curvature zero for every edge in the graph . they showed that if @xmath26 is a connected modified ricci - flat graph with girth @xmath62 , then @xmath26 is the infinite path , or a cycle @xmath65 with @xmath66 , the dodecahedral graph , the petersen graph , or the half - dodecahedral graph . in this paper we obtain exact expressions of ollivier s ricci - curvature for bipartite graphs and for the graphs with girth at least 5 . for a bipartite graph @xmath26 with @xmath36 , we show that the ricci - curvature has the form @xmath67 the explicit form of @xmath68 is given in theorem [ th : bipartite ] , and can be interpreted as a non - negative correction term which improves the lower bound in theorem [ th : jost ] to an exact equality . similarly , when @xmath26 is a graph with girth greater 4 and @xmath36 , the ricci - curvature has the form @xmath69 the explicit form of @xmath70 is given in theorem [ th : gfive ] , and as before , can be interpreted as a non - negative correction term .    to the best of our knowledge , exact formulas for ricci - curvature were only know for the graphs with girth at least six @xcite . our results not only subsume these results , but also provide the first exact formulas for ricci - curvature for a large class of non - trivial graphs , namely graphs with no odd - cycles and graphs with no cycles smaller than 5 . as a consequence of these results , we characterize the set of all ricci - flat graphs of girth at least 5 , where a graph @xmath26 is said to ricci - flat if @xmath71 for all @xmath36 . this is in analogue to the result on modified ricci - curvature of lin et al . @xcite in the context of ollivier s coarse ricci - curvature .    in theorem [ th : matching ] we prove a general lower bound on the ricci - curvature @xmath72 in terms of the size of the matching matching among the non - common neighbors of @xmath27 and @xmath28 in the graph @xmath26 . this bound is often tight , especially in regular graphs which have a perfect matching between the non - common neighbors of @xmath27 and @xmath28 . as the set of all transportation matrices in @xmath73-regular graphs is related to the famous birkhoff polytope , our lower bound result combined with the celebrated birkhoff - von neumann theorem gives a necessary and sufficient condition on the structure of ricci - flat regular graphs of girth 4 , which is detailed in corollary [ cor : ricciflat4 ] .    finally , we also study the ricci - curvature of random bipartite graphs @xmath0 ( theorem [ bp ] ) and random graphs @xmath1 ( theorem [ gnp ] ) , in various regimes of @xmath2 . using a stronger version of the hall s marriage theorem , and the existence of near - perfect matching in random bipartite graphs , we obtain the limiting behavior of the ricci - curvature in the regimes of @xmath2 where it has a constant limit in probability . we also show that when @xmath74 , that is , the graph is locally tree - like , the ricci - curvature converges in distribution to the tree formula of jost and lin @xcite . these are the first known results for ollivier s ricci - curvature for erds - renyi random graphs . the analogous version of these results using the modified ricci - curvature were obtained by lin et al . they showed almost sure convergence to constant limits , but could not capture all the different regimes of @xmath2 .    in section [ sec : preliminaries ] we prove several important lemmas which build the foundations for proving the main results . we show that the computation of ricci - curvature on a graph can be formulated as a totally unimodular linear programming problem , and so it suffices to optimize over integer valued 1-lipschitz functions . we also prove a crucially important reduction lemma where we identify the exact neighborhood an edge @xmath36 that needs to be considered while computing the ricci - curvature @xmath75 . in section [ sec : conclusions ] we summarize our work and give directions for future work .","summary":"in this paper we study ollivier s coarse ricci - curvature for graphs , and obtain exact formulas for the ricci - curvature for bipartite graphs and for the graphs with girth at least 5 . these are the first formulas for ricci - curvature which hold for a wide class of graphs . we also obtain a general lower bound on the ricci - curvature involving the size of the maximum matching in an appropriate subgraph . as a consequence , we characterize ricci - flat graphs of girth 5 , and give the first necessary and sufficient condition for the structure of ricci - flat regular graphs of girth 4 . finally , we obtain the asymptotic ricci - curvature of random bipartite graphs and random graphs , in various regimes of .","abstract":"in this paper we study ollivier s coarse ricci - curvature for graphs , and obtain exact formulas for the ricci - curvature for bipartite graphs and for the graphs with girth at least 5 . these are the first formulas for ricci - curvature which hold for a wide class of graphs . we also obtain a general lower bound on the ricci - curvature involving the size of the maximum matching in an appropriate subgraph . as a consequence , we characterize ricci - flat graphs of girth 5 , and give the first necessary and sufficient condition for the structure of ricci - flat regular graphs of girth 4 . finally , we obtain the asymptotic ricci - curvature of random bipartite graphs and random graphs , in various regimes of ."}
{"article_id":"1401.7319","section_id":"i","document":"the next set of axioms defines a particular type of relational symplectic groupoids which will allow us to relate the construction of relational symplectic groupoids for poisson manifolds to the usual symplectic groupoids for the integrable case . before this , we introduce the notion of immersed coisotropic submanifolds for weak symplectic manifolds .    _ a relational symplectic groupoid @xmath137 is called * regular * ( short rrsg ) if the following three axioms a.7 , a.8 and a.9 are satisfied . consider @xmath108 as a relation @xmath138 denoted by @xmath139 . _    * * * @xmath140 is an immersed submanifold of @xmath108 . @xmath124 is an equivalence relation in @xmath36_.    by equation [ invariance2 ] @xmath141 so @xmath124 is a relation on @xmath36 . by equation [ invariance2 ] , @xmath124 is transitive , by equation [ symmetric ] it is symmetric and , for any @xmath142 , by definition , there exists @xmath143 such that @xmath144 and by symmetry and transitivity of @xmath124 , we conclude that @xmath145 , hence , @xmath124 is an equivalence relation .    _ @xmath36 is an immersed coisotropic submanifold of @xmath108 . _    by definition of @xmath36 we get that @xmath146 and by a.6 . @xmath147 is a lagrangian subspace of @xmath148 . therefore @xmath149 if we restrict to the diagonal @xmath150 , we get that @xmath151 hence @xmath36 is coisotropic . the following proposition allows us ( in principle at the infinitesimal level ) , to regard the equivalence relation given by @xmath124 as the equivalence relation given by the characteristic foliation of @xmath36 . _ let @xmath152 where @xmath153 is the leaf of the characteristic foliation through the point @xmath142 . let @xmath154 . then @xmath155 _ first we will prove that @xmath156 . for this , consider @xmath157 , since @xmath158 , we get that @xmath159 since @xmath160 and @xmath124 is lagrangian @xmath161 combining equations [ e1 ] and [ e2 ] , we get that @xmath162 since the diagonal @xmath163 is contained in @xmath124 ( from corollary [ equi ] ) , then @xmath164 from equations and , we conclude that @xmath165 as we wanted . now we prove that @xmath166 is a lagrangian subspace of @xmath167 . for this , first observe that @xmath168 and that the canonical projection of @xmath166 in the symplectic reduction @xmath169 is @xmath163 , which is lagrangian . + applying lemma [ coisotropic ] we conclude that @xmath166 is lagrangian . now , since @xmath170 is also lagrangian by the axioms above and it contains @xmath166 as a subspace , it follows that @xmath171 hence @xmath172 , as we wanted . it follows from remark [ equiv ] that , in the case where @xmath108 and @xmath270 are both regular , an equivalence @xmath130 induces relations @xmath271 and @xmath272 satisfying @xmath273 this implies the following    _ the induced relation @xmath274 is the graph of a diffeomorphism between @xmath275 and @xmath276 . _    since the following diagram commutes : @xmath277^{f } |-{/}\\ar@{->}[d]_{s}&c_{\\mathcal h}\\ar@{->}[d]_{s}\\\\m_{\\mathcal g}\\ar@{->}[r]^{f_m } & m_{\\mathcal h}}\\ ] ] from theorem [ theo1poisson1 ] it follows also the following    _ the map @xmath274 is a poisson diffeomorphism . _    by a similar argument it can be easily checked that    [ poi ] _ if @xmath278 and @xmath279 are two equivalent regular relational symplectic groupoids , and if we assume that @xmath108 has coonected @xmath280- fibers , then there exists a unique poisson structure in @xmath281 such that the map @xmath282 is forward - dirac . _","summary":"this note introduces the construction of relational symplectic groupoids as a way to integrate every poisson manifold . examples are provided and the equivalence , in the integrable case , with the usual notion of symplectic groupoid is discussed .","abstract":"this note introduces the construction of relational symplectic groupoids as a way to integrate every poisson manifold . examples are provided and the equivalence , in the integrable case , with the usual notion of symplectic groupoid is discussed ."}
{"article_id":"1205.5209","section_id":"i","document":"topological insulators ( tis ) constitute a new state of matter with an insulating bulk and an odd number of metallic dirac cones at their surface @xcite . it was predicted @xcite and confirmed by angle - resolved photoemission spectroscopy ( arpes ) @xcite that the compounds bi@xmath0se@xmath1 , bi@xmath0te@xmath1 and sb@xmath0te@xmath1 possess such a single surface state ( ss ) . owing to this spin locking property , sss of tis are unique metallic systems for the study of fundamental magnetotransport properties and for the realization of future spintronics based devices . unfortunately such transport experiments have faced a major difficulty so far . indeed most tis samples present enough residual bulk conductance to overwhelm the actual surface contribution @xcite . the shubnikov - de haas oscillations reported in bi@xmath0se@xmath1 crystals originate exclusively from the bulk 3d bands indicating a low mobility for the surface dirac fermions @xcite . nevertheless recent progress has been achieved by using ultrathin films of bi@xmath0se@xmath1 @xcite or bi@xmath0te@xmath1 @xcite exfoliated on high - k dielectric insulator in order to improve the surface / bulk conductance ratio and to allow the gating of the surface state . from the gate voltage dependence of the total conductance , it was possible to separate bulk and surface contributions using a classical two - carrier model @xcite . most recently the surface conductance of strained hgte samples has been reported in truly 3d slabs with thicknesses exceeding @xmath2 nm and in the absence of significant bulk conductance @xcite . at low temperatures and for small samples , the quantum correction to transport was recently probed experimentally : the dependence of conductance on weak magnetic fields displays the expected weak antilocalization while the universal conductance fluctuations ( ucf ) were observed in some of those experiments @xcite . interestingly , the crossover between the symplectic and unitary universality classes upon breaking time - reversal symmetry has been observed in ultrathin samples of bi@xmath0te@xmath1 @xcite .    theoretically , describing the transport properties of topological insulator surface states amounts to consider the diffusion properties of two dimensional dirac fermions . indeed , at the lowest order in @xmath3 theory the ss fermi surface is circular with a spin winding in the plane . at low energy , this two dimensional conductor shares a lot of similarities with graphene but with the following important differences : the momentum is locked to a real spin as opposed to a a - b sublattice pseudo - spin in graphene , and it has a single dirac cone as opposed to the four - fold degeneracy of the dirac cone in graphene . for this simpler dirac metal , the conductivity and the induced in - plane spin polarization were calculated as functions of the 2d carrier concentration @xcite . far from the dirac point , surface spin - orbit may generically produce a significant hexagonal warping ( hw ) of the spin texture . as a result the fermi surface exhibits a snowflake or a nearly hexagonal fermi surface depending on the carrier density , and the spin gets tilted out of the plane @xcite . those effects have been confirmed by arpes and scanning tunneling microscopy ( stm ) experiments performed on bi@xmath0te@xmath1 crystals where hw is particularly strong @xcite , and also in bi@xmath0se@xmath1 @xcite . characterizing quantitatively the hw and therefore the amount of out - of plane spin polarization is a crucial issue in view of potential spintronics applications , and has been the subject of ab - initio studies @xcite and arpes experiments @xcite . this hexagonal warping is specific to the dirac metal at the surface of topological insulators , and different from the trigonal warping encountered at high energies in graphene . its amplitude is stronger in the metallic regime of high fermi energy which is of interest in the present paper : a full description of transport properties in this regime necessitates to include its presence in the model . it has been shown @xcite that hexagonal warping enhances perturbatively the classical drude conductivity with respect to the unwarped model @xcite . however , as we will show in this article a description of the effects of this hexagonal warping requires to go beyond the previous perturbative descriptions . in this paper , we develop a description of the diffusion of these surface states which is non - perturbative in the warping amplitude . we investigate theoretically the classical 2d charge diffusion within an hexagonally warped surface states using both a standard diagrammatic formalism and a boltzmann equation approach . in this classical regime , we find that the hexagonal warping on one hand strongly reduces the density of states and on the other hand increases the diffusion coefficient for the dirac surface states . the combination of both effects is found to correspond to an increase of the classical conductivity as a function of the warping amplitude . interestingly , as the warping amplitude increases with fermi energy , that dependence on the warping amplitude manifests itself in the behavior of the conductivity as a function of the fermi energy . in the second part of this article , we focus on the quantum correction to the conductivity , relevant in a phase coherent conductor . these quantum corrections are known to depend on the symmetry class of the associated anderson localization problem . similarly to graphene with only intra - valley disorder , the single dirac cone model is known to correspond to the symplectic / aii class . within this symplectic class the dirac model differs from graphene with long - range disorder or electrons with spin - orbit randomness by the presence of a topological term in the associated field theory @xcite . this topological term explains the absence of anderson localization for these topological insulators surface states @xcite , however it plays no role in the diffusive metallic regime . in this regime , the universal properties of both weak localization and conductance fluctuations are just the same as for any model on the two dimensional symplectic / aii class . we will recall these results , and show that the dependence of the diffusion coefficient on warping manifests itself in a dependence of the weak localization correction and conductance fluctuations away from their universal values . in particular , this diffusion constant parameterizes the universal cross - over from the symplectic / aii class to the unitary / a class when a magnetic field is applied perpendicular to the surface states . the shape of the associated cross - over functions now depends strongly on the warping amplitude , and thus the fermi energy . finally , we identify a property unique to the topological insulator surface states : a reduction of the conductance fluctuations by the application of a in - plane magnetic field . the paper is organized as follows . we present the model in section [ sec : model ] . the classical drude conductivity in presence of hw is derived using a boltzmann approach ( section [ sec : boltzmann ] ) and a diagrammatic method ( section [ sec : diagrams ] ) . in section [ sec : quantum ] , the quantum corrections to the average conductivity and the universal conductance fluctuations are respectively derived . the results and conclusions relevants for experiments are summarized in the conclusive section [ sec : results ] .","summary":"the transport properties of those two - dimensional surface states depend strongly on the amplitude of the hexagonal warping of their fermi surface . hence we develop a fully non - perturbative description of these effects . in particular , we find that the dependence of the warping amplitude on the fermi energy manifests itself in a strong dependence of the diffusion constant on this fermi energy , leading to several important experimental consequences","abstract":"we consider the transport properties of topological insulators surface states in the presence of uncorrelated point - like disorder , both in the classical and quantum regimes . the transport properties of those two - dimensional surface states depend strongly on the amplitude of the hexagonal warping of their fermi surface . it is shown that a perturbative analysis of the warping fails to describe the transport in experimentally available topological insulators , such as bise and bite . hence we develop a fully non - perturbative description of these effects . in particular , we find that the dependence of the warping amplitude on the fermi energy manifests itself in a strong dependence of the diffusion constant on this fermi energy , leading to several important experimental consequences . moreover , the combination of a strong warping with an in plane zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped dirac surface states ."}
{"article_id":"1205.5209","section_id":"i","document":"in this section , we summarize the main results of our approach focusing on the experimentally relevant aspects . in particular , we emphasize the effect of strong variation of the warping amplitude @xmath70 as the fermi energy is varied in a given material . universal properties of transport in the quantum regime are not affected by the presence of this warping . however , both the departure from these universal properties as well as the classical regime are entirely characterized by the diffusion constant @xmath173 which itself depends in the warping amplitude . the transport properties in the incoherent classical regime are characterized by both the density of states @xmath210 and the diffusion constant @xmath96 . the dependence on the fermi energy of both quantities is strongly affected by the presence of the warping of the fermi surface , whose amplitude @xmath70 itself depends on @xmath27 . this is shown on fig . [ fig : d_e],[fig : densitystates ] for two sets of parameters corresponding to the bi@xmath46se@xmath47 and bi@xmath46te@xmath47 compounds . as a consequence of these results , the conductivity @xmath211 acquires a strong fermi energy dependence shown on fig . [ fig : densitystates ] , which can be directly probed experimentally . h ]   corresponding to the bi@xmath46se@xmath47 and bi@xmath46te@xmath47 compounds . the results depend on the amplitude of disorder parameterized by the mean free path @xmath212 . here , they are normalized with respect to the diffusion constant in absence of warping @xmath213 which is independent of the fermi energy and incorporates the dependence on @xmath212.,title=\"fig:\",width=377 ]    [ ! h ]     , @xmath39 for bi@xmath46se@xmath47 and @xmath48 and @xmath49 corresponding to the bi@xmath46te@xmath47 compounds . on the left figure , the dotted lines corresponds to the standard linear density of states for dirac fermions without warping @xmath214 . on the right figure , the results are represented as a ratio with the conductivity in the absence of warping @xmath215 which is independent on the energy and incorporates the dependence on the disorder strength . , title=\"fig:\",width=302 ]   , @xmath39 for bi@xmath46se@xmath47 and @xmath48 and @xmath49 corresponding to the bi@xmath46te@xmath47 compounds . on the left figure , the dotted lines corresponds to the standard linear density of states for dirac fermions without warping @xmath214 . on the right figure , the results are represented as a ratio with the conductivity in the absence of warping @xmath215 which is independent on the energy and incorporates the dependence on the disorder strength . , title=\"fig:\",width=302 ]    similarly , the quantum corrections to transport depends strongly on the fermi energy through the dependence of the diffusion coefficient @xmath96 on the warping amplitude . indeed , the shape of the typical measurement of the weak ( anti-)localization correction through the dependence of the conductivity on a magnetic field perpendicular to the surface depends solely on the diffusion constant . this diffusion constant depending on the fermi energy , the associated anti - localization curve depends itself on this fermi energy as shown on fig . [ fig : locfaible_b ] . [ ! h ]     on the fermi energy for the values of @xmath216 corresponding to the bi@xmath46te@xmath47 ( left ) and bi@xmath46se@xmath47 ( right ) compounds . we have chosen to scale the magnetic field as @xmath217 where @xmath218 to avoid any energy ( or warping ) dependence of this rescaling field . the results show a clear dependence on energy of the magnetic field characteristic of weak localization decay . , title=\"fig:\",width=302 ]    on the fermi energy for the values of @xmath216 corresponding to the bi@xmath46te@xmath47 ( left ) and bi@xmath46se@xmath47 ( right ) compounds . we have chosen to scale the magnetic field as @xmath217 where @xmath218 to avoid any energy ( or warping ) dependence of this rescaling field . the results show a clear dependence on energy of the magnetic field characteristic of weak localization decay . , title=\"fig:\",width=302 ]    while the amplitude of conductance fluctuations are universal in the limit of an entirely coherent conductor , their amplitude in a realistic situation where @xmath219 will be parameterized by a universal function of the diffusion coefficient . we have shown moreover that these fluctuations depend in a remarkable way on an in - plane zeeman magnetic field . the amplitude of this effect depends on the ratio between the associated magnetic dephasing length @xmath220 and the mean free path @xmath221 . the dependence of this ratio on the fermi energy is shown on fig . [ fig : warping_zeeman_l ] for the two same sets of values used above . [ ! h ]   on the fermi energy for parameters corresponding to bi@xmath46te@xmath47 ( red ) and bi@xmath46se@xmath47 compounds . , title=\"fig:\",width=377 ]    in conclusion , we have shown that it is essential to take into account the hexagonal deformation of the dirac cone occurring at the surface of topological insulators such as bi@xmath0se@xmath1 and bi@xmath0te@xmath1 to accurately describe both their classical and quantum transport properties . in particular , we provide a formula describing the evolution of diffusion constant @xmath96 for arbitrary strength of the warping . since this warping amplitude increases with the fermi energy of the surface states , we predict a dependance on doping of transport properties different from those predicted for a perfect dirac cone . this work was supported by the anr under the project 2010-blanc-041902 ( isotop ) . jc also acknowledges support from eu / fp7 under contract temssoc .","summary":"it is shown that a perturbative analysis of the warping fails to describe the transport in experimentally available topological insulators , such as bise and bite .","abstract":"we consider the transport properties of topological insulators surface states in the presence of uncorrelated point - like disorder , both in the classical and quantum regimes . the transport properties of those two - dimensional surface states depend strongly on the amplitude of the hexagonal warping of their fermi surface . it is shown that a perturbative analysis of the warping fails to describe the transport in experimentally available topological insulators , such as bise and bite . hence we develop a fully non - perturbative description of these effects . in particular , we find that the dependence of the warping amplitude on the fermi energy manifests itself in a strong dependence of the diffusion constant on this fermi energy , leading to several important experimental consequences . moreover , the combination of a strong warping with an in plane zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped dirac surface states ."}
{"article_id":"1603.02590","section_id":"i","document":"the vast majority of known galaxies have effective surface brightnesses ( sbs ) which lie in a narrow peak within 2 or 3 magnitudes of the terrestrial sky ( roughly 22 magnitudes @xmath1 i.e. 22@xmath2 or @xmath3 ) . and yet , due to special circumstances , some few galaxies are known which span a vast range in intrinsic sb between 13@xmath2 and 30.5 @xmath2 i.e. a spread of ten million . we see the high sb tail of compact galaxies in the hubble deep field where tolman surface - brightness dimming by @xmath49 magnitudes , brings compact redshift 7 galaxies down into the normal range near 22 @xmath2 ( disney and lang 2012 ) , and we see the extreme low sb tail in the local group where their individual stars can be detected above galactic star counts ( e.g belukurov et al 2007 , koposov et al . 2015 , bechtol et al 2015 , beasley et al 2016 ) down to 30.5@xmath2 . the narrow peak in sb contrasted with the extremely broad range naturally suggests that dramatic selection effects are at work . and that wouldnt be surprising ; even outside the atmosphere the combination of scattered ( zodiacal ) sunlight and scattered starlight means that the background glare in our locality is 10 magnitudes brighter than one would expect it to be in intergalactic space ( 32 @xmath2 ) if only the summed intensity of @xmath5 populations of galaxies were responsible . theoretical analyses of the surface - brightness selection effects indeed show that the only galaxies with any hope of detection will lie in a very narrow wigwam - shaped peak less than 3 mags wide fwhm centred a couple of mags brighter than the sky ( disney and lang 2012 ) . apart from the above special cases there can be no hope of by - passing this glare in the optical itself ( see discussion and appendix c below ) so more ingenious indirect methods are necessary to unearth the potentially hidden population of dim and dark galaxies ( ddgs ) . for instance using redshift to discriminate between background and local signals  as in the 21 centimetre hydrogen line , or by using absorption where a galaxy much dimmer than the glare would nevertheless betray its presence through the absorption features it would impress on the spectrum of a background source such as a qso . over the past 20 years strenuous efforts have been made to find ddgs using both the above indirect techniques with , it has to be said , singular lack of success [ for instance the hipass survey carried out from parkes ( zwaan et al 2003 ) in which we participated , found more than 4000 blind hi sources in the southern hemisphere @xmath6 all of which turned out to have easily visible optical counterparts ( doyle et al 2005 ) . ] the trouble with all that negative evidence is that it s too good to be true , far too good . from time to time , usually by chance , odd observations turn up to refute it . for instance the colossal lsbg malin 1 , 200 kpc . in diameter and containing more than @xmath7 solar masses of hi , appeared by chance in the background ( at 25,000 kms ) during a modest arecibo survey targeted at individual dwarfs in the virgo cluster at @xmath4 1100 km @xmath8 ( bothun et al 1989 ) . surely it ca nt be unique @xmath6 and yet its analogues have never been found in the aforesaid blind hi surveys of almost the entire sky . and latterly deep optical observations of the coma cluster ( van dokkum et al 2014 , koda t et al 2015 ) reveal that it contains many galaxies of milky way size but with surface brightnesses up to 5 mags dimmer . indeed the failure of the 21 cm . and qsoals searches has become so egregious that one begins to suspect that some other explanation than the lack of the missing galaxies must be responsible . in this paper we claim it is the clustering of the ddgs with the normal ones  which leads to frequent confusions of identity . in the case of hi sources the poor resolution of the single - dish radio telescopes used to carry out the blind hi surveys means that it was all too easy to find a bright optical galaxy at approximately the right redshift to explain the hi signal when in fact a much dimmer galaxy clustered nearby was the true emitter . we back that suspicion up with high resolution observations recently made with the newly enhanced vla which confirm that the previous optical identifications were often incorrect and that ddgs are instead sometimes the seat of the signals . and in the case of qsoals , clustering means that ddgs within arc secs of the qso sight - lines are 30 times more likely to be responsible for the absorptions than the giant luminous galaxies arc minutes away with hypothetical giant halos hundreds of kilo - parsecs in extent which are invoked now ( indeed such halos would appear to be redundant ) . the rest of the paper is arranged by section as follows : ( 2 ) demonstrates the interplay between clustering and identification and the challenge it poses at both 21 cm and for qsoals . + ( 3 ) describes our recent observations with the uprated vla of hipass ids which show that our suspicions about their reliability are confirmed . moreover 12/19 of the new blind sources we find could be ddgs . + ( 4 ) extends the discussion to single - dish hi surveys in general to reach the disconcerting conclusion that increasing dish - size is of no help in solving the identification problem because , in general , larger dishes find their blind sources a correspondingly further distance away where their @xmath9 resolution , which is what matters for identification purposes , is no better . we then calculate the identification - ambiguity in existing single - dish blind surveys to find that they are all unreliable . + ( 5 ) examines whether the hosts of damped lyman - alpha qsoals s can be identified reliably using a combination of hst and ground based 8-metres . because of clustering , the majority , including dim and dark hosts , probably can not . thus the inferred existence of enormous gaseous halos around luminous spiral galaxies has to be questioned . the qsoals are more naturally explained as due to smaller dim and dark galaxies much closer to the lines of sight . + ( 6 ) the discussion returns to the general conjecture that there is a rich population of hidden galaxies still to be found . we examine , the hi , the qsoals and the deep ccd evidence and conclude that the many refutations of this conjecture so far published all founder on the difficulty of reliable identifications in a strongly clustered universe . a rich low surface brightness universe is a real possibility , and well worth looking for .","summary":"new very large array ( vla ) observations reveal that the identifications with bright optical objects claimed in previous single - dish blind hi surveys are often unreliable . for instance 14/36 of our high - resolution ( 5 arc sec , 13kpc . ) [ firstpage ]    surveys.galaxies:statistics ; galaxies : groups : general . cosmology : dark matter .","abstract":"we re - investigate the question of whether there is a significant population of dim ( low surface brightness ) and/or dark galaxies ( ddgs ) . we argue that if they are clustered with bright ones then a physical resolution of 10 kpc . will be needed to distinguish their 21-cm . and qso absorption line(qsoal ) counterparts from their brighter neighbours , leading to a real possibility of confusion . but until now such a resolution has not been available in this context . new very large array ( vla ) observations reveal that the identifications with bright optical objects claimed in previous single - dish blind hi surveys are often unreliable . for instance 14/36 of our high - resolution ( 5 arc sec , 13kpc . ) sample have no optical counterparts in the digital sky survey . this suggests that ddgs might be commonplace after all , and we go on to re - examine the main arguments that have been used against them .. we find that the qsoal argument founders on the aforementioned clustering while deep ccd surveys have so far covered too small an area to set set strong constraints on low surface brightness galaxies ( lsbgs ) . a cosmos filled with low surface brightness galaxies , dark galaxies and intergalactic gas clouds can no longer be ruled out .    [ firstpage ]    surveys.galaxies:statistics ; galaxies : groups : general . cosmology : dark matter . cosmology : re - ionization ."}
{"article_id":"1603.02590","section_id":"c","document":"the conjecture `` most of the galaxies , even in our neighbourhood remain to be discovered because galaxies are extremely hard to detect through our atmosphere and against our sky . '' is a natural one , with obvious implications for many areas of both astronomy and cosmology . it is also , epistemically speaking , a very healthy one because it both encourages exploration and invites refutation ( gauch , 2005 ) . broadly speaking there have been in recent years three approaches to examining the conjecture , none encouraging and some positively damning . optical observers have used increasingly more sensitive ccd detectors on increasingly larger telescopes to search in particular for low surface brightness galaxies @xmath6with meagre results . secondly radio astronomers have made blind hi surveys , only to claim that virtually every source so detected can be associated with a bright optical galaxy nearby with , to within the combined errors , the same radial velocity . and thirdly qsoal observers argue that their absorptions can be explained if they assume that @xmath15 galaxies have colossal gaseous haloes 300 kpc . or more in diameter . if that is the case then there is no need or indeed room , for any further dim or dark absorbers . we have already cast doubt on these last two arguments , and will return to them later , but first we must tackle the failure of the deep ccd surveys ( e.g. driver et al .2005 ) .    it has been widely supposed that because very few lsbgs have turned up in deep ccd surveys carried out with 4-m class telescopes that therefore they must be rare but , we argue next , that is not the case . finding a dim object is a signal - to - noise problem , a matter of counting object - photons as compared to sky - photons . to find a really dim object it must therefore be of large angular size , i.e. be relatively near by to us in space . but nearby objects are relatively rare ( e.g only 2 magellanic clouds ) and so to find them a large area of sky must be surveyed to a considerable depth@xmath6 an impracticability with a detector of small physical size like a ccd @xmath6 despite its high sensitivity . the argument is not completely obvious and requires some algebra [ which we do in appendix c ] but once grasped is manifestly true . it reveals that the number of galaxies of luminosity l and surface - brightness i that will turn up in a survey lasting a total time t is : + t(l ) ^3/2 \\{wq^3/2 }    where s is the surface - brightness of the sky , t the dwell - time per field , w the aerial on - sky fov of the detector and q its quantum efficiency , d the telescope diameter and @xmath97 the luminosity - function . the first bracket contains the properties of the galaxy , the second of the survey , the third of the detector .    from ( 14 ) we infer the following : ( i ) to acquire a certain number of galaxies of sb i : t ( ) ^3 thus , for a drop in surface brightness of 1 mag . the dwell - time t per field must be increased by 3 mag . or a factor of 16 . but the optimum visibility of galaxies , as we have long argued elsewhere ( e.g disney and phillipps 1983 ) lies within a narrow window of sb with a full - width - full maximum of only 2.5 mag . on the low - sb side [ see disney and lang 2012 ) ] . thus to escape entirely out of the window to see new populations of lsb galaxies we would need to increase the dwell - time t by 2.5 times 3 mag or a factor of one thousand!. we truly are imprisoned in a lighted cell . this far - from - obvious argument deserves to be more widely appreciated . \\(ii ) the detector figure - of - merit @xmath98 is higher for ccds than for schmidt photographic plates [ [ 36 sq . degs , q @xmath99 $ ] provided the ccds [ [ q@xmath100 ] have @xmath101 2000 pixels a side . the grasp of any survey is + @xmath102 $ ] + which means that 1-month - long ccd surveys with 4 metre - class telescopes will be an order of magnitude less effective for finding low surface brightness galaxies than the combined schmidt surveys covering the whole sky done 30 years ago . however if photon counting were the whole story then the sdss ought to beat the schmidt surveys by a factor of 5 to 10 , despite its very short dwell - time @xmath103 . unfortunately , very low sb galaxies can only be detected if they look apparently very large [ appx c ] when the unevenness of the sky background itself , not its photon statistics , becomes the predominant source of noise ( sabatini , roberts and davies 2003 , martinez - delgado et al 2010 ) . telescope size ( d ) may help but may run into serious pixel - matching problems as well as the aforementioned background fluctuations . large arrays of ccds , perhaps on medium - sized telescopes , might succeed eventually , but they will probably require observing strategies and software dedicated to the task . for the moment the photographic schmidt surveys of the 1950 s to 1990 s have , in this context , not been superseded . this is a sad admission because with a quantum efficiency of only one per cent , and saturation after an hour , they amount to no more than a 36 second glance at the universe . in summary then the hope we all had of finding a significant population of dim galaxies using deep ccd surveys has been frustrated by the need to find them nearby where large apparent size would be able to overcome low signal - to - noise per unit area . this frustration was not obvious and would have been difficult to recognise before the advent of linear panoramic detectors . the failure of the 21-cm attempts to refute the conjecture we have discussed . the earliest such attempt , using arecibo locked in transit mode ( zwaan et al , 1997 ) , was ingenious but seriously ill - found ( minchin r f et al 2003 ) . an internal comparison of their own data suffices to reveal this . if their data were as deep as they supposed , how could they pick up virtually all of their 66 sources in brief snapshots ( 20 mins ) with the smaller vla ? and why was their source - count at least an order of magnitude too low ? one suspects that they somehow failed to accumulate their daily scans , leaving a shallow single - transit survey setting few interesting limits . the failures with hopcat we have admitted and the weaknesses of alfalfa we have pointed out . both are faults of misidentification based on the plausible but fallacious idea that , in a highly clustered universe , positional and velocity information are more or less independent . our vla observations confirm only too well the outcome of the clustering calculations . up to a quarter of the ids we looked at proved to be wrong ; the incorrectly identified sources appear to be associated with faint , dim and even blank fields at the level of the dss . moreover of the 19 @xmath104 blind sources which turned up in those same fields 12 appear to have no obvious optical counterparts . the misidentification hypothesis also clears up the otherwise serious problem for blind hi surveys ; what we call the inchoate galaxy problem ( disney 2008 , appadoo et al 2009 ) . inchoate galaxies are extremely low surface brightness ( barely apparent in sdss ) dwarf objects , generally blue[(b - v ) as low as 0.3 ] embedded in large amounts of neutral hydrogen [ @xmath105 in solar units . ] @xmath6 the prototype being the so called proto - galaxy found serendipitously by giovanelli and haynes ( 1989 ) . the inchoate label for these objects derives from their apparent total lack of organisation . more irregular than irregulars they have no cores or obvious centres , and appear as merely haphazard enhancements of surface brightness at what appear to be hii regions . the dozen or so inchoates within our equatorial survey ( appadoo et al 2009 , disney et al 2008 ) of some 200 galaxies presented an inexplicable @xmath106 of properties . their high gas fractions indicate little integrated past star formation , while their blue colours can only be explained by a recent burst of star formation . either they are young@xmath6 in which case where are their totally dark hi predecessors ? or they are briefly bursting and will quickly fade away @xmath6 in which case where are their faded or totally darkened remains ? neither kind of object appears in hipass , an identical survey but with a different identification program . hence the mystery . but if many hipass sources are misidentified with brighter galaxies , all is explained(see disney and minchin 2003 for an alternative but now unnecessary explanation in terms of frozen hydrogen ) . this last argument can be reversed.the very existence in blind hi surveys of inchoate galaxies which , because of their blue colours , individually must have comparatively short lives , requires there to be a larger population of optically invisible hi clouds @xmath6 either the antecedents and/or the decendents of those that are presently observed to contain a predominant population of evanescent blue stars . that they are not presently detected suggests there is something seriously amiss with the existing identification process . +   + what of all the work that has subsequently been done on sources picked up in blind hi surveys and for which the identifications must now be so doubtful ? caveat emptor . we will speak here only of the equatorial survey which we carried out ourselves with the parkes multibeam as part of the hipass survey , and which covered 2 steradians and found 1100 sources ( appadoo et al 2009 ) . the part published comprises the 1700 sq . degs . which overlapped the sdss dr-2 release . originally that subset comprised 370 sources which we identified optically , using almost identical methods to hopcat . however we then threw out the 175 most doubtful ids leaving only 195 sources in our statistical analysis . the @xmath107 source density is @xmath4 195/0.6 @xmath108 sources / steradian ( a factor of 3 down on hopcat ) . comparing that fraction with our calculated q values suggests we must have thrown out most of the bad apples . there probably still are a handful , as we admitted at the time , but not enough to seriously challenge the largely statistical conclusions ( disney et al 2008 ) .    . the other strong refutation of the conjecture , claimed by the qsoals community is , if anything , more incredible @xmath6 but for the same basic reason . identifications were made with bright spirals typically 160 kpc . away from the qso line - of - sight ( sect 5 ) . but 160 kpc . is almost exactly the average distance from an @xmath15 galaxy to the nearest dwarf or dim galaxy in the group capable of causing the absorption . this is highly suspicious , and not at all supportive of a physical association , especially not one implying colossal halos without much other evidential support . those claims were mainly buttressed by the clear anti - correlation observed between impact - parameter and absorption equivalent - width e.g. lanzetta et al . however there is an alternative explanation for that under the clustering hypothesis : a qso sight - line passing through the inside of a group will be , statistically speaking , closer to both the real dim - or - dark absorber and to the nearest big visible spiral chosen spuriously to be the absorber , than a sight - line passing through the outer part of the group . the observed anti - correlation is thus naturally expected , without calling for any physical link(linder s , 1999 ) . the whole case for giant halos , which is venerable ( bahcall and spitzer , 1969 ) , needs to be re - examined . it is notable that qsoals observers first , then we blind - hi - observers second , fell into the same egregious trap . setting out to @xmath109 optical counterparts we , thanks to clustering , easily found visible galaxies nearby . then , when we checked the radial velocities @xmath6 lo , they matched . it was all very tempting and very natural to claim an identification . but had one started with a different mind - set @xmath6 to look out for dim and dark galaxies @xmath6 then most such tempting matches would be regarded sceptically , or dismissed out of hand . it is , like so many debates , a burden - of - proof issue . in the context of ruling out dim and dark galaxies the burden of proof here should surely lie on those who seek to claim identifications between sources and plausible visible objects in their neighbourhoods . if that is conceded , the existing confusion melts away . likewise the failure of optical observers to find dim galaxies with ccds on large telescopes . had we realised the odds were all against us we would have understood that the lack of positive evidence was not significant evidence of a negative kind . any would - be explorer of the unknown must nail the burden - of - proof issue first .    the hi data , the qsoals data and the failure of optical observers to find lsbgs , all seemed to provide cohering evidence against the existence of hidden galaxies and intergalactic gas clouds in any numbers . and yet , as we can now see , none of those claims stands up to examination . _ that is why it is necessary to be outspoken here_. what only matters is that the conjecture is still very much alive . there may well be a low surface brightness universe out there rich in both information and material . it may prove tricky to find , so the last thing needed is any false prejudice against its existence based on claims that are no longer credible . absence of evidence is certainly not evidence of absence here . an example of such prejudice at large was the storm of criticism ( see cho a , 2007 ) , especially from the expert hi community , directed at the one really plausible dark galaxy candidate that turned up in the blind hi surveys , namely virgohi21 ( davies ji et al 2004 , minchin et al 2005 , minchin et al 2007 ) . impressed perhaps by their own ability to find optical counterparts for every other hi source in the sky , they dismissed it as tidal debris ( e.g. haynes et al 2007 ) , @xmath6 which it could not be , simulated it away ( bekki et al 2005 , duc and bournand 2007 ) or proved it could never have formed in the first place ( taylor and webster 2005 ) . it is time to reconsider the favourable evidence @xmath6 which we contend is very strong ( minchin et a. 2007 ) @xmath6 . the point is that no dynamical simulation has been able to model the unique and abrupt change of gas velocity observed (   200 km.@xmath8 within 16 kpc . ) without invoking a massive ( @xmath110 solar masses ) dark object close to the line of sight ( vollmer , huchtmeir and van driel 2005 ; minchin et al 2007 ) . + we have so far only attacked the evidence against the conjecture as embodied in certain probable misidentifications ; we can not leave without at least mentioning the strong circumstantial evidence in its favour , evidence discussed at far more length in two recent iau conference proceedings : the low surface brightness universe (ed davies j i et al 1999 ) and `` dark galaxies and lost baryons''(ed davies ji and disney mj 2008 ) . but it is hard , very hard to ignore . there are so many independent coincidences in galaxy photometry @xmath6 half a dozen at least ( ellis gfr et al . 1984 ; disney,1999 ) @xmath6 that are explained if the the conjecture is true , that are a complete mystery if it is not : ( a ) optically discovered disc galaxies with a wide range of luminosities have surface brightnesses(sbs ) which cluster around a peak value ( freeman 1970 , disney 1976 . ( b ) the peak value is just such as to give discs the most prominence against the terrestrial sky ( disney 1976 ) . ( c ) optically discovered ellipticals with a wide range of luminosities have sbs which cluster around another peak value ( disney , 1976 ) . ( d ) that peak value , very different from ( b ) , is again just such as to render ellipticals most prominent against the earthly sky ( disney 1976 ) . ( e ) there is a complete lack of correlation between blue sb and blue ( b - v ) colour amongst discs @xmath6 when increased star - formation should push both parameters up together ( disney and phillipps 1985 , bothun , impey and mcgaugh 1997 . ( f ) a lack of correlation is observed between the apparent sbs of galaxies and their galactic latitude @xmath6 even in latitudes where the foreground absorption ought to be significant ( davies ji et al 1993 ) . ( g ) there is a close correspondence between the calculated visibility ( i.e the volume within which they can be detected ) of galaxies and their median observed distances in a large sample of spirals ( davies ji et al 1994 ) . and not the least is ( h ) the extraordinary discovery that virtually all the galaxies in the hubble deep field have the same apparent surface - brightness , irrespective of their redshifts and the same as galaxies nearby ( jones and disney 1997 , disney and lang 2012 ) . but hdf redshifts range from @xmath18 1 to 8 and surface brightnesses ought to vary as the tolman factor @xmath111 or by 10 magnitudes ! what we are probably seeing out there is the very high surface - brightness population of galaxies which we miss from the ground , because of strong selection effects . we could just as well be missing the low surface brightness population as well . a large helping of extra ( i.e. hidden ) galaxies at high redshift is exactly what we need to explain the re - ionisation of the universe ( e.g. robertson et al 2010 ) .","summary":"cosmology : re - ionization .","abstract":"we re - investigate the question of whether there is a significant population of dim ( low surface brightness ) and/or dark galaxies ( ddgs ) . we argue that if they are clustered with bright ones then a physical resolution of 10 kpc . will be needed to distinguish their 21-cm . and qso absorption line(qsoal ) counterparts from their brighter neighbours , leading to a real possibility of confusion . but until now such a resolution has not been available in this context . new very large array ( vla ) observations reveal that the identifications with bright optical objects claimed in previous single - dish blind hi surveys are often unreliable . for instance 14/36 of our high - resolution ( 5 arc sec , 13kpc . ) sample have no optical counterparts in the digital sky survey . this suggests that ddgs might be commonplace after all , and we go on to re - examine the main arguments that have been used against them .. we find that the qsoal argument founders on the aforementioned clustering while deep ccd surveys have so far covered too small an area to set set strong constraints on low surface brightness galaxies ( lsbgs ) . a cosmos filled with low surface brightness galaxies , dark galaxies and intergalactic gas clouds can no longer be ruled out .    [ firstpage ]    surveys.galaxies:statistics ; galaxies : groups : general . cosmology : dark matter . cosmology : re - ionization ."}
{"article_id":"0905.1691","section_id":"i","document":"it is estimated that 30% or more of the light emitted from stars in the universe is absorbed and re - emitted by dust in the infrared ( ir ) . the cosmic ir background , therefore , records the cumulative ir emission from galaxies at all redshifts and provides an important constraint on the global history of star formation . this emission is affected by dust evolution in galaxies , in particular at high redshift ( @xmath12 ) , where the presence of dust can influence the galaxy number counts and the evolution of quasars ( e.g. obscuring star - forming galaxies or active galactic nuclei ; smail , ivison & blain 1997 ; hughes et al . 1998 , maiolino et al . 2003a ) . evidence for the presence of dust at high redshifts comes from observations of damped ly@xmath13 systems ( pettini et al . 1994 ; prochaska & wolfe 2002 ; ledoux , bergeron & petitjean 2002 ) and from the detection of dust thermal emission from high redshift quasars ( qsos ) selected from the sloan digital sky survey ( sdss ) re - observed at millimetre wavelengths ( omont et al . 2001 ; carilli et al . 2001 ; bertoldi & cox 2002 ) . the inferred far - ir ( fir ) luminosities of samples of @xmath14 quasars are consistent with thermal emission from warm dust ( @xmath15  k ) , with dust masses in excess of @xmath16 ( bertoldi et al . 2003 ; robson et al . 2004 ; beelen et al . 2006 ) . despite the fact that these high redshift quasars are rare objects , hardly representative of the dominant star forming galaxy population , the fir and sub - mm observations indicate that early star formation leads to rapid enrichment of their host galaxies interstellar medium ( ism ) with metals and dust . this is consistent with the super - solar metallicities inferred from the optical emission - line ratios for many of these systems ( pentericci et al . 2002 ; freudling et al . 2003 ; maiolino et al . 2003b ) .    in present - day galaxies , the major sources of interstellar dust are believed to be low and intermediate - mass evolved stars during the asymptotic giant branch ( agb ) phase . since these stars take a long time to evolve to their dust producing stages , it is commonly believed that they can not be responsible for all of the dust seen at high redshifts . in fact , agb stellar lifetimes ( @xmath17 to @xmath18  yr ) are comparable to the age of universe at redshift @xmath19 ( morgan & edmunds 2003 ; marchenko 2006 ) . as a result , if the observed dust is produced by stellar processes , supernova ( sn ) ejecta appear to be the only viable sites of grain condensation fast enough to explain these large dust masses . this scenario has been tested through observations of the reddened quasar sdssj1048 + 46 at @xmath20 ( maiolino et al . 2004 ) and of the spectral energy distribution ( sed ) of the grb 050904 afterglow ( stratta et al . 2007 ) . in both sources , the inferred dust extinction curve is different with respect to any of the extinction curves observed at low z ( hopkins et al . 2004 ) , and it shows a very good agreement with the extinction curve predicted for dust formed in sn ejecta . this is an indication that the properties of dust evolve beyond @xmath21 . theoretical models , based on classical nucleation theory , predict that a few hundred days after the explosions silicate and carbon grains can form in expanding sn ejecta , with condensation efficiencies in the range @xmath22 . this implies @xmath23 of dust per sn for stellar progenitor masses in the range of core - collapse sn ( @xmath24 ) ( kozasa et al . 1991 ; todini & ferrara 2001 ; clayton , deneault & meyer 2001 ; nozawa et al . 2003 ) . there is now clear observational evidence for dust formation in core - collapse supernovae , but the quantity of dust formed within the ejecta is still a subject of debate . the observed ir emission for a limited number of sne , such as 1987a ( wooden et al . 1993 ) , 1999em ( elmhamdi et al . 2003 ) and 2003gd ( sugerman et al . 2006 ; meikle et al . 2007 ) implies dust masses which are generally smaller than @xmath25 , corresponding to condensation efficiencies which are at least two orders of magnitude smaller than what theory predicts . observations of young galactic sn remnants by the _ spitzer _ telescope provide unambiguous evidence of dust formation ( hines et al . the inferred total mass of freshly formed dust is @xmath26 for cas a ( rho et al . 2008 ) , and @xmath27 for 1e 0102.2 - 7219 ( rho et al . while masses up to @xmath28 have been estimated from fir and submm observations ( dunne et al . 2003 ) , the interpretation of these data is complicated by strong foreground contamination ( krause et al . 2004 ; wilson & batrla 2005 ) . the apparent discrepancies between observational estimates and theoretical models can be accomodated taking into account the partial destruction of newly synthesized dust in the reverse shock of the sn ( bianchi & schneider 2007 ) . the evolution of dust in the early universe is still poorly understood . models developed so far show that the current observational constraints on dust production in sne are still consistent with the scenario where most of the dust in qso at @xmath29 is produced by sne . however these estimates either neglect dust destruction by interstellar shocks ( maiolino et al . 2006 ) or make extreme assumptions on sn dust condensation factors ( dwek , galliano & jones 2007 ) . it is clear that our ability to interpret the observed properties of high redshift qsos depends on a detailed understanding of the star formation history and the history of metal and dust pollution in their host galaxies . this , in turn , requires an adequate description of metal and dust stellar yields .    in this work we study the evolution of dust produced by low , intermediate and high - mass stars as a function of time and metallicity , taking into account the stellar evolutionary timescales , i.e. without adopting an instantaneous recycling approximation . the aim of this study is to explore the relative importance of the two main stellar sources , agb stars and sne , in the evolution of dust at high redshift for galaxies with different star formation histories ( sfh ) and stellar initial mass function ( imf ) . the paper is organized as follows . in section 2 , we describe the adopted grid of dust yields for agb stars and sne with different initial metallicities . in section 3 we discuss the time evolution of the predicted dust mass for two different sfh . in this section we also explore the dependence of the results on the adopted imf and the stellar mass - lifetime relation . in section 4 we present a chemical evolution model which includes dust destruction by interstellar sn shocks and , in section 5 , we apply it to the qso sdss j1148 + 5251 at @xmath7 , using the star formation history of the host galaxy predicted by the numerical simulation of li et al . finally , in section 6 we discuss and summarize the results of our work . in what follows , we assume a @xmath30cdm cosmology with @xmath31 , @xmath32 , @xmath33 , and @xmath34  km / s / mpc . the age of the universe at a redshift @xmath7 is about 840 myr .","summary":"[ firstpage ]    galaxies : evolution , high - redshift , ism ; quasars : general ; stars : agb and post - agb , supernovae : general , ism : dust , extinction","abstract":"with the aim of investigating whether stellar sources can account for the dust masses inferred from mm / sub - mm observations of samples of quasars , we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes , taking into account dust destruction mechanisms . using a grid of stellar dust yields as a function of the initial mass and metallicity over the range and , we show that the role of agb stars in cosmic dust evolution at high redshift might have been over - looked . in particular , we find that ( i ) for a stellar population forming according to a present - day larson initial mass function ( imf ) with , the characteristic timescale at which agb stars dominate dust production ranges between 150 and 500  myr , depending both on the assumed star formation history and on the initial stellar metallicity ; ( ii ) this result is only moderately dependent on the adopted stellar lifetimes , but it is significantly affected by variations of the imf : for a , dust from agb starts to dominate only on timescales larger than 1 gyr and sne are found to dominate dust evolution when . we apply the chemical evolution model with dust to the host galaxy of the most distant quasar at , sdss j1148 + 5251 . given the current uncertainties on the star formation history of the host galaxy , we have considered two models : ( i ) the star formation history obtained in a numerical simulation by li et al . ( 2007 ) which predicts that a large stellar bulge is already formed at , and ( ii ) a constant star formation rate of/yr , as suggested by the observations if most of the fir luminosity is due to young stars . the total mass of dust predicted at by the first model is , within the range of values inferred by observations , with a substantial contribution (% ) of agb - dust . when a constant star formation rate is adopted , the contribution of agb - dust decreases to% but the total mass of dust formed is a factor 2 smaller . both models predict a rapid enrichment of the ism with metals and a relatively mild evolution of the carbon abundance , in agreement with observational constraints . this supports the idea that stellar sources can account for the dust observed but show that the contribution of agb stars to dust production can not be neglected , even at the most extreme redshifts currently accessible to observations .    [ firstpage ]    galaxies : evolution , high - redshift , ism ; quasars : general ; stars : agb and post - agb , supernovae : general , ism : dust , extinction"}
{"article_id":"0905.1691","section_id":"c","document":"in this work we show that the role of agb stars in cosmic dust evolution at high redshift might have been over - looked . we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes , taking into account dust destruction mechanisms . we use a grid of stellar dust yields as a function of the initial mass and metallicity over the range @xmath2 and @xmath3 . we adopt the stellar dust yields by zhukovska et al . ( 2008 ) for agb stars with stellar masses in the range @xmath187 and the model of bianchi & schneider ( 2007 ) to account for dust production and destruction in the reverse shock of sne , with progenitor stellar masses in the range @xmath24 . our results can be summarized as follows :    * a comparison of dust yields expected from agb stars and sne shows that carbon grains are the dominant dust component . silicates and other dust components can only be produced by agb stars with solar metallicities and by sne when @xmath188 but are always sub - dominant with respect to carbon grains . this is at odd with what has been generally adopted in chemical evolution models which , assuming a dust condensation efficiency of 1 for all refractory elements present in the ejecta , predict that sne dominate silicate dust production and that agb stars lead to a delayed injection of carbon dust ( dwek 1998 ; dwek 2005 ; galliano , dwek & chanial 2008 ) . * at early times , dust production is dominated by sne as a consequence of the shorter lifetimes of their progenitor stars . agb stars start to produce dust after about 30  myr ( i.e. when a @xmath189 star evolves off the main sequence to the agb phase ) . for our reference model , where we adopt a larson imf with @xmath4 and stellar lifetimes from raiteri et al . ( 1996 ) , we find that the characteristic timescale at which agb stars dominate dust production ranges between 150 and 500  myr , depending both on the assumed star formation history and on the initial stellar metallicity . hence , we conclude that these stellar dust sources must be taken into account at early cosmic epochs . * this conclusion is only moderately dependent on the adopted stellar lifetimes , but it is significantly affected by variations of the imf : for a @xmath5 , dust from agb starts to dominate only on timescales larger than 1 gyr , and sne are found to dominate dust evolution when @xmath6 . thus , variations of the stellar characteristic mass over cosmic history due to the smaller gas metallicity and/or to the larger cosmic microwave background temperature ( see , e.g. , omukai et al . 2005 ) might significantly affect the origin and properties of dust in the high redshift universe . * we apply the chemical evolution model with dust to the host galaxy of the most distant qso at @xmath7 , sdss j1148 + 5251 . given the current uncertainties on the star formation history of the host galaxy , we have considered two models : ( i ) the star formation history obtained in a numerical simulation by li et al . ( 2007 ) which predicts that a large stellar bulge is already formed at @xmath7 , in agreement with the local smbh - stellar mass relation , through a series of strong bursts triggered by galaxy mergers in the hierarchical evolution of the system and ( ii ) a constant star formation rate of @xmath8/yr , as suggested by the observations if most of the fir luminosity is due to young stars . in the latter case , the stellar mass at @xmath170 is compatible with estimates of the dynamical mass derived by observations . the total mass of dust predicted at @xmath7 by the first model is @xmath9 , within the range of values inferred by observations , with a substantial contribution ( @xmath10% ) of agb - dust . when a constant star formation rate is adopted , the contribution of agb - dust decreases to @xmath11% but the total mass of dust formed is a factor 2 smaller . both models predict a rapid enrichment of the ism with metals and a relatively mild evolution of the carbon abundance , in agreement with observational constraints . the evolution of dust in the high - redshift universe is still very uncertain . some of the chemical evolution models with dust developed so far have been aimed at reproducing the elemental abundances of the gas and dust phases of the ism of our galaxy ( dwek 1998 ; falceta - goncalves 2008 ; zhukovska et al . 2008 ) and of local ellipticals and dwarf irregulars ( calura , pipino & matteucci 2008 ) . in early galaxies , a crucial unknown is the relative contribution of sne and agb stars . it is generally found that there is no difficulty in producing highly dusty galaxies at @xmath190 if sne are an important contributor to interstellar dust . however , the models developed so far assume that all refractory elements present in sn ejecta form dust grains with a condensation efficiency of 1 ( dwek et al . 2007 ) or neglect dust destruction mechanisms ( morgan & edmunds 2003 ) . the evolution of metals and dust in the host galaxy of the most distant quasar at @xmath170 sdss j1148 + 5251 has been also investigated by dwek et al . ( 2007 ) which show that an average sn must condense a dust mass of @xmath191 to reproduce the dust - to - gas ratio inferred from the observations ( 0.0067 ) , when a gas mass of @xmath192 and a dust mass of @xmath193 are assumed . since the observed dust yield is much lower ( the largest observed dust yield is @xmath194 , rho et al . 2008 ) , the authors suggest that mc - grown dust or dust formed around the agn ( i.e. in outflows from the broad line regions , elvis et al . 2002 ) must be taken into account . our results suggest the alternative possibility that agb stars might significantly contribute to dust production even at redshifts @xmath100 . for a comparison , we can infer from figure 8 in dwek et al . ( 2007 ) that , in order to reproduce the dust - to - gas ratios predicted by our sfr models for sdss j1148 + 5251 ( @xmath195 at @xmath7 ) , a dust yield per sn of about @xmath196 would be required . this is larger than our adopted sn yields , the difference being compensated by the additional contribution to the dust budget provided by agb stars . more recently , li et al . ( 2008 ) have applied a three - dimensional monte carlo radiative transfer code to the hydrodynamic simulations of li et al . ( 2007 ) to model the dust properties of j1148 + 5251 and find that a supernova - origin dust model may be able to explain the observed dust properties . yet , dust destruction in the ism is not explicitely taken into account . moreover , these models make the a - priori assumption that at redshift above 6 , when the age of the universe is less than 1 gyr , the major alternative source of interstellar dust , namely agb stars , have not yet evolved to their dust - production stage . our results show that stellar sources can account for the huge dust masses inferred from observations of distant qsos . although the star formation history of the qso host galaxies is still largely unknown , our analysis indicate that the contribution of agb stars to dust production can not be neglected , even at the most extreme redshifts currently accessible to observations . yet , since agb winds are not efficient to disperse dust through the galaxy , sne are still required to efficiently re - distribute dust on galactic scales ( jones 2005 ) . the nature and properties of the grains responsible for dust extinction in high - redshift qsos and grbs host galaxies ( maiolino et al . 2004 ; stratta et al . 2007 ; gallerani et al . in prep ) are likely to depend more on the specific host galaxy star formation history than on redshift . future observations aimed at constraining the properties of dust in high redshift qsos might be a powerful probe of star formation and qso feedback regulating the bh - galaxy coevolution .","summary":"with the aim of investigating whether stellar sources can account for the dust masses inferred from mm / sub - mm observations of samples of quasars , we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes , taking into account dust destruction mechanisms . using a grid of stellar dust yields as a function of the initial mass and metallicity over the range and , we show that the role of agb stars in cosmic dust evolution at high redshift might have been over - looked . in particular , we find that ( i ) for a stellar population forming according to a present - day larson initial mass function ( imf ) with , the characteristic timescale at which agb stars dominate dust production ranges between 150 and 500  myr , depending both on the assumed star formation history and on the initial stellar metallicity ; ( ii ) this result is only moderately dependent on the adopted stellar lifetimes , but it is significantly affected by variations of the imf : for a , dust from agb starts to dominate only on timescales larger than 1 gyr and sne are found to dominate dust evolution when . we apply the chemical evolution model with dust to the host galaxy of the most distant quasar at , sdss j1148 + 5251 . given the current uncertainties on the star formation history of the host galaxy , we have considered two models : ( i ) the star formation history obtained in a numerical simulation by li et al . ( 2007 ) which predicts that a large stellar bulge is already formed at , and ( ii ) a constant star formation rate of/yr , as suggested by the observations if most of the fir luminosity is due to young stars . the total mass of dust predicted at by the first model is , within the range of values inferred by observations , with a substantial contribution (% ) of agb - dust . when a constant star formation rate is adopted , the contribution of agb - dust decreases to% but the total mass of dust formed is a factor 2 smaller . both models predict a rapid enrichment of the ism with metals and a relatively mild evolution of the carbon abundance , in agreement with observational constraints .","abstract":"with the aim of investigating whether stellar sources can account for the dust masses inferred from mm / sub - mm observations of samples of quasars , we develop a chemical evolution model which follows the evolution of metals and dust on the stellar characteristic lifetimes , taking into account dust destruction mechanisms . using a grid of stellar dust yields as a function of the initial mass and metallicity over the range and , we show that the role of agb stars in cosmic dust evolution at high redshift might have been over - looked . in particular , we find that ( i ) for a stellar population forming according to a present - day larson initial mass function ( imf ) with , the characteristic timescale at which agb stars dominate dust production ranges between 150 and 500  myr , depending both on the assumed star formation history and on the initial stellar metallicity ; ( ii ) this result is only moderately dependent on the adopted stellar lifetimes , but it is significantly affected by variations of the imf : for a , dust from agb starts to dominate only on timescales larger than 1 gyr and sne are found to dominate dust evolution when . we apply the chemical evolution model with dust to the host galaxy of the most distant quasar at , sdss j1148 + 5251 . given the current uncertainties on the star formation history of the host galaxy , we have considered two models : ( i ) the star formation history obtained in a numerical simulation by li et al . ( 2007 ) which predicts that a large stellar bulge is already formed at , and ( ii ) a constant star formation rate of/yr , as suggested by the observations if most of the fir luminosity is due to young stars . the total mass of dust predicted at by the first model is , within the range of values inferred by observations , with a substantial contribution (% ) of agb - dust . when a constant star formation rate is adopted , the contribution of agb - dust decreases to% but the total mass of dust formed is a factor 2 smaller . both models predict a rapid enrichment of the ism with metals and a relatively mild evolution of the carbon abundance , in agreement with observational constraints . this supports the idea that stellar sources can account for the dust observed but show that the contribution of agb stars to dust production can not be neglected , even at the most extreme redshifts currently accessible to observations .    [ firstpage ]    galaxies : evolution , high - redshift , ism ; quasars : general ; stars : agb and post - agb , supernovae : general , ism : dust , extinction"}
{"article_id":"1006.1319","section_id":"i","document":"gauge symmetry is no doubt the underlying principle of contemporary particle theory . it is a mathematical or geometrical input rather than a dynamical consequence . however , some people wonder if there is any physical or dynamical reason that necessitates gauge symmetry@xcite . aside from such attempts , one suggestion was made decades ago@xcite that when spin - one bosons are generated as tightly bound composite particles their couplings obey gauge invariance in the limit of vanishing mass . this was indeed demonstrated in a solvable model with fermions as constituents@xcite . as in most other attempts , the model was based on the lagrangian of the nambu - jona - lasinio type with a vector coupling and was , therefore , unrenormalizable , which is the price to pay for solvability . the conclusion was that all gauge - symmetry breakings as well as unrenormalizability are transformed into the mass of the composite spin - one bosons and that the composite boson mass can be made as small as one likes , but never zero , by making the binding force stronger , that is , infinitely close to gauge bosons but not exactly . failure to realize genuine gauge invariance is obvious since the lagrangian written in the fields of fermion constituents explicitly violates gauge invariance ; perfect gauge symmetry should not arise where underlying dynamics explicitly violates it . nonetheless , it is remarkable that gauge noninvariance is entirely transformed into the composite boson mass term . the gauge boson sector of the electroweak model without a higgs boson was built by the present author@xcite along this line twenty years ago incorporating the proposal of bjorken@xcite and of hung and sakurai@xcite . consistency of the large @xmath0 expansion as an effective low - energy field theory was analyzed for this model by cohen , georgi , and simmons@xcite , who also suggested how to incorporate quarks and leptons in this heretic electroweak model . it was immediately after production of the @xmath1 and @xmath2 bosons were confirmed at cern for the first time . since then , precision of the experimental measurement on the electroweak interaction has risen to test the standard model at the level of the loop corrections . consequently , the phenomenological models of the late 1980 s are no longer viable , but other options may still exist . until we see an outcome of the large hadron collider experiment , we should be prepared for possible surprises and leave all options open for phenomenology . it should be emphasized , however , that the purpose of the present paper is not to build a phenomenologically viable alternative to the standard electroweak theory , but to obtain a better understanding of the generation mechanism of approximate gauge invariance . even if this mechanism may not turn out to be of use to model building in near future , it is an interesting theoretical subject of discussion in field theory . we shall find in this paper that the dynamical generation of approximate gauge symmetry is not an accident in the nambu - jona - lasinio model or special to the fermionic constituents . a natural question arises as to how general this phenomenon is and which inputs are really necessary for this phenomenon to occur . the present paper first investigates the original fermionic constituent model by a different method and then moves on to explore how the approximate gauge symmetries are generated in the case of bosonic constituents , if at all . after studying the bosonic case , we understand the generation mechanism better and feel more confident that the mechanism is quite general and independent of specific models . it may appear that our study has some technical resemblance with the phenomenon known as hidden symmetry , the name coined by bando , kugo , and yamawaki@xcite . however , the hidden symmetry is something that is built in a theory at the beginning in one way or another . in contrast , we are concerned with the dynamics in which a relevant local symmetry does not exist , hidden or otherwise , at the fundamental level , but emerges only as an approximate symmetry in the low - energy effective lagrangian . in our case the local symmetry is explicitly broken at all levels . we study how the explicit breakings of local symmetries transform into the lagrangian of composite vector bosons . our study focuses on a different subject , technically and conceptually , as we shall later comment more .","summary":"although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair , we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way . the functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry , in particular , how the strong binding and global current conservation conspire to generate such an approximate symmetry . remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries .","abstract":"it can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding . although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair , we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way . the functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry , in particular , how the strong binding and global current conservation conspire to generate such an approximate symmetry . remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries ."}
{"article_id":"1006.1319","section_id":"i","document":"we would like to see whether the gauge - symmetry generation of the preceding section works in the bosonic constituent models or not . we emphasize that we do not slip an unbroken local symmetry in our models to look for massless vector bosons as dynamical gauge boson modes . such a study was done in the @xmath69 a few decades ago ; a local symmetry is present at the beginning as redundancy when its lagrangian is written in some form , then a composite massless vector boson is searched for . instead we choose models in which there is no local symmetry to start with . we study whether the explicit breaking can be transformed into the mass term alone in the case of tightly bound vector bosons . unlike the fermionic model , to our knowledge , our bosonic models have never been studied in the literature . they show us more clearly what realizes an approximate gauge symmetry as a consequence of compositeness . let us first study the case of an abelian vector boson since it gives us a good insight into the problem leaving out unnecessary complications . we form a neutral composite vector boson ( a massive photon ) with charged spinless bosons like @xmath70 having heavy mass @xmath3 . we introduce @xmath0 families of the heavy @xmath70 for the large @xmath0 expansion . our fundamental lagrangian is written in the nonpolynomial form as @xmath71 with the charged spinless bosons @xmath72 and @xmath73 ( @xmath74 ) of @xmath0 families . no constraint is imposed on the fields @xmath75 and the classical vacuum is at @xmath76 so that the lagrangian is invariant under the global u(1 ) charge rotation , @xmath77 and trivially invariant under global u(n ) family rotations . the current - current interaction has been so chosen that not only a tightly bound state can be formed but also its mass is explicitly calculable in the large @xmath0 limit.$ ] in this lagrangian has some vague resemblance with that of the @xmath69 model written in the constrained fields@xcite . but our @xmath78 are unconstrained here . ] a natural extension of the fermionic model might suggest the current - current interaction @xmath79 of @xmath78 in the bosonic case . however , this simple current - current interaction does not generate a tightly bound vector boson in the scattering amplitude for the following reasons :    \\1 . the current @xmath80 , is a conserved current in the case that the interaction is @xmath81 . because derivatives of @xmath78 enter @xmath81 , the conserved current that originates from the kinetic energy term alone . ] @xmath82 derivable by the noether theorem in the abelian case , @xmath83 contains a term which depends on the interaction @xmath79 . if we went ahead with this naive current - current interaction @xmath84 , the current @xmath85 would not conserve , @xmath86 . its immediate consequence is that the self - energy loop @xmath87 is not transverse ( @xmath88 ) and an additional term of quadratic divergence @xmath33 arises with the coefficient @xmath89 . this moves the pole to @xmath90 that can not be physically interpreted as mass square of a bound state . \\2 . from the standpoint of the functional formalism , choosing the simple interaction @xmath81 would amount to postulating that the composite vector field @xmath12 be proportional to @xmath85 and consequently lead to @xmath91 . that is , @xmath12 would not be purely a field of spin - one , but contain a spin - zero component . we were fortunate in the model of fermionic constituents since the binding interaction contains no derivative of fields and therefore the choice of the interaction was deceptively simple . in contrast , for the bosonic constituents we must choose the interaction carefully such that the auxiliary composite field @xmath12 is proportional to the noether current . if so chosen , the field @xmath12 obeys @xmath92 and its proper self - energy part @xmath87 turns out to be transverse . only in this situation can the composite boson mass be made as small as one likes by increasing the binding interaction constant @xmath11 . the factor @xmath93 $ ] in the denominator of the interaction in eq . ( [ lb ] ) serves this purpose and realizes @xmath94 . [ see the second relation in eq . ( [ gm ] ) . ]      a neutral vector bound - state is formed with the loop and bubble diagrams of @xmath78 . we compute for the bound - state in elastic scattering @xmath95 although we are interested in physics at large @xmath11 , we can not make the @xmath96 expansion in the lagrangian since the potential term behaves at large @xmath11 as @xmath97.\\ ] ] the behavior of @xmath98 at @xmath99 makes the perturbative vacuum ill - defined and prevents diagram calculation . we must instead perform diagram calculation in the perturbative expansion in powers of @xmath11 to all orders , sum up the perturbative series and then take @xmath11 to large values . such computation is possible only in the leading @xmath0 order . in the large @xmath0 limit the relevant diagrams are chains of loops with bubbles added . ( see fig . each loop comes from the diagram of @xmath100 , while the bubble diagram arise from @xmath101 in the power series expansion of the factor @xmath102 $ ] . if the loops and the bubbles of @xmath103 in the @xmath104 channel sum into the transverse form as @xmath105 the perturbation series turns into the total scattering amplitude in the form of eq . ( [ pi ] ) so that the bound - state mass @xmath21 comes out to be @xmath106 . transversality of eq . ( [ se ] ) is indeed realized after summing the loops and the bubbles of the same order in the power of @xmath11 , as shown in fig . 3 . in @xmath107 the tree diagram is the only diagram [ fig . 3(a ) ] . a single - loop diagram and a single - bubble diagram enter @xmath108 [ fig . the single - loop diagram alone would not make @xmath87 transverse in @xmath108 , as we know from the photon self - energy in electrodynamics of the charged pions in which the bubble generated by the interaction @xmath109 makes the photon self - energy transverse and keeps the photon massless even after loop corrections . in @xmath110 we sum a diagram with two bubbles , a pair of diagrams with one - loop and one - bubble , and the diagram of two bubbles [ fig . 3(c ) ] . we can keep on going to higher orders of @xmath11 and obtain a scattering amplitude of the form of eq . ( [ se ] ) in the @xmath31 channel . consequently , the location of the pole is found at @xmath111 as we desire . in order to realize this behavior , therefore , the factor @xmath112 $ ] is needed in the interaction term of the lagrangian , eq . ( [ lb ] ) .    when we sum up an infinite series of the loop plus bubble diagrams of fig . 3 in a compact form , the resulting invariant amplitude for the elastic scattering of eq . ( [ scattering ] ) is @xmath113 ,    \\nonumber   \\\\       & = & \\biggl(\\frac{g}{n}\\biggr)\\frac{(p_3-p_4)_{\\mu }                 ( p_1-p_2)^{\\mu}}{1+g\\pi(q^2)},\\end{aligned}\\ ] ] where @xmath114.\\ ] ] the bound - state pole appears in @xmath115 at the location determined by @xmath28 . for large @xmath11 the mass of the bound state is found at @xmath116 and its coupling to @xmath117 is given by @xmath118 so that the bound - state mass and the coupling are related at @xmath119 by @xmath120 here again the composite mass vanishes if one takes the limit of @xmath35 in eq . ( [ m ] ) . going back to the original lagrangian , eq . ( [ lb ] ) , we find in this limit @xmath121 it is not difficult to check that this lagrangian is u(1)-gauge invariant under @xmath122 . the u(1)-gauge invariance is nontrivial in this form unlike that in the fermionic model . in the nonlinear representation , however , this limiting lagrangian turns out to be the free lagrangian of the radial fields and the phase fields do not enter . that is , this lagrangian is trivially gauge invariant and of little physical content . the noether current of eq . ( [ jn ] ) vanishes @xmath123 since there is not a conserved global u(1 ) current , the massless limit of our composite boson would not contradict the general theorem@xcite . but it is obvious that a massless vector boson can not be formed with the limiting lagrangian that contains only the hermitian radial field . the lagrangian of eq . ( [ llim ] ) would be identical to that of the @xmath124 model @xmath78 were constrained with @xmath125 . however , the @xmath78 fields are the unconstrained fields in our case ; we have gone through the feynman diagram calculation with the standard ( unconstrained ) spinless - boson propagator .      in the diagram computation above , we need careful bookkeeping in summing up the perturbation series into the scattering amplitude . after our study of the fermionic model , however , we are able to carry out an equivalent calculation by the functional integral method in a simpler way . we see underlying issues and their new aspects more clearly in a new light . the first step is to introduce the auxiliary neutral vector field @xmath12 . the lagrangian of eq . ( [ lb ] ) in @xmath78 suggests the form for the partition function , @xmath126 ,                         \\label{aba}\\ ] ] where @xmath127 is given by eq . ( [ lb ] ) and @xmath128 is defined by @xmath129 upon integration over @xmath12 , the factor @xmath93 $ ] in front of the first term of eq . ( [ lbaux ] ) generates @xmath130 $ ] , as is shown in the appendix , and cancels the last term of @xmath41 so that eq . ( [ aba ] ) reduces to the partition function written in @xmath131 alone , @xmath132 the diagrammatic content of this logarithmic term is also shown in the appendix . the infinite factor @xmath133 represents the total functional phase space @xmath134 , which should be properly regularized . physically , it is a large finite number since the unrenormalizable lagrangian of eq . ( [ lb ] ) is valid only up to some limited energy range . however , if one regularizes it dimensionally as the @xmath135 limit of @xmath136 one would set this @xmath133 to zero using the formula @xmath137 containing no derivative , the term @xmath138 is manifestly gauge invariant by itself and , in the leading @xmath0 order , does not contribute to the calculation of the bound state in the @xmath104 channel . it affects only the @xmath139 channel of @xmath140 scattering in the leading @xmath0 order . we leave this singular term as proportional to @xmath133 as it is , while it does not affect our diagrammatic calculation in the rest of the paper . when we sum @xmath127 and @xmath141 , no current - current interaction is left in the sum , @xmath142 in fact , we have chosen @xmath41 in eq . ( [ lbaux ] ) so that the current - current interaction is absent from the sum in eq . ( [ lphia ] ) . we have not obtained eq . ( [ lphia ] ) by simply gauging @xmath127 with @xmath143 in eq . ( [ lb ] ) . we identify the constant @xmath144 in front of @xmath145 with the gauge coupling @xmath17 in eq . ( [ lphia ] ) . therefore we obtain @xmath146 , which is the relation between @xmath51 and @xmath21 that has been obtained in eq . ( [ gmb ] ) by the diagram calculation . furthermore a new four - point interaction of @xmath147 arises in @xmath148 , @xmath149 which is equal to @xmath150 thanks to @xmath146 . therefore the lagrangian in eq . ( [ lphia ] ) can be rearranged into the gauge - invariant form up to the mass term of @xmath12 : @xmath151 the lagrangian of eq . ( [ lg ] ) leads to the equation of motion for @xmath12 , @xmath152 the noether current @xmath82 in terms of @xmath75 and @xmath153 can be computed with eq . ( [ jn ] ) from @xmath127 as @xmath154 therefore , the equation of motion , eq . ( [ eqofmotion ] ) , together with @xmath155 says that , with our choice of lagrangian , @xmath12 is proportional to the noether current @xmath82 of the constituent fields before propagation ; @xmath156 consequently it satisfies @xmath157 so that its self - energy is transverse . therefore , the bound - state mass square can behave as @xmath30 . the relation @xmath157 also tells that this vector boson is not a gauge boson since it holds by the equation of motion , not by choice of fixing ambiguities . nor does @xmath12 transform like @xmath158 under @xmath159 either . that is , we are studying something very different from the gauge boson of the @xmath69 model@xcite or its hidden symmetry@xcite . we now proceed to obtain the kinetic energy term through loop diagrams . no three - point function or nonderivative four - point function of @xmath12 is generated in the abelian case . it is only the two - point functions that arise from loop and bubble diagrams . the computation is straightforward by the diagrams of fig . 4 with the interaction @xmath160 .    since the interaction @xmath161 added with @xmath162 is gauge invariant and since the mass term of @xmath12 enters nowhere in this loop and bubble calculation , the resulting kinetic energy is also gauge invariant : @xmath163 where the constant @xmath61 is computed with the loop diagram from the lagrangian of eq . ( [ lg ] ) ; @xmath164 this constant @xmath61 is removed by the wave - function renormalization of the field @xmath12 and renormalization of the coupling @xmath17 , and the mass @xmath21 : @xmath165 the renormalized mass and coupling are what the diagram computation has given in eqs . ( [ m ] ) and ( [ g ] ) as in the fermionic model . even after they are renormalized , they maintain the relation @xmath146 of eq . ( [ gmb ] ) . we have thus confirmed the results of our preceding diagram calculation in the bosonic model and have reaffirmed our finding in the fermionic model : in the small limit of the composite boson mass the bosonic theory also approaches the gauge theory as closely as possible although the mass @xmath21 can never be brought to zero for any large but finite value of @xmath11 . we have a little deeper understanding of the relation between gauge invariance and the small composite boson mass in the bosonic constituent model than in the fermionic model . in the case of the bosonic constituents we must be very careful in choosing the binding interaction ; the composite boson mass approaches zero in the limit of strong coupling @xmath166 we multiply the naive current - current interaction with the factor @xmath167 $ ] . this factor conspires with @xmath168 and generates part of the gauge interaction @xmath150 with the correct strength when we move to the effective theory in terms of the composite field @xmath12 . the equation of motion for @xmath12 prior to generation of the kinetic energy is of the form , @xmath169 where the right - hand side is proportional to the noether current . expanding the denominator @xmath170 $ ] in the power series of @xmath171 , we interpret the series as the composite vector boson consisting not only of a single pair of @xmath171 in @xmath172 wave but also of many additional @xmath171 pairs in @xmath173 wave . even with this additional factor @xmath112 $ ] , the original lagrangian @xmath127 written in the @xmath78 fields is not gauge invariant at all . after we introduce the composite vector field @xmath12 , however , gauge noninvariance is swept entirely into its mass term and we reach the correct form of the gauge boson lagrangian ( up to mass ) .    before we proceed to the non - abelian case , we summarize what we have learned from the models that we have so far studied . in order to generate composite vector bosons with small mass , their proper self - energy part @xmath87 must be of the transverse form @xmath22 without an additional term @xmath174 ( @xmath175 since this transverse form guarantees that the composite mass square is inversely proportional to strength of binding interaction . this transversality is realized in our models with the conserved currents of a global symmetry . for this reason , presence of a global symmetry is a prerequisite for a generation of ( approximate ) gauge symmetry though it may not be surprising . if conserved currents of a global symmetry do not exist , the composite boson mass can not be made small . by turning the argument around , we may say that a tightly bound state of @xmath104 exists , there must be some dynamical reason why such tight binding occurs . without a good reason the bound - state mass would only be some fraction of @xmath176 . in the @xmath104 channel a very strong current - current interaction of right properties can generate a tightly bound state of mass scale much lower than @xmath176 , at least theoretically , as we have seen above . \\2 . keeping this observation in mind , we should set up a model lagrangian possessing a global symmetry and introduce nonpropagating composite vector - boson fields that are proportional to the noether currents . then the resulting lagrangian of the composite fields is gauge invariant except for the mass term . when the lagrangian is written in the constituent particle fields alone , gauge symmetry does not exist since it is broken by their kinetic energy and , in the case of boson constituents , by the binding interaction too . however , after composite vector bosons are generated dynamically , the gauge symmetry breaking is entirely absorbed into the boson mass term .","summary":"it can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding .","abstract":"it can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding . although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair , we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way . the functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry , in particular , how the strong binding and global current conservation conspire to generate such an approximate symmetry . remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries ."}
{"article_id":"0706.0028","section_id":"i","document":"in @xcite m. entov and l. polterovich establish an unexpected link between a group - theoretic notion of quasi - morphism , which has been found useful in symplectic geometry , and a recently emerged branch of functional analysis called the theory of quasi - states and quasi - measures . in this paper we show this connection for a recently discovered , due to p. py @xcite , calabi quasi - morphism on orientable surfaces of higher genus . the proof relies on hyperbolic geometry tools , surprisingly combined with combinatorial tools such as hall s marriage theorem . [ def : ham ] let @xmath1 be a symplectic manifold equipped with a symplectic form @xmath2 . let @xmath3 , @xmath4 be a smooth function , called * hamiltonian * function . the pointwise linear equation @xmath5 defines a vector field @xmath6 on @xmath1 denoted by @xmath7 . the flow generated by the hamiltonian vector field @xmath7 is denoted by @xmath8 . by assuming that the union over @xmath9 of the supports of @xmath10 is contained in a compact subset of @xmath1 , we can guarantee that the above equation has a well defined solution for all @xmath9 , and so @xmath8 is well defined . the time - one map @xmath11 , denoted by @xmath12 , will be called * the hamiltonian diffeomorphism generated by @xmath13*. the collection of hamiltonian diffeomorphisms has a group structure and this group is denoted by @xmath0 . for further details see @xcite . the following algebraic results on @xmath0 are due to banyaga @xcite . [ thm : banyaga1 ] let @xmath14 be a closed symplectic manifold , then @xmath15 is simple , i.e. , it has no non - trivial normal subgroup . [ thm : banyaga2 ] let @xmath14 be an open manifold with an exact symplectic structure , @xmath16 . then @xmath15 admits the calabi homomorphism : @xmath17 defined as @xmath18 whose kernel is equal to the commutator subgroup of @xmath15 . furthermore , this kernel is a simple group . note that @xmath19 is defined by @xmath13 , but it can be shown that @xmath19 depends only on @xmath12 and not on the specific @xmath13 . returning to the case where @xmath1 is closed , one can not hope to construct a non - trivial homomorphism to @xmath20 since @xmath0 is simple . however , for certain manifolds , one can find a map which is `` locally '' equal to the calabi homomorphism and globally is a homomorphism up to a bounded error . this map is called a calabi quasi - morphism . a precise definition is given in the following subsection . let @xmath21 be a group , a function @xmath22 is a called a * quasi - morphism * if there exists a constant @xmath23 , called the * defect * of @xmath24 , such that for each @xmath25 in @xmath21 @xmath26 if in addition @xmath27 for each @xmath28 and @xmath29 then the quasi - morphism is called * homogeneous*. given a quasi - morphism we can define a homogeneous quasi - morphism called its * homogenization * @xmath30 by @xmath31    for further reading see e.g. @xcite . +    let @xmath1 be a closed manifold with a symplectic form @xmath2 . let @xmath32 be open and connected . denote by @xmath33 the subgroup of @xmath0 generated by hamiltonians supported in @xmath34 . if @xmath2 is exact on @xmath34 then , by theorem [ thm : banyaga2 ] , @xmath33 admits the calabi homomorphism @xmath35 . a set @xmath32 is called displaceable if there exists @xmath36 such that @xmath37 . the following question was posed by m. entov and l. polterovich in @xcite . can one construct a homogeneous quasi - morphism on @xmath0 such that its restriction to @xmath33 , for any open , connected , exact and displaceable @xmath32 , is equal to the calabi homomorphism @xmath35 ?    a homogeneous quasi - morphism with the above property is called a * calabi quasi - morphism*.    m. entov and l. polterovich @xcite have constructed calabi quasi - morphisms for the case of the following symplectic manifolds : @xmath38 , a complex grassmannian , @xmath39 with a monotone product symplectic structure , the monotone symplectic blow - up of @xmath40 at one point . y. ostrover extended it to some non - monotone manifolds @xcite . the following result is due to p. py @xcite . [ thm : pi1 ] let @xmath1 be an oriented closed surface of genus @xmath41 , equipped with a symplectic form @xmath2 . then there exists a homogeneous quasi - morphism @xmath42 such that the restriction to the subgroups @xmath33 is equal to the calabi homomorphism , where @xmath34 is diffeomorphic to a disc or an annulus . in addition , p. py has also constructed a calabi quasi - morphism for the torus @xcite . a smooth function @xmath43 is called a * morse function * if all its critical points are non - degenerate . if in addition the critical values of @xmath13 are distinct then @xmath13 is called a * generic morse function*.    [ def : commute ] let @xmath43 be a generic morse function . let @xmath44 be the space of smooth functions on @xmath1 which commute with @xmath13 in the poisson sense , i.e. @xmath45 note that @xmath13 and @xmath46 commute in the poisson sense if and only if @xmath47 let @xmath48 be the set of time one maps corresponding to the flows generated by the hamiltonian functions in @xmath44 , i.e. @xmath49    clearly , @xmath48 is an abelian subgroup of @xmath0 . it is easy to show that if a homogeneous quasi - morphism is defined on an abelian group , then it is in fact a homomorphism . hence , the restriction of @xmath24 , defined in theorem [ thm : pi1 ] , on the subgroup @xmath48 is a homomorphism . in @xcite p. py has proved the following formula for @xmath24 on @xmath48 , assuming that the total area of @xmath1 is equal to @xmath50 ,    @xmath51 where @xmath52 and @xmath53 is a certain subset of the critical points of @xmath13 . a precise formulation of this theorem will be given in section [ sec : essential ] . the notion of a quasi - state originates in quantom mechanics @xcite , and has been a subject of intensive study in recent years following the paper @xcite by j. f. aarnes . here is the definition . denote by @xmath54 the commutative ( with respect to multiplication ) banach algebra of all continuous functions on @xmath1 endowed with the uniform norm . for a function @xmath55 denote by @xmath56 the uniform closure of the set of functions of the form @xmath57 , where @xmath58 is a real polynomial . a ( not necessarily linear ) functional @xmath59 is called a * quasi - state * , if it satisfies the following axioms : + * quasi - linearity . * @xmath60 is linear on @xmath56 for every @xmath55 . + * monotonicity . * @xmath61 for @xmath62 . + * normalization . * @xmath63 . it is easy to show that a quasi - state is lipschitz continuous with respect to the @xmath64-norm . +    * main result . * in the following , @xmath1 will be an oriented closed surface of genus @xmath41 , equipped with a symplectic form @xmath2 , and @xmath24 is py s quasi - morphism given in theorem [ thm : pi1 ] . in @xcite m. entov and l. polterovich construct a quasi - state from a calabi quasi - morphism , our goal is to show that this procedure is applicable to py s calabi quasi - morphism . in the following , we assume that the total area of @xmath1 , denoted by @xmath65 , is equal to @xmath50 . the quasi - state is obtained from @xmath24 in the following way : +    [ def : qs ] for a smooth function @xmath13 define    @xmath66 the main result of the thesis is that the functional @xmath60 related to py s quasi - morphism is a quasi - state . [ thm : state_1 ] the functional @xmath60 can be extended to @xmath54 , and the extension is a quasi - state . note that this result implies that @xmath60 is lipschitz continuous with respect to the @xmath64-norm . +    * organization of the work . * in the following section we prove the main theorem assuming the monotonicity and continuity theorems , which are proved later on . in sections [ sec : reeb ] , [ sec : essential ] , [ sec : pants ] , [ sec : eight ] we make the preparations for the monotonicity theorem , which is proved in section [ sec : monoton ] . in section [ sec : reeb ] we define the reeb graph which is the base for the following constructions . in section [ sec : essential ] we introduce the notion of essential critical points . in section [ sec : pants ] we construct a pair of pants decomposition . in section [ sec : eight ] we prove an intersection theorem of figure eights related to the pair of pants decomposition . in section [ sec : cont ] we prove the continuity theorem by analyzing py s construction of the quasi - morphism , this section can be read independently .","summary":"we show that py - calabi quasi - morphism on the group of hamiltonian diffeomorphisms of surfaces of higher genus gives rise to a quasi - state .","abstract":"we show that py - calabi quasi - morphism on the group of hamiltonian diffeomorphisms of surfaces of higher genus gives rise to a quasi - state ."}
{"article_id":"1603.06366","section_id":"i","document":"the study of multi - component nonlinear waves is one of the fascinating topics which has potential applications in bose - einstein condensates ( becs ) in atomic physics @xcite and optial fibers in nonlinear optics @xcite . the realization of becs in weakly interacting atomic gases has strongly stimulated a large number of studies on exploring nonlinear properties of matter waves such as envelope solitons , gap solitons , soliton chains and so on @xcite . the development in trapping techniques for becs has allowed experimentalists to simulataneously confine atomic clouds in different hyperfine spin states or different atomic species . the first experiment involving interaction between multiple - species becs was performed in rubidium atoms which demonstrated the possibility of producing long - lived multiple condensate systems @xcite . in particular , the experimental demonstration of trapped multi - species becs have spurred great excitement in atomic physics and stimulated interest in studying various properties of two - component becs @xcite . a mixture of becs can be produced experimentally by simultaneously trapping atoms in different hyperfine states or two isotopes of the same element or of different species @xcite . recent experimental observations have also shown that the dark - bright and dark - dark vector solitons can be formed in certain two - species trapped dilute - gas becs @xcite . in contrast to the single - component case , such multicomponent condensates can present novel and fundamentally different scenarios for the collective dynamics and coherent structures due to the intercomponent interactions .    rogue waves ( rws ) are random nonlinear waves which occasionally rise up in the ocean which can attain amplitudes more than twice the value of background wave field @xcite . they appear from nowhere and disappear without a trace @xcite . rws were also noticed in a variety of physical systems such as optical fibers @xcite , superfluids @xcite and capillary waves @xcite . it was observed that modulational instability @xcite is responsible for the sudden rise in the wave amplitude in the ocean @xcite . recently , higher order rational solutions have been shown to attain even higher amplitudes of wave in the description of the rw phenomenon @xcite . on the other hand , there has been a number of studies committed to rws in coupled nonlinear schrdinger equations ( cnlse ) . the cnlse also models water wave interactions @xcite and wave propagation in fiber communication system @xcite . the exact analytical rw solutions of the cnlse ( integrable manakov case ) @xcite and its generalized version have been presented in @xcite . further , becs have also been shown to constitute a good platform to explore the rws which allow one to understand deeply the nature and dynamics of rws under laboratory conditions . the possibility of identifying vector rws in multi - component becs provides us a rich phenomenology of nonlinear wave structures . serkin et al . have considered the nonautonomous scalar nls equation with linear and harmonic oscillator potentials and explored many specific features of the non - autonomous solitons @xcite . followed by this study , some further interesting studies of the nonautonomous nls models with external potentials have also been made @xcite . several works have been exclusively devoted to construct soliton , rw and breather solutions of one - component becs @xcite and a few studies have been made to identify the vector soliton and rw solutions of two coupled gross - pitaevskii equation ( gpe ) @xcite . dynamical evolutions of vector solitons and rws have been investigated through managing related physical variables , see refs . @xcite . very recently , babu mareeswaran et al . @xcite have studied the interaction of the rw with a dark - bright boomeranic soliton of a two - component variant of the nls equation of relevance to both atomic becs and nonlinear optics . furthermore , they have also examined the robustness of these structures in direct numerical simulation of the original nonautonomous system . in this paper , we focus our attention to study the characteristics of vector localized matter waves in two and three - component becs with a cigar - shaped trap . in this work , we first contruct several possible vector localized solutions for two - component becs , which can be described by a set of two coupled gpes with time - dependent scattering length ( which is the nonlinearity parameter ) and external trap potential . to capture localized solutions of this model we map the time - dependent two coupled gpes onto the coupled nlses through the similarity transformation method with an integrability condition between the time - dependent scattering length and the external trap potential . in particular , we consider three different forms of traps , namely ( i ) time - independent expulsive trap , ( ii ) time - dependent monotonic trap , and ( iii ) time - dependent periodic trap . we identify the possibility of vector localized solutions , namely rws , dark soliton - rw , bright soliton - rw and rw - breather - like structures depending upon the specific values of a particular parameter in the obtained solutions . we then investigate in detail how the nature of these localized density profiles gets modifed by adjusting the trap parameter . we depict and analyze the trajectories of the nonautonomous vector rws . we also construct the dark - dark rw solution for repulsive - repulsive interaction of the two coupled gpes and investigate their dynamical evolution when we tune the strength of the trap parameter . in the time - independent trap case our results show that for low values of the trap parameter the vector localized structures are more stable , due to their prolonged existence with respect to time . by increasing the trap parameter , the localized structures become more and more localized in time , that is localized structures are short - lived , whereas they get stretched or more delocalized in space in a constant density background . in the time - dependent monotonic trap case with high value of the trap parameter , we could not observe any localized structures while @xmath0 because of the form of the nature of potential . finally , by replacing the monotonic trap with the periodic trap potential , the localized structures exist on a periodic background when the trap parameter is tuned . one can also observe that the localized waves lose their stability by way of getting delocalized in space as the potential strength is increased slowly . while no rigorous quantitative criteria can be identified to locate the point of instability , this can be checked numerically in the original nonautonomous system . we then construct composite rw solutions for three - component becs which are described by a coupled set of three gpes with variable scattering length and external trap potential . again , we transform the time - dependent three coupled gpes to the three coupled nls equations under the integrability condition through similarity transformation method . in ref . @xcite , the authors restrict the parameter values in the obtained generalized rw solutions and discuss the feasibility of single , two and three composite rws for three - component nls systems . they in fact report that the rw solution exhibits a peculiar structure , namely a four - petaled structure , in contrast to the eye - shaped structure of rw . motivated by this work , we construct the rw ( single , two and three composite rw ) solutions and analyze how to control these localized density profiles in three - component becs . furthermore we investigate the characteristics of these localized density profiles when we tune the strength of the trap parameter in the above trap potentials . our results show that in the case of time - independent trap potential the rw structures maintain their stability when the trap parameter is small and the rw structures become more and more localized in time and stretched ( delocalized ) in space when we increase the trap parameter . next we consider the case of time - dependent monotonic trap , and here also we note that the rw structures are more localized in time , delocalized in space and reach the higher density background . finally , in the time - dependent periodic trap case , we observe that the rw structures exist on a periodic background when we adjust the trap parameter . the paper is organized as follows . in sec . ii , we present the mean - field model for the two - component becs , map the quasi - one - dimensional two coupled gpes to the coupled nlses by using the similarity transformation technique which is subjected to a constraint on the forms of the time - dependent scattering length and the external trap potential and obtain the general form of vector rw solutions . the obtained rw solutions can contribute to control the vector localized structures in two - component becs . in sec . iii , we identify different vector localized structures , namely rws , dark soliton - rw , bright soliton - rw and rw - breather - like waves for different parameteric values and examine their dynamical evolutions in a constant background when we tune the strength of the trap parameter in the time - independent and time - dependent monotonic traps as well as the time - dependent periodic trap . in sec . iv , we investigate the trajectories of the nonautonomous rws . in sec . v , we construct the dark - dark rw solution for repulsive - repulsive interaction of two - component becs and analyze the associated characteristics for the above three different kinds of traps . in sec . vi , we consider the mean - field model for the three - component becs and map the quasi - one - dimensional time - dependent three coupled gpes to a system of three coupled nlses again by using the similarity transformation method . we construct the rw solutions of the three coupled gpes by considering the different kinds of traps the obtained rw solutions contribute to control and to understand localized density profiles in three - component becs . we illustrate how the localized density profiles such as the single , two and three compoite rws deform in a constant background when we adjust the trap parameter . finally , in sec . vii , we present a summary of the results and conclusions .","summary":"we analyze vector localized solutions of two - component bose - einstein condensates ( becs ) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled gross - pitaevskii equations into a pair of coupled nonlinear schrdinger equations with constant coefficients under a specific integrability condition . in this analysis we consider three different types of external trap potentials : a time - independent trap , a time - dependent monotonic trap , and a time - dependent periodic trap . we point out the existence of different interesting localized structures , namely rogue waves , dark - and bright soliton - rogue wave , and rogue wave - breather - like wave for the above three cases of trap potentials . we show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter . further we investigate the nature of the trajectories of the nonautonomous rogue waves . we also construct the dark - dark rogue wave solution for repulsive - repulsive interaction of two - component becs and analyze the associated characteristics for the three different kinds of traps . we then deduce single , two and three composite rogue waves for three component becs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials .","abstract":"we analyze vector localized solutions of two - component bose - einstein condensates ( becs ) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled gross - pitaevskii equations into a pair of coupled nonlinear schrdinger equations with constant coefficients under a specific integrability condition . in this analysis we consider three different types of external trap potentials : a time - independent trap , a time - dependent monotonic trap , and a time - dependent periodic trap . we point out the existence of different interesting localized structures , namely rogue waves , dark - and bright soliton - rogue wave , and rogue wave - breather - like wave for the above three cases of trap potentials . we show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter . further we investigate the nature of the trajectories of the nonautonomous rogue waves . we also construct the dark - dark rogue wave solution for repulsive - repulsive interaction of two - component becs and analyze the associated characteristics for the three different kinds of traps . we then deduce single , two and three composite rogue waves for three component becs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials ."}
{"article_id":"0904.3388","section_id":"c","document":"in conclusion we presented a versatile scheme for the calculation of optical properties of correlated materials . geared at the use with a localized basis set , we devised a realistic extension of the peierls substitution approach . moreover , we developed means to incorporate transitions that involve high energy orbitals that were downfolded in the many - body treatment of the electronic structure . as an application , we evaluated the optical conductivity of 2  for both , the metallic and the insulating phase . while the metal is characterized by a rather isotropic response , the insulator revealed a noticeable polarization dependence . the agreement with experiments is overall satisfying . the high energy conductivity is reasonably described when using the lda band - structure for high lying orbitals . the lda+cdmft many - body calculation for the 2gorbitals correctly describes the low - energy behavior . in the rutile phase it accounts for life - time effects within the 2 g  orbitals and therewith also for the damping of oxygen to 2 g  transitions with respect to lda results . in the insulator , it allowed for a genuine reproduction of the experimental 2 g  response , capturing in particular the polarization dependence over a wide energy range . the congruity of experiment and theory for the 2 g  spectral weight can be interpreted as corroborating the validity of the underlying many - body calculation for the electronic structure along with its interpretation . the authors gratefully acknowledge discussions with l. baldassarre , n. bontemps , a. georges , k. haule , h. j. kim , g. kotliar , a.  i. lichtenstein , r. lobo , a.  i. poteryaev , m.  m. qazilbash , g. sangiovanni , and a. toschi . this work was supported by idris , orsay , under project no . 091393 , and the french anr under project correlmat .","summary":"the aim of the present paper is to present a versatile scheme for the computation of optical properties of solids , with particular emphasis on realistic many - body calculations for correlated materials . geared at the use with localized basis sets , we extend the commonly known lattice `` peierls substitution '' approach to the case of multi - atomic unit cells . we further devise an upfolding scheme to incorporate optical transitions , that involve high energy orbitals that had been downfolded in the underlying many - body calculation of the electronic structure . as an application of the scheme , we present results on a material of longstanding interest , vanadium dioxide , vo . using dynamical mean - field data of both , the metallic and the insulating phase","abstract":"the aim of the present paper is to present a versatile scheme for the computation of optical properties of solids , with particular emphasis on realistic many - body calculations for correlated materials . geared at the use with localized basis sets , we extend the commonly known lattice `` peierls substitution '' approach to the case of multi - atomic unit cells . we show in how far this generalization can be deployed as an approximation to the full fermi velocity matrix elements that enter the continuum description of the response of a solid to incident light . we further devise an upfolding scheme to incorporate optical transitions , that involve high energy orbitals that had been downfolded in the underlying many - body calculation of the electronic structure . as an application of the scheme , we present results on a material of longstanding interest , vanadium dioxide , vo . using dynamical mean - field data of both , the metallic and the insulating phase , we calculate the corresponding optical conductivities , elucidate optical transitions and find good agreement with experimental results ."}
{"article_id":"1402.0113","section_id":"i","document":"in this paper we study the behaviour near the origin of @xmath0 positive solutions @xmath1 and @xmath2 of the system @xmath16 where @xmath4 are continuous functions . more precisely , we consider the following question .    * question 1*. for which continuous functions @xmath17 do there exist continuous functions @xmath18 such that all @xmath0 positive solutions @xmath1 and @xmath2 of the system satisfy @xmath19 @xmath20 and what are the optimal such @xmath21 and @xmath22 when they exist ?    we call a function @xmath21 ( resp . @xmath22 ) with the above properties a pointwise bound for @xmath23 ( resp . @xmath24 ) as @xmath25 . question 1 is motivated by the results on the single semilinear inequality @xmath26 and its higher order version @xmath27 which are discussed in @xcite .    although the literature on semilinear elliptic systems is quite extensive , very little of it deals with semilinear inequalities . we mention the work of bidaut - vron and grillot @xcite in which the following coupled inequalities are studied : @xmath28 and @xmath29 another related system of semilinear elliptic inequalities appears in @xcite ( see also @xcite ) and contains as a particular case the model @xmath30 our system ( 1.1 ) is different in nature from , and and its investigation completes the general picture of semilinear elliptic systems of inequalities . in particular ( see theorem 3.7 ) , we will obtain pointwise bounds for positive solutions of the system @xmath31 which complement the studies of systems , or . [ rem1 ] let @xmath32 since @xmath33 is positive and harmonic in @xmath34 , the functions @xmath35 are always positive solutions of . hence , any pointwise bound for positive solutions of must be at least as large as @xmath36 and whenever @xmath36 is such a bound for @xmath23 ( resp . @xmath24 ) it is necessarily optimal . in this case we say that @xmath23 ( resp . @xmath24 ) is _ harmonically bounded _ at @xmath37 . we shall see that whenever a pointwise bound for positive solutions of exists , then @xmath23 or @xmath24 ( or both ) are harmonically bounded at 0 . our results reveal the fact that the optimal conditions for the existence of pointwise bounds for positive solutions of are related to the growth at infinity of the nonlinearities @xmath5 and @xmath6 . in dimension @xmath8 we prove that pointwise bounds exist if @xmath38 or @xmath10 grow at most linearly at infinity ( see theorems [ thm2.1 ] , [ thm2.2 ] and [ thm2.3 ] ) . in dimensions @xmath39 we will assume that @xmath5 and @xmath6 have a power type growth at infinity , namely @xmath40 @xmath41 with @xmath15 . in this setting , we will find ( see theorem [ thm3.4 ] ) that no pointwise bounds exist if the pair @xmath42 lies above the curve @xmath43 on the other hand , if @xmath42 lies below the curve then pointwise bounds for positive solutions of always exist and their optimal estimates depend on new subregions in the @xmath44 plane ( see theorems [ thm3.1 ] , [ thm3.2 ] , [ thm3.3 ] and [ thm3.4 ] ) . we note that the curve lies below the sobolev hyperbola @xmath45 which separates the regions of existence and nonexistence for lane - emden systems : @xmath46 ( see @xcite ) . our analysis of combines the brezis - lions representation formula for superharmonic functions ( see appendix [ seca ] ) , a moser type interation ( see lemma [ lem4.6 ] ) , and certain pointwise estimates ( see corollary [ cor1 ] ) for the nonlinear potential @xmath47 , @xmath48 , where @xmath49 is the newtonian potential operator over a ball in @xmath50 , @xmath51 , and @xmath6 is a nonnegative bounded function . section [ nonlin ] in this work is concerned with various pointwise and integral estimates of nonlinear potentials of havin - mazya type and their connections with wolff potentials . since the results in this section may be of independent interest , we state them in greater generality than is needed for our study of the system .    in any dimension @xmath52 , we prove that our pointwise bounds for positive solutions of are optimal . when these bounds are not given by @xmath36 , their optimality follows by constructing ( with the help of lemma [ lem4.1 ] ) solutions @xmath23 and @xmath24 of satisfying suitable coupled conditions on the union of a countable number of balls which cluster at the origin and are harmonic outside these balls . in this case , it is interesting to point out that although our optimal pointwise bounds are radially symmetric functions , these bounds are not achieved by radial solutions of , because nonnegative radial superharmonic functions in a punctured neighborhood of the origin are harmonically bounded as @xmath53 . we also consider the following analog of question 1 when the singularity is at @xmath7 instead of at the origin .    * question 2*. for which continuous functions @xmath17 do there exist continuous functions @xmath54 such that all @xmath0 positive solutions @xmath1 and @xmath2 of the system @xmath55 satisfy @xmath56 @xmath57 and what are the optimal such @xmath21 and @xmath22 when they exist ?    this paper is organized as follows . in sections [ sec2 ] and [ sec3 ] we state our main results in dimensions @xmath8 and @xmath39 respectively . in section [ nonlin ] we obtain , using hedberg inequalities and wolff potential estimates , some new pointwise and integral bounds for nonlinear potentials of havin - mazya type . using these estimates , we collect in section [ sec4 ] some preliminary lemmas while sections [ sec5 ] and [ sec6 ] contain the proofs of our main results .","summary":"we study the behavior near the origin of positive solutions and of the system where are continuous functions . we provide optimal conditions on and at such that solutions of this system satisfy pointwise bounds near the origin . in dimension  we show that this property holds if or grow at most linearly at infinity . in dimension  and under the assumption , as , ( ) , we obtain a new critical curve that optimally describes the existence of such pointwise bounds . our approach relies in part on sharp estimates of nonlinear potentials which appear naturally in this context .    _ keywords _ : pointwise bound ; semilinear elliptic system ; isolated singularity ; nonlinear potential estimate .","abstract":"we study the behavior near the origin of positive solutions and of the system where are continuous functions . we provide optimal conditions on and at such that solutions of this system satisfy pointwise bounds near the origin . in dimension  we show that this property holds if or grow at most linearly at infinity . in dimension  and under the assumption , as , ( ) , we obtain a new critical curve that optimally describes the existence of such pointwise bounds . our approach relies in part on sharp estimates of nonlinear potentials which appear naturally in this context .    _ keywords _ : pointwise bound ; semilinear elliptic system ; isolated singularity ; nonlinear potential estimate ."}
{"article_id":"hep-ph0304027","section_id":"i","document":"the exploration of cp violation through studies of @xmath19-meson decays is one of the most exciting topics of present particle physics phenomenology , the main goal being to perform stringent tests of the kobayashi  maskawa mechanism @xcite . here the central target is the unitarity triangle of the cabibbo  maskawa ( ckm ) matrix , with its angles @xmath20 , @xmath21 and @xmath4 ( for a detailed review , see @xcite ) . thanks to the efforts of the babar ( slac ) and belle ( kek ) collaborations , cp violation could recently be established in the neutral @xmath22-meson system with the help of @xmath23 and similar decays @xcite . these modes allow us to determine @xmath24 , where the present world average is given by @xmath25 @xcite , implying the twofold solution @xmath26 for the @xmath27@xmath28 mixing phase @xmath29 , which equals @xmath30 in the standard model . here the former solution would be in perfect agreement with the `` indirect '' range following from the standard - model `` ckm fits '' , @xmath31 @xcite , whereas the latter would correspond to new physics @xcite . measuring the sign of @xmath32 , the two solutions can be distinguished . several strategies to accomplish this important task were proposed @xcite ; an analysis using the time - dependent angular distribution of the decay products of @xmath33 k^\\ast[\\to\\pi^0k_{\\rm s}]$ ] @xcite is already in progress at the @xmath19 factories @xcite . = 4.4truecm = 4.4truecm    an important ingredient for the testing of the kobayashi  maskawa picture is provided by transitions of the kind @xmath34  @xcite and @xmath35  @xcite , allowing theoretically clean determinations of the weak phases @xmath16 and @xmath3 , respectively , where @xmath36 is the @xmath37-meson counterpart of @xmath29 , which is negligibly small in the standard model . it is convenient to write these decays generically as @xmath38 , so that we may easily distinguish between the following cases :    * @xmath39 : @xmath40 , @xmath41 , * @xmath42 : @xmath43 , @xmath44 .    in the discussion given below , we shall only consider @xmath38 decays , where at least one of the @xmath45 , @xmath46 states is a pseudoscalar meson . in the opposite case , for example the @xmath47 decay , the extraction of weak phases would require a complicated angular analysis @xcite@xcite . if we look at fig . [ fig : bqdu ] , we observe that @xmath38 originates from colour - allowed tree - diagram - like topologies , and that also a @xmath6 meson may decay into the same final state @xmath48 . the latter feature leads to interference effects between @xmath5@xmath6 mixing and decay processes , allowing the extraction of @xmath12 with an eightfold discrete ambiguity . since @xmath7 can be straightforwardly fixed separately @xcite , we may determine the angle @xmath4 of the unitarity triangle from this cp - violating weak phase .    in section  [ sec : ampl - obs ] , we focus on the @xmath49 decay amplitudes and rate asymmetries , and investigate the relevant hadronic parameters with the help of `` factorization '' . in this section , we shall also point out that a subtle factor @xmath9 arises in the expressions for the mixing - induced observables , where @xmath10 denotes the angular momentum of the @xmath48 system , and show explicitly the cancellation of phase - convention - dependent parameters within the factorization approach . after discussing the `` conventional '' extraction of @xmath12 and the associated multiple discrete ambiguities in section  [ sec : conv ] , we emphasize the usefulness of `` untagged '' rate measurements for efficient determinations of weak phases from @xmath49 decays in section  [ sec : untagged ] , and suggest several novel strategies . in section  [ sec : bounds ] , we then derive bounds on @xmath12 , and illustrate their potential power with the help of a few numerical examples . in section  [ sec : comb ] , we propose a _ combined _ analysis of @xmath50 and @xmath51 modes , which has important advantages with respect to the conventional separate determinations of @xmath16 and @xmath3 , offering various attractive new avenues to extract @xmath4 in an essentially unambiguous manner and to obtain valuable insights into hadron dynamics . finally , we conclude in section  [ sec : concl ] .","summary":"moreover , we emphasize that `` untagged '' rates are an important ingredient for efficient determinations of weak phases , not only in the presence of a sizeable width difference ; should be sizeable , the combination of `` untagged '' with `` tagged ''  observables provides an elegant and _ unambiguous _ extraction of , whereas the `` conventional '' determination of is affected by an eightfold discrete ambiguity . finally , we propose a _ combined _ analysis of  and  modes , which has important advantages , offering various interesting new strategies to extract in an essentially unambiguous manner .   ","abstract":"decays of the kind  and  allow us to probe and , respectively , involving the angle of the unitarity triangle and the mixing phases ( ) . analysing these modes in a phase - convention - independent way , we find that their mixing - induced observables are affected by a subtle factor , where denotes the angular momentum of the decay products , and derive bounds on . moreover , we emphasize that `` untagged '' rates are an important ingredient for efficient determinations of weak phases , not only in the presence of a sizeable width difference ; should be sizeable , the combination of `` untagged '' with `` tagged ''  observables provides an elegant and _ unambiguous _ extraction of , whereas the `` conventional '' determination of is affected by an eightfold discrete ambiguity . finally , we propose a _ combined _ analysis of  and  modes , which has important advantages , offering various interesting new strategies to extract in an essentially unambiguous manner .    cern - th/2003 - 084 + hep - ph/0304027    * new strategies to obtain insights into cp violation through +  and  decays *    robert fleischer + _ theory division , cern , ch-1211 geneva 23 , switzerland _    cern - th/2003 - 084 + april 2003"}
{"article_id":"hep-ph0304027","section_id":"c","document":"let us now summarize the main points of our analysis :    * we have shown that @xmath0   and @xmath18  decays can be described through the same set of formulae by just making straightforward replacements of variables . we have also pointed out that a factor of @xmath9 arises in the expressions for the mixing - induced observables . in the presence of a non - vanishing angular momentum @xmath10 of the @xmath11 decay products , this factor has properly to be taken into account in the determination of the sign of @xmath115 from @xmath112 . * should the width difference @xmath14 be sizeable , the combination of the `` tagged '' mixing - induced observables @xmath217 with their `` untagged '' counterparts @xmath411 offers an elegant determination of @xmath15 in an essentially unambiguous manner , which does not require knowledge of @xmath162 . another important aspect of untagged rate measurements is the efficient determination of the hadronic parameters @xmath174 . to accomplish this task , we may apply various untagged strategies , which do not rely on a sizeable value of @xmath13 . * we have derived bounds on @xmath12 , which can straightforwardly be obtained from the mixing - induced @xmath49 observables , and provide essentially the same information as the `` conventional '' determination of @xmath12 , which suffers from multiple discrete ambiguities . giving a few examples , we have illustrated the potential power of these constraints , and have seen that stringent bounds on @xmath4 may be obtained through a _ combined _ study of @xmath228 and @xmath339 modes . * if we perform a simultaneous analysis of @xmath349-spin - related decays , for example of the @xmath282 , @xmath250 system , we may follow various attractive avenues to determine @xmath4 from the corresponding mixing - induced observables @xmath412 . the differences between these methods are due to different implementations of the @xmath349-spin relations for the hadronic parameters @xmath413 and @xmath285 . for example , we may extract @xmath4 by assuming @xmath369 or @xmath359 . in comparison with the conventional @xmath49 approaches , the most important advantage of these strategies  apart from features related to discrete ambiguities  is that @xmath163 does not have to be fixed , and that @xmath162 may only enter through @xmath284 , i.e.  a moderate correction , which can straightforwardly be included through untagged @xmath37 rate measurements ; an accurate determination of @xmath163 and @xmath162 would only be interesting for the inclusion of @xmath349-spin - breaking corrections to @xmath169 . after various steps of refinement , we would eventually arrive at an unambiguous , theoretically clean value of @xmath4 , and could also obtain  as a by - product  valuable insights into @xmath349-spin - breaking effects . since @xmath338 modes will be accessible in the era of the lhc , in particular at lhcb , we strongly encourage a simultaneous analysis of @xmath37 and @xmath22 modes  especially of @xmath349-spin - related decay pairs  to fully exploit their very interesting physics potential . m. kobayashi and t. maskawa , _ prog . phys . _  * 49 * ( 1973 ) 652 . r. fleischer , _ phys . _  * 370 * ( 2002 ) 537 . babar collaboration ( b. aubert _ et al . _ ) , _ phys .  rev . lett . _  * 87 * ( 2001 ) 091801 ; + belle collaboration ( k. abe _ _ ) , _ phys .  rev . lett . _  * 87 * ( 2001 ) 091802 . y. nir , wis-35 - 02-dpp [ hep - ph/0208080 ] . buras , tum - hep-435 - 01 [ hep - ph/0109197 ] ; 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( b. aubert _ et al . _ ) , babar - conf-03 - 015 [ hep - ex/0307036 ] . e. jenkins and m.j . savage , _ phys . _  * b281 * ( 1992 ) 331 . b. grinstein , e. jenkins , a.v . manohar , m.j . savage and m.b . wise , _ nucl . _  * b380 * ( 1992 ) 369 . ukqcd collaboration ( k.c . _ ) , _ nucl _  * b619 * ( 2001 ) 507 . p. ball and v.m . braun , _ phys . _  * d58 * ( 1998 ) 094016 . r. fleischer , _ eur . j. _  * c10 * ( 1999 ) 299 ; + m. gronau and j.l . rosner , _ phys . _  * b482 * ( 2000 ) 71 ; + p.z . skands , _ jhep _ * 0101 * ( 2001 ) 008 . r. fleischer , _ phys . _  * b459 * ( 1999 ) 306 .","summary":"cern - th/2003 - 084 + hep - ph/0304027    * new strategies to obtain insights into cp violation through +  and  decays *    robert fleischer + _ theory division , cern , ch-1211 geneva 23 , switzerland _    cern - th/2003 - 084 + april 2003","abstract":"decays of the kind  and  allow us to probe and , respectively , involving the angle of the unitarity triangle and the mixing phases ( ) . analysing these modes in a phase - convention - independent way , we find that their mixing - induced observables are affected by a subtle factor , where denotes the angular momentum of the decay products , and derive bounds on . moreover , we emphasize that `` untagged '' rates are an important ingredient for efficient determinations of weak phases , not only in the presence of a sizeable width difference ; should be sizeable , the combination of `` untagged '' with `` tagged ''  observables provides an elegant and _ unambiguous _ extraction of , whereas the `` conventional '' determination of is affected by an eightfold discrete ambiguity . finally , we propose a _ combined _ analysis of  and  modes , which has important advantages , offering various interesting new strategies to extract in an essentially unambiguous manner .    cern - th/2003 - 084 + hep - ph/0304027    * new strategies to obtain insights into cp violation through +  and  decays *    robert fleischer + _ theory division , cern , ch-1211 geneva 23 , switzerland _    cern - th/2003 - 084 + april 2003"}
{"article_id":"1309.4099","section_id":"i","document":"in the thermal steady - state model for neutral hydrogen ( hi ) in the galactic interstellar medium ( ism ) , two distinct stable phases coexist in pressure equilibrium ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these are ( 1 )  a cold phase ( the cold neutral medium , cnm ) , with high density ( @xmath3 @xmath4 ) and a high hi-21 cm  optical depth that gives rise to the narrow absorption features seen towards continuum radio sources , and ( 2 )  a warm diffuse phase ( the warm neutral medium , wnm ) with low density ( @xmath5 @xmath4 ) , which contributes to the hi  emission , but is extremely difficult to detect in absorption due to its low optical depth . the models ( e.g. * ? ? ? * ) find that gas in the stable cnm phase would have kinetic temperatures @xmath6 k , while gas in the stable wnm phase would have kinetic temperatures of @xmath7k . over the last few decades , a number of hi-21 cm  studies have established that the ism indeed contains cold atomic gas in the temperature range @xmath8k , consistent with theoretical expectations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? however , observational estimates of wnm temperature are quite rare @xcite and very little is as yet known about physical conditions in the wnm .    in the two - phase models , hi  at intermediate temperatures is unstable and such gas is expected to quickly evolve into one of the stable phases . gas at intermediate temperatures is thus expected to exist `` only as a transient phenomenon '' @xcite . the thermal timescale derived from the heating or cooling rates is @xmath9  yr for the cnm , and about @xmath10 times larger for the wnm @xcite . on the other hand , the timescale between physical disturbances in the ism ( i.e. the typical time interval between significant pressure fluctuations ) due to the propagation of supernova shocks is @xmath11  yr @xcite . thus , while the cnm can be assumed to be in the thermal steady state , equilibrium conditions may not prevail in the wnm . however , @xcite argue that physical conditions in the wnm will evolve towards the steady state , and the steady state conditions could be thought to `` represent an average of the conditions to be expected in the actual wnm '' . recently , there have been suggestions , based both on hi-21 cm  observations and simulations , that a significant fraction of the galactic hi  may have kinetic temperatures in the unstable range , @xmath12 k @xcite . numerical simulations of the ism suggest that dynamical processes like turbulence may drive hi  from the stable cnm or wnm phases to the thermally unstable phase ( e.g. * ? ? ? * ; * ? ? ? this could result in significant amounts of unstable neutral gas , unlike the case of the standard two - phase models . observational evidence for the presence of unstable gas stems from the work of @xcite , who carried out high velocity resolution hi-21 cm  absorption and emission studies towards 79 compact radio sources with the arecibo telescope . they then modelled the hi-21 cm  absorption and emission spectra as the sum of thermally - broadened gaussian components to estimate the kinetic temperature and fraction of gas in the different temperature phases . the unstable phase was found to make up nearly 50% of the hi  along their sightlines @xcite . however , the single - dish spectra used in their analysis are subject to large systematic effects , both due to contamination from stray radiation coming through the large sidelobes of the arecibo telescope and the fact that single - dish hi-21 cm  absorption spectra must be corrected for the hi  emission in the beam . the sidelobe contamination in the emission spectra is especially important here , because the results pertaining to gas in the unstable phase were based on the fits to the emission spectra . conversely , @xcite carried out high velocity resolution _ cm  absorption studies along two sightlines using the australia telescope compact array ( atca ) , with multi - gaussian fits to the absorption spectra alone [ see also @xcite and @xcite for a similar approach in damped lyman-@xmath13 systems ] . @xcite found that a significant fraction of gas is in the thermally unstable phase ; however the sample was small , with only two lines of sight . such deep interferometric observations allow the possibility of obtaining an `` clean '' determination of the hi-21 cm  absorption profile , by resolving out the hi-21 cm  emission , and thus , of directly detecting the wnm in absorption . we have recently begun a large observational program to probe neutral atomic gas in the ism through interferometric hi-21 cm  absorption studies with the westerbork synthesis radio telescope ( wsrt ) and the giant metrewave radio telescope ( gmrt ) , following the approach of @xcite . the observations , data analysis , spectra and integrated properties for each of the 34 observed sightlines were presented by ( * ? ? ? * hereafter , paper i ) . in this paper , we describe the multi - gaussian parametrisation of the 33 absorption spectra with detected hi-21 cm  absorption , including the two atca targets of @xcite , and their implications for physical conditions in the interstellar medium .","summary":"we discuss physical conditions in galactic neutral hydrogen based on deep , high velocity resolution interferometric hi 21 cm absorption spectroscopy towards 33 compact extra - galactic radio sources . [ firstpage ]    ism : atoms  ism : general  ism : kinematics and dynamics  ism : structures  radio lines : ism","abstract":"we discuss physical conditions in galactic neutral hydrogen based on deep , high velocity resolution interferometric hi 21 cm absorption spectroscopy towards 33 compact extra - galactic radio sources . the hi 21 cm optical depth spectra have root - mean - square noise values per 1  km  s velocity channel , i.e. , sufficiently sensitive to detect hi 21 cm absorption by the warm neutral medium ( wnm ) . comparing these spectra with hi 21 cm emission spectra from the leiden - argentine - bonn ( lab ) survey , we show that some of the absorption detected on most sightlines must arise in gas with temperatures higher than that in the stable cold neutral medium ( cnm ) . a multi - gaussian decomposition of 30 of the hi 21 cm absorption spectra yielded very few components with line widths in the temperature range of stable wnm , with no such wnm components detected for sixteen of the thirty sightlines . we find that some of the detected hi 21 cm absorption along thirteen of these sightlines must arise in gas with spin temperatures larger than the cnm range . for these sightlines , we use very conservative estimates of the cnm spin temperature and the non - thermal broadening to derive strict upper limits to the gas column densities in the cnm and wnm phases . comparing these upper limits to the total hi column density , we find that typically at least 28% of the gas must have temperatures in the thermally unstable range (  k ) . our observations hence robustly indicate that a significant fraction of the gas in the galactic interstellar medium has temperatures outside the ranges expected for thermally stable gas in two - phase models .    [ firstpage ]    ism : atoms  ism : general  ism : kinematics and dynamics  ism : structures  radio lines : ism"}
{"article_id":"1309.4099","section_id":"c","document":"we have studied the temperature distribution of the neutral interstellar medium along 33 galactic sightlines , using deep , high velocity resolution ( @xmath39  kms@xmath1 ) hi-21 cm  absorption spectra obtained with the wsrt , the gmrt and the atca . the typical rms optical depth noise of the spectra is @xmath0 per 1  kms@xmath1  velocity channel , making the spectra sufficiently sensitive to detect hi-21 cm  absorption from gas in the warm neutral medium , with hi  column densities @xmath81@xmath34 and velocity widths comparable to the thermal width .    we used conservative assumptions regarding the cnm spin temperature ( @xmath82  k ) , the wnm spin temperature ( @xmath48  k ) and non - thermal broadening of the wnm ( line fwhm  @xmath54 ) to consider the canonical two - phase model of the ism wherein the hi-21 cm  absorption features arise in the cnm , while the emission profiles contain contributions from both stable cnm and wnm . we find that such a model can be ruled out for more than half our sightlines . some of the hi-21 cm  absorption that we detect _ must _ arise from gas with spin temperatures larger than that of the cnm ( i.e. must arise in the wnm or with gas with temperatures in the thermally unstable range ) . we then used a multi - gaussian decomposition of 30 of the hi-21 cm  absorption spectra to examine the possibility that some galactic hi  might be in the unstable temperature range , @xmath56  k. we found very few components with doppler line widths consistent with values expected from stable or non - thermally broadened wnm . for sixteen sightlines , we found no hi-21 cm   absorption components with line widths consistent with an origin in the wnm . thirteen of the sixteen spectra are sufficiently sensitive to detect any wnm along the sightline even if extreme non - thermal broadening results in line fwhms comparable to the @xmath66 of the hi-21 cm  emission profile . we can thus rule out the possibility that the neutral hydrogen along these sixteen sightlines is in two phases , with temperatures in the stable cnm and wnm ranges . some fraction of the hi-21 cm  absorption that we detect on these sightlines must arise from gas with temperatures in the intermediate , thermally unstable range ( at @xmath51k  @xmath83k ) of the two - phase model . for the above thirteen sightlines , we obtain a median lower limit of @xmath84% to the gas fraction in this unstable phase . our observations hence robustly indicate that a significant fraction of the gas in the galactic ism has a temperature outside the thermally stable ranges in two - phase models .","summary":"the hi 21 cm optical depth spectra have root - mean - square noise values per 1  km  s velocity channel , i.e. , sufficiently sensitive to detect hi 21 cm absorption by the warm neutral medium ( wnm ) . comparing these spectra with hi 21 cm emission spectra from the leiden - argentine - bonn ( lab ) survey , we show that some of the absorption detected on most sightlines must arise in gas with temperatures higher than that in the stable cold neutral medium ( cnm ) . a multi - gaussian decomposition of 30 of the hi 21 cm absorption spectra yielded very few components with line widths in the temperature range of stable wnm , with no such wnm components detected for sixteen of the thirty sightlines . we find that some of the detected hi 21 cm absorption along thirteen of these sightlines must arise in gas with spin temperatures larger than the cnm range . our observations hence robustly indicate that a significant fraction of the gas in the galactic interstellar medium has temperatures outside the ranges expected for thermally stable gas in two - phase models .   ","abstract":"we discuss physical conditions in galactic neutral hydrogen based on deep , high velocity resolution interferometric hi 21 cm absorption spectroscopy towards 33 compact extra - galactic radio sources . the hi 21 cm optical depth spectra have root - mean - square noise values per 1  km  s velocity channel , i.e. , sufficiently sensitive to detect hi 21 cm absorption by the warm neutral medium ( wnm ) . comparing these spectra with hi 21 cm emission spectra from the leiden - argentine - bonn ( lab ) survey , we show that some of the absorption detected on most sightlines must arise in gas with temperatures higher than that in the stable cold neutral medium ( cnm ) . a multi - gaussian decomposition of 30 of the hi 21 cm absorption spectra yielded very few components with line widths in the temperature range of stable wnm , with no such wnm components detected for sixteen of the thirty sightlines . we find that some of the detected hi 21 cm absorption along thirteen of these sightlines must arise in gas with spin temperatures larger than the cnm range . for these sightlines , we use very conservative estimates of the cnm spin temperature and the non - thermal broadening to derive strict upper limits to the gas column densities in the cnm and wnm phases . comparing these upper limits to the total hi column density , we find that typically at least 28% of the gas must have temperatures in the thermally unstable range (  k ) . our observations hence robustly indicate that a significant fraction of the gas in the galactic interstellar medium has temperatures outside the ranges expected for thermally stable gas in two - phase models .    [ firstpage ]    ism : atoms  ism : general  ism : kinematics and dynamics  ism : structures  radio lines : ism"}
{"article_id":"1205.4795","section_id":"i","document":"the advent of modern technology makes it easier to collect massive , large - scale data - sets . a common feature of these data - sets is that the number of covariates greatly exceeds the number of observations , a regime opposite to conventional statistical settings . for example , portfolio allocation with hundreds of stocks in finance involves a covariance matrix of about tens of thousands of parameters , but the sample sizes are often only in the order of hundreds ( e.g. , daily data over a year period [ @xcite ] ) . genome - wide association studies in biology involve hundreds of thousands of single - nucleotide polymorphisms ( snps ) , but the available sample size is usually in hundreds , also . data - sets with large number of variables but relatively small sample size pose great unprecedented challenges and opportunities for statistical analysis . regularization methods have been widely used for high - dimensional variable selection [ @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ] . yet , most existing methods such as penalized least - squares or penalized likelihood [ @xcite ] are designed for light - tailed distributions . @xcite established the irrepresentability conditions for the model selection consistency of the lasso estimator . @xcite studied the oracle properties of nonconcave penalized likelihood estimators for fixed dimensionality . @xcite investigated the penalized least - squares estimator with folded - concave penalty functions in the ultra - high dimensional setting and established a nonasymptotic weak oracle property . @xcite proposed and investigated the sure independence screening method in the setting of light - tailed distributions . the robustness of the aforementioned methods have not yet been thoroughly studied and well understood . robust regularization methods such as the least absolute deviation ( lad ) regression and quantile regression have been used for variable selection in the case of fixed dimensionality . see , for example , @xcite , @xcite , @xcite , @xcite . the penalized composite likelihood method was proposed in @xcite for robust estimation in ultra - high dimensions with focus on the efficiency of the method . they still assumed sub - gaussian tails . @xcite studied the @xmath0-penalized quantile regression in high - dimensional sparse models where the dimensionality could be larger than the sample size . we refer to their method as robust lasso ( r - lasso ) . they showed that the r - lasso estimate is consistent at the near - oracle rate , and gave conditions under which the selected model includes the true model , and derived bounds on the size of the selected model , uniformly in a compact set of quantile indices . @xcite studied the @xmath0-penalized lad regression and showed that the estimate achieves near oracle risk performance with a nearly universal penalty parameter and established also a sure screening property for such an estimator . @xcite obtained bounds on the prediction error of a large class of @xmath0-penalized estimators , including quantile regression . @xcite considered the nonconvex penalized quantile regression in the ultra - high dimensional setting and showed that the oracle estimate belongs to the set of local minima of the nonconvex penalized quantile regression , under mild assumptions on the error distribution . in this paper , we introduce the penalized quantile regression with the weighted @xmath0-penalty ( wr - lasso ) for robust regularization , as in @xcite . the weights are introduced to reduce the bias problem induced by the penalty . the flexibility of the choice of the weights provides flexibility in shrinkage estimation of the regression coefficient . wr - lasso shares a similar spirit to the folded - concave penalized quantile - regression [ @xcite , @xcite ] , but avoids the nonconvex optimization problem . we establish conditions on the error distribution in order for the wr - lasso to successfully recover the true underlying sparse model with asymptotic probability one . it turns out that the required condition is much weaker than the sub - gaussian assumption in @xcite . the only conditions we impose is that the density function of error has lipschitz property in a neighborhood around 0 . this includes a large class of heavy - tailed distributions such as the stable distributions , including the cauchy distribution . it also covers the double exponential distribution whose density function is nondifferentiable at the origin .    unfortunately , because of the penalized nature of the estimator , wr - lasso estimate has a bias . in order to reduce the bias , the weights in wr - lasso need to be chosen adaptively according to the magnitudes of the unknown true regression coefficients , which makes the bias reduction infeasible for practical applications .    to make the bias reduction feasible , we introduce the adaptive robust lasso ( ar - lasso ) . the ar - lasso first runs r - lasso to obtain an initial estimate , and then computes the weight vector of the weighted @xmath0-penalty according to a decreasing function of the magnitude of the initial estimate . after that , ar - lasso runs wr - lasso with the computed weights . we formally establish the model selection oracle property of ar - lasso in the context of @xcite with no assumptions made on the tail distribution of the model error . in particular , the asymptotic normality of the ar - lasso is formally established . this paper is organized as follows . first , we introduce our robust estimators in section  [ secnotation ] . then , to demonstrate the advantages of our estimator , we show in section  [ seclasso ] with a simple example that lasso behaves suboptimally when noise has heavy tails . in section  [ secoracle ] , we study the performance of the oracle - assisted regularization estimator . then in section  [ secselection ] , we show that when the weights are adaptively chosen , wr - lasso has the model selection oracle property , and performs as well as the oracle - assisted regularization estimate . in section  [ secan ] , we prove the asymptotic normality of our proposed estimator . the feasible estimator , ar - lasso , is investigated in section  [ secpenalty ] . section  [ secsimul ] presents the results of the simulation studies . finally , in section  [ secproof ] , we present the proofs of the main theorems . additional proofs , as well as the results of a genome - wide association study , are provided in the supplementary appendix [ @xcite ] .","summary":"heavy - tailed high - dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis . a  natural procedure to address this problem is to use penalized regression with weighted-penalty , called weighted robust lasso , in which weights are introduced to ameliorate the bias problem induced by the-penalty . in the ultra - high dimensional setting , where the can grow exponentially with the sample size , we investigate the model selection oracle property and establish the asymptotic normality of the wr - lasso . we show that only mild conditions on the model error distribution are needed . this two - step procedure is justified theoretically to possess the oracle property and the asymptotic normality . numerical studies demonstrate the favorable finite - sample performance of the ar - lasso .    ,","abstract":"heavy - tailed high - dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis . a  natural procedure to address this problem is to use penalized regression with weighted-penalty , called weighted robust lasso , in which weights are introduced to ameliorate the bias problem induced by the-penalty . in the ultra - high dimensional setting , where the can grow exponentially with the sample size , we investigate the model selection oracle property and establish the asymptotic normality of the wr - lasso . we show that only mild conditions on the model error distribution are needed . our theoretical results also reveal that adaptive choice of the weight vector is essential for the wr - lasso to enjoy these nice asymptotic properties . to make the wr - lasso practically feasible , we propose a two - step procedure , called adaptive robust lasso ( ar - lasso ) , in which the weight vector in the second step is constructed based on the-penalized quantile regression estimate from the first step . this two - step procedure is justified theoretically to possess the oracle property and the asymptotic normality . numerical studies demonstrate the favorable finite - sample performance of the ar - lasso .    ,"}
{"article_id":"0710.2425","section_id":"i","document":"the primal initial - boundary value problem of elastoplasticity consists in determining the generalized deformation state of a material subject to external mechanical actions . in particular , starting from some initial state and for a given load and traction , one shall determine the displacement @xmath0 of the body from the reference configuration , the inelastic ( plastic ) part @xmath1 of its strain , and , possibly , a vector of internal hardening variables @xmath2 . in the small deformation regime and within the frame of associative elastoplasticity , the problem is classically formulated in a variational form as that of finding the absolutely continuous trajectory @xmath3 \\mapsto y(t ) \\in y$ ] ( @xmath4 is a banach space ) such that @xmath5 where @xmath6 stands for the vector of unknown fields , @xmath7 ( dual ) is linear , continuous , and symmetric , and @xmath8 $ ] is the positively @xmath9-homogeneous and convex dissipation potential ( @xmath10 is the classical subdifferential in the sense of convex analysis , see below ) . moreover , @xmath11\\to y^*$ ] is a given and suitably smooth generalized load ( possibly including surface tractions ) and @xmath12 represents the initial state . the reader is referred to section [ mechanical_model ] for some brief mechanical motivation as well as to the classical monographs by duvaut & lions @xcite , han & reddy @xcite , lemaitre & chaboche @xcite , and simo & hughes @xcite for a comprehensive collection of results . the aim of this paper is that of investigating a global - in - time variational formulation of problem . in particular , we shall introduce the functional @xmath13 $ ] on trajectories as @xmath14 where @xmath15 stands for the conjugate @xmath16 of @xmath17 and @xmath18 denotes the duality pairing between @xmath19 and @xmath4 . the starting point of this analysis relies on the fact that solutions of and minimizers of @xmath20 fulfilling the initial condition coincide , namely ( see theorem [ characterization ] ) @xmath21    this variational characterization has a clear mechanical interpretation . indeed , since @xmath17 is positively @xmath9-homogeneous , its conjugate @xmath15 turns out to be the indicator function of the convex set @xmath22 . hence , @xmath23 is actually a constrained minimization problem and we have @xmath24 where we have used the notation @xmath25 . the first relation above expresses the so - called _ local stability _ @xcite of the trajectory whereas the second is nothing but the energy balance at time @xmath26 . more precisely , @xmath27 denotes the complementary energy at time @xmath28 for the state @xmath29 , @xmath30 represents the dissipation of the system on @xmath31 $ ] , and @xmath32 is the work of external actions on @xmath31 $ ] . hence , minimizing @xmath20 consists in selecting the ( only ) stable trajectory which conserves the energy . in this regards , the reader is referred to the pioneering papers by moreau  @xcite . the interest of variational characterization of the differential problem relies on the possibility of exploiting the general tools from the calculus of variations . some care is however required . indeed , although @xmath20 is convex and lower semicontinuous with respect to the weak topology of @xmath33 , the functional generally fails to be coercive . moreover , one is not just asked to minimize @xmath20 but also to prove that the minimum is @xmath34 . this considerations suggest that the direct method is hardly applicable in order to get solutions to via the characterization in  . the first issue of this paper is instead that of showing that the variational principle in is particularly well - suited for discussing general approximation issues . since solutions and minimizers coincide , a natural tool in order to frame an abstract approach to limiting procedures within is that of considering the corresponding minimum problems via @xmath35-convergence @xcite . as the value of the functional is directly quantified to be @xmath34 on the minimizers , what is actually needed here for passing to limits are so - called @xmath36-@xmath37 inequalities only and the latter are generally easily available . we shall specifically focus on the case of linear hardening elastoplasticity and apply the above - mentioned perspective in order to recover in a unified and more transparent frame and partly generalize some convergence results for conformal finite elements ( thm . [ space_approx ] ) , time - discretizations ( thm . [ convergence_theta ] ) , and fully - discrete space - time approximations ( thm . [ s_t ] ) . in particular , for time - discretization we develop a discrete version of the variational principle in the same spirit of the theory of _ variational integrators _ @xcite ( see subsection [ discrete_principle ] ) . this connection entails also some generalized view at the classical discrete time - schemes ( see subsection [ discrete_scheme ] ) . a second novel point of the present variational approach consists in the possibility of exploiting @xmath20 in order to estimate a posteriori some approximation error . by letting @xmath38 , we will check that ( cor . [ unif_dist ] ) @xmath39}\\frac12{\\left\\langle}a(y - v),y - v { \\right\\rangle}\\leq { { \\mathcal f}}(v)\\quad \\forall v \\in w^{1,1}(0,t;y ) , \\ \\ v(0)=y_0.\\ ] ] if @xmath40 shows some coercivity ( which is precisely the case of linearized hardening , see subsection [ a_coerc ] ) , and @xmath41 is the outcome of some approximation procedure , the estimate above may serve as the basis for some a posteriori estimation procedure , possibly headed to adaptivity ( see subsection [ adaptivity ] ) . let us stress that the latter and entail that the distance of a ( stable ) trajectory from the solution to can be uniformly estimated by means of its energy production along the path .    the variational characterization in stems from a reinterpretation in the present elastoplastic frame of the celebrated principle by brezis & elekand @xcite for gradient flows of convex functionals . since its introduction , the latter principle has continuously attracted attention . in particular , it has been exploited in the direction of proving existence @xcite ( note that the above - mentioned obstructions to the application of the direct methods again appear ) and the description of long - time dynamics @xcite . moreover , the brezis - ekeland approach has been adapted to the case of second order @xcite and doubly nonlinear equations @xcite as well . one has to mention that , of course , is not the only possible global - in - time variational characterization of . besides minimizing the @xmath42 space - time norm of the residual ( which might be little interesting since the order of the problem is doubled ) , one has at least to mention visintin @xcite , where generalized solutions are obtained as minimal elements of a certain partial - order relation on the trajectories , and the recent contribution by mielke & ortiz @xcite where the functional @xmath43 is minimized among trajectories with @xmath44 . under extra - smoothness conditions on @xmath17 ( not fulfilled in the current frame ) , the euler - lagrange equations of the latter functional are @xmath45 in particular , minimizing the functional in consists in performing a suitable elliptic ( in time ) regularization of the problem . in the specific case of @xmath17 positively @xmath9-homogeneous , the limit @xmath46 can be carried out and the minimizers of the functional in are proved to converge to the solution of . the latter approach is quite different form that of . on the one hand , it is much more general as it naturally applies to the non - smooth case as well ( no derivatives of @xmath17 and @xmath47 are involved ) . on the other hand , it relies on an intermediate and somehow unphysical ( not causal ) @xmath48-regularized problem and ( besides existence ) it seems not directly suited for recovering the full extent of our approximation results for the specific case of problem .","summary":", the novel characterization allows to recover and partly extend some known results and proves itself to be especially well - suited for discussing general approximation and convergence issues .","abstract":"we present a variational principle governing the quasistatic evolution of a linearized elastoplastic material . in case of linear hardening , the novel characterization allows to recover and partly extend some known results and proves itself to be especially well - suited for discussing general approximation and convergence issues . in particular , the variational principle is exploited in order to prove in a novel setting the convergence of time and space - time discretizations as well as to provide some possible a posteriori error control ."}
{"article_id":"1208.3379","section_id":"i","document":"the measurement of heavy quark production provides a test of many aspect of qcd . a considerable progress in the qcd calculations for heavy - quark production has been done in the recent years . the theoretical results presented at this workshop are reviewed in section  [ sec : th ] . many new results have been presented on the production of heavy quarks from different types of collisions : deep inelastic scattering , photoproduction , @xmath2 and @xmath3 , and nuclear collisions ( pbpb , auau , cucu , dau ) . results on charm and beauty production are summarized in section  [ sec : cb ] . due to space constraints the results from heavy - ion collisions , which would deserve a dedicated summary , are not discussed . the measurements of top quark production are discussed in section  [ sec : top ] with the new results on top properties . finally section  [ sec : other ] summarizes the updates in heavy hadron spectroscopy and on searches beyond the standard model exploiting b - hadron decays .","summary":"new measurements on charm and beauty production presented in the heavy flavor working group are summarized and discussed in comparison with qcd predictions .","abstract":"we review theoretical and phenomenological aspects of heavy flavour production as discussed in the heavy flavour working group of the dis 2012 . recent theoretical progress includes approximate nnlo calculations for heavy quark structure functions in deep inelastic scattering , the extension of the acot heavy flavour scheme to jet production , and advances in top physics where the highlight is clearly the first complete nnlo qcd prediction for top pair production in the annihilation channel . furthermore , state of the art phenomenological predictions for open charm and bottom , charmonium , and single top and top pair production are discussed in addition to other topics such as the effect of double parton scattering on heavy quark production . new measurements on charm and beauty production presented in the heavy flavor working group are summarized and discussed in comparison with qcd predictions . top quark strong and weak couplings as well as top quark properties are being measured with precision at the lhc and the tevatron . we summarize also recent results on spectroscopy of charmonia , bottomonia and-hadrons , along with studies of their decays and properties . searches for physics beyond standard model through precise measurements of rare decays of heavy flavours are discussed as well ."}
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pas - bph-10 - 018 . babar collab . , b.  aubert _ et  al . _ * 101 * , 071801 ( 2008 ) . belle collab . , et  al . _ phys . rev . * d 82 * , 091106 ( 2010 ) . belle collab . , a. bondar _ et  al . _ lett . * 108 * , 122001 ( 2012 ) . a. bondar _ _ arxiv:1105.4473 . belle collab . , i. adachi _ et  al . _ lett . * 108 * , 032001 ( 2012 ) . belle collab . , i. adachi _ _ arxiv:1110.3934 . atlas collab . et  al . _ lett . * 108 * , 152001 ( 2012 ) . d@xmath164 collab . _ arxiv:1203.6034 . these proceedings . ckmfitter group , http://ckmfitter.in2p3.fr/ dcollab . , v. m. abazov _ phys . rev . * d84 * , 052007 ( 2011 ) . cdf collab . , cdf note 10778 . lhcb collab . , r. aaij _ et al . lett . * 108 * , 101803 ( 2012 ) . lhcb collab . , r. aaij _ et al . _ arxiv:1203.4493 . cdf collab . , www-cdf.fnal.gov/physics/new/bottom/120209.bmumu10fb lhcb collab . , r. aaij _ et al . lett . * 108 * , 111602 ( 2012 ) . cdf collab . , cdf note 10784 . _ arxiv:1111.5000 .","summary":"recent theoretical progress includes approximate nnlo calculations for heavy quark structure functions in deep inelastic scattering , the extension of the acot heavy flavour scheme to jet production , and advances in top physics where the highlight is clearly the first complete nnlo qcd prediction for top pair production in the annihilation channel . furthermore , state of the art phenomenological predictions for open charm and bottom , charmonium , and single top and top pair production are discussed in addition to other topics such as the effect of double parton scattering on heavy quark production .","abstract":"we review theoretical and phenomenological aspects of heavy flavour production as discussed in the heavy flavour working group of the dis 2012 . recent theoretical progress includes approximate nnlo calculations for heavy quark structure functions in deep inelastic scattering , the extension of the acot heavy flavour scheme to jet production , and advances in top physics where the highlight is clearly the first complete nnlo qcd prediction for top pair production in the annihilation channel . furthermore , state of the art phenomenological predictions for open charm and bottom , charmonium , and single top and top pair production are discussed in addition to other topics such as the effect of double parton scattering on heavy quark production . new measurements on charm and beauty production presented in the heavy flavor working group are summarized and discussed in comparison with qcd predictions . top quark strong and weak couplings as well as top quark properties are being measured with precision at the lhc and the tevatron . we summarize also recent results on spectroscopy of charmonia , bottomonia and-hadrons , along with studies of their decays and properties . searches for physics beyond standard model through precise measurements of rare decays of heavy flavours are discussed as well ."}
{"article_id":"1007.1452","section_id":"i","document":"the problem of the collision of two shoockwaves in four dimensions ( with lorentz signature ) that result from boosting two black holes to the speed of light is well known and has been extensively studied in the literature . references @xcite provide only a subset of the work dedicated to the particular problem ( for some interesting recent developments see @xcite ) . in particular , @xcite deals with this problem pertubatively and in a series of three papers the authors compute the metric and derive a formula for the gravitational radiation . the collision is axisymmetric while the bulk matter that creates the shockwaves as well as the back - reaction effects are not taken into account . recently , the high energy physics community has also expressed special interest in the topic of shockwaves collisions in the framework of general relativity @xcite through the anti - de - sitter space / conformal field theory correspondence ( ads / cft ) @xcite . the ads / cft duality , allows to formulate a process that is associated with non - abelian gauge theories at strong coupling as a purely gravitational problem . as a result , one may map the problem of heavy ion collisions ( in four dimensions ) onto shockwaves collisions in gravity in five dimensions . recently , we have been involved in such problems @xcite in gauge theories at strong coupling whose dual five dimensional gravitational description , exhibits similar characteristics with those of shockwave collisions in ( ordinary ) four dimensional gravity . our goal in this work is to attempt to apply our earlier experience @xcite and especially apply the technique that we have developed in @xcite in ( ordinary gravity in ) four dimensions . we choose to work in a different coordinate system than @xcite in order to retain the geometrical insight of the collision and in addition we take into account the matter responsible for the creation of the shockwaves and the back - reaction effects as well . furthermore , the collision we consider here is not axisymmetric but is involves a non zero impact parameter . we organize the paper as follows .    in chapter [ sup ] we state the problem we want to solve and construct the main set up . our goal is to determine the evolution of the geometry assuming that we know it in some time interval ( negative times ) . the initial geometry is given by two shockwaves which correspond to a non zero stress - energy tensor . ) with the speed of light and begin to interact for positive times ] our method is to construct a perturbative approach by expanding the metric around the background given by the flat metric along with the two shockwaves . equation ( [ s12 ] ) shows the form of the metric at all times while figure [ interaction ] offers a diagrammatical intuition of the terms of the metric we attempt to calculate in this project .    in chapter [ b2b ] we take into account the interaction of the one particle with the gravitational field created from the other and vice versa . in terms of feynman diagrams , loosely speaking , these corrections correspond to the diagrams of figure [ selfint4d ] . the corrections to the stress - energy tensor corresponding to these diagrams along with the corrections of the metric tensor corresponding to diagram of figure [ interaction ] form a consistent set ) ) . ] of the corrections that have to been taken into account . we verify that the modified stress - energy tensor is conserved ( to the order of the expansion that we are working ) and we find that it is traceless . this last condition results into some pleasing simplifications for einstein s equations ( compare ( [ ein ] ) with ( [ ee ] ) ) . chapter [ fe ] deals with the field equations and the specification of the gauge . our attempt is to perform a perturbative calculation about a metric that looks almost flat but contains two shockwaves moving opposite to each other and colliding ( see ( [ s12 ] ) ) . the shockwaves provide an effective stress - energy tensor in addition to the ( actual ) stress - energy tensor ( see ( [ rmn2gtt ] ) ) that creates the two shockwaves ; these terms correspond to products of the form @xmath5 and @xmath6 of equation ( [ deq1 ] ) respectively . a suitable gauge choice simplifies the field equations ( [ deq1 ] ) to equations ( [ deq ] ) which are solved in the next chapter .    in chapter [ seq ] we specify the boundary conditions of the field equations ( [ deq ] ) and the corresponding green s function . in particular , we seek for causal solutions and therefore the associated green s function to the differential operator ( [ box ] ) is the retarded green s function . we show how the integrations on the light - cone and transverse plane may be performed omitting some of the intermediate steps for appendices [ a ] , [ b ] and [ c ] . eventually we derive a formula for the metric tensor , equation ( [ gmn2 ] ) , to the order we are working . this is our final result and it generally has the structure ( [ gmn ] ) . finally in chapter [ conc ] we discuss about the area of validity of our solution and summarize our conclusions . in particular , we argue that the presence of matter and the back - reaction effects may not be ignored as they result to an important contribution to the metric . we also see that as the impact parameter tends to zero , the metric diverges logarithmically . it is in our belief that this is a signal that a classical approach to the problem stops being valid and that a quantum description is required . lastly , we talk about the general form of the metric . although its evolution is constrained by casualty as expected ; this evolution takes place in an intuitive way : at a given ( proper ) time , any arbitrary point on the transverse plane evolves according from whether the signal from the center of the one or the other shockwave or both , has enough time to reach the point under consideration . we had encountered such a behavior in an analogous set up in @xcite although the geometry there was anti de sitter geometry in five dimensions . in @xcite we had claimed that a similar evolution of the metric should also be observed in four dimensions ; in this work we verify our conjecture .","summary":"therefore , using einstein s equations we predict the future of space - time using the fact that we know the past geometry . our solution respects causality as expected but this casual dependence takes place in an intuitive way . in particular , at any given point on the transverse plane at fixed evolves according from whether the propagation from the center of each of the shockwaves or from both shockwaves has enough proper time ( ) to reach the point under consideration or not . simultaneously around the center of each shockwave , the future metric develops a-function profile with radius ; therefore this profile expands outwards from the centers ( of the shockwaves ) with the speed of light . finally , we discuss the case of the zero impact parameter collision which results to the violation of conservation and we argue that this might be a signal for the formation of a black hole .    andrzej derdzinski and especially prof . also the author thanks prof . in addition he would like to thank prof . jean - francois lafont , daniel shapiro and joseph ferrar and particularly prof . james cogdell and alexander leibman for answering his endless emails with clarity , exactness and always availability . attending many of the required classes would had been impossible without the help of his best friend chen zang who baby sat the authors son , nikolas alexandrou taliotis , while the author and his wife maria alexandrou had to attend classes . the author owns special gratefulness to his physics advisor , prof . department of energy under grant no .","abstract":"the problem of collisions of shockwaves in gravity is well known and has been studied extensively in the literature . recently , the interest in this area has been revived trough the anti - de - sitter space / conformal field theory correspondence ( ads / cft ) with the difference that in this case the background geometry is anti de sitter in five dimensions . in a recent project that we have completed in the context of ads / cft , we have gained insight in the problem of shockwaves and our goal in this work is to apply the technique we have developed in order to take some farther steps in the direction of shockwaves collisions in ordinary gravity . in the current project , each of the shockwaves correspond to a point - like stress - energy tensor that moves with the speed of light while the collision is asymmetric and involves an impact parameter ( b ) . our method is to expand the metric in the background of flat space - time in the presence of the two shockwaves and compute corrections that satisfy causal boundary conditions taking into account back - reactions of the stress - energy tensor of the two point - like particles . therefore , using einstein s equations we predict the future of space - time using the fact that we know the past geometry . our solution respects causality as expected but this casual dependence takes place in an intuitive way . in particular , at any given point on the transverse plane at fixed evolves according from whether the propagation from the center of each of the shockwaves or from both shockwaves has enough proper time ( ) to reach the point under consideration or not . simultaneously around the center of each shockwave , the future metric develops a-function profile with radius ; therefore this profile expands outwards from the centers ( of the shockwaves ) with the speed of light . finally , we discuss the case of the zero impact parameter collision which results to the violation of conservation and we argue that this might be a signal for the formation of a black hole .    the author would like to thank prof . andrzej derdzinski and especially prof . gerlach ulrich for serving in his defense committee and also for stimulating discussions prior and during this thesis . also the author thanks prof . samir mathur for very informative discussions during the writing of this work . in addition he would like to thank prof . thomas kerler and herb clemens for making the transferring from the graduate program of the department of physics to the graduate program of the department of mathematics possible and in addition denise witcher for guiding him through all the steps of this process . completion of the graduate courses would nt be possible without the help and teaching enthusiasm of prof . jean - francois lafont , daniel shapiro and joseph ferrar and particularly prof . james cogdell and alexander leibman for answering his endless emails with clarity , exactness and always availability . his student mates corry christopherson , fatih olmez and zhi qui have played a crucial role during the coursework as not only they kept encouraging him but also have spent enormous time from their time in order to patiently answer all of his questions . attending many of the required classes would had been impossible without the help of his best friend chen zang who baby sat the authors son , nikolas alexandrou taliotis , while the author and his wife maria alexandrou had to attend classes . the author owns special gratefulness to his physics advisor , prof . yuri kovchegov , for teaching him physics , for teaching him how to see through the complicate mathematics and nail down the physical picture and especially for showing him how to undertake his responsibilities not only inside but also outside of the academia . special thanks to prof . tom banks , steve giddings , yuri kovchegov and krishna rajagopal for their encouragement in submitting this thesis on the arxiv after it was defended . lastly but most important , the author would like to thank maria alexandrou for all of her patience during these years and for lifting most of the weights of their journey in life while keep smiling and being an example of a kind human , a reliable partner and a wonderful woman : he delicates this work to her .    this work is sponsored in part by the u.s . department of energy under grant no . de - fg02 - 05er41377 and in part by the institution of governmental scholarships of cyprus ( iky ) .    born in nicosia , cyprus    b.sc . in physics ,    ms in physics    graduate research associate in the department of physics and graduate student in the department of mathematics of the ohio state university"}
{"article_id":"1303.0259","section_id":"i","document":"in recent years , there has been increasing interest in the optical properties of nanomaterials . nanostructured materials have potential applications in photovoltaics and photoelectrochemical cells@xcite as well as uses as optical sensors@xcite . quantum confinement and surface effects play a crucial role in the electronic properties of these materials@xcite , while their large number of atoms makes them much more challenging to treat with conventional electronic structure methods than their bulk counterparts . it is therefore vital to develop efficient ways of computing optical properties of large scale systems to high accuracy . time - dependent ( td ) density - functional theory ( dft)@xcite has become a very successful method in recent years in determining excitation energies and optical spectra of molecules and nanoclusters @xcite . for many commonly used approximations to the exchange - correlation functional , the energies of local excitations in a variety of systems are typically being predicted to within a few tenths of an ev , while non - local excitations are often significantly underestimated@xcite . tddft is appealing for large scale applications since it shows a greater flexibility in computational cost than more complicated many - body techniques like the @xmath0 approximation and the bethe salpeter equation @xcite . for local and semi - local exchange - correlation functionals , which already deliver a good description for excitations where the electron - hole interaction is not significant , tddft is considerably cheaper computationally than many - body techniques . more sophisticated functionals , which come at greater computational cost , can recover the full solution to the bethe - salpeter equation@xcite , thus allowing a balance between accuracy and computational effort in tddft calculations . continuous improvement in tddft algorithms over recent years@xcite means that calculations on hundreds of atoms are now computationally feasible . however , even though tddft in many commonly used approximations to the exchange correlation functional is computationally cheaper than more advanced methods of calculating optical spectra , it still exhibits a cubic scaling behaviour with system size in conventional implementations , putting a severe limitation on the system sizes that can be studied . in ground - state calculations with density - functional theory ( dft)@xcite , the development of _ linear - scaling _ methods@xcite has been specifically aimed at enabling the treatment of large scale systems with up to hundreds of thousands of atoms@xcite . linear - scaling dft calculations have been performed on large biomolecules and nanoparticles@xcite . thus ideally , one would like to extend the ideas of linear scaling which have proved to be so successful in ground state dft to excited state calculations in tddft . fully linear - scaling formulations of tddft have been known for almost a decade @xcite . however , these formulations rely on propagating the td kohn - sham equations explicitly in time . the time - dependent response of the system to an external field can be determined at any instance , which , after a fourier transform into the frequency domain , contains information about the frequency dependent - response and thus the optical spectrum @xcite . to ensure stability of the solution , the time step to integrate the td kohn - sham equations is chosen to be quite small ( typically of the order of @xmath1 fs ) and thus the number of time steps required to obtain a meaningful spectrum becomes prohibitively large for many practical applications@xcite . furthermore , in time domain tddft implementations , one loses any explicit information on individual excitations , as well as the ability to compute dipole - forbidden states . only the spectrum as a whole can be resolved @xcite .    for many of the applications mentioned above , one is mainly interested in the low energy optical response of the system , with energies in the region of visible and low energy ultraviolet light . additionally , properties of individual excitations such as oscillator strengths and response density distributions are important for analysing the spectrum and optimising spectral response for specific applications . a method which lends itself naturally to computing low energy excitations of a system is the linear response formalism @xcite , in which the tddft equations are cast into an effective eigenvalue equation that can be solved for its lowest eigenvalues @xcite . this formalism can also be made linear scaling @xcite , making it ideal for the large scale nanostructured systems we have in mind .    in this paper , we present a fully linear - scaling implementation of tddft in the linear response formalism , suitable for calculating the low energy excitation energies and spectrum of large systems . we will first give a brief overview of both linear - scaling dft in the @xmath2 code @xcite ( section [ chapter_onetep ] ) and linear response tddft ( section [ chapter_linear_response ] ) , mentioning only features that are important for our formalism . we will then present an outline of various aspects of the linear - scaling tddft formalism , making use of a double representation approach to represent the occupied and unoccupied kohn - sham space ( sections [ chapter_linear_scaling]-[chapter_unocc ] ) . we will present results on a number of test systems ( sections [ chapter_pentacene]-[chapter_chlorophyll ] ) , as well as a demonstration of the linear scaling of the computational effort with system size ( sections [ chapter_nanorod ] and [ chapter_nanotube ] ) . our conclusions are summarised in section [ chapter_conclusion ] .","summary":"we present an implementation of time - dependent density - functional theory ( tddft ) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures .","abstract":"we present an implementation of time - dependent density - functional theory ( tddft ) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures . the method avoids any explicit reference to canonical representations of either occupied or virtual kohn - sham states and thus achieves linear - scaling computational effort with system size . in contrast to conventional localised orbital formulations , where a single set of localised functions is used to span the occupied and unoccupied state manifold , we make use of two sets of _ in situ _ optimised localised orbitals , one for the occupied and one for the unoccupied space . this double representation approach avoids known problems of spanning the space of unoccupied kohn - sham states with a minimal set of localised orbitals optimised for the occupied space , while the _ in situ _ optimisation procedure allows for efficient calculations with a minimal number of functions . the method is applied to a number of medium sized organic molecules and a good agreement with traditional tddft methods is observed . furthermore , linear scaling of computational cost with system size is demonstrated on ( 10,0 ) carbon nanotubes of different lengths ."}
{"article_id":"1303.0259","section_id":"m","document":"all linear - scaling dft formalisms are developed around the idea of exploiting nearsightedness@xcite : this principle states that for any system with a band gap , the single particle density matrix decays exponentially with distance @xcite . a variety of different linear scaling methods based on this principle have been developed in recent years and have been reviewed extensively @xcite .    in @xmath2 the density matrix is expressed through a set of optimisable localised functions @xmath3 referred to as nonorthogonal generalised wannier functions ( ngwfs ) @xcite . the ngwfs are expanded in an underlying basis of periodic sinc functions ( psincs ) @xcite equivalent to a set of plane waves . the density matrix is then written in separable form @xcite @xmath4 where we assume an implicit summation over repeated greek indices . in the following sections , we will use latin indices to denote objects in the canonical representation and greek indices to denote objects involving the localised set of functions , while subscripts and superscripts in curly brackets are labels , rather than free indices . thus , @xmath5 are the elements of the valence density matrix in the representation of duals of ngwfs . locality is imposed through a spatial cutoff on the density matrix and a strict localisation of the ngwfs . the total energy of the system is minimised both with respect to the density matrix and the ngwfs . the underlying psinc basis of the ngwfs allows the method to achieve an accuracy equivalent to plane - wave methods @xcite . the _ in situ _ optimisation of the ngwfs during the calculation ensures that only a minimal number of @xmath3 are needed to span the occupied subspace .    in a @xmath2 calculation , there is no reference to individual kohn - sham eigenstates in their canonical representation . eigenstates can be obtained in a post - processing step by a single diagonalisation of the dft hamiltonian in ngwf representation . due to the minimal size of the set of ngwfs needed to represent the occupied subspace , this diagonalisation is generally cheap , but does not scale linearly with system size . occupied states are accurately represented by @xmath3 , however , unoccupied states are reproduced increasingly poorly with increasing energy @xcite . in general , the specific optimisation of @xmath3 in order to represent the occupied space leads to poor representation of the conduction space manifold . this shortcoming was addressed recently @xcite in a method where a second set of ngwfs @xmath6 is optimised in a non - self - consistent calculation following the determination of the ground - state . the method uses a hamiltonian that projects out the occupied states and minimises the energy with respect to a second conduction density matrix @xmath7 and the set of ngwfs @xmath6 in order to represent the low energy subspace of the conduction manifold . the conduction density matrix is then expressed using the conduction ngwfs : @xmath8 here , we use the subscript @xmath9 to denote conduction kohn - sham states and @xmath10 to denote the number of kohn - sham conduction states that @xmath7 is optimised to represent . the optimisation of both @xmath7 and @xmath11 scales linearly with system size . as in the ground - state calculation , the individual kohn - sham eigenstates can be calculated from a single diagonalisation of the hamiltonian in conduction ngwf representation if needed . the obtained conduction states are shown to be in excellent agreement with traditional plane - wave dft implementations@xcite . thus the ngwf approach allows the representation of both the occupied space and a low energy subset of the unoccupied space to plane - wave accuracy using two independently optimised sets of localised functions . the underlying psinc basis allows for a systematic improvement of the ngwfs and the individual optimisations ensure that only a minimal set of @xmath3 and @xmath6 have to be used in order to represent the valence and conduction space . in contrast to methods making use of a single set of localised orbitals , the double ngwf approach also allows for keeping a strict localisation on @xmath3 representing the valence space , while for @xmath6 a larger localisation radius can be chosen . these features make the conduction and valence ngwfs ideal for the application to the linear response tddft formalism , provided only low energy excitations are of interest . the main limitation of the ngwf representation is that the localised functions @xmath12 do not form a very natural representation of high energy delocalised and unbound conduction states . this limitation however is generally shared with other localised basis set methods and we expect the ngwf representation to perform no worse for these states than gaussian basis sets , with the advantage that the set of @xmath12 is significantly smaller in size .      in recent years , a number of reviews on different aspects of tddft have been published@xcite . in general , one differentiates between two main formalisms : the linear response formalism , which can be cast into an effective eigenvalue equation and the time propagation formalism , in which the time - dependent kohn - sham equations are propagated explicitly . linear response tddft has become the method of choice for calculating low energy excitations and spectra and is now widely used @xcite . in the linear response regime , the excitation energies can be expressed as the solution to the eigenvalue equation @xcite    @xmath13    where the elements of the block matrices @xmath14 and @xmath15 can be expressed in canonical kohn - sham representation as @xmath16 here , @xmath9 and @xmath17 denote kohn - sham conduction and valence states and * k * is the coupling matrix with elements given by @xmath18   \\\\ \\times \\psi^{\\textrm{\\scriptsize{ks}}*}_{c}(\\textbf{r})\\psi^{\\textrm{\\scriptsize{ks}}}_{v}(\\textbf{r})\\psi^{\\textrm{\\scriptsize{ks}}*}_{v'}(\\textbf{r}')\\psi^{\\textrm{\\scriptsize{ks}}}_{c'}(\\textbf{r}').\\end{aligned}\\ ] ] in the above expressions , we have omitted all spin indices for convenience and are limiting ourselves to the calculation of singlet states only . furthermore , the coupling matrix is taken to be static , a simplification that is known as the adiabatic approximation . @xmath19 is the exchange - correlation energy and its second derivative , evaluated at the ground - state density @xmath20 of the system , is known as the tddft exchange - correlation kernel . as in ground state dft , its exact functional form is not known . a commonly made choice is to use @xmath21 , which is known as the adiabatic local density approximation ( alda ) . a further simplification to the tddft eigenvalue equation can be achieved by making use of the tamm - dancoff approximation ( tda ) @xcite . in this approximation , we assume the off - diagonal coupling matrix elements @xmath22 to be small . the matrix equation then simply reduces to @xmath23 a matrix eigenvalue problem of half the size of the original one . more crucially , the tddft eigenvalue equation in the tda is hermitian , while the original equation is not @xcite . generally speaking , the tda gives good excitation energies but violates oscillator strength sum rules @xcite . however , due to its hermitian properties , the tda lends itself to solutions involving standard matrix eigenvalue solvers and will therefore be considered for the rest of this work .    in principle , the matrix @xmath14 can be built explicitly and eq . [ eval_eqn ] can be diagonalised to give all excitation energies of the system . clearly , this is not possible with linear scaling effort , as the dimensions of @xmath14 grow as @xmath24 with system size and the matrix is not sparse in the canonical representation . since every matrix element involves a double integral over product kohn - sham states , constructing @xmath14 scales as @xmath25 . however , in the limit of large systems when one is only interested in a comparatively small number of eigenvalues , it is much more advantageous to use iterative methods instead of direct diagonalisation to calculate the eigenvalues of @xmath14 . in order to do so one needs to define the action of @xmath14 on an arbitrary trial vector @xmath26 . following the formalism introduced by hutter @xcite we define @xmath27 where @xmath28 is the first order response density associated with the trial vector @xmath26 . defining the self - consistent field potential @xmath29 as a reaction to the response density as @xmath30 the action * q * of the tddft operator @xmath14 on the arbitrary trial vector * x * can be simply written as @xmath31 here , @xmath32 is given by @xmath33 one can then express the lowest excitation energy @xmath34 of a system in terms of @xmath35 @xmath36 which can be minimised variationally with respect to @xmath26 .    the formulation of the lowest tddft eigenvalue in terms of a variational principle as outlined in eq . [ omega_canonical ] is only valid in the tamm - dancoff approximation , as it requires the tddft eigenvalue matrix to be hermitian . however , the full non - hermitian tddft eigenvalue matrix consists of blocks of hermitian matrices and exploiting this structure , a more generalised version of the variational principle of eq . [ omega_canonical ] can be formulated @xcite . while it is beyond the scope of this paper , we point out that the linear - scaling tddft method developed in the next sections can be readily extended to the full tddft eigenvalue equation by making use of the generalised version of the variational principle . although the approach above is outlined in the canonical representation , it can be reformulated in terms of local orbitals or other basis functions . in many quantum chemistry codes , @xmath37 is constructed in a gaussian basis set representation , making use of highly optimised methods to perform four centre gaussian integrals @xcite . plane wave implementations typically make use of a mixed representation of canonical orbitals for the occupied states and plane waves for the virtual states @xcite . the main advantage of all these iterative methods is that no explicit construction , storage and diagonalisation of @xmath14 is required , which is prohibitive for large system sizes . however , the different basis set implementations mentioned above still make reference to individual kohn - sham states , thus calculating @xmath38 still shows an asymptotic scaling of @xmath39 with system size . to improve the scaling , one has to avoid any reference to the canonical representation@xcite . @xmath2 provides a set of optimised ngwfs @xmath11 spanning the low energy conduction space and @xmath40 spanning the valence space . together , they form a suitable representation to expand quantities like @xmath41 and @xmath42 . in the following section , for all expressions including the sets of localised ngwfs , we will differentiate between covariant and contravariant quantities by using lower and upper case greek indices respectively . for quantities involving the canonical kohn - sham states , this differentiation is unneccessary since the kohn - sham orbitals form an orthogonal basis . for a more in depth treatment of tensors in electronic structure theory , see @xcite . the kohn - sham orbitals are used in this section to derive the appropriate expressions in ngwf representation , as well as to highlight the equivalence to the canonical representation . note however , that there is no explicit reference to the canonical representation in the final expressions . starting with the response density , we can write @xmath43 here , the sum of the conduction states goes over all the states for which @xmath11 was optimised . we have again assumed an implicit summation over repeated greek indices . in principle , one has to sum over an infinite number of conduction states . however , for the lowest few optical energies in the system , @xmath41 is well described by a relatively small number of unoccupied states . this approximation can be rigorously tested by including a larger subset of the conduction space manifold in the optimisation of the conduction density matrix @xmath7 . in the spirit of the linear scaling dft formalism the above expression can be rewritten as @xmath44 where the effective response density matrix @xmath45 is defined as @xmath46 the above definition is analogous to the definitions of the valence and conduction density matrices in ngwf representations , where @xmath47    eq . [ kernel ] defines the full response density matrix in mixed conduction - valence ngwf representation . each tddft excitation energy can be written as a functional of a specific response matrix and thus @xmath48 plays the same role in the linear - scaling linear response formulation as the eigenvector * x * does in the canonical formulation outlined in the previous section . similarly to the response density , @xmath32 can be rewritten as @xmath49 furthermore , the diagonal part of @xmath35 consisting of kohn - sham conduction - valence eigenvalue differences becomes : @xmath50 it is now convenient to introduce a shorthand notation for the matrix elements of different quantities in terms of the different types of ngwfs . we denote the kohn - sham hamiltonian in conduction and valence ngwf representations as @xmath51 and @xmath52 respectively and the self consistent field response in mixed conduction - valence ngwf representation as @xmath53 : @xmath54    by inserting eq . [ diag_part ] and eq . [ scf_part ] into eq . [ y_canonical ] , multiplying with @xmath55 and @xmath56 from the left and right respectively and summing over the @xmath9 and @xmath17 indices , one can remove all references to the canonical representation from @xmath38 . using the definition of the response density matrix @xmath48 , the result of the tddft operator acting on a trial response matrix @xmath48 in ngwf representation reduces to the simple form @xmath57    note that in the linear - scaling formalism employed in @xmath2 , @xmath51 , @xmath52 , @xmath7 , @xmath58 and @xmath53 are all sparse matrices for sufficiently large system sizes @xcite . furthermore , the response potential @xmath59 is a functional of the response density only . constructing @xmath41 from eq . [ response_dens_eq ] only requires information from density matrix elements @xmath45 for which @xmath60 and therefore scales linearly with system size even for fully dense @xmath48 . evaluating @xmath29 from eq . [ vscf_defined ] also scales linearly for any semi - local exchange - correlation functional . thus constructing @xmath53 scales linearly with system size for fully dense @xmath48 . however , in evaluating the matrix operations in eq . [ operator ] , linear scaling can only be achieved if the response density matrix is truncated , just like the density matrix in linear - scaling dft . if this truncation can be performed , the response density matrix becomes sparse for sufficiently large systems and evaluating the action of the tddft operator on an arbitrary response matrix @xmath48 scales linearly with system size . using the action of the tddft operator in ngwf representation defined in equation [ operator ] , one can then rewrite the lowest excitation energy of the system as @xmath61}{\\textrm{tr}\\left[\\textbf{p}^{\\{1\\}\\dagger}\\textbf{s}^{\\chi}\\textbf{p}^{\\{1\\}}\\textbf{s}^\\phi\\right]}\\right\\}.\\ ] ] here , @xmath62 and @xmath63 denote the conduction and valence ngwf overlap matrices given by @xmath64 and @xmath65 . using the definitions of the involved quantities , as well as the invariance of the trace operation under cyclic permutation , it is trivial to show that eq . [ functional_ngwf ] is equivalent to eq . [ omega_canonical ] in the canonical representation . once the minimum excitation energy has been calculated through the variational principle of eq . [ functional_ngwf ] , its related oscillator strength ( in atomic units ) can be calculated as @xmath66    while in the above discussion on the linear scalability of calculating @xmath67 we have assumed semi - local exchange - correlation kernels , the formalism is equally valid for hybrid functionals . for hybrid functionals , one can split @xmath37 into @xmath68 containing the local part of the functional and @xmath69 containing the fraction of exact exchange . @xmath68 can be evaluated trivially in linear - scaling effort , while the expression for @xmath69 reduces to @xmath70 where @xmath71 denotes the fraction of hartree - fock exchange . we note that eq . [ hf_exchange ] is closely related to a term that needs to be evaluated in ground state dft using hybrid functionals , where it can be calculated in linear - scaling effort @xcite . thus the evaluation of the action @xmath67 can be made to scale linearly with system size even for hybrid exchange - correlation kernels .      in order to calculate the @xmath72 lowest excitation energies of a system with response density matrices @xmath73 and corresponding @xmath74 , we define the function @xmath75}{\\textrm{tr}\\left[\\textbf{p}^{\\{1\\}^\\dagger}_i\\textbf{s}^{\\chi}\\textbf{p}^{\\{1\\}}_i\\textbf{s}^\\phi\\right]}\\right]\\ ] ] which can be minimised with respect to @xmath76 under the constraint @xmath77=\\delta_{ij}.\\ ] ] again using the expression for @xmath76 and the invariance of the trace under cyclic permutations , it is clear that the above constraint is equivalent to the requirement that eigenvectors of the canonical tddft eigenvalue problem ( eq . [ eval_eqn ] ) are orthonormal to each other . when @xmath78 is minimised , @xmath79 span the same subspace as the @xmath72 lowest eigenvectors of the tddft operator * a*. in this work , the minimisation of @xmath78 is achieved using a conjugate gradient algorithm with gram - schmidt orthonormalisation . differentiating @xmath78 with respect to @xmath80 one can find the ( covariant ) gradient orthogonal to all current ( contravariant ) trial response matrices @xmath81 @xcite @xmath82 ( s^{\\chi})_{\\alpha\\gamma}(p^{\\{1\\}}_{j})^{\\gamma\\delta}(s^{\\phi})_{\\delta\\beta}\\end{aligned}\\ ] ] operating on the left and right with the inverse conduction and valence overlap matrices , the covariant gradient can be transformed into a contravariant gradient @xmath83 ( p^{\\{1\\ } } _ { j})^{\\alpha\\beta}\\end{aligned}\\ ] ] which can be used as a steepest descent search direction for a conjugate gradient algorithm . the exact form of the conjugate gradient algorithm used here has been outlined elsewhere @xcite ( with the difference that we do not make use of any preconditioner ) . here we just focus on how to choose a suitable starting guess for @xmath84 . since we do not have individual kohn - sham states available in the linear scaling formalism of the ground state calculation , we can not initialise @xmath80 to conduction - valence product kohn - sham states close to the band gap , which would otherwise form reasonable starting guesses . instead we initialise the set of @xmath85 to random starting configurations ( for other possible initialisation schemes , see @xcite ) . however , from eq . [ kernel ] it can be seen that any valid response density matrix must be invariant under the operation @xmath86 this operation can be understood as a projection into conduction and valence kohn - sham states in their ngwf representation . response density matrices that violate invariance under this projection contain elements that would correspond to forbidden transitions between two occupied or two unoccupied states , or contain contributions from unoptimised and thus badly represented high energy conduction states . the invariance requirement follows from an expansion of the density matrix idempotency constraint to first order for a given perturbation@xcite and must thus be fulfilled for all first order response density matrices . the need to enforce the idempotency constraint explicitly via the projection of eq . [ invariance ] can be viewed as the price to be paid for moving away from a formulation involving the canonical representation . the invariance requirement can be enforced by projecting the starting guess response matrices with @xmath87 and @xmath88 from the left and the right respectively . from eq . [ operator ] it can be seen that @xmath67 , the result of the tddft operator acting on a valid trial response density matrix , automatically shows the same invariance property as @xmath48 . therefore all gradients @xmath89 constructed using a valid set of @xmath90 obey the invariance requirement by construction . thus , every conjugate gradient derived from @xmath89 will have the specified invariance property and updating a valid response matrix with a gradient will preserve the invariance of that matrix under the projection ( eq . [ invariance ] ) . the orthogonality condition of eq . [ ortho ] is enforced using a gram - schmidt procedure , which has a nominal scaling of o(n@xmath91 , with @xmath92 and @xmath93 being the number of conduction and valence ngwfs respectively . both @xmath92 and @xmath93 grow as @xmath94 with system size , giving an overall scaling of @xmath24 with system size for the orthonormalisation procedure . however , if @xmath48 is truncated and thus sparse , the scaling of the gram - schmidt orthonormalisation reduces to @xmath94 , with a prefactor dependent on the square of the number of excitation energies @xmath95 .    thus , the whole algorithm outlined above scales linearly in memory with the number of excitation energies @xmath72 to solve for . since the @xmath72 individual resonse density matrices @xmath90 have to be kept orthogonal to each other using a gram - schmidt procedure , the asymptotic scaling of computational cost with the number of excitation energies is @xmath96 . however , for a fixed number of states required , the algorithm scales as @xmath94 with system size in both memory requirements and computational cost . since the algorithm developed in the previous sections only exhibits true linear - scaling properties if all involved density matrices @xmath58 , @xmath7 and @xmath48 can be truncated , one has to justify that the truncations are indeed possible . the truncation of @xmath58 originates from the nearsightedness principle @xcite and forms the basis of any linear - scaling dft implementation . in insulating systems , @xmath58 can be shown to decay exponentially with distance@xcite . for the conduction states , @xmath7 is only expected to exhibit an exponential decay if there is a second energy gap in the conduction band and @xmath7 spans the manifold of conduction states between the two bandgaps . in this case , the same argument to show exponential decay of the ground - state density matrix can be applied to @xmath7 @xcite . furthermore , by the same argument , the joint density matrix spanning the manifold defined by both @xmath58 and @xmath7 must be exponentially localised . the joint density matrix can be written as a block diagonal matrix with @xmath58 and @xmath7 as its diagonal entries . any response density matrix @xmath48 due to the application of a small perturbation described in this work corresponds to the off - diagonal blocks of said joint density matrix . however , the application of a small perturbation can not break the disentanglement of the joint manifold of @xmath58 and @xmath7 from the rest of the conduction manifold and thus can not break the exponential localisation of the joint block density matrix . the joint block density matrix can only be exponentially localised if all its constituent blocks are exponentially localised . we thus conclude that , in the special case described here , the tddft response density matrix @xmath48 is indeed expected to be exponentially localised .    the desired property of exponential localisation of the conduction density matrix and thus of the response density matrix can most likely be realised in 1d systems and molecular crystals , where the bands show little dispersion . however , it is evident from the above considerations that one can not present a generalised argument that @xmath48 can be truncated for all systems . this limitation is not unique to the linear response formulation of tddft presented here , but applies to linear - scaling time domain tddft as well , where the time - dependent response density matrix is truncated without a general formal justification . it was however noted by yam _ et al_.@xcite and chen _ et al_.@xcite , that for a number of systems studied the first order response density matrix retained the localisation of the ground - state density matrix to a good degree and thus could be truncated . in general , we expect this finding to be true for the relatively localised excited states of a variety of systems . whether a truncation of @xmath48 can be achieved for very delocalised high - energy excitations is doubtful . however , since the method presented here is mainly aimed at low energy excitations of large systems , we expect that the truncation of both @xmath97 and @xmath48 can indeed be carried out in practice for a certain class of systems and a linear scaling of computation time with system size can be achieved . truncation of @xmath48 adds an additional complication to the algorithm in that the invariance relation of eq . [ invariance ] only holds approximately . thus the gradient @xmath98 derived from a truncated @xmath48 only approximately preserves the invariance property and the accumulation of errors can lead to instabilities in the convergence . to measure the variations of @xmath48 from valid response matrices obeying the projection operation of eq . [ invariance ] , we define the positive - semidefinite norm @xmath99 $ ] : @xmath100=\\textrm{tr}\\left[\\left(\\textbf{p}^{\\{1\\}\\dagger}\\textbf{s}^{\\chi}\\textbf{p}^{\\{1\\}}\\textbf{s}^{\\phi}-\\textbf{p}^{\\{1\\ } ' \\dagger}\\textbf{s}^{\\chi}\\textbf{p}^{\\{1\\}'}\\textbf{s}^{\\phi } \\right)^2\\right]\\ ] ] where @xmath101 is constructed by applying the projections @xmath87 and @xmath88 to @xmath48 from the left and right respectively , enforcing that the resulting matrix @xmath101 has the same sparsity pattern as @xmath48 . for fully dense matrices @xmath48 initialised in the way described in the previous section , @xmath99 $ ] vanishes to numerical accuracy . for truncated response density matrices , @xmath99 $ ] can be forced to remain smaller than some threshold by iteratively applying the projection of eq . [ invariance ] to @xmath48 after each tddft iteration , thus stabilising the algorithm . the purpose of the algorithm described in this work is to enable the calculation of excitations that mainly consist of kohn - sham transitions into well - bound unoccupied states and are well described by @xmath11 and @xmath97 . however , even low energy excitations largely made up of well bound kohn - sham transitions often have significant contributions from high energy conduction states and including these unoccupied states in the calculation becomes important to achieve convergence . while in principle it is always possible to optimise @xmath11 for a larger number of unoccupied states , it is in practice not desirable to attempt to achieve a precise description of very delocalised , unbound states within a framework of localised orbitals . optimising @xmath12 for high energy conduction states generally comes at the cost of an increased ngwf localisation radius , which leads to a decrease of computational efficiency . a more efficient approach is to optimise @xmath11 for the subset of bound , low energy conduction states that form the most important contributions to the low energy excitations and to include the unbound continuum states in an approximate fashion . in order to do so , we redefine the conduction density matrix as a projector onto the entire unoccupied subspace : @xmath102 here , @xmath103 , the cross - overlap matrix between the two sets of ngwfs , and @xmath11 is specifically optimised for a low energy , well - bound subspace of the unoccupied space . we notice that under the above redefinition , @xmath97 is only strictly idempotent if @xmath104 is complete , a condition that is never realised in practice . thus initialising @xmath48 in the manner described in [ chapter_algorithm ] no longer guarantees for the invariance relation in eq . [ invariance ] to be met , even if no density matrix truncation is applied . to stabilise the convergence of the algorithm , the invariance projection in eq . [ invariance ] has to be applied iteratively to @xmath48 after each tddft conjugate gradient iteration in order to keep @xmath99 $ ] below a certain threshold .","summary":"the method avoids any explicit reference to canonical representations of either occupied or virtual kohn - sham states and thus achieves linear - scaling computational effort with system size . in contrast to conventional localised orbital formulations , where a single set of localised functions is used to span the occupied and unoccupied state manifold , we make use of two sets of _ in situ _ optimised localised orbitals , one for the occupied and one for the unoccupied space . this double representation approach avoids known problems of spanning the space of unoccupied kohn - sham states with a minimal set of localised orbitals optimised for the occupied space , while the _ in situ _ optimisation procedure allows for efficient calculations with a minimal number of functions .","abstract":"we present an implementation of time - dependent density - functional theory ( tddft ) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures . the method avoids any explicit reference to canonical representations of either occupied or virtual kohn - sham states and thus achieves linear - scaling computational effort with system size . in contrast to conventional localised orbital formulations , where a single set of localised functions is used to span the occupied and unoccupied state manifold , we make use of two sets of _ in situ _ optimised localised orbitals , one for the occupied and one for the unoccupied space . this double representation approach avoids known problems of spanning the space of unoccupied kohn - sham states with a minimal set of localised orbitals optimised for the occupied space , while the _ in situ _ optimisation procedure allows for efficient calculations with a minimal number of functions . the method is applied to a number of medium sized organic molecules and a good agreement with traditional tddft methods is observed . furthermore , linear scaling of computational cost with system size is demonstrated on ( 10,0 ) carbon nanotubes of different lengths ."}
{"article_id":"1303.0259","section_id":"r","document":"in this section , we will assess the performance of the method outlined above , as implemented in the @xmath2 code . in section [ chapter_pentacene ] we perform a detailed comparison of our method with well established conventional tddft codes , demonstrating the accuracy of the approach introduced here . in [ chapter_fullerene ] we demonstrate the scaling of the method with respect to the number of excitations converged , while [ chapter_chlorophyll ] contains a comparison with experimental data . in [ chapter_nanorod ] we show the behaviour of the method under the truncation of the response density matrix . finally , in [ chapter_nanotube ] we demonstrate that the method does scale fully linearly with system size .    unless specified otherwise , all calculations are carried out using the lda exchange correlation functional for the ground - state dft calculations and alda for the tddft calculations , both in the perdew - zunger parameterisation@xcite . norm conserving pseudopotentials@xcite are used throughout this work . unless specified otherwise , the localisation region for conduction and valence ngwfs were chosen by converging the conduction energy and ground state energy with respect to the conduction and valence ngwf radii .      as the first test system we chose pentacene ( c@xmath105h@xmath106 ) , as its moderate size allows for detailed comparisons to traditional tddft methods . the simulation box was chosen to be @xmath107 and the kinetic energy cutoff was 750 ev . the atomic positions were optimised at the lda level@xcite . in order to assess the accuracy of the tddft method we first performed a calculation in which the unoccupied subspace was limited to only contain states for which @xmath104 was specifically optimised . for this calculation , a minimal set of 1 ngwf per h and 4 ngwfs per c atom was chosen for both the occupied and the unoccupied state representations . the ngwf radius for both valence ngwf species was chosen to be @xmath108 , while @xmath109 was chosen for the conduction ngwfs . the conduction density matrix was optimised for the 10 lowest unoccupied states , covering all of the bound unoccupied states . this put the dimensions of the tddft operator at @xmath110 in a canonical representation and @xmath111 in a representation of conduction and valence ngwfs . the results obtained were compared to a calculation performed using the octopus code @xcite ( modified to allow for calculations within the tamm - dancoff approximation ) . for the octopus calculation , a grid spacing of @xmath112 , equivalent to the onetep grid , was used , while the basis was defined on this grid as the union of atom centered spheres with a radius of @xmath113 . the calculation was performed using the casida calculation mode within the tamm - dancoff approximation and the number of unoccupied states was limited to 10 in order to ensure a very high level of convergence for these states . for the 10 lowest excited states , we found a good agreement between the two methods , with a root mean squared ( rms ) difference of 30 mev in excitation energies and an identical ordering of states . thus , the iterative solution to the tddft equation in onetep gives results that are comparable to the explicit construction and diagonalisation of the eigenvalue equation in octopus if the unoccupied subspace is truncated to the same size . .results for the excited states of pentacene , as calculated using onetep with the projection onto the entire unoccupied subspace , in comparison with results generated by nwchem . results are shown for the 10 lowest excitations , as well as two selected higher energy states , one dark and one bright ( labelled ( d ) and ( b ) respectively ) . the first three columns correspond to onetep calculations using three different ngwf representations , where * a * denotes the minimal set of ngwfs for the conduction space , * b * uses 2 ngwfs per h and * c * uses 5 ngwfs per h. the nwchem calculations are performed using an aug - cc - pvtz basis . energies are given in ev , oscillator strengths in brackets . [ cols=\"^,^,^,^,^\",options=\"header \" , ]     .,scaledwidth=45.0% ]    while the two methods agree well for a conduction space truncated to contain the 10 lowest , well bound states , the tddft eigenvalue energies need to be converged with respect to the size of the conduction space . here , we make use of the projector onto the unoccupied subspace defined in [ chapter_unocc ] for the onetep calculations . in order to assess the convergence with the size of our representation , we form three different choices of ngwf representation for @xmath11 : a minimal set containing 1 ngwf per h and 4 per c and two sets where we augmented the h atoms to have 2 and 5 ngwfs respectively . the reason for doing so is that the minimal representation of ngwfs already gives a very good description of the bound unoccupied states , while the additional functions on h lead to a better description of the very delocalised unbound states . for the minimal representation , the ngwfs were optimised for the 10 bound states , while the increased variational freedom in the two larger sets meant we could explicitly optimise 4 more lightly bound conduction states as well , leading to a total number of 14 optimised conduction states . table [ table_pentacene2 ] summarises the results of the onetep calculations using the projector method with the three different ngwf representations , as well as a benchmark calculation performed in the quantum chemistry software package nwchem @xcite . the nwchem calculations were performed using an aug - cc - pvtz gaussian basis set , corresponding to 46 basis functions per c atom and 23 basis functions per h atom . this put the size of the active unoccupied space in the nwchem calculations at 1196 conduction states . comparing the onetep results to the reference calculation , we find that the minimal ngwf set using the projector method produces results that show an rms difference of just 16mev for the first 10 states compared to the nwchem results . it does however predict a significantly lower oscillator strength for the bright state . the ngwf set containing 2 localised functions per h atom gives results within 0.02 ev of the nwchem results and a very good agreement on oscillator strengths throughout . comparisons to the largest ngwf set used show that the lowest 10 states are essentially converged in both energy and oscillator strength for the medium set , while the bright state is predicted to be 0.03ev lower than the nwchem benchmark result for the largest onetep representation . we thus note that in order to achieve results that are comparable to gaussian basis set calculations using a relatively large aug - cc - pvtz basis , it is enough to use a @xmath12 containing just 2 ngwfs per h and 4 per c. we also note that some low energy states , namely the lowest and fourth lowest excitation , drop significantly in energy when introducing the the whole unoccupied subspace into the calculation by means of a projector ( up to 0.16 ev for the fourth state ) . while a decomposition of @xmath48 into kohn - sham transitions shows that no single transition into the unbound and unoptimised conduction states makes up more than 0.1% of the total tddft response density matrix , their collective effect is to significantly lower the energy of certain states . however , the approximate description of these states via a projector onto the unoccupied subspace leads to very good results , even if only a very small number of ngwfs is used . the benchmark tests show that our results are well converged with basis set size and the representation of the unoccupied subspace . however , the nature of the localisation constraint on the ngwfs means that we need to assess the convergence of the method with respect to the conduction ngwf radius as well . figure [ pentacene_convergence ] shows the convergence of three selected excited states with respect to the conduction ngwf radius for the medium sized basis set corresponding to 2 ngwfs per h atom . the ngwfs were optimised for 14 conduction states and the projector onto the unoccupied subspace was used . we note that the excitations corresponding to the 6th and 9th lowest states in table [ table_pentacene2 ] are well converged even for relatively small ngwf radii . however , in order to converge the excited state labelled as ( d ) in table [ table_pentacene2 ] , one needs to go to much larger ngwf radii . a breakdown of the corresponding response density matrices into kohn - sham transitions shows that the excited state labelled ( d ) is to 99% composed of a transition from the homo into the 9th unoccupied kohn - sham state . this unoccupied state is very lightly bound and delocalised and thus naturally shows an increased sensitivity to the localisation constraint imposed on the conduction ngwfs . however , even this very sensitive excitation is well converged for an ngwf radius of @xmath114 .      as a second test system , we use buckminsterfullerene ( c@xmath115 ) which has already been studied extensively both experimentally and using _ ab initio _ simulation techniques . here , we focus on how the iterative solution of the tddft eigenvalue equations scales with the number of excitations converged . calculations were performed in a simulation cell of @xmath116 , using a kinetic energy cutoff of 800 ev . a minimal number of 4 ngwfs was chosen for both conduction and valence representations , while the ngwf radius was chosen to be @xmath117 and @xmath118 respectively . the conduction ngwfs were explicitly optimised for a total of 30 states , while the rest of the conduction space is included into the calculation via the projector onto the unoccupied subspace . c@xmath115 shows a high number of dark transitions in the low energy range , transitions for which the oscillator strength is very small . thus to reproduce the main features of the spectrum up to an energy of 4.8 ev , 150 excitations had to be converged . the spectrum for fullerene is shown in fig . [ spectrum_fullerene ] . the most prominent features of the spectrum are the strong excitation peaks at 3.46 ev and 4.42 ev , which are in good agreement to the tddft energies and oscillator strengths obtained in @xcite using a gradient - corrected functional and a 6 - 31g+s gaussian basis set . while the results obtained by onetep predict slightly lower energies for the main two peaks compared to @xcite , we note that the gaussian basis set used in those calculations is relatively small , such that the authors estimate the errors introduced for the main excitations as being of the order of up to 0.1 ev . finally , the energies for the main peaks in the spectrum as calculated in onetep are also in perfect agreement with the 3.5 ev and 4.4 ev obtained in time - propagation tddft calculations using a basis of linear combinations of atomic orbitals by tsolakidis _ et al _ @xcite . experimentally , the peaks are reported to be at 3.78ev and 4.84 ev @xcite , in reasonable agreement with the tddft results . generated from the 150 lowest excitation energies . an artificial smearing width of 0.03 ev was used in generating this plot . the positions and oscillator strengths of three major excitations were taken from @xcite and are plotted here using the same artificial gaussian smearing to produce a reference spectrum . the two spectra were scaled according to their relative oscillator strengths.,scaledwidth=45.0% ]    the main purpose of the c@xmath115 benchmark test is to demonstrate the scaling of computational cost of the tddft calculation with the number of converged excitation energies @xmath72 . figure [ timings_fullerene ] shows the total calculation time versus the number of converged excitation energies as well as the total time taken in applying the tddft operator on the trial vector ( eq . [ operator ] ) . the cost of applying the tddft operator scales linearly with the number of excitation energies , as one would expect . however , it can be seen that for larger numbers of excitations , the @xmath96 scaling of the gram - schmidt orthonormalisation begins to dominate over the application of the tddft operator and the total calculation time deviates from the linear trend .    . the red line is a parabolic fit to the total calculation time while the blue line is a linear fit to the total time taken to apply the tddft operator on the set of trial vectors . the non - linear behaviour of the total calculation time due to the orthogonalisation of multiple excitations is clearly visible.,scaledwidth=45.0% ]      in many ways , chlorophyll a ( c@xmath119h@xmath120mgn@xmath121o@xmath122 ) provides an ideal application for the method outlined in this work . although it is too small to fully exploit all advantages of linear scaling with system size in both the dft and tddft calculation , its size represents the upper limit of systems that can be comfortably studied using plane wave tddft implementations @xcite . due to its importance in photosynthesis , chlorophyll has been studied in great detail both experimentally and in theoretical work using tddft . calculations on chlorophyll were performed using a kinetic energy cutoff of 800 ev . a minimal number of 4 ngwfs per n , h , c , o and mg atom and 1 ngwf per h atom was chosen for the set of valence ngwfs , while for the conduction ngwfs , 13 and 5 where chosen per atom respectively . for the valence ngwfs , a radius of @xmath118 was chosen throughout , while for the conduction ngwfs , a radius of @xmath123 was chosen . the 15 lowest unoccupied states were explicitly optimised and the projector unto the unoccupied subspace was used in order to approximately represent the high energy conduction states . the resulting spectrum produced by the 12 lowest excitation energies in comparison to the experimental spectrum of chlorophyll in diethyl ether @xcite can be found in fig . [ spectrum_chlorophyll ] . we predict the first bright peak of the spectrum at 2.06 ev , while the second bright peak is found to be at 2.80 ev . we compare the results obtained in onetep with those obtained by sundholm @xcite using an alda functional and a sv(p ) gaussian basis set . we note that this gaussian basis calculation predicts the two main peaks of the spectrum to be lower by 50mev . however , the sundholm calculations are carried out using the whole tddft eigenvalue equations while our calculations are based on the tamm - dancoff approximation , so a discrepancy between the two sets of results of the order of less than 0.1 ev is to be expected . with reference to the experimental results , the onetep tddft calculations show a blue shift of the first peak , while the second peak at 2.80 ev is slightly red - shifted compared to the experimental spectrum . a similar result can be seen in the spectrum produced by rocca _ _ @xcite using the pbe exchange correlation functional and a plane - wave basis set , its overall shape being in very good agreement with tddft calculations presented here . the main point that can be taken from the tddft calculation presented here is that almost the whole visible spectrum of chlorophyll a , from 1.8 to 3.0 ev , can be generated by just calculating the first 12 excited states of the tddft superoperator . since the number of states required is very small compared to the dimensions of the tddft operator , iterative methods based on linear response theory are much more efficient than calculations based on the time propagation of the time dependent kohn - sham equations . thus , systems like chlorophyll a , where the low energy spectrum is completely dominated by a few very strong excitations and there is only a very small number of dark , dipole forbidden states , provide a perfect application for the method discussed in this work . the accuracy of the method with truncated density matrices is tested on a gaas nanorod . a number of these nanorods with different terminations have already been studied in some detail @xcite . for our purposes here , we choose a nanorod with hydrogen termination , consisting of a total of 996 atoms and having a length of @xmath124 . the calculations were performed at a kinetic energy cutoff of 400 ev and a minimal number of 4 ngwfs per ga and as atom and 1 ngwf per hydrogen atom was chosen for both sets of ngwfs . an ngwf localisation radius of @xmath125 was chosen for all ngwfs . since the purpose of the calculations on the nanocrystal was to establish the magnitude of errors introduced by the response density matrix only , we performed all calculations with fully dense conduction and valence density matrices and only truncated @xmath48 to different degrees . the nanorods studied here exhibit a large dipole moment and thus a strong electrostatic potential along their long axes , causing the homo and lumo to be strongly localised to opposite ends of the rod . thus for any semi - local approximation to the exchange - correlation kernel , one would expect the lowest excitation energy of the system to correspond to a charge transfer state across the rod . when calculating the lowest eigenvalue for the system using a fully dense response density matrix , this charge transfer state is exactly what we obtain . however , once a density matrix cutoff is introduced , the tddft algorithm converges to an excited state fully localised on the as terminated end of the rod and considerably higher in energy ( see fig . [ gaas_excitations ] ) .        in fig . [ plot_gaas ] , the energy convergence of the localised excited state is plotted with respect to the density matrix truncation used . we find that although a density matrix cutoff does not allow us to converge charge - transfer type excitations , the more localised excitation on the as terminated end of the rod is determined to a high degree of accuracy . a density matrix truncation radius of @xmath126 introduces an error of less than 5 mev compared to the excitation calculated with the full density matrix , suggesting that calculating localised excitations with a truncated density matrix is indeed possible . the fact that the charge transfer states are predicted to be the lowest excited states in our calculations using a full density matrix is an artefact of the local nature of the alda kernel , which leads to a significant underestimation of any long range excitation@xcite . more sophisticated non - local functionals would correct this short - coming and push the charge transfer states significantly higher in energy . in a calculation with a truncated density matrix these corrected states would still be missing . we note however , that our alda calculations with a truncated density matrix allow us to retain those excitations that are well described by local functionals and correspond to those observed experimentally as lowest excitations in the system . thus excluding charge transfer states from a calculation might indeed be desired in certain systems , especially since they often correspond to states much higher in energy than the lowest excitation if appropriate functionals are used . we have shown that excluding these states can be achieved naturally in the linear - response tddft formulation presented here by applying a suitable truncation on the response density matrix .      to demonstrate the linear scaling of the method with the number of atoms , a test system of a single - walled ( 10,0 ) carbon nanotubes ( cnts ) in periodic boundary conditions is chosen . supercell sizes of 640 , 920 , 1240 , 1600 and 1920 atoms are chosen , corresponding to segments of 127 , 193 , 257 , 321 and 386 @xmath127 in length . due to the periodic boundary conditions in place , all supercells simulate an infinitely long ( 10,0 ) cnt . there are well - known problems associated with using local exchange - correlation kernels in infinite systems , which are widely discussed in the community @xcite . furthermore , the very delocalised nature of excitations in the infinite system means that the cnt is not an ideal candidate for introducing a cutoff on the response density matrix , as seen in the previous section . the calculation performed here should therefore be regarded as a demonstration of linear - scaling capabilities only , while the previous sections provide a general demonstration for the accuracy of the method . the calculations were performed at a kinetic energy cutoff of 700 ev and only the lowest excitation energy was converged . as in previous sections , a minimal representation of 4 ngwfs per c atom was used for both the conduction and the valence ngwf sets . a localisation radius of @xmath118 and @xmath123 was selected for the valence and conduction ngwfs respectively . the number of unoccupied states included explicitly in the calculation was chosen such that all bound states were included and thus was scaled up linearly as the supercell size was increased . for the largest segment of 1920 atoms , this corresponds to a tddft operator of dimension @xmath128 in canonical representation and @xmath129 in conduction - valence ngwf representation , prohibitively large for any non - iterative treatment of the eigenvalue problem . in order to achieve full linear scaling in both the ground state and the tddft calculation , a cutoff radius of @xmath130 was applied to both the valence and the conduction density matrix .    . , scaledwidth=45.0% ]    the calculation time for a single iteration of the tddft conjugate gradient algorithm with respect to the different supercell sizes of ( 10,0 ) cnts can be found in fig . [ cnt_timing ] . calculations have been performed for both a fully dense response matrix and a response matrix that has been truncated at @xmath131 . it can be seen that with a moderate response matrix truncation of @xmath131 , the calculation time of a tddft iteration scales fully linearly with system size . however from fig . [ cnt_timing ] it is also evident that even for fully dense response matrices , the algorithm exhibits a near linear scaling behaviour up to the largest supercell sizes . thus for system sizes tested here , the construction of the response potential matrix @xmath132 , which only depends on the density and thus scales linearly even for fully dense @xmath48 , dominates the computation time of the tddft algorithm . for even larger system sizes , it is expected that the cubic scaling associated with the fully dense matrix operations performed to construct the tddft gradient and conjugate search directions will start to strongly influence computation times , making a truncation of @xmath48 necessary . however , it is evident that the algorithm presented here exhibits an excellent scaling up to large system sizes ( 1920 atoms ) even without enforcing the truncation of the response density matrix .","summary":"furthermore , linear scaling of computational cost with system size is demonstrated on ( 10,0 ) carbon nanotubes of different lengths .","abstract":"we present an implementation of time - dependent density - functional theory ( tddft ) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures . the method avoids any explicit reference to canonical representations of either occupied or virtual kohn - sham states and thus achieves linear - scaling computational effort with system size . in contrast to conventional localised orbital formulations , where a single set of localised functions is used to span the occupied and unoccupied state manifold , we make use of two sets of _ in situ _ optimised localised orbitals , one for the occupied and one for the unoccupied space . this double representation approach avoids known problems of spanning the space of unoccupied kohn - sham states with a minimal set of localised orbitals optimised for the occupied space , while the _ in situ _ optimisation procedure allows for efficient calculations with a minimal number of functions . the method is applied to a number of medium sized organic molecules and a good agreement with traditional tddft methods is observed . furthermore , linear scaling of computational cost with system size is demonstrated on ( 10,0 ) carbon nanotubes of different lengths ."}
{"article_id":"1303.0259","section_id":"c","document":"we have presented a linear - scaling tddft algorithm in the linear response formalism . we have demonstrated the accuracy of the method on a number of test systems by comparing to results in the literature obtained with conventional methods . the method presented in this work is ideal for systems in which the low energy excitation spectrum is dominated by a few very strong transitions and only a relatively small number of dark states . for these systems , the advantages of an iterative treatment of the eigenvalue problem can be fully exploited and the method is expected to outperform standard time - evolution tddft algorithms . for systems with a very large number of dipole forbidden states , or nanocrystals with an indirect band gap , calculations become more demanding since a much larger number of states need to be converged in order to produce a meaningful spectrum . however , while the orthogonality requirement of different excited states means that the algorithm can not scale linearly but rather quadratically with the number of excitation energies converged , we note that the prefactor in the quadratic term is generally small , as demonstrated in the calculations on buckminsterfullerene .    furthermore , we have demonstrated that the method scales truly linearly with system size if all density matrices in the formalism can be treated as fully sparse . we have shown the validity of truncating the response density matrix on gaas nanorods for localised excitations , thus giving an example of a realistic system that can be studied while making full use of the advantages of the linear - scaling algorithm presented . while we find that the truncation of the response density matrix prevents us from calculating long - range charge transfer states , we note that these states are badly represented in local approximations to the tddft exchange - correlation kernel in any case . a response density matrix truncation can thus provide an effective way of excluding unwanted charge transfer type states from the calculation . while we have shown that truncations of the response matrix are not always possible for excitations of arbitrary systems , we note that the algorithm shows excellent scaling even for fully dense response density matrices up to a system size of over 2000 atoms . thus , we expect the method to enable large scale computations of optical excitations in important areas such as biophysics and nanoscience .    the authors would like to thank keith refson , leonardo bernasconi and dominik jochym for helpful discussions . the authors would also like to thank jian - hao li for performing a number of benchmark tests of the method implemented in the @xmath2 code . all calculations reported in this work were performed using the imperial college high performance computing service . tjz was supported through a studentship in the centre for doctoral training on theory and simulation of materials at imperial college funded by epsrc under grant number ep / g036888/1 . ndmh acknowledges the support of epsrc grants ep / g05567x/1 and ep / j015059/1 , a leverhulme early career fellowship , and the winton programme for the physics of sustainability . pdh acknowledges the support of a royal society university research fellowship . 99 a. j. nozik , appl . . lett . * 30 * , 567 ( 1977 ) . m. grtzel , nature * 414 * , 338 ( 2001 ) . d. a. tryk , a. fujishima , and k. honda , electrochim . acta * 45 * , 2363 ( 2000 ) . m. walter , e. warren , j. mckone , s. w. boettcher , q. mi , e. a. santori , and n. s. lewis , chem . rev . * 110 * , 6446 ( 2010 ) . j. shi , y. zhu , x. zhang , w. r. g. baeyens , and a. m. garca - 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portal , and r. m. martin , phys . b * 66 * , 235416 ( 2002 ) . r. bauernschmitt , r. ahlrichs , f. h. heinrich , and m. m. kappes , j. am . soc . * 120 * , 5052 ( 1998 ) . h. du , r. c. a. fuh , j. li , l. a. corkan , and j. s. lindsey , photochem . photobiol . * 68 * , 141 ( 1998 ) ; http://omlc.ogi.edu/spectra/photochemcad/html/123.html . d. sundholm , chem . . lett . * 302 * , 480 ( 1999 ) . p. w. avraam , n. d. m. hine , p. tangney , and p. d. haynes , phys . b * 83 * , 241402(r ) ( 2011 ) . p. w. avraam , n. d. m. hine , p. tangney , and p. d. haynes , phys . b * 85 * , 115404 ( 2012 ) .","summary":"the method is applied to a number of medium sized organic molecules and a good agreement with traditional tddft methods is observed .","abstract":"we present an implementation of time - dependent density - functional theory ( tddft ) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures . the method avoids any explicit reference to canonical representations of either occupied or virtual kohn - sham states and thus achieves linear - scaling computational effort with system size . in contrast to conventional localised orbital formulations , where a single set of localised functions is used to span the occupied and unoccupied state manifold , we make use of two sets of _ in situ _ optimised localised orbitals , one for the occupied and one for the unoccupied space . this double representation approach avoids known problems of spanning the space of unoccupied kohn - sham states with a minimal set of localised orbitals optimised for the occupied space , while the _ in situ _ optimisation procedure allows for efficient calculations with a minimal number of functions . the method is applied to a number of medium sized organic molecules and a good agreement with traditional tddft methods is observed . furthermore , linear scaling of computational cost with system size is demonstrated on ( 10,0 ) carbon nanotubes of different lengths ."}
{"article_id":"1305.5258","section_id":"i","document":"the mid - ir spectra of many galactic and extragalactic sources display the well - known unidentified infrared ( uir ) bands at 3.3 , 6.2 , 7.7 , 8.6 , 11.2 , and 12.7  ( c.f . @xcite ; @xcite ; @xcite ) . these broad emission features are generally attributed to the ir - relaxation of uv - pumped polycyclic aromatic hydrocarbon ( pah ) molecules (; @xcite , ) . observationally , the relative strengths , peak position , and profile of the pah features have been seen to vary considerably within a source and from source to source ( e.g. @xcite ; ; @xcite ) . the relative strengths of pah features also change drastically going from neutral molecules to ions in laboratory studies ( c.f . @xcite ) . in particular , the 3.3 and 11.2  features arise primarily from neutral pah molecules while the 6.2 , 7.7 , and 8.6  features are attributed to pah ions . this allows ratios involving the neutrals and ions , such as the 7.7/11.2 ratio , to be useful tools for probing the ionization state of the emitting molecules and hence for probing the local physical conditions ( e.g. @xcite ) . in addition , smaller molecules dominate the emission at shorter wavelengths while larger molecules emit predominantly at longer wavelengths @xcite .    despite the success of pah ratios as tracers of physical conditions within a source , dust extinction often hampers measuring and interpreting these ratios . while there is extinction across the whole ir range , the main issue for pahs is silicate extinction in the mid - ir which primarily affects the 8.6 and 11.2  pah bands . moreover , this extinction can vary spatially across a source , complicating the interpretation of the observed mid - ir pah features . @xcite investigated variations in the pah ratios in a variety of objects including m82 , and concluded that pah variations are being caused by the properties of the emitting pah population within the objects in their study . however , @xcite attribute the pah band variations in this source to extinction variations . indeed they posited that the variations in dust extinction are strong enough to affect the interpretation of their calculated pah ratios , which showed variations comparable to the variations in extinction . this presents a fundamental problem in interpreting pah ratios : are the variations in the band ratios intrinsic to the source ? are they the direct result of variations in the extinction due to dust ? or are they some combination of the two ? unfortunately , the only source in which this effect has been studied , m82 , is a very complex and distant source , so each spitzer / irs pixel contains unresolved structure which adds to the already considerable uncertainties on the extinction and pah measurements . on the other hand , many galactic h  ii regions can be spatially resolved at many wavelengths and the general principles of their structures are well understood ( e.g. ( * ? ? ? * chapter 7 ) ) . these properties greatly increase the precision of which the spatial variations of extinction can be studied within the target as well as giving access to multiple other methods of extinction measurement . as a result , studying the effects of extinction on pah variations in a galactic h  ii region instead of m82 should result in a prime testbed to address this question . understanding the characteristics of dust in regions of massive star formation is of key importance as dust extinction and reemission dominates the spectral energy distribution of these regions . studies on the properties of dust in h  ii regions around massive young stars have a long history dating back to the optical studies on light scattering by @xcite , infrared studies by @xcite , and sub millimeter @xcite . the advent of moderate resolution infrared spectrometers with wide coverage on ground - based and space based platforms has opened up novel ways of probing the dust characteristics in h  ii regions through comparisons of the strength of ir recombination lines and studies of this type have revealed distinct differences with dust properties in the diffuse ism ( e.g. ) . the absorption characteristics of dust in h  ii regions can also be gleaned from detailed studies of the ( infrared ) spectral energy distribution ( @xcite ; @xcite ; ) . the high sensitivity of the irs spectrometer on the spitzer space telescope has opened up the study of the characteristics of dust in molecular clouds through photometric and spectroscopic studies of background stars shining through the cloud ( @xcite ; @xcite ; ; @xcite ) . these observations reveal that the dust properties vary widely within molecular clouds and regions of star formation . these variations likely reflect the importance of coagulation of interstellar dust in larger and larger aggregates as the density increases (; ) . there are several well known ways to measure the extinction in an h  ii region of which three will be employed in this paper . the first two require observations of the ionized hydrogen emission from the center of the h  ii region . we will employ the recombination lines in the nir and this shall be referred to as the nir method . the second method , the radio method , involves comparing the strength of the nir hydrogen lines with the radio continuum generated by the same ionized hydrogen . the third method is independent of the first two , and fits the 9.8  silicate profile to the observed spectra , deriving the depth of the 9.8  silicate absorption feature ; this will be referred to as the ` spoon ' method @xcite . in addition , the code pahfit does a similar analysis to the spoon method in fitting the mir spectrum and provides the optical depth of the 9.8  silicate absorption feature . we have therefore obtained narrow band photometric observations of the paschen @xmath0 ( hereafter pa@xmath0 ) and brackett @xmath1 ( hereafter br@xmath1 ) hydrogen lines of the galactic h  ii region ( iras 12063 - 6259 , he 2 - 77 ) . we will combine these data with mid - ir spitzer / irs spectral maps and radio to create multiple extinction maps to ensure consistency . subsequently , we can use these extinction maps to correct our spitzer / irs observations in order to investigate the effects of extinction on the pah band ratios . section 2 will be devoted to background information about iras 12063 - 6259 , including the relevant prior observations . in sections 3 the data reduction processes relevant to the isaac , atca and spitzer / irs data are described . section 4 shows the derivations of extinction maps from these data along with relevant discussion . in section 5 , the measurement of the pah bands and their correlations in the reddened and dereddened data are presented . in section 6 , the morphology of iras 12063 - 6259 and the effects of extinction on pahs is discussed and section 7 presents conclusions .","summary":"they have never been observed for h ii regions .","abstract":"the spatial variations in pah band intensities are normally attributed to the physical conditions of the emitting pahs , however in recent years it has been suggested that such variations are caused mainly by extinction . to resolve this question , we have obtained near - infrared ( nir ) , mid - infrared ( mir ) and radio observations of the compact h ii region iras 12063 - 6259 . we use these data to construct multiple independent extinction maps and also to measure the main pah features ( 6.2 , 7.7 , 8.6 and 11.2 ) in the mir . three extinction maps are derived : the first using the nir hydrogen lines and case b recombination theory ; the second combining the nir data with radio data ; and the third making use of the spitzer / irs mir observations to measure the 9.8  silicate absorption feature using the spoon method and pahfit ( as the depth of this feature can be related to overall extinction ) . the silicate absorption over the bright , southern component of iras 12063 - 6259 is almost absent while the other methods find significant extinction . while such breakdowns of the relationship between the nir extinction and the 9.8  absorption have been observed in molecular clouds , they have never been observed for h ii regions . we then compare the pah intensity variations in the spitzer / irs data after dereddening to those found in the original data . it was found that in most cases , the pah band intensity variations persist even after dereddening , implying that extinction is not the main cause of the pah band intensity variations ."}
{"article_id":"1305.5258","section_id":"r","document":"the general formula for differential extinction @xmath21 between two different wavelengths @xmath22 and @xmath23 is given by :    @xmath24 \\label{eq:1}\\ ] ]    where @xmath25 is the intrinsic flux and @xmath26 is the observed flux of a line at @xmath22 . given an electron density of 10003000 @xmath4 and temperature of @xmath27 8800 k ( see section  [ sec : source ] ) , a linear interpolation between the nearest case b grid points provided by @xcite gives @xmath28 . equation  [ eq:1 ] can then be restated for this specific case as :    @xmath29    extinction in the nir ( @xmath27 13 ) is described by a power law , usually taken to be of the following form @xcite :    @xmath30    where @xmath31 is in  and the exponent @xmath2 is usually in the range of 1.72.0 for the ism ( e.g. @xcite ) . it is then possible to state both @xmath32 and @xmath33 in terms of @xmath34 by substituting eq  [ eq : ak ] as appropriate :    @xmath35    adopting @xmath2 = 1.8 ( e.g. @xcite ) .    upon substitution of our flux calibrated maps , this produces the extinction map shown in figure  [ fig2 ] . the area of highest extinction is correlated with the dark lane across the nebula ( figure  [ fig1 ] ) . the highest extinction values ( @xmath36 ) are observed at the same position as the radio a source ( and as such are compromised by a lack of signal to noise ) , the second radio source ( radio b ) is obscured to a much lower extent ( @xmath37 ) .     of 0.25 , 0.5 , 0.75 , 1.0 , 1.25 , 1.5 , 2 ; white contours represent the 4.8 ghz radio observations ( as in figure  [ fig1 ] ) . the red contours surrounding radio b and some bright stars represent the pa@xmath0 s / n level of 3 . solid black circles represent areas in which foreground stars have been masked out . the @xmath38 and @xmath39 axes refer to positions in pixels on the nir images ( 0.148  per pixel).,width=302 ]    the derived values of @xmath34 ( 0.6  2.5 ) are consistent with the average value of 0.8 derived by @xcite using iso - sws data . the @xcite value would be biased towards the lower values as the iso aperture ( 14x 20 , see figure 2 of @xcite ) included the brightest ( lowest extinction ) parts which dominate the emission line spectrum and lead to a lower overall estimate of extinction . this method will henceforth be referred to as the nir method .      from radio observations of the ionized hydrogen continuum at multiple frequencies it is possible to derive the intrinsic intensity of recombination lines that are also emitted . this can be used to measure extinction as the observed flux of a hydrogen line ( such as those discussed in the previous section ) can be compared to the flux predicted by the radio observations . in order to derive the flux implied by the radio observations , some other quantities ( such as the electron temperature and emission measure ) must also be derived . using the atca radio observations ( discussed in section  [ sec : atca ] ) a brightness temperature map for both 4.8 and 8.6 ghz observations can be calculated . the brightness temperature is defined as ( * ? ? ? * equation 7.70 ) :    @xmath40\\ ] ]    where @xmath41 is the frequency in hz , @xmath42 is the brightness temperature in k and @xmath43 is the source solid angle . the source solid angle has been explicitly included to facilitate the creation of brightness temperature maps ( i.e. per pixel ) , rather than the usual method of using the sum of all radio flux for the whole object . we can rearrange to find :    @xmath44 \\label{eq : tb_deriv}\\ ] ]    we will refer to the maps created using this equation as the  observed \" brightness temperature maps . the brightness temperatures are in general much higher for the 4.8 ghz map , peaking at around 300 k as opposed to 50 k for the 8.64 ghz map . the unusual configuration of the atca array means that the atca beam is an elliptical rather than a circular aperture . as it is necessary to combine the two maps , they were combined by smoothing the higher frequency ( 8.64 ghz ) map using the larger beam of the low frequency ( 4.8 ghz ) map , taking into account this ellipticity . the following equations then describe the relationship between the important quantities necessary for calculating the intrinsic emission of any hydrogen recombination line , namely the electron temperature , @xmath6 and emission measure , @xmath45 :    @xmath46 \\label{eq : tb}\\ ] ]    and :    @xmath47    where @xmath41 is the frequency of our radio observations , @xmath48 is the optical depth for that frequency and @xmath49 is a function of @xmath6 and @xmath41 and represents the ratio of the true optical depth to a simplified approximation @xcite . @xmath6 was then found using iterative calculations ( cf . @xcite ; @xcite ) after combining equations  [ eq : tb ] and [ eq : nu ] to find :    @xmath50^{-2.1 } }   \\right ) \\quad [ \\textrm{k } ] \\label{eq : fin}\\ ] ]    where @xmath51 is the observed 4.8 ghz brightness temperature map and the factor @xmath52^{-2.1}$ ] represents the optical depth at 4.8 ghz as implied by the 8.64 ghz measurements . for the first iteration , the temperatures measured by previous authors ( as mentioned in section  [ sec : source ] ) of around 9000 k was used for the whole map . the difference between the observed brightness temperature map and that calculated using equation  [ eq : fin ] was applied iteratively to correct our @xmath6 map until no further changes were observed . the resultant map shows that radio a has a slightly lower average temperature ( @xmath27  8000 k ) than radio b ( 9000 k ) and that the temperature throughout most of the emission is roughly constant at around 9000 k. knowing @xmath6 , equation  [ eq : nu ] can then be rearranged to calculate the emission measure ( @xmath45 ) for each pixel :    @xmath53\\textrm{. } \\label{eq : em}\\ ] ]    following @xcite , we then calculate the expected flux at br@xmath1 using the following equation :    @xmath54 \\label{eq : brg0}\\ ] ]    where it is assumed that the hydrogen abundance by number is 0.9 , h is planck s constant , @xmath55 is the frequency of a @xmath56 photon , @xmath43 is the solid angle subtended by the emitting source and    @xmath57    represents the effective recombination cross section @xcite .    to find a specific expression for @xmath58 , we can substitute eq .  [ eq : em ] into eq . [ eq : brg0 ] to yield :    @xmath59 \\label{eq : brg}\\ ] ]    which was calculated for each pixel of the map . the extinction a@xmath60 , is then calculated by comparing the observed and calculated br@xmath1 fluxes ( equation  [ eq : akrad ] ) . @xmath61    from this , the k band extinction , a@xmath62 , is found as before , using eq . [ eq : ak ] . the calculated br@xmath1 map ( equation  [ eq : brg ] ) , is shown along with the observed isaac br@xmath1 map smoothed to the same resolution , in figure  [ fig5 ] , along with the resultant extinction map . this method will be referred to as the radio method . = 2.3 ) and b ( spoon a@xmath62 = 0.0 ) respectively . the radio b spectrum has been offset from the radio a spectrum for clarity . the thin red and blue lines are the initial interpolated power law continua for both cases ( with the interpolation points marked with crosses ) , the black dashed line at @xmath31 = 9.8  shows the approximate location of the silicate feature . the red dotted and dashed lines are the spectrum of radio a after being dereddened using the non - iterative spoon method ( dotted ) and the iterative spoon method ( dashed ) and then normalized to the observed spectrum . , width=302 ]    @xcite proposed a method for measuring the depth of the 9.8  silicate absorption feature independent of any intrinsic profile of the absorption . the spoon method , for pah dominated spectra ( see @xcite ) , is as follows : interpolate a power law continuum using points at 5.5  and 14.5  of the form @xmath63 , then calculate the natural log of the ratio of the flux of this continuum at 9.8  and the observed flux at 9.8 . this value , called @xmath64 by @xcite , can be interpreted as the optical depth at 9.8 , @xmath65 . an example of this method employed on the spitzer / irs spectra of radio a and b is presented in figure  [ fig6 ] . as discussed by @xcite , if significant silicate extinction is present , the flux of the long wavelength continuum point will be affected by absorption because of the overlapping of the 9.8 and 18  bands . @xcite suggest that if a long - low ( ll ) irs cube is available , that the 14.5  continuum point can be abandoned in favor of one at 23  which is less susceptible to silicate absorption . ll data for iras 12063 - 6259 are not available , so a new approach , iteratively calculating the extinction using the spoon method in combination with a wavelength profile of the absorption , has been devised . when the 14.5  continuum point is affected by silicate absorption , the spoon method underestimates the continuum at 9.8   leading to an underprediction of @xmath66 . dereddening such irs spectra using this value of @xmath66 , will still leave unaccounted for silicate absorption ( this is shown in figure  [ fig6 ] , where the dashed red line is the result of dereddening the radio a spectrum in this way ) . the new method implemented here applies the spoon method again to such a dereddened spectrum , to find a new value of @xmath66 . this process of applying the spoon method and dereddening the spectrum continues until the flux of the continuum point at 14.5  ceases to change . the continuum point at 9.8  in the final continuum is then compared with the observed 9.8  flux in the original spectrum . for the spectra most affected by silicate absorption ( @xmath66 @xmath67 2.0 ) , the difference between the initial value provided by the spoon method and the final value was around 40% .     and @xmath39 axes refer to positions in pixels on the irs cube ( 1.8  per pixel ) . , width=302 ]    in practice , the @xcite description of the shape of the 9.8 and 18  silicate extinction features in the ism to is used to deredden the irs sl spectra at each stage . the @xcite model also gives a direct relationship between a@xmath68 and a@xmath62 , which turns out to be nearly equal to one ( 1.006 ) . this provides the following relation between @xmath66 and a@xmath62 :    @xmath69    so to within 10% , a@xmath62 is equal to @xmath66 under the conditions for which the @xcite description of the silicate features in the local ism are satisfied . this method will be referred to as the spoon method in future discussion . the map of extinction as measured by the spoon method is presented in figure  [ fig_sil ] .      before using the various extinction maps to deredden mid - ir observations , they can be compared for consistency and correlations . in each case , the higher spatial resolution observation must be binned to match the resolution of the lower and then the derived extinctions for each pixel can be compared . the three maps have pixels of size 0.15 , 0.3  and 1.8  for the nir , radio and irs data respectively . as such , s / n improves significantly upon binning . however , it is still likely that many nir points will be untrustworthy as a ) the native resolution measurements of pa@xmath0 which are used to create them are have very low s / n and b ) the morphology of the nir narrow band emission does not match that of the mir or radio emission . point b also applies to the radio method , as the br@xmath1 image is used for this method . morphologically , the only large scale comparison can be drawn between the nir map and the spoon map as they cover large areas . the nir map ( figure  [ fig2 ] ) shows the prominent bar ( @xmath34 = 1.5  2 ) running from east to west , with the highest extinction ( @xmath34 = 2.5 ) occurring very near to the location of radio a within the bar . the southern regions , near radio b but also covering the extended emission evident in the h@xmath2 map shown in figure  [ fig1 ] , display an @xmath34 of between 1 and 1.25 . in contrast , the spoon map ( figure  [ fig_sil ] ) shows zero extinction in the southern regions near radio b. it agrees with the nir map in that the peak extinction occurs near radio a ( although it underestimates the degree of extinction ) , but the ` bar ' of extinction visible in the nir is only somewhat present as it falls between the radio a peak and the large region of silicate absorption occurring to the east . ( resampled to the same resolution as the radio data ) against radio @xmath34 . the cluster of points are those from the radio b h  ii region . , width=302 ]    in figure  [ fig9 ] , the correlation between the extinction derived with the nir method against that derived with the radio data is shown ( after discarding points with pa@xmath0 s / n @xmath70 3 ) . the distribution of points is consistent with a 1:1 correlation at low extinction ( radio b ) , with both isaac and radio methods yielding @xmath34 @xmath27 1.5 . the valid nir method points do not cover the high extinction radio a source as there is very little pa@xmath0 flux in this region .     against radio @xmath34 ( resampled to spitzer / irs sl pixel size : 1.8 ) . high extinction points are associated with the pixels associated with radio a , whilst the low extinction points are from radio b. , width=302 ]    figure  [ fig11 ] shows the correlation between the extinction derived from the radio data against that derived using the spoon method . the high extinction points near radio a have been included as lower limits ( see later discussion ) . at low @xmath34 ( radio b ) , the radio method presents a value of around 1.4 , while the spoon method finds a value very close to zero ( @xmath70 0.2 ) .     against isaac @xmath34 . the radio b pixels from figure  [ fig11 ] are marked as black crosses , the remaining points are included as blue or red diamonds corresponding to regions away from or associated with the radio b h  ii region ( i.e. within the southern low extinction region in figure  [ fig_sil ] ) respectively . , width=302 ]    in figure  [ fig10 ] , the correlation between the extinction derived from the nir method versus that derived using the spoon method is shown . figure  [ fig10 ] includes all of the data for the region surrounding iras 12063 - 6259 in figure  [ fig10 ] as both the spitzer / irs map and the isaac data are valid away from the brightest regions of the source . in figure [ fig10 ] , the points associated with the radio b h  ii region have been indicated ( red points ) and all possess lower spoon extinction than those away from the radio b h  ii region ( blue points ) as is already obvious from a cursory inspection of the spectra ( c.f . figure  [ fig6 ] ) . in figure [ fig10 ] , the s / n threshold for including points was increased to 5 to better display the discrepancy between the area of low silicate absorption near radio b and the higher absorption in the surroundings . in principle the radio method is the most accurate at measuring the total extinction between the emitting source and the observer . the radio observations detect the total emission from the h  ii region and so reflect the true shape of the ionized region , while at br@xmath1 the morphology is more complex and does not totally match that in the radio . around radio b , the br@xmath1 and radio morphologies match and the extinction measured is the same as that of the nir method . however near radio a , it is debatable whether any of the detected br@xmath1 flux emanates from the radio a h  ii region at all . the morphology of the emission is certainly very different , indicating the possibility that this may be diffuse emission associated with ir 12063 or foreground emission . in that case , the extinction derived from the br@xmath1-radio continuum comparison provides a lower limit to the extinction of source a ( and an upper limit to the extinction associated with the surrounding diffuse h  ii component ) . near radio b , a consistent extinction is found with the nir and the radio methods , but a discrepant extinction , of around a@xmath62 @xmath27 0.2 , is found using the spoon method . the emission morphology around radio b is very similar in the radio and nir , so we can safely assume that the extinctions measured are the extinction between the radio b h  ii region and the observer for the isaac and radio methods . the discrepant measurement arising from the spoon method around radio b was checked using an independent measure of the silicate absorption feature : pahfit @xcite . both methods agree that the pixels coincident with radio b , marked with red diamonds in figure  [ fig10a ] , have low silicate optical depths ( @xmath71 ) in agreement with the spoon method , while the bulk of the rest of the points display much higher silicate absorption . at low optical depths , the points in figure  [ fig10a ] seem to agree , while at higher optical depths ( @xmath72 ) pahfit finds a higher optical depth ( by around a factor of two ) than the spoon method . @xcite found the opposite trend in that they quote a higher range of values for the spoon method rather than pahfit . pahfit was used to measure each pixel of the irs - sl cube of iras 12063 - 6259 , and the resulting correlation between the @xmath66 of pahfit against that of the spoon method is shown in figure  [ fig10a ] . it should be noted that pahfit is intended to fit full irs spectra ( 540 ) , and large uncertainties result from using pahfit with only the irs / sl range ( 514 ) because the longer wavelength continuum greatly aids the fitting process . however there exist no longer wavelength observations of iras 12063 - 6259 so the silicate absorption strength as measured by pahfit result from its application to only the irs / sl range . in order to achieve a sensible extinction result from pahfit , it was necessary to impose a floor of @xmath73 because it was found that pahfit frequently found fits to many of the pixels in the map with zero silicate absorption , even for pixels where the spoon method found considerable optical depth ( up to @xmath74 ) . some of even after imposing this floor , there is still evidence of this effect in figure  [ fig10a ] , where there is a line of points at @xmath75 and a range of spoon values from zero to around 0.8 . this implies that pahfit found an acceptable fit with effectively zero silicate absorption in spectra where the spoon method detects optical depths of 0.8 . from figure  [ fig10a ] we can also see the opposite effect , there are some pixels in which pahfit detects optical depths of up to 0.8 where the spoon method detects zero optical depth , so it seems that under low optical depth conditions , both methods carry large uncertainties .     against pahfit @xmath66 . the pixels from radio b have been indicated with filled red diamonds . the black line indicates a 1:1 correlation . , width=302 ]    in the diffuse ism , the 9.8  optical depth ( as provided by the spoon method ) and extinction derived in the nir have been found to follow a tight correlation ( e.g. @xcite and references therein ) . hints that there may be a different relationship between these quantities in some circumstances , i.e. possibly a shallower correlation , were found by @xcite . later studies confirmed this difference for molecular cloud sightlines and found that both the 9.8  silicate optical depth , and the total optical depth at 9.8  ( continuum + silicates ) correlate well with the nir extinction , albeit with a shallower dependence for molecular clouds than the diffuse ism ( e.g. @xcite ; @xcite ; @xcite ; ) . the data and correlations from these studies , along with that of iras 12063 - 6259 are shown in figure  [ figtau ] . none of the aforementioned studies found objects as extreme as radio b ( nir a@xmath62 = 1.5 , @xmath66 = 0.2 ) . the areas of diffuse emission around the radio b h  ii region are slightly above the general ism trend ( nir a@xmath62 @xmath27 1.5 , @xmath66 @xmath27 1.0 ; blue points in figure  [ fig10 ] ) .    in figure  [ figtau ] , a selection of h  ii regions have been included which were present in the @xcite sample and so have nir a@xmath62 measurements . the corresponding measurements of their silicate optical depth were found by applying the spoon methodto their iso - sws spectra . the large iso - sws beam means that both the nir a@xmath62 s and silicate optical depths are spatial averages across each h  ii region . in general the iso - sws h  ii region sample appear along the ism trend in figure  [ figtau ] . however three of them : iras 02219 + 6152 , iras 10589 - 6034 and iras 18434 - 0242 ( better known as g029.96 - 00.02 ) , appear in roughly the same place as radio b in figure  [ figtau ] . iras 10589 - 6034 is part of a larger complex of very bright h@xmath2 emission ( saturated in the shs ) and also appears with similar morphology in each of the 2mass bands . these points are much lower than either the molecular cloud or ism trends . the three sources mentioned all have higher values of @xmath66 shown in the literature , ( e.g. @xcite for iras 02219 + 6152 ) however , there is very little trace of absorption in the iso - sws spectra .    from inspection of figure [ figtau ] , it appears that h  ii regions follow the ism trend when spatially integrated but that under certain circumstances they can violate this trend and have low silicate absorption . in the case of iras 12063 - 6259 , the radio b points appear to follow the molecular cloud trend while the diffuse surroundings follow the diffuse ism trend . the three sources which appear near the radio b points in figure  [ figtau ] presumably represent objects with similar conditions to radio b , but without the surrounding deep silicate absorption that is seen in iras 12063 - 6259 as this would appear in the iso - sws spectrum . we note that the general picture is the same if pahfit silicate absorption measurements are used in place of the spoon measurements , except that the points representing the diffuse surroundings of radio b fall well above the dism trend . included in figure  [ figtau ] is the iso - sws measurement of iras 12063 - 6259 ( as indicated in the figure ) , which was treated in the same way as the other iso - sws spectra . the iso - sws aperture used for this observation ( shown in figure  [ fig1 ] ) , includes both the bright southern part of iras 12063 - 6259 as well as the surrounding areas of high silicate extinction . the iso - sws observation of iras 12063 - 6259 ( and by inference possibly the observations of the other h  ii regions ) represents a combination of both effects and as such the iras 12063 - 6259 point appears near , but below , the dism trend in figure  [ figtau ] . ( spoon ) and nir extinction with reference points representing the diffuse ism and molecular clouds ( black crosses , @xcite ) , a sample of h  ii regions observed with iso - sws (; black triangles , see text ) and the measurements of the area around radio b and the diffuse emission from around iras 12063 - 6259 ( red diamonds and blue diamonds respectively , the same points as in figure  [ fig10 ] ) . best fit lines for ism and molecular cloud sightlines are shown in black . , width=302 ]    the physical interpretation of the differing relationship between @xmath76 and the nir extinction is usually attributed to the effects of grain growth in molecular clouds . grain coagulation causes the nir opacity to rise relative to the 9.8  silicate absorption because silicates are more easily coagulated than carbonaceous material . while found that it was very difficult to reproduce the observed relationship between @xmath76 and the nir extinction without significantly altering the shape of the 9.8  feature profile , the shape of the 9.8  silicate absorption feature in the vicinity of radio b can not be directly measured as there is so little absorption ( see figure  [ fig6 ] ) . the other major possibility which could solve the discrepancy between the nir extinction and the silicate optical depth is that properties of the nir extinction , generated by carbonaceous materials is different in the vicinity of radio b. this possibility can be ruled out on the grounds that the radio and nir extinction measurements appear to be consistent with standard nir extinction laws ( e.g. eq .  [ eq : ak ] ) . the preceding discussion dramatically alters the picture of how the extinction maps can be applied to dereddening the mid - ir cube . it appears that each extinction map is valid in somewhat different regions . the nir extinction map , for example is only valid around radio b , where there is sufficient s / n to make an accurate determination of the extinction . the radio extinction map is also only accurate around radio b , and over a much smaller area than the nir map ( because the radio observations are not sensitive to structure on larger scales ) . the spoon and pahfit maps appear to not be trustworthy in the vicinity of radio a or b , as the previous discussion has shown that the ratio of silicate absorption to nir extinction around both is much lower than would be expected .      in order to investigate the effects of extinction on the ratios of the major pah bands , the irs cube ( as described in section  [ sec : irs ] ) was dereddened using the @xcite prescription for the extinction in the mid - ir relative to @xmath34 using the extinction maps described in the previous section . the regions for which the extinction maps are not thought to be trustworthy have been removed and are not presented in the following analysis . the continuum subtraction and flux measuring process as described in section  [ sec : irs ] was repeated for cubes dereddened using the spoon and nir methods in the areas of their validity . in this section the unaltered observations will be referred to as the ` observed ' data , while the dereddened data will be referred to by the extinction map which was used to create it , e.g. spoon or nir .    following the discussion in section [ sec : extdisc ] , the extinction maps were used for dereddening in areas where they are valid . therefore , in the case of the spoon extinction map , the area around both radio sources is likely untrustworthy and has been masked out . for the nir map , only the regions where the pa@xmath0 signal to noise is above three at native resolution are included . the radio extinction map has not been used for dereddening purposes as it covers a very small area and would produce very few dereddened points .     and @xmath39 axes refer to positions in pixels on the irs cube ( 1.8  per pixel ) . , width=302 ]     and @xmath39 axes refer to positions in pixels on the irs cube ( 1.8  per pixel ) . , width=302 ]    the spatial distributions of the pah bands ( shown in figures  [ fig12 ]  and  [ fig12a ] ) show strong spatial variations which seem to correlate with extinction . the 6.2 and 7.7  bands peak in absolute strength near radio a as well as being very similar morphologically ( see figure  [ fig12 ] for 6.2  map along with radio and silicate absorption contours ) . in both maps the radio a peaks are all slightly offset to the south of radio a , possibly attributable to the large gradient in extinction in this region . they also show additional emission extending west towards the edge of the map . the 6.2 and 7.7  maps also display isolated weak emission east of radio a. the 8.6 and 11.2  bands peak around radio b and also share the same morphology , with some extended emission towards radio a. figure  [ fig12a ] shows the morphology of the 8.6  emission , as compared to the radio emission and the strength of silicate absorption . a comparison of figures  [ fig12 ] and  [ fig12a ] shows the effects of the silicate absorption band on pahs in that the morphologies are dramatically different . the area around radio a , associated with the highest extinction values , has strong 6.2 and 7.7  and weak 8.6 and 11.2  emission .    in general , ratios of pah band intensities ( i.e. i@xmath77/i@xmath78 ) are taken to remove any influence that distance , abundance or variations in the intrinsic strength of the whole pah spectrum may play on the relationships between the bands . this allows unbiased inspection of the relative strengths of different bands . /i@xmath78 plotted against i@xmath79/i@xmath78 for the pixels surrounding radio a and b. the red triangles represent the observed ratios while the blue diamonds represent the same data after dereddening using the spoon extinction map and the green squares are similar using the isaac extinction map . best fit gradients for each set of points are shown in the same color . a dereddening vector corresponding to @xmath34 = 1 is shown in black . , width=302 ]    /i@xmath78 plotted against i@xmath79/i@xmath78 for the pixels surrounding radio a and b. the red , blue and green points are as in figure  [ fig14 ] . best fit gradients for each set of points are shown in the same color . a dereddening vector corresponding to @xmath34 = 1 is shown in black . , width=302 ]    /i@xmath78 plotted against i@xmath77/i@xmath78 for the pixels surrounding radio a and b. the red , blue and green points are as in figure  [ fig14 ] . best fit gradients for each set of points are shown in the same color . a dereddening vector corresponding to @xmath34 = 1 is shown in black . , width=302 ]    l l l p1.4 cm p1.4 cm data & slope & intercept & slope y(0)=0 & correlation coefficient +   +   + observed & 3.19@xmath30.06 & -0.60@xmath30.11 & 2.84@xmath30.01 & 0.961 + spoon & 2.27@xmath30.06 & 0.53@xmath30.07 & 2.72@xmath30.01 & 0.947 + nir & 3.66@xmath30.26 & -1.19@xmath30.25 & 2.47@xmath30.03 & 0.914 + ngc 2023@xmath7 & 2.04@xmath30.02 & -0.29@xmath30.03 & 1.89@xmath30.01 & 0.967 + m17@xmath10 & & & 1.96 & 0.81 +   +   + observed & 5.24@xmath30.15 & -1.71@xmath30.19 & 3.90@xmath30.03 & 0.954 + spoon & 17.01@xmath33.37 & -12.77@xmath33.17 & 3.42@xmath30.03 & 0.636 + nir & 2.17@xmath30.18 & 0.97@xmath30.13 & 3.57@xmath30.08 & 0.871 + ngc 2023@xmath7 & 4.40@xmath30.06 & 1.17@xmath30.03 & 6.31@xmath30.04 & 0.953 + m17@xmath10 & - & & 11.91 & 0.33 +   +   + observed & 1.66@xmath30.07 & -0.38@xmath30.09 & 1.37@xmath30.01 & 0.880 + spoon & 10.19@xmath32.82 & -8.40@xmath32.65 & 1.25@xmath30.01 & 0.593 + nir & 0.41@xmath30.08 & 0.70@xmath30.06 & 1.43@xmath30.05 & 0.676 + ngc 2023@xmath7 & 2.13@xmath30.03 & 0.72@xmath30.03 & 3.44@xmath30.02 & 0.949 +    @xmath7 : peeters et al . , 2013 in prep . + @xmath10 : @xcite    the most commonly quoted correlation , i@xmath77/i@xmath78 vs i@xmath79/i@xmath78 , is presented in figure  [ fig14 ] ) . similar trends are seen for both i@xmath80/i@xmath78 vs i@xmath79/i@xmath78 ( figure  [ fig16 ] ) and i@xmath80/i@xmath78 vs i@xmath77/i@xmath78 ( figure  [ fig17 ] ) in the observed data . fits to each of these correlations ( along with the dereddened correlations which are subsequently presented ) are presented in table  [ table_pahparms ] . separate gradients for each correlation are provided which pass through the origin or are allowed to vary their y - intercepts .    in each of figures  [ fig14 ] , [ fig16 ]  and  [ fig17 ] dereddened points have also been included . for the i@xmath77/i@xmath78 vs i@xmath79/i@xmath78 correlation , the points with the highest ordinate values correspond to the points of highest extinction around radio a. this collection of points ( i@xmath79/i@xmath78 @xmath67 5 ) clearly displays a different slope than the rest of the points for the low extinction parts of the source . the dereddened points in figure  [ fig14 ] remove the ` break ' in the slopes evident in the observed data . the general effect of extinction of the i@xmath77/i@xmath78 vs i@xmath79/i@xmath78 correlation is most straightforward to explain : the 11.2  pah band is affected by extinction from the 9.8  silicate feature to a greater degree than the 6.2 or 7.7  bands . therefore the effect of extinction is to preferentially reduce the 11.2  pah flux and increase both the i@xmath77/i@xmath78 and i@xmath79/i@xmath78 ratios . the major effect of dereddening this correlation is to decrease each of the ratios and as such move all points towards the origin .    comparing the data in table  [ table_pahparms ] for iras 12063 - 6259 to that of ngc 2023 , which was measured in the same way with the same software ( peeters et al . , 2013 , in prep . ) , it is clear that there is no agreement between any of the parameters of the correlations between the pah bands as observed for iras 12063 - 6259 and ngc 2023 . included in table  [ table_pahparms ] are the correlations derived by @xcite for the m17 galactic star formation complex , which is the only galactic h  ii region in the @xcite sample . the m17 correlation for i@xmath77/i@xmath78 vs i@xmath79/i@xmath78 gives a lower value than the 2.84  found for the non - dereddened iras 12063 - 6259 data . the values found for iras 12063 - 6259 are lowered by the dereddening process to as low as 2.42 , however this still significantly differs . nevertheless , even after dereddening a tight correlation exists the the iras 12063 - 6259 data . the other correlations listed in table  [ table_pahparms ] also disagree with those for ngc 2023 and m17 , however in these cases the effect of dereddening , as discussed above , does not narrow the gap between the iras 12063 - 6259 data and that of the other objects . the two dereddening methods employed twist the best fit correlations in opposite ways , i.e. for the map dereddened using the spoon method the gradient increases drastically ( by a factor of 36 ) . while the nir dereddened data yields a shallower best fit , giving reductions in the gradients by a factor of 23 . from inspection of the correlation plots ( figures  [ fig16 ] and [ fig17 ] ) this appears to be because the spoon method collapses the variation in the i@xmath80/i@xmath78 ratio to around one , while the nir method gives a range from around 0.2  1.2 .    /i@xmath79 vs i@xmath78/i@xmath79 for the area around iras 12063 - 6259 . the red , blue and green points are as in figure  [ fig14 ] . the two lines represent ionized ( lower ) and neutral ( upper ) pah tracks for a variety of pah molecule sizes ( increasing towards the left ) @xcite . a dereddening vector corresponding to @xmath34 = 1 is shown in black . , width=302 ]    in figure  [ fig13 ] , another commonly examined correlation i@xmath77/i@xmath79 vs i@xmath78/i@xmath79 is shown , which is considered to be a useful diagnostic of pah size and ionization @xcite . the tracks for ionized and neutral pahs at varying @xmath81 are adopted from @xcite . the observed iras 12063 - 6259 points fall between the tracks , indicating a mixture of ionized and neutral pahs , albeit at the lowest end of the @xmath81 values considered ( @xmath81 = 16 ! ) . however it is clear that the dereddening process has significantly altered the i@xmath78/i@xmath79 ratio , as might be expected given that @xmath82 at 11.2  is higher than the other pah bands . in fact , dereddening has increased the range of values of i@xmath78/i@xmath79 from @xmath270.15 to around 0.3 . the range of values in i@xmath77/i@xmath79 does not change significantly as the difference between @xmath82 at 6.2 and 7.7  are much smaller . /i@xmath78 plotted against i@xmath83/i@xmath78 for the area around iras 12063 - 6259 . the red , blue and green points are as in figure  [ fig14 ] . a dereddening vector corresponding to @xmath34 = 1 is shown in black . , width=302 ]    in addition to the main bands , the 12.7  band was measured as it should also be weakly affected by extinction . in figure  [ fig17a ] the observed i@xmath77/i@xmath78 vs i@xmath83/i@xmath78 correlation is shown , along with the dereddened versions as in previous figures . the ratio of i@xmath83/i@xmath78 is of particular note as its variation decreases the most after dereddening . dereddening via the spoon method in particular reduces variation in the i@xmath83/i@xmath78 ratio to almost zero .","summary":"we use these data to construct multiple independent extinction maps and also to measure the main pah features ( 6.2 , 7.7 , 8.6 and 11.2 ) in the mir . three extinction maps are derived : the first using the nir hydrogen lines and case b recombination theory ; the second combining the nir data with radio data ; and the third making use of the spitzer / irs mir observations to measure the 9.8  silicate absorption feature using the spoon method and pahfit ( as the depth of this feature can be related to overall extinction ) . the silicate absorption over the bright , southern component of iras 12063 - 6259 is almost absent while the other methods find significant extinction . while such breakdowns of the relationship between the nir extinction and the 9.8  absorption have been observed in molecular clouds , it was found that in most cases , the pah band intensity variations persist even after dereddening , implying that extinction is not the main cause of the pah band intensity variations .","abstract":"the spatial variations in pah band intensities are normally attributed to the physical conditions of the emitting pahs , however in recent years it has been suggested that such variations are caused mainly by extinction . to resolve this question , we have obtained near - infrared ( nir ) , mid - infrared ( mir ) and radio observations of the compact h ii region iras 12063 - 6259 . we use these data to construct multiple independent extinction maps and also to measure the main pah features ( 6.2 , 7.7 , 8.6 and 11.2 ) in the mir . three extinction maps are derived : the first using the nir hydrogen lines and case b recombination theory ; the second combining the nir data with radio data ; and the third making use of the spitzer / irs mir observations to measure the 9.8  silicate absorption feature using the spoon method and pahfit ( as the depth of this feature can be related to overall extinction ) . the silicate absorption over the bright , southern component of iras 12063 - 6259 is almost absent while the other methods find significant extinction . while such breakdowns of the relationship between the nir extinction and the 9.8  absorption have been observed in molecular clouds , they have never been observed for h ii regions . we then compare the pah intensity variations in the spitzer / irs data after dereddening to those found in the original data . it was found that in most cases , the pah band intensity variations persist even after dereddening , implying that extinction is not the main cause of the pah band intensity variations ."}
{"article_id":"1305.5258","section_id":"c","document":"the somewhat conflicting extinction maps suggest a geometry for iras 12063 - 6259 : radio a is actually a deeply embedded , highly extinguished h  ii region separated from the h  ii region around radio b. the pah bands are seen to sharply peak at the same position as radio a , which strongly argues for most of the emitting pahs being located in the pdr around the radio a h  ii region and not associated with the extended pah emission evident in the figure  [ fig12 ] . in this case , the radio a pah emission should suffer from a similar level of extinction as the ionized part of the h  ii region , yet the mir spectra reveal only modest silicate absorption . the fact that the spoon method finds a much lower extinction ( at least a factor of two ) than the lower limit given by the radio method is possibly another instance of the expected relationship between the nir extinction and the silicate absorption breaking down . the radio b source , on the other hand , suffers from a similar problem which we must tentatively attribute to silicate coagulation . the non zero nir extinction and near zero silicate optical depth are difficult to explain using other mechanisms especially as the nir extinction around radio b is consistent with standard extinction laws . radio b appears to have cast off its extinguishing material ( possibly due to it being a small cluster of stars as suggested by @xcite ) . it is also possible that radio b is simply older and has cast off its natal cloud . given the lack of extinguishing material on our line of sight , it seems that the stars making up radio b are the likely cause of the extended pah emission surrounding iras 12063 - 6259 . here we discuss the possible ramifications of our findings regarding the various methods of measuring extinction . it is important to note that each method , in isolation , presents a seemingly reliable measurement of extinction . it is only when compared to other independent measures of extinction that inconsistencies emerge . the spoon method is commonly used to classify external galaxies ( e.g. @xcite ) . in this role it provides a self - consistent way of determining the degree of silicate absorption , albeit not a very accurate in terms of the total extinction as it seems to systematically underestimate the degree of silicate optical depth ( as shown in section  [ sec : sil_abs ] where we developed a method of compensating for this effect ) . in addition , it does not seem to be linked to the overall extinction , as measured by the radio method , as has also been concluded from completely independent methods to measure the extinction associated with molecular cloud materials ( e.g. @xcite ; @xcite ; @xcite ; ) . spatial extinction maps also show that different regions of a small object can have vastly different extinction properties . if we regard the iso - sws spectra of iras 12063 - 6259 as an average of the whole object , it shows some silicate absorption as well as nir extinction . the spitzer / irs observations disentangle these two effects and show that they are spatially distinct on scales of the 0.4 pc separation between the two radio sources . in the case of iras 12063 - 6259 , this small separation is resolved , for the usual application of the spoon method ( galaxy classification ) variations on this scale will be entirely invisible .      the primary argument made by @xcite was that because the variations in pah band ratios were lower than the variations one would expect due to variations in the extinction ; one could not reliably ascribe these variations to any other cause . @xcite made this assertion based on the scatter in their plot of i@xmath77/i@xmath79 against i@xmath78/i@xmath79 ( which we show with our data in figure  [ fig13 ] ) , which was rather close to the expected dereddening vector . for iras 12063 - 6259 , it is observed that the range of points on this figure is maintained or even amplified upon dereddening ( regardless of the extinction map chosen ) . this implies that the variations in the pah band ratios are not due to variable extinction but are intrinsic . we find that correlations involving the 8.6  band are highly affected by extinction , as one might expect . however the combination of the band being weak and the second most heavily affected by extinction produce very scattered correlation plots ( e.g. figures  [ fig16 ] and [ fig17 ] ) with low correlation coefficients . this probably also arises from the uncertainty on the wavelength profile of the 9.8  silicate absorption feature which has been found to vary significantly . the different extinction maps used to deredden the irs cube have the largest effect on the 8.6/11.2 pah ratio . the data dereddened using the spoon map shows much lower dispersion than that dereddened using the nir map . there are three potential explanations for this effect , it could be a reflection of the nir extinction map being noisier than the spoon map , although if this were the case it would be expected that the nir points on the correlation plots would have a higher scatter without preferring any specific direction , which is not observed . secondly , it could be that the method of using an extinction law to measure extinction and then dereddening using the same extinction law introduces biases which cause the spoon dereddened points to cluster . lastly , it could be that the spoon method systematically fails at low @xmath34 , in this case the points at low extinction do not move at all ( as for low nir @xmath34 the spoon method seems to find @xmath34 = 0 ) while the high extinction points move towards them - decreasing the scatter . however , the agreement between the spoon method and pahfit on the lack of absorption in radio b spectra seems to rule out the final possibility being a systematic error and suggest that instead , the 8.6/11.2 pah ratio displays a lower variation than expected .    in general the pah intensity correlations found for iras 12063 - 6259 are consistent with those of previous studies of h  ii regions and also the reflection nebula ngc 2023 . the range of values over which each pah ratio was found to vary seems to be compressed for iras 12063 - 6259 as compared to other objects , with the exception of the 7.7 and 6.2 bands with respect to the 11.2 . the 12.7  pah feature in particular displays very little variation as compared to other studies . from figure  [ fig17a ] it is clear that the variation in 12.7 relative to 11.2 is consistent with 12.7/11.2 being constant at a value of 0.2 ( after dereddening the effect persists but the value is around 0.11 or 0.14 for cube dereddened using the nir or spoon extinction maps respectively ) . in contrast , the reflection nebula ngc 2023 shows a range of 0.2  0.6 for 12.7/11.2 ( peeters et al . 2013 ; in prep . ) . in this sense the pah population of iras 12063 - 6259 may not be the best test for the effect of extinction on pahs as there is very little variation in some of the pah intensity ratios . however there have been very few studies of the spatial distribution of pahs and their properties around h  ii regions .","summary":"the spatial variations in pah band intensities are normally attributed to the physical conditions of the emitting pahs , however in recent years it has been suggested that such variations are caused mainly by extinction . to resolve this question ,","abstract":"the spatial variations in pah band intensities are normally attributed to the physical conditions of the emitting pahs , however in recent years it has been suggested that such variations are caused mainly by extinction . to resolve this question , we have obtained near - infrared ( nir ) , mid - infrared ( mir ) and radio observations of the compact h ii region iras 12063 - 6259 . we use these data to construct multiple independent extinction maps and also to measure the main pah features ( 6.2 , 7.7 , 8.6 and 11.2 ) in the mir . three extinction maps are derived : the first using the nir hydrogen lines and case b recombination theory ; the second combining the nir data with radio data ; and the third making use of the spitzer / irs mir observations to measure the 9.8  silicate absorption feature using the spoon method and pahfit ( as the depth of this feature can be related to overall extinction ) . the silicate absorption over the bright , southern component of iras 12063 - 6259 is almost absent while the other methods find significant extinction . while such breakdowns of the relationship between the nir extinction and the 9.8  absorption have been observed in molecular clouds , they have never been observed for h ii regions . we then compare the pah intensity variations in the spitzer / irs data after dereddening to those found in the original data . it was found that in most cases , the pah band intensity variations persist even after dereddening , implying that extinction is not the main cause of the pah band intensity variations ."}
{"article_id":"1305.5258","section_id":"i","document":"the spatial variations in extinction across iras 12063 - 6259 have been mapped using multiple methods . we then used these maps to deredden mir observations and hence investigated the effects of the spatial extinction variations on pah intensity variations . we obtained nir , mir and radio observations of the h  ii region iras 12063 - 6259 . the nir observations were performed using the isaac instrument on the vlt and provided maps of the narrow band hydrogen recombination line emission . the mir data were acquired using the spitzer / irs instrument in mapping mode and the radio observations were obtained using the atca array . these data allowed the derivation of several independent extinction maps . the nir observations were used to make the first extinction map by comparing the ratio of the strengths of two hydrogen recombination lines to their intrinsic ratio as given by case b recombination theory . the second measure of extinction was calculated by using the continuum radio observations to find the intrinsic strength of the stronger of the two hydrogen lines measured in the nir and then comparing the two . the final method , measuring the depth of the mir silicate absorption feature , was measured in two ways , firstly using the spoon method and subsequently using pahfit . we showed that the spoon method systematically underestimates the magnitude of the silicate absorption at 9.8  in the absence of observations at wavelengths longer than 14.5 . this effect originates from the secondary , shallower , silicate absorption feature which reduces the flux of the 14.5  spline point used to derive the continuum by the spoon method . we correct for this problem by implementing an iterative spoon method which compensates for the lowered 14.5  flux by dereddening the spectrum and then reapplying the spoon method . the original spoon method appears to underestimate the 9.8  optical depth by around 40% in high extinction regions without using this iterative technique . the extinction measurements which use the ionized hydrogen observations ( nir , radio ) tend to agree , while measurements based on the 9.8  silicate absorption feature are in disagreement . different methods of measuring the mir silicate absorption yielded different results , with the spoon method finding much lower absorption than pahfit ( although the pahfit measurements were performed using only short wavelength irs data ) . comparing the silicate absorption to the nir extinction showed that the dust composition varies on different sightlines to iras 12063 - 6259 , being more like a molecular cloud on the radio b sightline and consistent with general ism trends away from the two radio sources . prompted by this discrepancy , iso - sws h  ii region spectra @xcite were measured in the same way and this effect was also found for the h  ii region iras 10589 - 6034 , while other h  ii regions were consistent with the ism relationship between silicate absorption and nir extinction . in addition , the radio extinction method showed a much higher than expected extinction compared to the silicate absorption for the radio a source . the silicate absorption observed in the mir does peak around radio a , but only appears to account for half of the total extinction . we conclude that the spatial variations in extinction appear to include not only the magnitude of the extinction but also the dust composition along each sightline . the two radio sources in iras 12063 - 6259 reported by @xcite possess remarkably different properties which have proven difficult to satisfactorily explain . radio a , seems to be a heavily extinguished object with an a@xmath62 greater than 4 , yet it is ostensibly encompassed in a larger surrounding h  ii region . there is a ` bar ' of extinction which appears to be related to iras 12063 - 6259 as there is diffuse emission associated with iras 12063 - 6259 emanating from this region . radio b , which @xcite suggest could be multiple stars , is coincident with the brightest part of the h  ii region and seems to have a much lower total extinction of around a@xmath62 @xmath27 1.5 ( of which very little is generated by silicates ) . the spitzer / irs spectral cube of iras 12063 - 6259 was dereddened using the extinction maps and the spectral features measured for each pixel in both the dereddened cubes as well as in the originally observed cubes . the standard correlation plots were then presented for both the observed and dereddened data . correcting for extinction changes the pah correlations , in most cases altering the gradients , moreover the range of each particular pah ratio can also change substantially . any correlation involving the 8.6  band tends to be degraded by both noise and the relative uncertainty in the shape of the blue wing of the 9.8  silicate absorption feature . in iras 12063 - 6259 , correcting for extinction using the spoon method removes variation in the 12.7 / 11.2 pah band ratio . in general though , the dereddening process does not seem to totally remove variations in the pah ratios as was suggested by @xcite .","summary":"we have obtained near - infrared ( nir ) , mid - infrared ( mir ) and radio observations of the compact h ii region iras 12063 - 6259 . we then compare the pah intensity variations in the spitzer / irs data after dereddening to those found in the original data .","abstract":"the spatial variations in pah band intensities are normally attributed to the physical conditions of the emitting pahs , however in recent years it has been suggested that such variations are caused mainly by extinction . to resolve this question , we have obtained near - infrared ( nir ) , mid - infrared ( mir ) and radio observations of the compact h ii region iras 12063 - 6259 . we use these data to construct multiple independent extinction maps and also to measure the main pah features ( 6.2 , 7.7 , 8.6 and 11.2 ) in the mir . three extinction maps are derived : the first using the nir hydrogen lines and case b recombination theory ; the second combining the nir data with radio data ; and the third making use of the spitzer / irs mir observations to measure the 9.8  silicate absorption feature using the spoon method and pahfit ( as the depth of this feature can be related to overall extinction ) . the silicate absorption over the bright , southern component of iras 12063 - 6259 is almost absent while the other methods find significant extinction . while such breakdowns of the relationship between the nir extinction and the 9.8  absorption have been observed in molecular clouds , they have never been observed for h ii regions . we then compare the pah intensity variations in the spitzer / irs data after dereddening to those found in the original data . it was found that in most cases , the pah band intensity variations persist even after dereddening , implying that extinction is not the main cause of the pah band intensity variations ."}
{"article_id":"1409.5838","section_id":"i","document":"the line broadening in excess of thermal broadening seen in optical spectroscopic studies of @xmath1 regions has been attributed to turbulence in the photoionized gas . there are many examples in the literature of attempts to identify the presence and characterize this turbulence , for example @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and references cited by these papers . in these studies , the variation of the point - to - point radial velocities with scale was investigated using structure functions following . a general finding of these studies is that the structure function derived from these observations does not follow that predicted by kolmogorov s law @xcite . the interpretation of this result is that kolmogorov s law for incompressible and subsonic turbulent flows can not be strictly applied to the photoionized gas in @xmath1 regions , which will be compressible and possibly mildly supersonic @xcite , or that energy does not cascade from larger to smaller scales but is input at many scales . moreover , the results differ according to which emission lines are used in the study , since the topology of the emitting gas will be different . for instance , the [ @xmath2@xmath35007 line comes from gas in the interior of an @xmath1 region , whereas the [ @xmath4@xmath36731 line comes from the vicinity of the ionization front , essentially a two - dimensional surface . the suggested mechanisms responsible for the generation and maintenance of the turbulent velocities in @xmath1 regions include photoevaporated flows from globules and stellar winds .    in order to construct the structure functions for the velocity fields , observations at many points in an @xmath1 region are needed . this can be achieved either by multiple longslit spectroscopic observations at many positions across a nebula , or by fabry - perot interferometry . longslit observations with high velocity resolution have enabled several velocity components to be identified for emission lines of metal ions for which the thermal widths are small , e.g. , [ @xmath2@xmath35007 . these observations have been used to determine the radial velocities of the principal components of the emitting gas at hundreds of positions within the nebula . fabry - perot observations produce datasets of thousands of radial velocities , but without the velocity resolution to distinguish between different velocity components . obviously , in order to obtain a structure function over a wide range of scales , very high quality data with an ample spatial coverage are required . in the case of longslit spectra , this is a non - trivial task , not least the calibrating of the positions of the slits . @xcite suggested that turbulence is ubiquitous in astrophysics and that it could be analysed statistically via the spectrum of the velocity field , which expresses the correlations between instantaneous velocity components at all possible pairs of points in the medium . turbulence develops in a fluid when velocity advection is dominant over dissipation ( high reynolds number ) , then continuous injection of energy is required in order to maintain the turbulent state . one of the main assumptions of the kolmogorov theory of turbulence is that energy is only injected at large scales and is dissipated only at small scales . this implies that the energy cascades from large to small scales without dissipation . another assumption of this theory is that in the range between injection and dissipation scales the energy is transferred at a constant rate , and this range is called the inertial range . turbulence is often described in terms of the energy spectrum @xmath5 , and the inertial range is represented by a power - law relationship @xmath6 , where @xmath7 is the wave number . for incompressible , homogeneous , isotropic , 3d turbulence @xcite , we have @xmath8 , while in the limit of high mach number , shock - dominated turbulence in one dimension @xcite , the power law is @xmath9 . it has proved more difficult to obtain exact results for the general case of 3d compressible , hydrodynamic turbulence . scaling laws suggest that the original kolmogorov energy spectrum scaling should be preserved even for highly compressible turbulence if the density weighted velocity @xmath10 is taken instead of the pure velocity @xmath11 . recent work by @xcite predicts the relation @xmath12 for compressible , isothermal turbulence with compressive driving , with a turnover around the sonic scale to @xmath13 . this has been confirmed by extremely high resolution numerical experiments @xcite . another important prediction of the kolmogorov theory is the scaling of the structure function of any order . the universality of such scaling laws has been tested by detailed numerical experiments . even in numerical experiments of incompressible , homogeneous and isotropic turbulence with energy injection at a fixed large scale , it is found that the exponents of the higher order structure functions have an anomalous behaviour , which has been interpreted as the result of spatial and/or temporal intermittency . intermittency is a sparseness in space and time of strong structures associated with the dissipation or injection of energy @xcite . since astrophysical turbulence driven by real physical phenomena is almost certainly intermittent , it is important to understand the possible effects of intermittency on the derived statistical properties of real @xmath1 regions . the three - dimensional properties of the density and velocity fields that describe the turbulence in the interstellar medium , in this case an @xmath1 region , must be deduced from the statistical properties of the observed quantities . for photoionized gas , the observations generally consist of spectra at different positions , from which centroid velocities and linewidths can be obtained . for optical line emission , the emissivity depends on density , temperature and ionization state and therefore an analysis of the emission lines will not just be providing information on the turbulent velocity fluctuations in the gas . the observations are a two - dimensional projection of the three - dimensional properties and much effort has been dedicated to the problem of recovering 3d information from 2d data . generally , some simplifying assumptions , such as isothermal gas and statistical isotropy of the turbulence , must be made . recent modeling of @xmath1 regions has addressed the origin of the irregular structures , filaments , and globules seen within and around the borders in optical images . morphologically , the simulated emission - line images are very reminiscent of observed @xmath1 regions and the global dynamics , as measured by the r.m.s . velocity , is also similar to observationally derived values . the internal dynamics of the simulated @xmath1 regions is due mainly to the interaction of photoevaporated flows from the heads of the filaments and clumps , which flow into the interior of the @xmath1 region , superimposed on the general expansion of the @xmath1 region . however , the dynamics of real @xmath1 regions could also be affected at large scales by the action of stellar winds from the ionizing star or stars , and at small scales by outflows from young , low - mass stars .    in this paper we investigate to what extent our numerical simulations of @xmath1 regions model observed statistical properties of real @xmath1 regions . in   [ sec : nummod ] we briefly describe the numerical methods used in the radiation - hydrodynamics simulations and in the calculation of the simulated emission - line radiation , and how the statistical information is obtained from these calculations . in   [ sec : results ] we describe our results for the expansion of an @xmath1 region in a turbulent , clumpy molecular cloud . we discuss these results in  [ sec : discuss ] , and comment on the extent to which the statistical properties of the numerical simulations agree with those of observed @xmath1 regions . in  [ sec : summary ] we summarize and present our conclusions .","summary":"[ firstpage ]    hydrodynamics  hii regions  ism : kinematics and dynamics  turbulence","abstract":"we investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent hii region and to what extent these may be studied observationally . we find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top - down turbulence driven at the largest scales . the traditional structure function approach to the observational study of velocity fluctuations is shown to be incapable of reliably determining the velocity power spectrum of our simulation . we find that a more promising approach is the velocity channel analysis technique of lazarian & pogosyan ( 2000 ) , which , despite being intrinsically limited by thermal broadening , can successfully recover the logarithmic slope of the velocity power spectrum to a precision of from high resolution optical emission line spectroscopy .    [ firstpage ]    hydrodynamics  hii regions  ism : kinematics and dynamics  turbulence"}
{"article_id":"1409.5838","section_id":"c","document":"at times later than 150,000  years , our second - order structure function results for the h@xmath23 and [ @xmath2@xmath35007 emission - line velocity centroids strongly suggest the presence of turbulence with an inertial range between 1  pc and the numerical dissipation scale of about 8 cells ( equivalent to 0.0625  pc ) . the [ @xmath24@xmath36584 and [ @xmath4@xmath36716 structure function results also suggest turbulence , with a smaller upper limit to the inertial range , which is consistent with these ions being confined to relatively thin layers near the ionization front . however , it is difficult to characterize this turbulence since the slope of the structure function for a given emission line varies with time in an unpredictable manner and also depends on the line of sight . although the results for the @xmath43-axis line of sight suggest an increase in slope with time , an examination of the distributions of the velocity centroids ( see fig . [ fig : histogram ] ) shows that this is due to a champagne - type flow in that direction , and other lines of sight do not show a definite trend with time . different emission lines originate in different volumes of ionized gas , and this is reflected in the different slopes for the structure functions from different emitters . the h@xmath23 line is produced throughout the volume and is brightest close to the ionization front around the bright edges of the photoionized gas . there is therefore a wide range of densities associated with the h@xmath23-emitting gas . the emissivity of the h@xmath23 recombination line depends on the square of the density and only weakly on the temperature in the photoionized gas ( see e.g. , * ? ? ? . indeed , the gradients of the 3d power spectra of the h@xmath23 emissivity and the square of the density are essentially the same . on the other hand , the emissivity of the [ @xmath2@xmath35007 collisional line depends more strongly on temperature . this line originates in the interior of the @xmath1 region , where the density is more uniform but weak shocks due to the collision of photoevaporated flows cause fluctuations in the temperature . a more uniform density distribution corresponds to a steeper density power spectrum and , indeed , the structure functions , 2d velocity channel power spectra , and 3d power spectrum of the [ @xmath2@xmath35007 line are all steeper than those for the h@xmath23 recombination line .    the stellar parameters for the simulations presented in this work correspond to a relatively hot ( 37,500  k ) o7 star . for these parameters , the [ @xmath24@xmath36584 and [ @xmath4@xmath36716 collisionally ionized lines come from regions close to the ionization front , where the density variations are strong , and this is reflected in the less steep structure function and 2d velocity channel power spectra gradients . in particular , the [ @xmath4 emission will come from very close to the ionization front where the acceleration of the ionized gas is strongest , and as a result the structure function and 2d velocity channel power - spectra gradients are shallowest for this line . other stellar parameters , e.g. , a cooler b0 star or a much hotter white dwarf , would produce photoionized regions with different ionization stratifications . figure  [ fig : ps ] shows that the power spectra of physical quantities are very well approximated by power laws over the range from @xmath100 to 32 ( scales of 1  pc to 0.125  pc ) . in particular , the ionized gas velocity shows a power - law slope of @xmath122 once the turbulence is fully developed . this is significantly shallower than the kolmogorov ( @xmath123 ) or burgers ( @xmath36 ) value , indicating more velocity structure at small scales than would be seen in a simple turbulent cascade of energy injected at the largest scale . as a consequence , the turbulent velocity dispersion is relatively insensitive to scale , varying as @xmath124 . one possible reason for the shallow velocity power spectrum may be that energy is injected over a variety of scales , corresponding to the different sizes of clumps and filaments responsible for the photoevaporated flows in the simulated @xmath1 regions . moreover , the energy injection will vary with time due to the global expansion of the @xmath1 region , which moves the sources of the photoevaporated flows generally outwards , and the destruction of the clumps and filaments as they are eroded by the ionizing radiation . the density power spectrum has a very similar slope to that of the velocity : @xmath122 , but of greater relevance are the slopes of the emissivities of the different emission lines , which are @xmath125 for [ @xmath2 , @xmath126 for @xmath127 , @xmath128 for [ @xmath24 , and @xmath129 for [ @xmath4 . these span the critical value of @xmath130 that divides `` steep '' from `` shallow '' power spectra . [ @xmath2 has a steep slope , indicating that large - scale fluctuations dominate , while [ @xmath24 and [ @xmath4 have shallow slopes , indicating that small - scale fluctuations dominate . the @xmath127 slope is very close to the critical value , indicating roughly equal contributions from fluctuations on all size - scales . it is interesting to study the question of whether the known power - law indices of the velocity and emissivity power spectra in our simulations can in practice be recovered from observational diagnostics . if this is not the case for a given diagnostic , then it would call into question its utility for studying real @xmath1 regions . in particular , we will concentrate on two commonly used diagnostics : the second - order structure function of the line velocity centroids , and the power spectra of the surface brightness in isovelocity channel maps ( velocity channel analysis ) . the structure function of the velocity centroids is an observationally attractive diagnostic because it is relatively immune to the effects of thermal broadening and poor spectral resolution , so long as sufficiently high signal - to - noise spectra are used . however , it has the disadvantage that relating the observed slope to the 3-dimensional velocity statistics depends on the geometry of the emitting region , see  [ subsec : projsmooth ] . for transverse separations larger than the characteristic line - of - sight depth of the emitting gas , the two - dimensional gradient should be equal to the three - dimensional one : @xmath131 whereas at smaller separations than this , projection smoothing , as described above , means that the two - dimensional gradient is steeper : @xmath132 based on our simulation s velocity power spectrum index at late times of @xmath133 ( see figs .  [ fig : ps ] and [ fig : psevol ] ) , the structure function slope should be @xmath134 in the large - scale limit and @xmath135 in the small - scale limit .    in fact , all of the measured slopes lie between these two limits , with a systematically increasing value from low to high - ionization lines : @xmath136 } ) = 0.33 \\pm 0.02 $ ] , @xmath137 } ) = 0.49 \\pm 0.03 $ ] , @xmath138 , @xmath139 } ) = 0.74 \\pm 0.04 $ ] , where the averages were performed for @xmath140  years . this is qualitatively consistent with expectations because the emission from lower - ionization lines is confined to thin layers near the ionization front , whereas higher ionization emission is more distributed over the volume and therefore subject to greater projection smoothing . if the line - of - sight depth were constant over the face of the @xmath1 region , then the structure function would show a break at a scale equal to that depth , but in reality the depth varies from point to point , so there will not be a sharp break . instead , the structure function is expected to show negative curvature , with the gradient gradually decreasing as one passes from smaller to larger scales . a small such effect is seen in the structure functions derived from our simulations ( fig . [ fig : sfunc ] to [ fig : sfuncyz ] ) : the fit to a power law is generally not so good as in the case of the power spectra , with negative residuals at both ends of the fitted range , indicative of a negative curvature . that the observed effect is so small is probably due to the fact that the distribution of line - of - sight depths strongly overlaps with the limited dynamic range in separations available from our simulations , bounded at small scales by numerical dissipation , and at large scales by the size of the ionized region . it is disappointing that none of the measured slopes reach either of the limiting cases discussed above . all that can be deduced from the structure function is that @xmath141})$ ] and @xmath142})$ ] , which implies @xmath143 to @xmath144 . although this is a rather wide range of allowed velocity power spectrum slopes , it does serve to clearly rule out the kolmogorov value of @xmath145 . furthermore , the `` true '' value of @xmath146 lies close to the middle of the allowed range . a further proviso to the use of the structure function is that systematic anisotropic flows can affect the measured slopes when the viewing angle is along the direction of the flow . such an effect is seen at later times for our simulation when viewed along the @xmath43-axis ( fig . [ fig : sfunc ] ) . in this case , the structure function tends to steepen at the large - scale end of our fitting range , producing a positive curvature , which is opposite to the more typical case of negative curvature discussed above . such cases may also be identified by the presence of a significant skew in the pdf of the line - of - sight velocity ( see fig .  [ fig : histogram ] ) . figure  [ fig : sf - vs - n ] illustrates these points by graphing the correlation between the structure function slope @xmath106 and the slope @xmath102 of the underlying 3d velocity fluctuations . the theoretical relation is shown by black diagonal lines , both with ( continuous line ) and without ( dashed line ) projection smoothing . it is apparent that a large part of the variation in @xmath106 is not driven by changes in @xmath102 . indeed , @xmath106 shows a larger or equal variation in the latter stages of evolution , when @xmath102 is approximately constant , than it does in the earlier stages , when @xmath102 is varying . note that the additional complication identified by @xcite , whereby correlations between density and velocity fluctuations affect the translation between @xmath106 and @xmath102 , is likely of minor importance in our case . @xcite show that this is most important for high mach number turbulence , where @xmath147 , whereas the transonic turbulence inside our simulated @xmath1 regions produces more modest density contrasts . figure  [ fig : vca - thin - vs - n ] shows the correlations between the slope of the velocity fluctuation power spectrum and the vca slopes found in   [ sssec : vca ] above ( see fig .  [ fig : vcatrends ] ) . the theoretical procedure @xcite for deriving one from the other is slightly different , depending on whether the power spectrum of the emissivity fluctuations is `` steep '' or `` shallow '' ( see   [ sec : stats - vca ] above ) . in the steep case , which applies to [ @xmath2 in our simulation , the slope of the average power spectrum of the brightness maps in the thin isovelocity channels is given by @xmath148 , where @xmath149 for our simulation . the derived value from the [ @xmath2 thin channel maps for @xmath121 is @xmath150 , which compares well with the value @xmath151 that is implied by the simulation s value of @xmath102 .    in the shallow case , it is the difference in slope between the thin and thick slices that is predicted to depend on the velocity fluctuations : @xmath152 . the derived values are @xmath153 , @xmath154 , and @xmath155 for @xmath127 , [ @xmath24 , and [ @xmath4 , respectively . these also compare tolerably well with the value of @xmath156 that is implied by the simulation s value of @xmath102 . note , however , that the large doppler width of the @xmath127 line means that the thin velocity slices are not useful in this case , since the thick and thin slices have identical slopes . the fact that this agrees with the theoretical prediction is merely a coincidence , due to our velocity spectrum having a slope that is close to @xmath157 . for the lines from heavier ions , [ @xmath2 , [ @xmath24 and [ @xmath4 , the difference between the thin and thick velocity slices is not erased by thermal broadening , but in these three cases there is a consistent difference of @xmath158 between the measured vca slope and the theoretically expected one . the origin of this difference is unclear , but it is small enough that it is not a significant impediment to the application of the vca method . the slopes of the power spectra of the thick slices themselves , which are simply the velocity - integrated surface brightness images are predicted @xcite to be equal to the slopes of the 3d power spectra of their respective emissivities . the comparison between these two quantities is shown in figure  [ fig : vca - thick - vs - n ] , from which it is clear that only in the case of [ @xmath2 are the two slopes equal . in the case of the other lines , @xmath120 is shallower than the emissivity s spectral index @xmath102 by 0.36 , 0.19 , 0.61 for @xmath127 , [ @xmath24 , and [ @xmath4 , respectively . the reason for this discrepancy is the increasingly `` sheet - like '' morphology of the emission in the lower ionization lines . as shown in   4.1 of @xcite , one should see a transition from @xmath159 to the shallower slope @xmath160 at transverse scales larger than the line - of - sight depth of the emitting region . non - thermal linewidths in @xmath1 regions have been interpreted as evidence for turbulence in the photoionized gas . galactic @xmath1 regions generally exhibit subsonic turbulent widths , while giant extragalactic @xmath1 regions can have supersonic turbulent motions . the majority of observational studies consider only the h@xmath23 line , but @xcite and examine the components of the [ @xmath2@xmath35007 line in the orion nebula , m42 , while @xcite and @xcite investigate the kinematics of the [ siii ] and [ oi ] lines of this same object . the giant extragalactic @xmath1 region ngc-595 was studied by who analyzed the h@xmath23 , [ @xmath2 and [ @xmath4 kinematics . the heavier ions have the advantage that their emission lines have low thermal broadening compared to the h@xmath23 line . observational studies of the spatial scales of velocity fluctuations have mostly focused on the structure function of velocity centroids . the results are rather disparate , partly because the methodology varies considerably between different studies . for instance , some authors attempt to filter out `` ordered '' large - scale motions before analysing the fluctuations @xcite , whereas others analyse the unfiltered observations @xcite . also , in some cases multiple gaussian velocity components are fitted to the line profiles @xcite , which are then assigned to a small number of velocity `` systems '' that are each analysed separately , whereas in most studies the mean velocity of the entire line profile is used .    despite these differences , there are interesting commonalities in the results : a rising structure function with @xmath161@xmath162 is nearly always found at the smallest scales , which transitions to a flat structure function with @xmath163 at larger scales . however , the scale at which the transition occurs varies enormously from object to object , from @xmath164@xmath165  pc in compact ( @xmath166 to 5  pc ) galactic @xmath1 regions @xcite , up to 50  pc in giant ( @xmath167  pc ) extragalactic regions @xcite . we comment that the sound - crossing time for a region of size 50  pc is about 5  myr , roughly the same as the estimated age of the ngc  595 nebula @xcite . for the full extent of ngc  595 , the sound crossing time is about 40  myr . it is therefore unlikely that the turbulence in such large regions is in a statistically steady state unless it is highly supersonic . indeed , @xcite suggest that in the case of large extragalactic @xmath1 regions , the large linewidths could be due to multiple velocity components , that is , parts of the @xmath1 region with separation greater than the distance a sound wave could travel within the current lifetime of the object are kinematically distinct . such giant @xmath1 regions show velocity centroid dispersions of @xmath168 on the largest scales , which is several times larger than is seen in compact single - star regions or in our simulations . we will therefore not consider them further since they are governed by additional physical processes , such as powerful stellar winds and the cluster gravitational potential , which are beyond the scope of the current paper . the explanations that have been offered for the break in the structure function slope are also varied . in the case of compact @xmath1 regions , it is often taken to indicate the characteristic line - of - sight depth of the emission zone @xcite , with projection smoothing steepening the slope at the smaller separations ( see   [ subsec : projsmooth ] above ) . if that were the case , then the correct three - dimensional structure function slope is the flat one : @xmath169 , corresponding to a velocity power spectrum slope of @xmath130 . this interpretation would be broadly consistent with our simulation results , which show a very similar velocity power spectrum ( fig . [ fig : ps ] ) . however , our simulated structure functions rarely show a clear break in the same way as the observations do , although they do show a slight negative curvature in many cases . this is probably because of the very limited useful dynamic range , roughly a factor of 10 , that the simulations allow between the small scales that are affected by numerical diffusion and the large scales , that are affected by systematic flows , anisotropies , and edge - effects . an alternative explanation for the observed break in the structure function is that it represents the scale of the largest turbulent eddies @xcite and that the fluctuations at larger scales are simply uncorrelated . in such a picture it would still be necessary to postulate a velocity spectrum considerably shallower than kolmogorov in order to explain the small - scale slope . based on the discussion of our simulation results above (   [ sssec : vca2 ] ) , it seems that velocity channel analysis would be a very useful complement to the structure function , since it is less affected by uncertainties in projection smoothing and gives a more consistent result between different emission lines ( at least , for our simulations ) .    in a forthcoming paper , we will present such an analysis of recent high - resolution echelle spectroscopy of multiple emission lines in the orion nebula @xcite .","summary":"we find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top - down turbulence driven at the largest scales .","abstract":"we investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent hii region and to what extent these may be studied observationally . we find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top - down turbulence driven at the largest scales . the traditional structure function approach to the observational study of velocity fluctuations is shown to be incapable of reliably determining the velocity power spectrum of our simulation . we find that a more promising approach is the velocity channel analysis technique of lazarian & pogosyan ( 2000 ) , which , despite being intrinsically limited by thermal broadening , can successfully recover the logarithmic slope of the velocity power spectrum to a precision of from high resolution optical emission line spectroscopy .    [ firstpage ]    hydrodynamics  hii regions  ism : kinematics and dynamics  turbulence"}
{"article_id":"1409.5838","section_id":"i","document":"1 .   we have investigated the statistics of fluctuations in physical conditions within a radiation - hydrodynamic simulation of the evolution of an @xmath1 region inside a highly inhomogeneous molecular cloud . we find that steady - state turbulence , corresponding to time - independent profiles of the 3d power spectra , is only established after about 1.5 sound - crossing times of the @xmath1 region . in these simulations , this corresponds to about 200,000 years (   [ sssec : pspec ] ) . we find a power - law behaviour for the 3d power spectra in the range from about 1 pc down to 0.125 pc , equivalent to 16 computational cells . the larger scale can be interpreted as the size of the largest photoevaporated flows , while the smaller scale is about twice the numerical dissipation scale . the power - spectrum slopes of the velocity and density fluctuations are very similar and always lie in the range @xmath170 . this is significantly shallower than the slope predicted for the inertial range of either incompressible or compressible turbulence ( @xmath171 to @xmath172 ) . this suggests that turbulent driving is occuring over all scales in our simulation , unlike the case of classical turbulence where energy is injected only at the largest scales . the power - spectrum slopes of the emissivities of optical lines are even shallower , increasingly so for lower ionization lines , indicating that the smallest scale fluctuations are dominant (   [ sssec : ips ] ) . 3 .   we investigate in detail the utility of observational diagnostics for inferring the power spectra of emissivity and velocity fluctuations in our simulation . we find that the traditional velocity centroid structure function technique gives ambivalent results because of the effects of projection smoothing , combined with the fact that the effective line - of - sight depth of the emitting gas does not have a single well - defined value . in addition , the presence of anisotropic motions such as champagne flows can yield misleading structure function slopes when the simulation is viewed from certain directions (   [ sssec : strfunc ] ) . 4 .   the more recently developed technique of velocity channel analysis is found to offer a more robust diagnostic of the three - dimensional velocity statistics of our simulation . the slope of the velocity power spectrum can be correctly recovered to a precision of @xmath0 from either high or low ionization lines , and with no significant dependence on viewing direction (   [ sssec : vca2 ] ) .","summary":"we investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent hii region and to what extent these may be studied observationally . we find that a more promising approach is the velocity channel analysis technique of lazarian & pogosyan ( 2000 ) , which , despite being intrinsically limited by thermal broadening , can successfully recover the logarithmic slope of the velocity power spectrum to a precision of from high resolution optical emission line spectroscopy .   ","abstract":"we investigate the scale dependence of fluctuations inside a realistic model of an evolving turbulent hii region and to what extent these may be studied observationally . we find that the multiple scales of energy injection from champagne flows and the photoionization of clumps and filaments leads to a flatter spectrum of fluctuations than would be expected from top - down turbulence driven at the largest scales . the traditional structure function approach to the observational study of velocity fluctuations is shown to be incapable of reliably determining the velocity power spectrum of our simulation . we find that a more promising approach is the velocity channel analysis technique of lazarian & pogosyan ( 2000 ) , which , despite being intrinsically limited by thermal broadening , can successfully recover the logarithmic slope of the velocity power spectrum to a precision of from high resolution optical emission line spectroscopy .    [ firstpage ]    hydrodynamics  hii regions  ism : kinematics and dynamics  turbulence"}
{"article_id":"1006.0011","section_id":"i","document":"let @xmath3 be a quasi - projective non - singular variety over complex numbers , and @xmath4 be an ample line bundle on @xmath3 ( throughout this paper we work over @xmath5 ) . hilbert scheme of @xmath6-points on @xmath3 parameterizes the set of all subschemes of @xmath3 with dimension zero and length @xmath6 . more precisely consider the contravariant functor @xmath7 from the category of schemes to sets    @xmath7 @xmath8 @xmath9    which is given by : @xmath10^i \\ar[dr]_{\\pi } & & s \\times t \\ar[dl]^{p_2 } \\\\                                         & t &   }   & \\begin{array}{l }                                         z \\text { is a closed subscheme of } s \\times t \\\\                                         \\pi\\text { is flat } \\\\ z_t \\text { has constant hilbert polynomial}\\\\                                         \\text {        equal to $ n$ , for all } t \\in t                                         \\end{array } \\end{array } \\right\\}\\ ] ]    since @xmath11 is flat all @xmath12 s have the same hilbert polynomial so the definition makes sense . by a theorem of grothendieck the following functor is representable by a scheme , that we denote it by @xmath13}$ ] .    for a scheme @xmath14 with @xmath15 the poincar polynomial and normalized poincar polynomial are defined by    @xmath16 , @xmath17    where @xmath18 is the @xmath19 betti number of @xmath14 . gttsche showed that the poincar polynomial of @xmath13}$ ] can be computed as follow :    @xcite,@xcite let @xmath3 be a quasi - projective nonsingular surface then the generating function of the poincar polynomial of hilbert scheme of @xmath6 points on @xmath3 is given by :    @xmath20}}(t)=\\prod_{m=1}^{\\infty}\\frac{(1+t^{2m-1}q^{m})^{b_{1}(x)}(1+t^{2m+1}q^{m})^{b_{3}(x)}}{(1-t^{2m-2}q^{m})^{b_{0}(x ) } ( 1-t^{2m}q^{m})^{b_{2}(x)}(1-t^{2m+2}q^{m})^{b_{4}(x)}}$ ]    where @xmath21 is the @xmath19 betti number of @xmath3 ,      let @xmath3 be a quasi - projective non - singular surface . there is a natural map between the hilbert scheme of @xmath6 points in @xmath3 and the @xmath22-symmetric product of @xmath3 given by :    @xmath23 } \\to x^{(n ) } , z \\mapsto \\displaystyle\\sum \\l(\\mathcal{o}_{z , p})p$ ]    for @xmath24 we define the cycles @xmath25\\subset \\displaystyle\\coprod_{n } x^{[n - i ] } \\times x^{[n ] } \\times x$ ] to be :    @xmath25:=\\displaystyle \\coprod_{n } \\ { ( \\mathcal{i}_1,\\mathcal{i}_2,p)\\in x^{[n - i ] } \\times x^{[n ] } \\times x \\hspace{2mm}|\\hspace{2 mm }   \\mathcal{i}_1\\supset\\mathcal{i}_2   , \\hspace{2 mm } \\rho(\\mathcal{i}_2)-\\rho(\\mathcal{i}_1)=n[p]\\}$ ]    and for @xmath26 we define it by interchanging @xmath27 and @xmath28 . let @xmath29 be the borel - moore homology of x , for @xmath30 and @xmath31 and @xmath24 we define two operators @xmath32 $ ] and @xmath33 $ ] by :    @xmath32 : h_{*}(x^{[n ] } ) \\to h_{*}(x^{[n - i]})$ ]    @xmath34)))$ ]    @xmath33 : h_{*}(x^{[n - i ] } ) \\to h_{*}(x^{[n]})$ ]    @xmath35)))$ ]    where @xmath36 and @xmath37 are projections of @xmath38 } \\times x^{[n ] } \\times x$ ] and @xmath38 } \\times x^{[n]}$ ] ( resp . ) to their @xmath39 coordinate . in other words these operators are given by the correspondences defined by @xmath40)$ ] and @xmath41)$ ] . @xcite,@xcite    \\(i ) we have the following relations :    @xmath42,p_{\\beta}[j]]= ( -1)^{i-1 } i \\delta_{i+j}<\\alpha,\\beta > id$ ] if @xmath43    @xmath44,p_{\\beta}[j]\\}=(-1)^{i-1 } i \\delta_{i+j}<\\alpha,\\beta > id$ ] otherwise    \\(ii ) @xmath45})$ ] is an irreducible representation of the heisenberg superalgebra associated to @xmath3 , with the highest weight vector being the generator of @xmath46})=\\mathbb{q}$ ]      let @xmath1 be a quasi - projective non - singular surface , and @xmath0 be a cartier divisor that has a smooth representative . we want to consider the hilbert scheme of points in @xmath1 relative to @xmath0 . this has been done in @xcite but since some of the ideas will be used later in our paper we will briefly describe the construction of this space . we start by taking the hilbert scheme of points of @xmath47 , which is not a proper scheme , and compactify it relative to @xmath0 . in order to do so we consider the expanded degeneration of @xmath1 relative to @xmath0 . to be more precise take @xmath48 to be the @xmath49-bundle over @xmath0 corresponding to @xmath50 , i.e. @xmath51 . since @xmath48 is the projecivization of a direct sum it comes with two natural sections which we call them zero section and the infinity section . take @xmath6 copies of @xmath48 and glue them together in a way that the zero section of the @xmath52 copy is identified with the infinity section of the @xmath19 copy , for @xmath53 , and also glue the zero section of the first bubble to the divisor @xmath0 in @xmath1 . we denote the resulting scheme by @xmath54 $ ] and call it the expanded degeneration of @xmath1 relative to @xmath0 of length @xmath6 . note that the normal bundle to the zero section in each copy of @xmath48 is @xmath55 , and the normal bundle to the infinity section is @xmath56 .    from this pictures its not hard to see that for a given @xmath6 there is an action of @xmath57 on the space @xmath54 $ ] , such the @xmath19 copy of @xmath58 acts on the @xmath19 copy of @xmath48 by fiber - wise multiplication . so this action can be lifted to an almost free action on the hilbert scheme of points of @xmath54 $ ] . we will give a moduli description for points that we add in order to compactify @xmath59}$ ] . if a point in @xmath47 moves toward @xmath0 , which means that we have a family of subschemes of @xmath47 over @xmath60 such that the support of a given point on the fiber above @xmath61 is going toward @xmath0 as the @xmath61 goes to zero . such family can be extended to a family above @xmath62 in a way that the resulting fiber over zero consists of a subscheme of @xmath47 plus a point supported in the normal bundle of @xmath0 . in order to do this , we take @xmath63 and we blow up @xmath64 , then such family is a flat subscheme of the resulting scheme over @xmath60 that can be extended to be family over @xmath62 . the point that we have to keep in mind is that if we change the parametrization of @xmath60 ( that is just multiplication by a nonzero scalar since zero should be fixed ) , then the resulting limit points will vary in a fiber of @xmath56 . but all these families are isomorphic as families of subschemes of @xmath47 , so their limit should be the same . this means that to this family we can assign a subscheme of @xmath65 $ ] but this point is well defined up to a @xmath58 action which means that we have to identify the points in the orbit of the @xmath58 action on the hilbert scheme of points of @xmath65 $ ] and glue the resulting quotient to @xmath59}$ ] . now if a point in the bubble goes toward the infinity section we can do the same and add another bubble . note that if all the points in a bubble go to the next one then we will delete the empty bubble , which shows that we can have at most @xmath6 bubbles glued to the @xmath66 .    in section 1 we compute the poincar polynomial of the relative hilbert scheme of points , and prove the following theorem :    the generating function for the normalized poincar polynomial of the relative hilbert scheme of points is given by :    @xmath67}_{d}}(t ) & = & \\frac{(t^{2}-1)\\hat{h}_{s}(q , t)}{t^{2}c_{d}(q , t)-c_{d}(q , t^{-1})}\\end{aligned}\\ ] ]    where @xmath68 is the normalized poincar polynomial of the hilbert scheme of point on @xmath1 and @xmath69 .    in section two we prove the following theorem which allows us to construct a set of generators for the cohomology ring of relative hilbert scheme of point on the projective plane . the natural map between the chow group and borel - moore homology of the relative hilbert scheme of point of the projective plane and a line on it is an isomorphism .    using this theorem we can pick a set of generators for the chow group of relative hilbert scheme of point on the projective plane , and they will also generate the cohomology of this space , since its a smooth stack . since through out this paper we only work with dm - stacks , every time we use the word stack we mean dm - stack unless otherwise is specified . it turns out that the construction of nakajima s basis can be modified to give us a set of generators for the relative case , and there will be some relations among these generators . there is a geometric way of constructing relations for this case , which comes from natural maps from different ways that we can move points in a given bubble . in section three we discuss all these relations , and in the last section we show that these geometric relations are all the relations in the cohomology group of the relative hilbert scheme of projective plane relative to a line .","summary":"let be a smooth divisor on a non singular surface . we compute betti numbers of the relative hilbert scheme of points of relative to . in the case of and a line in it , we give an explicit set of generators and relations for the cohomology groups of this space .    [ multiblock footnote omitted ]","abstract":"let be a smooth divisor on a non singular surface . we compute betti numbers of the relative hilbert scheme of points of relative to . in the case of and a line in it , we give an explicit set of generators and relations for the cohomology groups of this space .    [ multiblock footnote omitted ]"}
{"article_id":"cond-mat0512064","section_id":"i","document":"solving difficult classical combinatorial problems by adiabatically controlling a fictitious quantum hamiltonian is a fascinating route to quantum computation @xcite , which is alternative to the main - stream approach @xcite . the quantum annealing ( qa ) strategy @xcite is precisely based on the adiabatic switching off , as a function of time , of strong fictitious quantum fluctuations , suitably introduced by an extra kinetic term in the otherwise classical hamiltonian under consideration .    a number of authors have by now applied qa to attack a variety of optimization problems . some amount of success was obtained in several cases , notably in the folding of off - lattice polymer models @xcite , in the 2d random ising model annealing@xcite , in the lennard - jones clusters optimization@xcite , and in the traveling salesman problem @xcite .    despite these successes  mostly obtained by path - integral monte carlo ( pimc ) implementations of qa  there is no general theory addressing and even less predicting the performance of a qa algorithm . different optimization problems are characterized by different `` energy landscapes '' of barriers and valleys about which little is known but which clearly influence the annealing process@xcite . success of qa crucially depends on the efficiency with which the chosen kinetic energy and associated fictitious quantum fluctuations explores and influences these effective energy landscape . this is a uncomfortable situation , in view of the fact that it is _ a priori _ not obvious or guaranteed that a qa approach should do any better than , for instance , classical simulated annealing ( ca ) . indeed , for the interesting case of boolean satisfiability problems @xcite  more precisely , a prototypical np - complete problem such as 3-sat  a recent study has shown that pimc - qa performs definitely _ worse _ than simple ca @xcite .    in a previous paper @xcite , henceforth referred to as i , we compared classical and quantum annealing approaches in their performance to optimize the simplest potential landscape @xmath0 , namely the one - dimensional potential double - well . classical annealing was implemented by means of a fokker - planck ( fp ) equation with a time - dependent ( decreasing ) temperature @xmath1 . quantum annealing was performed through the schrdinger s equation , both in real and in imaginary time , describing a particle with a time - dependent ( decreasing ) inverse mass @xmath2 in the double - well potential @xmath0 . given the textbook simplicity of the problem , it was possible to correlate in detail the features of the landscape ( position and shape of valleys , barrier height ) with the outcome of the annealing process . one saw for instance that fokker - plank ca is sensitive only to the ratio @xmath3 of the energy splitting @xmath4 between the two wells , or valleys , and the barrier height @xmath5 , whereas on the contrary schrdinger qa is sensitive to the landau - zener tunneling gap , and hence , among other things , to the barrier width . unfortunately , such a direct approach is applicable , for practical purposes , only to insignificantly small sized optimization problems . to appreciate the difficulty , it is enough to consider that the number of possible configurations , and hence the hilbert space size , of a small 32@xmath632 square lattice ising model is @xmath7 , an astronomically large number which forbids any direct approach based on deterministic state evolution . hard instances of typical optimization problems involve an even larger number of variables . because of that , alternative strategies , based on monte carlo sampling , are mandatory . that notwithstanding , the various deterministic types of dynamics , fokker - planck , schrdinger , or monte carlo dynamics , classical or quantum , are not at all equivalent . there is in particular no relationship between the ( physical ) time appearing in the fokker - planck or in the schrdinger equation , and the corresponding classical or quantum monte carlo time - step . furthermore , _ many _ different types of monte carlo ( mc ) dynamics are possible . while sampling the same equilibrium probability distribution and hence providing the same equilibrium averages @xcite , they will generally perform very differently in an out - of - equilibrium situation . in order to appreciate that , given the large variability of the possible mc outcomes , it is once again wise to concentrate attention on landscapes which are well under control .    in this paper we implement and investigate different monte carlo annealing strategies , both classical and quantum , to the very same optimization problem  the one - dimensional double - well  which was studied in i by deterministic ( fokker - planck and schrdinger ) annealing approaches . we will first show ( sec . [ ca_intro : sec ] that the choice of the proposed move in a metropolis mc scheme strongly influences the annealing performance . such a strong influence of the move is seen to be correlated with the instantaneous spectrum of the markov transition matrix associated to the mc scheme , as shown in detail in sec . [ spectral : subsec ] . next , we will turn to quantum mc , specifically to path - integral monte carlo ( pimc ) , and show how the required tunneling dynamics is highly non - trivial . the outcome of an allegedly state - of - the - art pimc annealing of a simple double - well can even be very unsatisfactory , due to sampling difficulties of instanton events ( see secs . [ pimc : sec ] , [ results1:subsec ] , [ results2:subsec ] ) . finally , we will analyze the choice of kinetic energy in the qa hamiltonian , by testing the effectiveness of an alternative _ relativistic _ kind of dispersion , which proves much more effective than the usual non - relativistic choice ( sec . [ results3:subsec ] ) . section [ discussion : sec ] will finally contain a summary of the main results some discussion . technical details on the spectral analysis of the classical markov process , and on the generalization of the bisection algorithm of interest for the pimc study of sec . [ results3:subsec ] , are relegated to the two appendices .","summary":"we present results for a variety of monte carlo annealing approaches , both classical and quantum , benchmarked against one another for the textbook optimization exercise of a simple one - dimensional double - well . in classical ( thermal ) annealing , the dependence upon the move chosen in a metropolis scheme is studied and correlated with the spectrum of the associated markov transition matrix . in quantum annealing","abstract":"we present results for a variety of monte carlo annealing approaches , both classical and quantum , benchmarked against one another for the textbook optimization exercise of a simple one - dimensional double - well . in classical ( thermal ) annealing , the dependence upon the move chosen in a metropolis scheme is studied and correlated with the spectrum of the associated markov transition matrix . in quantum annealing , the path - integral monte carlo approach is found to yield non - trivial sampling difficulties associated with the tunneling between the two wells . the choice of fictitious quantum kinetic energy is also addressed . we find that a `` relativistic '' kinetic energy form , leading to a higher probability of long real space jumps , can be considerably more effective than the standard one ."}
{"article_id":"0802.2831","section_id":"i","document":"many situations involve the computation of an equilibrium or a stable configuration of some sort in a dynamic environment . sometimes it is the result of individual agents acting on their own noncompetitively but selfishly ( e.g. , nash and other economic equilibria ) , sometimes it is agents acting competitively against each other ( and perhaps nature / chance ) , sometimes the equilibrium is the limit of an iterative process that evolves in some direction until it settles . often the sought objects can be described mathematically as the fixed points of an equation @xmath0 . many models and problems from a broad variety of areas are of this nature . examples include : nash equilibria in games ; market equilibria ; computation of optimal strategies and the values of competitive games ( stochastic and other games ) ; stable configurations of neural networks ; analysis of basic stochastic models for evolution like branching processes , and for language like stochastic context - free grammars ; and models that incorporate the basic primitives of probability and recursion like recursive markov chains . most of these models and problems have been studied mathematically for a long time , leading to the development of rich theories . yet , some of their most basic algorithmic questions are still not resolved , in particular it is not known whether they can be solved in polynomial time .    despite the broad diversity of these problems , there are certain common computational principles that underlie many of these different types of problems , which are captured by the complexity classes pls , ppad , and fixp . in this paper we will review these principles , the corresponding classes , and the types of problems they contain . all the problems we will discuss are total search problems . formally , a _ search problem _ @xmath1 has a set of instances , each instance @xmath2 has a set @xmath3 of acceptable answers ; the search problem is _ total _ if @xmath4 for all instances @xmath2 . as usual , for computational purposes , instances are represented by strings over a fixed alphabet @xmath5 , and it is assumed that , given a string over @xmath5 one can determine in polynomial time if it represents an instance of a problem . the size @xmath6 of an instance is the length of its string representation . input numbers ( such as the payoffs of games , input probabilities of stochastic models , etc . ) are assumed to be rationals represented in binary by numerator and denominator . the underlying solution space from which answers are drawn may be finite and discrete , as in combinatorial problems , or it may be infinite and continuous . in the former ( the finite ) case , solutions are represented also as strings and the problem is : given an instance @xmath2 , compute a solution in @xmath3 . in the latter ( infinite / continuous ) case also , if there are rational - valued solutions ( as in linear programming for example ) , then the problem is to compute one of them . in several problems however , the solutions are inherently irrational , and we can not compute them exactly ( in the usual turing machine - based model of computation and complexity ) . in these cases we need to specify precisely which information about the solutions is to be computed ; this could be for example a yes / no question , such as , does an event in a stochastic model occur almost surely ( with probability 1 ) or does the value of a game exceed a given threshold , or we may want to compute an answer up to a desired precision . in any case , the computational tasks of interest have to be defined precisely , because different tasks can have different complexity .    in this paper we will discuss a variety of equilibria and fixed point problems , and the complexity classes which capture the essential aspects of several types of such problems . we discuss three classes , pls , ppad , and fixp , which capture different types of equilibria . some representative complete problems for these classes are : for pls pure nash equilibria in games where they are guaranteed to exist , for ppad ( mixed ) nash equilibria in 2-player normal form games , and for fixp ( mixed ) nash equilibria in normal form games with 3 ( or more ) players .","summary":"examples include nash equilibria in games ; market equilibria ; computing optimal strategies and the values of competitive games ( stochastic and other games ) ; stable configurations of neural networks ; analysing basic stochastic models for evolution like branching processes and for language like stochastic context - free grammars ; and models that incorporate the basic primitives of probability and recursion like recursive markov chains . it is not known whether these problems can be solved in polynomial time . there are certain common computational principles underlying different types of equilibria , which are captured by the complexity classes pls , ppad , and fixp . representative complete problems for these classes are respectively , pure nash equilibria in games where they are guaranteed to exist , ( mixed ) nash equilibria in 2-player normal form games , and ( mixed ) nash equilibria in normal form games with 3 ( or more ) players . this paper reviews the underlying computational principles and the corresponding classes .   ","abstract":"many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind . examples include nash equilibria in games ; market equilibria ; computing optimal strategies and the values of competitive games ( stochastic and other games ) ; stable configurations of neural networks ; analysing basic stochastic models for evolution like branching processes and for language like stochastic context - free grammars ; and models that incorporate the basic primitives of probability and recursion like recursive markov chains . it is not known whether these problems can be solved in polynomial time . there are certain common computational principles underlying different types of equilibria , which are captured by the complexity classes pls , ppad , and fixp . representative complete problems for these classes are respectively , pure nash equilibria in games where they are guaranteed to exist , ( mixed ) nash equilibria in 2-player normal form games , and ( mixed ) nash equilibria in normal form games with 3 ( or more ) players . this paper reviews the underlying computational principles and the corresponding classes .    mihalis yannakakis"}
{"article_id":"0802.2831","section_id":"c","document":"many problems , from a broad , diverse range of areas , involve the computation of an equilibrium or fixed point of some kind . there is a long line of research ( both mathematical and algorithmic ) in each of these areas , but for many of these basic problems we still do not have polynomial time algorithms , nor do we have hard evidence of intractability ( such as np - hardness ) . we reviewed a number of such problems here , and we discussed three complexity classes , pls , ppad and fixp , that capture essential aspects of several types of such problems . the classes pls and ppad lie somewhere between p and tfnp ( total search problems in np ) , and fixp ( more precisely , the associated discrete problems ) lie between p and pspace . these , and the obvious containment ppad @xmath251 fixp , are the only relationships we currently know between these classes and the other standard complexity classes . it would be very interesting and important to improve on this state of knowledge . furthermore , there are several important problems that are in these classes , but are not ( known to be ) complete , so it is possible that one can make progress on them , without resolving the relation of the classes themselves . k.  etessami and m.  yannakakis . recursive markov chains , stochastic grammars , and monotone systems of non - linear equations . , 2005 . ( full expanded version available from http://homepages.inf.ed.ac.uk/kousha ) .","summary":"many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind . mihalis yannakakis","abstract":"many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind . examples include nash equilibria in games ; market equilibria ; computing optimal strategies and the values of competitive games ( stochastic and other games ) ; stable configurations of neural networks ; analysing basic stochastic models for evolution like branching processes and for language like stochastic context - free grammars ; and models that incorporate the basic primitives of probability and recursion like recursive markov chains . it is not known whether these problems can be solved in polynomial time . there are certain common computational principles underlying different types of equilibria , which are captured by the complexity classes pls , ppad , and fixp . representative complete problems for these classes are respectively , pure nash equilibria in games where they are guaranteed to exist , ( mixed ) nash equilibria in 2-player normal form games , and ( mixed ) nash equilibria in normal form games with 3 ( or more ) players . this paper reviews the underlying computational principles and the corresponding classes .    mihalis yannakakis"}
{"article_id":"gr-qc0505029","section_id":"i","document":"the laser interferometer gravitational wave observatory ( ligo ) is a network of interferometric detectors aiming to make direct observations of gravitational waves . construction of the ligo detectors is essentially complete , and much progress has been made in commissioning them to ( a ) bring the three interferometers to their final optical configuration , ( b ) reduce the interferometers noise floors and improve the stationarity of the noise , and ( c ) pave the way toward long - term science observations . interleaved with commissioning , four `` science runs '' have been carried out to collect data under stable operating conditions for astrophysical gravitational wave searches , albeit at reduced sensitivity and observation time relative to the ligo design goals . the first science run , called s1 , took place in the summer of 2002 over a period of 17 days . s1 represented a major milestone as the longest and most sensitive operation of broad - band interferometers _ in coincidence _ up to that time . using the s1 data from the ligo and geo600 interferometers  @xcite , astrophysical searches for four general categories of gravitational wave source types  binary inspiral  @xcite , burst - like  @xcite , stochastic  @xcite and continuous wave  @xcite  were pursued by the ligo scientific collaboration ( lsc ) . these searches established general methodologies to be followed and improved upon for the analysis of data from future runs . in 2003 two additional science runs of the ligo instruments collected data of improved sensitivity with respect to s1 , but still less sensitive than the instruments design goal . the second science run ( s2 ) collected data in early 2003 and the third science run ( s3 ) at the end of the same year . several searches have been completed or are underway using data from the s2 and s3 runs  @xcite . a fourth science run , s4 , took place at the beginning of 2005 .    in this paper we report the results of a search for gravitational wave bursts using the ligo s2 data . the astrophysical motivation for burst events is strong ; it embraces catastrophic phenomena in the universe with or without clear signatures in the electromagnetic spectrum like supernova explosions  @xcite , the merging of compact binary stars as they form a single black hole  @xcite and the astrophysical engines that power the gamma ray bursts  @xcite . perturbed or accreting black holes , neutron star oscillation modes and instabilities as well as cosmic string cusps and kinks  @xcite are also potential burst sources . the expected rate , strength and waveform morphology for such events is not generally known . for this reason , our assumptions for the expected signals are minimal . the experimental signatures on which this search focused can be described as burst signals of short duration ( @xmath3 1  second ) and with enough signal strength in the ligo sensitive band ( 1001100  hz ) to be detected in coincidence in all three ligo instruments . the triple coincidence requirement is used to reduce the false alarm rate ( background ) to much less than one event over the course of the run , so that even a single event candidate would have high statistical significance . the general methodology in pursuing this search follows the one we presented in the analysis of the s1 data  @xcite with some significant improvements . in the s1 analysis the ringing of the pre - filters limited our ability to perform tight time - coincidence between the triggers coming from the three ligo instruments . this is addressed by the use of a new search method that does not require strong pre - filtering . this new method also provides an improved event parameter estimation , including timing resolution . finally , a waveform consistency test is introduced for events that pass the time and frequency coincidence requirements in the three ligo detectors . this search examines 9.98 days of live time and yields one candidate event in coincidence among the three ligo detectors during s2 . subsequent examination of this event reveals an acoustic origin for the signal in the two hanford detectors , easily eliminated using a `` veto '' based on acoustic power in a microphone . taking this into account , we set an upper limit on the rate of burst events detectable by our detectors at the level of 0.26 per day at an estimated 90% confidence level . we have used _ ad hoc _ waveforms ( sine - gaussians and gaussians ) to establish the sensitivity of the s2 search pipeline and to interpret our upper limit as an excluded region in the space of signal rate versus strength . the burst search sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude incident on earth lies in the range @xmath2  . both the upper limit ( rate ) and its applicability to signal strengths ( sensitivity ) reflect significant improvements with respect to our s1 result  @xcite . in addition , we evaluate the sensitivity of the search to astrophysically motivated waveforms derived from models of stellar core collapse  @xcite and from the merger of binary black holes  @xcite .    in the following sections we describe the ligo instruments and the s2 run in more detail ( section  [ sec : ligos2run ] ) as well as an overview of the search pipeline ( section  [ sec : pipeline ] ) . the procedure for selecting the data that we analyze is described in section  [ sec : dataselect ] . we then present the search algorithm and the waveform consistency test used in the event selection ( section  [ sec : etg_methods ] ) and discuss the role of vetoes in this search ( section  [ sec : vetoes ] ) . section  [ sec : evana ] describes the final event analysis and the assignment of an upper limit on the rate of detectable bursts . the efficiency of the search for various target waveforms is presented in section  [ sec : efficiency ] . our final results and discussion are presented in sections  [ sec : results ] and  [ sec : summaries ] .","summary":"this search is sensitive to bursts of duration much less than a second and with frequency content in the 1001100  hz range . the sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude lies in the range of  . we interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level .","abstract":"we perform a search for gravitational wave bursts using data from the second science run of the ligo detectors , using a method based on a wavelet time - frequency decomposition . this search is sensitive to bursts of duration much less than a second and with frequency content in the 1001100  hz range . it features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by ligo . improvements in the search method allow exploring weaker signals , relative to the detector noise floor , while maintaining a low false alarm rate , hz . the sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude lies in the range of  . no gravitational wave signals were detected in 9.98 days of analyzed data . we interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level . we combine this limit with measurements of the detection efficiency for given waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order - of - magnitude distance sensitivity to certain modeled astrophysical sources . both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad - band search for untriggered and unmodeled gravitational wave bursts to date ."}
{"article_id":"gr-qc0505029","section_id":"m","document":"an accurate knowledge of gravitational wave burst waveforms would allow the use of _ matched filtering _ @xcite along the lines of the search for binary inspirals  @xcite . however , many different astrophysical systems may give rise to gravitational wave bursts , and the physics of these systems is often very complicated . even when numerical relativistic calculations have been carried out , as in the case of core collapse supernovae , they generally yield roughly representative waveforms rather than exact predictions . therefore , our present searches for gravitational wave bursts use general algorithms which are sensitive to a wide range of potential signals . the first ligo burst search  @xcite used two event trigger generator ( etg ) algorithms : a time - domain method designed to detect a large `` slope '' ( time derivative ) in the data stream after suitable filtering  @xcite , and a method called tfclusters  @xcite which is based on identifying clusters of excess power in time - frequency spectrograms . several other burst - search methods have been developed by members of the ligo scientific collaboration . for this paper , we have chosen to focus on a single etg called waveburst which identifies clusters of excess power once the signal is decomposed in the wavelet domain , as described below . other methods which were applied to the s2 data include tfclusters ; the excess power statistic of anderson _ et al . _ @xcite ; and the `` block - normal '' time - domain algorithm  @xcite . in preliminary studies using s2 playground data , these other methods had sensitivities comparable to waveburst for the target waveforms described in section  [ sec : efficiency ] , but their implementations were less mature at the time of this analysis .    an integral part of our s2 search and the final event trigger selection is to perform a consistency test among the data streams recorded by the different interferometers at each trigger time identified by the etg . this is done using the @xmath11-statistic  @xcite , a time - domain cross - correlation method sensitive to the coherent part of the candidate signals , described in subsection c below . waveburst is an etg that searches for gravitational wave bursts in the wavelet time - frequency domain . it is described in greater detail in  @xcite . the method uses wavelet transformations in order to obtain the time - frequency representation of the data . bursts are identified by searching for regions in the wavelet time - frequency domain with an excess of power , coincident between two or more interferometers , that is inconsistent with stationary detector noise . waveburst processes gravitational wave data from two interferometers at a time . as shown in fig . [ fig : pipeline ] the analysis is performed over three ligo detectors resulting in the production of triggers for three detector pairs . the three sets of triggers are then compared in a `` triple coincidence '' step which checks for consistent trigger times and frequency components , as will be described in section  [ ss : triplecoinc ] .        for each detector pair , the waveburst etg performs the following steps : ( a ) wavelet transformation applied to the gravitational wave channel from each detector , ( b ) selection of wavelet amplitudes exceeding a threshold , ( c ) identification of common wavelet components in the two channels , ( d ) clustering of nearby wavelet components , and ( e ) selection of burst triggers . during steps ( a ) , ( b ) and ( d ) the data processing is independent for each channel . during steps ( c ) and ( e ) data from both channels are used . the input data to the waveburst etg are time series from the gravitational wave channel with duration of @xmath15 seconds and sampling rate of @xmath16  hz . before the wavelet transformation is applied the data are downsampled by a factor of two . using an orthogonal wavelet transformation ( based on a symlet wavelet with filter length of 60 ) the time series are converted into wavelet series @xmath17 , where @xmath18 is the time index and @xmath19 is the wavelet layer index . each wavelet layer can be associated with a certain frequency band of the initial time series . the time - frequency resolution of the waveburst scalograms is the same for all the wavelet layers ( @xmath20  sec @xmath21  hz ) . therefore , the wavelet series @xmath17 can be displayed as a time - frequency scalogram consisting of 64 wavelet layers with @xmath22 pixels ( data samples ) each . this tiling is different from the one in the conventional dyadic wavelet decomposition where the time resolution adjusts to the scale ( frequency )  @xcite . the constant time - frequency resolution makes the waveburst scalograms similar to spectrograms produced with windowed fourier transformations .    for each layer we first select a fixed fraction @xmath23 of pixels with the largest absolute amplitudes . these are called _ black pixels_. the number of selected black pixels is @xmath24 . all other wavelet pixels are called _ white pixels_. then we calculate rank statistics for the black pixels within each layer . the rank @xmath25 is an integer number from 1 to @xmath24 , with the rank 1 assigned to the pixel with the largest absolute amplitude in the layer . given the rank of wavelet amplitudes @xmath25 , the following non - parametric pixel statistic is computed @xmath26 for white pixels the value of @xmath27 is set to zero . the statistic @xmath27 can be interpreted as the pixel s _ logarithmic significance_. assuming gaussian detector noise , the logarithmic significance can be also calculated as @xmath28 where @xmath29 is the absolute value of the pixel amplitude in units of the noise standard deviation . in practice , the ligo detector noise is not gaussian and its probability distribution function is not determined _ a priori_. therefore , we use the non - parametric statistic @xmath27 , which is a more robust measure of the pixel significance than @xmath30 . using the inverse function of @xmath31 with @xmath27 as an argument , we introduce the _ non - parametric amplitude _ @xmath32 and the _ excess power ratio _ @xmath33 which characterizes the pixel excess power above the average detector noise . after the black pixels are selected , we require their time - coincidence in the two channels . given a black pixel of significance @xmath27 in the first channel , this is accepted if the significance of neighboring ( in time ) pixels in the second channel ( @xmath34 ) satisfies @xmath35 where @xmath36 is the _ coincidence threshold_. otherwise , the pixel is rejected . this procedure is repeated for all the black pixels in the first channel . the same coincidence algorithm is applied to pixels in the second channel . as a result , a considerable number of black pixels in both channels produced by fluctuations of the detector noise are rejected . at the same time , black pixels produced by gravitational wave bursts have a high acceptance probability because of the coherent excess of power in two detectors . after the coincidence procedure is applied to both channels a clustering algorithm is applied jointly to the two channel pixel maps . as a first step , we merge ( or ) the black pixels from both channels into one time - frequency plane . for each black pixel we define neighbors ( either black or white ) , which share a side or a vertex with the black pixel . the white neighbors are called _ halo _ pixels . we define a cluster as a group of black and halo pixels which are connected either by a side or a vertex . after the cluster reconstruction , we go back to the original time - frequency planes and calculate the cluster parameters separately for each channel . therefore , there are always two clusters , one per channel , which form a waveburst trigger . the cluster parameters are calculated using black pixels only . for example , the cluster size @xmath37 is defined as the number of black pixels . other parameters which characterize the cluster strength are the cluster excess power ratio @xmath38 and the cluster _ logarithmic likelihood _ @xmath39 . given a cluster @xmath40 , these are estimated by summing over the black pixels in the cluster : @xmath41 given the times @xmath42 of individual pixels , the cluster center time is calculated as @xmath43 as configured for this analysis , waveburst initially generated triggers with frequency content between 64  hz and 4096  hz . as we will see below , the cluster size , likelihood , and excess power ratio can be used for the further selection of triggers , while the cluster time and frequency span are used in a coincidence requirement . the frequency band of interest for this analysis , 1001100  hz , is selected during the later stages of the analysis . there are two main waveburst tunable input parameters : the black pixel fraction @xmath23 which is applied to each frequency layer , and the coincidence threshold @xmath36 . the purpose of these parameters is to control the average black pixel occupancy @xmath44 , the fraction of black pixels over the entire time - frequency scalogram . to ensure robust cluster reconstruction , the occupancy should not be greater than @xmath45% . for white gaussian detector noise the functional form of @xmath44 can be calculated analytically . this can be used to set a constraint on @xmath23 and @xmath36 for a given target @xmath44 . if @xmath23 is set too small ( less then a few percent ) , noise outliers due to instrumental glitches may monopolize the limited number of available black pixels and thus allow gravitational wave signals to remain hidden . to avoid this domination of instrumental glitches , we run the analysis with @xmath23 equal to 10% . this value of @xmath23 together with the occupancy target @xmath44 of 0.7% defines the coincidence threshold @xmath36 at 1.5 . all the tuning of the waveburst method was performed on the s2 playground data set ( section  [ sec : dataselect ] ) . for the selected values of @xmath23 and @xmath36 , the average trigger rate per ligo instrument pair was approximately @xmath46  hz , about twice the false alarm rate expected for white gaussian detector noise . the trigger rate was further reduced by imposing cuts on the excess power ratio @xmath38 . for clusters of size @xmath37 greater than @xmath45 we required @xmath38 to be greater than @xmath47 while for single pixel clusters ( @xmath48 ) we used a more restrictive cut of @xmath38 greater than @xmath49 . this selection on the event parameters further reduced the counting rates per ligo instrument pair to @xmath50  hz . the times and reconstructed parameters of waveburst events passing these criteria were written onto disk . this allowed the further processing and selection of these events without the need to re - analyze the full data stream , a process which is generally time and cpu intensive . further selection of waveburst events proceeds by identifying triple coincidences . the output of the waveburst etg is a set of coincident triggers for a selected interferometer pair @xmath51 . each waveburst trigger consists of two clusters , one in @xmath52 and one in @xmath53 . for the three ligo interferometers there are three possible pairs : ( l1,h1 ) , ( h1,h2 ) and ( h2,l1 ) . in order to establish triple coincidence events , we require a time - frequency coincidence of the waveburst triggers generated for these three pairs . to evaluate the time coincidence we first construct @xmath54 , , the average central time of the @xmath52 and @xmath53 clusters for the trigger . three such combined central times are thus constructed : @xmath55 , @xmath56 , and @xmath57 . we then require that all possible differences of these combined central times fall within a time window @xmath58  ms . this window is large enough to accommodate the maximum difference in gravitational wave arrival times at the two detector sites ( @xmath59  ms ) and the intrinsic time resolution of the waveburst algorithm which has an rms on the order of @xmath60  ms as discussed in section  [ sec : efficiency ] . we apply a loose requirement on the frequency consistency of the waveburst triggers . first , we calculate the minimum ( @xmath61 ) and maximum ( @xmath62 ) frequency for each interferometer pair @xmath63 @xmath64 where @xmath65 and @xmath66 are the low and high frequency boundaries of the @xmath52 and @xmath53 clusters . then , the trigger frequency bands are calculated as @xmath67 for all pairs . for the frequency coincidence , the bands of all three waveburst triggers are required to overlap . an average frequency is then calculated from the clusters , weighted by signal - to - noise ratio , and the coincident event candidate is kept for this analysis if this average frequency is above 64  hz and below 1100  hz . the final step in the coincidence analysis of the waveburst events involves the construction of a single measure of their combined significance . as we described already , triple coincidence events consist of three waveburst triggers involving a total of six clusters . each cluster has its parameters calculated on a per - interferometer basis . assuming white detector noise , the variable @xmath39 for a cluster of size @xmath37 follows a gamma probability distribution . this motivates the use of the following measure of the _ cluster significance _ : @xmath68 which is derived from the logarithmic likelihood @xmath39 of a cluster @xmath40 and from the number @xmath37 of black pixels in that cluster  @xcite . given the significance of the six clusters , we compute the _ combined significance _ of the triple coincidence event as @xmath69 where @xmath70 ( @xmath71 ) is the significance of the @xmath52 ( @xmath53 ) cluster for the @xmath63 interferometer pair .    in order to evaluate the rate of accidental coincidences , we have repeated the above analysis on the data after introducing an unphysical time shift ( `` lag '' ) in the livingston data stream relative to the hanford data streams . the hanford data streams are not shifted relative to one another , so any noise correlations from the local environment are preserved . figure  [ fig : signif ] shows the distribution of cluster significance ( equation  [ eq : clustersig ] ) from the three individual detectors , and the combined significance ( equation  [ eq : combsig ] ) , over the entire s2 data set , for both zero - lag and time - lag coincidences . using 46 such time - lag instances of the s2 playground data we have set the threshold on @xmath72 for this search in order to yield a targeted false alarm rate of @xmath73hz . without significantly compromising the pipeline sensitivity , this threshold was selected to be @xmath74 . in the 641100  hz frequency band , the resulting false alarm rate in the s2 playground analysis was approximately @xmath75hz . the coincident events selected by waveburst in this way are then checked for their waveform consistency using the @xmath11-statistic .          the @xmath11-statistic test  @xcite is applied as the final step of searching for gravitational wave event candidates . this test re - analyzes the raw ( unprocessed ) interferometer data around the times of coincident events identified by the waveburst etg . the fundamental building block in performing this waveform consistency test is the @xmath11-statistic , or the normalized linear correlation coefficient of two sequences , @xmath76 and @xmath77 ( in this case , the two gravitational wave signal time series ) : @xmath78 where @xmath79 and @xmath80 are their respective mean values . this quantity assumes values between @xmath81 for fully anti - correlated sequences and @xmath82 for fully correlated sequences . for uncorrelated white noise , we expect the @xmath11-statistic values obtained for arbitrary sets of points of length @xmath83 to follow a normal distribution with zero mean and @xmath84 . any coherent component in the two sequences will cause @xmath11 to deviate from the above normal distribution . as a normalized quantity , the @xmath11-statistic does not attempt to measure the consistency between the relative amplitudes of the two sequences . consequently , it offers the advantage of being robust against fluctuations of detector amplitude response and noise floor . a similar method based on this type of time - domain cross - correlation has been implemented in a ligo search for gravitational waves associated with a grb  @xcite and elsewhere  @xcite .    as will be described below , the final output of the @xmath11-statistic test is a combined confidence statistic which is constructed from @xmath11-statistic values calculated for all three pairs of interferometers . for each pair , we use only the absolute value of the statistic , @xmath85 , rather than the signed value . this is because an astrophysical signal can produce either a correlation or an anticorrelation in the interferometers at the two ligo sites , depending on its sky position and polarization . in fact , the @xmath11-statistic analysis was done using whitened ( see below ) but otherwise uncalibrated data , with an arbitrary sign convention . a signed correlation test using calibrated data would be appropriate for the h1-h2 pair , but all three pairs were treated equivalently in the present analysis .    the number of points @xmath83 considered in calculating the statistic in eq . ( [ eqn : rstat ] ) , or equivalently the _ integration time _ @xmath86 , is the most important parameter in the construction of the @xmath11-statistic . its optimal value depends in general on the duration of the signal being considered for detection . if @xmath86 is too long , the candidate signal is `` washed out '' by the noise when computing @xmath11 . on the other hand , if it is too short , then only part of the coherent signal is included in the integration . simulation studies have shown that most of the short - lived signals of interest to the ligo burst search can be identified successfully using a set of three discrete integration times with lengths of 20 , 50 and 100  ms .    within its ligo implementation , the @xmath11-statistic analysis first performs data `` conditioning '' to restrict the frequency content of the data to ligo s most sensitive band and to suppress any coherent lines and instrumental artifacts . each data stream is first band - pass filtered with an 8th - order butterworth filter with corner frequencies of 100  hz and 1572  hz , then down - sampled to a 4096  hz sampling rate . the upper frequency of 1572  hz was chosen in order to have 20  db suppression at 2048  hz and thus avoid aliasing . the lower frequency of 100  hz was chosen to suppress the contribution of seismic noise ; it also defines the lower edge of the frequency band for this gravitational wave burst search , since it is above the lower frequency limit of 64  hz for waveburst triggers . the band - passed data are then whitened with a linear predictor error filter with a 10  hz resolution trained on a 10  second period before the event start time . the filter removes predictable content , including lines that were stationary over a 10  second time scale . it also has the effect of suppressing frequency bands with large stationary noise , thus emphasizing transients  @xcite . the next step in the @xmath11-statistic analysis involves the construction of all the possible @xmath11 coefficients given the number of interferometer pairs involved in the trigger , their possible relative time - delays due to their geographic separation , and the various integration times being considered . relative time delays up to @xmath87  ms are considered for each detector pair , corresponding to the light travel time between the hanford and livingston sites . future analyses will restrict the time delay to a much smaller value when correlating data from the two hanford interferometers , to allow only for time calibration uncertainties . furthermore , in the case of waveburst triggers with reported durations greater than the integration time @xmath86 , multiple integration _ windows _ of that length are considered , offset from the reported start time of the trigger by multiples of @xmath88 . for a given integration window indexed by @xmath89 ( containing @xmath90 data samples ) , ordered pair of instruments indexed by @xmath91 @xmath92 , and relative time delay indexed by @xmath37 , the @xmath11-statistic value @xmath93 is calculated . for each @xmath94 combination , the _ distribution _ of @xmath93 for all values of @xmath37 is compared to the null hypothesis expectation of a normal distribution with zero mean and @xmath95 using the kolmogorov - smirnov test . if these are statistically consistent at the 95% level , then the algorithm assigns no significance to any apparent correlation in this detector pair . otherwise , a one - sided significance and its associated logarithmic confidence are calculated from the _ maximum _ value of @xmath93 for any time delay , compared to what would be expected if there were no correlation . confidence values for all ordered detector pairs are then averaged to define the combined correlation confidence for a given integration window . the final result of the @xmath11-statistic test , @xmath96 , is the maximum of the combined correlation confidence over all of the integration windows being considered . events with a value of @xmath96 above a given threshold are finally selected .    the @xmath11-statistic implementation , filter parameters , and set of integration times were chosen based on their performance for various simulated signals . the single remaining parameter , the threshold on @xmath96 , was tuned primarily in order to ensure that much less than one background event was expected in the whole s2 run , corresponding to a rate of o@xmath97hz . since the rate of waveburst triggers was approximately @xmath75hz , as mentioned in section  [ ss : triplecoinc ] , a rejection factor of around 150 was required . table  [ t : reject ] shows the rejection efficiency of the @xmath11-statistic test for two thresholds on @xmath96 when the test is applied to white gaussian noise ( 200 ms segments ) , to real s2 interferometer noise at randomly selected times ( 200 ms segments ) , and to the data at the times of time - lag ( , background ) waveburst triggers in the s2 playground . in the first two cases , 200  ms of data was processed by the @xmath11-statistic algorithm , whereas in the latter case , the amount of data processed was determined by the trigger duration reported by waveburst . the table shows that random detector noise rarely produced a @xmath96 value above @xmath98 , but the rejection factor for waveburst triggers was not high enough . a @xmath96 threshold of @xmath99 was ultimately chosen for this analysis , yielding an estimated rejection factor of @xmath100 for waveburst triggers . [ htb ]    .percentage of s2 background events rejected by the @xmath11-statistic for two different thresholds on @xmath96 . [ cols=\"<,<,<\",options=\"header \" , ] the waveburst algorithm estimates the signal strength from the measured excess power in the cluster pixels , expressed as @xmath101 as in equation  [ eq : hrss ] but with the integrand being the antenna - pattern - corrected @xmath102 given by equation  [ eq : hdet ] rather than the intrinsic @xmath103 of the gravitational wave . figure  [ fig : sg_hrss ] shows that this quantity is slightly overestimated on average , particularly for weak signals . several factors contribute to mis - estimation of the signal strength . waveburst limits the signal @xmath101 integration to within the detected time - frequency volume of an event and not over the entire theoretical support of a signal . errors in the determination of the signal s time - frequency volume due to thresholding may lead to systematic uncertainties in the determination of its strength . the @xmath101 shown in fig .  [ fig : sg_hrss ] also reflects the folding of the measurements from all three ligo instruments and thus it is affected by calibration errors and noise fluctuations in any instrument . our simulation analysis has shown that the detected signal s @xmath101 is the quantity most sensitive to detector noise and its variability ; for this reason , it is not used in any step of the analysis either as part of the coincidence analysis or for the final event selection .    ]      during the s2 data taking , as well as shortly before and after it , several run intervals were designated for hardware signal injections . these injections were intended to address any instrumental issues , including calibrations , and provide a robust end - to - end test of ligo s data analysis pipelines . they also provided an important tool for establishing the `` safety '' of the veto analysis , , the absence of any couplings between a real gravitational wave burst and the auxiliary channels we considered as potential vetoes ( section  [ sec : vetoes ] ) . an arbitrary function generator connected to the mirror position actuators provided the capability of exciting the mirrors according to a simulated gravitational wave pattern . the waveforms injected through this hardware calibration included several of the ones described in the target waveform section above . the signals were injected into all three ligo instruments at identical times , without attempting to mock up the relative time delays and amplitudes that would be produced by a source at a particular position in the sky . thus the coincidence analysis , using the end - to - end pipeline invoked in the analysis of the real data alone as well as with software injections , was not fully appropriate for the hardware injections . we have restricted ourselves to examining the performance of the ligo instruments and of the waveburst etg in detecting these events and reconstructing their signal parameters using each individual detector . both the time and frequency reconstruction by the waveburst algorithm on these hardware - injected signals is consistent with our software injections and within our expectations . the largest source of systematic error in the efficiency of this search is uncertainty in the absolute calibration of the detectors . several contributions to this uncertainty have been considered  @xcite . systematic uncertainties are less than 12% for l1 , 5% for h1 , and 6% for h2 over the frequency band used in this analysis . the calibration at any given point in time is subject to an additional uncertainty from detector noise affecting the measurement of the amplitude of the calibration lines . these random errors were especially large near the beginning of the run , when the h1 and l1 calibration lines were rather weak . however , the efficiency of the search , averaged over the run , is insensitive to these random errors . the overall systematic uncertainty on the triple - coincidence efficiency is a combination of the individual systematic uncertainties which depends on the relative sensitivities of the detectors , with the least sensitive detector having the greatest influence . as shown in fig . [ fig : s2sens ] , h2 was the least sensitive detector at low frequencies while h1 was the least sensitive at high frequencies . the net uncertainty in the efficiency is estimated to be less than 8% at all frequencies . no significant systematic error is attributed to the procedure we followed in order to perform the efficiency measurement . the various signal morphologies were superimposed over the entire s2 data sample and its full range of detector behavior . the statistical error attributed to the finite number of simulations used for the efficiency measurement is reflected in the goodness of the sigmoid - like fits and is estimated to be less than 5% . the efficiency measurement was performed in multiple slightly - varying ways all of which yielded results within one standard deviation . these variations included different sampling of the s2 data set , different versions of the calibration constants , and different number and placement of the signal injections .    combining all uncertainties , we estimate our efficiency to any given signal morphology to be accurate at the 10% level or better .","summary":"no gravitational wave signals were detected in 9.98 days of analyzed data .","abstract":"we perform a search for gravitational wave bursts using data from the second science run of the ligo detectors , using a method based on a wavelet time - frequency decomposition . this search is sensitive to bursts of duration much less than a second and with frequency content in the 1001100  hz range . it features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by ligo . improvements in the search method allow exploring weaker signals , relative to the detector noise floor , while maintaining a low false alarm rate , hz . the sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude lies in the range of  . no gravitational wave signals were detected in 9.98 days of analyzed data . we interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level . we combine this limit with measurements of the detection efficiency for given waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order - of - magnitude distance sensitivity to certain modeled astrophysical sources . both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad - band search for untriggered and unmodeled gravitational wave bursts to date ."}
{"article_id":"gr-qc0505029","section_id":"r","document":"as we have seen in section  [ sec : evana ] , using the zero - lag and background rate measurements we set an upper bound on the rate of gravitational wave bursts at the instruments at the level of @xmath104 events per day at the 90% confidence level . we will now use the measurement of the efficiency of the search as described in the previous section in order to associate the above rate bound with the strength of the gravitational wave burst events . this is the rate versus strength interpretation that we introduced in our previous search for bursts in ligo using the s1 data  @xcite .    the rate bound of our search as a function of signal strength @xmath101 is given by @xmath105 where the numerator @xmath36 is the upper bound on the rate of detectable signal events at a given confidence level ( sec . [ ss : ratelimit ] ) and the denominator is the fractional efficiency for signals of strength @xmath101 ( at the earth ) . this rate versus strength interpretation makes the same assumptions on the signal morphology and origin as the ones that enter in the determination of the efficiency . in fig . [ fig : gsg_exclude ] we show the rate versus strength upper limit for the sine - gaussian and gaussian waveform families . for a given signal strength @xmath101 these plots give the upper limit at the 90% confidence level on the rate of burst events at the instruments with strength equal to or greater than @xmath101 . in that sense , the part of the plot above and to the right of these curves defines the region of signal strength - rate excluded by this search at 90% confidence level . as one would expect , for strong enough signals the efficiency of the search is 1 for all the signal morphologies : this part of the plot remains flat at a level that is set primarily by the observation time of this search . for weaker signals the efficiency decreases and the strength - rate plot curves up . eventually , as the efficiency vanishes the rate limit reaches infinity asymptotically . these curves for the various waveforms are not identical , as the detailed trailing off of the efficiency is dependent on the waveform . the exclusion rate - strength plots obtained from the s2 analysis represent a significant improvement with respect to the s1 result  @xcite . as already noted in section  [ sec : evana ] , the horizontal part of the plot determined by the observation time is improved by a factor of 6 while the sensitivity - limited curved part of it reflects an improvement in the efficiency of a factor of 17 or better , depending on the waveform morphology . exclusion plots at the 90% confidence level derived from the ligo burst search using the s2 data . the top plot corresponds to burst events modeled by sine - gaussians of q=8.9 and frequencies ranging from 100  hz to 849  hz , while the bottom plot corresponds to ones events modeled by gaussians of the @xmath86 s shown . for comparison , the corresponding curves resulting from the s1 analysis are superimposed . , title=\"fig : \" ]   exclusion plots at the 90% confidence level derived from the ligo burst search using the s2 data . the top plot corresponds to burst events modeled by sine - gaussians of q=8.9 and frequencies ranging from 100  hz to 849  hz , while the bottom plot corresponds to ones events modeled by gaussians of the @xmath86 s shown . for comparison , the corresponding curves resulting from the s1 analysis are superimposed . , title=\"fig : \" ]      as mentioned in the introduction , potential sources of gravitational wave bursts targeted in this search include core collapse supernovae , merging compact binaries ( neutron stars and/or black holes ) and gamma ray bursts . in recent years there has been much effort devoted to predicting gravitational wave burst waveforms from astrophysical sources , generally relying on detailed numerical and approximation methods . our search is designed to be sensitive to a broad range of short - duration bursts , so we wish to evaluate how it performs for plausible astrophysical signals suggested by certain models . as part of our signal simulation analysis for this search , we focus in particular on the case of the core collapse of rapidly spinning massive stars  @xcite , and of binary black hole mergers  @xcite . the core collapse simulations employ detailed hydrodynamical models in two dimensions , enforcing axisymmetry of the rotating star throughout its evolution . the core collapse is initiated artificially ( , through a change in the adiabatic index of the core material  @xcite ) . an accelerating quadrupole moment is calculated in 2d from the distribution and flow of matter during the collapse , from which the gravitational wave signal is derived . the rapid spinning of the progenitor star may produce multiple bounces of the dense core , which is reflected in the waveform of the emitted waves . simple models of the differential rotation of material in the star also lead to significant differences in the resulting waveforms . relativistic effects  @xcite , if included , serve to effectively `` stiffen '' the core , shifting the waves to higher frequencies and shorter durations . the simulation is followed through the core collapse phase when most of the gravitational wave signal is produced ; it need not be continued through to the explosion of the outer layers ( and indeed , these simulations may not produce such explosions ) . the simulations attempt to sample the space of important parameters ( progenitor star angular momentum , differential angular momentum versus radius , density versus radius , adiabatic index of the core , ) , resulting in collections of waveforms with widely varying morphologies ; but of course the actual distributions of such parameters are poorly known . in ref . @xcite the authors employ updated progenitor models and nuclear equation of state . for the studies described here , we make use of 78 waveforms supplied in ref . @xcite , 26 from ref . @xcite , and 72 from ref . we emphasize that we are studying these waveforms only as a guide for evaluating our search algorithm ; we do not rely on accurately modelling a realistic population of progenitor stars . the binary black hole merger waveforms are taken from the lazarus project  @xcite , which combines numerical simulation of the vacuum einstein equations for the most significantly nonlinear part of the interaction with close - limit perturbation theory for the late - time dynamics . the authors in  @xcite generate waveforms from simulations of equal mass binary black holes with no intrinsic spin starting from near the innermost stable circular orbit following a binary black hole inspiral . it should be kept in mind that these waveforms include the ringdown phase of the binary system and would naturally occur after an inspiral waveform , which is searched for using matched filtering techniques  @xcite .    in all of these models , the simulations and calculations predict gravitational wave bursts with time durations ranging from a fraction of a millisecond to tens or hundreds of milliseconds and with a significant fraction of their power in ligo s most sensitive frequency band ( 1001100  hz ) . this observation motivates the choice of parameters for the sine - gaussian and gaussian waveforms used to optimize and evaluate the efficiency for our search pipeline , as discussed in section  [ sec : efficiency ] . after tuning our pipeline algorithms using these _ ad hoc _ waveforms , we evaluate the efficiency for our search to detect the waveforms predicted from the astrophysical simulations . the amplitudes of these waveforms are predicted by the simulations , so that in addition to evaluating the efficiency as a function of @xmath101 ( at the earth ) , we can also present them as a function of distance to the source ( for a particular source inclination ) . we have evaluated the efficiency versus actual distance , averaged over source directions and polarizations , assuming an isotropic distribution in source direction . this assumption becomes invalid for supernova progenitors in the galactic disk , when the ligo detectors become sensitive to supernovae at distances greater than the disk thickness ( on the order of 150  pc ) . it is also invalid for extra - galactic binary black hole mergers , since the distribution of nearby galaxies is far from isotropic at the 1  mpc scale . this evaluation of the efficiency as a function of distance is only to `` set the scale '' for the current and future astrophysical searches .    for the case of core collapse supernovae we considered the collections of waveforms from the three studies discussed above  @xcite . there are 176 such supernovae waveforms . they are generally broad - band in frequency ; for 115 of them their central frequency is within the sensitive band of this search ( 1001100  hz ) and for them we established strength and distance sensitivities . sources were uniformly distributed over the whole sky with random polarization and fixed , optimal inclination . for detecting these waveforms , @xmath101 amplitudes of a few times @xmath106  corresponding to source distances of the order of 100 pc were required . such close - by supernovae are , of course , quite rare . in fig . [ fig : sn2 ] we show the expected @xmath101 ( at the detectors ) and the central frequency for each of the 176 supernovae waveforms assuming they originate from a core collapse supernovae that is optimally oriented and polarized and is located at 100  pc from the detectors . superimposed , we show the sensitivity of the ligo instruments during s2 .     at the detectors versus central frequency for the 176 supernovae waveforms from the three models described in references  @xcite : the hydrodynamical model of ref . @xcite , labeled `` zm '' , the relativistic effects considered in ref .  @xcite and labeled `` dfm '' , and finally the hydrodynamical model employing realistic nuclear equation of state of ref . @xcite , labeled `` oblw '' . in all cases , the supernova events are positioned in optimal orientation and polarization at 100  pc from the detectors . the strain sensitivity of the l1 detector during the s2 run is shown for comparison . [ fig : sn2 ] ]    for the case of binary black hole mergers , we have considered systems of black hole mass in the range of 10 - 90  @xmath107 . the characteristic frequency of the resulting waveform is inversely proportional to the mass of the system and thus five different masses of 10 , 30 , 50 , 70 and 90  @xmath107 were chosen in order to span the nominal frequency band of this search , , the 1001100  hz band . moreover , the waveforms of these systems  @xcite come with two polarizations and they thus offered a check of the robustness of the waveform consistency test , the @xmath11-statistic , against complex morphologies . the efficiency is calculated over the whole sky considering the two polarization waveforms and a fixed inclination angle . the best performing mass system corresponds to 50  @xmath107 : the characteristic frequency of this system corresponds to the best operating point of the ligo instruments , , close to 250  hz . on the contrary , the two worst performing mass systems reflect frequencies at the two ends of the ligo instrument s sensitivities relevant to this search , , 100  hz and 1100  hz . as with the supernova waveforms , the black - hole simulations provide us with order - of - magnitude estimates of the distance to which our detectors were sensitive to such astrophysical systems during the s2 run . for the lazarus black - hole mergers our @xmath101 amplitudes of a few times @xmath106  correspond to distances of order 1  mpc . all four waveform families we have considered for our simulations , either _ ad hoc _ or astrophysically motivated , have frequency content that ranges over the entire band of our search . within each of these families , signal strengths in order to reach fixed efficiency ( , 50% ) range over approximately an order of magnitude ; this is primarily a manifestation of the different frequency content of each waveform and the fact that the ligo detectors frequency response is not flat ( and varies by an order of magnitude or more over the 1001100  hz band , as shown in fig . [ fig : s2sens ] ) . we are in the process of augmenting the waveform library to be considered in future ligo burst searches . this will give us further opportunities to test the robustness of our methods and the use of @xmath101 as a measure of the signal strength relevant to burst detection in ligo .","summary":"we combine this limit with measurements of the detection efficiency for given waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order - of - magnitude distance sensitivity to certain modeled astrophysical sources . both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad - band search for untriggered and unmodeled gravitational wave bursts to date .","abstract":"we perform a search for gravitational wave bursts using data from the second science run of the ligo detectors , using a method based on a wavelet time - frequency decomposition . this search is sensitive to bursts of duration much less than a second and with frequency content in the 1001100  hz range . it features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by ligo . improvements in the search method allow exploring weaker signals , relative to the detector noise floor , while maintaining a low false alarm rate , hz . the sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude lies in the range of  . no gravitational wave signals were detected in 9.98 days of analyzed data . we interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level . we combine this limit with measurements of the detection efficiency for given waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order - of - magnitude distance sensitivity to certain modeled astrophysical sources . both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad - band search for untriggered and unmodeled gravitational wave bursts to date ."}
{"article_id":"gr-qc0505029","section_id":"i","document":"we have presented a search for gravitational wave bursts using the data the three ligo detectors collected during their second science run . transients with sufficient energy in ligo s most sensitive band during the s2 run , 1001100  hz , were searched for . a search for gravitational wave bursts with frequency content above the 1100  hz range is being pursued in coincidence with the tama  @xcite detector and will be described in a separate publication  @xcite . our analysis yielded a single candidate event which was subsequently determined to be terrestrial in origin and was vetoed retroactively . incorporating this into a frequentist statistical approach , we set an upper limit on the rate of strong gravitational wave bursts of @xmath104 events per day at the 90% confidence level . this rate limit is a factor of 6 below our previously published value  @xcite , due primarily to the longer duration of the s2 run and to better data quality . the efficiency of this search was measured using various waveform morphologies . besides the families of _ ad hoc _ waveforms we introduced in our previous search , we also measured the efficiency of our search to astrophysically motivated waveforms resulting from numerical simulations of the core collapse supernovae and binary black hole mergers . for most of the waveforms considered , the values of @xmath101 at 50% efficiency lie in the @xmath108  range . the sensitivity attained by this search represents an improvement with respect to s1 by a factor of 17 or more for waveforms studied in both searches . this difference is frequency dependent and mainly reflects the instruments noise floor improvement by a factor of @xmath1410 . the rest is attributed to improvements of the search algorithm and the use of the waveform consistency test ( @xmath11-statistic ) , allowing a lower effective threshold on signal amplitude . the interpreted results of this search include the rate versus strength exclusion curves on a per waveform morphology basis . the improvements on the rate and signal strength sensitivity are both reflected in significantly more stringent regions now allowed in these rate versus strength plots .      in our s1 paper , we made a comparison with results from searches with broad - band interferometric detectors described in  @xcite . the upper limit set by these detectors is at the level of 0.94 events per day and with a signal strength sensitivity of @xmath109  , both of which are now surpassed by our s2 search . in our s1 paper we also compared with the results of the igec search for gravitational wave bursts  @xcite . ligo s broad band response allowed us to set better limits on bursts whose power was mainly at frequencies away from the bars resonances . at or near the bars resonant frequencies , however , the igec search benefited from a much longer observing time and somewhat better sensitivity at those frequencies , and thus was able to set rate limits far below what we were able to do in ligo . with improved sensitivity in s2 , it is interesting to again compare ligo s performance at a frequency near the bars resonance . in order to perform this comparison in our published s1 work  @xcite we chose the sine - gaussian simulations at 849  hz frequency and with q=8.9 . although this waveform morphology has significant signal power in the narrow frequency band ( 895930  hz ) of sensitivity for most of the igec detectors , it actually fails to maintain an approximately flat fourier spectrum over the broader range ( 694930  hz ) needed in order to encompass all of them . for this reason , in order to perform the same comparison in s2 we have used the gaussian of @xmath86=0.1  ms signal morphology which was the closest waveform with a flat spectrum in the 694930  hz range that we included in our s2 simulations . the igec analysis  @xcite set an upper limit of @xmath110 events / day at the 95% confidence level on the rate of gravitational wave bursts . the limit was derived assuming optimal source direction and polarization and was also given as a function of the burst fourier amplitude in a rate versus strength exclusion curve similar to ligo s . using ligo s s2 gaussian of @xmath86=0.1  ms simulations , the waveburst etg efficiency for sources with random linear polarizations is 50% at a strength of @xmath111  ( see table  [ tbl : adhoc ] ) . for the same sources all with _ optimal _ polarizations , the 50% efficiency point improves by roughly a factor of 3 , to @xmath112  . thus the optimally oriented rate versus strength curve looks similar to fig . [ fig : gsg_exclude ] , but shifted to the left . substituting the 95% confidence level ( cl ) event limit of @xmath113 for the 90% cl event limit of @xmath104 shifts the curve up . lastly , the igec excluded region from fig .  13 of  @xcite can be translated from bars natural units ( hz@xmath114 ) to units of @xmath101 ( ) . given the fourier transform h(f ) for a gaussian waveform h(t ) , @xmath115 @xmath116 we convert the igec values of spectral amplitude h(f ) into @xmath101 for a gaussian of @xmath86=0.1  ms signal morphology ( the conversion is a function of the assumed frequency of the igec result and may vary by a few percent over the 694930  hz range . ) the resulting comparison can be seen in fig .  [ fig : ligovsigec ] . exclusion curves at the 95% confidence level for optimally oriented gaussians of @xmath86=0.1  ms . the solid curve displays the 95% confidence level measurement obtained by ligo with this search . the igec exclusion region is shown shaded and it is adapted from fig .  13 of  @xcite . if the comparison were performed using q=8.9 , 849  hz sine - gaussians , the ligo and igec curves would move to smaller amplitudes by factors of 1.1 and @xmath143 , respectively . ]    with ligo and s2 we are able to stretch the excluded region substantially to the left ( , to weaker signals ) of the boundary of the excluded region in the rate versus strength curve of fig . 13 in  @xcite . however , although s2 s increased observing time allows a lower rate limit than could be set in s1 , it is still the case that the igec longer duration search allows substantially better rate limits to be set , for signals strong enough for its detectors to have seen them . furthermore , we are interested in a comparison with the results reported from the analysis of the explorer and nautilus 2001 data . in their 2002 paper  @xcite the rome group that analyzes the data of and operates these two resonant mass detectors reported a slight excess of events seen in sidereal hours between 3 and 5 . the events seen in concidence by the two detectors are of an average temperature of approximately 120mk which according to the authors corresponds to an optimally oriented gravitational wave burst fourier amplitude of @xmath117hz@xmath114 ( equation 4 from ref . the rate of such events is of order 200 events / year ( or 0.55 events / day )  @xcite . given the amplitude of the observed events by the resonant mass detectors , the corresponding @xmath101 of the hypothetical events in our ligo instruments will generally depend on the signal morphology . as with our aforementioned igec analysis , we considered the case of a gaussian of @xmath86=0.1  ms , for which the fourier amplitude of the observed events at the detectors average resonance frequency implies an @xmath101 of @xmath118  . keeping in mind that the suggested @xmath101 values refer to optimal orientation , we can see from fig . [ fig : ligovsigec ] that for this event strength the ligo s2 search set an upper bound to their flux at roughly @xmath119 events per day at the 95% cl . it should be noted , though , that depending on the assumptions of signal waveform ( for example a single cycle of a 914  hz sinusoid or a narrow - band sine - gaussian signal centered on the same frequency ) or considering the range of event strengths recorded by explorer and nautilus ( rather than their average value only ) the corresponding @xmath101 at the ligo detectors may come nearer to the threshold of our sensitivity and thus make our rate limits poorer . the signal strength and rate of the 2001 rome results come with enough uncertainties that given the ligo s2 sensitivity and exposure we can not make a definitive comparison . the significant improvements in sensitivity and longer observation times that we expect in new ligo searches in the near future will enable us to move in this direction . the search for gravitational wave bursts in ligo s s2 run has seen significant improvements introduced in the search methodology and interpretation with respect to s1 . this included the introduction of the waveform consistency cut and the use of astrophysically motivated waveforms as part of the search interpretation . additional improvements are currently under way . we expect them to bring stronger suppression of the background via the use of a burst amplitude consistency test between the ligo detectors as well as new ways of performing our event analysis within the context of a distributional analysis of their strength . moreover , we plan to make use of data taking periods corresponding to the double coincidence of the instruments that are not part of the triple coincidence dataset . we will continue investigating the optimization of search algorithms for specific types of waveforms and adding stronger astrophysical context in our search by invoking source population models or targeting plausible point sources . among the lessons learned in the s2 search has been the importance of the follow - up investigations dictated by coincident triggers revealed by the pipeline . as expected , with the detector performance nearing design sensitivity , potential couplings from the environment and the instrument itself will become apparent and will need to be identified and vetoed out . our on - going work for vetoes will become more prominent together with the need to define rigorous criteria and procedures for following up on such events . ligo s subsequent runs have already collected data of comparable duration and improved sensitivity with respect to s2 and they will present the next milestone of the search for bursts where a good number of these improvements will be exercised . the authors gratefully acknowledge the support of the united states national science foundation for the construction and operation of the ligo laboratory and the particle physics and astronomy research council of the united kingdom , the max - planck - society and the state of niedersachsen / germany for support of the construction and operation of the geo600 detector . the authors also gratefully acknowledge the support of the research by these agencies and by the australian research council , the natural sciences and engineering research council of canada , the council of scientific and industrial research of india , the department of science and technology of india , the spanish ministerio de educacion y ciencia , the john simon guggenheim foundation , the leverhulme trust , the david and lucile packard foundation , the research corporation , and the alfred p. sloan foundation .","summary":"we perform a search for gravitational wave bursts using data from the second science run of the ligo detectors , using a method based on a wavelet time - frequency decomposition .","abstract":"we perform a search for gravitational wave bursts using data from the second science run of the ligo detectors , using a method based on a wavelet time - frequency decomposition . this search is sensitive to bursts of duration much less than a second and with frequency content in the 1001100  hz range . it features significant improvements in the instrument sensitivity and in the analysis pipeline with respect to the burst search previously reported by ligo . improvements in the search method allow exploring weaker signals , relative to the detector noise floor , while maintaining a low false alarm rate , hz . the sensitivity in terms of the _ root - sum - square _ ( rss ) strain amplitude lies in the range of  . no gravitational wave signals were detected in 9.98 days of analyzed data . we interpret the search result in terms of a frequentist upper limit on the rate of detectable gravitational wave bursts at the level of 0.26 events per day at 90% confidence level . we combine this limit with measurements of the detection efficiency for given waveform morphologies in order to yield rate versus strength exclusion curves as well as to establish order - of - magnitude distance sensitivity to certain modeled astrophysical sources . both the rate upper limit and its applicability to signal strengths improve our previously reported limits and reflect the most sensitive broad - band search for untriggered and unmodeled gravitational wave bursts to date ."}
{"article_id":"0808.4128","section_id":"i","document":"supersymmetry ( susy )  @xcite is one of the most highly favoured extensions of the standard model ( sm ) , and is often considered to be a prime candidate for discovery at the large hadron collider ( lhc ) . with the start of experiments at the lhc now becoming imminent , it is natural and topical to make the best possible assessment of the likelihood that the lhc will indeed discover susy , based on the best available experimental , phenomenological and cosmological information . most of the current constraints on possible physics beyond the sm are negative , in the sense that they reflect the agreement of data with the sm , and set only lower limits on the possible masses of supersymmetric particles  @xcite . examples are direct constraints such as lower limits on specific sparticles , e.g. , the chargino , and indirect constraints such as the lower limit on the possible mass of a sm - like higgs boson  @xcite .    however , there are two observational constraints that , within the context of susy , may be used also to set upper limits on the possible masses of supersymmetric particles , since they correspond to measurements that can not be explained by the sm alone . these hints for new physics are the anomalous magnetic moment of the muon , @xmath2 , which appears to differ by over three standard deviations from the best sm calculation based on low - energy @xmath3 data  @xcite , and the density of cold dark matter , @xmath4 @xcite , which has no possible origin within the sm . each of these discrepancies has many possible interpretations , of which susy is just one . nevertheless , given the strong motivations for susy , which include the naturalness of the mass hierarchy and grand unification , as well as the existence of a plausible candidate for the astrophysical cold dark matter , it is natural to ask what @xmath2  and @xmath4 may imply for the parameters of supersymmetric models . any such analysis should also take into account the constraints imposed by precision measurements of electroweak observables ( ewpo ) and @xmath5-physics observables ( bpo ) such as br(@xmath6 ) , where most observables agree quite well with the sm .    in this paper we revisit the indirect information on supersymmetric model parameters obtainable in the light of these experimental , phenomenological and cosmological constraints , using a markov - chain monte carlo ( mcmc ) approach , see , e.g. , ref . @xcite and references therein . this is practical only in simplified versions of the minimal supersymmetric extension of the standard model ( mssm ) , in which some universality relations are imposed on the soft susy - breaking parameters . initially , we work in the framework of the constrained mssm ( cmssm ) , in which the scalar and gaugino mass parameters , @xmath7 , @xmath8 , and the trilinear coupling @xmath9 are each assumed to be equal at the input gut scale . furthermore as low - energy parameter we have @xmath10 , the ratio of the two vacuum expectation values of the two higgs doublets . at the end we also comment on the possible changes in our results if the common soft susy - breaking contribution to the higgs scalar masses - squared , @xmath11 , is allowed to differ from those of the squarks and sleptons , the single - parameter non - universal higgs model or nuhm1 . there have been many previous studies of the cmssm parameter space  @xcite , including estimates of the sparticle masses , and a number of these have used mcmc techniques  @xcite . these have been used to extract the preferred values for the cmssm parameters using low - energy precision data , bounds from astrophysical observables and flavour - related observables . these analyses differ in the precision observables that have been considered , the level of sophistication of the theory predictions that have been used , and the way the statistical analysis has been performed .    here we use the mcmc technique to sample efficiently the susy parameter space , and thereby construct the @xmath12 probability function , @xmath13 . this accounts correctly for the number of degrees of freedom , @xmath14 , and thus represents a quantitative measure for the quality - of - fit . hence @xmath13 can be used to estimate the absolute probability with which the cmssm describes the experimental data . our probabilistic treatment is explained in detail in sec . [ sec : mpfit ] . many previous analyses found evidence for a relatively low susy mass scale in the stau - coannihilation region , e.g. ,  @xcite , and a mild preference for @xmath15 was found in  @xcite . a comparison of bayesian analyses yielding varying results under different assumptions was made in  @xcite . some differences between analyses may also be traceable to the treatments of the br(@xmath6 )  and @xmath2  measurements , which we discuss in some detail below . our main objectives in this paper are threefold . one is to discuss explicitly the prospects for discovering sparticles in early lhc running , another is to discuss the robustness of the fit results by analyzing the implications of relaxing the constraints due to @xmath2 , br(@xmath6 ) , @xmath4 and other observables , and the third is to discuss the extension of the cmssm results to the nuhm1 , in which an extra parameter is introduced that allows a common degree of non - universality for the two higgs multiplets . we find that the 95%  c.l . area in the @xmath16 plane of the cmssm lies largely within the region that could be explored with 1  fb@xmath1 of integrated lhc luminosity at 14  tev in a single experiment , and that much of the 68%  c.l.area lies within the region that could be explored with 50  pb@xmath1 of integrated luminosity at 10  tev ( the projected initial lhc collision energy ) . a same - sign dilepton signal could well be visible in the 68%  c.l . area with 1  fb@xmath1 of integrated luminosity at 14  tev , and the lightest higgs boson might also be detectable in squark decays with 2  fb@xmath1 of integrated luminosity at 14  tev . we find that removing the @xmath4 constraint has little effect on the preferred regions of the cmssm parameter space in the @xmath0 , @xmath17 , and @xmath18 planes , apart from expanding the range of @xmath7 , particularly for @xmath19 . on the other hand , rescaling the present error in @xmath2  may have quite an important effect : the preferred ranges in @xmath8 and @xmath7 would expand quite significantly if the error on the present experimental discrepancy with the sm were to be increased . conversely , if this error could be reduced , e.g. , by a more precise measurement of @xmath2  and/or a more refined theoretical estimate within the sm , the predictions for sparticle masses could be significantly improved . we also discuss the effects of possible variations in the errors in br(@xmath6 )  and other observables . finally , we show that our results would not be greatly changed in the nuhm1 : we leave a more complete study of the nuhm1 and the nuhm2 ( in which the masses of the two higgs multiplets are independently non - universal ) for future work .","summary":"the 95% confidence - level area in the plane of the cmssm lies largely within the region that could be explored with 1  fb of integrated luminosity at 14  tev , and much of the 68% confidence - level area lies within the region that could be explored with 50  pb of integrated luminosity at 10  tev . a same - sign dilepton signal could well be visible in most of the 68% confidence - level area with 1  fb of integrated luminosity at 14  tev . we discuss the sensitivities of the preferred ranges to variations in the most relevant indirect experimental and cosmological constraints and also to deviations from the universality of the supersymmetry - breaking contributions to the masses of the higgs bosons .   ","abstract":"in view of the imminent start of the lhc experimental programme , we use the available indirect experimental and cosmological information to estimate the likely range of parameters of the constrained minimal supersymmetric extension of the standard model ( cmssm ) , using a markov - chain monte carlo ( mcmc ) technique to sample the parameter space . the 95% confidence - level area in the plane of the cmssm lies largely within the region that could be explored with 1  fb of integrated luminosity at 14  tev , and much of the 68% confidence - level area lies within the region that could be explored with 50  pb of integrated luminosity at 10  tev . a same - sign dilepton signal could well be visible in most of the 68% confidence - level area with 1  fb of integrated luminosity at 14  tev . we discuss the sensitivities of the preferred ranges to variations in the most relevant indirect experimental and cosmological constraints and also to deviations from the universality of the supersymmetry - breaking contributions to the masses of the higgs bosons .    cern - ph - th/2008 - 181 , dcpt/08/118 , ftpi - minn-08/33 , ippp/08/59 , umn - th-2715/08"}
{"article_id":"0808.4128","section_id":"r","document":"in fig .  [ fig : contours ] we display the best - fit value and the 68% and 95% likelihood contours for the cmssm @xmath0 plane , obtained as described in sect . [ sec : mpfit ] from a fit taking into account all experimental constraints listed in tab .  [ tab : constraints ] as well as the constraints from the additional electroweak observables listed in  @xcite . we also show in the upper panel of fig . [ fig : contours ] various lhc sparticle discovery contours for 1  fb@xmath1 of good - quality data in a single experiment at a centre - of - mass energy of 14  tev . the atlas and cms collaborations have each published 5-@xmath59 discovery contours in the cmssm @xmath16 plane for @xmath60 and @xmath61  @xcite . their contours are generally very similar , and the solid brown contour displayed is that published by cms for the most sensitive jets + missing @xmath62 search . this contour is insensitive to @xmath9 , which affects primarily the third - generation sparticle masses , since the main discovery channels involve gluinos and first - generation squarks . the discovery contours are also not very sensitive to @xmath63 , since the gluino mass is insensitive to this variable , and the first - generation squark masses are also not very sensitive to @xmath63 . therefore , it is a reasonable first approximation to compare our 68% and 95% likelihood contours directly with the discovery contours given for @xmath60 and @xmath64 fixed , particularly since the best fit has a similar value of @xmath63 . ( 300,400 ) ( 0 , 220 ) ( 250 , 205)@xmath7 [ gev ] ( -5 , 360 )    90@xmath8 [ gev ]    ( 0 , 0 ) ( 250 , -15)@xmath7 [ gev ] ( -5 , 140 )    90@xmath8 [ gev ]    the parameters of the best - fit cmssm point are @xmath65  gev , @xmath66  gev , @xmath67  gev , @xmath68 and @xmath69  gev  , yielding the overall @xmath70 ( 37.3% probability ) and @xmath71  gev   and the inclusion of more observables , that are generally highly consistent with the cmssm . ] . the overall value of the @xmath12 at the minimum is somewhat pushed up by the value of @xmath48 , which is uncomfortably low . however , it is acceptable within the higher - order calculational uncertainties expected in the feynhiggs code that we use here , @xmath72  3  gev  @xcite . as we discuss below , this slight tension is removed in the nuhm1 model , which correspondingly has a somewhat lower overall @xmath12 ( yielding a similar fit probability for the two models ) . the spectrum at the best - fit cmssm point is shown in the left panel of fig . [ fig : spectra ] . it is interesting to note that the best - fit cmssm point and the corresponding spectrum are quite similar to the well - known sps1a benchmark point  @xcite , whose phenomenology at future colliders has been studied in considerable detail ( see , e.g. , @xcite ) . ( 450,210 ) ( 5 , 10 ) ( 10 , 185 )    90@xmath73 [ gev ]    ( 140 , 200)cmssm ( 235 , 10 ) ( 240 , 185 )    90@xmath73 [ gev ]    ( 370 , 200)nuhm1    comparing the 95% likelihood contour provided by the multi - parameter fit with the 1  fb@xmath1 lhc discovery contour , we see that the former is almost entirely contained within the latter , implying that , if the cmssm were correct , the lhc would be almost ` guaranteed ' , with 95% confidence , to discover susy with 1  fb@xmath1 of good - quality data at 14  tev . we also display in the upper panel of fig . [ fig : contours ] contours representing the 5  @xmath59 discovery reach with 1  fb@xmath1 at 14  tev for 4-jet events with and without a charged lepton , for same - sign dileptons  @xcite , denoted by ss , and ( with 2  fb@xmath1 ) for the lightest mssm higgs boson produced in cascade decays of sparticles  @xcite , denoted by @xmath74 . we see that the same - sign dilepton discovery region largely covers the 68% likelihood region of the cmssm @xmath0 plane . thus , this signature could serve as a clean signal capable of confirming the supersymmetric interpretation of any jets + missing @xmath62 signal observed in initial lhc running . on the other hand , the region where the lightest higgs boson could be discovered in cascade decays of squarks with 2  fb@xmath1 at 14  tev lies largely between the 95% and 68% c.l . contours . we have used prospino2  @xcite to estimate the variation of the discovery reach of the lhc jets + missing @xmath62 search as a function of the integrated luminosity and the centre - of - mass energy . we display in the lower panel of fig . [ fig : contours ] ( green ) dot - dashed and ( red ) dashed contours representing , respectively , the discovery reaches expected with 100  pb@xmath1 at 14  tev and 50  pb@xmath1 at 10  tev . we see that the 68% likelihood contour is well covered by the 14  tev/100  pb@xmath1 discovery reach , and even the 10  tev/50  pb@xmath1 reach would be sufficient to discover susy at the best - fit point , indicated by a filled circle in fig . [ fig : contours ] . the lower panel of fig . [ fig : contours ] also displays the regions of the cmssm @xmath0 plane that are excluded by chargino searches at lep and by sparticle searches at the tevatron  @xcite . the region excluded by the lep higgs search is sensitive to @xmath63 and @xmath9 , is subject to theoretical uncertainties , and , moreover , the experimental higgs likelihood function is not a simple step function . hence , it is not shown in fig .  [ fig : contours ]  , @xmath61 and @xmath60 the evaluation with feynhiggs yields a nominal value of @xmath75  gev for @xmath76307  gev . ] . the above analysis assumed the default implementations of the experimental , phenomenological and cosmological constraints discussed in the previous section . we now discuss the possible effects of relaxing ( or strengthening ) some of the key constraints , starting with the relic cold dark matter density , @xmath4 . it is well - known that this constraint essentially reduces the dimensionality of the mssm parameter space by one unit , fixing one combination of the parameters with an accuracy of a few  % . for example , in the cmssm for any pair of fixed values of @xmath9 and @xmath63 , the @xmath4 constraint largely determines @xmath7 as a function of @xmath8 , except for a discrete ambiguity associated with the coannihilation strip , the focus - point strip and the rapid - annihilation funnel that appears at large @xmath63 . therefore , one might expect that dropping the @xmath4 constraint would have a strong effect on the preferred region of the cmssm @xmath16 plane shown in fig . [ fig : contours ] . there are various possible reasons why one might consider dropping the dark matter constraint . perhaps the neutralino is not the lsp ? perhaps @xmath77-parity is not quite conserved ? perhaps the early thermal history of the universe differed from that usually assumed when calculating the relic lsp density ? perhaps nature is described by some generalization of the cmssm such as a model with non - universal susy - breaking contributions to the higgs scalar masses ( nuhm ) , in which case values of @xmath7 very different from those in the cmssm might be permitted ? we show in fig . [ fig : wmap ] the effect of dropping the @xmath4 constraint . this is significant in the upper panels , which display the @xmath0 and @xmath18 planes , but is not so important in the @xmath78 and @xmath79  planes shown in the two lower panels of fig . [ fig : wmap ] . these behaviours can be understood by recalling the behaviour of the wmap coannihilation strips in the cmssm @xmath16 planes for different values of @xmath63 . for example , the value of @xmath7 favoured by @xmath4 for any given values of @xmath8 and @xmath9 increases as the value of @xmath63 increases , foliating the @xmath0 plane . thus , for any given value of @xmath8 and @xmath9 , a large range of values of @xmath7 can be attained for a suitable choice of @xmath63 , even if one does impose the @xmath4 constraint . concerning the range of @xmath8 , this is bounded above by @xmath2 , and , for any given value of @xmath63 , the allowed range actually decreases for the larger values of @xmath7 allowed if the @xmath4 constraint is dropped . thus , dropping the @xmath4 constraint has little overall effect on the ranges of @xmath8 , @xmath7 and @xmath9 . the primary effect is to enforce a correlation between @xmath63 and @xmath7 , as seen in the upper right panel of fig . [ fig : wmap ] . the range of @xmath7 decreases at any fixed value of @xmath63 when the @xmath4 constraint is imposed , because of the narrowness of the wmap strip for any fixed value of @xmath63 . ( 440,412 ) ( -10 , 220 ) ( 220 , 220 ) ( -10 , 0 ) ( 220 , 0 ) ( 10 , 360 )    90@xmath8 [ gev ]    ( 170 , 220)@xmath7 [ gev ] ( 240 , 360 )    90@xmath7 [ gev ]    ( 415 , 220)@xmath10 ( 10 , 148 )    90@xmath8 [ gev ]    ( 185 , 0)@xmath10 ( 240 , 140 )    90@xmath8 [ gev ]    ( 400 , 0)@xmath9 [ gev ]    thus , we find that the fit results obtained in the parameter planes of @xmath7 , @xmath8 , @xmath9 and @xmath10 displayed in fig .  [ fig : contours ] are rather robust with respect to imposing / dropping the @xmath4 constraint . on the other hand , as already noted , the @xmath4 constraint does reduce the dimensionality of the parameter space by essentially one unit . this can also be seen from the fact that without imposing the @xmath4 constraint the preferred parameter region obtained from the fit to the ewpo and bpo still yields a wide range of possible values of @xmath80 . specifically we find that the 68% c.l . region of the @xmath0 plane shown in fig . [ fig : contours ] yields @xmath81 , while considerably larger values of @xmath80 are allowed at the 95% c.l . eventually , susy particle mass measurements at the lhc ( see the discussion of fig .  [ fig : dileptons ] below ) may enable this estimate of @xmath80 to be refined considerably ( see , e.g. , @xcite ) . drilling down into the dependences of our results on uncertainties in the experimental and phenomenological constraints , we display in fig . [ fig : drill ] the results of studies of their sensitivities to some key observables . the observables tracked are @xmath2 , br(@xmath6 ) , @xmath80 , br(@xmath82 )  and @xmath83 . the left panel shows the percentage variation in the preferred region of the @xmath0 plane as the assumed errors in these quantities are rescaled , assuming that the future experimental central values agree with the current ones . the right panel shows the same for the area in the @xmath84 plane . larger errors could arise if we have underestimated the relevant systematic errors , and smaller errors could result from future improvements of the experimental errors and/or the theoretical predictions . as could be expected from the discussion in the previous paragraph , the preferred areas vary very little with the error in @xmath4 , and the areas are also relatively insensitive to that in br(@xmath82 ) . however , there are greater sensitivities to br(@xmath6 ) , @xmath83  and ( particularly ) @xmath2 . ( 450,155 ) ( 5 , 0 ) ( 235 , 0 ) ( 10,43 )    90relative change in area [ % ]    ( 77,0)relative change in uncertainty ( 120,138)@xmath85 ( 240,43 )    90relative change in area [ % ]    ( 307,0)relative change in uncertainty ( 350,138)@xmath86    the theoretical error in @xmath83  is much smaller than the current experimental error . it is encouraging that reducing the experimental error , as should be possible with future tevatron and lhc data , could have substantial effects on the preferred areas in the parameter planes . a reduction in the error by a factor two could reduce the areas by factors of about five , if the present central value ( which disagrees with the sm by about one @xmath59 ) is maintained . the same would be true for a reduction in the error in br(@xmath6 ) , but here reducing the theoretical error would also be necessary . this would require , in particular , a better understanding of the uncertainties in higher - order and non - perturbative qcd corrections . indeed , a very conservative approach to the combination of the current theoretical and experimental errors in br(@xmath6 )  might even motivate a larger error and hence larger preferred areas than in our default analysis . [ fig : drill ] also shows that varying the error in @xmath2  is potentially more important , particularly if the present error is underestimated . this might be the case if , e.g. , the weight of experimental evidence would shift towards using @xmath87 decay data to estimate the sm hadronic contribution to @xmath2 , or if the error in the light - by - light contribution were to be revised drastically   anomaly by changing the sm prediction of the hadronic contribution to @xmath88 is unlikely in view of a combined analysis of all electroweak data . ] . the rapid increases in the areas of the preferred regions reflect the fact that a more relaxed treatment of the @xmath2  error led in the past to ( parts ) of the focus - point strip at large @xmath7 being included within the preferred region , which does not occur in our default analysis .    in order to explore the sensitivity to the @xmath2  error in more detail , we show in the left panel of fig . [ fig : g-2 ] the effect in the cmssm @xmath89 plane of varying this error , while assuming the same central value . going from the outer to the inner contours we have assumed @xmath90 with @xmath91 , see tab . [ tab : constraints ] . the partially fuzzy shapes would be smoothed by higher statistics . we see that the preferred region expands rapidly if the @xmath2  error is increased . going to an increase by a factor of  1.5 ( not shown in the plot ) would open up the focus - point region , which is disfavoured in our analysis . conversely , decreasing this error , as would be possible with an accessible improvement of the previous bnl @xmath2  experiment  @xcite , would enable the preferred ranges of the cmssm mass parameters to be decreased impressively . ultimately , this together with the other ewpo and bpo could make possible a sensitive test of susy at the loop level , if the lhc does indeed discover sparticles and measure their masses . ( 450,186 ) ( 0 , 0 ) ( 225 , 0 ) ( 20,138 )    90@xmath8 [ gev ]    ( 175,5)@xmath7 [ gev ] ( 245,138 )    90@xmath8 [ gev ]    ( 400,5)@xmath7 [ gev ]    in the right panel of fig . [ fig : g-2 ] , we make a similar analysis of the sensitivity to the br(@xmath6 )  error . going from the outer to the inner contours we have again assumed @xmath90 with @xmath92 , see tab . [ tab : constraints ] . we see from the right panel of fig . [ fig : g-2 ] that treating the errors differently could have a significant effect . employing a larger error ( as done in  @xcite , for instance ) , would not only expand the allowed regions , but also allow larger @xmath10 values , as br(@xmath6 )   is particularly sensitive to @xmath10 . though in the present analysis we have focused on the @xmath93 solution , as favoured by the @xmath2  anomaly , we comment briefly here on the structure of the @xmath94 parameter space . in order to minimize the discrepancy with the @xmath2  constraint , for @xmath94 one would need a relatively heavy spectrum in order to suppress the susy effects with the wrong sign . this would be particularly true for increasing values of @xmath10 , since @xmath2  grows almost linearly with @xmath10 . br(@xmath6 )  is also highly sensitive to the sign of the @xmath21 parameter . in particular , within the cmssm the solution with @xmath94 unambiguously implies that all the dominant susy effects to br(@xmath6 )  have the same sign and interfere constructively with the sm amplitude . this implies more severe constrains with respect to the @xmath93 case , and again points toward a heavy spectrum . this is not the case for @xmath93 , where partial cancellations among susy effects in br(@xmath6)allow relatively light squarks . we have also considered possible improvements in the determination of the cmssm parameters that might be obtainable from early lhc measurements . missing @xmath62 measurements with or without single leptons are unlikely to constrain the model with high precision . on the other hand , in the parameter region preferred by the fit ( with @xmath95 ) there are good prospects for measuring the opposite - sign dilepton edge in @xmath96 ( @xmath97 ) decays with high precision , which is located at @xmath98 such a measurement would constrain a combination of sparticle masses and hence the cmssm parameter space in an interesting way . as an appetizer for what might be possible , we show in fig . [ fig : dileptons ] the possible impact of a measurement of the dilepton edge for the cmssm best - fit point described in the previous paragraph , which has @xmath99  gev , @xmath100  gev , @xmath101  gev , yielding an edge at @xmath102  gev . we assume experimental and theoretical errors of 3  gev each . we see in fig . [ fig : dileptons ] that the dilepton edge measurement would reduce the parameter space preferred at the 68% c.l . to two narrow strips in the @xmath0 plane , linked into a tilted ` vee ' shape at the 95% c.l . the best - fit point in the right wing of the ` vee ' has quite different parameter values from the overall best - fit point in the left wing of the ` vee ' : @xmath103  gev , @xmath104  gev , @xmath105  gev , @xmath106 , yielding @xmath107 and @xmath108  gev , @xmath109  gev , @xmath110  gev .    ( 325,186 ) ( 0 , 0 ) ( -5,149 )    90@xmath8 [ gev ]    ( 261,-13)@xmath7 [ gev ]      the above analysis of the cmssm is relatively encouraging for the early days of the lhc , but one might wonder to what extent the conclusions can be extended to more general incarnations of the mssm . the full parameter space of the mssm has so many dimensions that exploring it with the mcmc approach used here would require prohibitive amounts of cpu time . accordingly , we discuss briefly here only the simplest possible generalization of the cmssm , in which the soft supersymmetry - breaking scalar contributions to the higgs masses are allowed to differ by the same amount from those of the squarks and sleptons at the gut scale , the so - called non - universal higgs model 1 ( nuhm1 )  @xcite . overall , it is encouraging that the general sizes of the 68% and 95% c.l . regions are similar to those in the cmssm , as shown in fig . [ fig : nuhm1 ] , though the 68% c.l . region together with the best - fit point are shifted to lower @xmath8 , and the 95% c.l . region is more elongated in @xmath8 . as in the case of the cmssm , susy could be discovered over all of the 68% c.l . region with 100  pb@xmath1 of integrated luminosity at 14  tev in a single experiment , and even 50  pb@xmath1 of integrated luminosity at 10  tev would cover most of it . as in the cmssm , not all of the nuhm1 95% c.l . region would be covered by the lhc with 1  fb@xmath1 of integrated luminosity at 14  tev , whereas the same - sign dilepton search would cover all the 68% c.l . region in the nuhm1 . there are differences between the shapes of the preferred regions in the cmssm and the nuhm1 , particularly at low @xmath8 . this reflects the fact that the @xmath4 constraint can be obeyed away from the coannihilation strip at larger values of @xmath7 , if @xmath111 . this freedom can then be exploited to relax the slight tension induced by @xmath48 which arises in the cmssm . ( 300,400 ) ( 0 , 220 ) ( 250 , 205)@xmath7 [ gev ] ( -5 , 360 )    90@xmath8 [ gev ]    ( 0 , 0 ) ( 250 , -15)@xmath7 [ gev ] ( -5 , 140 )    90@xmath8 [ gev ]    the spectrum at the best - fit nuhm1 point is shown in the right panel of fig . [ fig : spectra ] . this point has @xmath112  gev , @xmath113  gev , @xmath114  gev , @xmath115 , @xmath116  gev@xmath117 and @xmath118  gev , yielding @xmath119 ( 39% probability ) and @xmath120  gev . the best - fit values of @xmath8 and @xmath63 are somewhat lower than those in the cmssm , whereas the value of @xmath7 is somewhat higher . the overall value of @xmath12 is also somewhat lower than in the cmssm , reflecting the relaxation of the slight tension in the value of @xmath48 that is possible when the higgs masses are allowed to become non - universal . comparing with the best - fit cmssm spectrum , we see that the masses of the sleptons and squarks are quite similar , as are the masses of the lighter neutralinos and chargino . however , the splitting between the stop mass eigenstates is larger  reflecting the larger value of @xmath121 , the heavier neutralinos and chargino are much heavier  reflecting the larger value of @xmath21 , the best - fit value of @xmath48 lies comfortably above the lep lower limit , and the heavier higgs bosons are lighter than in the cmssm  reflecting the extra freedom conferred by the non - universality in the nuhm1 . the lower values of the heavier higgs masses compensate other susy contributions to br(@xmath6 ) , and offer better prospects for detection at the lhc than those offered by the cmssm .","summary":"in view of the imminent start of the lhc experimental programme , we use the available indirect experimental and cosmological information to estimate the likely range of parameters of the constrained minimal supersymmetric extension of the standard model ( cmssm ) , using a markov - chain monte carlo ( mcmc ) technique to sample the parameter space .","abstract":"in view of the imminent start of the lhc experimental programme , we use the available indirect experimental and cosmological information to estimate the likely range of parameters of the constrained minimal supersymmetric extension of the standard model ( cmssm ) , using a markov - chain monte carlo ( mcmc ) technique to sample the parameter space . the 95% confidence - level area in the plane of the cmssm lies largely within the region that could be explored with 1  fb of integrated luminosity at 14  tev , and much of the 68% confidence - level area lies within the region that could be explored with 50  pb of integrated luminosity at 10  tev . a same - sign dilepton signal could well be visible in most of the 68% confidence - level area with 1  fb of integrated luminosity at 14  tev . we discuss the sensitivities of the preferred ranges to variations in the most relevant indirect experimental and cosmological constraints and also to deviations from the universality of the supersymmetry - breaking contributions to the masses of the higgs bosons .    cern - ph - th/2008 - 181 , dcpt/08/118 , ftpi - minn-08/33 , ippp/08/59 , umn - th-2715/08"}
{"article_id":"astro-ph9708101","section_id":"i","document":"the bright 5.75  ms pulsar j04374715 was discovered by johnston et al . ( 1993 ) during the parkes survey for millisecond pulsars . the pulsar is in a 5.74  d binary orbit with a cool ( @xmath13  k ) , low - mass ( @xmath14 ) white dwarf companion and is surrounded by a bow - shock nebula ( becker et al . 1993 ; bailyn 1993 ; bell , bailes & bessel 1993 ; danziger , baade & della valle 1993 ; bell et al . it is an old object , with a characteristic age @xmath15  yr , low magnetic field @xmath16  g , and rotational energy loss @xmath17  erg  s@xmath12 . the observed dispersion measure of 2.65  pc  @xmath18 implies a distance @xmath19  pc , making this the closest known millisecond pulsar . sandhu et al . ( 1997 ) reported the distance @xmath20  pc , from parallax measurements . the pulsar shows significant radio emission over at least 80% of the pulse period , with a complicated mean pulse shape varying with radio frequency . variation of the linear polarization position angle within the mean pulse interpreted in terms of the rotating vector model ( radhakrishnan & cooke 1969 ) yields the angle between the observer s line of sight and the rotation axis , @xmath21 , and the angle between the magnetic and rotation axes , @xmath22 ( manchester & johnston 1995 ) . @xmath0 observations of   with the position sensitive proportional counter ( pspc ) have revealed ( becker & trmper 1993 ; hereafter bt93 ) that this is also a bright ( count rate @xmath23  s@xmath12 ) soft x - ray pulsar with a single broad pulse and a pulsed fraction @xmath24 in the pspc energy range @xmath25  kev . bt93 found that the pulsed fraction varies with photon energy @xmath26 and peaks in the range @xmath27  kev , reaching @xmath28 . although the pulsar spectrum can be fitted with a single power law , indicative of a non - thermal origin of the soft x - ray radiation , the energy dependence of the pulsed fraction in the narrow energy range makes this interpretation hardly plausible . bt93 showed also that a single blackbody model does not fit the pspc spectrum leaving a residual hard excess above 0.4  kev . they suggested that the spectrum can consist of two components : a power law , representing magnetospheric or nebular emission , and a blackbody component of the temperature @xmath29  k emitted from an area of @xmath30 ( @xmath31 ) ; this thermal component was suggested by bt93 to be radiated from a hot spot on the neutron star ( ns ) surface . was also detected with the @xmath1 deep survey instrument ( dsi ) in the lexan band filter ( @xmath32  kev ) by edelstein , foster & bowyer ( 1995 ) and halpern , martin & marshall ( 1996 ; hereafter hmm96 ) . according to edelstein et al . ( 1995 ) , the dsi count rate of the source is @xmath33  s@xmath12 , whereas hmm96 report the count rate of @xmath34  s@xmath12 obtained with a much longer exposure ( 496  ks vs.  72  ks ) . edelstein et al .  ( 1995 ) ruled out the single power - law spectral model based on the improbably high hydrogen column density , @xmath35  @xmath9 , required by this model . they claimed that both the @xmath0 flux below 0.4  kev and the @xmath1 flux could arise from an isothermal blackbody with a temperature @xmath36  k , an emitting area of @xmath37  km@xmath38 , and an absorbing column of @xmath39  @xmath9 . on the other hand , hmm96 concluded that the combined analysis of the @xmath0 spectrum and @xmath1 flux is consistent with a single power - law spectrum of photon index @xmath40 and intervening column density @xmath41  @xmath9 . alternatively , the combined data can be interpreted as comprised of two components , e.  g. , a power law and a blackbody component emitted from a hot polar cap of radius 50600  m and temperature @xmath42  k. hmm96 observed the pulsar in the high time resolution mode , which enabled them to obtain the light curve and to measure the pulsed fraction @xmath43 in the @xmath1 dsi spectral range . thus , although very important data have been collected and analyzed , the true nature of the soft x - ray radiation from   remains elusive . the only firmly established facts are that the radiation is pulsed ( pulsed fraction apparently depends on energy ) , and the spectrum can not be fitted with a single blackbody model . the main question is whether the radiation is of a nonthermal ( magnetospheric ? nebular ? ) origin or at least a fraction of it can be interpreted as thermal ( or thermal - like ) radiation from some heated regions ( polar caps ? ) on the ns surface . virtually all the ( different ) models of radio pulsars ( e.  g. , cheng & ruderman 1980 ; arons 1981 ; michel 1991 ; beskin , gurevich & istomin 1993 ) predict these objects to have _ polar caps _ ( pcs ) around the ns magnetic poles heated up to x - ray temperatures by relativistic particles and gamma - quanta impinging onto the pole regions from the acceleration zones . a conventional assumption about the pc radius is that it is close to the radius within which open magnetic field lines originate from the ns surface . for , it gives @xmath44 km . expected pc temperatures , @xmath45  k , and luminosities , @xmath46  erg  s@xmath12 , are much less certain , being strongly dependent on the specific pulsar model . thus , one can not firmly predict pc properties because of the lack of a well - established pulsar model  rather a theoretical model should be chosen based on x - ray observations of radio pulsars . x - ray observations of other old pulsars ( e.  g. , psr b1929 + 10  yancopoulos , hamilton & helfand 1994 ; psr b0950 + 08  manning & willmore 1994 ) do show pulsed x - ray radiation which , in principle , could be the thermal pc radiation . however , the number of photons collected has been too small to make firm conclusions , and the opposite hypothesis , that this radiation is of a magnetospheric origin ( gelman 1995 ; becker & trmper 1997  hereafter bt97 ) , can not be excluded . in principle , one could also observe the pc radiation from younger pulsars and use these data to discriminate between different pc models . indeed , there are some indications that hard components of the soft x - ray spectra of , e.  g. , psr b0656 + 14 and psr b105552 ( greiveldinger et al . 1996 ) may consist of two subcomponents , a power law and a thermal subcomponent corresponding to emission from pcs of temperatures @xmath47  k ( for psr b0656 + 14 ) and @xmath48  k ( for psr b105552 ) . this interpretation , however , is not unique because it is difficult to separate the hard component from the soft one which is believed to originate from the ( cooler ) entire ns surface , and even more difficult to separate the two subcomponents of the hard spectral tail .    one can not also exclude _ a priori _ that the nonthermal radiation from the pulsar magnetosphere or a pulsar - powered compact nebula contributes to , or even dominates , the observed soft x - ray flux of . it is natural to assume that the spectrum of this radiation can be approximated by a power law in the relatively short @xmath1-@xmath0 range . one could also expect the magnetospheric ( but not nebular ) radiation to be pulsed with the radio pulsar period ; the pulses should be , as a rule , narrower than those of the thermal pc radiation , and the shape of the light curve should not vary considerably with photon energy . thus , if more data confirm the conclusion of bt93 that the pulsed fraction depends on @xmath26 , the radiation of   should either be thermal or consist of the thermal and nonthermal components . in the latter case , since the sources of the thermal and nonthermal radiation are expected to be spatially separated , it is natural to expect that pulsations of these two components should be phase - shifted due to the difference of travel times and aberration . for instance , if the nonthermal component is generated at a distance comparable to the light cylinder radius ( @xmath49 cm ) , the time delay leads to a phase shift of about 0.2 of the pulsar period . no energy - dependent phase shifts have been reported for this source , although it can be explained by the poor photon statistics in hard pspc channels . as in the case of thermal pc radiation , the current theoretical models of nonthermal high - energy pulsar emission ( e.  g. , sturner , dermer & michel 1995 ; romani 1996 ) are not enough elaborated to predict the intensity , spectrum and light curve for a given pulsar . there exist empirical formulae ( seward & wang 1988 ; gelman 1995 ; bt97 ) which relate the ( presumably nonthermal ) x - ray luminosity to the pulsar parameters , e.  g. , to the period and magnetic field . for instance , gelman ( 1995 ) pointed out that the observed soft x - ray luminosities satisfy , for 7 pulsars , the following equation : @xmath50  erg  s@xmath51 . bt97 fitted the luminosities of 26 pulsars observed in the @xmath0 range with the dependence @xmath52 . these pulsars represent a very wide range of spin - down luminosities ( @xmath53  erg  s@xmath12 ) , ages ( @xmath54  yr ) , magnetic field strength ( @xmath55  g ) and spin periods ( @xmath56  ms ) . the inferred dependence indicates that for most pulsars the bulk of observed radiation is directly connected with pulsar mechanisms , i.  e. , with production and acceleration of relativistic particles which carry away the ns rotational energy . the fact that x - rays from some of these pulsars ( e.  g. , crab ) are certainly nonthermal may allow one to assume that the radiation detected with the @xmath0 from most pulsars is of a nonthermal origin . on the other hand , a correlation between @xmath57 and @xmath58 should take place also for radiation emitted by the pulsar pcs because their ( thermal ) luminosity is also provided by relativistic particles generated in the magnetosphere and accelerated towards the ns surface , so that the pc luminosity should be a fraction of @xmath58 which goes to heating of the pcs . moreover , both theoretical ( see section 5.1 ) and observational estimates of the pc luminosities may happen to be very close to the values predicted by the @xmath59 dependence obtained by bt97 . for instance , the luminosity of the thermal component in the power - law plus blackbody fit for , @xmath60  erg  s@xmath12 ( bt93 ) , is close to the predicted value , @xmath61  erg  s@xmath12 . another example is psr b1929 + 10 whose luminosity @xmath62  erg  s@xmath12 inferred from the blackbody fit of both @xmath0 and @xmath63 data ( yancopoulos et al . 1994 ; wang & halpern 1997 ) perfectly matches the dependence derived by bt97 . in general case , we may expect that the pulsar x - ray radiation contains both thermal ( pc ) and nonthermal components , both growing with @xmath58 , and the relation between the thermal and nonthermal fluxes may be different for different objects , depending , in addition to @xmath58 , on other intrinsic pulsar parameters ( e.  g. , pulsar period @xmath64 , magnetic inclination @xmath65 ) , as well as on the rotational inclination @xmath66 ( because the radiation beam widths are different for the thermal and nonthermal components ) . thus , one can not rule out that the pc component dominates in some cases , and we explore this possibility for . an important evidence on the nature of radiation of   could come from deep observations of its high - energy tail , at energies above @xmath67  kev . although this object has been detected by @xmath63 ( two 20  ks observations ) below 3  kev , the results are still not very conclusive because of poor choice of observing modes which did not take into account the presence of a neighboring seyfert galaxy . nevertheless , preliminary results show that a spectrum of @xmath68 pulsar photons extracted from the ccd away from the seyfert galaxy is softer than a power law and resembles more a thermal - like spectrum ( kawai , tamura & saito 1996 ) . this conclusion , however , needs verification based on longer pointed observations in a mode minimizing contamination from the seyfert . the conclusion of bt93 and hmm96 that the pspc spectrum of   can not be fitted with a single thermal component is based on the assumption that its spectrum coincides with the spectrum of the blackbody radiation . however , spectra emitted by real bodies , including stars , are always different from the planck spectrum . in particular , if the temperature of a stellar atmosphere grows inward , and the absorption coefficient decreases with frequency ( e.  g. , @xmath69 for the kramers law ) , then the spectrum is harder than the blackbody spectrum at high frequencies because we see deeper and hotter layers . this means that if a ns is covered with a fully ionized plasma , whose opacity can be described by the kramers law , its spectrum is substantially harder at high energies , @xmath70 ( e.  g. , pavlov & shibanov 1978 ) . this general property has been demonstrated in models of hydrogen and helium atmospheres of cooling nss by romani ( 1987 ) , pavlov et al . ( 1995 ) , rajagopal & romani  ( 1996 ) , zavlin , pavlov & shibanov ( 1996 ; hereafter zps96 ) . one can expect that a ns has a purely hydrogen atmosphere if it experienced accretion of the interstellar matter  heavy elements of the accreted matter sink down rapidly due to the strong ns gravitation ( alcock & illarionov 1980 ) . since   is a very old object , it is quite plausible that it accreted some matter during its long life , and in this case we may expect that the excess of the observed flux at @xmath71  kev is due to the fact that , including its pcs , is covered by a fully ionized hydrogen atmosphere . the pc radiation should be inevitably pulsed unless the rotation axis coincides with either the line of sight or the magnetic axis . if it were the blackbody radiation , the shape of the light curves and the pulsed fraction @xmath72 would remain the same at all photon energies @xmath26 . however , the atmosphere radiation has a very important feature  it is anisotropic , with anisotropy ( and consequently light curves ) depending on energy ( pavlov et al .  1994 ; shibanov et al .  1995 ; zps96 ) . this dependence is different for different chemical compositions and surface temperatures . e.  g. , for atmospheres with relatively high temperatures @xmath73  k consisting of light elements ( hydrogen , helium ) , the anisotropy increases with increasing @xmath26 in the soft x - ray range . this also makes the spectra dependent on the rotation phase . the inter - dependence of the spectral and angular distributions means that the proper interpretation of the observed pc radiation implies fitting of _ both the spectra and the light curves with the same pc model_.    the above - described properties of radiation emitted by a pc covered with an atmosphere warrant a new investigation of the soft x - ray radiation observed from , based on the ns atmosphere models . to perform this investigation , we used the @xmath0 and @xmath1 data analyzed previously by bt93 and hmm96 and combined with the results of new observations carried out with the @xmath0 high - resolution imager ( hri ) and @xmath0 pspc ( becker et al . these observations are briefly described in section  2 . we show that with allowance for the properties of ns atmosphere radiation these joint @xmath0 and @xmath1 data can be interpreted as thermal radiation of two pcs , _ without invoking an additional nonthermal component_. in section  3 we explore a simplest single - temperature pc model which assumes that both pcs have equal radii @xmath74 and uniform temperatures @xmath75 , whereas the rest part of the ns surface has a much lower temperature and is invisible in x - rays . since the magnetic field of   is very low , it can not affect the radiative properties of the pc atmospheres . therefore , we use the low - field atmosphere models developed by zps96 . to calculate the flux as measured by a distant observer , we integrate the specific flux over the visible pc surface with allowance for the gravitational redshift and bending of the photon trajectories . for the case of small pcs ( @xmath76 ) with uniform temperatures , a convenient expression for the observable flux is given by zavlin , pavlov & shibanov ( 1995 ; see their eq . [ a15 ] ) ) . we show that this simple model is generally consistent with the observational data if the pcs are covered with hydrogen or helium , whereas the iron atmosphere model does not fit the spectra ( cf . pavlov et al . for the hydrogen and helium models , we estimate @xmath74 , @xmath75 and the interstellar hydrogen column density , @xmath77 . the fit with the simplest pc model is still not perfect . this is not surprising because it is hard to expect the real pcs to be uniformly heated . on the contrary , due to higher heat conduction of subphotospheric layers , where the energy of accreting relativistic particles is released , the heat can propagate along the surface , eventually heating surface layers out of the `` primary '' hot spot . this should result in a larger hot region with the temperature decreasing outward . in fact , this mechanism should be more efficient just for low - field pulsars because the strong magnetic fields of ordinary pulsars greatly reduce the transverse conductivity ( e.  g. , hernquist 1985 ) . to the best of our knowledge , there have been no reliable calculations of the temperature distribution around the pulsar magnetic poles . thus , to include this effect into consideration , we explore in section  4 a simple model : the distribution is assumed to be a two - step function ( `` core+rim '' ) with two temperatures , @xmath78 and @xmath79 , and two radii , @xmath80 and @xmath81 . we show that this model is fairly consistent , for hydrogen - covered pcs , with all the data available . we discuss the results and implications of our interpretation in section  5 and draw conclusions in section  6 .","summary":"the polar cap interpretation implies low column densities ,  , and a high degree of ionization ,% , of the interstellar hydrogen towards the pulsar .","abstract":"we show that the soft x - ray spectra and light curves observed with the and from the closest known millisecond pulsar j04374715 can be interpreted as thermal radiation from two hot polar caps whose emitting layers ( atmospheres ) are comprised of hydrogen . the simplest model yields a uniform temperature of  k within a cap radius of  km . the spectral fits indicate that the temperature may be nonuniformly distributed along the cap surface . the distribution can be approximated by a central core heated up to  k within a radius of  km , surrounded by a colder rim with temperatures  k extending out to  km . the polar cap interpretation implies low column densities ,  , and a high degree of ionization ,% , of the interstellar hydrogen towards the pulsar . the inferred bolometric luminosity of the polar caps ,  erg  s , is in excellent agreement with the predictions of the slot - gap model of radio pulsars developed by arons and his coworkers . similar polar cap radiation should be emitted by other millisecond pulsars , although in some of them ( e.  g. , psr b182124 ) the soft x - ray flux is dominated by the nonthermal radiation from pulsar magnetospheres ."}
{"article_id":"astro-ph9708101","section_id":"c","document":"it is interesting to compare the inferred pc properties with those predicted by different radio pulsar models . the _ slot - gap model _ ( arons & scharlemann 1979 ; arons 1981 ) predicts the following energy flux of relativistic particles incident on the stellar surface ( arons 1981 ) @xmath216 where @xmath217 is the magnetic moment in units of @xmath218  g  @xmath219 , @xmath220 is the the ratio of the dipole radius of curvature to the actual radius of curvature , @xmath221 for the parameters of . the model is applicable for @xmath222  ms ; this corresponds to @xmath223 for @xmath224  ms , and we adopt an intermediate value @xmath225 for estimates . if most of this energy is reradiated , the effective temperature and luminosity are @xmath226 @xmath227 where @xmath228 is the ratio of the polar cap area to its canonical value , @xmath229  km@xmath38 ( @xmath230 for the original slot - gap model which implies that the particle acceleration zone is associated with `` favorably curved '' open field lines ) . we see that the predicted temperature is @xmath231 lower than the temperature @xmath75 inferred from the single - temperature pc model , but it is higher than @xmath79 . the predicted luminosity is in excellent agreement , for @xmath225 and @xmath232 , with the observed value . since the observed luminosity is almost independent of the pc temperature distribution ( @xmath233  erg  s@xmath12 for both the single - temperature and two - temperature pc models ) , it is the most suitable parameter to compare with , and we should conclude that the slot - gap model agrees very well with the suggested interpretation of the soft x - ray radiation from .    according to the _ outer - gap model _ ( e.  g. , cheng , ho & ruderman 1986 ) ,   is near the pulsar `` death line '' , @xmath234  ms , that implies high efficiency of the gamma - ray radiation produced by primary e@xmath235 accelerated in vacuum gaps in the outer magnetosphere of the pulsar . the total ( maximum ) flux of relativistic e@xmath236 ( or e@xmath237 ) impinging on the pc from the starward end of the acceleration zone can be estimated as ~=1.410 ^ 31 ( ) ( ) ^2  s^-1  , and the luminosity is @xmath238 , where @xmath239 is the lorentz factor of particles when they reach the ns surface . while traveling to the surface , the particles loose a fraction of their initial energy @xmath240 via curvature radiation , so that ( cf .  halpern & ruderman 1993 ; hmm96 ) @xmath241^{-1/3 } = \\\\   \\left[\\frac{1}{\\gamma_i^3 } + \\left(\\frac{1}{3.65\\times 10 ^ 6}\\right)^3\\left(\\frac{5.65~{\\rm ms}}{p}\\right ) \\ln \\left(\\frac{r_{\\rm min}}{\\rns}\\right ) \\right]^{-1/3}~ ,   \\nonumber\\end{aligned}\\ ] ] where @xmath242 is the minimum distance of the accelerator from the ns center . adopting @xmath243  km , the first term in the square brackets can be neglected if @xmath244 ( the latter value is much lower than @xmath245 limited by the curvature radiation losses ) . in this case , @xmath246 , and the expected pc luminosity , @xmath247  erg  s@xmath12 , exceeds the observed value by a factor of 4060 . the model pc luminosity would agree with the observed one only if we assume @xmath248 . thus , we should conclude that either the @xmath249 energies at the starward accelerator end are much lower than those expected from the curvature radiation losses , or there exists a mechanism reducing the particle flux @xmath250 which may reach the ns surface . in particular , the estimate ( 5 ) assumes the relativistic particles impinge onto the canonical pc area @xmath251 if the actual area is @xmath252 times smaller ( a `` primary '' cap radius is @xmath253  m , compatible with our @xmath80 ) , then , at the same ( goldreich  julian ) current density , the estimated luminosity coincides with that observed . an evidence of the reduced efficiency of the particle accelerator is provided by the upper limit on the luminosity of gamma - rays above 100  mev , @xmath254 ( fierro et al . since the same particle accelerator is responsible for pc heating , hmm96 suggest that an upper limit for the luminosity of one pc can be evaluated as 0.04 times the above - estimated maximum value , @xmath255  erg  s@xmath12 , very comfortable with the observed range of @xmath256  erg  s@xmath12 .    in the _ model of beskin , gurevich and istomin _ ( 1993 ) , the energy of relativistic particles impinging onto the pcs per unit time is _ surf  , where @xmath257 and @xmath258 is a multiplication coefficient , the number of particles which are knocked out from the ns surface by an impacting relativistic particle . the temperature of the polar cap is estimated as t_eff= ( ) ^1/20  k  . this temperature is consistent with the observed values , @xmath259 , only for large multiplication coefficient , @xmath260 , much greater than the maximum values , @xmath261 and @xmath262 calculated by bogovalov & kotov ( 1989 ) for @xmath263 and @xmath264 , plausible lorentz factors for . moreover , the same calculations show that @xmath258 sharply decreases with decreasing @xmath265 from @xmath266  g and becomes @xmath267 at @xmath268  g. thus , we have to conclude that either this model strongly overestimates the pc temperature and luminosity , or the multiplication coefficient is much greater than calculated .      the fits of the spectra and of the light curves presented in this paper were obtained for fixed values of the angles @xmath158 and @xmath116 inferred by manchester & johnston ( 1995 ) from the phase dependence of the position angle of the radio polarization . since these angles were determined approximately , and it is not trivial to estimate their uncertainties from the radio data , we can not exclude that their true values may be different . we also adopted canonical values for the ns mass and radius , @xmath117 and @xmath118  km , whereas the true mass and radius may differ from these values . we have demonstrated ( see fig . 7 ) that the shape of the light curves is very sensitive to the values of @xmath66 , @xmath65 and @xmath269 . this opens a new opportunity to constrain these quantities using them as free parameters for the light curve fitting . this analysis is presented elsewhere ( pavlov et al . 1997 ) . here we only mention that for _ any _ allowed values of @xmath65 and @xmath66 , the mass - to - radius ratio is constrained as @xmath270 , whereas for @xmath116 , @xmath158 we obtained @xmath271 . the latter inequality means that if the ns mass equals @xmath272 , its radius is @xmath273  km . we have shown that interpretation of the soft x - ray data in terms of thermal - like radiation from pcs yields systematically lower values for the intervening hydrogen column density than the power - law fits of the spectrum . for instance , bt93 found @xmath274  @xmath9 for the one - component power - law fit , whereas we obtained @xmath275  @xmath276 and @xmath277  @xmath9 for the single- and two - temperature pc models , respectively . it is useful to compare these values with those inferred from observations of other objects close towards  ( @xmath278 , @xmath279 ; @xmath114  pc ) . the pulsar is in the southern third galactic quadrant ( @xmath280 , @xmath281 ) , apparently within the famous low hi column region that extends out to @xmath282  pc at @xmath283 ( at least for @xmath284  see , e.  g. , paresce 1984 ; welsh 1991 ) . for instance , two stars of close longitudes and distances , @xmath285  cma ( @xmath286 , @xmath287 , @xmath288  pc ) and @xmath289  cma ( @xmath290 , @xmath291 , @xmath292  pc ) , show the neutral hydrogen densities as low as @xmath293 and 18.218.4 , respectively ( fruscione et al . 1994 ; welsh 1991 ) . the densities in directions of two other stars within the low density region , re 0503289 ( @xmath294 , @xmath295 , @xmath296  pc ) and re 0457281 ( @xmath297 , @xmath298 , @xmath296  pc ) , with latitudes closer to that of the pulsar ( farther from the galactic plane ) , albeit with twice smaller distances , are even lower : @xmath299 and 17.117.9 . a white dwarf wd 0320540 ( @xmath300 , @xmath301 , @xmath302  pc ) , which is likely near the boundary of the low - density region , shows @xmath303 . based on these values and observations of other ( scarce ) stars in this region of the sky ( fruscione et al . 1994 , welsh 1991 ; and references therein ) , we expect that plausible neutral hydrogen column for   should not exceed @xmath304  @xmath9 . interstellar absorption of x - rays enters the spectral fits through the attenuation function , @xmath305 , where @xmath306 is the effective cross section per hydrogen atom calculated under the assumption that the interstellar hydrogen is not ionized ( e.  g. , morrison & mccammon 1983 ) . the effective hydrogen column density @xmath77 coincides , naturally , with @xmath307 for the nonionized ism , but for the partially ionized hydrogen we have @xmath308 , where @xmath309 is the total ( neutral plus ionized ) hydrogen column density . with the electron column density @xmath310  @xmath9 , known from the pulsar dispersion measure , we can restrict the mean ionization degree of hydrogen , @xmath311 , as @xmath312 . if we adopt @xmath313  @xmath9 as a plausible estimate , the ionization degree @xmath314 is noticeably greater , and the ( total ) mean number density in the direction towards , @xmath315 @xmath18 , is lower than the estimates , @xmath316 and @xmath317  @xmath18 , obtained from the power - law fit . the inferred high ionization is in line with @xmath318 found by gry , york & vidal - madjar ( 1985 ) in the direction to @xmath289 cma . it is worth noting that the mean number density inferred from our pc model fits is fairly close to the ism density of the ambient medium around the pulsar estimated by equating the ram pressure of the interstellar medium to the pulsar wind pressure at the apex of the pulsar wind s bow shock ( see , e.  g. , hmm96 ) : @xmath319  @xmath18 , where the distance from the pulsar to the apex of the bow shock , @xmath320  cm , and the velocity of the pulsar , @xmath321  km s@xmath12 , are evaluated for @xmath114  pc . the fact that all available x - ray and euv data are consistent with our interpretation still does not prove that this interpretation is unique  it often happens that the same data can be equally well fitted with quite different models . therefore , it is important to verify that the hypothesis does not contradict to observations of similar objects . according to bt97 , soft x - ray radiation has been observed from seven millisecond pulsars . at least one of them , psr b182124 ( @xmath322  ms , @xmath323  erg  s@xmath12 ) , shows a strong evidence that its radiation is of a nonthermal ( magnetospheric ) origin  its spectrum , observed with @xmath63 up to 10  kev , can be fitted with a power law , and its x - ray pulses are sharp ( saito et al . thus , if we assume that pcs is a phenomenon common for all millisecond pulsars , we must explain why this phenomenon is not observed for psr b182124 . this can be done with the use of the aforementioned pulsar models . if the correct estimate obtained for the pc luminosity from the slot - gap model is not a chance coincidence , we may expect that the luminosity is scaled as @xmath324 , and the bolometric luminosity from two pcs of psr b182124 can be estimated as @xmath325  erg  s@xmath12 . this estimate is much lower than the luminosity @xmath326  erg s@xmath12 inferred by saito et al . if we adopt the outer - gap model and assume that the accelerator efficiency is reduced by the same factor for all pulsars , then the luminosity is scaled as @xmath327 , which yields @xmath328  erg  s@xmath12 for psr b182124 , even less than for the slot - gap model . moreover , even the maximum possible pc luminosity predicted by the outer - gap model remains lower than observed . thus , it is not surprising that the pc radiation is not seen from this pulsar , being overwhelmed by a nonthermal soft x - ray radiation . saito et al .  ( 1997 ) speculate that the high luminosity of the nonthermal radiation may be associated with large values of the magnetic field at the light cylinder , @xmath329  g , close to that of the crab pulsar and much higher than @xmath330  g for . the nature of x - ray radiation from other five millisecond pulsars is much less certain because of small numbers of counts detected . their luminosities in the @xmath0 range , inferred under the assumption of a power - law spectrum with the photon index @xmath331 , obey the same dependence , @xmath332 , as ordinary pulsars ( bt97 ) , and they are greater than the pc luminosities predicted for these objects by the slot - gap model ( scaled to ) . however , the ratios of the observed to predicted luminosities , ranging from @xmath333 for psr j1012 + 5307 to @xmath334 for psr j0751 + 1907 , are smaller than @xmath335 for psr b182124 . since the power - law model always yields a higher luminosity than the pc model ( because of higher @xmath77 needed to suppress the intrinsically high low - energy flux ) , one may expect that the luminosities inferred from the pc interpretation would be compatible with those predicted by equation ( 3 ) . in addition , as arons ( 1981 ) emphasizes , equation ( 3 ) gives a _ minimum _ expected luminosity  although the luminosity of   coincides with that minimum , pc luminosities of other pulsars may be greater . thus , the soft x - ray radiation of at least some other millisecond pulsars can be partly supplied by their pcs , although a nonthermal component may also be present and may even dominate . to resolve the dilemma , and to separate the two components , further observations are needed . at present , we can only say that both possibilities should be explored , and complementary interpretations are still viable for some pulsars .","summary":"the inferred bolometric luminosity of the polar caps ,  erg  s , is in excellent agreement with the predictions of the slot - gap model of radio pulsars developed by arons and his coworkers .","abstract":"we show that the soft x - ray spectra and light curves observed with the and from the closest known millisecond pulsar j04374715 can be interpreted as thermal radiation from two hot polar caps whose emitting layers ( atmospheres ) are comprised of hydrogen . the simplest model yields a uniform temperature of  k within a cap radius of  km . the spectral fits indicate that the temperature may be nonuniformly distributed along the cap surface . the distribution can be approximated by a central core heated up to  k within a radius of  km , surrounded by a colder rim with temperatures  k extending out to  km . the polar cap interpretation implies low column densities ,  , and a high degree of ionization ,% , of the interstellar hydrogen towards the pulsar . the inferred bolometric luminosity of the polar caps ,  erg  s , is in excellent agreement with the predictions of the slot - gap model of radio pulsars developed by arons and his coworkers . similar polar cap radiation should be emitted by other millisecond pulsars , although in some of them ( e.  g. , psr b182124 ) the soft x - ray flux is dominated by the nonthermal radiation from pulsar magnetospheres ."}
{"article_id":"astro-ph9708101","section_id":"i","document":"we have shown that both the spectra and the light curves of the soft x - ray radiation of   observed with the @xmath0 pspc and hri and @xmath1 dsi can be interpreted as _ thermal radiation from two hydrogen - covered polar caps_. the simplest , single - temperature pc model allows us to estimate typical pc radius , @xmath336  km , and temperature , @xmath337  k. the successful fitting of the data with the two - temperature model indicates that the pc temperature may be non - uniform , decreasing from @xmath338  k at a pc core with a typical size @xmath339  m down to @xmath340  k at a much greater radius @xmath341  km , so that the heated area may comprise a considerable fraction of the ns surface . the bolometric luminosity of the two pcs is @xmath342  erg  s@xmath12 , that is @xmath343 of the total energy loss of the pulsar is absorbed and re - emitted by the pcs . we emphasize that the proposed interpretation is based essentially upon the _ neutron star atmosphere models _  the data can not be interpreted as purely thermal pc radiation with the simplistic blackbody model . moreover , with the aid of the ns atmosphere models we show that the emitting layers should be depleted of heavy elements , which can be naturally explained by the plausible assumption that the old ns has experienced accretion of the hydrogen - rich matter during its long life - time . the successful fits of the @xmath1 and @xmath0 light curves in different energy ranges with the pc models are possible only if the energy - dependent limb - darkening of the hydrogen atmospheres is taken into account . the shape of the light curves is also very sensitive to the bending of photon trajectories in the strong gravitational field of the ns and to the orientations of the rotational and magnetic axes of the pulsar . we obtained the satisfactory fits assuming @xmath344 and @xmath345  km , with the magnetic inclination angle , @xmath116 , and viewing angle , @xmath158 , inferred from radio observations . we have demonstrated that the effect of the gravitational bending on the light curves can provide important information on the ns mass - to - radius ratio . the hydrogen column density towards the , @xmath346  @xmath9 , as well as strong ionization of hydrogen , @xmath347 , estimated from the pc model fits are consistent with the ism properties obtained from observations of other objects in the vicinity of the pulsar , whereas the power - law fit yields greater @xmath77 and lower @xmath348 . this can be considered as one more argument in favor of thermal origin of the x - ray radiation of .    the inferred pc temperature , radius and , especially , luminosity are in excellent agreement with the predictions of the slot - gap pulsar model ( arons 1981 ) . the upper limit on the pc luminosity provided by the outer - gap pulsar model ( cheng et al . 1986 ) exceeds the observed value . this model becomes compatible with our results if a reduced efficiency of the particle accelerator , consistent with the upper limit on the gamma - ray flux from the pulsar , is assumed . radio pulsar models predict that heated pcs is a common phenomenon inherent to all active pulsars . by virtue of this , the dependence @xmath349 found by bt97 for 26 pulsars detected with the @xmath0 determines a fraction of the rotational energy loss re - emitted in x - rays _ by both nonthermal and thermal processes_. contributions of these two mechanisms to the total x - ray flux depend on various factors , such as pulsar period , radius , magnetic field , etc . in some pulsars ( e.  g. , psr b182124 ) the thermal - like soft x - ray radiation from pcs may happen to be less intensive than the nonthermal radiation generated in the pulsar magnetosphere . for instance , both the slot - gap and outer - gap models predict the luminosity of pcs of psr b182124 much lower than the luminosity observed with the @xmath0 and @xmath63 . although all the available observations of   are consistent with the suggested pc interpretation , and this interpretation is supported by the theoretical pulsar models and by indirect arguments , we still can not completely exclude that the same data , collected in the relatively narrow energy range , could be interpreted with another model  for instance , as a combination of the pc radiation and magnetospheric radiation . hence , the proposed interpretation can be considered as complementary to the nonthermal interpretation discussed by bt97 . a crucial test would be provided by observations of this object at energies @xmath350  kev , which would enable one to firmly discriminate between the power - law and thermal - like spectra , or to separate their contributions . such observations could be carried out by @xmath63 ( with a sufficiently long exposure ) and by the forthcoming @xmath351 , @xmath352 and @xmath353-@xmath26 missions . important data could be also obtained from observations of the pulsar in the uv range ( @xmath354   ) with the @xmath355 . in particular , such observations would enable one to measure the temperature of the entire ns surface ( cf . pavlov , stringfellow & crdova 1996a ) and to elucidate other possible heating mechanisms competing with the pc heating .    for more accurate and reliable interpretation of the future observations , more theoretical work is highly desirable . in particular , the temperature distribution over the ns surface within and around the pcs should be investigated ( and further used to fit the data ) , and the nonthermal x - ray spectrum and beam shape should be calculated . we are grateful to werner becker and jules halpern for providing us with the @xmath0 pspc / hri and @xmath1 dsi observational data prior to publication . we are greatly indebted to joachim trmper and werner becker for their collaboration and fruitful , stimulating discussions . v.  e.  zavlin acknowledges the max - planck fellowship . g.  g.  pavlov is thankful to the max - planck - institut fr extraterrestrische physik for the warm hospitality . this work was partially supported through the intas grant 94 - 3834 , dfg - rbrf grant 96 - 02 - 00177 g and nasa grant nag5 - 2807 .","summary":"we show that the soft x - ray spectra and light curves observed with the and from the closest known millisecond pulsar j04374715 can be interpreted as thermal radiation from two hot polar caps whose emitting layers ( atmospheres ) are comprised of hydrogen . the simplest model yields a uniform temperature of  k within a cap radius of  km . the spectral fits indicate that the temperature may be nonuniformly distributed along the cap surface . the distribution can be approximated by a central core heated up to  k within a radius of  km , surrounded by a colder rim with temperatures  k extending out to  km . similar polar cap radiation should be emitted by other millisecond pulsars , although in some of them ( e.  g. , psr b182124 ) the soft x - ray flux is dominated by the nonthermal radiation from pulsar magnetospheres .","abstract":"we show that the soft x - ray spectra and light curves observed with the and from the closest known millisecond pulsar j04374715 can be interpreted as thermal radiation from two hot polar caps whose emitting layers ( atmospheres ) are comprised of hydrogen . the simplest model yields a uniform temperature of  k within a cap radius of  km . the spectral fits indicate that the temperature may be nonuniformly distributed along the cap surface . the distribution can be approximated by a central core heated up to  k within a radius of  km , surrounded by a colder rim with temperatures  k extending out to  km . the polar cap interpretation implies low column densities ,  , and a high degree of ionization ,% , of the interstellar hydrogen towards the pulsar . the inferred bolometric luminosity of the polar caps ,  erg  s , is in excellent agreement with the predictions of the slot - gap model of radio pulsars developed by arons and his coworkers . similar polar cap radiation should be emitted by other millisecond pulsars , although in some of them ( e.  g. , psr b182124 ) the soft x - ray flux is dominated by the nonthermal radiation from pulsar magnetospheres ."}
{"article_id":"astro-ph9807244","section_id":"c","document":"in this paper we have presented an observational study of the b[e ] star hd 87643 . the observations include high dispersion spectroscopy , medium dispersion spectropolarimetry around h@xmath1  and imaging . the main conclusions drawn from them are as follows :    1 .   from the spectroscopic observations we have found that at least three different line forming regions contribute to the spectrum ; a fast outflow giving rise to extremely high velocity components up to 1800 km s@xmath0  in h@xmath1  and neutral helium , a slower outflow visible in the relatively low velocity central reversal absorption in the hydrogen lines and in broad ( fwhm @xmath13 100  150 km s@xmath0 ) feii lines , while a third , narrow , component ( fwhm @xmath13 40 km s@xmath0 ) is revealed by narrow forbidden lines , neutral fei lines and some weaker feii lines . 2 .    a disk - like structure surrounding the star is revealed by the medium resolution spectropolarimetry . the startling linear polarization changes across the h@xmath1  emission line immediately imply that there is scattering within the ionized line - forming region and that this volume is certainly not spherical . a comparison with published model calculations shows that a rotating , expanding disk qualitatively reproduces the observed polarization , and illustrates the need for more realistic model calculations . broad - band imaging of the large reflection nebula around hd 87643 , suggests that the geometry of the circumstellar material at large scales are comparable to those on the small scales traced in the polarimetry ; the intrinsic polarization angle aligns well with the two most conspicuous nebular components . interstellar extinction and kinematic evidence favours a distance to the object of order of several kiloparsecs . this implies that it is unlikely that hd 87643 is a young main sequence object . nevertheless , these data are not conclusive in deciding whether hd 87643 is a luminous b - type supergiant or a lower luminosity type b[e ] star such as those discussed by gummersbach et al . indeed a feature peculiar to hd  87643 is that the maximum outflow velocities seen in absorption in the h@xmath1 line ( @xmath13 1800 km s@xmath0 ) are significantly higher than those seen in other b[e ] stars luminous enough to be classified as supergiants . since this absorption can only arise in the stellar wind and so may be sensitive to the stellar photospheric escape velocity , a more compact star with a luminosity significantly below that of a supergiant is a possibility .    these results on hd  87643 fit into the general conceptual framework due to zickgraf et al . ( 1985,1986 ) in which b[e ] stars are described as the source of two winds  a fast wind in the polar direction and a slower equatorial disk - like wind . here we have proposed a model that provides a possible physical basis for zickgraf et al.s two - wind concept . our model consists of a star encircled by an _ optically - thick _ disk wherein radiation pressure is sufficient to power mass loss from both the star and disk . hydrodynamical calculations yield a fast wind emerging from the star s polar regions and a much slower wind flowing away from the disk . a feature of the calculations not anticipated in earlier qualitative b[e ] star models is that the combination of the irradiated disk and its outflow modify the stellar wind at intermediate latitudes , rendering it denser and slower than over the stellar pole . the new picture these calculations present offers considerable promise of explaining our observations of hd 87643 . an important next step will be to synthesise spectral line profiles from the model in order to make a direct quantitative comparison with observations . anna gatti is thanked for her help in obtaining the mssso spectra . we thank the staff at the mount stromlo and siding spring observatories ( mssso ) and the anglo - australian telescope for their expert advice and support . the allocation of time on the anglo - australian telescope was awarded by patt , the united kingdom allocation panel . computations were performed at the pittsburgh supercomputing center . rdo and dp are funded by the particle physics and astronomy research council of the united kingdom . ddw is supported in part by spanish grant dgicyt pb94 - 0165 . this research has made use of the simbad database , operated at cds , strasbourg , france . barbier r. , swings j.p . 1981 , iau symp . 98 `` be stars '' , eds . m. jaschek and h .- groth , p. 103 bjorkman j.e . , cassinelli j.p . 1993 , apj 409 , 429 carlson e.d . , henize k.g . 1979 , _ vistas in astronomy _ 23 , 213 carr j.s . 1989 , apj 345 , 522 castor j.i . , abbott d.c . , klein r.i . 1975 , apj 195 , 157 cohen r.s . , grabelsky d.a . , may j. , bronfman l. , alvarez h. , thaddeus p. 1985 , apj 290 , l15 de freitas pacheco j.a . , gilra d.p . , pottasch s.r . 1982 , a&a 108 , 111 de freitas pacheco j.a . , faria lopes d. , landaberry s.c . , selvelli p.l . 1985 , a&a 152 , 101 drew j.e . 1985 , mnras 218 , 41p drew j.e . , busfield g. , hoare m.g . , murdoch k.a . , nixon c.a . , oudmaijer r.d . 1997 , mnras 286 , 538 drew j.e . , proga d. , stone j.m . 1998 , mnras 296 , l6 gnedin iu . n. , kiselev n.n . , pogodin m.a . , rozenbush a.e . , rozenbush v.k . 1992 , azhl 18 , 454 grabelsky d.a . , cohen r.s . , bronfman l. , thaddeus p. 1987 , apj 315 , 122 gummersbach c.a . , zickgraf f .- j . , wolf b. 1995 , a&a 302 , 409 harries t.j . 1996 , a&a 315 , 499 harries t.j . , howarth i.d . 1996 , a&a 310 , 553 herbig g.h . , 1994 , in _ the nature and evolutionary status of herbig ae / be stars _ the , m.r . prez , e.p.j . van den heuvel , asp conf.sers . hiltner w.a . , stephenson c.b . , sanduleak n. 1968 , astrop . letters 2 , 153 hubeny i. 1990 , apj 351 , 632 ignace r. , cassinelli j.p . , bjorkman j.e . 1996 , apj 459 , 671 jenniskens p. , dsert , f .- x . 1994 , a&as 106 , 39 kenyon s.j . , hartmann l. 1987 , apj 323 , 714 lamers h.j.g.l.m . , pauldrach a.w.a . 1991 , a&a 244 , l5 lopes d.f . , daminelli neto a. , de freitas pacheco j.a . 1992 , a&a 261 , 482 magalhaes a.m. 1992 , apj 398 , 286 matthewson d.s . , ford v.i . , klare g. , neckel t. , krautter j. 1978 , _ bull . , 14 , 115 mcgregor p.j . , hyland a.r . , hillier d.j . 1988 , apj 324 , 1071 miroshnichenko a.s . 1998 , in `` workshop on b[e ] stars '' , eds . a.m. hubert , c. jaschek , in press munari u. , zwitter t. 1997 , a&a 318 , 269 oudmaijer r.d . , busfield g. , drew j.e . 1997 , mnras 291 , 797 owocki s.p . , gayley k.g . , cranmer s. r. 1998 , in _ properties of hot luminous stars _ , ed . i. d. howarth , asp conf.ser . 131 , p. 237 proga d. , stone j.m . , drew j.e . 1998 , mnras 295 , 595 schulte - ladbeck r.e . 1998 , in `` workshop on b[e ] stars '' , eds . a.m. hubert , c. jaschek , in press schulte - ladbeck r.e . , clayton g.c . , hillier d.j . , harries t.j . , howarth i.a . 1994 , apj 429 , 846 stephenson c.b . 1974 , apj 191 , 685 straiys v. , kuriliene g. 1981 , ap&ss 80 , 353 surdej j. , swings j.p . 1983 , a&a 117 , 359 surdej a. , surdej j. , swings j.p . , wamsteker w. 1981 , a&a 93 , 285 swings j.p . 1974 , a&a 34 , l33 tody , d. 1993 , in astronomical data analysis software and systems ii , a.s.p . conference ser . , vol 52 , eds . hanisch , r.j.v . brissenden , j. barnes , p. 173 torres c.a.o . , quast g. , de la reza r. , gregorio - hetem j. , lepine j.r.d . 1995 , aj 109 , 2146 wood k. , brown j.c . , fox g.k . 1993 , a&a 271 , 492 yudin r.v . , evans a. 1998 , a&as in the press zickgraf f .- j . 1998 , in `` workshop on b[e ] stars '' , eds . a.m. hubert , c. jaschek , in press zickgraf f .- j . , wolf b. , stahl o. , leitherer c. , klare g. 1985 , a&a 143 , 421 zickgraf f .- j . , wolf b. , stahl o. , leitherer c. , appenzeller i. 1986 , a&a 163 , 119 zickgraf f .- j . , wolf b. , stahl o. , humphreys r.m . 1989 , a&a 220 , 206 zickgraf f .- j . , humphreys r.m . , lamers h.j.g.l.m . , smolinski j. , wolf b. , stahl o. 1996 , a&a 315 , 510","summary":"new high resolution spectroscopic and medium resolution spectropolarimetric data , complemented with optical broad and narrow band imaging , of the b[e ] star hd 87643 are presented . the resulting configuration consists of a fast polar wind from the star and a slowly expanding disk wind . the model also predicts that the stellar wind at intermediate latitudes is slower and denser than in the polar region .    #","abstract":"new high resolution spectroscopic and medium resolution spectropolarimetric data , complemented with optical broad and narrow band imaging , of the b[e ] star hd 87643 are presented . the spectrum of hd 87643 exhibits the hybrid characteristics well known to be representative of the group of b[e ] stars ; a fast wind with an expansion velocity in excess of 1000 km s  is measured in the hydrogen and helium lines , while a slower component is traced by lower excitation lines and forbidden lines . clues to the geometry of the rapidly expanding circumstellar shell are provided by the startling polarization changes across h . comparison with published schematic calculations indicates that the polarizing material is located in a slowly rotating , expanding disk structure . a hydrodynamical model is then presented whose results are consistent with the original two - wind concept for b[e ] stars and exhibits kinematic properties that may well explain the observed spectral features in hd 87643 . the model calculations use as input a b star undergoing mass loss , surrounded by an optically thick disk . the resulting configuration consists of a fast polar wind from the star and a slowly expanding disk wind . the model also predicts that the stellar wind at intermediate latitudes is slower and denser than in the polar region .    # 1#2    # 1#2#1roman#2    = = = 1=1=0pt = 2=2=0pt    biblabel[1 ]    stars : circumstellar matter  stars : individual : hd 87643  stars : emission line , be  polarization  hydrodynamics"}
{"article_id":"cond-mat0510254","section_id":"i","document":"quantum dot is a small disordered or irregularly shaped conductor , connected to leads  @xcite , see fig . exact values of the conductance of a quantum dot are determined by electron wave functions in the system and are hard to calculate exactly for arbitrary configurations of the dot . moreover , the conductance changes significantly even for tiny changes in the position of impurities or the boundary of the dot . due to extreme sensitivity of the conductance on many parameters , the statistical description of the conductance is more appropriate  @xcite . the random fluctuations of the conductance from sample to sample of non - interacting systems are universal . the universality  @xcite means that the conductance statistics can be described by universal functions , which are independent from the shape of the dot or the details of the disordered potential . particularly , the variance of the conductance @xmath0 is of the order @xmath1 and is nearly independent from the sample geometry ( @xmath2 is the quantum of conductance for spin degenerate electrons ) . the other universal quantity is the weak localization correction to the conductance , defined as the difference of average values of the conductance over orthogonal ( zero magnetic field ) and unitary ( strong magnetic field ) ensembles . the weak localization correction to the conductance is also of the order of @xmath3  @xcite . a common description of electron transport through quantum dots is based on the landauer formalism  @xcite , when the transport characteristics of the system are described in terms of the scattering amplitudes between different conducting channels in the leads . there are several approaches for statistical description of electron transport . one approach is based on a diagram technique developed for disordered bulk metals  @xcite , when the scattering amplitudes are represented in terms of electron green functions  @xcite . alternative approaches are based on the description of the system by random matrices , when either an exact scattering matrix is replaced by a random unitary matrix , or an exact hamiltonian is replaced by a random hermitian matrix . in the first case , the unitary matrix is taken from dyson s circular ensemble of uniformly distributed random matrices  @xcite . in the hamiltonian approach , the hermitian matrix belongs to an ensemble of random matrices  @xcite with the gaussian distribution of its matrix elements  @xcite . the equivalence for statistical description of electron transport by both random matrix approaches was shown in  @xcite . although the random matrix approach is not based on microscopic description of electron system , their correspondence to microscopic problem has been proven for disordered metal grains  @xcite . the validity of such random matrix description of chaotic ballistic systems was addressed in  @xcite . we imply the following realization of the system , see fig .  1 a ) . negative voltages applied to the gates ( black areas ) confine electrons to a small region ( light gray ) , forming a quantum dot . electrons in the dot are connected to the electron reservoirs by narrow leads . electric current that flows through the dot can be measured as a function of the voltage bias @xmath4 between the reservoirs and the amplitudes of ac gate voltages @xmath5 . particularly , the current linear in bias @xmath4 is determined by the conductance of the dot . changing magnetic field or shape of the dot one can obtain different realizations of the quantum dot and experimentally study statistics of the quantum corrections to the conductance . the quantum corrections to the conductance are commonly characterized by the weak localization and the variance of conductance fluctuations . as any other quantum interference phenomena , they are very sensitive to inelastic processes , commonly referred to as dephasing  @xcite . a phenomenological description of the effect of dephasing on electron transport through open quantum dots was developed in refs . the dephasing rate due to electron  electron interaction in quantum dots was estimated in @xcite . another possible source of dephasing is a time - dependent perturbation , such as a microwave radiation or periodic deformation . in this case the hamiltonian of the system can be considered as a time - dependent random matrix  @xcite , and all transport quantities can be calculated as a function of various parameters ( e.g. strength and frequency ) of the time - dependent perturbation . the scattering matrix description of the system subject to time - dependent perturbation was developed in energy representation by bttiker , thomas and pretrein in refs . @xcite . in this case the scattering matrix describes processes when electron scattering between different channels in the leads is accompanied by the change of electron energy . alternatively , the analysis of the effect of time - dependent perturbation on the conductance can be carried out in time representation , see  refs . @xcite . in general , both the weak localization correction to the conductance and the variance of conductance fluctuations are suppressed by time - dependent perturbation . the suppression of the quantum corrections to the conductance by microwave radiation was observed experimentally in @xcite . time - dependent perturbation of quantum dots not only suppresses quantum corrections to the conductance , but also produces electric current through the system even at zero bias . this effect is related to the charge pumping , which occurs in systems with large tunnel barriers  @xcite . if the conductance of the system is very small , the electric current is quantized in units of @xmath6 , where @xmath7 is the period of the pump . at finite conductance , a countercurrent reduces the pumped current and thus violate the quantization of electric current  @xcite . for an open quantum dot , the countercurrent nearly compensates the pumped current and the current is no longer quantized .    in the low frequency limit , the magnitude of the pumped current is determined entirely by the evolution of the system in the parameter space , see fig . 1 b ) , under time dependent perturbations  @xcite . as frequency increases , the parametric description becomes insufficient and requires full analysis of electron dynamics in time - dependent fields  @xcite . the analysis of how the adiabatic description breaks down at finite frequency can be also found in refs . we note that the charge pumping through an open quantum dot is a manifestation of the photovoltaic effect , which occurs in systems without inversion center  @xcite . the photovoltaic effect was previously considered by falko and khmelnitskii  @xcite in mesoscopic microjunctions and by kravtsov , aronov and yudson  @xcite in normal metal rings . it turns out  @xcite that the photovoltaic current is sensitive to the actual electron distribution function in the dot . time - dependent perturbations may broaden the distribution function , resulting in heating . this broadening of the electron distribution occurs as a result the electron diffusion in the energy space . the effect of time - dependent perturbations on electron distribution function becomes even more interesting in closed systems , when the energy diffusion acquires quantum interference corrections . the latter leads to a dynamic localization  @xcite of the electrons in energy space  @xcite . photovoltaic current fluctuates not only with respect to different realizations of the quantum dot , but also for a given realization due to quantum and thermal fluctuations . such fluctuations are called current noise and are described by the fluctuations of the charge transported through the dot in a certain number of perturbation cycles . the statistics of such charge fluctuations was studied in refs.@xcite for temperatures @xmath8 and pumping frequencies @xmath9 much smaller than the inverse dwell time @xmath10 ( escape rate ) of electrons from the quantum dot . particularly , refs . @xcite addressed the full counting statistics at temperatures @xmath11 ( we use @xmath12 and the boltsmann constant @xmath13 ) . the mean square charge fluctuations for @xmath14 ( but for arbitrary relation between @xmath15 and @xmath8 ) were considered in ref . the variance of the photovoltaic current for arbitrary relation between the temperature @xmath8 , the frequency @xmath9 , the escape rate @xmath10 and the strength of the perturbation was calculated in ref . @xcite . experiments  @xcite were performed to detect the photovoltaic current in various mesoscopic systems  @xcite , including open quantum dots  @xcite in the adiabatic regime . the observed magnetic field symmetry and the amplitude of the current indicate that the measured current was likely related to the ac rectification  @xcite . a more detailed analysis of the zero - bias current in different regimes of microwave radiation shows that in some instances the photovoltaic current , and not the rectification current , was observed  @xcite . in this review we focus on the random matrix description of electron transport through open quantum dots in the limit of the large number of open channels @xmath16 connecting the dot to the leads . this condition allows us to neglect the electron  electron interaction that gives corrections of the @xmath17 order , see ref . the same condition permits the use of a diagrammatic technique , similar to that described in @xcite , to calculate ensemble averaging . we assume that the electron dynamics in the dot is fully chaotic and disregard classical fluctuations of the conductance  @xcite . we emphasize that the random matrix description is applicable for sufficiently small quantum dots , when the thouless energy @xmath18 is much greater than all other energy scales of the problem , such as the frequency @xmath9 of the perturbation or the temperature @xmath8 ( @xmath19 is the electron crossing time of the dot ) . larger systems ( @xmath20 ) can be treated by methods developed for bulk conductors  @xcite , see e.g. @xcite . we note that the derivation of the results will be performed within the hamiltonian formalism , following refs . @xcite , but the same results were derived within scattering matrix formalism in @xcite .","summary":"assuming that the hamiltonian belongs to a gaussian ensemble of random matrices , we investigate various statistical properties of the direct current in the ensemble . particularly , even at zero bias we discuss dependence of the photovoltaic current and its noise on the frequency and the strength of the perturbation .","abstract":"we review the random matrix description of electron transport through open quantum dots , subject to time - dependent perturbations . all characteristics of the current linear in the bias can be expressed in terms of the scattering matrix , calculated for a time - dependent hamiltonian . assuming that the hamiltonian belongs to a gaussian ensemble of random matrices , we investigate various statistical properties of the direct current in the ensemble . particularly , even at zero bias the time - dependent perturbation induces current , called photovoltaic current . we discuss dependence of the photovoltaic current and its noise on the frequency and the strength of the perturbation . we also describe the effect of time - dependent perturbation on the weak localization correction to the conductance and on conductance fluctuations ."}
{"article_id":"cond-mat0510254","section_id":"c","document":"in summary , we reviewed the random matrix description of electron transport through an open quantum dot , subject to time - dependent perturbations . we expressed the dc current through the dot in terms of the scattering matrices , and considered such components of the current as the photovoltaic current , independent from the bias voltage , and the linear in the bias current , characterized by the conductance . the scattering matrices are calculated in terms of time - dependent hamiltonian , that belongs to a gaussian ensemble of random matrices . we then presented the diagram technique to perform ensemble averaging and applied this technique to calculate different statistical properties of the electron transport through the dot . the main results can be summarized as follows . the weak localization correction to the conductance and conductance fluctuations are both suppressed by time - dependent perturbation . however , the suppression has different parametric dependence on perturbation frequency . the photovoltaic current can be represented as a sum of circular and linear terms . these term have different frequency dependence : the circular term dominates at low frequencies and represents the adiabatic charge pumping , while the linear term dominates at high frequencies . the photovoltaic current and its noise are determined by the actual width of the electron distribution function in the dot , on the other hand , the variance of the conductance fluctuations is determined by electron temperature in the leads . these results are in qualitative agreement with experiments , described in refs . @xcite . we described calculations using the hamiltonian approach to the statistical description of the electron transport , a detailed description of the scattering matrix approach for time - dependent system can be found in ref . @xcite , where the same results were obtained .    in this review we considered the electron system neglecting the interaction effects and assumed spin degeneracy . the effect of electron - electron interaction can be disregarded only in the limit of the large number of open channels , but as the number of open channels decreases , the interaction effects become more important  @xcite . the interplay of the interaction and time - dependent perturbation was addressed in  refs . @xcite .    in semiconductor quantum dots in absence of magnetic field electron spin states are nearly degenerate . however , if magnetic field is applied , the spin degeneracy is lifted and currents of electrons with opposite spin orientations are not identical . in this case a spin current can be generated by time - dependent perturbation , similar to the photovoltaic charge current  @xcite , this effect was studied experimentally in ref . another modification of the system , considered in the present review , is a quantum dot connected to superconducting leads and was studied theoretically in  @xcite , the experimental realization of such a system remains a challenging task .","summary":"we review the random matrix description of electron transport through open quantum dots , subject to time - dependent perturbations .","abstract":"we review the random matrix description of electron transport through open quantum dots , subject to time - dependent perturbations . all characteristics of the current linear in the bias can be expressed in terms of the scattering matrix , calculated for a time - dependent hamiltonian . assuming that the hamiltonian belongs to a gaussian ensemble of random matrices , we investigate various statistical properties of the direct current in the ensemble . particularly , even at zero bias the time - dependent perturbation induces current , called photovoltaic current . we discuss dependence of the photovoltaic current and its noise on the frequency and the strength of the perturbation . we also describe the effect of time - dependent perturbation on the weak localization correction to the conductance and on conductance fluctuations ."}
{"article_id":"1403.4967","section_id":"i","document":"the term ` veronese space ' refers , primarily ( and historically ) , to the structure of prisms in a projective space with ` double hyperplanes ' as the points ( see @xcite , @xcite ) ; after that it refers to an algebraic variety which represents this structure ( cf . e.g.  @xcite ) and as such it was generalized in recent decades , and its geometry was studied and developed ( see e.g.  @xcite , @xcite , @xcite , @xcite ) .    a task to find a synthetic approach to ( ` original ' ) veronese spaces was undertaken by the group of geometers around g. tallini in the 70-th s and the results are presented in @xcite , @xcite , @xcite , @xcite . the way in which veronese spaces were presented in those papers , where the points are two - element sets with repetitions with the elements being projective points , turned out to be fruitfully generalizable to an abstract construction , which associates with an arbitrary partial linear space ( or even more generally : with an arbitrary incidence structure ) another partial linear space ( incidence structure resp . ) ; this construction and its basic properties were presented in @xcite . the point universe of the constructed veronese space @xmath0 consists of the @xmath1-element sets with repetitions with the elements in the universe of the underlying ` starting ' structure @xmath2 ( cf .  definitions , ) . the construction discussed belongs to the family of , informally speaking , ` multiplying ' a given structure somehow in the spirit of ` manifold theory ' : the structure @xmath0 can be covered by a family of copies of @xmath2 so as through each point of it there pass @xmath1 copies of @xmath2 . any two distinct copies of @xmath2 in this covering do not share more than a single point . the abstract schemas ( in fact : partial linear spaces of particular type ) of the coverings induced by the construction of a veronese space were studied in more detail in @xcite .    in this paper we develop to some extent the theory of veronese spaces associated with spaces with some additional structures ( like a parallelism ) , we discuss possibilities to introduce parallelism in the veronese spaces and related questions , all in a sense referring to a broad problem :  hyperplanes and parallelisms \" . the main approach is determining a hyperplane in a veronese space associated with a linear space that contains hyperplanes ( say : with a projective space ) and delete this hyperplane . the obtained reduct can not be presented as a veronese space ( [ thm : verprodnotverred ] ) . nevertheless we could succeed in characterizing the hyperplanes in ( ` classical ' ) veronese spaces associated with projective spaces ( [ thm : hipainprojver ] ) and prove that ( similarly to the case when a hyperplane is deleted from a projective space ) from the obtained  the underlying veronese space can be recovered ( [ thm : verred2ver ] ) . we find also interesting examples of hyperplanes in veronese spaces associated with polar spaces and we generalize our construction to this class also . this completes the set of our main results .    in appendix we discuss another approach : defining the veronese space associated with a structure with a parallelism ( say : with an affine space ) . there is no simple way to introduce a parallelism on the defined ` veronese product ' ( [ thm : noparinver ] ) . in both approaches we obtain a structure which can be covered by several copies of an affine space . at the end of this paper we formulate several open problems . they are out of the scope of our main reasoning but they seem closely related to it .","summary":"we determine hyperplanes in veronese spaces associated with projective spaces and polar spaces , and analyse the geometry of parallelisms induced by these hyperplanes . we also discuss if parallelisms on veronese spaces associated with affine spaces can be imposed .    + keywords : veronese space , projective space , affine space , polar space , , affine , hyperplane , correlation .    veronese space , projective space , affine space , polar space , , affine , hyperplane , correlation .","abstract":"we determine hyperplanes in veronese spaces associated with projective spaces and polar spaces , and analyse the geometry of parallelisms induced by these hyperplanes . we also discuss if parallelisms on veronese spaces associated with affine spaces can be imposed .    ( # 1,#2 )    ( # 1)#1^    # 1 - 13mu # 1#2#3_#3    ( # 1)(#1 ) ( # 1)^(#1 )    ( # 1,#2)*p*_#1(#2 ) ( # 1,#2)*v*_#1(#2 ) ( # 1)*q*(#1 ) ( # 1,#2)*g*_#1(#2 ) ( # 1,#2)*g*^_#1(#2 )    mathematics subject classification ( 2010 ) : 51a15 , 51a05 . + keywords : veronese space , projective space , affine space , polar space , , affine , hyperplane , correlation .    veronese space , projective space , affine space , polar space , , affine , hyperplane , correlation ."}
{"article_id":"astro-ph0303221","section_id":"i","document":"the proposition that extrasolar planet host stars tend to be metal rich has implications for the planet formation community . this fact , as shown by e.g. gonzalez ( 1997 , 1998 ) , laughlin & adams ( 1997 ) and jeffery et al . ( 1997 ) , although interesting , has not yet been given a single , universally accepted theoretical explanation . two possibilities are reviewed well by @xcite and @xcite@xmath3 either planets form preferentially around stars which are intrinsically richer in heavy elements , or the over - abundance of metals is due to hydrogen deficient protoplanetary debris enriching the stellar photosphere . only stars which have shallow convection regions will show metal enrichment due to accretion ; when a star has a large convective region , the additional metals will be diluted beyond detection . for f stars and earlier , enrichment can occur during the early life as a main - sequence star , however , for g stars , enrichment is thought to occur only if the accretion has taken place after the first 10 myr of pre - main sequence evolution . at this time the convective region has decreased in size @xcite . later type stars should show no detectable enhancement , even if large amounts of material are accreted . current searches for planets include stars with vastly different chemical and formation histories . one good way to test the enrichment theory is by observing a star cluster , whose members were presumably formed from homogeneous material . the key is to look for star - to - star differences in heavy element content . stars showing higher amounts of metals would have had to be enriched in some way , notably from h deficient material being accreted onto the stellar atmosphere . similar programs have utilized this concept of eliminating initial composition variable by performing a differential abundance analysis of binary stars @xcite . and recently , a program similar to this one has been undertaken by @xcite . abundances of hyades stars have been determined by several groups over the past few decades . these studies have provided increasingly more accurate abundances , as atomic data have improved and as stellar atmosphere models have become closer approximations to physical reality . @xcite review the abundance studies of the hyades from @xcite through their own work . it is evident that the measurement of heavy elements have been studied in a - f stars , but a detailed analysis in the lower mass dwarfs is lacking . in addition , many of these studies only include 1 - 2 dozen stars . conti et al . studied various elements in 10 hyades stars . they were also interested in looking for star - to - star differences to determine if the protocluster nebula was homogeneous . this survey provided the first evidence that li in the hyades is not uniform , while the abundances of several other elements were . to within their stated error bars , conti et al . determined that the abundance of hyades members is constant for all elements but li . later , chemical composition studies ( excluding studies of only fe and/or li , which are more numerous ) were completed in a - f stars by @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite . for lower mass stars , heavy element abundance determinations were only completed by the following ( again excluding those studies only of fe and/or li ) : @xcite , @xcite and @xcite . papers also instrumental to the metallicity determination of the hyades cluster are @xcite , @xcite , @xcite , @xcite , and @xcite . @xcite have estimated the amount of fe that must be accreted onto the stellar photosphere in order to enrich the measured [ fe / h ] of a solar - type star appreciably . they derive that a quantity of 10 m@xmath4 of fe ( a rough upper limit to the fe core of jupiter ) would increase the [ fe / h ] of a solar - type star by 0.09 dex . within the errors of stellar abundance analysis and atomic data , variations of this magnitude within the cluster are detectable through a differential abundance analysis .    in this paper , one in a series exploring planets and planet formation in the hyades cluster ( e.g. cochran et al . 2002 , paulson et al . 2002 , 2003 ) we present abundance determinations for fe , si , ti , ca , na , mg and zn ( as well as differential measurements for each of these elements ) for a large sample of hyades members over a wide effective temperature range in search for evidence of stellar enrichment .","summary":"we present a differential abundance analysis of hyades f - k dwarfs in search for evidence of stellar enrichment from accreted hydrogen deficient disk material . metallicites and relative abundance ratios of several species have been determined .","abstract":"we present a differential abundance analysis of hyades f - k dwarfs in search for evidence of stellar enrichment from accreted hydrogen deficient disk material . metallicites and relative abundance ratios of several species have been determined . we derive a cluster mean [ fe / h ] 0.13.01 . two stars show abundances.2 dex larger than the cluster mean . additionally , one star , which was added by a recent study as a cluster member , shows significantly lower abundances than the cluster mean . these three stars have questionable membership characteristics . the remaining stars in the survey have an rms of 0.04 dex in the differential [ fe / h ] values . the hyades cluster members have apparently not been significantly chemically enriched . the abundance ratios of si , ti , na , mg , ca and zn with respect to fe are in their solar proportions ."}
{"article_id":"0902.2812","section_id":"i","document":"the luminosity functions ( lfs ) of galaxies provide fundamental clues to the evolution of galaxies . until recently , measurements of the galaxy lfs were largely confined to near - ir to uv wavelengths ( e.g. , blanton et al . 2003 ; brown et al .  2007 ; faber et al . 2007 ; cirasuolo et al . 2007 for recent results ) mainly due to the observational difficulties of covering large areas in the mid - ir . the early mid / far - ir studies of galaxies utilized the _ iras _ , _ iso _ , and _ cobe _  satellites and ground - based sub - millimeter observations . these early studies led to the discovery of strong far - ir background radiation ( puget et al . 1996 ; hauser et al . 1998 ; fixsen et al . 1998 ) , understanding the properties of luminous and ultra - luminous ir galaxies ( e.g. , soifer et al . 1987 ; sanders & mirabel 1996 ; barger et al . 1999 ) , and earlier measurements of lfs in the mid / far - ir bands ( e.g. , soifer et al . 1987 ; rowan - robinson et al . 1987 ; saunders et al . 1990 ; xu et al . the _ spitzer space telescope _ ( werner et al . 2004 ) , with its unprecedented capabilities , allows us to significantly expand on these results . in particular , the _ spitzer_/irac channels 14 cover wavelengths of 3.6 , 4.5 , 5.8 , and 8.0 @xmath0 m ( fazio et al . 2004 ) , respectively , providing unique windows for studies of galaxy properties . at low redshifts ( @xmath11 ) , the 3.6 @xmath0 m and 4.5 @xmath0 m channels lie on the rayleigh - jeans tail of the blackbody spectrum of stars , directly tracing the stellar mass with little sensitivity to the ism either through absorption or emission . the 8.0 @xmath0 m channel contains polycyclic aromatic hydrocarbon ( pah ) features whose luminosity is well correlated with star formation rates . the situation for the 5.8 @xmath0 m is more complicated since the galaxy flux is composed of mixture of starlight and pah features . overall , the _ spitzer_/irac channels provide a comprehensive view of galaxy physics in the mid - infrared . recently , several studies have measured luminosity functions in the near and mid - ir based on irac photometry in the chandra deep field south ( cdfs ) , hubble deep field north ( hdfn ) , great observatories origins deep survey ( goods ) , combo-17 , and _ spitzer _ wide - area infrared extra - galactic ( swire ) surveys , where the majority of the galaxy redshifts are photometric redshifts , complemented by spectroscopic redshifts from these surveys and the vimos vlt deep survey ( vvds , le fvre et al . in particular , there are studies using 2600 24@xmath0 m  sources with 1941 spectroscopic redshifts ( le floch et al . 2005 ) , 8000 24@xmath0 m  sources with photometric redshifts ( prez - gonzlez et al . 2005 ) , 1478 3.6@xmath0 m  sources with 47% spectroscopic redshifts ( franceschini et al . 2006 ) , 1349 24@xmath0 m  sources with photometric redshifts ( caputi et al . 2007 ) , 1730088600 3.624@xmath0 m  sources with photometric redshifts ( swire , babbedge et al . 2006 ) , and 21200 3.6@xmath0 m  sources with 1500 spectroscopic redshifts ( arnouts et al . 2007 ) . most of these studies use a combination of several photometric and redshift surveys . semi - analytical models of galaxy evolution have also been developed to provide theoretical basis for comparisons to the observed lfs ( e.g. , lacey et al . 2008 ) . one of the central questions involved in these studies is the assembly history of galaxies , which should depend on both galaxy type and luminosity . for example , franceschini et al . ( 2006 ) found that the most massive galaxies are in place at @xmath12 , while , including fainter galaxies , arnouts et al . ( 2007 ) found about 50% of quiescent and 80% of active galaxies are in place at @xmath12 . accurate lf measurements as a function of redshift are essential to such studies . unfortunately , dividing samples into redshift bins reduces the sample size and increases both statistical and systematic uncertainties . the situation is further complicated by the presence of cosmic variance both within and between surveys and the heavy dependence on photometric redshifts . while photometric redshifts are frequently necessary for achieving a large sample size or a longer luminosity baseline , they can also lead to systematic uncertainties in the shape and evolution of the luminosity functions . moreover , as we find in this study , the redshift dependence of the definition of luminosity can be a problem for estimates of evolution rates .    in this paper , we present mid - infrared galaxy luminosity functions for @xmath13 in the _ spitzer_/irac bands by combining the irac shallow survey ( eisenhardt et al . 2004 ) of the noao deep wide - field survey ( ndwfs , jannuzi & dey 1999 ) with redshifts from the agn and galaxy evolution survey ( ages , kochanek et al . 2008 , in preparation ) . for the 3.68.0@xmath0 m  irac bands we have well - defined samples with roughly 38005800 spectroscopic redshifts and a statistical power corresponding to samples of 46008000 objects through the use of random sparse sampling . we describe the sample selection , photometry , and redshifts in  2 , the lf measurement methods in  3 , and the lfs in  4 . we discuss our results in  5 . we assume that @xmath14 , @xmath15 , and @xmath16 , and use the vega magnitude system throughout the paper .","summary":"we present galaxy luminosity functions at 3.6 , 4.5 , 5.8 , and 8.0 m  measured by combining photometry from the irac shallow survey with redshifts from the agn and galaxy evolution survey of the noao deep wide - field survey botes field . the well - defined irac samples contain 38005800 galaxies for the 3.68.0 m  bands with spectroscopic redshifts and . we obtained relatively complete luminosity functions in the local redshift bin of for all four irac channels that are well fit by schechter functions . after analyzing the samples for the whole redshift range , we found significant evolution in the luminosity functions for all four irac channels that can be fit as an evolution in with redshift , .","abstract":"we present galaxy luminosity functions at 3.6 , 4.5 , 5.8 , and 8.0 m  measured by combining photometry from the irac shallow survey with redshifts from the agn and galaxy evolution survey of the noao deep wide - field survey botes field . the well - defined irac samples contain 38005800 galaxies for the 3.68.0 m  bands with spectroscopic redshifts and . we obtained relatively complete luminosity functions in the local redshift bin of for all four irac channels that are well fit by schechter functions . after analyzing the samples for the whole redshift range , we found significant evolution in the luminosity functions for all four irac channels that can be fit as an evolution in with redshift , . while we measured and in the 3.6 and 4.5 m  bands consistent with the predictions from a passively evolving population , we obtained in the 8.0 m  band consistent with other evolving star formation rate estimates . we compared our lfs with the predictions of semi - analytical galaxy formation and found the best agreement at 3.6 and 4.5 m , rough agreement at 8.0 m , and a large mismatch at 5.8 m . these models also predicted a comparable value to our luminosity functions at 8.0 m , but predicted smaller values at 3.6 and 4.5 m . we also measured the luminosity functions separately for early and late - type galaxies . while the luminosity functions of late - type galaxies resemble those for the total population , the luminosity functions of early - type galaxies in the 3.6 and 4.5 m  bands indicate deviations from the passive evolution model , especially from the measured flat luminosity density evolution . combining our estimates with other measurements in the literature , we found% of the present stellar mass of early - type galaxies has been assembled at .    # 1to 0pt#1"}
{"article_id":"0902.2812","section_id":"m","document":"we used both the parametric maximum - likelihood method ( sty , sandage et al .  1979 ) and the non - parametric stepwise maximum - likelihood method ( swml , efstathiou et al .  1988 ) to fit the luminosity functions . in the sty method , we parameterized the lf as a schechter function @xmath45 and we allowed @xmath3 to evolve as @xmath46 when fitting the lf , following the parameterization of lin et al . we did not allow the normalization @xmath47 or the slope @xmath48 of the lf to evolve since our sample size is not large enough to constrain the evolution of these parameters . estimates of @xmath47 will also suffer from cosmic variance at low redshifts where we have little volume . in the swml method , the lf is defined in bins @xmath49 with value @xmath50 . in both methods , the parameters of the lfs in the sty method ( @xmath3 , @xmath48 , and @xmath8 ) and the swml ( @xmath50 ) method are calculated by maximizing the likelihood functions . since the absolute normalization factor @xmath47 is not modeled in the likelihood function , the shape of the lf determined from the sty and swml methods is not sensitive to the effects of large scale structure . we calculated the normalization @xmath47 using the minimum variance method ( david & huchra 1982 ) . since the sty and minimum variance methods are widely used in determinations of lfs , we leave the details of the calculations to other references ( e.g. , lin et al . 1996 , 1999 ) . we checked the sty and swml calculations using both synthetic catalogs and by calculating the lfs using the @xmath51 method ( schmidt 1968 ; avni & bahcall 1980 ) . the lfs from the @xmath51 method are in very good agreement with those determined from the swml method , except for the very low luminosity bins where the @xmath51 results show a deficit of galaxies compared to the swml method , probably due to the effects of large scale structure . we only present the sty / swml results . each galaxy was assigned a weight based on the sampling strategy and the redshift completeness . the mean redshift completeness , @xmath52 , 0.93 , 0.93 and 0.96 for the [ 3.6][8.0 ] bands , depends little on magnitude , and the sampling fraction @xmath53 or 0.3 depends on the target magnitudes and the band ( see  2.2 table  1 and figure  [ fig : iraci ] ) . thus , each galaxy has an overall statistical weight of @xmath54 . we included both the irac and @xmath23 band selection limits in our lf measurements . we also carried out the calculations using only the irac selection limits , and the resulting lfs are consistent with the full analysis . this is expected , since at the irac magnitude limits we are losing few galaxies due to the optical flux limit ( see figure  [ fig : iraci ] ) . we measured the lfs using the sty and swml methods in three different ways for the [ 3.6][8.0 ] bands . first , we determine the lfs by applying the sty method to the entire redshift range ( @xmath13 ) . this is essentially a pure luminosity evolution model since we did not allow the normalization @xmath47 or the slope @xmath48 of the lf to evolve . second , we applied the sty method to the three redshift bins @xmath55 , @xmath56 , and @xmath57 . we chose the redshift bins as a balance between the number of galaxies ( statistical uncertainties ) and the bin width ( averaging over cosmic time ) . we fixed the slope @xmath48 and evolution parameter @xmath8 to the values obtained from the first method and fit only the normalization @xmath47 and @xmath3 in each redshift bin . this allows us to check whether the lfs evolve beyond the pure luminosity evolution model . third , we measured the binned lfs with the swml method in the three redshift bins and then fit them jointly with schechter functions , where we fixed the faint end slope @xmath48 to be the same in all bins but allowed the @xmath3 and the normalization @xmath47 to differ .","summary":"1to 0pt#1","abstract":"we present galaxy luminosity functions at 3.6 , 4.5 , 5.8 , and 8.0 m  measured by combining photometry from the irac shallow survey with redshifts from the agn and galaxy evolution survey of the noao deep wide - field survey botes field . the well - defined irac samples contain 38005800 galaxies for the 3.68.0 m  bands with spectroscopic redshifts and . we obtained relatively complete luminosity functions in the local redshift bin of for all four irac channels that are well fit by schechter functions . after analyzing the samples for the whole redshift range , we found significant evolution in the luminosity functions for all four irac channels that can be fit as an evolution in with redshift , . while we measured and in the 3.6 and 4.5 m  bands consistent with the predictions from a passively evolving population , we obtained in the 8.0 m  band consistent with other evolving star formation rate estimates . we compared our lfs with the predictions of semi - analytical galaxy formation and found the best agreement at 3.6 and 4.5 m , rough agreement at 8.0 m , and a large mismatch at 5.8 m . these models also predicted a comparable value to our luminosity functions at 8.0 m , but predicted smaller values at 3.6 and 4.5 m . we also measured the luminosity functions separately for early and late - type galaxies . while the luminosity functions of late - type galaxies resemble those for the total population , the luminosity functions of early - type galaxies in the 3.6 and 4.5 m  bands indicate deviations from the passive evolution model , especially from the measured flat luminosity density evolution . combining our estimates with other measurements in the literature , we found% of the present stellar mass of early - type galaxies has been assembled at .    # 1to 0pt#1"}
{"article_id":"0902.2812","section_id":"c","document":"the spectroscopy from the ages survey has allowed us to measure the mid - infrared ( 3.6 , 4.5 , 5.6 , and 8.0@xmath0 m ) luminosity functions for @xmath13 with greater precision than existing mid - ir surveys which have largely relied on photometric redshifts . the bluest bands agree well with local @xmath42-band luminosity functions , possibly with some effects from the pah feature in the 3.6@xmath0 m band . the early and late - type galaxies having similar characteristic magnitudes and the early - type galaxies have shallower faint end slopes . as we move to the redder bands , the early - type galaxies exhibit fainter break magnitudes and steeper faint end slopes relative to the late - type galaxies . in general our results agree well with other recent mid - ir studies based largely on photometric redshifts by franceschini et al . ( 2006 ) , babbedge et al . ( 2006 ) and arnouts et al . although we have better statistics and use only spectroscopic redshifts , our study is limited to lower redshifts . the one major exception is that we find that schechter function fits work reasonably well at 5.8 and 8.0@xmath0 m , as huang et al . ( 2007 ) also found for 8.0@xmath0 m based on a sub - sample of galaxies with @xmath72 in our field . this is in disagreement with the power - law fits adapted by babbedge et al . ( 2006 ) for these bands . photometric redshifts are known to work well for the typical galaxy ( e.g. ,  3.1 , babbedge et al . 2006 ) which is why our luminosity functions broadly agree with those based solely or largely on them . where spectroscopic redshifts have an edge is on the wings of the luminosity function , where magnitude limited samples have few objects because the high luminosity objects are rare and the volume in which low luminosity objects can be found is small . these parts of the luminosity function , well away from @xmath113 , are quickly altered given even a small number of catastrophic photo - z redshift errors for the far more numerous @xmath113 galaxies . the general tendency will be to weaken the exponential cutoff of a schechter function at high luminosity and to steepen the slope at low luminosity . while we have no direct evidence that this is the explanation , this is exactly the trend of our differences with the longer wavelength swire luminosity functions ( babbedge et al . 2006 ) . we find no convincing evidence for density evolution in our sample , and a pure luminosity evolution model appears to work reasonably well . the @xmath3 for the total galaxy population evolves as @xmath334 with @xmath3351.2 in the [ 3.6 ] and [ 4.5 ] bands , which probe the stellar mass , and the evolution rates are consistent with the @xmath42-band passive evolution models of arnouts et al . ( 2007 , @xmath336 ) . we measured the evolution rate @xmath337 in the [ 8.0 ] band , which is sensitive to star formation and consistent with other estimates for the evolution of star formation ( hopkins 2004 ; villar et al . the rate of evolution agrees well with the scalings from 2mass , arnouts et al . ( 2007 ) and babbedge et al . ( 2006 ) at @xmath338 m . at [ 3.6 ] and [ 4.5 ] , the evolution of @xmath3 and @xmath47 for early - type galaxies suggests possible deviations from passive evolution models , however , with large uncertainties . the evolution of luminosity density for early - type galaxies provides a more robust test for deviations from the passive evolution model and suggests that the stellar mass for early - type galaxies has increased by @xmath117% from @xmath10 to @xmath20 . we also compared our lfs with the recent semi - analytical model from lacey et al . while the match between the model and observations is excellent at [ 3.6 ] and [ 4.5 ] , it is worse at [ 8.0 ] , and at [ 5.8 ] the model failed to reproduce the [ 5.8 ] lfs . we can also extend measurements of the galaxy luminosity density at @xmath119 into the mid - ir . the luminosity density spectrum is that of a mildly star forming galaxy where the emission drops from the near - ir to a minimum near 5@xmath0 m and rises again due to pah emission . our results at low redshift would be significantly improved by combining our sample with a complete redshift survey of the brighter mid - ir sources in the wider area swire fields , to better constrain the low redshift , high luminosity sources , and with a fainter sample in a narrow field ( e.g. the deep2 results for the extended groth strip ) to better constrain the faint end of the luminosity function and extend the results to higher redshifts . within the botes field itself we can achieve many of the same goals using photometric redshifts . in particular , assef et al . ( 2008 ) have developed a set of templates that extend through all four irac bands , which would probably give better results than most existing studies which have truncated their templates near 4.5@xmath0 m band due to a lack of good templates for the longer wavelengths . since our present analysis used the rest - frame 8@xmath0 m results from the assef et al . ( 2008 ) templates , which is based on data which extends only to 5@xmath0 m for sources at @xmath339 , it would also be useful to extend the templates through the mips 24@xmath0 m band . we thank c. lacey for providing the theoretical models for the irac band luminosity functions , s. arnouts and t. babbedge for providing more detailed information on their results , and s. willner for helpful discussions . the ages observations were obtained at the mmt observatory , a joint facility of the smithsonian institution and the university of arizona . we are grateful to the expert assistance of the staff of kitt peak national observatory where the botes field observations of the ndwfs were obtained . the authors thank noao for supporting the noao deep wide - field survey . the research activities of a.  d. and b.  t.  j. are supported by noao , which is operated by the association of universities for research in astronomy ( aura ) under a cooperative agreement with the national science foundation . this work is based on observations made with the _ spitzer space telescope _ , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa .","summary":"combining our estimates with other measurements in the literature , we found% of the present stellar mass of early - type galaxies has been assembled at .    #","abstract":"we present galaxy luminosity functions at 3.6 , 4.5 , 5.8 , and 8.0 m  measured by combining photometry from the irac shallow survey with redshifts from the agn and galaxy evolution survey of the noao deep wide - field survey botes field . the well - defined irac samples contain 38005800 galaxies for the 3.68.0 m  bands with spectroscopic redshifts and . we obtained relatively complete luminosity functions in the local redshift bin of for all four irac channels that are well fit by schechter functions . after analyzing the samples for the whole redshift range , we found significant evolution in the luminosity functions for all four irac channels that can be fit as an evolution in with redshift , . while we measured and in the 3.6 and 4.5 m  bands consistent with the predictions from a passively evolving population , we obtained in the 8.0 m  band consistent with other evolving star formation rate estimates . we compared our lfs with the predictions of semi - analytical galaxy formation and found the best agreement at 3.6 and 4.5 m , rough agreement at 8.0 m , and a large mismatch at 5.8 m . these models also predicted a comparable value to our luminosity functions at 8.0 m , but predicted smaller values at 3.6 and 4.5 m . we also measured the luminosity functions separately for early and late - type galaxies . while the luminosity functions of late - type galaxies resemble those for the total population , the luminosity functions of early - type galaxies in the 3.6 and 4.5 m  bands indicate deviations from the passive evolution model , especially from the measured flat luminosity density evolution . combining our estimates with other measurements in the literature , we found% of the present stellar mass of early - type galaxies has been assembled at .    # 1to 0pt#1"}
{"article_id":"1302.2901","section_id":"i","document":"an equilibrium in nature is rare and it is rather an exception than the rule . a vast majority of natural processes , ranging from large - scale flows in the atmosphere to the electric charge transfer found throughout the technological realm , are out - of - equilibrium processes . yet , the physics of the equilibrium state is much more studied and better understood . a major difficulty impeding the similar progress in the research of the nonequilibrium processes is that while all thermodynamics - based science rests on the law that , in equilibrium , any system assumes the state with the minimal free energy , the equally powerful and fundamental principles that govern the far - from - equilibrium behaviors still wait to be revealed . there has been an important advance both theoretical and experimental@xcite employing a variety of approaches to out - of - equilibrium problems in electronic systems@xcite ; among them , those based on the keldysh technique@xcite seem to appear the most promising as paving a way towards general method which would allow treating interacting nonequilibrium systems on a common fundamental ground .    in this work we undertake the study of a disordered superconducting system employing the theory that has been proven to effectively tackle the low - energy excitation physics , the keldysh nonlinear sigma model @xcite . more specifically , we focus on the nonequilibrium phase transition between the normal and the superconducting state . in a vicinity of the transition , when the system is in the normal state , the behavior of the system is governed by fluctuations of the superconducting order parameter . fluctuation - induced short - living cooper pairs are formed and contribute critically both into the thermodynamic and transport characteristics of the systems@xcite . in disordered thin films the temperature range where fluctuations are essential is determined by the sheet resistance ( being in any case significantly larger than the one of bulk superconductors@xcite ) and depends on the particular process involved , extending often to temperatures well above the superconducting transition temperature@xcite .    here we study the influence of superconducting fluctuations on dynamic properties of a thin film in the fluctuational region of a normal state . the film is driven out of the equilibrium due to contacts with thermal reservoirs having different temperatures and chemical potentials . the keldysh ginzburg - landau - like action under nonequilibrium conditions and several effects of nonequilibrium superconducting fluctuations were addressed in refs .   for this setting . out - of - equilibrium fluctuation contributions to the dc electrical conductivity were calculated in ref .  . importantly , under nonequilibrium conditions the fluctuation - dissipation theorem ( fdt ) is generally violated and there is no fundamental relation between the current fluctuations ( i.e.  noise ) and conductivity , in contrast to close - to - equilibrium conditions where this relation holds . therefore , unlike in equilibrium systems , the nonequilibrium noise is not fully tied to the conductivity and can carry additional information , not contained in the conductivity . this poses a problem of the independent calculation of noise in out - of - equilibrium state . shot noise in noninteracting diffusive electron system was studied in refs .  . the influence of the coulomb interaction on shot noise in disordered systems was analyzed in refs . , while the influence of bardeen - cooper - schrieffer ( bcs ) interaction on shot noise due to electric current flow above the critical temperature was considered only up to the second order in the electric field in ref .  . in the present work , we focus on a film above the nonequilibrium superconducting transition and calculate nonlinear dependence of the nyquist noise on the temperatures and chemical potentials of the thermal baths that are in contact with the film , see fig .  [ fig : film ] . the paper is organized as follows . in sec . [ sec : nlsm ] we introduce the nonlinear sigma model for superconductors within the keldysh technique . in sec . [ sec : noninteracting ] we find the current correlation function for the case of noninteracting electrons in a nonequilibrium disordered thin film . we further consider the bcs interaction . in sec . [ sec : fluctuations1 ] we introduce nonequilibrium fluctuation propagators . then we proceed with calculations of different contributions to the current - current correlation function caused by superconducting fluctuations : the density of states contribution is calculated in sec . [ sec : dos ] , the maki - thompson in sec . [ sec : mt ] and the aslamazov - larkin in sec . [ sec : al ] . in sec . [ sec : conclusions ] we summarize our results . some calculation details are given in appendices .","summary":"we study out - of - equilibrium transport in disordered superconductors close to the superconducting transition .","abstract":"we study out - of - equilibrium transport in disordered superconductors close to the superconducting transition . we consider a thin film connected by resistive tunnel interfaces to thermal reservoirs having different chemical potentials and temperatures . the nonequilibrium longitudinal current - current correlation function is calculated within the nonlinear sigma model description and nonlinear dependence on temperatures and chemical potentials is obtained . different contributions are calculated , originating from the fluctuation - induced suppression of the quasiparticle density of states , maki - thompson and aslamazov - larkin processes . as a special case of our results , close - to - equilibrium we obtain the longitudinal ac conductivity using the fluctuation - dissipation theorem ."}
{"article_id":"1302.2901","section_id":"c","document":"to summarize , we have studied the influence of superconducting fluctuations on the current - current correlation function in a disordered superconducting film driven out - of - equilibrium . the film is assumed to be in the normal state , but close to the nonequilibrium transition into the superconducting state . we obtained and analyzed nonlinear dependence of the noise on temperatures of the reservoirs , difference of chemical potentials , and frequency . we first considered the effect of the nonequilibrium conditions on the current - current correlation function ( i.e. , noise ) in the case of noninteracting electrons . then , we studied the bcs interaction and calculated contributions of different physical nature and origin to the in - plane current fluctuations : the aslamazov - larkin given by eq . ( [ eq : finalal ] ) , the maki - thompson given by eq . ( [ eq : mtan ] ) and the density of states given by eqs . ( [ eq : dosresult ] ) and ( [ eq : dosdift ] ) . these results are new and relevant for future experiments . we find that the frequency dependence of different contributions is characterized by different relevant energy scales manifesting different underlying physical processes . as a special case of our results , in the equilibrium we obtained the ac longitudinal conductivity .","summary":"different contributions are calculated , originating from the fluctuation - induced suppression of the quasiparticle density of states , maki - thompson and aslamazov - larkin processes . as a special case of our results , close - to - equilibrium we obtain the longitudinal ac conductivity using the fluctuation - dissipation theorem .","abstract":"we study out - of - equilibrium transport in disordered superconductors close to the superconducting transition . we consider a thin film connected by resistive tunnel interfaces to thermal reservoirs having different chemical potentials and temperatures . the nonequilibrium longitudinal current - current correlation function is calculated within the nonlinear sigma model description and nonlinear dependence on temperatures and chemical potentials is obtained . different contributions are calculated , originating from the fluctuation - induced suppression of the quasiparticle density of states , maki - thompson and aslamazov - larkin processes . as a special case of our results , close - to - equilibrium we obtain the longitudinal ac conductivity using the fluctuation - dissipation theorem ."}
{"article_id":"1305.2207","section_id":"i","document":"the action is the most important quantity in classical physics . general relativity ( gr ) is the most important classical field theory . understanding the action of gr is therefore of the utmost interest . this is not diminished by the expectation that classical gr is just a limit of some quantum theory . indeed , whatever the underlying theory , we know that gr defines its effective large - distance action . as such , the gr action is the _ result _ of a quantum - gravitational path integral . thus , special properties of the gr action may tell us something about this path integral . such an approach has been successful in the euclidean derivation @xcite of black hole entropy @xcite . there , the bekenstein - hawking entropy was extracted from an imaginary euclidean action . recently , it was noticed @xcite that the gravitational action @xmath0 in a bounded _ region generically has an imaginary part . this imaginary part arises from the action s boundary term , when the latter is integrated over `` flip surfaces '' - codimension-2 surfaces where the boundary flips its signature and becomes momentarily null . such flip surfaces are always present for a closed boundary , though they may be `` hidden '' at topological corners . as the normal becomes null at a flip surface , the boundary s extrinsic curvature diverges . the resulting divergence in the action s boundary term can be resolved by a deformation of the integration contour into the complex plane . in the process , an imaginary part is picked up . it has thus become clear that an imaginary gravitational action is a feature not just of euclidean spacetimes , but also of finite , non - stationary regions of realistic lorentzian solutions . moreover , it turns out that the imaginary part of the lorentzian action reproduces the black hole entropy formula , in the following precise way : @xmath1 here , the sum is over all the `` flip surfaces '' in the region s boundary . @xmath2 is the result of evaluating the black hole entropy formula on each flip surface . the relation was derived in @xcite by explicit calculation for gr with minimally - coupled matter and for lovelock gravity . the derivation can be trivially extended to e.g. scalar fields with non - minimal couplings of the form @xmath3 . for lovelock gravity or non - minimal couplings , one should use in not the bekenstein - hawking entropy , but its generalization due to wald @xcite .    in higher - derivative theories , the entropy formula for a stationary black hole does nt extend unambiguously to non - stationary geometries . in this case , eq . selects a particular non - stationary formula for @xmath2 . for lovelock gravity , a non - trivial calculation in @xcite results in a formula that depends solely on the intrinsic geometry of the flip surface . this is consistent with the non - stationary entropy formula proposed in @xcite . eq . can not be applied to general diff - invariant theories , since it requires knowledge of the action s boundary term . thus , the result s natural scope is the class of theories that contain no more than two time derivatives . in such theories , the boundary term is determined by requiring a well - defined variational principle , with only the boundary metric ( along with other configuration fields ) held fixed . for pure gravity , the only such theories are of the lovelock type . thus , the only cases not covered in @xcite are non - minimal matter couplings . in this paper , we will explicitly consider mostly lovelock gravity . we do so with the understanding that adding minimally - coupled matter is trivial , and with the expectation that the same principles should apply to all two - time - derivative theories . as discussed in @xcite , the action s imaginary part does nt affect the action variations that one encounters in hamiltonian evolution . this is because such variations leave the intrinsic geometry of flip surfaces , and therefore @xmath4 , unchanged . we note here that one can also reverse that argument . having accepted a non - vanishing @xmath4 , one can use the reality of the action variations in hamiltonian evolution to _ explain _ the dependence of @xmath4 on only the intrinsic metric of the flip surfaces .    in this paper , we continue to explore the imaginary part of the gravity action . in section [ sec : derive ] , we rederive @xmath4 for lovelock gravity , with gr as a special case . in the process , we draw a parallel with the euclidean calculation in @xcite . this enables us to explain the relation between @xmath4 and the entropy formula , as well as to elucidate the topological structure of @xmath4 in lovelock gravity . in section [ sec : gh ] , we focus on stationary black hole solutions , and evaluate the action for lorentzian regions that mimic the euclidean spacetimes of @xcite . the result , given in eq . , features a clean separation between the action s real and imaginary parts : while the real part consists of terms related to conserved charges , the imaginary part consists of terms related to the entropy .    in section [ sec : diamonds ] , we evaluate @xmath4 for causal - diamond - like boundaries that span a maximal portion of some symmetric spacetime . such boundaries coincide , in part or in full , with killing horizons and with the spacetime s asymptotic boundary . the geometries studied include minkowski space , the rindler wedge , pure ads , ds and ds@xmath5 spaces , as well as stationary black holes with either flat or ads asymptotics . for the regions examined , we find that @xmath4 agrees with the relevant horizon entropy , with the exception of the de - sitter example ( there is a factor - of-2 discrepancy , which disappears if one studies ds@xmath5 instead ) . in section [ sec : near_horizon ] , we examine local near - horizon regions for both stationary and non - stationary black holes . the imaginary action for such regions again agrees with the black hole entropy . we propose a heuristic interpretation of these local regions as `` effective '' asymptotic spacetimes for highly accelerated near - horizon observers . for non - stationary black holes , the relevant horizon for this interpretation is the teleological event horizon . it should be kept in mind that the general physical meaning of the action s imaginary part is unclear . in a euclidean situation , it is usually understood that the imaginary action describes a partition function . in the lorentzian , not much can be said with certainty . considering transition amplitudes @xmath6 , one sees that while @xmath7 is a phase , @xmath4 determines the amplitude s absolute value @xmath8 . thus , a positive @xmath4 implies exponentially damped amplitudes , which one may associate with an exponentially large number @xmath9 of available states .    despite the lack of a detailed physical understanding , two circumstances should be kept in mind . first , a nonvanishing @xmath4 does come out in an honest evaluation of the boundary - term integral , and should thus be taken seriously . second , the result refers primarily to finite spacetime regions , where the physical content of quantum gravity is itself unclear . indeed , the only well - understood quantum gravity observables @xcite are the s - matrix in asymptotically flat space and boundary cft correlators in asymptotically ads space @xcite . in ads / cft , the relationship between cft observables and bounded regions in the bulk is not entirely clear . a notable exception is the poincare patch of ads , which is cleanly associated with observables on a conformal minkowski patch of the ads boundary . as for s - matrix elements in asymptotically flat space , they are associated with the conformally compact region containing the entire spacetime . in section [ sec : diamonds ] , we will argue that @xmath4 actually vanishes in these two special cases . thus , a generally non - vanishing @xmath4 does nt seem to contradict any existing knowledge , but may in fact further our understanding of observables in quantum gravity .    in the formulas and figures below , the spacetime metric @xmath10 has mostly - plus signature . the spacetime dimension is @xmath11 . we use indices @xmath12 for spacetime coordinates , @xmath13 for coordinates on a codimension-1 hypersurface , and @xmath14 for coordinates on a codimension-2 surface . the sign convention for the riemann tensor is @xmath15v^\\mu$ ] .","summary":"in the other two setups , the imaginary part coincides with the relevant entropy .","abstract":"we study the imaginary part of the lorentzian gravitational action for bounded regions , as described in arxiv:1301.7041 . by comparing to a euclidean calculation , we explain the agreement between the formula for this imaginary part and the formula for black hole entropy . we also clarify the topological structure of the imaginary part in lovelock gravity . we then evaluate the action s imaginary part for some special regions . these include cylindrical slabs spanning the exterior of a stationary black hole spacetime , `` maximal diamonds '' in various symmetric spacetimes , as well as local near - horizon regions . in the first setup , the black hole s entropy and conserved charges contribute to the action s imaginary and real parts , respectively . in the other two setups , the imaginary part coincides with the relevant entropy ."}
{"article_id":"1305.2207","section_id":"c","document":"in this paper , we expanded the study of the imaginary part of the lorentzian gravitational action . the surprising results of the brute - force calculations in @xcite were explained more abstractly , through a relation with euclidean geometries . we also turned around the discussion in @xcite concerning the reality of the hamiltonian , using it to _ explain _ the dependence of @xmath4 in lovelock gravity on only the intrinsic metric of the flip surfaces . we then evaluated @xmath4 for three classes of physically interesting regions . for spacelike - bounded regions describing time evolution outside a stationary black hole ( section [ sec : gh ] ) , we found that the black hole s entropy and conserved charges enter @xmath4 and @xmath7 , respectively . we also found that the `` transition probability '' @xmath217 is inversely proportional to the number of microstates @xmath9 implied by the black hole s entropy . it would be interesting to see if this can be fleshed out into a more detailed physical picture .    for null - bounded `` maximal diamonds '' in various symmetric spacetimes , we found that @xmath4 coincides with the entropy that is usually associated to each spacetime . this is an intriguing pattern that calls for a deeper understanding . in particular , it can be taken to support the notion @xcite that null boundaries are best suited for the study of quantum gravity . standard de - sitter space poses an exception to the @xmath200 pattern , which is resolved if one considers the `` elliptical '' de - sitter space ds@xmath5 instead . if one takes @xmath4 seriously as a window into quantum gravity , this may serve as yet another argument favoring ds@xmath5 over ds as the more appropriate spacetime asymptotics .    finally , we discussed regions composed of small 1 + 1d diamonds times codimension-2 surfaces @xmath40 . for all such regions , @xmath4 evaluates to the entropy as calculated from @xmath40 . we proposed a physical interpretation for this calculation in two setups : a near - bifurcation - surface region in a stationary black hole spacetime and a near - event - horizon region for a non - stationary black hole .    in the future , it would be interesting to try and relate @xmath4 to the concept of entanglement entropy , both in ads / cft @xcite and more generally in quantum field theory .    on a more fundamental note , one would like to address the conceptual issues that arise from the non - unitarity of amplitudes @xmath6 for complex @xmath0 . this may serve as a concrete starting point on the broader mystery of the physical content of quantum gravity in finite regions .","summary":"we also clarify the topological structure of the imaginary part in lovelock gravity . these include cylindrical slabs spanning the exterior of a stationary black hole spacetime , `` maximal diamonds '' in various symmetric spacetimes , as well as local near - horizon regions . in the first setup ,","abstract":"we study the imaginary part of the lorentzian gravitational action for bounded regions , as described in arxiv:1301.7041 . by comparing to a euclidean calculation , we explain the agreement between the formula for this imaginary part and the formula for black hole entropy . we also clarify the topological structure of the imaginary part in lovelock gravity . we then evaluate the action s imaginary part for some special regions . these include cylindrical slabs spanning the exterior of a stationary black hole spacetime , `` maximal diamonds '' in various symmetric spacetimes , as well as local near - horizon regions . in the first setup , the black hole s entropy and conserved charges contribute to the action s imaginary and real parts , respectively . in the other two setups , the imaginary part coincides with the relevant entropy ."}
{"article_id":"1204.3909","section_id":"i","document":"wave propagation in granular crystals has been studied quite intensively in the past ten years . granular crystals are thought to be closely - packed chains of elastically interacting particles , which obey the fermi - pasta - ulam ( fpu ) lattice equations with hertzian interaction forces . experimental work with granular crystals and their numerous applications @xcite stimulated theoretical and mathematical research on the granular chains of particles . existence of solitary waves in granular chains was considered with a number of analytical and numerical techniques . in his two - page note , mackay @xcite showed how to adopt the technique of friesecke and wattis @xcite to the proof of existence of solitary waves . english and pego @xcite used these results to prove the double - exponential decay of spatial tails of solitary waves . numerical convergence to the solitary wave solutions was studied by ahnert and pikovsky @xcite . stefanov and kevrekidis @xcite reviewed the variational technique of @xcite and proved that the solitary waves are bell - shaped ( single - humped ) . recently , the interest to granular crystals has shifted towards periodic travelling waves as well as travelling waves in heterogeneous ( dimer ) chains , as more relevant for physical experiments @xcite . periodic wave solutions of the differential advance - delay equation were considered by james in the context of newton s cradle @xcite and homogeneous granular crystals @xcite . in particular , numerical approximations in @xcite suggested that periodic waves with wavelength larger than a critical value are spectrally unstable . convergence to solitary waves in the limit of infinite wavelengths was also illustrated numerically and asymptotically in @xcite . more recent work @xcite showed non - existence of time - periodic breathers in homogeneous granular crystals and existence of these breathers in newton s cradle , where a discrete @xmath0-schrdinger equation provides a robust approximation . periodic waves in a chain of finitely many beads closed in a periodic loop were approximated by starosvetsky _ _ in monomers @xcite and dimers @xcite by using numerical techniques based on poincar maps . interesting enough , solitary waves were found in the limit of zero mass ratio between lighter and heavy beads in @xcite . it is explained in @xcite that these solitary waves are in resonance with linear waves and hence they do not persist with respect to the mass ratio parameter . numerical results of @xcite indicate the existence of a countable set of the mass ratio parameter values , for which solitary waves should exist , but no rigorous studies of this problem have been developed so far . recent work @xcite contains numerical results on existence of periodic travelling waves in granular dimer chains .    in our present work , we rely on the anti - continuum limit of the fpu lattice , which was recently explored in the context of existence and stability of discrete multi - site breathers by yoshimura @xcite . by using a variant of the implicit function theorem , we prove that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter . by the perturbation theory arguments ( which are similar to the recent work in @xcite ) , we also show that the periodic waves with the wavelength larger than a certain critical value are spectrally stable . our results are different from the asymptotic calculations in @xcite , where a different limiting solution is considered in the anti - continuum limit . the family of periodic nonlinear waves bifurcating from the anti - continuum limit are shown numerically to extend all way to the limit of equal masses for the dimer beads . the periodic travelling waves of the homogeneous ( monomer ) chains considered in @xcite are different from the periodic waves extended here from the anti - continuum limit . in other words , the periodic waves in dimers do not satisfy the reductions to the periodic waves in monomers even if the mass ratio is one . similar travelling waves consisting of binary oscillations in monomer chains were considered a while ago with the center manifold reduction methods @xcite . the paper is organized as follows . section 2 introduces the model and sets up the scene for the search of periodic travelling waves . continuation from the anti - continuum limit is developed in section 3 . section 4 gives perturbative results that characterize floquet multipliers in the spectral stability problem associated with the periodic waves near the anti - continuum limit . numerical results are collected together in section 5 . section 6 concludes the paper .","summary":"we show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable .","abstract":"we study bifurcations of periodic travelling waves in granular dimer chains from the anti - continuum limit , when the mass ratio between the light and heavy beads is zero . we show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable . numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads , where periodic travelling waves of granular monomer chains exist ."}
{"article_id":"1204.3909","section_id":"c","document":"we have studied periodic travelling waves in granular dimer chains by continuing these solutions from the anti - continuum limit , when the mass ratio between the light and heavy beads is zero . we have shown that every limiting periodic wave is uniquely continued for small mass ratio parameters . although the vector fields of the granular dimer chain equations are not smooth , we can still use the implicit function theorem to guarantee that the continuation is @xmath93 with respect to the mass ratio parameter . we have also used rigorous perturbation theory to compute characteristic exponents in the linearized stability problem . from this theory , we have seen that the periodic waves with the wavelength larger than a certain critical value are spectrally stable for small mass ratios . numerical computations are developed to show that the stability of these periodic waves with larger wavelengths extends all way to the limit of equal mass ratio . on the other hand , we have also computed periodic travelling waves that are continued from solutions of the granular monomer chains at the equal mass ratio , their spectral stability , and their terminations for smaller mass ratios .    among open problems , we have not clarified the nature of bifurcation , where the solutions of branch 2 terminate at a @xmath412 for @xmath413 . we have not been able to find another solution nearby for @xmath414 . safe coalescence of purely imaginary characteristic exponents @xmath170 of opposite krein signatures is also amazing and we have not been able to explain the hidden symmetry that would explain why the eigenvalues at the coalescence point remain semi - simple . these problems as well as analysis of the periodic travelling wave solutions for other values of @xmath39 will wait for further studies .","summary":"we study bifurcations of periodic travelling waves in granular dimer chains from the anti - continuum limit , when the mass ratio between the light and heavy beads is zero . numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads , where periodic travelling waves of granular monomer chains exist .","abstract":"we study bifurcations of periodic travelling waves in granular dimer chains from the anti - continuum limit , when the mass ratio between the light and heavy beads is zero . we show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable . numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads , where periodic travelling waves of granular monomer chains exist ."}
{"article_id":"0807.3956","section_id":"i","document":"astrophysical foreground contaminants are five orders of magnitude brighter than the @xmath6 mk redshifted 21  cm emission expected from neutral hydrogen in the intergalactic medium ( igm ) during the epoch of reionization ( eor ) . these foregrounds will severely complicate planned experiments and the interpretation of their results . galactic synchrotron radiation dominates the sky at radio frequencies near 150 mhz ( @xmath7 ) , accounting for @xmath8 of the 200 to 10,000  k total brightness temperature . extragalactic continuum point sources are also especially strong and numerous , presenting a sea of confused point sources and comprising the bulk of the remaining @xmath9 of the sky brightness temperature . galactic radio recombination lines ( rrls ) and free - free emission from electrons in both the galaxy and the igm will additionally complicate the planned measurements . initial analyses indicated that these foregrounds were an insurmountable obstacle @xcite because their angular variance dominates the expected fluctuations in the redshifted 21  cm background , but subsequent studies have suggested that multi - frequency observations and the application of appropriate statistical techniques should provide methods to separate the foregrounds from the redshifted 21  cm signal by exploiting the large coherence of the foregrounds with frequency @xcite . however , these studies have relied on a number simplifying assumptions , and in particular have neglected complications due to the frequency - dependent instrumental response . the point spread function and instrumental field - of - view are both frequency dependent , and can mix the angular structure that concerned @xcite and @xcite into the frequency direction , masking the eor signal . this transfer of power from the angular to frequency dimensions has been dubbed `` mode - mixing '' , and is a significant concern for redshifted 21  cm measurements .    in this paper we explicitly model the mode - mixing effect for confusion level contaminants and explore ways of minimizing this power transfer into the frequency domain . with these new techniques we show that , for the murchison widefield array ( mwa ) , contamination due to mode - mixing can be reduced well below that of the expected 21  cm signal strength during the reionization epoch for a reasonable foreground model . we begin in @xmath102 by defining our instrument and sky models and establishing the mathematical foundation of the subtraction technique . in @xmath103 we analyze the ability of the method to produce a model of the confusion - level foreground contamination and , in @xmath104 , we show that the input 21  cm power spectrum in our simulations can be recovered to within @xmath1% ( excluding thermal noise uncertainty ) over most scales in the planned mwa measurements . we conclude in @xmath105 with a brief discussion and an analytic approximation to provide context to the results of the simulation . a detailed study of the dependence of this foreground subtraction technique on the properties of the instrument and astrophysical sky has been conducted in parallel by @xcite for cases building on our fiducial mwa measurement framework . in addition , @xcite have recently developed a sophisticated astrophysical foreground model and applied it to analysis of subtraction techniques in the context of the expected antenna configuration of the low frequency array ( lofar ) . their results indicate that lofar should be able to constrain the reionization history over a wide range of redshifts by measuring the variance in image maps from individual spectral channels between 100 and 200  mhz . our present focus is on foreground subtraction in the context of three - dimensional power spectrum measurements including the full frequency - dependent instrumental properties of the mwa , but many of the results of all three investigations are relevant to both measurements and instruments , as well as other active redshifted 21  cm experiments including the precision array to probe the epoch of reionization ( paper ) , the reionization project with the giant metre - wave radio telescope ( gmrt ) , and the future square kilometer array ( ska ) .","summary":"they recover the one - dimensional spherically - binned input redshifted 21  cm power spectrum to within% over the scales probed most sensitively by the mwa ( mpc ) and demonstrate that realistic instrumental effects will not mask the eor signal .","abstract":"subtraction of astrophysical foreground contamination from `` dirty '' sky maps produced by simulated measurements of the murchison widefield array ( mwa ) has been performed by fitting a-order polynomial along the spectral dimension of each pixel in the data cubes . the simulations are the first to include the unavoidable instrumental effects of the frequency - dependent primary antenna beams and synthesized array beams . they recover the one - dimensional spherically - binned input redshifted 21  cm power spectrum to within% over the scales probed most sensitively by the mwa ( mpc ) and demonstrate that realistic instrumental effects will not mask the eor signal . we find that the weighting function used to produce the dirty sky maps from the gridded visibility measurements is important to the success of the technique . uniform weighting of the visibility measurements produces the best results , whereas natural weighting significantly worsens the foreground subtraction by coupling structure in the density of the visibility measurements to spectral structure in the dirty sky map data cube . the extremely dense-coverage of the mwa was found to be advantageous for this technique and produced very good results on scales corresponding to in the-plane without any selective editing of the-coverage ."}
{"article_id":"1208.5189","section_id":"i","document":"quantum descriptions of physical systems begin with the introduction of a vector space , generally defined over the complex number field @xmath2 , with elements of the space associated with states of the physical system under consideration . this space , in the traditional approach , is assumed to be a hilbert space @xmath3 , which for @xmath4-level systems is @xmath5 . the hilbert space @xmath3 possesses a natural inner product @xmath6 , which we denote @xmath7 it is customary to associate a dual - vector @xmath8 to each vector @xmath9 , with the same label @xmath10 , via @xmath11 so that @xmath12 the presence of the inner product allows the definition of hermitian conjugation of linear operators via @xmath13 and that of hermitian operators , to which physical observables are associated , via @xmath14 . it also allows for the definition of unitary operators via @xmath15 under which the states are assumed to evolve . there are two ways for the quantum description to make contact with physical reality . in the first approach , possible outcomes of a measurement of an observable @xmath16 are assumed to be given by its eigenvalues . let us denote the eigenvector associated with eigenvalue @xmath10 by @xmath17 : @xmath18 when the system is in the state represented by @xmath19 , the probability of obtaining the outcome @xmath20 as a result of a measurement of @xmath16 is given by @xmath21 where the sum in the denominator runs over all the eigenvalues of @xmath16 . the hermiticity of @xmath16 ensures that its eigenvalues are all real , and that the eigenvectors are mutually orthogonal and complete . normalizing the state vector and the eigenvectors of @xmath16 so that @xmath22 the above expression for the probability reduces to @xmath23 . there is an alternative way of making contact with reality , which is equivalent to the one above for conventional treatments . one begins with the quantity @xmath24 which is real for hermitan @xmath16 , and interprets the result as the expectation value for the associated observable in the state @xmath25 . if @xmath26 , the expression reduces to @xmath27 . note that this is the standard approach in quantum field theory ( qft ) where all physical predictions are expressed in terms of @xmath4-point correlation functions , _ i.e. _ , the vacuum expectation values of the products of @xmath4 field operators . this is most explicit in the path integral formulation of qft . to recover the probabilistic interpretation of the first approach , one asserts that the probability for obtaining the outcome @xmath10 for the measurement of @xmath16 on the state @xmath28 is given by @xmath29 no absolute values are invoked , and attention is shifted to moments of the relevant observable operator in the state in question ; in particular we do need the expectation values of powers of the operator . for canonical quantum descriptions using the hilbert space @xmath3 , these two starting points lead to identical results . the situation however changes when the underlying space is not a hilbert space . indeed , for spaces for which the inner product is ill - defined , one can expect different outcomes for these two approaches .    in refs . @xcite and @xcite ( inspired by @xcite , @xcite , and @xcite ) , we have explored the possibility of discretizing the fields over which the vector space is defined but retaining the physical interpretation provided by the first approach , namely , the definition of probabilities via eq . ( [ probdef ] ) . the fields we considered were finite galois fields @xmath30 , where @xmath31 and @xmath32 is a prime number . for the @xmath33 case , they are @xmath34 . vector spaces over @xmath30 do not have inner products since @xmath30 is not an ordered field , preventing any bilinear map to @xmath30 from being positive - definite ( or non - negative ) in a natural way . however , it was recognized that for eq . ( [ probdef ] ) to make sense , the dual - vectors that appear in the expression only need to constitute a basis for the dual - vector space with a possible outcome of a measurement associated with each one . the usual pairing of dual - vectors with vectors via the inner product is inessential . indeed , all the inner product does , in a sense , is connect the two approaches via the property @xmath35 so that we can write , @xmath36 where we have made the identification @xmath37 thus , for the first approach , inner products are not necessary , and once a basis of the dual - vector space and the associated set of outcomes is specified , we have an ` observable . '    to make contact with the outcome of measurements and probability distributions , we need a map from the galois field to that of non - negative reals . it is essential that this map preserves products , which is necessary to distinguish entangled states from product ones , and also for the actions of symmetry groups on the galois field . this is achieved in @xcite and @xcite through an absolute value function . ( [ probdef ] ) can be used as is to define the probability of each outcome via the absolute value function from @xmath30 to @xmath38 given by @xmath39 here , numbers and symbols with underlines are used to denote elements of @xmath30 , to distinguish them from elements of @xmath38 . note that this function is product preserving , i.e. @xmath40 , which is essential for probabilities of product states to factorize . applying this formalism to 2-level systems , we constructed spin - like observables for which the measurement outcomes were @xmath41 , and calculated the clauser - horne - shimony - holt ( chsh ) @xcite ( see also @xcite ) bound for the model and found that it was two , despite the fact that no hidden variable mimic could reproduce the model s predictions . for details , see refs . @xcite and @xcite .    in this paper , we explore consequences of starting with the second approach to interpretation , namely , the definition of expectation values via eq . ( [ evdef ] ) . again , we consider vector spaces over the finite galois field @xmath30 , which do not have inner products . thus , the concepts of normalizability of states , hermiticity of operators , and a dual - vector as a hermitian conjugate of a vector , must all be reexamined before we can apply eq . ( [ evdef ] ) . furthermore , working in a vector space over @xmath30 , the expression @xmath42 will generically lead to an element of @xmath30 , which must be mapped to an element of @xmath38 if the result is to represent the expectation value of a measurement of a physical observable . while we obtain results similar to our earlier ones for certain fields , we discover significant differences in others .    in the following , we will address these points one by one and define a ` mutant ' qm on vector spaces over the fields @xmath43 and then @xmath44}$ ] , where @xmath45 is the solution to the equation @xmath46 , which is irreducible in @xmath0 . in both cases , we will find that @xmath47 by construction , which will be mapped to a number in @xmath38 . because we are looking at the expectation values of observables , the range of this map need not be restricted to the non - negative reals as in the case of the absolute value function . in appendix b we show that the requirement that this map preserve products and actions of symmetry groups determines the map uniquely . it is the use of this map for specific expectation values , instead of the absolute value function on brackets , that distinguishes between the two approaches to interpretation . we will show below that the connection to probabilities given by eq . ( [ pdelta ] ) for canonical qm is no longer valid . in fact , individual probability distributions are not fixed in our approach , giving rise to indeterminacies beyond those of canonical qm . our earlier result in refs . @xcite and @xcite that the chsh bound for spin - like systems over galois fields can not be larger than 2 was predicated upon using the first approach starting with eq . ( [ probdef ] ) . we will find that in the second approach , the chsh bound for the @xmath0 case is also 2 . for the @xmath1 case , however , the chsh bound is 4 , the maximum possible value . as far as we are aware of , this is one of the first explicit examples of a non - trivial super - quantum theory .    before we proceed to the heart of the matter , we note that consideration of discrete mathematical structures is not only relevant from an academic point of view . we note that such considerations have been seriously undertaken in various approaches to the quantum structure of space and time , i.e. in various forms of quantum gravity . the more complete literature can be found in @xcite . the outline of the paper is as follows : in section ii we introduce what we call biorthogonal quantum mechanics , and in section iii we present a few examples of this construction . then in section iv we consider the chch bound and find an explicit example of a super - quantum theory . in section v we show that in such a theory probabilities are indeterminate . we close in section vi with detailed comments about the physical relevance of our results . various details not covered in the main text are presented in two appendices .","summary":"we propose mutant versions of quantum mechanics constructed on vector spaces over the finite galois fields and . the mutation we consider here is distinct from what we proposed in previous papers on galois field quantum mechanics . in this new mutation , the canonical expression for expectation values is retained instead of that for probabilities . in fact , probabilities are indeterminate . furthermore , it is shown that the mutant quantum mechanics over the finite field exhibits super - quantum correlations ( i.e. the bell - clauser - horne - shimony - holt bound is 4 ) .","abstract":"we propose mutant versions of quantum mechanics constructed on vector spaces over the finite galois fields and . the mutation we consider here is distinct from what we proposed in previous papers on galois field quantum mechanics . in this new mutation , the canonical expression for expectation values is retained instead of that for probabilities . in fact , probabilities are indeterminate . furthermore , it is shown that the mutant quantum mechanics over the finite field exhibits super - quantum correlations ( i.e. the bell - clauser - horne - shimony - holt bound is 4 ) . we comment on the fundamental physical importance of these results in the context of quantum gravity ."}
{"article_id":"1208.5189","section_id":"c","document":"one of the simplest realization of how quantum theory differs from its classical counterpart is given by the celebrated bell inequalities , or its slightly generalized version , the chsh inequalities @xcite . according to these inequalities the classical and quantum physics are clearly separated by @xmath148 effects . it has been pointed out in the literature that the purely statistical reasoning leads to the maximal `` super - quantum bound '' of 4 @xcite . in one of our previous papers we have pointed out the special nature of such a super - quantum theory @xcite . given the fact that the chsh inequalities rely on the knowledge of expectation values ( and not probabilities ) in this paper we have focused on the requirement that expectation values of a super - quantum theory should satisfy the bound of 4 . note that our present work is distinguished from other efforts that try to eliminate theories which violate the quantum bound or which claim the uniqueness of the canonical complex quantum theory because of the supposed unphysical nature of super - quantum theories ( see @xcite ) . as is well known , the expectation values and the probabilities are related by a quadratic map in canonical quantum theories and its real counterparts @xcite . that this map is quadratic can be argued on general grounds , and the robustness of the born rule @xcite , by pointing out the generic nature of the fisher metric on the space of measured events @xcite . the chsh observable relies only on the computation of the expectation values . in order to achieve the super - quantum bound of 4 , one immediately realizes ( at least on a heuristic level ) that the expectation values should be `` mutated '' so that the last term in the chsh observable changes its sign . given the canonical relation between the expectation values and the probabilities , such a `` mutation '' of the computation of the expectation values would , at least naively , influence the probabilities as well . this is precisely what we find in a concrete mathematical model explored in this paper : the chsh observable computed in the mutant quantum mechanics over the finite field @xmath1 is explicitly equal to 4 , which in turn implies that the probabilities are indeterminate in such a super - quantum theory . indeterminate probabilities are a consequence of our construction and , in this particular case , a necessary feature of such a super - quantum theory . note that this statement also goes against some efforts in the foundations of quantum theory , which try to base the canonical complex quantum theory solely on the concept of probability ( see for example @xcite ) . our point is that even though canonical quantum theory might be solely based on the concept of probability , super - quantum theory does not have to be . this reinforces the experience of modern qft ( especially the conformal qft s ) in which one operates only with correlation functions .    in appendix a , we show that , in the context of galois biorthogonal qm , the projective orthogonal and the projective unitary groups play the natural role of the orthogonal and unitary groups of canonical qm . this maintains a parallel with our previous papers on galois field qm @xcite where we have shown that the complex ( and real ) projective spaces , which define the geometry of canonical quantum theory , can be naturally replaced by their finite projective counterparts . similarly , in this work , the orthogonal and unitary groups that define the invariance of expectation values in the real and complex quantum theories are replaced by their projective counterparts . it is of course tempting to contemplate that the general structure of biorthogonal systems , the graded valuation of expectation values , and the indeterminate nature of probabilities is valid for more general constructions of super - quantum theories , including the ones that we expect to be relevant in quantum theory of gravity .    to summarize : in this paper we have presented perhaps the simplest model for quantum super - correlations . quantum super - correlations are realized in the model together with a signature feature : the physics of the model is entirely determined in terms of expectation values , whereas the probabilities are , in general , indeterminate . this feature is actually quite natural ( and desirable ) from various point of view suggested by different modern avenues of fundamental physics . we note that the fact that the probabilities are indeterminate in our explicit construction also meshes well with some expectations from various attempts at quantum theory of gravity ( including the ones in which conformal field theories are used to define a quantum theory of gravity in particular asymptotic geometries . ) indeed , that fundamental quantum theories can be defined in terms of expectation values ( which is most obvious in the path integral formulation ) , is a feature found in modern conformal field theories , which are quantum field theory formulated from a purely algebraic viewpoint , without the use of lagrangians ( or hamiltonians ) or feynman rules . for example , the familiar s - matrix of the canonical quantum field theory , which comes about from compounding expectation values ( correlation functions ) with wave - functions of external probes , is not a well - defined concept in conformal field theory . as is well known , conformal field theories , can be dual to ( quantum ) gravitational theories in certain background ( the ads spaces @xcite , and also in the context of the observed cosmological de sitter spacetimes @xcite ) . thus , this feature should be relevant in the context of quantum gravity as well . indeed , different approaches to non - perturbative quantum gravity and quantum cosmology @xcite , suggest that the individual probability for specific measurements could be indeterminate , and that the observables in that context are different from the usual observables found in the canonical quantum theory . the model considered here should be viewed as a concrete realization of this general expectation . the model sheds new light on the foundations of quantum theory , and attempts to understand the simplest set of reasonable axioms that lead to canonical quantum theory , which could lead to natural generalizations of quantum theory expected in the context of quantum theory of gravity @xcite .    finally , we note that this work presents an alternative pathway to constructing a quantum theory on a vector space without an inner product from the one introduced in refs . application of the two constructions to banach spaces @xcite would be a natural place to further clarify the difference between the two approaches , do away with the product preserving map from @xmath80 to @xmath38 , and search for models which may serve as closer representations of reality where various quantum gravitational ideas discussed above can be explored . we will return to these , and related issues in future works . we would like to thank rafael sorkin and chia tze for informative discussions . zl , dm and tt are supported in part by the u.s . department of energy , grant de - fg05 - 92er40677 , task a. dm thanks the perimeter institute and the aspen center for physics for providing stimulating working environments during the completion of this paper .","summary":"we comment on the fundamental physical importance of these results in the context of quantum gravity .","abstract":"we propose mutant versions of quantum mechanics constructed on vector spaces over the finite galois fields and . the mutation we consider here is distinct from what we proposed in previous papers on galois field quantum mechanics . in this new mutation , the canonical expression for expectation values is retained instead of that for probabilities . in fact , probabilities are indeterminate . furthermore , it is shown that the mutant quantum mechanics over the finite field exhibits super - quantum correlations ( i.e. the bell - clauser - horne - shimony - holt bound is 4 ) . we comment on the fundamental physical importance of these results in the context of quantum gravity ."}
{"article_id":"0801.1217","section_id":"i","document":"blazars represent a small subset of the most enigmatic class of radio - loud active galactic nuclei ( agn ) , exhibiting strong variability at all wavelengths of the whole electromagnetic ( em ) spectrum , strong polarization from radio to optical wavelengths , and usually core dominated radio structures . the radiation of blazars at all wavelengths is predominantly nonthermal . this class includes bl lacertae ( bl lac ) objects and flat - spectrum radio quasars ( fsrqs ) . bl lacs show largely featureless optical continuum . in a unified model of the radio - loud agn based on the angle between the line of sight and the emitted jet from the source , blazars jet make angle of @xmath2 10@xmath3 from the line of sight ( urry & padovani 1995 ) . the radiation emitted by the plasma , with bulk relativistic motion in the jet oriented at small viewing angles , is affected by relativistic beaming , which in turn implies a shortening of time scales by a factor @xmath4 , where @xmath5 is the doppler factor .    from observations of blazars , it is known that they vary on the diverse time scales . variability time scales of blazars can be broadly divided into 3 classes viz . intra - day variability ( idv ) or micro - variability , short term outbursts and long term trends . significant variations in flux of a few tenths of magnitude over the course of a day or less is often known as idv ( wagner & witzel 1995 ) . short term outburst and long term trends can have time scales range from few weeks to several months and several months to years , respectively . in last about two decades , variability of blazars in radio to optical bands on diverse time scales have been reported in a large number of papers ( e.g. miller et al . 1989 ; courvoisier , et al . 1995 ; heidt & wagner 1996 ; takalo et al . 1996 ; sillanp@xmath6 et al . 1996a , 1996b ; bai , et al . 1998 , 1999 ; fan et al . 1998 , 2002 , 2007 ; xie , et al . 2002a ; gupta et al . 2004 ; ciprini et al . 2003 , 2007 and references therein ) . we selected a sample of a dozen blazars which are prominent candidates for simultaneous multi - wavelength observing campaigns in their outburst phase . the motivation of the present work was to observe these blazars in search for idv , short term variability and also find out if there is any one being in the outburst state . blazar emission mechanism in the outburst state and detected idv is strongly supported by the jet based models of radio - loud agn . in general , blazar emission in the outburst state is nonthermal doppler boosted emission from jets ( blandford & rees 1978 ; marscher & gear 1985 ; marscher et al . 1992 , hughes et al . there are other models of agn that can explain the idv in any type of agn are optical flares , disturbances or hot spots on the accretion disk surrounding the black hole of the agn ( mangalam & wiita 1993 and references therein ) . models based on the instabilities on accretion disc are mainly supported blazars idv when the blazar is in the low - state . when a blazar is in the low - state , any contribution from the jets if at all present , is very weak . recently , it is noticed that , in the low luminosity agn , accretion disk is radiatively inefficient ( chiaberge et al . 2006 ; capetti et al . 2007 ) . so , there will be an alternative way to explain the idv in the low - state of blazars , in which a weak jet emission will be responsible for the idv . with this motivation we recently carried out optical photometric observations of the nine blazars : s2 0109@xmath1224 , ao 0235@xmath1164 , s5 0716@xmath1714 , pks 0735@xmath1178 , oj 287 , on 231 , 3c 279 and 1es 2344@xmath1514 in r passband and 3c 454.3 in v and r passbands . the paper is arranged as follows : section 2 describes observations and data analysis method , in section 3 we mentioned our results , discussion and conclusion of the present work is reported in section 4 .","summary":"we selected a sample of a dozen blazars which are the prime candidates for simultaneous multi - wavelength observing campaigns in their outburst phase . we searched for optical outbursts , intra - day variability and short term variability in these blazars . we observed densely sampled 1534 image frames of these nine blazars . out of six nights of observations of 3c 454.3 , intra - day variability was detected in three nights . , we found that the predicted optical outburst with the time interval of 8 years in ao 0235 and 3 years in s5 0716 have possibly occurred .","abstract":"we selected a sample of a dozen blazars which are the prime candidates for simultaneous multi - wavelength observing campaigns in their outburst phase . we searched for optical outbursts , intra - day variability and short term variability in these blazars . we carried out optical photometric monitoring of nine of these blazars in 13 observing nights during our observing run october 27 , 2006 march 20 , 2007 by using the 1.02 meter optical telescope equipped with ccd detector and bvri johnson broad band filters at yunnan astronomical observatory , kunming , china . from our observations , our data favor the hypothesis that three blazars : ao 0235 , s5 0716 and 3c 279 were in the outburst state ; one blazar : 3c 454.3 was in the post outburst state ; three blazars : s2 0109 , pks 0735 and oj 287 were in the pre / post outburst state ; one blazar : on 231 was in the low - state ; and the state of one blazar : 1es 2344 was not known because there is not much optical data available for the blazar to compare with our observations . we observed densely sampled 1534 image frames of these nine blazars . out of three nights of observations of ao 0235 , intra - day variability was detected in two nights . out of five nights of observations of s5 0716 , intra - day variability was detected in two nights . in one night of observations of pks 0735 , intra - day variability was detected . out of six nights of observations of 3c 454.3 , intra - day variability was detected in three nights . no intra - day variability was detected in s2 0109 , oj 287 , on 231 , 3c 279 and 1es 2344 in their 1 , 4 , 1 , 2 and 1 nights of observations respectively . ao 0235 , s5 0716 , oj 287 , 3c 279 and 3c 454.3 were observed in more than one night and short term variations in all these blazars were also noticed . from our observations and the available data , we found that the predicted optical outburst with the time interval of 8 years in ao 0235 and 3 years in s5 0716 have possibly occurred ."}
{"article_id":"0801.1217","section_id":"c","document":"from our observations , our data favor the hypothesis that three blazars : ao 0235@xmath1164 , s5 0716@xmath1714 and 3c 279 were in the outburst state ; one blazar : 3c 454.3 was in the post outburst state ; three blazars : s2 0109@xmath1224 , pks 0735@xmath1178 and oj 287 were in the pre / post outburst state ; one blazar : on 231 was in the low - state ; and the state of one blazar : 1es 2344@xmath1514 was not known because there is not much optical data available for the blazar . the available statistics is not sufficient to draw strong conclusions . detected outburst phase in ao 0235@xmath1164 possibly confirms the @xmath2 8 years period in optical bands which was predicted by raiteri et al . ( 2006b ) . ao 0235@xmath1164 has shown idv on two night out of 3 nights of observations . one night in which we did not detected any idv , observations duration were very short and no idv could be detected ( if it has really occurred on that night ) . idv can be broadly divided into intrinsic and extrinsic classes . extrinsic idv is caused by refractive interstellar scintillation and only relevant in the low - frequency radio observations . another extrinsic cause of idv is gravitational micro - lensing . optical imaging and spectroscopic observations of the source have revealed foreground absorbing systems at z = 0.524 and z = 0.851 ( cohen et al . 1987 ; nilsson et al . the flux of the source is contaminated and absorbed by foreground absorbing systems , the stars of which can act as gravitational micro - lenses . the reported optical idv in ao 0235@xmath1164 is well suited by the gravitational micro - lensing . day to day variations are also noticed in our observations in the blazar .    out of 5 nights observations of s5 0716@xmath1714 , idv is detected in 2 nights of observations . day to day variations are distinctly visible in all 5 nights of observations which confirms the variability detection on short time scale . detected outburst possibly confirm the long term periodic variation time scale of 3.0@xmath220.3 years . idv reported in s5 0716@xmath1714 is intrinsic one . the dominantly fundamental model for intrinsic variability is shocks propagating through the jet ( blandford & k@xmath29nigl 1979 ; marscher & gear 1985 ) . models to explain intrinsic idv are based on a relativistic shock propagating down a jet and interacting with irregularities in the flow ( marscher et al . 1992 ) or relativistic shocks changing directions in the jet ( nesci et al . another related model involves non - axisymmetric bubbles carried outward in relativistic magnetized jets ( camenzind & krockenberger 1992 ) . the idv reported here in s5 0716@xmath1714 can be explained by any one of these models .    out of 2 nights observations of 3c 279 , idv is not detected . day to day variations are shown in our two nights of observations of the source which confirms the variability detection on short time scale . we detected short term variation of @xmath2 1.5 magnitude in r passband in 42 days which is much larger than the earlier detected short term variation of 0.91 magnitude in 49 days ( xie et al . when we observed 3c 279 , the source was in outburst / high - state . in the densely sampled light curves in search for idv in the source at outburst / high - state has not shown any idv . no idv detection in 3c 279 shows the jet emission do not have any irregularities in the jet flow , relativistic shocks directions have also not changed from the line of sight , no non - axisymmetric bubbles were carried outward in the relativistic magnetized jets . two other blazars : pks 0735@xmath1178 and 3c 454.3 have shown idv in our observations . 3c 454.3 was in the post outburst phase and pks 0735@xmath1178 was in the pre / post outburst phase during our observations . the idv detected in these two blazars is well suited for shock - in - jet models described above . in 3c 454.3 , we have also noticed the short term variability . no idv was detected in s2 0109@xmath1224 , oj 287 , on 231 and 1es 2344@xmath1514 in our observations . in oj 287 , we have noticed the short term variability . we thankfully acknowledge the critical comments by the referee which helped us to improve the paper significantly . we are thankful to prof . w. yuan for careful reading of the manuscript . acg and jmb gratefully acknowledge the financial support from the national natural science foundation of china ( grant nos . nsfc 10533050 and nsfc 10573030 ) . jhf s work is supported by the national natural science foundation of china ( grant nos . nsfc 10573005 and nsfc 10633010 ) . andruchow , i. , cellone , s. a. , romero , g. e. , et al . 2003 , a&a , 409 , 857 bach , u. , 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xie , g. z. , li , h. k. , zhang , x. et al . 1999 , apj , 522 , 846 xie , g. z. , zhou , s. b. , dai , b. z. , et al . 2002a , mnras , 329 , 689 xie , g. z. , liang , e. w. , zhou , s. b. , et al . 2002b , mnras , 334 , 459 zhang , x. , zhang , l. , zhou , g. , et al . 2004 , aj , 128 , 1929 zhang , x. , zhao , g. , zheng , y. g. , et al . 2007 , aj , 133 , 1995    cccccccc s2 0109@xmath1224 & 01 12 05.7 & @xmath122 44 39.2 & @xmath170.4 & 11.01.2007 & r & 80 & 3.00 + ao 0235@xmath1164 & 02 38 38.9 & @xmath116 36 59.3 & 0.94 & 09.01.2007 & r & 4 & 0.26 + & & & & 10.01.2007 & r & 79 & 3.04 + & & & & 19.03.2007 & r & 6 & 0.40 + s5 0716@xmath1714 & 07 21 53.5 & @xmath171 20 36.4 & 0.3 ? , 0.52 ? & 10.01.2007 & r & 116 & 3.03 + & & & & 12.01.2007 & r & 185 & 3.56 + & & & & 23.02.2007 & r & 60 & 1.00 + & & & & 19.03.2007 & r & 82 & 1.58 + & & & & 20.03.2007 & r & 195 & 4.24 + pks 0735@xmath1178 & 07 38 07.4 & @xmath117 42 19.0 & 0.424 & 11.01.2007 & r & 90 & 3.88 + oj 287 & 08 54 48.9 & @xmath120 06 31.0 & 0.306 & 29.10.2006 & r & 15 & 1.14 + & & & & 17.11.2006 & r & 18 & 1.18 + & & & & 18.11.2006 & r & 16 & 1.06 + & & & & 10.01.2007 & r & 49 & 1.79 + on 231 & 12:21:31.7 & @xmath128:13:58.5 & 0.102 & 11.01.2007 & r & 72 & 3.24 + 3c 279 & 12 56 11.2 & @xmath005 47 21.5 & 0.5362 & 12.01.2007 & r & 208 & 4.00 + & & & & 23.02.2007 & r & 100 & 2.35 + 3c 454.3 & 22 53 57.7 & @xmath116 08 54.0 & 0.859 & 27.10.2006 & r , v & 15,9 & 1.59 + & & & & 28.10.2006 & r , v & 15,8 & 1.27 + & & & & 29.10.2006 & r , v & 15,10 & 1.76 + & & & & 30.10.2006 & r , v & 14,2 & 1.10 + & & & & 09.01.2007 & r & 11 & 0.68 + & & & & 10.01.2007 & r & 7 & 0.54 + 1es 2344@xmath1514 & 23 47 04.8 & @xmath151 42 17.9 & 0.044 & 12.01.2007 & r & 53 & 1.89 +    cccc s2 0109@xmath1224 & i & 12.11 ( 0.04 ) & 1 + & c1 & 14.72 ( 0.06 ) & 1 + & d & 14.09 ( 0.05 ) & 1 + & e & 14.94 ( 0.05 ) & 1 + ao 0235@xmath1164 & 1 & 12.69 ( 0.02 ) & 2 + & 2 & 12.23 ( 0.02 ) & 2 + & 3 & 12.48 ( 0.03 ) & 2 + & 6 & 13.64 ( 0.04 ) & 3 + & c1 & 14.23 ( 0.05 ) & 3 + s5 0716@xmath1714 & 2 & 11.12 ( 0.01 ) & 4 + & 3 & 12.06 ( 0.01 ) & 4 + & 5 & 13.18 ( 0.01 ) & 4 + & 6 & 13.26 ( 0.01 ) & 4 + & 8 & 13.79 ( 0.02 ) & 4 + pks 0735@xmath1178 & c & 13.85 ( 0.04 ) & 5 + & c1 & 12.89 ( 0.04 ) & 5 + & c2 & 12.79 ( 0.04 ) & 5 + & c4 & 13.80 ( 0.04 ) & 5 + & c7 & 14.70 ( 0.06 ) & 5 + oj 287 & c1 & 15.50 ( 0.07 ) & 6 + & c2 & 15.66 ( 0.08 ) & 6 + & 4 & 13.74 ( 0.04 ) & 6 + & 10 & 14.34 ( 0.05 ) & 6 + & 11 & 14.65 ( 0.05 ) & 6 + on 231 & a & 11.72 ( 0.04 ) & 6 + & c1 & 16.03 ( 0.10 ) & 6 + & d & 13.86 ( 0.04 ) & 6 + 3c 279 & 1 & 12.05 ( 0.02 ) & 7 + & 5 & 15.47 ( 0.02 ) & 7 + & 8 & 14.44 ( 0.00 ) & 8 + 3c 454.3 & 1 & 13.15 ( 0.02 ) & 7 + & 2 & 13.19 ( 0.02 ) & 7 + & 3 & 14.00 ( 0.02 ) & 7 + & 4 & 14.79 ( 0.02 ) & 7 + & 5 & 14.83 ( 0.02 ) & 7 + & 6 & 14.83 ( 0.03 ) & 7 + & 7 & 14.94 ( 0.02 ) & 7 + & 8 & 15.34 ( 0.02 ) & 7 + 1es 2344@xmath1514 & c1 & 12.25 ( 0.04 ) & 3 + & c2 & 14.20 ( 0.05 ) & 3 + & c2 & 15.40 ( 0.08 ) & 3 + blazar & star & v magnitude & reference@xmath31 + & no . & ( error ) & + 3c 454.3 & 1 & 13.71 ( 0.02 ) & 7 + & 2 & 13.80 ( 0.02 ) & 7 + & 3 & 14.44 ( 0.02 ) & 7 + & 4 & 15.21 ( 0.02 ) & 7 + & 5 & 15.30 ( 0.02 ) & 7 + & 6 & 15.34 ( 0.03 ) & 7 + & 7 & 15.74 ( 0.02 ) & 7 + & 8 & 15.94 ( 0.02 ) & 7 +    ccccccccccc 11.01.2007 & s2 0109@xmath1224 & 11.36 @xmath0 14.35 & r &  80 & 0.007 & 0.008 & 0.007 & nv & 1.07 &  + 09.01.2007 & ao 0235@xmath1164 & 12.60 @xmath0 12.86 & r &  4 & 0.007 & 0.009 & 0.004 & nv & 2.00 &  + 10.01.2007 & & 13.10 @xmath0 16.14 & r &  79 & 0.029 & 0.029 & 0.007 &  v & 4.14 & 13.7 + 19.03.2007 & & 11.96 @xmath0 12.36 & r &  6 & 0.040 & 0.042 & 0.011 &  v & 3.73 &  9.5 + 10.01.2007 & s5 0716@xmath1714 & 16.34 @xmath0 19.37 & r & 116 & 0.009 & 0.009 & 0.005 & nv & 1.80 &  + 12.01.2007 & & 13.92 @xmath0 17.71 & r & 185 & 0.019 & 0.021 & 0.007 &  v & 2.86 & 6.3 + 23.02.2007 & & 12.22 @xmath0 13.22 & r &  60 & 0.016 & 0.015 & 0.004 &  v & 3.88 &  5.2 + 19.03.2007 & & 12.60 @xmath0 14.18 & r &  82 & 0.006 & 0.013 & 0.010 & nv & 0.95 &  + 20.03.2007 & & 11.99 @xmath0 16.25 & r & 195 & 0.023 & 0.027 & 0.016 & nv & 1.56 &  + 11.01.2007 & pks 0735@xmath1178 & 14.57 @xmath0 18.45 & r &  90 & 0.012 & 0.012 & 0.003 &  v & 4.00 &  4.9 + 29.10.2006 & oj 287 & 19.58 @xmath0 20.72 & r &  15 & 0.027 & 0.044 & 0.049 & nv & 0.72 &  + 17.11.2006 & & 21.58 @xmath0 22.76 & r &  18 & 0.006 & 0.008 & 0.007 & nv & 1.00 &  + 18.11.2006 & & 21.69 @xmath0 22.75 & r &  16 & 0.013 & 0.028 & 0.028 & nv & 0.73 &  + 10.01.2007 & & 19.61 @xmath0 21.40 & r &  49 & 0.016 & 0.016 & 0.015 & nv & 1.07 &  + 11.01.2007 & on 231 & 18.93 @xmath0 22.17 & r &  72 & 0.010 & 0.009 & 0.009 & nv & 1.06 &  + 12.01.2007 & 3c 279 & 18.96 @xmath0 22.96 & r & 208 & 0.008 & 0.010 & 0.009 & nv & 1.00 &  + 23.02.2007 & & 17.82 @xmath0 20.17 & r & 100 & 0.005 & 0.009 & 0.007 & nv & 1.00 &  + 27.10.2006 & 3c 454.3 & 11.76 @xmath0 13.10 & r &  15 & 0.036 & 0.028 & 0.013 & nv & 2.46 &  + & & 12.05 @xmath0 13.35 & v &  9 & 0.022 & 0.023 & 0.011 & nv & 2.05 &  + 28.10.2006 & & 15.06 @xmath0 16.33 & r &  15 & 0.018 & 0.019 & 0.007 &  v & 2.64 &  5.1 + & & 15.44 @xmath0 16.11 & v &  8 & 0.041 & 0.034 & 0.021 & nv & 1.79 &  + 29.10.2006 & & 11.15 @xmath0 12.54 & r &  15 & 0.014 & 0.015 & 0.006 & nv & 2.42 &  + & & 11.44 @xmath0 12.90 & v &  10 & 0.042 & 0.036 & 0.013 &  v & 3.00 & 11.6 + 30.10.2006 & & 11.56 @xmath0 12.66 & r &  14 & 0.013 & 0.012 & 0.006 & nv & 2.08 &  + & & 11.86 @xmath0 11.95 & v &  2 & 0.013 & 0.000 & 0.013 & nv & 0.50 &  + 09.01.2007 & & 11.62 @xmath0 12.30 & r &  11 & 0.059 & 0.056 & 0.015 &  v & 3.83 & 17.1 + 10.01.2007 & & 11.95 @xmath0 12.49 & r &  7 & 0.054 & 0.077 & 0.037 & nv & 1.77 &  + 12.01.2007 & 1es 2344@xmath1514 & 11.61 @xmath0 13.50 & r &  53 & 0.010 & 0.013 & 0.008 & nv & 1.44 &  +    cc blazar name & date + s2 0109@xmath1224 & 11.01.2007 + ut & magnitude + 11.35889 & 14.148 + 11.39917 & 14.155 + 11.43583 & 14.142 + 11.47250 & 14.145 + 11.51083 & 14.139 + 11.54833 & 14.144 + 11.58556 & 14.138 + 11.62194 & 14.140 + 11.65917 & 14.140 + 11.69639 & 14.144 +","summary":"we carried out optical photometric monitoring of nine of these blazars in 13 observing nights during our observing run october 27 , 2006 march 20 , 2007 by using the 1.02 meter optical telescope equipped with ccd detector and bvri johnson broad band filters at yunnan astronomical observatory , kunming , china . from our observations , our data favor the hypothesis that three blazars : ao 0235 , s5 0716 and 3c 279 were in the outburst state ; one blazar : 3c 454.3 was in the post outburst state ; three blazars : s2 0109 , pks 0735 and oj 287 were in the pre / post outburst state ; one blazar : on 231 was in the low - state ; and the state of one blazar : 1es 2344 was not known because there is not much optical data available for the blazar to compare with our observations . out of three nights of observations of ao 0235 , intra - day variability was detected in two nights . out of five nights of observations of s5 0716 , intra - day variability was detected in two nights . in one night of observations of pks 0735 , intra - day variability was detected . no intra - day variability was detected in s2 0109 , oj 287 , on 231 , 3c 279 and 1es 2344 in their 1 , 4 , 1 , 2 and 1 nights of observations respectively .","abstract":"we selected a sample of a dozen blazars which are the prime candidates for simultaneous multi - wavelength observing campaigns in their outburst phase . we searched for optical outbursts , intra - day variability and short term variability in these blazars . we carried out optical photometric monitoring of nine of these blazars in 13 observing nights during our observing run october 27 , 2006 march 20 , 2007 by using the 1.02 meter optical telescope equipped with ccd detector and bvri johnson broad band filters at yunnan astronomical observatory , kunming , china . from our observations , our data favor the hypothesis that three blazars : ao 0235 , s5 0716 and 3c 279 were in the outburst state ; one blazar : 3c 454.3 was in the post outburst state ; three blazars : s2 0109 , pks 0735 and oj 287 were in the pre / post outburst state ; one blazar : on 231 was in the low - state ; and the state of one blazar : 1es 2344 was not known because there is not much optical data available for the blazar to compare with our observations . we observed densely sampled 1534 image frames of these nine blazars . out of three nights of observations of ao 0235 , intra - day variability was detected in two nights . out of five nights of observations of s5 0716 , intra - day variability was detected in two nights . in one night of observations of pks 0735 , intra - day variability was detected . out of six nights of observations of 3c 454.3 , intra - day variability was detected in three nights . no intra - day variability was detected in s2 0109 , oj 287 , on 231 , 3c 279 and 1es 2344 in their 1 , 4 , 1 , 2 and 1 nights of observations respectively . ao 0235 , s5 0716 , oj 287 , 3c 279 and 3c 454.3 were observed in more than one night and short term variations in all these blazars were also noticed . from our observations and the available data , we found that the predicted optical outburst with the time interval of 8 years in ao 0235 and 3 years in s5 0716 have possibly occurred ."}
{"article_id":"1108.2222","section_id":"r","document":"in this section we examine the constraints that can be imposed on general void models in which the bang time is allowed to vary . this generalizes the previous results that were summarized in section [ constraints ] .    as before , the observables we will use to constrain these models are the supernova distance moduli as functions of redshift , the cmb power spectrum on small scales , the local hubble rate , and the kinematic sunyaev - zeldovich effect . the specific data used for each observable will be explained in the subsections that follow . we use the parametrized ltb models of section [ model ] , and a metropolis - hastings markov chain monte carlo ( mcmc ) method to explore parameter space . the likelihood function for each set of parameters is modeled as a chi - squared distribution , such that @xmath91 , and ` goodness of fit ' is quantified by comparing to a @xmath66cdm model with @xmath92 and @xmath93 @xcite . we first proceed by considering each observable individually , and then go on to consider the constraints available from combinations of different observables . it is found that the additional freedom allowed by varying the bang time significantly weakens the constraints that each observable imposes by itself , but that the combined power of all observables is still enough to effectively rule out these models as a possible explanation of dark energy . in particular , we show that neither the cmb+@xmath2 observations , nor the upper bounds on the ksz effect for individual clusters , have the ability to rule out these models by themselves , as is the case when the bang time is assumed to be constant .      in the fits that follow we use the union2 compilation of 557 supernovae , which extends out to @xmath94 @xcite . other supernova data sets also exist , and void fitting procedures are known to exhibit some sensitivity to the data set that is chosen @xcite . we choose the union2 data as it is the most extensive catalog , and the most widely used in the literature . the absolute magnitude of the supernovae in the union2 data set is an unknown parameter , and is therefore fitted to each model individually as a nuisance parameter . we use the published errors in this data set , which includes an ` intrinsic error ' that is added to minimize the reduced @xmath95 of @xmath66cdm . the full union2 `` covariance matrix with systematics '' is used in performing all of the likelihood estimates that follow .    as with @xmath64constant , there is no problem fitting the supernova data without dark energy .      in flrw cosmology , and for our current purposes , the cmb power spectrum can be efficiently specified on small scales with only three pieces of information : ( i ) the acoustic horizon scale at decoupling , ( ii ) the acoustic scale at matter - radiation equality , and ( iii ) the projected scale of the cmb onto our sky . this information can be combined into three parameters in a number of different ways @xcite , but here we choose to specify it as the ` shift parameter ' , @xmath96 , the hubble rate at last scattering , @xmath97 , and the redshift of the last scattering surface , @xmath84 . the shift parameter is defined as @xmath98 , where @xmath99 is the angular diameter distance to the last scattering surface in a fiducial spatially flat flrw model with @xmath100 . this quantity corresponds to the change in scale of fluctuations on the sky that two observers in different space - times would see when looking at two identical last scattering surfaces .     and @xmath97 , found using wmap 7-year data and a modified version of cosmomc @xcite . shaded regions show the 68% , 95% , and 99.7% confidence regions . ]        here , for simplicity , we take @xmath101 , which is the redshift to the last scattering surface in @xmath66cdm and various other models @xcite . to be free would add an extra nuisance parameter to be fitted for in our mcmc runs , which would inevitably loosen the resulting constraints . as such , the cmb constraints we derive here should be considered to be conservative . ] it now remains to impose constraints on @xmath96 and @xmath97 . to do this , we enforce the condition that the region of space in which the last scattering surface forms is well - approximated as being homogeneous and isotropic , so that standard results from flrw cosmology can be applied in dealing with all of the physics up until the formation of the last scattering surface . we can then use cosmomc @xcite to calculate @xmath97 and @xmath102 for an observer in a spatially flat and dust dominated flrw universe looking at this surface . using the space - time geometry of our void models we can then calculate @xmath96 and @xmath2 for an observer at the center of the void looking at an identical last scattering surface , with identical hubble rate at last scattering , and at an identical redshift . this is the procedure followed in @xcite . we use the wmap 7-year data @xcite , with a modified version of cosmomc , to constrain our models . in this analysis we choose to only use data at @xmath103 , as the low-@xmath104 power spectrum is dominated by the isw effect ( see section [ obs - others ] for a brief discussion of this ) . this choice weakens the constraints that can be achieved on the scalar spectral index of the initial power spectrum , @xmath105 . conservatively , we fix @xmath106 here . the constraints that can then be imposed on @xmath96 and @xmath97 are shown in fig . [ fig - shift - constraints ] . the best fit values are found to be @xmath107 and @xmath108 kms@xmath68mpc@xmath68 . these values are consistent with those found in @xcite . note that the cosmomc cmb fits were not performed jointly with the void model mcmc ; instead , they were run beforehand to get likelihoods for @xmath96 and @xmath97 , which we then used as priors for the void model mcmc . as discussed in section [ constraints - cmb ] , it is possible to construct simple void models with @xmath64constant that satisfy the constraints on @xmath96 displayed in fig . [ fig - shift - constraints ] . this can be achieved by simply changing the spatial curvature of the model at large @xmath24 @xcite . the constraints on @xmath97 , however , are more difficult to satisfy . for simple gaussian voids with @xmath64constant , under the assumptions described above , the wmap 7-year data @xcite and the union2 supernova data set @xcite are enough to show that @xmath109 40 kms@xmath68mpc@xmath68 is required , which is in strong disagreement with the value of @xmath110 kms@xmath68mpc@xmath68 found by riess _ _ @xcite . allowing @xmath84 to vary can increase the upper bound on @xmath2 by around 5 kms@xmath68mpc@xmath68 , and changing the precise functional form of @xmath8 can also marginally change @xmath2 ( see @xcite ) . these are relatively small effects , however , and unless one is prepared to reject one or more of the assumptions given in section [ intro ] , models with @xmath64constant remain strongly inconsistent with recent measurements of @xmath2 . allowing the bang time function to vary significantly improves the ability of void models to fit the cmb+@xmath2 data @xcite . in fig . [ fig - sn - cmb - h0 ] we show the likelihood plots for the parameters @xmath111 , when constrained with the wmap 7-year data @xcite , the union2 data set @xcite , and the measurement of @xmath110 kms@xmath68mpc@xmath68 @xcite . good fits to the data are obtained for models with a bang time fluctuation of width 8000 mpc that makes the universe about 800 million years older in the center than it is at large @xmath10 . the curvature profile is narrower than this , with a width of 2500 mpc , and a depth of @xmath112 at the center . the preferred spatial curvature at large radii is only @xmath113 . it can be seen that in this case the model is able to produce an acceptably large value of @xmath2 , with a best - fit value of 73.6 kms@xmath68mpc@xmath68 . when compared to the best - fit @xmath66cdm model we find that @xmath66cdm is slightly preferred , with @xmath114 + 4.5 for 560 degrees of freedom . most of this difference is due to the void model having a poorer fit to the supernova data , even though it over - fits @xmath2 and the cmb data . voids with slightly more complicated spatial curvature profiles produce fits to the data that are at least as good as @xmath66cdm .    in the best fitting models the curvature profile , @xmath8 , is largely responsible for shaping the void at low redshift , with @xmath115 . in this region the bang time gradient is small , and so has little effect . in the region @xmath116 the curvature profile then flattens out and the bang time gradient begins to change rapidly . this produces large fluctuations in @xmath117 along our past null cone , such that @xmath118 can take lower values at large @xmath24 . the low value of @xmath97 required at last scattering can then be simultaneously accommodated with a large value of @xmath2 locally . the difference in profile widths therefore helps to explain how it is that a good fit to the data can be achieved . let us now consider the ksz effect in void models with varying bang times . the void - induced dipole , @xmath71 , can be calculated in an ltb model by following the procedure below :    1 .   on every point on our past null cone , solve the radial null geodesic equation for light rays traveling both into and out of the center of the void . 2 .   calculate the redshift to the last scattering surface along these geodesics using eq . ( [ eqn - redshift - central ] ) . 3 .   calculate the dipole , @xmath72 , using eq . ( [ ksz - dt ] ) . this can be converted into an effective velocity using @xmath119 . this procedure relies on knowing the location of the last scattering surface at different values of @xmath10 . for models with a constant bang time , this surface occurs at a constant time , @xmath120 . in models with varying bang time , however , it will not occur as a hypersurface of constant @xmath11 , as the presence of a bang time gradient changes the time evolution of the radial hubble rate and density at a given @xmath10 . we therefore approximate the location of the last scattering surface as a hypersurface of constant density , @xmath121 , rather than time , @xmath11 . the precise location of the last scattering surface will turn out to be important , and we will discuss the consequences of altering its position as we proceed . we use the upper limits on @xmath122 that have been measured from nine individual clusters @xcite , as collected in @xcite . these clusters span a redshift range of @xmath123 . the data have asymmetric statistical errors , and are subject to large systematic errors of up to @xmath124 kms@xmath68 . for further explanation of the uncertainties in this data set the reader is referred to @xcite . void models with constant @xmath125 have already been shown to be inconsistent with even this limited data set , as we discussed in section [ ksztest ] @xcite . within this class of models , and subject to the assumptions outlined in section [ intro ] , the best fitting voids are those that are either very shallow ( @xmath126 ) or very narrow ( @xmath127 gpc ) , with the latter of these possibilities only working because it restricts the inhomogeneity to redshifts at which there are currently no data . we find that the extra freedom afforded by allowing the bang time to vary relaxes these tight constraints , and admits the possibility of allowing @xmath90 to be small even in regions of the universe that are strongly inhomogeneous , with @xmath128 as large as @xmath129 .    , for models with constant bang time ( dashed blue line ) and non - constant bang time ( solid red line ) . both models have the same spatial curvature , @xmath8 . the data points are the upper limits for the nine clusters used in @xcite . the solid red curve has a bang time fluctuation that is the sum of two gaussians . lower panel : normalized density as a function of @xmath10 on a hypersurface of constant @xmath11 for the same two models . ]    fig . [ fig - ksz - comparison ] shows an example of a large void with varying bang time that produces small enough @xmath90 to be compatible with the data discussed above . a model with the same curvature profile , @xmath8 , but a constant bang time is also displayed . it can be seen that the additional freedom allowed by the varying bang time has a considerable impact on @xmath90 . the energy density profile for this model is also displayed in the figure . one should note , however , that the functional form of the bang time fluctuation required to produce this result is more complicated than the simple profile of eq . [ eqn - tb - profile ] . instead , a sum of two ( modified ) gaussian curves was used , of the form @xmath130 } \\right ) & \\\\ \\nonumber + & a_2 \\exp \\left ( -{\\left [ ( r- r_2)^2/\\lambda^2_2 + ( r- r_2)^{6}/\\lambda^6_2\\right ] } \\right ) , & \\end{aligned}\\ ] ] where @xmath131 , @xmath132 , and @xmath133 are the amplitude , offset from the origin and width of the gaussians respectively . despite the greatly increased freedom in this bang time profile , we were unable to find a model consistent with the ksz and supernova data simultaneously ; the best - fit model had @xmath134 with @xmath66cdm . it is plausible that the situation could be improved by considering yet more complicated functional forms for @xmath8 and @xmath13 , a possibility that we investigate in section [ results - complicated ] . for simplicity , we have assumed in fig . [ fig - ksz - comparison ] that the offset caused by systematic errors in the data is zero . in reality , the data points would likely move slightly toward the curve to which they are being fitted , in order to improve the likelihood . finding models that agree with the upper limits on the statistical ksz from act and spt is a more difficult task . the ksz power spectrum given by @xmath135 , in eq . ( [ eqn - ksz - power ] ) , depends on an integral of @xmath90 over redshift . deviations from @xmath136 at any redshift therefore accumulate , potentially producing a large ksz signal . it is possible that @xmath90 could be made to change sign so that negative contributions cancel the positive ones , but this would require a delicate balancing of the competing effects to satisfy the statistical and single - cluster ksz data simultaneously . one should bear in mind , however , that at large enough @xmath24 , the effect of the void on the observed ksz effect will decrease , as the angle subtended by the void on the distant observer s sky decreases , and the power in the dipole term of the anisotropy is shifted to higher multipoles @xcite .    in summary , we find that large void models with varying bang times may have enough extra freedom available to alleviate the constraints that can currently be imposed from observations of the ksz effect . as we discuss in the following section , however , it is unlikely that after doing this there will be enough remaining freedom to accommodate any other observables . let us now consider combining all of the observables we have discussed so far . these are the union2 supernova data , the wmap 7-year data , local measurements of @xmath2 , and the ksz effect .    in fig . [ fig - ksz - z ] we show the observed value of @xmath71 as a function of @xmath24 that a central observer would measure from the ksz effect in the models found in section [ results - sn - cmb - h0 ] . these models have been shown to provide good fits to the supernova data , and the cmb and @xmath2 data sets simultaneously . in fig . [ fig - ksz - h0 ] we show this information as a function of @xmath2 for redshifts @xmath137 , @xmath138 , @xmath139 , and @xmath140 . at all redshifts considered the distribution was bimodal , with some models having @xmath141 . such incredibly high velocities are completely inconsistent with the data , and so here we show only the models with lower @xmath142 . it can be seen that the value of the ksz signal that one would observe from the center of these models is extremely large , even at low redshift . such enormous ksz signals are not compatible with the data displayed in fig . [ fig - ksz - comparison ] , even with very large additional systematic uncertainties included .     as a function of redshift for the best fitting models to the supernova , cmb and @xmath2 data sets , from section [ results - sn - cmb - h0 ] . the corresponding value of @xmath142 is shown on the right - hand axis . the median and 68% and 95% confidence intervals are shown as the black line , and the light gray and dark gray bands , respectively . the actual distribution is bimodal , and here we show only the models with low @xmath72 . even for low redshifts , @xmath142 is a large fraction of the speed of light . ]     and @xmath143 kms@xmath68mpc@xmath68 , for off - center observers at @xmath137 , @xmath138 , @xmath139 and @xmath144 , for the mcmc sample constrained by sn+cmb+@xmath2 data . ] the principal reason for this large effect appears to be the large width of bang time fluctuation that is favored by the combination of supernova , cmb and @xmath2 data sets ( see fig . [ fig - sn - cmb - h0 ] ) . because of this , observers at @xmath145 look through regions in which the bang time gradient is large when they look through the void . as discussed in section [ tb ] , these regions host shell crossings when @xmath58 . this pushes the surface of last scattering to much later times , and causes significant modifications to the redshift that this surface is seen at when looking through the center of the void . the redshift of the last scattering surface when looking away from the void experiences no such effect , as it is effectively fixed in position by the cmb data we see from the center . as a result , the values of @xmath77 and @xmath78 in eq . [ ksz - dt ] differ significantly , and the value of @xmath71 is therefore even larger than in the constant bang time case . even at low @xmath24 , this is unacceptably high .     and @xmath143 kms@xmath68mpc@xmath68 , for off - center observers at @xmath146 , @xmath140 and @xmath147 , for the mcmc sample constrained by sn+cmb+@xmath2+ksz data . the @xmath72 are much lower than for the mcmc sample in fig . [ fig - ksz - h0 ] , but the hubble rate is too low to be considered consistent with observations . ]      one may now ask whether changing the specific forms of @xmath13 and @xmath8 that we have used so far affects our results . we showed in section [ results - combined ] that very poor agreement with the ksz data is obtained for the models that best - fit the supernova , cmb , and @xmath2 data , but in section [ results - sn - ksz ] we found that a good fit to the ksz data could be obtained if a more complicated bang time profile was used . to see if a good fit to all of the observables is possible with a more complicated model , we ran an mcmc simulation using the spatial curvature profile of eq . ( [ eqn - k - profile ] ) and the extended bang time profile given by eq . ( [ eqn - ksz - complicated ] ) . the mcmc was constrained by the supernova , cmb , @xmath2 , and ksz data simultaneously .    a plot of ksz @xmath72 against @xmath2 for these models is shown in fig . [ fig - ksz - h0-complex ] , and may be compared with fig . [ fig - ksz - h0 ] . the models that maximize the likelihood have a @xmath90 profile that is almost flat over the redshift range of interest ( slightly larger at small @xmath24 ) , and much less discrepant with the ksz data . relatively narrow spatial curvature and bang time profiles are preferred , extending out to only @xmath148 , and the bang time profiles are shifted towards the negative @xmath10 direction ( i.e. @xmath149 in eq . ( [ eqn - ksz - complicated ] ) ) . a preferred @xmath2 of only @xmath150 kms@xmath68mpc@xmath68 is obtained , and the fit to supernova and cmb data is also poor ; the best - fit model is inconsistent with the data , with @xmath151 compared to @xmath66cdm . we conclude that this is because the fit is most sensitive to the ksz data ; it is easy to find models that are wildly inconsistent with the ksz data , as evidenced by fig . [ fig - ksz - h0 ] , and so models that minimize the @xmath95 with the ksz data above all else are preferred . these tend to have low hubble rates and narrow density profiles , features that are difficult to reconcile with the supernova and @xmath2 data . as such , it seems that even with the significantly more complex bang time profile , a good fit to all of the data simultaneously is not possible .    to further investigate the sensitivity of our results to the choice of profile parametrization , we now consider the model found by clrier _ _ in @xcite that was constructed to reproduce the @xmath66cdm values of luminosity distance and hubble rate as a function of redshift , but without dark energy . the density profile on a hypersurface of constant @xmath11 takes the form of a `` hump '' in this model , rather than a void , and the bang time gradient at low @xmath24 is negative , so there are no shell crossings at early times . instead , this model has double - valued redshifts at high @xmath24 ( see section [ tb ] ) , which almost always result in large @xmath71 because @xmath77 and @xmath78 in eq . [ ksz - dt ] differ significantly . as such , this model is also strongly disfavored by current ksz data ( see fig . [ fig - cbk - ksz ] ) . in fact , for large fluctuations in the bang time function we expect that there will _ always _ be a large dipole seen by off - center observers at some range of redshifts , corresponding to lines of sight that pass near to regions with a non - zero bang time gradient . can be seen to fit current ksz data , these data only extend out to @xmath152 . even this model will have a large @xmath90 for some @xmath153 . ] it therefore appears that one can not simultaneously fit the supernova , cmb , @xmath2 and ksz observations with a single ltb model unless one is prepared to violate one or more of the assumptions made in section [ intro ] . , of the ltb model found in @xcite which reproduces the hubble rate , @xmath154 , and luminosity distance , @xmath65 , of @xmath66cdm . lower panel : velocity with respect to frame in which the cmb is isotropic , @xmath90 , for the same ltb model . @xmath155 rapidly becomes very large ( @xmath156 for @xmath157 ) , and produces a very poor fit to the ksz data . ]","summary":"the apparent accelerating expansion of the universe , determined from observations of distant supernovae , and often taken to imply the existence of dark energy , may alternatively be explained by the effects of a giant underdense void if we relax the assumption of homogeneity on large scales . recent studies have made use of the spherically - symmetric , radially - inhomogeneous lematre - tolman - bondi ( ltb ) models to derive strong constraints on this scenario , particularly from observations of the kinematic sunyaev - zeldovich ( ksz ) effect which is sensitive to large scale inhomogeneity . however , most of these previous studies explicitly set the ltb ` bang time ' function to be constant , neglecting an important freedom of the general solutions . we find that although the extra freedom allowed by varying the bang time is sufficient to account for some observables individually , it is not enough to simultaneously explain the supernovae observations , the small - angle cmb , the local hubble rate , and the ksz effect . this set of observables is strongly constraining , and effectively rules out simple ltb models as an explanation of dark energy .","abstract":"the apparent accelerating expansion of the universe , determined from observations of distant supernovae , and often taken to imply the existence of dark energy , may alternatively be explained by the effects of a giant underdense void if we relax the assumption of homogeneity on large scales . recent studies have made use of the spherically - symmetric , radially - inhomogeneous lematre - tolman - bondi ( ltb ) models to derive strong constraints on this scenario , particularly from observations of the kinematic sunyaev - zeldovich ( ksz ) effect which is sensitive to large scale inhomogeneity . however , most of these previous studies explicitly set the ltb ` bang time ' function to be constant , neglecting an important freedom of the general solutions . here we examine these models in full generality by relaxing this assumption . we find that although the extra freedom allowed by varying the bang time is sufficient to account for some observables individually , it is not enough to simultaneously explain the supernovae observations , the small - angle cmb , the local hubble rate , and the ksz effect . this set of observables is strongly constraining , and effectively rules out simple ltb models as an explanation of dark energy ."}
{"article_id":"1108.2222","section_id":"c","document":"in order to rigorously establish that @xmath158 , and that the concordance model of cosmology is correct , a model is required within which observations can be interpreted . the homogeneity and isotropy of the universe on large scales is often assumed , and most analyses are performed using the highly symmetric flrw solutions of general relativity . these are not the only viable ways to model the universe , however , and recent advances in observational cosmology allow us to empirically test alternatives rather than relying on assumed symmetries of space - time on the largest scales . in this paper we used the spherically - symmetric , dust - only lematre - tolman - bondi ( ltb ) class of general relativistic cosmological models , in their full generality , to test the radial homogeneity of the universe on large scales . in particular , we consider the magnitude of the kinematic sunyaev - zeldovich ( ksz ) effect , which measures the dipole anisotropy of the cmb through a shift in the spectrum of cmb photons reflected from hot gas in clusters of galaxies . the ksz effect is sensitive to large - scale inhomogeneity , as observers inhabiting an inhomogeneous universe would generically expect to see large anisotropies on their cmb skies .    in section [ model ] , we introduced the theoretical framework for specifying these models and calculating observables in them . we defined a simple parametrization of the ltb radial function @xmath8 that governs radial inhomogeneity at late times , and the function @xmath13 that governs it at early times . this has been used to investigate underdense ` voids ' which have previously been shown to produce good fits to the supernova data . we have discussed potential problems with models that are inhomogeneous at early times ( i.e. that have non - constant @xmath125 ) , including the potential for disruptions around our observed surface of last scattering . in models with a positive radial derivative of the bang time , @xmath159 , it is found that shell crossing singularities form at early times , which pushes the surface of last scattering to later times . in models with negative bang time gradient , @xmath160 , regions with a negative radial hubble rate , @xmath161 , form and the distance - redshift relation , @xmath62 , ceases to be monotonic . these features have observable effects that ultimately lead to predictions of a large cmb dipole anisotropy at low redshifts . in section [ constraints ] we reviewed some of the observational constraints that can be imposed on void models with constant bang time . three key sets of observables were considered : the distance moduli of supernovae , the small - angle cmb power spectrum plus local hubble rate , and upper limits on the magnitude of the ksz effect for individual clusters of galaxies . voids can fit the supernova data easily , but are unable to fit recent measurements of the cmb and @xmath2 simultaneously ( they predict a value of @xmath2 that is far too low ) . similarly , voids which fit the supernova data predict a large cmb dipole at redshifts up to @xmath162 , which is inconsistent with current ksz measurements .    in section [ results ] we considered the effect on these constraints of allowing the bang time to vary . this resulted in a significant increase in the freedom of the models , and allowed the supernovae and cmb+@xmath2 data sets to be fit simultaneously , even with our simple parametrization of the ltb radial functions . models with small ksz signals , consistent with the data , were also found , but these required more complex profiles and gave worse fits to the supernova data . we then proceeded to combine all of the observational constraints , and found that voids which are able to fit the supernovae , cmb and @xmath2 predict an extremely large ksz effect which is orders of magnitude greater than the measured upper limits . a joint fit to the supernova , cmb , @xmath2 , and ksz data with a significantly more complicated bang time profile also failed to produce good agreement with the data . we also argued that any void model with a significant bang time inhomogeneity will produce a large ksz effect at _ some _ redshift . given that a varying bang time is necessary to resolve the low-@xmath2 problem , it seems that the combination of supernovae , cmb+@xmath2 and ksz data is enough to effectively rule out ltb void models that attempt to explain cosmological data without dark energy , subject to the assumptions made in section [ intro ] . this goes some way toward demonstrating the homogeneity of the universe on large scales . we used the dipole approximation to calculate the magnitude of the ksz effect in our models , but this only holds if the dipole term dominates the anisotropy of an off - center observer s sky @xcite . otherwise , higher multipoles become important , and the dipole approximation overestimates the ksz effect . the dipole will dominate as long as most lines of sight on the observer s sky pass through the void , as will be the case if the observer is firmly inside it , for example . for the models in section [ results - sn - ksz ] and [ results - combined ] , and the clrier _ _ model in section [ results - complicated ] , the inhomogeneity extends out to @xmath163 , and so the dipole approximation will always be a good one for observers at @xmath164 , where the ksz data lie . the models with more complicated bang time profiles considered in section [ results - complicated ] have much narrower inhomogeneities , however , and so we would expect the dipole approximation to be worse . these models predict low ksz magnitudes and are close to being consistent with the ksz data , so any overestimate due to the dipole approximation will have little effect on their total @xmath95 , which is anyway dominated by the poor fits to the supernova , cmb and @xmath2 data . we therefore conclude that the dipole approximation is sufficient for our purposes .    as we have tried to make clear throughout , our results are subject to several caveats that are summarized in section [ intro ] the first , that we are exactly in the center of a perfectly spherically symmetric void , serves to simplify our calculations but is clearly unrealistic as it fails to take into account angular variations in , for example , the galaxy distribution . this could affect observables such as the dipole anisotropy of the cmb seen by off - center observers , potentially weakening the constraints we have derived using the ksz effect . considering ourselves as off - center observers @xcite and introducing linear perturbations @xcite would produce more realistic models and allow more observational data to be used ( e.g. the matter power spectrum ) at the expense of a significant increase in complexity . a better understanding of linear perturbations would also go some way toward addressing our second caveat , that the formation of the last scattering surface must be in an approximately - flrw region . in general , one could expect features such as the coupling of scalar and tensor modes in ltb perturbations to produce secondary effects such as large b - mode polarizations @xcite . this type of effect is completely absent in linear perturbation theory about flrw backgrounds . a particular limitation of ltb solutions as cosmological models is that they contain only dust , and cease to be applicable when radiation becomes important . if we want to approximate the universe as an ltb model at late times , we must therefore match it to an appropriate solution containing radiation at early times . solutions involving separate inhomogeneous matter and radiation fluids @xcite , spatially - varying physical quantities such as the photon - baryon ratio @xcite , and scale - dependent initial power spectra @xcite have been considered , and serve to give some idea of the extra freedom that might be obtained in more general models . specifically , altering the location and properties of the surface of last scattering can have a profound effect on the predicted ksz signal @xcite and the observed cmb @xcite , and if one is prepared to consider this additional freedom , then our present results should not be expected to hold . finally , let us consider ltb models in the context of general inhomogeneity . rather than allowing space - time to be described by a single ltb metric , it has been suggested that the ltb geometry could be used as an effective geometry to model the scale dependence of inhomogeneity after some averaging procedure has been applied to the fine - grained structure of the actual inhomogeneous geometry of the real universe @xcite . this is a considerable departure from the situation we have been considering here . in particular , if other observers are able to construct similar effective spherically symmetric geometries about their own locations then we should no longer expect distant clusters to see a large dipole in their cmb sky . this would completely relax the constraints that can be imposed from observations of the ksz effect .","summary":"here we examine these models in full generality by relaxing this assumption .","abstract":"the apparent accelerating expansion of the universe , determined from observations of distant supernovae , and often taken to imply the existence of dark energy , may alternatively be explained by the effects of a giant underdense void if we relax the assumption of homogeneity on large scales . recent studies have made use of the spherically - symmetric , radially - inhomogeneous lematre - tolman - bondi ( ltb ) models to derive strong constraints on this scenario , particularly from observations of the kinematic sunyaev - zeldovich ( ksz ) effect which is sensitive to large scale inhomogeneity . however , most of these previous studies explicitly set the ltb ` bang time ' function to be constant , neglecting an important freedom of the general solutions . here we examine these models in full generality by relaxing this assumption . we find that although the extra freedom allowed by varying the bang time is sufficient to account for some observables individually , it is not enough to simultaneously explain the supernovae observations , the small - angle cmb , the local hubble rate , and the ksz effect . this set of observables is strongly constraining , and effectively rules out simple ltb models as an explanation of dark energy ."}
{"article_id":"1610.06036","section_id":"i","document":"in the era of space missions such as @xmath0 and @xmath0 - 2 ( k2 ) which have been providing asteroseismic data of unprecedented quality for several types of pulsating stars ( including white dwarfs ) , we decided to revisit the problem of the seismic modeling of this latter type of pulsators using current techniques , typical of those developed quite successfully in recent years for pulsating hot b subdwarfs ( see , e.g. , charpinet et al . 2013 ) . to test these techniques in a white dwarf context , we first carried out a detailed analysis of the pulsation properties of two classical hot zz ceti stars  gd 165 and ross 548  using the best available data from the ground . those targets were chosen on the basis of the simplicity of their light curves ( associated with their locations near the blue edge of the zz ceti instability strip ) , their near spectroscopic twin nature , and the availability of time - series data sets of exceptional quality . the results of that analysis were presented by giammichele et al . ( 2015 ; 2016 ) who found a credible seismic model for each star able to reproduce simultaneously the six observed periods well within  @xmath1 on the average , which is comparable to the best results achieved so far in asteroseismology . the models provided robust mode identification and were found to be perfectly compatible with the expectations of linear pulsation theory in both its adiabatic and nonadiabatic versions . in addition , these seismic models were shown to be consistent with all the available external independent constraints such as estimates of the atmospheric parameters derived from time - averaged spectroscopy , estimates of distances provided by parallax measurements or spectrocopy , and even the measured rate of period change for one mode in ross 548 . the study of giammichele et al . ( 2015 ; 2016 ) thus firmly established that our approach to quantitative seismology  based on static , parametrized models of stars  can be extended reliably to the white dwarf domain . an unexpected result of the study of giammichele et al . ( 2016 ) is the finding that the pulsation periods detected in gd 165 bear only a weak dependence on the core composition , while those observed in ross 548 are , on the contrary , quite sensitive to a variation of the core composition . this a priori puzzling result finds a natural explanation in that all six modes in the gd 165 model have amplitudes and weight functions that do not extend into the deep core and , consequently , their periods are not sensitive to a variation of the core composition . in comparison , three of the six modes of interest in the ross 548 model are partly confined below its thin envelope and , therefore , bear a strong sensitivity on the core composition . this discovery of the existence of deeply confined modes in ross 548 and , potentially , in many other pulsating white dwarfs , opens up the most interesting possibility of using those modes as probes of the internal composition profile in the c - o core . in the giammichele et al . ( 2016 ) study , to keep things as simple as possible , it was assumed that the core composition is homogeneous , which is a crude approximation in the light of the rather complicated c - o stratification expected in the cores of former agb stars as revealed by detailed evolutionary calculations ( see , e.g. , salaris et al . 2010 or romero et al . in retrospect , such an approximation was amply sufficient in the case of gd 165 , but it is now clear that for stars such as ross 548 , with deeply confined modes , our modeling could be perfected by including a parametrized description of the chemical layering in the c - o core . presumably , this would lead to still more realistic seismic models of pulsating white dwarfs , with theoretical periods approaching the `` holy grail '' of asteroseismology , i.e. , perhaps able to reproduce the observed periods at the accuracy of the observations . currently , as indicated above , the best one can do is to obtain average dispersions of less than @xmath2 in periods , still a long way from the measurement uncertainties as indicated , for example , in tables 3 and 4 of giammichele et al . the advent of ultra - high precision photometry from space , in particular with the _ kepler _ mission , further enlarges this gap as some pulsation frequencies can be measured with outstanding precision of the order of nanohertz . six pulsating white dwarfs were extensively monitored with _ kepler _ ( see , e.g. , stensen et al . 2011 ; greiss et al . 2014 , 2015 ) and high precision data for more objects have been ( or will be ) delivered by the still ongoing k2 mission ( hermes et al . 2014 ; howell et al . thus , there are exceptionally high - quality data available for a handful of pulsating white dwarfs that should provide particularly stringent testbeds for asteroseismology . we present , in this paper , a prescription for parametrizing the c - o core of a white dwarf , with the hope of improving future seismic models of stars of this type . we also discuss series of tests that evaluate the precision that can potentially be achieved on stellar and structural parameters with our technique .","summary":"this effort is part of our ongoing quest for more credible and realistic seismic models of white dwarfs using static , parametrized equilibrium structures .","abstract":"we present a prescription for parametrizing the chemical profile in the core of white dwarfs in the light of the recent discovery that pulsation modes may sometimes be deeply confined in some cool pulsating white dwarfs . such modes may be used as unique probes of the complicated chemical stratification that results from several processes that occurred in previous evolutionary phases of intermediate - mass stars . this effort is part of our ongoing quest for more credible and realistic seismic models of white dwarfs using static , parametrized equilibrium structures . inspired from successful techniques developed in design optimization fields ( such as aerodynamics ) , we exploit akima splines for the tracing of the chemical profile of oxygen ( carbon ) in the core of a white dwarf model . a series of tests are then presented to better seize the precision and significance of the results that can be obtained in an asteroseismological context . we also show that the new parametrization passes an essential basic test , as it successfully reproduces the chemical stratification of a full evolutionary model ."}
{"article_id":"1610.06036","section_id":"c","document":"in this paper , we introduced and tested a new parametrization that can replicate smoothly one or two steep `` drops '' in the chemical profile of oxygen in the core of a white dwarf model in order to better reproduce the shape of the stratification usually predicted from evolutionary models . the flexibility of the new two - transition core parametrization was explored and proven to be both necessary and sufficient for recovering the structure expected from evolutionary calculations . to be clear , the evolutionary structures are not reproduced to perfection , but we showed that the method is amply sufficient for testing the most important features of the chemical profile of a white dwarf through asteroseismology . and if need be , in special cases , the flexibility of our approach could also be improved . this new parametrization will be of high interest in upcoming seismic studies of pulsating white dwarfs , particularly those with available _ kepler _ and _ k2 _ data , which we plan to analyze thoroughly with our optimization tools developed for asteroseismology .    for the future , we retain the following lessons from the current work . based on tests generated with random sequences of periods , we can roughly define a conservative threshold of @xmath32 s for the average period dispersion of the best - fit solution above which results from seismic analyses should not be considered as very robust ( i.e. , statistically significant ) . we showed that our seismic method , based on parametrized models in hydrostatic equilibrium , is perfectly capable of retrieving stellar and shape parameters from a reference star with different levels of precision in the `` observational '' data . if the limiting factor was purely observational , i.e. , only governed by the errors in measuring the pulsation frequencies ( periods ) , stellar and shape parameters could be recovered to a remarkable precision . however , although our asteroseismic method gives robust , precise , and accurate constraints on both stellar or shape parameters , the limiting factor is usually not the precision of the observations themselves , but the uncertainties associated with the constitutive physics involved in current stellar models which still dominate the error budget . the latter need to be addressed in order to go beyond current achievements and improve overall the quality of the seismic fits toward solutions that approach the very stringent limit of observational measurement errors . this work was supported in part by the nserc canada through a doctoral fellowship awarded to noemi giammichele , and through a research grant awarded to gilles fontaine . the latter also acknowledges the contribution of the canada research chair program . stphane charpinet acknowledges financial support from `` programme national de physique stellaire '' ( pnps ) of cnrs / insu , france , and from the centre national dtudes spatiales ( cnes , france ) . this work was granted access to the hpc resources of calmip under allocation number 2015-p0205 . akima , h.  1970 , jacm , vol . 17 , no . 4 , 589 althaus , l.  g. , serenelli , a.  m. , crsico , a.  h. , & benvenuto , o.  g.  2002 , , 330 , 685 althaus , l.  g. , crsico , a.  h. , bischoff - 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dalsgaard , j. , et al . 2010 , , 122 , 131 greiss , s. , gnsicke , b.t . , hermes , j.j . , et al . 2014 , , 438 , 3086 greiss , s. , gnsicke , b.t . , hermes , j.j . , et al . 2015 , 19th european workshop on white dwarfs , 493 , 169 hermes , j.j . , mullally , f. , stensen , r.h . , et al .  2011 , , 741 , l16 hermes , j.j . , charpinet , s. , barclay , t. , et al . 2014 , , 789 , 85 landolt , a.u . 1968 , , 153 , 151 matthews , j.m . 2007 , communications in asteroseismology , 150 , 333 mazzitelli , i. , & dantona , f.  1986 , , 308 , 706 mazzitelli , i. , & dantona , f.  1986 , , 311 , 762 metcalfe , t.  s.  2005 , , 363 , l86 michel , e. , baglin , a. , auvergne , m. , et al . 2008 , science , 322 , 558 stensen , r.h . , silvotti , r. , charpinet , s. , et al . 2011 , , 414 , 2860 stensen , r.h . , bloemen , s. , vukovi , m. , et al .  2011 , , 736 , l39 romero , a.d . , crsico , a.h . , althaus , l. , et al . 2012 , mnras , 420 , 1462 salaris , m. , domnguez , i. , garca - berro , e. , et al . 1997 , , 486 , 413 salaris , m. , cassisi , s. , pietrinferni , a. et al . 2010 , apj , 716 , 1241 straniero , o. , domnguez , i. , imbriani , g. , & piersanti , l.  2003 , , 583 , 878 tassoul , m. , fontaine , g. , & winget , d.e . 1990 , apjs , 72 , 335 van grootel , v. , charpinet , s. , brassard , p. , fontaine , g. , & green , e.m . 2013 , , 553 , a97 wood , m.  a.  1992 , , 386 , 539","summary":"we present a prescription for parametrizing the chemical profile in the core of white dwarfs in the light of the recent discovery that pulsation modes may sometimes be deeply confined in some cool pulsating white dwarfs . such modes may be used as unique probes of the complicated chemical stratification that results from several processes that occurred in previous evolutionary phases of intermediate - mass stars . inspired from successful techniques developed in design optimization fields ( such as aerodynamics ) , we exploit akima splines for the tracing of the chemical profile of oxygen ( carbon ) in the core of a white dwarf model .","abstract":"we present a prescription for parametrizing the chemical profile in the core of white dwarfs in the light of the recent discovery that pulsation modes may sometimes be deeply confined in some cool pulsating white dwarfs . such modes may be used as unique probes of the complicated chemical stratification that results from several processes that occurred in previous evolutionary phases of intermediate - mass stars . this effort is part of our ongoing quest for more credible and realistic seismic models of white dwarfs using static , parametrized equilibrium structures . inspired from successful techniques developed in design optimization fields ( such as aerodynamics ) , we exploit akima splines for the tracing of the chemical profile of oxygen ( carbon ) in the core of a white dwarf model . a series of tests are then presented to better seize the precision and significance of the results that can be obtained in an asteroseismological context . we also show that the new parametrization passes an essential basic test , as it successfully reproduces the chemical stratification of a full evolutionary model ."}
{"article_id":"astro-ph9908196","section_id":"i","document":"in this paper we investigate the origin and the consequences of the _ bi - stability jump _ of the stellar winds of early - type stars near spectral type b1 . this bi - stability jump is observed as a steep decrease in the terminal velocity of the winds from @xmath8 for supergiants of types earlier than b1 to @xmath9 for supergiants of types later than b1 ( lamers et al . we will show that this jump in the wind velocity is accompanied by a jump in the mass - loss rate with @xmath7 increasing by about a factor of five for supergiants with  between 27  500 and 22  500 k.    the theory of radiation driven winds predicts that the mass - loss rates and terminal velocities of the winds of early - type stars depend smoothly on the stellar parameters , with @xmath10 and @xmath11 ( castor et al . 1975 , abbott 1982 , pauldrach et al . 1986 , kudritzki et al . this theory has not yet been applied to predict the observed jump in the ratio @xmath0 for supergiants near spectral type b1 . the change from a fast to a slow wind is called the @xmath12-@xmath13 jump . if the wind momentum @xmath14 were about constant across the bi - stability jump , it would imply that the mass - loss rate would _ increase _ steeply by about a factor of two from stars with spectral types earlier than b1 to later than b1 . unfortunately , there are no reliable mass - loss determinations from observations for stars later than spectral type b1 . so far , a physical explanation of the nature of this bi - stability jump has been lacking . in this paper , we attempt to provide such an explanation and we investigate the change in mass - loss rate that is accompanied by the change in @xmath15 . the concept of a bi - stability jump was first described by pauldrach & puls ( 1990 ) in connection to their model calculations of the wind of the luminous blue variable ( lbv ) star p  cygni (= 19.3 kk ) . their models showed that small perturbations in the basic parameters of this star can either result in a wind with a relatively high mass loss , but low terminal velocity , _ or _ in a wind with relatively low , but high . their suggestion was that the mechanism is related to the behaviour of the lyman continuum . if the lyman continuum exceeds a certain optical depth , then as a consequence , the ionization of the metals shifts to a lower stage . this causes a larger line acceleration @xmath16 and finally yields a jump in @xmath7 . the models of pauldrach & puls ( 1990 ) for p cygni show that the wind momentum loss per second , @xmath14 , is about constant on both sides of the jump ( see lamers & pauldrach 1991 ) . so lamers et al . ( 1995 ) put forward the idea that the mass - loss rate for normal stars could increase by about a factor of two , if @xmath15 decreases by a factor of two , so that @xmath14 is constant on both sides of the jump .    whether this is indeed the case , is still unknown . to investigate the behaviour of the mass loss at the bi - stability jump , we will derive mass - loss rates for a grid of wind models over a range in . the main goal of the paper is to understand the processes that cause the bi - stability jump . although our results are based on complex numerical simulations , we have attempted to provide a simple picture of the relevant physics . we focus on the observed bi - stability jump for normal supergiants . nevertheless , these results may also provide valuable insight into the possible bi - stable winds of lbvs . it is worth mentioning that lamers & pauldrach ( 1991 ) and lamers et al . ( 1999 ) suggested that the bi - stability mechanism may be responsible for the outflowing disks around rapidly - rotating b[e ] stars . therefore our results may also provide information about the formation of rotation induced bi - stable disks . the paper is organized in the following way . in sect . [ sec : simple ] we describe the basic stellar wind theory . in particular we concentrate on the question : `` what determines  and ? '' . we show that  is determined by the radiative acceleration in the _ subsonic _ region . in sect . [ sec : method ] we explain the method that we use to calculate the radiative acceleration with a monte carlo technique and the mass - loss rates of a grid of stellar parameters . sect . [ sec : isa ] describes the properties of the models for which we predict . in sect . [ sec : predictions ] our predicted bi - stability jump in mass loss will be presented . then , in sect .  [ sec : origin ] we discuss the origin of this jump and show that it is due to a shift in the ionization balance of fe iv to fe iii . then , we discuss the possible role of the bi - stability jump in  on the variability of lbv stars in sect . [ sec : lbv ] . finally , in sect . [ sec : concl ] , the study will be summarized and discussed .","summary":"we study the origin of the bi - stability jump in the terminal velocity of the winds of supergiants near spectral type b1 . observations show that here the ratio drops steeply from about 2.6 at types earlier than b1 to a value of=1.3 at types later than b2 . to this purpose , we have calculated wind models and mass - loss rates for early - type supergiants in a grid covering the range between and . these models show the existence of a jump in mass loss around for normal supergiants , with  increasing by about a factor five from to 22  500 k for constant luminosity . we argue that the jump in mass loss is accompanied by a decrease of the ratio , which is the observed bi - stability jump in terminal velocity . using self - consistent models for two values of","abstract":"we study the origin of the bi - stability jump in the terminal velocity of the winds of supergiants near spectral type b1 . observations show that here the ratio drops steeply from about 2.6 at types earlier than b1 to a value of=1.3 at types later than b2 . to this purpose , we have calculated wind models and mass - loss rates for early - type supergiants in a grid covering the range between and . these models show the existence of a jump in mass loss around for normal supergiants , with  increasing by about a factor five from to 22  500 k for constant luminosity . the wind efficiency number also increases drastically by a factor of 2  -  3 near that temperature .    we argue that the jump in mass loss is accompanied by a decrease of the ratio , which is the observed bi - stability jump in terminal velocity . using self - consistent models for two values of , we have derived = 2.4 for  = 30 000 k and = 1.2 for  = 17 500 k. this is within 10 percent of the observed values around the jump .    up to now , a theoretical explanation of the observed bi - stability jump was not yet provided by radiation driven wind theory . to understand the origin of the bi - stability jump , we have investigated the line acceleration for models around the jump in detail . these models demonstrate that _  increases around the bi - stability jump due to an increase in the line acceleration of fe  iii _ below _ the sonic point_. this shows that the mass - loss rate of b - type supergiants is very sensitive to the abundance and the ionization balance of iron .    furthermore , we show that the elements c , n and o are important line drivers in the _ supersonic _ part of the wind . the _ subsonic _ part of the wind is dominated by the line acceleration due to fe . therefore , cno - processing is expected _ not _ to have a large impact on but it might have impact on the terminal velocities .    finally , we discuss the possible role of the bi - stability jump on the mass loss during typical variations of luminous blue variable stars ."}
{"article_id":"astro-ph9908196","section_id":"i","document":"we have investigated the nature of the observed jump in the ratio @xmath0 of the winds of supergiants near spectral type b1 . calculations for wind models of ob supergiants show that around @xmath4 the mass - loss rate  jumps due to an increase in the line acceleration of fe  iii below the sonic point . this jump in  is found in three different series of models . in all cases , the wind efficiency number @xmath235 increases significantly , by about a factor of 2  to 3 , if  decreases from about 27  500 k to about 22  500 k. observations show that the ratio @xmath0 drops by a factor of two around spectral type b1 . applying these values for @xmath0 , we predict a bi - stability jump in  of about a factor of five . so  is expected to increase by about this factor between 27  500 and 22  500 k.    we have argued that the mass loss is determined by the radiative acceleration in the subsonic part of the wind , i.e. below @xmath236 . we found that this radiative acceleration is dominated by the contribution of the fe  iii lines . therefore  is very sensitive to both the metal abundance and to the ionization equilibrium of fe . our models show that the ionization fraction of fe  iii and the subsonic radiative acceleration increases steeply between = 27  500 and 25  000 k. this explains the calculated increase in  in this narrow temperature range . the exact temperature of the bi - stability jump is somewhat ambiguous . observations indicate that the jump occurs around spectral type b1 , corresponding to @xmath1  @xmath237  21  000  k ( lamers et al . 1995 ) . if one would not completely trust the value of @xmath0 for the star hd 109867 ( number 91 in lamers et al . ( 1995 ) ) , because of its relatively large error bar , then @xmath1 of the observed jump can easily occur at a few kk higher . in fact we can not expect the bi - stability jump to occur at one and the same temperature for all luminosity classes , because the jump is sensitive to the ionization balance ( mainly of fe  iii ) in the subsonic region of the wind and hence to the gravity of the star . our models predict that the jump will occur near @xmath1 @xmath237  25  000  k. however , this is sensitive to the assumptions of the models : the adopted masses and luminosities and to the assumption of the modified nebular approximation for the calculation of the ionization equilibrium of iron ( see sect .  [ sec : isa ] ) . a more consistent treatment of the ionization and excitation equilibrium of the fe - group elements may have two effects : _ i ) _  predicted from @xmath153 may alter , and _ ii ) _ @xmath1 at which the ionization ratio of e.g. fe  iii / iv flips , may shift . nevertheless , in view of the very encouraging results using the modified nebular approximation in the modeling of uv metal - line forests ( de koter et al . 1998 ) , we expect the error in   at which the dominant ionization of fe switches from iv to iii to be at most a few kk . furthermore , if a more consistent treatment would yield a change in this would most likely produce a systematic shift . since we are essentially interested in relative shifts in @xmath7 , we do not expect that our conclusions regarding the nature of the bi - stability jump would be affected . it is relevant to mention that leitherer et al . ( 1989 ) calculated atmospheric models for lbvs and suggested that the recombination of iron group elements from doubly to singly ionized stages , which according to them , occurs around  = 10  000 k , can explain  increases when lbvs approach their maximum states . we have found a fe  iii / iv ionization / recombination effect around  = 25  000 k for normal supergiants . we also anticipate that somewhere , at a lower value of a similar ionization / recombination effect will occur for fe  ii / iii , causing a _ second _ bi - stability jump . lamers et al . ( 1995 ) already mentioned the possible existence of a second bi - stability jump around  = 10  000 k from their determinations of , but the observational evidence for this second jump was meagre . possibly , this second jump _ is _ real and we anticipate that this second jump could very well originate from a fe  ii / iii ionization / recombination effect . furthermore , we have shown that the elements c , n and o are important line drivers in the _ supersonic _ part of the wind , whereas the _ subsonic _ part of the wind is dominated by the line acceleration due to fe . therefore , we do _ not _ expect cno - processing to have a large impact on , but it might have impact on the terminal velocities .    finally , we would like to add that our calculations for  around @xmath4 have only been performed for _ one _ value of @xmath238 , @xmath202 and h / he abundance . is expected to depend on these stellar parameters , so calculating mass - loss rates for a wider range of stellar parameters will provide valuable information on the size of the bi - stability jump in  and  and will allow us to constrain its amplitude and location in the hrd . we thank an anonymous referee for several useful suggestions . jv acknowledges support from the netherlands foundation for research in astronomy ( nfra ) with financial aid from the netherlands organization for scientific research ( nwo ) . adk acknowledges support from a nwo `` pionier '' grant to l.b.f.m . waters ; from nwo spinoza grant 08 - 0 to e.p.j . van den heuvel and from a grant from the nasa astrophysics data program nra 95-adp-09 to s.r","summary":"the wind efficiency number also increases drastically by a factor of 2  -  3 near that temperature .    furthermore , we show that the elements c , n and o are important line drivers in the _ supersonic _ part of the wind . the _ subsonic _ part of the wind is dominated by the line acceleration due to fe . therefore , cno - processing is expected _ not _ to have a large impact on but it might have impact on the terminal velocities .    finally , we discuss the possible role of the bi - stability jump on the mass loss during typical variations of luminous blue variable stars .","abstract":"we study the origin of the bi - stability jump in the terminal velocity of the winds of supergiants near spectral type b1 . observations show that here the ratio drops steeply from about 2.6 at types earlier than b1 to a value of=1.3 at types later than b2 . to this purpose , we have calculated wind models and mass - loss rates for early - type supergiants in a grid covering the range between and . these models show the existence of a jump in mass loss around for normal supergiants , with  increasing by about a factor five from to 22  500 k for constant luminosity . the wind efficiency number also increases drastically by a factor of 2  -  3 near that temperature .    we argue that the jump in mass loss is accompanied by a decrease of the ratio , which is the observed bi - stability jump in terminal velocity . using self - consistent models for two values of , we have derived = 2.4 for  = 30 000 k and = 1.2 for  = 17 500 k. this is within 10 percent of the observed values around the jump .    up to now , a theoretical explanation of the observed bi - stability jump was not yet provided by radiation driven wind theory . to understand the origin of the bi - stability jump , we have investigated the line acceleration for models around the jump in detail . these models demonstrate that _  increases around the bi - stability jump due to an increase in the line acceleration of fe  iii _ below _ the sonic point_. this shows that the mass - loss rate of b - type supergiants is very sensitive to the abundance and the ionization balance of iron .    furthermore , we show that the elements c , n and o are important line drivers in the _ supersonic _ part of the wind . the _ subsonic _ part of the wind is dominated by the line acceleration due to fe . therefore , cno - processing is expected _ not _ to have a large impact on but it might have impact on the terminal velocities .    finally , we discuss the possible role of the bi - stability jump on the mass loss during typical variations of luminous blue variable stars ."}
{"article_id":"1307.5270","section_id":"i","document":"lattice gauge theory predicts that at high temperatures / densities a new state of matter is formed , a plasma of quarks and gluons ( qgp ) @xcite . there is strong circumstantial evidence that in ultrarelativistic heavy - ion collisions such a plasma is created for a short amount of time . it quickly expands and hadronizes . it is the main objective of the present experiments at the ultrarelativistic heavy ion colliders to study the properties of the qgp . the experiments of the last ten years at rhic as well as the first runs at lhc have revealed that the hadron multiplicities are compatible with the assumption that hadrons are produced in statistical equilibrium at a temperature compatible with the predictions of lattice gauge calculations for the chiral / confinement phase transition @xcite . therefore the hadrons which are formed from plasma constituents are only of very limited use for the understanding of properties of the qgp .    for the study of the properties of the qgp during its expansion one has to rely on probes which do not come to an equilibrium with the plasma constituents . high - momentum heavy hadrons , those which contain a charm or a bottom quark , are such a probe . due to the high energy required for their production heavy quarks are created in hard collisions during the initial phase of the reaction and do not annihilate in later phases  @xcite . the number of these collisions can be determined from the collision geometry and the initial momentum distribution of the heavy quarks can be calculated from perturbative qcd ( pqcd )  @xcite . during the expansion of the plasma the heavy quarks interact with the plasma constituents , light quarks and gluons , but their initial momentum distribution is so different from that of the plasma particles that they do not come to thermal equilibrium  @xcite . therefore , their final momentum distribution at hadronization contains the desired information on the properties of the plasma during its evolution and this information is transferred to the heavy hadrons whose kinematics is largely determined by that of the entrained heavy quark . the interpretation of the experimental ( open ) heavy flavor results is in reality a double challenge : one has to understand the elementary interaction of the heavy quarks with the plasma constituents but also the expansion of the plasma itself . for the same elementary interaction different expansion scenarios yield different results of the observables  @xcite . heavy quarks interact with the plasma constituents either by elastic collisions @xcite or by inelastic radiative collisions @xcite or both @xcite . whereas radiative collisions dominate the energy loss of light quarks , for the heavy quarks the relative importance of the elastic and of the radiative energy loss is debated . detailed calculations for an expanding plasma are not available yet and the approximate calculations , using a static plasma of a given length , indicate that both are of the same order of magnitude  @xcite . another complication for the judgement of the importance of the radiative energy loss is the landau pomeranchuck migdal ( lpm ) effect , which states that radiative collisions are not independent but that a second gluon can only be emitted after the first one is formed .    for energetic light quarks the lpm effect in an infinite medium with a constant temperature and with static scattering centers has been evaluated independently by zakharov  @xcite and by baier , dokshitzer , mueller , peign and schiff  @xcite . later it has been found that both approaches are identical  @xcite and the approach has been extended to an expanding medium by applying time - dependent transport coefficients @xcite or time - dependent parton densities  @xcite . more recently arnold , moore and yaffe  @xcite , using diagrammatic methods , extended these calculations to dynamical gauge fields . the influence of the lpm effect for heavy quarks in a static medium is , however , presently still under debate and the calculation of how it shows up in an expanding medium whose temperature is rapidly changing is a theoretical challenge which has not been met yet . a while ago we have advanced a pqcd - inspired calculation for the elastic collisions of heavy quarks with the qgp constituents which employs a running coupling constant and an infrared regulator which reproduces the energy loss of the heavy quarks in the hard thermal loop approach  @xcite . embedding these cross sections in the hydrodynamical description of the expanding plasma of heinz and kolb  @xcite we could show that the collisional energy loss underpredicts the measured energy loss of heavy mesons at large momenta as well as their elliptic flow by roughly a factor of two . it is the purpose of this article to provide the basis for an extension of our pqcd calculation toward the calculation of the radiative energy loss . some preliminary considerations have been published in @xcite , where the calculation of @xcite for the radiative cross section was extended to the case of a collision implying one heavy quark . in  @xcite , it is argued that for heavy quarks of intermediate energy , those which constitute the bulk of the production at rhic and lhc , the gluon formation - time is strongly reduced by mass effects , so that coherence effects can be discarded in first approximation . in this respect , we offer a complementary viewpoint to the works of  @xcite where heavy quarks are assumed to be ultrarelativistic and where the phase space boundaries are not of primary importance . the same viewpoint will be adopted in the present work in order to deduce and study the radiative cross section that will be later implemented in our monte carlo simulations in the same spirit as  @xcite . the colliding light partons will be naturally considered as genuine dynamical degrees of freedom  see @xcite as well  and not as fixed scattering centers , as it was the case in most of the aforementioned works .    starting out in section  [ sec : model ] from the standard qcd radiation matrix elements we calculate the gluon emission cross section for the collisions of a heavy quark with a light quark . the complexity of this result can be substantially reduced by realizing that matrix elements can be regrouped into three gauge invariant subgroups out of which one is dominating the energy loss . we then establish that pqcd and scalar qcd ( sqcd ) give only slightly different results as far as the energy loss of the heavy quark in a single collision is concerned . therefore we continue our calculation in the sqcd approach which allows to compare our results with previous work of gunion and bertsch for the light quark sector  @xcite . we then discuss in section  [ sec : gluon_distribution ] the radiated gluon distribution and in particular the `` dead cone '' effect , the suppression of almost collinear gluon emission . this effect has been proposed a while ago by dokshitzer and kharzeev  @xcite . we show that the emission of gluons with a small traverse momentum ( with respect to the direction of the incoming quark ) is reduced but remains finite as soon as this effect is calculated with gauge invariant matrix elements . in section  [ sec : rad_cross_section ] we calculate the fractional radiative energy loss cross section @xmath0 as well as its integral over @xmath1 entering the calculation of the radiative energy loss @xmath2 ; we pay a particular attention to the kinematic region for which @xmath3 but @xmath4 not @xmath5 , relevant for production of heavy quarks at intermediate @xmath6 in ultrarelativistic heavy ion collisions at rhic and lhc . in section  [ sec : gluon_mass ] we extend the model by introducing a finite gluon mass , as done in a number of phenomenological approaches to study heavy ion collisions . we study in detail the influence of such a mass for the radiative energy loss . in section [ sec : energy_loss ] , we then provide a comparison of radiative and collisional energy loss . in an upcoming publication we will embed these results into a numerical simulation of the radiative and collisional energy loss using the hydrodynamical expansion scenario of ref . preliminary results for this approach have been presented recently  @xcite .","summary":"employing scalar qcd we study the gluon emission of heavy quarks created by the interaction with light quarks considered as dynamical scattering centers . we justify why scalar qcd represents a good approximation to the full qcd approach for the energy loss of heavy quarks . in the regime of accessible phenomenology","abstract":"employing scalar qcd we study the gluon emission of heavy quarks created by the interaction with light quarks considered as dynamical scattering centers . we develop approximation formulas for the high energy limit and study when the full calculation reaches this high energy limit . for zero quark masses and in the high energy limit our model reproduces the gunion - bertsch results . we justify why scalar qcd represents a good approximation to the full qcd approach for the energy loss of heavy quarks . in the regime of accessible phenomenology we observe that the emission at small transverse momentum ( dead cone effect ) is less suppressed than originally suggested . we also investigate the influence of a finite gluon mass on the discussed results ."}
{"article_id":"1307.5270","section_id":"c","document":"we present in this paper an approach to describe gluon emission from a heavy quark in collision with a light quark at mid and forward rapidity , i.e. for @xmath298 . because this radiation is centered at @xmath299 and the correction are of @xmath300 we use for this approach the scalar qcd formalism which allows identifying the physical processes much easier . we separate the matrix elements into three gauge invariant subgroups where two of them are identical with the bremsstrahlung diagrams already observed in qed . in the paper we concentrate on the third group which is genuine to qcd and dominates the radiation in the central rapidity region . we compare the full result with a high energy approximation which can be analytically calculated and find fair agreement already for moderate @xmath69 values ( @xmath301 ) . in ultrarelativistic heavy ion collisions at rhic and lhc the typical @xmath69 value of collisions of heavy quarks with heat bath particles is lower and therefore the approximate formulas are not directly applicable . we show that the phase boundaries are responsible for a substantial part of the corrections at intermediate energies , so that a model based on asymptotic transition elements and exact phase space boundaries can be used for semi - quantitative purposes . we find that the mass of the heavy quark suppresses the emission of gluons at low transverse momentum ( dead cone effect ) but this suppression is less important and less universal than originally advocated . we study the influence of a finite gluon mass on the energy loss of heavy quarks in radiative collisions and find a quite strong dependence . for massless gluons , the energy loss of heavy quarks due to radiative collisions exceeds that due to elastic collisions for all heavy quark momenta , while for massive gluons the crossing happens at moderate but finite momenta . in all cases , we conclude that radiative collisions have to be included for a quantitative description of the energy loss of heavy quarks in a quark gluon plasma . we have carried out this study assuming a constant infrared regularization scale @xmath289 for the elastic cross section and leave calculation with hard thermal loop propagators for future studies .","summary":"we observe that the emission at small transverse momentum ( dead cone effect ) is less suppressed than originally suggested . we also investigate the influence of a finite gluon mass on the discussed results .","abstract":"employing scalar qcd we study the gluon emission of heavy quarks created by the interaction with light quarks considered as dynamical scattering centers . we develop approximation formulas for the high energy limit and study when the full calculation reaches this high energy limit . for zero quark masses and in the high energy limit our model reproduces the gunion - bertsch results . we justify why scalar qcd represents a good approximation to the full qcd approach for the energy loss of heavy quarks . in the regime of accessible phenomenology we observe that the emission at small transverse momentum ( dead cone effect ) is less suppressed than originally suggested . we also investigate the influence of a finite gluon mass on the discussed results ."}
{"article_id":"0903.3580","section_id":"i","document":"elliptic systems with coupled boundary conditions have been attracting broad attention at least since  @xcite . a classical approach is based on interpreting interface conditions of an elliptic system as boundary conditions of a vector - valued elliptic equation . this leads to introducing differential operators acting on spaces of vector - valued functions . a parabolic theory for this kind of operators has been recently developed , see e.g.  @xcite . a particularly interesting application of the theory of elliptic systems is given by so - called _ networks _ and _ quantum graphs _ , see e.g.  @xcite and references therein . their generalisation to @xmath1-dimensional problems has appeared already in  @xcite , where the related notion of _ ramified space _ has been proposed . having in mind applications to quantum graphs , kuchment has proposed in  @xcite a class of coupled , time - independent boundary conditions for @xmath2-dimensional elliptic systems . kuchment s formalism allows for a very efficient variational approach , but the tradeoff is that his boundary conditions are only a proper subset of those considered in  @xcite  or , in the specific context of quantum graphs , in  @xcite . however , it is remarkable that kuchment s conditions give rise exactly to _ all self - adjoint realisations _ of the schrdinger operator on a metric graph , under a mild locality assumption .    in the companion paper @xcite , cardanobile and the author have generalized kuchment s formalism to the case of @xmath1-dimensional vector - valued diffusion and characterized several properties of the parabolic problem in dependence on the chosen boundary conditions . the aim of this paper is to provide the extension of the theory in  @xcite to the case of _ dynamic _ boundary conditions of wentzell  robin - type . although we are soon going to consider the general case , let us start by briefly focusing on the @xmath2-dimensional setting of _ networks _ ( or _ quantum graphs _ ) . [ firstexa ] let @xmath3 and consider the prototypical case of a diffusion problem @xmath4 on a metric graph  more precisely , on a semi - infinite star with @xmath5 edges @xmath6 on whose center a dynamic kirchhoff - type boundary condition is imposed along with a standard continuity assumption . each edge is parametrized as a @xmath7-interval , where @xmath8 is identified as the center of the star . therefore , the function @xmath9 describing the diffusion on the edge @xmath10 maps @xmath11 to @xmath12 , while @xmath13 describes the time evolution of the common boundary value in the center . it is known that the associated initial value problem is well - posed , as discussed , e.g. in  @xcite . laplace operators with dynamic boundary conditions appear as limiting cases of approximation schemes considered in  @xcite . the cable model of a dendritical tree proposed by rall in  @xcite also leads to analogous network diffusion problems , cf . @xcite : a thorough biomathematical investigation of them has been performed in a series of four papers beginning with  @xcite . +    in 18,90,162,214,270,306 ( :0 cm )  ( : 1.8 cm ) ; ( : 1.85 cm )  ( : 1.9 cm ) ; ( : 1.95 cm )  ( : 2 cm ) ; ( : 2.05 cm )  ( : 2.1 cm ) ; ( 0:0 cm ) circle ( 2pt ) node[above left]@xmath8 ;     + _ a semi - infinite star with @xmath14 edges . _ +    we can rephrase @xmath15 by considering the orthogonal projection @xmath16 of @xmath17 onto the subspace @xmath18 spanned in @xmath17 by the vector @xmath19 observe that the unknown can be thought of as a function @xmath20 , so that the network diffusion problem simply becomes @xmath21 with suitable boundary conditions in @xmath8 . more precisely , the continuity condition in the star s center  given by the second equation in @xmath15  amounts to require that @xmath22 for all @xmath23 , i.e. , @xmath24 while the dynamic boundary condition equivalently reads @xmath25 hence , the dynamic boundary condition is an equation living in the ( @xmath2-dimensional ) _ boundary space _ @xmath26 . this kind of boundary conditions also arises in the mathematical modelling of string networks with masses at the nodes . they play an important role in the control theory of wave and beam equations : investigations in this direction go back at least to  ( * ? ? ? *  2.7 ) and  @xcite . the goal of the present article is to generalize the setting discussed in the above example . let @xmath27 be a smooth open domain in @xmath28 with boundary @xmath29 . let @xmath30 be a separable complex hilbert space . in particular , bochner spaces @xmath31 and @xmath32 become separable complex hilbert spaces when endowed with the canonical scalar products @xmath33 and @xmath34 let @xmath35 be a closed subspace of @xmath32 and hence a hilbert space in its own right with respect to the scalar product induced by @xmath32 . vector - valued sobolev spaces can be introduced recursively just like in the scalar - valued case . i.e. , one first lets @xmath36 , hence defines @xmath37 & \\qquad\\qquad\\qquad\\qquad\\left . \\int_\\omega f(x)\\nabla h(x ) dx=-\\int_\\omega g(x ) h(x ) dx\\hbox { for all } h\\in c^\\infty_c(\\omega;{\\mathbb c})\\right\\},\\qquad k=1,2,\\ldots , \\end{array}\\ ] ] and finally introduces spaces of fractional order by standard complex interpolation . ( here we denote by @xmath38 the hilbert space defined as the cartesian product of @xmath1 copies of @xmath30 . ) in particular , @xmath39 is a hilbert space with respect to the scalar product @xmath40 we emphasize that vector - valued sobolev spaces are introduced using scalar - valued test functions , hence the integral appearing in   is vector - valued ( i.e. , a bochner integral ) whereas those appearing in   are scalar - valued ( i.e. , lebesgue integrals ) . it is well - known that the usual trace and normal derivative operators @xmath41 extend to operators acting between sobolev spaces of scalar - valued functions . in fact , they can be canonically defined in the vector - valued case , too  e.g. by means of  ( * ? ? ? with an abuse of notation we therefore denote by @xmath42 and @xmath43 the trace and normal derivative ( in the sense of distributions ) of a function @xmath44 . we are now in the position to generalise the one - dimensional setting presented in example  [ firstexa ] by allowing for more general coupling conditions at the interface and consider the abstract boundary - value problem @xmath45 where @xmath46 denotes the orthogonal projection of @xmath32 onto the closed subspace @xmath35 . in the @xmath2-dimensional case of finite quantum graphs , the investigation of such a problem has been sketched in  ( * ? ? ? *  4 ) . [ dyenkirch ] let @xmath47 and @xmath48 , so that @xmath49 . take @xmath50 then @xmath51 and one sees that @xmath52 is just a reformulation of @xmath15 considered in example  [ firstexa ] . let again @xmath47 and @xmath48 . if @xmath53 and @xmath54 , then the first boundary condition in @xmath52 is void and @xmath52 is the reformulation of a scalar - valued heat equation with wentzell  robin boundary conditions , see e.g.  the recent contributions in  @xcite . if instead @xmath55 , then @xmath52 reduces to a heat equation with dirichlet boundary conditions . for @xmath53 , these are the only possible choices for @xmath35 , but for @xmath56 we have infinitely many new boundary conditions that in some sense interpolate between dirichlet and wentzell  robin ones . this is crucial when setting up a courant  fischer min - max formula , cf . @xcite . for @xmath48 the elliptic problem with _ dynamic interface conditions _  a vector - valued version of wentzell  robin boundary conditions  has been considered in  @xcite . in  @xcite , even more general elliptic interface problems have been considerd under the very general assumption that the given system can even consist of several metric spaces with different hausdorff dimensions , see also  @xcite , see also  @xcite . as already mentioned , the general case of a diffusion equation equipped with coupled ( either dynamic or time - independent ) boundary conditions is mostly motivated by the theories of quantum graphs and parabolic network equations , but it also appears in higher dimensional applications , in particular in biomathematical models  see e.g.  @xcite and references therein .    in this article we restrict to the case of dynamic boundary conditions only . however , the general case of mixed dynamic / time - independent boundary conditions ( typically appearing in models from the applied sciences , see e.g.  @xcite ) can be easily treated combining the results presented here and those from  @xcite .    in section  [ prelim ] we introduce our abstract framework and deduce a well - posedness result . the above examples suggest that the vector - valued setting  although equivalent to the that based on a network ( or ramified space ) formalism  is more efficient . in fact , its flexibility allows to simply introduce whole families of spaces @xmath35 . consequently , completely new questions arise . for example , one may wonder how the solution to the heat equation with boundary conditions as in @xmath52 depends on @xmath35 : it will be shown in theorem  [ olafrev ] that this dependence is continuous in norm under very natural assumptions . this result is interesting in that it does not have a scalar - valued _ pendant_. we also extend to the vector - valued case a result on continuous dependence on parameters obtained in the scalar - valued case in  @xcite . we consider invariance of order intervals and subspaces in section  [ posdom ] , showing in particular a tight relation beween the properties of the heat semigroup governing the problem with time - independent ( i.e. , robin - type vector - valued ) boundary conditions and its dynamic counterpart . we will observe some unexpected phenomena : e.g. , the semigroups governing these diffusion problems are in general not submarkovian  not even positivity preserving .    to discuss these behaviours in detail , in section  [ examplesect ] we focus on the setting of example  [ firstexa ] . it turns out that even in the simple context of diffusion on a semi - infinite star with finitely many edges , unexpected dynamics arises after chosing appropriate boundary conditions . finally , in section  [ dynneum ] we briefly discuss the general properties of a similar but different kind of dynamic boundary condition , where the normal derivative  rather than the trace  undergoes a time evolution .","summary":"motivated by diffusion processes on metric graphs and ramified spaces , we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class . beside well - posedness , we discuss positivity ,-contractivity and further invariance properties . furthermore , we prove continuous dependence of the solution to the parabolic problem on the boundary conditions in the considered class .","abstract":"motivated by diffusion processes on metric graphs and ramified spaces , we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class . beside well - posedness , we discuss positivity ,-contractivity and further invariance properties . we show that the parabolic problem with dynamic boundary conditions enjoy these properties if and only if so does its counterpart with time - independent boundary conditions . furthermore , we prove continuous dependence of the solution to the parabolic problem on the boundary conditions in the considered class ."}
{"article_id":"1012.1787","section_id":"i","document":"the flux variability of very high energy ( vhe ) gamma - rays on minute timescales detected from the bl lac object @xcite and mkr 501 @xcite challenges the standard scenarios suggested for the explanation of the nonthermal properties of tev blazars @xcite . the extremely short duration of the flares impose severe constraints on the size of the gamma - ray producing region , of lc 310 ^ 13_3 cm , [ eq_size_prop ] where @xmath5 and @xmath6  s are the proper production size and the variability timescale in the frame of the jet respectively and @xmath7 is the light speed . the proper variability time - scale , @xmath8 , is connected to the variability in the observer frame , @xmath9 , by the relation = , [ eq_var_tran ] where @xmath10 is the doppler factor of the moving source ( the blob ) : @xmath11 here the bulk lorentz factor , @xmath12 , accounts for the relativistic transformation of time , and @xmath13 is responsible for the kinematic shrinking of the duration of the radiation and @xmath14 . relativistic jets ejected from the central engines are common phenomena for different types of active galactic nuclei ( agn ) . in particular , apparent superluminal speeds @xmath15 ( in units of the speed of light  @xmath7 ) as high as @xmath16 have been detected for radio components on ( projected ) scales of @xmath17pc ( see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) in blazars - agn with jets directed to the observer . this implies very large lorenz factors of bulk motion given that @xmath18 .    because of the large bulk lorenz factors of tev blazars , the condition equation  ( [ eq_var_tran ] ) allows significant relaxation of the requirement supplied by equation  ( [ eq_size_prop ] ) . in particular , @xcite argued that if a perturbation is produced by the central engine , its size should exceed the gravitational radius of the black hole in the observer frame . consequently , the proper size of the production region is expected to be larger than @xmath19 , where @xmath20 cm is the gravitational radius of a black hole ( bh ) of mass @xmath21 . in this case , the variability time - scale @xmath22s imposes a strict upper limit on the gravitational radius : r_g<310 ^ 12 _ 2 cm  . [ rg ] thus , the detection of gamma - ray flux variability @xmath23  s constrains the bh mass , to be @xmath24 . in reality , since the main energy release occurs in the inner parts of the accretion disk of radius @xmath25 , the mass of the black hole should be close to @xmath26 . generally , in the case of an extreme kerr black hole , the energy release takes place at the gravitational radius . however , even in this case one needs an entire rotation period for an effective energy release , i.e. the characteristic time can not be much shorter than @xmath27 . this implies that even in this case the upper bound of the bh mass of @xmath26 can not be significantly relaxed . this conclusion is true , in particular , for the model of internal shocks . note , however , that it is based on the assumption that the perturbation ( the reason of the flare ) originates in the central engine . therefore it can not be unconditionally extended to other possible scenarios as is claimed by @xcite . indeed , equation  ( [ rg ] ) is not valid if perturbations are produced by an external source , e.g. by plasma condensations ( often called `` blobs '' ) which do not have a direct link to the central black hole . such blobs can be produced , in particular , by interactions of stars with the base of the jet , as proposed by @xcite to explain the tev flares of m  87 on scales of days ( see also * ? ? ? * ) , where the interaction of gas clouds from broad line regions are discussed ) . the jet power of m  87 is relatively modest , @xmath28 . the results of @xcite show that , while this power is sufficient to blow - up the envelope ( atmosphere ) of the star which initially has been pulled out by the tidal force of the bh , such a jet appears to be not sufficiently powerful for acceleration of the gas cloud to relativistic velocities . actually this works in a positive direction for m  87 , given the large aspect angle of the jet . otherwise , the gamma - ray flux could not be observed because of the doppler de - boosting effect . on the other hand , the suggested mechanism of formation of hadronic blobs in the jets can not apply to powerful gamma - ray blazars unless the blobs are accelerated to lorentz factors @xmath29 . remarkably , this can be realized in a quite natural way in powerful jets with @xmath30 . interestingly , such powerful jets can ablate the star atmosphere without help of tidal forces ( the interesting implications of this effect are discussed below ) . moreover , the powerful jets can drag and disrupt the star s envelope into an ensemble of blobs moving with large lorentz factors which , from the point of view of explanation of very short time variability is a quite comfortable situation . another important aspect of the short time variability is related to the efficiency of acceleration and radiation mechanisms . currently the most conventional approach for modeling of vhe emission production in active galaxies is based on the inverse compton ( ic ) scattering of relativistic electrons , the soft target photon field being either the synchrotron radiation of same electrons ( the so - called synchrotron - self compton ( ssc ) model ) , or provided by external sources ( eic model ) . the apparent advantage of ic models is the combination of two factors : ( 1 ) the acceleration of electrons to relatively modest energies ( @xmath31  tev ) can be effectively realized within different acceleration scenarios ; and ( 2 ) these electrons radiate readily in interactions of ambient radiation and magnetic fields . nevertheless , while the ic models allow rather satisfactory explanations of the energy spectra and variability patterns of many blazars in general , the parameters used to fit some specific objects appear incompatible with the parameters defined from observations . moreover , the observed short variability time - scale demands conditions which appear to be quite uncomfortable , in terms of the strength of magnetic field and related consequences concerning the strong deviation from equipartition between the energy density of relativistic electrons and magnetic fields . the requirement of weak , ( generally less than 1 g ) magnetic fields is one of the key postulates of the ic paradigm of gamma - ray production in blazars . moreover , in the case of some objects with unusually hard source spectra ( after correction for intergalactic absorption ) , such as 1es  0229 + 200 , the magnetic field is required to be as small as 1 mg @xcite . the magnetic field in the blazar jets can be reduced to such small values only at very large distances from the central engine , namely @xmath32 . although this idea has some observational support related to the transparency of blobs in the radio band @xcite , it is likely that regions of highly variable gamma - ray emission are located at smaller distances from the central engine @xcite . in particular , the eic models require the location of any gamma - ray emitter to be located closer to the bh into the so - called broad line regions ( blr ) , i.e typically at distances @xmath33  cm . this implies that any ic model can be realized only if one finds a way dramatically reduce the magnetic field in the jet . although this can not be excluded ( e.g. because of reconnection of the b - field @xcite or due to the effective bulk acceleration of plasma @xcite ) , strong magnetic fields exceeding 1  g remain a more favored option , as long as we deal with strong jets on sub - parsec scales . in this regard , the models which invoke high energy protons for the production of gamma - rays passes certain advantages despite a quite popular view that they are not effective emitters ( see e.g. * ? ? ? actually this is true only for proton - proton and proton - photon interactions . what concerns the synchrotron radiation of protons , with a key assumption on the acceleration of particles with a rate close to @xmath34 , where @xmath35 is the proton energy , coupled with a strong magnetic field between 10 to 100 gauss , and a large doppler factor , @xmath36 , it is that can provide relevant acceleration and radiation timescales , as well as explain the extension of gamma - ray spectra to tev energies ( see e.g. * ? ? ?","summary":"whilst for the external inverse compton model , parameters of , and the are required .","abstract":"we propose a new model for the description of ultra - short flares from tev blazars by compact magnetized condensations ( blobs ) , produced when red giant stars cross the jet close to the central black hole . our study includes a simple dynamical model for the evolution of the envelope lost by the star in the jet , and its high energy nonthermal emission through different leptonic and hadronic radiation mechanisms . we show that the fragmented envelope of the star can be accelerated to lorentz factors up to 100 and radiate effectively the available energy in gamma - rays predominantly through proton synchrotron radiation or external inverse compton scattering of electrons . the model can readily explain the minute - scale tev flares on top of longer ( typical time - scales of days ) gamma - ray variability as observed from the blazar . in the framework of the proposed scenario , the key parameters of the source are robustly constrained . in the case of proton synchrotron origin of the emission a mass of the central black hole of , a total jet power of and a doppler factor , of the gamma - ray emitting blobs , of are required . whilst for the external inverse compton model , parameters of , and the are required ."}
{"article_id":"1012.1787","section_id":"c","document":"the ultra - short tev gamma - ray flares of blazars detected in the case of @xcite and mkr 501 @xcite on 100  s timescales represent a serious challenge for current models of blazars . this challenge concerns the origin and the sites of formation of these flares , the acceleration and radiation mechanisms , the hydrodynamics of relativistic outflows , amongst others . since the upper limit on the size of production region , of @xmath259 , is smaller by an order of magnitude than the gravitational radius of a black hole of mass @xmath260 ( which is required to power distant blazars ) , the only way to avoid the situation of invoking quite uncomfortable upper limits on the mass of the central black hole ( as small as @xmath26 ) , is to invoke the doppler boosting . however , this can be realized only in the case of an external origin of the processes which cause these ultra - short flares . if the flares are initiated by disturbances originating from the central black hole ( e.g. , due to internal shocks ) , the linear size ( in the observer s frame ) of the flare production region can not be smaller than the gravitational radius of the black hole , independent of the doppler factor of the jet . the model suggested in this work readily solves the problem of connecting the flares to the interactions of the red giant stars with the powerful jets . due to these interactions the red giant loses a significant fraction its atmosphere . the cloud , accelerated by the magnetically driven jet up to a lorentz factor of @xmath261 , likely separates into many small fragments . these `` blobs '' represent the ideal sites for the production of flares , provided that a significant fraction of jet energy absorbed by the cloud is converted ( e.g. due to relativistic shock acceleration or magnetic reconnection ) to relativistic particles . the effective acceleration of particles is a necessary , but not a sufficient condition for the interpretation of the gamma - ray radiation of blazars . any successful model of tev blazars require adequate cooling times through gamma - radiation ; they should be comparable , or often even shorter compared to the characteristic timescales of other radiative and non - radiative processes . generally , leptonic models of gamma - ray loud blazars , through the realization of ssc or external ic scenarios , do provide adequate radiation timescales , but at the expense of the assumption of a rather weak magnetic field , typically less than 1 g , which in powerful blazars ( @xmath262 ) , is well below the magnetic field in the jet as long as it s concerned with sub - parsec distances ( see figure  [ magjet ] ) . this is a quite challenging requirement of the discussion of feasibility of , which is generally ignored in the literature . in the jrgi scenario suggested here the problem can be formally solved assuming that the magnetic field inside the blob is much smaller than in the jet . however , in the case of the ssc models , this assumption still does not allow a relaxation of the second requirement of an extremely large jet lorentz factor , @xmath263 . although such lorentz factors for the bulk motion can not be excluded , in particular at large , @xmath264pc distances from the bh ( see figure  [ magjet ] ) , in the proposed jrgi model it hardly can work . at such distance the jet ram pressure is not sufficient able to ablate the atmosphere of the star . the requirements on the magnetic field and the jet lorentz factor are more relaxed in the external ic model . nevertheless , one should note that within the jrgi scenario , the external compton model has some specific features . in order to avoid severe gamma - gamma absorption , the compton scattering should proceed in the thomson regime . this can be fulfilled if the radiation region is located at large distances , i.e. regions still with quite a large lorenz factors for the jet , @xmath265 . one of the main postulates of the jrgi scenario is the effective star - jet interaction . this requires the location of the blobs that emit gamma - rays to be at small distances from the bh , typically @xmath266  cm . in the case of powerful jets , @xmath267 , this implies a very large magnetic field , @xmath211  g and a moderate lorenz factor , @xmath268 . both parameters match nicely with the interpretation of the tev gamma - ray flares as a result of proton - synchrotron radiation by highly magnetized blobs , formed and accelerated in jet - star interactions . this model demands the acceleration of protons to energies of @xmath269ev , and implies the acceleration of protons with a rate close to the maximum ( theoretically possible ) rate of , @xmath270 . this is quite a robust requirement , which however , can be provided , in principle , by certain acceleration mechanisms . another challenge of the proposed scenario is related to the power of the jet . namely , the proton synchrotron model of tev gamma - rays can be effective , provided that : ( i ) the mass of bh does not significantly exceed @xmath271 and ; ( ii ) the jet power is not significantly below @xmath272 . an unambiguous implication of these two requirements ( working in two different directions ) is that the jet should have a super - eddington luminosity . although this could seem like quite a dramatic assumption , we note the requirement of super - eddington luminosities seems to be an unavoidable , model - independent conclusion for grbs and also likely for powerful gamma - ray blazars @xcite . an important question in the suggested scenario is the expected rate of the flaring events , which is related to the number density of rgs at the relevant jet scales . the jet region suitable for the production of the powerful flares ( similar to the burst detected from ) , can be defined as @xmath273 , and the corresponding side cross section of the jet is @xmath274 . thus , the number of flaring events per year can be estimated as @xmath275 . equation  ( [ sv ] ) provides an estimate for the density of rgs required to produce @xmath276 flaring events per year : @xmath277 unfortunately , there are no direct measurements of the stellar density in the vicinity of bhs . thus , depending on the assumed distribution law , the number of rgs in the vicinity of the bh may or may not be sufficient . however , we note that studies of possible stellar density profiles in the vicinity of the bh in agns ( see e.g. @xcite ) show that densities similar to the one required ( @xmath278  pc@xmath279 ) are rather feasible . moreover , under the influence of x - ray radiation close to bhs , normal stars can drastically increase the rate of their stellar wind . thus , wind - fed clouds can be formed during the jet  star interaction . this interaction can mimic the interaction of rg atmosphere with the jet ( dorodnitsyn , private communications ) . since , the stellar density of normal stars is higher up to 2 orders of magnitude than the density of rgs , this effect can significantly relax the requirement imposed by equation  ( [ eq : density_rg ] ) on the stellar density in the vicinity of bhs .","summary":"we propose a new model for the description of ultra - short flares from tev blazars by compact magnetized condensations ( blobs ) , produced when red giant stars cross the jet close to the central black hole .","abstract":"we propose a new model for the description of ultra - short flares from tev blazars by compact magnetized condensations ( blobs ) , produced when red giant stars cross the jet close to the central black hole . our study includes a simple dynamical model for the evolution of the envelope lost by the star in the jet , and its high energy nonthermal emission through different leptonic and hadronic radiation mechanisms . we show that the fragmented envelope of the star can be accelerated to lorentz factors up to 100 and radiate effectively the available energy in gamma - rays predominantly through proton synchrotron radiation or external inverse compton scattering of electrons . the model can readily explain the minute - scale tev flares on top of longer ( typical time - scales of days ) gamma - ray variability as observed from the blazar . in the framework of the proposed scenario , the key parameters of the source are robustly constrained . in the case of proton synchrotron origin of the emission a mass of the central black hole of , a total jet power of and a doppler factor , of the gamma - ray emitting blobs , of are required . whilst for the external inverse compton model , parameters of , and the are required ."}
{"article_id":"hep-ph0511102","section_id":"i","document":"many models of supersymmetry ( susy ) breaking predict that at least one of the susy partners of the top quark is sufficiently light such that pair production is possible at a future linear collider with c.m.energies below 1  tev . in such a scenario threshold studies are feasible , where squark pairs are produced with small relative velocities , and which allow for precise measurements of squark masses , lifetimes or couplings in close analogy to threshold measurements at the top - antitop pair threshold  @xcite . if the susy partner of the gluon is ( as is general expected ) not much lighter than the electroweak scale , then the low - energy qcd dynamics of squarks is , up to the fact that we are dealing with a colored spinless state , based on standard qcd with interactions carried by spin-1 gluons in the adjoint representation . it is a special feature of pair production of heavy colored particles close to the two - particle threshold that multi - gluon exchange leads to singular terms @xmath0 and @xmath1 in the amplitude at @xmath2-loop perturbation theory , where @xmath3 is the relative particle velocity . thus for @xmath4 , which corresponds to a region in c.m.energy of roughly @xmath5 , @xmath6 being the heavy particle mass , the singular terms have to be summed to all orders in @xmath7 . this is achieved most efficiently within an effective field theory . for top pair threshold production the effective theory vnrqcd (  velocity non - relativistic qcd \" )  @xcite was developed to carry out this summation program aiming for nnll order precision , i.e.accounting for @xmath8 qcd  @xcite as well as @xmath9 electroweak corrections  @xcite . for squark - antisquark pair threshold production previous studies involved leading - logarithmic ( ll ) precision  @xcite . higher order qcd or electroweak effects were not taken into account in a systematic manner , although it is known from the top threshold that corrections to the ll approximation can be substantial .    in this work we present the vnrqcd lagrangian for a particle - antiparticle pair of heavy non - relativistic colored scalars in the fundamental representation of qcd . we provide matching conditions and anomalous dimensions required for renormalization group improved computations of threshold pair production at next - to - leading logarithmic ( nll ) order and scalar - antiscalar bound state energies at nnll order in the non - relativistic expansion . for our presentation we follow closely the conventions and notations of refs .  @xcite . among the crucial elements of the construction are that vnrqcd is obtained by a single matching procedure at the hard scale @xmath6 and that the soft and the ultrasoft renormalization scales , @xmath10 and @xmath11 , are correlated according to the non - relativistic energy - momentum relation of a heavy particle at all times . thus we have @xmath12 , where @xmath13 is the dimensionless renormalization group scaling parameter of vnrqcd . ( for corresponding computations in the pnrqcd approach  @xcite see ref.@xcite . ) for convenience , for the most part of the paper , we call the scalars in the fundamental representation of qcd simply `` squarks '' and the scalar versions of vnrqcd and qcd frequently just vnrqcd and qcd , respectively . the outline of the paper is as follows : in sec . [ sectionbasic ] we present the terms of the scalar vnrqcd lagrangian relevant for this work together with their matching conditions . a special set of operators generated by ultrasoft renormalization is discussed in sec . [ sectionbasic]b . the running of all relevant potentials is discussed in sec . [ sectionpot ] . finally , sec . [ sectioncurrent ] is devoted to the anomalous dimensions of the s- and p - wave squark - antisquark production currents . conclusions are given in sec . [ sectionconclusion ] .","summary":"the vnrqcd lagrangian for colored heavy scalar fields in the fundamental representation of qcd and the renormalization group analysis of the corresponding operators are presented . the results are an important ingredient for renormalization group improved computations of scalar - antiscalar bound state energies and production rates at next - to - next - to - leading - logarithmic ( nnll ) order .","abstract":"the vnrqcd lagrangian for colored heavy scalar fields in the fundamental representation of qcd and the renormalization group analysis of the corresponding operators are presented . the results are an important ingredient for renormalization group improved computations of scalar - antiscalar bound state energies and production rates at next - to - next - to - leading - logarithmic ( nnll ) order ."}
{"article_id":"0810.3080","section_id":"i","document":"non - leptonic kaon decay has been a focus for both theoretical and experimental physics for over 40 years since the discovery of cp violation by christenson , cronin , fitch and turlay  @xcite in @xmath3 . since then the origin of cp violation has long been a challenge to many theoretical models . the recent data from various experiments have yielded a clear non - vanishing direct cp - violation parameter  @xcite : @xmath4 which ruled out the so - called superweak theory where no direct cp violation appears in the decay  @xcite . at present , a full theoretic explanation to the origin of this phenomenon is still lacking . in the framework of the standard model ( sm ) , direct cp violation can be generated by the non - zero phase in the quark flavor - mixing matrix ( ckm matrix ) , as was suggested by kobayashi and maskawa  @xcite . a precision calculation of the effect , however , is extremely hard due to the non - perturbative nature of the strong interactions at low energy . results from several groups utilizing different methods differ widely , with error bars much larger than that of the experimental result  @xcite . the unsatisfying situation of the theoretical calculations have attracted much interest in attributing part of the phenomenon to physics beyond sm .    to be able to pin down the contribution to @xmath2 from models containing new physics , one has to make precision calculations of the strong - interaction physics associated with the non - perturbative structure of kaons and pions . various methods have been used to calculate the hadronic matrix elements , such as lattice  @xcite , qcd - inspired models  @xcite , chiral expansion together with large-@xmath5 @xcite , and parametrizations  @xcite . at present , the lattice field theory is the only approach based on first principles , with controllable systematic errors . there are difficulties in lattice calculations which are associated with the fact that the final state contains more than one particle . by maiani - testa theorem  @xcite , it is impossible to extract the physical kaon decay matrix elements by taking the limit @xmath6 in the euclidean space . in practise , there are several ways to avoid it : one can either work with an unphysical choice of momenta  @xcite , utilize an unphysical set of meson masses  @xcite , or derive the physical matrix elements by unphysical , but calculable ones . all of these methods need chiral perturbation theory ( chpt ) . chpt assumes an approximate chiral symmetry exists in @xmath7 and describes the low - energy qcd physics under a chiral breaking scale @xmath8 by the pseudo - goldstone particles , namely pions , kaons and eta . then the low - energy physics can be perturbatively expanded in powers of the particles external momenta and masses . it further assumes that , the wilson coefficients of the qcd operators expanded in terms of meson operators are independent of the external states . therefore the amplitudes of a large number of reactions can be determined by a relatively small set of coefficients , which gives us the predicting power . in the case of kaon decay , chpt is used to connect the desired matrix element @xmath9 with some unphysical quantities , such as @xmath10 and @xmath11 . the results in chpt are needed before doing relevant lattice calculations . here we will neglect some subtleties in the chpt ( such as quadratic divergence cancelations , zero pion mass corrections , etc ) and focus on possible operator structures as well as their chiral logarithm corrections for the kaon decay process . it is the goal of this paper to examine the chiral structures of possible qcd operators responsible for @xmath12 decay in generic beyong - sm theories and to calculate the large chiral logarithms associated with them . previous calculations have been made for operators present in the sm  @xcite . our work extends these studies to all possible operators in new physics models . the paper is organized as follows : we start from the operator basis in sm for the kaon decay , as well as possible new operators coming from physics beyond sm . a chiral perturbation theory calculation will be presented in the following section , with all corresponding operators and their one - loop corrections of the matrix elements . we end this section by applying our result to a specific example . concluding remarks and outlook are presented in the last section .","summary":"we study the chiral logarithms in kaon decay amplitudes from new flavor physics in beyond - standard - model theories .","abstract":"we study the chiral logarithms in kaon decay amplitudes from new flavor physics in beyond - standard - model theories . we systematically classify the chiral structures of dimension-5 , 6 and 7 effective qcd operators constructed out of light - quark ( up , down and strange ) and gluon fields . using the standard chiral perturbation theory , we calculate the leading chiral - logarithms associated with these operators . the result is useful for lattice calculations of the qcd matrix elements in decay necessary , for example , to understand the physical origin of the direct cp violation parameter . as a concrete example , we consider the new operators present in minimal left - right symmetric models ."}
{"article_id":"astro-ph0204184","section_id":"i","document":"m31 is the nearest galaxy with a normal bulge where there is good evidence for the existence of a supermassive black hole ( sbh ) of @xmath10 ( e.g. kormendy & bender 1999 ; kormendy 1987 ; dressler & richstone 1988 ; richstone , bower , & dressler 1990 ) . early stratosphere ii balloon observations ( light et al . 1974 ) saw that m31 appeared to have a dense nucleus embedded on top a galaxy bulge . nieto et al . ( 1986 ) showed that the nucleus was off centered slightly from the bulge and asymmetric , which was hinted at in light et al . it was not until _ hst ( hubble space telescope ) _ wfpc ( wide field and planetary camera ) and foc ( faint object camera ) observations , that the nucleus was resolved into double components ( lauer et al . 1993 [ l93 ] ; king , stanford , & crane 1995 [ k95 ] ; lauer et al . 1998 [ l98 ] ) . figure 1 shows a grey scale @xmath1-band @xmath11 image of the nucleus from _ hst _ wfpc2 in @xmath1 , which was deconvolved and kindly provided by t. lauer ( see l98 ) . the brighter of the double peak in the @xmath1-filter is designated as p1 , and it is separated from the fainter p2 by @xmath12 , or 1.8 pc ( l93 ) . in the far - uv , however , k95 discover that p2 is actually more luminous than p1 . there is a striking uv peak ( upturn ) on top of p2 which stands apart in color from both p2 and p1 . in literature , p2 is synonymous with the uv peak , but here i make the distinction because the peak is not centered on p2 , as shown later . in the infrared , the contrast between the two nucleus is not quite as strong as in the optical , and the peak seen in uv - light all but disappears , either because it is intrinsically faint or is smeared away by the psf ( corbin , oneil , & rieke 2001 ) . dust is ruled out as being the cause for the appearance and asymmetry of the double nucleus based on color images of the optical , far - uv , and near - infrared h - k ( corbin , oneil , & rieke 2001 ; mould et al . 1989 ) , as well as a two - dimensional decomposition by k95 , who impose the assumption that both p1 and p2 components are smooth .    despite the prominence of p1 in optical images , l93 and l98 show that it is the uv peak which corresponds more closely to the center of the galaxy bulge , using isophotal centroids . they also suggest it is the location of the sbh . from rotation curves , kormendy & bender ( 1999 [ kb99 ] ) , bacon et al . ( 2001 [ ba01 ] ) , and statler et al . ( 1999 [ s99 ] ) find that the uv peak of p2 also lies close to the dynamical center . the most precise measurements put the zero - velocity center at @xmath13 ( kb99 ) and @xmath14 ( ba01 ) from the uv peak of p2 , in the direction of p1 . however , the peak of the velocity dispersion is @xmath15 from p2 , _ away _ from p1 ( kb99 , ba01 ) . kb99 locate the sbh near the center of the uv peak . k95 speculate that the strong uv peak may be due to a non - thermal , low - level , active galactic nucleus ( agn ) , coincident with x - ray and radio emissions , but acknowledge it is unclear whether it is truly resolved in pre - costar _ _  images . moreover , it has the energy output of only a single post asymptotic giant star ( k95 ) . l98 find that the uv peak is resolved by _ hst _ wfpc2 , leading them to hypothesize that the bluish color may not be an agn , but instead is caused by a population of late b to early a - type stars in a cluster , possibly in a region with high metallicity abundance ( e.g. burstein et al . 1988 , and k95 ) . forming such a cluster may be difficult , however , because of the tidal influence of a nearby @xmath16 black hole . the agn speculation about the uv peak has not been clarified despite chandra observations . garcia et al . ( 2000 ) discover x - ray emission in proximity to p2 with an unusual spectrum indicating possible relation to an active nucleus . the error circle , however , is 1(twice the separation between p1 and p2 ) , and is not alone  there are a number of other x - ray sources farther away around the bulge . if the uv peak is in fact agn related , it is curious that it does not have a counterpart in the near - ir where the emissions are often seen more clearly than in the optical due to a typical rise in the agn spectrum and diminished extinction ( quillen et al . 2001 ) . several empirical evidences indicate that the nucleus and the bulge have a different formation history . within @xmath17 of p1 , l98 show that the color is redder in @xmath18 ( @xmath19 ) than the surrounding bulge ( @xmath20 ) . but in @xmath21 , p1 ( = 2.29 ) and its anti - p2 direction ( @xmath21=2.18 ) appear to be bluer than the bulge ( @xmath21=2.39 ) . this is in contrast to ba01 who find both p1 and anti - p2 to also be redder . nonetheless , both their findings indicate that the nucleus has a stellar population , metallicity , and perhaps origins , different from that of stars in the bulge . silchenko , burenkov , & vlasyuk ( 1998 [ sbv98 ] ) show that the nucleus is more metal rich than the surrounding . in the two regions , the spectral indices differ by , @xmath22 and @xmath23 . kb99 confirm that p1 and p2 have a similar stellar population , have higher metal line strengths , and are more similar to each other than to the bulge or to any globular cluster . sbv98 also use @xmath24 $ ] to show that stars in the nucleus are younger by roughly @xmath25 gyrs . the compactness of the p1 and p2 peaks is particularly interesting and challenging to explain from the standpoint of galaxy formation and dynamical evolution . kb99 determine the combined mass of the double nucleus to be @xmath26 , comparable to the mass of the sbh . that such a configuration exists at all with such close separation ( 1.7 pc ) is surprising , and a natural interpretation is that p1 is either a merger remnant or a captured star cluster . emsellem & combes ( 1997 ) model this scenario with n - body simulations in a sbh potential and find that , although they can reproduce the geometry , the lifetime is on the order of 0.5 myr . if the cluster is massive enough to survive disruption , in most cases , dynamical friction would cause p1 to spiral in and coalesce with p2 within several dynamical times , unless somehow p1 co - rotates with the bulge ( k95 ) . although the short life span of an accreting scenario is not in itself conclusive proof , the discovery of other similar such systems ( e.g. ngc 4486b , lauer et al . 1996 ) favors a scenario which has a much longer lifespan . moreover , s99 find that the sinking star cluster of emsellem & combes ( 1997 ) model does not reproduce either the rotation curve or the dispersion profile . tremaine ( 1995 ) proposes an eccentric disk model to explain the nuclear configuration which currently stands as the favorite model . the thick eccentric disk , nearly keplerian , is composed of stars in ring orbits around a black hole , and p1 is caused by a bottleneck of stars slowing down at the turnaround radius ( apocenter ) . this model also predicts that the velocity center is displaced by @xmath27 from p2 in the direction of p1 . moreover , it predicts that the stars in p1 and p2 should have a similar stellar population because they belong to the same system , which might not be the case if p1 is a merger remnant . with spectroscopic data , kb99 show that the shift of the rotation center is in the right sense of the prediction , even if the amount is somewhat lower than prediction . moreover , p1 and p2 have more similar stellar populations to each other than to the bulge in accord with the model prediction . however , the missing element in the tremaine model is an explanation for how the ring orbits maintain alignment under precession : the original model has no self gravity . since then , several workers have proposed enhancements . among them , salow & statler ( 2001 ) propose a semi - analytic eccentric disk with self - gravity around a black hole , where the disk is made up of a superposing set of keplerian orbits dispersed in eccentricity and orientation according to a certain distribution function . it predicts that the line - of - sight velocity distributions of the disk near the black hole should have a distinctive double peak , which provides a further observational constraint to test the eccentric disk model . using a different formalism , with integrable models , jalai & rafiee ( 2001 ) show that the double nucleus geometry can be sustained with four general types of regular orbits in a stckel potential , even in the absence of a sbh . however , the requirement that the nuclei be cuspy , with surface density @xmath28 is a stringent requirement , and is not seen in m31 . furthermore , it is not clear why the nucleus would be asymmetric . bekki ( 2000 [ be00 ] ) , ba01 , and sambhus & sridhar ( 2001 [ ss01 ] ) , propose scenarios for how such an eccentric disk might be formed and sustained under precession with self - gravity . in be00 n - body simulation , an inward bound @xmath29 star cluster is completely disrupted by the tidal shear of a @xmath30 black hole , consequently forming a thick , eccentric , stellar system . the alternative scenario by ba01 involves a circular disk , already present in the bulge , that gets excited into an eccentric disk by a natural @xmath0 perturbation . the excitation may either be caused by a passing giant molecular cloud or globular cluster , which can induce the lopsidedness in the disk ( seen in fig . 1 ) that persists for @xmath31 years in their simulations . however , for the non - axisymmetric waves to develop , the disk needs to be thin . they furthered considered a model in which a black hole was shifted from the center of the potential , and another where its velocity was perturbed . too many particles escaped in the simulations for them to be viable . the model proposed by sambhus & sridhar ( 2001 ) extends tremaine s ( 1995 ) eccentric disk to simulate a larger disk mass ( @xmath32 ) which involves a shredding of @xmath33 globular cluster near the vicinity of the sbh . subsequently , the cluster stars merge into a pre - existing disk of few @xmath34 , orbiting the central black hole on both prograde and retrograde , quasi - periodic , loop orbits . the @xmath0 instability which causes the large eccentricity is induced by resonant response to the counter - rotating orbits . in this model , lopsidedness of the eccentric disk geometry is created in response to the presence of retrograde orbits . all three models roughly reproduce the double nucleus geometry and the dynamics , such as the offset in the velocity dispersion profile from p2 by @xmath35 , to varying degrees of accuracy . however , one important difference between be00 and ba01 + ss01 scenarios is that the be00 model requires the stellar cluster be much less massive than ( @xmath36 ) the black hole so that it can be disrupted . by contrast , the ba01 and ss01 models are constructed to have a much larger disk , about @xmath37 of the total central mass concentration . these two scenarios can be directly tested if a mass estimate of the disk can be robustly measured , and the uncertainty can be quantified . the ambiguity in the bulge decomposition is reflected in the available photometry of p1 , which can significantly differ in brightness from different studies . furthermore , thus far it is not clear how much of p2 is part of the bulge or the eccentric disk . in addition to the eccentric disk , the bulge structure of m31 and how it fits into the developing picture of galaxy formation are interesting on their own merits . however , their studies have been complicated by the double nucleus . the steepness of galaxy nuclei and correlations with other structural parameters ( e.g. faber et al . 1997 ) reflect the manner by which bulges are formed . numerical simulations show that black hole mergers can flatten galaxy cores by ejecting stars from the center ( e.g. ebisuzaki , makino , & okumura 1991 ; nakano & makino 1999 ; and milosavljevi & merritt 2001 ) . this scenario appears promising for explaining the correlation found between large bulges and low central surface brightness . in this paper , i study the detailed properties of the m31 bulge by decomposing optical images to provide new structural parameters . with detailed decomposition one can address the following issues : are there subtle structures in the bulge that are not obvious in full light ? what are the relative contributions of the bulge , p1 , and p2 components ? what are their shapes ? what is the bulge profile and how sharply is it peaked ? finally , i discuss what the new photometry of p1 and p2 reveal about the two competing scenarios that explain the formation of the eccentric disk . although some of these questions can be addressed from other data in previous studies , this new analysis provides a unique look at the double nucleus based on a more flexible range of assumptions than foregoing studies .    in the sections to follow , section 2 discusses the data , section 3 briefly describes the analysis algorithm used to deblend the bulge . section 4 discusses the decomposition , followed by the environment of the bulge in section 5 . section 6 compares the eccentric disk formation models . conclusions follow in section 7 .    throughout the discussion i assume that the distance to m31 is @xmath38 kpc , following kb99 . i also assume that the galactic extinction is @xmath39 ( burstein & heiles 1984 ) , which is similar to @xmath40 determined by schlegel et al . kormendy ( 1988 ) and kb99 dynamical models also suggest that @xmath41 for the bulge stars . this is similar to star formation models of bell & de jong ( 2001 ) , from which one can derive @xmath42 based on the @xmath18 color of the bulge .","summary":"-band to study the bulge structure and to address competing formation scenarios of the eccentric disk . p2 appear to be embedded inside an intermediate component ( ) that is nearly spherical ( ) , while the main galaxy bulge is more elliptical ( ) . the spherical bulge mass ( ) , being coincident with the supermassive black hole mass ( ) , conjoined with a shallow bulge cusp , are consistent with the scenario that the bulge was scoured by spiraling binary supermassive black holes . in the 2-d decomposition , the bulge is consistent with being centered near the uv peak of p2 , but the exact position is difficult to pinpoint because of dust in the bulge .","abstract":"the double nucleus geometry of m31 is currently best explained by the eccentric disk hypothesis of tremaine , but whether the eccentric disk resulted from the tidal disruption of an inbounding star cluster by a nuclear black hole , or by an perturbation of a native nuclear disk , remains debatable . i perform detailed 2-d decomposition of the m31 double nucleus in the _ hubble space telescope _ -band to study the bulge structure and to address competing formation scenarios of the eccentric disk . i deblend the double nucleus ( p1 and p2 ) and the bulge simultaneously using five srsic and one nuker components . p1 and p2 appear to be embedded inside an intermediate component ( ) that is nearly spherical ( ) , while the main galaxy bulge is more elliptical ( ) . the spherical bulge mass ( ) , being coincident with the supermassive black hole mass ( ) , conjoined with a shallow bulge cusp , are consistent with the scenario that the bulge was scoured by spiraling binary supermassive black holes . in the 2-d decomposition , the bulge is consistent with being centered near the uv peak of p2 , but the exact position is difficult to pinpoint because of dust in the bulge . p1 and p2 are comparable in mass . within a radius of p2 , the relative mass fraction of the nuclear components is , assuming the luminous components have a common mass - to - light ratio of 5.7 . the eccentric disk as a whole ( p1+p2 ) is massive , , comparable to the black hole and the local bulge mass . as such , the eccentric disk could not have been formed entirely out of stars that were stripped from an inbounding star cluster . hence , the more favored scenario is that of a disk formed in situ by an perturbation , caused possibly by the passing of a giant molecular cloud , or the passing / accretion of a small globular cluster ."}
{"article_id":"astro-ph0204184","section_id":"c","document":"i decompose m31 with galfit to accurately extract the double nucleus . the large scale bulge is made up of two components : a small , spherical structure , embedded at the center of a large , and moderately elliptical component . i then use the decomposition to study the structural parameters of the bulge , finding that the break radius , @xmath77 , correlates with other galaxy parameters that are found in faber et al . ( 1997 ) for a large sample of early - type galaxies . the spherical component extracted has a mass of @xmath182 , which is surprisingly similar to the mass of m31 s supermassive black hole . it remains to be seen whether this is the result of binary black hole mergers , as predicted by milosavljevic & merritt ( 2001 ) n - body simulations , or a mere coincidence . the inferred mass of p1 and p2 combined is comparable to the black hole mass , and the bulge mass contained in a small region out to the radius of @xmath121 from uv peak , with relative masses @xmath183 . the inferred mass of p1+p2 is insensitive to the bulge parameters , as others ( e.g. ba01 ) had also found . coupled with the large impact parameter suggested by the disk , it seems a cluster that resulted in the eccentric disk of p1+p2 ( @xmath184 ) could not have been disrupted enough by the black hole ( @xmath185 ) to form an eccentric disk around it . in such a scenario , the progenitor of p1+p2 would have to be still larger than my mass estimate . the large mass of the disk is consistent with a scenario in which a stellar disk was formed in the nucleus , then became more eccentric after an @xmath0 perturbation , by , for example , passing giant molecular clouds or globular clusters ( ba01 ) . another possibility is that an approaching globular cluster of mass @xmath186 might have come within , and was shredded by , the sbh , then was integrated into the pre - existing disk ( ss01 ) . despite how well the current n - body simulations reproduce the kinematics and morphologies , given that all the components within @xmath104 of the bulge are comparable in mass , a perturbation that would excite the @xmath0 mode in the disk might also perturb the bulge . thus it is unclear whether their mutual tidal interactions need to be further considered in n - body simulations , or might a smooth bulge potential suffice . the n - body simulations , coupled with a hypothetical shroud of dust at the nucleus , might explain both the eccentric disk geometry as well as the slight color difference between the bulge and the nucleus . however , it can not be the whole story : kb99 show that p1 and p2 have metal line strengths stronger than any globular cluster , hence they are unlikely to be the digested remnant of a globular cluster or an elliptical galaxy . a more complete picture also needs to account for the differing bulge and nuclear stellar ages inferred by sbv98 . one viable scenario as suggested by l98 is that the disk formation was a separate event that occurred well after the formation of the bulge . this may be the case because the bulge formation event would have disrupted any pre - existing sub - structure at the center . to grow a disk to @xmath173 , one scenario is by the disruption of several globular clusters . however , this possibility is remote because angular momentum conservation and scattering by the sbh would tend to produce a more spheroidal geometry . a more likely explanation , in private communication with l.  c. ho , is that a significant amount of gas and dust roughly @xmath174 had accreted into the center . indeed , extended dust structures in figures 7 and 8 , as well as sbv98 , strongly suggest it was a possibility . through gravitational settling , a circular gas+dust disk enriched with reprocessed material could have grown steadily , out of which young stars would then form . this might explain the metallicity enhancement and the younger stellar population in the nucleus compared to the bulge . the disk might have subsequently experienced a kick from a passing gmc or a globular cluster that increased the eccentricity . however , it is unclear at the moment how long ago or how such a massive @xmath187 disk could have settled into the center . assuming that the accretion occurred in the form of gas , the rate is limited by the near absence of non - thermal agn activity at the m31 nucleus . perhaps a significant amount of wind from star formation near the center might quench the agn activity by blowing fuel away from the central engine ( c.  d. impey , private communication ) . the accretion + wind scenario is attractive for explaining the possible presence of a uv star cluster at the center , and for the absence of dust lanes in the immediate vicinity of the double nucleus , despite there being a large and extended dust structure mere @xmath188 away ( figs . 7 and 8) . * acknowledgments . * i thank peter strittmatter for financial support . i also thank luis ho and chris impey for comments and reading the original draft ; alice quillen , and dennis zaritsky , and roelof de jong , for general discussions ; daniel eisenstein for assistance in the error propagation ; and tod lauer for providing the deconvolved images of m31 , and for discussions about the sbf and fitting of the double nucleus . i also thank the referee for helpful and insightful comments . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . lauer , t. r. , faber , s. m. , groth , e. j. , shaya , e. j. , campbell , b. , code , a. , currie , d. g. , baum , w. a. , ewald , s. p. , hester , j. j. , holtzman , j. a. , kristian , j. , light , r. m. , lynds , c. r. , oneil , & e. j. jr . 1993 , , 106 , 1436 . [ l93 ]                                                      llrrrrrrrrrrrrrl solution 1 : & srsic & @xmath189 & @xmath190 & 0.004 & 0.002 & 19.07 & 0.08 & 0.42 & & & 0.63 & 70.4 & 0.67 & 1.30 & uv peak + nuker bulge & srsic & @xmath191 & @xmath192 & 0.24 & 0.15 & 14.17 & 0.87 & 0.98 & & & 0.66 & 54.3 & 0.05 & & p2 + & srsic & 0.31 & 0.42 & 0.26 & 0.16 & 13.88 & 1.00 & 1.31 & & & 0.62 & 64.8 & @xmath191 & & p1a + 13.10 , 12.20 mag & srsic & 0.49 & 0.37 & 0.08 & 0.05 & 15.46 & 0.37 & 0.69 & & & 0.92 & @xmath193 & 0.57 & & p1b + & srsic & 0.13 & @xmath194 & 0.11 & 0.16 & 12.76 & 3.21 & 0.83 & & & 0.97 & 56.0 & 0.14 & & spherical bulge + @xmath195 , & nuker & @xmath194 & @xmath192 & 0.29 & 0.45 & 17.76 & 66.48 & 1.10 & 1.99 & 0.17 & 0.81 & 50.1 & 0.05 & & bulge + @xmath196 & offset & & & 0.01 & 0.01 & 20.4 & & & & & & & & & mag / arcsec@xmath110 + solution 2 : & srsic & @xmath190 & @xmath190 & 0.005 & 0.002 & 18.86 & 0.09 & 0.41 & & & 0.67 & 60.7 & 1.99 & 1.30 & uv peak + srsic bulge & srsic & @xmath197 & @xmath198 & 0.27 & 0.18 & 13.98 & 0.90 & 1.00 & & & 0.69 & 55.6 & 0.01 & & p2 + & srsic & 0.33 & 0.43 & 0.28 & 0.20 & 13.83 & 0.90 & 1.20 & & & 0.66 & 64.9 & @xmath199 & & p1a + 13.10 , 12.20 mag & srsic & 0.51 & 0.38 & 0.07 & 0.04 & 15.77 & 0.36 & 0.68 & & & 0.88 & @xmath200 & 0.83 & & p1b + & srsic & 0.00 & 0.16 & 0.08 & 0.11 & 13.51 & 2.40 & 0.44 & & & 0.96 & 56.6 & 0.08 & & spherical bulge + @xmath195 , & srsic & 0.10 & @xmath201 & 0.29 & 0.47 & 4.97 & 214.71 & 2.00 & & & 0.81 & 52.0 & 0.06 & & bulge + @xmath196 & offset & & & 0.01 & 0.01 & 20.4 & & & & & & & & & mag / arcsec@xmath110 + uncertainties & & 0.02 & 0.02 & & & 0.2 & 2% & 0.03 & 0.02 & 0.02 & 0.03 & 2 & 0.02 & & +","summary":"the double nucleus geometry of m31 is currently best explained by the eccentric disk hypothesis of tremaine , but whether the eccentric disk resulted from the tidal disruption of an inbounding star cluster by a nuclear black hole , or by an perturbation of a native nuclear disk , remains debatable . p1 and p2 are comparable in mass . within a radius of p2 , the eccentric disk as a whole ( p1+p2 ) is massive , , comparable to the black hole and the local bulge mass . as such , the eccentric disk could not have been formed entirely out of stars that were stripped from an inbounding star cluster . hence , the more favored scenario is that of a disk formed in situ by an perturbation , caused possibly by the passing of a giant molecular cloud , or the passing / accretion of a small globular cluster .","abstract":"the double nucleus geometry of m31 is currently best explained by the eccentric disk hypothesis of tremaine , but whether the eccentric disk resulted from the tidal disruption of an inbounding star cluster by a nuclear black hole , or by an perturbation of a native nuclear disk , remains debatable . i perform detailed 2-d decomposition of the m31 double nucleus in the _ hubble space telescope _ -band to study the bulge structure and to address competing formation scenarios of the eccentric disk . i deblend the double nucleus ( p1 and p2 ) and the bulge simultaneously using five srsic and one nuker components . p1 and p2 appear to be embedded inside an intermediate component ( ) that is nearly spherical ( ) , while the main galaxy bulge is more elliptical ( ) . the spherical bulge mass ( ) , being coincident with the supermassive black hole mass ( ) , conjoined with a shallow bulge cusp , are consistent with the scenario that the bulge was scoured by spiraling binary supermassive black holes . in the 2-d decomposition , the bulge is consistent with being centered near the uv peak of p2 , but the exact position is difficult to pinpoint because of dust in the bulge . p1 and p2 are comparable in mass . within a radius of p2 , the relative mass fraction of the nuclear components is , assuming the luminous components have a common mass - to - light ratio of 5.7 . the eccentric disk as a whole ( p1+p2 ) is massive , , comparable to the black hole and the local bulge mass . as such , the eccentric disk could not have been formed entirely out of stars that were stripped from an inbounding star cluster . hence , the more favored scenario is that of a disk formed in situ by an perturbation , caused possibly by the passing of a giant molecular cloud , or the passing / accretion of a small globular cluster ."}
{"article_id":"1701.01065","section_id":"i","document":"let us describe the periodic homogenization theory of hamilton - jacobi equations . for each @xmath1 , let @xmath2 be the viscosity solution to @xmath3 here , the hamiltonian @xmath4 is of separable form with @xmath5 , which is coercive ( i.e. , @xmath6 ) , and @xmath7 , which is @xmath8-periodic . the initial data @xmath9 , the set of bounded , uniformly continuous functions on @xmath10 . it was proven by lions , papanicolaou and varadhan @xcite that @xmath11 converges to @xmath12 locally uniformly on @xmath13 as @xmath14 , and @xmath12 solves the effective equation @xmath15 the effective hamiltonian @xmath16 is determined in a nonlinear way by @xmath17 and @xmath18 through the cell problems as following . for each @xmath19 , it was shown in @xcite that there exists a unique constant @xmath20 such that the following cell problem has a continuous viscosity solution @xmath21 where @xmath22 is the @xmath23-dimensional flat torus @xmath24 . although there is a vast literature on homogenization of hamilton - jacobi equations in different settings after @xcite , characterizing the shape of @xmath25 remains largely open even in basic situations . let us summarize quickly what is known in the literature about @xmath0 . it is not hard to see that @xmath0 is coercive thanks to the coercivity of @xmath17 . if one assumes furthermore that @xmath17 is convex , then @xmath0 is also convex and the graph of @xmath0 can contain some flat parts ( i.e. , @xmath26 has interior points ) . see @xcite and the works of concordel @xcite . furthermore , in this convex setting , we have the following representation formula , thanks to the results of contreras , iturriaga , paternain and paternain @xcite , and gomes @xcite , @xmath27 note that the above representative formula still holds if @xmath17 is quasiconvex ( level - set convex ) , in which case @xmath0 is also quasiconvex . more interestingly , in case @xmath28 , @xmath29 and @xmath30 , a deep result of bangert @xcite says that the level curve @xmath31 for every @xmath32 must contain line segments ( i.e. , not strictly convex ) unless @xmath18 is a constant function . bangert s result relies on detailed information about the structure of aubry - mather sets in two dimension ( @xcite ) . see also jing , tran , yu @xcite for discussion regarding locations of line segments of the level curves for ma type hamiltonians . the first numerical computation of effective hamiltonians is due to qian @xcite based on the so called _ big - t method _ , that is , @xmath33 , where @xmath34 is the unique viscosity solution to @xmath35 for other numerical schemes , we refer to gomes , oberman @xcite , falcone , rorro @xcite , achdou , camilli , capuzzo - dolcetta @xcite , oberman , takei , vladimirsky @xcite , luo , yu , zhao @xcite and the references therein . it is worth mentioning that cell problem and representation formula appear also in weak kam theory ( see e @xcite , evans , gomes @xcite , fathi @xcite for the convex case , and cagnetti , gomes , tran @xcite for the nonconvex case ) . in fact , a central goal of the weak kam theory is to find information of underlying dynamical system encoded in the effective hamiltonian .    in the case where @xmath17 is nonconvex , to identify the shape of @xmath0 is highly nontrivial even in the one dimensional space . this was settled only very recently by armstrong , tran , yu @xcite , and gao @xcite . one fundamental feature obtained is the  _ quasi - convexification _ \" phenomenon , that is , the effective hamiltonian @xmath25 becomes quasiconvex ( level - set convex ) when the oscillation of @xmath18 is large enough . see section [ sec : quasi ] for more precise statements . in multi - dimensional spaces , armstrong , tran , yu @xcite obtained a qualitative shape of @xmath0 for a representative case where @xmath36 . other than @xcite , very little is known about finer properties of nonconvex @xmath0 in multi - dimensional spaces , partly due to the extreme complexity of dynamics associated with nonconvex hamiltonians . furthermore , as far as the authors know , there is no numerical study of @xmath0 in this case . let us also call attention to an extrinsic way to study @xmath0 via inverse problems . see luo , tran , yu @xcite .      reducing a complex quantity to relatively simpler objects is a very natural and common idea in mathematics . for a class of nonconvex hamiltonians @xmath17 , we introduce a new decomposition method to obtain min - max type representation formulas for @xmath0 . these formulas consist of effective hamiltonians of quasiconvex hamiltonians which are presumably less challenging to analyze . the most general statement is given by inductive formulas ( theorem [ maintheorem ] ) . two specific ( but important ) cases of theorem [ maintheorem ] are provided in theorem [ thm : rep1 ] and lemma [ thm : rep2 ] . one immediate corollary is the evenness of @xmath25 associated with a certain class of radially symmetric hamiltonians , which is otherwise not obvious at all . given the vast variety of nonconvex functions , our surgical approach is only a preliminary step toward understanding the shape of nonconvex @xmath25 . in section 2.4 , we present some natural obstacles to decomposing a nonconvex @xmath25 . in particular , there is a connection between  non - decomposability \" and loss of evenness .    as another interesting application , the method and the representation formulas are robust enough that we are also able to prove stochastic homogenization for the same class of nonconvex @xmath17 in the appendix . for instance , theorem [ thm : random ] includes the result in @xcite as a special case with a much shorter proof . the detailed discussion on this ( including a brief overview of stochastic homogenization ) is left to the appendix . we would like to point out that a priori identification of shape of @xmath25 is currently the only available way to tackle homogenization of nonconvex hamilton - jacobi equations in general stationary ergodic setting .    in section 3 , we provide various numerical computations of @xmath0 in multi - dimensional spaces for general radially symmetric hamiltonians and a double - well type hamiltonian . these provide insights on how the changes of potential energy @xmath18 affect the changes in shape of effective hamiltonian @xmath0 . the important  quasi - convexification \" phenomenon is observed in multi - dimensional cases as well . nevertheless , verifying it rigorously seems to be quite challenging . interesting connections between decomposition , loss of evenness and quasi - convexification are demonstrated in section 2.4 and remark [ rem : conj ] . several open problems are provided based on the numerical evidences we have in this section .","summary":"this paper is the first attempt to systematically study properties of the effective hamiltonian arising in the periodic homogenization of some coercive but nonconvex hamilton - jacobi equations . firstly , we introduce a new and robust decomposition method to obtain min - max formulas for a class of nonconvex . , we show that our new method and those a priori formulas from the periodic setting can be used to obtain stochastic homogenization for same class of nonconvex hamilton - jacobi equations .","abstract":"this paper is the first attempt to systematically study properties of the effective hamiltonian arising in the periodic homogenization of some coercive but nonconvex hamilton - jacobi equations . firstly , we introduce a new and robust decomposition method to obtain min - max formulas for a class of nonconvex . secondly , we analytically and numerically investigate other related interesting phenomena , such as  quasi - convexification \" and breakdown of symmetry , of from other typical nonconvex hamiltonians . finally , in the appendix , we show that our new method and those a priori formulas from the periodic setting can be used to obtain stochastic homogenization for same class of nonconvex hamilton - jacobi equations . some conjectures and problems are also proposed ."}
{"article_id":"astro-ph0607544","section_id":"i","document":"the grbs are to our best knowledge the most energetic phenomena in the universe . so far intense efforts have been made both on the observational and theoretical grounds toward understanding of their natures , but their origins still remains to be investigated . one of the most important finding recently is that grbs are involved with relativistic collimated flows . to account for the observations , an extremely high bulk lorentz factor , typically more than 100 , is required @xcite . grbs are known to be composed of two classes : long - duration grbs ( with duration being longer than a few seconds ) and short - duration grbs ( with duration being less than a second ) . at least , some of the long - duration grbs are known to be associated with supernovae ( sne ) . good examples of grb - sn connection are grb980425/sn1998bw @xcite and grb030329/sn2003dh @xcite . these provide strong evidences that the central engines of ( at least part of ) the long - duration grbs are sne . such association was theoretically predicted by @xcite and @xcite . a signature of a supernova contribution is actually found in the afterglow spectra of these grbs . these supernovae are categorized in the type ic whose progenitor has lost its hydrogen and helium envelope when the core - collapse occurs . another possible grb associated with sn is grb021211 . a strong absorption feature is observed in the spectrum of the afterglow @xcite . they concluded that the absorption is due to caii which is synthesized by the associated supernova explosion . further , the discovery of the host galaxy of the long duration grbs being star forming galaxies @xcite also strengthens the idea of strong grb - sn connection . it has been suggested that even supernovae , in which no associated grb was found , might have a link with grb . for example , the peculiar sn2002ap recorded a high velocity component of @xmath12 and huge kinetic energy of the jet of @xmath13 ergs , at least . these values are similar to those of grbs , indicating a similar explosion mechanism of sn2002ap to that of grbs . @xcite concluded that sn2002ap is one example of the supernovae which failed to make a grb . recently , a number of x - ray - rich grbs ( xrrs ) and xrfs , very similar phenomena to grbs but with significantly lower peak energy , have been successively discovered thanks to the good performance of hete-2 ( see @xcite and @xcite ) . interestingly , the event rates of xrrs and xrfs are similar to that of the long duration grbs @xcite . the origin of these events is poorly understood , but similar burst properties of grb , xrrs , and xrfs except for peak energy leads to an idea that they all might have the same origins but with different viewing angles ( nakamura 2000 ) or with variable opening angles ( lamb et al . 2005 ) .    in this paper , we elucidate the theory of xrfs , xrrs , and grbs in the context of the so - called collapsar model . the collapsar is a death of a massive star in the last stage of the stellar evolution . the collapsar model for grbs was proposed by woosley ( 1993 ; see also macfadyen & woosley 1999 ) , for a central engine of grbs . in this model , strong outflows , or jets , emerge from deeply inside the collapsar and propagate into the interstellar medium ( ism ) , producing gamma - ray bursts . @xcite performed two dimensional hydrodynamic simulations based on this model . assuming annihilation of neutrino and anti - neutrino , they deposited thermal energy around the center of the core which had been collapsed and become a black hole . their initial mass density profile is very flattened due to rotation of the progenitor . the gas around the center , where the high thermal energy is deposited , expands and forms very collimated outflow ; i.e. , a `` jet '' . the outflow successfully became a bipolar outflow . unfortunately , however , their calculations were not relativistic one , so the relativistic effects which are important to understand grbs were not included . since the mass density of the progenitor is quite high , it is not a trivial issue whether or not the formed outflow can always keep collimated structure and break out from the progenitor surface as a jet . it has been pointed out through the agn jet simulations that the multi - dimensional effects are so important for the dynamics of the `` light jet '' into some dense gas ( see , e.g. , @xcite , and references therein ) . here , light jet stands for the jet , the mass density of which is smaller than that of the ambient gas . at least two dimensional hydrodynamic calculations are indispensable to investigate the outflow propagation and its dynamics inside and outside the progenitor .    multi - dimensional , relativistic hydrodynamic simulations have been so far performed by several groups in the context of collapsar model @xcite . @xcite , for example , performed relativistic hydrodynamic simulations based on the model by @xcite . they have found that a bipolar flow is created and it breaks out from the progenitor . interestingly , the maximum lorentz factor of about 40 has been achieved , when the jet breaks out of the progenitor . another type of relativistic hydrodynamic simulations of the outflow have also been performed by @xcite , @xcite , and @xcite . they modeled a mainly very hot jet , i.e. an initially thermal energy dominated jet . injected jets from the computational boundary , which is assumed to be very close to the collapsed center of the progenitor , always successfully propagate in the progenitor keeping good collimation and break out the progenitor . it is still open question , however , whether a collimated outflow emerging from the center of the progenitor can always break out or not . although several provenance studies have demonstrated successful propagation throughout the progenitor and breakout of the input outflow , they might have assumed unrealistically large energy input in the initial condition . we should be aware that the formation mechanism of the outflow from the center of the collapsed progenitor has been poorly understood . in other words , we still do not know the physical conditions ( density , thermal energy , kinetic energy , magnetic energy , opening angle etc ) for generating outflows . further , it is not completely clear yet what discriminates between sne associated with grbs and those without grb association . the connection between xrfs and grbs is another important issue . a key factor may be attributed to the different dynamics of the outflow propagation .    motivated by these questions we perform series of relativistic hydrodynamic simulations of the outflow propagation in the progenitor and ism . in these simulations , we fix the total input energy power of @xmath14 but vary the bulk lorentz factor ( @xmath6 ) and the specific internal energy of the initial outflow ( @xmath9 which excludes the rest mass energy ) . we discuss what types of outflow can emerge from the central system for a wide range of parameters , @xmath6 and @xmath9 . this paper is organized as follows . in sec . [ method ] we introduce our model and then explain the numerical methods and the initial background and outflow conditions . the results of the numerical simulations are presented in sec . [ results ] , where we will demonstrate the emergence of two distinct types of outflows : a collimated jet and an expanding outflow . we then discuss the dynamics and structure of the outflow , focusing on the distinctions between the two types of flows in sec . [ discussion ] . the final section is devoted to conclusions .","summary":"initially , we locally inject an outflow near the center of a progenitor . we calculate 25 models , in total , by fixing its total input energy to be and radius of the injected outflow to be cm while varying its bulk lorentz factor , , and its specific internal energy , ( with being speed of light ) . the injected outflow propagates in the progenitor and drives a large - scale outflow or jet . our finding will explain a smooth transition between the grbs , x - ray rich grbs ( xrrs ) and x - ray flashes ( xrfs ) by the same model but with different values .","abstract":"we investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma - ray bursts ( grbs ) through two dimensional axisymmetric relativistic hydrodynamic simulations . initially , we locally inject an outflow near the center of a progenitor . we calculate 25 models , in total , by fixing its total input energy to be and radius of the injected outflow to be cm while varying its bulk lorentz factor , , and its specific internal energy , ( with being speed of light ) . the injected outflow propagates in the progenitor and drives a large - scale outflow or jet . we find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models . the opening angle of the outflow ( ) is sensitive to ; we find for . the maximum lorentz factor is , on the other hand , sensitive to both of and ; roughly . in particular , a very high lorentz factor of is achieved in one model . a variety of opening angles can arise by changing , even when the maximum lorentz factor is fixed . the jet structure totally depends on . when is high , a strong bow shock appears and generates a back flow . high pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow , relativistic jet . a number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability . when is low , on the contrary , the outflow expands soon after the injection , since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow . our finding will explain a smooth transition between the grbs , x - ray rich grbs ( xrrs ) and x - ray flashes ( xrfs ) by the same model but with different values ."}
{"article_id":"astro-ph0607544","section_id":"m","document":"our model is based on the collapsar model ( see , e.g. , woosley 1993 ) . according to this model the release of the gravitational energy is the main energy source of the energetic phenomena . this model explains the formation of an outflow as follows : when an iron core of the massive star collapses , a system consisting of a black hole or a proto - neutron star and an accretion disk is formed at the center of the progenitor . some fraction of the collapsing gas can produce an outflow , although the formation mechanism of this outflow is not fully understood yet , as in the case of agn jets . annihilation of neutrinos and anti - neutrinos emitted from the accretion disk or via mhd process is a possible scenario to generate such outflows . the progenitor is expected to spin rapidly . the gas along the rotational axis can freely fall into the center while the gas along the equatorial plane only gradually falls because of stronger centrifugal force . as a result , a tenuous regions are created along the rotational axis . after the core collapse , the outer envelopes begin to fall freely . the free fall timescale of the envelopes is longer than the dynamical time scale for the jet to propagate within the progenitor and to hit its surface . after the formation of the outflow , it should propagate in the progenitor and break out the surface of the progenitor into ism . finally the outflow is observed as a grb and an afterglow . we adopt the radial mass profile from @xcite , assuming that the progenitor is spherically symmetric when the iron core was collapsed ( see however @xcite for recent calculations on the effects of the angular momentum and magnetic fields ) . at least near the core , the profile along the equatorial axis is very similar to that used by @xcite and @xcite . the progenitor had a mass of about 40 solar masses in the main sequence and has 16 solar masses in the pre - supernovae stage . the hydrogen envelope has already been lost by the stellar wind . although our progenitor includes helium envelope which would produce type ib sn , main properties of the outflow dynamics , such as , collimated jet or expanding outflow described below , strongly depend on the mass profile around the injection point , i.e. silicon , carbon , and oxygen envelopes . our main conclusion is not affected whether we adopt the progenitor which includes helium envelope or not . figure [ 1ddensity ] shows the radial mass density profile from the center to the surface of the progenitor . the mass density decreases from @xmath15 to @xmath16 from the center to the surface located at 3.7 @xmath17 cm from the center . the lower boundary of the computational domain ( @xmath18 ) is set to be @xmath19 cm from the center of the progenitor . the center of the progenitor is set to be @xmath20 ( see figure [ condition_fig ] for a schematic view of the progenitor and the location of the computational box ) . note that the total mass of the progenitor within this radius is about two solar masses ; that is , here we postulate the situation that material of about two solar masses collapses towards the center and forms the system of a proto - neutron star or black hole and a surrounding accretion disk . this distance between the center of the progenitor and the computational lower boundary is the same as that adopted by @xcite . we will also calculate an additional case study , in which the lower boundary is set to be at @xmath21 cm from the center , following @xcite , in which thermal energy is deposited as a driver of the outflow . since the pressure becomes very high due to the strong bow shock , the pressure of the progenitor can be negligible . the initial thermal energy in the progenitor is set to be very low . the formation mechanism of the outflows around the core is not fully understood yet . we assume injection of an initial outflow from the lower boundary and that the direction of the initial outflow is parallel to that of the cylindrical ( @xmath22 ) axis . this method is basically the same as that adopted by @xcite @xcite and @xcite , although the injected outflows calculated by @xcite and @xcite had a finite opening angles and were not initially parallel flow . in the present study the radius ( @xmath23 ) and power ( @xmath24 ) of the injected outflow is fixed to be @xmath25 and @xmath26 , respectively . in this paper the subscript 0 stands for the values of the injected outflow and @xmath24 does not include the rest mass energy . the energy flux ( @xmath27 ) does not depend on radius . the net injected energy during the first ten seconds amounts to @xmath28 ergs . this values is close to the explosive energy of sn1998bw and sn2003dh and is higher than the normal explosive energy of @xmath29 ergs @xcite . such energetic supernovae are sometimes categorized as hypernovae . two more parameters are necessary to specify the outflow condition . the bulk lorentz factor ( @xmath6 ) and specific internal energy ( @xmath9 ) are chosen in this paper . these parameters characterize the kinetic and thermal energy per particle in the injected outflow , respectively . as @xmath9 and/or @xmath6 increases , so does the kinetic and/or thermal energy per particle . the rest mass density and pressure of the injected outflow can be derived from these two parameters , assuming an equation of state . the larger @xmath9 and/or @xmath6 is , the smaller becomes the rest mass density . for example , the rest mass density ( @xmath30 ) is given as @xmath31^{-1 }      [ \\pi r_{0}^2]^{-1},\\end{aligned}\\ ] ] where @xmath32 is adiabatic index . the ideal gas equation of state , @xmath33 , is employed , where @xmath34 is pressure , and the definition of specific enthalpy @xmath35 is used . the equation ( [ density_1 ] ) is derived from @xmath36 . figure [ epsilon_gamma ] shows rest mass density in the ( @xmath37 ) plane for fixed total energy , @xmath26 and the radius , @xmath25 , of the injected outflow . the symbols in the plane present the calculated models . assuming that all the initial total energy is efficiently converted to kinetic energy , we can estimate the maximum bulk lorentz factor from the energy conservation law , @xmath38 @xcite where @xmath39 is baryon mass of the outflow . approximately the total energy is the sum of the rest mass , kinetic , and thermal energy , @xmath40 $ ] . then the maximum lorentz factor of a fire - ball can be estimated as ( piran 1999 ) @xmath41 which means almost all thermal energy is converted to kinetic energy during expansion like sn explosion @xcite . we will systematically vary @xmath6 and @xmath9 to survey any possible physical situations , since we are unaware which is the case . the condition which determines these parameters should depend on the formation mechanism of the outflow from the center of the progenitor , i.e. , we should know in detail how the mass and the angular momentum are distributed in the progenitor , how a massive star collapses , how the neutrino transport occurs , and how the magnetic field grows and affects the dynamics . for example , a rapidly rotating massive star can form geometrically thick accretion disk around a new - born black hole or proto - neutron star after the core - collapse . the amount of the neutrino and anti - neutrino emission from such an accretion disk could be large . then the annihilation rate of neutrino and anti - neutrino will be large enough so that thermal dominated outflow may be generated . if the accretion disk is thin due to a lack of rapid rotation of the progenitor , conversely , the annihilation rate will be small , which may results in the formation of a baryon rich outflow . note , however , that these conclusions may not be firm , since we still do not know the formation mechanism of this outflow . magnetic fields could be a key here . since there is a possibility that a non - relativistic but collimated outflow is generated from the center of the progenitor , we explore both the relativistic and non - relativistic outflows . the bulk lorentz factor , @xmath6 , is varied from the relativistic to the non - relativistic regimes , @xmath42 and @xmath43 ( which correspond to @xmath44 0.98 , 0.97 , 0.94 , 0.87 , 0.7 , 0.6 , 0.5 , 0.4 , and 0.3 , respectively . ) . the specific internal energy , @xmath45 , is changed from 30 , 5 , 1.0 , and 0.5 . as a result , the rest mass density of the outflow is in the range from @xmath46 [ the fastest and hottest outflow : @xmath47 to @xmath48 [ the slowest and coldest outflow : @xmath49 . the pressure of the outflow also changes . table [ conditions ] summarizes 25 calculated models .    to compare with @xcite we also list the ratio of the total energy to kinetic energy , @xmath50 , is presented in the table , where the rest mass energy is excluded from the total energy ; @xmath51 ( see @xcite ) . because the definition of @xmath50 in @xcite was changed to be the ratio of kinetic energy to total energy , we also show the inverse of @xmath50 in the table . our model a300 , ( @xmath52)=(5,30 ) is similar one studied by @xcite . the theoretically estimated lorentz factor @xmath53 from eq . ( [ maxgam ] ) is also shown in table [ conditions ] . some cases , for example @xmath54 ) , produce subsonic flow and are , hence , difficult to calculate . we exclude such cases from table [ conditions ] to assure good numerical accuracy . since the mass density of the progenitor in the innermost region for the computation is about @xmath55 , all our models produce initially so - called light jet . if the flow can keep the collimated structure in the progenitor , such an outflow is expected to interact with the back flow @xcite and has complex internal structures in the jet . from eq . ( [ maxgam ] ) we understand that the most predominant case for the grbs is the outflow with very high @xmath6 and high @xmath9 ; i.e. , model a300 ( @xmath56 ) . the second one is model a50 ( @xmath57 ) . we numerically solve two dimensional relativistic hydrodynamic equations , assuming the axisymmetric geometry . the basic equations are , @xmath58 @xmath59 ( @xmath60 ) is the @xmath61-th velocity component . the equations are written in the unit that the speed of light is unity . the updated version of numerical hydrodynamic code used in @xcite is employed in this study . the code adopts godunov - type scheme which is advantageous for capturing strong shocks with a few grid points in good accuracy . in this version the physical values , such as , pressure , rest mass density and the space components of 4-velocity , are used for this interpolation using the piecewise parabolic method ( ppm ) which allows us to get third order accuracy in space . the version of third order accuracy in space is used . the results of 1d and 2d test calculations are presented in the appendix .    in this study , we calculate the propagation of the outflow crossing through the progenitor for 10 seconds after the outflow injection . since the outflow crossing timescale is shorter than the free - fall timescale , we neglect the gravitational field by the core . we also ignore self - gravity , for simplicity . when an outflow propagates from the inner boundary towards the surface of the progenitor , a strong bow shock appears and drives the progenitor gas to high pressure and temperature . nucleosynthesis could occur in the such a hot and high density medium . since produced entropy due to the nucleosynthesis is much smaller than that by the strong shock , we do not consider nucleosynthesis as an energy source in the energy equation ( eq . [ energy ] ) . we assume the ideal gas equation of state , that is @xmath62 , where @xmath63 ) is adiabatic index . we used non - uniform grid points . logarithmically uniform 500 grid points are spaced for @xmath64 . we also set uniform 120 zones for @xmath65 cm and logarithmically uniform 130 zones for @xmath66 cm . some of our results , especially those having slower injection velocity ( @xmath67 ) , exhibit spreading outflow , which has a large transverse component of the flow with respect to the direction of the injected flow . we find in the test calculations of 1d shock tube problem with relativistic transverse velocity ( see , [ shtranseverse ] ) that the limited resolution of our numerical codes produces some numerical errors ( numerical errors in both positional and absolute values of density , pressure , 3-velocity , up to several tens of percent ) . however , in some slower models , such as , models g01 , h01 , and i01 , the flow is close to non - relativistic flows and the errors caused by the relativistic transverse velocity are negligible . in some faster models , such as , models a300 , a50 , a10 , a05 , etc , the relativistic flow in mainly appear in the collimated jet and propagates along the cylindrical axis . since the transverse velocity is not so large , the numerical errors caused by the transverse velocity are also negligible . we can thus conclude that the errors in mildly relativistic and spreading models may affect to the opening angle , but does not alter our main conclusion of a smooth transition from the collimated jet to the expanding outflow that is discussed in sec . [ results ] . the achieved maximum lorentz factors in each simulations are not affected by this numerical error . the boundary condition at @xmath68 cm is reflective except the inner 7 grid points which are used to inlet outflow . the reflective boundary condition is also employed at cylindrical axis . the outflow boundary condition is employed at @xmath69 cm and @xmath70 cm . we compellingly replace the numerical flux at the boundary using injection conditions , such as , @xmath30 , @xmath9 , and @xmath6 , to inlet the outflow . the numerical fluxes of the mass , momentum for @xmath22 direction , and energy at the injection points ( @xmath71 ) are given as @xmath72 , @xmath73 , and @xmath74 , respectively .","summary":"we find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models . the opening angle of the outflow ( ) is sensitive to ; we find for . a variety of opening angles can arise by changing , even when the maximum lorentz factor is fixed . the jet structure totally depends on . when is high , a strong bow shock appears and generates a back flow .","abstract":"we investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma - ray bursts ( grbs ) through two dimensional axisymmetric relativistic hydrodynamic simulations . initially , we locally inject an outflow near the center of a progenitor . we calculate 25 models , in total , by fixing its total input energy to be and radius of the injected outflow to be cm while varying its bulk lorentz factor , , and its specific internal energy , ( with being speed of light ) . the injected outflow propagates in the progenitor and drives a large - scale outflow or jet . we find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models . the opening angle of the outflow ( ) is sensitive to ; we find for . the maximum lorentz factor is , on the other hand , sensitive to both of and ; roughly . in particular , a very high lorentz factor of is achieved in one model . a variety of opening angles can arise by changing , even when the maximum lorentz factor is fixed . the jet structure totally depends on . when is high , a strong bow shock appears and generates a back flow . high pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow , relativistic jet . a number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability . when is low , on the contrary , the outflow expands soon after the injection , since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow . our finding will explain a smooth transition between the grbs , x - ray rich grbs ( xrrs ) and x - ray flashes ( xrfs ) by the same model but with different values ."}
{"article_id":"astro-ph0607544","section_id":"c","document":"we observe a dramatic but smooth transition from collimated structure to expanding one in the outflow propagation by changing the lorentz factor and specific internal energy of the injected outflow . what is the key physics which is responsible for the transition ? one of them is the pressure of the injected outflow . the pressure of the injected outflow in the models of the collimated jet is lower than that of expanding outflow . additionally , we , here , point out that the appearance of the ( internal ) reconfinement shock could be a key , since the lateral expansion is suppressed by the presence of the reconfinement shock @xcite , thus leading to a formation of the collimated jet structure . in fact , high - pressure regions driven by a bow shock can keep the collimated structure . models which have expanding structure have no or less internal structure in the reverse and side shocks . then the injected flow is bi - forked . on the contrary , models which keep the collimated structure have a number of internal oblique shocks within the jet . the existence of a back flow also enhances the appearance of such shocks . such shocks may allow the magnetic field generation in the jet ( discussed later ) . the internal shock model was introduced by rees & meszaros ( 1994 ; see also kobayashi et al . 1997 , and spada et al . 2001 ) to explain very short time variation of grbs . it is predicted that the outflow has up to a few hundred internal structures or `` shells '' and multiple two shell collisions occur at the distance of @xmath112 cm from the fire ball which emits gamma - rays . a simple linear analysis by @xcite and @xcite concludes that the timescale for a jet to propagate to the progenitor surface is long enough for perturbations to grow to form internal shocks and variability in grbs . the instability is caused by the shear flow or perturbation in pressure , density , and/or velocity in lateral direction in the jet . the derived growth rate of the shear instability monotonically increases with the decrease of the wavelengths @xcite . although with our current resolution it is impossible to resolve such fine structure , we can estimate the timescale of the instability , assuming the specific internal structure , say , that seen in fig [ 1dpressure ] . taking the wavelength to be a typical interval of the oblique shocks , @xmath113 cm , and bulk lorentz factor to be @xmath114 , we find that the timescale of the shortest mode in model a50 is on the order of @xmath115 s. this growing timescale is sufficiently shorter than the dynamical one ; that is , there is ample time for perturbations to grow to shocks , as was claimed by @xcite . in addition to the shear instability scenario , there exists another possible cause of the internal oblique shocks ; that is the interaction between the jet and the back flow . as the path of the back flow is not straight , the boundary between main jet and the back flow is not smooth but dynamically perturbed . since the dynamics is so complicated and is non - linear , it is hard to specify which mechanism , either the growth of the instability in the jet or the interaction between the jet and the back flow , is dominant for the appearance of the internal shocks . the detailed structure should depend on the resolution of the calculation . for this reason , we have calculated the same model as model a50 but with twice higher resolutions than that of model a50 ; that is model a50c . fig . [ panels4]a shows the results of model a50c ( see the bottom panel of fig . [ 1dpressure ] for comparison ) . the discontinuities still clearly appear in a50c , as well , but the number of discontinuity has increased than that of model a50 . the cocoon has fine structures and vortices . the emergence of vortices enhances the mixing of the back flow and shocked progenitor gas . the appearance of the oblique shocks in the jet could be a key to the collimation . whether such internal shocks appear or not strongly depends on how high pressure can be achieved by the presence of the bow shock . but it is difficult to predict whether the outflow expands or keeps collimated structure by a simple formula . what is clearly demonstrated through our simulations is that the large lorentz factor and/or internal energy of the outflow can make a strong bow shock ahead of the outflow , leading to a good confinement of an exploding hot outflow .    before closing this section , we wish to remark on the role of magnetic fields . the grbs quite generally exhibit power - law and non - thermal spectra produced by synchrotron emission . then , we need moderately strong magnetic fields within the jet , but it is not well understood how the magnetic field can be generated and grows in grbs . a plausible mechanisms for creating magnetic fields is the weibel instability which sets out when the velocity field is not isotropic and which can amplify magnetic fields quickly . further , the particle acceleration to highly relativistic regime can take place in the shocks . @xcite showed relativistic electrodynamics particle simulations of launching jet into the ambient medium . they observed the amplification of non - uniform and small - scale magnetic fields by the weibel instability . although they studied the shock at the head of the jet , magnetic fields can also be amplified in internal shocks within the jet . if the magnetic field grows up , it will inevitably affect the emissivity of pre - cursors and emissivity of gamma - rays of grbs after breakout from the progenitor . if large - scale magnetic fields can be created , they should affect the dynamics of the outflow . we need further studies in this field . finally we discuss the astrophysical implications of our results . we have shown different types of outflow dynamics which can arise even by the input of the same total energy power through the initial outflow . the input outflows may propagate , keeping a collimated structure in the progenitor , or showing an expanding structure . the change of the outflow shape with changes in @xmath9 and @xmath6 is gradual ( see fig . [ epsilon_gamma ] ) . although we can not directly observe the propagation of the outflow within the progenitor due to a large optical depth , different dynamics will produce observable effects after the outbreak of the outflow . different outflow dynamics may account for a variety of phenomena . the outflow with significant collimation and high lorentz factor ( @xmath116 ) will produce grbs . when the lorentz factor in the collimated jet is a bit smaller , so is the peak energy of the emission . such an outflow could be observed as xrfs . some of our simulations show an expanding outflow even when @xmath6 and/or @xmath9 are relatively small . such outflows may be observed as less energetic explosions as xrfs , even if the viewing angle is relatively small . these cases may correspond to the high velocity but non - relativistic flow , such as sn2002ap , since the flow still has a directivity . there is another factor for explaining the differences between grbs and xrfs ; that is the viewing angle to the jet . recently the unified model has been proposed by @xcite and by @xcite who claim that the different phenomena are attributed to different viewing angles , although the bursts themselves are identical . if the viewing angle is less or near the jet opening angle , the object will be observed as a grb . if not , it will be identified as an xrf . @xcite derived the observational energy as a function of the viewing angle based on their simulations . the third but less unlikely possibility has been pointed out through the discovery of soft gamma - ray repeaters ( sgr ) 1806 - 20 . because of its proximity its spectral and light variations have been recorded in unprecedent details @xcite . such an event may be observed as a short gamma - ray bursts , if it explodes in nearby galaxies , although its spectrum is basically blackbody and does not agree with those of grbs . finally , we comment on the synthesis of heavy elements . the large cross section of the forward bow shock is advantageous for the synthesis of heavy elements , since then wider regions are available for the nucleosynthesis ( macfadyen and woosley 1999 ; nagataki et al . we find that the outflows have an expanding structure in some cases . this expansion is reminiscent of the cases of aspherical explosions of supernova or hypernova as was shown in nagataki et al . 2003 ( 1998 , see also nagataki 2000 , maeda & nomoto 2003 , nagataki et al . 2006 ) . a large amount of heavy elements is expected to be synthesized by such an aspherical expansion , since the effective cross section of the bow shock is very large . the difference of the expansion should affect the amount of the synthesized elements . the viewing angle is also an important parameter for this type of outflow and is expected to explain the observed features of sne @xcite . @xcite calculated explosive nucleosynthesis by hydrodynamic calculations along the line of the collapsar model . it is also possible that the nucleosynthesis of heavy elements can occur in the accretion disk surrounding the black hole @xcite . @xcite showed that @xmath117ni is synthesized in the jet like outflow and concluded that the amount of @xmath117ni becomes larger when the energy deposition occurs in a short time , since then the deposited energy is effectively converted to thermal energy by the strong shock . such calculations can be a good diagnostic tool to compare with the observations , since the amount of synthesized elements can be estimated .","summary":"a number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability .","abstract":"we investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma - ray bursts ( grbs ) through two dimensional axisymmetric relativistic hydrodynamic simulations . initially , we locally inject an outflow near the center of a progenitor . we calculate 25 models , in total , by fixing its total input energy to be and radius of the injected outflow to be cm while varying its bulk lorentz factor , , and its specific internal energy , ( with being speed of light ) . the injected outflow propagates in the progenitor and drives a large - scale outflow or jet . we find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models . the opening angle of the outflow ( ) is sensitive to ; we find for . the maximum lorentz factor is , on the other hand , sensitive to both of and ; roughly . in particular , a very high lorentz factor of is achieved in one model . a variety of opening angles can arise by changing , even when the maximum lorentz factor is fixed . the jet structure totally depends on . when is high , a strong bow shock appears and generates a back flow . high pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow , relativistic jet . a number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability . when is low , on the contrary , the outflow expands soon after the injection , since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow . our finding will explain a smooth transition between the grbs , x - ray rich grbs ( xrrs ) and x - ray flashes ( xrfs ) by the same model but with different values ."}
{"article_id":"astro-ph0607544","section_id":"c","document":"we investigate the propagation and dynamics of the outflows in the progenitor in the context of collapsar model for a central engine of grbs by means of hydrodynamical simulations . we assume a fixed power input of the initial outflow of @xmath26 and the radius of the injected outflow @xmath118 cm , and follow the propagation of hot outflow for different values of @xmath9 and @xmath6 over the ranges of @xmath119 and @xmath120 . the net energy for 10-second injection satisfies the explosive energy of so - called hypernovae @xmath121 ergs . our conclusions can be summarized as follows :    1 . the propagation dynamics of the outflow dramatically changes from the collimated structure to the expanding one as @xmath6 decreases . if the lorentz factor is high enough , say @xmath122 , the outflow can propagate throughout the progenitor , keeping a very collimated structure . the half opening angle is @xmath7 for @xmath8 . but the opening angle has weak dependence on @xmath9 , as well ; we get @xmath123 even for smaller @xmath6 but with small @xmath124 . the maximum lorentz factor is , on the other hand , sensitive to both of @xmath6 and @xmath9 ; roughly @xmath10 . 2 .   in the relativistic , collimated flow , a back flow , which is anti - parallel to the main jet , appears . during the propagation in the progenitor , we can see some internal structures caused by the instability grown by the shear flow in the jet or by the interaction between the jet and back flow in the collimated jets . such oblique shocks can help the reconfinement of the jet . the maximum lorentz factor of the jet follows a simple formula derived from energy conservation relation . after the breakout the outflow expands into the interstellar space , although there still remains a high velocity component along the @xmath22-axis . its half opening angle if a few degrees . this could be observed as grbs . another flow component which surrounds the central high velocity component can also be seen . it originates from the back flow during the propagation in the progenitor and shocked progenitor gas . 3 .   when the lorentz factor ( or the initial velocity ) of the outflow is not large , say , @xmath125 ( @xmath126 ) , the outflow no longer keeps the collimation and thus expands to the forward and lateral directions . eventually the outflow breaks out like an aspherical supernova explosion . this is because with the small outflow velocity the bow shock is weak and can not drive the progenitor gas to high enough pressure . as a result , the reconfinement shocks , which are necessary for the collimation , does not appear . thus , the structure is relatively featureless in the outflow . as the cross section of the reverse shock increases with time , the mass is collected at the head of the outflow . this enhances lateral expansion . high lorentz factor ( @xmath127)is needed to explain energetic phenomena , such as grbs and xrfs , but the different initial internal energy affects the opening angle of the outflow for injected outflows of smaller lorentz factor , i.e. slower velocity , thereby producing a marked difference in its observable . rather low internal energy , @xmath124 , and relatively small lorentz factor ( @xmath128 5 ) leads to collimated non - relativistic jets , which will be observed as a failed grb . high internal energy , @xmath129 , leads to un - collimated relativistic jets , which could be observed as xrfs . we can thus phenomenologically explain different types of explosions , grbs xrfs , and failed grb along the same line but with different values of @xmath9 for slower injected velocity . however , a cause of producing a variety of @xmath9 and @xmath6 is still unknown . it should be investigated in future work . we thank w. zhang for his comments on the definition of @xmath50 in their paper . we appreciate s. woosley for his helpful comments to this manuscript . we gratefully acknowledge m. a. aloy , e. mller , a. macfadyen , n. ohnish , and m. horikoshi for the discussion on the numerical method . one of the authors ( a.m. ) was supported by a research fellowship of the japan society for the promotion of science . this work was supported in part by the grants - in - aid of the ministry of education , science , culture , and sport ( 14079205 , a.m. and s.m ) , ( 16340057 s.m . ) and ( 14102004 , 14079202 , and 16740134 , s.n . ) , this work was supported by the grant - in - aid for the 21st century coe `` center for diversity and universality in physics '' from the ministry of education , culture , sports , science and technology ( mext ) of japan . this work was carried out on nec sx5 , cybermedia center and institute of laser engineering , osaka university , sx8 at yitp in kyoto university , and fujitsu vpp5000 of national observatory of japan . we appreciate computational administrators for technical supports .","summary":"we investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma - ray bursts ( grbs ) through two dimensional axisymmetric relativistic hydrodynamic simulations . the maximum lorentz factor is , on the other hand , sensitive to both of and ; roughly . in particular , a very high lorentz factor of is achieved in one model . when is low , on the contrary , the outflow expands soon after the injection , since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow .","abstract":"we investigate the dynamics of an injected outflow propagating in a progenitor in the context of the collapsar model for gamma - ray bursts ( grbs ) through two dimensional axisymmetric relativistic hydrodynamic simulations . initially , we locally inject an outflow near the center of a progenitor . we calculate 25 models , in total , by fixing its total input energy to be and radius of the injected outflow to be cm while varying its bulk lorentz factor , , and its specific internal energy , ( with being speed of light ) . the injected outflow propagates in the progenitor and drives a large - scale outflow or jet . we find a smooth but dramatic transition from a collimated jet to an expanding outflow among calculated models . the opening angle of the outflow ( ) is sensitive to ; we find for . the maximum lorentz factor is , on the other hand , sensitive to both of and ; roughly . in particular , a very high lorentz factor of is achieved in one model . a variety of opening angles can arise by changing , even when the maximum lorentz factor is fixed . the jet structure totally depends on . when is high , a strong bow shock appears and generates a back flow . high pressure progenitor gas heated by the bow shock collimates the outflow to form a narrow , relativistic jet . a number of internal oblique shocks within the jet are generated by the presence of the back flow and/or shear instability . when is low , on the contrary , the outflow expands soon after the injection , since the bow shock is weak and thus the pressure of the progenitor gas is not high enough to confine the flow . our finding will explain a smooth transition between the grbs , x - ray rich grbs ( xrrs ) and x - ray flashes ( xrfs ) by the same model but with different values ."}
{"article_id":"quant-ph0510096","section_id":"c","document":"we have presented a hashing protocol to distill multipartite css states , an important class of stabilizer states . starting with @xmath0 copies of a mixed state that is diagonal in the @xmath23-basis , the protocol consists of local clifford operations that result in a permutation of all @xmath4 tensor products of css states , followed by pauli measurements that extract information on the global state . to find these local clifford operations , we used the efficient binary matrix description of stabilizer states and clifford operations . with the aid of the information - theoretical notion of a strongly typical set , it is possible to calculate the minimal number of copies that have to be measured in order to end up with copies of a pure css state , for @xmath0 approaching infinity . as a result , the yield of the protocol is formulated as the solution of a linear programming problem .","summary":"we present a hashing protocol for distilling multipartite css states by means of local clifford operations , pauli measurements and classical communication . it is shown that this hashing protocol outperforms previous versions by exploiting information theory to a full extent an not only applying cnots as local clifford operations . using the information - theoretical notion of a strongly typical set , we calculate the asymptotic yield of the protocol as the solution of a linear programming problem .","abstract":"we present a hashing protocol for distilling multipartite css states by means of local clifford operations , pauli measurements and classical communication . it is shown that this hashing protocol outperforms previous versions by exploiting information theory to a full extent an not only applying cnots as local clifford operations . using the information - theoretical notion of a strongly typical set , we calculate the asymptotic yield of the protocol as the solution of a linear programming problem ."}
{"article_id":"math0502437","section_id":"i","document":"we will work in the smooth category . for simplicity , all 3-manifolds @xmath0 will be the interior of compact manifolds @xmath1 with tori or klein bottle boundary components . a map @xmath2 from a surface @xmath3 into @xmath0 is called @xmath4-injective if the induced map @xmath5 is one - to one . by an abuse of notation , we will call @xmath3 ( or @xmath6 ) incompressible , if @xmath7 is a @xmath4-injective embedding . we will suppose throughout that all the boundary components of @xmath1 are incompressible . all 3-manifolds will be assumed to be irreducible and @xmath8-irreducible , i.e every embedded 2-sphere bounds a 3-ball and there are no embedded 2-sided projective planes . such a 3-manifold @xmath0 will be called atoroidal , if given any @xmath4-injective map @xmath9 from a torus or klein bottle into @xmath0 , @xmath7 is homotopic to a map into one of the boundary components of @xmath1 . any surface or map which is homotopic into a boundary surface of @xmath1 will be called peripheral .    for basic 3-manifold theory , see either @xcite or @xcite . an ideal triangulation @xmath10 of @xmath0 will be a cell complex which is a decomposition of @xmath0 into tetrahedra @xmath11 glued along their faces and edges , so that the vertices of the tetrahedra are all removed . moreover the link of each such missing vertex will be a klein bottle or torus . we call these links the peripheral surfaces of @xmath0 . note that tetrahedra may have faces and edges self - identified . using moise s construction of triangulations of 3-manifolds @xcite , one can convert a triangulation of @xmath1 into such an ideal triangulation , by collapsing the boundary surfaces to ideal vertices and also collapsing edges which join the ideal vertices to the interior vertices . see @xcite for a discussion of such collapsing procedures . one has to ensure that at each stage of such collapsings , that the topological type of @xmath0 does not change . we now summarize haken s theory of normal surfaces @xcite , as extended by thurston to deal with spun normal surfaces in ideal triangulations ( see also @xcite , @xcite ) . given an abstract tetrahedron @xmath12 with vertices @xmath13 , there are four normal triangular disk types , cutting off small neighborhoods of each of the four vertices . there are also three normal quadrilateral disk types , which separate pairs of opposite edges , such as @xmath14 . each tetrahedron @xmath15 of @xmath10 contributes 7 coordinates which are the numbers @xmath16 of each of the normal disk types . we can form a vector of integers of length @xmath17 from a list of these coordinates @xmath16 , @xmath18 .    a normal surface @xmath19 is formed by gluing finitely many normal disk types together and its coordinate vector is denoted by @xmath20 $ ] . @xmath20 $ ] is called the normal class of @xmath19 . there are @xmath21 compatibility equations for the coordinates of a normal surface , each of the form @xmath22 , where the left side of the equation gives the number of normal triangles and quadrilaterals with a particular normal arc type in the boundary , e.g the arc running between edges @xmath23 in @xmath12 . if the face @xmath24 is glued to @xmath25 of the tetrahedron @xmath26 , then @xmath27 are the number of normal triangles and quadrilaterals with the boundary normal arc type running between @xmath28 in @xmath29 . note that we allow self identifications of tetrahedra and hence also of normal disk types . note that normal surfaces may be embedded , immersed or branched . it turns out that the solution space @xmath30 of these compatibility equations in @xmath31 has dimension @xmath32 , i.e. there are @xmath33 redundant compatibility equations . the non - negative integer solutions in @xmath30 are then normal surfaces and we can regard @xmath32 as the dimension of the space of these surfaces . for a proof , see @xcite . also in @xcite , the dimension of the space @xmath34 of spun and ordinary normal surfaces is computed . in fact , if @xmath35 is the number of tori and klein bottle boundary components of @xmath1 , then it is shown there that the dimension of @xmath34 is @xmath36 .    in an ideal triangulation @xmath10 , a spun normal surface @xmath19 is formed by gluing infinitely many normal disk types together . by definition , there are finitely many quadrilaterals and infinitely many triangular disks in such a spun normal surface . a connected neighborhood ( in @xmath19 ) of these quadrilaterals can be formed by adding finite regions of triangles , yielding a compact core @xmath37 of @xmath19 . then the closure of @xmath38 is a collection of non - compact triangular regions of @xmath19 . it is easy to see that these regions must then all be half open annuli . the reason is that any such region projects onto a boundary surface of @xmath1 , which becomes a triangulated klein bottle or torus , when pushed into @xmath0 as a normal surface . the projection is locally one - to - one and so the region must be an annulus winding around the boundary surface .    now to form a vector space @xmath34 of spun and ordinary normal surfaces @xmath19 , we will consider only the quadrilateral coordinates of each @xmath19 . so @xmath34 will be a subspace of @xmath39 . this idea has been studied previously in @xcite , in the case of ordinary normal surface theory in standard ( closed ) triangulations and is called @xmath40 normal surface theory . for spun normal surfaces , @xmath40 theory has been investigated in @xcite,@xcite . there are @xmath33 compatibility equations for the quadrilaterals and in @xcite , it is shown there are @xmath35 redundancies . in an ideal triangulation , the solutions to these equations are naturally either normal or spun normal surfaces . the only surfaces which are not ` seen ' by this theory , are the boundary klein bottles and tori , formed entirely of triangular disk types . if we added these in also , the theory would have dimension @xmath41 . however these boundary surfaces play no significant role , so it is reasonable to leave them out of consideration . spun normal surfaces have been used in an interesting way by stefan tillmann @xcite , to study essential splitting surfaces arising from representation varieties in culler - shalen theory . finally we briefly discuss the theory of ( generalised ) almost normal surfaces , which turns out to give an elegant way of describing the combinatorial obstruction to deform a taut structure into an angle structure . the disks of generalised almost normal surface theory are properly embedded in the tetrahedra and have boundary loops consisting of normal arcs . it is an elementary exercise to check that such loops can be described as the boundary of a regular neighbourhood of an embedded arc in the boundary of a tetrahedron , where the latter arc runs between two vertices and consists of normal arcs plus two arcs from the vertices to interior points of edges not containing the vertices . ( see figure 1 ) . as a consequence , every such disk , which is not a triangle or quadrilateral , has length @xmath42 and we will refer to it as a @xmath42-gon . we will find an interesting connection between these @xmath42-gons , for @xmath43 , and branch points of normal classes ! = 2.5 in    in our work , it turns out to be sufficient to use normal and generalised almost normal surfaces . however , there is an interesting interaction with spun normal surface theory , which we will mention for completeness .","summary":"ideal triangulations are the basis of the computer program snappea of weeks and the program snap of coulson , goodman , hodgson and neumann . .525 cm","abstract":"this is the second in a series of papers in which we investigate ideal triangulations of the interiors of compact 3-manifolds with tori or klein bottle boundaries . such triangulations have been used with great effect , following the pioneering work of thurston . ideal triangulations are the basis of the computer program snappea of weeks and the program snap of coulson , goodman , hodgson and neumann . casson has also written a program to find hyperbolic structures on such 3-manifolds , by solving thurston s hyperbolic gluing equations for ideal triangulations .    in this second paper , we study the question of when a taut ideal triangulation of an irreducible atoroidal 3-manifold admits a family of angle structures . we find a combinatorial obstruction , which gives a necessary and sufficient condition for the existence of angle structures for taut triangulations . the hope is that this result can be further developed to give a proof of the existence of ideal triangulations admitting ( complete ) hyperbolic metrics .    our main result answers a question of lackenby . we give simple examples of taut ideal triangulations which do not admit an angle structure . also we show that for ` layered ' ideal triangulations of once - punctured torus bundles over the circle , that if the manodromy is pseudo anosov , then the triangulation admits angle structures if and only if there are no edges of degree 2 . layered triangulations are generalisations of thurston s famous triangulation of the figure 8 knot space . note that existence of an angle structure easily implies that the 3-manifold has a cat(0 ) or relatively word hyperbolic fundamental group .    .525 cm"}
{"article_id":"1304.7472","section_id":"i","document":"by a result of winkelmann ( see @xcite ) , every connected real lie group @xmath1 can be realized as the automorphism group of some complex stein manifold @xmath0 , which may be chosen complete , and hyperbolic in the sense of kobayashi . subsequently , kan showed in @xcite that we may further assume @xmath2 . we shall obtain a somewhat similar result for connected algebraic groups . we first introduce some notation and conventions , and recall general results on automorphism group schemes .    throughout this article , we consider schemes and their morphisms over a fixed field @xmath3 . schemes are assumed to be separated ; subschemes are locally closed unless mentioned otherwise . by a _ point _ of a scheme @xmath4 , we mean a @xmath5-valued point @xmath6 for some scheme @xmath5 . a _ variety _ is a geometrically integral scheme of finite type . we shall use @xcite as a general reference for group schemes . we denote by @xmath7 the neutral element of a group scheme @xmath1 , and by @xmath8 the neutral component . an _ algebraic group _ is a smooth group scheme of finite type . given a projective scheme @xmath0 , the functor of automorphisms , @xmath9 is represented by a group scheme , locally of finite type , that we denote by @xmath10 . the lie algebra of @xmath10 is identified with the lie algebra of global vector fields , @xmath11 ( these results hold more generally for projective schemes over an arbitrary base , see @xcite ; they also hold for proper schemes of finite type over a field , see ( * ? ? ? * thm .  3.7 ) ) . in particular , the neutral component , @xmath12 , is a group scheme of finite type ; when @xmath3 is perfect , the reduced subscheme , @xmath13 , is a connected algebraic group . as a consequence , @xmath12 is a connected algebraic group if @xmath14 , since every group scheme of finite type is reduced under that assumption . yet @xmath12 is not necessarily reduced in prime characteristics ( see e.g.  the examples in @xcite ) . we may now state our first result :    [ thm : aut ] let @xmath1 be a connected algebraic group , and @xmath15 its dimension .    if @xmath14 , then there exists a smooth projective variety @xmath0 such that @xmath16 and @xmath17 . if @xmath18 and @xmath3 is perfect , then there exists a normal projective variety @xmath0 such that @xmath19 and @xmath17 ( resp . @xmath16 and @xmath20 . this result is proved in section [ sec : aut ] , first in the case where @xmath14 ; then we adapt the arguments to the case of prime characteristics , which is technically more involved due to group schemes issues . we rely on fundamental results about the structure and actions of algebraic groups over an algebraically closed field , for which we refer to the recent exposition @xcite . theorem [ thm : aut ] leaves open many basic questions about automorphism group schemes . for instance , can one realize every connected algebraic group over an arbitrary field ( or more generally , every connected group scheme of finite type ) as the full automorphism group scheme of a normal projective variety ? also , very little seems to be known about the group of components , @xmath21 , where @xmath0 is a projective variety . in particular , the question of the finite generation of this group is open , already when @xmath0 is a complex projective manifold .    as a consequence of theorem [ thm : aut ] , we obtain the following characterization of lie algebras of vector fields :    [ cor : der ] let @xmath22 be a finite - dimensional lie algebra over a field @xmath3 of characteristic @xmath23 . then the following conditions are equivalent :    1 . @xmath24 for some proper scheme @xmath0 of finite type . @xmath22 is the lie algebra of a linear algebraic group .    under either condition , @xmath0 may be chosen projective , smooth , and unirational of dimension @xmath25 , where @xmath26 . if @xmath3 is algebraically closed , then we may further choose @xmath0 rational . this result is proved in subsection [ subsec : der ] . the lie algebras of linear algebraic groups over a field of characteristic @xmath23 are called algebraic lie algebras ; they have been characterized by chevalley in @xcite . more specifically , a finite - dimensional lie algebra @xmath22 is algebraic if and only if its image under the adjoint representation is an algebraic lie subalgebra of @xmath27 ( see ) . moreover , the algebraic lie subalgebras of @xmath28 , where @xmath29 is a finite - dimensional vector space , are characterized in ( * ? ? ? ii ,  14 ) . also , recall a result of hochschild ( see @xcite ) : the isomorphism classes of algebraic lie algebras are in bijective correspondence with the isomorphism classes of connected linear algebraic groups with unipotent center .    in characteristic @xmath30 , one should rather consider restricted lie algebras , also known as @xmath31-lie algebras . in this setting , characterizing lie algebras of vector fields seems to be an open question . this is related to the question of characterizing automorphism group schemes , via the identification of restricted lie algebras with infinitesimal group schemes of height @xmath32 ( see ( * ? ? ? viia , thm .  7.4 ) ) . next , we turn to the monoid schemes of endomorphisms of projective varieties ; we shall describe their connected subsemigroup schemes . for this , we recall basic results on schemes of morphisms .    given two projective schemes @xmath0 and @xmath33 , the functor of morphisms , @xmath34 is represented by an open subscheme of the hilbert scheme @xmath35 , by assigning to each morphism its graph ( see @xcite , and @xcite , @xcite for more details ) . we denote that open subscheme by @xmath36 . the composition of morphisms yields a natural transformation of functors , and hence a morphism of schemes @xmath37 where @xmath38 is another projective scheme .    as a consequence of these results , the functor of endomorphisms of a projective scheme @xmath0 is represented by a scheme , @xmath39 ; moreover , the composition of endomorphisms equips @xmath39 with a structure of monoid scheme with neutral element being of course the identity , @xmath40 . each connected component of @xmath39 is of finite type , and these components form a countable set . the automorphism group scheme @xmath10 is open in @xmath39 by @xcite ( see also ( * ? ? ? i.1.10.1 ) ) . if @xmath0 is a variety , then @xmath10 is also closed in @xmath39 , as follows from ( * ? ? ? 4.4.4 ) ; thus , @xmath10 is a union of connected components of @xmath39 . in particular , @xmath12 is the connected component of @xmath40 in @xmath39 .    as another consequence , given a morphism @xmath41 of projective schemes , the functor of sections of @xmath42 is represented by a scheme that we shall denote by @xmath43 : the fiber at @xmath44 of the morphism @xmath45 every section of @xmath42 is a closed immersion ; moreover , @xmath43 is identified with an open subscheme of @xmath46 by assigning to each section its image ( see @xcite again ; our notation differs from the one used there ) . given a section @xmath47 , we may identify @xmath33 with the closed subscheme @xmath48 ; then @xmath42 is identified with a _ retraction _ of @xmath0 onto that subscheme , i.e. , to a morphism @xmath49 such that @xmath50 , where @xmath51 denotes the inclusion . moreover , the endomorphism @xmath52 of @xmath0 is _ idempotent _ , i.e. , satisfies @xmath53 . conversely , every idempotent @xmath3-rational point of @xmath39 can be written uniquely as @xmath54 , where @xmath55 is the inclusion of the image of @xmath56 ( which coincides with its fixed point subscheme ) , and @xmath57 is a retraction . when @xmath0 is a variety , @xmath33 is a projective variety as well . we now analyze the connected component of @xmath56 in @xmath39 :    [ prop : end ] let @xmath0 be a projective variety , @xmath58 an idempotent , and @xmath59 the connected component of @xmath56 in @xmath39 . write @xmath54 , where @xmath55 denotes the inclusion of a closed subvariety , and @xmath57 is a retraction .    1 . the morphism @xmath60 restricts to an isomorphism from the connected component of @xmath61 in @xmath62 , to @xmath59 . moreover , @xmath59 is a subsemigroup scheme of @xmath39 , and @xmath63 for any @xmath64 . the morphism @xmath65 restricts to an isomorphism of semigroup schemes @xmath66 . in particular , @xmath67 is a group scheme with neutral element @xmath56 . 3 .   @xmath68 restricts to an isomorphism from the connected component of @xmath61 in @xmath69 , to the subscheme @xmath70 of idempotents in @xmath59 . moreover , @xmath71 for all @xmath72 ; in particular , @xmath70 is a closed subsemigroup scheme of @xmath59 . the morphism @xmath73 is an isomorphism of semigroup schemes , where the semigroup law on the left - hand side is given by @xmath74 . this is proved in subsection [ subsec : end ] , by using a version of the rigidity lemma ( see @xcite ) . as a straightforward consequence , the maximal connected subgroup schemes of @xmath39 are exactly the @xmath75 with the above notation ( this fact is easily be checked directly ) .    as another consequence of proposition [ prop : end ] , the endomorphism scheme of a projective variety can have everywhere nonreduced connected components , even in characteristic @xmath23 . consider for example a ruled surface @xmath76 where @xmath33 is an elliptic curve and @xmath77 is a locally free sheaf on @xmath33 which belongs to a nonsplit exact sequence @xmath78 ( such a sequence exists in view of the isomorphisms @xmath79 ) . let @xmath55 be the section associated with the projection @xmath80 . then the image of @xmath61 yields an isolated point of @xmath46 with zariski tangent space of dimension @xmath81 ( see e.g. ( * ? ? ? 4.6.7 ) ) . thus , the connected component of @xmath61 in @xmath69 is a nonreduced fat point . by proposition [ prop : end ] ( iv ) , the connected component of @xmath52 in @xmath39 is isomorphic to the product of that fat point with @xmath82 , and hence is nonreduced everywhere . this explains a posteriori why we have to be so fussy with semigroup schemes . a further consequence of proposition [ prop : end ] is the following :    [ prop : semi ] let @xmath0 be a projective variety , @xmath4 a connected subsemigroup scheme of @xmath39 , and @xmath83 the closed subscheme of idempotents . assume that @xmath4 has a @xmath3-rational point .    1 . @xmath84 is a connected subsemigroup scheme of @xmath4 , with semigroup law given by @xmath71 . moreover , @xmath84 has a @xmath3-rational point . 2 .   for any @xmath85 , the closed subsemigroup scheme @xmath86 is a group scheme . moreover , the morphism @xmath87 is an isomorphism of semigroup schemes . 3 .   identifying @xmath4 with @xmath88 via @xmath89 , the projection @xmath90 is the unique retraction of semigroup schemes from @xmath4 to @xmath84 . in particular , @xmath91 is independent of the choice of the @xmath3-rational idempotent @xmath56 . this structure result is proved in subsection [ subsec : semi ] ; a new ingredient is the fact that a subsemigroup scheme of a group scheme of finite type is a subgroup scheme ( lemma [ lem : unit ] ) . the case where @xmath4 has no @xmath3-rational point is discussed in remark [ rem : nopoint ] at the end of subsection [ subsec : semi ] . proposition [ prop : semi ] yields strong restrictions on the structure of connected subsemigroup schemes of @xmath39 , where @xmath0 is a projective variety . for example , if such a subsemigroup scheme is commutative or has a neutral element , then it is just a group scheme .    as another application of that proposition , we shall show that the dynamics of an endomorphism of @xmath0 which belongs to some algebraic subsemigroup is very restricted . to formulate our result , we need the following :    [ def : end ] let @xmath0 be a projective variety , and @xmath42 a @xmath3-rational endomorphism of @xmath0 . we say that @xmath42 is _ bounded _ , if @xmath42 belongs to a subsemigroup of finite type of @xmath39 . equivalently , the powers @xmath92 , where @xmath93 , are all contained in a finite union of subvarieties of @xmath39 . we say that a @xmath3-rational point @xmath94 is _ periodic _ , if @xmath95 is fixed by some @xmath92 . [ prop : bound ] let @xmath42 be a bounded endomorphism of a projective variety @xmath0 .    1 . there exists a smallest closed algebraic subgroup @xmath96 such that @xmath97 for all @xmath98 . moreover , @xmath1 is commutative . when @xmath3 is algebraically closed , @xmath42 has a periodic point if and only if @xmath1 is linear . if @xmath0 is normal , this is equivalent to the assertion that some positive power @xmath92 acts on the albanese variety of @xmath0 via an idempotent . this result is proved in subsection [ subsec : bound ] . as a direct consequence , every bounded endomorphism of a normal projective variety @xmath0 has a periodic point , whenever the albanese variety of @xmath0 is trivial ( e.g. , when @xmath0 is unirational ) ; we do not know if any such endomorphism has a fixed point . in characteristic @xmath23 , it is known that every endomorphism ( not necessarily bounded ) of a smooth projective unirational variety @xmath0 has a fixed point : this follows from the woods hole formula ( see ( * ? ? ? * thm . 2 ) , ( * ? ? ? iii , cor .  6.12 ) ) in view of the vanishing of @xmath99 for all @xmath100 , proved e.g. in ( * ? ? ? * lem .  1 ) . also , it would be interesting to extend the above results to endomorphism schemes of complete varieties . in this setting , the rigidity lemma of @xcite still hold . yet the representability of the functor of morphisms by a scheme is unclear : the hilbert functor of a complete variety is generally not represented by a scheme ( see e.g. ( * ? ? ? 5.5.1 ) ) , but no such example seems to be known for morphisms .","summary":"we first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety . then we show that very few connected algebraic semigroups can be realized as endomorphisms of some projective variety , by describing the structure of all connected subsemigroup schemes of end( ) .","abstract":"we first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety . then we show that very few connected algebraic semigroups can be realized as endomorphisms of some projective variety , by describing the structure of all connected subsemigroup schemes of end( ) ."}
{"article_id":"1305.4526","section_id":"i","document":"a formulation of general relativity called teleparallel equivalent of general relativity ( tegr ) has not been yet used as a starting point for a quantization of gravity @xcite . since nowadays no existing approach to quantum gravity seems to be fully successful it is worth to check whether it is possible to construct a model of quantum gravity based on tegr . in this paper we will address an issue of constructing a space of quantum states for tegr which could be applied in the procedure of canonical ( or a canonical - like ) quantization of the theory . a hamiltonian analysis of tegr @xcite shows that it is a constrained system . since we do not expect that constraints on the phase space of tegr can be solved classically we would like to apply the dirac s approach to canonical quantization of constrained systems . according to this approach one first constructs a space of kinematic quantum states , that is , quantum states which correspond to classical states constituting the unconstrained phase space , next among kinematic quantum states one distinguishes physical quantum states as those corresponding to classical states which satisfy all constraints . thus our goal is to construct a space of kinematic quantum states for tegr . since tegr is a background independent theory it is desirable to construct a space of quantum states for it in a background independent manner . methods which provide a construction of this sort are known from loop quantum gravity ( lqg)see e.g. @xcite and references therein  but because of a reason explained below they are rather not applicable to tegr . therefore we are going to construct the desired space for tegr by means of a general method @xcite deliberately developed for this purpose . this method works as follows . the starting point for the method is a phase space of a theory of the form @xmath0 , where @xmath1 is a space of momenta , and @xmath2 is a ( hamiltonian ) configuration space ( that is , a space of `` positions '' ) . one starts the construction by choosing a set @xmath3 of real functions on @xmath2 called _ configurational elementary degrees of freedom_. analogously , one chooses a set of _ momentum elementary degrees of freedom _ consisting of some real functions on @xmath1 . next , one defines a special directed set @xmath4each element of this set corresponds to a finite collection of both configurational and momentum elementary d.o.f.and with every element @xmath5 of @xmath6 one associates a set of quantum states denoted by @xmath7 .    given @xmath8 , the set @xmath7 of quantum stated is constructed as follows . the element @xmath5 corresponds to a finite set @xmath9 of configurational d.o.f .. one uses the d.o.f . in @xmath9 to reduce `` infinite - dimensional '' space @xmath2 to a finite dimensional space @xmath10this reduction consists in identifying all points of @xmath2 for which each d.o.f . in @xmath9 gives the same value . then one defines a hilbert space of functions on @xmath10 square integrable with respect to a measure on @xmath10 . the set @xmath7 is a set of all density operators ( i.e. positive operators of trace equal @xmath11 ) on this hilbert space  because density operators represent some ( mixed , in general , ) quantum states one can treat @xmath7 as a set of such states .    in this way one obtains a family @xmath12 of sets of quantum states . if the set @xmath4 is chosen properly then it naturally generates on @xmath12 the structure of a projective family . finally , the desired space of kinematic quantum states related to the original phase space @xmath0 is defined as the projective limit of the family . as shown in @xcite , the task of constructing such a space of quantum states reduces to a construction of a directed set @xmath4 satisfying some assumptions  these assumptions are imposed both on elementary d.o.f . constituting elements of @xmath6 and the relation @xmath13 . since now a directed set @xmath4 satisfying all these assumption will be called _ proper directed set @xmath4 . _ the goal of the present paper is to find variables on the ( hamiltonian ) configuration space @xmath2 of tegr which are suitable for constructing a proper directed set @xmath4 for the theory . more precisely , we are looking for variables on the configuration space which provide a set @xmath3 of configurational d.o.f . such that    1 .   d.o.f . in @xmath3 separate points of @xmath2 ; [ as - sep ] 2 .   d.o.f . in @xmath3 are defined via integrals of functions of components of the variables ; the functions are polynomials of the components of degree @xmath11 ; [ as - poly ] 3 . there exists a directed set elements of which are finite subsets of @xmath3 such that for every element @xmath9 of the directed set there exists a natural bijection from @xmath10 onto @xmath14 , where @xmath15 is the number of d.o.f . in @xmath9 ; [ as - bij ] 4 . d.o.f . in @xmath3 are defined in a background independent way i.e. without application of any background field . [ as - bgi ]    the first three * assumptions * above correspond to some assumptions imposed in @xcite on a proper set @xmath4 . the present assumption [ as - sep ] can be found in section 2 of @xcite containing preliminaries and the assumption [ as - poly ] above describes a practical way to satisfy assumption 3b of @xcite ( see section 3.2 and section 6.2 in that paper ) . the present assumption [ as - bij ] corresponds to assumption 2 of @xcite ( see section 3.2 in that paper ) . let us note that the original assumption 2 is imposed on every finite subset @xmath9 of @xmath3 which ( together with a finite set @xmath16 of momentum d.o.f . ) constitute an element of @xmath4 : `` if @xmath17 , then ... '' . but we do not have any set @xmath4 for tegr yet  we are at a stage of preparations for constructing such a set  and therefore we can not impose the original assumption 2 as it is formulated in @xcite . instead , we require the existence of a directed set consisting of some special finite subsets of @xmath3formulating in this way the present assumption [ as - bij ] we hope that a directed set of this sort may facilitate a construction of a proper directed set @xmath4 for tegr . finally , assumption [ as - bgi ] express our wish to construct quantum states for tegr in a background independent manner . results of our inquiries can be summarized as follows : we will find two kinds of variables on the configurations space @xmath2 of tegr which not only satisfy the four assumptions above but can be actually used in a background independent manner to construct two distinct spaces of quantum states for tegr . one of these variables are natural configurational variables on the phase space of tegr , that is , one - forms @xmath18 , @xmath19 , defined on a three - dimensional manifold being a space - like slice of a spacetime . we will show , however , that the space of quantum states derived from these variables possesses an undesired property . therefore we will transform the natural variables obtaining a family of new variables such that some elements of the family can be used to build a space of quantum states for tegr free of that property  a construction of this space will be presented in @xcite . let us emphasize that the analysis of variables suitable for constructing a space of quantum states for tegr will be continued in an accompanying paper @xcite where we will analyze more closely the family of new variables . some constructions presented in the present paper are similar to ( elements of ) a construction of a space of kinematic quantum states for a simple background independent theory called degenerate plebaski gravity ( dpg)the latter construction is described in @xcite . it seems to us that it may be quite helpful for the reader to study first the construction in @xcite since it is simpler that ones described here . let us finally explain why the lqg methods of constructing quantum states do not seem to be applicable to tegr . the reason is quite simple : the methods require finite dimensional spaces @xmath20 to be _ compact_. ] and it is rather difficult to obtain naturally such spaces in the case of tegr .    the paper is organized as follows : section 2 contains preliminaries , in section 3 we consider the natural variables @xmath18 and explain why the space of quantum state constructed from them does not seem to be very promising for canonical quantization of tegr . in section 4 we present the family of new variables . section 5 contains a short summary and an outline of the analysis to be presented in the accompanying paper @xcite . in appendix we prove two very important lemmas which guarantee that both kinds of variables considered in this paper provide d.o.f . satisfying assumption [ as - bij ] above .","summary":"we present the first part of an analysis aimed at introducing variables which are suitable for constructing a space of quantum states for the teleparallel equivalent of general relativity via projective techniques  the space is meant to be applied in a canonical quantization of the theory . we show that natural configuration variables on the phase space of the theory can be used to construct a space of quantum states which however possesses an undesired property . we introduce then a family of new variables such that some elements of the family can be applied to build a space of quantum states free of that property .    _ institute of theoretical physics , warsaw university + ul . hoa 69 , 00 - 681 warsaw , poland + oko@fuw.edu.pl_","abstract":"we present the first part of an analysis aimed at introducing variables which are suitable for constructing a space of quantum states for the teleparallel equivalent of general relativity via projective techniques  the space is meant to be applied in a canonical quantization of the theory . we show that natural configuration variables on the phase space of the theory can be used to construct a space of quantum states which however possesses an undesired property . we introduce then a family of new variables such that some elements of the family can be applied to build a space of quantum states free of that property .    _ institute of theoretical physics , warsaw university + ul . hoa 69 , 00 - 681 warsaw , poland + oko@fuw.edu.pl_"}
{"article_id":"1404.2930","section_id":"i","document":"many observational studies have measured dark matter halo masses in order to find correlations with the properties of the galaxies they host . various works have utilized gravitational lensing of background objects @xcite , virial temperatures derived from x - rays and dynamics of satellites @xcite . these methods have achieved high accuracy , but are also observationally expensive to carry out on large samples and for small haloes , which limits the statistical strength and range of application . a less direct but more comprehensive method of linking galaxies to haloes is abundance matching , which uses the merger trees from @xmath10-body dark matter simulations as input and assumes that the halo mass is the main determinant of galaxy luminosity and stellar mass . the basic idea is to cumulatively match observed galaxy luminosity functions and halo mass functions by placing progressively less luminous galaxies in less massive haloes . by design , this method reproduces the luminosity ( or stellar mass ) function , and is able to predict the clustering of galaxies in many cases @xcite . + direct measurements of galaxy clustering are another powerful way to connect galaxies with the underlying dark matter distribution . as a function of physical separation @xmath11 , clustering is commonly measured in the form of the two - point spatial correlation function @xmath12 ( scf ; peebles 1980 ) . the relation between the distributions of galaxies and dark matter can be parametrized through the galaxy bias @xmath13 , which is given by the scaling between the scfs of these two fields : @xmath14 the scf of dark matter depends on the cosmology , and can be prescribed analytically given those parameters @xcite . thus , the bias of a galaxy sample is directly determined by its scf . in general , the bias depends on the spatial scale and redshift @xcite , since galaxies and dark matter do not evolve in the exact same manner in time or space . the measurement of @xmath15 can therefore reveal a precise description of the connection between galaxies and dark matter . + many studies up to intermediate redshifts ( @xmath16 ) have investigated galaxy clustering with samples selected in different ways @xcite . the most common conclusion is that clustering strength is correlated with luminosity , red color and morphology ( towards early - type ) . galaxies on the extreme of these properties are highly biased and therefore they live in massive haloes . + these conclusions can be obtained just by analyzing the overall amplitude of the bias . however , the precise form of this observable as a function of spatial separation contains more information about the inner structure of the haloes . the halo occupation distribution ( hod ) is a simple parametric framework to accurately model the bias . it considers galaxies to be either centrals or satellites , and the number of these that a halo can host is fully determined by the halo mass . + one of the advantages of the hod framework is that its parameters have a clear physical meaning , and thus when fitting the clustering one can gain a deeper insight into the connection between the galaxies and their host haloes . for example , the hod framework can directly relate the average stellar mass of the central galaxies to a particular halo mass . as shown in many studies at @xmath17 , the ratio of these masses is highest around a halo mass of @xmath18 @xcite . this implies that there is a characteristic halo mass where galaxy formation has been more efficient . the qualitative explanation for this is that at low halo masses the gravitational potential is not deep enough to halt the expulsion of gas due to stellar winds @xcite , while high - mass haloes have heated up the intra - halo medium by gravitational heating and agn feedback @xcite so that infalling gas gets heavily shocked and can not easily cool and condense . these two trends can be reduced to a comparison between dynamical and gas cooling times in haloes , such that @xmath19 for low masses and @xmath20 for high - masses . a possible consequence is that the peak halo mass @xmath21 is related to a characteristic quenching mass @xmath22 that sets @xmath23 @xcite and marks a transition between star forming and quenched haloes . indeed , massive red galaxies with little star formation have been shown to live in massive haloes @xcite , supporting the idea of the red sequence of galaxies arising when they become quenched @xcite . this blue / red dichotomy is present in the nearby universe @xcite , and starts its build - up around @xmath24 @xcite . thus , when haloes become large enough , they quench their star formation . a consequence of this is that the most massive galaxies today have no significant ongoing star formation . this effect has been called archeological downsizing @xcite , and is also inferred from the lack of evolution in the massive end of the stellar mass function @xcite . hod models have shown that the stellar - to - halo mass ratio ( shmr ) evolves in the sense that the peak moves to lower halo masses with increasing time , at least since @xmath25 @xcite . this trend has been predicted to persist up to @xmath26 by extensions of hod that use conditional stellar mass functions @xcite and abundance matching studies @xcite . a possible mechanism for this would involve evolution in @xmath22 , which is supported by the idea that the universal gas fraction drops with time and therefore star formation becomes more difficult with time at fixed halo mass @xcite . however , this is still a matter of debate . for instance , @xcite present evidence in favor of this evolution being set by quenching below a critical galaxy - halo mass ratio instead of a critical halo mass . such a mechanism would also shift the shmr toward lower masses with time . + we have described the basic processes that can determine @xmath21 , based on the comparison of @xmath27 and @xmath28 as a function of halo mass . this basic model can be extended to include modes of galactic outflows , which are then directly constrained by the observed slope of the shmr . the stellar mass growth of a galaxy is heavily regulated by the expulsion of gas , which could be mainly sourced by supernovae feedback @xcite . the stellar mass loss rate , @xmath29 , can be broken down in two contributions : pressure - supported energy injection ( energy - driven winds ) and coherent momentum transfer ( momentum - driven winds ) . the energy and momentum deposition rates , @xmath30 and @xmath31 , can be related from first principles to the mass via a proxy of the kinetic velocity field , @xmath32 : @xmath33 and @xmath34 . this suggests that galaxies with low velocity fields , and therefore low masses , may have their outflows dominated by energy - driven winds @xcite . thus , a larger contribution from this type of wind would result in a steeper low mass slope of the shmr . + at high masses ( and high @xmath32 ) , these arguments would point to a dominance of momentum - driven winds . however , the winds in this regime are also sourced by radiative agn feedback , which is expected to have a strong contribution @xcite . in addition , a large merger rate between central galaxies will result in a flattening of the shmr @xcite . with all these processes at play , the high - mass slope is less straightforward to interpret than the low - mass one , but it can still offer important constraints on this combination of mechanisms . + galaxy clustering combined with hod modeling provide particularly solid measurements of the shmr whenever the selection of galaxies spans the relevant range of stellar masses . at @xmath35 , such measurements have proven to be very difficult given the lack of large volume - limited samples . @xcite use the 0.25 deg@xmath0 newfirm survey @xcite , but the low number statistics made it difficult to map the turnover of the shmr . in this study , we use a 94 deg@xmath0 mid - infrared survey to select galaxies with stellar masses ranging from @xmath2 and fit an hod model to the angular correlation function . we present the most robust measurement to date of the peak of the shmr at @xmath9 . + in addition , the hod yields particularly strong constraints on the satellite population of a given galaxy sample . we determine what fraction of the galaxies are satellites , and how the abundance of these depends on the halo mass . moreover , we measure a proxy for the occurrence of galaxy pairs of similar mass , and find that it mildly decreases toward high luminosities . although we do not achieve a robust detection , this represents the opposite trend to what is seen at low - redshift . the processes that produce this relationship are strongly tied to the accretion and merger events between galaxies and haloes , as well as the quenching of star formation in satellites . + the paper is organized as follows . in section [ s_datasets ] , we describe all datasets that are used . in section [ s_ctrlsamples ] we describe how we adapt redshift and stellar mass distributions from a reference optical + mid - ir survey . in section [ s_2pt ] we define the two - point clustering statistic and the method used to compute it . in section [ s_placing ] , we describe the model that links galaxies to haloes . in section [ s_fits ] , we explain the fitting procedure of the hod to the observed clustering . in sections [ s_shmr ] , [ s_satellites ] and [ s_bg ] we discuss the results obtained regarding the shmr , the satellite galaxies and the large - scale bias , respectively . we end with a short summary in section [ s_summary ] . for the reader that is only interested in the results , we recommend reading sections [ s_shmr ] and beyond . + additionally , we include several appendices where many of the details are covered . appendix [ s_photsims ] presents a calibration of systematic effects in the photometry . appendix [ a_evsc ] compares the results obtained from using different reference catalogs to draw redshift and stellar mass distributions . appendix [ s_ic ] calculates the systematic offset in the clustering amplitude due to the geometry of the survey . appendix [ a_halo ] presents the formalism of the halo model . appendix [ nosc ] investigates the removal of low - redshift sources from the sample using optical data . appendix [ a_tests ] explores different choices of free parameters used in the hod fits to the clustering . + throughout this paper we use the following cosmology : @xmath36 , @xmath37 and @xmath38 @xmath39mpc@xmath40 . all magnitudes are in the vega system and masses are in units of @xmath41 .","summary":"the mid - infrared photometry efficiently selects galaxies at in the stellar mass range , making this sample the largest used so far to study such a distant population . we fit halo occupation distributions and determine how the central galaxy s stellar mass and satellite occupation depend on the halo mass . we measure a prominent peak in the stellar - to - halo mass ratio at a halo mass of , 4.5 times higher than the value . this supports the idea of an evolving mass threshold above which star formation is quenched . we also find that , above a given stellar mass limit , the fraction of galaxies that are in similar mass pairs is higher at than at . in addition , we measure that this fraction mildly increases with the stellar mass limit at , which is the opposite of the behavior seen at low - redshift .    [ firstpage ]    cosmology : observations  galaxies : evolution  galaxies : high - redshift  galaxies : halos  large scale structure of universe","abstract":"we present an analysis of the clustering of high - redshift galaxies in the recently completed 94 deg _ spitzer_-spt deep field survey . applying flux and color cuts to the mid - infrared photometry efficiently selects galaxies at in the stellar mass range , making this sample the largest used so far to study such a distant population . we measure the angular correlation function in different flux - limited samples at scales ( corresponding to physical distances mpc ) and thereby map the one- and two - halo contributions to the clustering . we fit halo occupation distributions and determine how the central galaxy s stellar mass and satellite occupation depend on the halo mass . we measure a prominent peak in the stellar - to - halo mass ratio at a halo mass of , 4.5 times higher than the value . this supports the idea of an evolving mass threshold above which star formation is quenched . we estimate the large - scale bias in the range and the satellite fraction to be , showing a clear evolution compared to . we also find that , above a given stellar mass limit , the fraction of galaxies that are in similar mass pairs is higher at than at . in addition , we measure that this fraction mildly increases with the stellar mass limit at , which is the opposite of the behavior seen at low - redshift .    [ firstpage ]    cosmology : observations  galaxies : evolution  galaxies : high - redshift  galaxies : halos  large scale structure of universe"}
{"article_id":"astro-ph0612696","section_id":"i","document":"cataclysmic variables ( cvs ) are binary stars consisting of a white dwarf ( wd ) and a late spectral type secondary which fills , or almost fills , its roche lobe and transfers mass to the wd . cvs divide into a number of subclasses @xcite and the object of our study , mv lyrae , is a novalike cv of the vy scl subclass . a defining characteristic of this subclass is a non - periodic alternation between high and low luminosity states , differentiated by a change in mean brightness of more than one magnitude between states . this alternation usually takes place on intervals of hundreds of days . the orbital period of mv lyr , @xmath2 , places it close to the long - period end of the period gap @xcite . its high - low range is 12.2 - 18 , inferred from fig.4 of @xcite . while it is widely argued that evolution of cvs with periods longer than the period gap is controlled by magnetic braking @xcite , and evolution shortward of the gap is driven by gravitational radiation @xcite , this scenario has been recently challenged by , e.g. , @xcite , @xcite , and @xcite . patterson ( 1984 ) developed an empirical mass transfer relationship for cvs which predicts a mass transfer rate of @xmath3 at the orbital period of mv lyr . a theory of magnetic braking @xcite shows that the mass transfer rate from the secondary is a decreasing function with decreasing orbital period , reaching a value of @xmath4 at the top of the period gap , where mv lyr is found , for the parameters used in their study . some authors , as discussed below , adopt even larger mass transfer rates at the top of the period gap .    if the magnetic braking mechanism that drives evolution of the secondary star is suddenly turned off at an orbital period of @xmath5 , then the secondary approaches thermal equilibrium on a kelvin - helmholtz timescale . consequently , mass transfer continues at a decreasing rate for @xmath6 @xcite . but the alternation between high and low states in vy scl stars is on a much shorter timescale and requires a separate mechanism to switch the mass transfer on and off . @xcite discuss the problem and propose starspots on the secondary star , which pass across the l1 point and cause reduced mass transfer . this proposal has been further developed @xcite with application of a time - dependent code to model the variable accretion disk . ( see also @xcite ) . but the @xcite model produced the unwanted result of dwarf - nova type outbursts in the low state , after mass transfer had been switched off . a suggested escape was maintenance of the inner accretion disk in a permanent high state through irradiation by the wd ( leach et al . 1999 , hereafter l1999 ) . l1999 concluded that the presence of a 40,000k wd does suppress dwarf nova outbursts . the l1999 study adopted a high state mass transfer rate of @xmath7 that was chosen to guarantee that hydrogen is fully ionized at the outer accretion disk boundary . according to l1999 , cessation of mass transfer produces a rapid transition to a state of low but non - zero viscosity . the accretion disk remains nearly intact during the low state , transferring only a few percent of the accretion disk mass to the wd . because of non - zero viscosity , the accretion disk still radiates at a low level during the low state . hameury & lasota ( 2002 , hereafter hl02 ) show that the adopted wd mass in l1999 ( 0.4@xmath8 ) is important to the suppression of outbursts , and that a wd mass of 0.7@xmath8 would have produced outbursts . hl02 alternatively propose that vy scl stars have magnetic wds and that the magnetic field truncates the accretion disk . hl02 show that , for a wd mass of 0.7@xmath8 and a magnetic moment of @xmath9 , no outbursts occur and the change in the @xmath10 magnitude , from high state to low state , is 5 magnitudes . hoard et al . ( 2004 , hereafter h2004 ) used the binsyn suite @xcite to calculate a system model and corresponding synthetic spectrum for mv lyr in a recent low state . the synthetic spectrum accurately fits _ fuse _ spectra and contemporaneous optical spectra , as well as _ iue _ spectra from a prior low state . the h2004 discussion considers the connection of the low state study to earlier investigations of mv lyr and shows that the low state can be understood in terms of a naked hot wd with a temperature of 47,000k , a photosphere log @xmath11 of 8.25 , and a metallicity of 0.3 solar . the log @xmath11 , together with the mass - radius relation for zero - temperature carbon wd models @xcite selects a model with @xmath12 , estimated error of @xmath13 , and radius of @xmath14 . the secondary star fills its roche lobe and is cooler than 3500k ; it contributes nothing to the fuv flux and a varying amount to the optical flux , from 10% at 5200  to 60% at 7800 . if an accretion disk is present it contributes negligibly to the observed spectra . assuming no disk is present , the model optical light curve , for a system orbital inclination of @xmath15 taken from the literature , has an amplitude approximately 50% larger that of the observed optical light curve . the scaling of the model spectrum to the observed data leads to a distance of @xmath16pc to mv lyr .    in  2 of this paper we describe the program suite used to analyze the observed spectra . in  3 we further investigate the low state and derive improved system parameters . in  4 we show that it is possible to augment the low state system with an accretion disk with artificially elevated @xmath1 at large radii and achieve a close fit to intermediate state _ iue _ archival spectra . in  5 we show that our models produce a predicted @xmath17 , low state to intermediate state , that is one magnitude larger than observed , indicating a problem with the models . in  6 we show that an isothermal 14,000k accretion disk extending half way to the tidal cutoff radius resolves the @xmath17 problem and provides a fair fit to the _ iue _ spectra .  7 presents a model fit to a new high state hst spectrum ,  8 considers the predicted luminosity change low state to high state , a general discussion is in  9 and  10 summarizes our results .","summary":"archival _ iue _ spectra of the vy scl system mv lyr , taken during an intermediate state , can be best fit by an isothermal accretion disk extending half way to the tidal cutoff radius . these fits use component star parameters determined from a study of mv lyr in a low state .","abstract":"archival _ iue _ spectra of the vy scl system mv lyr , taken during an intermediate state , can be best fit by an isothermal accretion disk extending half way to the tidal cutoff radius . in contrast , a recent hst spectrum , while mv lyr was in a high state , can be best fit with a standard profile for an accretion disk extending from an inner truncation radius to an intermediate radius with an isothermal accretion disk beyond . these fits use component star parameters determined from a study of mv lyr in a low state . model systems containing accretion disks with standard profiles have continua that are too blue . the observed high state absorption line spectrum exhibits excitation higher than provided by the profile , indicating likely line formation in a high temperature region extending vertically above the accretion disk . the absorption lines show a blue shift and line broadening corresponding to formation in a low velocity wind apparently coextensive with the high temperature region . lines of n v , si iv , c iv , and he ii are anomalously strong relative to our synthetic spectra , indicating possible composition effects , but unmodeled excitation effects could also produce the anomalies .    an analysis of a low state of mv lyrae , considered in an earlier study and extended in this paper , sets a limit of 2500k for the of an accretion disk that may be present in the low state . this limit is in conflict with two recent models of the vy scl phenomenon ."}
{"article_id":"astro-ph0612696","section_id":"c","document":"the significant result from our low state study is that , to within observational error , the system spectrum can be represented by a combination of a wd spectrum and an irradiated , @xmath108k secondary component . there is no observational evidence for accretion disk emission in the mv lyr low state . our newly calculated contribution of the secondary star is an interpolation among nextgen models and includes allowance for irradiation of the secondary by the wd . both l1999 and hl02 model the low state of mv lyr with a truncated accretion disk that retains most of its mass from the high state , and emits radiation at a level consistent with residual viscosity . our results limit possible low state accretion disk emission to values well below those predicted by both l1999 and hl02 . @xcite discuss the occasional sudden drops in luminosity of v974 aql and show that the drops can be explained within the accretion disk limit cycle theory in terms of back and forth propagation of cooling and heating transition fronts . as with l1999 and hl02 , @xcite find that the accretion disk undergoes little net mass loss while mass transfer from the secondary is turned off . hl02 discuss slow passage of an accretion disk system from an initial stable state through the instability region and show that outside - in outbursts would occur but are unobserved . the only solution to the vy scl phenomenon that they visualize , to meet the constraint imposed by the case of tt ari @xcite , is a magnetic field sufficiently large ( b@xmath109 mg ) to truncate the residual low state accretion disk at a radius large enough to suppress accretion disk formation . however , as hl02 note , if a magnetic field is present , then circular polarization should also be present . @xcite chronicles that repeated attempts to measure the circular polarization in mv lyr always found a value less than 0.13% . robinson et al . also note that , if there is a magnetic field present that is strong enough to disrupt the accretion disk , zeeman - splitting of absorption lines should be detected ; it is not . thus , there is no evidence for a strong magnetic field associated with the mv lyr wd .    both the intermediate state spectra and the high state hst spectra are inconsistent with our calculated standard models , having flatter flux profiles . our subsequent thin disk simulations , using tlusty annulus models , differ from the standard model by assuming a flatter @xmath0 profile ; they are able to produce fairly good fits to the observed continua . confirmation that the tlusty annuli represent a thin disk model is provided by the output data for an annulus at @xmath110 and for a mass transfer rate of @xmath46 , close to the value of our high state model . for this annulus , whose radius is @xmath111 cm , a rosseland optical depth of 0.81 is located at @xmath112 cm , one dex smaller than the radius . a rosseland optical depth of 0.001 occurs at @xmath113 cm , indicating line formation in a thin photosphere . smak ( 1994 ) has discussed peculiar ( i.e. , non - standard model ) , @xmath0 distributions . the departures from the standard model in the systems he cites ( e.g. , @xcite ) are in the direction of a too flat @xmath0 profile , as we find for mv lyr . smak argues that the departures for systems with @xmath114 result from the assumption of a flat accretion disk . that explanation is not applicable for mv lyr because of its low inclination . smak suggests that , for low @xmath53 cases , heating of the outer part of the accretion disk by the stream collision could be the explanation . buat - mnard , hameury & lasota ( 2001 ) discuss the effect of stream impact heating and tidal effects . as our high state model indicates , if stream impact heating is the physical cause of anomalous heating in the outer accretion disk region , the heating effects extend over an appreciable fraction of the accretion disk radius . this effect differs from a bright spot , for which the radial extent amounts to a few percent of the component separation ( see * ? ? ? * sect.2.6.5 ) . we stress the importance of the low orbital inclination in mv lyr and the consequential absence of eclipses . all of the systems cited by smak were shown to have peculiar @xmath0 distributions by application of the mem technique ( @xcite ) and so were restricted to systems showing eclipses . the spectrum synthesis method used in this paper represents an alternative and independent technique that is applicable to both eclipsing and non - eclipsing systems . the presence of high - excitation absorption lines in the mv lyr system imply their formation in a high temperature region above ( both faces of ) the accretion disk , possibly similar to a chromosphere or corona . accretion disk coronae are considered in @xcite , @xcite , and @xcite . we have presented evidence for formation of both the intermediate state emission lines and the high state absorption lines in a wind , apparently coextensive with the high temperature region . it would be of interest to search for a p - cygni profile , possibly in the infra - red . we thank the referee for this suggestion . @xcite summarizes known properties of winds from cvs . @xcite discuss a model of radiation - driven winds from accretion disks , and @xcite discuss the stability of line - driven winds . table  2 lists the fwhm wavelength ranges for the principal absorption lines in the hst spectrum . in most cases , several transitions contribute to a given line . the low mv lyr @xmath53 value nominally would imply narrow disk lines , distinctly different from the observations . the observed broadening is consistent with lines of sight that traverse a range of radial velocities before reaching an optical depth of 1.0 . the @xmath115 blue shift of the absorption lines is smaller than typically found for winds from accretion disks . our tlusty annuli models are in lte and apply default values for the internal parameters , leading to a negative temperature gradient perpendicular to the surface of the annulus . line formation in a vertically extended wind violates our model assumption of hydrostatic equilibrium ; addition of a wind model , @xcite , might provide improved representation of the mv lyr spectral data . @xcite combined tlusty disk models with a representation of a biconical wind in a study of ss cyg . we speculate that continuum formation takes place under conditions different from the assumptions of our annulus models and that difference may explain our failure to achieve an accurate continuum fit , especially in the intermediate state . @xcite discusses conditions for hot upper layers of accretion disk annuli to exist . he shows that the z - direction profile of viscosity strongly affects the formation of these regions . @xcite discuss the treatment of viscosity as implemented in tlusty , in particular the steps taken to prevent a high temperature z - direction anomaly . the authors also emphasize the importance of nlte effects . it is widely believed that the physical cause of accretion disk viscosity is the magnetorotational instability @xcite . @xcite discusses issues in the implementation of the instability in accretion disk models . the magnetohydrodynamical simulations of @xcite find an increase in viscosity toward the accretion disk surface , leading to increased z - direction heating .    the flatter spectral profile of the intermediate state _ iue _ spectrum , as compared to the hst high state spectrum ( fig . 11 ) is of particular interest . the isothermal accretion disk extending only half way to the tidal cutoff radius in the intermediate state has the attractive feature that it provides a ready explanation for emission lines ( the line emission region is seen extending beyond the edge of the accretion disk ) , while the same lines are seen in absorption in the high state ( the accretion disk now extends to the tidal cutoff radius ) . this scenario indirectly supports the absence of an accretion disk in the low state , again in disagreement with l1999 and hl02 . an explanation of the flat @xmath0 profile , both intermediate and high , must differ from the case of dw uma @xcite , also a vy scl star . in dw uma there is also a flat @xmath0 profile , but it is explained by self - occultation by a puffed - up outer accretion disk rim and an orbital inclination large enough to produce eclipses of the wd .","summary":"in contrast , a recent hst spectrum , while mv lyr was in a high state , can be best fit with a standard profile for an accretion disk extending from an inner truncation radius to an intermediate radius with an isothermal accretion disk beyond . the observed high state absorption line spectrum exhibits excitation higher than provided by the profile , indicating likely line formation in a high temperature region extending vertically above the accretion disk .","abstract":"archival _ iue _ spectra of the vy scl system mv lyr , taken during an intermediate state , can be best fit by an isothermal accretion disk extending half way to the tidal cutoff radius . in contrast , a recent hst spectrum , while mv lyr was in a high state , can be best fit with a standard profile for an accretion disk extending from an inner truncation radius to an intermediate radius with an isothermal accretion disk beyond . these fits use component star parameters determined from a study of mv lyr in a low state . model systems containing accretion disks with standard profiles have continua that are too blue . the observed high state absorption line spectrum exhibits excitation higher than provided by the profile , indicating likely line formation in a high temperature region extending vertically above the accretion disk . the absorption lines show a blue shift and line broadening corresponding to formation in a low velocity wind apparently coextensive with the high temperature region . lines of n v , si iv , c iv , and he ii are anomalously strong relative to our synthetic spectra , indicating possible composition effects , but unmodeled excitation effects could also produce the anomalies .    an analysis of a low state of mv lyrae , considered in an earlier study and extended in this paper , sets a limit of 2500k for the of an accretion disk that may be present in the low state . this limit is in conflict with two recent models of the vy scl phenomenon ."}
{"article_id":"astro-ph0612696","section_id":"i","document":"\\(1 ) based on the excellent fit of a system synthetic spectrum to fuse , _ iue _ , and optical low state spectra ( h2004 ) , any accretion disk that may be present in the low state must have a @xmath1 less than 2500k . this result agrees with a study of the cv system tt ari @xcite . a comparison of our results ( fig . 3 ) with two models ( l1999 and hl02 ) of the vy scl phenomenon demonstrates a discrepancy with those models . \\(2 ) using tlusty annulus models , and corresponding synthetic spectra , to simulate an intermediate state for which _ iue _ spectra are available , we show that a standard model ( see text ) can not produce a system synthetic spectrum that satisfactorily fits the _ iue _ spectra . a rough fit is possible with a standard model with a mass transfer rate of @xmath4 but the model synthetic spectrum is too blue . a fairly good fit is possible with a mass transfer rate of @xmath116 , a truncation radius of @xmath44 , and with @xmath0=9500k beyond @xmath117 . but this model produces a change in @xmath10 magnitude between the low and intermediate states that is about one magnitude larger than the observational value . an isothermal 14,000k accretion disk with a radius that is half of the tidal cutoff radius produces agreement with the v magnitude change ; this model is slightly bluer than the _ iue _ spectra . \\(3 ) study of a high state demonstrates that no combination of mass transfer rate and truncation radius can produce a standard model system synthetic spectrum whose continuum satisfactorily fits our recent hst spectrum . all synthetic spectra are too blue . a fairly good fit is possible for a mass transfer rate of @xmath96 , a truncation radius of @xmath44 , and @xmath0=12,000k beyond @xmath118 . this model produces a calculated system flux at 7228.5  that is in reasonable agreement with a measurement of hst optical flux . \\(4 ) the absorption lines in our mv lyr hst spectrum show a range of excitations , and corresponding temperatures , that are higher than the nearly flat continuum would imply . this result is consistent with line formation in a large @xmath119 high temperature region . anomalous line strengths of c , n , si , and he have a possible interpretation in terms of composition effects , but excitation effects can not be disentangled . \\(5 ) the slight blue shift of the absorption lines ( @xmath120 ) , as compared with the system radial velocity of @xmath121 , indicates that the absorption lines are formed in a low velocity wind , which is coextensive with the large @xmath119 high temperature region . there is no apparent difference in velocity between the emission line intermediate state spectrum and the high state absorption line spectrum ; the wind and high temperature structures appear to be present in both the intermediate and high states . \\(6 ) the difference between the physical conditions under which the absorption and emission lines form in a wind and the physical conditions assumed by our hydrostatic equilibrium annulus models , used to calculate the synthetic spectra , may explain our difficulty in fitting the high state and intermediate state continua accurately . the same problem may explain the failure of our synthetic spectra to represent the high excitation absorption lines in the high state hst spectra .","summary":"the absorption lines show a blue shift and line broadening corresponding to formation in a low velocity wind apparently coextensive with the high temperature region . an analysis of a low state of mv lyrae , considered in an earlier study and extended in this paper , sets a limit of 2500k for the of an accretion disk that may be present in the low state . this limit is in conflict with two recent models of the vy scl phenomenon .","abstract":"archival _ iue _ spectra of the vy scl system mv lyr , taken during an intermediate state , can be best fit by an isothermal accretion disk extending half way to the tidal cutoff radius . in contrast , a recent hst spectrum , while mv lyr was in a high state , can be best fit with a standard profile for an accretion disk extending from an inner truncation radius to an intermediate radius with an isothermal accretion disk beyond . these fits use component star parameters determined from a study of mv lyr in a low state . model systems containing accretion disks with standard profiles have continua that are too blue . the observed high state absorption line spectrum exhibits excitation higher than provided by the profile , indicating likely line formation in a high temperature region extending vertically above the accretion disk . the absorption lines show a blue shift and line broadening corresponding to formation in a low velocity wind apparently coextensive with the high temperature region . lines of n v , si iv , c iv , and he ii are anomalously strong relative to our synthetic spectra , indicating possible composition effects , but unmodeled excitation effects could also produce the anomalies .    an analysis of a low state of mv lyrae , considered in an earlier study and extended in this paper , sets a limit of 2500k for the of an accretion disk that may be present in the low state . this limit is in conflict with two recent models of the vy scl phenomenon ."}
{"article_id":"astro-ph0002062","section_id":"i","document":"@xcite and @xcite have summarized the relative importance of star formation , gas inflow , and gas outflow in the galactic center ( gc ) . gas from the inner disk flows into the nucleus , perhaps driven by a bar potential @xcite , and some of the stellar mass - loss from the bulge may fall into the gc @xcite . @xcite have proposed that this inflow of disk gas results in sustained star formation in a  central molecular zone \" ( cmz ) within a radius from the gc of @xmath3 200 pc . the gc is observed to be currently forming stars in the cmz at a rate of 0.30.6 m@xmath4 yr@xmath5 @xcite . some of the gc gas incorporated into stars , enriched by stellar nucleosynthesis , will be returned to the gc interstellar medium by stellar mass - loss and supernovae . x - ray observations of hot gas in the gc suggest that some gas could be driven temporarily or permanently from the gc by a galactic fountain or wind @xcite , however , making it unclear how much enriched material is incorporated into following generations of star formation . the presence of strong magnetic fields in the gc also likely plays a role in whether enriched gas is driven from or is retained within the gc . continued star formation in the central few hundred parsecs of the galaxy may lead to higher metallicities within the cmz . chemical abundances in the disks of spiral galaxies are observed to reach their highest values at the center ( see * ? ? ? * ; * ? ? ? h ii regions , planetary nebulae , and ob associations in the milky way also show a radial metallicity gradient @xcite . chemical evolution models strive to explain these gradients by considering the relative star formation and gas infall / outflow rates , and the metal abundance of the gas compared to the stars ( see * ? ? ? * ; * ? ? ? the metallicity of gc stars is needed in order to constrain models and understand the stellar processes in the central parsecs of our galaxy . measurements of stellar metallicities in the center of the milky way galaxy , which is obscured by approximately 30 mag of extinction at @xmath6 , are only now beginning to be feasible through infrared studies . @xcite found a solar fe abundance in irs 7 , an m supergiant at a distance of @xmath7 0.2 pc from the gc , from a detailed abundance analysis of cshell ( @xmath8 = 40,000 ) @xmath1band spectra . our work analyzes similar data for several m supergiant and giant stars located in the central cluster , within 0.5 pc of the gc , and also one m supergiant star located in the quintuplet cluster , 30 pc away from the gc .","summary":"we present measurements of [ fe / h ] for six m supergiant stars and three giant stars within 0.5 pc of the galactic center ( gc ) and one m supergiant star within 30 pc of the gc .","abstract":"we present measurements of [ fe / h ] for six m supergiant stars and three giant stars within 0.5 pc of the galactic center ( gc ) and one m supergiant star within 30 pc of the gc . the results are based on high - resolution ( 40,000 )band spectra , taken with cshell at the nasa infrared telescope facility . we determine the iron abundance by detailed abundance analysis , performed with the spectral synthesis program moog . the mean [ fe / h ] of the gc stars is determined to be near solar , [ fe / h ] = + 0.12 0.22 . our analysis is a _ differential _ analysis , as we have observed and applied the same analysis technique to eleven cool , luminous stars in the solar neighborhood with similar temperatures and luminosities as the gc stars . the mean [ fe / h ] of the solar neighborhood comparison stars , [ fe / h ] = + 0.03 0.16 , is similar to that of the gc stars . the width of the gc [ fe / h ] distribution is found to be narrower than the width of the [ fe / h ] distribution of baade s window in the bulge but consistent with the width of the [ fe / h ] distribution of giant and supergiant stars in the solar neighborhood ."}
{"article_id":"astro-ph0002062","section_id":"c","document":"we present the first measurement of stellar [ fe / h ] for ten stars in the galactic center ( gc ) , at distances from the gc of @xmath12 30 pc . nine gc stars are located in the central cluster ( @xmath12 0.5 pc ) and one star is located in the quintuplet cluster ( @xmath13 = 30 pc ) . the abundance analysis is based on high - resolution ( @xmath0 40,000 ) @xmath1band spectra . the mean [ fe / h ] of the gc is determined to be near solar , [ fe / h ] = + 0.12 @xmath2 0.22 , and also similar to the mean [ fe / h ] for cool , luminous stars in the solar neighborhood , [ fe / h ] = + 0.03 @xmath2 0.16 , observed and analyzed in the same way . the width of the gc [ fe / h ] distribution , which ranges from [ fe / h ] = 0.3 to + 0.5 , is found to be significantly narrower than the width of the [ fe / h ] distribution of baade s window , which ranges from [ fe / h ] = 1.0 to + 0.8 . the gc [ fe / h ] distribution is consistent with the [ fe / h ] distribution of supergiant stars in the solar neighborhood . this suggest that the most luminous stars in the gc are unlikely to be dominated by bulge - like stars , and that the evolutionary path of the gc , while unique , is closer to the disk s than to the bulge s . the quintuplet star at @xmath13 = 30 pc has a similar [ fe / h ] to stars located in the central cluster at @xmath12 0.5 pc . in the future , abundance measurements of cno and @xmath44elements are planned to provide a complete view of the abundance patterns of the stars in the central regions of the milky way . support for this work was generously provided by the national science foundation through nsf grant ast-9619230 to k.s . and r.d.b . s.v.r . also gratefully acknowledges support from a gemini fellowship ( grant # gf-1003 - 97 from the association of universities for research in astronomy , inc . , under nsf cooperative agreement ast-8947990 and from fundacin andes under project c-12984 ) , from an ohio state presidential fellowship , and from an ohio state alumni research award . s.c.b . acknowledges support from nsf grants ast-9618335 and ast-9819870 , and j.s.c . from the office of naval research . s.v.r . would like to thank e. luck , r. kraft , b. plez , a. pradhan , r. pogge , a. gould , a. sills , and c. sneden for useful suggestions and enlightening comments . we thank d. figer for his generosity in sharing his spectrum of irs 7 in advance of publication . electronic versions of our spectra are available upon request to s.v.r . llcccccc hr 6146 & m6 iii & 45 & 3250@xmath2100 & -5.5 & 0.2@xmath20.3 & 2.0@xmath20.5 & 9.6@xmath21.1 + hr 6702 & m5 ii - iii & 36 & 3300@xmath2100 & -3.4 & 0.7@xmath20.3 & 2.0@xmath20.5 & 7.8@xmath21.8 + hr 7442 & m5 iiias & 36 & 3450@xmath2100 & -4.0 & 0.5@xmath20.3 & 2.4@xmath20.2&10.5@xmath22.7 + hr 8062 & m4 iiias & 34 & 3450@xmath2100 & -3.5 & 0.7@xmath20.3 & 1.7@xmath20.2 & 8.9@xmath20.5 + @xmath18 ori&m1 - 2 iab - a&305 & 3540@xmath2260 & -7.4 & 0.0@xmath20.3 & 2.8@xmath20.2&14.7@xmath20.5 + hr 8383 & m2 iape+ & 100 & 3480@xmath2250 & -6.8 & 0.0@xmath20.3 & 2.7@xmath20.2&14.4@xmath22.1 + hd 202380&m3 ib & 46 & 3600@xmath2200 & -5.7 & 0.6@xmath20.5 & 2.5@xmath20.2&16.2@xmath20.5 + hd 163428&k5 ii & 67 & 3800@xmath2200 & -5.5 & 0.6@xmath20.5 & 2.3@xmath20.2&11.5@xmath23.2 + bd+59 594&m1 ib & 49 & 4000@xmath2200 & -6.6 & -0.9@xmath20.3 & 3.1@xmath20.2&18.2@xmath21.0 + hd 232766&m1 iab & 38 & 4000@xmath2200 & -6.6 & 0.2@xmath20.3 & 2.2@xmath20.2&11.5@xmath23.7 + hr 8726 & k5 iab & 57 & 4000@xmath2200 & -5.2 & 0.5@xmath20.3 & 2.4@xmath20.2&11.4@xmath20.5    ccc 21781.82 & 3.415 & 4.485 + 22381.27 & 5.844 & 1.458 + 22386.90 & 5.033 & 0.481 + 22391.22 & 5.320 & 1.600 + 22398.98 & 5.099 & 1.249 + 22818.82 & 5.792 & 1.296 + 22838.60 & 5.099 & 1.325 + 22852.17 & 5.828 & 0.612 lcccccccc irs 7 & i & 52&3470@xmath2250&9.0&17@xmath23 & 0.6@xmath20.2 & 3.3@xmath20.4 & 20.6@xmath22.7 + vr 5 - 7 & i & 30&3500@xmath2300&7.8&14@xmath22 & 0.2@xmath20.3 & 2.9@xmath20.5 & 12.6@xmath21.6 + irs 19 & i & 75&3650@xmath2300&7.2&14@xmath22 & 0.1@xmath20.3 & 2.7@xmath20.5 & 13.4@xmath22.0 + irs 22 & i & 25&3550@xmath2300&6.4&10@xmath22 & 0.3@xmath20.3 & 2.5@xmath20.5 & 12.8@xmath21.6 + bsd 124 & i & 10&3600@xmath2300&5.5 & 7@xmath23 & 0.4@xmath20.3 & 2.4@xmath20.5 & 12.7@xmath22.7 + bsd 129 & i & 13&3650@xmath2300&5.3 & 7@xmath23 & 0.5@xmath20.3 & 2.4@xmath20.5 & 12.3@xmath22.7 + bsd 72 & i & 13&3750@xmath2300&4.5 & 5@xmath22 & 0.8@xmath20.3 & 2.1@xmath20.5 & 11.0@xmath22.7 + bsd 114 & iii&15&3100@xmath2280&5.8 & 3@xmath21 & 0.2@xmath20.5 & 2.9@xmath20.6 & 9.0@xmath23.0 + irs 11 & iii&16&3100@xmath2280&5.3 & 3@xmath21 & 0.0@xmath20.5 & 2.8@xmath20.6 & 9.1@xmath22.2 + bsd 140 & iii&13&3100@xmath2280&4.8&2.5@xmath21&0.1@xmath20.5 & 2.9@xmath20.6 & 9.0@xmath23.0    lccccccc hr 6146 & 90@xmath2 6 & 355@xmath2 8 & 162@xmath2 7 & 210@xmath2 7 & 130@xmath2 6 & 277@xmath2 7 & 211@xmath2 7 + hr 6702 & 67@xmath2 5 & 332@xmath2 9 & 136@xmath2 7 & 189@xmath2 7 & 119@xmath2 6 & 234@xmath2 7 & 220@xmath2 7 + hr 7442 & 60@xmath2 5 & 339@xmath2 9 & 143@xmath2 8 & 174@xmath2 8 & 141@xmath2 8 & 294@xmath2 8 & 246@xmath2 8 + hr 8062 & 65@xmath2 5 & 351@xmath2 9 & 149@xmath2 7 & 199@xmath2 6 & 110@xmath2 6 & 208@xmath2 7 & @xmath45 + @xmath18 ori & 101@xmath2 8 & 520@xmath210 & 218@xmath210 & 319@xmath210 & 178@xmath210 & 339@xmath210 & 271@xmath210 + hd 202380 & 102@xmath2 8 & 476@xmath211 & 180@xmath2 9 & 311@xmath2 9 & 137@xmath2 8 & 299@xmath2 9 & @xmath45 + hr 8383 & 86@xmath2 7 & 466@xmath210 & 183@xmath2 9 & 285@xmath2 9 & 112@xmath2 8 & 261@xmath2 9 & 233@xmath2 9 + hd 163428 & 87@xmath2 7 & 430@xmath2 9 & 172@xmath2 9 & 241@xmath2 9 & 113@xmath2 8 & 263@xmath2 8 & @xmath45 + bd+59 594 & 107@xmath2 9 & 522@xmath211 & 171@xmath212 & 329@xmath212 & 96@xmath2 9 & 289@xmath213 & 226@xmath212 + hd 232766 & 66@xmath2 6 & 410@xmath2 8 & 159@xmath2 9 & 228@xmath2 9 & 97@xmath2 8 & 216@xmath2 9 & 173@xmath2 9 + hr 8726 & 71@xmath2 6 & 397@xmath2 8 & 158@xmath2 8 & 234@xmath2 8 & 115@xmath2 8 & 239@xmath2 8 & 186@xmath2 8    lcccccccc hr 6146 & 0.05 & + 0.05 & 0.20 & 0.00 & 0.30 & + 0.15 & + 0.25 & + 0.10 + hr 6702 & 0.05 & 0.05 & 0.25 & 0.05 & 0.30 & + 0.20 & + 0.10 & + 0.30 + hr 7442 & + 0.10 & + 0.10 & 0.25 & + 0.10 & 0.60 & + 0.20 & + 0.20 & + 0.20 + hr 8062 & + 0.10 & 0.10 & 0.05 & + 0.05 & 0.20 & + 0.10 & 0.05 & @xmath45 + @xmath18 ori & + 0.15 & 0.00 & + 0.05 & + 0.05 & 0.10 & + 0.20 & + 0.10 & 0.00 + hd 202380 & + 0.10 & + 0.10 & + 0.10 & 0.00 & + 0.10 & + 0.10 & + 0.10 & @xmath45 + hr 8383 & 0.05 & 0.10 & 0.10 & 0.10 & 0.20 & 0.15 & 0.25 & 0.10 + hd 163428 & + 0.07 & 0.00 & 0.00 & 0.02 & 0.25 & 0.05 & 0.05 & @xmath45 + bd+59 594 & 0.10 & 0.00 & 0.25 & 0.25 & 0.25 & 0.30 & 0.35 & 0.35 + hd 232766 & 0.10 & 0.20 & 0.15 & 0.15 & 0.40 & 0.20 & 0.40 & 0.40 + hr 8726 & + 0.15 & 0.10 & 0.00 & 0.05 & 0.20 & 0.00 & 0.10 & 0.20 +    lcccccccc irs 7 & + 0.35 & + 0.22&0.15&0.10 &  & + 0.38&0.30 &  + & @xmath20.05&@xmath20.07&@xmath20.10&@xmath20.05 & & @xmath20.05&@xmath20.05 & + vr 5 - 7 & + 0.12 & + 0.20&0.30 & + 0.15&0.40 & + 0.10 & + 0.15 &  + & @xmath20.03&@xmath20.07&@xmath20.10&@xmath20.05&@xmath20.10&@xmath20.05&@xmath20.07 & + irs 19 & + 0.30 & + 0.40&0.30 & + 0.40&0.05 & + 0.45&0.05 &  + & @xmath20.05&@xmath20.05&@xmath20.10&@xmath20.07&@xmath20.10&@xmath20.05&@xmath20.10 & + irs 22 & + 0.30&0.05&0.40 & + 0.15&0.40 & + 0.20 & + 0.35 & + 0.30 + & @xmath20.05&@xmath20.05&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10 + bsd 124 &  & + 0.22 & + 0.20 & + 0.20&0.10 & + 0.20 & + 0.20 &  + & & @xmath20.07&@xmath20.10&@xmath20.20&@xmath20.10&@xmath20.05&@xmath20.10 & + bsd 129 &  & + 0.50 & + 0.50 & + 0.70 & + 0.20 & + 0.60 & + 0.60 &  + & & @xmath20.20&@xmath20.10&@xmath20.20&@xmath20.10&@xmath20.10&@xmath20.10 & + bsd 72 &  & + 0.10 & + 0.40 & + 0.35 & + 0.05 & + 0.35&0.20 &  + & & @xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10 & + bsd 114 &  & 0.20&0.85&0.10&0.70 &  0.00&0.30 &  + & & @xmath20.10&@xmath20.20&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10 & + irs 11 & 0.15 & + 0.25&0.80&0.20&0.80&0.15&0.50 &  + & @xmath20.05&@xmath20.05&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10&@xmath20.10 & + bsd 140 &  &  0.00&0.40 & + 0.10&0.40 &  0.00 &  0.00 &  + & & @xmath20.20&@xmath20.20&@xmath20.20&@xmath20.20&@xmath20.10&@xmath20.10 &    lcccccc hr 6146 & @xmath390.03 & @xmath20.10 & @xmath390.11 & @xmath20.08 & @xmath20.07 & @xmath20.19 + hr 6702 & @xmath390.03 & @xmath20.10 & @xmath390.11 & @xmath20.13 & @xmath20.08 & @xmath20.22 + hr 7442 & @xmath390.03 & @xmath20.10 & @xmath390.04 & @xmath20.19 & @xmath20.11 & @xmath20.25 + hr 8062 & @xmath390.03 & @xmath20.10 & @xmath390.04 & @xmath20.04 & @xmath20.04 & @xmath20.13 + @xmath18 ori&@xmath390.07 & @xmath20.10 & @xmath390.04 & @xmath20.04 & @xmath20.03 & @xmath20.14 + hd 202380 & @xmath390.05 & @xmath20.17 & @xmath390.04 & @xmath20.04 & @xmath20.02 & @xmath20.19 + hr 8383 & @xmath390.07 & @xmath20.10 & @xmath390.04 & @xmath20.15 & @xmath20.03 & @xmath20.20 + hd 163428 & @xmath390.05 & @xmath20.17 & @xmath390.04 & @xmath20.22 & @xmath20.04 & @xmath20.29 + bd+59 594 & @xmath390.05 & @xmath20.10 & @xmath390.04 & @xmath20.07 & @xmath20.05 & @xmath20.15 + hd 232766 & @xmath390.05 & @xmath20.10 & @xmath390.04 & @xmath20.26 & @xmath20.05 & @xmath20.29 + hr 8726 & @xmath390.05 & @xmath20.10 & @xmath390.04 & @xmath20.04 & @xmath20.04 & @xmath20.13 +    lcccccc irs 7 & @xmath390.07 & @xmath20.07 & @xmath390.09 & @xmath20.19 & @xmath20.13 & @xmath20.27 + vr 5 - 7 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.11 & @xmath20.11 & @xmath20.23 + irs 19 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.14 & @xmath20.13 & @xmath20.26 + irs 22 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.11 & @xmath20.12 & @xmath20.24 + bsd 124 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.19 & @xmath20.06 & @xmath20.26 + bsd 129 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.19 & @xmath20.08 & @xmath20.27 + bsd 72 & @xmath390.08 & @xmath20.10 & @xmath390.11 & @xmath20.19 & @xmath20.10 & @xmath20.27 + bsd 114 & @xmath390.08 & @xmath20.17 & @xmath390.13 & @xmath20.21 & @xmath20.16 & @xmath20.35 + irs 11 & @xmath390.08 & @xmath20.17 & @xmath390.13 & @xmath20.15 & @xmath20.18 & @xmath20.33 + bsd 140 & @xmath390.08 & @xmath20.17 & @xmath390.13 & @xmath20.21 & @xmath20.10 & @xmath20.32    lccclcc hr 6146 & 8 & 0.01@xmath20.19 & & irs 7 & 6 & + 0.09@xmath20.27 + hr 6702 & 8 & 0.02@xmath20.22 & & vr 5 - 7&7 & + 0.09@xmath20.23 + hr 7442 & 8 & + 0.01@xmath20.25 & & irs 19 & 7 & + 0.29@xmath20.26 + hr 8062 & 7 & 0.03@xmath20.13 & & irs 22 & 8 & + 0.09@xmath20.24 + @xmath18 ori & 8 & + 0.05@xmath20.14 & & bsd 124 & 6 & + 0.17@xmath20.26 + hd 202380 & 7 & + 0.07@xmath20.19 & & bsd 129 & 6 & + 0.49@xmath20.27 + hr 8383 & 8 & 0.14@xmath20.20 & & bsd 72 & 6 & + 0.17@xmath20.27 + hd 163428 & 7 & 0.05@xmath20.29 & & bsd 114 & 6 & 0.29@xmath20.35 + bd+59 594 & 8 & 0.24@xmath20.15 & & irs 11 & 7 & 0.16@xmath20.33 + hd 232766 & 8 & 0.26@xmath20.29 & & bsd 140 & 6 & 0.06@xmath20.32 + hr 8726 & 8 & 0.07@xmath20.13 & & & & +                                                      livingstone , w. & wallace , l. , 1991 , an atlas of the solar spectrum in the infrared from 1850 to 9000 @xmath46 ( 1.1 to 5.4 @xmath26 m ) , n.s.o . technical report # 91 - 001 , ( tucson : national solar observatory )","summary":"the mean [ fe / h ] of the gc stars is determined to be near solar , [ fe / h ] = + 0.12 0.22 . the mean [ fe / h ] of the solar neighborhood comparison stars , [ fe / h ] = + 0.03 0.16 , is similar to that of the gc stars . the width of the gc [ fe / h ] distribution is found to be narrower than the width of the [ fe / h ] distribution of baade s window in the bulge but consistent with the width of the [ fe / h ] distribution of giant and supergiant stars in the solar neighborhood .","abstract":"we present measurements of [ fe / h ] for six m supergiant stars and three giant stars within 0.5 pc of the galactic center ( gc ) and one m supergiant star within 30 pc of the gc . the results are based on high - resolution ( 40,000 )band spectra , taken with cshell at the nasa infrared telescope facility . we determine the iron abundance by detailed abundance analysis , performed with the spectral synthesis program moog . the mean [ fe / h ] of the gc stars is determined to be near solar , [ fe / h ] = + 0.12 0.22 . our analysis is a _ differential _ analysis , as we have observed and applied the same analysis technique to eleven cool , luminous stars in the solar neighborhood with similar temperatures and luminosities as the gc stars . the mean [ fe / h ] of the solar neighborhood comparison stars , [ fe / h ] = + 0.03 0.16 , is similar to that of the gc stars . the width of the gc [ fe / h ] distribution is found to be narrower than the width of the [ fe / h ] distribution of baade s window in the bulge but consistent with the width of the [ fe / h ] distribution of giant and supergiant stars in the solar neighborhood ."}
{"article_id":"1309.4877","section_id":"c","document":"in this paper we studied a holographic p - wave superconductor model in a four dimensional einstein - maxwell - complex vector field theory with a negative cosmological constant . the complex vector field @xmath0 is charged under the maxwell field . taking the back reaction of matter fields into consideration , we managed to construct hairy black hole solutions which satisfy all asymptotic conditions . we found the model presents a rich phase structure controlled by the mass @xmath5 and charge @xmath2 of the vector field @xmath0 . we investigated possible phase transitions in detail . it turns out that there exist zeroth order , first order and second order phase transitions in this model . hairy black holes were also found in the unusual higher temperature range @xmath11 , which always have free energy higher than the normal phase . the phase diagrams in terms of the temperature and charge were constructed . our numerical calculation suggests the existence of a critical @xmath6 denoted as @xmath96 . when @xmath93 , we have a second order phase transition from the normal phase to the condensed phase for the weak back reaction case . this transition becomes a first order one as we increase the strength of the back reaction . the transition temperature @xmath7 decreases as we decrease the value of @xmath2 , which means that the increase of the back reaction makes the transition more difficult . when @xmath95 , the thermodynamic behavior of the system changes a lot . starting from the high temperature region , one can find the following transitions : for @xmath119 , the system undergoes a second order phase transition from the normal phase to the condensed phase at @xmath8 and as the temperature decreases to @xmath9 , there is a zeroth order transition back to the normal phase ; for @xmath120 , the system first undergoes a first order phase transition from the normal phase to the condensed phase at @xmath10 , then at the lower temperature @xmath9 , it comes back to the normal phase by a zeroth order transition ; for @xmath121 , we can only get hairy black hole solutions that are always subdominant in the free energy referred to as  retrograde condensation \" . here the concrete values of @xmath163 and @xmath164 depend on the mass squared @xmath6 of the vector field @xmath165 . it was argued in ref . @xcite that the holographic free energy can be thought of as a sort of generalized version of landau - ginzburg free energy . in landau - ginzburg theory , it is usually assumed that the quadratic term depends on the temperature linearly while the fourth order term is not strongly temperature dependent . in our present study , we found the behaviors deviating from the mean field theory . in the context of landau - ginzburg theory , such deviation would be a sign of an unusual temperature dependence of the higher order terms . it should be stressed that our model is dual to a strongly coupled system . a priori the dual system does not obey the usual assumption for the free energy . it is in principle possible that there is some new temperature scale at which the coefficients of higher order terms change their signs , giving rise to non - standard phase transitions in the framework of landau - ginzburg theory .    our study can be straightforwardly generalized to the higher dimensional case and other gravitational backgrounds , such as the ads soliton backgrounds which can mimic the superconductor / insulator phase transition  @xcite . in a recent paper  @xcite , we studied the effect of an applied magnetic field effect on the ads soliton background , and found that the magnetic field can induce the ads soliton instability due to the non - minimal coupling of the vector field and the background magnetic field . by comparing our complex vector field model to the su(2 ) p - wave model with a constant non - abelian magnetic field , we found that the su(2 ) p - wave model can be recovered by the restriction @xmath142 and @xmath166 in our model with the ansatz in ref . it suggests that in some sense , the charged vector model is a generalization of the su(2 ) p - wave model to the case with a general mass squared @xmath6 and gyromagnetic ratio @xmath167 for the vector field . due to the adjustable parameter @xmath5 , we can see in this paper that our model shows a much richer phase structure than the su(2 ) p - wave model , thus can be used to describe more phenomena in dual strongly coupled systems .    in the present paper , we limited ourselves to a simple case with @xmath23 non - vanishing only . in principle , in order to understand the full phase structure of the model at fixed chemical potential , one should search for the dominant thermodynamic configuration not only in this given sector but in a more general setup , especially turning on the temporal component of the charged vector @xmath168 . this would of course be much more involved , since one should search for the hairy black hole configuration with the least free energy among all possible configurations . we will leave this issue for further study .    as a phenomenological approach , we consider the model as a p - wave superconducting ( superfluid ) one . indeed , this toy model could be applicable in a wide variety of condensed matter systems and beyond . indeed , as we have discussed in ref . @xcite , it may also be revelent for holographically mimicking the phenomenon that the qcd vacuum undergoes a phase transition to an exotic phase with charged @xmath50-meson condensed in a sufficiently strong magnetic field  @xcite .    as we have mentioned above , according to the symmetry of the macroscopic wave function or condensate of cooper pairs in the real superconducting materials , the superconductor can be classified by s - wave , p - wave , d - wave and so on . the holographic s - wave model has well studied ( especially with back reaction ) in the literature . adopting the present p - wave model , it is quite interesting to study holographic models with multiple superconducting order parameters , including the competition or coexistence between s - wave order and p - wave order or between two p - wave orders . we will leave all these issues for further study . finally we like to mention that with suitable parameters @xmath5 and @xmath2 , our model shows the normal / superconducting / normal phase transition ( see figure  [ phasediagn ] ) as one lowers the temperature continuously . such a phase transition is called reentrant phase transition in the literature  @xcite . the reentrant phase transition usually happens in the binary and multicomponent liquid mixtures . but it is interesting to note that such a phase transition also appears in some superconducting materials , for example , granular @xmath169 compound  @xcite and cuprate superconductors  @xcite . thus it would be of some interest to see whether our model is relevant to these superconducting phase transitions .","summary":"we study a holographic p - wave superconductor model in a four dimensional einstein - maxwell - complex vector field theory with a negative cosmological constant . the complex vector field is charged under the maxwell field . , we find a rich phase structure : zeroth order , first order and second order phase transitions can happen in this model . we construct the phase diagram for this system in terms of the temperature and charge of the vector field .","abstract":"we study a holographic p - wave superconductor model in a four dimensional einstein - maxwell - complex vector field theory with a negative cosmological constant . the complex vector field is charged under the maxwell field . we solve the full coupled equations of motion of the system and find black hole solutions with the vector hair . the vector hairy black hole solutions are dual to a thermal state with the u(1 ) symmetry as well as the spatial rotational symmetry broken spontaneously . depending on two parameters , the mass and charge of the vector field , we find a rich phase structure : zeroth order , first order and second order phase transitions can happen in this model . we also find  retrograde condensation \" in which the hairy black hole solution exists only for the temperatures above a critical value with the free energy much larger than the one of the black hole without the vector hair . we construct the phase diagram for this system in terms of the temperature and charge of the vector field ."}
{"article_id":"1612.02922","section_id":"i","document":"the dusty torus around active galactic nucleus ( agn ) is a key component in a unification theory of agns ( @xcite ; see also @xcite for a recent review ) . such torus is originally introduced to hide broad line region , another key component in the unification theory , from observers line - of - sight for type-2 agns in the optical and near - infrared ( nir ) wavelengths . in the unification theory , the torus is also responsible for major characteristics of agns at x - ray and mid - infrared ( mir ) wavelengths . x - ray emission , especially in the soft x - ray band , from the central part of the agn is absorbed by gas within the torus . the observed absorption is larger for type-2 agns due to the dusty torus intercepting along the line - of - sight , and most x - ray emission below 10  kev is absorbed in the extreme compton - thick case ( @xmath5  @xmath6 , where @xmath7 is the hydrogen column density ) . mir emission from the agn is dominated by thermal emission of the dusty torus heated by the agn . silicate feature around 9.7  @xmath2 m is often seen either in absorption or emission when the torus is seen edge - on or pole - on , respectively , by the observers . recent mir studies have provided us with much more realistic view of the central part of the agns . _ spitzer _ studies of nearby compton - thick agns have shown that even compton - thick agns , especially low - luminosity ones , often show only modest  moderate silicate absorption at 9.7@xmath8 m ( e.g. , @xcite ) . classical smooth torus model , such as one of @xcite , predicts deeper absorption in proportion to the x - ray absorption column density . on the other hand , if the torus is made of collection of clouds , each cloud is heated to @xmath9  k to emit mir emission while absorbing the background light when the foreground cloud is cooler than the one behind . the radiation transfer effect among the clouds significantly reduces the net silicate absorption even when the torus is seen edge - on @xcite . meanwhile , recent mir interferometric studies of nearby agns have started to directly reveal the dust distribution in the vicinity of the agns at parsec scales . in some best studied agns , extended optically - thin dust emission elongated toward the system s polar direction ( e.g. , direction of the extended narrow line region or outflow ) is typically found in addition to the compact disk - like component ( e.g. , @xcite ; see also @xcite for the single dish study ; see @xcite for a review ) . such extended polar emission is clearly inconsistent with the classical idea of the dusty torus in the unification theory , and its nature is under debate . some proposed ideas are that it originates from the inner funnel of an extended dust distribution above and below the torus and/or the dusty outflow within the ionizing cone that is radiatively driven from the inner wall of the compact dusty torus ( e.g. , @xcite ) . m51 ( ngc  5194 ) is a very nearby ( 7.1  mpc ; @xcite ; @xmath10 corresponds to 34.4  pc ) compton - thick agn . it is one of the nearest agns , and is even closer than the best studied compton - thick agn ngc  1068 ( 14.4  mpc ) . although the agn in m51 ( 0.07  jy for the unresolved core component at a resolution of 04 full - width at half maximum ( fwhm ) at 11.2  @xmath2 m ;  [ radial_profile_analysis ] ) is much fainter than that of ngc  1068 ( 8.7  jy within a central 04 aperture at 11.6  @xmath2 m ; @xcite ) , it has been studied in great detail , thanks to its proximity . the hard x - ray emission from the agn was discovered by _ ginga _ @xcite , and its compton - thick spectra have been analyzed in more detail by using the succeeding x - ray satellites @xcite . extended agn - related activities such as radio jet ( e.g. , @xcite ) , optical narrow line region nebula ( e.g. , @xcite ) , and soft x - ray nebula @xcite have been known . torus - like structures at @xmath11  pc scale have been claimed in the 1990s by several authors , although they are not likely the torus in light of recent advanced high - resolution infrared interferometric studies of nearby agns ( e.g. , @xcite ) . those include disk - like rotating dense molecular gas cloud at @xmath11  pc scale with hcn ( @xmath12 ) emission @xcite and `` x''-shaped nuclear dust lanes at several tens  pc scale in _ hst _ optical images @xcite . recently , @xcite found that most molecular gas is associated with circumnuclear outflowing structures at several tens  pc scale , with little nuclear concentration . they argued that the hydrogen column density toward the nucleus is apparently much smaller ( by more than two orders of magnitude ) than the expectation from the compton - thick x - ray properties ( see also @xcite ;  [ discussion_torus ] ) . high spatial - resolution mir imaging of one of the nearest agns in m51 would enable us to examine details of the agn structure and its circumnuclear region . in the @xmath1-band ( 813  @xmath2 m ) , ground - based 810  m telescopes can achieve diffraction - limited resolution of 0304 , or @xmath13  pc at a distance of m51 . note that the most powerful high - resolution imaging / spectral mapping machine at mir , very large telescope interferometer ( vlti ) with midi ( mid - infrared interferometric ) instrument , can not observe this galaxy due to its declination . in addition , space - based mir imaging and spectroscopy provide the best sensitivity over the larger field of view and larger wavelength coverage at modest spatial resolution , enabling detailed spectral analysis of the agn and its circumnuclear region . therefore , we performed subaru mir imaging observation and analyzed the archival _ data of the agn in m51 to characterize the agn inner structure and effect of the agn on the circumnuclear region .","summary":"spitzer _ irs spectrum processed to mimic our chopping observation of the nucleus , and the published radiative - transfer model seds of the agn clumpy dusty torus .","abstract":"we performed near - diffraction - limited ( fwhm )-band imaging of one of the nearest active galactic nucleus ( agn ) in m51 with 8.2 m subaru telescope to study the nuclear structure and spectral energy distribution ( sed ) at 813  m . we found that the nucleus is composed of an unresolved core ( at  pc resolution , or intrinsic size corrected for the instrumental effect of  pc ) and an extended halo ( at a few tens  pc scale ) , and each of their seds is almost flat . we examined the sed by comparing with the archival _ spitzer _ irs spectrum processed to mimic our chopping observation of the nucleus , and the published radiative - transfer model seds of the agn clumpy dusty torus . the halo sed is likely due to circumnuclear star formation showing little polycyclic aromatic hydrocarbon ( pah ) emission due to the agn . the core sed is likely dominated by the agn because of the following two reasons . firstly , the clumpy torus model seds can reproduce the red mid - infrared continuum with apparently moderate silicate 9.7  m absorption . secondly , the core 12  m luminosity and the absorption - corrected x - ray luminosity at 210  kev in the literature follow the mid - infrared  x - ray luminosity correlation known for the nearby agns including the compton - thick ones ."}
{"article_id":"1612.02922","section_id":"r","document":"the comics core+halo sed of the m51 nucleus is quite different from typical sed of star - forming objects and the irs off - nuclear spectrum of m51 ( top panel of figure  [ sed ] ) , and is instead consistent with the chopped nuclear irs spectrum showing little pah features ( middle panel of figure  [ sed ] ) . when compared to the michelle photometries of the m51 nucleus @xcite , the comics uir11.2 ( 11.2  @xmath2 m ) flux is consistent with the michelle si-5 ( 11.6  @xmath2 m ) flux , whereas the comics [ ne  ii ] ( 12.8  @xmath2 m ) flux is notably higher than the michelle si-6 ( 12.5  @xmath2 m ) flux (  [ comp_michelle ] ) . in an attempt to explain the difference , we made the synthetic photometries of the chopped nuclear irs spectrum for the two michelle filters ( top and middle panels of figure  [ sed ] ) . we found that the comics [ ne  ii ] flux is larger than the si-6 flux because the [ ne  ii ] filter just covers the [ ne  ii ] line whereas the si-6 filter also covers the adjacent continuum due to its wider filter width . therefore , both comics core+halo and michelle photometries are consistent with the chopped nuclear irs spectrum after considering difference in the filter widths . the _ spitzer _ and ground - based photometries match to each other despite of their different spatial resolutions , suggesting that a single compact core+halo component is located at the nucleus over the extended host - galaxy component showing the typical pah features . the relatively weaker pah feature strength in the nuclear irs spectrum ( top panel of figure  [ sed ] ; @xcite ) is apparently due to this core+halo component showing little pah features . the comics core sed can be interpreted as either the pah - deficient chopped nuclear irs spectrum or the agn emission . the bottom panel of figure  [ sed ] directly compares the synthetic photometries of the scaled chopped nuclear irs spectrum with the comics core sed to illustrate a good match given the error bars . here , the scaling is to account for the flux ratio between the core and core+halo seds (  [ radial_profile_analysis ] ) . this indicates that the core sed can be explained by spectrum showing little pah features in the same way for the core+halo sed . alternatively , the core sed can be explained by an absorbed power - law continuum of the agn . to demonstrate this , we applied an absorption on type-1 agn sed template of @xcite by an apparent optical depth at 9.7  @xmath2 m ( @xmath79 ) of @xmath80 ( top panel of figure  [ agnsed ] ) . here , we assumed simple foreground dust absorption with an extinction curve of @xcite toward the galactic center . we found that this model , though it is unrealistically simple , can reproduce the observation reasonably well , except for n8.8 where the photometry quality is the worst . note that this optical depth is much larger than that measured with irs ( @xmath810.00.04 ; @xcite ) . this is most likely due to less contamination at the comics resolution by circumnuclear less - absorbed star - forming region . we further examine the agn models for the core sed by using the recent sophisticated agn sed models with clumpy torus . it has been known that the observed shallower silicate absorption at 9.7  @xmath2 m even in the compton - think agns can be reproduced by the agn clumpy torus ( e.g. , @xcite ) . recent more advanced radiative - transfer calculations for the clumpy torus medium not only successfully reproduce the mir seds of both type-1 and type-2 agns but also provide the basis to compare with the observed spatial distribution of the infrared emission in the central parsec - scale regions of agns in the interferometric studies ( e.g. , @xcite ) . there are three groups in the model parameters : those that define the intrinsic radiation from the accretion disk , dusty torus properties such as size and density distribution as well as the dust composition , and observer s viewing angle of the torus . the agn luminosity sets overall flux scale of the emergent sed , not the relative sed shape , as long as the inner torus radius is set at the dust sublimation temperature , due to scaling relation of the agn torus radiation ( e.g. , @xcite ) . the relative sed shape is then determined mostly by overall torus shape ( opening angle of the central dust - free zone of the torus and outer radius of the torus ) , distribution of dusts ( or dust clouds ) within the torus , average optical depth ( or mean optical depth of each clump and the average number of the clumps ) along the torus equatorial plane , as well as the viewing angle . in particular , two most important characteristics of the observed mir sed , the apparent depth of the silicate absorption at 9.7  @xmath2 m and the overall slope ( redness ) of the continuum , are mostly determined by the combination of the radial dust distribution , the average optical depth along the torus equatorial plane , and the viewing angle ( e.g. , @xcite ) . we performed the model fitting of the core sed by using two representative agn sed models with clumpy torus , cat3d @xcite and skirtor 2.0 ( @xcite ; see also @xcite ) . these two models are very similar in overall settings of the accretion disk radiation and the torus geometry / distributions of the dusts within the torus , although there are numbers of differences in the details of the parameterization of the models , as well as the technical details of the calculations . the agn luminosity is estimated by using the core [ ne  ii]-filter flux ( @xmath82(12.3  @xmath2m)@xmath83 erg s@xmath84 ) and the mir bolometric correction factor estimated by using equation ( 5 ) of @xcite , which is based on their mir and x - ray luminosity correlation and the x - ray bolometric correction factor of @xcite . some parameters that do not affect the mir sed very much , such as dust composites ( both in cat3d and skirtor 2.0 ) , outer radius of the torus ( in cat3d ) , and fraction of the total dust mass within the clump ( in skirtor 2.0 ) , are fixed to the fiducial values according to the model papers . middle and bottom panels of figure  [ agnsed ] show all acceptable model seds for the two models , and table  [ sedfit ] summarizes their parameters . in both models , relatively larger average optical depth in the equatorial plane of the torus ( @xmath85 in cat3d and @xmath86 in skirtor 2.0 ; see table  [ sedfit ] ) and flatter radial distribution of the dusts ( near - zero power - law index as a function of the distance from the center ; @xmath87 in cat3d and @xmath88 in skirtor 2.0 ; see table  [ sedfit ] ) are preferred . this , combined with the nearly edge - on viewing angle , provides preferred conditions to see the silicate feature in absorption on the redder continuum @xcite . lcc parameter name and its description & parameter space & acceptable parameter range +   + @xmath87 : radial dust cloud distribution index ( @xmath89 ) & 0.0 ... @xmath90 ( in steps of 0.5 ) & 0.0 .. @xmath91 ( mostly 0.0 ) + @xmath92 : optical depth of the individual clouds at @xmath93 band & 30 , 50 , 80 & 80 + @xmath94 : number of clouds along an equatorial line - of - sight & 2.5 ... 10 ( in steps of 2.5 ) & 7.5 .. 10 ( mostly 10.0 ) + @xmath95 : half - opening angle of the torus & 5@xmath96 , 30@xmath96 , 45@xmath96 , 60@xmath96 & 5@xmath96 .. 60@xmath96 + @xmath97 : outer radius of the torus & 150 & 150 + @xmath98 : inclination angle & 0@xmath96 .. 90@xmath96 ( in steps of 15@xmath96 ) & 60@xmath96 .. 90@xmath96 ( mostly 90@xmath96 ) + dust composition & `` standard '' ism & `` standard '' ism +   + @xmath88 : radial gradient of dust density ( @xmath99 ) & 0.0 ... 1.5 ( in steps of 0.5 ) & 0.0 .. 1.0 ( mostly 0.0 .. 0.5 ) + @xmath100 : dust density gradient with polar angle ( exp(@xmath101 ) ) & 0.0 ... 1.5 ( in steps of 0.5 ) & 0.0 .. 1.5 ( mostly 0.0 .. 0.5 ) + @xmath86 : average edge - on optical depth at 9.7  @xmath2 m & 3 .. 11 ( in steps of 2 ) & 7 .. 11 + @xmath102 : angle between the equatorial plan and edge of the torus & 10@xmath96 .. 80@xmath96 ( in steps of 10@xmath96 ) & 50@xmath96 + @xmath103 : outer - to - inner torus radius ratio ( @xmath97/@xmath104 ) & 10 , 20 , 30 & 20 , 30 + @xmath105 : fraction of total dust mass inside clumps & 0.97 & 0.97 + @xmath98 : inclination angle & 0@xmath96 .. 90@xmath96 ( in steps of 10@xmath96 ) & 60@xmath96 .. 90@xmath96 ( mostly 80@xmath96 .. 90@xmath96 ) +      the halo sed is similar to the chopped nuclear irs spectrum , because the core and halo seds are similar to each other (  [ radial_profile_analysis ] ) , and the core+halo sed is consistent with the chopped nuclear irs spectrum (  [ results_core_halo ] ) . in particular , the [ ne  ii ] 12.8  @xmath2 m emission is likely associated with the halo . this is because the [ ne  ii ] emission is present around the nucleus at the core+halo scale as demonstrated by the difference between the comics core+halo sed and the michelle sed at around 12.512.8  @xmath2 m (  [ comp_michelle ] ; [ results_core_halo ] ) , and the core sed is most likely the dust thermal emission around the agn as we discuss next (  [ nature_core ] ) .","summary":"we examined the sed by comparing with the archival _","abstract":"we performed near - diffraction - limited ( fwhm )-band imaging of one of the nearest active galactic nucleus ( agn ) in m51 with 8.2 m subaru telescope to study the nuclear structure and spectral energy distribution ( sed ) at 813  m . we found that the nucleus is composed of an unresolved core ( at  pc resolution , or intrinsic size corrected for the instrumental effect of  pc ) and an extended halo ( at a few tens  pc scale ) , and each of their seds is almost flat . we examined the sed by comparing with the archival _ spitzer _ irs spectrum processed to mimic our chopping observation of the nucleus , and the published radiative - transfer model seds of the agn clumpy dusty torus . the halo sed is likely due to circumnuclear star formation showing little polycyclic aromatic hydrocarbon ( pah ) emission due to the agn . the core sed is likely dominated by the agn because of the following two reasons . firstly , the clumpy torus model seds can reproduce the red mid - infrared continuum with apparently moderate silicate 9.7  m absorption . secondly , the core 12  m luminosity and the absorption - corrected x - ray luminosity at 210  kev in the literature follow the mid - infrared  x - ray luminosity correlation known for the nearby agns including the compton - thick ones ."}
{"article_id":"1612.02922","section_id":"c","document":"our upper limit of the core size and the core photometry give very high mir surface brightness lower limit , but we can not exclude a possibility of a very compact nuclear star cluster . @xcite compiled nuclear surface brightness of nearby agns at @xmath106 m measured with 810  m telescopes . they demonstrated that the surface brightness of the agns is @xmath107 @xmath108/pc@xmath109 , and showed that the surface brightness of @xmath110 @xmath108/pc@xmath109 is a useful diagnostic threshold to separate agns from compact nuclear starbursts . the mir luminosity of the m51 core is @xmath82(11.2  @xmath2m)@xmath111 erg s@xmath84 ( from the core uir11.2-filter flux ) , and the core size upper limit is 6  pc ( fwhm ;  [ radial_profile_analysis ] ) . we found that the surface brightness is @xmath112 @xmath108/pc@xmath109 , indicating that the core mir surface brightness is almost comparable to that of known agns . we caution that the surface brightness of the m51 core is less than the threshold by a factor of two , and very compact nuclear starbursts can have comparably large surface brightness of @xmath113 @xmath108/pc@xmath109 @xcite . therefore , we can not conclude that the agn dominates the core in mir emission on the basis of the mir surface brightness argument . we examine mir - to - x - ray luminosity ratio of the core in an attempt to identify its nature , because both an absorbed agn and a compact star - forming cluster with deficient pah features can explain the mir sed (  [ results_core ] ) . agns are much more luminous in x - ray at @xmath114  kev than star - forming clusters for given mir luminosity ( e.g. , @xcite ) , and we test if the ratio of the absorption - corrected intrinsic x - ray and mir luminosities of the core is consistent with the agns . @xcite showed that the mir luminosity and the intrinsic x - ray ( 210  kev ) luminosity corrected for the absorption based on the x - ray spectral fitting show a good linear correlation among the local agns ( see also @xcite ) . they used single - dish mir observations with 8m - class telescopes , like our observation with subaru 8.2 m telescope . high spatial - resolution mir photometry is essential to reduce the contamination by the circumnuclear regions and isolate the properties of the agns ( e.g. , @xcite ) . the correlation is found independent of the two types of the agns including the compton - thick agns , although the compton - thick agns show slightly lower mir luminosity by @xmath115 dex for the same x - ray luminosity when compared to the rest . note that this mir luminosity offset is smaller than the overall scatter of the correlation ( @xmath116 dex ) , making this correlation useful to diagnose the agn nature of the mir core in the compton - thick agn of m51 . @xcite already included m51 in their correlation analysis by using their own michelle photometry data @xcite , and showed that m51 dose follow the correlation . by using equation ( 2 ) of @xcite , we predict the intrinsic x - ray luminosity as @xmath117(210  kev)@xmath118 erg s@xmath84 from the core 12  @xmath2 m luminosity ( @xmath119 erg s@xmath84 from the core [ ne  ii]-filter flux ) . for comparison , the observed absorbed - corrected x - ray luminosity ( converted to our assumed distance of 7.1  mpc ) is log @xmath117(210  kev)@xmath120 erg s@xmath84 @xcite . this measurement is based on multi - epoch observations with _ chandra _ and _ xmm - newton _ satellites , and the uncertainty includes differences among the observations ( see @xcite and references therein ) . note that this result is consistent with the _ bepposax _ measurement ( @xmath117(210  kev)@xmath121 erg s@xmath84 ) by @xcite . we found that the observed x - ray luminosity is @xmath122 dex larger than the prediction from the mir luminosity for general agn populations , or is @xmath123 dex larger for the compton - thick agns if we consider the above - mentioned systematic offset . because this difference is smaller than the uncertainty of the observed x - ray luminosity ( 0.6 dex ) , we conclude that our core mir photometry is consistent with the mir  x - ray luminosity correlation of the agns .    how can we explain discrepancy between the mir and x - ray measurements of the hydrogen column density toward the agn ? in the simple absorbed agn model with foreground absorption (  [ results_core ] ) , the apparent optical depth at the silicate absorption ( @xmath124 ) corresponds to @xmath125 @xmath6 . this order - of - magnitude estimate is based on the @xmath126 conversion ( @xmath127 ; @xcite ) and a standard gas - to - dust ratio within the galactic interstellar medium ( @xmath7/@xmath128 @xmath6 mag@xmath84 ) . this absorption is much smaller than expected for the compton - thick column density measured in the x - ray ( @xmath129 @xmath6 ; @xcite ; @xmath130 @xmath6 ; @xcite ) in spite of considerable uncertainties in this very simple model and the conversion factors . however , the clumpy agn torus is known not to create very deep silicate absorption even in the compton - thick condition (  [ intro ] ) . in fact , we found that the model seds of the agn clumpy torus ( cat3d ; @xcite ; skirtor 2.0 ; @xcite ) reproduce the observed core sed reasonably well (  [ results_core ] ) . as expected , the hydrogen column density of the acceptable models is much larger than the estimate based on the apparent small optical depth at 9.7  @xmath2 m : for example , with cat3d models , the average total optical depth in the equatorial plane of the torus is @xmath131 ( table  [ sedfit ] ) , corresponding to @xmath132 @xmath6 in the edge - on viewing angle with the same standard gas - to - dust ratio . therefore , the agn clumpy torus models acceptable for the mir core sed are consistent with the x - ray observations in terms of the hydrogen column density toward the agn . we need to caution that , although we successfully demonstrated that the agn clumpy torus models can reproduce the core mir sed , there is no direct hint to suggest that the torus structure dominates the mir emission in m51 . even though such model seds are known to represent agn seds in general reasonably well ( e.g. , @xcite ) , there is mounting evidence recently to indicate that most of the mir emission comes from the extended polar region of the agns , rather than from the torus as expected in the agn unification theory (  [ intro ] ) . in addition , although our argument based on the mir and x - ray luminosity correlation indicates that the agn dominates the core mir sed , this dose not mean that the emission comes from the agn torus . @xcite showed based on their 8 m single - dish observations of nearby agns at mir that some small fraction of their sample with sufficiently good observations shows the polar extensions , suggesting that such polar extension commonly exists in agns . because the mir and x - ray luminosity correlation we used in our discussion is based on the total mir luminosities of the compact nucleus including the ( not well resolved ) polar components @xcite , our correlation analysis may suggest similar polar component in the m51 agn at mir . therefore , we need to wait for the future mir interferometric observations to reveal the structure of the mir core in m51 . we found a signature of agn influence in the nuclear irs spectrum that shows remarkable differences from the off - nucleus one , and in the irac ch4/ch3 flux ratio map . previously , the agn influence is found in the nuclear concentration of the hot ( @xmath1344001000 k ) h@xmath75 gas @xcite , the enhanced high - ionization ( 97.1  ev ) line of [ ne  v ] ( @xcite ;  [ spitzer_data_analysis ] ) , and pah deficiency at the nucleus at the irs resolution ( @xcite ; see also  [ results_core_halo ] ) . the pah - deficient mir spectrum is typically seen in agns ( e.g. , @xcite ) , and is most likely due to destruction of pah particles in the circumnuclear region due to intense hard photons from agn and/or strong shock associated with agn jet ( e.g. , @xcite ) . in addition , we found the smaller irac ch4/ch3 flux ratio at @xmath135  pc scale around the nucleus well beyond the irac resolution ( @xmath136 fwhm or 70  pc ; figure  [ findingchart ] ) , which is likely due to deficient pah features in the ch4 ( the 7.7 and 8.6  @xmath2 m features ) that are typically very bright in the star - forming regions (  [ spitzer_data_analysis ] ) . the region with the smaller ch4/ch3 flux ratio roughly coincides with the extended radio jet ( e.g. , @xcite ) , optical narrow - line region nebula ( e.g. , @xcite ) , the soft x - ray nebula @xcite , and the jet - entrained shocked outflowing molecular - gas clouds @xcite . the irac flux ratio is smallest near the nucleus , where the chopped nuclear irs spectrum shows little pah emission (  [ results_core_halo ] ) . these characteristics indicate more pronounced pah destruction near the agn . the nuclear [ ne  v ] emission also suggests significant agn contribution at the nucleus at the irs resolution , because this line is usually considered as a tracer of either excitation by agn hard photons or strong shock ( e.g. , @xcite ) . the observed [ ne  ii]/[ne  v ] flux ratio ( @xmath27 ;  [ spitzer_data_analysis ] ) is only one tenth of the one in star - forming regions ( @xmath137 ) and is much closer to the one in seyfert galaxies ( @xmath138 ; @xcite ) . what is the nature of the extended halo found in the comics images at a few tens  pc scale ? the halo sed is similar to the chopped nuclear irs spectrum (  [ results_halo ] ) , suggesting the circumnuclear star formation showing little pah emission as we discussed above . alternatively , the halo could be the very extended polar mir emission of agns sometimes seen even with the single - dish observations ( e.g. , @xcite ;  [ intro ] ) . in fact , the mir - to - x - ray luminosity ratio by using the combined comics core+halo flux , log @xmath117(@xmath139m)/@xmath117(210  kev)@xmath140 , is still consistent with the agns in general in the sample of @xcite . however , the former star formation model seems preferred to explain the strong [ ne  ii ] emission in the halo (  [ results_halo ] ) . this is because strong [ ne  ii ] is typically associated with the star forming region ( e.g. , @xcite ) , whereas the dust continuum emission dominates , without any significant [ ne  ii ] emission , in the extended polar regions in the interferometric spectroscopies of the best - studied nearby agns showing the polar emission ( e.g. , @xcite ) . if this is the case , the halo is likely the circumnuclear star - forming regions affected by the central agn , like in the case of the more extended region traced by the smaller irac ch4/ch3 flux ratio . previous molecular line observations in mm / sub - mm wavelength have shown much smaller hydrogen column density toward the m51 nucleus than expected for the compton - thick agn . this discrepancy , however , can be explained if the molecular gas is mostly associated with an one - parsec - scale torus . @xcite found a compact nuclear molecular - gas concentration at @xmath141 resolution , which is likely associated with the mir core , because the halo is more extended to @xmath142 fwhm . they calculated the h@xmath75 column density of @xmath143  @xmath6 ( or @xmath144 @xmath6 ) toward the nucleus . here , they measured the emission - line luminosity and converted it to the hydrogen number by assuming metallicity and excitation conditions of the gas . they also assumed that the source extends just over the observing beam . @xcite then studied physical conditions of the molecular gas based on multi - line / multi - transition molecular - line analysis , and found that effect of gas excitation and metallicity alone can not explain apparently very small column density reported earlier . on the other hand , the beam dilution effect seems to significantly affect the column density measurement . we showed in this study that the mir core is unresolved with the 039 ( 13  pc ) fwhm beam , and the one - sigma upper limit is 018 ( 6  pc ) fwhm (  [ radial_profile_analysis ] ) . if we adopt 1  pc as a fiducial torus size following statistics of nearby agns studied by infrared interferometry @xcite and assume that most of the molecular gas is associated with this very compact torus , the column density is now calculated to be @xmath145  @xmath6 . @xcite already did the same calculation , but we now have better size constraint of the m51 core as well as better statistics of the agn torus size in infrared . @xcite argued that mean gas density of the torus in this case is @xmath146 @xmath147 , being roughly consistent with their multi - line / multi - transition molecular - line analysis results ( @xmath148 @xmath147 ) . therefore , a model of one - parsec - scale , dusty , and molecular - gas - rich torus can solve the apparent column density discrepancy between the x - ray and molecular - line measurements . although we can not conclude in this study that the mir core is attributed to the agn torus (  [ nature_core ] ) , future study of the m51 agn at even higher spatial resolution in both infrared and sub - mm / mm wavelengths would provide us a direct view of not only the material distribution but also the fueling and feedback processes in the vicinity of the agn .","summary":"the halo sed is likely due to circumnuclear star formation showing little polycyclic aromatic hydrocarbon ( pah ) emission due to the agn . the core sed is likely dominated by the agn because of the following two reasons . secondly , the core 12  m luminosity and the absorption - corrected x - ray luminosity at 210  kev in the literature follow the mid - infrared  x - ray luminosity correlation known for the nearby agns including the compton - thick ones .","abstract":"we performed near - diffraction - limited ( fwhm )-band imaging of one of the nearest active galactic nucleus ( agn ) in m51 with 8.2 m subaru telescope to study the nuclear structure and spectral energy distribution ( sed ) at 813  m . we found that the nucleus is composed of an unresolved core ( at  pc resolution , or intrinsic size corrected for the instrumental effect of  pc ) and an extended halo ( at a few tens  pc scale ) , and each of their seds is almost flat . we examined the sed by comparing with the archival _ spitzer _ irs spectrum processed to mimic our chopping observation of the nucleus , and the published radiative - transfer model seds of the agn clumpy dusty torus . the halo sed is likely due to circumnuclear star formation showing little polycyclic aromatic hydrocarbon ( pah ) emission due to the agn . the core sed is likely dominated by the agn because of the following two reasons . firstly , the clumpy torus model seds can reproduce the red mid - infrared continuum with apparently moderate silicate 9.7  m absorption . secondly , the core 12  m luminosity and the absorption - corrected x - ray luminosity at 210  kev in the literature follow the mid - infrared  x - ray luminosity correlation known for the nearby agns including the compton - thick ones ."}
{"article_id":"1612.02922","section_id":"c","document":"we performed near - diffraction - limited ( @xmath0 fwhm resolution ) @xmath1-band imaging of one of the nearest compton - thick agns in m51 with comics at the subaru telescope to study the nuclear structure and sed at 813  @xmath2 m . we also analyzed the archival _ mir imaging and spectroscopy data . we then characterized properties of the agn and the circumnuclear region at 10100  pc scale . here we summarize our main findings and the implications . we decomposed the m51 nucleus into an unresolved ( at 039 fwhm resolution at @xmath149 m ) core and an extended halo at @xmath33 scale in the @xmath1-band . we estimated the intrinsic core size corrected for the instrumental effect as @xmath150  pc ( @xmath151 ) . we measured the mir surface brightness of the m51 core at 11.2  @xmath2 m to be @xmath112 @xmath108/pc@xmath109 . although this surface brightness is almost comparable to that of known agns ( @xmath107 @xmath108/pc@xmath109 ; @xcite ) , it is not high enough to exclude a possibility of a very compact nuclear star cluster as an origin of the core . the core+halo sed is almost flat with slightly increasing flux at longer wavelength . in order to interpret this sed , we made the `` chopped '' nuclear irs spectrum to follow the comics chopping observation by subtracting the off - nuclear `` sky '' spectrum from the nucleus one . this shows continuum - dominated spectrum with molecular hydrogen and [ ne  ii ] 12.8  @xmath2 m emission lines but little pah emission . we found that the core+halo sed is reproduced by this pah - deficient starburst spectrum . the sed of the halo alone is similar to the core+halo sed , and is also reproduced by similar pah - deficient spectrum with the [ ne  ii ] . in addition , we found that the irac 8.0  @xmath2m/5.6  @xmath2 m flux ratio is smaller within @xmath152  pc from the nucleus , also suggesting deficient pah 7.7 and 8.6  @xmath2 m features that are typically very bright in the star - forming regions . the pah particles in the circumnuclear region are likely destroyed either by intense hard photons from the agn and/or strong shock associated with the agn jet . the core sed is similar to the core+halo sed , and it can be reproduced by a star - forming cluster within the core showing the pah - deficient spectrum . alternatively , the agn clumpy torus model seds @xcite can reproduce the red mir continuum with moderate apparent silicate 9.7  @xmath2 m absorption ( @xmath153 ) . although we can not discriminate the two possibilities on the basis of the mir sed examination , we found that the observed ratio of the mir and absorption - corrected intrinsic x - ray ( 210  kev ) luminosities is consistent with the one for agns in general . therefore , the core is likely dominated by the agn in mir emission . both yo and sm are supported by the national science council ( nsc ) and the ministry of science and technology ( most ) of taiwan , most 104 - 2112-m-001 - 034- ( yo ) , 105 - 2112-m-001 - 024- ( yo ) , nsc 100 - 2112-m-001 - 006-my3 ( sm ) , and most 103 - 2112-m-001 - 032-my3 ( sm ) . this work is based in part on observations made with the _ spitzer _ space telescope , obtained from the nasa / ipac infrared science archive , both of which are operated by the jet propulsion laboratory , california institute of technology under a contract with the national aeronautics and space administration . antonucci , r.  1993 , , 31 , 473 asmus , d. , hnig , s.  f. , gandhi , p. , smette , a. , & duschl , w.  j.  2014 , , 439 , 1648 asmus , d. , gandhi , p. , hnig , s.  f. , smette , a. , & duschl , w.  j.  2015 , , 454 , 766 asmus , d. , hnig , s.  f. , & gandhi , p.  2016 , , 822 , 109 ballantyne , d.  r.  2008 , , 685 , 787 bradley , l.  d. , kaiser , m.  e. , & baan , w.  a.  2004 , , 603 , 463 brightman , m. , & nandra , k.  2011 , , 413 , 1206 brunner , g. , sheth , k. , armus , l. , et al . 2008 , , 675 , 316 burtscher , l. , meisenheimer , k. , tristram , k.  r.  w. , et al . 2013 , , 558 , a149 cecil , g. , & rose , j.  a.  1984 , , 287 , 131 chiar , j.  e. , & tielens , a.  g.  g.  m.  2006 , , 637 , 774 cohen , m. , walker , r.  g. , carter , b. , et al . 1999 , , 117 , 1864 crane , p.  c. , & van der hulst , j.  m.  1992 , , 103 , 1146 diamond - 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diffraction - limited ( fwhm )-band imaging of one of the nearest active galactic nucleus ( agn ) in m51 with 8.2 m subaru telescope to study the nuclear structure and spectral energy distribution ( sed ) at 813  m . firstly , the clumpy torus model seds can reproduce the red mid - infrared continuum with apparently moderate silicate 9.7  m absorption .","abstract":"we performed near - diffraction - limited ( fwhm )-band imaging of one of the nearest active galactic nucleus ( agn ) in m51 with 8.2 m subaru telescope to study the nuclear structure and spectral energy distribution ( sed ) at 813  m . we found that the nucleus is composed of an unresolved core ( at  pc resolution , or intrinsic size corrected for the instrumental effect of  pc ) and an extended halo ( at a few tens  pc scale ) , and each of their seds is almost flat . we examined the sed by comparing with the archival _ spitzer _ irs spectrum processed to mimic our chopping observation of the nucleus , and the published radiative - transfer model seds of the agn clumpy dusty torus . the halo sed is likely due to circumnuclear star formation showing little polycyclic aromatic hydrocarbon ( pah ) emission due to the agn . the core sed is likely dominated by the agn because of the following two reasons . firstly , the clumpy torus model seds can reproduce the red mid - infrared continuum with apparently moderate silicate 9.7  m absorption . secondly , the core 12  m luminosity and the absorption - corrected x - ray luminosity at 210  kev in the literature follow the mid - infrared  x - ray luminosity correlation known for the nearby agns including the compton - thick ones ."}
{"article_id":"astro-ph0407125","section_id":"i","document":"it is believed that accretion disks around black holes are powering in many kinds of celestial objects . the most important scale in the description of accretion disks is the critical accretion rate , defined by @xmath2 g / s , where the accretion efficiency @xmath3 is for schwarzschild black holes whose gravity effects are approximated by the pseudo - newtonian potentials . the structures of accretion disks rely greatly on the mass of the black hole ( @xmath4 ) , the accretion rate ( @xmath5 ) and the viscosity ( @xmath6 ) , and hence the emergent spectrum from the disk . according to the dimensionless accretion rate @xmath7 , the disk structures can be classified : ( 1 ) optically thin advection - dominated accretion flows ( adafs ; narayan & yi 1994 ) , advection - dominated inflow - outflows ( adios ; blandford & begelman 1999 ) and convection - dominated accretion flows ( cdafs ; narayan et al . 2000 ; quataert & gruzinov 2000 ) when @xmath8 , ( 2 ) optically thick and geometrically thin disks ( shakura & sunyaev 1973 ) if @xmath9 , ( 3 ) slim disks ( muchotrzeb & paczyski 1982 ; abramowicz et al . 1988 ; chen & taam 1993 ) once @xmath10 . chen et al . ( 1995 ) presented a unified model , but they _ assumed _ a keplerian angular momentum distribution in the disk . the unified model to cover all these regimes has not been sufficiently understood , especially we still lack the emergent spectrum of such a model for the comparison with observations . there is growing evidence from current observations that the accretion rates of a significant fraction of celestial objects span quite wide ranges from very low to super - critical in x - ray binaries , microquasars and active galactic nuclei ( agns ) . in our galaxy , some ultra - luminous compact x - ray sources ( ulxs ) , microquasars such as grs 1915 + 105 and ss 433 , show large bolometric luminosities and high color temperatures ( > 1 kev ) in their high states ( makishima et al . 2000 ; watarai et al . 2001 ; ebisawa et al . this provides strong evidence for the appearance of slim disks in these objects . the eddington ratios ( @xmath11 ) in agns and quasars have been reliably estimated for revealing the structures of the disks in agns and quasars , since the black hole masses can be estimated by the reverberation mapping relation ( kaspi et al . 2000 ) and the relation with their host galaxies ( e.g. mclure & dunlop 2001 ) . it has been suggested that some of agns have close or super critical accretion rates ( collin et al . 2002 ; netzer 2003 ; vestergaard 2003 ; wang 2003 ; szuszkiewicz 2003 ) , whose luminosities seemingly exceed @xmath12 ( if the estimations of black hole masses are reliable ) . collin et al . ( 2002 ) have shown that about half of the 34 agns , of which the masses are determined by reverberation mapping , have super - critical accretion rates . vestergaard ( 2003 ) extended the empirical relation of reverberation mapping in the sample of kaspi et al . ( 2000 ) to the cases of high redshit quasars ( see also mclure & jarvis 2002 ) . she found there are a significant number of quasars with super - eddington luminosities , in either intermediate redshift range @xmath13 or high redshift range @xmath14 . willott et al . ( 2003 ) found that the quasar sdss j1148 + 5251 at @xmath15 is radiating at the eddington luminosity with the estimated mass @xmath16 . wang ( 2003 ) has also discovered a handful of the candidate super - critical accretors , using the limit relation between the black hole mass and fwhm(h@xmath17 ) , @xmath18^{6.67}m_\\odot$ ] . this relation is a result by combining the empirical reverberation mapping and the features of the emergent spectra from slim disks . although the spectra of 110 bright agns in the sample of laor ( 1990 ) are fitted well by standard thin disks ( shakura & sunyaev 1973 ) , those super - eddington objects can never be explained within the framework of the standard disk theory . a wide range of dimensionless accretion rates should exist in various kinds of celestial objects , but there is not a unified model of accretion disks to describe the varieties of accretion .    [ taueff ] 0.2 cm    the significance of slim disks has been exhibited when they are applied to narrow line seyfert 1 galaxies ( nls1s ; wang et al . 1999 ; mineshige et al . 2000 ; wang & netzer 2003 ; kawaguchi 2003 ) , galactic black hole candidates ( watarai et al . 2000 , fukue 2000 ) and ulxs ( watarai et al . 2001 ) for the strong soft x - ray emission and the violent variability . however , slim disk models in above literatures suffer from the problem that the effective optical depth is smaller than unity in the inner disk region . the slim disks have been thought to work in these objects with high accretion rates , but the emergent spectra from the disks are not satisfactory enough . we list the models and spectra studied by far in table 1 , in which the main assumptions and features in these models are also given . the emergent spectra from the accretion disks of a wide range of @xmath19 remain open so far , especially only wang & netzer ( 2003 ) calculated the spectrum from the slim disk with hot corona based on the self - similar solution . we noted that most of the models assumed a low viscosity so that the transition to an optically - thin region does not appear in their models ( see equation 1 ) . szuszkiewicz et al . ( 1996 ) calculated the emergent spectrum with the modified blackbody radiation and explained the soft x - ray excesses claimed for some agns with slim disks . the vertical structures and the continuum spectra have been computed by wang et al . ( 1999 ) and shimura & manmoto ( 2003 ) . szuszkiewicz et al . ( 1996 ) presented the optically thin region with a small viscosity parameter @xmath20 and the accretion rates @xmath21 . kawaguchi ( 2003 ) also pointed out these regions in the accretion disks around super massive black holes ( smbhs ) . but they did not provide a reasonable treatment in the optically - thin hot region . in this paper , we show that a much wider region , where the effective optical depth @xmath22 , appears when the viscosity increases to @xmath23 for a stellar - mass black hole accretion ( fig . it can be seen that the transition radii from optically thick to thin locate at least several decades @xmath24 ( @xmath25 , the schwarzschild radius ) for the accretion rates @xmath26 . in such large inner regions , the diffusion approximation for radiative transfer in the slim disks ( abramowicz et al . 1988 ) breaks down . we can not avoid the calculations of the emergent spectra from such disks having transition regions and hot corona , if connect the slim disks with observations . 0.2 cm    [ cols=\"<,^,^,^,^,^,<\",options=\"header \" , ]     this paper is organised by following : the basic formulations for the calculations of structures and spectra are given in  2 , and the numerical results are presented in  3 . we find that the transonic location changes due to the presence of transition region . so does the structure in the inner disk region . we pay our attentions on how the emergent spectrum gradually changes with the accretion rate increasing from sub- to super - critical . the transition to an optically - thin region modifies the emergent spectrum , especially in the euv and soft x - ray bands . we apply the present slim disk model with transition region to galactic black hole candidates , one microquasar , and two nls1s sources in  4 . the conclusions are laid in the final section .","summary":"slim disks have been received much attention because of the increasing evidence for the super - critical accreting objects . in this paper , we make an attempt to construct a unified model , in which the viscosity and the dimensionless accretion rate can span rather wide ranges . thus this allows us to investigate the structures of and the emergent spectra from slim disks in a wider parameter space , covering transition regions from optically thick to optically thin . the emergent spectra from the unified model of the accretion disk have been calculated .","abstract":"slim disks have been received much attention because of the increasing evidence for the super - critical accreting objects . in this paper , we make an attempt to construct a unified model , in which the viscosity and the dimensionless accretion rate can span rather wide ranges . we replace blackbody radiation under diffusion approximation with a bridged formula , which accounts for both blackbody radiation and thermal bremsstrahlung in optically - thick and -thin cases , respectively . thus this allows us to investigate the structures of and the emergent spectra from slim disks in a wider parameter space , covering transition regions from optically thick to optically thin . we show that there is a maximum transition radius , roughly when . the emergent spectra from the unified model of the accretion disk have been calculated . a simple model of hot corona above the slim disk is taken into account for the hard x - ray spectrum in this paper based on wang & netzer ( 2003 ) . we have applied the present model to the microquasar grs 1915 + 105 , narrow line seyfert 1 galaxies re j1034 + 396 and akn 564 . our model can explain well the broadband x - ray spectra of narrow line seyfert 1 galaxies , microquasars and possible ultra - luminous compact x - ray sources . the present model can be widely applied to the candidates of super - critical accreting objects ."}
{"article_id":"astro-ph0407125","section_id":"r","document":"the equations ( 2 - 7 ) can be reduced to two first - order differential equations about two variables , @xmath38 and @xmath53 . we use the shooting method to solve these equations with appropriate boundary conditions . we assume an outer boundary at @xmath103 @xmath104 , where shakura - sunyaev solutions ( the gas pressure - dominated and @xmath105 ) are available . at this boundary , we firstly choose the derivatives of @xmath38 and @xmath53 obtained from shakura - sunyaev disk solutions , substitute them into the two differential equations , then calculate the values of @xmath38 and @xmath53 by iterations . although they are very close to shakura - sunyaev values , the new values of @xmath38 and @xmath53 allows the inward integration to run on the right way . the general relativistic effects are simulated by the pseudo - newtonian potential near the horizon of black holes . fourth - order runge - kutta method is employed to integrate the two differential equations to the inner disk edge @xmath106 , where @xmath106 is taken as a free parameter as other authors did ( e.g. mineshige et al . 2000 ; wang & netzer 2003 ) . we use the torque - free condition at the inner boundary . the shooting method determines the eigen angular momentum @xmath47 , provided the solution satisfies the regularity condition at the critical point close to the transonic radius . after we obtain the global transonic solutions , the basic physical quantities in the accretion flow and its emergent spectrum are given for stellar black holes ( @xmath107 ) and smbhs ( @xmath108 ) in this section . we show in detail how the transition to an optically thin region appears with the change of accretion rate . [ transonic ] 0.2 cm    [ sonicpoint ] 0.2 cm    [ sshape ]    0.1 cm    the detailed transonic situations are analysed here , and they are compared with the cases of slim disks without the correct treatment of transition regions . fig . 2 presents the exact distributions of the angular momentum ( @xmath44 ) , totoal pressure ( @xmath37 ) and radial velocity ( @xmath42 ) in the vicinity of transonic position , with the viscosity parameter @xmath23 and @xmath109 . the cases of @xmath110 and @xmath111 are both exhibited . from this figure , it can be seen that the curves of @xmath110 of our model are almost the same as those of the classical slim disk model . comparing with the classical slim disk , in the slim disk with transition regions , the angular momentums shift upward , total pressures decrease and the ratios of radial velocity to sound speed increase at the innermost radius , due to the effects of optically thin region . in the inner disk region where the effective optical depth is smaller than unity , the diffusion approximation for blackbody radiation is invalid , and the radiative cooling becomes inefficient . thus the temperature is higher than that of the classical slim disk , where local blackbody radiation is assumed in the entire disk . at the same time , the lower total pressure resulting from the decreased radiation pressure due to @xmath112 , leads to the smaller viscous tensor ( @xmath113 ) . therefore , the curve of angular momentum is flatter ( see equation 3 ) and the flow becomes more dense . the accretion flow reaches the sonic point earlier than the classical slim disk , since the sound speed @xmath114 is much smaller and the ratio @xmath115 becomes larger . this explains why the transonic positions shift outwards , compared with those in abramowicz et al . ( 1988 ) . as well known , the accretion flow has four types of transonic cases , according to which kind of pressure ( gas or radiation ) is dominant at the sonic point and the magnitude of the viscosity parameter . for low @xmath6 , it is total pressure that pushes the flow pass through the sonic point . while for large @xmath6 , the action of viscosity drives the flow across the transonic point . fig . 3 shows the dependency of the transonic radius on the accretion rate and the viscosity parameter for a black hole of 10 @xmath81 . it is apparent that the transition to an optically thin region moves the transonic point out , when the accretion rate is in the range @xmath116 and the viscosity parameter is @xmath117 . in other parameter space comprising @xmath118 and @xmath6 , the transonic location in our result is almost the same as that of the classical slim disk . the transonic flows with transition regions of high viscosity can be compared with the flows of low viscosity . first , they are both radiation pressure dominated for super - critical accretion rates . second , they are different in some properties . one of them is manifested in the optical depth . the accretion flow is almost entirely optically thick for a small viscosity parameter , e.g. @xmath119 . while the transition region appears for a large @xmath6 ( if @xmath6 is large enough , the inner flow can be purely optically thin and gas - pressure dominated ) . another distinct feature lies in the position of the sonic point . for low @xmath6 , the flow can not acquire enough velocity to transonic until it is near the marginal bound orbit ( 2 @xmath24 ) , since the sound speed is relatively high and the viscosity - driven process is not efficient . on the contrary , the sound speed of the flow with large @xmath6 is small , the sonic point locates far outside of the last stable orbit ( 3 @xmath24 ) . therefore , we conclude that the transonic situation of the accretion flow with transition region is , to some extent , between the case of low viscosity and that of high viscosity in the classical slim disk .    the s - shaped curves for different parameters are shown in fig . 4 . it is found that they are strongly affected by the transition region when the viscosity is high . for the case of stellar - mass black holes , the upper adaf and the middle unstable branches change much . the upper branch due to advection is modified , and the unstable branch is compressed . the appearance of the transition to an optically thin region lowers the radiation efficiency , hence the advection becomes more important . in the accretion flows of smbhs , the s - shaped curves are less altered , as shown in panels ( c ) and ( d ) in fig . it is easy to understand the curves are not seriously influenced in the outer region , since there the optical depth is large and it tends to be the classical slim disk . the distorted s - shaped curves may have observational features in stellar black hole accretions . the transition timescale from the upper to the lower branches , @xmath120 , will be shorter than that of the classical slim disk . for example with the same parameters , the difference at @xmath121 has a factor of @xmath122 . but the transition timescale from the lower branch to the upper , @xmath123 , is unchanged and greater than @xmath120 . this would be of interest in the explanation of x - ray transient objects . the variation of state - transition timescales in stellar black holes is also one of the crucial characteristics of the transition to optically thin regions in slim disks . [ str - mdot ]      fig . 5 provides the physical quantities such as the half - thickness , density , midplane temperature ( including surface temperature ) , effective optical depth and the ratio of gas pressure to total pressure for slim disks of both stellar - mass black holes and smbhs . the results of the classical slim disks are also shown in the figure with grey lines . the transition region influences greatly the structure in inner disk region , especially for the accretion flow around a stellar - mass black hole . first is the half - thickness . for all the super - critical accretion rates @xmath124 , @xmath125 , indicating the flow is geometrically slim . the thickness increases with the accretion rate , which is consistent with the result of the classical slim disk . at the outer boundary radius , the disk is always geometrically thin , and the solutions can be approximated by shakura - sunyaev solutions . because of @xmath32 , the lower sound speed results in the reduction of half - thickness , in comparison with the classical slim disk model . the reduced height favors the trapped photons to escape from the disk . this shape of the accretion flow is somewhat analogical with the funnels in thick disks .    with the emergence of the transition region , the temperature and density of the disk are both larger than those in the classical slim disks . there are still considerable radiation fluxes in the innermost region after the flow passes through the sonic point , which is pointed out by watarai et al . the effective optical depth has also been shown in fig . it should be noted that there is a large zone of @xmath22 when @xmath126 , e.g. more than 30 @xmath24 ( 15 @xmath24 ) for the disk of a black hole of @xmath111 ( @xmath127 ) solar masses . the lowest effective optical depth reaches 0.03 . more important is that , in the accretion flows of both stellar - mass and supermassive black holes , there are wider regions of at least 100 @xmath24 showing @xmath128 for a moderate super - critical accretion rate @xmath129 . in such large transition regions , blackbody radiation is not adequate to describe the radiative transfer . accordingly , a new radiation formula valid for any optical depth , as adopted in the present work , is necessary . when the accretion rate tends to very large , for example @xmath130 , in the inner disk region the advected energy dominates over the surface cooling , i.e. @xmath131 , the flow will have self - similar behaviors ( wang & zhou 1999 ) . we find that the global solution indeed shows the self - similar signatures : the radial velocity @xmath132 , total pressure @xmath133 , the density @xmath134 , the temperature @xmath135 and @xmath136 weakly depends on the radius , except in the vicinities of the inner disk edge . watarai & mineshige ( 2003 ) have also shown these properties . [ dotm - tr ] 0.2 cm    fig . 6 shows the dependence of the transition region on the accretion rate . we find the relation can be well fitted by an analytical formula @xmath137 there is a maximum transition radius @xmath138 at @xmath139 . this is clearly different from that in the standard disk model , i.e. @xmath140 ( see equation 1 ) . our calculations show that there is no transition radius when @xmath141 , and it drops quickly if @xmath142 . the maximum radius of the transition region can be understood from the s - shaped curves in fig . 4 . near the turning point between the upper and the middle branch , the surface density is the lowest and at the same time the very high temperature makes the absorption opacity be small . the father from this area , the larger effective optical depth due to the increase of either the surface density or the absorption opacity , or of both . this is an interesting result since the intermediate super - critical accretion has the largest transition radius , where the gravitational energy is mostly released . we briefly discuss the viscosity effect on the disk structure . 7 is the @xmath6-dependency of the global disk structure . in the slim disks , @xmath6 has only a little effect on the disk half - thickness . in our model large @xmath6 such as @xmath143 , reduces much height , increases the density and temperature in the inner region , which differs with that discussed by kawaguchi ( 2003 ) . at the outer radius , the situation is similar as the result in kawaguchi ( 2003 ) : the larger viscosity , the lower density , midplane temperature and also the optical depth , but the higher surface temperature . this is because of more efficient angular momentum transfer outwards and more trapped advection energy in the flow . [ str - alpha ] 0.2 cm    fig . 8 is the dependence of the transition radius on the viscosity @xmath6 . it can be found that the results from our calculations are not in agreement with the shakura - sunyaev disk , even at a small viscosity ( @xmath144 ) . this is because that the shakura - sunyaev disk breaks down when @xmath145 . the dependence of the transition radius on @xmath6 becomes very strong , roughly @xmath146 for @xmath147 and @xmath148 for @xmath144 , while @xmath149 in the shakura - sunyaev disk . the high viscosity drives the accreting gas to fall into the black hole more rapidly , leading to a low density region . this region then becomes absorption weak , enlarging the transition region . since the radial motion and the advection effect is neglected in the standard disk , its prediction does not hold when either the accretion rate or the viscosity is large .    in the end , we should pay attention that the properties of the effective optically thin region discussed here are completely different from optically - thin adafs . firstly , the flow is only effective optically thin . the volumn density and the surface density are still larger than those of optically - thin adafs . the thomson scattering is very important and the comptonization is significant . that the optical depth becomes effectively thin is because of the transparancy to photon absorption at a high temperature . in optically - thin adafs , the plasma density is very low and the thomson scattering optical depth is rather small . secondly , the temperature in the present slim disk model is not so high as that of optically - thin adaf ( @xmath150 k ) . thirdly , the pressure is still radiation - pressure dominated . while for the adaf , it has merely gas pressure , the radiation pressure can be neglected . however , we believe that slim disks ( optically - thick adafs ) are possible to transit to optically - thin adafs in inner region , once the viscosity is large enough . we leave this topic in the later paper . [ alpha - tr ] 0.2 cm    [ compton - y ]    0.2 cm      [ spectra - mdot ]    0.2 cm    [ spectra - alpha ]    0.2 cm    we have shown that the global structures of the slim disks with transition regions are quite different from those slim disks in abramowicz et al . ( 1988 ) . with the presence of transition region , only the theoretically predicted spectrum based on the global structure is of great significance to the observations . the emergent spectra of slim disks have been extensively studied . szuszkiewicz et al . ( 1996 ) were the first to calculate the spectrum with modified blackbody radation , and explained the soft - x excesses of quasars . wang et al . ( 1999 ) calculated the vertical structures and emergent spectra from slim disks . two prominent features appear : the saturated total luminosity and the constant cutoff energy . mineshige et al . ( 2000 ) and watarai et al . ( 2001 ) used purely blackbody radiation approximation , though it is not adequate in inner disk region . wang & netzer ( 2003 ) and kawaguchi ( 2003 ) employed the method of czerny & elvis ( 1987 ) to consider thompson electron scatterings and comptonization in accretion disks . however , since they did not treat the phenomena of optically thin , their results are only available for low viscosity parameter . as for the case of high viscosity parameter , the local radiation in spectral calculations tends to thermal bremsstrahlung when the optical depth is small , while local blackbody radiation that holds only for optically thick medium is assumed to determine the disk structure . this inconsistent treatment between structure and spectral calculations leads to the problem of temperature invertion ( czerny & elvis 1987 ) , namely , the calculated surface temperature is even higher than the midplane temperature in the accretion flow ( see the grey lines in the middle panels of fig . 5 ; in the classical slim disk , @xmath85 is much larger than @xmath53 at several @xmath24 ) . the reason is that the blackbody approximation predicts too much energy loss than the realistic radiation in optically - thin flows . thus , the radiated flux is heavily overestimated at high energies . we have solved the problem in this paper . by adopting the bridged formula which can describe the radiation energy for both optically - thick and -thin cases , the calculated surface temperature is not larger than the midplane temperature , as shown in figs . 5 and 7 . except that the thompson electron scattering modifies the radiation to deviate blackbody , the inelastic scattering also exchange the energy between photons and electrons . the comptonization effect has been stressed in wang & netzer ( 2003 ) and kawaguchi ( 2003 ) . we can give a more detailed estimation of the importance of this process . the effective compton parameter @xmath151 where @xmath152 , the absorption opacity is taken as @xmath153 ( @xmath154 ) , and 30 times value for smbhs . fig . 9 shows the parameter @xmath155 for different photon energies , accretion rates and black hole masses . when @xmath156 , comptonization can not be neglected and the emergent spectrum will be strongly modified . fig . 9 clearly shows how important the comptonization process is for disks with different parameters . we can draw a conclusion that the comptonization effect is very important in the inner region of super - critical accretion flows . saturated comptonization process is inevitable for less massive black hole disk ( @xmath157 ) . this confirms the conclusion of wang & netzer ( 2003 ) . the comptonization is less important for a @xmath158 black hole disk unless the disk has highly super - critical accretion rate , which agrees with laor & netzer ( 1989 ) . the higher accretion rate , the more important comptonization process . we adopt the scheme described in  2.2 to calculate the spectra from slim disks , taking into account the comptonization effect by a simple but practical method .    figs . 10 and 11 show the details of the emergent spectra from the slim disks with transition regions . we would like to stress that the present calculations have two advantages : 1 ) we include the transition region ; 2 ) the model covers wide ranges of the accretion rate and the viscosity . thus the present model involves all the known disk models ( except for the optically thin adios and cdafs ) . 10 clearly shows the spectra from the accretion disks of which the central black hole masses are 10 and @xmath127 @xmath159 . we start the accretion rate from sub - critical ( @xmath160 ) to super - critical ( @xmath161 ) . we find the spectrum shifts toward high energy with the increasing accretion rate . this is due to the increases of temperature and of the importance of comptonization with the accretion rate . the spectra show very strong humps at high energies for both stellar and supermassive black holes . the spectral flux is proportional to the accretion rate for the sub - critical accretion flow . the distinct spectral characteristic of super - critical disks is its broadness and flatness . the cutoff energies of the spectra almost keep constant when the accretion rate @xmath19 is above 10 , and the total radiated luminosity from the disk tends to be saturated . the _ constant _ cutoff energy was first found in wang et al . ( 1999 ) , which is caused by _ advection_. the feature of the saturated luminosity has also been found in abramowicz et al . ( 1988 ) , which is caused by the advection effect : most of the dissipated energy is swallowed by the central black hole . the maximum cutoff energy is about 100 kev ( 4 kev ) for a black hole of 10 ( @xmath127 ) solar masses . the saturated luminosity is about several eddington limit ( @xmath162 and @xmath163 erg / s for 10 and @xmath127 @xmath81 black holes , respectively ) . this extreme slim disk with very high accretion rate can be explained by the behaviors of self - similar solution ( wang & zhou 1999 ; wang & netzer 2003 ) . the features of the broad and flat spectrum , constant cutoff energy and saturated luminosity are very useful in explaining the x - ray spectra of microquasars , ulxs and narrow line seyfert 1 galaxies .    for a comparison with the spectra from the classical slim disks , we draw them as grey lines in fig . 10 . we use the same computation scheme for the spectra from the classical slim disks . we find that the emergent spectra are quite different from those based on the present model with transition region , when the accretion rate is above the critical value . the cutoff energy in the classical slim disk is unrealistically higher than the present model . thus the present model provides an improved version for the slim disk . we investigate the effect of the viscosity on the spectrum . for all the accretion rates , larger viscosity parameter causes the spectrum to extend to higher frequency . this is the contribution of the more significant elastic electron scatterings and comptonization . from czerny & elvis ( 1987 ) , the critical temperature is @xmath164 , above which the modification due to electron scattering is important . if @xmath6 increases , the transition region will enlarge and the surface temperature will increase . in such a flow the comptonization effect becomes stronger . thus the emergent spectrum is broader and flatter with the higher viscosity parameter . usually the cutoff energy strongly relies on both the accretion rate and the viscosity parameter . but in a saturated accretion system , it is only affected by @xmath6 . this may be utilized to determine the unknown viscosity parameter through x - ray observations of ultra - luminous objects . finally , with the detailed calculations , we verify the importance of photon trapping in the super - critical flows . if the diffusion timescale @xmath165 is longer than the accretion timescale @xmath166 in a flow , the photons can not escape from the disk at the same radius . this causes the so - called photon trapping . such a case has been recognized in early time ( katz 1977 ; begelman 1978 ) , but the quantitative features have been discussed by wang & zhou ( 1999 ) ; ohsuga et al . ( 2002 , 2003 ) and shimura & manmoto ( 2003 ) . let us compare the two timescales . 12 shows @xmath167 in the entire @xmath168 region for any @xmath169 . this means that the viscosity works for the disk , transporting the angular momentum and dissipating the gravitational energy . when @xmath170 , in the inner region @xmath171 , the photons are hardly radiated out so that trapped in the accretion flow . in this trapped region , energy transport in the form of advection is the main cooling mechanism . in this sense , the slim disk is often called optically thick adaf . after comparisons , we conclude that the photon trapping effect is still significant , but it is not so severe as that in the classical slim disk . this is mainly because of the greatly reduced disk height . the present model does not treat the photon trapping carefully , but see ohsuga et al . ( 2002 , 2003 ) , who treated the photon trapping with the given disk structure . wang & zhou ( 1999 ) have shown that the radiated luminosity is of @xmath172 erg / s for an extreme super - critical disk , which is as small as one third of the eddington luminosity . in fact , in physics the photon trapping effect makes it difficult to estimate the real accretion rate from the saturated observed spectrum , when the black hole has a super - critical accretion rate . one of the goals in this paper is to investigate the physics of the transition region . for a moderate super - critical rate @xmath173 , the photon trapping effect is not so strong , our present model does work for our applications in next section . the model coupling the photon trapping effects is just in preparation . considering the photon trapping effect , we believe that the super - critical accretors in microquasars and nls1s are more than the number we know at the present . kawaguchi ( 2004 ) realized the role of the self - gravitation in the optical spectrum of nls1s . we did not consider the self - graviation in the present work . the general relativistic effects are not included either . future work will solve the equations of the general relativistic disk with transition region , as well as calculate the spectrum from the disk . [ timescale ] 0.2 cm","summary":"we replace blackbody radiation under diffusion approximation with a bridged formula , which accounts for both blackbody radiation and thermal bremsstrahlung in optically - thick and -thin cases , respectively . we show that there is a maximum transition radius , roughly when . our model can explain well the broadband x - ray spectra of narrow line seyfert 1 galaxies , microquasars and possible ultra - luminous compact x - ray sources .","abstract":"slim disks have been received much attention because of the increasing evidence for the super - critical accreting objects . in this paper , we make an attempt to construct a unified model , in which the viscosity and the dimensionless accretion rate can span rather wide ranges . we replace blackbody radiation under diffusion approximation with a bridged formula , which accounts for both blackbody radiation and thermal bremsstrahlung in optically - thick and -thin cases , respectively . thus this allows us to investigate the structures of and the emergent spectra from slim disks in a wider parameter space , covering transition regions from optically thick to optically thin . we show that there is a maximum transition radius , roughly when . the emergent spectra from the unified model of the accretion disk have been calculated . a simple model of hot corona above the slim disk is taken into account for the hard x - ray spectrum in this paper based on wang & netzer ( 2003 ) . we have applied the present model to the microquasar grs 1915 + 105 , narrow line seyfert 1 galaxies re j1034 + 396 and akn 564 . our model can explain well the broadband x - ray spectra of narrow line seyfert 1 galaxies , microquasars and possible ultra - luminous compact x - ray sources . the present model can be widely applied to the candidates of super - critical accreting objects ."}
{"article_id":"astro-ph0407125","section_id":"c","document":"the detailed structure and spectral calculations of the slim disk with transition region ( the effective optical depth @xmath223 ) have been presented . we have shown that there is a quite large transition region in the slim disk . this region becomes larger with the increase of viscosity parameter . we get an empirical formula for the transition radius , i.e. @xmath224 . the maximum transition radius reaches @xmath225 @xmath226 at @xmath139 for a fixed viscosity @xmath6 . in the slim disk regime , the transition radius is @xmath227 for a fixed accretion rate ( e.g. @xmath228 ) and @xmath147 . the transition region affects not only the global disk structure , but also the emergent spectrum . the transonic location moves outward and the local radiated spectrum departs from blackbody radiation , because of the presence of the transition region . in comparison with the classical slim disk , we have made more accurate treatment with the optically thin region , in the calculations of both structure and spectrum . the present model covers a rather wide parameter space . we have also shown how the soft x - ray spectrum changes from sub - critical , moderate super - critical to the extreme super - critical accretion rate . we calculate the comptonization parameter for the slim disk , and show that the comptonization is very essential for stellar - mass black holes and less massive black holes ( @xmath229 @xmath159 ) , whereas it is not very important for more massive black holes with the masses larger than @xmath80 @xmath159 . this shows that the comptonization process play a key role in the formation of spectra in luminous objects . the present model can be widely applied to microquasars , ultra - luminous x - ray sources and narrow line seyfert 1 galaxies . the authors thank the helpful discussions with j.f . lu , m. wu . detailed reading of the manuscript and productive comments from the refree , ewa szuszkiewicz , are also appreciated . jmw thanks the support from national science foundation of china and special funds for major state basic research . 99 abramowicz , m.a . , czerny , b. , lasota , j.p . , & szuszkiewicz , e. 1988 , apj , 332 , 646 artemova , i.v . , bisnovatyi - 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ph/0310278 vaughan , s. , reeves , j. , warwick , r. , & edelson , r. 1999 , mnras , 309 , 113 veon - cetty , m .- p . , veon , p. & goncalves , a.c . 2001 , a&a , 372 , 730 vestergaard , m. 2003 , preprint ( astro - ph/0309521 ) wandel , a. , & liang , e.p . 1991 , apj , 380 , 84 wang , j .- m . 2003 , aj , 125 , 2859 wang , j .- m . , & netzer , h. 2003 , a&a , 398 , 927 wang , j .- szuszkiewicz , e. , lu , f .- j . , & zhou , y .- y . 1999 , apj , 522 , 839 wang , j .- m . , & zhou , y .- y . 1999 , apj , 513 , 420 watarai , k. , fukue , j. , & takeuchi , m. 2000 , pasj , 52 , 133 watarai , k. , mizuno , t. , & mineshige , s. 2001 , apj , 549 , l77 watarai , k. , & mineshige , s. 2003 , apj , 596 , 421 willott , c.j . , mclure , r.j . , & jarvis , m.j . 2003 , apj , 587 , l15 zampieri , l. , turolla , r. , & szuszkiewicz , e. 2001 , mnras , 325 , 1266","summary":"the present model can be widely applied to the candidates of super - critical accreting objects .","abstract":"slim disks have been received much attention because of the increasing evidence for the super - critical accreting objects . in this paper , we make an attempt to construct a unified model , in which the viscosity and the dimensionless accretion rate can span rather wide ranges . we replace blackbody radiation under diffusion approximation with a bridged formula , which accounts for both blackbody radiation and thermal bremsstrahlung in optically - thick and -thin cases , respectively . thus this allows us to investigate the structures of and the emergent spectra from slim disks in a wider parameter space , covering transition regions from optically thick to optically thin . we show that there is a maximum transition radius , roughly when . the emergent spectra from the unified model of the accretion disk have been calculated . a simple model of hot corona above the slim disk is taken into account for the hard x - ray spectrum in this paper based on wang & netzer ( 2003 ) . we have applied the present model to the microquasar grs 1915 + 105 , narrow line seyfert 1 galaxies re j1034 + 396 and akn 564 . our model can explain well the broadband x - ray spectra of narrow line seyfert 1 galaxies , microquasars and possible ultra - luminous compact x - ray sources . the present model can be widely applied to the candidates of super - critical accreting objects ."}
{"article_id":"hep-ph9609525","section_id":"i","document":"there is currently an unfortunate dichotomy in analytical approaches to qcd . one either calculates using lagrangian methods and , with the exception of monte carlo simulations , is limited to perturbative calculations , or one employs low energy models of qcd and eschews the known high energy behavior of the theory . there are only a few approaches where , for example , the calculation of hadronic form factors may be connected to the expected quark counting behavior at high energies . these include qcd sum rules  @xcite , nrqcd  @xcite , and to some extent light cone quantization  @xcite . this paper develops a formalism by which the known high energy behavior of qcd ( pqcd ) may be rigorously joined to standard phenomenological models of hadrons . this is achieved by using the renormalization group to run the scale of the qcd hamiltonian to the hadronic regime where it smoothly joins a fixed phenomenological behavior . this approach imposes important constraints on the low energy portion of the model . if one wishes to recover pqcd , one must work with current quarks . thus the low energy theory must also deal with current quarks . however phenomenology indicates that constituent quarks are the relevant degrees of freedom at low energy . thus , one must allow for spontaneous chiral symmetry breaking in the model . this , in turn , means that a nontrivial vacuum must be incorporated into the theory . finally , we see that one must use many - body techniques when calculating observables . the hamiltonian - based renormalization group we employ is particularly useful in this regard because it allows for the use of nonperturbative many - body techniques . we call this approach the `` dynamical quark model '' ( dqm ) . the fact that the low energy behavior of the dqm evolves directly from pqcd is very helpful when analyzing the dynamical structure of the low energy portion of the model . for example , we are able to rigorously establish that the non - abelian coulomb interaction is responsible for the quark structure of confinement in the heavy quark limit . we are also able to resolve ambiguities in the separation of short and long distance phenomena when evaluating current matrix elements . this brings us to a final important reason for employing the renormalization group improved ( rgi ) hamiltonian . as stated , we are obliged to use many - body methods while working with the model . the major tools at our disposal are the tamm - dancoff approximation ( tda ) and the random phase approximation ( rpa ) . these build , for example , meson bound states of the type @xmath0 or @xmath1 respectively . if one wants to allow for mixing to , for example , @xmath2 or @xmath3 states then these must be explicitly included in the calculation . such coupled channel problems are rather difficult to solve . thus it is imperative to include as much of the physics of fock sector mixing as possible directly into the hamiltonian . for example , the phenomenologically important hyperfine splittings can be incorporated by iterating the @xmath2 vertex , thereby adding an effective transverse gluon exchange operator to the hamiltonian . using the rgi hamiltonian automatically achieves this goal . the remainder of this paper is organized as follows . a model based on the coulomb gauge qcd hamiltonian is introduced in section ii and its high energy behavior is analyzed . to do this we impose a chiral invariant regulator and then calculate the rgi hamiltonian . the counter - term structure and possible perturbative and nonperturbative renormalization schemes are then discussed . in section iii we show how effective operators are constructed and examine the ultraviolet behavior of the quark creation operator , the axial current , and the scalar quark density . section iv presents nonperturbative , one - loop , many - body calculations of the vacuum gap equation , the quark condensate , and the dynamical quark mass . we summarize and conclude in section v.","summary":"furthermore , the hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale . this method has the benefit of allowing radiative corrections to be directly incorporated into nonperturbative many - body techniques . finally , the formalism is applied to the vacuum gap equation , the quark condensate , and the dynamical quark mass .","abstract":"a model which combines the perturbative behavior of qcd with low energy phenomenology in a unified framework is developed . this is achieved by applying a similarity transformation to the qcd hamiltonian which removes interactions between the ultraviolet cutoff and an arbitrary lower scale . iteration then yields a renormalization group improved effective hamiltonian at the hadronic energy scale . the procedure preserves the standard ultraviolet behavior of qcd . furthermore , the hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale . this method has the benefit of allowing radiative corrections to be directly incorporated into nonperturbative many - body techniques . it is applied to coulomb gauge qcd supplemented with a low energy linear confinement interaction . a nontrivial vacuum is included in the analysis via a bogoliubov - valatin transformation . finally , the formalism is applied to the vacuum gap equation , the quark condensate , and the dynamical quark mass ."}
{"article_id":"1008.3391","section_id":"c","document":"in order to examine how accurate the fastica + wt separation algorithm is , we randomly select three identified clusters with different redshifts and brightness temperatures ( table 2 ) to extract and study their radial brightness temperature profiles and spectra , and compare them with the input model , under the assumptions of @xmath3 g and @xmath100 g for the icm , respectively . to correctly obtain a cluster s image in the 65 mhz channel ( @xmath254 ) , here we define a local circular region , which is large enough to cover the whole cluster ( fig . 7@xmath237 & 7@xmath238 ) , and feed the fake 21cma survey maps extracted in this local region in five adjacent channels ( @xmath23961 , 63 , 65 , 67 and 69 mhz , @xmath272 mhz for each channel ) into the fastica program . the separated images ( fig . 8) are obtained with the same fastica + wt algorithm and are rescaled in the same way as described in @xmath273 . by repeating this process , we obtain separated images of each cluster in the 80 , 95 , 110 , 125 , 140 , 155 , 170 , and 185 mhz ( @xmath272 mhz for each channel ) channels , respectively . within a radius at which the brightness temperature drops to 1/10 of its central value , we extract the brightness temperature profiles and spectra of each cluster from the separated images ( fig . 9 ) . at a given radius @xmath274 as measured from the cluster s center @xmath275 , the systematic error is calculated as the mean deviation @xmath276 ^ 2}/{n_{\\rm pixel}|_{{|{\\bf r}-{\\bf r}_0|=r } } } } $ ] , where @xmath277 is the brightness temperature averaged at @xmath274 , and @xmath278 is the area .    in figure 9 , we also show the original input radio brightness temperature profiles and spectra of the three selected clusters , as well as the difference between the extracted and input distributions as residuals . in each case we find that the extracted and input distributions agree very well with each other within the error bars . consequently , we conclude that the fastica + wavelet algorithm will enable us to separate and study the brightest ( @xmath268 ) clusters in the 21cma fov , whose number is expected to be about 37 if @xmath3 g ( or 15 if @xmath4 g ) .    at 65 mhz , we successfully identify about @xmath2 ( 37 out of 48 if @xmath3 g , or 15 out of 18 if @xmath4 g ) of the simulated clusters that possess a central brightness temperature of @xmath279 , comparing to the average brightness temperature of @xmath280 of the foreground galactic emission . the detected clusters are distributed in a mass range of @xmath281 , and a redshift range of @xmath282 if @xmath3 g , or @xmath283 if @xmath4 g . all of them are bright enough for a direct model study to determine their spectral properties . we ascribe the failure of detection of the remaining 14 clusters ( 11 clusters if @xmath3 g , or three clusters if @xmath4 g ) to the following three reasons . first , six out of the 14 undetected clusters exhibit relatively flat spectra , which makes it difficult to disentangle them from the galaxy component , the spectral index of which ranges from @xmath284 to 2.9 . second , five out of the 14 clusters are faint and less extended , either embeded in brighter clusters or overlapped by bright discrete sources . and third , three out of the 14 clusters are less extended and are masked along with adjacent bright discrete sources . we also find that 10 ( if @xmath3 g ) or four discrete sources ( if @xmath4 g ) are misidentified as galaxy clusters . this mistake can be corrected by examining the brightness temperature profiles and spectra of the sources .    for the cosmological 21 cm signals survey projects such as the 21cma , although our separation approach can only extract bright clusters , which are more than two orders of magnitude brighter than the cosmological 21 cm signals , from the images , the analysis on the cluster component can deepen our understanding on cluster characters ( e.g. , brightness , shape , spatial distribution , spectrum ) in the low - frequency radio sky , the information of which is valuable when detecting the cosmological 21 cm signals in both image and frequency spaces .      in the frame of the most popular model for cluster radio halos , i.e. , the turbulent re - acceleration model ( e.g. , ferrari et al . 2008 ) , every cluster should host a radio halo after experiencing a major merger . however , since the halo s radio emission decays quickly as the relativistic electrons lose their energy , radio halos are expected in only about @xmath285 of massive ( @xmath286 ) clusters and in @xmath287 of less massive ( @xmath288 ) clusters ( cassano et al . 2006 ) , in other words , in the whole sky @xmath289 50 clusters are found to host a bright radio halo at 1.4 ghz according to the obsevational works ( cassano et al . 2006 ; giovannini et al . 2009 ; brunetti et al . 2009 ) . using this halo number density we estimate that @xmath290 radio halo shall appear at 1.4 ghz in the 21cma fov , which is consistent with the 1.4 ghz detection of abell 2294 in this field . on the other hand , by calculating the evolution of the power density @xmath291 of cluster radio halos ( see appendix ) , we find that among 1084 simulated clusters only one ( if @xmath3 g ) or none ( if @xmath4 g ) cluster ( fig . 10 ) is brighter than the standard vla detection threshold at 1.4 ghz , given an intergration time of @xmath292 hrs ( giovannini et al . this shows that our work is nicely consistent with current observations performed at higher frequencies , and the prediction for the apperence of more than one dozen low - frequency cluster radio halos in the 21cma fov is reliable . this work is accomplished based on the predictions of the standard turbulent re - acceleration model , which assumes that most cluster radio halos are formed in major merger events . however , in alternative models ( e.g. , the magneto - hydrodynamic ( mhd ) model ; brunetti et al . 2004 ; cassano 2009 ) , some radio halos , although relatively small and weak , can also be produced on cluster scales via minor mergers , so that much more halos are expected in the low - frequency radio sky . the survey of galaxy clusters with upcoming facilities working in the band of a few hundred of mhz will help distinguish these models .","summary":", we prove that , with a cumulative observation of one month with the 21cma array , about of galaxy clusters ( 37 out of 48 clusters assuming a mean magnetic field of g in the icm , or 15 out of 18 clusters assuming g ) with central brightness temperatures of at 65 mhz can be safely identified and separated from the overwhelmingly bright foreground . by examining the brightness temperature images and spectra extracted from these identified clusters , we find that the morphological and spectroscopic distortions are extremely small as compared to the input simulated clusters , and the reduced of brightness temperature profiles and spectra are controlled to be and , respectively . these results robustly indicate that in the near future a sample of dozens of bright galaxy clusters will be disentangled from the foreground in 21cma observations , the study of which will greatly improve our knowledge about cluster merger rates , electron acceleration mechanisms in cluster radio halos , and magnetic field in the icm .","abstract":"in this work we simulate the mhz radio sky that is constrained in the field of view ( radius ) of the 21 centimeter array ( 21cma ) , a low - frequency radio interferometric array constructed in the remote area of xinjiang , china , by carrying out monte - carlo simulations to model the strong contaminating foreground of the redshifted cosmological reionization signals , including emissions from our galaxy , galaxy clusters , and extragalactic discrete sources ( i.e. , star - forming galaxies , radio - quiet agns , and radio - loud agns ) . as an improvement of previous works , we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi - band observations , but also evolution of radio halos in galaxy clusters , assuming that relativistic electrons are re - accelerated in the intra - cluster medium ( icm ) in merger events and lose energy via both synchrotron emission and inverse compton scattering with cosmic microwave background ( cmb ) photons . by introducing a new approach designed on the basis of independent component analysis ( ica ) and wavelet detection algorithm , we prove that , with a cumulative observation of one month with the 21cma array , about of galaxy clusters ( 37 out of 48 clusters assuming a mean magnetic field of g in the icm , or 15 out of 18 clusters assuming g ) with central brightness temperatures of at 65 mhz can be safely identified and separated from the overwhelmingly bright foreground . by examining the brightness temperature images and spectra extracted from these identified clusters , we find that the morphological and spectroscopic distortions are extremely small as compared to the input simulated clusters , and the reduced of brightness temperature profiles and spectra are controlled to be and , respectively . these results robustly indicate that in the near future a sample of dozens of bright galaxy clusters will be disentangled from the foreground in 21cma observations , the study of which will greatly improve our knowledge about cluster merger rates , electron acceleration mechanisms in cluster radio halos , and magnetic field in the icm ."}
{"article_id":"1008.3391","section_id":"i","document":"by carrying out monte - carlo simulations we model the foreground of the cosmological reionization signals , including emissions from our galaxy , galaxy clusters , and extragalactic discrete sources ( i.e. , star - forming galaxies , radio - quiet agns , and radio - loud agns ) . as an improvement of previous works , we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi - band observations , but also evolution of radio halos in galaxy clusters , assuming that relativistic electrons are re - accelerated in the icm in merger events and lose energy via both synchrotron emission and inverse compton scattering with cmb photons . with these we create the fake @xmath0 mhz sky as will be observed with the 21cma array . we show that about @xmath2 ( 37 out of 48 if @xmath3 g , or 15 out of 18 if @xmath4 g ) of the clusters with a central brightness temperature of @xmath5 at 65 mhz can be successfully disentangled from the fake sky maps , if an ica+wavelet detection algorithm is applied . we thank the referee for the valuable comments on our manuscript . this work was supported by the national science foundation of china ( grant no . 10673008 , 10878001 and 10973010 ) , the ministry of science and technology of china ( grant no . 2009cb824900 , 2009cb824904 ) , and the ministry of education of china ( the ncet program ) .","summary":"in this work we simulate the mhz radio sky that is constrained in the field of view ( radius ) of the 21 centimeter array ( 21cma ) , a low - frequency radio interferometric array constructed in the remote area of xinjiang , china , by carrying out monte - carlo simulations to model the strong contaminating foreground of the redshifted cosmological reionization signals , including emissions from our galaxy , galaxy clusters , and extragalactic discrete sources ( i.e. , star - forming galaxies , radio - quiet agns , and radio - loud agns ) . as an improvement of previous works , we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi - band observations , but also evolution of radio halos in galaxy clusters , assuming that relativistic electrons are re - accelerated in the intra - cluster medium ( icm ) in merger events and lose energy via both synchrotron emission and inverse compton scattering with cosmic microwave background ( cmb ) photons . by introducing a new approach designed on the basis of independent component analysis ( ica ) and wavelet detection algorithm","abstract":"in this work we simulate the mhz radio sky that is constrained in the field of view ( radius ) of the 21 centimeter array ( 21cma ) , a low - frequency radio interferometric array constructed in the remote area of xinjiang , china , by carrying out monte - carlo simulations to model the strong contaminating foreground of the redshifted cosmological reionization signals , including emissions from our galaxy , galaxy clusters , and extragalactic discrete sources ( i.e. , star - forming galaxies , radio - quiet agns , and radio - loud agns ) . as an improvement of previous works , we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi - band observations , but also evolution of radio halos in galaxy clusters , assuming that relativistic electrons are re - accelerated in the intra - cluster medium ( icm ) in merger events and lose energy via both synchrotron emission and inverse compton scattering with cosmic microwave background ( cmb ) photons . by introducing a new approach designed on the basis of independent component analysis ( ica ) and wavelet detection algorithm , we prove that , with a cumulative observation of one month with the 21cma array , about of galaxy clusters ( 37 out of 48 clusters assuming a mean magnetic field of g in the icm , or 15 out of 18 clusters assuming g ) with central brightness temperatures of at 65 mhz can be safely identified and separated from the overwhelmingly bright foreground . by examining the brightness temperature images and spectra extracted from these identified clusters , we find that the morphological and spectroscopic distortions are extremely small as compared to the input simulated clusters , and the reduced of brightness temperature profiles and spectra are controlled to be and , respectively . these results robustly indicate that in the near future a sample of dozens of bright galaxy clusters will be disentangled from the foreground in 21cma observations , the study of which will greatly improve our knowledge about cluster merger rates , electron acceleration mechanisms in cluster radio halos , and magnetic field in the icm ."}
{"article_id":"math0107003","section_id":"i","document":"in this paper we study the spaces of conformal blocks for one dimensional lattice vertex operator algebras .    spaces of conformal blocks or modular functor ( see @xcite ) play an important role in conformal field theory . they can be defined for a wide class of vertex operator algebras and they parameterizes the states of the corresponding field theory . to avoid cumbersome notion let us describe our approach for affine algebras ( which corresponds to the wznw theory ) . first , recall the definition of the space of conformal blocks . let @xmath1 be a simple lie algebra , by @xmath2 denote the central extension of the lie algebra of @xmath1valued laurent polynomials . fix a level @xmath3 , that is , identify the central element of @xmath2 with the positive integer @xmath3 . as a geometric part of the data consider a complex curve @xmath4 and a set of pairwise distinct points @xmath5 with a local coordinate in a small vicinity of each point . then define the lie algebra @xmath6 of @xmath1-valued meromorphic functions on @xmath4 with poles only at @xmath7 . clearly we have the inclusion @xmath8 mapping any @xmath1-valued function to its laurent expansions at the points @xmath9 . another part of the data is a set of integrable representations @xmath10 of @xmath2 at level @xmath3 . their external tensor product is a representation of @xmath11 and , therefore , of @xmath12 . then the space of conformal block is defined as the space of coinvariants @xmath13 i.e. the quotient of @xmath14 by the action of @xmath15 . it is well known that these spaces are finite - dimensional and form a flat family over the module space of curves with punctures .    in @xcite another construction is proposed . let , as above , @xmath4 be a curve , @xmath9 and @xmath16 be pairwise distinct points on @xmath4 . then consider the subalgebra @xmath17 of functions with zeroes at @xmath9 and the subalgebra @xmath18 of functions whose values at @xmath9 belongs to the nilpotent borel subalgebra @xmath19 . then for any integrable representation @xmath20 at level @xmath3 we have the natural isomorphisms ( see @xcite ) @xmath21 where sum goes over all the sets of integrable representations at level @xmath3 and @xmath22 denotes the finite - dimensional representation of @xmath1 generated by the highest vector of @xmath23 . so the space of coinvariants of a single representation @xmath20 contains the spaces of conformal blocks where @xmath20 appears . an advantage of this construction is that these spaces of coinvariants is well defined if some of the points @xmath24 coincides . in this case we just consider zeroes with multiplicities . for multiple points we have not isomorphisms  ,  , but it is easy to show that these spaces form a coherent sheaf over the variety @xmath25 of sets of points on @xmath4 . first question is whether the dimension of the space of coinvariants preserves when some points coincides . indeed , this question is local and it is enough to check this when @xmath4 is the riemann sphere . the answer is positive for @xmath26 ( see @xcite for @xmath27 and @xcite for @xmath28 ) and negative for @xmath29 . also there is the positive answer for the similar question about the @xmath30-minimal models of the virasoro algebras ( see @xcite ) . but the general case is far from been studied . here we prove the equality of dimensions in the case of one dimensional lattice voas . another question is about the natural filtration on these spaces . namely , the affine lie algebra @xmath1 and its integrable representations are graded by the action of the energy element . but the subalgebras defined above are not homogeneous ( except the case of riemann sphere and @xmath31 ) , hence the spaces of coinvariants can be considered only as filtered spaces . nevertheless we consider the hilbert polynomials @xmath32 of the adjoint graded spaces and interpret them as a @xmath0-analog of the correspondent verlinde numbers ( which are dimensions of spaces of conformal blocks ) . this object is interesting even in the case of the riemann sphere ( and well studied only in this case ) . in @xcite there is a conjecture that expresses @xmath32 in terms of generalized @xmath0-supernomial coefficients . for @xmath30-minimal models of the virasoro algebras the polynomials @xmath32 take part in the andrews - gordon identities and therefore can be decomposed into sums of @xmath0-multinomial coefficients as well . in this paper we prove a formula ( see theorem  [ th : char ] , ( ii ) ) which expresses @xmath32 for one - dimensional lattice voas as a sum of @xmath0-supernomial coefficients . note that this formula can be considered as another definition of @xmath0-supernomials . these two question are connected . namely , suppose that the dimension preserves when the points coincides . then in the case of the riemann sphere it is enough to find @xmath32 for the graded subalgebra with @xmath31 . it makes possible to degenerate the algebra together with the subalgebra into an abelian one or a rather simple voa and obtain a fermionic type ( in terms of @xcite ) formula for @xmath32 . such a formula exists for @xmath33 ( see @xcite , @xcite , @xcite ) , for @xmath30-minimal models of the virasoro algebra ( see @xcite ) and for one - dimensional lattice voas ( see theorem  [ th : char ] , ( i ) ) .    in more general cases ( @xmath34-algebras , lattice voas , etc . ) it is not evident which subalgebras should be chosen instead of @xmath35 and @xmath36 . let us explain what we are doing in the case of affine lie algebras . introduce some `` elementary '' graded subalgebras @xmath37 . as the subalgebras are graded , they consist of @xmath1-valued functions with some local conditions at the zero point . then define the `` fused '' subalgebra @xmath38 of functions with pole only in @xmath16 and local conditions in @xmath7 prescribed by the subalgebras @xmath39 . then we have @xmath40 in particular , the subalgebra @xmath41 is fused from @xmath42 copies of the affine nilpotent borel subalgebra @xmath43 and the subalgebra @xmath44 is fused from @xmath42 copies of the affine nilpotent parabolic subalgebra @xmath45 , so and follows from . the paper is organized as follows .    in sec . [ sec : lvoa ] we recall some facts about lattice vertex operator algebras ( `` voa '' ) and their representations . in sec .  [ sec : ass ] we introduce an associative algebra that acts in each representation of the voa . in this way representations of the voa can be obtained as induced representations of the associative algebra .    in sec .  [ sec : verlinde ] we introduce spaces of coinvariants and give basic statements about their dimensions . in sec . [ sec : element - sub ] elementary subalgebras are introduced and the fused subalgebras are studied .    sec . [ sec : algebras ] and  [ sec : combinator ] are rather technical . in sec . [ sec : algebras ] the character of some auxiliary space of coinvariants is calculated . in sec . [ sec : combinator ] we show that characters of these auxiliary spaces can be expressed in terms of @xmath0-supernomial coefficients . this allows us to prove the main results of the paper in sec . [ sec : main - result ] . we use the standard notation for the @xmath0-binomial coefficients @xmath46_{q } } =    \\begin{cases }      \\frac{(q)_n}{(q)_{n - m}(q)_m},&n\\geq m\\geq0,\\\\      0,&\\text{otherwise } ,    \\end{cases}\\qquad\\text{where}\\quad    ( q)_n=(1-q)\\dots(1-q^n).\\ ] ]","summary":"we propose an alternative definition of-supernomial coefficients as characters of coinvariants for one dimensional lattice vertex operator algebras . this gives a new formula for-supernomial coefficients . along = 1.6pt","abstract":"we propose an alternative definition of-supernomial coefficients as characters of coinvariants for one dimensional lattice vertex operator algebras . this gives a new formula for-supernomial coefficients . along the way we prove that the spaces of coinvariants form a bundle over the configuration space of complex points ( the configuration space includes diagonals ) .    = 1.6pt"}
{"article_id":"1606.00793","section_id":"i","document":"there has been growing interest recently in the properties of the exotic quasi - particles arising in topologically ordered systems such as certain fractional quantum hall states @xcite or two - dimensional frustrated quantum magnets @xcite . one - dimensional lattice models for these non - abelian anyons have been constructed starting from a consistent set of fusion and braiding rules and the collective phases realized in many - body anyon models with pairwise interactions have been studied , mostly numerically , to identify a variety of critical phases and the conformal field theories describing their low energy properties , see e.g.  @xcite . the gapless states in these phases are protected by the topological symmetry present in these chains and can be realized at interfaces between different topological phases where they provide insights into nature of the adjacent quantum liquids @xcite . integrable models are known to be another important source ( complementary to numerical approaches ) of un - biased information on the properties of correlated many - body systems , in particular in low - dimensional systems where quantum fluctuations are strong . in fact , some of the anyonic lattice models mentioned above can be derived in the hamiltonian limit of a class of integrable statistical lattice models with interactions round the face ( also called irf or face models ) , such as the restricted solid on solid ( rsos ) models @xcite and their generalizations @xcite . motivated by this connection several integrable chains of interacting non - abelian anyons have been constructed and studied recently , see e.g.  @xcite .    here we consider one of the deformations of @xmath5 quantum spin chains leading to an anyonic models studied by gils _ et al_.  @xcite , namely the @xmath6 spin-@xmath2 or , equivalently , @xmath0 anyon model , see also refs . @xcite . as pointed out in ref . @xcite this model can be related to one of the paradigms of integrable quantum chains , i.e.  the xxz heisenberg spin chain , under a particular spin - anyon ( or face - vertex ) correspondence @xcite . based on this correspondence we have been able to embed the anyonic hamiltonian into a family of commuting operators generated by an irf transfer matrix . interestingly , and unlike the usual @xmath5 spin-@xmath2 chain with bilinear and biquadratic exchange or , e.g. , the model of interacting @xmath7 non - abelian anyons @xcite , this embedding is possible for arbitrary coupling constants . specifically , the spectrum of the anyon chain can be related to that of the xxz spin chain subject to properly chosen boundary conditions depending on the topological sector of the former . the independence of thermodynamic properties on these boundary conditions this allows to relate the phase diagram of the anyon chain to that known from the exact solution of the heisenberg model , see fig . [ fig : d3-phases ] . = [ circle , draw , thin , fill = blue!40,minimum size=5pt , inner sep=0pt ] = [ ]    ( z3 ) at ( -1.5,0.15 ) ; ( z3j ) at ( -1.5,0.02 ) ; ( z2 ) at ( 1.5,0.15 ) ; ( z2j ) at ( 1.5,0.02 ) ; ( zc ) at ( 0,0.25 ) ; ( zc ) at ( 2,0.02 ) ;    ( -2,0 )  ( -1,0 ) ; ( -1,0 )  ( 1,0 ) ; ( 1,0 )  ( 2,0 ) ; ( -1.0,-0.0 )  ( -1.0,0.5 ) ; ( 1.0,-0.2 )  ( 1.0,0.5 ) ; at ( -0.939693 , ) ; at ( -0.766044 , ) ; at ( -0.5 , ) ; at ( -0.173648 , ) ; at ( 0.173648 , ) ; at ( 0.5 , ) ; at ( 0.766044 , ) ; at ( 0.939693 , ) ; at ( 1,0.0 ) ; ( -1 * , )  ( -1.01 * , ) ; ( -1 * , )  ( -0.93 * , ) ; ( -0.93969,0 . )  ( -0.93969 * , ) ; ( -1.,0 . )  ( -1 . * , ) ; ( -1 . * , )  + ( 0.,-0.2 ) ; at ( -0.9396926208 * , ) ; at ( -0.9848077530 * , ) ; at ( -0.9932383577 * , ) ; at ( -0.9961946981 * , ) ;    we find that , while the low energy properties of the anyon and the spin chain in the critical phases are both described by conformal field theories ( cfts ) with central charge @xmath8 their operator content is different as a consequence of the change in boundary conditions and the presence of additional selection rules on a @xmath9 charge ( i.e.the magnetization for the spin chain ) for the anyon model : the continuum limit of the critical heisenberg model is known to a free boson with compactification radius @xmath10 depending on the anisotropy . the critical properties of the anyon model , on the other side are @xmath4 orbifolds of a boson compactified on a circle with radius @xmath11 . @xcite . ] for rational values of @xmath12 these cfts have an extended symmetry allowing for their formulation in terms of a finite number of primary fields . from the exact solution of the @xmath0 anyon chain the location of these special points in the phase diagram can be given in terms of the coupling constant of the microscopic model . these include the special rational cfts corresponding to compactification radii @xmath13 with integer @xmath14 that have been identified previously in the numerical investigation of ref . @xcite , see fig . [ fig : d3-phases ] . we note that the sequence of these field theories for _ arbitrary _ integer @xmath15 is realized for the coupling constant corresponding to the dual radius , @xmath16 . the paper is organized as follows : first we recall some basic facts related to the integrability of the xxz heisenberg chain ( or six - vertex model ) and its formulation as a @xmath0 symmetric spin chain . the @xmath0 group algebra can be extended to form a quasi - triangular hopf algebra which allows to construct related chains of anyons obeying @xmath0 fusion rules with an integrability structure closely related to that of the xxz model . based on this structure we employ functional bethe ansatz methods to solve the spectral problem of the @xmath0 anyon model . using this solution we perfom a finite - size analysis of the spectrum in the critical regime to identify the field theory describing the collective behaviour of the anyons at low energies","summary":"commuting transfer matrices for linear chains of interacting non - abelian anyons from the two - dimensional irreducible representation of the dihedral group ( or , equivalently , the integer sector of the spin- chain ) are constructed using the spin - anyon correspondence to a-symmetric formulation of the xxz heisenberg spin chain . the resulting spectrum can be related to that of the xxz spin- heisenberg chain with boundary conditions depending on the topological sector of the anyon chain . the properties of this model in the critical regime are studied by finite size analysis of the spectrum . in particular , points in the phase diagram where the anyon chain realizes some of the rational orbifold theories are identified .    = 1","abstract":"commuting transfer matrices for linear chains of interacting non - abelian anyons from the two - dimensional irreducible representation of the dihedral group ( or , equivalently , the integer sector of the spin- chain ) are constructed using the spin - anyon correspondence to a-symmetric formulation of the xxz heisenberg spin chain . the spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional bethe ansatz methods . the resulting spectrum can be related to that of the xxz spin- heisenberg chain with boundary conditions depending on the topological sector of the anyon chain . the properties of this model in the critical regime are studied by finite size analysis of the spectrum . in particular , points in the phase diagram where the anyon chain realizes some of the rational orbifold theories are identified .    = 1"}
{"article_id":"1201.2064","section_id":"i","document":"this paper concerns the classification of finite dimensional pointed hopf algebras with finite cyclic groups . recently heckenberger established one - to - one correspondence between arithmetic root systems and nichols algebras of diagonal type having a finite set of ( restricted ) poincare - birkhoff - witt generators @xcite and between twisted equivalence classes of arithmetic root systems and generalized dynkin diagrams @xcite . in this latter work , arithmetic root systems were also classified in full generality . the theory of nichols algebras is dominated by the classification of finite dimensional pointed hopf algebras ( see e.g. @xcite ) . nichols algebras appear in the construction of quantized kac - moody algebras and their @xmath3-graded ( see @xcite ) and @xmath4-graded versions @xcite . they are natural quantum groups and are connected to the bicovariant differential calculus initiated by woronowicz @xcite . bicovariant differential calculi on quantum groups have been studied by klimyk and schmdgen in their book @xcite ( see especially part iv of this book ) . nichols algebras play a central role in the theory of ( pointed ) hopf algebras . any braided vector space has a canonical nichols algebra . the easiest braidings are those of diagonal type , that is , the vector space v has a basis @xmath5 such that the braiding @xmath6 is given by @xmath7 for some nonzero numbers @xmath8 , for all @xmath9 the braided vector spaces of diagonal type with finite - dimensional nichols algebra were essentially classified by heckenberger . in this paper we study diagonal braidings and their nichols algebras coming from yetter- drinfeld modules over finite cyclic groups . this is a substantial restriction , and it turns out . we classify finite dimensional nichols algebras with diagonal type of connected finite dimensional yetter - drinfeld ( yd ) modules over finite cyclic group @xmath0 . we first determine which braided vector space @xmath1 is a @xmath0-yd module by means of equation systems in @xmath0 . using the classification of arithmetic root systems , we find all finite dimensional nichols algebras with diagonal type of connected finite dimensional @xmath0-yd modules . this paper is organized as follows . in sections 1 and 2 we find all finite dimensional nichols algebras with diagonal type of connected 2-dimensional and 3-dimensional @xmath0-yd modules , respectively . in section 3 we prove that nichols algebra of connected @xmath0-yd module @xmath1 with @xmath2 is infinite dimensional .    throughout , @xmath10 is a field of characteristic zero , which contains a primitive @xmath11th root of unit . let @xmath12 be a finite abelian group . let @xmath13 and @xmath14 is a primitive @xmath11th root of unit@xmath15 . if @xmath16 is a cyclic group with order @xmath11 and @xmath17 with basis @xmath18 , then there exist @xmath19 , such that @xmath20 and @xmath21 for any @xmath22 , @xmath23 let @xmath24 such that @xmath25 . thus @xmath26 and @xmath27 for @xmath28    if @xmath1 is a vector space with a basis @xmath29 and @xmath30 for @xmath31 such that map @xmath32 then @xmath33 is called a braided vector space of diagonal type . denote by @xmath34 the braiding matrix of @xmath33 under the basis @xmath29 . then @xmath35 is also written as @xmath36 let @xmath37 be vertexes of a diagram . there is a line between vertexes @xmath38 and @xmath39 if @xmath40 . label vertex @xmath38 by @xmath41 and line between @xmath38 and @xmath39 by @xmath42 . this diagram is called generalized dynkin diagram ( written as gdd in short ) of matrix @xmath34 or @xmath43 @xmath1 is said to be connected if the generalized dynkin diagram is connected . let @xmath44 be a basis of @xmath45 . let @xmath46 and @xmath47 then @xmath1 is a @xmath45 graded vector space if one defines @xmath48 . let @xmath49 and @xmath50 .","summary":"all finite dimensional nichols algebras with diagonal type of connected finite dimensional yetter - drinfeld modules over finite cyclic group are found . it is proved that nichols algebra of connected yetter - drinfeld module over with is infinite dimensional .","abstract":"all finite dimensional nichols algebras with diagonal type of connected finite dimensional yetter - drinfeld modules over finite cyclic group are found . it is proved that nichols algebra of connected yetter - drinfeld module over with is infinite dimensional ."}
{"article_id":"1701.00990","section_id":"i","document":"hitherto , the main exoplanet detection technique relies on spectroscopic and photometric transits . if a planet passes in front of a star , the star will be partially eclipsed and its flux will be dimmed by the successive coverage and uncoverage of the stellar surface by the transiting planet , resulting in detectable dips in the stellar light curve . in the optical and infrared bands , where most of the transit detection occurred , those transit depths are of the order of 13% , e.g. , 1.6% for hd  209458b @xcite , and 2.45% for hd  189733b @xcite . if the photospheric disk has a uniform emission ( i.e. , there is no limb - darkening ) , these depths are equal to the square of the ratio of the exoplanet radius ( @xmath4 ) to the stellar radius ( @xmath5 ) . from multi - wavelength light curves , it becomes possible to characterize the atmosphere and exosphere of giant exoplanets ( e.g. , * ? ? ? * ) , but additional measurements are needed to estimate the mass of the planet , the orbital parameters , and the inclination angle . these results can be achieved thanks to radial velocity measurements , orbital brightness modulations , gravitational microlensing , direct imaging , astrometry , and polarimetry . the later is probably one of the most delicate methods since the anticipated white light polarization degree ( about 10@xmath6 , @xcite ) resulting from scattering of stellar photons onto the atmospheric layers of hot jupiters is expected to be just about detectable given the current limits of current optical , broad - band , stellar polarimeters @xcite . @xcite reported to have successfully achieved a @xmath7-band polarimetric detection of hd  189733b and found a peak polarization of 2@xmath810@xmath9 ( i.e. 0.02  % ) and a cosine - shaped distribution of polarization over the orbital period . from those results , @xcite inferred additional constraints on the size of the scattering atmosphere of hd  189733b , and on the orientation of the system with respect to the earth - primary line of sight . yet there is no reliable measurement of the true scattered light polarization from hd  189733b in the @xmath7-band , as @xcite and @xcite reported an absence of large amplitude polarization variations . even if their observations are consistent with a plausible polarization amplitude from the planet , the low significance of the polarimetric observations can not be used as a claim for detection . this highlights the difficulty of _ polarimetric _ measurements of exoplanets in the optical band . however , _ spectroscopic _ detection of exoplanets has been quite successful at all wavebands , except at x - rays energies . it is unfortunate since x - ray photometry , spectroscopy , and polarimetry could help to constrain the composition and morphology of the exoplanet s atmosphere . @xcite reported for hd  189733 the detection in the 0.252  kev energy band of a transit depth estimate ranging from 4.0@xmath102.7% to 7.3@xmath102.5% ( see in their table  6 the limb - brightened model ) , which might be larger than the transit depth in optical of 2.391@xmath100.001% , computed for a uniformly emitting disk using the planetary radius of @xcite . these values of transit depths in x - rays were obtained by fitting the x - ray broad - band light curve using the analytic chromospheric transit of @xcite that assumes a geometrically thin emission . however , the corona of the sun ( a normal star ) is by definition located above the chromosphere and the solar coronal plasma is extended above the photosphere ( see for a review on the solar corona , e.g. , * ? ? ? * ) , therefore , a zero thickness is not appropriate to describe the geometry of the corona of hd  189733a , a moderately active star . moreover , the normalized phase - folded x - ray light curve of hd  189733a is affected for a phase binning of 0.005 ( corresponding to 958  s ) by large statistical noise ( @xmath05% ; poisson noise from added - up raw count rate out transit in table  5 of @xcite ) and astrophysical ( white noise ) scatter ( @xmath04% ; see bottom right panel of fig . 12 in the appendix of @xcite ) that hinders any fitting . therefore , more sensitive x - ray observations of the transit of hd  189733b are mandatory to obtain an accurate measurement of the shape of the planetary transit of the corona of hd  189733a and to better constrain its maximum depth .    in any case , the first indirect detection of an extra - solar planet in the 0.1  10  kev energy range opens new questions : what is the expected x - ray absorption radius and scattered flux from giant exoplanets ? is a _ direct _ detection of giant exoplanets feasible in this energy band ? is , similarly to the optical band , a polarimetric detection within the reach of future instruments ? to solve those issues , it is necessary to estimate the host - star flux reprocessed by the exoplanet gaseous surface first , and then to compute the resulting scattering - induced polarization . it is a particularly relevant issue since we have known for decades that stellar x - ray polarimetry is a very powerful diagnostic tool ( e.g. , * ? ? ? .    in this regards , hd  189733b is one of the best laboratories for giant exoplanet studies . hd  189733 is a binary system , situated at a distance of about 19.45  pc from the sun @xcite . the primary component hd  189733a is a main - sequence star of stellar type k1.5  v , mass 0.846  @xmath11 @xcite , radius 0.805  @xmath12 @xcite and rotational period 11.953 days @xcite . hd  189733a emits about 10@xmath13erg.s@xmath14 in the 0.25  2  kev band , corresponding to @xmath15 times its bolometric luminosity , which is about 10 times larger than the ratio of x - ray to bolometric luminosity observed from the sun at its maximum @xcite . the secondary component of spectral type m4  v is located at an angular separation of 11@xmath164 ( @xmath0 216  au ) from hd  189733a with an orbital period is 3200  years @xcite and it is approximatively two orders of magnitude fainter in x - rays than hd  189733a @xcite . the exoplanet hd  189733b with mass 1.162  @xmath17 @xcite and radius 1.26  @xmath18 , was discovered by transit observations in optical @xcite . orbiting around hd  189733a in 2.219 days @xcite , this hot jupiter is situated at only 0.031  au from its host star . due to its proximity from earth and its favorable observing geometrical conditions  its orbital plane is parallel within about 4@xmath19 of our line of sight @xcite and its orbit is nearly circular @xcite  hd  189733b stands as the perfect object for observations and numerical modeling . hence , in this paper , we aim to investigate the hd  189733a planetary system in terms of photometry and continuum polarization . focusing our study on soft x - rays , where the stellar coronal emission peaks , we build in sect . [ model ] a template x - ray spectrum for the corona of hd  189733a and a model for the atmosphere of hd  189733b according to the latest observational constraints . we present the monte - carlo code that we used to perform our calculations of radiative transfer and report the very first estimations of the reprocessed flux emerging from the outer atmospheric layers of hd  189733b , along with its resulting x - ray polarization , in sect .  [ results ] . in sect . [ discussion ] , we discuss our results in the context of present and future x - ray facilities , and conclude our paper in sect . [ conclusion ] .","summary":"what makes the detection of exoplanets so difficult in this band ? to answer this question , we run monte - carlo radiative transfer simulations to estimate the amount of x - ray flux reprocessed by hd  189733b despite its extended evaporating - atmosphere , we find that the x - ray absorption radius of hd  189733b at 0.7  kev , the mean energy of the photons detected in the 0.252 kev energy band by xmm - newton , is.01 times the planetary radius for an atmosphere of atomic hydrogen and helium ( including ions ) , and produces a maximum depth of.1% at  min from the center of the planetary transit on the geometrically thick and optically thin corona . additionally , the degree of linear polarization emerging from hd 189733b is.003% , with maximums detected near planetary greatest elongations .","abstract":"thousands of exoplanets have been detected , but only one exoplanetary transit was potentially observed in x - rays from hd  189733a . what makes the detection of exoplanets so difficult in this band ? to answer this question , we run monte - carlo radiative transfer simulations to estimate the amount of x - ray flux reprocessed by hd  189733b despite its extended evaporating - atmosphere , we find that the x - ray absorption radius of hd  189733b at 0.7  kev , the mean energy of the photons detected in the 0.252 kev energy band by xmm - newton , is.01 times the planetary radius for an atmosphere of atomic hydrogen and helium ( including ions ) , and produces a maximum depth of.1% at  min from the center of the planetary transit on the geometrically thick and optically thin corona . we compute numerically in the 0.252  kev energy band that this maximum depth is only of.6% at  min from the transit center , and little sensitive to the metal abundance assuming that adding metals in the atmosphere would not dramatically change the density - temperature profile . regarding a direct detection of hd  189733b in x - rays , we find that the amount of flux reprocessed by the exoplanetary atmosphere varies with the orbital phase , spanning between 35 orders of magnitude fainter than the flux of the primary star . additionally , the degree of linear polarization emerging from hd 189733b is.003% , with maximums detected near planetary greatest elongations . this implies that both the modulation of the x - ray flux with the orbital phase and the scattered - induced continuum polarization can not be observed with current x - ray facilities ."}
{"article_id":"1701.00990","section_id":"r","document":"we present the outcomes of our simulations in fig  [ fig : results ] . results are plotted with respect to the orbital phase of hd  189733b , also converted into transit hours . each data - point is associated with its 1@xmath183 monte carlo error bars resulting from the simulation . the monte carlo statistical error is estimated using the standard deviation @xmath183 that is roughly proportional to @xmath184/@xmath185 for large @xmath186 , with @xmath186 the number of photons sampled in the direction of the observer and var(x ) the variance of the estimate .      the top panel of fig  [ fig : results ] shows the light curve of hd  189733a at 0.7  kev , normalized to unity . the exoplanet orbits in front of hd  189733a from orbital phase -0.25 to orbital phase + 0.25 , with an eclipse of the stellar corona ( i.e. , a planetary transit ) occuring between orbital phases -0.0169 and + 0.0169 . during this planetary transit , the 0.7 kev flux decreases by 2.00@xmath100.15  % between the first and second contacts , as the exoplanet starts to cover the x - ray corona , then rises to 1.07@xmath100.15  % at orbital phase 0 . it then decreases back to 2.02@xmath100.15  % between the third and fourth contacts before resuming to the non - eclipsed flux , showing no more variation during the remainder of the orbit of hd  189733b . a close up representation of the transit is shown in fig . [ fig : transit ] for clarity purposes . we find a perfect agreement between numerical and simulation results within the monte - carlo statistical error of our modeling . using the stokes code , we isolated photons that are re - emitted / scattered from hd  189733b , and plotted the resulting light curve ( normalized with respect to the unitary flux of hd  189733a ) in fig  [ fig : results ] ( second panel from the top ) . to increase the statistics of the photon - starved results , the phase resolution of the re - emitted / scattered radiation has been decreased compared to fig . [ fig : transit ] . due to the strong photoelectric absorption processes that prevail at soft x - ray energies , the x - ray flux from the exoplanet is found to be three to five orders of magnitude lower than the photon flux from the main star . from the hd  189733a flux of @xmath187  erg  @xmath53  s@xmath14 at 0.7  kev , the flux of hd  189733b is about @xmath188  @xmath189  erg  @xmath53  s@xmath14 , depending on the orbital phase of the planet . the flux reprocessed onto the atmospheric layers of hd  189733b strongly depends on the angle between the source , the exoplanet atmosphere and the observer ; this effect is due to the differential scattering phase function of incoherent scattering , as presented in fig . [ fig : electronbound ] ( bottom ) . in the case of rayleigh scattering , forward and backward reprocessing prevails while , for incoherent scattering onto bound electrons , forward and perpendicular scattering are less probable . however , backscattering is very strong and when the gaseous planet passes beyond the plane - of - the - sky , its reprocessed flux rises up to a normalized flux of @xmath0  4.7 @xmath8 10@xmath9 . then , hd  189733b disappears behind its star and flux drops to zero . the middle panel of fig  [ fig : results ] is a visualization of the linear continuum polarization degree @xmath178 , ranging from 0 ( unpolarized ) to 100  % ( fully polarized ) . it is the polarization resulting from scattered light only , i.e. not diluted by the unpolarized stellar flux . the shape of the polarization curve is very similar to the results obtained by @xcite , who evaluated the spectra of visible to near - infrared starlight reflected by jupiter - like extrasolar planets . as @xcite , we find polarization maximums close to orbital phases @xmath190 , i.e. , near planetary greatest elongations , with @xmath178 = 64.9@xmath102.9  % which is slightly larger than in infrared . since the planet s orbital plane is inclined by 4@xmath19 , the polarization degree does not drop to zero at zero orbital phase as a small fraction of photons scatters onto the top of the atmospheric layers towards the earth . hence , we are sure that our model produces correct results and extends the near - infrared / optical investigation of @xcite to x - ray energies . the fourth panel of fig  [ fig : results ] also shows the star+planet linear polarization , now taking into account polarization dilution by the unpolarized stellar photons , i.e. , @xmath191 . the overall shape of the polarization curve , associated with a polarization degree below 0.003  % , is quite different from the intrinsic @xmath178 . in fact , maximum polarization is found when the exoplanet transits behind the plane - of - the - sky , with a local diminution to zero when hd  189733b is occulted by its primary star . the departure from a purely sinusoidal waveform is again due to the scattering phase function of incoherent scattering that promotes backscattering . associated with maximum fluxes from hd  189733b that are not located at maximal planetary elongations , the net diluted polarization degree peaks at orbital phases + 0.35 and + 0.65 . the highest degrees of @xmath178 are of the order of 0.0025  @xmath10  0.0002  % at 0.7  kev , similarly to the polarization found in the optical band @xcite . finally , the bottom panel of fig  [ fig : results ] presents the absolute polarization position angle @xmath180 to be observed with an x - ray polarimeter . when hd  189733b does not transit on hd  189733a , its polarization angle is equal to 90@xmath19 ( the @xmath192-vector of the radiation is aligned with the projected rotational axis of the orbit ) . however , when the planet is about to transit in front of its primary star , @xmath180 oscillates around 90@xmath19 . the canceling contribution of unpolarized fluxes from the star and the 90@xmath19 oriented polarization position angle resulting from scattering prevent the @xmath180 value from stabilizing , resulting in a chaotic signal . this behavior is strengthened due to the edge - on orientation of the exoplanet s orbit . as the illuminated side of hd  189733b , producing the scattering - induced polarization signal , is facing the star , an observer situated on earth no longer detects the bright side of the atmosphere and the signal is almost canceled . only photons that have scattered on the top of the atmosphere carry a non - random polarization signal . since most of the radiation comes from hd  189733a , the resulting polarization signal is highly diluted and thus @xmath180 randomly oscillates . another variation of @xmath180 is detected when the planet passes behind hd  189733a : at the ingress ( egress ) point , the polarization position angle increases ( decreases ) by @xmath0  30@xmath19 , due to the partial obscuration of the reprocessing target . the inclination of the system and the partial obscuration of the planetary disk suppresses the averaging of polarization and results in @xmath180 variations before a pure cancellation of polarization due to the planet disappearance . the amplitude of the fluctuation of @xmath180 is directly correlated with the orbital inclination of the exoplanet and could be , in principle , used to estimate the impact parameter of the transit .","summary":"thousands of exoplanets have been detected , but only one exoplanetary transit was potentially observed in x - rays from hd  189733a .","abstract":"thousands of exoplanets have been detected , but only one exoplanetary transit was potentially observed in x - rays from hd  189733a . what makes the detection of exoplanets so difficult in this band ? to answer this question , we run monte - carlo radiative transfer simulations to estimate the amount of x - ray flux reprocessed by hd  189733b despite its extended evaporating - atmosphere , we find that the x - ray absorption radius of hd  189733b at 0.7  kev , the mean energy of the photons detected in the 0.252 kev energy band by xmm - newton , is.01 times the planetary radius for an atmosphere of atomic hydrogen and helium ( including ions ) , and produces a maximum depth of.1% at  min from the center of the planetary transit on the geometrically thick and optically thin corona . we compute numerically in the 0.252  kev energy band that this maximum depth is only of.6% at  min from the transit center , and little sensitive to the metal abundance assuming that adding metals in the atmosphere would not dramatically change the density - temperature profile . regarding a direct detection of hd  189733b in x - rays , we find that the amount of flux reprocessed by the exoplanetary atmosphere varies with the orbital phase , spanning between 35 orders of magnitude fainter than the flux of the primary star . additionally , the degree of linear polarization emerging from hd 189733b is.003% , with maximums detected near planetary greatest elongations . this implies that both the modulation of the x - ray flux with the orbital phase and the scattered - induced continuum polarization can not be observed with current x - ray facilities ."}
{"article_id":"1701.00990","section_id":"c","document":"in this paper , we adopted the @xcite s model of the atmosphere of hd 189733b to run a monte - carlo radiative transfer code to estimate the amount of x - ray photons emitted from the corona of hd  189733a reprocessed on this hot - jupiter like exoplanet . we obtained the predictive x - ray transit light curve of hd  189733a and quantified the flux and polarization emerging from scattering onto the atmospheric layers . we have found that the maximum depth of the planetary transit on the geometrically thick and optically thin corona of hd  189733a in the 0.252  kev energy band is @xmath01.7% . with the assumption that adding metals in the atmosphere would not change dramatically the density - temperature profile , we have estimated that the maximum transit depth is little sensitive to the metal abundance . since the maximum depth of the x - ray transit of hd  189733b estimated from the current modeling of its atmosphere is small , forthcoming deeper observations with the current x - ray observatories may not have the required x - ray sensitivity to accurately constrain the transit shape . the next generation of large x - ray mission from the esa , athena , thanks to its larger mirror area ( e.g. , the proposed athena+ mission had at 1  kev a mirror area about 14 times larger than the fm2-pn mirror of xmm - newton ; @xcite ) should allow deeper investigations of the x - ray planetary transits of hd  189733a @xcite .    we have quantified the amount of flux reprocessed onto the hot jupiter surface . the exoplanet s flux is three to five orders of magnitude fainter than its primary star , with maximums at egress and ingress points due to the asymmetrical scattering phase function of compton and rayleigh scattering . at most , the reprocessed flux is lower than 1.0@xmath810@xmath194erg  @xmath53  s@xmath14 . a detection of the flux modulation with orbital phase is in pratical not achievable since requiring tremendous exposure time . the reprocessed flux is associated with a very weak , diluted , amount of linear polarization . the polarization degree being less than to 0.003  % , it is impossible to measure it with the current technology of x - ray polarimeters . however , the direct detection of the x - rays scattered by hd  189733b might be considered in the future with the possible advent of interferometric facilities in x - rays , e.g. , _ the black hole mapper _ visionary - mission with ( sub)microarcsecond resolution ( see _ nasa astrophysics in the next three decades _ , @xcite ) . this research has been supported by the academy of sciences of the czech republic , the cost action mp1104 `` polarization as a tool to study the solar system and beyond '' , and the european union seventh framework programme ( fp7/2007 - 2013 ) under grant agreement no . 312789 `` stronggravity '' . fm is grateful to sylvain bugier ( ) for his artwork of the hd  189733 system . 99 agol , e. , cowan , n.  b. , knutson , h.  a. , et al . 2010 , apj , 721 , 1861 anders , e. , & ebihara , m.  1982 , geochim . acta , 46 , 2363 anders , e. , & grevesse , n.  1989 , geochim . acta , 53 , 197 aschwanden , m.  j.  2004 , physics of the solar corona . an introduction , praxis publishing ltd . 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hutter , d. , et al . 2015 , apj , 813 , 48 wilms , j. , allen , a. , & mccray , r.  2000 , apj , 542 , 914 yelle , r.  v.  2004 , icarus , 170 , 167","summary":"we compute numerically in the 0.252  kev energy band that this maximum depth is only of.6% at  min from the transit center , and little sensitive to the metal abundance assuming that adding metals in the atmosphere would not dramatically change the density - temperature profile . regarding a direct detection of hd  189733b in x - rays , we find that the amount of flux reprocessed by the exoplanetary atmosphere varies with the orbital phase , spanning between 35 orders of magnitude fainter than the flux of the primary star .","abstract":"thousands of exoplanets have been detected , but only one exoplanetary transit was potentially observed in x - rays from hd  189733a . what makes the detection of exoplanets so difficult in this band ? to answer this question , we run monte - carlo radiative transfer simulations to estimate the amount of x - ray flux reprocessed by hd  189733b despite its extended evaporating - atmosphere , we find that the x - ray absorption radius of hd  189733b at 0.7  kev , the mean energy of the photons detected in the 0.252 kev energy band by xmm - newton , is.01 times the planetary radius for an atmosphere of atomic hydrogen and helium ( including ions ) , and produces a maximum depth of.1% at  min from the center of the planetary transit on the geometrically thick and optically thin corona . we compute numerically in the 0.252  kev energy band that this maximum depth is only of.6% at  min from the transit center , and little sensitive to the metal abundance assuming that adding metals in the atmosphere would not dramatically change the density - temperature profile . regarding a direct detection of hd  189733b in x - rays , we find that the amount of flux reprocessed by the exoplanetary atmosphere varies with the orbital phase , spanning between 35 orders of magnitude fainter than the flux of the primary star . additionally , the degree of linear polarization emerging from hd 189733b is.003% , with maximums detected near planetary greatest elongations . this implies that both the modulation of the x - ray flux with the orbital phase and the scattered - induced continuum polarization can not be observed with current x - ray facilities ."}
{"article_id":"cond-mat0407497","section_id":"i","document":"the pseudogap in the cuprates is widely believed to hold an important clue to the fundamental nature of these systems.@xcite through angular resolved photoemission studies@xcite of the variation around the fermi surface of the leading edge of the electron spectral density , it has been established that the pseudogap has d - wave symmetry as does the superconducting gap . a smooth evolution of the superconducting gap into the pseudogap is also observed in tunneling@xcite which shows that , in the underdoped regime , the gap fills in with increasing temperature but does not close as one goes through @xmath0 . these ideas have led to a school of thought that believes that the pseudogap is a precursor to superconductivity . one model is the preformed pair@xcite model with phase coherence lost at the superconducting @xmath0 , but the pairs remain till the higher pseudogap temperature @xmath1 . another model includes finite momentum pairs@xcite , which exist at any finite temperature below @xmath1 but do not contribute to the superfluid stiffness . no zero momentum cooper pairs remain above @xmath0 where superconductivity is lost . a second school of thought envisages that the pseudogap has its origin in a competing order parameter.@xcite the ddw theory is found among this group . it establishes a charge density wave order which has d - wave symmetry and which opens at the antiferromagnetic brillouin zone as the competing order parameter . the ddw model@xcite breaks time reversal symmetry because it introduces bond currents which also have small orbital magnetic moments . the two dimensional @xmath2 brillouin zone is halved into a lower and an upper antiferromagnetic brillouin zone . the ddw model can be included in the group of models associated with unconventional density waves ( udw ) , which have been proposed to explain some phases of correlated electron systems . for instance , udws have been used to understand quasi - two dimensional organic conductors , such as @xmath3 , with @xmath4 and @xmath5.@xcite unconventional density waves have a gap which averages to zero on the fermi surface ( although in contrast , the ddw gap , not opening at the fermi surface , can only average to zero over the brillouin zone ) . likewise , there is no periodic modulation in the charge or spin density , which makes them difficult to detect experimentally . for this reason it is very important to have predictions for transport properties in order to look for features that may characterize them .    in this paper , we calculate the optical conductivity and the electronic raman response for the ddw model . for tight - binding bands with first - nearest - neighbours only , the chemical potential acts as the lower cutoff on the interband signal in both optical responses as first discussed by yang and nayak@xcite in the case of optical conductivity . as the second - nearest - neighbour hopping is increased from zero , the cutoff remains , but shifts and is no longer at twice the chemical potential . the role of the chemical potential in the optical response is intimately related to the fact that the ddw order parameter opens at the antiferromagnetic brillouin zone . as a consequence optical spectral weight is transferred from intraband to interband transitions in the energy range of the gap with little change in total spectral weight . we obtain a peak in the real part of the conductivity coming from the interband contribution . this feature is robust with respect to different dispersion relations with second - nearest - neighbours . it is modified by impurities and by inelastic scattering , which shift the energy of the structure and obscure the cutoff , making an unambiguous determination of the pseudogap difficult . as the temperature is increased , the interband spectral weight loses intensity . it is fully depleted at the pseudogap temperature @xmath1 at which point it has all been transferred to the intraband . a similar peak is found in the optical scattering rate , but it can be shifted in energy . this feature can be used to test for the ddw state , but so far , it has not been seen in the cuprates .    the paper is organized as follows . in the next section , we present the ddw model , then in section [ sec : one - part ] , we discuss the one - particle properties relevant for our problem . section [ sec : conduc ] treats the problem of the optical conductivity and of the optical spectral weight . section [ sec : raman ] deals with the electronic raman response . in section [ sec : scatt ] , we consider the effects of elastic and inelastic scattering , and in the final section our conclusions are presented .","summary":"we have calculated the optical conductivity and the raman response for the d - density wave model , proposed as a possible explanation for the pseudogap seen in high cuprates .","abstract":"we have calculated the optical conductivity and the raman response for the d - density wave model , proposed as a possible explanation for the pseudogap seen in high cuprates . the total optical spectral weight remains approximately constant on opening of the pseudogap at fixed temperature . this occurs because there is a transfer of weight from the drude peak to interband transitions across the pseudogap . the interband peak in the optical conductivity is prominent but becomes progressively reduced with increasing temperature , with impurity scattering , which distributes it over a larger energy range , and with inelastic scattering which can also shift its position , making it difficult to have a direct determination of the value of the pseudogap . corresponding structure is seen in the optical scattering rate , but not necessarily at the same energies as in the conductivity ."}
{"article_id":"cond-mat0407497","section_id":"c","document":"we have calculated the optical conductivity and the raman response for a ddw system . there is a cutoff at low frequencies in the interband response for both the optical conductivity and the raman response . this cutoff is at @xmath50 if there is no imperfect nesting term in the dispersion relation . the imperfect nesting adds directly to the chemical potential and shifts the cutoff to lower frequency but does not eliminate it . including scattering makes the cutoff harder to discern .    as the chemical potential is changed we find a readjustment of the spectral weight between the inter- and intraband conductivities . that part of the interband contribution , ranging from frequencies zero to @xmath50 , is transferred at zero temperature to the drude weight as the chemical potential is increased with increasing doping . however , contrary to a first expectation there is little loss in the total spectral weight with the opening of the pseudogap . this result agrees with experiments.@xcite    as mentioned above , the @xmath50 cutoff also appears in the electronic raman scattering . the best channels to observe the cutoff at @xmath50 are @xmath147 and @xmath148 . the @xmath146 channel projects out the antinodal region where the gap is biggest , and the low intensity of the raman scattering at small @xmath129 , where it goes like @xmath164 , may make the cutoff difficult to see .    the behaviour with temperature of the optical conductivity has two characteristics : 1 ) the expected shift of the @xmath114 feature to lower frequencies , for a mean field theory with order parameter vanishing at @xmath1 , and 2 ) the transfer of spectral weight from interband to intraband as the interband contribution collapses . there is also a filling of the depression between low frequencies and @xmath50 . an important result of this paper is that there is a peak in the real part of the optical conductivity in the region @xmath232 that comes from the interband conductivity with @xmath233 for @xmath44 . this peak is robust against different dispersion relations including second - nearest - neighbours . it is reduced by the impurity scattering and by the inelastic scattering , which can also shift it . it is washed out with increasing temperature vanishing completely at the pseudogap critical temperature . similar structure is found in the optical scattering rate , but it is shifted relative to that in the optical conductivity . with strong inelastic scattering , as may be found in the mfl model , the @xmath50 cutoff and @xmath114 features become more difficult to determine directly . to the best of our knowledge , this interband structure has not yet been identified in experiments on cuprates . ejn acknowledges funding from nserc and the government of ontario ( premier s research excellence award ) , and the university of guelph . jpc acknowledges support from nserc and the ciar . we thank l. benfatto , w. kim , and d. basov for helpful discussions . 99 t. timusk and b. statt , rep . 62 * , 61 ( 1999 ) and references therein . h. ding , t. yokoya , j. c. campuzano , t. takahashi , m. randeria , m.r . norman , t. mochiku , k. kadowaki , and j. giapintzakis , nature ( london ) * 382 * , 51 ( 1996 ) . loeser , z .- x . shen , d.s . dessau , d.s . marshall , c.h . park , p. fournier , and a. kapitulnik , science * 273 * , 325 ( 1996 ) . renner , b. revaz , j .- y . genoud , k. kadowaki , and o. fischer , phys . lett . * 80 * , 149 ( 1998 ) . v. j. emery and s.a . kivelson , nature ( london ) * 374 * , 134 ( 1995 ) . e. carlson , v.j . emery , s.a . kivelson , and d. orgad in _ the physics of conventional and unconventional superconductors _ edited by k.h . bennemann and j.b . ketterson ( springer - 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{"article_id":"astro-ph0406608","section_id":"i","document":"cosmological observations suggest that the universe is dominated by an exotic form of matter which is responsible for the present phase of accelerated expansion @xcite . several scenarios have been proposed to account for the observations , but the nature of this dark energy still remains unknown . the simplest minimal model to fit the experimental data assumes the presence of a cosmological constant @xmath2 , representing the vacuum energy contribution to the spatial curvature of the space - time . in spite of the success of this concordance @xmath2cdm model , there is no reasonable explanation why the observed value of @xmath2 is extremely small compared to particle physics expectations @xcite . alternatively , a light scalar field , called quintessence , rolling down a flat effective potential has been proposed to account for the missing energy in the universe @xcite . in particular quintessence models manifesting tracker properties allow the scalar field to dominate the present universe independently of the initial conditions @xcite . different realizations of the original quintessence idea have been studied in the literature including the possibility of a scalar field evolution driven by a non - canonical kinetic term @xcite and a non - minimal coupling between quintessence and dark matter @xcite . on the other hand unified models of dark matter and dark energy have been considered @xcite . despite the proliferation of scalar field models of dark energy , we still lack of a fully consistent particle physics formulation . nonetheless distinguishing between a dynamical form of dark energy and a cosmological constant is of immense importance as it would give us a hint on the nature of this component . the recent wmap satellite measurements of the cosmic microwave background , by providing an accurate determination of the anisotropy power spectrum , offer the opportunity to have a better insight into the physics of the dark energy . the quintessence hypothesis has been tested with different methods using pre - wmap cmb data and sn - ia data or the 2df power spectrum @xcite . these analysis have constrained the dark energy equation of state @xmath3 without ruling out the possibility of a time dependence . in this article we carry out an analysis of the time evolution of the dark energy equation of state . our aim is to constrain a set of parameters characterizing the dark energy properties and the standard cosmological parameters by performing a likelihood analysis of the wmap first year data @xcite and the sn - ia luminosity distance measurements @xcite . the paper is organized as follows : in section  [ met ] and the appendices we describe the method and the data , in section  [ like ] we explain the evaluation of the likelihood , in section  [ res ] we discuss our results and finally in section  [ conc ] we present our conclusions .","summary":"detecting dark energy dynamics is the main quest of current dark energy research . addressing the issue demands a fully consistent analysis of cmb , large scale structure and sn - ia data with multi - parameter freedom valid for all redshifts . here we undertake a ten parameter analysis of general dark energy confronted with the first year wmap , 2df galaxy survey and latest sn - ia data . despite the huge freedom in dark energy dynamics","abstract":"detecting dark energy dynamics is the main quest of current dark energy research . addressing the issue demands a fully consistent analysis of cmb , large scale structure and sn - ia data with multi - parameter freedom valid for all redshifts . here we undertake a ten parameter analysis of general dark energy confronted with the first year wmap , 2df galaxy survey and latest sn - ia data . despite the huge freedom in dark energy dynamics there are no new degeneracies with standard cosmic parameters apart from a mild degeneracy between reionisation and the redshift of acceleration , both of which effectively suppress small scale power . breaking this degeneracy will help significantly in detecting dynamics , if it exists . our best - fit model to the data has significant late - time evolution at . phantom models are also considered and we find that the best - fit crosses which , if confirmed , would be a clear signal for radically new physics . treatment of such rapidly varying models requires careful integration of the dark energy density usually not implemented in standard codes , leading to crucial errors of up to 5% . nevertheless cosmic variance means that standardcdm models are still a very good fit to the data and evidence for dynamics is currently very weak . independent tests of reionisation or the epoch of acceleration ( e.g. isw - lss correlations ) or reduction of cosmic variance at large scales ( e.g. cluster polarisation at high redshift ) may prove key in the hunt for dynamics ."}
{"article_id":"astro-ph0406608","section_id":"r","document":"in this section we discuss different aspects of our results . we start by taking a look at the best - fit models and at the goodness - of - fit of both quintessence and models . then we show that the introduction of a time - varying equation of state for the dark energy component does not significantly alter the constraints on the basic cosmological parameters . this allows us to discuss constraints on the time evolution of the quintessence equation of state . in section [ lss ] we use large - scale structure data instead of the supernova data to break the geometric degeneracy . we also check if the combination of both data sets improves the constraints . finally , we discuss limits on toy `` phantom energy '' models where we allow @xmath53 . our global best fit qcdm model is characterized by the following dark energy parameters : @xmath54 , @xmath55 , @xmath56 and @xmath57 , which correspond to a fast transition in the equation of state at redshift of @xmath58 . the total @xmath59 of this model is @xmath60 , while the best - fit model has @xmath61 . however , the total number of degrees of freedom is 1514 , so that all our fits are rather bad . this is mainly due to the wmap data ( see the discussion in @xcite ) . in table [ chi ] we report the corresponding @xmath59 values for the cmb and sn data and best fit values of the standard cosmological parameters for these two models . notice that the qcdm model provides the best fit to both the cmb and sn data . cccccccccc model & @xmath62 & @xmath63 & @xmath64 & @xmath6 & @xmath18 & @xmath30 & @xmath25 & @xmath65 & @xmath24 +   + @xmath2cdm & @xmath66 & @xmath67 & @xmath68 & @xmath69 & @xmath70 & @xmath71 & @xmath72 & @xmath73 & @xmath74 + qcdm & @xmath75 & @xmath76 & @xmath60 & @xmath69 & @xmath77 & @xmath78 & @xmath79 & @xmath80 & @xmath81 +   +    it is intriguing that such a model has a time evolving equation of state @xmath4 similar to that reconstructed from the best fit to the sn data in @xcite . in figure  [ cmb ] we plot the temperature anisotropy power spectrum for these two models . it is remarkable how perfectly the two completely different models agree at intermediate @xmath82 , demonstrating the power of the wmap cmb data . at low multipoles the additional freedom of the qcdm models allows a slightly better fit . in fact due to a different distribution of the isw , these qcdm best fit models have less power at low multipoles than the one . however we want to remark that this part of the cmb spectrum is most likely affected by galactic contamination effects @xcite and without a more accurate investigation we should not place too much emphasis on this suppression of power . it is worth noticing that the difference in the best - fit cosmological parameters between qcdm and will lead to different tt power spectra at higher multipoles , @xmath83 . this suggest that an accurate detection of the third peak may increase the statistical weight in favour or against the qcdm model . cmb power spectrum for the qcdm ( red solid line ) and ( blue dashed line ) best fit models.,title=\"fig:\",width=302 ] +    the fact that the @xmath59 improves by @xmath84 through the addition of the three new dark energy parameters , is to be expected . nevertheless we see that some quintessence models provide a better fit to the data than standard , as opposed to analyses which assume that @xmath3 is constant . as we will discuss later , the limits on the time evolution of the dark energy equation of state are still compatible with a number of proposed scalar field scenarios .    studying the distribution of the @xmath59 values in the mcmc chains for the models , we find that @xmath85 for the models at @xmath86 ( 68.3% cl ) and @xmath87 at @xmath88 ( 95.4% cl ) . in the gaussian case , this corresponds to about @xmath89 independent degrees of freedom , slightly less than the number of cosmological parameters used ( @xmath90 ) . for the quintessence models we find @xmath91 for @xmath86 and @xmath92 for @xmath88 . assuming gaussian errors , this would mean that we are dealing with about @xmath93 independent degrees of freedom , many less than the @xmath90 cosmological and @xmath94 dark energy parameters used in the analysis . we conclude that we are unable to constrain all the additional parameters . is the improved @xmath59 of the best fit qcdm models a positive evidence for the additional dark energy parameters ? the answer to this question requires an estimation of the information criteria associated with the model @xcite . in general adding more parameters tends to improve the fit to data , however one should reward thoes models that can produce the same goodness - of - fit with fewer parameters . this can be achieved through the akaike information criterion ( aic @xcite ) and bayesian information criterion ( bic @xcite ) , respectively defined as @xmath95 and @xmath96 where @xmath97 is the maximum likelihood , @xmath98 is the number of parameters of the model and @xmath99 is the number of datapoints . the models have an aic of @xmath100 , while the qcdm models of @xmath101 . based on this difference of @xmath102 we conclude that four parameter dark energy models are not necessarily favoured . the bic disfavours the new parameters even more strongly . the information criteria therefore suggest that current data provide no positive evidence that the dark energy is anything more complex than a cosmological constant . this is not surprising , but should not be used as a reason to stop searching for ways of detecting evidence of evolution . the rewards from finding such evidence would be huge . the class of quintessence models could _ a priori _ contain new , severe degeneracies which change completely the preferred values of the cosmological parameters . if this were the case , then all the standard results of the wmap analysis @xcite would only be valid in the context of a model . we have found this not to be the case . the new dark energy parameters are degenerate amongst themselves but do not introduce any new degeneracy with the other cosmological parameters . this can be seen in figure [ cpar ] where quintessence model results are compared with those obtained for models only . unless specifically stated , the quoted results have been obtained using a linear parametrisation of @xmath8 and a logarithmic one of @xmath9 in the mcmc . this maximises the weight of models with a late rapid transition , other parametrisations lead to an even slightly better agreement between and qcdm . marginalized likelihoods for the various cosmological parameters in the scenario ( blue solid curve ) and including the qcdm models ( yellow shaded region ) . also shown are qcdm models with a prior on the baryon energy density @xmath103 ( red dashed line ) . the results agree very well in all cases.,title=\"fig:\",width=302 ] +    we notice that all parameters , with the possible exception of the reionisation optical depth @xmath24 , are well determined in both cases . also , their values are very similar and can not be distinguished even at one standard deviation . table [ tablep ] lists the best fit values of the cosmological parameters for the @xmath2cdm and the dark energy models . the constraint on @xmath19 is consistent with the hst measurement @xcite , while the amount of clustering matter @xmath104 is in agreement with large scale structure estimates @xcite . the physical baryon density is consistent with the big - bang nucleosynthesis expectations @xcite . this provides an important cross - check that all viable models have to pass . the background universe is therefore largely independent of the details of the dark energy . ccc parameter & @xmath2cdm & qcdm +   + @xmath104 & @xmath105 & @xmath106 + @xmath25 & @xmath107 & @xmath108 + @xmath30 & @xmath109 & @xmath110 + @xmath65 & @xmath111 & @xmath112 + @xmath24 & @xmath113 & @xmath114 +   +    we find nonetheless some differences , but they can be explained quite easily . firstly , these are the marginalised likelihoods . the remaining degeneracy in @xmath104 , @xmath30 and @xmath6 is therefore translated into a slight shift to lower values in both @xmath104 and @xmath30 . the degeneracy between the physical baryon density , @xmath25 , and the scalar spectral index , @xmath23 , becomes slightly worse ( see figure  [ ob_ns ] ) , leading to somewhat longer tails in their likelihood distributions . this is a consequence of the larger integrated sachs - wolfe ( isw ) effect produced in time dependent dark energy models with the respect to the @xmath2cdm case @xcite . in fact the isw boosts power on the large angular scales of the cmb , therefore less power of the primordial fluctuation power spectrum at small wavenumber @xmath98 is required to match the data . consequently slightly blue shifted spectral index values are preferred . the same effect is also responsible for the spread of the likelihood distribution of the reionisation optical depth through the degeneracy between @xmath65 and @xmath24 . for larger values of @xmath65 the excess of power at the low multipoles of the te spectrum requires larger values of the optical depth ( see figure  [ ns_tau ] ) . since the reionisation suppresses the contribution at high @xmath82 with a factor of @xmath115 a better determination of the cmb peak structure as well as better polarisation data will help to break this degeneracy . we hope that the latter will be available shortly , when wmap releases the two - year data . the degeneracy between the scalar spectral index , @xmath23 , and the physical baryon density @xmath116 . the filled contour are the 1 and 2 @xmath117 limits of the quintessence models , while the black solid contours are those of the models.,title=\"fig:\",width=302 ] +     the degeneracy between the scalar spectral index , @xmath23 , and the optical depth @xmath24 . the filled contour are the 1 and 2 @xmath117 limits of the quintessence models . the black lines show the corresponding limits for the case.,title=\"fig:\",width=302 ] +    figure [ cpar ] shows also the effect of introducing a prior on @xmath25 , namely @xmath103 . as we can see , the prior only affects the cosmological parameters @xmath24 , @xmath23 and @xmath25 and removes some of their high values . none of the dark energy parameters are affected ( see figure  [ depar ] ) . we should note that all cases use a top - hat prior @xmath118 . as we have seen in the previous section , the additional parameters which describe the dark energy do not introduce any new degeneracies with the standard cosmological parameters . however we expect the dark energy parameter space to have an internal degeneracy . for instance @xmath6 and @xmath7 both act on physical observables as an equation of state parameter . therefore slowly varying models with @xmath119 may look indistinguishable from models with the same value of @xmath6 and a rapid transition at very early time from whatever value of @xmath7 . as anticipated in section  [ good ] , the consequence of such degeneracy is that we can strongly constrain only one of the dark energy parameters , which turns out to be @xmath6 . in particular , the one - dimensional marginalized likelihood gives @xmath120 at @xmath88 , which is consistent with the upper limits quoted in other time dependent dark energy analyses @xcite . of course what this really implies is that the equation of state at a redshift of order z=0.1 is being constrained . we can not say anything about its true value today , but in what follows we use @xmath6 with this caveat in mind . the same applies when we take the limit of @xmath121 in the relevant figures . the other dark energy parameters are weakly constrained . in particular , as expected from the arguments discussed in section  [ like ] , we find that the inferred confidence intervals may depend on the parametrisation of @xmath8 and @xmath9 used in the mcmc . for the standard case , we find @xmath122 at @xmath88 , on the other hand @xmath8 and @xmath9 remain unconstrained . we refer to @xcite for a discussion on breaking such a degeneracy with an estimate of the value of @xmath20 from large scale structure . a parametrisation in @xmath123 would place more emphasis on early transitions , so that the effective redshift where @xmath124 is evaluated is moved to higher values . in this case the limits on @xmath124 become even weaker , and we conclude that @xmath124 as a parameter is difficult to interpret . on the other hand , the limits on @xmath4 as a function of redshift are less dependent of the parametrisation of @xmath8 , as we derive them at all redshifts separately . we therefore advocate these limits , as plotted in figure [ wz ] , as a better illustration of the constraints on dark energy models . likelihoods for the dark energy parameters in the qcdm models without prior on @xmath25 ( yellow shaded area ) and with the prior ( solid blue line ) . the prior does not affect the dark energy parameters significantly . we also show the relative goodness of fit of the best model in each bin ( red dashed lines).,title=\"fig:\",width=302 ] +    these limits , derived with the markov - chain approach , rest solely on the local density of the accepted models . if the assumption of gaussian errors holds approximately , then we can derive the same limits using the actual likelihood values instead . in this case , and considering a single variable , models with @xmath125 occur 95.4% of the time . we find that models with @xmath126 have @xmath127 , consistent with the limits from the markov chain . in order to put limits on the equation of state as a function of redshift , we proceed as follows : we compute @xmath4 for each model and then take either the @xmath128 confidence region over all models in the chain ( shaded area in figure  [ wz ] ) or compute the highest @xmath4 for models with @xmath129 ( dashed line ) . @xmath88 confidence region on @xmath4 derived by taking the 95% models with lowest @xmath4 from our main chain ( yellow shaded area ) and the `` exclusion zone '' where _ all _ models have @xmath130 from the best - fit model in our main chain ( blue hatched area ) . we also show the @xmath4 of the best - fit model ( black solid line ) . is acceptable at @xmath88.,title=\"fig:\",width=302 ] +    the shaded area is _ a priori _ the proper marginalised result , representing the @xmath128 limits on @xmath4 . however it is worth remarking that this constraint may suffer from a potential problem with the choice of the measure that we introduce to integrate the marginalised parameters over ( see discussion in section [ like ] ) . on the other hand the dashed line relies only on the goodness of fit , and can be interpreted as an exclusion limit . in other words models with a @xmath4 that enter the hatched area are a `` bad '' fit to the data . this does not include any information about how likely these models are , given the variation in the other parameters . our interpretation of this is as follows : if we want to judge if a single , specific model is ruled out or not , then we should be using the dashed line as an upper limit for @xmath4 . if we are more interested in what we would expect as the value of @xmath4 , given our additional knowledge about the other variables , then we should look at the shaded region as providing a limit on the equation of state parameter . as we can see in figure [ wz ] , models with @xmath131 at @xmath132 and with a fast transition occurring at @xmath133 are a bad fit to the data , being beyond the dashed blue line . physically this is because models where the transition from @xmath124 to @xmath17 occurs at redshifts @xmath134 with @xmath135 give rise to a non - negligible dark energy energy contribution at decoupling , which is strongly constrained by cmb data . however , models with @xmath136 and @xmath137 for which the transition occurs at redshift @xmath138 are consistent with the data as their early energy contribution is negligible . as mentioned earlier , the apparent exclusion of these models based on the likelihood for @xmath124 in figure  [ depar ] is an artifact of our parametrisation of @xmath8 . this can also be seen by noticing that the maximised results ( dashed curve ) does not fall to zero for @xmath139 , indicating that there are acceptable models in this part of the parameter space . however these models will be indistinguishable from a pure @xmath2cdm scenario and are thus not very interesting when we try to rule out one from the other . the limits on @xmath4 can be reinterpreted as constraints on the evolution of the dark energy density ( see figure  [ oqz ] ) . models with @xmath140 above the dashed line are ruled out , thus limiting the amount of dark energy available during matter domination to be @xmath141 ( see also @xcite ) . these results undoubtedly have an effect for quintessence model building , and we will be investigating this aspect in a future paper . limits on @xmath140 corresponding to those on @xmath4 in figure [ wz].,title=\"fig:\",width=302 ] +    for now though we restrict ourselves to a few general remarks . the limits on @xmath4 previously obtained allow us to constrain a large class of quintessence models . for instance the exclusion plot in figure [ wz ] suggests that models with a perfect tracking behavior , for which @xmath142 during the matter era up to @xmath143 , and with a late time fast transition , are disfavoured by the data . as we have seen before , this is because @xmath144 must be negligible at early times . this class of models , for some particular choice of the parameters of the scalar field potential , include the two exponential potential @xcite and the albrecht - skordis model @xcite . of course , if they leave their tracking behaviour before then , the constraint is weakened . these models satisfy the constraints only if the slope of the scalar field potential , where the quintessence is initially rolling down , is very steep and then followed by a nearly flat region such that the equation of state @xmath145 at the present time . on the other hand models with a non - perfect tracking behavior and a slowly varying equation of state with @xmath136 are consistent with the data . this is the case of quintessence models with an inverse power law potential @xcite , supergravity inspired potentials such as the one proposed in @xcite or off - tracking quintessence models , such as those studied in @xcite . models of late time transition @xcite which show features of our best fit model can also be consistent with the data . one important question is whether the supernova data contains any severe systematic effects that may strongly bias our results . to test for this possibility , we replace the supernova data by the 2df galaxy redshift survey power spectrum from ref . the bias is added as a new , free parameter . this means that only the form of @xmath146 is constrained , not its amplitude . the solid lines in figures [ cpar_lss ] and [ depar_lss ] show the resulting likelihoods of the cosmological and the dark energy parameters respectively . comparing them to the cmb+sn - ia results ( shaded yellow regions ) , we find that the results are consistent , but that the supernovae allow us to place stronger constraints on @xmath104 , @xmath30 and @xmath6 when combined with the cmb . there is no evidence for any systematic problems in the sn - ia data set . additionally , we can use the combination of all three data sets . in @xcite we found that the large scale structure ( lss ) does not add any strong constraints , beyond those found with cmb+sn - ia data , as long as no constraints on the bias parameter are imposed . as the dashed curve in figures [ cpar_lss ] and [ depar_lss ] shows , this is still the case , and the bias parameter is strongly correlated with the clustering strength , @xmath20 . the constraints on the bias found in @xcite do not apply to our analysis , since they were obtained by combining the sdss 3d matter power spectrum with the wmap results on @xmath20 which are correct only for @xmath2cdm cosmologies . constraints on the cosmological parameters when adding the 2dfgrs data to cmb and sn - ia data ( blue dashed line ) and when only using cmb+2dfgrs ( black solid line ) , compared to the cmb+sn - ia case ( yellow shaded region ) . , title=\"fig:\",width=302 ] +     constraints on the dark energy parameters when adding the 2dfgrs data to cmb and sn - ia data ( blue dashed line ) and when only using cmb+2dfgrs ( black solid line ) , compared to the cmb+sn - ia case ( yellow shaded region ) . , title=\"fig:\",width=302 ] +    for standard quintessence models one can thus either use supernovae or large scale structure data , with the supernova data giving the stronger constraints . the situation changes if additional parameters need to be constrained , e.g. non - zero neutrino masses . in this case it is crucial to have very good clustering data on small scales where the neutrinos impose a distinct signal on @xmath146 . several authors have suggested that dark energy models with a super - negative equation of state , for which @xmath53 , can provide a better fit to the cmb and the sn - ia data @xcite . on the other hand all these analyses are biased in favour of phantom dark energy models since they use a constant equation of state parameter @xcite . in this scenario the dark energy violates the weak energy condition ( wec ) which leads to a number of problems @xcite . for this reason we feel that these models are disfavoured on theoretical grounds . nevertheless it remains an interesting question whether they are compatible with the current cosmological observations ? constraining time dependent phantom energy models allows us the opportunity to test these models against the observational data without the bias induced by assuming a constant equation of state parameter . however the main problem for this class of models is the existence of tachyon instabilities which lead to an exponential growth of phantom energy perturbations on small scales . in addition our formalism does not allow us to follow the evolution of the dark energy perturbations for phantom models which cross the @xmath1 value ( see discussion in appendix  [ scaleq ] ) . on the other hand we can account for the perturbations in models which violate the weak energy condition at all times .    in order to be self - consistent we therefore extend our analysis to two different classes of dark energy models , those which always satisfy / violate the wec and those which cross the wec boundary value @xmath1 . the latter are assumed to be homogeneous and consequently our analysis for these class of models accounts only for the effects they produce on the background expansion . although this is not physical , we are unaware of a unique prescription for handling these cases . we therefore suggest that the reader sees this section more as a speculative treatment . it is interesting to note that in these `` toy '' phantom models , the allowed values of the cosmological parameters do not change very much , in that they lie somewhere between the and the qcdm case ( see fig . [ cpar_phantom ] ) . constraints on the cosmological parameters for all phantom models ( solid lines ) and those that respect the weak energy condition ( @xmath147 ) ( shaded ) , compared to the models ( dashed).,title=\"fig:\",width=302 ] +     constraints on the dark energy parameters for all phantom models ( red dashed lines ) and those that respect the weak energy condition ( @xmath148 ) ( solid black line ) . the dotted line is from models that do not cross @xmath1.,title=\"fig:\",width=302 ] +    the models which cross @xmath1 provide a slightly improved best - fit . in particular we find a best - fit model with @xmath149 . it has @xmath150 and @xmath151 , i.e.  the equation of state crosses over that of the cosmological constant , @xmath152 . this behaviour is most likely driven by the supernova data , as we find a similar result if we only use this data set @xcite . constraints on the dark energy equation of state parameter @xmath4 . the shaded area corresponds to models which do not cross @xmath1 and for which perturbations are taken into account , while the hatched area corresponds to all models , including those crossing @xmath1 , but without perturbations.,title=\"fig:\",width=302 ] +    for the standard parametrisation of @xmath8 and @xmath9 , the median for @xmath6 is @xmath153 and for @xmath7 is @xmath154 . the 95% confidence intervals are @xmath155 and @xmath156 . for the models that do not cross @xmath1 , but always remain either with @xmath157 or @xmath148 , the results give the median for @xmath6 to be @xmath69 and for @xmath7 to be @xmath158 . the overall best - fit model is the same as for the standard qcdm models , but as the above median values show there are about the same number of accepted models on both sides of the divide .    thus there is no evidence for any deviation from in this extended framework . the parameter which does show some change is the clustering amplitude , @xmath159 , which lies now in the 95% confidence interval @xmath160 as opposed to the dark energy models satisfying the weak energy condition @xmath148 for which @xmath161 . the limits on @xmath4 are shown in figure  [ wlim_phantom ] . the shaded regions correspond to all models which do not cross @xmath1 and for which perturbations are included , while the hatched area corresponds to all models which cross @xmath1 .","summary":"our best - fit model to the data has significant late - time evolution at . nevertheless cosmic variance means that standardcdm models are still a very good fit to the data and evidence for dynamics is currently very weak .","abstract":"detecting dark energy dynamics is the main quest of current dark energy research . addressing the issue demands a fully consistent analysis of cmb , large scale structure and sn - ia data with multi - parameter freedom valid for all redshifts . here we undertake a ten parameter analysis of general dark energy confronted with the first year wmap , 2df galaxy survey and latest sn - ia data . despite the huge freedom in dark energy dynamics there are no new degeneracies with standard cosmic parameters apart from a mild degeneracy between reionisation and the redshift of acceleration , both of which effectively suppress small scale power . breaking this degeneracy will help significantly in detecting dynamics , if it exists . our best - fit model to the data has significant late - time evolution at . phantom models are also considered and we find that the best - fit crosses which , if confirmed , would be a clear signal for radically new physics . treatment of such rapidly varying models requires careful integration of the dark energy density usually not implemented in standard codes , leading to crucial errors of up to 5% . nevertheless cosmic variance means that standardcdm models are still a very good fit to the data and evidence for dynamics is currently very weak . independent tests of reionisation or the epoch of acceleration ( e.g. isw - lss correlations ) or reduction of cosmic variance at large scales ( e.g. cluster polarisation at high redshift ) may prove key in the hunt for dynamics ."}
{"article_id":"astro-ph0406608","section_id":"c","document":"in this paper we have made the first attempt to constrain dynamical models of dark energy by combining cmb , 2dfgrs and type - ia supernova data . on the positive side , we find that by allowing the dark energy equation of state to vary as a function of time , we do not introduce any strong degeneracies that would adversely affect the standard cosmological parameter estimation , apart from perhaps a mild degeneracy between the reionisation optical depth , @xmath24 and the redshift of the commencement of acceleration . its effect is to alter the isw contribution to large angles and hence , after cobe normalisation uniformly alters the heights of the peaks @xcite . breaking this degeneracy by some means will significantly enhance our ability to constrain dark energy dynamics . this might be done through a number of routes : other astrophysical constraints on @xmath24 ; by probing the redshift of acceleration using isw - lss correlations ; by measuring the non - gaussianity of cmb from weak lensing induced by structure formation @xcite or by beating cosmic variance using cluster polarisation at high redshift @xcite . the remaining cosmic parameters are only mildly affected by the new freedom given to dark energy and are similar to their @xmath2cdm counterparts . on the down side , with regard to the dark energy parameters , the currently available data set means that only the present value of the equation of state @xmath6 is well constrained . we find @xmath136 at 95% confidence level . by studying the behaviour of @xmath4 , we conclude that the constraints become weak for any redshifts larger than about unity .    however , there are some clear results that emerge . for example in the large class of quintessence models that have periods of perfect tracking behaviour , i.e. @xmath142 during the matter dominated era , only those which track for during the period @xmath162 are acceptable . quintessence models with a very late departure from tracking , or any dark energy models with a late transition from a high value of @xmath3 , are disfavoured as a consequence of the fact that early contributions of dark energy are constrained to be negligible . we have also found a point of practical importance in the hunt for dark energy dynamics . since only rapidly varying models at low redshift have a distinct signature as opposed to @xmath2cdm @xcite including such models in ones likelihood analysis is very important , otherwise the results will be biased towards no detection of dynamics . however these rapidly varying models are the most susceptible to numerical errors , which we have found can be as large as @xmath16 . we therefore have used a code specially adapted to handle these `` kink '' cases , and this is described in appendix [ boltz ] . we have also studied toy models for which @xmath53 is possible . in this case the perturbations are generically unstable , and so we turned them off for any model which enters @xmath53 at any point . in this case models that have @xmath3 slightly larger than @xmath163 at early times and show a rapid , late transition to a super - negative equation of state , @xmath164 , are slightly , but not significantly , preferred . in a slightly more physical model where @xmath1 can not be crossed , allowing us to compute the perturbations , we find no preference for these `` phantom '' models . overall , we conclude that dynamical models of dark energy are by no means ruled out and provide a slightly better fit to current data than . the latter is still perfectly acceptable and , given its simplicity , seems in many ways the preferred model at the current time . whether observations and theoretical prejudice maintain this conclusio over the coming years will have a profound impact on our understanding of fundamental physics we are grateful to michael doran for testing our models with cmbeasy and for the very useful discussions and suggestions . thank axel de la macorra for the interesting discussions and the hospitality at the mexico university . is supported by columbia university academic quality fund , m.k . and d.p . are grateful to pparc for financial support and b.a.b . is grateful to z. chacko for discussions and funding from royal society / jsps . simulations were performed on cosmos iv , the origin 3800 supercomputer , funded by sgi , hefce and pparc . the completion of this paper was made possible thanks to the early elimination of italy , switzerland and england from the european championships . we are grateful to the players of those teams for being so aware of our need to finish this work .","summary":"there are no new degeneracies with standard cosmic parameters apart from a mild degeneracy between reionisation and the redshift of acceleration , both of which effectively suppress small scale power . breaking this degeneracy will help significantly in detecting dynamics , if it exists . phantom models are also considered and we find that the best - fit crosses which , if confirmed , would be a clear signal for radically new physics . treatment of such rapidly varying models requires careful integration of the dark energy density usually not implemented in standard codes , leading to crucial errors of up to 5% . independent tests of reionisation or the epoch of acceleration ( e.g. isw - lss correlations ) or reduction of cosmic variance at large scales ( e.g. cluster polarisation at high redshift ) may prove key in the hunt for dynamics .","abstract":"detecting dark energy dynamics is the main quest of current dark energy research . addressing the issue demands a fully consistent analysis of cmb , large scale structure and sn - ia data with multi - parameter freedom valid for all redshifts . here we undertake a ten parameter analysis of general dark energy confronted with the first year wmap , 2df galaxy survey and latest sn - ia data . despite the huge freedom in dark energy dynamics there are no new degeneracies with standard cosmic parameters apart from a mild degeneracy between reionisation and the redshift of acceleration , both of which effectively suppress small scale power . breaking this degeneracy will help significantly in detecting dynamics , if it exists . our best - fit model to the data has significant late - time evolution at . phantom models are also considered and we find that the best - fit crosses which , if confirmed , would be a clear signal for radically new physics . treatment of such rapidly varying models requires careful integration of the dark energy density usually not implemented in standard codes , leading to crucial errors of up to 5% . nevertheless cosmic variance means that standardcdm models are still a very good fit to the data and evidence for dynamics is currently very weak . independent tests of reionisation or the epoch of acceleration ( e.g. isw - lss correlations ) or reduction of cosmic variance at large scales ( e.g. cluster polarisation at high redshift ) may prove key in the hunt for dynamics ."}
{"article_id":"1604.07458","section_id":"i","document":"the hydrodynamic equation is expressed in terms of macroscopic quantities such as the pressure , particle number density , and fluid velocity , and takes a universal form irrespective of the microscopic dynamics of the system . the detailed microscopic properties of the system are renormalized into transport coefficients such as the shear viscosity , heat conductivity and so on . therefore , the elaborate investigation of the transport coefficients is one of the most important tasks to reveal the microscopic properties of the fluid . for instance , the fluid with a tiny shear viscosity is realized in the experiment of ultracold fermi gases at the unitarity @xcite : the value of its shear viscosity is close to a quantum bound that is theoretically proposed @xcite , implying the realization of the strongly correlated systems at the unitarity @xcite . the hydrodynamic behavior with a small shear viscosity is also discovered in the ultra - relativistic heavy ion collision experiments at the relativistic heavy ion collider ( rhic ) at the brookhaven national laboratory and the large hadron collider ( lhc ) at cern , which may again suggest that the created matter , i.e. , quark - gluon plasma ( qgp ) is a strongly coupled system ( see refs . @xcite , for instance ) . it is noteworthy that , in spite of very large difference of the energy scale , these systems share common hydrodynamic properties , and the hydrodynamic equation provides us with a unified way to study their dynamics .    however , there is a problem in the application of the navier - stokes equation , besides the causality problem typical to the relativistic hydrodynamics : in finite systems , there are the central region where the density is large enough to apply the naive viscous hydrodynamic equation , and the peripheral region where the naive hydrodynamic description breaks down due to the small density . in the latter , since the system slowly approaches the thermal equilibrium state due to the lack of enough collision rate , we need to take into account more microscopic dynamics . to this end , we should incorporate the relaxation process of dissipative currents , which is characterized by viscous relaxation times @xcite . the second - order hydrodynamic equation describes the mesoscopic dynamics including the relaxation of the dissipative currents , in addition to the ordinary hydrodynamic behavior described by the navier - stokes equation . it should be emphasized that , though the importance of the second - order hydrodynamics has been recognized and many attempts has been done to derive it , its formulation is still controversial @xcite .    in this paper , we derive the second - order hydrodynamic equation from the boltzmann equation for non - relativistic systems by using the renormalization group ( rg ) method @xcite . in the rg method , we faithfully solve the boltzmann equation and extract the hydrodynamics as a low - energy effective dynamics of the kinetic theory . it has been applied to derive the first- and second - order hydrodynamic equations for both relativistic and non - relativistic systems @xcite , and desirable properties have been already shown for the resultant equation such as causality , stability , positivity of the entropy production rate , and the onsager s reciprocal relation without imposing any assumption a priori @xcite . moreover , the microscopic expressions obtained for the transport coefficients such as the shear viscosity , heat conductivity and so on coincide with those derived in the celebrated chapman - enskog method , while the novel microscopic expressions of the viscous relaxation times written in terms of the relaxation functions allow physically natural interpretations as the relaxation times . as an extension of ref . @xcite , we take account of the effect of quantum statistics and external forces . as an application , we use our microscopic expressions to calculate the shear viscosity , heat conductivity , and viscous relaxation times of the stress tensor and heat flow of the cold fermionic atoms in a quantitative way , where the transition amplitude in the collision term is given explicitly in terms of the @xmath1-wave scattering length @xmath2 : the microscopic expressions given in forms of correlation functions are converted to linear integral equations , which we solve numerically without recourse to any approximation . on the basis of the numerical results , we discuss the quantum statistical effects , temperature dependence , and scattering - length dependence of the first - order transport coefficients and the viscous relaxation times : it is shown that at low temperatures , quantum statistics acts so effectively that the transport coefficients and the relaxation times increase rapidly because pauli principle almost forbids particle scatterings other than the forward ones . on the other hand , as @xmath2 is increased up to unitarity , these quantities decrease monotonically and become vanishingly small at unitarity because of the strong coupling . we also examine how well the relation @xmath3 and its analog for the heat conductivity are satisfied , where @xmath5 is the viscous relaxation time of the stress tensor , @xmath6 the shear viscosity , and @xmath7 the pressure . these relations are obtained from the boltzmann equation with use of the relaxation - time approximation ( rta ) , which has been widely applied to a lot of studies of the kinetic theory @xcite . although the rta might happen to be valid for a system close to the local equilibrium , its quantitative reliability is unclear and has been hardly checked even apart from the fact that the relaxation times should have different values depending on the realization process : we are only aware of @xcite in which the validity of the rta is analytically examined up to some approximations . we show that the relation @xmath3 holds quite well , while the similar relation for the relaxation time @xmath4 of the heat conductivity is satisfied only approximately with a considerable error . here we should mention that a brief report of the present work is already given in ref . @xcite , and the present paper give the detailes of not only the analytic but also numerical calculations . this paper is organized as follows : in sec . [ sec : sec2 ] , we briefly summarize the properties of the boltzmann equation . in sec . [ sec : sec3 ] , we derive the second - order hydrodynamic equation by using rg method , and show the resultant equations and microscopic expressions of the transport coefficients . in sec . [ sec : sec4 ] , we reduce the microscopic expressions of the transport coefficients and the viscous relaxation times for the numerical calculations . in sec . [ sec : sec5 ] , we show the numerical results of the transport coefficients and the viscous relaxation times , and discuss the physical properties of the numerical results with temperature and the scattering length being varied . convergence of the numerical results are confirmed in the last part of this section . in sec . [ sec : sec6 ] , we give the concluding remarks . in appendix .  [ sec : app1 ] , we give a useful formula which is used to solve the boltzmann equation . in appendix . [ sec : app2 ] , we present the detailed derivation of the relaxation equation .","summary":"we give a detailed derivation of the second - order ( local ) hydrodynamics for boltzmann equation with an external force by using the renormalization group method . in this method , we solve the boltzmann equation faithfully to extract the hydrodynamics without recourse to any ansatz . our method leads to microscopic expressions of not only all the transport coefficients that are of the same form as those in chapman - enskog method but also those of the viscous relaxation times that admit physically natural interpretations . as an example , we apply our microscopic expressions to calculate the transport coefficients and the relaxation times of the cold fermionic atoms in a quantitative way , where the transition probability in the collision term is given explicitly in terms of the-wave scattering length . we thereby discuss the quantum statistical effects , temperature dependence , and scattering - length dependence of the first - order transport coefficients and the viscous relaxation times : it is shown that as the temperature is lowered , the transport coefficients and the relaxation times increase rapidly because pauli principle acts effectively . on the other hand , as is increased , these quantities decrease and become vanishingly small at unitarity because of the strong coupling . the numerical calculation shows that the relation , which is derived in the relaxation - time approximation and used in most of literature without almost any foundation , turns out to be satisfied quite well , while the similar relation for the relaxation time of the heat conductivity is satisfied only approximately with a considerable error .","abstract":"we give a detailed derivation of the second - order ( local ) hydrodynamics for boltzmann equation with an external force by using the renormalization group method . in this method , we solve the boltzmann equation faithfully to extract the hydrodynamics without recourse to any ansatz . our method leads to microscopic expressions of not only all the transport coefficients that are of the same form as those in chapman - enskog method but also those of the viscous relaxation times that admit physically natural interpretations . as an example , we apply our microscopic expressions to calculate the transport coefficients and the relaxation times of the cold fermionic atoms in a quantitative way , where the transition probability in the collision term is given explicitly in terms of the-wave scattering length . we thereby discuss the quantum statistical effects , temperature dependence , and scattering - length dependence of the first - order transport coefficients and the viscous relaxation times : it is shown that as the temperature is lowered , the transport coefficients and the relaxation times increase rapidly because pauli principle acts effectively . on the other hand , as is increased , these quantities decrease and become vanishingly small at unitarity because of the strong coupling . the numerical calculation shows that the relation , which is derived in the relaxation - time approximation and used in most of literature without almost any foundation , turns out to be satisfied quite well , while the similar relation for the relaxation time of the heat conductivity is satisfied only approximately with a considerable error ."}
{"article_id":"cond-mat9911008","section_id":"i","document":"much attention has been paid in the last twenty years to low frequency dynamics of dna due to its relevance to biological processes . vibrational modes involving collective motions of groups of atoms have been experimentally investigated by means of various techniques as neutron scattering  @xcite , spectroscopy measurements  @xcite , nmr ,  ... among the latters , raman studies carried out by h.  urabe  _ et al._@xcite have revealed particulary useful to gain information on the dependence of low frequency vibrations properties of dna upon external conditions e.g. water content , ionic concentration , temperature . the observation of the raman scattering intensity in the low frequency region is technically very difficult because the strong solvent rayleigh scattering near zero frequency masks the dna response . nevertheless a broad band ranging from 60 @xmath5 to @xmath8  @xmath5 has been evidenced and associated to hydrogen bonded base pair vibrations  @xcite . moreover experiments focusing on oriented solid dna fibers have also exhibit sharp peaks in the raman intensity at @xmath9  16  @xmath5 , that shifts toward lower frequency region when rising the degree of hydration  @xcite . the origin of this peak is far from being obvious . in particular , its interhelical or intrahelical origine has been debated for a long time  @xcite .    to reach a better understanding of the above experimental findings , detailed theoretical analysis of dna vibrational motions have been proposed . devoting a particular attention to hydrogen bond stretching modes , prohofsky and his collaborators  @xcite have been able to find back a vibration mode at 85  @xmath5 and confirm its origin . their approach is based on a detailed description of the dna molecule at the atomic level  @xcite and a variational calculation method , called modified self - consistent phonon approximation ( mspa ) . within mspa , the molecule at ambient temperature is reduced to an effective ( and complex ) harmonic lattice the force constants of which are determined in a self - consistent way . this approach has been very useful in calculating many properties of dna , e.g. the melting of dna s of different sequences @xcite,@xcite , the temperature and salt dependence of the b to z conformation change @xcite and the stability of drug - dna complex @xcite .    a qualitative weakness of mspa , that also arises in other simplified theoretical approaches  @xcite lies in the _ a priori _ nature of modes . though effective elastic constants depends on temperature , normal modes indeed conserve a plane wave structure  @xcite . as a consequence , dispersion relations for the normal modes are well defined as for phonons in crystals  @xcite . in other words , the coherence length is infinite and the momentum selection rule give rise to a discrete set of lines in the theoretical predictions for raman spectra@xcite . on the contrary , amorphous materials or more generally thermally disordered systems give rise to normal modes with short coherence lengths , whose power spectrum displays a finite width  @xcite . as a result , momentum selection rules break down and light scattering processes may occur from essentially all normal modes  @xcite . correspondingly for a dna molecule in solution , the raman spectrum is continuous and does not depend on the wave length of the incident laser beam nor on the scattering angle  @xcite .    understanding the vibrations of a system in presence of thermal ( or configurational ) disorder is a difficult task  @xcite . non - harmonicities in the interactions between constituents may modify deeply the usual phonon picture of wave propagation in solids and generally forbid any rigorous analytical treatment of the dynamical equations . an interesting approach to circumvent this difficulty has been proposed in the context of liquid state dynamics  @xcite . the idea is to start from a randomly chosen configuration at thermodynamical equilibrium . then , the equations of motion around this fixed initial configuration can be linearized , defining some instantaneous normal modes ( inm ) and their corresponding relaxation times _ i.e. _ frequencies . all these quantities may then be averaged over the initial configuration chosen from the gibbs ensemble at the desired temperature . one obtains this way a precise description of the short times dynamics based on the average spectrum of relaxation times and the statistical properties of the inm  @xcite . as a major advantage , the inm approach takes into account thermal disorder through the choice of the random initial configuration and gives rise to highly disordered normal modes with finite autocorrelation length as expected at finite temperature . due to the linearization procedure , the information available through inm calculations is restricted to short times dynamics . this limitation is however not serious in the range of frequencies mentioned above for dna collective dynamics as we shall see later .    from a theoretical point of view , the calculation of the inm around a fixed intial configuration is a hard task that can be performed analytically for simple enough models only@xcite . in this paper we describe the torsional and hydrogen bond stretching vibrations of a very simple dna model by normal modes that are not plane waves using the inm approach . we are able in particular to calculate the frequency dependent density of state at a given temperature , the coherence length of the normal modes and some pseudo dispersion relations at ambient temperature . the model that we consider has been introduced in a previous article to study the dna denaturation driven by temperature or mechanically induced by a torque  @xcite . this study was motivated by the recent development of micromanipulation techniques@xcite that have allowed the direct observation of dna denaturation induced by an external torsional stress  @xcite . our model describes the dna molecule at the base pair level , and for each base pair we have just two degrees of freedom that is the base pair radius and twist angle . as a result , the potential energy is sufficiently simple to allow for sophisticated analytical calculations of normal collective modes . from a technical point of view , our calculation is inspired from a recent study of instantaneous modes in an one dimensional disordered system  @xcite , that mixes techniques used in localization theory ( the resolvent calculation ) , disordered system ( replica trick)@xcite and a variational gaussian wave function method . as we shall see , the interest of the calculation is two - fold . first , it gives theoretical predictions for the spectrum of modes , the effective dispersion relations and damping width at ambient temperature that can be directly confronted with raman spectroscopy and to neutron scattering data . secondly , it is a way to check the validity of ( and eventually improve ) our model in very different experimental conditions from the the ones it was originally designed for . the paper is organized as follows . in section  ii , we define the dna model and explain how to compute its statistical physics properties . the choice of the force constants and the main thermodynamical features are then exposed . section  iii is devoted to dynamics and to the definiton of the instantaneous modes . the relationship between the latters and raman spectra is evoked . the analytical framework necessary to calculation the properties of inm is presented in section  iv . results are given and compared to experiments in section  v. finally , we present some conclusions and perspectives in section  vi .","summary":"the instantaneous normal modes corresponding to base pair vibrations ( radial modes ) and twist angle fluctuations ( angular modes ) of a dna molecule model at ambient temperature are theoretically investigated . due to thermal disorder , normal modes are not plane waves with a single wave number but have a finite and frequency dependent damping width .","abstract":"the instantaneous normal modes corresponding to base pair vibrations ( radial modes ) and twist angle fluctuations ( angular modes ) of a dna molecule model at ambient temperature are theoretically investigated . due to thermal disorder , normal modes are not plane waves with a single wave number but have a finite and frequency dependent damping width . the density of modes , the average dispersion relation as well as the coherence length are analytically calculated . the gibbs averaged resolvent is computed using a replicated transfer matrix formalism and variational wave functions for the ground and first excited state . our results for the density of modes are compared to raman spectroscopy measurements of the collective modes for dna in solution and show a good agreement with experimental data in the low frequency regime  . radial modes extend over frequencies ranging from 50  to 110  . angular modes , related to helical axis vibrations are limited to  . normal modes are highly disordered and coherent over a few base pairs only ( ) in good agreement with neutron scattering experiments ."}
{"article_id":"cond-mat9911008","section_id":"r","document":"we first compute the ground state wave function @xmath71 and the corresponding eigenvalue @xmath241 , see section ii.b , by means of kellog s method @xcite . the integration range @xmath257 $ ] over @xmath258 is discretized into a set of @xmath259 points @xmath260 , @xmath261 with @xmath262 and @xmath263 . self - consistent equations ( [ opt1 ] ) for @xmath264 can then be solved iteratively . as can be checked at zero temperature , convergence is improved by iterating the equations for @xmath265 rather than for @xmath264 itself . we stop the iteration process as soon as the differences between the @xmath266 s and their images through the iteration become smaller than @xmath267 for all @xmath268 . numerical difficulties come from the limits @xmath269 and @xmath270 . this can be best seen for base pairs vibrations in the simplest case @xmath271 . the exact solution to equations ( [ opt1 ] ) is @xmath272 . in other words , eigenvalues @xmath273 and radii @xmath258 are in simple correspondance  : to any permitted eigenvalue @xmath113 is associated one ( or a few ) radius @xmath274 such that @xmath275 and the density of states reads @xmath276 in practice however , the integral in ( [ nume1 ] ) is discretized as follows @xmath277 consider the eigenvalue @xmath278 corresponding to radius @xmath279 for some arbitrary integer @xmath280 . dominant @xmath281 contributions to the density @xmath282 in ( [ nume2 ] ) come from @xmath283 in the range @xmath284 with @xmath285 . problems arise when @xmath286 is close to unity . when @xmath273 scans the interval @xmath287 $ ] , the index of the only ( for @xmath288 ) contributing term to @xmath289 jumps from @xmath290 to @xmath291 at some intermediate @xmath113 which will be a local minimum of the density @xmath292 . such local fluctuations are pure artifacts of the discretization procedure and must be removed by keeping @xmath293 , that is @xmath294 . typical suitable values of the parameters are @xmath295 , @xmath296 , giving a spectrum @xmath289 almost normalized to unity ( with a small error @xmath297 ) . note that the same reasoning holds for the numerical calculation of the torsional spectrum . the discretization of the integral over @xmath298 must be replaced by a sum involving a large number @xmath299 of terms to reach a good accuracy of the results . radial mode spectra obtained for different choices of @xmath25 and @xmath87 are displayed figure  5 . they exhibit smooth shapes and van hove divergences have been smeared out by thermal disorder , compare to figure  4 . as at zero temperature , the overall width of the spectrum is an increasing function of @xmath87 .    for @xmath81 , the general form of @xmath1 is reminiscent of the density of states at zero temperature , with a shoulder in @xmath300  @xmath5 and a maximum in @xmath301  @xmath5 , in correspondence with the edges of the zero temperature spectrum , @xmath302  @xmath5 and @xmath303  @xmath5 . a careful analysis even show a quantitative agreement between the density of states at @xmath72  k and @xmath36  k for frequencies lying in the range 110  @xmath304  @xmath5 . a similar behaviour , that is the robustness of the central part of the spectrum to ( weak ) disorder was also observed in  @xcite .    at a weaker stiffness @xmath305 , a single bump is observed . the range of allowed frequencies at zero temperatures @xmath306  @xmath307  @xmath5 is indeed too narrow and both peaks merge under the action of thermal disorder . note that a very small fraction of modes seem to be unstable and give rise to imaginary frequencies , see section  iii.b . we however discard them since their integrated sum is smaller than the accuracy @xmath308 of the calculation . figure  6 shows the dispersion relations at ambient temperature for radial modes . the frequency @xmath309 is an increasing function of the wave number over the interval @xmath310 . since the range of allowed frequencies is much larger at @xmath72  k than at @xmath36  k , there is no general coincidence with the zero temperature dispersion relations as can be seen for @xmath305 . for larger stiffness constants , the dispersion relations for both temperatures however coincide for medium wave numbers , _ i.e. _ when @xmath311 roughly . in agreement with the above analysis of the density of states , the effective thermal disorder gets weaker and weaker as the stiffness constant @xmath87 grows . when @xmath87 increases , the molecule becomes more and more rigid since radii @xmath11 less and less fluctuate from base pair to base pair . the wave function @xmath312 gets more and more concentrated around the minimum of the morse potential @xmath313 , see figure  2 and the region of integration over @xmath258 that mostly contributes to the density of states in ( [ spec87 ] ) becomes narrower and narrower . on the opposite , for small @xmath87 , @xmath71 mainly reflects the structure of the morse well whose flanks are not accessible at zero temperature . the tails of @xmath314 are large and give rise to some tails for the density of states . the cross - over between both regimes takes place at @xmath315 , that is of the order of a few @xmath316 . the inverse coherence length @xmath317 is plotted figure  7 as a function of frequency . in the central ragion of the spectra , the corresponding autocorrelation lengths are @xmath318 for @xmath319 and @xmath320 for @xmath321 with a more sensitive dependence on @xmath125 in the latter case . as expected from the above discussion , @xmath322 increases with @xmath87 . the values of the coherence length @xmath322 are in good agreement with the equilibrium correlation distance @xmath323 defined through @xmath324 a thermodynamical calculation of @xmath323 can be carried out from the knowledge of the excited states of the transfer matrix @xmath69 confined to the morse potential @xcite . results are @xmath325 for @xmath319 and @xmath326 for @xmath321@xcite . note that @xmath323 is the inverse damping with of the static structure factor whereas @xmath327 is an energy ( frequency ) dependent coherence length . we now turn to the angular spectrum . the density of modes is shown on figure  8 . we first concentrate on positive , that is real frequencies . the band edge @xmath328  @xmath5 of the zero temperature spectrum visible on figure  4 disappears at finite temperature . a sharp maximum now takes place at @xmath329  @xmath5 . as expected from zero temperature calculations , the width of the peak is smaller than for radial modes and can be estimated to @xmath330  @xmath5 . the densities of states at @xmath319 and @xmath321 coincide within @xmath331 . we have numerically checked that the angular mode spectrum depends extremely weakly on the stiffness constant @xmath87 over the whole range @xmath332 . in other words , unlike radial modes , angular modes are not sensitive to the width of the ground state wave function @xmath74 , _ i.e. _ to fluctuations of the base pair radius @xmath258 , see figure  2 . this observation is supported by inspection of the variational parameter @xmath264 entering wave function  ( [ trwf ] ) . at fixed frequency , both imaginary and real parts of @xmath264 are indeed almost constant on the whole range of radius @xmath333 . the robustness of the spectrum displayed fig . 8 can be understood by looking at the variations of @xmath334 around the thermal average positions @xmath335 and @xmath336 . the second derivative of @xmath159 with respect to @xmath258 at fixed twist angle equals @xmath337 while the range of fluctuations of @xmath258 is given by the largest squared width of @xmath74 ( corresponding to @xmath271 ) and reads @xmath338 . therefore the fluctuations of the radius @xmath258 modifies @xmath159 by @xmath339 , that is by less than @xmath340 of @xmath159 typically . repeating the same calculation for twist - induced fluctuations , we obtain @xmath341 and @xmath342 . the resulting variations of @xmath159 due to changes of twist are of the order of @xmath343 that is comparable to @xmath159 . consequently , an excellent approximation of the angular mode spectrum may be obtained by the following simple argument . let us call @xmath344 the diagonal element of @xmath345 ( [ hess ] ) where we have for simplicity identified @xmath346 with @xmath347 since @xmath348 at @xmath72  k ) . the twist angle @xmath163 is approximately distributed with the gibbs measure , see ( [ mu ] ) , @xmath349 then we may substitute the variational equation ( [ opt1 ] ) on @xmath264 with @xmath350 which involves a single parameter @xmath235 . solving equation ( [ opt10 ] ) , the density of angular modes equals @xmath351im(@xmath352)@xmath353 and is in excellent agreement with figure  8 . from a numerical point of view , this approximation is much less time consuming than the full resolution of ( [ opt1 ] ) . in fact , equation ( [ opt1 ] ) required the integral over @xmath163 to be computed for each value of @xmath258 ( and at each iteration step ) and the solving time was therefore @xmath259 times larger than for ( [ opt10 ] ) . close to zero frequency , the density of states vanishes as @xmath354 since the density of eigenvalues @xmath355 is finite in @xmath356 , see ( [ ris ] ) . we now turn to negative , that is imaginary frequencies . computing the integrated density of unstable modes , we see that the latters represent roughly @xmath357 of angular modes . they extend down to frequencies equal to @xmath358  @xmath5 with a maximum in @xmath359  @xmath5 . we shall come back to the physical implications of these modes in next section . the relation of dispersion @xmath360 for the angular modes is displayed figure  9 over the whole range of real and imaginary frequencies . we also show on figure  10 the inverse autocorrelation length @xmath361 . as for radial modes , the dispersion relations at @xmath72  k gets close to its zero temperature counterpart at intermediate wave numbers @xmath362 corresponding to frequencies @xmath363  @xmath364  @xmath5 . this coincidence is accompagnied by small values of @xmath220 on this interval of frequencies , giving rise to a coherence length of the order of @xmath365 . conversely , large frequencies correspond to highly disordered modes : @xmath366 and monotonously increasing @xmath367 , with @xmath368 at @xmath369  @xmath5 . notice that the statical correlation length is the same as for radial modes , see section  v.b . unstable modes have also short autocorrelation lengths , e.g. @xmath370 at @xmath371  @xmath5 . however , their wave numbers are much smaller and can be considered as contant ( and zero ) for @xmath372 . the autocorrelation function of unstable eigenmodes ( [ corr73 ] ) therefore do not change sign over a typical distance @xmath373 . unstable modes can be seen as unstable acoustic phonons , involving coherent rotations of the molecule extending over regions of size @xmath374 .    to end with , notice that the dispersion relation and the inverse coherence length both exhibit an inflection point in @xmath375 as shown fig . 9  and  10 . this is an artefact of the representation of unstable modes as negative frequencies . consider for instance the damping width @xmath220 close to zero frequency . in the natural @xmath113 eigenvalue parametrization , we expect a non singular behaviour in the vicinity of @xmath356 : @xmath376 . for positive eigenvalues @xmath113 , the frequency @xmath125 is defined as @xmath377 ( [ eq ] ) while using the negative - imaginary convention of section  iii.b , @xmath378 for negative eigenvalues . the expansion of the inverse coherence length as a function of ( small ) frequencies thus reads : @xmath379 and is singular with an inflection point in @xmath380 . our calculation shows that the coherence length of normal modes is finite and remains of the order of unity . eigenvectors at finite temperature are thus far from being plane waves as in the zero temperature case . the power spectrum , that is the fourier transform of the autocorrelation function at frequency @xmath125 ( [ rel2 ] ) acquires a lorentzian form centered around a certain wave number @xmath381 with a width @xmath382 . this behaviour is experimentally observed in neutron scattering experiments  @xcite . furthermore , the calculation justifies _ a posteriori _ the absence of selection rule on momentum in raman experiments . indeed , the coherence length of the disordered phonons is of the order of @xmath383 and is negligible with respect to optical wavelengths @xmath384 , see section  iii.c . both radial and angular spectra are superposed in figure  11 . the total spectrum @xmath385 equals @xmath386 is normalized to unity ( half of modes originate from angular degree of freedom , and the remaining half from radial ones ) . the torsion peak appears much more narrow and higher than its radial counterpart . the width of the latter amounts to @xmath387  @xmath5 ( respectively @xmath388  @xmath5 ) for @xmath305 ( resp . for @xmath81 ) whereas ( stable ) torsional modes spread over a range of @xmath389  @xmath5 . while for @xmath81 , torsional and radial spectra do not intersect each other , there is an overlap region at smaller stiffness constant around @xmath390  @xmath5 . nevertheless , both fluctuations take place on basically two distinct scale times . angular vibrations are associated to a typical frequency of @xmath391  @xmath5 , or equivalently to a typical time @xmath392  s. radial modes are present at frequencies @xmath393  @xmath5 that is involve dynamical processes on a scale @xmath394  s. at low frequencies @xmath395  @xmath5 , the presence of unstable modes threatens the validity of the linearization procedure used in section  iii.b . a more refined analysis taking into account non linear terms in the dynamical equations is needed to understand how unstable modes ( with low wave numbers @xmath0 ) are coupled to stable mode ( with larger @xmath0 ) and modify the frequencies of the latters . the influence of viscous friction upon modes in this frequency regime would also deserve to be further studied as mentioned section  iii.a . conversely , the absence of unstable modes at frequencies larger than @xmath396  @xmath5 indicate that the inm predictions are reliable for time scale smaller than @xmath397  s. this is enough to identify the range of allowed frequencies for torsional modes : @xmath398  @xmath5 . the inm prediction for the location of the torsional peak @xmath399  @xmath5 can not be trust blindly but it reasonably lies in the middle of the zero temperature band , see section  iii.d . we now turn to the comparison with spectroscopy measurements . to establish the link between the density of states and the raman intensity , the knowledge of the light - to - vibrations coupling @xmath129 is necessary as seen section  iii.c . in the absence of precise information on the latter , we have rescaled the density of modes @xmath400 according to formula ( [ rescaraman ] ) for the three different choices @xmath401 , @xmath402 and @xmath403 ( note that the second hypothesis for @xmath404 is the most plausible one ) . the resulting theoretical raman intensities are shown figure  12.a for @xmath305 and figure  12.b for @xmath81 . from the one hand , the overall shape of the spectra change with @xmath404 with respect to @xmath124 . in particular for @xmath405 and @xmath402 , the torsional peak diverges at small frequencies and the radial modes bump acquires a shoulder from , located in the right flank of the torsional modes . on the other hand , the band of allowed frequencies remains unaltered by the choice of @xmath404 and extends over @xmath406  @xmath5 for @xmath319 and @xmath407  @xmath5 for @xmath321 . in the latter case , the radial region of the spectrum exhibit two local maxima at the same height for @xmath402 . the rescaled spectrum of fig  12.a for @xmath408 closely agrees with intensity curves obtained from raman experiments at @xmath409c and shown figure  2 of ref.@xcite on the range of frequencies @xmath406  @xmath5 . the latter measurement was performed on calf thymus in solution ( 10 mm phb , ph=7 ) . this allows us to think that @xmath319 is a better choice for the stiffness constant than @xmath321  @xcite . our results do not show drastic variations with temperature for @xmath58 ranging from 300  k to the melting temperature @xmath410  k. at @xmath76 the double helix structure disappears and so do all angular and radial vibrations . since denaturation is described as a first order phase transition by the present model , there is no gradual destabilization of the modes and no relevant change in @xmath124 can be seen as mentioned above . the experimental raman measurements shown on figure  2 of ref.@xcite nevertheless show a smooth change in the shape of the intensity curves over the temperature interval @xmath411c@xmath412c . this apparent paradox can be easily explained by the fact that our model describes a homogeneous sequence of bases . for the latter , the fraction of open base pairs versus temperature exhibits an abrupt jump from zero to one at @xmath76  @xcite . in the case of a heterogeneous sequence as in the experiments of ref.@xcite , the denaturation temperature of at rich regions can be inferred to be @xmath413c  @xcite and the fraction of open base pairs smoothly increases from zero to one over the range of temperatures @xmath411c@xmath414c . we now turn to angular modes . raman measurements on fibers at 100% of relative humidity ( r.h . ) have given evidence for a narrow band at @xmath415@xmath5 , see fig .  1 of ref.@xcite . this peak shifts down to lower frequencies ( @xmath416@xmath5 ) when increasing the hydration degree of dna in gels and disappears in the central component for dna in solution@xcite . other measurements on b - dna fibers al lower @xmath417% r.h . by lindsay et al . have reported a similar band at a higher frequency @xmath418@xmath5 that shifts to lower values as the r.h . increases in good agreement with urabe et al.s data  @xcite . the observed softening of the frequence may come from the weakening of external e.g. interhelical interactions as well as from the influence of the ( rigid ) primary and ( viscous ) secondary water shells , see section  iii.a . note that this modes seems to appear when the scattering vector @xmath419 gets parallel to the helical axis . other molecular system as crystals of atp or guanosine monosphosphate ( gmp ) that present a columnar stacking of bases ( even without hydrogen bond interactions ) exhibit similar low frequency spectra . the intensity of the low frequency ( @xmath420@xmath5 ) mode was found to depend mostly on the stacking degree of bases in a column  @xcite . our calculation predicts , despite the presence of unstable inm and the absence of friction terms in the dynamical equations ( [ eqm ] ) that angular modes are predominant for @xmath6@xmath5 . at such low frequencies , radial modes can be neglected and twist fluctuations are responsible for collective vibrations of interplane distances @xmath421 . in agreement with experiments , our calculation thus predicts that low frequency modes ( @xmath6@xmath5 ) are related to vibrations of the base pairs column . a quantitative comparison of our dispersion relations for angular modes with experimental results is difficult to the lack of available data . neutron scattering measurements have shown that pseudo - dispersion relations with a finite damping width can be obtained for low frequencies but these experiments have been performed on crystalline dna fibers . our model ( and the values of parameters exposed section  ii.c ) are valid for dna in solution where the interaction with surrounding water is radically different and interhelical effects are absent . more precisely , we find that at fixed momentum @xmath0 , the experimental frequency @xmath125 for fibers is larger than the theoretical predictions for diluted dna . the additional mass due to primary water shells for dna in solution may account for the reduction of frequency to a large extent  @xcite . conversely , the extrapolated value of @xmath220 is constant and equal to 0.48 in good agreement with the theoretical minimum @xmath422 shown fig .","summary":"our results for the density of modes are compared to raman spectroscopy measurements of the collective modes for dna in solution and show a good agreement with experimental data in the low frequency regime  . radial modes extend over frequencies ranging from 50  to 110  .","abstract":"the instantaneous normal modes corresponding to base pair vibrations ( radial modes ) and twist angle fluctuations ( angular modes ) of a dna molecule model at ambient temperature are theoretically investigated . due to thermal disorder , normal modes are not plane waves with a single wave number but have a finite and frequency dependent damping width . the density of modes , the average dispersion relation as well as the coherence length are analytically calculated . the gibbs averaged resolvent is computed using a replicated transfer matrix formalism and variational wave functions for the ground and first excited state . our results for the density of modes are compared to raman spectroscopy measurements of the collective modes for dna in solution and show a good agreement with experimental data in the low frequency regime  . radial modes extend over frequencies ranging from 50  to 110  . angular modes , related to helical axis vibrations are limited to  . normal modes are highly disordered and coherent over a few base pairs only ( ) in good agreement with neutron scattering experiments ."}
{"article_id":"cond-mat9911008","section_id":"i","document":"in this article , we have shown how to apply the inm framework to a simple model of dna molecule and reproduce the main features of collective vibration modes at finite temperature . scale time separation between atomic vibrations and collective modes allows to obtain good results at low frequencies without resorting to a detailed description of dna at the atomic level . this simplified modelization of dna permits in turn a deeper analytical understanding of the structure of the modes than e.g. within mspa . the model we had introduced to reproduce thermally and mechanically - induced dna denaturation transitions has proven to be also capable of describing accurately the pico - second dynamics seen through spectroscopy measurements . this robustness has been obtained without any modification of the model or any new fit of the constant force or geometrical parameters . remarkably , the comparison with raman experiments has permitted us to decide the value of the only parameter known with some uncertainty from the denaturation experiments , that is the stacking stiffness @xmath87 . the success of the present model to account for completely different experiments comes from its mesoscopic nature , that lies at an intermediate level between microscopic modelizations , e.g. studies by prohofsky _ et al._@xcite or numerical simulations by lavery and collaborators@xcite and elasticity theories as the worm - like - chain model@xcite and its recent extensions@xcite . our calculation gives access to the density of modes @xmath385 and some statistical properties of the normal modes as the dispersion relation @xmath2 and the autocorrelation length @xmath423 . the dispersion relations provide the power spectrum of the modes which exhibit a finite damping width @xmath367 at ambient temperature . let us summarize briefly our main quantitative result . through a rescaling of the density of modes taking into account the light - to - vibrations coupling @xmath404 , we have related the density of modes to raman intensity measurements . the choice of parameters @xmath424 , @xmath305 offers a good agreement with the experiments by urabe et al . ( see figure  12.a and figure  2 in @xcite ) . the range of frequencies @xmath425  @xmath426  @xmath5 corresponding to radial , _ i.e. _ base pair stretching modes do not qualitatively depend on @xmath404 . furthermore , it remains roughly unchanged in the whole interval of temperatures @xmath427c@xmath428 where @xmath429c is the denaturation temperature . indeed , our model describes a homogeneous sequence for which the melting transition is very abrupt and not smooth as for disordered dna .    it would be very interesting to compare our theoretical results for @xmath430 and @xmath309 with neutron scattering experiments which to our best knowledge are not available for dna in solution over the range of frequencies mentioned above . a fundamental feature of the modes is that the coherence length @xmath322 is of the order of unity : decorrelation between components of the same mode takes place on a few angstrms . this prediction agrees well with results for the static correlation distance @xmath323 obtained from statistical mechanics calculations as seen section  v.b . as for angular modes , the predicted characteristic frequencies @xmath431  @xmath5 coincide with the raman measurements @xmath432  @xmath5@xcite . the value of the coherence length in the center of the spectrum , @xmath433 is compatible with data obtained through neutron scattering experiments on dna fibers @xcite . however , as far as angular modes are concerned , the present approach suffers from two weaknesses . first , we have not taken into account in the dynamical equations the viscous forces that might become relevant at very low frequencies . secondly , inm can become unstable at small @xmath125 and the linearization approximation we have used throughout the study reveals dangerous . further information about the non linear couplings between modes would be extremely useful to circumvent this difficulty . it is however not clear how such a study could be technically pursued . .5 cm * acknowledgments  :* we are particularly grateful to w.  baumruk and p.y .  turpin for motivating and enligthening discussions on the experimental aspects of this work . we also thank j.f . leger , l.  bourdieu , a.  colosimo , d.  chatenay , m.  peyrard and h.  urabe for advises and discussions .","summary":"the density of modes , the average dispersion relation as well as the coherence length are analytically calculated . normal modes are highly disordered and coherent over a few base pairs only ( ) in good agreement with neutron scattering experiments .","abstract":"the instantaneous normal modes corresponding to base pair vibrations ( radial modes ) and twist angle fluctuations ( angular modes ) of a dna molecule model at ambient temperature are theoretically investigated . due to thermal disorder , normal modes are not plane waves with a single wave number but have a finite and frequency dependent damping width . the density of modes , the average dispersion relation as well as the coherence length are analytically calculated . the gibbs averaged resolvent is computed using a replicated transfer matrix formalism and variational wave functions for the ground and first excited state . our results for the density of modes are compared to raman spectroscopy measurements of the collective modes for dna in solution and show a good agreement with experimental data in the low frequency regime  . radial modes extend over frequencies ranging from 50  to 110  . angular modes , related to helical axis vibrations are limited to  . normal modes are highly disordered and coherent over a few base pairs only ( ) in good agreement with neutron scattering experiments ."}
{"article_id":"1412.4694","section_id":"i","document":"from the first spectroscopic observations of ( ultra)luminous infrared galaxies ( ( u)lirgs ) in the far - infrared ( far - ir ) domain with the infrared space observatory ( iso ) , evidence was found that the strength of fine - structure lines ( from both ions and atoms ) in emission are generally anticorrelated with the depth and excitation of the molecular lines observed in absorption @xcite . the most commonly observed line , the fine - structure [ c ii]157.7 @xmath0 m transition ( hereafter [ c ii ] ) , tends to exhibit a strong deficit with respect to the far - ir luminosity in ulirgs relative to less luminous systems @xcite . in normal galaxies , the [ c ii]/fir luminosity ratio remains nearly constant ( @xmath20% ) , while it decreases in galaxies with warmer far - ir colors @xcite . on the other hand , studies of individual templates ( arp  220 and mrk  231 ) indicated that high far - ir radiation densities associated with the nuclear regions of galaxies with [ c ii ] deficits , are required to account for the observed high - lying molecular absorption ( * ? ? ? * ; * ? ? ? * hereafter g - a08 ) . the launch of the _ herschel _ space observatory @xcite has dramatically improved the sensitivity of these measurements . observations with the pacs spectrometer @xcite soon revealed that the observed deficit of [ c ii ] relative to the far - ir emission applies to all far - ir fine - structure lines ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter g - c11 ) . g - c11 also showed that the deficits are better correlated with @xmath21 than with @xmath22 , while pacs observations of three ( u)lirgs with strong line deficits , ngc  4418 , arp  220 , and mrk  231 , showed deep absorption in high - lying molecular lines ( * ? ? ? * ; * ? ? ? * hereafter g - a12 and g - a14 ) . ngc  4418 is a case in point , as it shows the highest [ c ii ] deficit , a moderate @xmath23  but a high @xmath24 /(g - c11 ) , and the highest - lying  absorption among all galaxies with full fir spectra ( g - a12 ) .    to explore the connection between intense far - ir fields and both the highly excited molecular gas and the [ c ii ] deficit , we investigate the relationship between the oh @xmath25 transition at @xmath26 @xmath0 m ( hereafter oh65 ) with @xmath4 k , and the [ c ii ] line , @xmath21 , the @xmath7 @xmath0 m silicate absorption , and the far - ir colors , also using measurements of the oh @xmath27 transition at @xmath28 @xmath0 m ( hereafter oh71 , @xmath10 k ) in galaxies for which it is available . oh is a versatile molecule with high abundances in active regions including photodissociated regions ( pdrs ) , cosmic - ray dominated regions ( crdrs ) , and x - ray dominated regions ( xdrs ) ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and traces powerful galactic - scale molecular outflows in some sources ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * hereafter v13 ; g - a14 ) mostly associated with large agn luminosity fractions and luminosities . in extragalactic sources , the oh65 doublet ( when detected ) is absorption - dominated , indicating that the excitation of the lower @xmath29 level is governed by radiative ( rather than collisional ) processes followed by oh65 absorption is not dominant owing to the high @xmath30einstein coefficient of the 84 @xmath0 m ( @xmath31 ) transition ; efficient oh65 absorption involves a high radiation density such that it will also dominate the excitation of @xmath29 under reasonable physical condictions . ] . the oh65 pumping thus involves successive absorptions in the 119 , 84 , and finally in the 65 @xmath0 m doublet with high @xmath30einstein coefficients ( @xmath32 , @xmath33 , and @xmath34 s@xmath35 , see the energy level diagram of oh in g - a14 ) , thus ensuring an excellent probe of strong far - ir fields . 65 @xmath0 m @xmath36 continuum - normalized spectra in all galaxies in the sample , with the velocity plotted relative to the rest - frame wavelength of the blue component of the doublet ( @xmath37 line at @xmath38 @xmath0 m ) . the spectra are grouped according to the values of the equivalent width measured between @xmath39 and @xmath40  around the blue component ( indicated by the solid vertical lines and listed in table  [ tbl-2 ] ) . the dotted vertical lines indicate the positions of the two components of the doublet . the green , red , and blue spectra are vertically shifted for clarity . ] 71 @xmath0 m @xmath41 continuum - normalized spectra in all 15 galaxies for which it is available , with the velocity plotted relative to the rest - frame wavelength of the blue component of the doublet at @xmath42 @xmath0 m . the dotted vertical lines indicate the positions of the two @xmath43-components of the doublet , which are blended into a single spectral feature . the spectra are grouped according to the values of the equivalent width measured between @xmath39 and @xmath44  ( indicated by the vertical solid lines and listed in table  [ tbl-2 ] ) . the red and blue spectra are vertically shifted for clarity . the position of the  @xmath45 line ( @xmath46 k ) is indicated . ]         and @xmath40  around the blue component of the doublet , and ( b ) the [ c ii]158 @xmath0 m line to fir ratio , as a function of the the far - ir to co ( 1 - 0 ) luminosity ratio in our galaxy sample . symbol colors and shapes have the same meaning as in fig .  [ correl ] . ]","summary":"_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 m line ( ) with lower level energy k , is anticorrelated with the [ c ii]158 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 m far - infrared color . while all sources are in the active /  mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at /. in the most buried sources , oh65 probes material partially responsible for the silicate m absorption . combined with observations of the oh 71 m doublet ( k ) ,","abstract":"_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 m line ( ) with lower level energy k , is anticorrelated with the [ c ii]158 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 m far - infrared color . while all sources are in the active /  mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at /. in the most buried sources , oh65 probes material partially responsible for the silicate m absorption . combined with observations of the oh 71 m doublet ( k ) , radiative transfer models characterized by the equivalent dust temperature , , and the continuum optical depth at 100 m , , indicate that strong [ c ii]158 m deficits are associated with far - ir thick ( , ) , warm ( k ) structures where the oh 65 m absorption is produced , most likely in circumnuclear disks / tori / cocoons . with their high ratios and columns , the presence of these structures is expected to give rise to strong [ c ii ] deficits .  probes the fraction of infrared luminosity arising from these compact / warm environments , which is% in sources with high . sources with high have surface densities of both and higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution ."}
{"article_id":"1412.4694","section_id":"c","document":"absorption in high - lying transitions of molecules with high dipolar moment and level spacing ( i.e. mostly light hydrides ) , represented by oh65 and oh71 , has been shown here to be strong in most local ulirgs ( @xmath531% ) and in several lirgs . despite the high columns inferred in galaxies with high @xmath68 , their low [ c ii]/fir and low @xmath532 suggest that both are associated with a `` deficit '' in @xmath19 relative to the far - ir continuum emission , accompanied by additional effects such as significant optical depth in the [ c ii ] line and high excitation of co. high columns and  but low @xmath533 are indicative of high radiation densities and small volumes , with the high columns of gas and dust confined to small regions ( an upper limit of which is the observed luminosity ) with its calculated value , @xmath534 , where @xmath535 stands for the projected surface and @xmath536 is the continuum optical depth at frequency @xmath537 along the corresponding line of sight . for reference , the effective radius is @xmath538 pc for @xmath539  ( @xmath540 ) , @xmath541 k , and @xmath512 , which is a lower limit to the physical size in some galaxies owing to clumpiness . the diagnostics in fig . [ correl ] and model results in fig . [ models ] are nevertheless independent of sizes and adopted distances.[foot : size ] ] around the bright , buried illuminating source(s ) ( nearly ) dominating the galaxy output . the relationship between the model parameterization used here and that in terms of the dominant exciting source ( agn or starburst ) , volume and column densities , and ionization parameter ( * ? ? ? * ; * ? ? ? * g - c11 ) , as well as the origin of the deficit in fine - structure lines other than [ c ii ] , will be explored in future work . the inferred column densities associated with @xmath494 , @xmath13 , are higher than those derived from the silicate strength at @xmath7 @xmath0 m . models by @xcite indicate that the observed @xmath542 can be explained with @xmath543 ( @xmath544 ) . since the oh65 regions / structure will block all the inner mid - ir emission passing through it , the observed mid - ir emission and associated silicate absorption are biased toward relatively unabsorbed mid - ir emitting regions . likewise , several sources in the sample show mid - ir agn signatures as [ ne v ] emission ( iras  05189 - 2524 and mrk  273 ; * ? ? ? * v09 ) or an optical broad line region ( e.g. mrk  231 ) , and our direct view of this emission indicates tiny absorbing columns in comparison with those inferred from oh65 . if the oh65 absorption is generated in a circumnuclear disk / torus / cocoon , either the combination of scale height / inclination , and/or clumpiness are required to account for the apparent decrease of extinction with decreasing wavelength . in sources with high contrast in mid - to - far infrared extinction , either extreme clumpiness or important inclination effects are necessarily involved . in other sources , extinction of the mid - ir emission by the oh65 structure is consistent with their low @xmath299 ratio . though these structures are variably clumpy , the oh65 bimodality ( fig . [ distrib]b - c ) suggests that they are coherent and quickly formed , and provide an effective way to obscure the signposts of agns at shorter wavelengths in some sources .    in the direction of the warm , optically thick regions / structure where the oh65 absorption is produced , the surface density of both @xmath18 and h@xmath545 mass are significantly higher than the average values previously estimated for the areas within the half - light radius ( from co or optical / uv ) . the grey parallelogram in fig . [ fig4]b indicates the location of the @xmath506 component for the ten sources where both oh65 and oh71 are detected : @xmath546  pc@xmath547 ( @xmath548 ) and @xmath549  kpc@xmath547 ( @xmath504 k ) . the latter high fluxes are consistent with previous estimates using sizes derived from radio emission and strengthen the role of radiation pressure support ( * ? ? ? * ; * ? ? ? * see their fig . 3 ) . for starburst - dominated sources and using a @xcite imf , the corresponding sfrs are @xmath550  yr@xmath35 kpc@xmath547 . for hot _ sub_components in some sources like the @xmath551 component of ngc  4418 , @xmath552  kpc@xmath547 and @xmath553 ( @xmath554 ) on spatial scales of @xmath56 pc ( g - a12 , * ? * ; * ? ? ? * ; * ? ? ? * ) .    the solid , dashed , and dotted black lines in fig . [ fig4]b are extrapolations of the fits found in previous studies for subsamples of ( u)lirgs / mergers / smgs . a pure sf scenario involves the shadowing of @xmath555 ( for @xmath556 ) star - forming regions , each with @xmath557 mag and @xmath558 , on spatial scales of @xmath559 pc ; on spatial scales of a few parsecs , there is apparently no analog star - forming region close to the galactic center .  as measured with _ @xcite , consistent with its moderate effective @xmath560 k , @xmath561  kpc@xmath547 , and @xmath562 /  for a gas - to - dust ratio by mass of 100 @xcite . oh65 is not detected towards sgr  a@xmath563 and its circumnuclear disk @xcite , and is detected in emission towards the orion bar pdr indicating collisional excitation in warm and dense gas @xcite . ] the implied gas consumption timescales are @xmath564 myr for @xmath565 k , comparable to those estimated for extreme sources exhibiting powerful oh outflows driven by buried agns @xcite . on the other hand , 21 sources in our sample were analyzed in the oh 119 @xmath0 m transition by v13 , and 12 ( 9 with @xmath293 ) were found to have @xmath566  ( the velocity below which 84% of the absorption takes place ) , most likely indicative of significant agn feedback . the oh65-(u)lirg phase may thus represent the starburst - agn co - evolution phase in its shortlived most buried / active stage . pacs has been developed by a consortium of institutes led by mpe ( germany ) and including uvie ( austria ) ; ku leuven , csl , imec ( belgium ) ; cea , lam ( france ) ; mpia ( germany ) ; inafifsi / oaa / oap / oat , lens , sissa ( italy ) ; iac ( spain ) . this development has been supported by the funding agencies bmvit ( austria ) , esa - prodex ( belgium ) , cea / cnes ( france ) , dlr ( germany ) , asi / inaf ( italy ) , and cicyt / mcyt ( spain ) . e.g - a is a research associate at the harvard - smithsonian cfa , and thanks the spanish ministerio de economa y competitividad for support under projects aya2010 - 21697-c05 - 0 and fis2012 - 39162-c06 - 01 . e.g - a and h.a.s . acknowledge partial support from nhsc / jpl rsa 1455432 ; h.a.s acknowledges nasa grant nnx14aj61 g . basic research in ir astronomy at nrl is funded by the us - onr ; j.f . acknowledges support from nhsc / jpl subcontracts 139807 and 1456609 . s.v . and m.m . acknowledge partial support from nhsc / jpl rsa 1427277 and 1454738 . this research has made use of nasa s astrophysics data system and of gildas ( http://www.iram.fr/iramfr/gildas ) . aalto , s. , radford , s. j. e. , scoville , n. z. , & sargent , a. i. 1997 , , 475 , l107 abel , n. p. , dudley , c. , fischer , j. , satyapal , s. , & van hoof , p. a. m. 2009 , , 701 , 1147 armus , l. , charmandaris , v. , bernard - salas , j. , et al . 2007 , , 656 , 148 brauher , j. r. , dale , d. a. , & helou , g. 2008 , , 178 , 280 burlon , d. , ajello , m. , greiner , j. , comastri , a. , merloni , a. , & gehrels , n. , 728 , 58 casoli , f. , willaime , m .- c . , viallefond , f. , & gerin , m. 1999 , a&a , 346 , 663 chabrier , g. 2003 , , 586 , l133 chung , a. , narayanan , g. , yun , m. s. , heyer , m. , & erickson , n. r. 2009 , aj , 138 , 858 costagliola , f. , aalto , s. , sakamoto , k. , martn , s. , beswick , r. , muller , s. , & klckner , h .- r . 2013 , a&a , 556 , a66 daddi , e. , elbaz , d. , walter , f. , et al . 2010 , , 714 , l118 daz - santos , t. , armus , l. , charmandaris , v. , et al . 2013 , , 774 , 68 daz - santos , t. , armus , l. , charmandaris , v. , et al . 2014 , , in press ( arxiv:1405.3983 ) downes , d. , solomon , p. m. , & radford , s. j. e. 1993 , , 414 , l13 etxaluze , m. , goicoechea , j. r. , cernicharo , j. , polehampton , e. t. , noriega - crespo , a. , molinari , s. , swinyard , b. m. , wu , r. , & bally , j. 2013 , a&a , 556 , a137 farrah , d. ; 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sturm , e. , et al . 2013 , apj , 776 , 27 ( v13 ) vron - cetty , m .- & vron , p. 2006 , a&a , 455 , 773 wei , a. , walter , f. , & scoville , n. z. 2005 , a&a , 438 , 533","summary":"sources with high have surface densities of both and higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution .","abstract":"_ herschel_/pacs observations of 29 local ( ultra-)luminous infrared galaxies , including both starburst and agn - dominated sources as diagnosed in the mid - infrared / optical , show that the equivalent width of the absorbing oh 65 m line ( ) with lower level energy k , is anticorrelated with the [ c ii]158 m line to far - infrared luminosity ratio , and correlated with the far - infrared luminosity per unit gas mass and with the 60-to-100 m far - infrared color . while all sources are in the active /  mode as derived from previous co line studies , the oh65 absorption shows a bimodal distribution with a discontinuity at /. in the most buried sources , oh65 probes material partially responsible for the silicate m absorption . combined with observations of the oh 71 m doublet ( k ) , radiative transfer models characterized by the equivalent dust temperature , , and the continuum optical depth at 100 m , , indicate that strong [ c ii]158 m deficits are associated with far - ir thick ( , ) , warm ( k ) structures where the oh 65 m absorption is produced , most likely in circumnuclear disks / tori / cocoons . with their high ratios and columns , the presence of these structures is expected to give rise to strong [ c ii ] deficits .  probes the fraction of infrared luminosity arising from these compact / warm environments , which is% in sources with high . sources with high have surface densities of both and higher than inferred from the half - light ( co or uv / optical ) radius , tracing coherent structures that represent the most buried / active stage of ( circum)nuclear starburst - agn co - evolution ."}
{"article_id":"hep-ex9603005","section_id":"i","document":"the high center of mass ( cms ) energy of @xmath107 available at the electron proton collider hera has led to a renewed interest in the study of @xmath0 production in lepton proton scattering . the production cross section  is dominated by photoproduction , i.e. by the interaction of almost real photons , @xmath108 , where @xmath109 is the negative four momentum transfer squared to the scattered lepton . the topic of this paper is an analysis of photoproduction of @xmath0  mesons in _ elastic _ and _ inelastic _ processes . several mechanisms have been suggested to describe photoproduction of @xmath0  mesons @xmath110 for the description of the _ elastic _ ( or _ exclusive _ ) process where @xmath111 , a diffractive mechanism has been proposed by donnachie and landshoff  @xcite . the mechanism is based on regge phenomenology where @xmath0  production is mediated by pomeron exchange ( fig . 1(a ) ) and can be extended to include also _ proton dissociation _ ( fig . measurements at hera are expected to shed new light on the diffractive production mechanism and the nature of the pomeron  @xcite . + at lower center of mass  energies pomeron exchange was successfully used in the framework of the vector dominance model ( vdm )  @xcite to describe the production of _ light _ vector mesons . the predicted slow variation with energy of the elastic cross section was confirmed and an exponentially falling @xmath112 distribution was found , where @xmath112 is the squared four momentum transfer to the scattered proton . when applied to @xmath0 meson production at low center of mass  energies the prediction of the vdm model was found to be more than an order of magnitude above the data but other features like energy dependence and @xmath112 distributions agreed within errors . attempts have been made to describe _ elastic _ @xmath0  production in perturbative qcd . in the approach by ryskin  @xcite the interaction between the proton and the charm quark is mediated by the exchange of a gluon ladder ( fig . non perturbative effects are included in the gluon distribution of the proton which enters the production cross section quadratically . a measurement of elastic @xmath0 production could therefore be a sensitive probe of the gluon density in the proton . recently higher order effects have been calculated in this model and a comparison to preliminary hera data  @xcite was carried out  @xcite . the ryskin model predicts a different energy dependence of the elastic @xmath0 cross section than the donnachie - landshoff approach . the energy dependence in the ryskin model is coupled to the low @xmath113 behaviour of the gluon density in the proton . using a gluon density increasing towards low @xmath113 which describes recent measurements of the structure function @xmath114 at hera@xcite , results in a fast increase of the cross section  for elastic photoproduction of @xmath0  @xcite .    in _ elastic _ @xmath0  production at small momentum transfer the @xmath0  meson retains approximately the full photon energy ( @xmath115 with @xmath116 in the proton rest system ) . @xmath0  production _ with proton dissociation _ although strictly speaking an inelastic process also leads to @xmath117 values close to 1 . in contrast , _ inelastic _ processes will have @xmath117 values below 1 and a high mass hadronic state is formed . the principal inelastic process proposed is the photon gluon fusion mechanism where the photon emitted by the incoming lepton interacts with a gluon from the proton via the charm quark ( fig . this mechanism is calculable in perturbative qcd due to the hard scale given by the mass of the charm quark . attempts have been made to determine the gluon density in the proton from this reaction in several fixed target experiments  @xcite . in the colour singlet model  @xcite for photoproduction of @xmath0 , which is based on this picture , the formation of a @xmath0 state is accompanied by the emission of a hard gluon . comparing predictions of the colour singlet model to data a discrepancy in absolute magnitude was found which was attributed to missing higher order calculations (  k  factor \" ) . subsequently several improvements have been proposed which led to better agreement with the data  @xcite . recently , complete next - to - leading order ( nlo ) calculations have been performed  @xcite and compared successfully to fixed target data and to preliminary hera data . ( 14.0,8.0 ) ( -1.0,-11.0 )    motivated by tevatron data on inelastic @xmath0  and @xmath5   production  @xcite which may require colour octet contributions to explain the measured cross sections , calculations have been performed for possible colour octet contributions in photoproduction at hera  @xcite . both groups attempt to estimate the colour octet  contributions to @xmath0  mesons at high @xmath117 ; in  @xcite the contribution to _ inelastic _ @xmath0  production is estimated . we present here an analysis of elastic and inelastic @xmath0 production in positron proton collisions near @xmath118 for @xmath4 cms energies up to @xmath119 . the analysis is based on @xmath0 decays to leptons , @xmath120 or @xmath121 . the data were collected with the h1 detector at hera and correspond to an integrated luminosity of @xmath122 . the _ inelastic _ process is analysed for the first time in h1 ; preliminary results have also been shown by the zeus collaboration  @xcite . the analysis of the _ elastic _ process is an update of a previous letter  @xcite where we have presented a measurement of @xmath123 which showed a strong increase of the cross section with @xmath124 , the photon proton center of mass  energy , compared to experiments at lower cms energy . this increase was faster than expected from the donnachie - landshoff prediction . at that time contributions from processes with proton dissociation could however not be excluded completely . with the increased statistics now available and an improved analysis method these inelastic processes can be efficiently recognised . the fast increase of the elastic cross section  with @xmath124  was also observed by the zeus collaboration  @xcite . the paper is organised as follows . after a brief introduction of the kinematics ( section 2 ) , the experimental conditions and the pre - selection of the data sample are described in section 3 . the analysis of the _ elastic _ @xmath0  samples follows in section 4 , which includes the energy dependence of the total @xmath4  cross section  and the distribution of @xmath125 , the transverse momentum of the @xmath0 . the second part of section 4 contains the analysis of the _ proton dissociation _ process and the decay angle distribution of diffractively produced @xmath0  mesons . in section 5 the selection of the inelastic events is discussed and results are presented including the energy dependence of the @xmath4  cross section , the distributions of @xmath125   and of the elasticity @xmath117 of the @xmath0 . a first cross section for @xmath5  production in the hera energy range is given in the last section .","summary":"results on  production in interactions in the h1 experiment at hera are presented . the  mesons are produced by almost real photons ( ) and detected via their leptonic decays . is observed to increase strongly with the center of mass  energy . diffractive  production has been observed and a first estimate of the ratio to  production in the hera energy regime is given .    plus 2 mm minus 2 mm    desy 96 - 037 + march 1996 +    * elastic and inelastic photoproduction + of  mesons at hera + *    h1 collaboration +    s.  aid , v.  andreev , b.  andrieu , r .- d .  appuhn , m.  arpagaus , a.  babaev , j.  bhr , j.  bn , y.  ban , p.  baranov , e.  barrelet , r.  barschke , w.  bartel , m.  barth , u.  bassler , h.p .  behrend , a.  belousov , ch .  contreras , c.  cormack , j.a .  hess , w.  hildesheim , k.h .  hilton , j.  hladk , k.c .  mcmahon , a.  mehta , k.  meier , t.  merz , a.  meyer , a.  meyer , h.  meyer , j.  meyer , p .- o .  robertson , p.  robmann , h.e .  shtarkov , g.  siegmon , u.  siewert , y.  sirois , i.o .  institut der rwth , aachen , germany + iii . 115/e-743/spub / p03/109/95 and 2  p03b  244  08p01 , and stiftung fr deutsch - polnische zusammenarbeit , project no.506/92 + supported in part by usdoe grant de  f603  91er40674 + supported by the deutsche forschungsgemeinschaft + supported by the swedish natural science research council + supported by ga r , grant no .","abstract":"results on  production in interactions in the h1 experiment at hera are presented . the  mesons are produced by almost real photons ( ) and detected via their leptonic decays . the data have been taken in 1994 and correspond to an integrated luminosity of . the cross section for elastic  production is observed to increase strongly with the center of mass  energy . the cross section for diffractive production with proton dissociation is found to be of similar magnitude as the elastic cross section . distributions of transverse momentum and decay angle are studied and found to be in accord with a diffractive production mechanism . for inelastic  production the total cross section , the distribution of transverse momenta , and the elasticity of the   are compared to nlo qcd calculations in a colour singlet model and agreement is found . diffractive  production has been observed and a first estimate of the ratio to  production in the hera energy regime is given .    plus 2 mm minus 2 mm    desy 96 - 037 + march 1996 +    * elastic and inelastic photoproduction + of  mesons at hera + *    h1 collaboration +    s.  aid , v.  andreev , b.  andrieu , r .- d .  appuhn , m.  arpagaus , a.  babaev , j.  bhr , j.  bn , y.  ban , p.  baranov , e.  barrelet , r.  barschke , w.  bartel , m.  barth , u.  bassler , h.p .  beck , h .- j .  behrend , a.  belousov , ch .  berger , g.  bernardi , r.  bernet , g.  bertrand - coremans , m.  besanon , r.  beyer , p.  biddulph , p.  bispham , j.c .  bizot , v.  blobel , k.  borras , f.  botterweck , v.  boudry , a.  braemer , w.  braunschweig , v.  brisson , d.  bruncko , c.  brune , r.  buchholz , l.  bngener , j.  brger , f.w .  bsser , a.  buniatian , s.  burke , m.j .  burton , g.  buschhorn , a.j .  campbell , t.  carli , f.  charles , m.  charlet , d.  clarke , a.b .  clegg , b.  clerbaux , s.  cocks , j.g .  contreras , c.  cormack , j.a .  coughlan , a.  courau , m .- c .  cousinou , g.  cozzika , l.  criegee , d.g .  cussans , j.  cvach , s.  dagoret , j.b .  dainton , w.d .  dau , k.  daum , m.  david , c.l .  davis , b.  delcourt , a.  de  roeck , e.a .  de  wolf , m.  dirkmann , p.  dixon , p.  di  nezza , w.  dlugosz , c.  dollfus , j.d .  dowell , h.b .  dreis , a.  droutskoi , d.  dllmann , o.  dnger , h.  duhm , j.  ebert , t.r .  ebert , g.  eckerlin , v.  efremenko , s.  egli , r.  eichler , f.  eisele , e.  eisenhandler , r.j .  ellison , e.  elsen , m.  erdmann , w.  erdmann , e.  evrard , a.b .  fahr , l.  favart , a.  fedotov , d.  feeken , r.  felst , j.  feltesse , j.  ferencei , f.  ferrarotto , k.  flamm , m.  fleischer , m.  flieser , g.  flgge , a.  fomenko , b.  fominykh , j.  formnek , j.m .  foster , g.  franke , e.  fretwurst , e.  gabathuler , k.  gabathuler , f.  gaede , j.  garvey , j.  gayler , m.  gebauer , a.  gellrich , h.  genzel , r.  gerhards , a.  glazov , u.  goerlach , l.  goerlich , n.  gogitidze , m.  goldberg , d.  goldner , k.  golec - biernat , b.  gonzalez - pineiro , i.  gorelov , c.  grab , h.  grssler , r.  grssler , t.  greenshaw , r.  griffiths , g.  grindhammer , a.  gruber , c.  gruber , j.  haack , d.  haidt , l.  hajduk , m.  hampel , w.j .  haynes , g.  heinzelmann , r.c.w .  henderson , h.  henschel , i.  herynek , m.f .  hess , w.  hildesheim , k.h .  hiller , c.d .  hilton , j.  hladk , k.c .  hoeger , m.  hppner , d.  hoffmann , t.  holtom , r.  horisberger , v.l .  hudgson , m.  htte , h.  hufnagel , m.  ibbotson , h.  itterbeck , a.  jacholkowska , c.  jacobsson , m.  jaffre , j.  janoth , t.  jansen , l.  jnsson , k.  johannsen , d.p .  johnson , l.  johnson , h.  jung , p.i.p .  kalmus , m.  kander , d.  kant , r.  kaschowitz , u.  kathage , j.  katzy , h.h .  kaufmann , o.  kaufmann , s.  kazarian , i.r .  kenyon , s.  kermiche , c.  keuker , c.  kiesling , m.  klein , c.  kleinwort , g.  knies , t.  khler , j.h .  khne , h.  kolanoski , f.  kole , s.d .  kolya , v.  korbel , m.  korn , p.  kostka , s.k .  kotelnikov , t.  krmerkmper , m.w .  krasny , h.  krehbiel , d.  krcker , u.  krger , u.  krner - marquis , h.  kster , m.  kuhlen , t.  kura , j.  kurzhfer , d.  lacour , b.  laforge , r.  lander , m.p.j .  landon , w.  lange , u.  langenegger , j .- f .  laporte , a.  lebedev , f.  lehner , c.  leverenz , s.  levonian , ch .  ley , g.  lindstrm , m.  lindstroem , j.  link , f.  linsel , j.  lipinski , b.  list , g.  lobo , h.  lohmander , j.w .  lomas , g.c .  lopez , v.  lubimov , d.  lke , n.  magnussen , e.  malinovski , s.  mani , r.  maraek , p.  marage , j.  marks , r.  marshall , j.  martens , g.  martin , r.  martin , h .- u .  martyn , j.  martyniak , t.  mavroidis , s.j .  maxfield , s.j .  mcmahon , a.  mehta , k.  meier , t.  merz , a.  meyer , a.  meyer , h.  meyer , j.  meyer , p .- o .  meyer , a.  migliori , s.  mikocki , d.  milstead , j.  moeck , f.  moreau , j.v .  morris , e.  mroczko , d.  mller , g.  mller , k.  mller , p.  murn , v.  nagovizin , r.  nahnhauer , b.  naroska , th .  naumann , p.r .  newman , d.  newton , d.  neyret , h.k .  nguyen , t.c .  nicholls , f.  niebergall , c.  niebuhr , ch .  niedzballa , h.  niggli , r.  nisius , g.  nowak , g.w .  noyes , m.  nyberg - werther , m.  oakden , h.  oberlack , u.  obrock , j.e .  olsson , d.  ozerov , p.  palmen , e.  panaro , a.  panitch , c.  pascaud , g.d .  patel , h.  pawletta , e.  peppel , e.  perez , j.p .  phillips , a.  pieuchot , d.  pitzl , g.  pope , s.  prell , r.  prosi , k.  rabbertz , g.  rdel , f.  raupach , p.  reimer , s.  reinshagen , h.  rick , v.  riech , j.  riedlberger , f.  riepenhausen , s.  riess , e.  rizvi , s.m .  robertson , p.  robmann , h.e .  roloff , r.  roosen , k.  rosenbauer , a.  rostovtsev , f.  rouse , c.  royon , k.  rter , s.  rusakov , k.  rybicki , n.  sahlmann , d.p.c .  sankey , p.  schacht , s.  schiek , s.  schleif , p.  schleper , w.  von  schlippe , d.  schmidt , g.  schmidt , a.  schning , v.  schrder , e.  schuhmann , b.  schwab , f.  sefkow , m.  seidel , r.  sell , a.  semenov , v.  shekelyan , i.  sheviakov , l.n .  shtarkov , g.  siegmon , u.  siewert , y.  sirois , i.o .  skillicorn , p.  smirnov , j.r .  smith , v.  solochenko , y.  soloviev , a.  specka , j.  spiekermann , s.  spielman , h.  spitzer , f.  squinabol , r.  starosta , m.  steenbock , p.  steffen , r.  steinberg , h.  steiner , b.  stella , a.  stellberger , j.  stier , j.  stiewe , u.  stlein , k.  stolze , u.  straumann , w.  struczinski , j.p .  sutton , s.  tapprogge , m.  taevsk , v.  tchernyshov , s.  tchetchelnitski , j.  theissen , c.  thiebaux , g.  thompson , p.  trul , j.  turnau , j.  tutas , p.  uelkes , a.  usik , s.  valkr , a.  valkrov , c.  valle , d.  vandenplas , p.  van  esch , p.  van  mechelen , y.  vazdik , p.  verrecchia , g.  villet , k.  wacker , a.  wagener , m.  wagener , a.  walther , b.  waugh , g.  weber , m.  weber , d.  wegener , a.  wegner , t.  wengler , m.  werner , l.r .  west , t.  wilksen , s.  willard , m.  winde , g .- g .  winter , c.  wittek , e.  wnsch , j.  ek , d.  zarbock , z.  zhang , a.  zhokin , m.  zimmer , f.  zomer , j.  zsembery , k.  zuber , and m.  zurnedden    i. physikalisches institut der rwth , aachen , germany + iii . physikalisches institut der rwth , aachen , germany + institut fr physik , humboldt - universitt , berlin , germany + school of physics and space research , university of birmingham , birmingham , uk + inter - university institute for high energies ulb - vub , brussels ; universitaire instelling antwerpen , wilrijk ; belgium + rutherford appleton laboratory , chilton , didcot , uk + institute for nuclear physics , cracow , poland + physics department and iirpa , university of california , davis , california , usa + institut fr physik , universitt dortmund , dortmund , germany + cea , dsm / dapnia , ce - saclay , gif - sur - yvette , france + department of physics and astronomy , university of glasgow , glasgow , uk + desy , hamburg , germany + i. institut fr experimentalphysik , universitt hamburg , hamburg , germany + ii . institut fr experimentalphysik , universitt hamburg , hamburg , germany + physikalisches institut , universitt heidelberg , heidelberg , germany + institut fr hochenergiephysik , universitt heidelberg , heidelberg , germany + institut fr reine und angewandte kernphysik , universitt kiel , kiel , germany + institute of experimental physics , slovak academy of sciences , koice , slovak republic + school of physics and chemistry , university of lancaster , lancaster , uk + department of physics , university of liverpool , liverpool , uk + queen mary and westfield college , london , uk + physics department , university of lund , lund , sweden + physics department , university of manchester , manchester , uk + cppm , universit daix - marseille ii , in2p3-cnrs , marseille , france + institute for theoretical and experimental physics , moscow , russia + lebedev physical institute , moscow , russia + max - planck - institut fr physik , mnchen , germany + lal , universit de paris - sud , in2p3-cnrs , orsay , france + lpnhe , ecole polytechnique , in2p3-cnrs , palaiseau , france + lpnhe , universits paris vi and vii , in2p3-cnrs , paris , france + institute of physics , czech academy of sciences , praha , czech republic + nuclear center , charles university , praha , czech republic + infn roma and dipartimento di fisica , universita `` la sapienza '' , roma , italy + paul scherrer institut , villigen , switzerland + fachbereich physik , bergische universitt gesamthochschule wuppertal , wuppertal , germany + desy , institut fr hochenergiephysik , zeuthen , germany + institut fr teilchenphysik , eth , zrich , switzerland + physik - institut der universitt zrich , zrich , switzerland + visitor from yerevan phys . inst . , armenia + on leave from lbl , berkeley , usa + supported by the bundesministerium fr forschung und technologie , frg , under contract numbers 6ac17p , 6ac47p , 6do57i , 6hh17p , 6hh27i , 6hd17i , 6hd27i , 6ki17p , 6mp17i , and 6wt87p + supported by the uk particle physics and astronomy research council , and formerly by the uk science and engineering research council + supported by fnrs - nfwo , iisn - iikw + supported by the polish state committee for scientific research , grant nos . 115/e-743/spub / p03/109/95 and 2  p03b  244  08p01 , and stiftung fr deutsch - polnische zusammenarbeit , project no.506/92 + supported in part by usdoe grant de  f603  91er40674 + supported by the deutsche forschungsgemeinschaft + supported by the swedish natural science research council + supported by ga r , grant no . 202/93/2423 , ga av r , grant no . 19095 and ga uk , grant no . 342 + supported by the swiss national science foundation +"}
{"article_id":"hep-ex9603005","section_id":"r","document":"the data were taken in 1994 with the h1 detector operating at the electron proton storage ring hera , where positrons of 27.5  collide with protons of 820 . in 1994 hera was operated with 153 colliding positron and proton bunches . the integrated luminosity used for this analysis is @xmath156 for the decay @xmath157   and @xmath158 for @xmath159 . the h1 detector is described in  @xcite . we repeat here the essential features of the detector components used for the analysis . the central tracking system is mounted concentrically around the beamline and covers polar angles  axis pointing in the proton beam direction , hence the polar angle @xmath160 is measured with respect to the proton beam direction . the region of small polar angles is called  forward \" . the plane perpendicular to the @xmath117 axis is named @xmath161 plane . ] between @xmath162 and @xmath163 . measurements of charge and momenta of charged particles are provided by two coaxial cylindrical drift chambers ( central jet chambers , cjc )  @xcite . two sets of cylindrical drift chambers for measurement of the @xmath117-coordinate and multiwire proportional chambers  ( mwpc ) for triggering are placed at two radial positions . one set surrounds the beamline within the inner cjc and the other is mounted in between the two jet chambers . the central tracking system is complemented by a forward tracking system which covers polar angles @xmath164 . in the present analysis the forward tracker is only used to detect events with tracks other than the @xmath0 decay leptons . the tracking system is surrounded by a highly segmented liquid argon ( lar ) sampling calorimeter  @xcite with an inner electromagnetic section consisting of lead absorber plates with a total depth of 20 to 30 radiation lengths and an outer hadronic section with steel absorber plates . polar angles between @xmath165 and @xmath166 are covered by the calorimeter and the total depth is 4.5 to 8 interaction lengths depending on the polar angle . the backward region , @xmath167 , is covered by a lead scintillator calorimeter where the scattered positron is detected for @xmath168 . the magnetic field of 1.15  t is produced by a superconducting solenoid surrounding the lar calorimeter . the iron flux return yoke surrounding the superconducting solenoid is instrumented with limited streamer tubes to provide muon identification ; it is segmented into 10 iron plates of 7.5  thickness and instrumented with up to 16 layers of streamer tubes . muon tracks are reconstructed in the region @xmath169 with a spatial resolution of the order of 1 . in addition to this central muon detector there is a toroidal muon spectrometer outside the main h1 magnet covering small polar angles . in the present analysis its driftchambers which cover @xmath170 , are used for the recognition of events with proton dissociation . for the same purpose a system of scintillators  the proton tagger  is placed 24  m downstream the proton beam around the beampipe , covering an angular range of approximately @xmath171 . the luminosity is measured using the radiative process @xmath172 where the photon is detected in a luminosity monitor  @xcite . the background rate at hera is high , mainly due to interactions of the beam protons with gas in the beam pipe or surrounding material and due to photoproduction of light quarks . therefore a restrictive trigger is necessary which can not use the distinctive signature of the scattered positron since for photoproduction the positron stays in the beampipe ) with the bulk of the @xmath0  data which are at @xmath173 . ] . the trigger essentially has to rely on the decay leptons of the @xmath0 .    compared to our previous report @xcite the trigger for muons and for electrons from @xmath0  decays has been improved resulting in an approximate efficiency for electron pairs of 50% and for muon pairs of nearly 60% with a tolerable background rate . the following triggers are utilized :    1 . * track triggers from multi wire proportional chambers  ( mwpc ) *  @xcite demanding the origin of the tracks in the @xmath117 direction to be near the nominal vertex region . a * coplanar track trigger * constructed from the mwpcs which demands exactly two tracks of transverse momentum @xmath174 , roughly coplanar with the beams . 3 .   a * driftchamber track trigger *  @xcite demanding one track in the cjc with a transverse momentum @xmath175 which originates from the interaction point in the plane perpendicular to the beams within @xmath176 . muon triggers * demanding a penetrating particle detected in the central muon systems . a * calorimetric trigger * for low energy electromagnetic clusters with @xmath177 roughly aligned with a track candidate in the proportional chambers . these triggers are combined such that each event class is triggered by at least two different trigger combinations which can be compared with each other for determination of the efficiency .    for exclusive @xmath0 meson production in both leptonic decay modes a combination of elements 1 , 2 and 3 gives a trigger based purely on tracking chambers . a trigger for muons  which is used for elastic and inelastic processes  is based on track triggers 1 and 3 and the muon trigger 4 . for electrons the combination of track triggers 1 and 3 with the calorimetric trigger 5 is used imposing a requirement of low track multiplicity in the mwpcs therefore only sensitive to elastic and proton dissociationprocesses . the event selection starts from tracks found in the central drift chambers cjc which have been associated to the primary @xmath178 interaction point ( vertex ) in a constrained fit which helps to increase momentum resolution and to reduce pattern recognition ambiguities . _ electrons _ are identified in the electromagnetic section of the lar calorimeter by linking a reconstructed drift chamber track to a calorimeter cluster with energy @xmath179 and demanding the measured energy to be comparable with the momentum ( @xmath180 ) . the efficiency for electron identification is @xmath181 for @xmath182 . a particle is identified as a _ muon _ if the track in the drift chamber is either linked to a track element reconstructed in the central muon detector or if it is identified as a minimum ionizing particle in the lar calorimeter . for the link with a track in the central muon system a drift chamber track is extrapolated taking into account the deflection in the magnetic field , the energy loss in the material of the detector and multiple scattering . the @xmath183 probability comparing the parameters of the two tracks is required to be above @xmath184 . a muon signature in the lar calorimeter is defined by an energy deposit below @xmath185 around the extrapolated track , at least three active cells in the hadronic part of the calorimeter , and the particle has to penetrate at least 90 % of the calorimeter . with these requirements the thresholds are 0.8  for the identification of muons in the lar calorimeter ( @xmath186 efficiency above @xmath187 ) and 1.5  in the central muon system ( @xmath188 efficiency above @xmath189 ) . monte carlo ( mc ) techniques are used in order to determine the geometrical acceptance , the trigger and selection efficiencies . events are generated using models and the detector response is simulated in detail . the simulated events are subjected to the same reconstruction and analysis chain as the data . two models are used to simulate @xmath0  production . inelastic @xmath0   production is simulated by the generator epjpsi  @xcite which is based on the colour singlet  model in leading order . diffractive @xmath0  production  elastic and proton dissociation  is modelled by the monte carlo generator diffvm  @xcite . diffractive events are generated with an energy dependence proportional to @xmath190 , an exponential @xmath112 distribution @xmath191 with a fixed slope of @xmath192 in the elastic mode and @xmath193 for proton dissociation . the proton dissociation mode has an additional parameter , the mass @xmath194  of the dissociated proton . events are generated with a @xmath195 distribution for @xmath196 above @xmath197 . below @xmath197 the distribution is closely modelled to diffractive proton dissociation data obtained from deuterium measurements  @xcite . the system @xmath198 is fragmented at masses above 2  by treating it as a system of quark and diquark and using the lund string model  @xcite . below 2  it is treated as a nucleon resonance and decays into nucleon and pions according to the known branching ratios . the detector response in the monte carlo simulation is checked in detail by comparing to the data . after applying small overall correction factors the dependence of the efficiencies for track reconstruction , particle identification and triggering on the polar angle and the momentum of the @xmath0 decay particles is well described by the simulation . this tuned monte carlo simulation is then used for correcting the data and remaining differences between data and monte carlo are included in the systematic errors . elastic and inelastic @xmath0   events in general look quite different in the detector , elastic events having only the decay leptons measured while inelastic events are characterized by additional tracks . initially a common selection aims to identify lepton pairs in the @xmath0  mass region irrespective of any other activity in the detector . two tracks are selected with a common origin at the beam interaction point in the @xmath161 plane and momenta above @xmath200 in the range of polar angles @xmath201 . both tracks have to be identified as muons or electrons . the @xmath117-coordinate of the event vertex has to be within @xmath202 of the average beam collision point .    for low multiplicity events , one of the main backgrounds is due to cosmic ray muons , which are efficiently rejected by demanding the angle between the lepton candidates to be less than @xmath203 . photoproduction events are selected by requiring no scattered positron be visible in the calorimeter , i.e. below a polar angle of @xmath204 . rejecting energy clusters above @xmath205 restricts the photon virtuality to @xmath206 .","summary":"bsser , a.  buniatian , s.  burke , m.j .  campbell , t.  carli , f.  charles , m.  charlet , d.  clarke , a.b .  coughlan , a.  courau , m .- c .  kotelnikov , t.  krmerkmper , m.w .  nguyen , t.c .  202/93/2423 , ga av r , grant no .","abstract":"results on  production in interactions in the h1 experiment at hera are presented . the  mesons are produced by almost real photons ( ) and detected via their leptonic decays . the data have been taken in 1994 and correspond to an integrated luminosity of . the cross section for elastic  production is observed to increase strongly with the center of mass  energy . the cross section for diffractive production with proton dissociation is found to be of similar magnitude as the elastic cross section . distributions of transverse momentum and decay angle are studied and found to be in accord with a diffractive production mechanism . for inelastic  production the total cross section , the distribution of transverse momenta , and the elasticity of the   are compared to nlo qcd calculations in a colour singlet model and agreement is found . diffractive  production has been observed and a first estimate of the ratio to  production in the hera energy regime is given .    plus 2 mm minus 2 mm    desy 96 - 037 + march 1996 +    * elastic and inelastic photoproduction + of  mesons at hera + *    h1 collaboration +    s.  aid , v.  andreev , b.  andrieu , r .- d .  appuhn , m.  arpagaus , a.  babaev , j.  bhr , j.  bn , y.  ban , p.  baranov , e.  barrelet , r.  barschke , w.  bartel , m.  barth , u.  bassler , h.p .  beck , h .- j .  behrend , a.  belousov , ch .  berger , g.  bernardi , r.  bernet , g.  bertrand - coremans , m.  besanon , r.  beyer , p.  biddulph , p.  bispham , j.c .  bizot , v.  blobel , k.  borras , f.  botterweck , v.  boudry , a.  braemer , w.  braunschweig , v.  brisson , d.  bruncko , c.  brune , r.  buchholz , l.  bngener , j.  brger , f.w .  bsser , a.  buniatian , s.  burke , m.j .  burton , g.  buschhorn , a.j .  campbell , t.  carli , f.  charles , m.  charlet , d.  clarke , a.b .  clegg , b.  clerbaux , s.  cocks , j.g .  contreras , c.  cormack , j.a .  coughlan , a.  courau , m .- c .  cousinou , g.  cozzika , l.  criegee , d.g .  cussans , j.  cvach , s.  dagoret , j.b .  dainton , w.d .  dau , k.  daum , m.  david , c.l .  davis , b.  delcourt , a.  de  roeck , e.a .  de  wolf , m.  dirkmann , p.  dixon , p.  di  nezza , w.  dlugosz , c.  dollfus , j.d .  dowell , h.b .  dreis , a.  droutskoi , d.  dllmann , o.  dnger , h.  duhm , j.  ebert , t.r .  ebert , g.  eckerlin , v.  efremenko , s.  egli , r.  eichler , f.  eisele , e.  eisenhandler , r.j .  ellison , e.  elsen , m.  erdmann , w.  erdmann , e.  evrard , a.b .  fahr , l.  favart , a.  fedotov , d.  feeken , r.  felst , j.  feltesse , j.  ferencei , f.  ferrarotto , k.  flamm , m.  fleischer , m.  flieser , g.  flgge , a.  fomenko , b.  fominykh , j.  formnek , j.m .  foster , g.  franke , e.  fretwurst , e.  gabathuler , k.  gabathuler , f.  gaede , j.  garvey , j.  gayler , m.  gebauer , a.  gellrich , h.  genzel , r.  gerhards , a.  glazov , u.  goerlach , l.  goerlich , n.  gogitidze , m.  goldberg , d.  goldner , k.  golec - biernat , b.  gonzalez - pineiro , i.  gorelov , c.  grab , h.  grssler , r.  grssler , t.  greenshaw , r.  griffiths , g.  grindhammer , a.  gruber , c.  gruber , j.  haack , d.  haidt , l.  hajduk , m.  hampel , w.j .  haynes , g.  heinzelmann , r.c.w .  henderson , h.  henschel , i.  herynek , m.f .  hess , w.  hildesheim , k.h .  hiller , c.d .  hilton , j.  hladk , k.c .  hoeger , m.  hppner , d.  hoffmann , t.  holtom , r.  horisberger , v.l .  hudgson , m.  htte , h.  hufnagel , m.  ibbotson , h.  itterbeck , a.  jacholkowska , c.  jacobsson , m.  jaffre , j.  janoth , t.  jansen , l.  jnsson , k.  johannsen , d.p .  johnson , l.  johnson , h.  jung , p.i.p .  kalmus , m.  kander , d.  kant , r.  kaschowitz , u.  kathage , j.  katzy , h.h .  kaufmann , o.  kaufmann , s.  kazarian , i.r .  kenyon , s.  kermiche , c.  keuker , c.  kiesling , m.  klein , c.  kleinwort , g.  knies , t.  khler , j.h .  khne , h.  kolanoski , f.  kole , s.d .  kolya , v.  korbel , m.  korn , p.  kostka , s.k .  kotelnikov , t.  krmerkmper , m.w .  krasny , h.  krehbiel , d.  krcker , u.  krger , u.  krner - marquis , h.  kster , m.  kuhlen , t.  kura , j.  kurzhfer , d.  lacour , b.  laforge , r.  lander , m.p.j .  landon , w.  lange , u.  langenegger , j .- f .  laporte , a.  lebedev , f.  lehner , c.  leverenz , s.  levonian , ch .  ley , g.  lindstrm , m.  lindstroem , j.  link , f.  linsel , j.  lipinski , b.  list , g.  lobo , h.  lohmander , j.w .  lomas , g.c .  lopez , v.  lubimov , d.  lke , n.  magnussen , e.  malinovski , s.  mani , r.  maraek , p.  marage , j.  marks , r.  marshall , j.  martens , g.  martin , r.  martin , h .- u .  martyn , j.  martyniak , t.  mavroidis , s.j .  maxfield , s.j .  mcmahon , a.  mehta , k.  meier , t.  merz , a.  meyer , a.  meyer , h.  meyer , j.  meyer , p .- o .  meyer , a.  migliori , s.  mikocki , d.  milstead , j.  moeck , f.  moreau , j.v .  morris , e.  mroczko , d.  mller , g.  mller , k.  mller , p.  murn , v.  nagovizin , r.  nahnhauer , b.  naroska , th .  naumann , p.r .  newman , d.  newton , d.  neyret , h.k .  nguyen , t.c .  nicholls , f.  niebergall , c.  niebuhr , ch .  niedzballa , h.  niggli , r.  nisius , g.  nowak , g.w .  noyes , m.  nyberg - werther , m.  oakden , h.  oberlack , u.  obrock , j.e .  olsson , d.  ozerov , p.  palmen , e.  panaro , a.  panitch , c.  pascaud , g.d .  patel , h.  pawletta , e.  peppel , e.  perez , j.p .  phillips , a.  pieuchot , d.  pitzl , g.  pope , s.  prell , r.  prosi , k.  rabbertz , g.  rdel , f.  raupach , p.  reimer , s.  reinshagen , h.  rick , v.  riech , j.  riedlberger , f.  riepenhausen , s.  riess , e.  rizvi , s.m .  robertson , p.  robmann , h.e .  roloff , r.  roosen , k.  rosenbauer , a.  rostovtsev , f.  rouse , c.  royon , k.  rter , s.  rusakov , k.  rybicki , n.  sahlmann , d.p.c .  sankey , p.  schacht , s.  schiek , s.  schleif , p.  schleper , w.  von  schlippe , d.  schmidt , g.  schmidt , a.  schning , v.  schrder , e.  schuhmann , b.  schwab , f.  sefkow , m.  seidel , r.  sell , a.  semenov , v.  shekelyan , i.  sheviakov , l.n .  shtarkov , g.  siegmon , u.  siewert , y.  sirois , i.o .  skillicorn , p.  smirnov , j.r .  smith , v.  solochenko , y.  soloviev , a.  specka , j.  spiekermann , s.  spielman , h.  spitzer , f.  squinabol , r.  starosta , m.  steenbock , p.  steffen , r.  steinberg , h.  steiner , b.  stella , a.  stellberger , j.  stier , j.  stiewe , u.  stlein , k.  stolze , u.  straumann , w.  struczinski , j.p .  sutton , s.  tapprogge , m.  taevsk , v.  tchernyshov , s.  tchetchelnitski , j.  theissen , c.  thiebaux , g.  thompson , p.  trul , j.  turnau , j.  tutas , p.  uelkes , a.  usik , s.  valkr , a.  valkrov , c.  valle , d.  vandenplas , p.  van  esch , p.  van  mechelen , y.  vazdik , p.  verrecchia , g.  villet , k.  wacker , a.  wagener , m.  wagener , a.  walther , b.  waugh , g.  weber , m.  weber , d.  wegener , a.  wegner , t.  wengler , m.  werner , l.r .  west , t.  wilksen , s.  willard , m.  winde , g .- g .  winter , c.  wittek , e.  wnsch , j.  ek , d.  zarbock , z.  zhang , a.  zhokin , m.  zimmer , f.  zomer , j.  zsembery , k.  zuber , and m.  zurnedden    i. physikalisches institut der rwth , aachen , germany + iii . physikalisches institut der rwth , aachen , germany + institut fr physik , humboldt - universitt , berlin , germany + school of physics and space research , university of birmingham , birmingham , uk + inter - university institute for high energies ulb - vub , brussels ; universitaire instelling antwerpen , wilrijk ; belgium + rutherford appleton laboratory , chilton , didcot , uk + institute for nuclear physics , cracow , poland + physics department and iirpa , university of california , davis , california , usa + institut fr physik , universitt dortmund , dortmund , germany + cea , dsm / dapnia , ce - saclay , gif - sur - yvette , france + department of physics and astronomy , university of glasgow , glasgow , uk + desy , hamburg , germany + i. institut fr experimentalphysik , universitt hamburg , hamburg , germany + ii . institut fr experimentalphysik , universitt hamburg , hamburg , germany + physikalisches institut , universitt heidelberg , heidelberg , germany + institut fr hochenergiephysik , universitt heidelberg , heidelberg , germany + institut fr reine und angewandte kernphysik , universitt kiel , kiel , germany + institute of experimental physics , slovak academy of sciences , koice , slovak republic + school of physics and chemistry , university of lancaster , lancaster , uk + department of physics , university of liverpool , liverpool , uk + queen mary and westfield college , london , uk + physics department , university of lund , lund , sweden + physics department , university of manchester , manchester , uk + cppm , universit daix - marseille ii , in2p3-cnrs , marseille , france + institute for theoretical and experimental physics , moscow , russia + lebedev physical institute , moscow , russia + max - planck - institut fr physik , mnchen , germany + lal , universit de paris - sud , in2p3-cnrs , orsay , france + lpnhe , ecole polytechnique , in2p3-cnrs , palaiseau , france + lpnhe , universits paris vi and vii , in2p3-cnrs , paris , france + institute of physics , czech academy of sciences , praha , czech republic + nuclear center , charles university , praha , czech republic + infn roma and dipartimento di fisica , universita `` la sapienza '' , roma , italy + paul scherrer institut , villigen , switzerland + fachbereich physik , bergische universitt gesamthochschule wuppertal , wuppertal , germany + desy , institut fr hochenergiephysik , zeuthen , germany + institut fr teilchenphysik , eth , zrich , switzerland + physik - institut der universitt zrich , zrich , switzerland + visitor from yerevan phys . inst . , armenia + on leave from lbl , berkeley , usa + supported by the bundesministerium fr forschung und technologie , frg , under contract numbers 6ac17p , 6ac47p , 6do57i , 6hh17p , 6hh27i , 6hd17i , 6hd27i , 6ki17p , 6mp17i , and 6wt87p + supported by the uk particle physics and astronomy research council , and formerly by the uk science and engineering research council + supported by fnrs - nfwo , iisn - iikw + supported by the polish state committee for scientific research , grant nos . 115/e-743/spub / p03/109/95 and 2  p03b  244  08p01 , and stiftung fr deutsch - polnische zusammenarbeit , project no.506/92 + supported in part by usdoe grant de  f603  91er40674 + supported by the deutsche forschungsgemeinschaft + supported by the swedish natural science research council + supported by ga r , grant no . 202/93/2423 , ga av r , grant no . 19095 and ga uk , grant no . 342 + supported by the swiss national science foundation +"}
{"article_id":"hep-ex9603005","section_id":"i","document":"@xmath0  meson production in the photoproduction limit is analysed in the elastic channel . corrections for contributions from events with proton dissociation are applied almost entirely on an event to event basis . the following results are found :    * the total @xmath4 cross section is observed to increase with energy as @xmath290 with @xmath358 for h1 data alone , and @xmath252 including the zeus and low energy data . this increase is faster than predicted in soft diffractive models ( @xmath253 ) . * a calculation using the model by ryskin in the framework of perturbative qcd results in a good description of the energy dependence if the gluon distribution from the set mrsa is used . * the @xmath125 distribution of the elastic @xmath0  data below @xmath359 can be fitted with an exponential @xmath360 , @xmath361 . the @xmath4 cross cross section for @xmath0 meson production with proton dissociation was determined . the @xmath4  cross section  is as large as the elastic one and its energy dependence is slightly steeper than the elastic cross section , @xmath291 . the @xmath125 distribution is flatter than for the elastic process . the slope parameter is approximately a factor 2 smaller than for elastic data . the angular distribution in the helicity frame was determined for the complete diffractive data sample , i.e. including elastic and proton dissociation   contributions . the distribution in the helicity frame is consistent with s - channel helicity conservation , @xmath299 , where @xmath297 is the fraction of transversely polarised @xmath0  mesons . inelastic @xmath0 meson production can be described well by a qcd calculation in nlo of the colour singlet model if cuts are used which demand the emitted gluon to be hard , @xmath362 and @xmath332 , in order to make perturbation theory applicable . the agreement is observed in the shape of the @xmath124 , @xmath125 and @xmath117 distributions . the absolute normalization between data and theory agrees within the experimental errors of @xmath363 , using any gluon distribution function which describes the @xmath114 data at low @xmath113 . a comparison to the relative energy distribution @xmath117 of inelastic @xmath0   production with @xmath338 calculated in a colour octet  model shows disagreement at high values and makes a large colour octet  contribution unlikely . we are very grateful to the hera machine group whose outstanding efforts made this experiment possible . we acknowledge the support of the desy technical staff . we appreciate the big effort of the engineers and technicians who constructed and maintained the detector . we thank the funding agencies for financial support of this experiment . we wish to thank the desy directorate for the support and hospitality extended to the non  desy members of the collaboration . we wish to thank m. krmer from the desy theory group for many enlightening discussions and good collaboration . thanks to r. roberts ( ral ) for providing us with his numerical results for elastic @xmath0  production . 99 a.  donnachie and p.v . landshoff , _ phys . _ b348 ( 1995 ) 213 ; 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coremans , m.  besanon , r.  beyer , p.  biddulph , p.  bispham , j.c .  bizot , v.  blobel , k.  borras , f.  botterweck , v.  boudry , a.  braemer , w.  braunschweig , v.  brisson , d.  bruncko , c.  brune , r.  buchholz , l.  bngener , j.  brger , f.w .  burton , g.  buschhorn , a.j .  cousinou , g.  cozzika , l.  criegee , d.g .  cussans , j.  cvach , s.  dagoret , j.b .  dainton , w.d .  dau , k.  daum , m.  david , c.l .  de  wolf , m.  dirkmann , p.  dixon , p.  di  nezza , w.  dlugosz , c.  dollfus , j.d .  dowell , h.b .  dreis , a.  droutskoi , d.  dllmann , o.  dnger , h.  duhm , j.  ebert , t.r .  ebert , g.  eckerlin , v.  efremenko , s.  egli , r.  eichler , f.  eisele , e.  eisenhandler , r.j .  ellison , e.  elsen , m.  erdmann , w.  erdmann , e.  evrard , a.b .  fahr , l.  favart , a.  fedotov , d.  feeken , r.  felst , j.  feltesse , j.  ferencei , f.  ferrarotto , k.  flamm , m.  fleischer , m.  flieser , g.  flgge , a.  fomenko , b.  fominykh , j.  formnek , j.m .  foster , g.  franke , e.  fretwurst , e.  gabathuler , k.  gabathuler , f.  gaede , j.  garvey , j.  gayler , m.  gebauer , a.  gellrich , h.  genzel , r.  gerhards , a.  glazov , u.  goerlach , l.  goerlich , n.  gogitidze , m.  goldberg , d.  goldner , k.  golec - biernat , b.  gonzalez - pineiro , i.  gorelov , c.  grab , h.  grssler , r.  grssler , t.  greenshaw , r.  griffiths , g.  grindhammer , a.  gruber , c.  gruber , j.  haack , d.  haidt , l.  hajduk , m.  hampel , w.j .  haynes , g.  heinzelmann , r.c.w .  henderson , h.  henschel , i.  herynek , m.f .  hiller , c.d .  hoeger , m.  hppner , d.  hoffmann , t.  holtom , r.  horisberger , v.l .  hudgson , m.  htte , h.  hufnagel , m.  ibbotson , h.  itterbeck , a.  jacholkowska , c.  jacobsson , m.  jaffre , j.  janoth , t.  jansen , l.  jnsson , k.  johannsen , d.p .  johnson , l.  johnson , h.  jung , p.i.p .  kalmus , m.  kander , d.  kant , r.  kaschowitz , u.  kathage , j.  katzy , h.h .  kaufmann , o.  kaufmann , s.  kazarian , i.r .  kenyon , s.  kermiche , c.  keuker , c.  kiesling , m.  klein , c.  kleinwort , g.  knies , t.  khler , j.h .  khne , h.  kolanoski , f.  kole , s.d .  kolya , v.  korbel , m.  korn , p.  kostka , s.k .  krasny , h.  krehbiel , d.  krcker , u.  krger , u.  krner - marquis , h.  kster , m.  kuhlen , t.  kura , j.  kurzhfer , d.  lacour , b.  laforge , r.  lander , m.p.j .  landon , w.  lange , u.  langenegger , j .- f .  ley , g.  lindstrm , m.  lindstroem , j.  link , f.  linsel , j.  lipinski , b.  list , g.  lobo , h.  lohmander , j.w .  lomas , g.c .  lopez , v.  lubimov , d.  lke , n.  magnussen , e.  malinovski , s.  mani , r.  maraek , p.  marage , j.  marks , r.  marshall , j.  martens , g.  martin , r.  martin , h .- u .  martyn , j.  martyniak , t.  mavroidis , s.j .  morris , e.  mroczko , d.  mller , g.  mller , k.  mller , p.  murn , v.  nagovizin , r.  nahnhauer , b.  naroska , th .  naumann , p.r .  newman , d.  newton , d.  neyret , h.k .  nicholls , f.  niebergall , c.  niebuhr , ch .  niedzballa , h.  niggli , r.  nisius , g.  nowak , g.w .  noyes , m.  nyberg - werther , m.  oakden , h.  oberlack , u.  obrock , j.e .  olsson , d.  ozerov , p.  palmen , e.  panaro , a.  panitch , c.  pascaud , g.d .  patel , h.  pawletta , e.  peppel , e.  perez , j.p .  phillips , a.  pieuchot , d.  pitzl , g.  pope , s.  prell , r.  prosi , k.  rabbertz , g.  rdel , f.  raupach , p.  reimer , s.  reinshagen , h.  rick , v.  riech , j.  riedlberger , f.  riepenhausen , s.  riess , e.  rizvi , s.m .  skillicorn , p.  smirnov , j.r .  smith , v.  solochenko , y.  soloviev , a.  specka , j.  spiekermann , s.  spielman , h.  spitzer , f.  squinabol , r.  starosta , m.  steenbock , p.  steffen , r.  steinberg , h.  steiner , b.  stella , a.  stellberger , j.  stier , j.  stiewe , u.  stlein , k.  stolze , u.  straumann , w.  struczinski , j.p .  sutton , s.  tapprogge , m.  taevsk , v.  tchernyshov , s.  tchetchelnitski , j.  theissen , c.  thiebaux , g.  thompson , p.  trul , j.  turnau , j.  tutas , p.  uelkes , a.  usik , s.  valkr , a.  valkrov , c.  valle , d.  vandenplas , p.  van  esch , p.  van  mechelen , y.  vazdik , p.  verrecchia , g.  villet , k.  wacker , a.  wagener , m.  wagener , a.  walther , b.  waugh , g.  weber , m.  weber , d.  wegener , a.  wegner , t.  wengler , m.  werner , l.r .  west , t.  wilksen , s.  willard , m.  winde , g .- g .  winter , c.  wittek , e.  wnsch , j.  ek , d.  zarbock , z.  zhang , a.  zhokin , m.  zimmer , f.  zomer , j.  zsembery , k.  zuber , and m.  zurnedden    i. physikalisches institut fr experimentalphysik , universitt hamburg , hamburg , germany + physikalisches","abstract":"results on  production in interactions in the h1 experiment at hera are presented . the  mesons are produced by almost real photons ( ) and detected via their leptonic decays . the data have been taken in 1994 and correspond to an integrated luminosity of . the cross section for elastic  production is observed to increase strongly with the center of mass  energy . the cross section for diffractive production with proton dissociation is found to be of similar magnitude as the elastic cross section . distributions of transverse momentum and decay angle are studied and found to be in accord with a diffractive production mechanism . for inelastic  production the total cross section , the distribution of transverse momenta , and the elasticity of the   are compared to nlo qcd calculations in a colour singlet model and agreement is found . diffractive  production has been observed and a first estimate of the ratio to  production in the hera energy regime is given .    plus 2 mm minus 2 mm    desy 96 - 037 + march 1996 +    * elastic and inelastic photoproduction + of  mesons at hera + *    h1 collaboration +    s.  aid , v.  andreev , b.  andrieu , r .- d .  appuhn , m.  arpagaus , a.  babaev , j.  bhr , j.  bn , y.  ban , p.  baranov , e.  barrelet , r.  barschke , w.  bartel , m.  barth , u.  bassler , h.p .  beck , h .- j .  behrend , a.  belousov , ch .  berger , g.  bernardi , r.  bernet , g.  bertrand - coremans , m.  besanon , r.  beyer , p.  biddulph , p.  bispham , j.c .  bizot , v.  blobel , k.  borras , f.  botterweck , v.  boudry , a.  braemer , w.  braunschweig , v.  brisson , d.  bruncko , c.  brune , r.  buchholz , l.  bngener , j.  brger , f.w .  bsser , a.  buniatian , s.  burke , m.j .  burton , g.  buschhorn , a.j .  campbell , t.  carli , f.  charles , m.  charlet , d.  clarke , a.b .  clegg , b.  clerbaux , s.  cocks , j.g .  contreras , c.  cormack , j.a .  coughlan , a.  courau , m .- c .  cousinou , g.  cozzika , l.  criegee , d.g .  cussans , j.  cvach , s.  dagoret , j.b .  dainton , w.d .  dau , k.  daum , m.  david , c.l .  davis , b.  delcourt , a.  de  roeck , e.a .  de  wolf , m.  dirkmann , p.  dixon , p.  di  nezza , w.  dlugosz , c.  dollfus , j.d .  dowell , h.b .  dreis , a.  droutskoi , d.  dllmann , o.  dnger , h.  duhm , j.  ebert , t.r .  ebert , g.  eckerlin , v.  efremenko , s.  egli , r.  eichler , f.  eisele , e.  eisenhandler , r.j .  ellison , e.  elsen , m.  erdmann , w.  erdmann , e.  evrard , a.b .  fahr , l.  favart , a.  fedotov , d.  feeken , r.  felst , j.  feltesse , j.  ferencei , f.  ferrarotto , k.  flamm , m.  fleischer , m.  flieser , g.  flgge , a.  fomenko , b.  fominykh , j.  formnek , j.m .  foster , g.  franke , e.  fretwurst , e.  gabathuler , k.  gabathuler , f.  gaede , j.  garvey , j.  gayler , m.  gebauer , a.  gellrich , h.  genzel , r.  gerhards , a.  glazov , u.  goerlach , l.  goerlich , n.  gogitidze , m.  goldberg , d.  goldner , k.  golec - biernat , b.  gonzalez - pineiro , i.  gorelov , c.  grab , h.  grssler , r.  grssler , t.  greenshaw , r.  griffiths , g.  grindhammer , a.  gruber , c.  gruber , j.  haack , d.  haidt , l.  hajduk , m.  hampel , w.j .  haynes , g.  heinzelmann , r.c.w .  henderson , h.  henschel , i.  herynek , m.f .  hess , w.  hildesheim , k.h .  hiller , c.d .  hilton , j.  hladk , k.c .  hoeger , m.  hppner , d.  hoffmann , t.  holtom , r.  horisberger , v.l .  hudgson , m.  htte , h.  hufnagel , m.  ibbotson , h.  itterbeck , a.  jacholkowska , c.  jacobsson , m.  jaffre , j.  janoth , t.  jansen , l.  jnsson , k.  johannsen , d.p .  johnson , l.  johnson , h.  jung , p.i.p .  kalmus , m.  kander , d.  kant , r.  kaschowitz , u.  kathage , j.  katzy , h.h .  kaufmann , o.  kaufmann , s.  kazarian , i.r .  kenyon , s.  kermiche , c.  keuker , c.  kiesling , m.  klein , c.  kleinwort , g.  knies , t.  khler , j.h .  khne , h.  kolanoski , f.  kole , s.d .  kolya , v.  korbel , m.  korn , p.  kostka , s.k .  kotelnikov , t.  krmerkmper , m.w .  krasny , h.  krehbiel , d.  krcker , u.  krger , u.  krner - marquis , h.  kster , m.  kuhlen , t.  kura , j.  kurzhfer , d.  lacour , b.  laforge , r.  lander , m.p.j .  landon , w.  lange , u.  langenegger , j .- f .  laporte , a.  lebedev , f.  lehner , c.  leverenz , s.  levonian , ch .  ley , g.  lindstrm , m.  lindstroem , j.  link , f.  linsel , j.  lipinski , b.  list , g.  lobo , h.  lohmander , j.w .  lomas , g.c .  lopez , v.  lubimov , d.  lke , n.  magnussen , e.  malinovski , s.  mani , r.  maraek , p.  marage , j.  marks , r.  marshall , j.  martens , g.  martin , r.  martin , h .- u .  martyn , j.  martyniak , t.  mavroidis , s.j .  maxfield , s.j .  mcmahon , a.  mehta , k.  meier , t.  merz , a.  meyer , a.  meyer , h.  meyer , j.  meyer , p .- o .  meyer , a.  migliori , s.  mikocki , d.  milstead , j.  moeck , f.  moreau , j.v .  morris , e.  mroczko , d.  mller , g.  mller , k.  mller , p.  murn , v.  nagovizin , r.  nahnhauer , b.  naroska , th .  naumann , p.r .  newman , d.  newton , d.  neyret , h.k .  nguyen , t.c .  nicholls , f.  niebergall , c.  niebuhr , ch .  niedzballa , h.  niggli , r.  nisius , g.  nowak , g.w .  noyes , m.  nyberg - werther , m.  oakden , h.  oberlack , u.  obrock , j.e .  olsson , d.  ozerov , p.  palmen , e.  panaro , a.  panitch , c.  pascaud , g.d .  patel , h.  pawletta , e.  peppel , e.  perez , j.p .  phillips , a.  pieuchot , d.  pitzl , g.  pope , s.  prell , r.  prosi , k.  rabbertz , g.  rdel , f.  raupach , p.  reimer , s.  reinshagen , h.  rick , v.  riech , j.  riedlberger , f.  riepenhausen , s.  riess , e.  rizvi , s.m .  robertson , p.  robmann , h.e .  roloff , r.  roosen , k.  rosenbauer , a.  rostovtsev , f.  rouse , c.  royon , k.  rter , s.  rusakov , k.  rybicki , n.  sahlmann , d.p.c .  sankey , p.  schacht , s.  schiek , s.  schleif , p.  schleper , w.  von  schlippe , d.  schmidt , g.  schmidt , a.  schning , v.  schrder , e.  schuhmann , b.  schwab , f.  sefkow , m.  seidel , r.  sell , a.  semenov , v.  shekelyan , i.  sheviakov , l.n .  shtarkov , g.  siegmon , u.  siewert , y.  sirois , i.o .  skillicorn , p.  smirnov , j.r .  smith , v.  solochenko , y.  soloviev , a.  specka , j.  spiekermann , s.  spielman , h.  spitzer , f.  squinabol , r.  starosta , m.  steenbock , p.  steffen , r.  steinberg , h.  steiner , b.  stella , a.  stellberger , j.  stier , j.  stiewe , u.  stlein , k.  stolze , u.  straumann , w.  struczinski , j.p .  sutton , s.  tapprogge , m.  taevsk , v.  tchernyshov , s.  tchetchelnitski , j.  theissen , c.  thiebaux , g.  thompson , p.  trul , j.  turnau , j.  tutas , p.  uelkes , a.  usik , s.  valkr , a.  valkrov , c.  valle , d.  vandenplas , p.  van  esch , p.  van  mechelen , y.  vazdik , p.  verrecchia , g.  villet , k.  wacker , a.  wagener , m.  wagener , a.  walther , b.  waugh , g.  weber , m.  weber , d.  wegener , a.  wegner , t.  wengler , m.  werner , l.r .  west , t.  wilksen , s.  willard , m.  winde , g .- g .  winter , c.  wittek , e.  wnsch , j.  ek , d.  zarbock , z.  zhang , a.  zhokin , m.  zimmer , f.  zomer , j.  zsembery , k.  zuber , and m.  zurnedden    i. physikalisches institut der rwth , aachen , germany + iii . physikalisches institut der rwth , aachen , germany + institut fr physik , humboldt - universitt , berlin , germany + school of physics and space research , university of birmingham , birmingham , uk + inter - university institute for high energies ulb - vub , brussels ; universitaire instelling antwerpen , wilrijk ; belgium + rutherford appleton laboratory , chilton , didcot , uk + institute for nuclear physics , cracow , poland + physics department and iirpa , university of california , davis , california , usa + institut fr physik , universitt dortmund , dortmund , germany + cea , dsm / dapnia , ce - saclay , gif - sur - yvette , france + department of physics and astronomy , university of glasgow , glasgow , uk + desy , hamburg , germany + i. institut fr experimentalphysik , universitt hamburg , hamburg , germany + ii . institut fr experimentalphysik , universitt hamburg , hamburg , germany + physikalisches institut , universitt heidelberg , heidelberg , germany + institut fr hochenergiephysik , universitt heidelberg , heidelberg , germany + institut fr reine und angewandte kernphysik , universitt kiel , kiel , germany + institute of experimental physics , slovak academy of sciences , koice , slovak republic + school of physics and chemistry , university of lancaster , lancaster , uk + department of physics , university of liverpool , liverpool , uk + queen mary and westfield college , london , uk + physics department , university of lund , lund , sweden + physics department , university of manchester , manchester , uk + cppm , universit daix - marseille ii , in2p3-cnrs , marseille , france + institute for theoretical and experimental physics , moscow , russia + lebedev physical institute , moscow , russia + max - planck - institut fr physik , mnchen , germany + lal , universit de paris - sud , in2p3-cnrs , orsay , france + lpnhe , ecole polytechnique , in2p3-cnrs , palaiseau , france + lpnhe , universits paris vi and vii , in2p3-cnrs , paris , france + institute of physics , czech academy of sciences , praha , czech republic + nuclear center , charles university , praha , czech republic + infn roma and dipartimento di fisica , universita `` la sapienza '' , roma , italy + paul scherrer institut , villigen , switzerland + fachbereich physik , bergische universitt gesamthochschule wuppertal , wuppertal , germany + desy , institut fr hochenergiephysik , zeuthen , germany + institut fr teilchenphysik , eth , zrich , switzerland + physik - institut der universitt zrich , zrich , switzerland + visitor from yerevan phys . inst . , armenia + on leave from lbl , berkeley , usa + supported by the bundesministerium fr forschung und technologie , frg , under contract numbers 6ac17p , 6ac47p , 6do57i , 6hh17p , 6hh27i , 6hd17i , 6hd27i , 6ki17p , 6mp17i , and 6wt87p + supported by the uk particle physics and astronomy research council , and formerly by the uk science and engineering research council + supported by fnrs - nfwo , iisn - iikw + supported by the polish state committee for scientific research , grant nos . 115/e-743/spub / p03/109/95 and 2  p03b  244  08p01 , and stiftung fr deutsch - polnische zusammenarbeit , project no.506/92 + supported in part by usdoe grant de  f603  91er40674 + supported by the deutsche forschungsgemeinschaft + supported by the swedish natural science research council + supported by ga r , grant no . 202/93/2423 , ga av r , grant no . 19095 and ga uk , grant no . 342 + supported by the swiss national science foundation +"}
{"article_id":"1007.5194","section_id":"i","document":"the dynamics of quantum systems under the influence of time - periodic driving fields is a long - standing problem in quantum mechanics @xcite . an extensive review on this topic , covering both non - dissipative and dissipative systems , can be found in ref .  . for a more concise review with an accurate description of the floquet - theoretical method , it is recommended to consult chapter 5 in ref . @xcite .    in the past two decades , the study of driven quantum systems has sparked renewed interest after the discovery of the phenomenon of coherent destruction of tunneling @xcite . in the original work @xcite , the authors considered the problem of a particle moving in a double - well potential and perturbed by a monochromatic driving field . the analysis of the floquet spectrum of the system allowed them to show that , by an appropriate choice of the parameter values of the driving field , the tunneling of the particle through the potential barrier can be brought to a standstill . among the possible applications of this phenomenon , one can mention the laser - induced trapping of an electron in a quantum - well structure @xcite , and the control of proton or electron transfer reactions . recently , the phenomenon of coherent destruction of tunneling has been experimentally verified in an optical double well system @xcite , in a bose - einstein condensate in a strongly driven optical lattice @xcite and in single - particle tunneling in strongly driven double - well potentials @xcite .    in order to clarify the mechanism of coherent destruction of tunneling reported in ref . @xcite , it has turned out to be useful to consider a simplified two - state model @xcite . in this model , all the spatial information contained in the floquet modes is neglected , and only the influence of the lowest quasienergy doublet is taken into account . the study of this approximate two - state model makes it possible to determine simple conditions for the appearance of the phenomenon of coherent destruction of tunneling . for instance , in the high - frequency limit , an averaging procedure shows that this phenomenon occurs when the ratio of the amplitude of the monochromatic driving field to its frequency is a zero of the zeroth - order bessel function of the first kind @xcite . it is worthwhile to point out that the phenomenon of coherent destruction of tunneling in a two - state model resembles that of dynamic localization observed in a driven , infinite tight - binding system @xcite . a discussion of their similarities and differences can be found in sec .  4 of ref .  . recently , the internal relationship between these two phenomena has been clarified in ref . @xcite .    in the last decade , several works have been published which describe alternative approaches , beyond the averaging procedure , for the analytical study of a driven two - state quantum system @xcite . in particular , in refs . @xcite the authors propose a convergent strong - coupling expansion free of secular terms . in refs . @xcite the method is based on dual dyson series and renormalization techniques . finally , in ref . @xcite the author applies a multiple scale expansion in the inverse of the driving frequency for the calculation of the floquet states and the quasienergies . one of the main conclusions of these works is that , for high but finite values of the driving frequency , the coherent destruction of tunneling in a two - state quantum system is only temporary . more precisely , in the high - frequency limit , coherent destruction of tunneling occurs only for time values much smaller than a characteristic time scale proportional to the driving frequency squared . this is a consequence of the fact that the quasienergy degeneracy predicted by the averaging procedure when the ratio of the amplitude of the monochromatic driving field to its frequency is a zero of the zeroth - order bessel function of the first kind is exact only in the mathematical limit of infinite driving frequency . for high but finite values of the driving frequency , there is a quasienergy splitting of the order of the inverse of the driving frequency squared ( see , for instance , ref . @xcite ) .    in the present paper , we take up again the problem of a spin-@xmath0 particle in the presence of a rotating magnetic field , originally studied by rabi  @xcite . this same model has been considered in ref .   to study the suppression of quantum coherence induced by circularly polarized driving fields . as is well known , under the influence of a rotating magnetic field , the dynamics of a spin-@xmath0 particle displays a resonant behavior ( see , for instance , sec . 11.2 of ref . @xcite or the beginning of sec . [ results ] of the present paper ) . in this work , we are interested in analyzing how this resonant behavior is affected by the application of an additional high - frequency magnetic field along the rotation axis . as will be shown in this paper , there is a remarkable similarity between the problem considered here and the problem of coherent destruction of tunneling in a two - state quantum system driven by a monochromatic field . the paper is organized as follows . in the following section , we introduce the model and apply an averaging method to work out an analytical expression for the time evolution operator . in sec . [ mssection ] , we use multiple scale techniques to obtain an improved expression for the time evolution operator which is valid in a wider range of time scales than the one obtained by the previous averaging procedure . in sec . [ results ] , we apply the analytical results in the previous sections to the study of the effects of the high - frequency magnetic field on the dynamics of the system . in particular , we examine in detail its effects on the above mentioned resonant behavior . in that section , we also compare our analytical results with those obtained from the numerical solution of the schrdinger equation . finally , in sec . [ conclusions ] , we present conclusions for the main findings of our work .","summary":"the analytical results achieved by applying these two methods are compared with those obtained from the numerical solution of the schrdinger equation . , the averaging method predicts the complete destruction of the resonant behavior by an appropriate choice of the parameter values of the high - frequency magnetic field .","abstract":"in this paper , we investigate the role of a high - frequency magnetic field in the resonant behavior displayed by a spin- particle under the influence of a rotating magnetic field . we propose two alternative methods for analyzing the system dynamics , namely , the averaging method and the multiple scale method . the analytical results achieved by applying these two methods are compared with those obtained from the numerical solution of the schrdinger equation . this comparison leads to the conclusion that the multiple scale method provides a better understanding of the system dynamics than the averaging method . in particular , the averaging method predicts the complete destruction of the resonant behavior by an appropriate choice of the parameter values of the high - frequency magnetic field . this conclusion is disproved both by the numerical results , and also by the results obtained from the multiple scale method .    coherent destruction of tunneling , resonant behavior , spin- particle , rotating magnetic field , high - frequency fields , two - state systems"}
{"article_id":"1007.5194","section_id":"r","document":"we begin this section with a brief description of the resonant behavior displayed by a spin-1/2 particle under the influence of the rotating magnetic field in eq . ( [ mf ] ) , when the high - frequency magnetic field in eq . ( [ hff ] ) is absent ( i.e. , when @xmath60 ) . then , according to eqs . ( [ defthetadet ] ) and ( [ thamiltonian ] ) , the hamiltonian @xmath247 becomes time independent and equal to @xmath248.\\ ] ] taking into account eqs . ( [ utransformation ] ) and ( [ evolutionoperator2 ] ) , the time evolution operator will be then given by @xmath249    henceforth , we will be interested in studying the time dependence of the expected value of @xmath250 . if we take as initial condition an arbitrary state @xmath18 , this expected value can easily be evaluated from the time evolution operator by using the expression @xmath251 let us assume that we take as initial condition @xmath252 , with @xmath253 being the eigenvectors of @xmath250 corresponding to the eigenvalues @xmath254 . then , from eqs . ( [ tevolutionoperator0 ] ) and ( [ expforexpvalsigz ] ) , together with eqs . ( [ rotation1 ] ) and ( [ rotation2 ] ) with @xmath65 replaced by @xmath255 and @xmath130 by @xmath40 , it is easy to see that @xmath256\\right\\},\\ ] ] where @xmath257 and @xmath258 .    from the exact expression ( [ expvalsigma0 ] ) one can see that , in the absence of the high - frequency magnetic field , @xmath259 is a periodic function of time of period @xmath260 . the average of this function over a period is @xmath261 , and the amplitude of the oscillations is given by @xmath262 this amplitude as a function of @xmath263 displays a resonant behavior with a maximum at @xmath161 . this behavior is depicted with a solid line in fig . [ resonance1 ] for the case @xmath264 .     for @xmath264 and @xmath60 , @xmath265 and @xmath266 . solid line : exact result for the case @xmath60 obtained from eq . ( [ amplitude0 ] ) . dashed and dotted lines : analytical results obtained from eq . ( [ amplitudernonzero ] ) for @xmath267 ( dashed line ) and @xmath268 ( dotted line ) . symbols : results obtained from the numerical solution of eqs . ( [ evolutionoperator1])-([hamiltonian ] ) , and the use of eq . ( [ expforexpvalsigz ] ) with @xmath269 . the parameter values of the high - frequency magnetic field used in the numerical calculations are : @xmath270 , @xmath271 , @xmath267 ( crosses ) and @xmath268 ( pluses ) . ]    when the high - frequency magnetic field is present , we do not have an exact expression for the time evolution operator and have to resort to eqs . ( [ amsolution2 ] ) or ( [ mssolution ] ) , depending on whether one uses the averaging method or the multiple scale method . let us consider first the case in which @xmath203 is not a zero of @xmath67 , so that @xmath145 . then , from eqs . ( [ effhamiltonian ] ) , ( [ amsolution2 ] ) and ( [ expforexpvalsigz ] ) , together with eqs .  ( [ rotation1 ] ) and ( [ rotation2 ] ) , the averaging method yields @xmath272 ^ 2}{\\omega_{\\mathrm{eff}}^2 } \\left[\\cos(\\omega_{\\mathrm{eff } } t)-1\\right]\\right\\}.\\nonumber\\\\ \\!\\!\\!\\!\\!&&\\!\\!\\!\\!\\!\\end{aligned}\\ ] ]    however , if one uses the multiple scale method , from eqs . ( [ mshamiltoniann0 ] ) and ( [ mssolution ] ) one obtains @xmath273 ^ 2}{\\omega_{\\mathrm{eff}}^2 } \\left[\\cos(\\omega_{\\mathrm{ms } } t)-1\\right]\\right\\},\\nonumber\\\\ \\!\\!\\!\\!\\!&&\\!\\!\\!\\!\\!\\end{aligned}\\ ] ] with the multiple scale frequency @xmath274 notice that both methods lead to the same expression @xmath275 ^ 2}{\\omega_{\\mathrm{eff}}^2}=\\frac{\\left[\\omega_{\\perp}j_0(r)\\right]^2}{(1+\\omega_{\\parallel})^2+\\left[\\omega_{\\perp}j_0(r)\\right]^2}\\ ] ] for the amplitude of the oscillations of the function @xmath259 . according to eq . ( [ amplitudernonzero ] ) , the resonant peak at @xmath161 persists in the presence of a high - frequency magnetic field when @xmath203 is not a zero of @xmath67 . since the width of the peak is related to @xmath276 , the presence of the high - frequency magnetic field gives rise to a narrowing of the resonant peak with respect to the case @xmath60 . these analytical results are shown in fig . [ resonance1 ] for @xmath264 with a dashed line ( @xmath267 ) and a dotted line ( @xmath268 ) . in fig . [ resonance1 ] , we also show the amplitude values obtained from the numerical solution of eqs . ( [ evolutionoperator1])-([hamiltonian ] ) , and the use of eq . ( [ expforexpvalsigz ] ) with @xmath269 . the numerical integration of the differential equation ( [ evolutionoperator1 ] ) has been performed using the function ` ndsolve ` of the software package mathematica with the option ` maxsteps ` @xmath277 . in order to have a well - defined amplitude value , the high - frequency and small - amplitude oscillations observed in the numerical values of @xmath278 have been removed by performing a time average of @xmath278 over a high - frequency period . the parameter values of the high - frequency magnetic field used in the numerical calculations are : @xmath270 , @xmath271 , @xmath267 ( crosses ) and @xmath268 ( pluses ) . notice that there is a very good agreement between the analytical and the numerical results .    although the analytical expressions for @xmath259 obtained by the averaging method [ eq .  ( [ expvalsigmaav ] ) ] and the multiple scale method [ eq .  ( [ expvalsigmams ] ) ] look very similar , there exists a slight difference @xmath279 between the frequencies of the oscillations predicted by both methods . this slight difference becomes important for large values of @xmath40 . in particular , for time scales @xmath280 , the expected values @xmath281 and @xmath282 are @xmath283 radians out of phase with each other . for instance , for @xmath264 , @xmath161 , @xmath267 and @xmath270 , this situation occurs for @xmath284 . to work out this number , we have used the value @xmath285 , obtained numerically from eq . ( [ defgamma1 ] ) , for the calculation of @xmath245 [ see eq . ( [ etadef ] ) ] . the integral appearing in the definition of @xmath286 [ see eq . ( [ defgamma1 ] ) ] has been evaluated numerically using the function ` nintegrate ` of the computer algebra program mathematica .    in fig . [ timebehavior1 ] , it is shown the time dependence of @xmath278 in the intervals @xmath287 $ ] ( upper panel ) and @xmath288 $ ] ( lower panel ) , for the above mentioned parameter values . the results obtained from eq . ( [ expvalsigmaav ] ) ( averaging method ) have been plotted with dashed lines , and those obtained from eq . ( [ expvalsigmams ] ) ( multiple scale method ) with solid lines . we also depict with crosses the results obtained from the numerical solution of eqs . ( [ evolutionoperator1])-([hamiltonian ] ) ( for @xmath271 ) , and the use of eq . ( [ expforexpvalsigz ] ) with @xmath269 . for short time scales ( upper panel ) , both the averaging and the multiple scale methods agree very well with the numerical results . in fact , the dashed line is completely hidden by the solid one . nevertheless , in the time interval @xmath289 $ ] only the multiple scale method reproduces the numerical results , whereas the averaging method predicts a time dependence which is approximately @xmath283 radians out of phase with respect to these ones .     in the time intervals @xmath290 $ ] ( upper panel ) and @xmath291 $ ] ( lower panel ) . dashed lines : analytical results obtained from eq . ( [ expvalsigmaav ] ) ( averaging method ) . solid lines : analytical results obtained from eq . ( [ expvalsigmams ] ) ( multiple scale method ) . crosses : results obtained from the numerical solution of eqs . ( [ evolutionoperator1])-([hamiltonian ] ) , and the use of eq . ( [ expforexpvalsigz ] ) with @xmath269 . the parameter values are : @xmath264 , @xmath161 , @xmath267 , @xmath270 and @xmath271 . in the upper panel the dashed line is hidden by the solid line . ] now let us consider the case in which @xmath203 is equal to one of the zeros of the bessel function @xmath67 , for instance , the @xmath229-th zero @xmath228 . if we also assume that @xmath292 , it is easy to see that eqs . ( [ expvalsigmaav ] ) and ( [ expvalsigmams ] ) remain valid , since the condition that @xmath145 still holds . consequently , from eqs . ( [ expvalsigmaav ] ) and ( [ expvalsigmams ] ) one obtains that @xmath293 for @xmath227 and @xmath292 .    for @xmath227 and @xmath294 the averaging and the multiple scale methods lead to different expressions for @xmath295 . if one uses the averaging method and takes into account eqs . ( [ amsolution2 ] ) and ( [ expforexpvalsigz ] ) , the result is @xmath296 , since the effective hamiltonian in eq . ( [ effhamiltonian ] ) vanishes when @xmath227 and @xmath294 . by contrast , if one uses the multiple scale method and takes into account that for these parameter values @xmath160 , from eqs . ( [ mshamiltonian0 ] ) and ( [ mssolution ] ) one obtains @xmath297 with the multiple scale frequency @xmath298    from these results one concludes that , for @xmath227 , the averaging method predicts that @xmath299 for all the values of @xmath263 and , consequently , the complete disappearance of the resonant behavior . by contrast , the multiple scale method predicts that @xmath300 i.e. , the resonant peak at @xmath294 persists but its width becomes zero . this last behavior is depicted in fig . [ resonance2 ] with a dashed line . in fig . [ resonance2 ] , we also show with crosses the amplitude values obtained numerically , by the numerical procedure described previously , for the parameter values @xmath264 , @xmath301 , @xmath270 and @xmath271 . the numerical results highlight the existence of an extremely narrow peak around @xmath161 and , consequently , confirm the prediction made by the multiple scale method . nevertheless , the multiple scale method is not able to explain the finite width of the resonant peak observed in the numerical results shown in fig . [ resonance2 ] . this fact shows up the inability of the analytical expression in eq . ( [ simazavmsrnonzero ] ) to describe properly the time behavior of @xmath295 in a small neighborhood around @xmath161 . this inability is not surprising if one takes into account that the expression for @xmath302 in eq . ( [ simazavmsrnonzero ] ) does not converge to the result in eq . ( [ msexpvalsigzrzero ] ) in the limit @xmath303 . in order to avoid this discontinuity , we suspect that it is necessary to extend the multiple scale method described in sec . [ mssection ] to a larger number of time scales .     for @xmath301 [ first zero of the bessel function @xmath67 ] . dashed line : analytical results obtained by the multiple scale method [ eq .  ( [ mswidthzero ] ) ] . crosses : numerical results obtained following the same procedure as in fig . [ resonance1 ] . the parameter values used in the numerical calculations are : @xmath264 , @xmath270 and @xmath271 . the scale of abscissa has been magnified with respect to fig . [ resonance1 ] in order to make visible the finite width of the resonant behavior observed numerically . ]    to illustrate this point , in fig . [ timebehavior2 ] it is shown the time dependence of @xmath278 for @xmath301 and five values of @xmath263 around @xmath161 . the rest of the parameter values are : @xmath264 , @xmath270 and @xmath271 . the analytical results obtained using the averaging method [ i.e. , eq . ( [ simazavmsrnonzero ] ) for all the values of @xmath263 ] are plotted with dashed lines , and those obtained from the multiple scale method [ i.e. , eq . ( [ simazavmsrnonzero ] ) for @xmath292 , and eq .  ( [ msexpvalsigzrzero ] ) for @xmath161 ] with solid lines . we also show with symbols the results obtained numerically . in the upper panel , it is considered the case @xmath307 . in this case , the value of @xmath263 is not too close to the resonant value @xmath161 , and both the averaging and the multiple scale methods reproduce properly the numerical results depicted by crosses . in the middle panel , it is considered the cases @xmath308 ( pluses ) , @xmath309 ( circles ) and @xmath310 ( triangles ) . as @xmath263 gets closer to the resonant value @xmath161 , the disagreement between the analytical results in eq . ( [ simazavmsrnonzero ] ) and the numerical ones becomes more pronounced , and the numerical results converge gradually to the multiple scale solution in eq . ( [ msexpvalsigzrzero ] ) . since the averaging and the multiple scale solutions coincide when @xmath292 [ see eq . ( [ simazavmsrnonzero ] ) ] , the dashed lines are hidden by the solid lines in the upper and middle panels . finally , in the lower panel it is shown the case @xmath161 . in this case , only the multiple scale expression in eq . ( [ msexpvalsigzrzero ] ) is able to reproduce the numerical results depicted by squares . to calculate the multiple scale frequency in eq . ( [ msfrequencyrzero ] ) , we have used the value @xmath311 , which has been obtained numerically from eq . ( [ defgamma1j ] ) using the function ` nintegrate ` of the program mathematica .     for @xmath301 [ first zero of the bessel function @xmath67 ] and five values of @xmath263 around @xmath161 . the rest of the parameter values are : @xmath264 , @xmath270 and @xmath271 . dashed lines : analytical results obtained from eq . ( [ simazavmsrnonzero ] ) for all the values of @xmath263 ( averaging method ) . solid lines : analytical results obtained from eq . ( [ simazavmsrnonzero ] ) for @xmath292 , and eq .  ( [ msexpvalsigzrzero ] ) for @xmath294 ( multiple scale method ) . symbols : numerical results . upper panel : @xmath307 ( crosses ) . middle panel : @xmath308 ( pluses ) , @xmath309 ( circles ) and @xmath310 ( triangles ) . lower panel : @xmath161 ( squares ) . in the upper and middle panels the dashed lines are hidden by the solid lines . ] we finish this section with a brief discussion of the role played by the phase shift @xmath312 between @xmath26 and @xmath27 in the system dynamics . since the frequencies @xmath159 , @xmath313 and @xmath314 do not depend on @xmath312 , the analytical results obtained up to now in this section are also independent of this parameter . as we shall see below , this is so due to the initial conditions considered , namely @xmath252 . in the numerical results , the value of @xmath312 affects only slightly the high - frequency and small - amplitude oscillations observed in @xmath259 ( see fig . [ timebehavior3 ] ) .     for @xmath161 , @xmath264 , @xmath270 , @xmath301 [ first zero of the bessel function @xmath67 ] , @xmath271 ( upper panel ) and @xmath315 ( lower panel ) . dashed line : analytical results obtained by the multiple scale method [ eq .  ( [ msexpvalsigzrzero ] ) ] . solid lines : numerical results . ] a more interesting situation arises when one considers an arbitrary initial condition of the form @xmath316 $ ] and @xmath317 . in this case , it is straightforward to see from eqs . ( [ mssolution ] ) and ( [ expforexpvalsigz ] ) that , if we write explicitly the dependence of the expected value of @xmath17 on the parameters @xmath312 and @xmath318 , it results that @xmath319 where @xmath320 . that is , in order to calculate the expected value of @xmath17 by the multiple scale method , a high - frequency magnetic field with a phase shift @xmath312 can be replaced by another one with a phase shift equal to @xmath321 , if the phase @xmath318 of initial state is also replaced by another value @xmath320 . from eqs . ( [ amsolution2 ] ) and ( [ expforexpvalsigz ] ) , it is easy to see that this result also holds if one uses the averaging method .    as an example of this property , let us consider the case in which @xmath227 and @xmath161 . for these parameter values , the effective hamiltonian in eq . ( [ effhamiltonian ] ) vanishes and , consequently , from eqs . ( [ amsolution2 ] ) , ( [ expforexpvalsigz ] ) and ( [ ic1 ] ) , the averaging method yields @xmath322 which is independent of @xmath312 and @xmath318 . by contrast , if one uses the multiple scale method , from eqs . ( [ mshamiltonian0 ] ) , ( [ mssolution ] ) , ( [ expforexpvalsigz ] ) and ( [ ic1 ] ) , one obtains @xmath323 which depends on @xmath312 and @xmath318 through @xmath324 .    in order to compare these analytical expressions with the numerical results , in fig . [ timebehavior4 ] it is shown the time dependence of @xmath325 for the following parameter values : @xmath161 , @xmath264 , @xmath270 and @xmath301 . in the upper panel , it is considered a phase shift @xmath271 and an initial condition of the form ( [ ic1 ] ) with @xmath326 and @xmath327 . in the lower panel , it is assumed a phase shift @xmath315 and the same initial condition as before but with @xmath328 . according to eq . ( [ msarbitraryis ] ) , the multiple scale method leads to the same conclusion in both panels ( solid lines ) . the analytical results obtained using the averaging method [ eq . ( [ avarbitraryis ] ) ] are plotted with dashed lines . we also show with crosses the results obtained numerically . once again , only the multiple scale method is able to reproduce the numerical results , with exception of the high - frequency and small - amplitude oscillations .     for @xmath161 , @xmath264 , @xmath270 , @xmath301 [ first zero of the bessel function @xmath67 ] and an initial condition of the form ( [ ic1 ] ) with @xmath326 . upper panel : @xmath271 and @xmath327 . lower panel : @xmath315 and @xmath328 . dashed lines : analytical results obtained from eq . ( [ avarbitraryis ] ) ( averaging method ) . solid lines : analytical results obtained from eq . ( [ msarbitraryis ] ) ( multiple scale method ) . crosses : numerical results . ]","summary":"in this paper , we investigate the role of a high - frequency magnetic field in the resonant behavior displayed by a spin- particle under the influence of a rotating magnetic field . this conclusion is disproved both by the numerical results , and also by the results obtained from the multiple scale method .   ","abstract":"in this paper , we investigate the role of a high - frequency magnetic field in the resonant behavior displayed by a spin- particle under the influence of a rotating magnetic field . we propose two alternative methods for analyzing the system dynamics , namely , the averaging method and the multiple scale method . the analytical results achieved by applying these two methods are compared with those obtained from the numerical solution of the schrdinger equation . this comparison leads to the conclusion that the multiple scale method provides a better understanding of the system dynamics than the averaging method . in particular , the averaging method predicts the complete destruction of the resonant behavior by an appropriate choice of the parameter values of the high - frequency magnetic field . this conclusion is disproved both by the numerical results , and also by the results obtained from the multiple scale method .    coherent destruction of tunneling , resonant behavior , spin- particle , rotating magnetic field , high - frequency fields , two - state systems"}
{"article_id":"1007.5194","section_id":"c","document":"we have studied how the resonant behavior displayed by a spin-@xmath0 particle under the influence of a rotating magnetic field is affected by the application of an additional high - frequency magnetic field along the rotation axis . analytical expressions for the time evolution operator and the expected value of @xmath17 have been obtained by using two alternative methods , namely , the averaging method and the multiple scale method . when the ratio of the strength of the high - frequency magnetic field to its frequency ( in dimensionless units ) is not a zero of the bessel function @xmath67 , both methods lead to the same conclusion about the effect of the high - frequency magnetic field on the resonant behavior . specifically , its presence only gives rise to a narrowing of the resonant peak . by contrast , when this ratio coincides with a zero of @xmath67 , both methods lead to different predictions . more precisely , the averaging method predicts the complete disappearance of the resonant behavior , whereas according to the multiple scale method the resonant peak persists but its width becomes zero . this discrepancy in the conclusions of both methods is similar to the one appearing in the study of the phenomenon of coherent destruction of tunneling . there , the averaging method predicts the complete destruction of tunneling , whereas other more accurate methods , among them the multiple scale method , conclude that this destruction is only temporary . in our case , the numerical results show up the existence of an extremely narrow resonant peak and , consequently , confirm the prediction made by the multiple scale method . an open problem which arises in this context is how to extend the multiple scale method proposed in this paper in order to explain the finite width of the resonant peak observed in the numerical solution . comparison of the analytical results for the expected value of @xmath17 with the numerical ones shows that the multiple scale method also allows a better description of the time evolution than the averaging method , above all in the long - time limit . finally , we have studied the role played by the phase shift between the high - frequency and the rotating magnetic fields in the system dynamics . from this study it follows that a modification of this phase shift is basically equivalent to a change in the phase of the initial state .","summary":"we propose two alternative methods for analyzing the system dynamics , namely , the averaging method and the multiple scale method . this comparison leads to the conclusion that the multiple scale method provides a better understanding of the system dynamics than the averaging method . in particular coherent destruction of tunneling , resonant behavior , spin- particle , rotating magnetic field , high - frequency fields , two - state systems","abstract":"in this paper , we investigate the role of a high - frequency magnetic field in the resonant behavior displayed by a spin- particle under the influence of a rotating magnetic field . we propose two alternative methods for analyzing the system dynamics , namely , the averaging method and the multiple scale method . the analytical results achieved by applying these two methods are compared with those obtained from the numerical solution of the schrdinger equation . this comparison leads to the conclusion that the multiple scale method provides a better understanding of the system dynamics than the averaging method . in particular , the averaging method predicts the complete destruction of the resonant behavior by an appropriate choice of the parameter values of the high - frequency magnetic field . this conclusion is disproved both by the numerical results , and also by the results obtained from the multiple scale method .    coherent destruction of tunneling , resonant behavior , spin- particle , rotating magnetic field , high - frequency fields , two - state systems"}
{"article_id":"astro-ph9901027","section_id":"i","document":"uv observations of euv - detected stars have revealed the presence of about 15 hot white dwarf companions to bright stars in non - interacting binary systems ( e.g. , burleigh , barstow , & fleming 1997 ) . at optical wavelengths , these wds are hidden because of their close proximity to much more luminous companions which are main sequence ( spectral type k or earlier ) or evolved stars . a fascinating variety of objects are known or proposed to contain white dwarf ( wd ) stars in interacting binary systems . a partial list includes novae , cataclysmic variables , symbiotic stars , ba and ch giants , feige  24-type systems and dwarf carbon stars ( green & margon 1994 ) . these systems offer great insights to evolution and dynamical processes in binaries . a number of interacting binary systems where the white dwarf is the primary ( i.e. , optically brightest ) star have also been found among euv - detected systems ( e.g. , 6 close , interacting white dwarf / red dwarf binaries by vennes & thorstensen 1994 ) . optical or ultraviolet spectral observations are most commonly used to detect companions to wd primaries , by searching for ( 1 ) the presence of narrow balmer line emission overlying the broad smooth balmer absorption of the wd , ( 2 ) a composite white dwarf + main sequence spectrum , or ( 3 ) radial velocity ( rv ) variations . however , only wds with very close , or intrinsically active companions will be found by method ( 1 ) . for hot white dwarf systems , composite spectra ( 2 ) are only expected to be visible if the companion s spectral type is early enough . rv variations ( 3 ) require multiple observations at high spectral resolution , and detection strongly favors close and/or massive companions . all the discoveries mentioned above have been strongly dominated by these selection effects , with companions biased to earlier types than predicted by the simulations of dekool & ritter ( 1993 ) and others . scaling from dekool & ritter s results , vennes & thorstensen ( 1994 ) estimate that `` at least twice as many close binary systems remain to be identified from euv surveys , most of them with a low mass secondary . '' the resulting sample of binaries known to date therefore must diverge strongly from the intrinsic distribution , in overall normalization , as well as in mass and spectral type of the main sequence companions .    the current study , conceived as a complement to optical studies , began as a near - ir photometric survey for low mass companions to hot white dwarfs ( wds ) . by investigating only euv - detected wds , we obtain a very reasonably - sized but complete sample of young wds , next to which very late - type dwarf companions can be detected in the near - infrared by searching for a @xmath1 excess over that expected from the white dwarf . many hot white dwarfs ( @xmath2k ; finley et al . 1993 ) have been detected in the recent euv all - sky surveys . euv detection of these hot wds depends primarily on their temperature , distance , and the intervening galactic ism . our sample of euv wds ( whose selection we define below ) offers excellent flux contrast in the ir relative to optical ; cool companions will almost always be brighter in the @xmath1 band than the hot wds .    to know what @xmath1 mag to expect for the wds , we benefit from constraints on log@xmath3 , radius , and @xmath4 derivable from optical spectra for the wds in our sample , using nlte model atmosphere fits ( napiwotzki et al .  1993 , napiwotzki 1997 ) . the resulting predictions for @xmath1 magnitudes allow a direct search for any ir excess from a cool companion . in some cases , ir colors will also provide a preliminary spectral type . results from the ir survey will be presented in an upcoming paper . an additional motivation is the study of the white dwarf mass distribution . since the pioneering work of koester , schulz & weidemann ( 1979 ; ksw ) it is well established that the masses of white dwarfs cluster in a narrow range around @xmath5 , remarkable given that white dwarfs stem from progenitors with masses ranging from below @xmath6 up to @xmath7@xmath8 . precise knowledge of the white dwarf mass distribution puts constraints on the theory of stellar evolution , especially the poorly understood mass loss process during the final stages of stellar evolution . with two recent exceptions ( beauchamp et al . 1996 and dreizler & werner 1996 , who analyzed samples of helium - rich db and do white dwarfs , respectively ) the mass distribution has only been determined for hydrogen - rich da white dwarfs . however , this is not a severe limitation , because this spectral class comprises about 80% of all known white dwarfs . the analysis of ksw , along with other follow - up investigations in the early eighties , used photometric data of which the strmgren and greenstein multichannel colors were the most suitable . both systems provide temperature- and gravity - sensitive indices . alternatively , ksw and others used trigonometric parallax measurements to directly calculate the stellar radius . however , the latter method is practical only for a small sample and suffers from considerable measurement uncertainty . unfortunately , the photometric indices have their highest sensitivity near 10000k . at this temperature da white dwarfs have a convective atmosphere and the results depend critically on the adopted parameters of mixing length theory . the situation improved at the beginning of the nineties , when the development of modern , highly efficient detectors made it possible to obtain high - quality spectra of large numbers of white dwarfs and determine the stellar parameters from a fit to the detailed profiles of the balmer lines . this method yields sufficient accuracy for white dwarfs hot enough to have a radiative envelope . the first comprehensive sample of white dwarfs analyzed by this method was presented by bergeron , saffer & liebert ( 1992 ; hereafter bsl ) . as attributed to higher precision of spectroscopic methods , this investigation yielded a white dwarf mass distribution even narrower than found by ksw and other previous studies . at the same time , kidder ( 1991 ) analyzed a sample of hot da white dwarfs discovered through positional coincidences of catalogued hot da white dwarfs in existing soft x - ray databases . three soft x - ray sources corresponding to white dwarfs were found , having relatively low effective temperatures , @xmath925,000k , determined independently using complementary optical and uv spectroscopy . kidder et al . ( 1992 ) analyzed an expanded sample to derive photospheric he abundances for the hotter objects and establish an effective observational low - temperature threshold for the detection of pure hydrogen da white dwarfs at soft x - ray wavelengths .    in 1997 three groups ( marsh et al . 1997 , m97 ; vennes et al . 1997 , v97 ; finley , koester & basri 1997 , fkb ) published results on the mass distribution of extreme ultraviolet ( euv ) selected white dwarfs . due to the selection criterion , these samples contain the hottest white dwarfs ( @xmath10@xmath11k ) , as cooler white dwarfs do not emit significant euv radiation . the derived mass distributions in the euv - selected samples are similar to that of bsl , but show some interesting deviations in detail . the frequency of very high mass white dwarfs is much larger , and that of very low mass white dwarfs much smaller , than in bsl . these findings can at least partly be explained by selection effects ( see the discussion in fkb ) . more serious is a trend of the peak mass with temperature . v97 found that their mass distribution peaks at @xmath12 , while the bsl distribution peaks at @xmath13 , with masses computed using wood s ( 1995 ) mass - radius relation with `` thick '' layers ( @xmath14 , @xmath15 ) . this discrepancy diminishes slightly , if the `` very thin layer '' ( @xmath16 , no hydrogen layer ) mass - radius relations are used ( peak masses of @xmath17 and @xmath18 for the v97 and bsl sample , respectively ) . v97 interpreted this as evidence for a very thin hydrogen layer of the da white dwarfs . however , the effects are small so this result depends strongly on the accuracy of the derived stellar parameters . fkb estimated the internal accuracy of different analysis methods from monte carlo simulations . the precision reachable by balmer line fitting is very compelling : @xmath19 @xmath10/ @xmath10@xmath20 for @xmath10@xmath21k . however , for spectra with very high signal - to - noise ratios ( s / n ) , errors introduced by details of the observation and reduction techniques ( e.g. , extraction , flat fielding , flux and wavelength calibration ) might be more important , but are very difficult to determine . additionally , one has to take into account differences in the model atmosphere calculations and fitting procedure . together with the results presented in this paper , we now have four samples of hot white dwarfs , analyzed in a similar way , and with significant overlap . this offers the opportunity to determine the real accuracy of the spectral analysis of hot white dwarfs , including many possible systematic effects . we present the selection criteria of our sample in sect .  2 and the observations and data reduction procedures in sect . details on our model atmospheres are given in sect . the results and a detailed comparison with the previous analyses of euv selected white dwarfs are presented in sect . we finish with a discussion of our results and an outlook .","summary":"we present new determinations of effective temperature , surface gravity , and masses for a sample of 46 hot da white dwarfs selected from the euve and rosat wide field camera bright source lists in the course of a near - ir survey for low mass companions . the structure of very hot or low mass white dwarfs depends sensitively on their history . however , we do not confirm a trend of peak mass with temperature reported in two previous analyses .    this feature very likely results from a decreased relative sample volume for low mass white dwarfs caused by interstellar absorption in euv selected samples .","abstract":"we present new determinations of effective temperature , surface gravity , and masses for a sample of 46 hot da white dwarfs selected from the euve and rosat wide field camera bright source lists in the course of a near - ir survey for low mass companions . our analysis , based on hydrogen nlte model atmospheres , provides a map of lte correction vectors , which allow a thorough comparison with previous lte studies . we find previous studies underestimate both the systematic errors and the observational scatter in the determination of white dwarf parameters obtained via fits to model atmospheres .    the structure of very hot or low mass white dwarfs depends sensitively on their history . to compute white dwarf masses , we thus use theoretical mass - radius relations that take into account the complete evolution from the main sequence . we find a peak mass of our white dwarf sample of , in agreement with the results of previous analyses . however , we do not confirm a trend of peak mass with temperature reported in two previous analyses .    analogous to other euv selected samples , we note a lack of low mass white dwarfs , and a large fraction of massive white dwarfs . only one white dwarf is likely to have a helium core . while the lack of helium white dwarfs in our sample can be easily understood from their high cooling rate and therefore low detection probability in our temperature range , this is not enough to explain the large fraction of massive white dwarfs . this feature very likely results from a decreased relative sample volume for low mass white dwarfs caused by interstellar absorption in euv selected samples ."}
{"article_id":"astro-ph9901027","section_id":"r","document":"atmospheric parameters of our da white dwarfs are obtained by simultaneously fitting line profiles of the observed balmer lines with the nlte model spectra described above . we use the least - square algorithm described in bsl . the observed and theoretical balmer line profiles are normalized to a linear continuum ( both spectra are @xmath43 ) in a consistent manner . wavelength shifts are determined with a cross - correlation method and applied consistently to each complete spectrum . the synthetic spectra are convolved to the observational resolution with a gaussian and interpolated to the actual parameters with bicubic splines , and interpolated to the observed wavelength scale . the atmospheric parameters @xmath10 and @xmath44 are then determined by minimizing the @xmath45 value by means of a levenberg - marquardt steepest descent algorithm ( press et al . several tests revealed that our interpolation routine is rather robust concerning spacing of our model grid and yields reliable results even at the edge of the model grid . finally , an estimate of the internal errors can be derived from the covariance matrix . in contrast to bsl , we estimate the noise of the spectra ( @xmath46 ) used for the @xmath45 fit from the neighboring continuum of each line . the s / n is adopted to be constant throughout the line . rlr@@xmath47lr@@xmath47lrl 0007 + 331 & gd2 & 46493&514 & 7.83&0.05 & 0.602 & 6 jan 1996 + 0134@xmath25160&gd984 , phl1043&44866&667 & 7.77&0.05 & 0.572 & 5 jan 1996 + 0237@xmath25122 & phl1400 & 32077&177 & 8.45&0.04 & 0.890 & 5 jan 1996 + 0348@xmath25005 & gd50 & 39508&464 & 9.07&0.06 & 1.215 & 4 jan 1996 + 0427 + 740 & & 48587&1044 & 7.93&0.08 & 0.646 & 5 jan 1996 + 0457@xmath25280 & mct0455@xmath252812&51199&786 & 7.72&0.05 & 0.570 & 4 jan 1996 + 0512@xmath25004 & & 31733&139 & 7.40&0.03 & 0.458 & 5 jan 1996 + 0521@xmath25102 & & 33186&301 & 8.60&0.06 & 0.980 & 5 jan 1996 + 0841 + 032 & & 38293&252 & 7.75&0.03 & 0.544 & 4 jan 1996 + 0902@xmath25040 & & 23218&160 & 7.84&0.02 & 0.544 & 4 jan 1996 + 0907 + 505 & pg0904 + 511 & 32167&338 & 8.11&0.07 & 0.695 & 4 jan 1996 + 0940 + 502 & pg0937 + 506 & 36034&283 & 7.69&0.04 & 0.519 & 9 apr 1997 + 0957 + 852 & & 51311&1348 & 8.37&0.10 & 0.866 & 5 jan 1996 + 1019@xmath25140 & & 31524&102 & 7.92&0.02 & 0.606 & 9 apr 1997 + 1029 + 450 & pg1026 + 454 & 35518&247 & 7.70&0.04 & 0.520 & 9 apr 1997 + 1032 + 532 & & 43587&506 & 7.95&0.05 & 0.644 & 4 jan 1996 + 1033@xmath25114 & g162@xmath2566 , ltt3870 & 24685&252&7.85&0.03 & 0.553 & 4 jan 1996 + 1036 + 460 & gd123 & 29361&251 & 8.02&0.05 & 0.648 & 4 jan 1996 + 1043 + 490 & & 41132&1178 & 7.94&0.13 & 0.635 & 5 jan 1996 + 1044 + 574 & pg1041 + 580 & 30338&153 & 7.81&0.03 & 0.550 & 4 jan 1996 + 1100 + 713 & pg1057 + 719 & 41104&814 & 7.84&0.09 & 0.593 & 4 jan 1996 + 1112 + 240 & ton61 & 39824&636 & 7.78&0.07 & 0.563 & 5 jan 1996 + 1122 + 434 & pg1120 + 439 & 26996&151 & 8.31&0.02 & 0.803 & 9 apr 1997 + 1126 + 183&pg1123 + 189 & 54334&1983 & 7.76&0.13 & 0.594 & 4 jan 1996 + 1128@xmath25025 & pg1125@xmath25026 & 30699&380 & 8.24&0.08 & 0.767 & 4 jan 1996 + 1148 + 183 & pg1145 + 188 & 25758&299 & 7.91&0.04 & 0.587 & 4 jan 1996 + 1235 + 233&pg1232 + 238 & 46569&523&7.83&0.05 & 0.602 & 11 + 12 may 1996 + 1257 + 220&gd153 & 38926&142 & 7.78&0.02 & 0.560 & 4 jan 1996 , 12 may 1996 + 1336 + 694 & pg1335 + 701 & 29607&87 & 8.34&0.02 & 0.824 & 10 may 1996 + 1431 + 370 & gd336 & 34404&115 & 7.91&0.02 & 0.608 & 11 may 1996 + 1446 + 632 & & 37947&254 & 7.79&0.04 & 0.562 & 11 may 1996 + 1629 + 780 & & 41043&338 & 7.92&0.04 & 0.627 & 11 may 1996 + 1638 + 350 & pg1636 + 351 & 35404&142 & 7.98&0.02 & 0.642 & 10 may 1996 + 1643 + 411&pg1642 + 414 & 28815&81&8.22&0.02 & 0.753 & 9 may 1996 + 1650 + 403 & & 38144&211 & 7.97&0.03 & 0.643 & 9 may 1996 + 1711 + 664 & & 48989&757&8.89&0.06 & 1.141 & 12 may 1996 , 9 apr 1997 + 1726 + 583&pg1725 + 586 & 53561&542&8.23&0.04 & 0.795 & 9 may 1996 + 1800 + 683 & kuv18004 + 6836&44723&424 & 7.80&0.04 & 0.585 & 10 may 1996 + 1820 + 580 & & 44099&264 & 7.78&0.03 & 0.574 & 9 may 1996 + 1845 + 682 & kuv18453 + 6819&36120&189 & 8.23&0.03 & 0.770 & 10 may 1996 + 2116 + 735&kuv21168 + 7338 & 50812&354&7.72&0.03 & 0.569 & 5 jan 1996 , 9 may 1996 + 2207 + 252 & & 26964&174 & 8.27&0.03 & 0.779 & 5 jan 1996 + 2312 + 104 & gd246 & 53088&968 & 7.85&0.07 & 0.624 & 4 jan 1996 +    the results are given in table  [ t : results ] , with illustrative examples shown in fig . [ f : sampleres ] . we adopt , for the moment , the usual practice and indicate in table  [ t : results ] the internal errors estimated from the quality of the @xmath45 fit . however , one should keep in mind that these errors can only serve as lower limits . we will show below ( sect . [ s : comparison ] ) that these formal errors derived from the @xmath45 fit significantly underestimate the real errors . external errors can be estimated from multiple observations and analysis of the same star . we obtained repeat observations for a subsample of 6 stars , for which results are given in table  [ t : repeat ] . the gravity values of all six stars agree within the estimated internal errors . the same is true for four temperature comparisons , too . however , the differences found for rej1650 + 403 and rej2116 + 735 are significantly larger . this is in line with the external errors we estimate from a comparison with the studies of m97 , v97 , and fkb ( see sect .  [ s : comparison ] ) . rr@@xmath47lr@@xmath47lr@@xmath47lr@@xmath47l 1235 + 233 & 46308&837 & 7.85&0.08 & 46737&670 & 7.82&0.06 + 1257 + 220 & 39349&317 & 7.76&0.04 & 38820&159 & 7.78&0.02 + 1643 + 411 & 28813&120 & 8.23&0.02 & 28818&111 & 8.21&0.02 + 1650 + 403 & 37798&245 & 7.94&0.04 & 39126&413 & 8.01&0.05 + 1726 + 583 & 52712&927 & 8.27&0.06 & 54003&669 & 8.20&0.05 + 2116 + 735 & 50131&384 & 7.71&0.03 & 54604&906 & 7.76&0.06 +      five stars in our sample , rej0134 - 160 , rej1036 + 460 , rej1043 + 490 , rej1126 + 183 , and rej1629 + 780 , show clear signs of binarity in the red part of their spectra . two more stars , rej1711 + 664 and rej2207 + 502 , are members of visual binaries . [ [ rej1629780 ] ] rej1629 + 780 : + + + + + + + + + + + +    the red part of the spectrum of rej1629 + 780 is heavily contaminated by a m type main sequence companion . the composite spectrum and the spectrum of the m star after subtracting the white dwarf component are shown in fig . [ f : compspek ] . the characteristic bands of tio are easily recognizable . cataln et al . ( 1995 ) determined a spectral type dm4 . the h@xmath48  and h@xmath49  lines are seen in emission , which indicates a chromospherically active me star . sion et al.(1995 ) detected a flare - like increase of the balmer line emission . the comparison in fig . [ f : compspek ] demonstrates that the blue part ( @xmath50 ) of the white dwarf spectrum is not disturbed by the m dwarf . thus , we excluded h@xmath49  and the core of h@xmath51  from the fit and derived the parameters @xmath10@xmath52k and @xmath53 from h@xmath51  to h@xmath54 . these parameters are in reasonable agreement with the results of cataln et al . ( @xmath10@xmath55k ; @xmath42 ) , who however included h@xmath49 , and kidder ( 1991 ; @xmath10@xmath56k , @xmath57 ) , who fitted lyman-@xmath48 and the balmer lines h@xmath49  and h@xmath51 . [ [ rej1036460-rej1043490-rej1126183 ] ] rej1036 + 460 , rej1043 + 490 , rej1126 + 183 : + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    three more white dwarfs of our observed sample are known binaries ( rej1036 + 460 , rej1126 + 183 : green , schmidt , & liebert 1986 , rej1043 + 490 : schwartz et al . 1995 ) and show red excesses in our spectra : since the h@xmath49  lines of the white dwarfs are contaminated they were excluded from the fit . h@xmath51  and higher balmer lines are virtually uncontaminated . a discussion of these stars and newly discovered binaries will be given in a forthcoming paper . [ [ rej0134 - 160-gd984 ] ] rej0134 - 160 ( gd984 ) : + + + + + + + + + + + + + + + + + + + +    although our spectrum ends at only 5600  a red excess is obvious . subtraction of the theoretical white dwarf flux leaves an m star spectrum . the m dwarf contribution is much smaller than in rej1629 + 780 and we excluded only the cores of h@xmath49  and h@xmath51 , filled in by the balmer line emission , from the fit . bues & aslan ( 1995 ) suspected a hot third component in rej0134 - 160 . however , outside of the h@xmath49  and h@xmath51  cores , the balmer lines are well reproduced by our best fit without any indication of a third component . indeed , a subdwarf component as suggested by bues & aslan ( 1995 ) is almost certainly not present , since its flux would dominate in the blue . [ [ rej1711664 ] ] rej1711 + 664 : + + + + + + + + + + + +    since a late type star is separated from the white dwarf by only @xmath58 , we took care to get an uncontaminated white dwarf spectrum . we obtained a spectrum under good seeing conditions . no excess is present up to the red limit at 8500 . [ [ rej2207252 ] ] rej2207 + 252 : + + + + + + + + + + + +    this white dwarf has a red companion @xmath59 away . schwartz et al . ( 1995 ) estimated spectral type k4v and distance 65pc from its colors . with the parameters from table  [ t : results ] a white dwarf distance of 62pc results . thus it is likely that both stars form a physical pair . the angular separation corresponds to @xmath9500au . two white dwarfs of our sample show zeeman splitting of the balmer line cores , indicative of a magnetic field . rej1659 + 440 ( pg1658 + 441 ) is a well known star , already analyzed by schmidt et al . the discovery of the magnetic nature of rej1440 + 750 ( hs1440 + 7518 ) was announced by dreizler et al . ( 1994 ; note the naming confusion corrected in dreizler et al . 1995 : hs1412 + 6115 should have been hs1440 + 7518 ) . although rej1440 + 750 was analyzed by v97 , they did not remark on its magnetic nature . this is likely due to the lack of coverage of the h@xmath48  line , which displays the most pronounced zeeman effect . flux calibrated spectra of the magnetic white dwarfs are displayed in fig . [ f : magwd ] . the pg1658 + 441 analysis of schmidt et al.(1992 ) resulted in @xmath10@xmath60k and @xmath61 . the magnetic splitting was best reproduced by a 3.5megagauss ( mg ) dipole inclined @xmath62 to the line of sight ( producing a mean surface field strength @xmath63 mg ) . from the linear zeeman effect we estimated a mean magnetic strength of 8 mg for rej1440 + 750 , consistent with the estimate given in dreizler et al . ( 1994 ) . the temperature and gravity of rej1440 + 750 were derived from a fit of the higher balmer lines h@xmath51  to h@xmath54 , which are less affected by the magnetic splitting . results are given in table  [ t : magwd ] supplemented by the schmidt et al . ( 1992 ) fit of pg1658 + 441 . our own fit gave similar results albeit with lower accuracy . our fits of rej1440 + 750 can only provide a rough estimate of the stellar parameters . accurate results can only be expected from a detailed treatment of the magnetic effects . rlr@@xmath47lr@@xmath47lrrl 1440 + 750 & hs1440 + 7518 & 36154&275 & 8.87&0.05 & 1.128 & 7.7 & 10 may 1996 + 1659 + 440&pg1658 + 441 & 30510&200&9.36&0.07 & 1.311 & 2.3 & 10 may 1996 +      we have now presented the results of a homogeneous analysis of a sample of 46 hot , euv selected white dwarfs based on balmer line fitting . three other large samples analyzed with the same method were recently published by m97 , v97 , and fkb . since considerable overlap exists between all four samples , this allows a direct check for systematic errors and the individual scatter on a star by star basis for white dwarfs hotter than 25000k . since in contrast to previous works , our analysis is based on nlte model atmospheres , we applied the correction vectors given in fig . [ f : ltevectors ] to correct for the lte assumption . since for the hottest white dwarfs these corrections become large , while the accuracy of temperature and gravity estimates decreases for both lte and nlte analyses , one should exclude comparison of stars with @xmath10@xmath64k . this does not affect our sample , which has a maximum temperature closer to 54000k . differences ( after correction to nlte ) in @xmath10and @xmath44 between studies for stars in common with m97 , v97 , and fkb are displayed in fig . [ f : diffteff ] as function of @xmath10 . the magnetic white dwarfs and the binaries , which show significant contamination of the white dwarf spectrum by the companion , are excluded . one can now focus on systematic differences between pairs of studies , e.g.  our results ( ngs ) versus fkb ( fkb@xmath25ngs ) , v97@xmath25ngs , m97@xmath25ngs , fkb@xmath25m97 , m97@xmath25v97 , and so on . however , we chose another approach and performed an optimization that simultaneously took into account all values from all stars in common between any samples . in other words , the values given for the systematic differences between our study and the m97 , v97 , and fkb samples form a system for direct transformation between , say , fkb and the three other samples . the running averages computed this way are plotted in fig . [ f : diffteff ] as a solid line . the actual value was computed in 1000k steps for all white dwarfs in the respective temperature intervals @xmath10@xmath65 . although this curve does not represent the best fit to the data plotted in fig . [ f : diffteff ] alone , it is a fairly good representation of the differences computed directly between our measurements and those of m97 , v97 , and fkb . since the distribution is highly non - gaussian with many outliers , as evident in fig . [ f : diffteff ] , we decided to adopt an underlying lorentzian ( or cauchy ) distribution for the optimization . the tails of the cauchy distribution are much larger than that of the corresponding gaussian , yielding a much lower weight for deviant points ( see discussion in press et al . the dotted lines represent the @xmath66 confidence interval _ of the mean _ , computed conservatively from the rms deviations . first , we notice a considerable scatter , larger than expected from the internal error estimates ( see the discussion below ) . if one ignores the hot end , the agreement between the fkb and our temperature scale is good ; differences are below 1% , smaller than the maximum model differences to the koester models ( cf .  sect .  4 ) , which were used by fkb . the same atmospheres are used in m97 , and it is therefore surprising that significant differences with m97 are present . these trends are most likely caused by different reduction and analysis techniques . offsets of the same order are found in our comparison with v97 , where a different lte model atmosphere code is used . although basically the same input physics is included , this might at least partly explain those shifts in @xmath10and @xmath44 . lr@@xmath47lr@@xmath47lr@@xmath47l @xmath10@xmath67k & @xmath250.023&0.006 & 0.032&0.005 & 0.007&0.005 + @xmath68k & @xmath250.013&0.003 & 0.017&0.003 & 0.004&0.003 + @xmath69k & 0.036&0.006 & 0.050&0.006 & 0.046&0.007 + all with @xmath70k&@xmath250.006&0.003&0.024&0.003 & 0.012&0.003 +    lr@@xmath47lr@@xmath47lr@@xmath47l @xmath71k & @xmath250.112&0.017 & @xmath250.001&0.016 & @xmath250.064&0.018 + @xmath68k & @xmath250.086&0.017 & 0.026&0.016 & @xmath250.034&0.016 + @xmath69k & @xmath250.066&0.030 & @xmath250.067&0.026 & @xmath250.062&0.027 + all with @xmath70k&@xmath250.084&0.013&@xmath250.002&0.012 & @xmath250.047&0.012 +    our results are quantified in tables  [ t : dteff ] and  [ t : dlogg ] . we divided the white dwarfs into three groups according to their temperature : a cool group with @xmath72k , a hotter one with @xmath73k , and the hottest considered group with @xmath74k . nlte effects are still negligible in the range of effective temperatures of the two coolest groups . mean shifts and the confidence range of the mean ( computed as described above ) are provided for these groups and the complete sample ( except stars with @xmath75k ) . the shifts discussed above and shown in fig  [ f : diffteff ] are statistically significant and reach values of @xmath95% in @xmath76 in the hottest bin . in @xmath44 the difference between our results and m97 reach @xmath90.1dex for the coolest bin . however , we emphasize that all four analyses are based on state - of - the - art model atmospheres and @xmath45 fitting techniques . since there are no strong arguments to favor or discard one analysis , it seems these are the systematic shifts characteristic of modern analyses of hot white dwarfs . lrr @xmath71k & 0.023 & 0.075 + @xmath68k & 0.023 & 0.101 + @xmath69k & 0.034 & 0.128 + all with @xmath70k & 0.026 & 0.107 +    if we take the systematic shifts into account , we can use the samples to derive estimates of the observational scatter , which can be compared with the internal error estimates . since we have approximately the same scatter for different combinations of the samples , we compute a mean scatter @xmath77 for all possible combinations ( weighted by the number of stars in common ) . for this purpose we correct for the systematic shifts calculated for each of the three @xmath76 bins , whose temperature intervals are given in table  [ t : scatter ] . the individual measurement errors @xmath78 add quadratically , and if we assume that the inherent scatter is the same for all analyses ( and we found no reason to discard this assumption ) , the individual measurement errors can be estimated as @xmath79 . not surprisingly , the smallest scatter is found for the `` cool '' group ( @xmath72k ) with @xmath80% and @xmath81dex . it increases to @xmath82% and @xmath83dex for the hottest bin . this trend is expected from the statistical analysis presented in fkb ( their fig .  1 ) . however , the values are larger by a factor of three or more than the internal parameter errors for a well exposed spectrum ( see e.g.  table  [ t : results ] ) . therefore , we conclude that the accuracy is not limited by the noise for good spectra , and we suggest that other effects , such as details of the extraction or fluxing and normalization procedures , contribute more . considering these systematic uncertainties , the 0.3dex difference between the gravity determinations of fkb and napiwotzki et al . ( 1993 ) for hz43a is only a @xmath84 deviation and therefore not as serious as considered by fkb . once the temperature and gravity of the white dwarfs are known the mass can be determined from theoretical mass - radius relations . the recent investigations of m97 , v97 , and fkb based their interpretation on the model sequences of wood ( 1995 ) . the applied models have h- and he - layer masses of @xmath85 and @xmath86 , respectively ( `` thick layers '' ) and a carbon core . these model sequences are based on a set of pre - white dwarf models with end masses of @xmath87 and @xmath88 computed by kawaler ( see wood 1994 ) . starting models for other masses were constructed by homology transformations . the mass - radius relations we use are based on the evolutionary calculations of blcker ( 1995 ) . these models are calculated _ ab initio _ from the main sequence . the resulting white dwarfs show important differences compared to wood s models . in contrast with the carbon core models widely used for mass determination , the degenerate core contains a mass - dependent mixture of carbon and oxygen ( and trace elements ) . however , note that wood ( 1995 ) also presented some white dwarf sequences with c / o cores . the h- and he - layer masses resulting from evolutionary calculations depend on the stellar mass ( blcker 1995 ; blcker et al . while the canonical thick hydrogen layer mass of @xmath89 is met for a @xmath90 white dwarf , it decreases from several @xmath91 for @xmath92 down to @xmath93 for @xmath94 . this results in a mass - radius relation which is steeper than a relation based on a constant layer mass . consequently , the derived mass distribution will be narrower , if evolutionary layer masses are used . the lower mass limit for a c / o core white dwarf is @xmath95 , the limiting mass for central helium burning in low mass stars ( sweigart et al . thus , white dwarfs with a lower mass possess a helium core . at the current age of the universe he white dwarfs have not been produced by single star evolution , but are the result of binary evolution where the hydrogen - rich envelope was stripped away along the ( first ) red giant branch ( kippenhahn 1967 ; iben & tutukov 1986 ) . we use the recent evolutionary models of he white dwarfs calculated by driebe et al . ( 1998 ) based on this scenario .    the combined tracks of blcker ( 1995 ) and driebe et al . ( 1998 ) cover the mass range @xmath96 to @xmath97 . we supplemented this set with the 1.0 , 1.1 , and @xmath98 carbon core sequences of wood ( 1995 ) with `` thin '' layers . since the hydrogen envelope mass decreases with increasing white dwarf mass in blcker s models , their highest mass models effectively correspond to `` thin layer '' models . since high mass white dwarfs are already close to the zero - temperature configuration , the remaining departures from consistent evolutionary calculations can be ignored for practical purposes .    the position of the analyzed white dwarfs in the temperature / gravity plane is shown in fig . [ f : tracks ] along with the tracks used for the mass determination . the individual white dwarf masses are given in table  [ t : results ] , and the resulting mass distribution is shown in fig . [ f : mass ] . we have also redetermined masses for the bsl sample with the blcker / driebe mass - radius relations and supplement fig . [ f : mass ] with the resulting distribution . our mass distribution possesses the same basic features as found in the euv selected samples of m97 , v97 , and fkb . the sharp peak centered at @xmath99 is in principal agreement with the earlier investigations of ksw , weidemann & koester ( 1984 ) , and bsl , with a sharp falloff towards lower masses , and a less steep decline towards higher masses with a tail of high mass white dwarfs . considering the relatively large observational scatter we found in sect . [ s : comparison ] , the _ underlying _ distribution may be extremely sharp . the mean mass is @xmath100 . however , this value is strongly biased by the few very high mass white dwarfs . we decided to follow the recipe of fkb and fitted the mass peak with a gaussian . although a gaussian is not a good representation of the white dwarf mass distribution , it gives a robust estimate of the peak mass . the fit result is , in principle , dependent on the adopted binning of the mass intervals . however , in some test calculations we found effects exceeding a few @xmath101 only if the bin width was larger than @xmath102 . the values given in this paper were derived by fitting gaussians to virtually unbinned mass distributions ( formal bin width @xmath101 ) . we were concerned by the possibility that the different fraction of low and high mass white dwarfs found in different samples ( see discussion below ) may skew the gaussian fit of the main peak to higher or lower masses . we tested this by fitting the bsl , and fkb and our mass distributions with multi - component gaussians , which fitted the secondary high and low mass peaks separately . we found no deviation higher than @xmath103 in any case and concluded that the single gaussian fit of the main peak yields a rather stable estimate .    with this method , we derived a peak mass of our sample of @xmath104 . we reanalysed the fkb , m97 , and v97 samples with our mass - radius relations . we applied the corrections to nlte and excluded the white dwarfs with temperatures in excess of 70000k . the peaks masses are @xmath105 ( fkb ) , @xmath106 ( m97 ) , and 0.582 ( v97 ) . these differences reflect the systematic differences in @xmath76 and @xmath44 determinations discussed above and probably different selection criteria in the case of fkb .    the probable he core white dwarf rej0512 - 004 is the only object in our sample with a mass below @xmath107 , but four white dwarfs have masses in excess of @xmath108 . the frequency of low and high mass white dwarfs found in our and other euv selected samples is qualitatively different from that found in optically selected samples such as bsl . bsl detected in their sample of 129 white dwarfs 16 objects with masses below the limiting mass for c / o core white dwarfs and a total of 28 white dwarfs with @xmath109 . these numbers are reduced to 10 and 16 respectively , if we redetermine the masses with the mass - radius relations of blcker ( 1995 ) and driebe et al . ( 1998 ) . however , that is still a much higher fraction than we find in our euv selected sample .      why do optical and euv selected samples contain different fractions of high and low mass white dwarfs ? all helium white dwarfs from the bsl sample have temperatures below 30000k ; the only helium white dwarf candidate in our sample has @xmath11032000k . this implies that the detection probability of low mass white dwarfs in euv selected samples is much lower , because the fraction of low mass white dwarfs at higher @xmath76 is much lower than it is for @xmath71k . this viewpoint is supported by the helium white dwarf sequences calculated by driebe et al . we have plotted the variation of temperatures with time for white dwarfs with helium and c / o cores in fig . [ f : tevol ] . the detection probability in a given evolutionary stage goes as the inverse of the rate of temperature decrease at that stage . new he white dwarfs cool down rapidly to a certain ( mass dependent ) temperature , whereafter the cooling rate drops drastically and the star remains on a temperature plateau for a long time . this behavior is most pronounced for the lowest masses . hydrogen shell burning plays an important role for this plateau phase . although the energy production by hydrogen burning drops down dramatically after the star enters the white dwarf sequence , it still produces a significant fraction of the total luminosity , enough to bring the cooling to a standstill . we can conclude from fig . [ f : tevol ] that it is extremely unlikely to detect a helium white dwarf during its first rapid cooling phase . it is easier to find them during their plateau phase or afterwards . this means there is a strong bias towards detecting helium white dwarfs in samples of relatively `` cool '' da stars ( like bsl ) instead of the overall much hotter euv selected samples . we can explain in a similar fashion why high mass white dwarfs are found preferentially in the @xmath111k range . due to the drop in neutrino cooling , the evolutionary speeds of massive white dwarfs are relatively low in this range , as demonstrated by the @xmath112 track , the most massive stellar remnant calculated by blcker ( 1995 ) . this increases the detection probability of more massive white dwarfs in euv selected samples . even if we restrict our comparisons to hot subsamples of white dwarfs , the fraction of massive white dwarfs is much higher in the euv selected samples than it is in optically selected ones . an extensive discussion of this problem is carried out by fkb . fkb argue that the number of high mass white dwarfs discovered per sky area is similar for the whole sky euv surveys and the optical palomar - green ( pg ) survey ( green et al . 1986 ) , which covered roughly 25% of the sky . in other words , a whole sky version of the pg survey should have discovered all but one of the euv detected white dwarfs with @xmath113 . at a given temperature , white dwarfs with lower masses are larger , consequently more luminous , and detectable to larger distances . for instance at 30000k , a white dwarf of @xmath107 is detectable at distances @xmath114 larger than a @xmath115 white dwarf . at the maximum distance sampled by , e.g. , the pg survey , the probability is very high that interstellar matter effectively absorbs all euv radiation . thus the dominant effect in euv surveys is not a selection for massive white dwarfs as suggested by v97 , but a selection _ against _ low mass white dwarfs , due to a sample volume strongly affected by interstellar absorption . fkb noted a moderate apparent trend of the white dwarf peak mass with temperature . since their sample also included optically selected white dwarfs , they analyzed a considerably higher fraction of stars with @xmath116k and therefore have a larger temperature baseline than pure euv samples . analogous to this finding , v97 found an @xmath117 offset between the peak of the mass distribution in their euv selected sample and the ( cooler ) white dwarfs analyzed by bsl . in both cases this temperature dependence decreases if wood s models with `` very thin '' layers ( @xmath16 , no hydrogen layer ) instead of the canonical thick layer models ( @xmath118 ) are used . however , part of the trend noted in v97 may be related to the systematic differences between the analyses discussed in sect  5.3 . since v97 compared results from two different analyses , it is not possible to judge if the offset is real or just an artifact . the case of fkb is stronger , because they based their case on a homogeneously analyzed sample . fkb warned that the temperature dependence of the mass distribution peak may be caused by inadequacies remaining in the model atmospheres . a more detailed discussion is given in the next section . some evidence that part of the temperature trend stems from the analyses comes from our intercomparisons presented in sect  5.3 . we showed that systematic differences between the four investigated samples exist that vary with effective temperature . this might mimic a temperature dependence of the sample peak mass . a gravity offset of 0.1dex transforms into mass offsets of 0.050@xmath119 , @xmath120 , and @xmath121 for a @xmath5 white dwarf with 25000k , 40000k , and 60000k , respectively . even a relatively small systematic @xmath44 difference of 0.05dex ( cf.table  [ t : dlogg ] ) corresponds to a @xmath122 offset . the scatter @xmath46 of _ individual _ gravity determinations reported in table  [ t : scatter ] corresponds to @xmath123 , nearly independent of @xmath76 . another part of the @xmath76 dependence of the mass peak may be caused by the use of wood s cooling tracks by fkb and v97 . these tracks are not completely self - consistent since not all model sequences were not calculated _ ab initio _ from the main sequence . this is not important for cooler white dwarfs but may cause deviations from _ ab initio _ tracks especially for the hottest white dwarfs , where structure depends sensitively on the evolutionary history ( blcker & schnberner 1990 ) . we redetermined the masses of the bsl white dwarfs with the blcker / driebe mass - radius relations and derived a peak mass of @xmath124 . that is @xmath117 lower than our peak mass , but having in mind the range of mass determination derived for the euve selected samples , we can not consider this a significant difference . fkb divided their sample into cool ( @xmath125k ) and a hot ( 35000k @xmath12675000k ) subsamples and derived a @xmath127 higher peak mass for the hot sample . our reanalysis of the fkb lte results with the blcker / driebe mass - radius relation yields virtually the same offset : @xmath128 . however , the difference is brought down to @xmath129 ( @xmath130 vs.  @xmath131 ) if we apply corrections to nlte . one can imagine that a difference of this order ( if significant at all ) can easily be produced by our neglect of metallicity effects ( cf . lanz et al . 1996 , barstow et al . 1998 ) . therefore , given the combination of sample selection and systematic effects in analyses to date , our results do not confirm the presence of intrinsic , systematic mass differences between hot and cool white dwarfs .","summary":"our analysis , based on hydrogen nlte model atmospheres , provides a map of lte correction vectors , which allow a thorough comparison with previous lte studies . analogous to other euv selected samples , we note a lack of low mass white dwarfs , and a large fraction of massive white dwarfs . while the lack of helium white dwarfs in our sample can be easily understood from their high cooling rate and therefore low detection probability in our temperature range , this is not enough to explain the large fraction of massive white dwarfs .","abstract":"we present new determinations of effective temperature , surface gravity , and masses for a sample of 46 hot da white dwarfs selected from the euve and rosat wide field camera bright source lists in the course of a near - ir survey for low mass companions . our analysis , based on hydrogen nlte model atmospheres , provides a map of lte correction vectors , which allow a thorough comparison with previous lte studies . we find previous studies underestimate both the systematic errors and the observational scatter in the determination of white dwarf parameters obtained via fits to model atmospheres .    the structure of very hot or low mass white dwarfs depends sensitively on their history . to compute white dwarf masses , we thus use theoretical mass - radius relations that take into account the complete evolution from the main sequence . we find a peak mass of our white dwarf sample of , in agreement with the results of previous analyses . however , we do not confirm a trend of peak mass with temperature reported in two previous analyses .    analogous to other euv selected samples , we note a lack of low mass white dwarfs , and a large fraction of massive white dwarfs . only one white dwarf is likely to have a helium core . while the lack of helium white dwarfs in our sample can be easily understood from their high cooling rate and therefore low detection probability in our temperature range , this is not enough to explain the large fraction of massive white dwarfs . this feature very likely results from a decreased relative sample volume for low mass white dwarfs caused by interstellar absorption in euv selected samples ."}
{"article_id":"astro-ph9901027","section_id":"c","document":"we have obtained temperatures , gravities , and masses for a sample of 46 extreme ultraviolet selected da white dwarfs . these data complement a near infrared survey for low mass companions . the stellar parameters were determined by fitting the hydrogen balmer line profiles with nlte model spectra . a map of lte correction vectors was constructed , which allows the transformation of lte results to the nlte scale . these shifts become important for temperatures above 50000k ( see also napiwotzki 1997 ) . three recent analyses of da white dwarfs have a considerable overlap with our sample and allow a direct check for systematic errors and individual measurement scatter . although all four analyses applied similar model atmospheres and fitting techniques , we recognized systematic shifts up to 5% in temperature and 0.1dex in gravity determinations . these systematic errors have to be considered when the results are interpreted and compared to other studies . the individual measurement errors increase with temperature : @xmath132 from 2.3% to 3.3% and @xmath133 from 0.07dex to 0.13dex . this is larger than the typical errors computed with @xmath45 fit procedures for a well - exposed spectrum and indicates that accuracy is limited by noise in combination with other effects such as details of the extraction , fluxing or normalization procedures . it is unclear if these @xmath46 values indicate lower limits , or scale ( at least partially ) with the s / n ratio of the spectra . it will be a challenge to resolve this question . repeated observations performed by one observer , at one telescope , reduced the same way and analysed with one method as performed by bsl , fkb , and us ( table  2 ) do not reveal all effects . independent observations analysed independently are necessary . masses have been inferred from theoretical mass - radius relations based on the evolutionary calculations of blcker ( 1995 ) for c / o white dwarfs and driebe et al . ( 1998 ) for he white dwarfs . an important feature of these calculations are the hydrogen and helium layer masses which depend on stellar mass . we find a sharp peak centered at @xmath9@xmath0 in agreement with the previous investigations of ksw and bsl . we redetermined masses of the bsl white dwarfs with the blcker / driebe mass - radius relation and derived a peak mass of @xmath134 . at first glance this seems to confirm the systematic offset reported by v97 . however , this offset could be explained by systematic differences of the model atmosphere analyses as well . our reanalysis of the homogeneous fkb sample showed that the temperature dependence of the mass peak nearly vanishes , when corrected for their lte assumption . we conclude that the observational data presented here and in similar studies are well explained by canonical stellar evolution theory , i.e. white dwarfs with thick envelopes . we find only one object ( rej0512 - 004 ) with a mass below @xmath107 , which is a possible helium core white dwarf , but four white dwarfs with masses in excess of @xmath108 . this ratio of high- and low - mass white dwarfs is quite different from that found by bsl . this can partly be understood as the result of variable evolutionary time scales of high and low mass white dwarfs . we agree with fkb that another part can be explained by a selection _ against _ low mass white dwarfs in euv selected samples . the principal aim of our project is the search for and study of cool main sequence companions of our white dwarf sample . five white dwarfs already show red contamination in our optical spectra . a comprehensive discussion of these and other binaries will be given in a forthcoming paper presenting ir photometry for the white dwarf sample . in this article we provided the basic white dwarf data necessary to interpret our binary sample . we thank t.  driebe , f.  herwig , and t. blcker for providing us with their tracks and computing the white dwarf masses and d.koester , who made some model spectra available for our model comparison . we are grateful to steward observatory for an unexpected , generous award of six nights of unclaimed 2.3-m time , which made possible simultaneous optical and infrared observations of our sample of stars . we thank perry berlind for obtaining several white dwarf spectra . pjg acknowledges support through nasa contract nas8 - 39073 ( asc ) . barstow m. a. , hubeny i. , holberg j. b. 1998 , mnras , 299 , 520 beauchamp a. , wesemael f. , bergeron p. , liebert j. , saffer r. a. 1996 , in : hydrogen - deficient stars , eds . c. s.  jeffery & u.  heber , asp conf . 96 , p.  295 bergeron p. 1993 , in : white dwarfs : advances in observation and theory , ed . m. a.  barstow , kluwer , dordrecht , p. 267 bergeron p. , saffer r. a. , & liebert j. 1992 , 394 , 228 ( bsl ) blcker t. 1995 , 299 , 755 blcker t. & schnberner d. 1990 , , 240 , l11 blcker t , herwig f , driebe t. , bramkamp h. , & schnberner d. 1997 , in : white dwarfs , eds . i.  isern et al . , kluwer , dordrecht , p.  57 bues i. , aslan t. 1995 , in : white dwarfs , eds . d.  koester & k.  werner , springer , berlin , p.  259 burleigh , m. r. , barstow , m. a. , & fleming , t. a. 1997 , mnras , 287 , 381 cataln m. s. , sarna m. j. , jomaron c. m. , & smith r. c. 1995 , mnras , 275 , 153 dekool , m. & ritter , h. 1993 , a&a , 267 , 397 dreizler s. , heber u. , jordan s. , & engels d. 1994 , in : hot stars in the galactic halo , eds . s. j.  adelman , a. r.  upgren , c. j.  adelman , cambridge university press , p.  228 dreizler s. & werner k. 1996 , 314 , 217 dreizler s. , werner k. , & heber u. 1995 , in : white dwarfs , eds . d.  koester & k.  werner , springer , berlin , p.  160 driebe t. , schnberner d. , blcker t. , herwig f. 1998 , , 339 , 123 filippenko a. v. 1982 , , 94 , 715 finley , d. s. , et al . 1993 , apj , 417 , 259 finley d. s. , koester d. , & basri g. 1997 apj 488 , 375 ( fkb ) green , p. j. & margon , b. 1994 , apj , 423 , 723 green r. f. , schmidt m. , & liebert j. 1986 apjs 61 , 305 hubeny i. , hummer d. g. , & lanz t. 1994 , , 282 , 151 hummer d. g. & mihalas d. 1988 , 331 , 794 iben , i. jr . & tutukov a. v. 1986 , 311 , 742 jordan s. , heber u. , weidemann v. 1991 , in : white dwarfs , ed . g.  vauclair & e. m.  sion , kluwer , dordrecht , p. 121 kidder , k. m. 1991 , phd thesis , university of arizona kidder , k. m. , holberg , j. b. , barstow , m. a. , tweedy , r. w. , & wesemael , f. 1992 , apj , 394 , 288 kippenhahn r. , kohl k. , & weigert a. 1967 , zeitschrift f.   astrophys .  66 , 58 koester d. , schulz h. , & weidemann v. 1979 , , 76 , 262 ( ksw ) lanz t. , barstow m. a. , hubeny i. , & holberg j. b. 1996 , , 473 , 1089 lemke m. 1997  122 , 285 liebert j. , bergeron p. , & saffer r. a. 1990 pasp , 102 , 1126 malina , r. et al . 1994 , aj , 107 , 751 marsh m. c. , barstow , m. a. , buckley d. a. et al . 1997 , mnras , 286 , 369 ( m97 ) massey p. , strobel s. , barnes j. v. , & anderson e. 1988 , , 328 , 315 napiwotzki r. 1997 , 322 , 256 napiwotzki r. , barstow m. a. , fleming t. , holweger h. , jordan s. , & werner k. 1993 , 278 , 478 pounds , k. et al . 1993 , mnras , 260 , 77 press w. h. , flannery b. p. teukolsky s. a. , & vetterling w. t. 1986 , numerical recipes , cambridge university press schmidt g. d. , bergeron p. , liebert j. , & saffer r. a. 1992 , , 394 , 603 schwartz r. d. , dawkins d. , findley d. , & chen d. 1995 , 107 , 667 sion e. m. , holberg j. b. , barstow m. a. , & kidder , k. m. 1995 , , 107 , 232 sweigart a. v. , greggio l. , & renzini a. 1990 , 364 , 527 vennes , s. & thorstensen , j. r. 1994 , apj , 433 , l29 vennes s. , thejll p. a. , galvan g. g. , & dupuis j. 1997 , , 480 , 714 ( v97 ) vennes s. , christian d. j. & thorstensen j. r. 1998 apj , 502 , 763 vidal c. r. , cooper j. , & smith e. w. 1970 jqsrt 10 , 1011 weidemann v. & koester d. 1984 , , 132 , 195 werner k. 1986 , 161 , 177 wonnacott d. , kellett b. j. , & stickland d. j. 1993 , mnras , 262 , 277 wood , m. 1994 , in iau coll . 147 : the equation of state in astrophysics , eds . g. chabrier and e. schatzmann ( cambridge u. press : cambridge ) p.  612 . wood m. 1995 , in : white dwarfs , eds . d.  koester & k.  werner , springer , berlin , p.  41","summary":"we find a peak mass of our white dwarf sample of , in agreement with the results of previous analyses . only one white dwarf is likely to have a helium core .","abstract":"we present new determinations of effective temperature , surface gravity , and masses for a sample of 46 hot da white dwarfs selected from the euve and rosat wide field camera bright source lists in the course of a near - ir survey for low mass companions . our analysis , based on hydrogen nlte model atmospheres , provides a map of lte correction vectors , which allow a thorough comparison with previous lte studies . we find previous studies underestimate both the systematic errors and the observational scatter in the determination of white dwarf parameters obtained via fits to model atmospheres .    the structure of very hot or low mass white dwarfs depends sensitively on their history . to compute white dwarf masses , we thus use theoretical mass - radius relations that take into account the complete evolution from the main sequence . we find a peak mass of our white dwarf sample of , in agreement with the results of previous analyses . however , we do not confirm a trend of peak mass with temperature reported in two previous analyses .    analogous to other euv selected samples , we note a lack of low mass white dwarfs , and a large fraction of massive white dwarfs . only one white dwarf is likely to have a helium core . while the lack of helium white dwarfs in our sample can be easily understood from their high cooling rate and therefore low detection probability in our temperature range , this is not enough to explain the large fraction of massive white dwarfs . this feature very likely results from a decreased relative sample volume for low mass white dwarfs caused by interstellar absorption in euv selected samples ."}
{"article_id":"1104.2769","section_id":"i","document":"the local density approximation ( lda ) ( ref .  ) in density functional theory ( dft ) ( ref .  ) has shown fantastic performance in understanding and even predicting material properties@xcite in spite of its relatively simple treatment of the exchange - correlation energy @xmath2 $ ] as a functional of the electron density @xmath3 ; e.g. , for many materials , lattice and elastic constants are generally reproduced . the deviations from experimental values are within less than 1 - 2 % and several percent , respectively , in lda . yet lda fails to describe some of properties including ground - state magnetic orderings even for bulk iron@xcite and for some transition - metal oxides.@xcite it also tends to overestimate the bonding strength , leading to an absolute error of molecular atomization energies.@xcite    some of limitations of lda are remedied by the generalized gradient approximation ( gga ) in which the exchange - correlation energy is expressed in terms of not only the electron density but also its gradient . the molecular atomization energies are calculated with the error of several tenths of ev,@xcite and the ground state of the bulk iron is correctly predicted to be a ferromagnetic body - center phase.@xcite the prevailed functional form of gga ( pbe ) ( ref .  ) generally provides better accuracy for structural properties of variety of solids and activation energies in chemical reactions than lda does .    the local ( lda ) and semilocal ( gga ) approximations are still insufficient to describe some of important properties , however . the ground states of strongly correlated materials are incorrectly predicted and the energy band gaps of most semiconductors and insulators are substantially underestimated . the meta - gga scheme@xcite extending the exchange - correlation functionals with including the kinetic energy density further improves the lda and gga results for molecular systems@xcite but not succeed to remedy above failures in condensed matters .    the failure of lda and gga is occasionally discussed in terms of the self - interaction error ( sie).@xcite an electron is under the electrostatic potential due to other electrons . yet the expression of the electrostatic potential in the ( semi)local approximations includes the spurious interaction with the electron itself . when we consider the hartree - fock ( hf ) exchange potential with kohn - sham orbitals , this spurious self - interaction is cancelled by a term in the exchange potential . in the ( semi)local expression of the exchange potential , however , this cancellation is incomplete so that each electron is affected by the self - interaction . this sie causes delocalization of the electron , predicting the incorrect fractional - charged ground state of , e.g. , h@xmath4 with large nucleus separation.@xcite    the sie affects the band gaps substantially . the band gap @xmath5 is formally defined as the ionization energy subtracted by the electron affinity so that @xmath6 where @xmath7 is the total energy of the @xmath8-electron system . in dft with the exact exchange - correlation energy , the band gap is expressed as the difference between the highest occupied kohn - sham level @xmath9 of the @xmath10-electron system and its counterpart of the @xmath8-electron system @xmath11 : i.e. , @xmath12.@xcite when we introduce a fractional electron system with @xmath13 electrons as a mixed state of real integer - electron systems , then the total energy @xmath14 becomes linear for @xmath15 and shows discontinuity at the integer value @xmath8 for finite - gap systems . using janak theorem@xcite which relates the kohn - sham level to the derivative of the total energy as @xmath16 , the linearity of @xmath17 leads to the constant @xmath18 as a function of @xmath19 . in the ( semi)local approximations , however , the kohn - sham level @xmath20 [ @xmath21 increases ( decreases ) with increasing @xmath19 due to the self - interaction , leading to the concave shape of @xmath14 this may cause an underestimate of the energy gap.@xcite    the hf approximation ( hfa ) is free from the self - interaction . yet the calculated band gaps in hfa are substantially overestimated due to the lack of the correlation energy . an approach called the optimized effective potential@xcite which is incorporated in dft ( refs .  ) intending to remedy the issue is still in an immature stage in a view of applications to polyatomic systems . hence the hybrid functionals combining lda or gga with hfa may be effective to break the limitation of the semilocal approximations . the hybrid approach has begun in empirical ways : the hf - exchange energy was mixed with the lda exchange - correlation energy in the half and half way@xcite and then three mixing parameters were introduced@xcite to mix the lda , gga , and hfa energies ; the latter scheme is called b3lyp and has widely been used to clarify thermochemical properties of molecules.@xcite a rationale for the hybrid functional is provided@xcite in the light of the adiabatic - connection theorem,@xcite @xmath22 = \\int_0 ^ 1 d\\lambda \\ e_{\\rm xc,\\lambda } \\ , \\label{adconn}\\ ] ] where @xmath23 is the energy of the exchange and correlation in a system , where the electron - electron interaction @xmath24 is reduced by the factor @xmath25 but the external potential @xmath26 is added to reproduce the electron density @xmath27 of the real system ( @xmath28 ) . here @xmath29 is the ground - state many - body wave function . by assuming that @xmath30 is the 4th polynomial of @xmath25 with particular asymptotic forms for @xmath31 and @xmath28 , perdew , ernzerhof , and becke have proposed a parameter - free hybrid functional called pbe0@xcite in which the hf and pbe exchange energies are mixed with the ratio of 1:3 . its applicability has been examined for molecular systems.@xcite    screening of the coulomb potential is effective in polyatomic systems . hence it may be effective to apply the non - local hf - exchange operator only to the short - range part of the coulomb potential.@xcite this is conveniently done by introducing the error function splitting the coulomb potential into short - range and long - range components . the hybrid functional which is constructed in this way from the pbe0 functional is proposed by heyd , sucseria , and ernzerhof ( hse).@xcite this treatment reduces computational cost substantially and opens a possibility to apply the hybrid functionals to condensed matters . the structural properties as well as the band gaps of several solids have been calculated and significant improvements on semi - local functionals are achieved.@xcite    on the other hand , effects of the exchange interaction for the long - range component of the coulomb potential are certainly important@xcite in a view of reducing sie . hirao and his collaborators have proposed a long - range corrected ( lc ) functional in which the long - range component is treated by the hf exchange energy and the short - range component is by the lda exchange.@xcite they have applied to various molecular systems and obtained relatively successful results.@xcite further application of the lc functional to molecular systems and its comparison with other functionals have been done and the applicability of the lc functional have been recognized.@xcite the lc functional has also been applied to structural properties and band gaps of several condensed matters and the results are compared with those obtained from other functionals.@xcite    at the present stage , several hybrid functionals have been implemented in different packages and the assessment of the validity of each functional has been done mainly to molecular systems . applicability of the pbe0 and hse functionals to condensed matters have been examined.@xcite the structural and electronic properties such as lattice constants , bulk moduli , and also the band gaps of condensed matters are obtained only after careful examinations of various calculation parameters . obviously , numerical precision should not be neglected . in order to assess the validity of each hybrid functional , it is thus imperative to perform the computation in a single reliable calculation scheme . furthermore , the split of the coulomb potential into the short - range and long - range parts requires another parameter @xmath32 being the exponent of the error function . the @xmath32 dependence of the results should certainly be examined for better understanding and further improvements on the hybrid functionals . the aim of the present paper is to implement several important hybrid functionals in the well - established plane - wave - basis total - energy band - structure calculation code and examine validity and limitation of each functional . a plane - wave code we adopt in this work is _ tokyo ab initio program package _ ( tapp).@xcite we have calculated lattice constants , bulk moduli , band gaps , and band widths of various semiconductors and insulators with the pbe0 , hse , and lc hybrid functionals as well as ( semi)local gga functional . comparison of the obtained results unequivocally elucidates the validity and the limitation of the hybrid functionals .    in section [ hybrid ] , we briefly describe each of the hybrid functionals used in the present paper . section [ computation ] presents details of our computational scheme . the calculated results are shown in section [ result ] , and our finding is summarized in section [ conclusion ] .","summary":"the three hybrid functionals , pbe0 by perdew , ernzerhof , and becke , hse by heyd , sucseria , and ernzerhof , and a long - range corrected ( lc ) functional , are implemented in a well - established plane - wave - basis - set scheme combined with norm - conserving pseudopotentials , thus enabling us to assess applicability of each functional on equal footing to the properties of the materials . the materials we have examined in this paper range from covalent to ionic materials as well as a rare - gas solid whose energy gaps determined by experiments are in the range of 0.6 ev - 14.2 ev : i.e. , ge , si , batio ,-gan , diamond , mgo , nacl , licl , kr , and lif . we find that the calculated bulk moduli by the hybrid functionals show better agreement with the experiments than the generalized gradient approximation ( gga ) provides , whereas the calculated lattice constants by the hybrid functionals and gga show comparable accuracy . = 0.0em","abstract":"we present a systematic study that clarifies validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators . the three hybrid functionals , pbe0 by perdew , ernzerhof , and becke , hse by heyd , sucseria , and ernzerhof , and a long - range corrected ( lc ) functional , are implemented in a well - established plane - wave - basis - set scheme combined with norm - conserving pseudopotentials , thus enabling us to assess applicability of each functional on equal footing to the properties of the materials . the materials we have examined in this paper range from covalent to ionic materials as well as a rare - gas solid whose energy gaps determined by experiments are in the range of 0.6 ev - 14.2 ev : i.e. , ge , si , batio ,-gan , diamond , mgo , nacl , licl , kr , and lif . we find that the calculated bulk moduli by the hybrid functionals show better agreement with the experiments than the generalized gradient approximation ( gga ) provides , whereas the calculated lattice constants by the hybrid functionals and gga show comparable accuracy . the calculated energy band gaps and the valence - band widths for the ten prototype materials show substantial improvement using the hybrid functional compared with gga . in particular , it is found that the band gaps of the ionic materials as well as the rare - gas solid are well reproduced by the lc - hybrid functional , whereas those of covalent materials are well described by the hse functional . we also examine exchange effects due to short - range and long - range components of the coulomb interaction and propose an optimum recipe to the short - range and long - range separation in treating the exchange energy .    = 0.0em"}
{"article_id":"1104.2769","section_id":"r","document":"l@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r + [ 2pt ] + [ -4pt ] & pbe & hf & pbe0 & & & expt . + [ 2pt ] + [ -4pt ] & & & & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & +   + ge & 0&4.75&1.00&0.76 & 0.54 & 0.43 & 0.27&1.05&2.05&2.66&3.69&0.74 + si & 0.61&6.03&1.72 & 1.20 & 0.94 & 0.80&0.73&2.24&3.85&4.19&4.63&1.17 + batio@xmath0&2.14&11.62 & 4.21 & 3.57 & 3.12&2.83&2.73&4.59&6.26&7.45&8.01&3.2 + @xmath1-gan&2.06&8.84 & 3.51 & 3.02 & 2.65&2.42&2.26&3.95&5.58&6.55&7.36&3.30 + c & 4.01&12.44&5.87 & 5.28 & 4.88 & 4.62&4.45&5.06&6.80&7.95&8.73&5.48 + mgo & 4.95&14.21&6.99 & 6.62 & 6.14 & 5.79&5.52&6.38&8.33&9.88&11.12&7.7 + nacl & 5.13&13.38&6.95 & 6.46 & 6.00 & 5.69&5.49&7.03&8.90&10.22&11.12&8.5 + licl & 6.33&14.85&8.60 & 8.14 & 7.67 & 7.36&7.15&8.53&10.45&11.75&12.66&9.4 + lif & 9.70&21.57&12.51&12.02&11.45&11.02&10.68&11.59&13.87&15.65&17.06&14.30 + kr & 7.09&15.22&9.14 & 8.46 & 7.98 & 7.68 & 7.48 & 9.85&11.75&13.00&13.75 & 11.65 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 42.5&179.7&19.7&12.4&19.9&26.4&31.5&28.2&62.3&88.9&117.4 + mre ( % ) & @xmath13342.5&179.7&5.7&@xmath1339.0&@xmath13319.9&@xmath13326.4&@xmath13331.5&11.1&61.7&88.9&117.4 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 49.1&303.1&25.4&5.8&16.0&25.5&33.2&40.8&119.0&158.8&205.4 + mre ( % ) & @xmath13349.1&303.1&25.4&0.9&@xmath13316.0&@xmath13325.5&@xmath13333.2&37.8&119.0&158.8&205.4 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 35.9&56.3&14.0&19.0&23.9&27.3&29.8&15.6&5.6&18.9&29.4 + mae ( % ) & @xmath13335.9&56.3&@xmath13314.0&@xmath13319.0&@xmath13323.9&@xmath13327.3&@xmath13329.8&@xmath13315.6&4.4&18.9&29.4 +    we have performed total - energy electronic - structure calculations using pbe , hf , pbe0 , hse , lc exchange - correlation functionals for ten materials , including covalent semiconductors , ionic insulators , dielectric compounds , and a rare - gas solid : i.e. , si , ge , gan , diamond , mgo , nacl , licl , lif , batio@xmath0 , and kr . the calculated results elucidate capability and limitation of each functional in discussing electronic and structural properties of these prototype materials . we first present calculated electron states of these materials and compare them with experimental results in the subsection [ ele_state ] . then we present the results of structural optimization in the subsection [ structure ] . l@  r@  r@  r @  r@  r@  r @  r@  r@  r @  r + [ -2pt ] + [ 2pt ] + [ -4pt ] & pbe&hf&pbe0 & & & expt . + [ 2pt ] + [ -4pt ] & & & & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & + [ 2pt ] + [ -4pt ] ge&12.85&18.22&14.50&13.80&13.47&13.11&14.23&15.54&16.36&12.9@xmath1340.2 + si&11.95&16.90&13.37&13.28&12.99&12.65&12.19&13.45&14.52&12.5@xmath1340.6 + batio@xmath0 & 4.53&6.37&5.08&5.03&4.95&4.85&4.85&5.34&5.72 & + @xmath1-gan&6.73&8.27&7.20&7.11&7.02&6.93&7.11&7.44&7.91 & + c&21.65&30.09&23.64&23.51&23.28&22.96&24.15&25.00&26.19 & 24.2@xmath1341 ,  21@xmath1341 + mgo & 4.43&6.16&4.97 & 4.80 & 4.70 & 4.60&5.21&5.56&5.92 & + nacl&1.65&2.24&1.84 & 1.77 & 1.71 & 1.67&2.04&2.25&2.38 & + licl&2.82&4.33&3.39 & 3.16 & 3.16 & 3.09&3.59&3.91&4.17 & + kr & 1.50&1.93&1.61 & 1.59 & 1.55 & 1.52&1.57&1.74&1.85 & + lif & 2.83 & 3.66&3.09 & 2.96 & 2.92 & 2.87 & 2.94&3.09&3.27 & +    figure [ si_band ] shows calculated band structures of si with five exchange - correlation functionals . for the hse and lc functionals , the band structures with different choices of @xmath32 [ 0.1 , 0.2 , and 0.3 ( @xmath52 ) ] in eq . ( [ split ] ) are shown . the overall features of the band structures obtained by the five functionals are similar to each other . yet the bandwidths and the fundamental gaps are different quantitatively . when the ratio of the hf exchange to the total - exchange functional is large , the resulting bandwidth and gap become large ; these quantities become larger in the order of pbe , pbe0 , hse , lc , and hf . notice that the band gaps obtained by the lc functional are always larger than those by the hse functional , indicating that the correction to the long - range part of the exchange potential tends to make the band gap large . we also show the calculated energy bands of the dielectric compound batio@xmath135 and the ionic insulator nacl in figs . [ batio3_band ] and [ nacl_band ] , respectively . we find the general tendency similar to that in si : i.e. , the overall features of the energy bands are insensitive to the difference in the functionals ; the lc functional provides larger energy gaps compared with the hse functional . table  [ bandgap ] and [ bandwidth ] summarize the calculated bandwidths and band gaps for the ten materials . for assessment of validity of each functional , it is convenient to introduce two quantities , the mean relative error ( mre ) which is the mean of the calculated value minus the experimental value over the ten materials , and the mean absolute relative error ( mare ) which is the mean of the absolute value of the difference between the calculated and the experimental values over the ten materials . the mre is a measure of under- or over - estimates of the experimental values since each functional predicts either smaller or larger values than the experimental values for most of the ten materials . on the other hand , mare is a measure of closeness between the calculated and experimental values . in the discussion below , we categorize the ten materials into group i and group ii : group i , i.e. , diamond , gan , batio@xmath0 , si and ge has covalent characters in which the band gaps are less than 7 ev ; group ii , i.e. , lif , kr , nacl , licl and mgo , consists of ionic solids and a rare - gas solid in which the experimental band gaps are larger than 7 ev . the calculated band gap by the pbe functional for each material is substantially smaller than the corresponding experimental value , as is reported in literature . the calculated mre for the ten materials is @xmath13342.5 % . on the other hand , hfa largely overestimates the band gaps for all the ten materials : mre is 179.7 % . the pbe0 functional provides better values . the calculated mre by the pbe0 for the materials in group i is 25.4 % , whereas it gives @xmath13314.0 % for the materials in group ii . the hse and lc functional also provide better agreement of the band gap with the experiments than the pbe does . further when we choose optimum values of @xmath32 , the hse and lc results show nice agreement with the experimental values . in the hse functional , a general trend is the decrease in the band gap with increasing @xmath32 . we have found that the value @xmath32 = 0.1 @xmath52 produces the band gaps close to the experimental values within mre = 0.9 % for the materials in group i. it produces worse values for the materials in group ii . the calculated mre is @xmath13319.0 % for the materials in group ii , but still hse being the better approximation than pbe . the lc functional provides good agreement with the experimental values for the materials in group ii : when we choose the optimum value of @xmath136 , the calculated mre is nicely small , 4.4 % for the materials in group ii . yet the lc provides worse values for the materials in group i , showing its limitation as an universally valid approximation . figure  [ theory_vs_expt ] is a summary of our calculated band gaps by the pbe , hse and lc functionals . for hse and lc , we show the calculated results with the optimum @xmath32 values : @xmath32 = 0.1 @xmath52 for hse and @xmath32 = 0.2 @xmath52 for lc . it is clearly shown that the calculated band gaps by hybrid functionals , hse and lc , are in better agreement with the experimental values than the pbe ( gga ) approximation , indicating the promising possibility of the hybrid functionals . the degree of the agreement is close to the greens - function - based gw approximation in which there are several ambiguities in theoretical treatments.@xcite however , this figure also shows the limitation ; hse is reasonably good for only the group i materials , whereas lc is good for only the group ii materials . our finding here is that hse is a good approximation for relatively small - gap materials and that lc is a good approximation for the relatively large - gap materials . screening of the coulomb interaction depends on the materials . hence the best treatment of the short - range and long - range parts of the coulomb interactions should change material by material . what we have found here is natural in the sense . however , another point we have shown here is that the appropriate choice of @xmath32 with each exchange - correlation functional provides reasonable agreement with the calculated band gaps for rather wide range of materials ; hse with @xmath32 @xmath137 0.1 @xmath52 for the materials with their band gaps smaller than 7 ev and lc with @xmath32 @xmath137 0.2 @xmath52 for the materials with their band gaps larger than 7 ev . this information certainly provides a practical recipe to obtain reliable band gaps for various materials .        the calculated bandwidths by the pbe functional are in good agreements with the experimental values available ( table  [ bandwidth ] ) . other hybrid functionals also provide reasonable agreement , in particular , with appropriate choices of the @xmath32 parameter for the hse and lc functionals . on the other hand , hfa shows substantial overestimate for each material . l@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r + [ -4pt ] + [ 2pt ] + [ -4pt ] & pbe & hf & pbe0 & & & expt . + [ 2pt ] + [ -4pt ] & & & & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & + [ 2pt ] + [ -4pt ] ge&5.589&5.574&5.615&5.546&5.556&5.566&5.571&5.579&5.534&5.508&5.490&5.652 + si&5.463&5.387&5.431&5.435&5.441&5.446&5.452&5.459&5.434&5.416&5.403&5.430 + batio@xmath0&4.139&4.048&4.068&4.102&4.106&4.111&4.116&4.137&4.120&4.102&4.088&4.000 + @xmath1-gan&4.539&4.380&4.434&4.455&4.457&4.441&4.461&4.502&4.511&4.491&4.452&4.520 + c&3.563&3.485&3.506&3.522&3.540&3.543&3.547&3.560&3.556&3.543&3.531&3.567 + mgo&4.202&4.198&4.198&4.117&4.136&4.141&4.146&4.178&4.175&4.157&4.138&4.207 + nacl&5.541&5.416&5.444&5.500&5.505&5.509&5.514&5.525&5.503&5.487&5.472&5.595 + licl&5.175&5.107&5.133&5.145&5.147&5.155&5.158&5.165&5.140&5.117&5.115&5.106 + kr & 10.86&10.06&10.74&10.79&10.81&10.86&10.86&10.69&10.49&10.05&10.05&9.94 + lif&4.115&4.006&4.030&4.041&4.071&4.073&4.076&4.103&4.098&4.091&4.080&4.010 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 1.20&1.37&1.10&1.40&1.37&1.41&1.35&1.25&1.21&1.34&1.54 + mre ( % ) & 0.68&@xmath1331.10&@xmath1330.49&@xmath1330.47&@xmath1330.22&@xmath1330.16&@xmath1330.03&0.40&0.10&@xmath1330.27&@xmath1330.62 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 1.15&1.75&1.20&1.44&1.34&1.40&1.32&1.17&1.13&1.33&1.62 + mre ( % ) & 0.66&@xmath1331.27&@xmath1330.51&@xmath1330.39&@xmath1330.20&@xmath1330.17&0.00&0.41&0.10&@xmath1330.31&@xmath1330.74 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 1.26&0.88&0.99&1.34&1.41&1.41&1.39&1.35&1.32&1.34&1.44 + mre ( % ) & 0.72&@xmath1330.87&@xmath1330.47&@xmath1330.58&@xmath1330.24&@xmath1330.14&@xmath1330.06&0.38&0.11&@xmath1330.22&@xmath1330.48 + [ 2pt ]    we next examine performance of the hybrid functionals in describing structural properties . table  [ lattice ] and [ bm ] show calculated lattice constants @xmath138 and bulk moduli @xmath139 , respectively , of the ten materials . the @xmath138 and @xmath139 values are determined by fitting parameters in the murnaghan equation of state to the calculated total energy as a function of the volume . in mare and mre presented in table  [ lattice ] , the calculated value for solid kr is not included . as shown in this table , the calculated lattice constant of kr is substantially larger than the experimental value : it is overestimated by 1.1 - 9.2 % in gga and in the hybrid approximations , and by 1.2 % in hfa . this is because van der waals interaction which is unable to be treated in the approximations examined in this paper plays an essential role in solid kr . we thus exclude the value for kr from the statistical assessment . the results obtained by pbe reasonably agree with the experimental values ( mre = 0.68 % and mare = 1.20 % for @xmath138 and mre = @xmath1337.1 % and mare = 8.3 % for @xmath139 ) . the accuracy of hfa is slightly inferior to that of pbe ( mre = @xmath1331.10 % and mare = 1.37 % for @xmath138 and mre = 13.7 % and mare = 13.7 % for @xmath139 ) . the pbe0 functional shows better accuracy with the mre = @xmath1330.49 % and mare = 1.10 % for @xmath138 , and mre = @xmath1331.7 % and mare = 5.1 % for @xmath139 . the calculated lattice constants using the hse and lc functionals are insensitive to the choice of @xmath32 : the difference obtained from different @xmath32 values is within 1 % . the difference in the calculated bulk modulus from different @xmath32 values are not so small as in the lattice constant partly because the fitting by the murnaghan equation is incomplete . for the hse functional , the value @xmath32 = 0.1 @xmath52 produces best agreement with the experiments : mre = @xmath1330.47 % and mare = 1.40 % for @xmath138 , and mre = 1.7 % and mare = 3.6 % for @xmath139 . for the lc functional , we have found that @xmath32 = 0.2 @xmath52 produces best results : mre = 0.10 % and mare = 1.21 % for @xmath138 , and mre = 2.0 % and mare = 5.5 % for @xmath139 . these optimum values for @xmath32 for the hse and lc functionals are identical to the optimum values determined from the calculated mre and mare for band gaps , corroborating the appropriate choice of @xmath32 . l@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r@  r + [ -4pt ] + [ 2pt ] + [ -4pt ] & pbe & hf & pbe0 & & & expt . + [ 2pt ] + [ -4pt ] & & & & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & @xmath32=0.1 & @xmath32=0.2 & @xmath32=0.3 & @xmath32=0.4 & + [ 2pt ] + [ -4pt ] ge&69.0&76.0&68.8&76.3&75.8&73.3&72.7&71.8&85.3&89.0&95.8&75.8 + si&91.1&116.3&98.1&95.9&93.8&92.0&90.4&90.4&98.0&104.3&109.0&99.2 + batio@xmath0&146.0&184.0&167.0&164.0&162.0&159.0&156.0&150.0&167.0&166.0&175.0&162.0 + @xmath1-gan&173.0&274.6&220.3&215.5&213.3&203.5&189.1&192.2&195.0&218.1&249.3&210.0 + c & 456.0&534.0&488.0&485.0&483.0&478.0&473.0&469.0&472.0&490.0&508.0&443.0 + mgo & 152.0&181.0&169.0&166.0&164.0&162.0&160.0&152.0&154.0&161.0&169.0&165.0 + nacl&27.3&32.7&29.3&29.0&28.9&28.7&28.4&28.6&29.1&29.9&30.9&26.6 + licl&30.7&37.3&33.6&33.6&33.5&33.3&33.1&34.2&36.3&35.1&36.0&35.4 + kr & 2.4 & 6.4 & 3.8 & 3.8 & 3.5 & 3.1 & 2.7 & 3.2 & 3.5 & 4.7 & 5.1 & 3.4 + lif & 67.2&72.0&69.9&69.8&69.8&69.6&69.2&73.1&69.3&67.9&72.0&69.8 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 8.3&13.7&5.1&3.6&3.4&4.4&5.6&6.6&5.5&6.4&11.2 + mre ( % ) & @xmath1337.1&13.7&1.7&1.7&0.9&@xmath1330.9&@xmath1332.6&@xmath1332.6&2.0&5.1&11.2 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 9.5&16.5&5.7&3.5&3.2&4.7&6.7&7.2&6.1&7.9&15.5 + mre ( % ) & @xmath1338.3&16.5&1.6&2.1&1.0&@xmath1331.5&@xmath1334.0&@xmath1334.8&2.8&7.9&15.5 + [ 2pt ] + [ -4pt ] + [ 2pt ] mare ( % ) & 6.9&10.3&4.5&3.7&3.7&4.0&4.3&5.9&4.8&4.6&5.9 + mre ( % ) & @xmath1335.6&10.3&1.9&1.1&0.7&0.0&@xmath1330.9&0.2&1.1&1.6&5.9 + [ 2pt ]","summary":"in particular , it is found that the band gaps of the ionic materials as well as the rare - gas solid are well reproduced by the lc - hybrid functional , whereas those of covalent materials are well described by the hse functional .","abstract":"we present a systematic study that clarifies validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators . the three hybrid functionals , pbe0 by perdew , ernzerhof , and becke , hse by heyd , sucseria , and ernzerhof , and a long - range corrected ( lc ) functional , are implemented in a well - established plane - wave - basis - set scheme combined with norm - conserving pseudopotentials , thus enabling us to assess applicability of each functional on equal footing to the properties of the materials . the materials we have examined in this paper range from covalent to ionic materials as well as a rare - gas solid whose energy gaps determined by experiments are in the range of 0.6 ev - 14.2 ev : i.e. , ge , si , batio ,-gan , diamond , mgo , nacl , licl , kr , and lif . we find that the calculated bulk moduli by the hybrid functionals show better agreement with the experiments than the generalized gradient approximation ( gga ) provides , whereas the calculated lattice constants by the hybrid functionals and gga show comparable accuracy . the calculated energy band gaps and the valence - band widths for the ten prototype materials show substantial improvement using the hybrid functional compared with gga . in particular , it is found that the band gaps of the ionic materials as well as the rare - gas solid are well reproduced by the lc - hybrid functional , whereas those of covalent materials are well described by the hse functional . we also examine exchange effects due to short - range and long - range components of the coulomb interaction and propose an optimum recipe to the short - range and long - range separation in treating the exchange energy .    = 0.0em"}
{"article_id":"1104.2769","section_id":"c","document":"we have studied validity of hybrid exchange - correlation functionals in density functional theory by implementing three hybrid functionals in a well - established plane - wave - basis - set code named tapp and by calculating structural properties and electron states of representative ten materials where the experimental energy gaps range from 0.67 ev to 14.20 ev . the three hybrid exchange - correlation functionals examined in this paper are pbe0 proposed by perdew , burke , and ernzerhoff , hse proposed by heyd , scuseria , and ernzerhoff , and lc originally proposed by savin and by hirao and his collaborators . for comparison , results from the generalized gradient approximation , i.e. , pbe , and hfa have been presented . the ten materials we have examined are ge , si , gan , batio@xmath0 , diamond , mgo , licl , nacl , kr , and lif which are representatives of covalent , ionic , and rare - gas solids . we have found that the structural properties such as lattice constants are already well reproduced by the pbe functional and also by hfa and that the hybrid functionals show better agreement with the experimental values . we have determined appropriate values of @xmath32 in the separation of the short - range and long - range parts in the coulomb interaction : the optimum value is @xmath32 = 0.1 @xmath52 for the hse functional and @xmath32 = 0.2 @xmath52 for the lc functional . by choosing the appropriate value of @xmath32 in the hse and lc functionals , we have achieved better agreement in the lattice constants and further substantial improvement in description of elastic constants such as bulk moduli for the ten materials . dramatic success of the hybrid functionals are observed in the calculated band gaps . we have found that the calculated band gaps by the lc functional for the wide band - gap materials satisfactorily agree with the experimental values with mean relative error ( mre ) of 3.0 % , whereas the band gaps by the hse functional for the small band - gap materials agree well with the experimental values with mre = 0.7 % . this good description of the band gaps is unprecedented in density functional theory where lda and gga produce the value of mre @xmath137 40 - 50 % , and is comparable with or better than what the gw approximation produces . the @xmath32 value leading to the best agreement with the experiments is 0.1 @xmath52 for the hse functional and 0.2 @xmath52 for the lc functional . these @xmath32 values are identical to the optimum values determined from the examination of the structural properties . the calculated valence - band widths by the hybrid functionals also agree satisfactorily with the experimental values . it is now established that the hse and lc functionals with appropriate choice of the @xmath32 parameter are useful to describe structural and electronic properties of various materials . rigorous justification of the choice of the form of the hybrid functionals along with a guiding principle of choice of @xmath32 would offer further developments in the first - principles calculations .    the work is partly supported by a grant - in - aid project from mext , japan ,  scientific research on innovative areas : materials design through computics - complex correlation and non - equilibrium dynamics - \" under the contract number 22104005 . computations were done at supercomputer center , institute for solid state physics , university of tokyo , and at research center for computational science , national institutes of natural sciences . w. kohn and l. j. sham , phys . rev . * 140 * , a1133 ( 1965 ) . p. hohenberg and w. kohn , phys . rev . * 136 * , b864 ( 1964 ) . for a review , _ theory of the inhomogeneous electron gas _ , edited by s. lundqvist and n. h. march , ( plenum pres ny , 1983 ) . t. asada and k. terakura , phys . rev . b 46 , 13 599 ( 1992 ) , and references therein . a. oshiyama , n. shima , t. nakayama , k. shiraishi and h. kamimura , in _ mechanisms of high temperature superconductivity _ , edited by h. kamimura and a. oshiyama , ( springer - verlag , 1989 ) p111 . j. p. perdew and s. kurth , in _ a premier in density functional theory _ , edited by c. fiolhais , f. nogueira and m. a. l. marques ( springer , berlin 2003 ) . for a review , s. kmmel and l. kronik , rev . phys . * 80 * , 3 ( 2008 ) . j. p. perdew , k. burke and m. ernzerhof , phys . lett . * 77 * , 3865 ; 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","abstract":"we present a systematic study that clarifies validity and limitation of current hybrid functionals in density functional theory for structural and electronic properties of various semiconductors and insulators . the three hybrid functionals , pbe0 by perdew , ernzerhof , and becke , hse by heyd , sucseria , and ernzerhof , and a long - range corrected ( lc ) functional , are implemented in a well - established plane - wave - basis - set scheme combined with norm - conserving pseudopotentials , thus enabling us to assess applicability of each functional on equal footing to the properties of the materials . the materials we have examined in this paper range from covalent to ionic materials as well as a rare - gas solid whose energy gaps determined by experiments are in the range of 0.6 ev - 14.2 ev : i.e. , ge , si , batio ,-gan , diamond , mgo , nacl , licl , kr , and lif . we find that the calculated bulk moduli by the hybrid functionals show better agreement with the experiments than the generalized gradient approximation ( gga ) provides , whereas the calculated lattice constants by the hybrid functionals and gga show comparable accuracy . the calculated energy band gaps and the valence - band widths for the ten prototype materials show substantial improvement using the hybrid functional compared with gga . in particular , it is found that the band gaps of the ionic materials as well as the rare - gas solid are well reproduced by the lc - hybrid functional , whereas those of covalent materials are well described by the hse functional . we also examine exchange effects due to short - range and long - range components of the coulomb interaction and propose an optimum recipe to the short - range and long - range separation in treating the exchange energy .    = 0.0em"}
{"article_id":"cond-mat0401515","section_id":"i","document":"since the discovery of magnetic quantum tunneling ( mqt ) in [ mn@xmath0o@xmath0(ch@xmath4coo)@xmath5(h@xmath6o)@xmath7@xmath8 2ch@xmath4cooh@xmath9h@xmath6o ( mn@xmath0-ac),@xcite single molecule magnets ( smms ) have become the focus of considerable experimental and theoretical interest due to their novel quantum properties @xcite and possible future use in quantum computational devices.@xcite mn@xmath0-ac remains the most widely studied smm due to its large spin ground state ( @xmath10 , see refs [ ] ) , together with a considerable easy - axis magneto - crystalline anisotropy.@xcite these combined factors result in a sizeable kinetic barrier against spin reversal at the molecular level , leading to slow magnetization relaxation and hysteresis ( bistability ) at low temperatures ( below  @xmath113  k).@xcite when a dc magnetic field is applied parallel to the easy - axis of a single crystal of mn@xmath0-ac , sharp steps are observed in its hysteresis loops at well defined field strengths.@xcite the enhanced magnetization relaxation at these steps is the result of resonant mqt . while a clearer picture concerning the mechanism of mqt in mn@xmath0-ac is beginning to emerge , @xcite many interesting problems remain . in particular , current theoretical models assume the presence of quadratic and quartic transverse crystal - field interactions in the spin hamiltonian [ @xmath12 and @xmath13 , where the former has been ascribed to solvent disorder.@xcite however , these interactions , which contain only even powers of the raising and lowering operators , _ do not _ provide an explanation for the observation of odd mqt steps in the hysteresis loops , i.e. tunneling via resonances between levels whose spin projections ( @xmath14 ) differ by an odd integer.@xcite it is generally recognized that the underlying mechanism _ must _ involve internal transverse fields,@xcite but their source has yet to be identified . prokofev and stamp@xcite proposed that hyperfine interactions might provide the answer ; however , the calculated mqt rates were too small . subsequently , garanin and chudnovsky@xcite suggested that strains or structural defects in the crystal lattice ( dislocations ) could lead to a distribution of tilts of the magnetic easy - axes at the mn@xmath0-ac cluster sites ; upon application of an external magnetic field , such tilts would result in a distribution of transverse fields , even when the field is applied parallel to the global symmetry ( @xmath2- ) axis of the crystal . while this model was in qualitative agreement with the fact that experiments revealed significant distributions in the finite field mqt rates,@xcite the measured distributions were considerably narrower than those predicted by garanin and chudnovsky.@xcite    although some preliminary spectroscopic data have been reported in support of dislocations,@xcite a more plausible model leading to easy - axis - tilting was recently suggested by cornia et al.@xcite based on a detailed analysis of existing x - ray diffraction data and some approximate electronic structure calculations , they propose that such a local symmetry lowering and easy - axis - tilting can be ascribed to the presence of the two acetic acids of crystallization in the unit cell . experiments in support of this model were recently published by us,@xcite and by del  barco et al.@xcite however , evidence for the easy - axis - tilting was lacking in these investigations , though we note that tilts have recently been reported for a related mn@xmath0 complex in a separate study by del barco et al.@xcite here we report electron paramagnetic resonance ( epr ) measurements on precisely ( in - situ ) aligned mn@xmath0-ac single crystals under large applied fields in the transverse direction . at relatively low frequencies ( @xmath15  ghz ) , as the field is rotated away from the hard plane , simulations show that the epr intensity should oscillate between two series of resonances excited from  even \" and  odd \" spin states ( labeled @xmath16 and @xmath17 respectively , see following section ) . the magnetic dipole matrix elements and transition frequencies associated with these  even \" and  odd \" resonances are extremely sensitive to the field orientation ( providing @xmath18 resolution ) , allowing for a precise appraisal of the cornia model . indeed , experiments reveal a significant overlap of the @xmath16 and @xmath17 resonances , providing conclusive evidence for the presence of tilts . however , we find that the magnitude of the tilts is a factor of @xmath19 larger than predicted by cornia et al.,@xcite which should be of both theoretical and experimental significance in regards to understanding the spin dynamics of mn@xmath0-ac . our conclusions also provide an explanation for several previously reported anomalous epr transitions ( labeled @xmath17-resonances ) which can not be explained within the widely accepted giant spin ( @xmath20 ) model described below.@xcite    we emphasize from the outset that our conclusions are based upon the angle - dependent behavior of epr fine structures which have previously been explained@xcite within the context of the cornia solvent - disorder picture,@xcite and have been independently supported by magnetization measurements.@xcite the easy axis tilting is inferred from the persistence of epr peaks for field orientations which are tilted significantly away from the angles where the intensity should have vanished if all molecules were aligned . the discrete nature of the tilting can then be seen from the fact that the different fine structures exhibit distinct angle dependencies . this behavior is completely reproducible in mn@xmath0-ac samples prepared by different methods and by different groups.@xcite furthermore , our method of analysis is not sensitive to the intricacies associated with lineshape analyses , which could be influenced by complex many - body effects , e.g. magnetic spin - spin interactions.@xcite finally , we note that all of the unusual solvent - induced anomalies reported in this paper for mn@xmath0-ac are absent in the epr spectra for a related high - symmetry ( @xmath21 ) mn@xmath0 complex [ mn@xmath0o@xmath0(o@xmath22cch@xmath22br)@xmath5(h@xmath22o)@xmath234ch@xmath6cl@xmath6 ] which possesses a full compliment of four ch@xmath6cl@xmath6 solvent molecules per mn@xmath0.@xcite","summary":"et al . _ , phys . rev . the effect is considerably larger than deduced from x - ray diffraction analyses . these data constitute the sought - after evidence for the presence of transverse fields in mn-acetate , and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low - temperature hysteresis experiments for this system .","abstract":"the variation with microwave frequency and temperature of previously reported anomalous peaks in the epr spectra of mn-acetate , under large transverse fields , reveals that the molecular easy magnetization axes are tilted with respect to the global symmetry direction . more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra we infer that the tilt distribution must be discrete , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [ s. hill _ et al . _ , phys . rev . lett . * 90 * , 217204 ( 2003 ) ] . the tilts are confined to two orthogonal planes , and the distribution extends up to degrees away from the the global easy (- ) axis . we ascribe the tilting to the hydrogen - bonding effect associated with the disordered acetic acid solvent molecules . the effect is considerably larger than deduced from x - ray diffraction analyses . these data constitute the sought - after evidence for the presence of transverse fields in mn-acetate , and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low - temperature hysteresis experiments for this system ."}
{"article_id":"cond-mat0401515","section_id":"i","document":"the basis of our experiment is illustrated in fig . 1 , which shows the spin energy level diagram for mn@xmath0-ac ( fig . 1a ) , based on an exact diagonalization of the standard @xmath3 spin hamiltonian @xcite under a transverse magnetic field @xmath25 , and assuming @xmath21 symmetry :     @xmath26    here , @xmath27 is the projection of the spin operator @xmath28 along @xmath2 , and @xmath29 ( @xmath30 ) is the uniaxial anisotropy parameter ; the second term is the zeeman interaction ; and the remaining terms represent higher order crystal field interactions ( the operators @xmath31 and @xmath32 have their usual meaning).@xcite we have used acceptable parameters for the simulations in fig .  1 : @xmath33 @xmath34 , @xmath35 = @xmath36 @xmath34 and @xmath37 = @xmath38 @xmath34 . we note that this parameter set yields the optimum agreement with a large body of single crystal epr data,@xcite including the present study , which additionally considers the effects of _ e_-strain and easy axis tilting . at this stage , we do not explicitly include lower symmetry interactions in eq .  1 due to disorder , e.g. second - order rhombicity , or easy - axis tilting . we begin by considering a single molecule and the effect of field - mis - alignment away from the hard plane . we then compare experimental data with simulations in order to quantify the easy - axis tilting caused by the solvent - disorder in mn@xmath0-ac . finally , we consider the rhombic anisotropy associated with this disorder . we note that an account of the influence of the solvent - disorder - induced rhombic anisotropy [ @xmath39 , and its affect on the transverse field epr fine structure , has been presented previously by us.@xcite in the following , we use polar coordinates to parameterize the field orientation : @xmath40 represents the angle between the applied field and the global easy ( @xmath2- ) axis of the single crystal ; @xmath41 represents the azimuthal angle , i.e. the angle between the intrinsic hard four - fold ( @xmath42- ) @xmath43 axis and the projection of the applied field onto the hard plane .    in the high - field limit ( @xmath44*b *  @xmath45 ) , and for the standard epr geometry ( microwave field * h*@xmath46*b * ) , one expects a total of 20 @xmath47 epr transitions between the 21 ( @xmath48 ) spin - states for @xmath3 . for clarity , only a few of the lowest - lying levels are shown in fig . 1a for the case of a magnetic field applied precisely along the medium four - fold axis of a single molecule ( i.e. @xmath49 and @xmath50 ) ; these levels are labeled on the right - hand - side of fig . 1a according to an @xmath51 basis , where @xmath52 (=  integer ) is the projection of the total spin along the applied field axis . the high - field epr spectra are dominated by transitions between adjacent levels , i.e. @xmath53 . if one follows the epr spectra to lower fields , into a region where the zeeman and axial terms in eq . 1 become comparable ( @xmath54*b *  @xmath55 ) , one finds that the transitions may be grouped into two categories : i ) those between levels which evolve from @xmath56 ( @xmath57  integer ) zero - field doublets , which we label @xmath16 ( represented by blue sticks in fig . 1a ) ; and ii ) those between levels which evolve from adjacent zero - field doublets , which we label @xmath17 ( represented by red solid circles in fig .  1a ) . this distinction between @xmath16 and @xmath17 resonances is based on a zero - field @xmath58 basis , where @xmath59 is the projection of the total spin along the uniaxial direction of the crystal @xmath60 the levels are labeled according to this convention on the left - hand - side of fig . 1a . throughout the remainder of the paper , we number all transitions according to the absolute value of @xmath52 ( high - field @xmath51 representation ) associated with the level from which the transition was excited , preceded by either @xmath16 or @xmath17 ( low - field @xmath58 representation ) in order to distinguish between the two categories of resonances . therefore , the highest field blue stick in fig . 1a corresponds to @xmath61 , while the highest field red circle corresponds to @xmath62.@xcite    in order to set the scene , we first review the status of earlier single - crystal epr studies . the observation most pertinent to the present work is seen in fig . 1b , which compares various calculations of the @xmath16 and @xmath17 transition frequencies with actual 8  k epr peak positions.@xcite for these earlier experiments , data were obtained with the field applied parallel to the hard plane of a single - crystal sample to within an accuracy of @xmath63 ( @xmath64 ) . within the hard plane , a crude attempt was made to align the magnetic field along the medium four - fold axis . based on our more recent angle dependent studies on accurately aligned single crystals ( section  iii and ref . [ ] ) , we estimate that such an alignment was achieved to within an accuracy of approximately @xmath65 ( i.e. @xmath66 ) . for the purposes of the following discussion , any mis - alignment within the hard plane is not important . in the absence of tilting , the calculated @xmath16 transition frequencies decrease smoothly to zero ( thick blue curves in fig . 1b ) , whereas the @xmath17 transition frequencies ( thick red curves in fig . 1b ) go through minima which are on the order of 90  ghz for the three highest field branches . the actual @xmath17-transition data , on the other hand , deviate significantly from these predictions , i.e. they do not exhibit a minimum frequency , but instead follow monotonic curves to the lowest frequencies investigated . the same trend has been noted for field alignment along different directions within the hard plane.@xcite for comparison , fig . 2 displays representative experimental epr spectra obtained with the field approximately along the hard four - fold axis ( @xmath67 ) , also within @xmath68 of the hard / medium plane ( @xmath69);@xcite note that the @xmath17-resonances are again seen to the lowest frequencies studied ( 44  ghz ) . following our more recent angle - dependent studies that provided clear indications for a breakdown of the four - fold symmetry of mn@xmath0-ac,@xcite and in light of the cornia model,@xcite we conjecture that the anomalous behavior of the @xmath17 transitions might be explained in terms of tilts of the easy - axes of magnetization at a local scale . to better illustrate this idea , we have included tilted field calculations in fig . 1b ( thin curves : blue@xmath70 , red@xmath71 ) for a few of the highest field transitions . each tilted field curve belongs to a family of curves which deviate successively ( in @xmath72 increments ) from one of the zero - tilt curves ( @xmath49 , thick lines ) ; the tilted field curves have been truncated at low fields in order to simplify the figure . tilting the field away from the hard plane results in a field component parallel to the easy axis . this  longitudinal \" field ( @xmath73 ) has the effect of lifting the degeneracy of the of the @xmath56 zero - field doublets in zeroth order.@xcite consequently , instead of tending to zero - frequency , the @xmath16 resonance frequencies tend to successively larger offsets as the field is tilted away from the hard plane , as seen by the thin blue curves and indicated by the blue arrow ( for @xmath61 ) in fig . the opposite is true for the @xmath17 transitions . since the longitudinal field splits the low - field @xmath56 doublets , this results in a reduction in the closest approach of levels in adjacent doublets @xmath60 hence , to a reduction in the minimum frequency of the @xmath17 transitions ; again , this behavior is born out by the thin red curves and indicated by the red arrow ( for @xmath62 ) in fig . thus , tilting could explain the continuation of the @xmath17 resonance data to frequencies well below the theoretical minima given by the thick red curves ( @xmath49 , or @xmath74 ) in fig . however , the observed trend can not be ascribed to a simple mis - alignment of the sample , because the @xmath61 ( highest field blue squares ) and @xmath62 ( highest field red circles ) resonances are both seen to frequencies below 50  ghz ( see also fig .  2 ) . the observation of @xmath62 at 45  ghz would imply a sample mis - alignment of @xmath75 , which is completely incompatible with the observed behavior of the @xmath61 data which tracks the thick blue curve ( @xmath49 , or @xmath74 ) in fig . 1b ; note that each successive thin curve corresponds to an additional @xmath72 of tilt away from the hard plane . thus , it would appear that the data in figs .  1 and 2 reflect several molecular orientations . a rigorous comparison between experiment and eq .  1 , in this frequency / field range where the zeeman and axial terms are comparable , requires calculation of magnetic dipole matrix elements , i.e. a full simulation of the epr spectra . 3 and  4 show 15  k epr simulations , as a function of the polar angle @xmath40 between the applied field and the easy axis of a single molecule , and for two of the lowest frequencies used in our experiments ( 44  ghz and 62  ghz ) ; the simulations are limited to the @xmath76 to @xmath77 range in @xmath78 increments . in figs  3a and  4a , the vertical scale represents microwave absorption while , in figs  3b and  4b , absorption is indicated by the darker shaded regions . the simulations were generated using the software package sim;@xcite no rhombic ( @xmath79 ) term was included at this stage , and the simulations assume perfect alignment of all molecules in the sample , i.e. no orientational averaging was employed . as expected , the simulations confirm that only the @xmath16 peaks are observed for fields parallel to the hard plane ( @xmath80 ) , for @xmath81  ghz . however , tilting the field away from the hard plane leads to a very abrupt suppression of the magnetic dipole matrix elements ( epr selection rules ) for the @xmath16 transitions @xmath60 this behavior was not obvious from fig .  1 . in just @xmath82 of rotation , @xmath61 vanishes completely at 44  ghz ( @xmath63 for 62  ghz ) . this is then followed by a range of almost @xmath83 where neither @xmath61 nor @xmath62 are observed at the lowest frequency of 44  ghz , i.e. @xmath62 does not appear until the field is tilted about @xmath84 away from the hard plane . similar trends are seen at both frequencies for @xmath85 and @xmath86 , etc .. , albeit over differing angle ranges . remarkably , the simulations are suggestive of a symmetry effect in the transverse - field ( @xmath87 ) epr spectra , as a function of the longitudinal field component ( @xmath88 ) . the dashed curves on the contour plots in figs . 3b and  4b indicate lines of constant @xmath73 , demonstrating that all of the @xmath16 resonances disappear ( and all of the @xmath17 resonances appear ) at roughly the same longitudinal field strengths . subsequently , the @xmath17 resonances disappear and the @xmath89 resonances re - appear . this behavior is reminiscent of the tunnel - splittings seen in the fe@xmath90 smm as a function of transverse field , for different static longitudinal fields.@xcite indeed , closer inspection of fig . 1b reveals that the @xmath17 transition frequencies tend to zero at certain values of @xmath73 , while the simulations in figs . 3 and 4 suggest that the @xmath17 transitions matrix elements tend to zero as well at these same angles . thus , the analogy with the quenching of the ground - state tunnel splittings in fe@xmath90 is significant , albeit the degeneracies involve excited levels evolving from different zero - field doublets in the present case . we shall not pursue this analogy further here . however , we note that the @xmath17 series of resonances is exactly what one would expect from a spin @xmath91 system in a perpendicular field with the same hamiltonian parameters as the parent @xmath20 system;@xcite meanwhile @xmath92 corresponds to the first expected peak in a series belonging to a spin @xmath93 system , and so on . furthermore , all resonances except for @xmath61 occur from excited levels . thus , the tilted field data have the appearance of spectra from excited multiplets having successively lower total spin , as was originally proposed by us as an explanation for the anomalous @xmath17 resonances.@xcite    an intensity analysis of the measured low - frequency ( @xmath15  ghz ) @xmath62 peaks in fig .  2 yields an ( approximate ) activation energy consistent with an excitation from the @xmath94 state within the @xmath20 manifold . we should point out that , in order to precisely fit the @xmath95 intensity , one must first fully comprehend its origin ( we save such an analysis until the end of this article ) . the clearest indication that @xmath62 likely occurs within the @xmath20 manifold can be seen by noting that the temperature dependencies of the @xmath95 and @xmath96 transitions in fig . 2 are very similar , suggesting that they both involve energy levels which are close in energy . thus , in the following sections , we _ do not _ consider the possibility of excitations within excited state ( @xmath97 ) manifolds . however , the simultaneous observation of @xmath61 and @xmath62 down to a frequency of 44  ghz ( fig . 2 ) _ is not _ consistent with the simulations in fig .  3 , which assume aligned molecules . for this reason , we argue that the molecular easy - axes are not perfectly aligned , i.e. we propose a distribution of easy - axis alignments centered about the global four - fold axis of the crystal . this would result in overlapping angle dependent features ( such as those in figs . 3 and  4 ) from different parts of the distribution , i.e. for a given field orientation one may observe @xmath17 peaks from tilted ( aligned ) molecules together with @xmath16 peaks due to aligned ( tilted ) molecules . as already discussed , the origin for such a distribution can be understood in terms of solvent disorder . indeed , the calculations by cornia et al . predict easy - axis tilts of up to @xmath72.@xcite the absence of either @xmath61 or @xmath62 over an approximately @xmath83 range in the simulation in fig . 3 suggests that the tilt distribution extends at least @xmath98 , since both @xmath61 and @xmath62 are observed in the 44  ghz spectra ( fig .  2 ) .","summary":"lett . * 90 * , 217204 ( 2003 ) ] .","abstract":"the variation with microwave frequency and temperature of previously reported anomalous peaks in the epr spectra of mn-acetate , under large transverse fields , reveals that the molecular easy magnetization axes are tilted with respect to the global symmetry direction . more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra we infer that the tilt distribution must be discrete , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [ s. hill _ et al . _ , phys . rev . lett . * 90 * , 217204 ( 2003 ) ] . the tilts are confined to two orthogonal planes , and the distribution extends up to degrees away from the the global easy (- ) axis . we ascribe the tilting to the hydrogen - bonding effect associated with the disordered acetic acid solvent molecules . the effect is considerably larger than deduced from x - ray diffraction analyses . these data constitute the sought - after evidence for the presence of transverse fields in mn-acetate , and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low - temperature hysteresis experiments for this system ."}
{"article_id":"cond-mat0401515","section_id":"c","document":"the origin of two separate angle dependencies finds a natural explanation if one assumes that the easy - axis tilting and rhombicity are connected ( as predicted by cornia ) , and that the tilting is confined to directions determined by the principal axes of the rhombic zero - field tensor . we now assume that two of the mn@xmath0 variants originally discussed by cornia et al . ( @xmath111 and @xmath112)@xcite have their easy axes tilted significantly , and that these tilts are confined to two orthogonal planes defined by the associated rhombic zero - field tensor and the global four - fold ( @xmath2- ) axis . the @xmath111 and @xmath112 variants comprise @xmath109 of the total number of molecules in cornia s model , and both species are predicted to have significant @xmath79 values ( @xmath113  @xmath34).@xcite of this @xmath109 , half of the molecules ( @xmath114 of the total @xmath60 the * a * molecules ) are expected to have their hard two - fold axes aligned along a single direction within the hard plane . then , because there exist four equivalent positions for the acetic acid of crystallization related by a four - fold rotation about @xmath2 , the remaining half of the @xmath111 and @xmath112 species ( @xmath114 of the total @xmath60 the * b * molecules ) will have their hard axes aligned @xmath77 away from the hard axes of the * a * molecules , i.e. parallel to the medium two - fold axes of the * a * molecules . this situation is depicted by the polar ( @xmath41- ) plot in the lower panel of fig . the two - fold hard axes are denoted @xmath115 , with the subscript * a * or * b * to distinguish between the two sub - sets of molecule . the orientations of these axes relative to the four - fold hard - axes ( @xmath116 at @xmath117 , @xmath77 , @xmath118 , and @xmath119 ) is based on previous angle - dependent epr investigations for rotations within the hard plane , where it was determined that the principal axes of the @xmath79 and @xmath43 tensors were mis - aligned by @xmath120.@xcite next , we assume that the easy axis tilts are also confined along these two distinct / discrete directions , as indicated by the shaded regions in the lower panel of fig .  6 . in other words , the well defined rhombic distortion and molecular easy axis tilting are directly related . based on the ensuing analysis , we find that molecules tilted in one of the two orthogonal planes have their @xmath115 axes perpendicular to that plane , as shown in the upper panel of fig . thus , the * a * ( * b * ) molecules are tilted in a plane containing the @xmath121 ( @xmath122 ) axis . it is now possible to see how one might expect two distinct angle dependencies for different parts of the epr spectrum , i.e. the shoulders and the main peaks . the thick purple arrow along @xmath123 ( and @xmath124 ) in the lower panel of fig . 6 represents the best estimate ( _ vide infra _ ) of the plane of rotation for the epr spectra presented in fig . this plane is inclined closer to @xmath122 ( @xmath125 and @xmath126 ) than to @xmath121 ( @xmath127 and @xmath128 ) . therefore , for fields close to the hard plane ( @xmath49 ) , the rhombic term ( @xmath129 ) associated with the @xmath111 and @xmath112 variants will lead to different epr peak - position - shifts for the * a * and * b * molecules , thereby enabling one to resolve their contributions to the epr spectra for a sufficiently large @xmath79 value . in our experiments , the plane of rotation is closer to the tilt - plane for the * b * molecules than for the * a * molecules ( @xmath130 as opposed to @xmath131 ) . thus , the projection of the tilt distribution onto the plane of rotation is correspondingly greater for the * b * molecules than for the * a * molecules . the magnitudes of these projections scale as the @xmath132 of the angle ( @xmath133 ) between the field rotation plane and the corresponding tilt - plane . indeed , as explained later , it is on this basis that we deduced the orientation of the plane of rotation relative to @xmath122 and @xmath121 for the experiments presented in fig . the molecules having the greater projection of tilts onto the rotation plane will , thus , be expected to exhibit the greater spread in their associated epr spectra away from the hard plane . in this scenario , one may attribute the shoulders on the high - field sides of the main peaks in fig .  5 to the * a * molecules in fig . 6 , since their tilt distribution will have a narrower projection onto the rotation plane ( see projections onto field rotation plane represented by blue and red dashed lines in fig . furthermore , the fact that the rotation plane is close to the hard axes of the * a * molecules is fully consistent with the appearance of the shoulder on the high - field sides of the main peaks ( assuming @xmath134 ) . meanwhile , the contribution of the * b * molecules is buried within the main peak , as explained below .    based on the geometry depicted in fig .  6 , we set out to simulate the data in fig . the discussion above concerns only @xmath109 of the possible variants in cornia s model,@xcite i.e. the two dominant species possessing a significant @xmath79-term . furthermore , only half of these ( @xmath114 of the total ) are tilted in the plane of rotation . for the sake of simplicity , we assume that the remaining @xmath109 of the molecules ( * c * ) do not possess a significant @xmath79-value . this is a slight simplification of cornia s model , since it is known that the @xmath135 trans species ( comprising @xmath136 of the molecules ) are predicted to have an @xmath79-value comparable to the @xmath111 and @xmath112 variants.@xcite however , one should first recall that cornia s calculations are approximate , and that our previous epr studies have indicated that the magnitudes of the @xmath79-values may have been underestimated.@xcite second , introducing too many different species would result in an over - parameterization of our model . the main purpose of the following simulation is to demonstrate that one can explain essentially all aspects of the single - crystal epr spectra for mn@xmath0-ac based on a simple model involving three just three molecular species , together with discrete easy - axis tilting , in the spirit of the original cornia proposal . it is not our intent that this model be viewed as definitive . 7 shows three gray - scale contour plots representing the expected angle ( @xmath40- ) dependent contributions to the epr intensity for the three species * a * , * b * , and * c * ; they assume the same experimental conditions as figs .  4 and 5 , i.e. t  @xmath137  15  k and a frequency of 62  ghz . the simulations in figs . 7a and  b assume that the * a * and * b * molecules are tilted respectively along the @xmath122 and @xmath121 directions ( @xmath138 and @xmath139 ) i.e. the orientations of the tilt planes are  discrete . \" meanwhile , we assume a non - discrete distribution of the tilt angles along these two directions , which cuts - off at @xmath140 , as indicated by the shaded region in the lower panel of fig . 6 . in addition , we assume an @xmath79-value of @xmath141  @xmath34 for the * a * and * b * species . the simulation in fig . 7c assumes no @xmath79-value . consequently , the epr intensity due to the * c * molecules contributes to the bulk of the central portion of the summed epr peaks ( fig . we included a small random ( i.e. not confined to planes ) distribution of tilts ( @xmath98 ) for the * c * molecules as a means of taking into account possible variations in the zero - field parameters / orientations associated with the four cornia variants ( @xmath142 , @xmath143 , @xmath135 cis and trans ) which comprise this remaining @xmath109 of the molecules . it is the finite @xmath79-value associated with the * a * and * b * species which enables us to resolve the discrete nature of their tilting directions . we can not rule out similar properties for the remaining species ( * c * ) , but their smaller @xmath79-values do not allow us to observe such discrete behavior . thus , the choice of random tilts for the * c * molecules is quite arbitrary . nevertheless , this distribution provides better overall qualitative agreement with the observed out - of - plane angle dependence in fig . agreement between experiment ( fig .  5 ) and the subsequent summation of the simulated spectra ( fig . 8) is rather sensitive to the precise cut - off angle of @xmath140 for the tilt distribution of the * a * and * b * molecules ; however , it is not so sensitive to the exact shape of the distribution . for example , a discrete distribution with the * a * and * b * molecules all having precisely @xmath140 tilts along @xmath122 and @xmath121 reproduces many aspects of the experiments . however , such simulations contain many more fine structures which are averaged out by considering a smoother distribution such as the one employed in the fig . 8 simulations . once again , we stress that this parameter set should not be viewed as definitive . however , we emphasize that , in order to simulate the main qualitative trends in the data ( e.g. the distinct angle dependencies of the main peaks and high - field shoulders ) , a discrete tilt distribution is necessary . as discussed above , the simulations are not so sensitive to the shape of the tilt distribution within each tilt plane . thus , it is not easy to make direct comparisons with the distributions of tilts inferred by other methods.@xcite however , we note that only a small subset of the molecules ( @xmath114 ) , corresponding to half of the lowest symmetry cornia variants,@xcite are able to contribute to the anomalous epr intensity in our experiment . of these molecules , we can conclude that fewer than half ( @xmath144 of the total ) are tilted by more than @xmath82 . while comparisons between the gray - scale plots are not so sensitive to the @xmath79-value , comparisons between simulated and actual experimental spectra are extremely sensitive to @xmath79 ( see fig .  10 below ) ; the value of @xmath145  @xmath34 gives the best agreement with a wide body of single - crystal data collected over several years.@xcite this @xmath79 value is also in excellent agreement with a recent first principles calculation by park et al.@xcite    as discussed above , the relative angle ( @xmath133 ) between the field rotation plane and the * a * and * b * tilt - planes ( @xmath121 and @xmath122 respectively ) was chosen so that the epr peaks corresponding to the * a * and * b * molecules ( figs . 7a and  b ) cover the same angle ranges as the high - field shoulders ( @xmath146 for @xmath61 ) and the central portions of the peaks ( @xmath147 for @xmath61 ) respectively in fig . the best agreement was obtained with the field rotation plane oriented @xmath130 away from @xmath122 ( fig . thus , we estimate that the @xmath122 and @xmath121 axes are oriented @xmath148 and @xmath149 with respect to the sample faces , while the hard four - fold axes are roughly @xmath150 away ( see fig . 6 ) , which also agrees with magnetic and structural data.@xcite the simulated spectra obtained according to the aforementioned procedure were then normalized and summed in the ratio * a*:*b*:*c *  @xmath151  @xmath152 . the results of this summation are displayed in fig . agreement with the experimental data in fig . 5 is quite impressive . first and foremost , the simulations including tilts account for essentially all of the anomalous aspects of the data which could not be explained without tilts ( fig .  4 ) . for example : the @xmath61 and @xmath62 peaks overlap by about @xmath83 between roughly @xmath153 and @xmath154 ; the @xmath62 peak disappears ( below the @xmath155 level ) over a roughly @xmath156 range either side of @xmath157 . there is also clear evidence for a shoulder on the high - field sides of the main epr peaks , although this shoulder is more apparent in fig . 5a than 5b . the overall widths and shapes of the resonances are also reproduced fairly well , including the broad low - field tail and the fairly abrupt decrease in intensity on the high - field sides of the peaks ( a 0.1  tesla gaussian lineshape was employed in the individual simulations in fig . we note from fig .  5 that an extremely weak @xmath95 signal persists even for fields parallel to the hard plane . we were unable to reproduce this behavior in the simulations while , at the same time , maintaining good agreement with other aspects of the experimental data , e.g. the angle range of overlap between the @xmath16 and @xmath17 resonances . we therefore speculate that this weak remnant signal may be due to excitations within a higher lying @xmath91 state , as previously proposed by us.@xcite however , more careful temperature dependent studies will be required in order to establish the location of this excited state relative to the @xmath20 ground state . indeed , recent measurements on a related high symmetry mn@xmath0 species ( without significant easy axis tilting ) have enabled precisely such an analysis.@xcite    having satisfactorily reproduced the spectra for out - of - plane rotations ( figs .  5 and  8) , we consider previously published spectra obtained as a function of the field orientation @xmath41 within the hard plane.@xcite one of the puzzling questions concerning these earlier measurements concerned the observation of only a single satellite peak ( shoulder ) on the high - field side of resonances for some field orientations . the modulation of the widths of the epr peaks was originally explained in terms of the cornia model.@xcite so why does one never see both low - field and high - field shoulders , corresponding to the positive and negative epr line - position - shifts induced by the different signs of the rhombic term ? we note that , for a field along @xmath122 ( @xmath121 ) , one expects an upward ( downward ) shift in field of the absorption due to the * a * molecules , together with a downward ( upward ) shift due to the * b * molecules . the apparent explanation is illustrated in fig . 9 , which displays the evolution of absorption due to one of the tilted species ( either * a * or * b * ) as a function of the field orientation ( within the hard plane ) relative to the hard two - fold axis for that species ; note @xmath105 this is not the same as the angle @xmath41 . with the field along the hard two - fold axis @xmath115 ( @xmath158 in fig .  9 ) , the resonance occurs at the highest field position , while the projected distribution of tilts onto the rotation plane is at its narrowest . consequently , the epr peak is narrow . conversely , with the field along the medium two - fold axis ( @xmath159 in fig . 9 ) , the resonance occurs at the lowest field position , and the projected distribution of tilts onto the rotation plane is at its broadest , resulting in a broader epr peak . conservation of the area under the peaks additionally requires that the @xmath160 peak be more intense at its maximum than the @xmath161 peak . the result is that the broad low - field shoulder does not quite get resolved from the main * c * peak , whereas the sharp high - field peak is resolved for several of the resonances @xmath105 particularly @xmath61 and @xmath85 . in fact , the low - field @xmath161 peak contributes significantly to the slow decay of the @xmath61 resonance on its low - field side , thus accounting for another previously unexplained feature of the mn@xmath0-ac single - crystal epr spectra . we note that recent experiments on deuterated samples reveal shoulders on both the low and high field sides of the main resonances.@xcite    knowing the relative orientations of the principal axes associated with the @xmath79 and @xmath43 tensors , we can simulate the full hard - plane angle dependence published previously,@xcite as shown in figs . 10 to  12 . we note that , while the misalignment of the @xmath79 and @xmath43 tensors has previously been suggested from x - ray structure measurements , the epr studies in ref . [ ] clearly illustrate that the magnetic properties of mn@xmath0-ac reflect this misalignment . 10 displays the simulated spectra as a function of the field orientation @xmath41 relative to one of the hard four - fold axes ( @xmath116 ) . these spectra can be compared directly with fig .  1 of ref . [ ] , albeit that the frequencies are slightly different ( 50  ghz in ref .  [ ] and 62  ghz in the present case ) . the previously published spectra do not include the highest field @xmath61 resonance due to the limitations of the split - pair magnet used in those investigations ; one should also be careful to note the different labeling scheme used in this and earlier studies.@xcite the splitting of @xmath85 ( highest field peak in ref . [ ] ) is reproduced very precisely , as are the amplitudes of the linewidths ( full - width - at - half - maximum @xmath105 fwhm ) variations with angle , as displayed in fig .  11 for peaks @xmath162 to @xmath85 . again , these are the same four linewidths plotted in fig .  2a of ref . the maximum linewidth or splitting caused by the disorder - induced rhombic anisotropy is observed at @xmath163 and @xmath164 relative to the @xmath116 axes ( see fig . 6 ) , and the widths are in fair agreement with the @xmath79-value used in the present simulations . the orientations of the linewidth maxima , which correspond to the hard and medium two - fold axes ( @xmath122 and @xmath121 ) are , therefore , oriented at @xmath149 and @xmath148 relative to the crystal faces . the @xmath165 and @xmath166 symbols are used here to reflect the inversion symmetry of the crystal . we note that the linewidth minima are somewhat deeper in the simulation ( fig . 11 ) , as compared to experiment.@xcite this is most likely due to other sources of line broadening ( d - strain , g - strain , etc .. ) which were not taken into consideration in our model . the main point of this simulation is to once again show that the four - fold oscillation in the linewidth / splitting is related to the @xmath79-strain , and that the model employed in this study is in complete agreement with our earlier investigations . the contour plot in fig . 12 clearly illustrates the four - fold variation in the line positions caused by the intrinsic four - fold @xmath167 transverse anisotropy . the orientation of one the @xmath116 axes , together with one of the @xmath115 axes , is indicated at the top of the figure , as is the orientation of the rotation plane corresponding to the data in fig . overall , fig . 12 is an excellent reproduction of the contour plot in fig .  1 of ref . we remind the reader that the linewidth / shape analysis was employed in ref .  [ ] to estimate the rhombic @xmath79-term associated with the low - symmetry mn@xmath0 variants , and is supported by independent magnetization studies.@xcite contrary to recent assertions,@xcite the epr linewidths are not used in our determination of the easy - axis tilting , which has been inferred entirely from the angle - dependent intensities of the epr spectra .    finally , having reproduced the full angle dependence at a single temperature of 15  k , we display in fig .  13 a simulation of the older temperature dependent data shown in fig .  2 . we found it necessary to include a small mis - alignment ( @xmath82 , or @xmath168 ) of the field away from the hard plane in order to obtain the appropriate relative intensities of the @xmath16 and @xmath17 resonances , i.e. we suspect an approximately @xmath82 mis - alignment in the original experiment ( we note that these earlier studies were performed in a cryostat which did not allow for in - situ alignment of the sample ) . within the hard plane , the simulation assumes that the field was applied along the @xmath116 axis ( i.e. @xmath169 ) . agreement between the simulations and the experiment is extremely good .","summary":"the tilts are confined to two orthogonal planes , and the distribution extends up to degrees away from the the global easy (- ) axis .","abstract":"the variation with microwave frequency and temperature of previously reported anomalous peaks in the epr spectra of mn-acetate , under large transverse fields , reveals that the molecular easy magnetization axes are tilted with respect to the global symmetry direction . more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra we infer that the tilt distribution must be discrete , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [ s. hill _ et al . _ , phys . rev . lett . * 90 * , 217204 ( 2003 ) ] . the tilts are confined to two orthogonal planes , and the distribution extends up to degrees away from the the global easy (- ) axis . we ascribe the tilting to the hydrogen - bonding effect associated with the disordered acetic acid solvent molecules . the effect is considerably larger than deduced from x - ray diffraction analyses . these data constitute the sought - after evidence for the presence of transverse fields in mn-acetate , and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low - temperature hysteresis experiments for this system ."}
{"article_id":"cond-mat0401515","section_id":"i","document":"using angle - resolved single - crystal high - frequency epr measurements , we have clearly demonstrated that the molecular easy axes associated with the widely studied mn@xmath0-ac single - molecule magnet are tilted on a local scale . this tilting provides the much sought - after source of the transverse fields necessary to explain the observation of odd resonant tunneling steps in hysteresis experiments , i.e. the tilt distribution results in a transverse internal field distribution , even when the field is applied precisely parallel to the global easy - axis of the crystal . more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra , we infer that the tilts are constrained along orthogonal planes , i.e. there is a discrete aspect to the tilts , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy.@xcite this behavior is completely reproducible in mn@xmath0-ac samples prepared by different methods and by different groups.@xcite furthermore , our analysis is insensitive to the intricacies associated with lineshape analyses , which could be influenced by complex many - body effects , e.g. magnetic spin - spin interactions.@xcite therefore , this study provides compelling support for the recent predictions by cornia et al.,@xcite who have suggested that a discrete form of disorder associated with the acetic acid of crystallization provides the dominant source of transverse anisotropy responsible for the magnetic quantum tunneling in mn@xmath0-ac . thus , one can rule out suggestions that dislocations may be responsible for the symmetry lowering at the local scale , since one would not expect the easy axis tilting to be confined to discrete planes under such a scenario.@xcite    while our data agree with many qualitative aspects of the cornia model,@xcite the magnitudes of the easy - axis tilting angles ( up to @xmath170 ) , and the rhombic anisotropy associated with the tilted molecules ( @xmath79 up to @xmath141  @xmath34 ) , are both significantly larger than the predicted values ( by a factor of about 5 ) . these results should , therefore , be of significant theoretical interest , forming a basis for more refined structure calculations such as those recently published by park et al.@xcite we tentatively ascribe the observed tilting to the hydrogen - bonding between the two acetic acid solvent molecules per mn@xmath0-ac . this conjecture is supported by earlier observations that hydrogen bonding must be important to the magnetization dynamics in the mn@xmath0 cluster because deuteration leads to a significant slowing down of the magnetization reversal dynamics as measured by high - frequency ac susceptibility.@xcite we note also that all of the unusual solvent - induced anomalies reported in this paper for mn@xmath0-ac are absent in the epr spectra for a related high - symmetry ( @xmath21 ) mn@xmath0 complex [ mn@xmath0o@xmath0(o@xmath22cch@xmath22br)@xmath5(h@xmath22o)@xmath234ch@xmath6cl@xmath6 ] which possesses a full compliment of four ch@xmath6cl@xmath6 solvent molecules per mn@xmath0 , and none of the low symmetry hydrogen bonding environments present in cornia s model.@xcite","summary":"more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra we infer that the tilt distribution must be discrete , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [ s. hill _ we ascribe the tilting to the hydrogen - bonding effect associated with the disordered acetic acid solvent molecules .","abstract":"the variation with microwave frequency and temperature of previously reported anomalous peaks in the epr spectra of mn-acetate , under large transverse fields , reveals that the molecular easy magnetization axes are tilted with respect to the global symmetry direction . more importantly , on the basis of the angle - dependence of fine structures observed in the epr spectra we infer that the tilt distribution must be discrete , as was previously suspected from studies which demonstrated the presence of a locally varying rhombic anisotropy [ s. hill _ et al . _ , phys . rev . lett . * 90 * , 217204 ( 2003 ) ] . the tilts are confined to two orthogonal planes , and the distribution extends up to degrees away from the the global easy (- ) axis . we ascribe the tilting to the hydrogen - bonding effect associated with the disordered acetic acid solvent molecules . the effect is considerably larger than deduced from x - ray diffraction analyses . these data constitute the sought - after evidence for the presence of transverse fields in mn-acetate , and provide a possible explanation for the lack of selection rules in the resonant quantum tunneling behavior seen in low - temperature hysteresis experiments for this system ."}
{"article_id":"math0212403","section_id":"i","document":"-5 mm    the organisers requested a talk which would both be a colloquium style talk understandable to a wide spectrum of mathematicians and one which would survey the recent developments in the subject . i have found it hard to meet both desiderata , and have opted to concentrate on the former . thus the first three sections of this paper contain a simple presentation of a web of deep conjectures connecting galois representations to algebraic geometry , complex analysis and discrete subgroups of lie groups . this will be of no interest to the specialist . my hope is that the result is not too banal and that it will give the non - specialist some idea of what motivates work in this area . i should stress that nothing i write here is original . in the final section i briefly review some of what is known about these conjectures and _ very briefly _ mention some of the available techniques . i also mention two questions which lie outside the topic we are discussing , but which would have important implications for it . maybe someone can make progress on them ? we will let @xmath1 denote the field of rational numbers and @xmath2 denote the field of algebraic numbers , the algebraic closure of @xmath1 . we will also let @xmath3 denote the group of automorphisms of @xmath2 , that is @xmath4 , the absolute galois group of @xmath1 . although it is not the simplest it is arguably the most natural galois group to study . an important technical point is that @xmath3 is naturally a ( profinite ) topological group , a basis of open neighbourhoods of the identity being given by the subgroups @xmath5 as @xmath6 runs over subextensions of @xmath7 which are finite over @xmath1 .    to my mind the galois theory of @xmath1 is most interesting when one looks not only at @xmath3 as an abstract ( topological ) group , but as a group with certain additional structures associated to the prime numbers . i will now briefly describe these structures .    for each prime number @xmath8 we may define an absolute value @xmath9 if @xmath10 with @xmath11 and @xmath12 integers coprime to @xmath8 . if we complete @xmath1 with respect to this absolute value we obtain the field of @xmath8-adic numbers @xmath13 , a totally disconnected , locally compact topological field . we will write @xmath14 for its absolute galois group , @xmath15 . the absolute value @xmath16 has a unique extension to an absolute value on @xmath17 and @xmath14 is identified with the group of automorphisms of @xmath17 which preserve @xmath16 , or equivalently the group of continuous automorphisms of @xmath17 . for each embedding @xmath18 we obtain a closed embedding @xmath19 and as the embedding @xmath18 varies we obtain a conjugacy class of closed embeddings @xmath19 . slightly abusively , we shall consider @xmath14 a closed subgroup of @xmath3 , suppressing the fact that the embedding is only determined up to conjugacy . this can be compared with the situation ` at infinity ' . let @xmath20 denote the usual archimedean absolute value on @xmath1 . the completion of @xmath1 with respect to @xmath20 is the field of real numbers @xmath21 and its algebraic closure is @xmath22 the field of complex numbers . each embedding @xmath23 gives rise to a closed embedding @xmath24 as the embedding @xmath23 varies one obtains a conjugacy class of elements @xmath25 of order @xmath26 , which we refer to as complex conjugations . there are however many important differences between the case of finite places ( i.e. primes ) and the infinite place @xmath27 is an infinite extension and @xmath17 is not complete . we will denote its completion by @xmath28 . the galois group @xmath14 acts on @xmath28 and is in fact the group of continuous automorphisms of @xmath28 .    the elements of @xmath13 ( resp . @xmath17 ) with absolute value less than or equal to @xmath29 , form a closed subring @xmath30 ( resp . @xmath31 ) . these rings are local with maximal ideals @xmath32 ( resp . @xmath33 ) consisting of the elements with absolute value strictly less than @xmath29 . the field @xmath34 is an algebraic closure of the finite field with @xmath8 elements @xmath35 , and we will denote it by @xmath36 . thus we obtain a continuous map @xmath37 which is surjective . its kernel is called the inertia subgroup of @xmath14 and is denoted by @xmath38 . the group @xmath39 is procyclic and has a canonical generator called the ( geometric ) frobenius element and defined by @xmath40 in many circumstances it is technically convenient to replace @xmath14 by a dense subgroup @xmath41 , which is referred to as the weil group of @xmath13 and which is defined as the subgroup of @xmath42 such that @xmath43 maps to @xmath44 we endow @xmath41 with a topology by decreeing that @xmath38 with its usual topology should be an open subgroup of @xmath41 . we will take a moment to describe some of the finer structure of @xmath38 which we will need for technical purposes later . first of all there is a ( not quite canonical ) continuous surjection @xmath45 such that @xmath46 for all @xmath47 . the kernel of @xmath48 is a pro-@xmath8-group called the wild inertia group . the fixed field @xmath49 is obtained by adjoining @xmath50{p}$ ] to @xmath51 for all @xmath52 coprime to @xmath8 and @xmath53{p } = \\zeta_n^{t(\\sigma ) } \\sqrt[n]{p},\\ ] ] for some primitive @xmath54-root of unity @xmath55 ( independent of @xmath43 , but dependent on @xmath48 ) . i want to focus here on attempts to describe @xmath3 via its representations . perhaps the most obvious representations to consider are those representations @xmath58 with open kernel , and these so called artin representations are already very interesting . however one obtains a richer theory if one considers representations @xmath59 which are continuous with respect to the @xmath60-adic topology on @xmath61 . we refer to these as _ @xmath60-adic representations_.      1 .   a choice of embeddings @xmath23 and @xmath62 establishes a bijection between isomorphism classes of artin representations and isomorphism classes of @xmath60-adic representations with open kernel . thus artin representations are a special case of @xmath60-adic representations : those with finite image . 2 .   there is a unique character @xmath63 such that @xmath64 for all @xmath60-power roots of unity @xmath65 . this is called the @xmath60-adic _ cyclotomic character_. 3 . if @xmath66 is a smooth projective variety ( and we choose an embedding @xmath67 ) then the natural action of @xmath3 on the cohomology @xmath68 is an @xmath60-adic representation . for instance if @xmath69 is an elliptic curve then we have the concrete description @xmath70({\\overline{{{{\\mathbb{q } } } } } } ) , { \\overline{{{{\\mathbb{q}}}}}}_l ) \\cong { \\overline{{{{\\mathbb{q}}}}}}_l^2,\\ ] ] where @xmath71 $ ] denotes the @xmath72-torsion points on @xmath73 . we will write @xmath74 for the twist @xmath75    before discussing @xmath60-adic representations of @xmath3 further , let us take a moment to look at @xmath60-adic representations of @xmath14 . the cases @xmath76 and @xmath77 are very different . consider first the much easier case @xmath78 . here @xmath60-adic representations of @xmath14 are not much different from representations of @xmath41 with open kernel . more precisely define a _ wd - representation _ of @xmath41 over a field @xmath73 to be a pair @xmath79 and @xmath80 where @xmath81 is a finite dimensional @xmath73-vector space , @xmath82 is a representation with open kernel and @xmath83 is a nilpotent endomorphism which satisfies @xmath84 for every lift @xmath85 of @xmath86 . the key point here is that there is no reference to a topology on @xmath73 , indeed no assumption that @xmath73 is a topological field . given @xmath82 there are up to isomorphism only finitely many choices for the pair @xmath87 and these can be explicitly listed without difficulty . a wd - representation @xmath87 is called _ unramified _ if @xmath88 and @xmath89 . it is called frobenius semi - simple if @xmath82 is semi - simple . any wd - representation @xmath87 has a canonical frobenius semi - simplification @xmath90 ( see @xcite ) . in the case that @xmath91 we call @xmath87 @xmath60-integral if all the eigenvalues of @xmath92 have absolute value @xmath29 . this is independent of the choice of frobenius lift @xmath93 . if @xmath78 , then there is an equivalence of categories between @xmath60-integral wd - representations of @xmath41 over @xmath94 and @xmath60-adic representations of @xmath14 . to describe it choose a frobenius lift @xmath85 and a surjection @xmath95 . up to natural isomorphism the equivalence does not depend on these choices . we associate to an @xmath60-integral wd - representation @xmath87 the unique @xmath60-adic representation sending @xmath96 for all @xmath97 and @xmath47 . the key point is grothendieck s observation that for @xmath78 any @xmath60-adic representation of @xmath14 must be trivial on some open subgroup of the wild inertia group . we will write @xmath98 for the wd - representation associated to an @xmath60-adic representation @xmath99 . note that @xmath98 is unramified if and only if @xmath100 . in this case we call @xmath99 _ unramified_.    the case @xmath77 is much more complicated because there are many more @xmath8-adic representations of @xmath14 . these have been extensively studied by fontaine and his co - workers . they single out certain @xmath8-adic representations which they call _ de rham _ representations . i will not recall the somewhat involved definition here ( see however @xcite and @xcite ) , but note that ` most ' @xmath8-adic representations of @xmath14 are not de rham . to any de rham representation @xmath99 of @xmath14 on a @xmath17-vector space @xmath81 they associate the following .    1 .   a wd - representation @xmath98 of @xmath41 over @xmath17 ( see @xcite and @xcite ) . 2 .   a multiset @xmath101 of @xmath102 integers , called the hodge - tate numbers of @xmath99 . the multiplicity of @xmath103 in @xmath101 is @xmath104 where @xmath105 denotes @xmath28 with @xmath14-action @xmath106 times the usual ( galois ) action on @xmath28 . we now return to the global situation ( i.e. to the study of @xmath107 ) . the @xmath60-adic representations of @xmath3 that arise ` in nature ' , by which i mean ` from geometry ' , have a number of very special properties which i will now list . let @xmath108 be a subquotient of @xmath74 for some smooth projective variety @xmath66 and some integers @xmath109 and @xmath110 .    1 .   ( grothendieck ) the representation @xmath99 is unramified at all but finitely many primes @xmath8 . ( fontaine , messing , faltings , kato , tsuji , de jong , see e.g. @xcite , @xcite ) the representation @xmath99 is de rham in the sense that its restriction to @xmath111 is de rham . ( deligne , @xcite ) the representation @xmath99 is _ pure _ of weight @xmath112 in the following sense . there is a finite set of primes @xmath113 , such that for @xmath114 , the representation @xmath99 is unramified at @xmath8 and for every eigenvalue @xmath115 of @xmath116 and every embedding @xmath117 @xmath118 in particular @xmath115 is algebraic ( i.e. @xmath119 ) . an amazing conjecture of fontaine and mazur ( see @xcite and @xcite ) asserts that any irreducible @xmath60-adic representation of @xmath3 satisfying the first two of these properties arises from geometry in the above sense and so in particular also satisfies the third property . [ cfm ] suppose that @xmath120 is an irreducible @xmath60-adic representation which is unramified at all but finitely many primes and with @xmath121 de rham . then there is a smooth projective variety @xmath66 and integers @xmath109 and @xmath110 such that @xmath81 is a subquotient of @xmath74 . in particular @xmath99 is pure of some weight @xmath122 . algebraic geometers have formulated some very precise conjectures about the action of @xmath3 on the cohomology of varieties . we do nt have the space here to discuss these in general , but we will formulate , in an as algebraic a way as possible , some of their conjectures .      1 .   for each prime @xmath60 and for each embedding @xmath124 @xmath125 is an irreducible subrepresentation of @xmath126 . 2 .   for all indices @xmath110 and for all primes @xmath8 there is a wd - representation @xmath127 of @xmath41 over @xmath2 such that @xmath128 for all primes @xmath60 and all embeddings @xmath129 . 3 .   there is a multiset of integers @xmath130 such that 1 . for all primes @xmath60 and all embeddings @xmath129 @xmath131 2 . and for all @xmath132 @xmath133 is the multiplicity of @xmath11 in @xmath134 . if one considers the whole of @xmath135 rather than its pieces @xmath136 , then part 2 . is known to hold up to frobenius semisimplification for all but finitely many @xmath8 and part 3 . is known to hold ( see @xcite ) . it follows from a theorem of faltings @xcite that the whole conjecture is true for @xmath137 of an abelian variety . the putative constituents @xmath136 are one incarnation of what people call ` pure motives ' . if one believes conjectures [ cfm ] and [ cgeo ] then ` geometric ' @xmath60-adic representations should come in compatible families as @xmath60 varies . there are many ways to make precise the notion of such a compatible family . here is one .    by a _ weakly compatible system of @xmath60-adic representations _ @xmath138 we shall mean a collection of semi - simple @xmath60-adic representations @xmath139 one for each pair @xmath140 , where @xmath60 is a prime and @xmath141 , which satisfy the following conditions . * there is a multiset of integers @xmath142 such that for each prime @xmath60 and each embedding @xmath129 the restriction @xmath143 is de rham and @xmath144 . * there is a finite set of primes @xmath113 such that if @xmath114 then @xmath145 is unramified for all @xmath60 and @xmath146 . * for all but finitely many primes @xmath8 there is a frobenius semi - simple wd - representation @xmath147 over @xmath2 such that for all primes @xmath78 and for all @xmath146 we have @xmath148      * we call @xmath149 _ strongly compatible _ if the last condition ( the existence of @xmath147 ) holds for all primes @xmath8 . * we call @xmath149 _ irreducible _ if each @xmath150 is irreducible . * we call @xmath149 _ pure _ of weight @xmath151 , if for all but finitely many @xmath8 and for all eigenvalues @xmath115 of @xmath152 , where @xmath153 , we have @xmath154 for all embeddings @xmath132 . * we call @xmath149 _ geometric _ if there is a smooth projective variety @xmath66 and integers @xmath109 and @xmath110 and a subspace @xmath155 such that for all @xmath60 and @xmath146 , @xmath156 is @xmath3 invariant and realises @xmath150 .        1 . if @xmath157 is a continuous semi - simple de rham representation unramified at all but finitely many primes then @xmath99 is part of a weakly compatible system . any weakly compatible system is strongly compatible . any irreducible weakly compatible system @xmath149 is geometric and pure of weight @xmath158 . a famous theorem of cebotarev asserts that if @xmath159 is any galois extension in which all but finitely many primes are unramified ( i.e. for all but finitely many primes @xmath8 the image of @xmath38 in @xmath160 is trivial ) then the frobenius elements at unramified primes @xmath161 are dense in @xmath160 . it follows that an irreducible weakly compatible system @xmath149 is uniquely determined by @xmath147 for all but finitely many @xmath8 and hence by one @xmath150 . conjectures [ cfm ] and [ ccs ] are known for one dimensional representations , in which case they have purely algebraic proofs based on class field theory ( see @xcite ) . otherwise only fragmentary cases have been proved , where amazingly the arguments are extremely indirect involving sophisticated analysis and geometry . we will come back to this later . @xmath0-functions are certain dirichlet series @xmath162 which play an important role in number theory . a full discussion of the role of @xmath0-functions in number theory is beyond the scope of this talk . the simplest example of an @xmath0-function is the riemann zeta function @xmath163 it converges to a holomorphic function in the half plane @xmath164 and in this region of convergence it can also be expressed as a convergent infinite product over the prime numbers @xmath165 this is called an _ euler product _ and the individual factors are called euler factors . lying deeper is the fact that @xmath166 has meromorphic continuation to the whole complex plane , with only one pole : a simple pole at @xmath167 . moreover if we set @xmath168 then @xmath169 satisfies the functional equation @xmath170 encoded in the riemann zeta function is lots of deep arithmetic information . for instance the location of the zeros of @xmath166 is intimately connected with the distribution of prime numbers . moreover its special values at negative integers ( where it is only defined by analytic continuation ) turn out to be rational numbers encoding deep arithmetic information about the cyclotomic fields @xmath171 . another celebrated example is the @xmath0-function of an elliptic curve @xmath73 : @xmath172 in this case the @xmath0-function is defined as an euler product ( converging in @xmath173 ) @xmath174 where @xmath175 is a rational function , and for all but finitely many @xmath8 @xmath176 with @xmath177 being the number of solutions to the congruence @xmath178 in @xmath179 . it has recently been proved @xcite that @xmath180 can be continued to an entire function , which satisfies a functional equation @xmath181 for some explicit positive integer @xmath182 . a remarkable conjecture of birch and swinnerton - dyer @xcite predicts that @xmath183 has infinitely many rational solutions if and only if @xmath184 . again we point out that it is the behaviour of the @xmath0-function at a point where it is only defined by analytic continuation , which is governing the arithmetic of @xmath73 . this conjecture has been proved ( see @xcite ) when @xmath180 has at most a simple zero at @xmath167 . one general setting in which one can define @xmath0-functions is @xmath60-adic representations . let us look first at the local setting . if @xmath87 is a wd - representation of @xmath41 on an @xmath73-vector space @xmath81 , where @xmath73 is an algebraically closed field of characteristic zero , we define a local l - factor @xmath185 ( @xmath186 is the subspace of @xmath81 where @xmath38 acts trivially and @xmath88 . ) one can also associate to @xmath87 a conductor @xmath187 , which measures how deeply into @xmath38 the wd - representation @xmath87 is nontrivial , and a local epsilon factor @xmath188 , which also depends on the choice of a non - trivial character @xmath189 with open kernel . ( see @xcite . ) if @xmath190 is an @xmath60-adic representation of @xmath3 which is de rham at @xmath60 and pure of some weight @xmath151 , and if @xmath191 we will define an @xmath0-function @xmath192 which will converge to a holomorphic function in @xmath193 . for example @xmath194 and if @xmath69 is an elliptic curve then @xmath195 ( for any @xmath146 ) . note the useful formulae @xmath196 also note that @xmath197 determines @xmath198 for all @xmath8 and hence @xmath199 for all but finitely many @xmath8 . hence by the cebotarev density theorem @xmath197 determines @xmath99 ( up to semisimplification ) . write @xmath200 for the multiplicity of an integer @xmath103 in @xmath101 and , if @xmath201 , define @xmath202 by : @xmath203 assume that @xmath204 are integers , i.e. that @xmath205 . then we can define a @xmath206-factor , @xmath207 , which is a product of functions @xmath208 as @xmath11 runs over a set of integers depending only on the numbers @xmath200 and @xmath204 . we can also define an epsilon factor @xmath209 which again only depends on @xmath200 , @xmath204 and a non - trivial character @xmath210 . set @xmath211 and @xmath212 ( which makes sense as @xmath213 for all but finitely many @xmath8 ) and @xmath214 where @xmath215 . [ cfe ] suppose that @xmath99 is an irreducible @xmath60-adic representation of @xmath3 which is de rham and pure of weight @xmath151 . then @xmath216 for all @xmath8 , so that @xmath217 . moreover the following should hold . it is tempting to believe that something like properties 1 . , 2 . and 3 . should characterise those euler products which arise from @xmath60-adic representations . we will discuss a more precise conjecture along these lines in the next section . why galois representations should be * the * source of euler products with good functional equations seems a complete mystery . let @xmath223 denote the profinite completion of @xmath224 , i.e. @xmath225 a topological ring . also let @xmath226 denote the topological ring of finite adeles @xmath227 where @xmath223 is an open subring with its usual topology . as an abstract ring , @xmath226 is the subring of @xmath228 consisting of elements @xmath229 with @xmath230 for all but finitely many @xmath8 . however the topology is not the subspace topology . we define the topological ring of adeles to be the product @xmath231 note that @xmath1 embeds diagonally as a discrete subring of @xmath232 with compact quotient @xmath233    we will be interested in @xmath234 , the locally compact topological group of @xmath235 invertible matrices with coefficients in @xmath232 . we remark that the topology on @xmath234 is the subspace topology resulting from the closed embedding @xmath236 @xmath237 is a discrete subgroup of @xmath234 and the quotient @xmath238 has finite volume . if @xmath239 is an open subgroup with @xmath240 , then @xmath241 note that @xmath242 is a subgroup of @xmath243 of finite index . most of the statements we make concerning @xmath234 can be rephrased to involve only @xmath244 , but at the expense of making them much more cumbersome . to achieve brevity ( and because it seems more natural ) we have opted to use the language of adeles . we hope that this extra abstraction will not be too confusing for the novice .    before continuing our introduction of automorphic forms let us digress to mention class field theory , which provides a concrete example of the presentational advantages of the adelic language . it also implies essentially all the conjectures we are considering in the case of one dimensional galois representations . indeed this article is about the search for a non - abelian analogue of class field theory . class field theory gives a concrete description of the abelianisation ( maximal continuous abelian quotient ) @xmath245 of @xmath3 and @xmath246 of @xmath41 . first the local theory asserts that there is an isomorphism @xmath247 with various natural properties , including the facts that @xmath248 is the image of the inertia group @xmath38 in @xmath246 , and that the induced map @xmath249 takes @xmath8 to the geometric frobenius element @xmath86 . secondly the global theory asserts that there is an isomorphism @xmath250 such that the restriction of @xmath251 to @xmath252 coincides with the composition of @xmath253 with the natural map @xmath254 . thus @xmath251 is defined completely from a knowledge of the @xmath253 ( and the fact that @xmath251 takes @xmath255 to complex conjugation ) and the reciprocity theorem of global class field theory can be thought of as a determination of the kernel of @xmath256 . we now return to our ( extended ) definition of automorphic forms . for each partition @xmath257 let @xmath258 denote the subgroup of @xmath259 consisting of matrices of the form @xmath260 let @xmath261 denote the orthogonal subgroup . let @xmath262 denote the centre of the universal enveloping of @xmath263 , the complexified lie algebra of @xmath244 ( i.e. @xmath264 with @xmath265=xy - yx$ ] ) . via the harish - chandra isomorphism ( see for example @xcite ) we may identify homomorphisms @xmath266 with multisets of @xmath52 complex numbers . we will write @xmath267 for the homomorphism corresponding to a multiset @xmath268 . thus @xmath262 acts on the irreducible finite dimensional @xmath263-module with highest weight @xmath269 ( @xmath270 ) by @xmath271 . fix such a multiset @xmath268 of cardinality @xmath52 . the space of cusp forms with infinitesimal character @xmath268 , @xmath272 is the space of smooth bounded functions @xmath273 satisfying the following conditions .    1 . ( @xmath6-finiteness ) the translates of @xmath274 under @xmath275 ( where @xmath276 denotes the orthogonal group ) span a finite dimensional vector space ; 2 . ( infinitesimal character @xmath268 ) if @xmath277 then @xmath278 ; 3 . ( cuspidality ) for each partition @xmath257 , @xmath279      one would like to study @xmath283 as a representation of @xmath234 , unfortunately it is not preserved by the action of @xmath244 ( because the @xmath6-finiteness condition depends on the choice of a maximal compact subgroup @xmath261 ) . it does however have an action of @xmath284 and of @xmath263 , which is essentially as good . more precisely it is an admissible @xmath285-module in the sense of @xcite . in fact it is a direct sum of irreducible , admissible @xmath286-modules each occurring with multiplicity one . we will ( slightly abusively ) refer to these irreducible constituents as cuspidal automorphic representations of @xmath234 with infinitesimal character @xmath268 . @xmath287 is just the space of locally constant functions on @xmath288 and so cuspidal automorphic representations of @xmath289 with infinitesimal character @xmath290 , are just the ( finite order ) complex valued characters of @xmath291 , i.e. dirichlet characters . @xmath292 is simply obtained from @xmath293 by twisting by @xmath294 , where @xmath295 is the product of the absolute values @xmath296 . thus in the case @xmath297 cuspidal automorphic representations are essentially dirichlet characters . the case @xmath298 is somewhat more representative . in this case we have @xmath299 unless @xmath300 , @xmath301 or @xmath302 . it is conjectured that the third possibility can not arise unless @xmath303 . let us consider the case @xmath304 a little further . if @xmath305 then it turns out that the irreducible constituents of @xmath306 are in bijection with the weight @xmath307 holomorphic cusp forms on the upper half plane , which are normalised newforms ( see for example @xcite ) . thus in some sense cuspidal automorphic representations are are also generalisations of classical holomorphic normalised newforms . note that if @xmath308 is a character of @xmath309 and if @xmath310 is a cuspidal automorphic representation of @xmath234 with infinitesimal character @xmath268 then @xmath311 is also a cuspidal automorphic representation with infinitesimal character @xmath268 and the contragredient ( dual ) @xmath312 of @xmath310 is a cuspidal automorphic representation with infinitesimal character @xmath313 . one of the main questions in the theory of automorphic forms is to describe the irreducible constituents of @xmath283 . if we are to do this we first need some description of all irreducible admissible @xmath314-modules , and then we can try to say which occur in @xmath283 .    just as a character @xmath315 can be factored as @xmath316 where @xmath317 ( resp . @xmath318 ) , so an irreducible , admissible @xmath286-module can be factorised as a restricted tensor product ( see @xcite ) @xmath319 where @xmath320 is an irreducible , admissible @xmath321-module ( see for example @xcite ) , and each @xmath322 is an irreducible smooth ( i.e. stabilisers of vectors are open in @xmath323 ) representation of @xmath323 with @xmath324 for all but finitely many @xmath8 . to the factors @xmath325 one can associate various invariants ( see @xcite ) . ( we also remark that @xmath262 acts via a character @xmath266 on any irreducible , admissible @xmath321-module @xmath332 . this character is called the infinitesimal character of @xmath332 . ) now we may attach to @xmath310    * a central character @xmath333 ; * an @xmath0-function @xmath334 ( which may or may not converge ) ; * an extended @xmath0-function @xmath335 ; * a conductor @xmath336 ( which makes sense because @xmath337 when @xmath324 ) ; * and an epsilon constant @xmath338 where @xmath339 is any non - trivial character . the following theorem and conjecture describe the ( expected ) relationship between automorphic forms and @xmath0-functions with euler product and functional equation . we suppose @xmath340 . a similar theorem to theorem [ gjt ] is true for @xmath297 , except that @xmath341 may have one simple pole . in this case it was due to dirichlet . conjecture [ cct ] becomes vacuous if @xmath297 . [ gjt ] suppose that @xmath310 is an irreducible constituent of @xmath283 with @xmath340 . then @xmath341 converges to a holomorphic function in some right half complex plane @xmath342 and can be continued to a holomorphic function on the whole complex plane so that @xmath343 is bounded in all vertical strips @xmath344 . moreover @xmath343 satisfies the functional equation @xmath345    [ cct ] suppose that @xmath310 is an irreducible , admissible @xmath314-module such that the central character of @xmath310 is trivial on @xmath346 and such that @xmath341 converges in some half plane . suppose also that for all characters @xmath347 the @xmath0-function @xmath348 ( which will then converge in some right half plane ) can be continued to a holomorphic function on the entire complex plane , which is bounded in vertical strips and satisfies a functional equation @xmath349 ( @xmath350 also automatically converges in some right half plane . ) then there is a partition @xmath351 and cuspidal automorphic representations @xmath352 of @xmath353 such that @xmath354    this conjecture is known to be true for @xmath298 ( @xcite , @xcite ) and @xmath355 ( @xcite ) . for @xmath356 a weaker form of this conjecture involving twisting by higher dimensional automorphic representations is known to hold ( see @xcite , @xcite ) . these results are called ` converse theorems ' . the reason for us introducing automorphic forms is because of a putative connection to galois representations , which we will now discuss . but first let us discuss the local situation . it has recently been established ( @xcite , @xcite , @xcite ) that there is a natural bijection , @xmath357 , from irreducible smooth representations of @xmath323 to @xmath52-dimensional frobenius semi - simple wd - representations of @xmath41 over @xmath22 . the key point here is that the bijection should be natural . we will not describe here exactly what this means ( instead we refer the reader to the introduction to @xcite ) . it does satisfy the following . now suppose that @xmath365 and that @xmath99 is a de rham @xmath60-adic representation of @xmath3 which is unramified at all but finitely many primes . using the local reciprocity map @xmath357 , we can associate to @xmath99 an irreducible , admissible @xmath285-module @xmath366 where @xmath367 is a tempered irreducible , admissible @xmath321-module with infinitesimal character @xmath368 and with @xmath369 . the definition of @xmath370 depends only on the numbers @xmath200 and @xmath204 . then we have the following conjectures .    [ cgfa ] suppose that @xmath268 is a multiset of @xmath52 _ integers _ and that @xmath310 is an irreducible constituent of @xmath283 . identify @xmath67 . then each @xmath371 can be defined over @xmath2 and there is an irreducible geometric strongly compatible system of @xmath60-adic representations @xmath149 such that @xmath372 and @xmath373 for all primes @xmath8 . [ cafg ] suppose that @xmath120 is an irreducible @xmath60-adic representation which is unramified at all but finitely many primes and for which @xmath121 is de rham . let @xmath374 . then @xmath375 is a cuspidal automorphic representation of @xmath234 . conjecture [ cafg ] is probably the more mysterious of the two , as only the case @xmath297 and fragmentary cases where @xmath298 are known . this will be discussed further in the next section . note the similarity to the main theorem of global class field theory that @xmath376 has kernel @xmath346 . [ kt ] suppose that @xmath268 is multiset of @xmath52 _ distinct _ integers and that @xmath310 is an irreducible constituent of @xmath283 . let @xmath191 . suppose moreover that @xmath377 for some character @xmath378 , and that either @xmath379 or for some prime @xmath8 the representation @xmath322 is square integrable ( i.e. @xmath371 is indecomposable ) . then there is a continuous representation @xmath380 with the following properties . this was established by finding the desired @xmath60-adic representations in the cohomology of certain unitary group shimura varieties . it seems not unreasonable to hope that similar techniques might allow one to improve many of the technical defects in the theorem . however clozel has stressed that in the cases where @xmath268 does not have distinct elements or where @xmath387 , there seems to be no prospect of finding the desired @xmath60-adic representations in the cohomology of shimura varieties . it seems we need a new technique . let us first summarise in a slightly less precise way the various conjectures we have made , in order to bring together the discussion so far . fix an embedding @xmath23 and let @xmath268 be a multiset of integers of cardinality @xmath340 . then the following sets should be in natural bijection . one way to make precise the meaning of ` natural ' is to require that two objects @xmath388 and @xmath389 should correspond if the local l - factors @xmath390 and @xmath391 are equal for all but finitely many @xmath8 . note that in each case the factors @xmath390 for all but finitely many @xmath8 , completely determine @xmath388 .    1 .   [ af ] irreducible constituents @xmath310 of @xmath272 . [ lf ] near equivalence classes of irreducible , admissible @xmath285-modules @xmath310 with the following properties . ( we call two @xmath314-modules , @xmath310 and @xmath392 nearly equivalent if @xmath393 for all but finitely many @xmath8 . ) 1 . @xmath332 has infinitesimal character @xmath268 . the central character @xmath359 is trivial on @xmath394 . 3 .   for all characters @xmath395 the @xmath0-function @xmath396 converges in some right half plane , has holomorphic continuation to the entire complex plane so that it is bounded in vertical strips and satisfies the functional equation @xmath397 4 . ( see @xcite for an explanation of this condition . ) there is a finite set of primes @xmath113 containing all primes @xmath8 for which @xmath371 is ramified , such that , writing @xmath398 for @xmath114 , @xmath399 is bounded as @xmath400 from the right . + in this case @xmath401 . + ( lr ) : :    [ lr ] ( fix    @xmath402 . )    irreducible @xmath60-adic representations    @xmath403    which are unramified at all but finitely many primes and for which    @xmath121 is de rham with    @xmath404 . in    this case ( wcs ) : :    [ cs ] irreducible weakly compatible systems of @xmath60-adic    representations @xmath149 with    @xmath372 . in this case ( gcs ) : :    [ gcs ] irreducible geometric strongly compatible systems of    @xmath60-adic representations @xmath149 with    @xmath372 . in this case @xmath406 .    for @xmath297 we must drop the item @xmath407 , because it would need to be modified to allow @xmath408 to have a simple pole , while , in any case condition ( lf ) ( b ) would make the implication @xmath409 trivial . this being said , in the case @xmath297 all the other four sets are known to be in natural bijection ( see @xcite ) . this basically follows because global class field theory provides an isomorphism @xmath410    i would again like to stress how different are these various sorts of objects and how surprising it is to me that there is any relation between them . items ( af ) and ( lf ) both concern representations of adele groups , but arising in rather different settings : either from the theory of discrete subgroups of lie groups or from the theory of @xmath0-functions with functional equation . items ( lr ) and ( wcs ) arise from galois theory and item ( gcs ) arises from geometry .      not much . trivially one has @xmath411 . the passage @xmath412 is ok by theorem [ gjt ] . as discussed in section [ s3 ] we have significant partial results in the directions @xmath409 and @xmath413 , but both seem to need new ideas . ( though i should stress that i am not really competent to discuss converse theorems . ) one way to establish the equivalence of all five items would be to complete the passages @xmath409 and @xmath414 and to establish the passage @xmath415 . it is these implications which have received most study , though it should be pointed out that in the function field case the equivalence of the analogous objects was established by looking at the implications @xmath416 ( see @xcite . it is the use of techniques from grothendieck s @xmath60-adic cohomology to prove the first of these implications which is most special to function fields . ) however it is striking that in the case of number fields all known implications from items ( lr ) , ( wcs ) or ( gcs ) to ( lf ) go via ( af ) . for the rest of this article we will concentrate on what still seems to be the least understood problem : the passage from ( lr ) or ( wcs ) to ( af ) or ( lf ) . although the results we have are rather limited one should not underestimate their power . perhaps the most striking illustration of this is that the lifting theorems discussed in section [ s4.2 ] ( combined with earlier work using base change and converse theorems ) allowed wiles @xcite to finally prove fermat s last theorem . the discussion in the rest of this paper will of necessity be somewhat more technical . in particular we will need to discuss automorphic forms , @xmath60-adic representations and so on over general number fields ( i.e. fields finite over @xmath1 ) . we will leave it to the reader s imagination exactly how such a generalisation is made . in this connection we should remark that if @xmath417 is a finite extension of number fields and if @xmath99 is a semi - simple de rham @xmath60-adic representation of @xmath418 which is unramified at all but finitely many primes , then ( see @xcite ) @xmath419 ( formally if the @xmath0-functions do nt converge ) . in fact this is true euler factor by euler factor and similar results hold for conductors and @xmath420-factors ( see @xcite ) . this observation can be extremely useful . suppose that @xmath421 is a group , @xmath268 a normal subgroup such that @xmath422 is cyclic with generator of @xmath43 . it is an easy exercise that an irreducible representation @xmath82 of @xmath268 extends to a representation of @xmath421 if and only if @xmath423 as representations of @xmath268 . if one believes conjectures [ cgfa ] and [ cafg ] , one might expect that if @xmath417 is a cyclic galois extension of number fields of prime order , if @xmath43 generates @xmath424 and if @xmath310 is a cuspidal automorphic representation of @xmath425 with @xmath426 , then there should be a cuspidal automorphic representation @xmath427 of @xmath428 , such that for all places @xmath429 of @xmath0 we have @xmath430 . this is indeed the case . for @xmath297 we have @xmath431 , langlands @xcite proved it for @xmath298 using the trace formula and arthur and clozel @xcite generalised his method to all @xmath52 . one drawback of this result is that if @xmath432 is a place of @xmath6 inert in @xmath0 then there is no complete recipe for @xmath433 in terms of @xmath310 . this can be surprisingly serious . it can however be alleviated , if we know how to associate irreducible @xmath60-adic representations to both @xmath427 and @xmath310 . langlands used this to show that many two dimensional artin representations ( i.e. @xmath60-adic representations with finite image ) were automorphic ( i.e. associated to a cuspidal automorphic representation ) . in fact using additional results from the theory of @xmath0-functions , particularly the converse theorem for @xmath434 ( see section [ s4.4 ] ) , he and tunnell ( @xcite ) were able to establish the automorphy of all continuous two dimensional artin representations with soluble image . suppose that @xmath82 is a representation of a finite group @xmath421 . then there are soluble subgroups @xmath435 , one dimensional representations @xmath436 of @xmath437 and integers @xmath438 such that as virtual representations of @xmath421 we have @xmath439      let @xmath365 . suppose that @xmath403 is an @xmath60-adic representation with _ finite image_. then the @xmath0-function @xmath440 has meromorphic continuation to the entire complex plane and satisfies the expected functional equation . artin s argument runs as follows . let @xmath421 denote the image of @xmath99 and write @xmath441 as in brauer s theorem . let @xmath442 be the galois extension with group @xmath421 cut out by @xmath99 and let @xmath443 . then one has equalities @xmath444 by class field theory for the fields @xmath445 , the character @xmath436 is automorphic on @xmath446 and so @xmath447 has holomorphic continuation to the entire complex plane ( except possibly for one simple pole if @xmath448 ) and satisfies a functional equation . it follows that @xmath197 has meromorphic continuation to the entire complex plane and satisfies a functional equation . the problem with this method is that some of the integers @xmath438 will usually be negative so that one can only conclude the meromorphy of @xmath197 , not its holomorphy .        as cogdell and piatetski - shapiro point out , conjecture [ cct ] would have very important implications for galois representations . for instance the cases @xmath298 and @xmath449 played a key role in the proof of the automorphy of two dimensional artin representations ( see [ s4.1 ] ) . conjecture [ cct ] combined with brauer s theorem and a result of jacquet and shalika @xcite in fact implies that many ( all ? - certainly those with soluble or perfect image ) artin representations are automorphic . a similar argument shows that in many other cases , in order to check the automorphy of an @xmath60-adic representation of @xmath3 , it suffices to do so after a finite base change . for instance one has the following result . _ assume conjecture [ cct ] . let @xmath191 and let @xmath159 be a finite , totally real galois extension . suppose that @xmath427 is a cuspidal automorphic representation of @xmath428 with infinitesimal character corresponding to a multiset @xmath268 consisting of @xmath52 distinct integers . if @xmath450 also suppose that @xmath433 is square integrable ( i.e. @xmath451 is indecomposable ) for some finite place @xmath432 of @xmath6 . let @xmath403 be an @xmath60-adic representation such that @xmath452 for some character @xmath308 of @xmath3 , and such that @xmath453 is irreducible . suppose finally that @xmath454 and @xmath427 are associated , in the sense that , for all but finitely many places @xmath432 of @xmath6 , we have @xmath455 then there is a regular algebraic cuspidal automorphic representation @xmath310 of @xmath234 associated to @xmath99 in the same sense . _        to describe this sort of theorem we first remark that if @xmath157 is continuous then after conjugating @xmath99 by some element of @xmath61 we may assume that the image of @xmath99 is contained in @xmath456 and so reducing we obtain a continuous representation @xmath457    the lifting theorems i have in mind are results of the general form if @xmath99 and @xmath458 are @xmath60-adic representations of @xmath3 with @xmath458 automorphic and if @xmath459 then @xmath99 is also automorphic . very roughly speaking the technique ( pioneered by wiles @xcite and completed by the author and wiles @xcite ) is to show that @xmath460 arises from automorphic forms for all @xmath82 by induction on @xmath82 . as @xmath461 is an abelian group one is led to questions of class field theory and galois cohomology . i should stress that such theorems are presently available only in very limited situations . i do not have the space to describe the exact limitations , which are rather technical , but the sort of restrictions that are common are as follows .    1 . if @xmath190 then there should be a character @xmath462 and a non - degenerate bilinear form @xmath463 on @xmath81 such that * @xmath464 and * @xmath465 . + ( this seems to be essential for the method of @xcite . ) 2 . @xmath99 should be de rham with distinct hodge - tate numbers . ( this again seems essential to the method of @xcite , but see @xcite . ) either @xmath99 and @xmath458 should be ordinary ( i.e. their restrictions to @xmath111 should be contained in a borel subgroup ) ; or @xmath99 and @xmath458 should be crytsalline ( not just de rham ) at @xmath60 with the same hodge - tate numbers and @xmath60 should be large compared with the differences of elements of @xmath101 . ( the problems here are connected with the need for an integral fontaine theory , but they are not simply technical problems . there are some complicated results pushing back this restriction in isolated cases , see @xcite , @xcite , @xcite , but so far our understanding is very limited . ) the image of @xmath466 should not be too small ( e.g. should be irreducible when restricted to @xmath467 ) , though in the case @xmath298 there is beautiful work of skinner and wiles ( @xcite and @xcite ) dispensing with this criterion , which this author has unfortunately not fully understood . in addition , all the published work is for the case @xmath298 . however there is ongoing work of a number of people attempting to dispense with this assumption . using a very important insight of diamond @xcite , the author , together with l.clozel and m.harris , has generalised to all @xmath52 the so called minimal case ( originally treated in @xcite ) where @xmath99 is no more ramified than @xmath466 . one would hope to be able to deduce the non - minimal case from this , as wiles did in @xcite for @xmath298 . in this regard one should note the work of skinner and wiles @xcite and the work of mann @xcite . however there seems to be one missing ingredient , the analogue of the ubiquitous ihara lemma , see lemma 3.2 of @xcite ( and also theorem 4.1 of @xcite ) . as this seems to be an important question , but one which lies in the theory of discrete subgroups of lie groups , let us take the trouble to formulate it , in the hope that an expert may be able to prove it . it should be remarked that there are a number of possible formulations , which are not completely equivalent and any of which would seem to suffice . we choose to present one which has the virtue of being relatively simple to state . suppose that @xmath468 is a unitary group which becomes an inner form of @xmath259 over an imaginary quadratic field @xmath73 . suppose that @xmath469 is compact . let @xmath60 be a prime which one may assume is large compared to @xmath52 . let @xmath470 and @xmath471 be distinct primes different from @xmath60 with @xmath472 and @xmath473 . let @xmath474 be an open compact subgroup of @xmath475 and consider the representation of @xmath476 on the space @xmath477 of locally constant @xmath478-valued functions on @xmath479 ( note that @xmath480 is a discrete cocompact subgroup of @xmath481 . ) suppose that @xmath482 is an irreducible _ sub - representation _ of @xmath483 with @xmath484 generic . then @xmath485 is also generic . the most serious problem with applying such lifting theorems to prove an @xmath60-adic representation @xmath99 is automorphic is the need to find some way to show that @xmath466 is automorphic . the main success of lifting theorems to date , has been to show that if @xmath73 is an elliptic curve over the rationals then @xmath486 is automorphic , so that @xmath73 is a factor of the jacobian of a modular curve and the @xmath0-function @xmath180 is an entire function satisfying the expected functional equation ( @xcite , @xcite,@xcite ) . this was possible because @xmath487 happens to be a pro - soluble group and there is a homomorphism @xmath488 splitting the reduction map . the artin representation @xmath489 is automorphic by the langlands - tunnell theorem alluded to in section [ s4.1 ] . i would like to discuss one other technique which has been some help if @xmath298 and may be helpful more generally . we will restrict our attention here to the case @xmath298 and @xmath490 . we have said that the principal problem with lifting theorems for proving an @xmath60-adic representation @xmath491 is automorphic is that one needs to know that @xmath466 is automorphic . this seems to be a very hard problem . nonetheless one can often show that @xmath466 becomes automorphic over some galois totally real field @xmath159 . ( because @xmath6 is totally real , if @xmath492 and @xmath493 then @xmath494 . so this ` potential automorphy ' is far from vacuous ) . the way one does this is to look for an abelian variety @xmath495 with multiplication by a number field @xmath496 with @xmath497=\\dim a$ ] , and such that @xmath466 is realised on @xmath498 $ ] for some prime @xmath499 , while for some prime @xmath500 the image of @xmath501 on @xmath502 $ ] is soluble . one then argues that @xmath502 $ ] is automorphic , hence by a lifting theorem @xmath503 is automorphic , so that ( tautologically ) @xmath498 $ ] is also automorphic , and hence , by another lifting theorem , @xmath454 is automorphic . one needs @xmath6 to be totally real , as over general number fields there seems to be no hope of proving lifting theorems , or even of attaching @xmath60-adic representations to automorphic forms . in practice , because of various limitations in the lifting theorems one uses , one needs to impose some conditions on the behaviour of a few primes , like @xmath60 , in @xmath6 and some other conditions on @xmath504 . the problem of finding a suitable @xmath504 over a totally real field @xmath6 , comes down to finding a @xmath6-point on a twisted hilbert modular variety . this is possible because we are free to choose @xmath6 , the only restriction being that @xmath6 is totally real and certain small primes ( almost ) split completely in @xmath6 . to do this , one has the following relatively easy result . suppose that @xmath66 is a smooth geometrically irreducible variety . let @xmath113 be a finite set of places of @xmath1 and suppose that @xmath505 has a point over the completion of @xmath1 at each place in @xmath113 . let @xmath506 be the maximal extension of @xmath1 in which all places in @xmath113 split completely ( e.g. @xmath507 is the maximal totally real field ) . then @xmath505 has a @xmath506-point .    in this regard it would have extremely important consequences if , in the previous proposition , one could replace @xmath506 by @xmath508 , the maximal soluble extension of @xmath1 in which all places in @xmath113 split completely . i do not know if it is reasonable to expect this . [ mer ] suppose that @xmath149 is an irreducible weakly compatible system of two dimensional @xmath60-adic representations with @xmath509 where @xmath510 . suppose also that @xmath511 for one ( and hence for all ) pairs @xmath140 . then there is a galois totally real field @xmath159 and a cuspidal automorphic representation @xmath310 of @xmath512 such that      in particular @xmath149 is pure of weight @xmath517 . moreover @xmath149 is strongly compatible and @xmath518 has meromorphic continuation to the entire complex plane and satisfies the expected functional equation .    the last sentence of this theorem results from the first part and brauer s theorem . we remark that conjecture [ cct ] would imply that this theorem could be improved to assert the automorphy of @xmath149 over @xmath1 . aaaa e.artin , _ zur theorie der l - reihen mit allgemeinen gruppencharakteren _ , hamburg 8 ( 1930 ) , 292306 . j.arthur and l.clozel , _ simple algebras , base change and the advanced theory of the trace formula _ , annals of math . studies 120 , pup 1989 . l.berger , _ reprsentations @xmath8-adiques et quations diffrentielles _ , invent . 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( 1997 ) , 379391 . j.dixmier , _ algbres enveloppantes _ , gauthier villars 1974 . g.faltings , _ endlichkeitsstze fr abelsche varietten ber zahlkrpern _ , 73 ( 1983 ) , 349366 . d.flath , _ decomposition of representations into tensor products _ , in `` automorphic forms , representations and @xmath0-functions i '' ams 1979 . m.fontaine , talk at `` mathematische arbeitstagung 1988 '' , maz - planck - institut fr mathematik preprint no . 30 of 1988 . m.fontaine , _ le corps des priodes @xmath8-adiques _ , astrisque 223 ( 1994 ) , 59111 . m.fontaine , _ reprsentations @xmath8-adiques semi - stables _ , astrisque 223 ( 1994 ) , 113184 . m.fontaine , _ reprsentations @xmath60-adiques potentiellement semi - stables _ , astrisque 223 ( 1994 ) , 321347 . m.fontaine and b.mazur , _ geometric galois representations _ , in elliptic curves , modular forms and fermat s last theorem ( j.coates and s .- t.yau eds . ) , international press 1995 . godement and h.jacquet , _ zeta functions of simple algebras _ , lnm 260 , springer 1972 . m.harris , _ on the local langlands correspondence _ , these proceedings . g.henniart , _ une preuve simple des conjectures de langlands pour @xmath519 sur un corps @xmath8-adiques _ , invent . 139 ( 2000 ) , 439455 . m.harris and r.taylor , _ the geometry and cohomology of some simple shimura varieties _ , pup 2001 . y.ihara , _ on modular curves over finite fields _ , in `` proceedings of an international colloquium on discrete subgroups of lie groups and applications to moduli '' oup 1975 . l.illusie , _ cohomologie de de rham et cohomologie tale @xmath8-adique _ , astrisque 189190 ( 1990 ) , 325374 . h.jacquet , _ principal @xmath0-functions of the linear group _ , in `` automorphic forms , representations and @xmath0-functions 2 '' ams 1979 . h.jacquet and r.langlands , _ automorphic forms on @xmath520 _ , lnm 114 , springer 1970 . h.jacquet , i.piatetski-shapiro and j.shalika , _ automorphic forms on @xmath521 _ , annals of math . 109 ( 1979 ) , 169258 . h.jacquet and j.shalika , _ on euler products and the classification of automorphic representations ii _ , 103 ( 1981 ) , 777815 . v.kolyvagin , _ on the mordell - weil group and the shafarevich - tate group of modular elliptic curves _ , in `` proceedings of the kyoto international congress of mathematicians '' math . japan 1991 . r.kottwitz , _ on the @xmath522-adic representations associated to some simple shimura varieties _ , invent . ( 1992 ) , 653665 . l.lafforgue , _ drinfeld varieties and the langlands program _ , these proceedings . r.p.langlands , _ automorphic representations , shimura varieties and motives . ein mrchen . _ in `` automorphic forms , representations and @xmath0-functions ii '' ams 1979 . langlands , _ base change for @xmath523 _ , annals of math . studies * 96 * , princeton univ .   press , princeton , 1980 . w.r.mann , _ local level - raising for @xmath259 _ , preprint . l.moret-bailly , _ groupes de picard et problmes de skolem ii _ , ann . ens 22 ( 1989 ) , 181194 . t.miyake , _ modular forms _ , springer 1989 . f.pop , _ embedding problems over large fields _ , annals of math 144 ( 1996 ) , 134 . k.ribet , _ congruence relations between modular forms _ , in `` proceedings of the warsaw icm '' polish scientific publishers 1984 . d.savitt , _ modularity of some potentially barsotti - tate galois representations _ , p.serre , _ abelian @xmath60-adic representations and elliptic curves _ , benjamin 1968 . c.skinner and a.wiles , _ residually reducible representations and modular forms _ , inst . hautes etudes sci . ( 1999 ) , 5126 . c.skinner and a.wiles , _ base change and a problem of serre _ , duke math . j. 107 ( 2001 ) , 1525 . c.skinner and a.wiles , _ nearly ordinary deformations of irreducible residual representations _ , annales de la facult de sciences de toulouse x ( 2001 ) , 185215 . j.tate , _ number theoretic background _ , in a.borel and w.casselman `` automorphic forms , representations and @xmath0-functions '' , proc . symposia in pure math . 33 ( 2 ) , ams 1979 . r.taylor , _ on the meromorphic continuation of degree two @xmath0-functions _ , preprint available at http://www.math.harvard.edu/~rtaylor . j.  tunnell , _ artin s conjecture for representations of octahedral type _ , bull . ams * 5 * ( 1981 ) , 173175 . r.taylor and a.wiles , _ ring theoretic properties of certain hecke algebras _ , annals of math . 141 ( 1995 ) , 553572 . n.wallach , _ representations of reductive lie groups _ , in `` automorphic forms , representations and @xmath0-functions i '' ams 1979 . a.weil , _ ber die bestimmung dirichletscher reihen durch funktionalgleichungen _ , ( 1967 ) , 149156 . a.wiles , _ modular elliptic curves and fermat s last theorem _ , annals of math . 141 ( 1995 ) , 443551 .","summary":"in the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of galois groups with algebraic geometry , complex analysis and discrete subgroups of lie groups . in the second part we briefly review some limited recent progress on these conjectures . 4.5 mm    * 2000 mathematics subject classification : * 11f80 .    * keywords and phrases : * galois representations ,-function , automorphic forms .","abstract":"in the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of galois groups with algebraic geometry , complex analysis and discrete subgroups of lie groups . in the second part we briefly review some limited recent progress on these conjectures . 4.5 mm    * 2000 mathematics subject classification : * 11f80 .    * keywords and phrases : * galois representations ,-function , automorphic forms ."}
{"article_id":"astro-ph0508076","section_id":"i","document":"a certain kind of stellar explosion , known as _ type ia supernovae _ among astronomers , is currently explained by the thermonuclear explosion of an electron - degenerate stellar remnant @xcite . such an object , which is called a white dwarf , emanates from the burn - out of stars comparable in mass to our sun and is mainly composed of carbon and oxygen . if the white dwarf has a companion star in close orbit , it can grow by accreting material from the companion . under certain conditions , the white dwarf s mass will steadily increase and finally approach the _ chandrasekhar limit _ , which is the maximal mass that can be supported by the degeneracy pressure of electrons @xcite . as the temperature and density are increasing , thermonuclear burning of carbon and oxygen gradually sets in . close to the chandrasekhar mass , the conditions in the core of the white dwarf eventually pass a critical threshold @xcite . at this point , the rate of thermonuclear reactions rises rapidly , and a runaway is initiated , which incinerates and disrupts the whole star within a few seconds . the total energy release is of the order @xmath4 @xcite .    the thermonuclear combustion of degenerate carbon and oxygen of density in the range @xmath5 proceeds in the form of a deflagration @xcite . since the nuclear ash produced by the burning process has less specific weight than the surrounding unprocessed material , it becomes rayleigh - taylor unstable . since turbulence is subsequently produced , the flames get corrugated and folded @xcite . in consequence , there is a positive feedback mechanism of turbulence enhancing the burning and , according to state - of - the - art numerical simulations , eventually results in an explosion @xcite . although it can not be ruled out that a transition from the deflagration to a detonation might set in at some stage @xcite , turbulent deflagration plays a crucial role in the theoretical modelling of thermonuclear supernovae in any case . the subject of this article is the dynamics of flame fronts on length scales much smaller than the size of a chandrasekhar - mass white dwarf . to that end , an artificial scenario was set up . a turbulent flow is produced by means of stochastic stirring in a cubic domain subject to periodic boundary conditions @xcite . thermonuclear burning is ignited in small spherical regions and subsequently evolved by means of the _ level set method _ the complicated network of thermonuclear reactions encountered in a type ia supernova is substituted by the effective fusion of equal mass fractions of @xmath6c and @xmath7o to @xmath8ni and @xmath9he as representative reaction @xcite . the equation of state is dominated by the degenerate gas of relativistic free electrons . thus , the approximate relation @xmath10 applies , while the temperature has virtually no influence on the pressure . this is actually the reason for the runaway , because the negative feedback between heating and expansion in non - degenerate matter is absent . the exact equation of state has no analytic solution and must be integrated numerically . moreover , contributions from nuclei , photons and pair electron - positron pair creation at temperatures of the order @xmath11 are taken into account ( section 3.2 of @xcite ) . the fluid dynamics is treated by means of the piece - wise parabolic method ( ppm ) within the framework of the euler equations @xcite .    in the corrugated flamelet regime of combustion , the flame propagation is affected by turbulence on length scales ranging from the gibson length up to the integral length scale @xcite . in general , only the the largest length scales can be resolved in a numerical simulation . in order to account for the wrinkling of the flame surface on length scales smaller than the cutoff scale of a simulation , an effective propagation speed , the so - called turbulent flame speed , must be calculated . this involves a subgrid scale ( sgs ) model for the local budget of turbulence energy contained in numerically unresolved modes . in this article , we present a numerical study in which different variants of the sgs turbulence energy model are compared ( section 4.3 in @xcite ) . in particular , we adopted a dynamical procedure for the computation of sgs closure parameters . this procedure was proposed by kim and menon for the application in les of gas turbine combustor flows @xcite .","summary":"the fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the chandrasekhar limit . the options of either including or suppressing inverse energy transfer in the turbulence production term are compared . in combination with the piece - wise parabolic method for the hydrodynamics , our results favour the latter option . +   + keywords : _ combustion , thermonuclear , turbulence , large eddy simulation , level set method _","abstract":"we study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing . the fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the chandrasekhar limit . the level set method is applied to represent the flame fronts numerically . the computational domain for the numerical simulations is cubic , and periodic boundary conditions are imposed . the goal is the development of a suitable flame speed model for the small - scale dynamics of turbulent deflagration in thermonuclear supernovae . because the burning process in a supernova explosion is transient and spatially inhomogeneous , the localised determination of subgrid scale closure parameters is essential . we formulate a semi - localised model based on the dynamical equation for the subgrid scale turbulence energy . the turbulent flame speed is of the order . in particular , the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales , which has been successfully applied to combustion problems in engineering . the options of either including or suppressing inverse energy transfer in the turbulence production term are compared . in combination with the piece - wise parabolic method for the hydrodynamics , our results favour the latter option . moreover , different choices for the constant of proportionality in the asymptotic flame speed relation , , are investigated . +   + keywords : _ combustion , thermonuclear , turbulence , large eddy simulation , level set method _"}
{"article_id":"astro-ph0508076","section_id":"c","document":"the numerical simulation of thermonuclear deflagration in a box subject to stochastic stirring was utilised as a test problem for the study of flame speed models . the evolution of the flame front was computed by means of the level set method in the so - called passive implementation . essentially , an effective flame propagation speed must be calculated , if the gibson scale is small compared to the resolution of the computational grid . a subgrid scale ( sgs ) model based on the budget of turbulence energy determines a velocity scale which is proportional to the propagation speed of flame fronts in the fully turbulent regime . some of the closure parameters of the sgs model are locally calculated with dynamical procedures . thus , we have a semi - localised model .    particularly , we compared two variants of this model . in one case , inverse energy transfer from subgrid toward resolved scales was included , in the other case it was suppressed . inverse energy transfer is also known as backscattering . for a consistent treatment of backscattering , complete coupling of the sgs model and the resolved hydrodynamics is indispensable . in combination with the piece - wise parabolic method , this entails difficulties stemming from the significant numerical viscosity of the scheme . but we obtained sensible results when suppressing backscattering and applying a simplified sgs model with partial coupling . depending on the constant of proportionality @xmath80 in the asymptotic flame speed relation , we found the transition from laminar to turbulent burning at noticeably different points in the course of turbulence production . this transition comes about once the sgs turbulence velocity must exceed the laminar burning speed in a significant volume fraction of the computational domain . then the nuclear energy generation grows at a much higher rate , and the flame surface develops an intricate structure due to the stretching and folding caused by turbulent vortices . if @xmath94 is about unity , the peak of nuclear energy release appears roughly when the turbulent flow becomes statistically stationary and homogeneous . for larger values of @xmath94 , most of the fuel is consumed in advance of turbulence becoming fully developed . we propose to consider @xmath94 as a control parameter , which regulates the overall rapidness of the burning process . the semi - localised sgs model presented here is especially suitable for any kind of transient and inhomogeneous turbulent combustion process . it is the first implementation of this kind of sgs model for an astrophysical application , namely , the numerical simulation of thermonuclear supernovae .","summary":"moreover , different choices for the constant of proportionality in the asymptotic flame speed relation , , are investigated .","abstract":"we study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing . the fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the chandrasekhar limit . the level set method is applied to represent the flame fronts numerically . the computational domain for the numerical simulations is cubic , and periodic boundary conditions are imposed . the goal is the development of a suitable flame speed model for the small - scale dynamics of turbulent deflagration in thermonuclear supernovae . because the burning process in a supernova explosion is transient and spatially inhomogeneous , the localised determination of subgrid scale closure parameters is essential . we formulate a semi - localised model based on the dynamical equation for the subgrid scale turbulence energy . the turbulent flame speed is of the order . in particular , the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales , which has been successfully applied to combustion problems in engineering . the options of either including or suppressing inverse energy transfer in the turbulence production term are compared . in combination with the piece - wise parabolic method for the hydrodynamics , our results favour the latter option . moreover , different choices for the constant of proportionality in the asymptotic flame speed relation , , are investigated . +   + keywords : _ combustion , thermonuclear , turbulence , large eddy simulation , level set method _"}
{"article_id":"1602.05306","section_id":"i","document":"plasmonic electron phenomena in semiconductors could enable advanced terahertz ( thz ) devices  @xcite . in particular , the thz detectors using the non - linear plasmonic properties of two - dimensional electron gas ( 2degs )  @xcite have proved to be very effective devices operating at room temperature @xcite . the resonant excitation of the plasma oscillations in the gated and ungated 2degs by incoming thz radiation could support relatively large electric - field oscillations and , hence , rather large rectified current components . using the nonlinearity of the current - voltage characteristics ( such as the nonlinearity of the thermionic or tunneling channel - gate leakage or injection currents ) to enhance the hydrodynamic nonlinearity of plasma oscillations  @xcite , the pertinent detectors can exhibit marked advantages . in particular , the combination of the plasmonic properties of the 2deg channel with the contact nonlinearity can be realized in lateral schottky diodes @xcite . the detection of thz radiation in lateral device structures based on carbon nanotubes ( cnts ) was demonstrated in refs . the detection mechanisms in the devices with nonuniform cnt networks  @xcite are associated with nonuniform heating of the electron or hole system by the absorbed thz radiation or with the structure asymmetry due to metal contacts with different nonlinear properties leading to the rectification of the ac current induced by this radiation . different cnt - base photodetectors and mechanisms of their operation were reviewed in ref . @xcite the incident thz radiation can excite the plasma oscillations in lateral cnt networks ( with the wavelength larger that the average distance between the cnts ) in a similar way as in the 2deg channels in the standard heterostructures or in the graphene - based heterostructures . the plasmonic nature of the thz response in cnt systems was discussed in a number of publications ( see , for example , refs . the role of the plasmonic effects in the aligned cnts and disordered cnt networks was experimentally confirmed in refs . the interpretation of the experimental findings , relied on the concept of 1d plasmons propagating along the cnt and having cylindrical symmetry of the potential distribution ( see , for example , ref . however , in sufficiently dense lateral cnt , different cnts interact with each other and , as a result , the plasma oscillations excited by the thz radiation can be associated with the _ collective coherent _ motion of the carriers belonging to many cnt responding to the ac _ self - consistent _ electric fields . this collective motion reveals the 2d - nature of the response , especially pronounced when the plasma wavelength markedly exceeds the average distance between the cnts .    in this paper , in contrast to the previous works focused on the dilute cnt systems ( including the composite materials with randomly dispersed , randomly oriented cnts ) , we study the 2d plasma oscillations excited by the thz radiation in lateral _ dense _ cnt disordered networks consisting of a mixture of the single - wall semiconducting cnts ( s - cnts ) and quasi - metallic cnts ( m - cnts ) of the p-type.also , we consider the networks of relatively long cnts connecting two highly conducting contacts with distinct properties and focus on the role of the hole collective motion , i.e. , on the plasmonic effects on the thz radiation detection and the characteristics of thz detectors based on such cnt networks .    the cnt device structure with relatively dense cnt network under consideration is similar to that fabricated and studied experimentally recently ( type b devices for sub - thz and thz detection  @xcite and for transistor applications  @xcite ) . we demonstrate that the hole system in the lateral cnt network can be treated as a 2d hole gas ( 2dhg ) , exhibiting pronounced plasmonic properties , and that the excitation of the plasma oscillations can result in a resonant enhancement rectified current component . such cnt - based structures can be used in uncooled cnt - detectors with elevated responsivity exploiting the rectification mechanism .","summary":"* keywords : * carbon nanotube network , schottky contact , two - dimensional carrier system , terahertz radiation , plasmonic resonance we consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube ( cnt ) networks forming the device channel with asymmetric electrodes . we develop the device model for response of the lateral cnt networks which comprise a mixture of randomly oriented semiconductor cnts ( s - cnts ) and quasi - metal cnts ( m - cnts ) .","abstract":"* keywords : * carbon nanotube network , schottky contact , two - dimensional carrier system , terahertz radiation , plasmonic resonance we consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube ( cnt ) networks forming the device channel with asymmetric electrodes . one electrode is the ohmic contact to the cnt network and the another contact is the schottky contact . these structures can serve as detectors of the terahertz ( thz ) radiation . we develop the device model for response of the lateral cnt networks which comprise a mixture of randomly oriented semiconductor cnts ( s - cnts ) and quasi - metal cnts ( m - cnts ) . the proposed model includes the concept of the two - dimensional plasmons in relatively dense networks of randomly oriented cnts ( cnt `` felt '' ) and predicts the detector responsivity spectral characteristics . the detection mechanism is the rectification of the ac current due the nonlinearity of the schottky contact current - voltage characteristics under the conditions of a strong enhancement of the potential drop at this contact associated with the plasmon excitation . we demonstrate that the excitation of the two - dimensional plasmons by incoming thz radiation the detector responsivity can induce sharp resonant peaks of the detector responsivity at the signal frequencies corresponding to the plasmonic resonances . the detector responsivity depends on the fractions of the s- and m - cnts . the burning of the near - contact regions of the m - cnts or destruction of these cnts leads to a marked increase in the responsivity in agreement with our experimental data . the resonant thz detectors with sufficiently dense lateral cnt networks can compete and surpass other thz detectors using plasmonic effects at room temperatures ."}
{"article_id":"1602.05306","section_id":"r","document":"+        we compare the above theoretical results with the recent experimental data related to the thz detectors based on asymmetric devices with one the ohmic and the schottky contacts and the conduction channels are formed by lateral arrays of cnts  @xcite and some new our experimental results shown below . assuming @xmath300  a , @xmath301 , and @xmath302  k , we obtain @xmath303  a / v@xmath304 , that is consistent with the experimental value  @xcite @xmath305a / v@xmath304 . for @xmath306 ( @xmath69 ) , and @xmath307 , eq . ( 46 ) yields @xmath308  a / w . taking into account that in the experiments  @xcite @xmath309 and setting also @xmath310 , we find @xmath311  a / w and somewhat lower values for @xmath312  ghz ( that is markedly smaller than the plasmonic frequency ) . taking into account that @xmath313 , for the sub - thz frequency range we obtain @xmath314  v / w . these values of the current and voltage responsivities are in a reasonable agreement with the data obtained experimentally  @xcite . to achieve higher responsivities , the devices with higher antenna efficiency should be used . another opportunity is to realize the resonant plasmonic response predicted above using the structures with relatively high ratios @xmath217 or @xmath191 . as predicted above , the elimination of the m - cnts might also lead to a substantial increase in the responsivity . to verify this , we fabricated and measured device structures similar to those fabricated and studied as in ref . the spacing between the contacts and the gate thickness are @xmath315  nm and @xmath316  nm , respectively . it includes eight cnts connecting the electrodes ( so that @xmath317  @xmath108 ) and was supplied with a spiral antenna . the sem image of such a cnt device is shown in fig . the structure corresponds to that schematically shown in fig .  1 . originally the cnt network was formed with a mixture of the s- and m - cnts . this is confirmed by the analysis of the device transfer characteristics . the response of the structure was measured at the negative gate voltage @xmath318  v ) as a function of the radiation frequency in the sub - thz range from 140 to 220 ghz the cnt network was coupled to the radiation by a spiral antenna . then the m - cnts that provided a substantial current path between the electrodes were destroyed , so that the current between the electrodes was associated with the s - cnts . the response of this structure after the destruction of of the m - cnts was measured as a function of the radiation frequency ( at the same gate voltage and in the same frequency range as in the case of original structure ) . the results of the transfer characteristics measurements are shown in fig . 7 . as seen from fig .  7 , the maximum device conductance ( on - conductance ) at the negative gate voltage originally was about of @xmath319s . after some cnts were destroyed , the conductance droped down to @xmath320s . this implies that the contribution of the destroyed m - cnts was about of @xmath321s , and that the hole density in the s - cnts was about one fifth of the net density . the minimum conductance ( off - conductance ) of the original structure was about of @xmath322s .    as seen from fig . 8 , the voltage responsivity of the device with the destructed m - cnts in the frequency range 150 - 160   ghz is much larger ( about five times ) than that of the original device with a mixture of the m- and s - cnts .     versus radiation frequency @xmath288 before ( mixed cnt network ) and after m - cnt destruction ( s - cnt network ) at @xmath323  v. , width=226 ]     versus frequency @xmath288 calculated for low - density cnt detectors with a cnt mixture and with destructed m - cnts : disconnected ( solid line ) and fragmented ( dashed line ) m - chts . , width=226 ]    first of all , our model describes the mechanism of the thz response of the devices under consideration in terms of the rectification of the signals at the schottky contacts of the s - cnts and the electrode . as shown , the shunting effect caused by relatively low contact resistance of m - cnts can substantially suppress the effect of rectification . the elimination ( disconnection from the electrode or destruction ) of the cnts lead to an efficient increase in the responsivity . this is confirmed by the data shown in fig . second , the device model developed above predicts the resonant response of the cnt devices under consideration to the thz radiation associated with the excitation of the 2d - plasmons . although the experimental data shown in figs .  7 and 8 are related to rather delute cnt networks , we apply the obtained above formulas for , at least , qualitative consideration of the experimental situation .    since the gate layer thickness @xmath316  nm is close the quantity @xmath324  nm , @xmath325 , so that both eqs . ( 21 ) and ( 36 ) can be used for rough estimates . there are two plausible scenario : ( a ) due to burning , the m - cnts are disconnected from the electrode , which forms the schottky contacts with the s - cnts , and ( b ) the m- cnts are fragmented into small fractions much shorter than the spacing between the electrodes .    in the case `` a '' , the holes belonging to the both types of the cnts contribute to the plasma frequencies @xmath99 and @xmath266 . the analysis of the measurement results provides the hole density induced by the gate voltage @xmath318  v about of @xmath326  @xmath110 . the acceptor - induced hole density could be roughly estimated from the threshold gate voltage ( @xmath327 , see fig . 6 ) to be about @xmath328  @xmath110 . setting @xmath329 , @xmath330  g , @xmath150 , @xmath318  v , and @xmath331  @xmath110 , from eqs . ( 20 ) and ( 35 ) we obtain @xmath332  ghz . in contrast , in the case `` b '' , when only the holes in the s - cnts determine the plasma frequencies , assuming @xmath333  @xmath110 , we arrive at @xmath334  ghz . we calculated the current and voltage responsivities of the detectors with the above parameters in a wide range of hole collision frequencies @xmath28 . figure  9 shows an example of the voltage responsivity @xmath291 as a function of the signal frequency @xmath335 calculated using eqs . ( 44 ) - ( 48 ) for the cnt structures with a mixture of the m- and s - cnts with @xmath336  ghz and for the cnt structure with disconnected m - cnts with @xmath336  ghz ) as well as fragmented m - cnts with @xmath337  ghz assuming the hole collision frequency @xmath338  s@xmath158 and the pertinent charging time @xmath339  s . in line with fig .  7 , it is also assumed that the ratio of the conductance @xmath340 for the structure with the cnt mixture and for the structure with destroyed m - cnts is equal to five . according to fig . 9 ( as well as according to the calculations with other values of @xmath341 ) , the frequency dependences of the voltage responsivity are monotonically decreasing not exhibiting any resonant peaks . this can be attributed to relatively low quality factor ( @xmath342 in the case of fragmented m - cnts ) and to the signal frequencies well below the plasmonic resonance frequency in the case of the mixed cnt array and the array with disconected m - cnts ) . due to this , t the responsivity maxima in fig.8 are most probably attributed to to antenna shape -induced effects .","summary":"the detector responsivity depends on the fractions of the s- and m - cnts .","abstract":"* keywords : * carbon nanotube network , schottky contact , two - dimensional carrier system , terahertz radiation , plasmonic resonance we consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube ( cnt ) networks forming the device channel with asymmetric electrodes . one electrode is the ohmic contact to the cnt network and the another contact is the schottky contact . these structures can serve as detectors of the terahertz ( thz ) radiation . we develop the device model for response of the lateral cnt networks which comprise a mixture of randomly oriented semiconductor cnts ( s - cnts ) and quasi - metal cnts ( m - cnts ) . the proposed model includes the concept of the two - dimensional plasmons in relatively dense networks of randomly oriented cnts ( cnt `` felt '' ) and predicts the detector responsivity spectral characteristics . the detection mechanism is the rectification of the ac current due the nonlinearity of the schottky contact current - voltage characteristics under the conditions of a strong enhancement of the potential drop at this contact associated with the plasmon excitation . we demonstrate that the excitation of the two - dimensional plasmons by incoming thz radiation the detector responsivity can induce sharp resonant peaks of the detector responsivity at the signal frequencies corresponding to the plasmonic resonances . the detector responsivity depends on the fractions of the s- and m - cnts . the burning of the near - contact regions of the m - cnts or destruction of these cnts leads to a marked increase in the responsivity in agreement with our experimental data . the resonant thz detectors with sufficiently dense lateral cnt networks can compete and surpass other thz detectors using plasmonic effects at room temperatures ."}
{"article_id":"1602.05306","section_id":"c","document":"as it was assumed in the model under consideration , each electrons interact with a large number of others . this is in line with the consideration of the collective effects in different plasmonic media with a large number of charged particles in the debye sphere  @xcite .    in our case , assuming for simplicity that the debye screening length @xmath17 is the same as in the standard 2deg with effective ( or fictituous ) mass @xmath343  g , @xmath344 , and @xmath275  @xmath110 , for the number of the electron inside the region with the area @xmath345 ( inside the `` debye circle '' ) @xmath346 we find @xmath347 . setting @xmath275  @xmath110 , we obtain @xmath348 . however , one needs to point out that the effects of the self - consistent electric field can really be important in different plasmas even if the parameter of ideality @xmath349 . the value @xmath275  @xmath110 ( which is determined either by the gate voltage and doping level ) can correspond to @xmath350  @xmath108 . the quantity @xmath351 @xmath108 implies that the average distance between cnts is about of @xmath352  nm , which is orders of magnitude larger that the size of the electron localization around the cnts ( slightly larger than the diameter the cnts under consideration @xmath353  nm ) , so that the overlap of the electron wave functions of individual cnts is negligible . as was mentioned above , the crossing of the cnts , at which the cnts touch each other , can play the role of the electron scattering ( collision ) points . due to the deformation mechanism of such scattering the effective collision frequency is smaller than the frequency of the crossing of these points by electrons . for @xmath354  @xmath108 and the average electron velocity along the cnts @xmath355  cm / s , this yields for the pertinent collision frequency the following estimate : @xmath356  s@xmath158 . the interaction of the electrons belonging to different cnts near the crossing of the latter , does not change the momentum of the pairs of colliding electrons , and , hence , does not contribute to the electron momentum relaxation and the quantity @xmath28 . the latter implies that the `` crossing '' collision mechanisms in question should not suppress the plasmonic resonant response when @xmath357  thz . the absorption of the thz radiation in the cnt network and similar sistemscan lead to a heating of the hole system in the cnts ( see , for example , refs . the excitation of the plasmonic oscillation can result in the enhancement of the absorption at the plasmonic resonances . in this case , apart from the rectified current , an extra dc current associated with the difference of the electron temperature in the cnt network and the contacts can appear if the contacts have different thermal properties . the calculation of the bolometric contribution to the responsivity under the conditions of the plasmonic effects , requires a more complex model than that used above . the spatial distribution of the effective hole temperature might be essentially nonuniform due to the nonuniform spatial distribution of the ac electric field ( which heats the dhg in the cnt network under consideration ) and due to thermal flows from the cnt network toward the contacts . therefore , the equations of more strict device model should be supplemented by the heat conductivity equation and related boundary conditions accounting for the contact properties . this model will be considered elsewhere . below we estimate the bolometric contribution to the responsivity using a fairly simple model .    assuming that ( 1 ) the variation of the current due to the hole heating is associated primarily with the variation of the schottky contact electrical conductivity ( due to higher thermal conductivity of the ohmic contact and , hence , smaller temperature gradient near the latter ) , ( 2 ) the variation of the effective hole temperature near the schottky contact is close to that averaged over the entirely cnt network and the plasmonic oscillation period @xmath358 , and ( 3 ) only the s - cnts contribute to the effect in question . in such a situation , the expression for the density of the rectified current given by eqs .  ( 41 ) and ( 42 ) should be generalized as follows :    @xmath359    where @xmath360\\exp[-e(\\phi_s - v_0)/t ] =   2\\beta_s(\\phi_s - v_0)/e$ ] characterized the variation of the current density trough the schottky contact due to an increase of the hole effective temperature in the s - cnts . since @xmath361 is determined by the balance between the thz power absorbed by the cnt network and the power which goes to the lattice ( and the contact ) , one can write @xmath362 , where @xmath363 is the effective energy relaxation time . considering this , one can arrive at the the following formulas for the rectified current density @xmath239 and the net responsivity @xmath364 ( associated with both the rectification and bolometric effects ) :    @xmath365    and @xmath366 here @xmath367 is the ratio of the hole bolometric response and the effect of the rectification , where @xmath368 . setting @xmath369  mev , @xmath70  g , and @xmath370 m , @xmath276  s@xmath158 at @xmath371  thz , we obtain @xmath372 . this implies that @xmath373 can be comparable with unity or exceed it if the hole energy relaxation time @xmath363 is sufficiently long . according to these estimates , there should @xmath374  s for the sub - thz frequencies and @xmath375  s for the frequencies about 1 thz . at sufficiently low temperatures , the latter conditions can be satisfied . if the hole heating leads to stronger hole current from the cnt network to the ohmic contact due to , in particular , special thermal isolation of the pertinent cnt network ( as in device a in ref . @xcite ) , the bolometric responsivity can be relatively high and exhibit the opposite sign .","summary":"one electrode is the ohmic contact to the cnt network and the another contact is the schottky contact . the proposed model includes the concept of the two - dimensional plasmons in relatively dense networks of randomly oriented cnts ( cnt `` felt '' ) and predicts the detector responsivity spectral characteristics . the detection mechanism is the rectification of the ac current due the nonlinearity of the schottky contact current - voltage characteristics under the conditions of a strong enhancement of the potential drop at this contact associated with the plasmon excitation . the burning of the near - contact regions of the m - cnts or destruction of these cnts leads to a marked increase in the responsivity in agreement with our experimental data .","abstract":"* keywords : * carbon nanotube network , schottky contact , two - dimensional carrier system , terahertz radiation , plasmonic resonance we consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube ( cnt ) networks forming the device channel with asymmetric electrodes . one electrode is the ohmic contact to the cnt network and the another contact is the schottky contact . these structures can serve as detectors of the terahertz ( thz ) radiation . we develop the device model for response of the lateral cnt networks which comprise a mixture of randomly oriented semiconductor cnts ( s - cnts ) and quasi - metal cnts ( m - cnts ) . the proposed model includes the concept of the two - dimensional plasmons in relatively dense networks of randomly oriented cnts ( cnt `` felt '' ) and predicts the detector responsivity spectral characteristics . the detection mechanism is the rectification of the ac current due the nonlinearity of the schottky contact current - voltage characteristics under the conditions of a strong enhancement of the potential drop at this contact associated with the plasmon excitation . we demonstrate that the excitation of the two - dimensional plasmons by incoming thz radiation the detector responsivity can induce sharp resonant peaks of the detector responsivity at the signal frequencies corresponding to the plasmonic resonances . the detector responsivity depends on the fractions of the s- and m - cnts . the burning of the near - contact regions of the m - cnts or destruction of these cnts leads to a marked increase in the responsivity in agreement with our experimental data . the resonant thz detectors with sufficiently dense lateral cnt networks can compete and surpass other thz detectors using plasmonic effects at room temperatures ."}
{"article_id":"1602.05306","section_id":"c","document":"we investigated the hole transport and the plasmonic oscillations excited by incoming thz radiation in the device structures with lateral cnt networks and asymmetric contacts ( one ohmic contact and one schottly contact ) and evaluated their effect on the operation of the thz detectors using such structures . we developed the device models accounting for the 2d nature of the collective behavior of the hole system in lateral cnt networks , i.e. , treating this system as a 2dhg , including both the s- and m - cnts and the specifics of the contact phenomena . as demonstrated , the rectification of the ac current stimulated by the thz radiation at the schottky contact of the s - cnts ( associated with the nonlinearity of the current - voltage characteristics of this contact ) is an effective mechanism of the thz detection . the excitation of plasmonic oscillations of the self - consistent electric field by the thz radiation can lead to a substantial increase in the rectified current and , hence , to the elevated detector responsivity . due to the resonant character of the plasmons excitation , the responsivity can exhibit sharp resonant peaks . the positions of these peaks can be controlled by the gate voltage . we showed that the disconnection ( or fragmentation ) of the m - cnts from the contact electrode results in a marked increase in the responsivity due to the elimination of the partial shunting of the schottky contact . this was confirmed experimentally by comparing the cnt structures with natural ratio of the s- and m - cnts densities ( usually two to one ) with the structures with the destructed m - cnts . the resonant thz cnt detectors with sufficiently high density s - cnt networks can surpass other thz detectors using plasmonic effects at room temperatures .","summary":"the resonant thz detectors with sufficiently dense lateral cnt networks can compete and surpass other thz detectors using plasmonic effects at room temperatures .","abstract":"* keywords : * carbon nanotube network , schottky contact , two - dimensional carrier system , terahertz radiation , plasmonic resonance we consider the carrier transport and plasmonic phenomena in the lateral carbon nanotube ( cnt ) networks forming the device channel with asymmetric electrodes . one electrode is the ohmic contact to the cnt network and the another contact is the schottky contact . these structures can serve as detectors of the terahertz ( thz ) radiation . we develop the device model for response of the lateral cnt networks which comprise a mixture of randomly oriented semiconductor cnts ( s - cnts ) and quasi - metal cnts ( m - cnts ) . the proposed model includes the concept of the two - dimensional plasmons in relatively dense networks of randomly oriented cnts ( cnt `` felt '' ) and predicts the detector responsivity spectral characteristics . the detection mechanism is the rectification of the ac current due the nonlinearity of the schottky contact current - voltage characteristics under the conditions of a strong enhancement of the potential drop at this contact associated with the plasmon excitation . we demonstrate that the excitation of the two - dimensional plasmons by incoming thz radiation the detector responsivity can induce sharp resonant peaks of the detector responsivity at the signal frequencies corresponding to the plasmonic resonances . the detector responsivity depends on the fractions of the s- and m - cnts . the burning of the near - contact regions of the m - cnts or destruction of these cnts leads to a marked increase in the responsivity in agreement with our experimental data . the resonant thz detectors with sufficiently dense lateral cnt networks can compete and surpass other thz detectors using plasmonic effects at room temperatures ."}
{"article_id":"1611.04801","section_id":"i","document":"admm ( alternating direction method of multipliers ) is one of the most popular first order methods for non - smooth optimization and regularization problems widely used in signal processing and imaging @xcite . admm was first introduced in @xcite , and extensive studies can be found in  @xcite and so on . it aims at the following general constrained optimization problem , @xmath0 where @xmath1 , @xmath2 , @xmath3 and @xmath4 are real hilbert spaces with @xmath5 denoting the corresponding proper , convex and lower semi - continuous function spaces  @xcite . and @xmath6 , @xmath7 , where @xmath8 denotes the spaces of linear and continuous operators mapping from hilbert spaces @xmath9 to @xmath10 . with appropriate conditions @xcite , this problem is equivalent to the following saddle - point problem , and assume there exists a bounded saddle - point , @xmath11 where @xmath12 is the lagrangian function and @xmath13 is the lagrangian multiplier . also the associated fenchel - rockafellar dual problem of reads as follows @xcite , @xmath14 once writing the following augmented lagrangian , @xmath15 what follows is the admm method by solving the sub minimization problems @xmath16 and @xmath17 consecutively in , and updating the lagrangian multipliers at last , @xmath18,\\\\ p^{k+1 }   & = ( r b^*b + \\partial g)^{-1}[b^ * ( -rau^{k+1 } - \\bar{\\lambda}^{k } + rc ) ] ,        \\\\ \\bar{\\lambda}^{k+1 } & = \\bar{\\lambda}^{k } + r(au^{k+1 } + bp^{k+1}-c ) . \\\\            \\end{aligned }      \\right.\\ ] ] here and following , we assume @xmath19 such that @xmath20 and @xmath21 exist and are lipschitz continuous .    it is known the convergence of method in finite dimensional spaces is clear , see @xcite and @xcite . however , the weak convergence is not quite clear in infinite dimensional hilbert space except @xcite . it is also well known that one can get admm through applying douglas - rachford splitting method to the dual problems while @xmath22 , @xmath23 @xcite , and there are some weak convergence results of douglas - rachford splitting method in infinite dimensional hilbert spaces , see @xcite and the recent paper @xcite . however , as our analysis in remark [ rem : weakdr : not : weakadmm ] of section [ sec : admm - equavi - dr ] , the weak convergence of douglas - rachford splitting method in @xcite could not lead to weak convergence of the corresponding admm directly . the reason is that the resolvent operators @xmath24 and @xmath25 of could not preserve the weak convergence , although the weak convergence of multipliers could be guaranteed . more analysis is needed to obtain the weak convergence of admm . the weak convergence of preconditioned admm is analysed in @xcite in infinite dimensional hilbert spaces , under the framework of general proximal point iterations with moderate conditions . here we extend the results to overrelaxed variants by a different approach . actually , admm could be seen as a special case of the following  fully \" relaxed and preconditioned version of , @xmath26,\\\\ p^{k+1 }   & = ( m + \\partial g)^{-1}[b^ * ( -r \\rho_{k } au^{k+1 } + r(1-\\rho_{k})bp^{k } - \\bar{\\lambda}^{k } + r\\rho_{k}c ) + ( m - rb^*b)p^k ] ,        \\\\ \\bar{\\lambda}^{k+1 } & = \\bar{\\lambda}^{k } + r(\\rho_{k } au^{k+1 } + bp^{k+1}-(1-\\rho_{k})bp^{k}-\\rho_{k}c ) ,            \\end{aligned }      \\right.\\ ] ] with assumption on relaxation parameters @xmath27 throughout this paper , @xmath28 and @xmath29 , @xmath30 are both self - adjoint operators , and satisfy , @xmath31 actually , the updates of @xmath32 and @xmath33 in could be reformulated as follows , @xmath34,\\\\ p^{k+1 }   & = p^{k } + ( m + \\partial g)^{-1}[b^ * ( -r \\rho_{k } au^{k+1 } + r(1-\\rho_{k})bp^{k } - \\bar{\\lambda}^{k } + r\\rho_{k}c ) - ( \\partial g+ rb^*b)p^k ] ,      \\end{aligned }      \\right.\\ ] ] where @xmath35 and @xmath36 could be seen as generalized  preconditioners \" for the operator equations for calculating @xmath32 and @xmath33 in classical . it is shown in @xcite that one could benefit from efficient preconditioners for solving the implicit problems approximately with only one , two , or three cheap preconditioned iterations without controlling the errors , to guarantee the ( weak ) convergence of the iterations without relaxation . it is not surprising that while @xmath37 ( or @xmath38 ) is a quadratical form @xcite , the update of @xmath39 ( or @xmath40 ) above is just the classical preconditioned iteration in numerical linear algebra in finite dimensional spaces . and various preconditioning techniques are efficient and are widely used . even for nonlinear @xmath37 or @xmath38 , there are still some preconditioning techniques available , see @xcite for diagonal preconditioning , and @xcite for nonlinear symmetric gauss - seidel preconditioning .    actually , is equivalent to the following iterations involving the augmented lagrangian , @xmath41 here @xmath42 and @xmath43 are weighted norm , i.e. , @xmath44 , and they are called as proximal terms as in @xcite . could also be recovered from by setting @xmath45 , @xmath46 and @xmath47 .    motivated by the  partial \" primal - dual gap analysis in @xcite and @xcite , we prove the weak convergence of the fully preconditioned and relaxed in infinite dimensional hilbert spaces , together with the corresponding ergodic convergence rate , under only conditions , and , by employing the detailed analysis of a kind of  partial \" primal - dual gap . similar but different partial gap function could be found in @xcite . the main contributions belong to the following parts . first , we prove weak convergence of original and its relaxed version as in @xcite in infinite dimensional hilbert space with conditions , and , through a different approach compared to @xcite . and no additional condition is needed as in @xcite where the proximal terms must both be positive definite , i.e. , @xmath48 and @xmath49 . this kind of relaxation is different from @xcite that only focused on relaxation for the updates of lagrangian multipliers . second , we proposed a relaxed admm with different relaxation parameters for separable components of the @xmath17 and @xmath13 , which could help us to get a kind of relaxed and preconditioned admm easily , by applying the weak convergence of relaxed to a specially designed modified constrained optimization problems , when only the update of @xmath32 is preconditioned , i.e. , @xmath50 . the case the added proximal term for update of @xmath32 in is positive definite , is discussed in @xcite , which is mainly focused on linearization strategy in finite dimensional spaces , i.e. , @xmath51 and @xmath50 . however the positive definiteness of @xmath52 or @xmath53 could prevent lots of interesting applications including the efficient symmetric ( block ) red - black gauss - seidel preconditioner for tv ( or tgv ) denosing problems , where @xmath52 is not positive definite , see @xcite . similar linearized admm with overrelaxation is also considered in @xcite while @xmath54 , where estimating the largest eigenvalue of @xmath55 or @xmath56 is necessary , which would be very expensive while @xmath55 is large and is not well - conditioned . besides , by applying douglas - rachford splitting method to the dual problems , while @xmath50 in , we found that the primal - dual gap stopping criterion in imaging @xcite could be used for admm , while applying to basic rof denoising model . third , we prove the weak convergence of  fully \" preconditioned admm with relaxation and give the corresponding ergodic convergence rate . and to the best knowledge of the author , the weak convergence and ergodic convergence rate of seem to be figured clear for the first time both in finite dimensional spaces and infinite dimensional hilbert spaces . we need to point out that the convergence of without relaxation , i.e. , @xmath45 , in finite dimensional spaces could be found in @xcite , and @xcite while @xmath22 and @xmath23 . the paper is organized as follows , we first consider the weak convergence and ergodic convergence rate of the fundamental in section [ sec : esti : admm ] by employing the  partial \" gap analysis . then we consider the weak convergence and the corresponding ergodic convergence rate for relaxation variant of , by similar but adjusted  partial \" gap analysis in section [ sec : relax : admm ] . in section [ sec : pre : admm : relax ] , by applying the results for relaxed admm in section [ sec : relax : admm ] to a modified constrained problem , we get a kind of preconditioned admm and its relaxation formally , with only preconditioning for the update of @xmath32 . furthermore , we present the relation to douglas - rachford splitting method , and show the limited equivalent weak convergence results for admm benefited from the existing weak convergence results of douglas - rachford method as in @xcite . in section [ sec : full : pre : admm ] , we discuss the weak convergence and the corresponding ergodic convergence rate of , with the help of adjusted  partial \" gap analysis and the analysis in the previous sections . in the last section , some numerical tests are conducted to demonstrate efficiency of the proposed schemes in this paper .","summary":"alternating direction method of multipliers ( admm ) is a powerful first order methods for various applications in signal processing and imaging . however , there is no clear result on the weak convergence of admm with relaxation studied by eckstein and bertsakas in infinite dimensional hilbert spaces . in this paper , by employing a kind of  partial \" gap analysis , we prove the weak convergence of general preconditioned and relaxed admm in infinite dimensional hilbert spaces , with preconditioning for solving all the involved implicit equations under mild conditions . we also give the corresponding ergodic convergence rates respecting to the  partial \" gap function . furthermore , the connections between certain preconditioned and relaxed admm and the corresponding douglas - rachford splitting methods are also discussed , following the idea of gabay in . numerical tests also show the efficiency of the proposed overrelaxation variants of preconditioned admm .    [ [ key - words . ] ] key words . + + + + + + + + + +    alternating direction method of multipliers , douglas - rachford splitting , relaxation , linear preconditioners technique , weak convergence analysis , partial primal - dual gap    [ [ ams - subject - classifications . ] ] ams subject classifications . + + + + + + + + + + + + + + + + + + + + + + + + + + + +    65k10 , 49k35 , 90c25 , 65f08 .","abstract":"alternating direction method of multipliers ( admm ) is a powerful first order methods for various applications in signal processing and imaging . however , there is no clear result on the weak convergence of admm with relaxation studied by eckstein and bertsakas in infinite dimensional hilbert spaces . in this paper , by employing a kind of  partial \" gap analysis , we prove the weak convergence of general preconditioned and relaxed admm in infinite dimensional hilbert spaces , with preconditioning for solving all the involved implicit equations under mild conditions . we also give the corresponding ergodic convergence rates respecting to the  partial \" gap function . furthermore , the connections between certain preconditioned and relaxed admm and the corresponding douglas - rachford splitting methods are also discussed , following the idea of gabay in . numerical tests also show the efficiency of the proposed overrelaxation variants of preconditioned admm .    [ [ key - words . ] ] key words . + + + + + + + + + +    alternating direction method of multipliers , douglas - rachford splitting , relaxation , linear preconditioners technique , weak convergence analysis , partial primal - dual gap    [ [ ams - subject - classifications . ] ] ams subject classifications . + + + + + + + + + + + + + + + + + + + + + + + + + + + +    65k10 , 49k35 , 90c25 , 65f08 ."}
{"article_id":"astro-ph0108096","section_id":"i","document":"the population of seyfert 1 galaxies has a widely - used sub - classification into narrow - line seyfert 1 galaxies ( nls1s ) and broad - line seyfert 1 galaxies ( bls1s ) . while the scheme appears to make an arbitrary distinction based primarily upon the widths of the optical emission lines ( nls1s having h@xmath5 @xmath6 , @xcite ) , this turns out to be an extremely useful terminology as the x - ray properties of the two sub - classes are systematically different . rapid and large - amplitude variability ( * ? ? ? * hereafter bbf96 ; @xcite ) is a characteristic of nls1s , with the excess variance @xcite typically an order of magnitude larger than that observed for samples of bls1s with the same luminosity distribution @xcite . spectral properties also vary across the seyfert population with nls1s showing systematically steeper photon indices than those of bls1s across both soft and hard x - ray bands , @xcite . the anti - correlations between h@xmath7 @xmath8 and both x - ray spectral slope @xcite and excess variance @xcite reveal a continuous range of parameter values between the nls1 and bls1 extremes of the population ; the observed differences are now thought to be driven by a range in a fundamental physical parameter , such as the accretion rate . a popular idea , originally proposed by @xcite , draws an analogy between seyfert 1 galaxies and galactic black - hole candidates . the latter show steepening in the high state . in this scenario , nls1s are sources in the high - state , emitting at higher fractions of their eddington luminosity , hence having higher fractional accretion rates ( @xmath9 ) . given that nls1s have comparable luminosity to that of the bls1s , it has often been suggested that they also have relatively small central black holes , i.e. , @xmath10 , as opposed to @xmath11 , which is typical for bls1s ( e.g. , * ? ? ? * ; * ? ? ? smaller black - hole masses naturally explain both the narrowness of the optical emission lines , which are generated in clouds that have smaller keplerian velocities  hence smaller widths  and the extreme x - ray variability , since the primary emission would originate in a smaller region around the central engine ( e.g. , * ? ? ? higher accretion rates lead to some observational predictions , such as a hotter accretion disk leading ( via inverse compton scattering ) to enhanced soft x - ray emission and an ionized surface for the accretion disk @xcite . support for the ionized disk is found in the form of k@xmath1 emission from ionized states of fe in six nls1s ( @xcite , @xcite , @xcite , @xcite , @xcite ; @xcite ) . however , the observation of similar lines in some bls1s , may point to the luminosity of the central source playing as important a role as accretion rate ( e.g. , * ? ? ? alternative explanations of the extreme properties in nls1s are that ( 1 ) the broad - line regions ( blr ) of nls1s have larger radii ( i.e. , the blr gas is more distant from the nucleus ) than in the bls1s @xcite then the narrow width of the lines is a reflection of the lower orbital velocity ; ( 2 ) the nls1s may be low - inclination ( i.e. , observed nearly face on ) systems @xcite . assuming the motions around the central source to be virialized , the narrowness of the lines is due to the fact that the gas is moving preferentially on a plane that is almost perpendicular to the line of sight , hence the line widths are reduced by a factor of @xmath12 , where @xmath13 is face - on . one way to distinguish between these models is to measure the the size and virial mass of the blr via reverberation techniques @xcite ; @xcite and @xcite find that the blrs of nls1s and bls1s have comparable size , while nls1s have virial masses one order of magnitude smaller than bls1s , but can not exclude the second model solely on the basis of reverberation results . however , @xcite and @xcite disfavor the low - inclination model , while @xcite show that the inner regions of bls1s also appear to be observed close to face - on . tonantzintla ( ton ) s180 ( phl 912 ) is a bright nls1 with a low galactic column density along the line - of - sight ( @xmath14 @xmath15 ; * ? ? ? this source has fwhm h@xmath1 and h@xmath16 900 km s@xmath17 and a redshift z=0.06198 @xcite . ton  s180 has a relatively high luminosity , with absolute magnitude @xmath18 mag . ton  s180 was observed by _ asca _ on 1999 december 3 to 15 , during a multi - wavelength monitoring campaign that included observations from _ hst _ , _ rxte _ , _ chandra _ , _ euve _ , _ fuse _ , in addition to optical  ir observations obtained from ground - based observatories . the results of the long - baseline timing project using _ rxte _ , _ euve _ and _ asca _ are reported in @xcite . the _ hst _ and _ fuse _ data were obtained contemporaneously with _ chandra _ and _ asca _ and were undertaken to determine the spectral - energy - distribution of the source , as reported in @xcite . spectral result is reported in @xcite . in this paper we present the results from the @xmath2 400ks _ asca _ observation of ton  s180 . this long observation has allowed us to study the variability of the spectral components on different timescales , from 12 days to @xmath19 day . this is particularly interesting since the results of a 35-day long observational campaign on the nls1 arakelian ( akn ) 564 indicate that superimposed on a fast - varying continuum component that dominates the spectrum is a slower - varying soft excess emission @xcite . in  [ dataobs ] we describe our observations and data reduction . in  [ timevar ] we discuss the time variability of the source . in  [ meansp ] we analyze the mean spectrum and in  [ ciccio ] we discuss time - resolved spectroscopy . in  [ results ] we present a summary of our observational results , and in  [ comptonakn ] a comparison with the properties of akn  564 . finally , in  [ discussion ] we discuss the results .","summary":"we present an analysis of the x - ray variability properties of the narrow - line seyfert 1 galaxy , based upon a 12-day continuous observation with _ our timing analysis and time - selected spectroscopy indicate that the x - ray emission originates within 12 schwarzschild radii .","abstract":"we present an analysis of the x - ray variability properties of the narrow - line seyfert 1 galaxy , based upon a 12-day continuous observation with _ asca_. examination of the light curves reveals flux variations of a factor of 3.5 in the 0.71.3kev band and 3.9 in the 210kev band . time - resolved spectroscopy , using approximately daily sampling , reveals that the broad `` soft hump '' component at energieskev shows flux variations on timescales as short as 1 day that are well correlated with the photon index and the 210kev band flux . a broad fe k emission is detected . there is also a statistically significant evidence for a narrow fe k line at 6.8kev , indicating an origin in ionized material . we do not detect significant variations of the fe k line flux or equivalent width on timescales of 1 day1 week .    despite evidence for correlated events in the power - law and soft hump on timescales of a day , the flux correlations clearly do not exist on all timescales . in particular , the softness ratio reveals spectral variability on timescales as short ass , indicating that the power - law continuum and soft hump fluxes are not well correlated on this timescale . the softness ratio also shows a slow decline across the observation , due to a combination of the different time - variability of the power - law continuum and soft hump flux on timescales of 1 week .    our timing analysis and time - selected spectroscopy indicate that the x - ray emission originates within 12 schwarzschild radii . the amplitudes and timescales of the rapid variations we observed are consistent with those expected within disk - corona models . furthermore , the observed fast variability of the soft hump rules out an origin of the soft emission in large scale components , such as circumnuclear starburst . thesoft hump correlation is consistent with the soft hump being produced by up - scattering of the accretion disk radiation within a patchy , flaring disk corona ."}
{"article_id":"astro-ph0108096","section_id":"i","document":"1 .   on a 12-day baseline , the x - ray flux of ton  s180 presents trough - to - peak variations by a factor 3.5 in the 0.71.3kev band , and 3.9 in the 210kev band when sampled using 256s bins . the mean photon index , calculated from the continuum fit of the mean spectrum , is @xmath125 . time - resolved spectroscopy reveals significant changes on timescales of @xmath2 1 week . we confirm the presence of a separate `` soft hump '' component at energies @xmath0kev . this component shows flux variations down to timescales of @xmath2 1 day , ranging by a factor of 2.3 in normalization over the 12 days of our observations . some flux changes appear to match changes in the 210kev flux on this timescale although the soft hump shows a drop in ew from 100 to 84ev across the observation . minor changes in the shape of the soft hump are apparent on timescales of a few days . 4 .   in our approximately daily sampling the photon index is correlated with the flux of the soft x - ray hump . 5 .   variations in both the photon index and soft hump strength contribute to the change in softness ratio observed across the _ asca _ observation . the softness ratio reveals spectral variability down to timescales of @xmath3s in addition to the slow decline across the observation . the power - law and soft hump show divergent behavior on very short ( 1000s ) or long ( 2 weeks ) timescales . 7 . the fe k@xmath1 line emission is detected with a narrow component peaking at @xmath2 6.8kev , indicating an origin in ionized material . a broad line component ( ew @xmath126ev ) is also evident . we do not detect significant variations of the fe k@xmath1 line strength or equivalent width , on timescales of @xmath2 1 day12 days .","summary":"a broad fe k emission is detected . there is also a statistically significant evidence for a narrow fe k line at 6.8kev , indicating an origin in ionized material . we do not detect significant variations of the fe k line flux or equivalent width on timescales of 1 day1 week .    despite evidence for correlated events in the power - law and soft hump on timescales of a day","abstract":"we present an analysis of the x - ray variability properties of the narrow - line seyfert 1 galaxy , based upon a 12-day continuous observation with _ asca_. examination of the light curves reveals flux variations of a factor of 3.5 in the 0.71.3kev band and 3.9 in the 210kev band . time - resolved spectroscopy , using approximately daily sampling , reveals that the broad `` soft hump '' component at energieskev shows flux variations on timescales as short as 1 day that are well correlated with the photon index and the 210kev band flux . a broad fe k emission is detected . there is also a statistically significant evidence for a narrow fe k line at 6.8kev , indicating an origin in ionized material . we do not detect significant variations of the fe k line flux or equivalent width on timescales of 1 day1 week .    despite evidence for correlated events in the power - law and soft hump on timescales of a day , the flux correlations clearly do not exist on all timescales . in particular , the softness ratio reveals spectral variability on timescales as short ass , indicating that the power - law continuum and soft hump fluxes are not well correlated on this timescale . the softness ratio also shows a slow decline across the observation , due to a combination of the different time - variability of the power - law continuum and soft hump flux on timescales of 1 week .    our timing analysis and time - selected spectroscopy indicate that the x - ray emission originates within 12 schwarzschild radii . the amplitudes and timescales of the rapid variations we observed are consistent with those expected within disk - corona models . furthermore , the observed fast variability of the soft hump rules out an origin of the soft emission in large scale components , such as circumnuclear starburst . thesoft hump correlation is consistent with the soft hump being produced by up - scattering of the accretion disk radiation within a patchy , flaring disk corona ."}
{"article_id":"astro-ph0108096","section_id":"c","document":"ton  s180 reaffirms the rapid and large - amplitude x - ray variations which are a characteristic of the nls1 class . during our 12-day observation , the light curves sampled on 256s timescales show trough - to - peak flux variations by a factor of @xmath2 3.5 in the soft band ( 0.7 - 1.3kev ) , and up to a factor of @xmath2 4 in the hard band ( 210kev ) . further examination of these light curves shows variations up to a factor of @xmath127 occurring on timescales of @xmath2 1000 s which are sometimes accompanied by spectral changes . there is a strong correlation ( @xmath128 ) between the soft- and hard - band light curves , with a 95% confidence upper limit on the lag of hard with respect to soft of @xmath129d . the strength of this correlation , the short lag , and the fact that @xmath2 72% of the flux in the soft band is contributed by the power - law continuum while the hard flux is driven by the power - law , indicate that this correlation is dominated by the variations of the power - law continuum itself . we used these timing data to obtain an estimate of some fundamental parameters for ton  s180 . our estimate of the accretion efficiency is @xmath130% , marginally above the limit for the efficiency in the schwarzschild geometry , perhaps favoring a kerr geometry . however , large uncertainties are associated with this estimate ( see * ? ? ? light - crossing time arguments yield a radius @xmath131 for the emitting region , @xmath132 for @xmath133 . the 1000s timescale for variability observed in ton  s180 indicates that neither thermal nor viscous / radial drift phenomena can be held responsible for the observed fast variability . the values of these parameters are consistent with what is generally found for other seyfert 1s . @xcite discuss a model where soft thermal photons from the accretion disk are compton - upscattered in localized blobs of coronal plasma , constrained by magnetic loops from the disk . the resulting x - rays from the blobs then illuminate the disk and produce the so - called compton hump and fe k@xmath1 emission line . the amplitudes and timescales of the rapid variations observed in ton  s180 are consistent with those expected as a result of stochastic noise in the number of reprocessing blobs , which depend on the formation and reconnection of magnetic loops . the continuum fit to the mean spectrum yields a photon index @xmath62 . our time - selected spectral fits give @xmath134 ( 1-@xmath46 error ) with variations from 2.38 to 2.62 . the steep index and the range ( @xmath135 ) are comparable with that observed in akn  564 ( @xmath136 , @xmath137 , * ? ? ? * ) , though the variations on a @xmath19day timescale are significant in the case of akn  564 and not for ton  s180 ( where we detect variations of @xmath4 in @xmath19week timescale ) . the range of indices is also consistent with that found for the bls1 ngc  7469 ( @xmath138 , * ? ? ? this may indicate a fundamental similarity in the process which causes slope fluctuations , over a range of different agn . we confirm the presence of the soft x - ray emission component at energies @xmath0kev previously observed by @xcite , @xcite , and @xcite . this component rises above the power - law continuum @xmath139kev , and has recently been shown to be a smooth continuum component rather than a blend of features , not only in ton  s180 @xcite , but also in the nls1 ngc  4051 @xcite . therefore , our time - selected spectroscopic analysis is particularly well suited to study its variability properties in particular and understand the nature of the soft hump in nls1s in general . the soft hump shows flux variations on timescales as short as @xmath19day ( the shortest timescales our time - selected spectroscopy can study ) , ranging by a factor of 2.3 in flux over the observation , but always being present . we note that the fast variability observed in the soft hump of ton  s180 rules out an origin of the soft emission in large - scale components , such as circumnuclear starburst ( as also concluded for the soft hump in akn  564 , @xcite ) . the hard flux , when similarly binned on timescales of a day , has a range of a factor 1.65 . the softness ratio shows spectral variability on timescales as short as @xmath3s . in ton s180 such fast spectral variability can be attributed either to rapid changes in photon index or in the relative strengths of the soft hump and power - law . in addition to this evidence for divergent behavior on very short timescales , the soft hump and power - law show different trends on timescales of @xmath19 week . the higher value of @xmath52 measured in the soft than in the hard band is probably due to the combined effects of a larger amplitude of variation of the soft hump over the baselines of the observation , and the changes in spectral slope ( which could preferentially affect the soft band if the pivot point lies within the hard band ) . the correlation observed between the soft hump flux and the photon index in ton  s180 is expected in disk - corona models where an increase of the flux in the soft x - ray / uv component can cool the corona and steepen the power - law continuum @xcite . this is not the case for akn  564 , where @xcite suggest the corona cooling might be saturated . iron k@xmath1 line emission is detected , with a broad , asymmetric profile . it is best parameterized by two gaussian components ; the narrow component peaks at @xmath140kev , which is consistent with emission from highly ionized gas , the broad component consistent with emission from either neutral or ionized gas . we caution about the reliability of this result because the signal - to - noise in this range is low and the errors on the fitted parameters are correspondingly large ( table  [ kafitstab ] ) . therefore it seems that the best parametrization for the fe k@xmath1 line is a broad ionized line , which is consistent with previous _ bepposax _ @xcite and _ asca _ @xcite observations . the broad component is generally thought to originate in the innermost regions of the accretion disk around the central black hole ( e.g. , * ? ? ? * and references therein ) , and so it is due to highly ionized fe , while the narrow component is thought to be generated in the putative obscuring torus that extends on a parsec scale @xcite , and so is believed to be due to neutral material . in this context , the result of an ionized narrow fe k@xmath1 component is therefore somewhat suprising . note , however , that observations of such a feature are not unprecedented : @xcite and @xcite detected narrow lines due to highly ionized iron in _ chandra _ observations of mkn  3 and ngc  4151 , respectively . the fe k@xmath1 emission line has a very large equivalent width , ew @xmath141ev , as previously observed in other _ asca _ and _ bepposax _ observations of ton  s180 , akn  564 , and other nls1s @xcite . these ews are interesting compared to a sample taken across the seyfert 1 population @xcite , which found an average ew @xmath142ev . one interpretation is in terms of an extreme fe abundance in nls1s , as proposed by @xcite for akn  564 ; this may , in turn , support the proposition that nls1s are seyfert galaxies in an early stage of evolution @xcite . alternatively , @xcite show that the expected ews for predominantly h- and he - like fe can be a factor of a few higher than those from neutral fe . we do not detect significant variations of the fe k@xmath1 line , on timescales of @xmath2 1 day or of @xmath2 1 week . we note that given our signal - to - noise in the k@xmath1 energy range for the 14 time - selected spectra , the line flux would have had to varied by at least a factor 2 for us to have detected the variation at @xmath143% confidence level . pr acknowledges support through nasa adp grant nag5 - 9346 - 1 . tjt is pleased to acknowledge support for this work by nasa through grant number nag5 - 7385 ( ltsa ) . sm acknowledges support through nasa grant nag5 - 8913 ( ltsa ) . we also acknowledge support from hst  go08265.01a from the space science telescope institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nss5 - 226555 . we thank the _ asca _ team for their operation of the satellite , and tahir yaqoob for discussions on the _ asca _ calibration . we thank brad peterson for use of the cross - 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ph/0105238 ) turner , t.  j. , et al . 2001c , in preparation vaughan , s. , pounds , k.  a. , reeves , j. , warwick , r. , & edelson , r.  1999 , , 308 , l34 vaughan , s. , reeves , j. , warwick , r. , & edelson , r.   1999 , , 309 , 113 wandel , a. , & boller , th . 1998 , , 331 , 884 white , r.  j. , & peterson , b.  m.  1994 , , 106 , 879 wisotzki , a. , dreizler , s. , engels , d. , fink , h.  h. , & heber , u.  1995 , , 297 , l55 yaqoob , t. , et al . 2000 , _ asca _ gof calibration memo , asca - cal-00 - 06 - 01 , v1.0 yaqoob , t. , george , i.  m. , nandra , k. , turner , t.  j. , serlemitsos , p.  j. , & mushotzky , r.  f.  2001 , , 546 , 759    lllcc @xmath144 & 0.06198 & 0.0247 & 1 & 2 + galactic @xmath145 ( @xmath15 ) & 1.52@xmath146 & 6.4@xmath146 & 3 & 4 + @xmath147 ( mag ) & 14.4 & 14.6 & 5 & 6 + @xmath148 ( 10@xmath149 ^-1 ergs s@xmath17 ) & 4.9 & 2.4 & 7(3 ) & 8(3 ) + @xmath39 soft band & 3.5 & 16 & 7(3 ) & 8(3 ) + @xmath39 hard band & 3.9 & 14 & 7(3 ) & 8(3 ) + @xmath39 soft hump & 2.33 @xmath58 0.45 & 6.44 @xmath58 3.30 & 7(5.3 ) & 8(5.3 ) + @xmath39 210kev & 1.65 @xmath58 0.02 & 3.97 @xmath58 0.06 & 7(5.3 ) & 8(5.3 ) + @xmath52 ( 12 d , soft ) ( % ) & 19.12 @xmath58 0.58 & 35.81 @xmath58 0.81 & 7(3.1 ) & 7 + @xmath52 ( 12 d , hard ) ( % ) & 17.26 @xmath58 0.65 & 35.73 @xmath58 0.70 & 7(3.1 ) & 7 + @xmath52 ( 1 d , soft ) ( % ) & variable & variable & 7(3.1 ) & 8(3.1 ) + correlates with x - ray & no & no & 7(3.1 ) & 8(3.1,7 ) + @xmath52 ( 1 d , hard ) ( % ) & variable , @xmath150 soft & variable , @xmath150 soft & 7(3.1 ) & 8(3.1 ) + correlates with x - ray & no & no & 7(3.1 ) & 8(3.1,7 ) + iccf @xmath45 ( soft  hard band ) & 0.748 & 0.942 & 7(3 ) & 8(7 ) + iccf @xmath47 ( 95% limit , d ) & @xmath151 & @xmath150 0.02 & 7(3 ) & 8(7 ) + @xmath4 ( mean spectrum ) & 2.44 @xmath580.02 & 2.538 @xmath58 0.005 & 7(4 ) & 8(4 ) + @xmath152@xmath153 & 2.382.62 & 2.452.72 & 7(5.2 ) & 8(5.2 ) + @xmath154 & 0.24 & 0.27 & 7(5.2 ) & 8(5.2 ) + pl soft band contribution ( % ) & 72 & 75 & 7(4.1 ) & 8(3.1 ) + soft hump gaussian fits : @xmath155 ( kev ) & 0.17 @xmath58 0.17 & 0.57 @xmath58 0.2 & 7(4.1 ) & 8(4.1 ) + fwhm ( kev ) & 1.01@xmath156 & 0.36 @xmath58 0.01 & 7 & 8 + @xmath157 ( @xmath158 ph s@xmath17 @xmath15 ) & 1.50@xmath159 & 1.25@xmath160 & 7 & 8 + ew ( ev ) & 94@xmath161 & 110@xmath162 & 7 & 8 + k@xmath1 diskline fits : @xmath155 ( kev ) & @xmath163 & @xmath164 & 7(4.2 ) & 8(4.2 ) + ew ( ev ) & @xmath165 & 351@xmath58 85 & 7 & 8 + @xmath166 ( deg ) & @xmath167 & 26@xmath582 & 7 & 8 + k@xmath1 laor fits : @xmath155 ( kev ) & @xmath168 & @xmath169 & 7(4.2 ) & 8(4.2 ) + ew ( ev ) & @xmath170 & @xmath171 & 7 & 8 + @xmath166 ( deg ) & @xmath172 & @xmath173 & 7 & 8 +","summary":"time - resolved spectroscopy , using approximately daily sampling , reveals that the broad `` soft hump '' component at energieskev shows flux variations on timescales as short as 1 day that are well correlated with the photon index and the 210kev band flux . the amplitudes and timescales of the rapid variations we observed are consistent with those expected within disk - corona models . furthermore , the observed fast variability of the soft hump rules out an origin of the soft emission in large scale components , such as circumnuclear starburst . thesoft hump correlation is consistent with the soft hump being produced by up - scattering of the accretion disk radiation within a patchy , flaring disk corona .","abstract":"we present an analysis of the x - ray variability properties of the narrow - line seyfert 1 galaxy , based upon a 12-day continuous observation with _ asca_. examination of the light curves reveals flux variations of a factor of 3.5 in the 0.71.3kev band and 3.9 in the 210kev band . time - resolved spectroscopy , using approximately daily sampling , reveals that the broad `` soft hump '' component at energieskev shows flux variations on timescales as short as 1 day that are well correlated with the photon index and the 210kev band flux . a broad fe k emission is detected . there is also a statistically significant evidence for a narrow fe k line at 6.8kev , indicating an origin in ionized material . we do not detect significant variations of the fe k line flux or equivalent width on timescales of 1 day1 week .    despite evidence for correlated events in the power - law and soft hump on timescales of a day , the flux correlations clearly do not exist on all timescales . in particular , the softness ratio reveals spectral variability on timescales as short ass , indicating that the power - law continuum and soft hump fluxes are not well correlated on this timescale . the softness ratio also shows a slow decline across the observation , due to a combination of the different time - variability of the power - law continuum and soft hump flux on timescales of 1 week .    our timing analysis and time - selected spectroscopy indicate that the x - ray emission originates within 12 schwarzschild radii . the amplitudes and timescales of the rapid variations we observed are consistent with those expected within disk - corona models . furthermore , the observed fast variability of the soft hump rules out an origin of the soft emission in large scale components , such as circumnuclear starburst . thesoft hump correlation is consistent with the soft hump being produced by up - scattering of the accretion disk radiation within a patchy , flaring disk corona ."}
{"article_id":"quant-ph9812049","section_id":"i","document":"quantum computers  @xcite offer the possibility of faster combinatorial search by operating simultaneously on all search states . for instance , quantum computers can factor integers in polynomial time  @xcite , a problem thought to be intractable for classical machines .    at first sight , quantum computers seem particularly well - suited for np search problems  @xcite due to their efficiently - computable test of whether a given search state is a solution . quantum computers can apply this test to exponentially many search states in about the same time as a conventional ( `` classical '' ) computer tests just one and a variety of search algorithms have been proposed  @xcite . however , extracting a definite answer from this simultaneous evaluation appears to still give an exponentially growing search cost in the worst case  @xcite .    for general np searches , amplitude amplification  @xcite , using a test of whether a search state is a solution , quadratically improves performance of heuristics consisting of many independent trials  @xcite . this is the best possible improvement for `` unstructured '' quantum methods , i.e. , those using only such a test  @xcite . moreover , this technique does not apply to more complex heuristics , e.g. , those involving backtracking , tabu lists , parameters adjusted based on unsuccessful trials , cached nogoods or other forms of learning , abstraction or extensive preprocessing . such heuristics often provide the best known performance , at least on average , for a variety of combinatorial searches . a focus on _ typical _ behavior of large problems is important because often the worst cases are far harder than most instances encountered in practice . thus , as a practical matter , there remain the questions of whether using problem structure in quantum algorithms can give more than quadratic improvement for the heuristics consisting of independent trials , any improvement at all for other types of heuristics , and less than exponential cost for at least some typical problems arising in practice . as one example , further improvement is possible for a quantum algorithm using detailed information on the distance of search states to solutions  @xcite , but in practice , such information is not readily available for most searches . addressing these questions requires developing algorithms using problem structure and determining their behavior for large problems . as with classical heuristics , such algorithms are often difficult to analyze theoretically due to complicated dependencies among successive search choices . thus one is often forced to use empirical evaluation with a sample of problems . while quite common for evaluating classical heuristics , this approach is limited to small problems for quantum algorithms on current machines due to the exponential increase in time and memory required for the classical simulation . another approach , applied in this paper , evaluates average behavior over a simple ensemble of problems . such ensemble - based analyses provide insight into typical behavior for large problems  @xcite . an extreme case is single - step quantum search , i.e. , algorithms using only a single evaluation of structure associated with a problem . single - step search is very effective for highly constrained problems  @xcite , outperforming both unstructured quantum search and classical heuristics in these cases . can the technique used for highly constrained problems be extended to the more challenging case of hard search problems with an intermediate number of constraints  @xcite ? conversely , to what extent does the restriction to a single step limit the extent to which the capabilities of quantum computers can be used ? single - step search is particularly well - suited for an ensemble - based analysis , since it avoids the dependencies found in multistep quantum algorithms or classical heuristics . furthermore , single - step methods require far less coherence time than the unstructured algorithm with its exponentially many steps , and hence should be easier to implement . this is because maintaining coherence over many computational steps is difficult  @xcite . while this difficulty is unlikely to be a fundamental limitation  @xcite and small quantum computations have been implemented  @xcite , algorithms that minimize the required coherence time simplify hardware implementation . this paper gives an ensemble analysis for a single - step algorithm using the number of conflicts in each search state . we evaluate the asymptotic average scaling behavior directly , rather than relying on simulations . this result allows optimizing the algorithm , and also demonstrates a general technique for studying the average behavior of quantum search algorithms . we compare the asymptotic predictions to evaluations of small cases accessible to simulation , showing good correspondence even for small problems .    in the remainder of this paper , we first summarize the np - complete satisfiability search problem and then describe a class of one - step quantum algorithms for it . this class includes both the previous unstructured and highly constrained methods as special cases . we identify the best performing algorithms for satisfiability problems with differing degrees of constraint in the following two sections . we then present some additional behaviors of the algorithm and briefly consider extensions to more complex algorithms suggested by these results . details of the derivation are in the appendices .    as a note on notation , to compare the growth rates of various functions we use  @xcite @xmath0 to indicate that @xmath1 grows no faster than @xmath2 as a function of @xmath3 when @xmath4 . conversely , @xmath5 means @xmath1 grows at least as fast as @xmath2 , and @xmath6 means both functions grow at the same rate .","summary":"the structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties . the analytic techniques introduced here also apply to other quantum algorithms , supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of np search problems .","abstract":"the structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties . the structure of random k - sat allows determining the asymptotic average behavior of these algorithms , showing they improve on quantum algorithms , such as amplitude amplification , that ignore detailed problem structure but remain exponential for hard problem instances . compared to good classical methods , the algorithm performs better , on average , for weakly and highly constrained problems but worse for hard cases . the analytic techniques introduced here also apply to other quantum algorithms , supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of np search problems ."}
{"article_id":"quant-ph9812049","section_id":"c","document":"we have shown how an analysis based on ensemble averages helps design quantum search algorithms . the result was evaluated for satisfiability problems in the hard region as well as the easier weakly and highly constrained cases . compared to unstructured search , this gives exponentially better average behavior . moreover , this performance uses only a single evaluation of the assignment properties rather than the exponentially large number of repeated evaluations required by the unstructured method . thus this single - step algorithm requires much less coherence time for the quantum operations . the algorithm can be combined with amplitude amplification  @xcite , giving an additional quadratic performance improvement , but then requiring coherence time extending for the full algorithm rather than just for each trial separately . classical heuristics use more problem properties than the algorithm described here . these properties include the difference between the number of conflicts in an assignment and those of its neighbors , and the conflicts associated with partial assignments . we illustrated how additional phase variation allows incorporating such information in the quantum algorithm , and how the analyses techniques developed here can be extended to identify suitable parameters . thus these techniques can help evaluate a variety of quantum algorithms that are not easily addressed theoretically and hence would otherwise require slow classical simulation . this evaluation requires only that the properties of assignments used by the algorithm and the nature of the ensemble allow for an explicit determination of the ensemble averages , in analogy with eq . ( [ eq.psolnrandom ] ) . furthermore , in many respects this analysis is simpler than that for heuristic classical methods . this is because classical searches introduce dependencies in their path through a search space based on a series of heuristic choices . these dependencies are difficult to model theoretically . by contrast , the quantum search , by in effect exploring all search paths simultaneously , avoids this difficulty thereby giving relatively simple analytic expressions for the average behavior . on the other hand , this analysis is restricted to simple quantities , such as the average probability of finding a solution . how well this reflects typical search costs remains to be seen , though the discussion of  [ sect.costs ] suggests it gives a reasonable estimate , as well as determining good parameter values . classical heuristics often rely on behavior of states near solutions as guides , and can become stuck in local minima or among large collections of assignments with the same number of conflicts  @xcite . for the quantum algorithm , local minima are not an issue : instead the limited correlation between distance and conflicts for states _ far _ from solutions prevents efficient search . because of these very different characteristics , an interesting direction for future work is identifying individual problems or problem ensembles where the correlations are stronger even though the local minima for states relatively near solutions remain . in such cases , quantum algorithms could perform much better than classical heuristics . an important advantage of basing the algorithm on ensembles is the use of averages rather than requiring detailed knowledge of an individual search problem . this contrasts with the unstructured search method which requires knowledge of the number of solutions for a particular problem , or various values must be tried repeatedly  @xcite . an interesting open question is whether the algorithm , e.g. , the choice of @xmath86 and @xmath87 , could be improved by adjusting the parameters prior to search based on readily computed characteristics of an individual problem instance . in effect this would amount to using a more specific ensemble whose instances are more likely to be similar to the given instance than random problems . more generally , the variation in performance suggests a portfolio approach  @xcite would be effective for combining quantum algorithms using different parameter choices along with various classical methods . another possibility is combining this quantum algorithm more directly with classical heuristics consisting of independent trials , just as is possible for amplitude amplification . in this case , the heuristic is described not just by the probability to find a solution but by the probabilities it finds assignments with various numbers of conflicts , enhancing assignments with relatively few conflicts . then instead of starting with a uniform superposition of assignments , the initial state for the corresponding quantum algorithm would have amplitudes proportional to the square root of these probabilities . if the probabilities have a simple analytic form , the asymptotic analysis could be repreated , allowing optimal selection of the phase parameters for use with the classical heuristic . otherwise samples of the classical heuristic s behaviors could be used to estimate the relevant probabilities . while the resulting analysis will be more complicated than for amplitude amplificiation with nonuniform initial state  @xcite , using additional information in the quantum operations ( namely the number of conflicts in assignments rather than just whether they are solutions ) may allow for similar improvements as seen here for uniform initial conditions . these results show the usefulness of ensemble - based analyses for designing quantum algorithms . this is particularly helpful because empirical evaluation , through classical simulation , is limited to small cases . because quantum algorithms use properties of the entire search space , not just a small , carefully selected sample as with classical heuristics , ensemble averages are likely to be more useful for quantum algorithm development than is the case classically . thus quantum computing is likely to benefit from continued study of the properties of search problem ensembles , particularly for developing heuristic methods that work well for typical problems .","summary":"compared to good classical methods , the algorithm performs better , on average , for weakly and highly constrained problems but worse for hard cases .","abstract":"the structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties . the structure of random k - sat allows determining the asymptotic average behavior of these algorithms , showing they improve on quantum algorithms , such as amplitude amplification , that ignore detailed problem structure but remain exponential for hard problem instances . compared to good classical methods , the algorithm performs better , on average , for weakly and highly constrained problems but worse for hard cases . the analytic techniques introduced here also apply to other quantum algorithms , supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of np search problems ."}
{"article_id":"1304.3272","section_id":"i","document":"early investigations of black hole accretion flows indicated that tenuous flows can develop a two - temperature structure , with proton temperature sufficient to produce a significant @xmath0-ray luminosity above 10 mev through @xmath9 production ( e.g.  dahlbacka , chapline & weaver 1974 ) . the two - temperature structure is an essential feature of the optically - thin , advection dominated accretion flow ( adaf ) model , which has been extensively studied and successfully applied to a variety of black hole systems ( see , e.g. , reviews in yuan 2007 , narayan & mcclintock 2008 , yuan & narayan 2013 ) over the past two decades , following the work of narayan & yi ( 1994 ) . mahadevan , narayan & krolik ( 1997 ; hereafter m97 ) pointed out that @xmath0-ray emission resulting from proton - proton collisions in adafs may be a signature allowing to test their fundamental nature . the model of m97 relied on a non - relativistic adaf model and their computations were improved by oka & manmoto ( 2003 ; hereafter om03 ) who used a fully general relativistic ( gr ) model of the flow . however , both m97 and om03 neglected the doppler and gravitational shifts of energy as well as gravitational focusing and capturing by the black hole , which is a major deficiency because the @xmath0-ray emission is produced very close to the black hole s horizon . furthermore , both works neglected the internal absorption of @xmath0-ray photons to pair creation , which effect should be important in more luminous systems . adafs are supposed to power low - luminosity agns , like fanaroff - riley type i ( fr i ) radio galaxies or low - luminosity seyfert galaxies , and a measurement , or even upper limits on their @xmath0-ray emission , may put interesting constraints on the properties of the source of high - energy radiation in such objects . m97 and om03 considered only the _ cgro_/egret source in the direction of the galactic center for such an analysis . significant progress in exploration of the @xmath0-ray activity of agns which has been made after their works , thanks to the _ fermi _ mission , motivates us to develop a more accurate model of the hadronic @xmath0-ray emission from adafs . detections of @xmath0-ray emission from objects with misaligned jets ( e.g.  abdo et al . 2010b ) are most relevant for our study . their @xmath0-ray radiation is usually explained as a jet emission ; we show that emission from an accretion flow may be a reasonable alternative , at least in some fr is . we focus on modelling of radiation in 100 mev  10 gev energy range , relevant for the _ fermi_-lat measurements of the fr i radio galaxies ( abdo et al . 2010b ) and over which the upper limits in seyfert galaxies are derived ( ackermann et al . 2012 ) . the dependence of the @xmath0-ray luminosity on the black hole spin parameter makes a particularly interesting context for such an investigation . already a rough estimate by shapiro , lightman & eardley ( 1976 ) indicated a strong dependence of the @xmath0-ray luminosity from a two - temperature flow on the spin of the black hole and , then , they suggested that this effect may serve as a means to measure the spin value ( see also eilek & kafatos 1983 and colpi , maraschi & treves 1986 ) . om03 , who made gr calculations for the modern adaf model , found a dramatic dependence of the @xmath0-ray luminosity on the spin value in models with thermal distribution of proton energies , however , they concluded that the dependence is weak if protons have a nonthermal distribution . in this work we extend the analysis of this issue and clarify some related properties . we find global solutions of the hydrodynamical adaf model , which follows manmoto ( 2000 ) , and use them to compute the @xmath0-ray emission . similarly to m97 and om03 we take into account emission resulting from thermal and nonthermal distribution of proton energies ; we use similar phenomenological models , with some modifications which allow to illustrate separately effects due to local distribution of proton energies and to radial profile of @xmath0-ray emissivity . we also use our recently developed model of global comptonization ( niedwiecki , xie & zdziarski 2012 ; hereafter n12 , see also xie et al . 2010 ) to compute the x - ray emission , which allows to investigate the internal absorption of @xmath0-ray photons to pair creation in the flow .    in our computations we assume a rather weak magnetic field , with the magnetic pressure of 1/10th of the total pressure , supported by results of the magnetohydrodynamic ( mhd ) simulations in which amplification of magnetic fields by the magneto - rotational instability typically saturates at such a ratio of the magnetic to the total pressure ( e.g.  machida , nakamura & matsumoto 2004 , hirose et al . 2004 , hawley & krolik 2001 ) . we investigate the dependence on the poorly understood parameter in adaf theory , @xmath10 , describing the fraction of the turbulent dissipation that directly heats electrons in the flow . we take into account only one value of the accretion rate , but the considered ranges of the spin and @xmath10 parameters yield a rather large range of bolometric luminosities of @xmath11 to @xmath12 of the eddington luminosity . in our paper we present both the spectra affected by @xmath13 absorption and those neglecting the absorption effect ; the latter may be easily scaled to smaller accretion rates , for which the @xmath13 absorption becomes unimportant .","summary":"we use a fully general relativistic description of both the radiative and hydrodynamic processes , which allows us to study the dependence on the black hole spin . [ firstpage ]    accretion , accretion discs  black hole physics  gamma - rays : theory","abstract":"we present a model of-ray emission through neutral pion production and decay in two - temperature accretion flows around supermassive black holes . we refine previous studies of such a hadronic-ray emission by taking into account ( 1 ) relativistic effects in the photon transfer and ( 2 ) absorption of-ray photons in the radiation field of the flow . we use a fully general relativistic description of both the radiative and hydrodynamic processes , which allows us to study the dependence on the black hole spin . the spin value strongly affects the-ray emissivity within gravitational radii . the central regions of flows with the total luminosities of the eddington luminosity ( ) are mostly transparent to photons with energies below 10 gev , permitting investigation of the effects of space - time metric . for such , an observational upper limit on the-ray ( 0.1  10 gev ) to x - ray ( 2  10 kev ) luminosity ratio of can rule out rapid rotation of the black hole ; on the other hand , a measurement of can not be regarded as the evidence of rapid rotation , as such a ratio can also result from a flat radial profile of-ray emissivity ( which would occur for nonthermal acceleration of protons in the whole body of the flow ) . at , the-ray emission from the innermost region is strongly absorbed and the observed-rays do not carry information on the value of . we note that if the x - ray emission observed in centaurus a comes from an accretion flow , the hadronic-ray emission from the flow should contribute significantly to the mev / gev emission observed from the core of this object , unless it contains a slowly rotating black hole and protons in the flow are thermal .    [ firstpage ]    accretion , accretion discs  black hole physics  gamma - rays : theory"}
{"article_id":"1304.3272","section_id":"i","document":"we have studied the @xmath0-ray emission resulting from proton - proton interactions in two - temperature adafs . our model relies on the global solutions of the gr hydrodynamical model , same as om03 , but we improve their computations by taking into account the relativistic transfer effects as well as the @xmath13 absorption and by properly describing the global comptonization process . we have found that the spin value is reflected in the properties of @xmath0-ray emission , but the effect is not thrilling . the speed of the black hole rotation strongly affects the @xmath0-ray emission produced within the innermost @xmath52 . if emission from that region dominates , the observed @xmath0-ray radiation depends on the spin parameter noticeably ; the intrinsic @xmath0-ray luminosities of flows around rapidly - rotating and non - rotating black holes differ by over a factor of @xmath1 . however , if the @xmath0-ray emitting region extends to larger distances , the dependence is reduced . in the most extreme case with protons efficiently accelerated to relativistic energies in the whole body of the flow , the regions within and beyond @xmath52 give comparable contributions to the total emission , reducing the difference of @xmath0-ray luminosities between high and low values of @xmath8 to only a factor of @xmath102 . the radial emissivity profile of @xmath0-rays is very uncertain ( as the acceleration efficiency may change with radius ) , then , the level of the @xmath0-ray luminosity can not be regarded as a very sensitive probe of the spin value . still , it may be possible to assess a slow rotation in a low luminosity object by putting an upper limit on the @xmath0-ray luminosity at the level of @xmath254 of the x - ray luminosity . the presence of nonthermal protons may be easily assessed from the @xmath0-ray spectrum as for a purely thermal plasma the total @xmath0-ray emission would be observed only at energies lower than 1 gev . we have considered the accretion rate of @xmath46 , for which our model gives the bolometric luminosities between @xmath255 and @xmath256 . such @xmath75 , with the corresponding range of @xmath257 , seems to be favoured for investigation of the hadronic @xmath0-ray emission , with the related effects of the space - time metric , because the internal @xmath0-ray emission is large and its attenuation by @xmath13 absorption is weak . flows with @xmath258 can produce observable @xmath0-ray radiation only if the emitting region extends out to a rather large distance of several tens of @xmath106 . we have found the x - ray to @xmath0-ray luminosities ratio as a function of the black hole spin and the efficiency of the direct heating of electrons . the @xmath180 ratios reaching @xmath259 , with the corresponding levels of the @xmath0-ray luminosities which may be probed in nearby agns at the current sensitivity of _ fermi_-lat surveys , encourage to consider contribution from an accretion flow to the @xmath0-ray emission observed in low - luminosity objects . we point out that such a contribution should be strong at least in cen a.    the @xmath0-ray luminosity decreases rapidly ( @xmath260 ) with decreasing @xmath75 . m87 and sgr a@xmath224 are the obvious , however possibly also unique , objects for which the @xmath0-ray emission from the flow can be searched at @xmath261 . obviously , contribution from other @xmath0-ray emitting sites should be properly subtracted to establish the luminosity of an accretion flow , which may be particularly difficult in sgr a@xmath224 . the adaf model with a hard ( acceleration index @xmath262 ) nonthermal proton distribution can explain the @xmath0-ray detections of both sgr a@xmath224 ( above 100 gev ) and m87 , however , it does not allow for strong reduction of the accretion rate by outflows . nevertheless , it seems intriguing that in both nearby , low accretion - rate objects , in which the @xmath0-ray radiation is not suppressed by @xmath13 absorption , observations reveal very high energy components , consistent with predictions of such a model . in both objects the model requires a large black hole spin . the luminosity ratio should decrease rather slowly ( @xmath263 , as the radiative efficiency of hot flows varies as @xmath264 at small @xmath75 ; cf . xie & yuan 2012 ) with decreasing @xmath75 . the presence of the @xmath0-ray signal in low - luminosity agns is often considered as the evidence for the origin of their radiation in a jet ( see , e.g. , takami 2011 ) . we note that such a diagnostic is not valid because accretion flows may produce a similarly strong @xmath0-ray emission as jets in such objects .","summary":"the spin value strongly affects the-ray emissivity within gravitational radii .","abstract":"we present a model of-ray emission through neutral pion production and decay in two - temperature accretion flows around supermassive black holes . we refine previous studies of such a hadronic-ray emission by taking into account ( 1 ) relativistic effects in the photon transfer and ( 2 ) absorption of-ray photons in the radiation field of the flow . we use a fully general relativistic description of both the radiative and hydrodynamic processes , which allows us to study the dependence on the black hole spin . the spin value strongly affects the-ray emissivity within gravitational radii . the central regions of flows with the total luminosities of the eddington luminosity ( ) are mostly transparent to photons with energies below 10 gev , permitting investigation of the effects of space - time metric . for such , an observational upper limit on the-ray ( 0.1  10 gev ) to x - ray ( 2  10 kev ) luminosity ratio of can rule out rapid rotation of the black hole ; on the other hand , a measurement of can not be regarded as the evidence of rapid rotation , as such a ratio can also result from a flat radial profile of-ray emissivity ( which would occur for nonthermal acceleration of protons in the whole body of the flow ) . at , the-ray emission from the innermost region is strongly absorbed and the observed-rays do not carry information on the value of . we note that if the x - ray emission observed in centaurus a comes from an accretion flow , the hadronic-ray emission from the flow should contribute significantly to the mev / gev emission observed from the core of this object , unless it contains a slowly rotating black hole and protons in the flow are thermal .    [ firstpage ]    accretion , accretion discs  black hole physics  gamma - rays : theory"}
{"article_id":"cond-mat0305221","section_id":"i","document":"in the preceding paper,@xcite we have developed the dynamical theory for x - ray resonant magnetic specular reflectivity using the self - consistent method in the distorted - wave born approximation ( dwba ) . it is important to bear in mind , however , that specular reflectivity , which measures the density profile normal to the surface averaged over the in - plane directions , can yield only information corresponding to the root - mean - square roughness ( or equivalently , the average width ) of the interfaces . a more complete description of the morphology of the roughness can only be obtained from off - specular or diffuse scattering studies . the first such studies of resonant x - ray magnetic diffuse scattering studies were carried out recently by mackay @xmath0 @xmath1.@xcite from these measurements , quantities , such as the in - plane correlation length of the roughness , the interlayer roughness correlations and the roughness exponent , can be deduced . these quantities are of considerable importance . in the case of magnetic films , freeland @xmath0 @xmath1.@xcite found little correlation of the variations in the magnetic coercive force @xmath2 for a variety of samples with the average roughness ( chemical or magnetic ) but a systematic dependence on the roughness correlation length . in the case of giant magnetoresistance ( gmr ) films , contradictory results have been found in studying how the magnitude of the gmr effect depended on the chemical roughness alone , and it is likely that the effect depends on a more detailed set of parameters related to the magnetic ( as well as possibly the chemical ) roughness.@xcite barna and palasantzas@xcite have carried out calculations of the manner in which self - affine roughness at an interface affects electronic transport . methods were developed earlier to calculate analytically the offspecular components of the charge scattering of x - rays by rough surfaces and interfaces using the born approximation ( ba ) and the distorted - wave born approximation ( dwba).@xcite we present here the generalization of these methods to the case of resonant magnetic x - ray scattering from surfaces or interfaces of ferromagnetic materials possessing both structural and magnetic roughness . for this purpose , in the preceding paper@xcite we have represented the deviations from a smooth magnetic interface in terms of a `` rough '' magnetic interface , distinct from the structural interface ( but possibly correlated strongly with it ) , with its own self - affine roughness parameters and parameters representing the correlation of the structural with the magnetic roughness height fluctuations . components of the magnetization at the interface , which are disordered on much shorter length scales , are ignored in this treatment , as they will scatter at much lager @xmath3-values than those of interest here . the ba results have been previously presented in an earlier publication@xcite and already applied in interpreting x - ray resonant magnetic diffuse scattering measurements from magnetic multilayers.@xcite we also note that the analogous case of off - specular neutron scattering by magnetic roughness was treated earlier by sinha@xcite and more recent treatment has been given by toperverg.@xcite    the plan of this paper is as follows . in sec . ii , we derive the expression for the magnetic scattering in the ba , which is presented here in detail for completeness , although a brief account has been published earlier.@xcite in sec . iii , we discuss the magnetic diffuse scattering from magnetic domains in the ba . in sec . iv , we present the derivation of the resonant magnetic diffuse scattering in the dwba for a single magnetic interface and discuss numerical results . finally , in sec . v , we discuss the extension of the formalism to the case of diffuse scattering from magnetic multilayers and present some numerical results with experimental data from a gd / fe multilayer , which were analyzed earlier in the ba.@xcite","summary":"the theoretical formulation of x - ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse ( off - specular ) scattering , and general expressions are derived in both the born approximation ( ba ) and the distorted - wave born approximation ( dwba ) for both single and multiple interfaces . for this purpose , structural and magnetic interfaces are defined in terms of roughness parameters related to their height - height correlation functions and the correlations between them .","abstract":"the theoretical formulation of x - ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse ( off - specular ) scattering , and general expressions are derived in both the born approximation ( ba ) and the distorted - wave born approximation ( dwba ) for both single and multiple interfaces . we also give in the ba the expression for off - specular magnetic scattering from magnetic domains . for this purpose , structural and magnetic interfaces are defined in terms of roughness parameters related to their height - height correlation functions and the correlations between them . the results are generalized to the case of multiple interfaces , as in the case of thin films or multilayers . theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of mangetic diffuse scattering from a gd / fe multilayer ."}
{"article_id":"cond-mat0305221","section_id":"c","document":"we have shown in this paper and the preceding paper i@xcite that one can generalize the conventional theory of ordinary ( thomson ) x - ray scattering from surfaces possessing self - affine structural roughness to the case of resonant magnetic x - ray scattering from surfaces or interfaces of ferromagnetic materials possessing both structural and magnetic roughnesses . for this purpose , we have represented the deviations from a smooth magnetic interface in terms of `` rough '' magnetic interface , distinct from the structural interface ( but possibly correlated strongly with it ) , with its own self - affine roughness parameters and parameters representing the correlation of the structural with the magnetic roughness height fluctuations . components of the magnetization at the interface which are disordered on much shorter length scales are ignored in this treatment , as they will scatter at much lager @xmath3-values than those of interest here . the decrease of the in - plane averaged magnetization as a function of distance from the interface is taken into account by a form factor @xmath76 which is the fourier transform with respect to @xmath18 of the derivative of graded average magnetization density , and a magnetic dead layer is taken into account by allowing for a possible separation @xmath47 along the @xmath18-axis of the average structural and magnetic interfaces . in addition to magnetic roughness , magnetic domains can also give rise to offspecular scattering and their effect has also been included in the formalism . formulae have been derived both in the born approximation ( ba ) and the distorted - wave born approximation ( dwba ) for both single and multiple interfaces . numerical illustrations have been given for typical examples of each of these systems and compared with the experimental data from a gd / fe multilayer . we hope that the expressions given here and in the preceding paper i@xcite will be useful in helping to analyze the rapidly increasing amount of magnetic x - ray scattering data currently being accumulated from magnetic thin film and multilayer systems and in extracting meaningful parameters regarding to both the structural and magnetic roughness . this information will help in the understanding of the magnetic and magnetotransport properties of these multilayered systems . the codes for the calculations in this paper and the preceding one are also available in c language by emailing to d.r.l . ( drlee@aps.anl.gov ) . work at argonne is supported by the u.s . doe , office of basic energy sciences , under contract no . w-31 - 109-eng-38 .","summary":"theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of mangetic diffuse scattering from a gd / fe multilayer .","abstract":"the theoretical formulation of x - ray resonant magnetic scattering from rough surfaces and interfaces is given for the diffuse ( off - specular ) scattering , and general expressions are derived in both the born approximation ( ba ) and the distorted - wave born approximation ( dwba ) for both single and multiple interfaces . we also give in the ba the expression for off - specular magnetic scattering from magnetic domains . for this purpose , structural and magnetic interfaces are defined in terms of roughness parameters related to their height - height correlation functions and the correlations between them . the results are generalized to the case of multiple interfaces , as in the case of thin films or multilayers . theoretical calculations for each of the cases are illustrated as numerical examples and compared with experimental data of mangetic diffuse scattering from a gd / fe multilayer ."}
{"article_id":"math0101262","section_id":"i","document":"let @xmath19 be a convex set in a real vector space and let @xmath20 . then according to hyers and ulam  @xcite for @xmath21 , @xmath22 is @xmath23-approximately convex iff @xmath24.\\ ] ] in  @xcite they show that if @xmath22 is @xmath23-approximately convex and @xmath25 then there is a convex function @xmath26 and a constant @xmath27 only depending on the dimension so that @xmath28 . in a previous paper we show the sharp constant is @xmath29 ( here @xmath30 is the floor , or greatest integer function , and @xmath31 is the ceiling function , that is @xmath32 is the smallest integer greater than or equal to @xmath33 . ) in the present paper we generalize the notion of approximate convexity and give the sharp constants in the corresponding hyers - ulam type theorems . this is done by finding the extremal approximately convex function on the simplex that vanishes on the vertices . let us put the these problems in a somewhat larger setting . first , by replacing @xmath22 by @xmath34 in  , there is no loss of generality in assuming that @xmath35 . then many natural notions of generalized convexity are covered in the following definition . let @xmath36 be the standard @xmath1-dimensional simplex . [ def : s - almost ] let @xmath37 a vector space over the reals and let @xmath38 be a convex set and let @xmath39 . then a function @xmath3 is * _ _ * @xmath4-almost convex on @xmath19 iff for all @xmath5 and @xmath6 the inequality @xmath40 holds . we denote by @xmath41 the set of almost convex functions @xmath3 . the case of @xmath42 corresponds to the case studied by hyers and ulam  @xcite and others ( cf . the book  @xcite for more information and references ) . when @xmath43 the @xmath4-almost convex functions are just the functions that satisfy @xmath44 which are the approximately midpoint convex functions , ( sometimes called the approximately jensen convex functions ) which also have been studied by several authors . we give a general theory of @xmath4-almost convex functions . in particular when @xmath4 has at least one point that is not a vertex we construct ( definition  [ def : e ] and theorem  [ e - extr ] ) a bounded @xmath4-almost convex function @xmath45 such that if @xmath10 is bounded , @xmath4-almost convex , and @xmath11 on the vertices of @xmath9 then @xmath46 for all @xmath13 . then the number @xmath47 is the sharp constant in stability theorems of hypers - ulam type and the function @xmath48 is the function that shows it is sharp ( see theorem  [ stability ] . )    probably the most natural choices , for @xmath4 are @xmath49 , a simplex , and @xmath14 , the barycenter of a simplex . in these cases we are able to give very explicit formulas both for the extremal function @xmath50 and for the constant @xmath51 . ( for the case @xmath49 this was done in our earlier paper  @xcite where @xmath52 for the case of @xmath4 the barycenter of @xmath15 see theorem  [ main - bary ] , where the value is given as @xmath53 ( this differs from the notation of theorem  [ main - bary ] by the substitution @xmath54 . ) ) there is an interesting dichotomy in these two cases . when @xmath49 then @xmath50 is a concave piecewise linear function that is continuous on the interior @xmath55 of @xmath9 and the maximum occurs at the barycenter of @xmath9 . ( see  @xcite . ) however when @xmath14 is the barycenter of @xmath15 then @xmath50 is discontinuous on a dense subset of @xmath9 and the graph of @xmath50 is a fractal with a large number of self similarities and the maximum does _ not _ occur at the barycenter of @xmath15 . see figure  [ e - graph ] . we also note the somewhat surprising fact , that , as functions of @xmath56 , both @xmath57 and @xmath58 have the same order of growth , i.e. @xmath59 . this paper is not completely self - contained . several of the results have proofs that are very similar to the proofs in our earlier paper  @xcite and at several places we refer the reader to  @xcite for proofs . let @xmath60 be the standard @xmath1-dimensional simplex . for the rest of this section we fix a subset @xmath61 it follows easily from the definition of @xmath4-almost convex that @xmath62 is a convex subset of the vector space of all functions from @xmath19 to @xmath63 . it is useful to make a distinction between two cases :    [ def : cases ] if @xmath64 then    1 . if @xmath65 for any finite @xmath66 then @xmath4 is of * _ _ * infinite type . if @xmath67 for some @xmath66 then @xmath4 is of * _ _ * finite type . if further @xmath68 for some @xmath1 then @xmath4 is * _ _ * homogeneous . [ s - compact ] if we assume that the union @xmath69 is disjoint and has the natural topology ( @xmath70 is open iff @xmath71 is open in @xmath15 for all @xmath1 ) then it is not hard to see that @xmath4 is of finite type if and only if it has compact closure in @xmath72 . when considering @xmath4-almost convex functions there is no real distinction between @xmath4 of finite type and @xmath4 homogeneous . [ 1delta ] let @xmath67 . for @xmath73 let @xmath74 be the inclusion @xmath75 and set @xmath76\\subseteq \\delta_n$ ] . let @xmath77 . then for any convex subset @xmath19 of a real vector space @xmath78 . this is a more or less straightforward chase though the definition . the proof of the following is also straightforward and left to the reader . [ symmetric]let @xmath68 and let @xmath79 where @xmath80 is the group of all permutations of @xmath81 . then for any convex subset @xmath19 of a real vector space @xmath78 . the following is also trivial . [ incl ] let @xmath82 . then for any convex subset @xmath19 of a real vector space @xmath83 . the following can be used to reduce certain questions about @xmath4-almost convex functions to the case where @xmath84 . [ s - part ] let @xmath85 and let @xmath86 be a nonempty subset of @xmath87 for some @xmath1 . let @xmath88 be a partition of the set @xmath81 into @xmath89 nonempty sets and let @xmath90 where @xmath91 then @xmath92 for any convex subset @xmath19 of a real vector space . in particular if @xmath5 and for some @xmath93 we set @xmath94 and @xmath95 then any @xmath4 almost convex function @xmath22 will satisfy @xmath96 . let @xmath19 be a convex subset of a real vector space and let @xmath97 , @xmath98 and @xmath99 . let @xmath100 be defined by @xmath101 as @xmath98 there is a @xmath102 so that @xmath103 . then as @xmath104 is @xmath4-almost convex @xmath105 thus @xmath106 . it is useful to understand when an @xmath4-almost convex function is bounded . [ leb - bded ] let @xmath85 and assume that @xmath4 contains at least one point that is not a vertex ( that is there is @xmath5 with @xmath107 ) . let @xmath108 be a convex open set in @xmath109 . then any @xmath4-almost convex function @xmath110 which is lebesgue measurable is bounded above and below on any compact subset of @xmath108 . let @xmath5 with @xmath107 . then there is a @xmath111 so that if @xmath112 and @xmath95 , then @xmath113 , @xmath114 and by proposition  [ s - part ] @xmath115 we assume that @xmath116 , the case of @xmath117 having a similar proof . as any compact subset of @xmath108 is contained in a bounded convex open subset of @xmath108 we can also assume , without loss of generality , that @xmath108 is bounded . let @xmath118 be compact and let @xmath119 . for any @xmath120 let @xmath121 be the open ball of radius @xmath122 about @xmath33 . then for any @xmath123 we have @xmath124 . for @xmath123 define @xmath125 by @xmath126 then it is easy to check that @xmath127 for all @xmath128 and @xmath129 for all @xmath130 . also @xmath131 is a dilation in the sense that @xmath132 for all @xmath133 . as @xmath127 and @xmath134 this implies @xmath135=b_a((\\alpha/\\beta)r)\\subseteq b_a(r)$ ] . let @xmath136 be lebesgue measure on @xmath109 . then for any measurable subset @xmath137 of @xmath109 @xmath138)=(\\alpha/\\beta)^n{{\\mathcal l}}^n(p).\\ ] ] choose a positive real number @xmath23 so that @xmath139 where @xmath140 is the open ball of radius @xmath122 about the origin . because @xmath22 is measurable and @xmath141 there is a positive @xmath142 so large that @xmath143 therefore if @xmath144 then @xmath145 . let @xmath146 . we now claim that @xmath147 $ ] has positive measure . for if not then @xmath148 and @xmath149 $ ] would be essentially disjoint subsets of @xmath150 and therefore , using that @xmath151)=(\\alpha/\\beta)^n{{\\mathcal l}}^n(a)$ ] , @xmath152)\\\\ & = { \\left(}1+{\\left(}\\frac\\alpha\\beta{\\right)}^n{\\right)}{{\\mathcal l}}^n(a)\\\\ & \\ge { \\left(}1+{\\left(}\\frac\\alpha\\beta{\\right)}^n{\\right)}({{\\mathcal l}}^n(b_a(r))-{\\varepsilon})\\end{aligned}\\ ] ] which can be rearranged as @xmath153 contradicting  . therefore @xmath154)>0 $ ] as claimed . let @xmath155)$ ] . then @xmath33 and @xmath156 are both in @xmath157 and therefore @xmath158 . thus @xmath159 which shows that @xmath22 is bounded above on @xmath160 .    to show that @xmath22 has a lower bound on compact subsets of @xmath108 , let @xmath161 and let @xmath162 be small enough that the closed ball @xmath163 is contained in @xmath108 . then @xmath163is compact so by what we have just done there is a constant @xmath164 so that @xmath165 for all @xmath166 . let @xmath166 . then , again as above , @xmath167 , and therefore @xmath168 which can be solved for @xmath169 to give @xmath170 therefore @xmath104 is bounded below on @xmath171 . but any compact subset of @xmath108 can be covered by a finite number of such open balls and thus @xmath104 is bounded below on all compact subsets of @xmath108 . the following will be needed later . [ 1d - bded ] let @xmath172\\to { { \\mathbf r}}$ ] be a lebesgue measurable function so that @xmath173 for some @xmath174 with @xmath114 ( that is @xmath104 is @xmath4-almost convex with @xmath175 ) . then @xmath104 is bounded above on @xmath176 $ ] .    by doing a linear change of variable ( which preserves @xmath4-almost convexity ) we can assume that @xmath176=[0,1]$ ] . also by replacing @xmath104 by @xmath177 we can assume that @xmath178 . let @xmath179 . then by theorem  [ leb - bded ] there is a constant @xmath180 such that @xmath181 on @xmath182 $ ] . let @xmath183 we now show that @xmath184 on @xmath185 $ ] . if @xmath186 , @xmath187 , or @xmath188 $ ] this is clear . let @xmath189 then the choice of @xmath190 ensures that there is a @xmath191 $ ] such that @xmath192 for some positive integer @xmath193 . also , as @xmath194 $ ] , @xmath195 . therefore @xmath196 if @xmath197 a similar calculation shows that @xmath198 ( or this can be reduced to the case @xmath189 by the change of variable @xmath199 ) . this completes the proof . we will show that on the @xmath56-dimensional simplex @xmath9 there is a pointwise largest bounded @xmath4-almost convex function that vanishes on the vertices of @xmath15 . we start with some definitions . [ tree ] a * _ _ * tree , @xmath200 , is a collection of points @xmath201 , called * _ _ * nodes , and a set of ( directed ) * _ _ * edges connecting some pairs of nodes with the following properties : the set @xmath201 is a disjoint union @xmath202 where @xmath203 contains exactly one point , the * _ _ * root of the tree , each @xmath204 is a finite set and if @xmath205 then @xmath206 is a disjoint union @xmath207 of nonempty sets where @xmath208 is the set of * _ _ * successors of @xmath209 . the ( directed ) edges of the tree leave a node and connect it to its successors and there are no other edges in the tree ( cf . figure  [ fig : s - tree ] ) . if @xmath210 is a node of the tree then @xmath211 where @xmath212 is the * _ _ * rank of @xmath210 . a * _ _ * branch of the tree is a sequence of nodes @xmath213 where @xmath214 is the root , @xmath215 , and there is an edge from @xmath216 to @xmath217 . we now consider trees with extra structure , a labeling of the edges in a way that will be used in defining the extremal @xmath4-almost convex function . [ def : ranked - tree ] let @xmath218 be nonempty . then an * _ _ * @xmath4-ranked tree is a tree @xmath200 with its edges labeled by non - negative real numbers in such a way that for any node @xmath210 of the tree there is an element @xmath219 so that there are exactly @xmath220 edges leaving @xmath210 and these are labeled by @xmath221 . the number @xmath222 is the * _ _ * weight of the edge it labels . figure  [ fig : s - tree ] shows a typical @xmath4-ranked tree . ( 260,150 ) ( 80,150 ) ( 40,100 ) ( 120,100 ) ( 20,50 ) ( 60,50 ) ( 90,50 ) ( 120,50 ) ( 150,50 ) ( 40,100)(4,5)40 ( 120,100)(-4,5)40 ( 20,50)(2,5)20 ( 60,50)(-2,5)20 ( 90,50)(3,5)30 ( 150,50)(-3,5)30 ( 120,50)(0,1)50    ( 20,50)(10,25)(0,0 ) ( 20,50)(20,25)(20,0 ) ( 20,50)(30,25)(40,0 )    ( 60,50)(55,25)(50,0 ) ( 60,50)(65,25)(70,0 )    ( 90,50)(85,25)(80,0 ) ( 90,50)(95,25)(100,0 )    ( 120,50)(115,25)(110,0 ) ( 120,50)(125,25)(130,0 ) ( 120,50)(120,25)(120,0 )    ( 150,50)(145,25)(140,0 ) ( 150,50)(155,25)(160,0 ) ( 150,50)(150,25)(150,0 )    ( 48,125)@xmath223 ( 103,125)@xmath224    ( 17,70)@xmath225 ( 54,70)@xmath226    ( 90,70)@xmath227 ( 142,70)@xmath228 ( 122,70)@xmath229    ( 100,147)the root @xmath230 unique node of rank @xmath231 . ( 140,97)the rank one nodes . ( 170,47)the rank two nodes . we now describe how an @xmath4-ranked tree determines a probability measure on the set of branches of the tree . let @xmath200 be an @xmath4-ranked tree and let @xmath232 be the set of all branches of @xmath200 . if @xmath233 are two elements of @xmath234 we can define a distance between them as @xmath235 where @xmath236 is the smallest index with @xmath237 ( and @xmath238 if @xmath239 ) . while we will not need to use this fact , it is not hard to check that this makes @xmath234 into a compact metric space which is homeomorphic to the cantor set . [ def : s - ranked - meas ] let @xmath85 be nonempty and let @xmath200 be an @xmath4-ranked tree . then @xmath200 defines a measure on @xmath234 , the set of branches of @xmath200 , as follows . for @xmath210 a node of @xmath200 let @xmath240 be the set of branches of @xmath200 that pass through @xmath210 . if @xmath241 is the rank of @xmath210 then let @xmath242 be the initial segment of a branch passing through @xmath210 ( so that @xmath243 ) and for @xmath244 let @xmath245 be the weight of the edge from @xmath246 to @xmath209 . then @xmath247 is the measure on @xmath234 such that @xmath248 ( that is @xmath249 is the product of the weights of the edges along an initial segment of a branch connecting the root to @xmath210 . ) a measure arising in this way will be called an * _ _ * @xmath4-ranked probability measure . it follows from this definition that if @xmath210 is a node of @xmath200 and @xmath250 are the successors of @xmath210 and @xmath219 labels the edges from @xmath210 in such a way that @xmath222 labels the edge from @xmath210 to @xmath209 then @xmath251    it is useful to give a description of an @xmath4-ranked probability measure that does not rely directly on its construction from an @xmath4-ranked tree . [ def : s - meas ] an * _ _ * @xmath4-ranked probability measure is an ordered triple @xmath252 where @xmath234 is a nonempty set , @xmath253 a sequence of finite partitions of @xmath234 into nonempty subsets such that @xmath254 and @xmath255 refines @xmath256 , @xmath247 is a measure defined on the @xmath257-algebra , @xmath258 , generated by @xmath259 so that for all @xmath260 and all @xmath261 , there exists @xmath5 such that if @xmath262 then @xmath263 if @xmath264 then the * _ _ * rank of @xmath265 is @xmath266 where @xmath267 . ( the union @xmath259 is disjoint so this is well defined . )    given an @xmath4-ranked probability measure @xmath252 we can construct an @xmath4-ranked tree by using for the set of nodes of the tree @xmath268 , letting @xmath269 be the set of nodes of rank @xmath193 . there is an edge from @xmath270 to @xmath271 iff @xmath272 in this case the weight of this edge is the @xmath222 such that @xmath273 . in most of what follows we will work with the alternative definition of @xmath4-ranked probability  [ def : s - meas ] , but will think of any such measure as being constructed from an @xmath4-ranked tree as above . [ example1 ] suppose @xmath4 consists of a single point @xmath274 in the interior of @xmath15 ( so that each @xmath222 is positive ) . then there is only one @xmath4-ranked probability measure i.e.  @xmath275 the product measure on @xmath276^{{\\mathbf n}}$ ] where @xmath276=\\{0,1{,\\dots,}m\\}$ ] and @xmath277 and @xmath278 is given on @xmath276 $ ] by @xmath279 . this uniqueness is clear when viewed in terms of @xmath4-ranked trees as when @xmath4 is a one point set there is clearly only one @xmath4-ranked tree . [ note1 ] let @xmath5 and for each @xmath280 with @xmath281 , let @xmath282 be an @xmath4-ranked probability measure on a set @xmath283 where we assume @xmath284 for @xmath285 . we let @xmath286 ( the disjoint union of the @xmath283 ) and let @xmath254 . for @xmath287 , set @xmath288 . ( this gives @xmath289 . ) define a measure @xmath247 on @xmath258 by @xmath290 . then @xmath252 is an @xmath4-ranked probability measure . note that if @xmath291 then @xmath292 and @xmath293 . [ def : divides ] if @xmath294 and @xmath295 is a probability sequence in @xmath296 ( that is @xmath297 and @xmath298 ) then * _ _ * @xmath33 divides @xmath299 , written as @xmath300 , iff @xmath301 can be partitioned into sets @xmath302 such that @xmath303 -22pt    [ def : e ] define @xmath304 by @xmath305 where the infimum is taken over all @xmath4-ranked probability measures @xmath252 and all disjoint sequences @xmath306 with @xmath307 ( this can be rephrased using disjoint sequences @xmath308 which are either finite or countable . but it is notationally more convenient to take a finite sequence @xmath309 and extend it to a sequence @xmath310 with @xmath311 for @xmath312 . )    in much of what follows it will be clear that the domain of @xmath313 is @xmath9 and we will just write @xmath16 or just @xmath313 rather than @xmath50 . [ note2 ] for each @xmath4-ranked probability measure @xmath252 we let @xmath314 denote the finite algebra with elements of @xmath315 as its atoms . then in the last definition let @xmath316 be a disjoint sequence so that   holds and let @xmath317 be a partition of @xmath318 so that @xmath319 . then set @xmath320 . then @xmath321 therefore we could also define @xmath322 by @xmath323 where the infimum is taken over all @xmath4-ranked probability measures , and all disjoint sequences @xmath324 so that @xmath325 -32pt    the following sum will be used later in this section and in section  3 . the proof is left to the reader .    [ lemma : sum ] let @xmath326 with @xmath327 and @xmath193 an integer . then @xmath328 -20pt    [ prop1 ] for any nonempty @xmath329 we have @xmath330 for all vertices of @xmath9 and if @xmath13 is not a vertex then @xmath331 . if @xmath4 contains a point @xmath274 which is not a vertex , i.e.  @xmath332 , then @xmath16 is bounded on @xmath9 and in fact has the upper bound @xmath333 on @xmath9 . thus if @xmath334 ( for example when @xmath335 ) then @xmath313 is given by @xmath336 and @xmath337 for @xmath13 and @xmath33 not a vertex .    if @xmath33 is a vertex of @xmath15 , which without lost of generality we can take to be @xmath338 , then let @xmath252 be any @xmath4-ranked probability measure and let @xmath339 and @xmath311 for @xmath340 . partition @xmath318 as @xmath341 and @xmath342 an arbitrary partition of @xmath343 . then @xmath344 and @xmath345 for @xmath340 and therefore @xmath346 thus @xmath347 . now assume that @xmath33 is not a vertex and let @xmath252 be an @xmath4-ranked probability measure and @xmath348 with @xmath349 and @xmath350 . then as @xmath33 is not a vertex we have that @xmath351 for @xmath352 and therefore @xmath353 . thus @xmath354 and therefore @xmath355 . this gives @xmath356 taking an infimum then gives that @xmath357 . now assume that @xmath4 contains a point that is not a vertex and note that if @xmath358 then @xmath359 for all @xmath33 . thus it suffices to show that @xmath360 is bounded when @xmath4 is a single point @xmath274 with @xmath361 . suppose @xmath362 . we let @xmath247 be the product measure as in example  [ example1 ] and we let @xmath363 as in remark  [ note2 ] and use the alternative definition of @xmath16 given in remark  [ note2 ] . for each @xmath193 , @xmath352 , we select inductively a set @xmath364 with @xmath365 pairwise disjoint such that @xmath366 note that if @xmath367 , then @xmath368 . we carry out the the inductive selection as follows : let @xmath369 then @xmath370 if @xmath371 , let @xmath372 . if @xmath373 let @xmath225 be the first integer such that @xmath374 since @xmath375 , @xmath376 let @xmath377 . continue choosing from @xmath378 to obtain @xmath379 . note that by  , the supply of atoms in @xmath380 is sufficient to choose the sets @xmath381 . for @xmath382 we have @xmath383 which implies @xmath384 for @xmath382 . as @xmath385 we can use lemma  [ lemma : sum ] ( with @xmath386 ) to compute @xmath387 thus , in the notation of remark  [ note2 ] , @xmath388 which bounds @xmath313 as required . [ prop2 ] the function @xmath389 is @xmath4-almost convex on @xmath9 . let @xmath390 and @xmath391 . for @xmath281 , let @xmath392 be an @xmath4-ranked probability measure . we let @xmath393 be a disjoint sequence such that @xmath394 . now let @xmath247 be the @xmath4-ranked probability measure on @xmath286 as in remark  [ note1 ] , i.e.  @xmath395 . it is easily checked that @xmath396 ( and @xmath397 ) . thus @xmath398t_i\\mu^{(i)}\\big(i^{(i)}_j\\big)\\\\ & = 1+\\sum_{i=0}^m t_i\\bigg(\\sum_{j=1}^\\infty \\big(r_{\\mu^{(i)}}i^{(i)}_j\\big)\\mu^{(i)}\\big(i^{(i)}_j\\big)\\bigg).\\end{aligned}\\ ] ] taking the infimum over all @xmath399 on the right hand side of this gives @xmath400 which completes the proof . [ e - extr ] the function @xmath389 is the extremal @xmath4-almost convex function on @xmath9 in the sense that if @xmath104 is a bounded @xmath4-almost convex function on @xmath9 with @xmath401 for @xmath402 , then @xmath403 for all @xmath13 . let @xmath13 . also let @xmath252 be an @xmath4-ranked probability measure and @xmath404 a disjoint sequence in @xmath405 such that @xmath406 where @xmath318 is partitioned by @xmath302 and @xmath407 . if @xmath408 ( the @xmath257-algebra generated by @xmath409 ) , i.e.   @xmath410 , we define ( for @xmath411 , so that @xmath412 ) @xmath413 then the map @xmath414 is a vector measure on @xmath415 . note that @xmath416 ( as @xmath417 except for a set of @xmath247-measure zero so that @xmath418 ) . for each @xmath419 let @xmath420 note that if @xmath421 , then @xmath422 for some @xmath423 . since @xmath424 each @xmath425 is ( except for a set of @xmath247-measure zero ) a disjoint union of countable many sets @xmath426 with @xmath421 so that @xmath427 . we require the following lemma to complete the proof . [ lemma1 ] with @xmath22 as in the statement of theorem  [ e - extr ] @xmath428\\mu(j).\\ ] ]    before proving the lemma we show that it implies the theorem . as @xmath104 is bounded there is an @xmath142 so that @xmath429 for all @xmath430 . therefore by the lemma    @xmath431    since @xmath432 this yields @xmath433 . taking the infimum over @xmath247 gives @xmath403 and completes the proof of theorem  [ e - extr ] . the proof is by induction on @xmath1 . the base case is @xmath434 which amounts to @xmath435\\mu(x)$ ] , which is in fact an equality . now assume for some @xmath436 that the inequality   holds . consider @xmath437 . then @xmath438 divides into sets @xmath439 such that @xmath440 since @xmath441 the @xmath4-almost convexity of @xmath104 implies @xmath442 multiplying this by @xmath443 @xmath444\\mu(j_i).\\end{aligned}\\ ] ] if we let @xmath445 and apply the above to each @xmath437 @xmath446\\mu(j)\\le \\sum_{j\\in \\mathcal{s}_m}[m+1 + h(x_j)]\\mu(j).\\ ] ] if @xmath447 and @xmath448 for some @xmath280 then @xmath449 , where @xmath450 . thus the term for @xmath438 satisfies @xmath451\\mu(j)=[m+1 + h(e_k)]\\mu(i_i)\\le(m+1)\\mu(i_i)=r_\\mu(i_i)\\mu(i_i)\\ ] ] since @xmath452 and @xmath11 . now @xmath453 . thus @xmath454\\mu(j)\\\\ & \\le \\sum_{r_\\mu(i_i)\\le m}r_\\mu(i_i)\\mu(i_i )      + \\sum_{j\\in\\mathcal{s}_m}[m+1 + h(x_j)]\\mu(j)\\\\ & \\le\\sum_{r_\\mu(i_i)\\le m}r_\\mu(i_i)\\mu(i_i )      + \\sum_{r_\\mu(i_i)=m+1}r_\\mu(i_i)\\mu(i_i)\\\\ & \\quad\\qquad      + \\sum_{j\\in\\mathcal{r}_{m+1}}[m+1 + h(x_j)]\\mu(j)\\\\ & = \\sum_{r_\\mu(i_i)\\le m+1}r_\\mu(i_i)\\mu(i_i )      + \\sum_{j\\in\\mathcal{r}_{m+1}}[m+1 + h(x_j)]\\mu(j).\\end{aligned}\\ ] ] this closes the induction and completes the proof of the lemma . let @xmath64 and assume that @xmath4 contains at least one point that is not a vertex , that is a point @xmath274 with @xmath455 . then , letting @xmath45 be as in definition  [ def : e ] , set @xmath456 by proposition  [ prop1 ] the number @xmath18 is finite and we will show that it is given by  . the function @xmath50 and the number @xmath18 are extremal in several analytic and geometric inequalities involving @xmath4-almost convex functions and sets . an example of this is the sharp form of the hyers - ulam stability theorem ( theorem  [ stability ] ) in which @xmath18 is the best constant and the example showing that this is the case is the function  @xmath457 . the exact value of @xmath18 for some natural choices of @xmath4 are given in later sections . as a preliminary to theorem  [ stability ] we show that @xmath4-almost convex functions with minimal regularity ( borel measurability ) are locally bounded so that theorem  [ e - extr ] can be applied . recall that in a metric space the borel sets are the members of the @xmath257-algebra generated by the open sets and if @xmath458 is a function between metric spaces then it is borel measurable iff @xmath459 $ ] is a borel subset of @xmath234 for every open subset @xmath108 of @xmath460 . [ borel - bded ] assume that @xmath4 has at least one point that is not a vertex . let @xmath461 be a borel measurable @xmath4-almost convex function . then @xmath462    by replacing @xmath104 by @xmath463 , which will still be @xmath4-almost convex , we may assume that @xmath464 for @xmath465 . if @xmath104 is bounded then @xmath466 by theorem  [ e - extr ] . so to finish the proof it is enough to show that @xmath104 is bounded . in doing this we can use proposition  [ s - part ] and note that there are @xmath174 with @xmath114 so that if @xmath467 then @xmath104 is @xmath468-almost convex . ( to be a bit more precise let @xmath5 with @xmath469 and then the choice @xmath470 and @xmath471 works . )    with this choice of @xmath468 we now prove by induction on @xmath56 that if @xmath461 is @xmath468-almost convex and vanishes on the vertices of @xmath9 then @xmath472 . the base case is @xmath473 . then as a borel measurable function is lebesgue measurable corollary  [ 1d - bded ] implies @xmath104 is bounded . but then theorem  [ e - extr ] implies @xmath474 .    for the induction step let @xmath475 be @xmath468-almost convex and suppose @xmath22 vanishes on the vertices of @xmath9 let @xmath476 be the function @xmath477 . then @xmath478 is @xmath468-almost convex , vanishes on the vertices of @xmath479 and is borel measurable . therefore by the induction hypothesis @xmath480 . let @xmath481 and consider the function @xmath482\\to { { \\mathbf r}}$ ] given by @xmath483 then this is @xmath468-almost convex on @xmath185 $ ] and is borel measurable . therefore another application of corollary  [ 1d - bded ] implies that @xmath484 bounded and as @xmath484 vanishes at the endpoints of @xmath185 $ ] we have that @xmath485 . this implies @xmath486 but every @xmath13 can be expressed as @xmath487 for some @xmath488 and some @xmath489 $ ] . therefore @xmath104 is bounded on @xmath9 . then theorem  [ e - extr ] implies @xmath490 . this closes the induction and completes the proof . [ gen - bds ] let @xmath108 be a convex set in a normed vector space and let @xmath491 be an @xmath4-almost convex function which is bounded above on compact subsets of @xmath108 . assume that @xmath4 contains at least one point which is not a vertex . then for any @xmath492 the inequalities @xmath493 hold for all @xmath494 . if @xmath108 is compact , @xmath56-dimensional and @xmath37 is the set of extreme points of @xmath108 then @xmath495    let @xmath496 be given by @xmath497 . then @xmath498 is @xmath4-almost convex , bounded ( as @xmath22 is bounded on the convex hull of @xmath499 as it is compact ) and vanishes on the vertices of @xmath9 . therefore by theorem  [ e - extr ] @xmath500 which implies  .    if @xmath108 is compact and @xmath56 dimensional with extreme points @xmath37 , then @xmath108 is the convex hull of @xmath37 . by carathodory s theorem for any @xmath501 there are @xmath502 and @xmath503 so that @xmath504 which , along with  , implies .    we can now give the sharp version of the hyers - ulam stability theorem for @xmath4-almost convex functions . [ stability ] let @xmath85 so that @xmath4 contains at least one point that is not a vertex . assume that @xmath505 , @xmath21 , and that @xmath110 is bounded above on compact subsets of @xmath108 and satisfies @xmath506 for all @xmath219 and points @xmath507 . then there exist convex functions @xmath508 such that @xmath509 . the constant @xmath18 is the best constant in these inequalities . note that if @xmath104 satisfies   then @xmath34 is @xmath4-almost convex . therefore , by theorem  [ leb - bded ] , if @xmath108 is open and @xmath104 is lebesgue measurable then @xmath104 will automatically be bounded on compact subsets of @xmath108 . likewise if @xmath108 is a borel set and @xmath22 is borel measurable then by proposition  [ borel - bded ] @xmath22 will be bounded above on the convex hull of any finite number of points and this is enough for the proof of the theorem .    in the special case that @xmath510 a proof , based on ideas of hyers and ulam  @xcite and cholewa  @xcite , can be found in  @xcite . as the details in the present case are identical we omit the proof .","summary":"let be the standard-dimensional simplex . let , then a function with domain a convex set in a real vector space is * _ _ *-almost convex iff for all and the inequality holds if contains at least one point that is not a vertex , then an extremal-almost convex function is constructed with the properties that it vanishes on the vertices of and if is any bounded-almost convex function with on the vertices of , then for all . in the special case , the barycenter of , very explicit formulas are given for and . these are of interest as and are extremal in various geometric and analytic inequalities and theorems .","abstract":"let be the standard-dimensional simplex . let , then a function with domain a convex set in a real vector space is * _ _ *-almost convex iff for all and the inequality holds . a detailed study of the properties of-almost convex functions is made . if contains at least one point that is not a vertex , then an extremal-almost convex function is constructed with the properties that it vanishes on the vertices of and if is any bounded-almost convex function with on the vertices of , then for all . in the special case , the barycenter of , very explicit formulas are given for and . these are of interest as and are extremal in various geometric and analytic inequalities and theorems ."}
{"article_id":"math0101262","section_id":"r","document":"we now assume that @xmath511 is compact . by remark  [ s - compact ] this implies that @xmath4 is of finite type . therefore by proposition  [ 1delta ] there is no loss in generality in assuming that @xmath512 for some @xmath1 . let @xmath513 be a compact convex set and let @xmath37 be the set of extreme points of @xmath160 . if @xmath514 is a function , then @xmath515 has * _ _ * extreme values equal to @xmath516 iff @xmath517 . two functions @xmath518 * _ _ * have the same extreme values iff they agree on @xmath37 . if @xmath514 is a bounded function and @xmath68 then let @xmath519 be the set of bounded @xmath4-almost convex functions @xmath515 so that @xmath520 . then the * _ _ * extremal @xmath4-almost convex function with extreme values @xmath516 is @xmath521 if @xmath4 contains at least one point which is not a vertex , then theorem  [ gen - bds ] implies that @xmath522 is finite valued and in fact @xmath523 . as the pointwise supremum of @xmath4-almost convex functions is @xmath4-almost convex , the function @xmath522 is the pointwise largest @xmath4-almost convex function with @xmath524 on @xmath37 . if @xmath513 is a compact convex set and @xmath37 is the set of extreme points of @xmath160 then for any function @xmath515 define @xmath525 by @xmath526 where it is assumed that @xmath527 . we can then define @xmath4-almost convex functions in terms of this operator by the following , for any bounded function @xmath528 , @xmath529 this operator satisfies a maximum principle and can be used to prove that extremal @xmath4-almost convex functions are lower semi - continuous . [ max - prin ] let @xmath513 be a compact convex set with extreme points @xmath37 . assume that @xmath530 is compact and has at least one point which is not a vertex . let @xmath531 be bounded functions so that @xmath532 and @xmath533 is @xmath4-almost convex ( that is @xmath534 ) then @xmath535 and if @xmath536 is the lower semi - continuous envelope of @xmath498 , @xmath537 then @xmath538    the proof here follows the basic outline of the proof of corresponding result , ( * ? ? ? * theorem  2.8 p.9 ) , in the case @xmath539 . however the technical details are trickier in the case when @xmath4 is infinite . but most of the rest of the results of  ( * ? ? ? * section  2.2 ) go through with only minor changes to the proofs . the proofs of   and   are similar , with the proof of   being the simpler of the two , so we will give the details in the proof of  . the inequality @xmath540 implies for @xmath541 and any @xmath21 there is a @xmath219 and @xmath527 such that @xmath542 as @xmath498 and @xmath533 are bounded we can assume , by adding appropriate positive constants to @xmath498 and @xmath533 , that @xmath543 for some @xmath544 . set @xmath545 we need to show that @xmath546 ( as @xmath547 is clear ) . we may assume that @xmath548 , for if @xmath549 then @xmath550 and there is nothing to prove . [ step - down ] let @xmath551 , but @xmath552 and assume for some @xmath21 that @xmath553 then there is a @xmath554 so that @xmath555    we now prove theorem  [ max - prin ] from the lemma . let @xmath21 . we now choose a finite sequence @xmath556 with @xmath557 as follows . from the definition of @xmath190 there is a @xmath551 with @xmath558 . if @xmath559 we stop . if @xmath560 , then by the lemma , there is a @xmath554 with @xmath561 and @xmath562 . if @xmath563 then stop , otherwise use the lemma ( with @xmath564 replacing @xmath565 and @xmath566 replacing @xmath23 ) to get a @xmath567 with @xmath568 . if @xmath569 , stop if @xmath570 then we continue to use the lemma to get @xmath571 with @xmath572 for @xmath573 . this implies that @xmath574 . but as @xmath575 this process must terminate for some @xmath557 with @xmath576 . then @xmath577 letting @xmath578 in this implies @xmath579 which completes the proof . let @xmath565 be as in the statement of the lemma . from the definition of @xmath536 there is a sequence @xmath580 so that @xmath581 and @xmath582 . by there is a sequence @xmath583 and sequences @xmath584 so that ( replacing @xmath585 by the appropriate subsequence ) . @xmath586 for some non - negative real number @xmath19 . by compactness of @xmath4 and @xmath160 we can assume , by possibly going to a subsequence , that @xmath587 and @xmath588 and that @xmath589 for some @xmath590 , @xmath591 and @xmath592 . then @xmath593 and from the definition of @xmath536 , @xmath594 . therefore @xmath595 this is turn implies that @xmath596 because @xmath533 is @xmath4-almost convex , @xmath597 combining   and   yields @xmath598    we now claim there is an @xmath599 so that @xmath600 to see this partition @xmath81 into two sets @xmath601 and @xmath602 where @xmath603 and @xmath604 . note that as @xmath544 we have @xmath605 so that @xmath606 . for @xmath607 let @xmath608 then @xmath609 . using  , @xmath610 we have already seen that @xmath611 and therefore @xmath612 . thus @xmath613 where we have used that @xmath614 and that @xmath615 is decreasing for @xmath544 . as @xmath609 this implies there is at least one @xmath616 with @xmath617 . for this @xmath599 the claim   holds . letting @xmath599 be so that   holds and using that @xmath618 , and that @xmath619 for all @xmath280 in  , we have @xmath620 this implies @xmath621 as @xmath622 this gives @xmath623 letting @xmath624 completes the proof of the lemma . [ extr - lsc ] let @xmath513 be a compact convex set with extreme points @xmath37 . assume that @xmath514 is uniformly continuous . let @xmath68 be compact and contain at least one point that is not a vertex . then the extremal @xmath4-almost convex function @xmath522 is lower semi - continuous and satisfies @xmath625 . this can be derived from theorem  [ max - prin ] in the same way that ( * ? ? ? * theorem  2.12 p.  13 ) is derived from ( * ? ? ? * theorem  2.8 p.  9 ) . one complication in definition  [ def : e ] is that the infimum is taken over a collection of measures that are not all defined on the same measure space . when @xmath68 it is possible to have all the measures involved defined on the same space . suppose @xmath68 . we may regard each @xmath4-ranked probability measure as a ( borel ) probability measure on @xmath626^{{\\mathbf n}}$ ] , with @xmath276=\\{0,1{,\\dots,}m\\}$ ] . let @xmath627 be the space of probability measures on @xmath234 . then @xmath628 and in the weak@xmath629 topology @xmath627 is compact and metrizable ( as @xmath630 is separable ) . we let @xmath631 then every @xmath632 has @xmath633 given by @xmath634^j , \\\\ i=\\{x\\in x : x(1)=i_1{,\\dots,}x(j)=i_j\\}.\\end{array}\\right.\\ ] ] or what is the same thing @xmath261 if and only if @xmath635 where @xmath636 with @xmath637 $ ] for all @xmath280 . since each @xmath638 has the same sequence @xmath639 , we let @xmath640 which is defined independently of the choice of @xmath632 . .    finally note that if @xmath642 and @xmath643 , then @xmath148 is a clopen ( i.e.  both open and closed ) set in @xmath234 . consequently @xmath644 . in this case we have @xmath642 and thus the function @xmath645 is continuous on @xmath627 and thus on @xmath646 . [ prop3 ] with this notation , if @xmath530 is closed , then @xmath646 is closed in @xmath627 and thus is weak@xmath629 compact . notice that if @xmath647 , then @xmath632 if and only if for every @xmath648 , there exists @xmath390 such that @xmath649 where @xmath261 and @xmath265 is the disjoint union of @xmath650 . let @xmath651 and define a function @xmath652 by @xmath653 then this is continuous on @xmath627 . let @xmath654= \\{\\mu\\in { { \\mathcal p}}(x ) : \\mu(i)=\\sum_{i=0}^mt_i\\mu(i_i)\\text { for some } t\\in s\\}.\\ ] ] then @xmath655 . as an intersection of closed sets is closed , to finish the proof it is enough to show that each @xmath656 is closed . let @xmath657 and suppose @xmath658 in @xmath627 . for each @xmath659 there is a @xmath660 such that @xmath661 . since @xmath4 is compact , by passing to a subsequence , if necessary , we may assume that @xmath662 . thus @xmath663 therefore @xmath656 is closed . [ prop4 ] suppose that @xmath664 is closed and that @xmath4 contains a point that is not a vertex ( so that by proposition  [ prop1 ] @xmath389 is bounded ) . then    1 . @xmath313 is lower semi - continuous , 2 . if @xmath13 , then there exists a @xmath632 and a pairwise disjoint sequence @xmath665 such that @xmath666 and @xmath667 thus the infimum that defines @xmath322 is a minimum .    [ alt - lsc ] the lower semi - continuity of @xmath313 also follows from theorem  [ extr - lsc ] , but we include another proof here both because it is short and also to have a proof that is independent of  @xcite .    [ lemma2 ] suppose that @xmath4 is a closed subset of @xmath15 . further suppose    1 . [ 1 ] @xmath585 is a sequence in @xmath9 with @xmath668 , 2 . [ 2 ] @xmath669 is a sequence in @xmath646 with @xmath670 , 3 . [ 3 ] for all @xmath671 , there exists a disjoint sequence @xmath672 such that @xmath673 , 4 .   [ 4 ] @xmath674 , and 5 .   [ 5 ] there is an @xmath675 so that for all @xmath671 @xmath676    then there exists a disjoint sequence @xmath677 such that    1 . [ i ] @xmath678 2 . [ ii ] @xmath350 3 . [ iii ] @xmath679 . first we select a subsequence @xmath680 of @xmath681 for some infinite @xmath682 by first choosing sets @xmath683 and @xmath684 as follows : for each @xmath685 , we can use point  ( [ 4 ] ) to partition the terms of @xmath686 into @xmath687 sequences @xmath688 where @xmath689 and @xmath690 . we may assume that for every @xmath691 that @xmath692 . if @xmath693 , let @xmath694 and @xmath695 , otherwise @xmath696 is bounded for some infinite set of @xmath697 . since for any integer @xmath536 , there are only finitely many sets in @xmath698 of rank @xmath699 , there is an @xmath700 so that @xmath701 on an infinite subset @xmath702 of @xmath318 . similarly choose @xmath703 infinite in @xmath702 and @xmath704 such that either @xmath705 and @xmath706 or @xmath707 for all @xmath708 . continue selecting infinite sets @xmath709 of @xmath318 and @xmath684 such that @xmath710 and either @xmath711 and @xmath712 or @xmath713 for all @xmath714 . the inequalities @xmath692 yield @xmath715 and therefore @xmath716 also the sets @xmath717 are pairwise disjoint .    now let @xmath533 be an infinite set in @xmath318 such that each @xmath718 is finite . let @xmath719 . assumption  ( [ 5 ] ) implies @xmath720 thus for fixed @xmath721 and @xmath193 @xmath722 and therefore @xmath723 hence @xmath724 where @xmath725 . it follows that @xmath726 but since the sets @xmath727 are pairwise disjoint @xmath728 but this implies that there must be equality for each @xmath729 : @xmath730    once again fix @xmath719 . for @xmath721 suitably large in @xmath533 , @xmath713 if @xmath731 . thus @xmath732 ( all the sums are finite so there is no problem in interchanging the limit with the summation . ) since this holds for all large @xmath719 , @xmath733 now splice the sequences @xmath734 into a single sequence @xmath735 . this sequence satisfies the conclusion of the lemma . we first show the lower semi - continuity of @xmath313 . suppose that @xmath585 is a sequence in @xmath9 and that @xmath668 . further suppose that @xmath736 is convergent . for each @xmath671 , select a measure @xmath737 and a sequence @xmath686 in @xmath698 such that @xmath738 , @xmath739 , and @xmath740 . by passing to a subsequence , if necessary , we may assume that @xmath741 . by lemma  [ lemma2 ] , there is a sequence @xmath404 in @xmath698 so that @xmath742 , @xmath743 and @xmath744 thus @xmath313 is lower semi - continuous . we now show the second conclusion of proposition  [ prop4 ] . let @xmath13 . select @xmath745 a sequence in @xmath646 and for each @xmath721 choose a sequence @xmath686 in @xmath698 such that @xmath746 , @xmath747 and @xmath748 by passing to a subsequence , if necessary , @xmath749 for some @xmath750 . let @xmath751 be the sequence obtained by lemma  [ lemma2 ] . then for the measure @xmath247 and the sequence @xmath310 the equality  [ inf = min ] holds . this completes the proof .","summary":". a detailed study of the properties of-almost convex functions is made .","abstract":"let be the standard-dimensional simplex . let , then a function with domain a convex set in a real vector space is * _ _ *-almost convex iff for all and the inequality holds . a detailed study of the properties of-almost convex functions is made . if contains at least one point that is not a vertex , then an extremal-almost convex function is constructed with the properties that it vanishes on the vertices of and if is any bounded-almost convex function with on the vertices of , then for all . in the special case , the barycenter of , very explicit formulas are given for and . these are of interest as and are extremal in various geometric and analytic inequalities and theorems ."}
{"article_id":"1106.5384","section_id":"i","document":"the inflationary paradigm @xcite solves successfully the problems of the big bang model and also provides us with a mechanism to generate the primordial perturbations from quantum fluctuations that are later imprinted as anisotropies in the cosmic microwave background ( cmb ) radiation and in the large - scale structure of the universe . in particular , regarding the cmb power spectrum , we now know that it is nearly scale invariant @xcite , mostly of adiabatic origin and it contains almost all the information about the primordial perturbations ( i.e. the perturbations are nearly gaussian ) . this is in agreement with the predictions of many models of inflation . however , a small amount of non - gaussianity is still allowed by the cmb data and recently there have been several claims of detection of non - gaussianity of the primordial perturbations @xcite . if the values of the non - gaussianity parameters are of the order of magnitude claimed then nasa s satellite , planck @xcite , which is already up in the sky taking data , should be able to measure these values at many standard deviations @xcite . these are exciting times for theoretical cosmologists that for the past ten years or so have been trying to construct models where large non - gaussianity is produced . it is well known that the simplest and most popular inflationary model , a single scalar field with standard kinetic term satisfying the slow - roll conditions and with standard initial conditions for the vacuum state of the quantum perturbation predicts a level of non - gaussianity that is small and unobservable @xcite , even for the planck satellite @xcite . therefore , the previously mentioned observations have the potential if confirmed to rule out a large and most popular class of models . it is good on itself to rule out many models in one go and even better that a detection of non - gaussianity ( the same applies to the tensor - to - scalar ratio ) would allows us to progress significantly in our understanding of the mechanism that drove inflation in the early universe , this is because higher - order statistics contain much more information about the dynamics that the power spectrum .    our searches for inflationary models producing large observable non - gaussianity have been fruitful . many possibilities have been found , for example models with non - canonical kinetic terms ( like dbi - inflation , k - inflation , ghost - inflation ) @xcite , multiple field models of inflation @xcite , temporary violations of the slow - roll conditions and small departures of the initial vacuum state from the standard bunch - davies vacuum @xcite . for recent reviews about these mechanisms to produce non - gaussian perturbations see @xcite . both at the bispectrum level ( three - point correlation function ) and the trispectrum level ( four - point correlation function ) many observationally distinct shapes of these higher - order correlations have been found @xcite . some of these shapes of non - gaussianity have been constrained with cmb data @xcite and large - scale structure data @xcite . current limits on the amplitude of the bispectrum , taken from the 7-year wmap @xcite data at 95% confidence level are @xcite : @xmath0 , @xmath1 and @xmath2 for the local , equilateral and orthogonal shapes respectively . ref . @xcite has a more recent analysis of the cmb bispectrum ( see @xcite for the trispectrum analysis ) including many other shapes . planck satellite will improve all these constraints significantly and will also improve existing constraints on the amplitude of the trispectrum . for some review papers on observational aspects of non - gaussianity see for instance @xcite .    in this paper , in order to produce large and observable non - gaussianity , we shall study a model where the slow - roll conditions are temporarily violated . this model can be included in the class of models with  features \" ( i.e. non - scale invariant models ) in the potential or more generally in the field s lagrangian @xcite . there are several other reasons that motivate the study of  feature(s ) \" models . for instance , it has been shown that these models can provide better fits to the power spectrum of the cmb anisotropies than the @xmath3 model @xcite . in these models , this is achieved thanks to the introduction of new parameters ( and scales ) that can be tuned to coincide with well known  glitches \" @xmath4 in the cmb spectrum data . these models are also of theoretical interest because they have very distinct bispectrum signatures like scale - dependence ( e.g.  ringing \" and localization of @xmath5 ) . the features often have a more fundamental physical explanation , like for example they might be localized sharp features due to particle production during inflation @xcite , due to a duality cascade in brane inflation @xcite , periodic features due to the production of instantons in axion monodromy inflation @xcite or phase transitions @xcite . the study of these more realistic scenarios might eventually allows us to identify the underlying microscopic theory of inflation .    in particular , in this paper we will study a model where the mass of the inflaton field suddenly changes . we will describe this using a toy model where the change is approximated by a heaviside step function . for example , this might be a toy model for a first order phase transition . we will compute the power spectrum and the bispectrum of the curvature perturbation and show that its amplitude can be large and that its shape is new with very distinctive features . this paper is divided into the following sections . in section [ sec : model ] , we introduce the model and give the analytical background solution under some approximations . in section [ sec : pert ] we discuss linear perturbations , present an analytical approximation for the mode function of the primordial curvature perturbation and finally calculate the analytical power spectrum and compare it with the numerical result . in section [ sec : bispectrum ] , we compute the dominant contribution to the bispectrum of the curvature perturbation in two interesting limits , namely the equilateral limit and the squeezed limit . section [ sec : conclusion ] is devoted to the conclusion .","summary":"we present an analytical approximation for the mode function of the curvature perturbation , obtain the power spectrum analytically and compare it with the numerical result . we also compute the dominant contribution to the bispectrum in the equilateral and the squeezed limits and find new shapes . in the equilateral and","abstract":"we study an inflationary model driven by a single minimally coupled standard kinetic term scalar field with a step in its mass modeled by an heaviside step function . we present an analytical approximation for the mode function of the curvature perturbation , obtain the power spectrum analytically and compare it with the numerical result . we show that , after the scale set by the step , the spectrum contains damped oscillations that are well described by our analytical approximation . we also compute the dominant contribution to the bispectrum in the equilateral and the squeezed limits and find new shapes . in the equilateral and squeezed limits the bispectrum oscillates and it has a linear growth envelope towards smaller scales . the bispectrum size can be large depending on the model parameters ."}
{"article_id":"1106.5384","section_id":"c","document":"in this paper , we introduced an inflationary model driven by a single standard kinetic term scalar field . the field s potential is dominated by the vacuum energy and the mass term changes abruptly at a point . this abrupt change is modeled by an heaviside step function . this might be seen as a simple toy model for a first order mass phase transition occurring during inflation .    under the vacuum domination assumption , we have solved the background evolution analytically . as expected for large step sizes and for some time after the transition the slow - roll approximation breaks down . we have considered linear perturbations and presented an analytical approximation for the mode function that for scales different from the step scale @xmath59 is a good approximation to the numerical mode function for any time . we have computed the power spectrum of the curvature perturbation and showed that for scales smaller than @xmath59 it contains damped oscillations with  angular frequency \" @xmath230 . this behavior is captured well by our analytical approximation of the spectrum . models with temporary violations of slow - roll are expected to produce large non - gaussianity . for our choice of parameters , we showed that the dominant contribution to the bispectrum comes from the terms containing @xmath54 in the third - order interaction hamiltonian . using the analytical approximation of the mode function , we have computed ( analytically when it was possible , otherwise numerically ) the bispectrum produced by these terms in certain interesting limits . we analyzed two well known limiting triangle configurations of the three momentum vectors on which the bispectrum depends on . first , for the equilateral limit , we found that for scales much larger than @xmath59 the quantity @xmath231 decreases with the square of the ratio @xmath190 which implies that for values of @xmath12 of order one , its value is too small to be of observational interest . for scales much smaller than @xmath59 it oscillates with an  angular frequency \" of approximately @xmath232 . on these scales @xmath233 is linearly enhanced towards large @xmath68 as @xmath234 . this enhancement may be used to push the value of @xmath218 to within observational range even for a small amplitude @xmath12 of the step . it would be interesting to consider observational constraints on this kind of strongly scale dependent and oscillatory bispectrum models but this is outside the scope of the present paper .    secondly , we considered the squeezed limit of the bispectrum . for scales much smaller than @xmath59 , again we found an oscillatory behavior in @xmath68 with  angular frequency \" @xmath230 . when the size of the smallest side of the squeezed triangle is @xmath235 then the quantity @xmath183 has as enhancement factor of @xmath236 . this might have important consequences regarding the detectability of the present signal in the data . for larger scales , we found that the quantity @xmath182 is suppressed by the square of the ratio @xmath190 which implies that for values of @xmath12 of order one , its value is too small to be observational relevant . we have shown that for a wide choice of the model parameter @xmath12 , the squeezed and equilateral limits of the bispectrum can be large for scales much smaller than @xmath59 . this represents a significant enhancement with respect to the canonical single field slow - roll model result . in particular , the squeezed limit of the bispectrum can be large in comparison with any single field model of inflation known to the authors . see however refs . @xcite for non - vacuum initial state scenarios which also give significant enhancement factors but which have been shown @xcite not to be enough to put the cmb bispectrum within the reach of the planck satellite . it would be very interesting to repeat that analysis for the present model . the analytical approximation for the mode function used in this paper breaks down for scales close to the scale set by the transition so the present method can not be applied to compute the bispectrum at these scales . in order to perform that computation one has to numerically integrate the equation of motion for the curvature perturbation and then calculate the bispectrum integral numerically . we leave this for future work . finally , it would also be interesting to study the trispectrum of this model and this will be presented in a forthcoming publication . we would like to thank xingang chen , kazuya koyama and takahiro tanaka for interesting discussions and useful comments on an early version of the manuscript . fa is also thankful to the organizers of the workshop  the cosmological perturbation and the cosmic microwave background \" , march 2011 at the yukawa institute for theoretical physics , kyoto university for their invitation and financial support during which part of this work was done . finally , he thanks the asia pacific center for theoretical physics for its hospitality and support during the @xmath237 ieu - apctp focus program on cosmology and fundamental physics , june 2011 . fa acknowledges the support by the world class university grant no . r32 - 10130 through the national research foundation , ministry of education , science and technology of korea . aer is supported by the taiwan nsc under project no . nsc97 - 2112-m-002 - 026-my3 , by taiwan s national center for theoretical sciences ( ncts ) . ms is supported in part by jsps grant - in - aid for scientific research ( a ) no .  21244033 , and by jsps grant - in - aid for creative scientific research no . this work was also supported in part by mext grant - in - aid for the global coe program at kyoto university ,  the next generation of physics , spun from universality and emergence \" and by korea institute for advanced study under the kias scholar program . a.  a. starobinsky , jetp lett . * 30 * , 682 ( 1979 ) . d.  kazanas , astrophys . j. * 241 * , l59 ( 1980 ) . k.  sato , mon . not . soc . * 195 * , 467 ( 1981 ) . a.  h. guth , phys . * d23 * , 347 ( 1981 ) . a.  d. linde , phys . * b108 * , 389 ( 1982 ) . a.  albrecht and p.  j. steinhardt , phys . rev . lett . * 48 * , 1220 ( 1982 ) . e.  komatsu _ et  al . _ , astrophys . j. suppl . * 192 * , 18 ( 2011 ) , 1001.4538 . a.  p.  s. yadav and b.  d. wandelt , phys . * 100 * , 181301 ( 2008 ) , 0712.1148 . j .- et  al . _ , . j. * 717 * , l17 ( 2010 ) , 1003.3451 . b.  hoyle , r.  jimenez , and l.  verde , ( 2010 ) , 1009.3884 . k.  enqvist , s.  hotchkiss , and o.  taanila , jcap * 1104 * , 017 ( 2011 ) , 1012.2732 . http://www.rssd.esa.int/index.php?project=planck . e.  komatsu and d.  n. spergel , phys . rev . * d63 * , 063002 ( 2001 ) , astro - 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th/0506236 . d.  seery and j.  e. lidsey , jcap * 0506 * , 003 ( 2005 ) , astro - ph/0503692 . f.  arroja and t.  tanaka , jcap * 1105 * , 005 ( 2011 ) , 1103.1102 . c.  burrage , r.  h. ribeiro , and d.  seery , ( 2011 ) , 1103.4126 . h.  collins , ( 2011 ) , 1101.1308 . j.  ganc and e.  komatsu , jcap * 1012 * , 009 ( 2010 ) , 1006.5457 . o.  elgaroy , s.  hannestad , and t.  haugboelle , jcap * 0309 * , 008 ( 2003 ) , astro - ph/0306229 .","summary":"we study an inflationary model driven by a single minimally coupled standard kinetic term scalar field with a step in its mass modeled by an heaviside step function . the bispectrum size can be large depending on the model parameters .","abstract":"we study an inflationary model driven by a single minimally coupled standard kinetic term scalar field with a step in its mass modeled by an heaviside step function . we present an analytical approximation for the mode function of the curvature perturbation , obtain the power spectrum analytically and compare it with the numerical result . we show that , after the scale set by the step , the spectrum contains damped oscillations that are well described by our analytical approximation . we also compute the dominant contribution to the bispectrum in the equilateral and the squeezed limits and find new shapes . in the equilateral and squeezed limits the bispectrum oscillates and it has a linear growth envelope towards smaller scales . the bispectrum size can be large depending on the model parameters ."}
{"article_id":"1606.02778","section_id":"i","document":"these are notes for five lectures on moduli and degenerations of algebraic curves via tropical geometry . what do i mean by degenerations of algebraic curves ? the basic idea is that one can get information about the behavior of a smooth curve by studying one - parameter families of smooth curves , which degenerate in the limit to a singular curve , instead . the singular curve typically has many irreducible components , giving rise to a rich combinatorial structure . this technique obviously relies on having a robust notion of family of curves , that is , a moduli space . thus moduli spaces immediately come to the fore . tropical geometry is a modern degeneration technique . you can think of it , to begin with , as a very drastic degeneration in which the limiting object is entirely combinatorial . we will flesh out this picture over the course of the lectures . it is also a developing field : exactly _ what _ tropical geometry encompasses is a work in progress , developing rapidly . the powerful idea of using degenerations to study algebraic curves is at least several decades old and has already been very successful . but recent developments in tropical geometry make it timely to return to and expand upon these ideas . the focus of these lectures will be on one beautiful recent meeting point of algebraic and tropical geometry : the _ tropical moduli space of curves _ , its relationship with the deligne - mumford compactification by stable curves , and its implications for the topology of @xmath0 . i am not assuming any prior background in tropical geometry .","summary":"these are notes for a series of five lectures on `` moduli and degenerations of algebraic curves via tropical geometry '' delivered at the http://moduli2016.eventos.cimat.mx/node/304[cimpa-cimat-ictp school on moduli of curves ] , february 29-march 4 , 2016 in guanajuato , mexico .","abstract":"these are notes for a series of five lectures on `` moduli and degenerations of algebraic curves via tropical geometry '' delivered at the http://moduli2016.eventos.cimat.mx/node/304[cimpa-cimat-ictp school on moduli of curves ] , february 29-march 4 , 2016 in guanajuato , mexico ."}
{"article_id":"0905.3680","section_id":"i","document":"for today , the standard model is proved with a convincing variety of experiments . however , this theory can not shed light on some essential aspects of our understanding of the nature , which still remain obscure and are of great interest . among them is the _ quantum gravity _ , which is believed to play a major role at the _ planck scale of energies _ ( @xmath0gev ) . the standard model fails to incorporate the general relativity at the quantum level , since the quantization methods adopted in the former theory lead to a nonrenormalizable quantum gravity in this case . such theory is unacceptable as a fundamental theory . at the same time , there exist some candidates for such fundamental theory , string theories , for instance , taking the form of the standard model and the general relativity in appropriate low - energy limits . thus searching for signatures of the planck - scale physics at experimentally attainable energies would be a natural way to choose between these candidate theories , to constrain their parameters , and to clarify the essence of the quantum gravity . planck energies being far from experimental attainment , the _ standard model extension ( sme ) _ was elaborated . it is an effective theory ( applicable at the energies @xmath1 ) formulated axiomatically as a set of corrections to the lagrangian of the standard model , which fulfill some `` natural '' requirements @xcite , such as _ observer lorentz invariance , 4-momentum conservation , unitarity , and microcausality_. in what follows , we will focus on a subset of the sme referred to as the _ minimal _ sme in _ flat _ minkowsky spacetime , in which local @xmath2 gauge invariance and power - counting renormalizability are also required . a spectacular feature of such requirements is that they reduce the diversity of possible correction terms down to a _ finite _ number of them . each of them consists of a complex ( pseudo)tensor constant ( sme coupling ) contracted with conventional standard model fields and their spacetime derivatives . these constants are believed to stand for vacuum expectation values of the fields featuring in the hypothetic lorentz - covariant fundamental theory and condensed at low energies due to the spontaneous symmetry breaking mechanism . indeed , it has been shown that such lorentz symmetry breaking can occur in some theories beyond the standard model @xcite , leading subsequently to the sme . the sme can thus be used to reduce the complexity of these theories and related calculations in the low - energy limit . it also provides a standard for representation of the data obtained in experiments searching for lorentz violation . recently , a number of theoretical researches has been performed aimed at investigating the vacuum structure of this model ( see , e.g. , @xcite ) , and to study the assumed lorentz violation on various high - energy processes @xcite . such effects as the vacuum photon splitting , vacuum birefringence , and vacuum cherenkov radiation were studied . the effect of lorentz violation on the synchrotron radiation @xcite and the atomic spectrum and radiation properties @xcite were also analyzed . as a result of such theoretical investigations and subsequent precise experimental tests , the new constraints on lorentz violation were placed .    on the other hand , even in the conventional standard model , the quantum structure of the vacuum manifests itself in such effects as the casimir effect @xcite , that have been directly observed . this effect has been studied thoroughly within the standard model , including different approaches @xcite ( various regularization schemes , the calculations via the dyadic green function and the vacuum energy ) , setups ( two parallel plates , a sphere , a plate and a sphere ; non - perfect conductor plates , finite temperature , fermion casimir effect , etc . ) . the so - called _ maxwell - chern - simons ( mcs ) electrodynamics _ in @xmath3 dimensions was also considered in this concern @xcite . the casimir effect was also studied within the context of extra dimensions ( see , e.g. , @xcite ) and curved space @xcite . some attention was paid to this problem within the sme , namely , within extended quantum electrodynamics ( see sec . [ sec : mcsqed ] ) @xcite , which , in a certain particular case , takes the form quite analogous to the mcs electrodynamics . although the original version of casimir effect concerned electromagnetic field , this effect is much more general . it can be defined as the stress ( force per unit area ) on the bounding surfaces when a quantum field is confined within a finite volume of space . the boundaries can be material media and also the interfaces between different phases of the vacuum or topologies of space .    in our investigation , we focus on the extended electrodynamics , in order to find the signature of the lorentz violation in the electromagnetic casimir effect .    our paper is organized as follows . in sec . [ sec : mcsqed ] , we analyze the pure - photon sector of a particular case of the sme , namely , of the @xmath4-dimensional maxwell - chern - simons electrodynamics , in order to obtain the expression for the vacuum energy within this theory . we prove directly that the casimir force in such a theory remains gauge - invariant although the energy - momentum tensor does not . in sec . [ sec : photoneigenstates ] , we focus on finding the eigenstates and the energy spectrum of the photon between the two parallel perfectly conducting plates within the mcs electrodynamics . the one - photon energy spectrum , which follows from the implicit expression found in sec . [ sec : photoneigenstates ] , is then analyzed in sec . [ sec : spectrumnotes ] , where we show that when the plates are close enough to each other , the imaginary - energy ( tachyonic ) states are negligibly few , so the instability of the theory is also negligible ( see assertion [ finalassertion ] ) . in sec . [ sec : zetareg ] , using approximate energy eigenvalues , we find the leading correction to the zeta function corresponding to the one - photon energy - squared operator , and , in turn , the leading correction to the casimir energy . the contribution of the `` quasi - zero '' modes , which become trivial in the maxwell case , to the casimir force , is also discussed . in sec . [ sec : residuetheorem ] , we use the strict approach based on the residue theorem @xcite to explicitly sum the vacuum energy series , which contains the zeros of the transcendental function . we then renormalize the resulting complex plane integral and find the exact convergent expression for the real part of the casimir energy . section [ sec : conclusion ] summarizes the results obtained , and we discuss the constraints they place on the parameters of the lorentz violation .","summary":"we find the one - particle eigenstates of such a field , as well as the implicit expression for the photon energy spectrum . the resulting correction to the casimir force , which is attractive and quadratic in the chern - simons term , disagrees with the one obtained in [ m.  frank and i.  turan , phys .","abstract":"within the framework of the ( 3 + 1)-dimensional lorentz - violating extended electrodynamics including the cpt - odd chern - simons term , we consider the electromagnetic field between the two parallel perfectly conducting plates . we find the one - particle eigenstates of such a field , as well as the implicit expression for the photon energy spectrum . we also show that the tachyon - induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite . in order to find the leading chern - simons correction to the vacuum energy , we renormalize and evaluate the sum over all one - particle eigenstate energies using the two different methods , the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem . the resulting correction to the casimir force , which is attractive and quadratic in the chern - simons term , disagrees with the one obtained in [ m.  frank and i.  turan , phys . rev . d * 74 * , 033016 ( 2006 ) ] , using the misinterpreted equations of motion . compared to the experimental data , our result places a constraint on the absolute value of the chern - simons term ."}
{"article_id":"0905.3680","section_id":"c","document":"let us briefly discuss the results of our calculations . originally , m.  frank and i.  turan attempted to solve the problem we discussed here , using the green s function method , in @xcite . but they have used a wrong identity , namely , @xmath460 , in the mcs electrodynamics , that has reduced the dispersion relation for the mcs photon to that for a massive photon . the fact is , in 4 dimensions , the existence of the chern - simons term does not make the photons just massive , like it is in the 3-dimensional maxwell - chern - simons electrodynamics @xcite , instead , the photon possesses a more complicated dispersion relation ( see eq .  ) . the result we have obtained differs both in sign and in magnitude from the one obtained in @xcite . it should be also mentioned that the calculation of the green function within the mcs electrodynamics seems to be much more complicated than it was thought in @xcite , so in the present paper we have used the two other methods , namely , the zeta function regularization and the summation and renormalization of the discrete sum involving the residue theorem .    the zeta function analytical regularization is widely used for the calculations of the casimir effect in various physical situations @xcite . it automatically subtracts the vacuum energy of the infinite space ( i.e. , without the plates ) from the casimir energy . in our calculations , we used the `` true '' zeta function regularization , in which the complex regularization parameter @xmath461 , it depends on , controls the negative power of the frequencies in the series . sometimes ( see , e.g. , @xcite ) , the space dimensionality @xmath462 is chosen as the parameter of the analytical regularization , and , indeed , the expression for the vacuum energy depends on @xmath462 through the riemann zeta function . in our case , it would not be strict enough , since the transformations we would make during the calculation of the vacuum energy ( analogous to , , ) would not converge together for any @xmath463 . the regularization with the parameter @xmath461 avoids this problem , as it was mentioned in sec . [ sec : zetareg ] . the method we have used to find the sum of a discrete series using the complex plane integral , is a kind of generalization of the abel - plana formula which is also widely used in casimir effect calculations @xcite . indeed , one can generalize it to find the explicit integral expression for the series over the roots of a transcendental equation , including , e.g. , bessel functions @xcite . the approach we have used in section [ sec : residuetheorem ] is another generalization of this type , however , it does not follow the approach developed in @xcite . one should hold in mind that the calculations presented in our paper can not provide a direct way to make experimental predictions . for the experimental purposes , we should take into account the finite conductivity of the plates and the dispersion of their conductivity , as well as some other aspects . here we can only say how the presence of a small @xmath26 condensate , which violates lorentz invariance , affects the dependency of the casimir force on the distance between the plates . again , we conclude that the correction is quadratic in @xmath26 and strengthens the attraction between the plates at relatively large distances of the order @xmath464 . the relative magnitude of this additional force compared to the maxwell casimir force increases quadratically with distance @xmath391 , so large - separation casimir effect measurements could give tighter constraints on @xmath26 . recent observations @xcite showed the @xmath465% agreement between the experiment and the theory of the casimir effect based on the conventional standard model , at distances of about @xmath466 nanometer . thus we can conclude that the leading @xmath26-correction to the casimir force is less or about @xmath465% of its value for @xmath183 . this leads to the following constraint : @xmath467 some experiments measure the casimir effect at distances of several micrometers , with about a 10% accuracy @xcite , and this can at least make the above constraint @xmath468 times tighter . though this constraint is very loose compared to those astrophysical and some other observations place on @xmath26 , it demonstrates a property of a quantum vacuum within the extended standard model . moreover , this is the first constraint placed on the chern - simons lorentz - violating term based on the _ correct _ calculation of the casimir effect in ( 3 + 1 ) dimensions .","summary":"we also show that the tachyon - induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite . in order to find the leading chern - simons correction to the vacuum energy , we renormalize and evaluate the sum over all one - particle eigenstate energies using the two different methods , the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem .","abstract":"within the framework of the ( 3 + 1)-dimensional lorentz - violating extended electrodynamics including the cpt - odd chern - simons term , we consider the electromagnetic field between the two parallel perfectly conducting plates . we find the one - particle eigenstates of such a field , as well as the implicit expression for the photon energy spectrum . we also show that the tachyon - induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite . in order to find the leading chern - simons correction to the vacuum energy , we renormalize and evaluate the sum over all one - particle eigenstate energies using the two different methods , the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem . the resulting correction to the casimir force , which is attractive and quadratic in the chern - simons term , disagrees with the one obtained in [ m.  frank and i.  turan , phys . rev . d * 74 * , 033016 ( 2006 ) ] , using the misinterpreted equations of motion . compared to the experimental data , our result places a constraint on the absolute value of the chern - simons term ."}
{"article_id":"gr-qc0609074","section_id":"i","document":"the einstein - vlasov system describes a collisionless gas of particles that only interact via the smoothed relativistic gravitational field they generate collectively through their averaged stress - energy . in this article we study the equilibrium states of the spherically symmetric einstein - vlasov equations . this topic is of considerable physical and mathematical interest : fackerell , ipser , and thorne have used these models as models for relativistic star clusters  @xcite ( see also these references for references to earlier literature ) ; martin - garcia and gundlach studied these models in the context of critical collapse  @xcite ; rein and rendall approached the area from a more mathematical point of view  @xcite  this paper will be taken as the starting point for the present work . it is straightforward to work with particles with different masses , see e.g.  @xcite , but for simplicity we will restrict ourselves to particles with a single mass , @xmath0 , which yields the same mathematical problem . a collisionless gas is characterized by a non - negative phase space distribution @xmath1 defined on the future mass shell @xmath2 of the tangent space @xmath3 of the spacetime , i.e. , @xmath4 are spacetime coordinates and @xmath5 are local coordinates of the four - momentum with respect to the coordinate basis @xmath4 such that @xmath6 , @xmath7 , where @xmath8 , and where @xmath9 is the spacetime metric with signature @xmath10 ; throughout this article we set @xmath11 , where @xmath12 is the speed of light and @xmath13 is the gravitational constant .    for static spherically symmetric models , the metric can be written as @xmath14 and the vlasov equation as @xmath15 where @xmath16 is defined below . the non - negative energy - density and radial- and tangential pressures are given by    [ origrho ] @xmath17    the vlasov equation admits a stationary solution given by @xmath18 , where @xmath19 and @xmath20 are conserved quantities , interpreted as particle energy and angular momentum , per unit mass ; they are defined by @xmath21 where we have followed  @xcite and defined @xmath22 as @xmath23 , where @xmath24 and @xmath25 , where @xmath26 and @xmath27 ; @xmath28 is defined as @xmath29 , where @xmath30 and where @xmath31 is the radial coordinate component of @xmath5 . note that the above objects are associated with the spatial projection of the four - velocity : @xmath32 and that they thus differ from the physical three - velocity , @xmath33 , which is defined by @xmath34 and @xmath35 , where @xmath36 ; hence , e.g. , @xmath37 and @xmath38 .    using that @xmath39 yields :    [ rhop ] @xmath40    where @xmath41 . let @xmath42 $ ] denote the radius of support of the system , i.e. , @xmath43 when @xmath44 . we are interested in gravitationally bound systems in equilibrium that either have finite radii @xmath45 or possess a function @xmath46 that decreases sufficiently rapidly towards infinity so that in both cases @xmath47 . because of the equilibrium assumption , it follows that @xmath48 of the individual particles has to satisfy @xmath49 . we therefore require , since @xmath50 , that @xmath51 when @xmath52 , i.e. , we assume that there exists a cut - off energy that prevents particles from escaping the gravitational field they create collectively . the basic remaining equations of the einstein - vlasov system are given by    [ ein ] @xmath53    where @xmath54 . we define the mass function , @xmath55 , according to @xmath56 which , together with  ( [ lambda ] ) , yields @xmath57 consequently , eq .  ( [ mu ] ) takes the form @xmath58 since @xmath59 is assumed to be positive when @xmath60 , it follows that @xmath61 when @xmath62 , and that @xmath63 is a monotonically increasing function in @xmath64 ( or @xmath65 ) ; it also follows that @xmath66 when @xmath67 , where @xmath68 denotes the adm mass . in this paper we will consider distribution functions of the type @xmath69 where @xmath70 is a non - negative function such that @xmath71 when @xmath72 ; we also assume that @xmath73 . let us make the basic definitions @xmath74 rewriting   in terms of @xmath75 results in @xmath76 note that @xmath75 is closely related to the redshift , @xmath77 , measured at the surface @xmath45 : @xmath78 . for distributions of the type  ( [ d1 ] ) the density and the radial pressure take the following form :    [ prho ] @xmath79\\:,\\end{aligned}\\ ] ] where the constant @xmath80 is given by @xmath81 here , @xmath82 denotes the gamma function . the functions @xmath83 are defined by @xmath84^{i}\\,d{{\\cal e}}\\:.\\ ] ]    where , with a slight abuse of notation , @xmath85 ; note that @xmath86 and @xmath87 . the tangential pressure is given by @xmath88 ,    throughout the paper , the ratio @xmath89 will play an important role : @xmath90 note that this inequality is equivalent to @xmath91 , where @xmath92 and where @xmath93 is the isotropic pressure ; the limit @xmath94 , or equivalently @xmath95 , corresponds to the ultra - relativistic limit , i.e. , radiation .    the equations  ( [ meq ] ) and  ( [ etaeq ] ) form the einstein - vlasov system for equilibrium states ; it is a two - dimensional non - autonomous system ( recall that @xmath96 ) ; the system is closed via  ( [ prho ] ) which provides the relation between @xmath97 and @xmath46 through the definition of @xmath83 in ( [ gidef ] ) . however , note that the system  ( [ meq ] ) and ( [ etaeq ] ) is not just relevant for kinetic theory , but also for any fluid with an anisotropic pressure @xmath88 and an equation of state that relates @xmath97 and @xmath46 ( the system reduces to one for an isotropic perfect fluid when @xmath98 so that @xmath99 ) . the fundamental assumption in kinetic theory that the distribution function be non - negative automatically leads to natural physical conditions on @xmath46 , @xmath100 , and @xmath101 ; in particular , the density and @xmath100 are positive when @xmath62 . since @xmath102 it follows that @xmath103 as well ( the limiting case @xmath104 describes a gas of non - colliding particles with purely radial motion , or a fluid with no tangential pressure ) . from a mathematical point of view one can regard the kinetic case as a special anisotropic fluid case that corresponds to a certain class of equations of state , implicitly determined by ( [ p ] ) , ( [ rho ] ) and ( [ gidef ] ) ; however , recall that @xmath105 in the kinetic case .    if we assume the usual weak differentiability conditions so that @xmath106 , where @xmath107 is the energy - momentum tensor , then we obtain the equation @xmath108 which , when ( [ etaeq ] ) is inserted , yields the analogue of the tolman - oppenheimer - volkov equation . from  ( [ pretolop ] ) it follows that we can write @xmath109 in the form @xmath110^{-1}\\:.\\ ] ] the outline of the paper is as follows . in sec . [ dynsys ] we derive the dynamical system formulation : the einstein - vlasov system is reformulated as an autonomous system of differential equations on a bounded state space . this dynamical system is subsequently analyzed in sec . [ dynanalys ] . the results are then interpreted in the standard physical variables to yield our main theorems in sec . [ physinterpretation ] ; these theorems formulate various criteria that guarantee solutions of the einstein - vlasov system to have finite masses and radii ; hereby we generalize earlier work  @xcite . we conclude with a brief discussion in sec . [ concl ] . in appendix  [ appdiff ] we investigate various differentiability conditions that are needed in the paper and derive properties of the prominent function @xmath111 . in appendix  [ appexist ] we discuss existence and uniqueness of solutions . in appendix  [ appcenter ] we perform a center manifold analysis , which allows us to sharpen one of the theorems when certain asymptotic differentiability conditions are imposed . finally , in appendix d we present an extension of the monotonicity principle given in  @xcite .","summary":"we study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the einstein - vlasov system for collisionless matter . we recast the equations into a regular three - dimensional system of autonomous first order ordinary differential equations on a bounded state space . pacs number(s ) : 02.90.+p , 04.40.-b , 98.20.-d .","abstract":"we study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the einstein - vlasov system for collisionless matter . we recast the equations into a regular three - dimensional system of autonomous first order ordinary differential equations on a bounded state space . based on a dynamical systems analysis we derive new theorems that guarantee that the steady state solutions have finite radii and masses .    pacs number(s ) : 02.90.+p , 04.40.-b , 98.20.-d ."}
{"article_id":"gr-qc0609074","section_id":"c","document":"in this paper we have recast the stationary spherically symmetric einstein - vlasov equations for distribution functions of the form @xmath416 into a three - dimensional dynamical system with compact closure . this has allowed us to derive new theorems formulating conditions under which solutions have finite radii and masses ; our theorems naturally extend previous work , see e.g. ,  @xcite and the newtonian analysis in  @xcite .    in the present paper we have focused on distributions that can be bounded by asymptotic polytropes in the low @xmath75 regime . additional results can be obtained if one also makes restrictions that lead to controlled behavior in the large @xmath75 regime ; e.g. , one can investigate classes of distributions that yield asymptotically linear relations between the pressures and @xmath46 , which in turn may make it possible to obtain theorems about mass - radius diagrams of the type given in  @xcite for perfect fluids with asymptotically linear equations of state in the high pressure regime . the theorems presented in this article may be less sharp than one would wish , since the natural kinetic assumptions imply non - trivial restrictions on the effective implicit equation of state that have not been investigated here . the connection between the distribution function and the effective equation of state is given via the integrals of section  [ introduction ] ; it is an interesting question whether it is possible obtain more comprehensive information about this relation , e.g. , by finding classes of functions @xmath70 that lead to certain types of equations of state . simple results in this direction are due to fackerell  @xcite : it could be excluded that models with constant energy density possess a kinetic interpretation . in this context one should note that the assumption @xmath417 implies that the density and the pressures depend on both @xmath64 and @xmath75 ; however , the function @xmath109 appearing on the r.h.s .  of the equations is a function of @xmath75 alone . hence the mathematical correspondence between fluids with equations of state and kinetic models amounts to a correspondence in @xmath111 alone  which equations of state yield @xmath111 with kinetic interpretations ?","summary":"based on a dynamical systems analysis we derive new theorems that guarantee that the steady state solutions have finite radii and masses .   ","abstract":"we study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the einstein - vlasov system for collisionless matter . we recast the equations into a regular three - dimensional system of autonomous first order ordinary differential equations on a bounded state space . based on a dynamical systems analysis we derive new theorems that guarantee that the steady state solutions have finite radii and masses .    pacs number(s ) : 02.90.+p , 04.40.-b , 98.20.-d ."}
{"article_id":"astro-ph9612150","section_id":"i","document":"the nature of gamma - ray bursts ( grbs ) remains an enigma , even nearly 30 years after their discovery with the vela satellites in 1967 ( klebesadel et al . the bursts detected with the burst and transient source experiment ( batse ) on board the _ compton gamma - ray observatory _ ( cgro ) show that their positions are completely consistent with isotropy . for the subsample of 1005 grbs in the 3b batse catalogue the galactic dipole moment is within @xmath5 of the value expected for isotropy , and the observed galactic quadrupole moment deviates only @xmath6 ( briggs et al . 1996 ) from isotropy . thus , grbs are distributed significantly more isotropic than any known galactic population and most of the galactic models are no longer in agreement with the data ( cf .  e.g.  briggs et al . 1996 , hartmann et al . a spherical dark matter halo model could still be consistent with the measured burst positions , but requires a core radius larger than necessary to explain the galaxy s rotation curve ( hakkila et al . 1994 ; caldwell & ostriker 1981 ; briggs et al . 1996 ) . extended halo models have to place the typical batse grb farther away than about 100 kpc in order to obtain the measured isotropy . on the other hand , the observed bursts must be closer than about 350 kpc , because no excess of bursts is observed in the direction of m31 . neutron stars born with velocities exceeding the local galactic escape velocity have been proposed to match these requirements ( podsiadlowski 1995 ) , but in order to obtain isotropy of bursts , only a very small fraction of low - velocity neutron stars are allowed to burst in this model . moreover , a delayed turn - on is necessary to avoid a concentration of bursts to the galactic disk ( see e.g.  li & dermer 1992 ; briggs et al . 1996 ) .    the alternative possibility , a burst location at cosmological distances , does not require to postulate additional restrictions ( paczyski 1986 ) . also , the observed inhomogeneity of the bursts radial distribution can be regarded as supportive evidence for this idea . the number of faint bursts shows a deficit with respect to the power law of slope @xmath7 of a homogeneous distribution in euclidean space ( schmidt et al . this can be explained naturally if faint bursts are located at high redshift ( paczyski 1991 ; dermer 1992 ; piran 1992 ) . there have been many attempts to estimate the redshift range of grb sources from their brightness distribution ( e.g. fenimore 1993b ; fenimore & blom 1995 ) . whereas a redshift of about 0.1 for the nearest bursts seems likely , only a very crude estimate of the redshift of the faintest bursts can be made ( @xmath8 through @xmath9 ) . apart from the uncertainty in the cosmological parameters , such studies suffer from the unknown evolution function of the burst sources and the corresponding emission rate ( see sect . 4.1 ) as function of redshift ( rutledge et al . 1995 ) . the realization that gamma - ray measurements alone may be not sufficient to solve the grb mystery has prompted increasing attempts for counterpart searches of grbs at various wavelengths . two different methods are possible to search for grb counterparts :    * ( 1 ) * because of the typically large errors of burst positions and the huge number of quiescent objects within each grb error box , one method consists of simultaneous observations at other wavelengths ( x - ray , optical , ir , radio ) to search for transient sources during the grb event ( see recent reviews by hartmann 1995 , greiner 1995 ) . as a result of these studies , there is solid evidence that gamma - ray bursts do not produce simultaneous optical flashes brighter than about 5@xmath10 mag for an assumed duration of 1 sec ( greiner 1996 ) or simultaneous radio emission stronger than 10@xmath11 erg @xmath12 s@xmath13 ( cortiglioni 1981 ; inzani 1982 ) . * ( 2 ) * the second , more statistical approach is the search for positional coincidences of grb locations with comparison samples of any other known class of astronomical object . various types of catalogued objects , both galactic and extragalactic , were compared with the batse gamma - ray error boxes , but any correlation between these and the bursts was compatible with random expectation . ( i ) webber et al . ( 1995 ) looked for catalogued counterparts of 60 bursts with the smallest error boxes available ( @xmath14 ) and found no position coincidences above random expectation for extragalactic objects ( see , however , sect . 5.2.2 . for our investigation of the latter sample ) . ( ii ) gorosabel ( 1995 ) found no significant correlation between 44 grbs localized by the watch instrument to less than one square degree and objects ( galactic and extragalactic ) listed in 33 different catalogues . ( iii ) extremely rare events in external galaxies , for example merging neutron stars , are one possibility to explain an extragalactic origin of grbs ( eichler 1989 ; paczyski 1991 ) . under such a hypothesis a correlation between burst positions and the large - scale structure of matter should be expected . the concentration of nearby galaxies towards the super - galactic plane offers the possibility to search for counterparts up to a redshift of @xmath15 . hartmann et al . ( 1996 ) found no compelling evidence for a concentration of grbs to the super - galactic plane in the 3b catalogue . ( iv ) with a likelihood method that compares the counts - in - cell distribution of gamma - ray bursts with the one expected from the known large - scale structure of the universe , quashnock ( 1996 ) argued that the nearest bursts originate at a redshift @xmath16 and the farthest ones at @xmath17 . ( v ) however , searches for a correlation between grb and the direction of rich clusters of galaxies ( situated right in the above redshift range ) did not arrive at consistent results ( howard et al . 1993 , nemiroff 1994 , deng et al . 1995 , kolatt & piran 1996 , marani 1996 ) . from a comparison of the angular correlation functions of grbs and that of extragalactic radio sources , kurt & komberg ( 1995 ) concluded that gamma - ray bursts do not belong to a normal population of galaxies with @xmath18 . if we assume that grbs are emitted at cosmological distances and keep in mind that no clear correlation was found with either clusters of galaxies or the super - galactic plane then it seems unlikely that any normal constituents of galaxies can cause gamma - ray bursts . the most promising sources with a different nature are quasars and active galactic nuclei ( agn ) . they had been suggested as grb sources by prilutski & usov ( 1975 ) shortly after the discovery of grbs ( klebesadel 1973 ) . both , the number of bursts with relatively small error boxes , and the number of identified agn and quasars are increasing permanently . webber et al .  ( 1995 ) used the 1989 version of the vron - cetty & vron compilation of qsos and agn . the fact that the number of known quasars and agn has doubled since then has motivated us to check their results with improved statistics . a further chance to find correlations arises if only a certain subclass of the agn or quasars are counterparts of grb . in that case the mean distance between the members of the sample will increase and the error of the gamma - ray burst position will play a less important role . we have therefore not only repeated the work of webber ( 1995 ) with larger samples , but extended the search for correlations to various subclasses of agn . our paper is arranged as follows . in the first part of sect . 2 the grb sample and the methods used to search for correlations are introduced . in the second part we provide the samples of agns and quasars as well as different subclasses . our search for correlations between grbs and various subclasses is given in the first part of sect . in the second part we study in more detail those subclasses which show a positive correlation . the final results are described in sect . 4 and we elaborate on the one positive correlation found . finally , we discuss our results in the light of previous studies in sect . 5 and conclude with some remarks in sect .","summary":"an analysis of a smaller sample of well - localized interplanetary network gamma - ray burst positions supports this result . this correlation strongly favours the cosmological origin of gamma - ray bursts and enables to estimate its distance scale . the average luminosity of those gamma - ray bursts which we associate directly with radio - quiet quasars is of the order of erg ( assuming isotropic emission ) .   ","abstract":"we study positional coincidences between gamma - ray bursts in the batse 3b catalogue and quasars / agn taken from the vron - cetty & vron compilation . for most classes of agn , for bl lac objects and for radio - loud quasars , we find no excess coincidences above random expectation , and we give upper limits for their burst emission rate .    however , surprising evidence is found for a positional correlation between gamma - ray bursts and radio - quiet quasars . a total of 134 selected bursts with a position error radius and the nearest and intrinsically brightest radio - quiet quasars ( and ) have a probability of.7% to be associated with each other . an analysis of a smaller sample of well - localized interplanetary network gamma - ray burst positions supports this result . this correlation strongly favours the cosmological origin of gamma - ray bursts and enables to estimate its distance scale . the average luminosity of those gamma - ray bursts which we associate directly with radio - quiet quasars is of the order of erg ( assuming isotropic emission ) .   "}
{"article_id":"astro-ph9612150","section_id":"r","document":"we first summarize all classes for which no coincidences in excess of random expectation were found . in the second subsection we will strengthen the case for a correlation between grbs and radio - quiet quasars . .upper limits [ cols=\"<,<,^,>,^ , > , > \" , ]     @xmath34 : per source in 10@xmath368 yr@xmath13      quasars and agn are often discussed in the frame of the standard model assuming a massive compact object in the center , most probably a super - massive black hole . many spectral features , like optical polarization or radio - loudness , are interpreted as evidence of a nuclear jet . most of the samples and subsamples of qso and agn analyzed here show no evidence for a correlation with grbs . however , the measured values can be used to estimate upper limits for the emission of grbs . to determine the 3@xmath29 upper limit we use always our analysis + the @xmath32 18 burst sample which reaches the highest significance . the 3@xmath29 upper limit is given by : @xmath369 where @xmath212 is the number of coincidences with the real grbs , and @xmath370 is the number of coincidences expected for a simulated burst sample . @xmath371 is approximated by the standard deviation of @xmath370 as provided in table 2 , together with the other two values . the resulting upper limits are listed in table [ ul ] . as a quantity independent of the amount of members in the different subclasses we define the emission rate , @xmath372 : @xmath373    cccccrrrr + & & & + & + & & & @xmath25 & & @xmath25 & +   +   + 23.0  24.1 & @xmath374 & & 836 & & @xmath144&@xmath185 / @xmath375 & @xmath376&@xmath166 / @xmath377 + 24.2  25.0 & @xmath378 & & 847 & & @xmath379&@xmath135 / @xmath380 & @xmath381&@xmath166 / @xmath382 + 25.1  25.6 & @xmath383 & & 784 & & @xmath384&@xmath385 / @xmath386 & @xmath387&@xmath148 / @xmath388 + 25.7  26.1 & @xmath389 & & 820 & & @xmath390&@xmath391 / @xmath392 & @xmath393&@xmath60 / @xmath394 + 26.2  26.6 & @xmath395 & & 910 & & @xmath396&@xmath385 / @xmath397 & @xmath398&@xmath218 / @xmath399 + 26.7  27.1 & @xmath400 & & 875 & & @xmath401&@xmath240 / @xmath402 & @xmath403&@xmath266 / @xmath404 + 27.2  27.9 & @xmath405 & & 993 & & @xmath144&@xmath406 / @xmath407 & @xmath376&@xmath60 / @xmath408 + 28.0  31.9 & @xmath409 & & 871 & & @xmath410&@xmath411 / @xmath412 & @xmath413&@xmath280 / @xmath414 +   +    this rate is given by the derived upper limits divided by the size @xmath415 of the comparison sample , and by the observation time of batse ( 3.42 years ) . further it is corrected for the 68% confidence interval we used , and the probability of detecting a burst ( 38% , cf . meegan et al . all numbers refer to the 134 grbs in the 3b catalogue having @xmath32 18 . our initial positive result for a correlation of grbs with `` active galaxies '' ( ag ) was not confirmed in the previous chapter . thus we give an upper limit for ags in table [ ul ] . the positive result obtained initially might be due to the non - homogeneity of the sky distribution of ag . however , an additional bias due to a small - scale structure of the grb distribution can not be excluded at this point .      because of the inverse relation between burst flux and positional error radius we expected to strengthen the result obtained in our first search for correlation for the low - redshift quasars . in sect . we were able to show that the result is influenced neither by the distance to the nearest neighbour , nor the small - scale structure of the burst locations , nor by the non - homogeneity of their sky distribution . in this section we will try to strengthen our positive correlation for radio - quiet quasars . seyfert galaxies are closely related to radio - quiet quasars . because many radio - quiet quasars show a seyfert - like spectrum , it appears that the main difference between these two classes is the absolute magnitude . given the negative result obtained for the seyfert galaxies , it seems reasonable to presume that the absolute magnitude influences the emission rate of grbs . therefore , we also defined subsamples according to absolute magnitude as listed in the compilation of vron - cetty & vron ( 1996 ) . again , the values obtained were compared with randomly simulated grb samples and the results are provided in table 7 . the probability levels do not support coincidences in excess of random expectation for the fainter magnitudes ( @xmath416 ) at more than the 95%-level . however , excess coincidences are indeed found for quasars brighter than @xmath417 . it appears that only intrinsically bright quasars show a detectable emission rate of grbs . this interpretation is in agreement with the negative result found for the seyfert galaxies . crrrr & & + & @xmath25 & & @xmath25 & +   +   + 1 & @xmath418&@xmath124 / @xmath419 & @xmath420&@xmath421 / @xmath422 + 2 & @xmath423&@xmath124 / @xmath424 & @xmath425&@xmath421 / @xmath419 + 3 & @xmath426&@xmath218 / @xmath419 & @xmath427&@xmath124 / @xmath428 +    @xmath429 numbers denote the different samples : 1 = simulated control sample ; 2 = shifted control sample ; 3 = singular coincidences    we conclude that there is an increased probability for the _ nearby _ and for the absolutely _ brighter _ radio - quiet quasars to correlate with grbs . it is therefore tempting to construct an `` optimized quasar sample '' with even higher probability for emitting grbs . we defined such a sample by @xmath430 and @xmath431 . it contains 967 radio - quiet quasars and was tested with the three methods described in sect . 2 , for the two grbs samples with the smaller error radii . results are provided in table 8 . the corresponding distribution of the positional coincidences for the null - hypothesis of the `` optimized quasar sample '' are plotted in fig . the value expected at random is shown as a dotted line and the value obtained for the real grbs is indicated by a dashed line . for all six comparisons the probability for a real correlation with grbs exceeds 99.7% . moreover , in four of the six comparisons the 1000 simulations of grbs positions did not show a single case with a number of coincidences as high as for the real grbs . frequently , two catalogues of objects detected in different wavebands are cross - identified from a study of the radial histogram of the distances between suspected counterparts . we did not use this method until this point because many bursts have more than one qso or agn in their error circle , which would significantly increase the chance coincidences at large distances between grbs and objects of the comparison sample . however , the `` optimized quasar sample '' ( @xmath430 and @xmath431 ) allows to illustrate our result with the radial histogram of the distances between suspected counterparts . the differential distribution of coincidences is given by the number of quasars , @xmath432 in an annulus between a radius @xmath433 and @xmath434 . the distribution of the real coincidences is a function of the positional errors which is not very well determined . however , the real coincidences must be located within a distance less than 3 times the positional error radius , @xmath435 , assuming a two - dimensional gaussian distribution . the number of randomly expected coincidences is proportional to the cumulative area of all annuli . thus , the number of sources in a given annulus as a function of the radius is given by    @xmath436 where a(r ) is the probability for real coincidences per unit area , and b is the probability for chance coincidences per unit area . we divide by @xmath433 and set    @xmath437    thus , we may rewrite :    @xmath438    to allow for the very different sizes of the grb positional errors we scale the distance between grb and radio - quiet quasars in units of the positional error @xmath29 , i.e.  we choose @xmath439 to obtain the normalized differential distribution , which should be constant for @xmath440 . in fig . 5 the normalized differential distribution for the optimized quasar sample is given . in the normalized differential distribution every coincidence between a gamma - ray burst and a quasar is counted . this results in a doubling of the background value for the first bin as opposed to counting every grb only once . nevertheless , the coincidences we find in excess of random expectation between 2@xmath29 and 5@xmath29 more than compensate for the poor statistical significance of the first bin ( cf . fig.5 ) .    by substituting @xmath441 with ( @xmath442 ) in equation 2 we obtain the emission rate for the detected radio - quiet quasars : @xmath443 using the results obtained for the `` optimized quasar sample '' given in the first line of table 8 we determine an emission rate of burst of 0.0146@xmath300.004 y@xmath13 per radio - quiet quasar .","summary":"however , surprising evidence is found for a positional correlation between gamma - ray bursts and radio - quiet quasars .","abstract":"we study positional coincidences between gamma - ray bursts in the batse 3b catalogue and quasars / agn taken from the vron - cetty & vron compilation . for most classes of agn , for bl lac objects and for radio - loud quasars , we find no excess coincidences above random expectation , and we give upper limits for their burst emission rate .    however , surprising evidence is found for a positional correlation between gamma - ray bursts and radio - quiet quasars . a total of 134 selected bursts with a position error radius and the nearest and intrinsically brightest radio - quiet quasars ( and ) have a probability of.7% to be associated with each other . an analysis of a smaller sample of well - localized interplanetary network gamma - ray burst positions supports this result . this correlation strongly favours the cosmological origin of gamma - ray bursts and enables to estimate its distance scale . the average luminosity of those gamma - ray bursts which we associate directly with radio - quiet quasars is of the order of erg ( assuming isotropic emission ) .   "}
{"article_id":"astro-ph9612150","section_id":"c","document":"we have found evidence that intrinsically bright radio - quiet quasars with @xmath444 coincide with grbs from the 3b catalogue at a confidence level of more than 99% . the correlation with low - redshift objects is not surprising . for statistical reasons our study had to be restricted to grbs with the smallest positional errors , which tend to be the brightest grbs . these grbs are preferably nearby since the luminosity distribution of grbs can not be very flat ( hakkila 1995 ) , and thus one introduces a strong selection effect for low - redshift quasars . based on the different methods which we applied to test our results , we are confident to have excluded any bias from an inhomogeneous sky distribution of quasars . in addition , we showed our result to be robust against a possible small - scale structure in the sky distribution of @xmath282-ray bursts .    the restriction to intrinsically bright quasars with @xmath445 seems to be a real physical selection indicating that the grb emission rate is at least lower for intrinsically faint quasars . this interpretation is supported by the negative result obtained for the seyfert galaxies which are intrinsically fainter than radio - quiet quasars but otherwise have very similar properties . we can not exclude that other classes of agn and qsos emit bursts with a comparable rate since the derived 3@xmath29 upper limits ( see table [ ul ] ) are above the emission rate of the radio - quiet quasars ( 0.0146 y@xmath13 per quasar ) . the lower emission rate of radio - loud quasars argues against a direct connection between radio jets and grb emission . two previous studies may appear in contradiction with our results . however , a thorough analysis shows that one of these is not comparable with our study , and that the other in fact does not contradict our results . kurt & komberg ( 1995 ) compared the two - point angular correlation function of 458 gamma - ray bursts with the two - point angular correlation function of a sample of 413 unresolved extragalactic radio sources ( qso , bl lac and radio galaxies ) . they found that the correlation function of grbs does not differ from a random distribution over all angular scales while the one for the radio sources shows significant autocorrelation on small angular scales at a level of @xmath446 . kurt & komberg conclude that grbs do not belong to a normal population of galaxies with @xmath447 . this may not be correct in this generalization , particularly since these authors dealt with compact radio sources and did not consider radio - quiet objects . moreover , drinkwater & schmidt ( 1996 ) have recently pointed out the very different clustering properties of radio galaxies and radio - loud quasars , both of which are well - mixed in kurt & komberg s sample . because we found only coincidences in excess of random expectation for radio - quiet quasars , our result is not in contradiction to that of kurt & komberg ( 1995 ) . furthermore , we found no hint for a correlation between radio - loud objects and grbs which agrees with their conclusion . webber et al . ( 1995 ) compared @xmath44860 grbs located to within very small error boxes of @xmath4480.25 deg@xmath449 or less with several catalogues of extragalactic objects . more than half of their sample of grbs was taken from the first interplanetary network ( ipn ) grb catalog ( atteia et al . 1987 ) , seven grbs from the comptel catalogue of bursts ( hanlon et al . 1994 ) and 16 bursts from the third ipn ( hurley , private comm . ) . they find that any correlation between these catalogued extragalactic objects and the grbs are consistent with chance expectation . in order to compare the bursts with the extragalactic objects they count the number of the closest bursts falling in bins of width 05 in radial separation independent of the actual shape of the error box . they found two coincidences : qso 2219@xmath450420 ( z=1.3 ) in the error box of grb 790419 and qso 0116288 ( @xmath451 ; which was discovered in a deep optical follow - up search of the grb error box by pedersen 1983 ) in the error box of grb 781119 ( obviously mis - printed as grb 791119 in webber et al . webber et al . ( 1995 ) simulated 100 sets of quasar positions and obtained a background value of @xmath452 . motivated by the large increase of known quasars since the 1989 compilation of agn and qsos by vron - cetty & vron as used by webber et al . ( 1995 ) , we reanalyzed webber s sample of grbs with the 1995 compilation of radio - quiet qso . because the error boxes of the seven bursts localized by comptel have areas well within @xmath4480.25 deg@xmath449 , which is larger than most of the error boxes of the ipn grb catalog , we excluded the former here . for the 28 bursts from the first ipn grb catalog ( atteia et al . 1987 ) , we compared the positions of radio - quiet qso with the exact ( elongated ) shape of the error boxes and arrived at the same result as webber et al . ( 1995 ) : one quasar each is located in the error boxes of grb 790419 and grb 781119 . then we determined the expected background value with 1000 simulations for the 28 burst positions . accepting quasars within a bin width of 05 we derive the same result as reported by webber et al . ( 1995 ) , namely that a correlation between quasars and the grbs is consistent with chance expectation . in a second approach , rather than using a standard radial distance of 05 for all bursts , we converted the area of a given error box to a corresponding error circle for each burst . with this approach we expect @xmath453 random coincidences as compared to the above value of @xmath452 . thus , the probability to find two radio - quiet quasars in the error boxes of the grbs is only 1.2% . this result corresponds to a probability of 98.8% for a positive correlation , i.e.  much higher than derived by webber et al . ( 1995 ) and confirming our results .      our result of a correlation between grbs and intrinsically bright , radio - quiet quasars does not necessarily imply that grbs are produced in the nuclei of these quasars , but possibly in their host galaxies . thus , there are two different questions related to the hosts of grb sources : are host galaxies bright enough to be detectable in previous or future deep searches ? what do we know about the host galaxies of radio - quiet quasars ? earlier deep optical searches of small grb error boxes ( by imaging in bandpasses from u to k ) did not find suitable host galaxies ( schaefer 1992 ) . this has become known as the  no - host \" problem for cosmological grb scenarios ( fenimore 1993a ) . recently , near - infrared imaging of six small grb error boxes ( a sample of grbs different from that used by schaefer ( 1992 ) ) in the jhk@xmath454 bands has shown that the  no - host \" problem does not exist ( larson 1996 ) . on the contrary , even an overabundance of brighter ( k @xmath455 15.5 mag ) galaxies was found . whether these might be hosts for radio - quiet quasars remains to be seen . as the detectability of quasars is concerned , the lack of excess quasars in grb error boxes is neither contradicting our results nor surprising . in photometric studies , radio - quiet quasars are not separated from other types of agn or radio - loud quasars , and thus the existence of any excess of radio - quiet quasars is easily missed . we should note here that a recent deep optical imaging ( vrba 1995 ) has revealed marginal evidence for a quasar excess at the rate of one per high galactic latitude grb error box . further studies able to distinguish between the different types of agn are certainly needed to clarify this situation . in addition , there are two probable kinds of quasars which are difficult to detect in optical , photometric searches . first , there are only a few quasars showing seyfert 2 type spectra . if the ratio of sy1/sy2 type spectrum quasars were equally large as the ratio of sy1/sy2 galaxies , then a large number of quasars will have been missed in optical studies . ultra - luminous infrared galaxies discovered by iras ( sanders et al . 1988 ) might be a second possibility to explain bursts lacking optical counterparts . these are suggested to be young quasars in a dust - enshrouded initial phase .      until quite recently radio - quiet quasars were thought to be associated mainly with spiral galaxies , and radio - loud ones with elliptical galaxies ( see bahcall et al . 1995 for an overview of references to previous , apparently contradicting results ) . however , very recent deep images taken with the _ hubble space telescope _ suggest that quasars reside in a wide variety of environments , not confirming the above preconception . if radio - quiet quasars are indeed equally likely to be associated with both spirals and ellipticals , then their clustering properties are difficult to predict . together with the reasonable assumption that grbs are an extremely rare phenomenon in the life of a galaxy , the lack of autocorrelation among grbs seems more natural . on the other hand , the production of grbs must be related to some specific property of the quasar , otherwise one would expect also a correlation of grbs with normal spirals , which is not observed . in the next section it is shown that the detected number of grb and the total number of quasars is in agreement with the emission rate determined in section 4.2 . because the number of spirals exceeds the number of quasars by a factor of order @xmath456 , our result argues strongly against a relation between grb and normal spirals .      in a friedmann universe with zero cosmological constant the luminosity distance d@xmath457 is defined as    @xmath458 \\right\\ } , \\ ] ]    whith @xmath459 the hubble constant , @xmath460 the deceleration parameter and @xmath461 the velocity of light . the comoving volume @xmath462 can be approximated by :    @xmath463    for @xmath464 this correspond to :    @xmath465    assuming @xmath466 mpc@xmath13 km s@xmath13 . from figure 2 in hewett 1993 ) the cumulative space density of quasars @xmath467 for the optimized quasar sample can be estimated . assuming @xmath468 we get @xmath469 for the redshift range @xmath470 and @xmath471 for the redshift range @xmath472 , respectively . to derive the total number of quasars we further assumed that @xmath473 holds for redshifts below @xmath474 and that 15% of the quasars are radio - loud . under these assumptions we can estimate that in total 2.9 10@xmath475 quasars meet the criteria of the optimized quasar sample . the number of quasars studied , 967 , therefore corresponds to 3.4% of the total sample . this number has to be compared with the percentage of grbs cross - identified with a radio - quiet qso . according to table 8 we found counterparts to 12.5 grbs for a total sample of 134 bursts studied , or a detection rate of 9.3%@xmath302.8% . thus , the expected detection rate is within two sigma of the observed one , a reasonable agreement given the small number statistics . one should also be aware that there are two biasing effects which increase the rate of optical counterparts . the first is that more luminous quasars at a similar redshift show a higher probability to be detected in most kinds of surveys . our finding that more luminous quasars have a higher probability of being a grb counterpart suggest that the basic quasar sample used is already biased towards a higher rate of counterparts . a further bias towards a higher rate of counterparts is caused by the clustering of radio - quiet quasars ( shanks & boyle 1994 ) . because the clustering occurs on small scales it does not affect our results given the large error boxes of the grbs . on the other hand , unknown quasars show a higher probability to be located near to a known quasar in comparison to an arbitrary location on the sky .      merging neutron stars and black holes are one possibility to explain quasars as counterparts of grbs and are discussed in the first of the following subsections . there are not many publications explaining grb with emission by the active nucleus itself . because our result strongly suggests such a mechanism we show in a second subsection that the gamma - ray emission of radio - quiet quasars / agn can reach the energy range of grbs . finally , we discuss the model of leiter ( 1980 ) which may explain the observed correlation . an interesting scenario to explain grb from agn and quasars was proposed by epstein et al . ( 1993 ) . because compact - star binaries have a higher mass than normal stars they settle to the center of the nuclear stellar cluster ( fraction of a parsec ) before they coalesce . the binary merging will typically occur in a time span of a second and will accelerate debris to very high velocities reaching almost the speed of light . the quiescent emission of the quasar nucleus is then up - scattered to the range of gamma - rays by this accelerated hot material ( debris ) , i.e. the spectrum is shifted by @xmath476 in photon energy and the flux is boosted by @xmath477 . the grb spectra and their light curves are therefore explained by the relative orientation between the observer , the beam direction of the emission of the active nucleus , and the path of the accelerated material . this scenario predicts that the spectra and variability of the grbs would be correlated with that of the host agn . already the heao-1 observations ( rothschild et al .  1983 ) revealed agn to show emission up to the 100kev energy range ( mainly from seyfert 1s ) . emission up to 100mev was detected from radio - loud quasars and bl lac objects , for which synchrotron emission is the favoured mechanism . however , no emission above 500kev was detected from radio - quiet agn or qsos with the three cgro instruments batse , comptel and osse ( schnfelder 1994 ) . it appears that two different mechanisms are at work in the high - energy band depending on the radio - loudness of the objects . the existence of two mechanisms is supported by the well - established difference between radio - loud and radio - quiet qsos seen in x - rays ( cf e.g.  wilkes & elvis 1987 ; schartel et al . our result fits into this phenomenological picture , because we found grb counterparts only for radio - quiet quasars . on the other hand , the maximum energy of photons from grbs reaches up to several gev and thus is significantly higher than the observed steady 500kev emission from radio - quiet agn and qsos . thus , there is a clear difference in the gamma - ray spectra of grbs and the steady emission of radio - quiet quasars . possibly , the miso and ariel 5 observations of ngc 4151 ( perotti et al .  1981 ) , a radio - quiet seyfert galaxy , may give some clues the understanding of our results . the flux above @xmath448500kev from ngc  4151 was found to be variable by a factor of 3 to 10 on a time scale up to 1 year as measured with ariel 5 in december 1976 , and miso in may 1977 and september 1979 . the observed @xmath282-ray fluxes are more than an order of magnitude higher than the limits reported from the osse / comptel monitoring of ngc  4151 ( schnfelder 1994 ) or any previous measurement . therefore , such a possible gamma - ray high state seems to be extremely rare . the variability by a factor of 3 to 10 in the @xmath3500kev range on a time scale of less than one year should be compared with a hard x - ray variability of only up to a factor of two ( perotti et al . 1981 ) . one model to explain the variability found at the highest measured energies was suggested by leiter ( 1980 ) . if a massive ( m @xmath478 ) kerr black hole exists in the nucleus of ngc  4151 , then the penrose compton - scattering mechanism can lead to the production of @xmath282-rays with a cutoff at an energy of about 3 mev . the burst is triggered by sporadic injection of hot plasma caused by turbulence in the inner region of the accretion disk . the resulting @xmath282-ray burst is emitted within an angle of 40 from the equatorial plane of the kerr black hole . the duration of such an event is given by the size of the target region divided by the speed of light which is located between the event horizon and the ergosphere . in most unified models it is usually assumed that radio - loud quasars contain a rotating black hole matching the criteria of leiter s simulations . but for radio - quiet quasars black holes without rotation are generally favoured . however , the accretion of matter through an accretion disk permanently transfers angular momentum to the black hole . the increasing angular momentum causes an increase of the ergosphere . finally , the ergosphere is larger than the event horizon creating a very small target region for penrose compton - scattering . further investigations have strengthened the possibility to produce grbs in hot tori around black holes ( jaroszynski 1996 ) .    if we assume that at least a part of the optical luminosity of the quasar is caused by turbulence in the accretion disk , then the positional coincidence we found between grb and intrinsically _ bright _ quasars can be explained with a higher injection rate of hot plasma and a higher transfer of angular momentum according to leiter s model . since particularly the x - ray emission of quasars is interpreted as a measure of the activity of the inner part of the accretion disk , a search for positional coincidences between _ x - ray bright _ , radio - quiet quasars and grbs would be most promising . it is interesting that the model proposed by leiter already predicts a focusing orthogonal to the angular momentum of the black hole . this may explain our negative result obtained for radio - loud quasars and bl lac objects if we assume that the radio - jet is emitted along the rotation axis .","summary":"we study positional coincidences between gamma - ray bursts in the batse 3b catalogue and quasars / agn taken from the vron - cetty & vron compilation . for most classes of agn , for bl lac objects and for radio - loud quasars , we find no excess coincidences above random expectation , and we give upper limits for their burst emission rate .   ","abstract":"we study positional coincidences between gamma - ray bursts in the batse 3b catalogue and quasars / agn taken from the vron - cetty & vron compilation . for most classes of agn , for bl lac objects and for radio - loud quasars , we find no excess coincidences above random expectation , and we give upper limits for their burst emission rate .    however , surprising evidence is found for a positional correlation between gamma - ray bursts and radio - quiet quasars . a total of 134 selected bursts with a position error radius and the nearest and intrinsically brightest radio - quiet quasars ( and ) have a probability of.7% to be associated with each other . an analysis of a smaller sample of well - localized interplanetary network gamma - ray burst positions supports this result . this correlation strongly favours the cosmological origin of gamma - ray bursts and enables to estimate its distance scale . the average luminosity of those gamma - ray bursts which we associate directly with radio - quiet quasars is of the order of erg ( assuming isotropic emission ) .   "}
{"article_id":"astro-ph9612150","section_id":"c","document":"the aim of our study was to develop a method to handle the large error boxes of grbs and to study the positional coincidences with qsos and agn . we found the surprising result that the nearest and intrinsically brightest radio - quiet quasars have a probability of @xmath399.7% of being associated to the 134 best localized ( and thus in general brightest and nearest ) grbs of the 3b catalogue . while previous claims of correlations have usually been found spurious in light of improved ( and larger ) data samples , it is not the fact of the mere correlation which is surprising , but rather the high probability we find . if our results are confirmed in future studies with improved statistics then bright quasars emit @xmath282-ray bursts at an emission rate of @xmath479 bursts per year and quasar for the batse sensitivity limit , based on a comparison of the 134 brightest batse bursts with 967 quasars of an `` optimized quasar '' sample . in order to determine the energy emitted during a burst we consider only the 20 grbs with a single quasar in their error box . for 16 of them the fluxes are given in the 3b catalog , thus yielding a mean total emission of @xmath480 erg for the 2050kev band , of @xmath481 erg in the 50100kev band , and @xmath482 erg in the 100300kev range , respectively . an isotropic emission over @xmath483 @xmath484 was assumed and the following parameters were used : h@xmath485=50 km s@xmath13mpc@xmath13 , and @xmath486 assuming power law spectra with @xmath487 .    the deviation of the cumulative peak flux distribution of grbs from the 3/2 slope should then be used with caution to study the curvature of space - time , because quasars themselves show an intrinsic evolution . we neither wish to discuss the implications of our results on models , nor to build a theoretical scenario of grb emission from radio - quiet quasars . however , the brief review of the scenarios proposed by epstein ( 1993 ) and leiter ( 1980 ) shows that there are already theoretical ideas matching our findings , and ( in the case of leiter s scenario ) that phenomena related to neutron stars ( or stellar - sized compact objects ) are not the only possible explanation for grbs . also , the measurements of ngc  4151 provide evidence for emission from radio - quiet agn and qso in the energy range required for grbs . this implies that in the epstein ( 1993 ) scenario the boosting during the grb is rather moderate . thus , our finding of a positive correlation of grbs with radio - quiet agn combined with some previously suggested scenarios of cosmological grbs may provide a new avenue towards understanding the grb puzzle . we thank w. wamsteker and d. reimers for fruitful discussions . we appreciate the comments of two anonymous referees . jg is supported by the deutsche agentur fr raumfahrtangelegenheiten ( dara ) gmbh under contract no . fkz 50 or 9201 .","summary":"a total of 134 selected bursts with a position error radius and the nearest and intrinsically brightest radio - quiet quasars ( and ) have a probability of.7% to be associated with each other .","abstract":"we study positional coincidences between gamma - ray bursts in the batse 3b catalogue and quasars / agn taken from the vron - cetty & vron compilation . for most classes of agn , for bl lac objects and for radio - loud quasars , we find no excess coincidences above random expectation , and we give upper limits for their burst emission rate .    however , surprising evidence is found for a positional correlation between gamma - ray bursts and radio - quiet quasars . a total of 134 selected bursts with a position error radius and the nearest and intrinsically brightest radio - quiet quasars ( and ) have a probability of.7% to be associated with each other . an analysis of a smaller sample of well - localized interplanetary network gamma - ray burst positions supports this result . this correlation strongly favours the cosmological origin of gamma - ray bursts and enables to estimate its distance scale . the average luminosity of those gamma - ray bursts which we associate directly with radio - quiet quasars is of the order of erg ( assuming isotropic emission ) .   "}
{"article_id":"0911.2530","section_id":"i","document":"galaxy formation and evolution is strongly dependent on environment and on galaxy mass ( e.g. , @xcite ) . galaxies in high density regions are systematically older than those in lower density regions , and massive galaxies are on average older than lower mass galaxies in stellar ages . it seems that massive galaxies in the high density regions form first and galaxy formation activity is propagated to lower density regions and to lower - mass galaxies with time . such dependence on environment and mass can be understood by intrinsic effects and extrinsic effects . intrinsic effects are those determined by the initial condition of galaxy formation and extrinsic effects are those in effect during the evolution of galaxies after formation .    the environmental dependence can be partly understood by the intrinsic effect called `` galaxy formation bias '' ( e.g. , @xcite ) where high density regions should have started off from the largest initial density fluctuations that collapse first in the universe , and galaxy formation takes place earliest in such regions and subsequent evolution is prompted . in lower density regions , however , galaxy formation is delayed and time scales of star formation and mass assembly are longer . likewise , the mass dependence of galaxy formation called `` down - sizing '' ( e.g. , @xcite ) may be partly understood by the scaled - down version of the bias on galactic scale , where more massive galaxies today correspond to higher initial density fluctuations on galactic scale and their formation such as star formation and assembly of building blocks take place earlier than less massive galaxies . galaxies are also subject to external effects from their surrounding environments , such as galaxy - galaxy interactions / mergers and ram - pressure stripping in dense environments ( e.g. , @xcite ) . such interactions may enhance and/or quench the star formation activity in galaxies preferentially in high density regions , which would therefore result in conspicuous dependence of galaxy properties on environments .    however , the relative importance of the intrinsic effects and the extrinsic effects is almost totally unknown yet . one of the most effective methods to verify the existence of the intrinsic effects is to go back in time and directly see the galaxies in the distant universe . by doing so , we may eventually reach the epoch when galaxies are forming rapidly in the biased cluster core , while galaxies are not yet formed or only slowly forming in lower density regions . also , as we go back in time , host galaxies of star formation would be shifted to higher mass systems and we may eventually see the active star formation in action in massive galaxies in the cluster core .    in the low redshift universe , star formation activity is a monotonically decreasing function of local density . however , we have not yet known the dependence of star formation activity on environments at high redshifts in detail . according to recent studies , it seems that star formation is in fact biased at high density region at high redshifts . @xcite reported for the first time in the goods north / south surveys that at @xmath14 the galaxies at denser environment tend to have higher star formation rates ( sfrs ) , in contrast to the local universe . @xcite and @xcite also showed similar trends for [ oii ] emitters at @xmath14 in deep2 and cosmos surveys , respectively . at a slightly lower redshift , @xmath15 , based on the mid - infrared observation of the rx  j1716.4 + 6708 cluster , @xcite reported that the star formation activity is probably enhanced in the medium density region , such as cluster outskirts or galaxy groups , rather than in the highest density region . @xcite also suggested that sfrs of galaxies may have a peak at intermediate densities at @xmath16=0.40.8 based on the ediscs survey . these observational findings may imply that the environment that hosts active star formation is shifted towards denser regions at higher redshifts . on the other hand , it is well - known as the `` butcher - oemler ( b - o ) effect '' that more distant clusters show higher fraction of blue galaxies up to @xmath17 , suggesting the enhancement of star formation activity in higher-@xmath16 clusters ( e.g. , @xcite ) . however , the fraction of blue galaxies decreases with cluster centric radius , and red galaxies still dominate in the core regions at @xmath17 ( @xcite ) . such studies of the b - o effect in clusters have been extended up to @xmath14 . @xcite found that the fraction of active galaxies in the central regions of clusters is higher at @xmath180.70.9 compared to @xmath180.20.5 . however , @xcite suggested that the fraction of galaxies with strong [ oii ] emission in the cluster cores at @xmath19 is not significantly dependent on redshift . it thus seems that we have not yet reached a bursting phase of massive galaxy formation in cluster cores even at @xmath14 , although the global activity of star formation within clusters is already enhanced .    in this paper , we present an [ oii ] emitter survey of the xmmxcs  j2215.9 - 1738 cluster ( hereafter 2215 cluster ) with a narrow - band filter @xmath1 on suprime - cam ( figure [ fig;transmission ] ) , and discuss spatial distribution of star formation activity ( see also @xcite , which presents our h@xmath20 emitter survey of the rx  j1716.4 + 6708 cluster at @xmath15 ) . the 2215 cluster is the most distant cluster to date at @xmath16=1.46 with a detection of extended x - ray emission ( @xcite ) . @xcite have confirmed dozens of the cluster members by spectroscopy , and found that velocity dispersion of the member galaxies is @xmath21 [ km s@xmath22 . with the @xmath1 filter , we can survey [ oii ] emissions from the galaxies with the line - of - sight velocities between @xmath232794 @xmath24 @xmath25 [ km s@xmath22 @xmath24 1598 with respect to the velocity centre of the cluster . our @xmath1 filter thus perfectly matches this cluster , and should be able to detect all the [ oii ] emission lines from the cluster members to a certain flux limit without introducing any bias ( figure [ fig;transmission ] ) . therefore , our survey is unique , and the 2215 cluster is an ideal target for us to investigate the environmental dependence of star formation activity over a wide range in environment at this high redshift . the x - ray luminosity and inter - cluster medium temperature for the 2215 cluster are @xmath26[erg  s@xmath22 , and @xmath27[kev ] , respectively ( @xcite ) . the luminosity is fainter than what is expected from the temperature compared to the local @xmath28 relation . @xcite thus point out that this cluster may experience a merger within the last few gyr . it is also found that colour - magnitude diagram in this cluster shows red sequence ( @xcite ) . @xcite investigated the morphologies of bright member galaxies , and found that about 60% of members are e or s0 galaxies . even at @xmath0 , cluster core is already dominated by early - type galaxies , as far as morphology is concerned . the structure of this paper is as follows . the observations and data reduction are described in   [ sec;obs ] . in   [ sec;selection ] , we describe how we select the [ oii ] emitters associated to the cluster at @xmath0 from the photometric catalogues . we show the spatial distribution , sfrs , and equivalent widths of the [ oii ] emitters , and investigate the star forming activity in the 2215 cluster in  [ sec;results ] . we also discuss the deficit of faint red galaxies and its evolution . a summary is given in  [ sec;summary ] . throughout this paper , magnitudes are in the ab system , and we adopt cosmological parameters of @xmath29 , @xmath30 and @xmath31 . vega magnitudes in @xmath6 and @xmath7 , if preferred , can be obtained from our ab magnitudes using the relations : @xmath6(vega)=@xmath6(ab)@xmath230.92 and @xmath7(vega)=@xmath7(ab)@xmath231.80 . filter ( @xmath2=9139 , @xmath3=134 ) . upper x - axis shows peculiar velocity with respect to the velocity centre of the cluster at @xmath0 . the histograms show the velocity distribution of the spectroscopically confirmed member galaxies of the 2215 cluster ( @xcite ) . , width=264 ]","summary":"moreover , we find a deficit of galaxies on the red sequence at magnitudes fainter than on the colour - magnitude diagram . this break magnitude is brighter than that of lower redshift clusters , and it is likely that we are seeing the formation phase of more massive red galaxies in the cluster core at .","abstract":"we present an unbiased deep [ oii ] emission survey of a cluster xmmxcs  j2215.9 - 1738 at , the most distant cluster to date with a detection of extended x - ray emission . with wide - field optical and near - infrared cameras ( suprime - cam and moircs , respectively ) on subaru telescope , we performed deep imaging with a narrow - band filter ( = 9139 ,=134 ) as well as broad - band filters ( , , and ) . from the photometric catalogues , we have identified 44 [ oii ] emitters in the cluster central region of down to a dust - free star formation rate of 2.6 m/yr ( 3 ) . interestingly , it is found that there are many [ oii ] emitters even in the central high density region . in fact , the fraction of [ oii ] emitters to the cluster members as well as their star formation rates and equivalent widths stay almost constant with decreasing cluster - centric distance up to the cluster core . unlike clusters at lower redshifts ( ) where star formation activity is mostly quenched in their central regions , this higher redshift 2215 cluster shows its high star formation activity even at its centre , suggesting that we are beginning to enter the formation epoch of some galaxies in the cluster core eventually . moreover , we find a deficit of galaxies on the red sequence at magnitudes fainter than on the colour - magnitude diagram . this break magnitude is brighter than that of lower redshift clusters , and it is likely that we are seeing the formation phase of more massive red galaxies in the cluster core at . these results may indicate inside - out and down - sizing propagation of star formation activity in the course of cluster evolution .    [ firstpage ]    galaxies : clusters : general  galaxies : clusters : individual : xmmxcs j2215.9 - 1738  galaxies : evolution ."}
{"article_id":"0911.2530","section_id":"r","document":"emitters to the cluster members as a function of radius from a cluster centre . the contribution of field galaxies is statistically subtracted from our colour - selected cluster member candidates . the error - bars indicate the statistical errors associated to both [ oii ] emitters and the cluster members . , width=264 ]     regions for xcs2215 cluster at @xmath0 ( left ) and rxj1716 cluster at @xmath15 ( right ) . blue open squares show [ oii ] emitters for 2215 cluster and h@xmath20 emitters for rxj1716 cluster , respectively . dots show cluster member candidates selected in  [ sec;clmember ] for the 2215 cluster , and member galaxies selected by photometric redshifts of @xmath72 for rxj1716 cluster ( @xcite ) , respectively . both panels show the areas of similar physical scales ( 0.51mpc / arcmin at @xmath0 and 0.45mpc / arcmin at @xmath15 , respectively ) . , width=317 ]            figure [ fig;map_member ] shows that there are many [ oii ] emitters in the central region of the 2215 cluster . if we assume that [ oii ] lines are emitted from ionized gas in / around the star forming regions , it seems that the 2215 cluster is still actively forming stars even at its core region . this is not the case in lower-@xmath16 clusters where star forming activity is much lower in the central region . to be more quantitative , we estimate a fraction of [ oii ] emitters to cluster members as a function of cluster - centric distance in figure  [ fig;oii_fraction ] . here , the amount of remaining contamination from foreground / background galaxies are estimated from the sdf sample , and it is statistically subtracted from the colour - selected sample of cluster member candidates . figure [ fig;oii_fraction ] suggests that the 2215 cluster maintains a high fraction of star forming galaxies in the central region , @xmath73% , even at the most inner part within 0.25  mpc in physical scale ( 1=0.51mpc at @xmath0 ) . this fraction is higher than the [ oii ] fraction in the cluster cores in @xcite , which is @xmath74% at @xmath19 . @xcite recently reported a distribution of spectroscopic sample of [ oii ] emitters in a cluster xmmu  j2235.3 - 2557 at @xmath75 , a similar redshift to that of the 2215 cluster . while there are no galaxies in the very core within 90  kpc in radius that show star forming activity , [ oii ] lines are detected from more than half of galaxies near the centre . this result is similar to ours on the [ oii ] emitters in 2215 cluster at a similar ( slightly higher ) redshift of 1.46 . it seems likely that distant x - ray detected clusters at @xmath76 are actively forming new stars even in the central region within a few hundreds kpc in radius . we have recently conducted a narrow - band h@xmath20 emitter survey for rx  j1716.4 + 6708 cluster at @xmath16=0.81 ( @xcite in preparation ) . this survey reveals quite a different situation where no h@xmath20 emitters are observed in the core region within a radius of 0.25  mpc ( figure [ fig;1716 ] ) . a difference in spatial distribution of the emitters is very impressive . the h@xmath20 emitters in the 1716 cluster are selected with a combination of @xmath77 ( @xmath2 = 11885 , @xmath3=141 ) and @xmath6 filters on subaru / moircs . the h@xmath20 survey reached to the depth of a limiting line flux of @xmath124.1@xmath3210@xmath55 erg s@xmath56 @xmath57 , which corresponds to a dust - free sfr of @xmath78m@xmath9yr@xmath56 . the h@xmath20 survey for the 1716 cluster is , thus , more sensitive to star forming galaxies with slightly lower sfr than the [ oii ] survey for the 2215 cluster , presented in this paper .    although the lines are different between the two clusters , h@xmath20 and [ oii ] lines , considering the fact that h@xmath20 line is much less affected by dust extinction than [ oii ] line , the intrinsic difference in spatial distribution of the emitters would be more significant . furthermore , @xcite find that the fraction of star forming galaxies decreases as one goes to denser region , which is different from what we see for the 2215 cluster . similar trends are also found in lower redshift clusters at @xmath16=0.40.8 ( @xcite ) . @xcite have also unveiled the star forming activities hidden by dust in the 1716 cluster based on the mid - infrared imaging with akari . these studies conclude that star formation activity has already been quenched in the cluster core , while it comes to an peak in the medium density regions away from the cluster core . these facts may imply that we find galaxy formation bias in the highest density region at @xmath79 . recent studies also support the biased star formation in a relatively dense environment at @xmath80 ( @xcite ) . the difference of critical environments in star formation at various redshifts may suggest that galaxy formation bias plays an important role in the dependence of galaxy properties on environments . in such a comparison between different clusters at different redshifts , we must keep in mind that the size and mass of the clusters can be different . in fact , the bolometric x - ray luminosity of 1716 cluster is @xmath81 times larger than that of 2215 cluster ( @xcite ) . also , the sub - structures of 1716 cluster is more prominent ( @xcite ) . we can not therefore conclude whether the difference seen in spatial distribution is largely due to time evolution or due to different masses or characteristics . but it may be the case that we are witnessing the evolution in star forming activity in the core of high-@xmath16 clusters from @xmath79 to @xmath82 . on the other hand , @xcite report a diversity in distribution of h@xmath20 emitters in the cores of clusters at @xmath16=0.70.8 . two among their three clusters at similar redshifts show a decrease in h@xmath20 fraction toward the cluster centre , while the other cluster shows an opposite trend . this fact may imply that it is not only the star formation bias that causes the high fraction of [ oii ] emitters in the core of the 2215 cluster . it is thus crucial to observe more clusters at @xmath83 , and to evaluate to what extent the presence of star forming galaxies in the cluster core is a general property at @xmath80 . the @xmath28 relation of the 2215 cluster suggests that it is possible that it experienced a merger event within the last few gyr ( @xcite ) . this can be another possible reason for the high fraction of [ oii ] emitters , since the cluster merging event might cause an enhancement of star formation activity in galaxies in the cluster core . also , since the distribution of [ oii ] emitters is projected on celestial sphere , it may be possible that some member galaxies in the outskirt of the cluster happen to be seen in the direction to the cluster centre , which may result in apparent high fraction of [ oii ] emitters at the centre . however , the number density of galaxies in the outskirt is likely to be much lower than that of galaxies in the core region ( figure [ fig;bzk](b ) ) , and such projection effect would be small in the direction to the centre . it is also possible that an active galactic nucleus ( agn ) enhances [ oii ] line flux . recent studies suggest that a fraction of agns in clusters increases with redshifts . @xcite have found an overdensity of agns within a radius of 0.25  mpc in clusters at @xmath84 , and that the density of x - ray selected agns in clusters at @xmath85 is 0.102 arcmin@xmath86 , which is @xmath87 times larger than that of clusters at @xmath88 . it indicates that it is possible that 34 agns reside in the central 33.8 arcmin@xmath89 region of the 2215 cluster . @xcite also show a monotonous increase of agn fraction in clusters from @xmath90 to @xmath91 . it is worth mentioning that @xcite report no obvious x - ray point source in the cluster core , although we can not completely exclude the presence of any point source . we thus consider that agn contribution is small . @xcite suggest that [ oii ] emitters in the red sequence tend to be agns , most commonly liners , and that [ oii ] line can be valid as an indicator of star formation activity only for blue galaxies . we find four red [ oii ] emitters with @xmath38 colours redder than @xmath92 ( see  [ sec;cmd ] and figure [ fig;cmd_lf](a ) ) , which are located near the centre ( figure [ fig;map_member ] ) . even if all these red [ oii ] emitters are agns , the enhancement of galaxy activity in the core would be still valid , since the presence of agn is also a sign of activity . this would then provide us with the clues to understanding the influence of agns on the evolution of massive galaxies in the cluster core , such as quenching of star formation . it is essential therefore to obtain nir spectra of these four [ oii ] emitters in order to constrain the origin of the [ oii ] lines .      according to @xcite , [ oii ] line flux [ ergs s@xmath56 @xmath57 ] and continuum flux density [ ergs  s@xmath56 @xmath57 @xmath22 for 44 [ oii ] emitters are calculated from flux densities in @xmath1 and @xmath5 bands ( @xmath94 and @xmath95 ) , respectively , as follows ; @xmath96})=f_{nb912}\\delta_{nb912}\\frac{1-(f_{z'}/f_{nb912})}{1-(\\delta_{nb912}/\\delta_{z ' } ) } , \\label{eq;fline}\\ ] ] @xmath97 where @xmath98 and @xmath99 indicate fwhms of the filters , and @xmath100  and @xmath101 .    in order to estimate dust - corrected sfr of our [ oii ] emitters , we use the empirical sfr calibration for [ oii ] parametrized in terms of the @xmath4-band luminosity developed by moustakas , kennicutt & tremonti ( 2006 ) for local star forming galaxies . the @xmath4-band luminosity was regarded as a proxy of stellar mass . they were aware that the mass - to - light ratios of star forming galaxies span a wide range and that the @xmath4-band luminosity would not be a perfect indicator of stellar mass . however , they empirically found that the amount of dust extinction and metallicity are correlated with the @xmath4-band luminosity ( see figure 16 in moustakas et al . ( 2006 ) ) . they also found that the correlation for star forming galaxies at 0.5@xmath24@xmath16@xmath241.5 is roughly consistent with that for local galaxies . it should be noted , however , that there is a larger uncertainty in the derived sfr for individual galaxies at high redshifts . we apply their correction scheme of dust extinction to our [ oii ] emitters at @xmath0 . we infer the rest - frame @xmath4-band fluxes from the @xmath6-band fluxes and @xmath102 colours and use them to correct for dust extinction . figure [ fig;sfr_ew](a ) shows thus derived dust - corrected sfrs of our [ oii ] emitters as a function of distance from the cluster center . stellar masses of the [ oii ] emitters are estimated from @xmath7 total magnitudes using the equation given in @xcite . @xcite estimate the stellar masses for @xmath45-selected galaxies at @xmath103 using k20 survey data . mass to @xmath45-band luminosity ratio is derived from multi - wavelength data from @xmath104 to @xmath45 with @xcite imf ( @xcite ) . the relation is calibrated with @xmath105 colour , which can reduce the dispersion of derived stellar mass to @xmath106 . we also derive specific sfr by dividing sfr by stellar mass . figure [ fig;sfr_ew](b ) shows the specific sfrs for [ oii ] emitters as a function of radius from a centre . the observed equivalent width of an [ oii ] emission is also derived from [ oii ] line flux and continuum flux density ( equations ( [ eq;fline ] ) and ( [ eq;fcont ] ) ) . figure [ fig;sfr_ew](c ) shows the observed equivalent widths for the [ oii ] emitters as a function of radius from a centre . figure [ fig;sfr_ew ] suggests that star formation activities of the [ oii ] emitters in denser regions are as active as those in the outskirt of the cluster . the equivalent widths are not correlated with the position of galaxies in the cluster . these facts also suggest active star formation in the central region of the 2215 cluster . on the other hand , the specific sfrs may show a mild correlation in the sense that [ oii ] emitters at the inner regions tend to have lower specific sfrs . since the similar correlation is not seen in their sfrs , this is due to the fact that massive galaxies tend to reside near the centre of the cluster . this tendency may be due to the galaxy formation bias that massive galaxies are formed in the cluster core , or may be a result of efficient mass assembly due to merging that can be more effective in high density regions . figure [ fig;sfr_ew](b ) also shows that the red [ oii ] emitters tend to have lower specific sfrs . this may be because we underestimate their intrinsic sfrs due to the strong dust extinction for the red galaxies . otherwise , this may imply that these galaxies are just quenching their star formation activities . figure [ fig;cmd_lf](a ) shows a colour - magnitude diagram of @xmath38 vs. @xmath7 for cluster member candidates in the central @xmath107 region . note that the @xmath7-selected galaxy sample is used in this section . the use of the @xmath1-selected sample may cause incompleteness in the number of galaxies at faint @xmath5 magnitudes . the solid line in the figure shows the expected location of the colour - magnitude relation ( cmr ) of passively evolving galaxies at @xmath0 formed at @xmath108 inferred from the @xcite model which is calibrated to reproduce the cmr of elliptical galaxies in the coma cluster at @xmath109 ; @xmath110 we define the red sequence galaxies as those falling in - between @xmath111 from the predicted cmr as shown by the broken lines in figure [ fig;cmd_lf](a ) . the number of the red sequence galaxies seems to decrease at magnitude fainter than @xmath11221.5 . the long - dashed and dotted lines show the 5@xmath10 and 3@xmath10 confidence levels of @xmath38 colours , respectively . therefore the decrease in the number of the red galaxies is not driven by incompleteness . @xcite and @xcite also examine colour - magnitude diagrams , and find that there is a well defined cmr of red galaxies in the 2215 cluster . in @xcite , however , shallowness of the data does not allow us to discuss the faint end of the red sequence . @xcite use deeper data to investigate the cmr , and colour - magnitude diagram of figure  6 in @xcite shows a deficit of red galaxies at magnitudes fainter than @xmath113 . this is consistent with our result . since all the cluster member candidates are plotted in figure [ fig;cmd_lf](a ) , some galaxies actually do not belong to the cluster . in order to correctly evaluate the deficit of the red galaxies , we derive the field - corrected @xmath7-band luminosity function in the central @xmath107 region by statistically subtracting the field contamination . the detection completeness is also corrected for as follows . artificial objects with gaussian profile are randomly generated and embedded in the raw @xmath7 image , and detection of these objects is conducted with the same manner as in  [ sec;selection_nbcatalogue ] . the assumed distribution of brightness of the artificial objects is uniform within each magnitude bin . the completeness thus estimated in each bin is always as high as @xmath11490% . the resulting luminosity function of the red sequence galaxies is shown in figure [ fig;cmd_lf](b ) . it is clear that the number of red member galaxies decreases at @xmath115 . this magnitude corresponds to @xmath116 + 0.5 with respect to the passively evolving galaxies at @xmath0 @xcite . in the 2215 cluster at @xmath0 , the red sequence is visible only down to @xmath12@xmath116 + 0.5 and truncated at that magnitude . such truncation is seen , if any , at fainter magnitudes ( @xmath117 + 0.5 ) in the cores of lower redshift clusters . for example , @xcite find no deficit of galaxies on red sequence down to @xmath118 in the ms1054.4 - 0321 cluster at @xmath16=0.83 . @xcite suggest that the build - up of the cmr depends on x - ray luminosity of clusters at @xmath82 , and find that the cmr is established down to @xmath119 even for a x - ray fainter cluster rxj1716 + 6708 at @xmath15 . @xcite and @xcite study cmr for the rdcs  j1252.9 - 2927 cluster at @xmath16=1.24 . while the red sequence galaxies only appear down to @xmath120 in sub - clumps in the outskirt of the cluster ( @xcite ) , faint red galaxies clearly exist down to @xmath121 in the main cluster ( @xcite ) . @xcite also find that there are red faint galaxies down to @xmath122 in the core region of the xmmu  j2235.3 - 2557 cluster at @xmath16=1.39 . we also note that @xcite show that the cmr of proto - clusters at much higher redshifts ( @xmath123 ) becomes less conspicuous , and even the bright - end of the red sequence seems to disappear in proto - clusters at @xmath124 .    in figure [ fig;cmd_lf](a ) , we mark the [ oii ] emitters with blue open squares . most of the [ oii ] emitters have bluer colours as expected since they are likely to be still forming stars . the galaxies that are fainter in @xmath7 hence less massive galaxies tend to be slightly bluer . this may suggest that star formation activity in more massive galaxies tends to be truncated at earlier times . we draw three iso - stellar mass curves of @xmath125m@xmath9 , @xmath126m@xmath9  and @xmath127m@xmath9 , respectively , using the equation given in @xcite . if the [ oii ] emitters cease their star formation , they would move along these curves until they reach on to the red sequence . if an [ oii ] emitter has a sfr of 50m@xmath9/yr , which is close to the median sfr in our [ oii ] emitter sample , and keeps this rate constant until @xmath128 , its stellar mass would increase by @xmath129m@xmath130@xmath131m@xmath9 . if we assume that an [ oii ] emitter gradually becomes red while increasing its stellar mass at a constant sfr , the faint end of the red sequence would be filled up by @xmath91 . if this is the case , the [ oii ] emitters with @xmath132m@xmath9  may be good progenitors of the faint galaxies on the red sequence . however , we do not know yet the mechanisms of changing galaxy colours and quenching their star formation . as described in the last paragraph of  [ sec;sf_activity ] , contribution of agns to the [ oii ] emitters on the red sequence can be large ( @xcite ) . perhaps agn feedback is one of the key mechanisms to reduce the star formation activities .    combining with the previous studies of cmr ( see above ) , we come up with the following scenario of formation of red sequence in clusters at @xmath79 . the most massive galaxies brighter than @xmath116 ( i.e. , @xmath133m@xmath9 ) are formed at @xmath134 , and become red by quenching the star formation in early epoch . some galaxies on the red sequence may still be keeping residual star formation activities . on the other hand , less massive galaxies are actively growing at @xmath135 , and we hardly see galaxies fainter than @xmath116 on the red sequence . star forming galaxies with @xmath136m@xmath9  at @xmath79 may evolve into faint red sequence galaxies by @xmath91 . this suggest down - sizing propagation of star formation in high redshift clusters .","summary":"interestingly , it is found that there are many [ oii ] emitters even in the central high density region . in fact , the fraction of [ oii ] emitters to the cluster members as well as their star formation rates and equivalent widths stay almost constant with decreasing cluster - centric distance up to the cluster core . unlike clusters at lower redshifts ( ) where star formation activity is mostly quenched in their central regions , this higher redshift 2215 cluster shows its high star formation activity even at its centre , suggesting that we are beginning to enter the formation epoch of some galaxies in the cluster core eventually .","abstract":"we present an unbiased deep [ oii ] emission survey of a cluster xmmxcs  j2215.9 - 1738 at , the most distant cluster to date with a detection of extended x - ray emission . with wide - field optical and near - infrared cameras ( suprime - cam and moircs , respectively ) on subaru telescope , we performed deep imaging with a narrow - band filter ( = 9139 ,=134 ) as well as broad - band filters ( , , and ) . from the photometric catalogues , we have identified 44 [ oii ] emitters in the cluster central region of down to a dust - free star formation rate of 2.6 m/yr ( 3 ) . interestingly , it is found that there are many [ oii ] emitters even in the central high density region . in fact , the fraction of [ oii ] emitters to the cluster members as well as their star formation rates and equivalent widths stay almost constant with decreasing cluster - centric distance up to the cluster core . unlike clusters at lower redshifts ( ) where star formation activity is mostly quenched in their central regions , this higher redshift 2215 cluster shows its high star formation activity even at its centre , suggesting that we are beginning to enter the formation epoch of some galaxies in the cluster core eventually . moreover , we find a deficit of galaxies on the red sequence at magnitudes fainter than on the colour - magnitude diagram . this break magnitude is brighter than that of lower redshift clusters , and it is likely that we are seeing the formation phase of more massive red galaxies in the cluster core at . these results may indicate inside - out and down - sizing propagation of star formation activity in the course of cluster evolution .    [ firstpage ]    galaxies : clusters : general  galaxies : clusters : individual : xmmxcs j2215.9 - 1738  galaxies : evolution ."}
{"article_id":"0911.2530","section_id":"i","document":"we performed a unique , unbiased [ oii ] line survey of star forming galaxies in the xmmxcs  j2215.9 - 1738 cluster at @xmath0 , which is currently the most distant cluster ever identified with a detection of extended x - ray emission . we have obtained wide - field optical ( @xmath4 , @xmath5 , @xmath1 ) and near - infrared ( @xmath6 and @xmath7 ) data with suprime - cam and moircs , respectively . with a combination of @xmath1 narrow - band filter ( @xmath2 = 9139 , fwhm=134 ) and the @xmath5-band filter , we detect 69 @xmath1 emitters in the central @xmath8 region where near - infrared data are also available . among them , 44 emitters are identified as [ oii ] emitters associated to the cluster based on the @xmath37 and @xmath38 colours , down to a dust - free star formation rate of 2.6 m@xmath9yr@xmath56 ( 3@xmath10 ) . we find that many [ oii ] emitters reside in the central high density region even within a radius of 0.25 mpc ( physical scale ) . we also find that the fraction of [ oii ] emitters to cluster members remains high up to the core region . this suggests that the 2215 cluster is still actively forming stars even at the central region , in contrast to lower redshift clusters , where old passively evolving elliptical galaxies dominate . this indicates an inside - out propagation of star formation in high redshift clusters , and we may be eventually beginning to enter the epoch of biased galaxy formation in the densest region at @xmath0 . sfrs , specific sfrs , and equivalent widths are derived for 44 [ oii ] emitters . it is found that the emitters have similar sfrs and equivalent widths irrespective of the location within the cluster . it seems however that the specific sfrs tend to decrease slightly toward the cluster core , probably due to the fact that more massive [ oii ] emitters exist near the centre . we may be approaching to the formation phase of massive galaxies at the cluster core . moreover , the colour - magnitude diagram in the 2215 cluster shows a deficit of red sequence galaxies fainter than @xmath12@xmath13 , while the red sequence in lower redshift clusters extends to much fainter magnitudes . while some bright [ oii ] emitters are located on the red sequence , all the faint [ oii ] emitters with @xmath137@xmath138 have blue colours . it is likely that those blue [ oii ] emitters become redder once they truncate their star formation , and they would eventually reach and fill the faint end of the red sequence at lower redshifts . this indicates a down - sizing propagation of star formation in high redshift clusters .","summary":"we present an unbiased deep [ oii ] emission survey of a cluster xmmxcs  j2215.9 - 1738 at , the most distant cluster to date with a detection of extended x - ray emission . with wide - field optical and near - infrared cameras ( suprime - cam and moircs , respectively ) on subaru telescope , we performed deep imaging with a narrow - band filter ( = 9139 ,=134 ) as well as broad - band filters ( , , and ) . from the photometric catalogues , we have identified 44 [ oii ] emitters in the cluster central region of down to a dust - free star formation rate of 2.6 m/yr ( 3 ) . these results may indicate inside - out and down - sizing propagation of star formation activity in the course of cluster evolution .    [ firstpage ]    galaxies : clusters : general  galaxies : clusters : individual : xmmxcs j2215.9 - 1738  galaxies : evolution .","abstract":"we present an unbiased deep [ oii ] emission survey of a cluster xmmxcs  j2215.9 - 1738 at , the most distant cluster to date with a detection of extended x - ray emission . with wide - field optical and near - infrared cameras ( suprime - cam and moircs , respectively ) on subaru telescope , we performed deep imaging with a narrow - band filter ( = 9139 ,=134 ) as well as broad - band filters ( , , and ) . from the photometric catalogues , we have identified 44 [ oii ] emitters in the cluster central region of down to a dust - free star formation rate of 2.6 m/yr ( 3 ) . interestingly , it is found that there are many [ oii ] emitters even in the central high density region . in fact , the fraction of [ oii ] emitters to the cluster members as well as their star formation rates and equivalent widths stay almost constant with decreasing cluster - centric distance up to the cluster core . unlike clusters at lower redshifts ( ) where star formation activity is mostly quenched in their central regions , this higher redshift 2215 cluster shows its high star formation activity even at its centre , suggesting that we are beginning to enter the formation epoch of some galaxies in the cluster core eventually . moreover , we find a deficit of galaxies on the red sequence at magnitudes fainter than on the colour - magnitude diagram . this break magnitude is brighter than that of lower redshift clusters , and it is likely that we are seeing the formation phase of more massive red galaxies in the cluster core at . these results may indicate inside - out and down - sizing propagation of star formation activity in the course of cluster evolution .    [ firstpage ]    galaxies : clusters : general  galaxies : clusters : individual : xmmxcs j2215.9 - 1738  galaxies : evolution ."}
{"article_id":"1203.5579","section_id":"i","document":"recently a multi - purpose fixed - target experiment using the proton and lead - ion beams of the large hadron collider ( lhc ) extracted by a bent crystal , referred to as after in the following , was proposed by brodsky , fleuret , hadjidakis and lansberg  @xcite . such an extraction mode will not alter the performance of the collider experiments at the lhc . the center - of - mass energy is @xmath8 gev with the lhc-@xmath9 tev proton beam and @xmath10 gev with the a lead running with @xmath11 tev - per - nucleon beam , and it can be even higher by using the fermi motion of the nucleons in a nuclear target . this project will provide a unique opportunity to study the nucleon partonic structure , spin physics , nuclear matter properties , deconfinement in heavy ion collisions , @xmath12 and @xmath4 productions , exclusive , semi - exclusive and backward reactions , and even further potentialities of a high - energy fixed target set - up . we concentrate our study on some issues related to the spin physics for the after proposal . the study of the three - dimensional or the intrinsic transverse momentum dependent distribution functions ( 3dpdfs or tmds ) has received much attention in recent years  @xcite . such new quantities of the nucleon provide us a significant perspective on understanding the three - dimensional structure of hadrons and the non - perturbative properties of quantum chromodynamics ( qcd ) . the intrinsic transversal momentum of partons may cause special effects in high energy scattering experiments  @xcite . azimuthal asymmetries of unpolarized and single polarized drell  yan processes are among the most challenging issues of qcd spin physics  @xcite . the first measurement of the angular distribution of drell  yan process , performed by na10 collaboration for @xmath13 , indicates a sizable @xmath3 azimuthal asymmetry  @xcite which can not be described by leading and next - to - leading order perturbative qcd  @xcite . furthermore , the violation of the lam  tung relation  @xcite which is obtained from the spin-@xmath14 nature of quarks and the spin-@xmath15 nature of gluons , just like the callan  gross relation in the deep - inelastic scattering  @xcite , was measured by fermilab e615 collaboration  @xcite . this violation was also tested by e866/nusea collaboration through the @xmath1 and @xmath0 drell  yan dimuon processes in recent year  @xcite . large single spin asymmetries ( ssas ) were observed experimentally in the process @xmath16 two decades ago  @xcite . ssas in semi - inclusive deeply inelastic scattering ( sidis )  @xcite with one colliding nucleon transversely polarized have also been measured by several experiments . standard perturbtive qcd based on collinear factorization to leading twist failed to explain these asymmetries  @xcite . the drell  yan process is an ideal ground for testing the perturbative qcd and for probing the 3dpdfs or tmds , as it contains only the distribution functions with no fragmentation functions , and its differential cross section is well described by next - to - leading order qcd calculations  @xcite . in this paper , we calculate azimuthal asymmetries of @xmath0 and @xmath1 dilepton production processes in drell  yan continuum region and around the @xmath4-pole through a fixed - target experiment using the lhc proton beams with the proton or deuteron target unpolarized and transversally or longitudinally polarized . the paper is organized as follows . in sect .  2 and 3 , we respectively calculate the azimuthal asymmetries in unpolarized and single polarized @xmath0 and @xmath1 processes . in sect .  4 , we present the numerical results of these asymmetries . then , a brief discussion and conclusion is contained in sect .","summary":"a multi - purpose fixed - target experiment using the proton and lead - ion beams of the lhc was recently proposed by brodsky , fleuret , hadjidakis and lansberg , and here we concentrate our study on some issues related to the spin physics part of this project ( referred to as after ) . we study the nucleon spin structure through and processes with a fixed - target experiment using the lhc proton beams , for the kinematical region with 7  tev proton beams at the energy in center - of - mass frame of two nucleons gev .","abstract":"a multi - purpose fixed - target experiment using the proton and lead - ion beams of the lhc was recently proposed by brodsky , fleuret , hadjidakis and lansberg , and here we concentrate our study on some issues related to the spin physics part of this project ( referred to as after ) . we study the nucleon spin structure through and processes with a fixed - target experiment using the lhc proton beams , for the kinematical region with 7  tev proton beams at the energy in center - of - mass frame of two nucleons gev . we calculate and estimate the azimuthal asymmetries of unpolarized and dilepton production processes in the drell  yan continuum region and at the-pole . we also calculate the , and azimuthal asymmetries of and dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the drell  yan continuum region and around resonances region . we conclude that it is feasible to measure these azimuthal asymmetries , consequently the three - dimensional or transverse momentum dependent parton distribution functions ( 3dpdfs or tmds ) , at this new after facility ."}
{"article_id":"1203.5579","section_id":"r","document":"in this section , we calculate the azimuthal asymmetries of the @xmath0 and @xmath1 dilepton production processes with the proton or deuteron target unpolarized and longitudinally or transversally polarized in drell  yan continuum region and @xmath4 resonance region respectively . we present a numerical estimation of these azimuthal asymmetries for measurement at a fixed - target experiment using the lhc beams proposed by brodsky , fleuret , hadjidakis and lansberg  @xcite . with the @xmath9 tev proton beams , the center - of - mass frame energy @xmath2 gev for two nucleons . the cross section of drell  yan process can also be expressed depending on @xmath81 and @xmath82 instead of @xmath83 and @xmath84 with just a jacobian multiplied as @xmath85 at the region @xmath70 , we have the following relation : @xmath86 the @xmath83 and @xmath84 can also be expressed with @xmath87 and @xmath82 @xmath88 and @xmath89 @xmath83 is the momentum fraction of the parton in the beam proton , and @xmath84 is that of the parton in the target nucleon . for the single polarized processes , @xmath84 is the momentum fraction of the parton in the polarized target nucleon , sometimes labeled as @xmath90 in the literature . to calculate the azimuthal asymmetries depending on @xmath91 , @xmath87 or @xmath92 , we need to integrate over the other variables in the numerator and the dominator of the expression of the asymmetries respectively . the rapidity is cut in @xmath93 $ ] which is the easiest region to carry on measurements as discussed in  @xcite , and this is where the momentum fraction of the parton inside the polarized nucleons is the largest .    in our calculation , we adopt the boer  mulders function @xmath21 extracted from the unpolarized @xmath1 and @xmath0 drell  yan data  @xcite . the parametrization of @xmath21 for both valence and sea quarks has the form : @xmath94 where the subscript `` bm '' stands for the boer  mulders functions , and @xmath95 , @xmath58 , @xmath57 and @xmath59 . the possible range of the parameters @xmath96 allowed by the positivity bound  @xcite can be described by a coefficient @xmath97 which balance the contributions of quark and antiquark . @xmath98 for @xmath95 , @xmath58 and @xmath99 for @xmath100 , @xmath59 will not change the calculated @xmath3 asymmetry in the unpolarized @xmath0 and @xmath1 drell  yan data . the range of @xmath97 is @xmath101 , and we choose the case @xmath102 , which corresponds to the central values of @xmath96 , in our calculation .    in figs . [ unppcont1 ] and  [ unpdcont1 ] , we show the @xmath3 azimuthal asymmetry depending on @xmath91 from @xmath103 gev to @xmath104 gev of the unpolarized @xmath0 and @xmath1 drell  yan process at after including @xmath4 taken into account . [ unppcontxf2 ] ,  [ unppcontxf5 ] ,  [ unpdcontxf2 ] and  [ unpdcontxf5 ] respectively show the @xmath3 azimuthal asymmetry depending on @xmath87 of the unpolarized @xmath0 and @xmath1 processes with @xmath105 gev and @xmath106 gev as for low and mid @xmath91 drell  yan regions at after . [ unppz ] and  [ unpdz ] respectively show this azimuthal asymmetry of @xmath0 and @xmath1 processes at the @xmath4 pole at after . azimuthal asymmetry depending on @xmath87 of unpolarized @xmath0 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath87 of unpolarized @xmath0 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath92 of unpolarized @xmath0 process in @xmath4 resonance region.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath92 of unpolarized @xmath0 process in @xmath4 resonance region.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath87 of unpolarized @xmath1 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath87 of unpolarized @xmath1 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath92 of unpolarized @xmath1 process in @xmath4 resonance region.,scaledwidth=50.0% ]     azimuthal asymmetry depending on @xmath92 of unpolarized @xmath1 process in @xmath4 resonance region.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target proton polarized @xmath0 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath91 of target deuteron polarized @xmath1 drell  yan process with both @xmath44 and @xmath4 taken into account.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath105 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target proton polarized @xmath0 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath107 depending on @xmath87 of target deuteron polarized @xmath1 drell  yan process at @xmath106 gev.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target proton polarized @xmath0 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target proton polarized @xmath0 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target proton polarized @xmath0 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target deuteron polarized @xmath1 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target deuteron polarized @xmath1 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]     azimuthal asymmetry @xmath108 depending on @xmath92 of target deuteron polarized @xmath1 dilepton production process at the @xmath4 pole.,scaledwidth=50.0% ]    to calculate the ssas of the @xmath0 and @xmath1 dilepton production processes at after , we also need the distribution functions @xmath63 , @xmath65 and @xmath67 besides the boer  mulders function @xmath21 . in our calculation , we adopt ansatz of these @xmath23-even distribution functions calculated from the light - cone quark - diquark model . in this model , the melosh  wigner rotation , which is important to understand the proton spin puzzle due to the relativistic effect of quark transversal motions  @xcite , is taken into account . this model has been applied to calculate helicity distributions  @xcite , transversity distributions  @xcite and some other 3dpdfs or tmds  @xcite , and has been used to analysis related azimuthal spin asymmetries in sidis processes  @xcite . the model results of these distribution functions are expressed as  @xcite @xmath109w_s^j(x,\\bm{k}_t^2)\\nonumber\\\\ & -\\frac{1}{6}f_{1d}^{v}(x,\\bm{k}_t^2)w_v^j(x,\\bm{k}_t^2),\\\\ j_d^{v}(x,\\bm{k}_t^2 ) = & -\\frac{1}{3}f_{1d}^{v}(x,\\bm{k}_t^2)w_v^j(x,\\bm{k}_t^2 ) , \\label{tevenpdf}\\end{aligned}\\ ] ] where @xmath110 , @xmath63 , @xmath65 , and the superscript @xmath111 stands for valence quark distributions . the factors @xmath112 are the melosh  wigner rotations for scalar or axial vector spectator - diquark respectively , having the forms : @xmath113 where @xmath114    the distribution functions @xmath67 , @xmath63 , @xmath65 of sea quarks are constrained by the positivity bounds  @xcite : @xmath115 when considering the effects of these distribution functions of sea quarks contributing to the asymmetries , we can get the upper and lower limits of the azimuthal asymmetries by saturating the positivity bounds .    in figs . [ sppcont1a]-[sppcont1c ] , we respectively show the @xmath5 , @xmath6 and @xmath7 azimuthal asymmetries depending on @xmath91 from @xmath103 gev to @xmath104 gev of the target proton polarized @xmath0 drell  yan process at after including @xmath4 taken into account , and the corresponding results for deuteron target polarized @xmath1 process are shown in figs . [ spdcont1a]-[spdcont1c ] . these asymmetries in the far backward region , with rapidity cut @xmath116 $ ] , are shown in figs . [ sppcont2a]-[spdcont2c ] , with @xmath91 running from @xmath15 gev to @xmath117 gev . in figs . [ sppcontxf2a]-[spdcontxf5c ] , we respectively show the @xmath5 , @xmath6 and @xmath7 azimuthal asymmetries depending on @xmath87 of the target proton and deuteron polarized @xmath0 and @xmath1 drell  yan processes at after with @xmath105 gev and @xmath106 gev as for low and mid @xmath91 regions . [ sppza][sppzc ] show the @xmath5 , @xmath6 and @xmath7 azimuthal asymmetries of the target proton polarized @xmath0 process around the @xmath4-pole at after . the corresponding azimuthal asymmetries of @xmath1 processes with target deuteron transversally or longitudinally polarized are shown in figs . [ spdza][spdzc ] .","summary":"we also calculate the , and azimuthal asymmetries of and dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the drell  yan continuum region and around resonances region .","abstract":"a multi - purpose fixed - target experiment using the proton and lead - ion beams of the lhc was recently proposed by brodsky , fleuret , hadjidakis and lansberg , and here we concentrate our study on some issues related to the spin physics part of this project ( referred to as after ) . we study the nucleon spin structure through and processes with a fixed - target experiment using the lhc proton beams , for the kinematical region with 7  tev proton beams at the energy in center - of - mass frame of two nucleons gev . we calculate and estimate the azimuthal asymmetries of unpolarized and dilepton production processes in the drell  yan continuum region and at the-pole . we also calculate the , and azimuthal asymmetries of and dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the drell  yan continuum region and around resonances region . we conclude that it is feasible to measure these azimuthal asymmetries , consequently the three - dimensional or transverse momentum dependent parton distribution functions ( 3dpdfs or tmds ) , at this new after facility ."}
{"article_id":"1203.5579","section_id":"c","document":"in this paper , we calculate the @xmath3 azimuthal asymmetries of unpolarized @xmath0 and @xmath1 dilepton production processes in the drell  yan continuum region and around the @xmath4 resonance region . we also calculate the @xmath5 , @xmath6 and @xmath7 azimuthal asymmetries of single transversally or longitudinally polarized @xmath0 and @xmath1 dilepton production processes in these regions . our calculations are concentrated on some issues related to the spin physics part of the after project , a multi - purpose fixed - target experiment using the proton and lead - ion beams of the lhc extracted by a bent crystal , proposed by brodsky , fleuret , hadjidakis and lansberg  @xcite . we present an estimation of the azimuthal asymmetries for a fixed - target experiment using the lhc 7  tev proton beams with the proton or deuteron target unpolarized and transversally or longitudinally polarized . as the target is conveniently polarized , it is an ideal ground to study the spin physics at after with @xmath2 gev and high luminosity . it is feasible to measure these azimuthal asymmetries at after . this will help us to study the three dimensional or transverse momentum dependent parton distributions ( 3dpdfs or tmds ) , and consequently help understand and test the qcd and hadron structure at such a high laboratory energy . this work is partially supported by national natural science foundation of china ( grants no .  11021092 , no . 10975003 , no . 11035003 , and no . 11120101004 ) , by the research fund for the doctoral program of higher education ( china )    s.  j.  brodsky , f.  fleuret , c.  hadjidakis and j.  p.  lansberg , arxiv:1202.6585 [ hep - 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ph/0209114 ] .","summary":"we calculate and estimate the azimuthal asymmetries of unpolarized and dilepton production processes in the drell  yan continuum region and at the-pole . we conclude that it is feasible to measure these azimuthal asymmetries , consequently the three - dimensional or transverse momentum dependent parton distribution functions ( 3dpdfs or tmds ) , at this new after facility .","abstract":"a multi - purpose fixed - target experiment using the proton and lead - ion beams of the lhc was recently proposed by brodsky , fleuret , hadjidakis and lansberg , and here we concentrate our study on some issues related to the spin physics part of this project ( referred to as after ) . we study the nucleon spin structure through and processes with a fixed - target experiment using the lhc proton beams , for the kinematical region with 7  tev proton beams at the energy in center - of - mass frame of two nucleons gev . we calculate and estimate the azimuthal asymmetries of unpolarized and dilepton production processes in the drell  yan continuum region and at the-pole . we also calculate the , and azimuthal asymmetries of and dilepton production processes with the target proton and deuteron longitudinally or transversally polarized in the drell  yan continuum region and around resonances region . we conclude that it is feasible to measure these azimuthal asymmetries , consequently the three - dimensional or transverse momentum dependent parton distribution functions ( 3dpdfs or tmds ) , at this new after facility ."}
{"article_id":"0707.3766","section_id":"c","document":"to summarize , we have defined , in terms of the spanning tree variables , two new boundary conditions in the two - dimensional abelian sandpile model , and we have explored their nature in terms of a logarithmic cft with central charge @xmath0 . together with the well - known open and closed boundary conditions , they lead to seven new boundary condition changing fields @xmath232 , with scaling dimensions in the set @xmath233 . we have examined many 3- and 4-point amplitudes within the conformal setting , and have found a full agreement with the corresponding lattice data . this brings further support to the consistency and relevance of the conformal description , and adds new entries in this description . it is worth stressing again the peculiarities and unusual features that these new boundary conditions have .    1 .   the arrow boundary conditions carry an intrinsic orientation . to our knowledge , this is the first instance of oriented boundary conditions . a direct consequence of this is that the boundary condition changing fields which involve arrows have a vanishing two - point function , or , formulated in another way , the metric on the space of states is off - diagonal in the representation basis . they can not be uniformly imposed on a whole boundary . the reason for this is very clear in the sandpile model . the recurrent configurations are in one - to - one correspondence with spanning trees . since a uniform arrow boundary condition on a boundary introduces a loop , it can not be part of a spanning tree and therefore does not correspond to an allowed height configuration in the sandpile . in the conformal description however , this is a rather strange and new situation . the full implications of this from the general point of view of boundary cft need to be clarified . all boundary condition changing fields are primary , but two of them , @xmath234 and @xmath235 , belong to an indecomposable representation @xmath141 with rank 2 jordan cells . the physical meaning of this and the physical interpretation of the lowest logarithmic partners ( the @xmath236 and @xmath237 fields ) remain to be understood . a third boundary condition changing field , namely @xmath149 , is the lowest lying state of an indecomposable representation @xmath142 . in @xmath142 this field is degenerate at level 5 but possesses a singular descendant at level 2 . even though this singular descendant has been seen to decouple in a number of amplitudes , we have no conclusive argument that it is actually null , and so we leave this question open . the same question as in point 3 regarding the physical interpretation of the field @xmath154 remains . besides the questions raised above , there is clearly a number of other problems that need be answered before we can pretend to understand the sandpile model with boundaries . among the most pressing and important ones , one can first mention the classification of all the observables which either preserve or interpolate between the four boundary conditions discussed here . then one should also classify all conformally invariant boundary conditions present in the sandpile model , find their conformal description and determine the corresponding spectra of boundary fields . this is obviously much more challenging since an infinite number of boundary conditions are expected .","summary":"we continue our investigation of the two - dimensional abelian sandpile model in terms of a logarithmic conformal field theory with central charge , by introducing two new boundary conditions . these have two unusual features : they carry an intrinsic orientation , and , more strangely , they can not be imposed uniformly on a whole boundary ( like the edge of a cylinder ) . they lead to seven new boundary condition changing fields , some of them being in highest weight representations ( weights and ) , some others belonging to indecomposable representations with rank 2 jordan cells ( lowest weights 0 and 1 ) .","abstract":"we continue our investigation of the two - dimensional abelian sandpile model in terms of a logarithmic conformal field theory with central charge , by introducing two new boundary conditions . these have two unusual features : they carry an intrinsic orientation , and , more strangely , they can not be imposed uniformly on a whole boundary ( like the edge of a cylinder ) . they lead to seven new boundary condition changing fields , some of them being in highest weight representations ( weights and ) , some others belonging to indecomposable representations with rank 2 jordan cells ( lowest weights 0 and 1 ) . their fusion algebra appears to be in full agreement with the fusion rules conjectured by gaberdiel and kausch ."}
{"article_id":"1212.0917","section_id":"i","document":"quantum fisher information ( qfi ) , which is one of the most important quantities for both quantum estimation theory and quantum information theory , has been widely studied @xcite . in the field of quantum estimation , the main task is to determine the value of an unknown parameter labeling the quantum system , and a primary goal is to enhance the precision of the resolution @xcite . the inverse of the qfi provides the lower bound of error of the estimation @xcite . hence , how to increase the qfi become the key problem to be solved . moreover , the qfi can be used to measure the statistical distinguishability on the space of the density operators in the quantum information geometry @xcite . recently , the qfi flow was proposed as a quantitative measure of the information flow and provides a novel perspective on observing the non - markovian behavior in open quantum systems @xcite . there are several variants of quantum versions of fisher information , among which the one based on the symmetric logarithmic derivative ( sld ) operator has been used most widely and possesses many good properties @xcite , such as convexity , remaining invariant under the unitary evolution , and the total amount of the qfi equivalent to the summation of the qfis of all subsystem being uncorrelated . in this paper , we also study another variant of the quantum version of the fisher information , which is closely related with the skew information @xcite . the skew information was proposed to measure the amount of information that a quantum state contains with respect to the observable which does not commute with additive conserved quantities , such as hamiltonians , momenta @xcite . it is also used to measure the quantum uncertainty @xcite and quantify quantum correlations in bipartite state in a recent work @xcite . in the following , we shall show that the two qfis formally possess many similar features @xcite , but they are different not only for the concrete expressions of the definitions , but also for their applications . as is mentioned previously , the qfi based on sld operator is mainly applied in the quantum metrology , however , the variant version of the qfi plays an important role in quantum state discrimination @xcite .    from the information theory , both two different qfis characterize the content of information contained in the quantum systems . a crucial property of these two information quantities is that they decrease monotonically under the completely positive and trace - preserving ( cpt ) maps  @xcite . the monotonicity property manifests the information loss under the cpt map . just as the introduction of the qfi flow @xcite , can we observe the non - markovian properties from the other information quantities perspective ? here , we will address this problem by calculating these two qfis for a single qubit and derive the explicit formulas in the bloch representation , which greatly facilitates the computing of these two quantities . the main results in this paper are that the dynamical qfis , in the presence of decoherences , are analytically solved . here , the irreversible processes are modeled via three decoherence channels @xcite : phase - damping channel  ( pdc ) , depolarizing channel  ( pdc ) , and the generalized amplitude damping channel  ( gadc ) @xcite . the analytical results for the two information quantities under those channels are obtained . we will show that the values of the two qfis monotonically decrease with time , apart from the isolated case that the qfi based on the sld operator about the amplitude parameter @xmath1 remain invariant under the pdc . in order to further identify the behaviors of the two qfis subject to quantum noise , we discuss a simple model of a two - level system coupled to a reservoir with a lorentzian spectral density @xcite . by using the hierarchy equation method , we numerically analyze the dynamics of the two qfis , and compare these with the analytical solutions by using the rotating - wave approximation ( rwa ) . we further generalize the results to the qudit system . meanwhile , we verify that they are also applicable for the @xmath2-qubit system with symmetry exchange . for the sake of clarity , we calculate the dynamical quantum fisher information in the presence of collisional dephasing . this paper is organized as follows . in sec . [ qfs ] , we first review two different definitions of the qfi , and give the explicit formulae for the qfis for a single qubit system . in sec . [ qfi_qubit ] , we obtain the analytical results for the two quantities under three different decoherence channels , and the numerical results are given . moreover , in sec .  [ qfi_qudit](a ) , we generalize the expressions of the two qfis for a qudit system , and the qfi in a noisy environment for an @xmath2-qubit system is discussed in sec . [ qfi_qudit](b ) . finally , the conclusion are given in sec . [ conclusion ] .","summary":"moreover , we obtain analytical results for them under three different decoherence channels , which are expressed as affine transformation matrices . using the hierarchy equation method , we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating - wave approximation .","abstract":"the dynamics of two variants of quantum fisher information under decoherence are investigated from a geometrical point of view . we first derive the explicit formulas of these two quantities for a single qubit in terms of the bloch vector . moreover , we obtain analytical results for them under three different decoherence channels , which are expressed as affine transformation matrices . using the hierarchy equation method , we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating - wave approximation . we further express the two information quantities in terms of the bloch vector for a qudit , by expanding the density matrix and hermitian operators in a common set of generators of the lie algebra . by calculating the dynamical quantum fisher information , we find that the collisional dephasing significantly diminishes the precision of phase parameter with the ramsey interferometry ."}
{"article_id":"hep-ph0102181","section_id":"i","document":"supersymmetry ( susy ) models with r - parity invariance offers a leading candidate for the dark matter observed in the universe at large and locally in the milky way galaxy . thus in models of this type , the lightest neutralino , @xmath12 , is generally the lightest supersymmetric particle ( lsp ) and hence is absolutely stable . the observed dark matter is then the relic neutralinos left over after the big bang . susy models are predictive since they can calculate simultaneously the amount of relic density expected , milky way detection signals and the production cross sections at accelerators . thus cosmological , astronomical and accelerator constraints simultaneously constrain the susy parameter space .    the procedure for calculating the relic density of neutralinos is well known . ( for a review , see @xcite . ) over the past decade , a number of refinements of the analysis needed to get accurate answers have been included . thus the treatment of threshold and s - channel resonances in the annihilation cross section in the early universe was discussed in @xcite . in calculating the relic density , in most of the parameter space it is sufficient to use the two body neutralino annihilation cross section , since the effects of heavier particles are suppressed by the boltzman factor . however , in special situations , the next to lightest supersymmetric particle ( nlsp ) may become nearly degenerate with the lsp , and the coupled annihilation channels of lsp - lsp , nlsp - lsp , nlsp - nlsp must be simultaneously considered  @xcite . this phenomena of coannihilation was considered within the framework of the minimal supersymmetric model ( mssm ) in @xcite for the situation when the lightest chargino , @xmath13 , becomes nearly degenerate with the @xmath12 . in this paper we consider supergravity ( sugra ) models with grand unification of the gauge coupling constants and soft susy breaking at the gut scale @xmath14 gev . the low energy properties of the theory is thus obtained by running the renormalization group equations ( rge ) from @xmath15 to the electroweak scale , where susy breaking at @xmath15 triggers @xmath16 breaking at the electroweak scale . aside from being in accord with the lep data implying grand unification , radiative breaking of @xmath16 greatly enhances the predictiveness of the theory as it reduces the number of susy parameters , and one finds generally for such models that the @xmath12 is mostly bino , and the @xmath13 is mostly wino ( when the soft breaking masses are less than 1 tev ) . then the @xmath12 and @xmath13 do not become nearly degenerate and this type of coannihilation does not generally take place . ( an exception for a class of d - brane models is discussed below . ) more recently it was pointed out that in sugra models , the sleptons ( particularly the lightest stau , @xmath17 ) can become nearly degenerate with the @xmath12 leading to a new type of coannihilation , and this was explored for low and intermediate values of @xmath18  @xcite . ( here @xmath19 give rise to ( @xmath20,@xmath21 ) quark masses ) . in this paper we examine this effect for the full range of @xmath0 , i.e. @xmath22  @xcite . further , in addition to @xmath23 coannihilation , we find the possibility of light stop @xmath24 coannihilation as well as light sbottom @xmath25 coannihilation . we consider these effects for a range of models based on grand unfication of the gauge coupling constants : ( 1 ) minimal supergavity model ( msugra )  @xcite where there is universal soft breaking masses at @xmath26 , ( 2 ) nonuniversal supergravity models  @xcite , where the first two generation soft breaking masses are kept universal at @xmath26 ( to suppress flavor changing neutral currents ) as well as the gaugino masses , but the higgs and third generation soft breaking masses are allowed to be nonuniversal , and ( 3 ) a d - brane model  @xcite based on type iib strings  @xcite where soft breaking masses at @xmath26 of the @xmath27 doublet squark , slepton and higgs are kept degenerate but distinct from the @xmath27 singlets , and similarly the gaugino @xmath27 doublet soft breaking mass is distinct from the @xmath27 singlets . while the first two models have been characterized as sugra models , they can also be realized in string models , and in fact any string model based on grand unification at a high @xmath26 scale with the standard model gauge group holding below @xmath26 , phenomenologically can be treated as a sugra model with an appropriate amount of nonuniversal soft breaking . thus the three models sample the possibilities of universal soft breaking , nonuniversal soft breaking in the squark , slepton and higgs sector but universal gaugino masses , and finally nonuniversality in the gaugino sector as well . since the milky way is perhaps 90@xmath28 dark matter , it is a  laboratory \" for studying the properties of dark matter ( dm ) . possible signals for dm include annihilation in the halo of the galaxy , annihilation in the center of the sun or earth , and direct detection from scattering by terrestial nuclear targets . of these , the last is most promising , and we restrict our discussion here to this . ( for recent discussions of the other possibilities see @xcite ) . in general , the neutralino - nucleus scattering has a spin independent and spin dependent part . however , for heavy nuclei ( aside from exceptional situations discussed below ) , the spin independent scattering dominates , giving rise to approximately equal scattering by neutrons ( @xmath29 ) and protons ( @xmath30 ) in the nucleus . it is thus possible to extract from any data the neutralino - proton cross section , @xmath31 ( subject to astronomical uncertainties about the milky way ) . current detectors ( dama , cdms , ukdmc ) are sensitive to cross sections @xmath32 with a one to two order of magnitude improvement possible in the near future . future detectors ( e.g. genius , cryoarray ) plan to be sensitive down to @xmath33 and thus it is of interest to see what parts of the susy parameter space can be examined by such detectors .    in order to obtain accurate calculations of both the relic density and @xmath31 for large @xmath0 , it is necessary to include a number of corrections in the analysis , and we list these here : ( i ) in relating the theory at @xmath26 to phenomena at the electroweak scale , the two loop gauge and one loop yukawa renormalization group equations ( rge ) are used , iterating to get a consistent susy spectrum . ( ii ) qcd rge corrections are further included below the susy breaking scale for contributions involving light quarks . ( iii ) a careful analysis of the light higgs mass @xmath34 is necessary ( including two loop and pole mass corrections ) as the current lep limits impact sensitively on the relic density analysis . ( iv ) l - r mixing terms are included in the sfermion ( mass)@xmath35 matrices since they produce important effects for large @xmath36 in the third generation . ( v ) one loop corrections are included to @xmath37 and @xmath38 which are again important for large @xmath36 . ( vi ) the experimental bounds on the @xmath39 decay put significant constraints on the susy parameter space and theoretical calculations here include the leading order ( lo ) and nlo corrections for large @xmath36 . note that we have not in the following imposed @xmath40 ( or @xmath41 ) yukawa unification or proton decay constraints as these depend sensitively on unknown post - gut physics . for example , such constraints do not naturally occur in the string models where @xmath42 ( or @xmath43 ) gauge symmetry is broken by wilson lines at @xmath26 ( even though grand unification of the gauge coupling constants at @xmath26 for such string models is still required ) .    in carrying out the above calculations we have included the latest lep bound on the light higgs mass , @xmath44 114 gev  @xcite and the recent nlo corrections for large @xmath0 for the @xmath39 decay  @xcite . ( we have checked numerically that @xcite and @xcite give identical results . ) since there are still some remaining errors in the theoretical calculation of @xmath34 as well as uncertainty in the top quark mass , @xmath45 gev , we will conservatively assume here that @xmath44 110 gev . in the mssm , the constraint on @xmath34 is @xmath0 dependent as @xmath46 production ( @xmath47 is the cp odd higgs ) when @xmath48 is possible for @xmath49 and this can be confused with @xmath50 production . however , in sugra models , radiative electroweak breaking eliminates this part of the parameter space , and so it is correct to impose the lep bound on @xmath34 for the full range of @xmath0 . lep also gives the bound  @xcite @xmath51 102 gev , and the tevatron bound for the gluino @xmath52 is @xcite @xmath53270 gev ( for squark ( @xmath54 ) and gluino masses approximately equal ) . we assume an allowed 2@xmath55 range from the cleo data for the @xmath39 branching ratio  @xcite : @xmath56    in calculating the relic density we will assume the bounds @xmath57 where @xmath58 , @xmath59 is the relic density of the @xmath60 , @xmath61 ( @xmath62 is the present hubble constant and @xmath63 is the newton constant ) and @xmath64kms@xmath65mpc@xmath65 . the lower bound on @xmath66 is somewhat lower than more conventional estimates ( @xmath67 ) , and allows us to consider the possibility that not all the dm are neutralinos . ( in the following , we will mention when results are sensitive to this lower bound . ) accurate determinations by the map and planck satellites of the dark matter relic density will clearly strengthen the theoretical predictions , and already , analyses using combined data from the cmb , large scale structure , and supernovae data suggests that the correct value of the relic density lies in a relatively narrow band in the center of the region of eq . ( [ eq4 ] )  @xcite . we will here , however , use the conservative range given in eq . ( [ eq4 ] ) . supersymmetry theory allows one to calculate the @xmath60-quark cross section and we follow the analysis of @xcite to convert this to @xmath68 scattering . for this one needs the @xmath69 @xmath55 term , @xmath70 @xmath71 and the quark mass ratio @xmath72 . we use here @xmath73 mev @xcite , and @xmath74@xcite . recent analyses , based on new @xmath75 scattering data gives @xmath76 mev@xcite . older @xmath75 data gave @xmath77 mev@xcite . we will use in most of the analysis below the larger number . if the smaller number is used , it would have the overall effect in most of the parameter space of reducing @xmath31 by about a factor of 3 . however , in the special situation for @xmath780 where there is a cancellation of matrix elements , the choice of @xmath79 produces a more subtle effect , and we will exhibit there results from both values . some of the results described below have been mentioned earlier in conference talks  @xcite . there have been in the recent past a number of calculations of @xmath31 in the literature @xcite . however , none include simultaneously all the corrections discussed above , the large @xmath0 range and the recent lep @xmath34 bounds . we find general numerical agreement with other calculations for regions of parameter space where the omitted corrections are small .","summary":"the d - brane models considered possess stau coannihilations regions similar to msugra , as well as small regions of chargino coannihilation . analytic explanations of much of the above phenomena are given .","abstract":"coannihilation effects in neutralino relic density calculations are examined for a full range of supersymmetry parameters including large and large for stau , chargino , stop and sbottom coannihilation with the neutralino . supergravity models possessing grand unification with universal soft breaking ( msugra ) , models with nonuniversal soft breaking in the higgs and third generation sparticles , and d - brane models with nonuniversal gaugino masses were analysed . unlike low where is generally small , stau coannihilation corridors with high are highly sensitive to , and large allows to become as large as 1tev . nonuniversal soft breaking models at high also allow the opening of a new annihilation channel through the s - channel pole with acceptable relic density , allowing a new wide band in the plane with gev and rising to 1 tev . the d - brane models considered possess stau coannihilations regions similar to msugra , as well as small regions of chargino coannihilation . neutralino - proton cross sections are analysed for all models and it is found that future detectors for halo wimps will be able to scan essentially the full parameter space with tev except for a region with where accidental cancellations occur when . analytic explanations of much of the above phenomena are given . the above analyses include current lep bounds on the higgs mass , large nlo correction to the decay , and large susy corrections to the and masses .    epsf.tex ( # 1 width # 2)=#2 # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )"}
{"article_id":"hep-ph0102181","section_id":"c","document":"we have considered in this paper coannihilation effects in dark matter neutalino - proton detection cross sections which arise for large @xmath0 and large values of @xmath1 for models which have grand unification of the gauge coupling constants at the gut scale @xmath26 . coannihilation can occur if the light stau ( @xmath319 ) , light chargino ( @xmath320 ) , light stop ( @xmath290 ) or light sbottom ( @xmath321 ) become nearly degenerate with the neutralino . in order to examine these effects for a wide range of models , we have considered sugra models with universal soft breaking ( msugra ) , nonuniversal soft breaking in the higgs and third generation squarks and sleptons , and finally a d - brane model based on type iib orientifolds which possess nonuniversal gaugino masses . in all these we have imposed the cosmological neutralino relic density constraints as well as accelerator constraints on the susy parameter space ( including in particular the large @xmath0 nlo corrections to the @xmath125 decay  @xcite as well as the large @xmath0 susy corrections to @xmath37 and @xmath38 ) . radiative breaking of @xmath322 at the electroweak weak scale also gives strong constraints on the theory . msugra illustrates some of the effects arising for large @xmath36 . thus for low @xmath36 , the regions in the @xmath323 plane allowed by the relic density constraint eq . ( [ eq4 ] ) is relatively insensitive to @xmath1 . however , for large @xmath36 , the @xmath9 constraint allows only the @xmath324 coannihilation corridors to remain ( except for some small islands when @xmath325 gev ) and as @xmath1 increases , these corridors have increasing @xmath2 . thus @xmath2 can rise to 1 tev for large @xmath80 . ( see e.g. fig . 1 . ) this lowers the value of @xmath281 and even though @xmath281 increases rapidly with @xmath36 , the value of @xmath281 at large @xmath36 and large @xmath1 can be smaller than @xmath281 at @xmath326 , as illustrated in fig.4 . for @xmath123 , however , one generally finds for the parameter space of eqs . ( 6 - 8 ) that @xmath327 pb , and so should be accessible to future detectors . in the high @xmath36 domain , the @xmath9 constraint produces a lower bound on @xmath80 , which decreases with increasing @xmath1 . thus one finds that @xmath328 gev ( @xmath329 gev ) for @xmath330 , @xmath331 , @xmath135 .    for @xmath7 , a special cancellation can occur in msugra allowing @xmath281 to become much less than @xmath306 pb , as has been previously noted for low and intermediate @xmath36  @xcite . the analytic origin of this effect is discussed in sec . 2 . the effect , however , occurs only for a fixed range of @xmath36 . thus the position of these minima begins for @xmath332 at @xmath333 gev , moves to lower @xmath80 until @xmath36 increases to 10 , and then increases to beyond @xmath333 gev at @xmath334 . ( see fig . we note that while the cancellation occurs at a fixed value of @xmath80 , the effects spread over a wide range of @xmath80 and in this region , halo dark matter would be inaccessible to current or planned detectors . however , if the recently reported anomaly in the muon gyromagnetic ratio  @xcite is indeed due to supersymmetry , then @xmath87 is positive and this case would be eliminated . the nonuniversal soft breaking models illustrate new phenomena at large @xmath284 not present in msugra , and one can also understand these effects analytically . thus the value of @xmath190 , obtained from radiative breaking of @xmath322 , is a major element in controlling the value of @xmath281 , and lowering @xmath190 increases @xmath281 . thus for one sign of the nonuniversalities , @xmath281 can be increased by a factor of 10 or more , allowing current detectors to sample the parameter space with @xmath36 as low as @xmath335 . ( see fig . 7 . ) for large @xmath36 a new effect can occur . the value of @xmath190 also controls the gaugino / higgsino content of the @xmath336 , and lowering @xmath190 increases the amount of higgsino in the @xmath336 . this then increases the amount of early universe annihilation via an off shell s - channel @xmath3 boson , which opens an additional allowed region in the @xmath4 plane , considerably wider than the @xmath319 coannihilation corridor and at much higher @xmath2 . ( see fig . 8 . ) ( other simple choices of nonuniversal parameters can also raise the values of @xmath2 for the @xmath319 coannihilation corridor , as illustrated in fig.9 . ) though @xmath2 is large for this @xmath3-channel annihilation , reducing @xmath281 , this effect is compensated by the fact that @xmath190 is decreased ( which raises @xmath281 ) . thus @xmath281 remains relatively large ( see figs . 10 , 11 ) , and this region of parameter space should become experimentally accessible in the relatively near future ( e.g. when cdms moves to the soudan mine ) . the d - brane model examined is quite constrained as all the squark and slepton nonuniversalities are controlled by a single parameter @xmath256 . current detectors are sampling parts of the parameter space where @xmath337 . because these models have also nonuniversal gaugino masses , the lep lower bound on @xmath283 is much smaller than in sugra models , i.e. the same as in the mssm : @xmath338 gev . however , the gaugino nonuniversality still allows the usual type of @xmath23 coannihilation to occur . a unique feature of the gaugino nonuniversality is that @xmath339 can become smaller than @xmath340 allowing the @xmath336 to become mostly wino and a @xmath341 coannihilation domain to exist . however , the near degeneracy of @xmath342 and @xmath336 occurs only for a very small region of parameter space ( when @xmath343 ) . the cancellation phenomena in @xmath281 for @xmath7 also occurs for these d - brane models , the minimum value of @xmath283 where the cancellation is complete occuring at @xmath344 gev for @xmath288 . nonuniversal sugra models also allow for @xmath24 coannihilation to occur . in this case , the light stop is mostly @xmath295 . then for @xmath345 , the landau pole contributions to @xmath300 are negative , and one can chose nonuniversal soft breaking so that the coefficient of @xmath194 is also negative . the @xmath290 then becomes nearly degenerate with the @xmath336 when @xmath346 gev , coannihilation setting in for that domain . actually , @xmath24 can also occur in msugra , but to achieve the near degeneracy one needs @xmath347 . similarly , this coannihilation can occur for the d - brane model but for @xmath310 tev .    in a similar fashion , @xmath25 coannihilation can occur for nonuniversal models when the @xmath321 is mainly @xmath312 . thus one may chose @xmath345 and nonuniversal parameters in @xmath348 so that the coefficient of @xmath194 is negative , making the @xmath321 nearly degenerate with the @xmath336 . this coannihilation only sets in , however , for @xmath349 tev .","summary":"coannihilation effects in neutralino relic density calculations are examined for a full range of supersymmetry parameters including large and large for stau , chargino , stop and sbottom coannihilation with the neutralino . supergravity models possessing grand unification with universal soft breaking ( msugra ) , models with nonuniversal soft breaking in the higgs and third generation sparticles , and d - brane models with nonuniversal gaugino masses were analysed . unlike low where is generally the above analyses include current lep bounds on the higgs mass , large nlo correction to the decay , and large susy corrections to the and masses .   ","abstract":"coannihilation effects in neutralino relic density calculations are examined for a full range of supersymmetry parameters including large and large for stau , chargino , stop and sbottom coannihilation with the neutralino . supergravity models possessing grand unification with universal soft breaking ( msugra ) , models with nonuniversal soft breaking in the higgs and third generation sparticles , and d - brane models with nonuniversal gaugino masses were analysed . unlike low where is generally small , stau coannihilation corridors with high are highly sensitive to , and large allows to become as large as 1tev . nonuniversal soft breaking models at high also allow the opening of a new annihilation channel through the s - channel pole with acceptable relic density , allowing a new wide band in the plane with gev and rising to 1 tev . the d - brane models considered possess stau coannihilations regions similar to msugra , as well as small regions of chargino coannihilation . neutralino - proton cross sections are analysed for all models and it is found that future detectors for halo wimps will be able to scan essentially the full parameter space with tev except for a region with where accidental cancellations occur when . analytic explanations of much of the above phenomena are given . the above analyses include current lep bounds on the higgs mass , large nlo correction to the decay , and large susy corrections to the and masses .    epsf.tex ( # 1 width # 2)=#2 # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )"}
{"article_id":"quant-ph9802062","section_id":"i","document":"it is quite possible that the first implementations of quantum computers will not be fully quantum mechanical . instead , they may have two parts : a quantum part and a classical part with a communication between two parts . in this case , the quantum part will be considerably more expensive than the classical part . therefore , it will be useful to make the quantum part as small as possible even if it leads to some ( reasonable ) increases in the size of the classical part . this motivates the study of systems with a small quantum mechanical part . quantum finite automata ( qfa ) is a theoretical model for such systems . @xcite introduced both 1-way and 2-way qfas , with emphasis on 2-way automata because they are more powerful . however , the model of 2-way qfas is not quite consistent with the idea of a system with a small quantum mechanical part . @xcite allows superpositions where different parts of superposition have the head of qfa at different locations . ( even more , using such superpositions was the main idea in the proof that 2-way qfas are more powerful than classical finite automata . ) this means that the position of the head must be encoded into quantum state . hence , the number of quantum states necessary to implement a 2-way qfa is not a constant but grows when the size of the input increases . this also makes state transformations more complicated ( and more difficult to implement ) . hence , we think that more attention should be given to the study of simpler models like 1-way qfas . a 1-way quantum automaton is a very reasonable model of computation and it is easy to see how it can be implemented . the finite dimensional state - space of a qfa corresponds to a system with finitely many particles . each letter has a corresponding unitary transformation on the state - space . a classical device can read symbols from the input and apply the corresponding transformations to the quantum mechanical part . results about 1-way qfas in @xcite were quite pessimistic . it was shown that the class of languages recognized by 1-way qfas is a proper subset of regular languages . we continue the investigation of 1-way qfas and show that , despite being limited in some situations , they perform well in other situations . our first results consider relations between 1-way qfas and 1-way reversible automata . clearly , a 1-way reversible automaton is a special case of a qfa and , therefore , can not recognize all regular languages . it is a natural question whether 1-way qfas are more powerful than 1-way reversible automata . interestingly , the answer depends on the accepting probability of a qfa . if a qfa gives a correct answer with a large probability ( greater than 7/9 ) , it can be replaced by a 1-way reversible automaton . however , this is not true for 0.68 ... and smaller probabilities . then , we show that qfas can be much more space - efficient than deterministic and even probabilistic finite automata . namely , there is a 1-way qfa that can check whether the number of letters received from the input is divisible by a prime @xmath0 with only @xmath1 states ( this is equivalent to @xmath2 bits of memory ) . any deterministic or probabilistic finite automaton needs @xmath0 states ( @xmath3 bits of memory ) . we think that this space - efficient quantum algorithm may be interesting for design of other quantum algoritms as well .    finally , we consider modifications of 2-way quantum automata where the head is always at the same position for all parts of superposition . modified 2-way qfas can be implemented with a quantum system of constant size . several modifications are proposed . in one of our models ( 1-way qfas with a probabilistic preprocessing ) , some non - regular languages can be recognized .","summary":"we show that , if an automaton is required to give the correct answer with a large probability ( greater than 7/9 ) , then any 1-way qfa can be simulated by a 1-way reversible automaton . however , quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata .    we think that this construction may be useful for design of other space - efficient quantum algorithms .    epsf.sty    6.5 in 8.25 in -0.25 in","abstract":"we study 1-way quantum finite automata ( qfas ) . first , we compare them with their classical counterparts . we show that , if an automaton is required to give the correct answer with a large probability ( greater than 7/9 ) , then any 1-way qfa can be simulated by a 1-way reversible automaton . however , quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata .    second , we show that 1-way qfas can be very space - efficient . we construct a 1-way qfa that is exponentially smaller than any equivalent classical ( even randomized ) finite automaton . we think that this construction may be useful for design of other space - efficient quantum algorithms .    third , we consider several generalizations of 1-way qfas . here , our goal is to find a model which is more powerful than 1-way qfas keeping the quantum part as simple as possible .    epsf.sty    6.5 in 8.25 in -0.25 in"}
{"article_id":"cs0605064","section_id":"i","document":"reasoning about topological relations between regions in space is recognized as one of the most important and challenging research areas within spatial reasoning in artificial intelligence ( ai ) and philosophy , spatial and constraint databases , and geographical information systems ( giss ) . research in this area can be classified according to the logical apparatus employed :     first - order theories of topological relations between regions , as studied in ai and philosophy @xcite , spatial databases @xcite and from an algebraic viewpoint in @xcite ;     purely existential theories formulated as constraint satisfaction systems over jointly exhaustive and mutually disjoint sets of topological relations between regions @xcite     modal logics of space with operators interpreted by the closure and interior operator of the underlying topological space and propositions interpreted as subsets of the topological space , see e.g. , @xcite .    a similar classification can be made for temporal reasoning : we have general first - order theories  @xcite , temporal constraint systems @xcite and modal temporal logics like prior s tense logics , ltl , and ctl @xcite . surprisingly , one of the most natural approaches to temporal reasoning has not yet found a fully developed analogue on the spatial reasoning research agenda : halpern and shoham s modal logic of intervals @xcite , in which propositions are evaluated at intervals ( rather than time points ) , and where reference to other intervals is enabled by modal operators interpreted by allen s 13 relations between intervals , see also @xcite . despite its bad computational behavior ( undecidable , usually not even r.e . ) , this framework proved rather fruitful and influential in temporal reasoning , see e.g.   @xcite .    in this paper , we consider modal logics in which propositions are evaluated at the regions of topological spaces , and reference to other regions is enabled by modal operators interpreted as topological relations . for defining such logics , the two most important decisions to be made are choosing an appropriate set of relations and identifying a suitable notion of a `` region '' in a topological space .    regarding the relations , in the initially mentioned research areas there appears to be consensus that the eight egenhofer - franzosa ( or @xmath1 ) relations , which have been independently introduced in @xcite and @xcite , and their coarser relative @xmath2 consisting of only five relations , are the most fundamental sets of relations between regions of topological spaces  both from a theoretical and a practical viewpoint , see e.g.  @xcite . therefore , in the current paper we concentrate on these two sets of relations . we should note that modal logics based on the egenhofer - franzosa relations have been suggested in an early paper by cohn @xcite and further considered in  @xcite . however , it proved difficult to analyze the expressive power and computational behavior of such logics : despite several efforts , to the best of our knowledge no results have been obtained so far . concerning the regions of a topological space , we adopt a rather relaxed view : we generally assume that regions are non - empty regular closed subsets of a topological space , but we do not require that _ every _ such subset is a region . this view allows us to consider logical structures , henceforth called _ region structures _ , that are based on various kinds of regions . among others , we consider the following options :     region structures in which the set of regions is _ exactly _ the set of non - empty regular closed subsets of a topological space .  in the euclidean space @xmath3 , region structures where regions are identified with all non - empty convex regular closed sets , or with all hyper - rectangles .  substructures of the above region structures : for example , we may admit region structures in which only some , but not all hyper - rectangles of @xmath4 are regions . to distinguish this case from the former two , we call region structures in which all regions of a particular kind are present _ full _ region structures .  finite substructures of the above region structures . the rationale behind the latter two choices of structures is that , for certain applications , it is sufficient to require the presence of only those regions in region structures that are inhabited by spatial objects . if it is known that there are only finitely many such objects , but their exact number is unknown , then finite substructures are the appropriate choice .    the main purpose of this paper is to _ introduce modal logics of topological relations in a systematic way , to perform an investigation of their expressiveness and relationships , and to analyze their computational behavior_. regarding expressiveness , our main result concerns the relationship to first - order theories of topological relations . the expressive power of our modal logics is incomparable with that standard theories of this kind since modal logics offer an infinite supply of propositional variables corresponding to unary predicates of first - order logic . in contrast , standard first - order theories of topological relations offer only eight binary predicates interpreted as topological relations , and no unary predicates  @xcite . therefore , we consider the extension of first - order theories of topological relations with an infinite number of `` free '' unary predicates . then , we can show that our logics based on the egenhofer - franzosa or relations has exactly the same expressive power as the two - variable fragment of first - order logic on the same set of relations ( indeed , this holds for any mutually disjoint and jointly exhaustive set of topological relations ) . we also show that first - order logic is exponentially more succinct . we argue that the availability of unary predicates is essential for a wide range of application areas : in contrast to describing only purely topological properties of regions , it allows one to also capture other properties such as being a country ( in a gis ) , a ball ( for a soccer - playing robot ) , or a protected area ( in a spatial database ) . in our modal logics , we can thus formulate constraints based on non - spatial properties such as `` there are no two overlapping regions that are both countries '' and `` every river is connected to an ocean or a lake '' . the main results of this paper concern the computational behavior of modal logics of topological relations . we prove a very general undecidability result that captures all modal logics of the relations that are determined by a class of region structures whose regions are ( not necesserily all ) non - empty regular closed sets , and that contains at least one infinite structure . it is interesting to note that this result also covers logics that are determined by _ substructures _ of region structures . in particular , it captures the substructures of the real line where regions are intervals , and thus improves upon undecidability results for interval temporal logics by halpern and shoham that do not capture substructures of interval structures @xcite . using a variation of the proof of our central theorem , we can even show that logics based on finite substructures of region structures are undecidable . although our results show that moving from full region structures to substructures does not help to regain decidability , there is an improvement in computational complexity : we show that most logics of relations based on full region structures are @xmath5-hard and thus not recursively enumerable . in contrast , we also prove that many logics determined by substructures _ are _ recursively enumerable . finally , we establish the undecidability of a number of modal logics based on the relations . the result is less general and , for example , does not cover the substructure case . recursive enumerability of -based logics is left as an open problem . this paper is organized as follows : in section  [ sect : structures ] , we introduce region structures as the semantical basis for modal logics of topological relations . the modal language is introduced in section  [ sect : languages ] . in this section , we also compare its expressiveness to that of first - order logic . additionally , we show that our modal logics are strictly more expressive than topological constraint satisfaction problems . in section  [ sect : logics ] , we introduce a number of natural modal logics based on the egenhofer - franzosa relations that are induced by different notions of regions , and briefly analyze their relationship . in section  [ sect : rcc8undec ] , we then prove the central undecidability result capturing basically all interesting modal logics of relations determined by sets of region structures containing at least one infinite structure . for logics of full region structures , this is strengthened to a @xmath5-hardness proof in section  [ sect : notre ] . we also prove recursive enumerability of many modal logics based on substructures of region structures . in section  [ sect : finite ] , we prove undecidability of logics determined by classes of finite region structures . finally , in section  [ sect : rcc5 ] we consider modal logics based on the relations .","summary":"logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems , spatial and constraint databases , and spatial reasoning in ai . in analogy with halpern and shoham s modal logic of time intervals based on the allen relations , we introduce a family of modal logics equipped with eight modal operators that are interpreted by the egenhofer - franzosa ( or ) relations between regions in topological spaces such as the real plane . we investigate the expressive power and computational complexity of logics obtained in this way . it turns out that our modal logics have the same expressive power as the two - variable fragment of first - order logic , but are exponentially less succinct . the complexity ranges from ( undecidable and ) recursively enumerable to-hard , where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces . as our undecidability results also capture logics based on the real line , they improve upon undecidability results for interval temporal logics by halpern and shoham . we also analyze modal logics based on the five relations , with similar results regarding the expressive power , but weaker results regarding the complexity .","abstract":"logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems , spatial and constraint databases , and spatial reasoning in ai . in analogy with halpern and shoham s modal logic of time intervals based on the allen relations , we introduce a family of modal logics equipped with eight modal operators that are interpreted by the egenhofer - franzosa ( or ) relations between regions in topological spaces such as the real plane . we investigate the expressive power and computational complexity of logics obtained in this way . it turns out that our modal logics have the same expressive power as the two - variable fragment of first - order logic , but are exponentially less succinct . the complexity ranges from ( undecidable and ) recursively enumerable to-hard , where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces . as our undecidability results also capture logics based on the real line , they improve upon undecidability results for interval temporal logics by halpern and shoham . we also analyze modal logics based on the five relations , with similar results regarding the expressive power , but weaker results regarding the complexity ."}
{"article_id":"cond-mat9906451","section_id":"i","document":"when a gas or vapour is brought into contact with a clean solid surface , parts of its molecules will become reversibly attached to the surface in the form of an adsorbed layer . knowledge of equilibrium and dynamical properties of such adsorbed layers is essential for many practical applications , including coating , gluing and lubrication .    following the seminal work of langmuir ( see , e.g. ref.@xcite ) , the equilibrium properties of adsorbed layers have been extensively studied and a great number of important developments have been made . in particular , further analysis included more realistic forms of intermolecular interactions or allowed for the possibility of multilayer formation . as a result , different possible phase transformations have been predicted and different forms of adsorption isotherms have been found , which well explain available experimental data ( see , e.g. refs.@xcite ) .    some effort has been also invested to the understanding of molecular diffusion in adsorbed layers , which has a strong impact on their global dynamical behavior . for instance , diffusional processes control the rates of spreading of molecular films on solid surfaces @xcite , spontaneous or forced dewetting of monolayers @xcite or island formation @xcite . here , some approximate analytical results have been obtained for both dynamics of an isolated adatom on a corrugated surface and collective diffusion , describing spreading of the macroscopic density fluctuations in interacting adsorbates being in contact with the vapour phase @xcite . on the other hand , most of available studies of the tracer diffusion in adsorbed layers , which provides a useful information about their intrinsic viscosity , pertain to strictly two - dimensional models excluding the possibility of particles adsorption and desorption ( see , e.g. refs.@xcite and references therein ) . except for ref.@xcite , which studied driven tracer dynamics in a somewhat artificial one - dimensional model , analysis of the tracer diffusion in adsorbed monolayers undergoing exchanges with the vapour phase seems to be lacking at present .    in this paper we study the diffusion properties of a driven tracer in a two - dimensional adsorbed monolayer undergoing continuous exchanges with the vapour . the system we consider consists of ( i ) a solid substrate , which is modeled in a usual fashion as a regular square lattice of adsorption sites supporting at most a single occupancy , ( ii ) a monolayer of adsorbed , mobile hard - core particles in contact with a vapour and ( iii ) a single , hard - core tracer particle . each monolayer particle moves randomly along the lattice by performing hopping motion on the vacant neighboring lattice sites . the monolayer particles undergo continuous exchanges with a vapour phase , i.e. may desorb from and adsorb onto the lattice with some prescribed rates dependent on the vapour pressure , temperature and the interactions with the solid substrate . on the contrary , the tracer particle is constrained to move on the two - dimensional lattice only , i.e. it can not desorb to the vapour , and it is subject to a constant external force @xmath4 . hence , the tracer performs a biased random walk , which is constrained by the hard - core interactions with the monolayer particles , and always remains within the monolayer , probing its response on the internal perturbancy or , in other words , its frictional properties . here we focus on the limit of sufficiently large external force , such that the tracer may move only in one direction , but not large enough to make it slide regardless of the surface corrugation . the results for the general case of arbitrary @xmath4 , which allow us to deduce the analog of the stokes formula for 2d adsorbed monolayers and to define the corresponding friction coefficient , will be presented elsewhere @xcite .    in terms of a mean - field - type approximation of ref.@xcite , which is based on the decoupling of the tracer - particle - particle correlation functions into the product of pair - wise correlations , we define the stationary density profiles of the monolayer particles , as seen from the moving tracer , and we determine analytically the terminal velocity @xmath0 of the tracer . we show that the adsorbed monolayer particles tend to accumulate in front of the driven tracer , creating a sort of a `` traffic jam '' , which impedes its motion . thus the density profile around the tracer is highly inhomogeneous : the local density of the monolayer particles in front of the tracer is higher than the average and approaches the average value as an exponential function of the distance from the tracer . the characteristic length and the amplitude of the density relaxation function are calculated explicitly . on the other hand , past the tracer the local density is lower than the average ; we show that depending on the condition whether the number of particles in the monolayer is explicitly conserved or not , the local density past the tracer may tend to the average value either as an exponential or as an @xmath5 function of the distance , revealing in the latter case especially strong memory effects and strong correlations between the particle distribution in the monolayer and the tracer position .    further on , we find that the terminal velocity of the tracer particle depends explicitly on the excess density in the `` jammed '' region in front of the tracer . this excess density , in turn , depends on the magnitude of the velocity , as well as on the rate of the adsorption / desorption processes and on the rate at which the particles can diffuse away of the tracer . the interplay between the jamming of the monolayer , produced by the tracer particle , and the rate of its homogenization due to diffusion and adsorption / desorption processes , manifests itself as a medium - induced frictional force exerted on the tracer , whose magnitude depends on the tracer velocity . as a consequence of such a non - linear coupling , in the general case , ( i.e. for arbitrary adsorption / desorption rates and particles diffusion coefficient ) , @xmath0 can be found only implicitly , as the solution of a certain non - linear equation relating @xmath0 to the system parameters . this equation simplifies considerably in the limit of small or large particles diffusivity , in which two cases exlicit asymptotic expressions for the tracer velocity are obtained . we finally remark , that a qualitatively similar physical effect was predicted recently for a different model system involving a charged particle moving at a constant speed at a small distance above the surface of an incompressible , infinitely deep liquid . it has been shown in refs.@xcite , that the interactions between the moving particle and the fluid molecules induce an effective frictional force exerted on the particle , producing a local distortion of the liquid interface , - a bump , which travels together with the particle and increases effectively its mass . the mass of the bump , which is analogous to the jammed region appearing in our model , depends itself on the particle s velocity resulting in a non - linear coupling between the medium - induced frictional force exerted on the particle and its velocity @xcite . the paper is structured as follows : in section 2 , we formulate the model and introduce basic notations . in section 3 , we write down the dynamical equations which govern the time evolution of the monolayer particles and of the tracer . section 4 is devoted to the analytical solution of these evolution equations in the limit @xmath6 ; here we also present some general results on the form of the density profiles around stationary moving tracer and on the tracer terminal velocity , which is given implicitly , as the solution of a transcendental equation . in section 5 , we derive explicit asymptotic results for the tracer terminal velocity in the limits of small and large particles diffusivities . as well , here we discuss the forms of the density profiles at intermediate scales . corresponding asymptotical behavior of the density profiles at large distances from the tracer is discussed in section 6 . finally , we conclude in section 7 with a brief summary and discussion of our results .","summary":"we study the dynamics of a tracer particle , which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard - core particles undergoing continuous exchanges with a vapour phase . in terms of a mean - field - type approach , based on the decoupling of the tracer - particle - particle correlation functions into the product of pairwise , tracer - particle correlations , we determine the density profiles of the monolayer particles , as seen from the stationary moving tracer , and calculate its terminal velocity , . in the general case the latter is determined implicitly , as the solution of a certain transcendental equation . in two extreme limits of slow and fast monolayer particles diffusion , we obtain explicit asymptotic forms of . we show next that the density profile in the monolayer is strongly inhomogeneous : in front of the stationary moving tracer the local density is higher than the average value , , and approaches as an exponential function of the distance from the tracer . past the tracer the local density is lower than and the approach to may proceed differently depending whether the particles number in the monolayer is not or is explicitly conserved . in the former case the approach is described by an exponential dependence with a different characteristic length , compared to the behavior in front of the tracer ; in the latter case , the density tends to algebraically . the characteristic lengths and the amplitudes of the density relaxation functions are also determined explicitly .   ","abstract":"we study the dynamics of a tracer particle , which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard - core particles undergoing continuous exchanges with a vapour phase . in terms of a mean - field - type approach , based on the decoupling of the tracer - particle - particle correlation functions into the product of pairwise , tracer - particle correlations , we determine the density profiles of the monolayer particles , as seen from the stationary moving tracer , and calculate its terminal velocity , . in the general case the latter is determined implicitly , as the solution of a certain transcendental equation . in two extreme limits of slow and fast monolayer particles diffusion , we obtain explicit asymptotic forms of . we show next that the density profile in the monolayer is strongly inhomogeneous : in front of the stationary moving tracer the local density is higher than the average value , , and approaches as an exponential function of the distance from the tracer . past the tracer the local density is lower than and the approach to may proceed differently depending whether the particles number in the monolayer is not or is explicitly conserved . in the former case the approach is described by an exponential dependence with a different characteristic length , compared to the behavior in front of the tracer ; in the latter case , the density tends to algebraically . the characteristic lengths and the amplitudes of the density relaxation functions are also determined explicitly .    * directed random walk in adsorbed monolayer *    * o.bnichou , a.m.cazabat , m.moreau and g.oshanin *    _ laboratoire de physique thorique des liquides ( cnrs - umr 7600 ) , universit pierre et marie curie , 4 place jussieu , 75252 paris cedex 05 , france + _    key words : hard - core lattice gas , langmuir adsorption / desorption model , biased tracer diffusion .    pacs numbers : 05.40-a , 66.30.lw , 68.45.da"}
{"article_id":"cond-mat9906451","section_id":"r","document":"\\(a ) for small @xmath148 , @xmath152 and @xmath149 , @xmath317 and @xmath318 which means that @xmath274 is logarithmically small with @xmath148 , while @xmath273 is large . note also that @xmath319 can be a non - monotonous function of @xmath171 when @xmath320 . + ( b ) for small @xmath148 , @xmath151 and @xmath149 , @xmath321 and @xmath322 i.e. , @xmath274 is logarithmically small with @xmath96 , while @xmath273 is large . + ( c ) for small @xmath148 , @xmath151 and @xmath150 , @xmath323 and @xmath324 hence , in this case @xmath325 is large , since it is inversely proportional to the small parameter @xmath96 , but @xmath319 is small . + ( d ) for @xmath154 and @xmath152 , @xmath326 and @xmath327 i.e. , here , likewise to the case ( c ) , @xmath274 appears to be large and @xmath273 is small . on the other hand , if we suppose that @xmath151 ( no adsorption / desorption ) and @xmath328 , we find a bit different forms of @xmath273 and @xmath274 ; namely , @xmath329 and @xmath330 i.e. , similarly to the above considered case , @xmath274 is large and @xmath273 is small . note also that , despite the fact that the tracer velocity in the cases @xmath152 and @xmath195 is given by the same expression in eq.([vel ] ) , the characteristic properties of the density profile appear to be different when @xmath92 is zero or @xmath160 . consider next the asymptotical behavior of @xmath290 and @xmath291 in the limit of slow and fast particles diffusion . + for small @xmath148 , @xmath152 and @xmath149 , which corresponds to the limit ( a ) in our previous notations , @xmath331 and @xmath332 i.e. @xmath291 tends to a constant value when @xmath164 , which means that here @xmath333 , while @xmath334 diverges when @xmath155 . note , however , that we evidently have @xmath335 . this means that in the limit ( a ) the density profiles around the tracer are strongly asymmetric ; in front of the tracer we have a condensed , `` traffic''-jam - like region , characterized by a high amplitude but of a relatively short spatial extent , while past the tracer there is a depleted region which extends on much longer scales but has a considerably smaller amplitude . + next , for high particles diffusivity and @xmath152 , which corresponds to the limit ( d ) , one encounters an exactly opposite situation . here the values of the characteristic lengths and the amplitudes of the condensed and the depleted regions almost coincide , i.e. @xmath336 and @xmath337 , where @xmath273 and @xmath274 are given by eqs.([2 ] ) and ( [ 1 ] ) . consider next the asymptotic forms of the decay amplitudes in eq.([am ] ) . using the results of the previous section , we find then the following asymptotical results : + in the limit of small @xmath148 , @xmath151 and @xmath149 , which corresponds to the limit ( b ) of section 5 , @xmath338 which means that the amplitude is large in this limit , since @xmath95 . + in the limit of small @xmath148 , @xmath151 and @xmath150 , ( limit ( c ) ) , @xmath339 since this limit can be only realized at sufficiently high particles densities , @xmath340 , we have then that in this case the amplitude should be small . + lastly , in the limit @xmath154 ( limit ( d ) ) we find @xmath341 i.e. which signifies that in this case the decay amplitude is small . m .- c.desjonqures and d.spanjaard , _ concepts in surface physics _ , ( springer verlag , berlin , 1996 ) d.j.shaw , _ introduction to colloid and surface chemistry _ , ( butterworth - heinemann ltd . , oxford , 1992 ) r.h.fowler and e.a.guggenheim , _ statistical thermodynamics _ , ( cambridge university press , london , 1939 ) s.f.burlatsky , g.oshanin , a.m.cazabat and m.moreau , phys . * 76 * , 86 ( 1996 ) s.f.burlatsky , g.oshanin , a.m.cazabat , m.moreau and w.p.reinhardt , phys . e * 54 * , 3892 ( 1996 ) d.ausserr , f.brochard-wyart and p.g.de gennes , c. r. acad . paris * 320 * , 131 ( 1995 ) b.n.j.persson and e.tosatti , phys . b * 50 * , 5590 ( 1994 ) g.oshanin , j.de coninck , a.m.cazabat and m.moreau , phys . rev . e * 58 * , r20 ( 1998 ) g.oshanin , j.de coninck , a.m.cazabat and m.moreau , j. mol . liquids * 76 * , 195 ( 1998 ) see , e.g. h.jeong , b.kahng and d.e.wolf , physica a * 245 * , 355 ( 1997 ) ; j.g.amar and f.family , phys . lett . * 74 * , 2066 ( 1995 ) and references therein r.gomer , rep . . phys . * 53 * , 917 ( 1990 ) h.j.kreuzer , in : _ diffusion at interfaces : microscopic concepts _ , springer series in surface science , vol . * 12 * ( springer - verlag , berlin , 1986 ) m.a.zaluska-kotur and l.a.turski , physica a * 195 * , 375 ( 1993 ) ; z.w.gortel , m.a.zaluska-kotur and l.a.turski , phys . rev . b * 52 * , 16916 ( 1995 ) r.ferrando , r.spadacini and g.e.tommei , phys . rev . e * 48 * , 2437 ( 1993 ) and references therein k.w.kehr and k.binder , in : _ application of the monte carlo method in statistical physics _ , ed . k.binder , ( springer - verlag , berlin , 1987 ) and references therein . k.nakazato and k.kitahara , prog . . phys . * 64 * , 2261 ( 1980 ) r.a.tahir-kheli and r.j.elliott , phys . b * 27 * , 844 ( 1983 ) h.van beijeren and r.kutner , phys . * 55 * , 238 ( 1985 ) m.brummelhuis and h.hilhorst , physica a * 156 * , 575 ( 1989 ) j.de coninck , g.oshanin and m.moreau , europhys . lett . * 38 * , 527 ( 1997 ) o.bnichou , a.m.cazabat , a.lemarchand , m.moreau and g.oshanin , cond - mat/9810163 o.bnichou , a.m.cazabat , m.moreau and g.oshanin , in preparation s.f.burlatsky , g.oshanin , a.mogutov and m.moreau , phys . a * 166 * , 230 ( 1992 ) ; s.f.burlatsky , g.oshanin , m.moreau and w.p.reinhardt , phys . e * 54 * , 3165 ( 1996 ) e.raphael and p.g.de gennes , europhys . lett . * 31 * , 293 ( 1995 ) e.raphael and p.g.de gennes , phys . e * 53 * , 3448 ( 1996 ) c.landim , s.olla and s.b.volchan , commun . phys . * 192 * , 287 ( 1998 ) h.s.wilf , _ generatingfunctionology _ , ( academic press , new york , 1990 ) e.montroll and g.weiss , j. math . * 6 * , 167 ( 1965 ) b.d.hughes , _ random walks and random environments _ , ( oxford science publ . , oxford , 1995 ) w.mccrea and f.whipple , proc . * 60 * , 281 ( 1940 ) ; see also f.spitzer , _ principles of random walk _ , ( van nostrand , princeton , new jersey , 1964 ) p.flajolet and a.m.odlyzko , siam journal on discrete math . * 3 * , 216 ( 1990 )     + fig.1 . two - dimensional lattice of adsorption sites partially occupied by identical , mobile hard - core particles ( grey spheres ) undergoing continuous exchanges with the reservoir - the vapor phase . particles desorption and adsorption probabilities are denoted by @xmath129 and @xmath128 , respectively . the dark grey sphere with an arrow denotes the tracer particle , whose motion is completely directed by external field @xmath4 . sketch of the density profiles at finite distances from the tracer . the black circle denotes the tracer particle and the arrow represents the direction of the external force exerted on the tracer . _ limit ( a ) _ : @xmath342 , and @xmath343 .","summary":"* directed random walk in adsorbed monolayer *    * o.bnichou , a.m.cazabat , m.moreau and g.oshanin *    _ laboratoire de physique thorique des liquides ( cnrs - umr 7600 ) , universit pierre et marie curie , 4 place jussieu , 75252 paris cedex 05 , france + _    key words : hard - core lattice gas , langmuir adsorption / desorption model , biased tracer diffusion .   ","abstract":"we study the dynamics of a tracer particle , which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard - core particles undergoing continuous exchanges with a vapour phase . in terms of a mean - field - type approach , based on the decoupling of the tracer - particle - particle correlation functions into the product of pairwise , tracer - particle correlations , we determine the density profiles of the monolayer particles , as seen from the stationary moving tracer , and calculate its terminal velocity , . in the general case the latter is determined implicitly , as the solution of a certain transcendental equation . in two extreme limits of slow and fast monolayer particles diffusion , we obtain explicit asymptotic forms of . we show next that the density profile in the monolayer is strongly inhomogeneous : in front of the stationary moving tracer the local density is higher than the average value , , and approaches as an exponential function of the distance from the tracer . past the tracer the local density is lower than and the approach to may proceed differently depending whether the particles number in the monolayer is not or is explicitly conserved . in the former case the approach is described by an exponential dependence with a different characteristic length , compared to the behavior in front of the tracer ; in the latter case , the density tends to algebraically . the characteristic lengths and the amplitudes of the density relaxation functions are also determined explicitly .    * directed random walk in adsorbed monolayer *    * o.bnichou , a.m.cazabat , m.moreau and g.oshanin *    _ laboratoire de physique thorique des liquides ( cnrs - umr 7600 ) , universit pierre et marie curie , 4 place jussieu , 75252 paris cedex 05 , france + _    key words : hard - core lattice gas , langmuir adsorption / desorption model , biased tracer diffusion .    pacs numbers : 05.40-a , 66.30.lw , 68.45.da"}
{"article_id":"1508.06156","section_id":"i","document":"remobilization concerns the in - vessel release of dust residing away from its production site , whereas the general term mobilization also includes the release of dust upon creation ( cracking , melt layer splashing , delamination , arcing ) . it has been long realised that dust remobilization is a major safety issue for iter and future fusion devices , owing to the possibility of radioactive or toxic dust release upon loss of vacuum accidents ( lovas)@xcite . in such scenarios , air ingress in the vacuum vessel creates an outward flow after pressure equilibration which leads to hydrodynamic forces that can potentially mobilize dust grains@xcite . moreover , dust remobilization upon disruptions has been consistently observed in multiple tokamaks by cameras@xcite and other diagnostics@xcite . in such cases , vibrations of plasma - facing components ( pfcs ) , thermal shocks@xcite or large currents induced by fast transients most probably provide the mobilizing forces . finally , dust can also be remobilized in normal operating conditions by plasma forces . regardless of the scenario , remobilization is a consequence of momentum imbalance in the `` dust - pfc contact '' . hence , the main differentiating factor between remobilization in lovas , disruptions and normal operating conditions is the mobilizing force or torque .    deeper understanding of the mechanism of remobilization by plasma forces can play an important role in diverse plasma - wall interaction issues .    * _ specification of realistic initial conditions for the ejection speed and angle of remobilized dust grains_. this will increase the predictive power of dust transport codes as far as the grain penetration depth and the amount of dust - associated impurities are concerned . consequently , this can lead to a more accurate modelling of transient impurity events@xcite , intense radiation spikes most likely associated with mobile dust re - distributed by a temporally adjacent disruptive discharge@xcite . * _ specification of realistic dust trajectory termination conditions_. so far , migraine is the only code that treats dust - wall interactions@xcite and thus has the potential to make predictions with respect to the in - vessel sites where dust will most likely accumulate . however , in the current version of migraine@xcite , dust trajectories terminate for impacts that satisfy the sticking condition since remobilization is not accounted for . we stress that identification of preferred dust accumulation sites is the first step in developing efficient _ in situ _ dust removal techniques . for instance , in iter , mechanical dust removal is envisaged and hence successful predictions of the location of such sites can lead to dust collection by the divertor remote handling system or the multi - purpose deployment system@xcite . * _ quantification of dust amassment in the grooves of castellated pfcs_. in iter , pfcs will be castellated , i.e. split into small segments separated by thin gaps@xcite . the gap entrance corresponds to a small fraction of the plasma - exposed area ( the gap width is @xmath0 mm ) , implying that dust trajectories directly terminating in the gaps can be considered rare . two mechanisms related with the physics of the dust - pfc contact can be more efficient : dust remobilization from neighbouring monoblocks ( provided that the release velocity is nearly tangential and low enough to ensure that the motion is governed not only by inertia but also by potential effects ) or dust impacting and subsequently rolling or sliding on neighbouring monoblocks . * _ evaluation of the gap trapping efficiency . _ a closely related issue concerns grains already residing in the gaps and in particular whether they are permanently stuck therein or can be remobilized during normal plasma conditions or by a disruption .    despite its importance , the remobilization of dust grains in normal operating conditions has not been properly considered thus far . there are no relevant experimental results , whereas previous theoretical investigations have either erroneously neglected the role of adhesion@xcite or adopted an oversimplifying description of the phenomenon@xcite . in this work , we carry out the first combined experimental and theoretical study of dust remobilization in fusion plasmas during normal operating conditions . the main theoretical aspects of remobilization are analyzed , the role of adhesion in both establishing and breaking the dust - pfc contact is highlighted , whereas generic remobilization conditions are formulated . an experimental technique is proposed based on controlled pre - adhesion of dust grains on samples and detailed mapping of the deposition profiles prior to and post plasma exposure . such a technique realistically mimics naturally occurring remobilization . proof - of - principle of the technique is provided by experiments with planar tungsten samples in the textor tokamak and the extrap - t2r reversed - field pinch . it is shown that plasma forces are sufficient to remobilize the grain and first quantitative estimates of the remobilization activity are performed . further experiments in the pilot - psi linear device enabled studies under varying plasma conditions and magnetic field topology . they were complemented by camera observations allowing for estimates of the ejection speed and angle .","summary":"the first combined experimental and theoretical studies of dust remobilization by plasma forces are reported . the main theoretical aspects of remobilization in fusion devices under steady state conditions are analyzed . in particular , the dominant role of adhesive forces is highlighted and generic remobilization conditions - direct lift - up , sliding , rolling - are formulated . a novel experimental technique is proposed , based on controlled adhesion of dust grains on tungsten samples combined with detailed mapping of the dust deposition profile prior and post plasma exposure . proof - of - principle experiments in the textor tokamak and the extrap - t2r reversed - field pinch are presented .","abstract":"the first combined experimental and theoretical studies of dust remobilization by plasma forces are reported . the main theoretical aspects of remobilization in fusion devices under steady state conditions are analyzed . in particular , the dominant role of adhesive forces is highlighted and generic remobilization conditions - direct lift - up , sliding , rolling - are formulated . a novel experimental technique is proposed , based on controlled adhesion of dust grains on tungsten samples combined with detailed mapping of the dust deposition profile prior and post plasma exposure . proof - of - principle experiments in the textor tokamak and the extrap - t2r reversed - field pinch are presented . the versatile environment of the linear device pilot - psi allowed for experiments with different magnetic field topologies and varying plasma conditions that were complemented with camera observations ."}
{"article_id":"1508.06156","section_id":"c","document":"the present studies refer exclusively to metallic dust remobilization from metallic surfaces under normal operating conditions ( in absence of transient events ) with the grain motion triggered by the action of plasma forces . as will be discussed in details below , camera observations in pilot - psi clearly illustrate that dust remobilization takes place _ during plasma exposure_. this is further supported by the reference samples not exposed to plasma ( see also subsection [ dummysubsection ] ) , which never exhibited any remobilization activity . our textor and extrap - t2r experimental results confirmed that remobilization does take place under steady state plasma operation and revealed that the condition for the grain release is not easily satisfied , since only a relative small fraction of the exposed populations has remobilized and among those mostly larger grains and small clusters . the interpretation of the pilot - psi data greatly benefits from being complemented by camera observations and from the multiple exposure of samples to identical plasma conditions . the experimental evidence from this device allow us to draw the following rather important conclusion : for a given `` dust - pfc contact '' , there appears to be a condition to satisfy for remobilization to occur , in case it is not fulfilled in the beginning of the plasma exposure , then the grain shall remain adhered provided that the plasma conditions are stationary . let us elaborate on this further . in pilot - psi the rise time of the magnetic field pulse is @xmath102s , whereas the first plasma reaches the samples at @xmath185ms . subsequently , the plasma density gradually builds up to its maximum value which it attains at the plateau . our exposures have been complemented by camera observations in several but not all discharges and altogether we have observed @xmath186 trajectories , that correspond to a small fraction of the detached grains as determined by the post exposure sem analysis ( @xmath187 ) . according to the cameras , all the observed dust remobilization events take place between @xmath188 and @xmath189s of plasma exposure . since the dust surface temperature can only increase in time and the cameras observe the hottest dust@xcite , we can conclude that after a certain time no dust is released from the samples . this is strongly supported by the results of the re - exposure experiments . namely , even samples with drastic remobilization activity upon their first exposure , did not exhibit a single incidence of remobilization after re - exposure to an identical discharge . this implies that , as the plasma profiles build up , once the plasma forces become strong enough to satisfy any of the three remobilization conditions for some of the grains , these grains are immediately displaced and further exposure to similar conditions will not lead to any additional activity .    the remobilization experiments were carried out under varying plasma and surface conditions ( @xmath190m@xmath128 , @xmath191ev , @xmath192ev , @xmath193 , @xmath194 , @xmath195 ) . in such a wide range of experimental conditions , we have identified a clear dependence on the dust size . in accordance with the theory , larger grains and agglomerates tend to remobilize much easier than smaller grains @xmath196 m . consequently , smaller grains can be expected to have a longer lifetime on pfcs . this is particularly important , in view of recent dust studies in full metal tokamaks which have revealed that w grains with sizes @xmath196 m are the dominant component of the tungsten dust inventory . for instance , in dust collection activities from the full tungsten asdex upgrade@xcite the majority of w dust has sizes less than @xmath176 m with a most probable size @xmath197 m , whereas in the first dust studies from jet with the iter - like wall@xcite @xmath198 m is a typical size of w dust . we shall now view the theoretical estimates presented in section [ theorysection ] and the postulations about the three remobilization conditions in light of the experimental results . our calculations of the pull - off force strength indicate that it is hard for plasma forces acting along the surface normal to compensate for adhesion and that sliding or rolling can be realized easier than direct lift - up . however , overall , a significant number of grains were detached from the samples during plasma exposure . there are three possible explanations for this discrepancy : * ( i ) * micrometer scale roughness acts as a ramp . while the remobilized dust grains initially slide or roll , they soon encounter an asperity that redistributes the local normal and tangential velocity components causing detachment . * ( ii ) * nanometer scale roughness decreases the ideal strength of the pull - off force by two orders of magnitude . theoretical models@xcite indicate that the influence of nano - roughness on adhesion depends on the value of the dimensionless adhesion parameter @xmath199 where @xmath200 is the mean asperity radius and @xmath201 is the standard deviation of asperity heights@xcite . according to experiments , for large values of the adhesion parameter , @xmath202 , the pull - off force can be decreased by at least one order of magnitude@xcite . such high values require that the materials have large young s moduli @xmath203 . in fact , refractory metals are characterized by large @xmath203 and especially tungsten has one of the largest values , @xmath204gpa . * ( iii ) * there are additional plasma induced forces acting on the normal direction apart from the ion drag force and the electrostatic sheath force . we consider this possibility as unlikely to occur and mention it for the sake of completeness . some examples are forces due to thermal shocks or @xmath205 forces . camera observations in the pilot - psi experiments reported here support the first explanation , since they never revealed evidence of a direct lift - up . in the perpendicular configuration all grains moved radially along the sample surface , whereas in the oblique configuration the initial phase of trajectory was either pure tangential or with a dominant tangential component . however , as aforementioned , we did not manage to resolve the starting point of the trajectories . in further support of the first explanation , there were events where the grains were either significantly or slightly displaced from their original position without leaving the sample . future dust remobilization experiments will focus on clarifying which of the three remobilization conditions is satisfied first . recently , we managed to drastically improve the camera resolution in the pilot - psi experiments to @xmath206m / pixel@xcite , which can assist in resolving dust trajectories closer to the remobilization instant as well as clarify whether the tangential trajectories observed are along the surface of the sample or along the plasma sheath . moreover , in experiments with mirror polished samples ( @xmath207 nm ) micron - roughness can be eliminated . finally , measurements of the pull - off force either by atomic force microscopy or by electrostatic mobilization can quantify the effect of nano - roughness for w on w adhesion . a quantitative analytical theory of dust remobilization is currently a formidable task . self - consistent modelling of remobilization requires a consideration of the influence of dust on the local plasma parameters . even for a single dust grain residing on the much larger pfc , while the global sheath structure will be unaffected , local effects will still be important owing to the strong dependence of the plasma forces on the micro - flows and on the details of the density profiles ( sheath within a sheath case ) . theoretical analysis can become even more complex for dust sizes comparable to the debye length , for multiple grains due to shadowing effects and agglomerates , for roughness values comparable to the debye length or for castellated pfcs . however , the static nature of the phenomenon implies that particle - in - cell numerical modelling@xcite is a viable candidate that can provide quantitative results . such investigations will be the subject of future work .    in view of such theoretical difficulties , controlled dust remobilization experiments in fusion environments are essential . the experimental technique proposed herein not only realistically mimics naturally occurring sticking impacts , but also allows for an unambiguous quantification of the dust remobilization activity .","summary":"the versatile environment of the linear device pilot - psi allowed for experiments with different magnetic field topologies and varying plasma conditions that were complemented with camera observations .","abstract":"the first combined experimental and theoretical studies of dust remobilization by plasma forces are reported . the main theoretical aspects of remobilization in fusion devices under steady state conditions are analyzed . in particular , the dominant role of adhesive forces is highlighted and generic remobilization conditions - direct lift - up , sliding , rolling - are formulated . a novel experimental technique is proposed , based on controlled adhesion of dust grains on tungsten samples combined with detailed mapping of the dust deposition profile prior and post plasma exposure . proof - of - principle experiments in the textor tokamak and the extrap - t2r reversed - field pinch are presented . the versatile environment of the linear device pilot - psi allowed for experiments with different magnetic field topologies and varying plasma conditions that were complemented with camera observations ."}
{"article_id":"cond-mat0309021","section_id":"i","document":"the vortex state in layered superconductors has a very rich phase diagram in the multidimensional space of temperature - field - anisotropy - field orientation . especially interesting subject is the vortex phases in layered superconductors with very high anisotropy such as bi@xmath0sr@xmath0cacu@xmath0o@xmath1 ( bscco ) . relatively simple vortex structures are formed when magnetic field is applied along one of the principal axes of the layered structure . a magnetic field applied perpendicular to the layers penetrates inside the superconductor in the form of pancake vortices ( pvs ) . @xcite pvs in different layers are coupled weakly via the josephson and magnetic interactions and form aligned stacks at low fields and temperatures ( pv stacks ) . these stacks are disintegrated at the melting point . in another simple case of the magnetic field applied parallel to the layers the vortex structure is completely different . such a field penetrates inside the superconductor in the form of josephson vortices ( jvs).@xcite the jvs do not have normal cores , but have rather wide nonlinear cores , of the order of the josephson length , located between two central layers . at small in - plane fields jvs form the triangular lattice , strongly stretched along the direction of the layers , so that jvs form stacks aligned along the @xmath2 direction and separated by a large distance in the in - plane direction . a rich variety of vortex structures were theoretically predicted for the case of tilted magnetic field , such as the kinked lattice , @xcite , tilted vortex chains @xcite , coexisting lattices with different orientation.@xcite a very special situation exists in highly anisotropic superconductors , in which the magnetic coupling between the pancake vortices in different layers is stronger than the josephson coupling . in such superconductors a tilted magnetic field creates a unique vortex state consisting of two qualitatively different interpenetrating sublattices.@xcite this set of crossing lattices ( or combined lattice @xcite ) contains a sublattice of josephson vortices generated by the component of the field parallel to the layers , coexisting with a sublattice of stacks of pancake vortices generated by the component of the field perpendicular to the layers . a basic reason for such an exotic ground state , as opposed to a simple tilted vortex lattice , is that magnetic coupling energy is minimal when pancake stacks are perfectly aligned along the @xmath2 axis . a homogeneous tilt of pancake lattice costs too much magnetic coupling energy , while formation of josephson vortices only weakly disturbs the alignment of pancake stacks .    even at high anisotropies jvs and pancake stacks have significant attractive coupling.@xcite the strong mutual interaction between the two sublattices leads to a very rich phase diagram with many nontrivial lattice structures separated by phase transitions . at sufficiently small c - axis fields ( 10 - 50 gauss ) a phase separated state is formed : density of the pancake stacks located at jvs becomes larger than the stack density outside jvs.@xcite this leads to formation of dense stack chains separated by regions of dilute triangular lattice in between ( mixed chain+lattice state ) . such structures have been observed in early decoration experiments @xcite and , more recently , by scanning hall probe @xcite , lorentz microscopy @xcite , and magnetooptical technique.@xcite at very small c - axis fields ( @xmath3 several gauss ) the regions of triangular lattice vanish leaving only chains of stacks.@xcite moreover , there are experimental indications @xcite and theoretical reasoning @xcite in favor of the phase transition from the crossing configuration of pancake - stack chains and jvs into chains of tilted vortices . jvs also modify the interaction between pancake stacks leading to an attractive interaction between the stacks at large distances.@xcite as a consequence , one can expect clustering of the pancake stacks at small concentrations . many unexpected observable effects can be naturally interpreted within the crossing lattices picture . the underlying jv lattice modifies the free energy of the vortex crystal state . an observable consequence of this change is a shift of the melting temperature . strong support for the crossing - lattices ground state is the linear dependence of the c - axis melting field on the in - plane field observed within a finite range of in - plane fields.@xcite in an extended field range several melting regimes have been observed @xcite indicating several distinct ground states of vortex matter in tilted fields . transitions between different ground state configurations have also been detected by the features in the irreversible magnetization.@xcite in this paper we consider in detail the properties of an isolated jv in the pancake lattice . we mainly focus on the regime of a dense pancake lattice , when many rows of the pancakes fit into the jv core . the pancake lattice forms an effective medium for jvs which determines their properties . the dense pancake lattice substantially modifies the jv structure . in general , the phase field of the jv is built up from the continuous regular phase and the phase perturbations created by pancake displacements . such a jv has a smaller core size and smaller energy as compared to the ordinary jv.@xcite the pancake lattice also strongly modifies the field and current distribution far away from the core region.@xcite    the key parameter which determines the structure of the jv core in the dense pancake lattice is the ratio @xmath4 , where @xmath5 is the in - plane london penetration depth , @xmath6 is the anisotropy ratio , and @xmath7 is the period of layered structure . the core structure experiences a smooth yet qualitative evolution with decrease of this parameter . when @xmath8 is small ( large anisotropies ) pancakes have only small displacements with respect to positions of the ideal crystal and the jv core occupies several pancakes rows . in this situation the renormalization of the jv core by the pancake vortices can be described in terms of the continuous vortex phase which is characterized by its own phase stiffness ( effective phase stiffness approach).@xcite at large @xmath8 ( small anisotropies ) the core shrinks to scales smaller than the distance between pancake vortices . in this case pancake stacks in the central row form soliton - like structure smoothly transferring between the neighboring lattice position . we consider dynamic properties of jvs in the case of small @xmath8 : the critical pinning force which sticks the jv to the pv lattice and the viscosity of the moving jv due to the traveling displacement field in the pv lattice . the pinning force has a nonmonotonic dependence on the c - axis magnetic field , @xmath9 , reaching maximum when roughly one pancake row fits inside the jv core region . at higher fields the pinning force decays exponentially @xmath10 . we study jv motion through the pv lattice and find that the lattice strongly hinders the mobility of jvs . the paper is organized as follows . section [ sec : jvstructure ] is devoted to the static structure of an isolated jv inside the pv lattice . in this section we    * consider small c - axis fields and calculate the crossing energy of jv and pv stack ( [ sec : cren ] ) ; * consider large c - axis fields and introduce the `` effective phase stiffness '' approximation , which allows for simple description of jv structure inside the dense pv lattice in the case of large anisotropy ( [ sec : effphstiff ] ) ; * investigate a large - scale behavior and jv magnetic field ( [ sec : largescale ] ) ; * analyze the jv core quantitatively using numeric minimization of the total energy and find crossover from the jv core structure to the soliton core structure with decrease of anisotropy ( [ sec : quantcore ] ) ; * formulate a simple model which describes the soliton core structure for small anisotropies ( [ sec : soliton ] ) . in section [ sec : jvpin ] we consider pinning of jv by the pancake lattice and calculate the field dependence of the critical current at which the jv detaches from the pv lattice . in section [ sec : jvvisc ] we consider possible jv dynamic regimes : dragging the pancake lattice by jvs and motion of jvs through the pancake lattice . for the second case we calculate the effective jv viscosity .","summary":"in very anisotropic layered superconductors a tilted magnetic field generates crossing vortex lattices of pancake and josephson vortices ( jvs ) . we study the properties of an isolated jv in the lattice of pancake vortices . jv induces deformations in the pancake vortex crystal , which , in turn , substantially modify the jv structure . the phase field of the jv is composed of two types of phase deformations : the regular phase and vortex phase . we find that the structure of the cores experiences a smooth yet qualitative evolution with decrease of the anisotropy . at large anisotropies pancakes have only small deformations with respect to position of the ideal crystal while at smaller anisotropies the pancake stacks in the central row smoothly transfer between the neighboring lattice positions forming a solitonlike structure .","abstract":"in very anisotropic layered superconductors a tilted magnetic field generates crossing vortex lattices of pancake and josephson vortices ( jvs ) . we study the properties of an isolated jv in the lattice of pancake vortices . jv induces deformations in the pancake vortex crystal , which , in turn , substantially modify the jv structure . the phase field of the jv is composed of two types of phase deformations : the regular phase and vortex phase . the phase deformations with smaller stiffness dominate . the contribution from the vortex phase smoothly takes over with increasing magnetic field . we find that the structure of the cores experiences a smooth yet qualitative evolution with decrease of the anisotropy . at large anisotropies pancakes have only small deformations with respect to position of the ideal crystal while at smaller anisotropies the pancake stacks in the central row smoothly transfer between the neighboring lattice positions forming a solitonlike structure . we also find that even at high anisotropies pancake vortices strongly pin jvs and strongly increase their viscous friction ."}
{"article_id":"0801.1081","section_id":"i","document":"the theory of stellar evolution has been tested extensively mainly through well - studied binary stars ( _ e.g. _ , popper 1980 , lastennet & valls - gabaud 2002 , ribas 2006 ) or simple , coeval stellar populations such as open and globular clusters ( _ e.g. _ vandenberg et al . 1996 , renzini & fusi pecci 1988 ) . it has been extraordinarily successful at explaining most stellar properties across the different evolutionary stages , by incorporating increasingly complex physics in both stellar interiors and atmospheres ( see salaris & cassisi 2006 for an updated and extensive review ) . in contrast , and perhaps somewhat paradoxically , the determination of the fundamental parameters of single stellar populations , such as distance , age , metallicity , reddening , convective parameters , etc , has seldom been the subject of a rigorous mathematical determination . more often than not , isochrones are `` fitted '' by eye , and very rough estimates of errors are given , if given at all . the reason for this state of affairs is perhaps the many degeneracies between these parameters , which makes it seemingly impossible to find a unique solution to the set of fundamental parameters . alternative , semi - empirical methods have been developed instead to infer _ relative _ quantities , rather than absolute ones . for instance , the so - called horizontal method relies on the difference in colour between the turn - off ( to ) point and the base of the red giant branch ( rgb ) , and is independent of the assumptions made on the convective theory . the vertical method , on the other hand , relies on the difference in apparent magnitude between horizontal branch ( hb ) stars and turn - off stars . both methods rely heavily on `` semi - empirical calibrations '' provided by stellar models , and are subject to many uncertainties ( _ e.g. _ , how to define properly the to point when photometric errors blur this region of the colour - magnitude diagram ? what is the vertical offset hb  to when the hb is not horizontal ? ) which nevertheless have been tackled with some success ( _ e.g. _ rosenberg et al . 1999 , salaris & weiss 2002 ) .    here we want to point out that many of the degeneracies are actually mere artifacts , and that a proper and rigorous mathematical technique can be formulated to measure these parameters in a robust and objective way . for example , the well - known age - metallicity degeneracy , which states that a given isochrone can be fitted with a different age provided the metallicity is changed appropriately , is a purely _ geometrical _ degeneracy : the _ shape _ of the isochrones is the same , yet stellar evolution predicts that stars with a different metal content will evolve at a different _ speed_. hence , the age - metallicity degeneracy is not a physical one , but simply a result of using the geometrical shape of isochrones as the only discriminant factor . clearly , a simple statistical estimator that would count the number of stars _ along _ the isochrones would give very different results for any pair of age / metallicity values that would give the same geometrical shape to the isochrones . in a more formal way , let us consider a curvilinear coordinate @xmath0 along an isochrone of given parameters ( say , distance , reddening , metallicity , age , alpha elements enhancement , etc ) . this position depends only on the age @xmath1 of that isochrone and on the mass @xmath2 of the star at that precise locus , so that @xmath3 only . an offset in age @xmath4 is reflected only through changes in mass @xmath2 and position @xmath0 along the isochrone of age @xmath1 since dt(m , s ) = .|_s dm + .|_m ds . for a star in this isochrone the offset is , by definition , zero , hence .|_t = - .|_s ( .|_m ) ^-1 . [ eq2 ] the first term is always finite . the second term is the evolutionary speed , the rate of change for a given mass @xmath2 of its coordinate along the isochrone when the age changes by some small amount . one can think of @xmath0 as representing some evolutionary phase , and so this term will be large when the phase is short - lived : a small variation in age yields a very large change in position along the isochrone . alternatively , for a given age , and since the first term is always finite , a wide variation in position implies a narrow range in mass . this is the case of the red giant branch or the white dwarf cooling sequence , for instance . on the other hand , slowly evolving phases such as the main sequence have small evolutionary speeds and wide ranges in mass for a given interval along an isochrone . clearly , the most important phases to discriminate between alternative ages and metallicities will be the post main - sequence ones , where the range of mass is small ( and hence insensitive to the details of the stellar mass function ) , and at the same time where evolutionary speeds are large . if we consider the mid- to lower main sequence , at fixed metallicity , isochrones of all ages trace the same locus , with only marginal changes in the density distribution of points amongst them . in this sense , one of the parameters , @xmath1 , is to a large extent absent from the main sequence , while phases beyond are always substantially a function of both age and metallicity . the density of stars along an isochrone is therefore = - ( ) ( . the first term is related to the initial stellar mass function ( imf ) , and , as discussed above , the second term is finite while the third is a strong function of the evolutionary speed . if the mass after the turn - off is assumed to be roughly constant , this implies that the _ ratio _ in the number of stars in two different evolutionary stages after the turn - off will only depend on the ratio of their evolutionary time scales .    in terms of observables , this well - know relation has been exploited using luminosity functions as a proxy ( as pioneered by paczyski 1984 ) , that is , number counts of stars as a function of apparent magnitude . this is not the isochrone coordinate @xmath0 , but rather the projection of the isochrone on the vertical axis of the colour - magnitude diagram . the fact that the sub - giant branch often appears nearly horizontal in cmds implies that luminosity bins in this regime will not be discriminant . this is unfortunate because this phase is more heavily populated than the red giant branch , and thus the use of luminosity functions is not optimal . likewise , the projection on the horizontal axis , a colour , is less sensitive to the details along the rgb . clearly , the optimal strategy is to use the full information provided by the observed density of stars along the isochrone .    to summarize existing methods , one approach has grown out of the fitting of geometrical indicators of the observed cmd to isochrones , from single particular indicators such as turn off point ( to ) , magnitude or colour difference between two points on the cmd , to vs. zero - age horizontal branch or tip of the rgb and rgb bump position and combinations thereof . examples can be found in renzini & fusi pecci ( 1988 ) , buonanno et al . ( 1998 ) , salaris & cassisi ( 1998 ) , salaris & weiss ( 1998 ) , vandenberg & durrel ( 1990 ) , ferraro et al . ( 1999 ) and rosenberg et al . the accuracy of these approaches has been extended by including several such geometrical indicators simultaneously ( e.g. vandenberg 2000 , meissner & weiss 2006 ) , or a complete geometrical comparison between observed cmd and isochrone ( e.g. straniero & chieffi 1991 ) . the reduction of the cmd to a few numbers , given the varied and complex physics which enters in determining them implies using only a subset of the information available in the cmd , while the unavoidable observational errors present necessarily lead to ambiguities in the identification of the key points to be used , which are hard to quantify formally , and which result in uncertain confidence intervals being assigned to the inferences derived . neglecting stellar evolutionary effects limits the information content of the isochrones against which the cmds are compared . on the other hand , approaches concentrating explicitly on the stellar evolutionary effects have grown out of the already mentioned analysis of luminosity functions presented by paczyski ( 1984 ) , a projection of the cmd onto the vertical axis . extensions have mostly centered on the easy to measure and age sensitive features of the rgb luminosity function ( _ e.g. _ jimenez & padoan , 1998 , and zoccali & piotto 2000 ) . here again , observational errors together with the binning adopted in generating luminosity functions , imply a limited use of the information available in the observation , while not including the information encoded by the geometry of both the cmd and isochrones limits the accuracy of the inferences .    there are have been a few attempts in the past at using the full information available in a colour - magnitude diagram , as pioneered by flannery & johnson ( 1982 ) and further developed by wilson & hurrey ( 2003 ) and naylor & jeffries ( 2006 ) . unfortunately all these approaches , while mathematically correct , fail to include properly the key discriminating factor discussed above , the stellar evolutionary speed , resulting in wide uncertainties in the inferred parameters . the only other attempt we are aware of , in the context of inferring parameters from a stellar population , was made by jrgensen & lindegren ( 2005 ) , who adapted our formalism developed in a previous paper ( hernandez , valls - gabaud & gilmore 1999 ) to derive stellar ages . the present paper is a further and robust extension of this approach . paper ii in this series ( valls - gabaud & hernandez 2007 ) will apply the method to different sets of observations of stellar populations .    in section 2 we present the rigorous probabilistic model , which is tested with synthetic cases in section 3 . in section 4 we explore and quantify the effects of systematic uncertainties , in section 5 we present an application of the method to a real case , ngc  3201 . finally in section 6 we present our conclusions on this novel approach .","summary":"the basic properties of these simple populations , systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities . here we show that systematic uncertainties due to field contamination , unresolved binaries , initial or present - day stellar mass function are either negligible or well under control .","abstract":"the colour - magnitude diagrams of resolved single stellar populations , such as open and globular clusters , have provided the best natural laboratories to test stellar evolution theory . whilst a variety of techniques have been used to infer the basic properties of these simple populations , systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities . here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable : the number of stars along the isochrone . through extensive monte carlo simulations we show that , for instance , we can infer the four main parameters ( age , metallicity , distance and reddening ) in an objective way , along with robust confidence intervals and their full covariance matrix . we show that systematic uncertainties due to field contamination , unresolved binaries , initial or present - day stellar mass function are either negligible or well under control . this technique provides , for the first time , a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations , in an easy - to - implement algorithm .    [ firstpage ]    methods : statistical  stars : statistics  globular clusters : general  open clusters and associations : general  galaxy : stellar content"}
{"article_id":"0801.1081","section_id":"c","document":"we have presented a method which treats the inference of structural parameters of single stellar populations in a fully rigorous statistical manner , within a bayesian approach , to construct a merit function for the comparison of an observed cmd in relation to a point in the 4-d parameter space of age , metallicity , distance modulus and reddening .    implementing a genetic algorithm simulation we have shown through various examples using synthetic cmds with parameters as appropriate for current observations of galactic single stellar populations , that the method accurately recovers the input parameters , and yields reliable confidence intervals , including naturally an analysis of the covariances and correlations between the recovered parameters .    by performing extensive monte carlo experiments with systematic effects , which surely apply to real cases and which are explicitly excluded from the formalism presented , we have evaluated the consequences these effects are expected to have on the results of our method . we found that although the error ranges on the recovered parameters typically increase , no systematic offsets appear , at least within the reasonable ranges tested . this implies that our formalism , which explicitly takes into account the number density of stars along isochrones , can tentatively test stellar evolution models when using clusters with well - measured abundances , distances and reddenings . this , along with the absolute dating of clusters with precise photometry , will be presented in the second paper of this series ( valls  gabaud & hernandez 2007 ) .","summary":"the colour - magnitude diagrams of resolved single stellar populations , such as open and globular clusters , have provided the best natural laboratories to test stellar evolution theory . whilst a variety of techniques have been used to infer we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable : the number of stars along the isochrone . through extensive monte carlo simulations we show that , for instance , we can infer the four main parameters ( age , metallicity , distance and reddening ) in an objective way , along with robust confidence intervals and their full covariance matrix . this technique provides , for the first time , a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations , in an easy - to - implement algorithm .   ","abstract":"the colour - magnitude diagrams of resolved single stellar populations , such as open and globular clusters , have provided the best natural laboratories to test stellar evolution theory . whilst a variety of techniques have been used to infer the basic properties of these simple populations , systematic uncertainties arise from the purely geometrical degeneracy produced by the similar shape of isochrones of different ages and metallicities . here we present an objective and robust statistical technique which lifts this degeneracy to a great extent through the use of a key observable : the number of stars along the isochrone . through extensive monte carlo simulations we show that , for instance , we can infer the four main parameters ( age , metallicity , distance and reddening ) in an objective way , along with robust confidence intervals and their full covariance matrix . we show that systematic uncertainties due to field contamination , unresolved binaries , initial or present - day stellar mass function are either negligible or well under control . this technique provides , for the first time , a proper way to infer with unprecedented accuracy the fundamental properties of simple stellar populations , in an easy - to - implement algorithm .    [ firstpage ]    methods : statistical  stars : statistics  globular clusters : general  open clusters and associations : general  galaxy : stellar content"}
{"article_id":"0902.1991","section_id":"i","document":"it is quite remarkable that elements heavier than helium exist in the intergalactic medium ( igm ) only @xmath14gyr after the big bang , as indicated by the presence of metal absorption lines associated with the ly@xmath15  forest of high redshift qsos ( songaila 2001 ; becker et al . 2006 ; ryan - weber , pettini & madau 2006 ; simcoe 2006 ) . for these elements to be observed there needs to be significant star formation prior to redshift @xmath16 , and the nucleosynthetic products of such early stars need to be expelled beyond the gravitational influence of their host galaxies . the production of early metals is closely linked to the emission of the lyman continuum ( lyc ) photons responsible for ionizing the igm and ending the so - called `` dark ages '' ( gnedin & ostriker 1997 ; fan , carilli , & keating 2006 ) , a process which could have started as early as @xmath17 and continued until completion at @xmath18 ( dunkley et al . 2009 ) . clearly , some galaxies were already actively forming stars at @xmath19 . the current record for a spectroscopically confirmed galaxy is held by the ly@xmath15  emitter at @xmath20 discovered by iye et al . ( 2006 ) , but several candidates selected via the redshifted lyman break have been found at @xmath21 ( stark et al . 2007 ; richard et al . 2008 ; bouwens et al . 2008 and references therein ) . furthermore , analyses of the broad - band spectra of galaxies at redshifts @xmath22 have in several cases revealed objects with ` mature ' stellar populations , suggesting that star formation in these galaxies was underway well before @xmath16 ( shapley et al . 2001 ; shapley et al . 2005 ; yan et al . 2006 ; eyles et al . 2007 ) . whether the level of star formation so far accounted for at @xmath19 is in fact sufficient to maintain reionization is far less certain , because it depends on a number of essentially unknown parameters , especially the escape fraction of lyman continuum photons from the sites of star formation , the degree of clumping of the sources and of the igm , and the slope of the faint end of the galaxy luminosity function at these early times ( madau , haardt , & rees 1999 ) . using the luminosity function of bouwens et al . ( 2006 ) at @xmath23 and assuming an escape fraction of 20% , bolton & haehnelt ( 2007 ) concluded that there may be _ just enough _ lyc photons to keep the igm ionised , suggesting that cosmic reionization was a ` photon starved ' process ( see also gnedin 2008 ) . qsos are unlikely to help matters , since their contribution to the metagalactic photoionization rate at these redshifts is estimated to be at most 15% ( srbinovsky & wyithe 2007 ) . bolton & haehnelt ( 2007 ) proposed that , in order to complete reionization by @xmath23 , either the escape fraction of lyc photons must have been higher at earlier times , or the ionizing spectrum must have been harder ( or both ) . alternatively , the faint end slope of the luminosity function may have been steeper at @xmath19 compared to the luminosity function determined by bouwens et al . ( 2006 ) , as indeed proposed by stark et al . ( 2007 ) .    the cosmic budget of elements produced via stellar nucleosynthesis ( loosely referred to as metals ) provides an entirely different , and complementary , census of the star - formation activity prior to a given epoch . indeed , at redshifts @xmath24 there appears to be an approximate agreement ( within a factor of about two ) between the observed metal budget  summing together the contributions of stars , igm and diffuse gas in galaxies  and expectations based on the integral of the cosmic star formation rate density over the first 2 - 3gyr of the universe history ( pettini 2006 ; bouch et al . 2007 ) .    at higher redshifts , we rely increasingly on the ly@xmath15  forest and gamma - ray burst afterglows to trace metals in the igm and in galaxies , since at @xmath0 the spectra of even the most luminous galaxies are too faint to be studied in detail with current instrumentation . the most commonly encountered metal lines associated with the ly@xmath15  forest are the civ  @xmath25 doublet ( cowie et al . 1995 ; ellison et al . photoionisation modelling ( schaye et al . 2003 ; simcoe , sargent , & rauch 2004 ) suggests that at redshifts @xmath24 the carbon abundance is a function of the gas density , as expected ( cen & ostriker 1999 ) , and that the mean metallicity of the igm is @xmath26 . interestingly , the comoving mass density of triply ionised carbon , obtained by integrating the distribution of column densities @xmath27(civ ) , appears to be approximately constant from @xmath28 to @xmath29 : expressed as a fraction of the critical density , @xmath30 ( songaila 2001 ; pettini et al . 2003mpc@xmath31 , @xmath32 and @xmath33 cosmology used in this paper . ] ) over a period of @xmath34gyr which saw the peak of the cosmic star - formation and massive black hole activity ( e.g. reddy et al . 2008 and references therein ) . this surprising result has led to conflicting interpretations as to the source of these intergalactic metals , with some authors ( e.g. madau , ferrara , & rees 2001 ; porciani & madau 2005 ) proposing an origin in low - mass galaxies at @xmath35 , when the pollution of large volumes of the igm would have been easier , while others ( e.g adelberger 2005 ) place them much closer to the massive galaxies responsible for most of the metal production at redshifts @xmath365 . while both processes presumably contribute , their relative importance has yet to be established with certainty ( songaila 2006 ) . the most extensive theoretical work in this area has been published by b.  d.   oppenheimer and collaborators . in a series of papers ( oppenheimer & dav 2006 , 2008 ; dav & oppenheimer 2007 ) these authors analysed the output of cosmological simulations of galaxy formation which include feedback in the form of momentum - driven winds . they found that the apparent lack of evolution of @xmath11 from @xmath37 to 1.5 can be explained as the result of two countervailing effects : an overall increase of the cosmic abundance of carbon , reflecting the on - going pace of star formation , and an accompanying reduction in the fraction of carbon which is triply ionised .    whether this is the true picture or not , it is clear that determining @xmath11 at @xmath0 is the next observational priority ; in any case , metal lines are our only remaining probe of the igm at these high redshifts where the ly@xmath15  forest itself becomes effectively opaque . such an extension of metal - line surveys in qso spectra necessitates observations at moderate spectral resolution and signal - to - noise ratio at near - infrared ( near - ir ) wavelengths , a regime which has only recently begun to be exploited for such purposes ( e.g. kobayashi et al . 2002 ; nissen et al . 2007 ) . in a pilot study ( ryan - weber , pettini , & madau 2006 ) , we demonstrated that qso absorption line spectroscopy could indeed be performed in the near - ir to the levels required to detect intergalactic civ absorption . from observations of two qso at redshifts @xmath38 and 5.99 we discovered two strong civ doublets at absorption redshifts @xmath39 and 5.8290 . these two absorbers , which were confirmed by an independent study by simcoe ( 2006 ) , would  if typical imply that a high concentration of civ was already in place in the igm at @xmath23 , but clearly much better statistics than those afforded by only two qso sight - lines are necessary to assess the true level of @xmath11 .    given the success of our pilot study , in the last two years we have conducted an observational campaign on the keck and eso - vlt telescopes aimed at securing near - ir spectra of as many as possible of the 19 known qsos with @xmath1 and infrared magnitude @xmath40 . the results of this programme are presented here . specifically , we have observed 13 qsos and obtained useful data for ten of them . this sample represents an increase by a factor of seven in the pathlength probed , from the absorption distance @xmath41 covered by ryan - weber et al . ( 2006 ) to @xmath42 . is defined so that @xmath43 , where @xmath44 is the hubble parameter . populations of absorbers with constant physical cross sections and comoving number densities maintain constant line densities @xmath45 as they passively evolve with redshift . ] with this extended data set , we find the first evidence for a _ decrease _ in @xmath11 from @xmath46 to @xmath47 , in broad agreement with the predictions of the cosmological simulations by oppenheimer , dav , & finlator ( 2009 ) .    this paper is organised as follows . section  2 describes the observations , followed by brief comments on each qso in section  3 . in section 4 we deduce the value of implied from our three detections of absorbers within the redshift range @xmath48 . in sections 5 and 6 , we consider the completeness of the survey , and discuss the evidence for a drop in  as we look back to redshifts @xmath49 . the implications of these results for early star formation and reionisation are discussed in section  7 . we finally summarise our main conclusions in section  8 .    throughout this paper we use a ` 737 ' cosmology with @xmath50mpc@xmath31 , @xmath32 and @xmath33 . much of the previous work ( including our own ) with which we compare the present results was based on an einstein - de sitter cosmology ; in all cases , we have converted the quantities of interest to the cosmology adopted here .    [ cols=\"<,^,<,^,>,^,>,>,^ \" , ]     @xmath51signal - to - noise ratio over wavelength range sampled . + @xmath52redshift range covered for civ absorption . + @xmath53when available , we quote values of @xmath54 measured from the civ  @xmath55 broad emission line in our nirspec spectra . as is well known , + the qso systemic redshift , @xmath56 , can be higher than the value measured from high ionisation lines such as civ , by up to several thousand km  s@xmath31 + ( e.g. richards et al . 2002 ) . + @xmath57bal qso ; not included in the survey statistics . + @xmath58with a small gap between two wavelength settings . + @xmath59two wavelength settings , with exposure times of 14400 and 18000s respectively . + @xmath60kurk et al . + @xmath61observations reported in ryan - weber et al . . + @xmath62jiang et al . ( 2007 ) . + @xmath63 in three , partially overlapping , wavelength settings , with exposure times of 39600 , 7200 and 36000s respectively . + @xmath64@xmath54 measured from the siiv  @xmath65 broad emission line in our nirspec spectrum . + [ tab : obs ]","summary":"[ firstpage ]    quasars : absorption lines , intergalactic medium , cosmology : observations","abstract":"we present the results of the largest survey to date for intergalactic metals at redshifts , using near - ir spectra of nine qsos with emission redshifts . we detect three strong  doublets at.8 , two low ionisation systems at , and numerous mgii absorbers at.8 . we find , for the first time , a change in the comoving mass density of  ions as we look back to redshifts . at a mean , we deduce which implies a drop by a factor of compared to the value at , after accounting for the differing sensitivities of different surveys . the observed number of  doublets is also lower by a similar factor , compared to expectations for a non - evolving column density distribution of absorbers .    these results point to a rapid build - up of intergalactic  over a period of onlymyr ; such a build - up could reflect the accumulation of metals associated with the rising levels of star formation activity from indicated by galaxy counts , and/or an increasing degree of ionisation of the intergalactic medium ( igm ) , following the overlap of ionisation fronts from star - forming regions . if the value of we derive is typical of the igm at large , it would imply a metallicity . the early - type stars responsible for synthesising these metals would have emitted only about one lyman continuum photon per baryon prior to ; such a background is insufficient to keep the igm ionised and we speculate on possible factors which could make up the required shortfall .    [ firstpage ]    quasars : absorption lines , intergalactic medium , cosmology : observations"}
{"article_id":"0902.1991","section_id":"c","document":"to summarise , by extending our previous searches for intergalactic  to near - ir wavelengths , we have found that both the number of such absorbers per unit absorption distance and the comoving mass of triply ionised carbon are approximately three times lower at @xmath229 than at @xmath8 . although our results refer to the stronger  systems in the column density distribution function , with @xmath230 , the evolution appears to extend at least to absorbers with half this column density ( becker et al . 2009 ) .    before considering the implications of these results , we reflect briefly on possible caveats . as already mentioned , we may have underestimated the column densities of  through line saturation ; we do not expect this effect to be so severe as to cause ( spuriously ) the fall in  evident in figure  [ fig : o_civb ] , but only higher resolution observations will quantify the corrections required ( if any ) . it must also be borne in mind that the distribution of  at @xmath231 seems to be extremely patchy : of the nine sight - lines sampled , seven show no absorption , while two absorbers are found in the direction of one qso . thus , our statistics are very prone to what in galaxy counts is referred to as ` cosmic variance ' . this can explain why the pilot observations by ryan - weber et al . ( 2006 ) suggested a higher value of the first stage of our survey fortuitously found one - third of the @xmath232 of the whole sample presented here , even though it covered only @xmath233 of the total @xmath227 . conversely , becker et al . ( 2009 ) detected _ no _ absorbers in their higher resolution nirspec spectra of four qsos ( three in common with our sample ) over less than half of the @xmath227 of our survey . in future , better statistics will undoubtedly improve the accuracy of determinations of  at @xmath0 ; for the moment we shall proceed on the assumption that our estimate of the error on this quantity , as shown in figure  [ fig : o_civb ] , is realistic . the downturn in  we have discovered as we approach @xmath234 is clear evidence of important changes taking place in the universe at , or before , this epoch . in the following discussion we shall find it more convenient to ` turn the time arrow around ' , and to think of the evolution as time progresses from higher to lower redshifts . the rise in  we see in figure  [ fig : o_civb ] could result either from an increase in the amount of intergalactic carbon , or from changes in the ionisation balance favouring the fraction of carbon which is triply ionised , or both . indeed , there are indications from previous work that both effects may be at play .    by integrating the galaxy luminosity function down to 1/5 of the fiducial luminosity at @xmath235 ( that is , considering galaxies with @xmath236 ) , bouwens et al . ( 2008 ) found that the cosmic star - formation rate density increased by a factor of @xmath237 over the 400myr period from @xmath238 to @xmath16 . the growth in intergalactic we see at @xmath239 may well be a reflection of this enhanced star - formation activity , as the products of stellar nucleosynthesis accumulate in the igm , presumably transported by galactic outflows . note that this is carbon produced by massive stars , with evolutionary time - scales of less than 10myr ( pettini et al . 2008b ; pettini 2008 ) ; it is therefore quite conceivable that over @xmath240myr the products of typeii supernovae could have travelled considerable distances from their production sites .    on the other hand , fan et al . ( 2006c ) have argued for a marked increase in the transmission of the ly@xmath15  forest at @xmath241 , which has been interpreted as marking the overlap of the hydrogen ionisation fronts from star - forming galaxies , as the igm became transparent to lyman continuum photons ( e.g. gnedin & fan 2006 ) . opinions are still divided , however , as to the correct interpretation of the ly@xmath15  forest evolution at these high redshifts ( e.g. becker , rauch , & sargent 2007 and references therein ) . coupled with the rise in the comoving density of bright qsos ( fan 2006 ) , a higher igm transmission would quickly ionise a larger fraction of carbon into .    to make progress beyond these qualitative remarks , detailed modelling is necessary . as mentioned in the introduction , b. oppenheimer and collaborators have devoted considerable attention to this problem and shown , in particular , how momentum - driven winds from star - forming galaxies can reproduce the behaviour of  at redshifts @xmath242 . it is therefore of interest to consider their model predictions for earlier epochs . their latest models ( oppenheimer , dav , & finlator 2009 ) do indeed entertain a marked growth in  from @xmath243 to 5 , driven by _ both _ effects mentioned above . in their scenario , the overall density of carbon increases by a factor of @xmath244 between @xmath13 and 4.7 . the accompanying rise in  depends on the spectral shape of the radiation field which dominates the ionisation equilibrium . oppenheimer et al . ( 2009 ) consider two possibilities : the metagalactic background in the formulation by haardt & madau ( 1996 ) with recent updates , and a more local field dominated by early - type stars in the nearest galaxy to the  absorbers , in recognition of the fact that cosmic reionisation was likely to be very patchy at these early epochs . the former produces the larger change in  ( for the reasons explained above ) , which grows by a factor of @xmath245 between @xmath13 and 4.7 ; the latter results in a more modest rise , by a factor of @xmath246 . given our warnings about the effects of ` cosmic variance ' on the current observational determinations of , it would be quite premature to compare in detail these theoretical predictions with the data in figure  [ fig : o_civb ] and , for example , draw conclusions on the shape of the ionising background at these early epochs . it is encouraging , nevertheless , that models and data concur in a general trend towards a build - up of  over the relatively short cosmic period between @xmath234 and 5 . two ingredients of the simulations by oppenheimer et al . ( 2009 ) need to be clarified , however . the first , and more important one , is that in their scenario the galaxies responsible for most of the igm enrichment are of low mass and with luminosities well _ below _ the current observational limit @xmath236 . we know very little , if anything at all , about the galaxies at the faint end of the luminosity function at @xmath0 , and this situation is unlikely to be remedied until the launch of the james webb space telescope in the next decade . a second concern is the resonant opacity of the igm at the frequencies of the heii lyman series which has been neglected until recently , and which may affect the distribution of carbon among its highly ionised states ( madau & haardt 2009 ) . the average metallicity of the igm at a given epoch reflects the accumulation of the heavy elements synthesised by previous generations of stars and expelled from their host galaxies . the massive stars which explode as typeii supernovae and seed the igm with metals are also the sources of nearly all of the lyman continuum photons produced by a burst of star formation . consequently , it is relatively straightforward to link a given igm metallicity with a minimum number of lyc photons which must have been produced up until that time . the close correspondence between the sources metals and photons makes the conversion from one to the other largely independent of the details of the stellar initial mass function ( imf ) . for example , madau & shull ( 1996 ) calculate that changing the index of a power - law formulation of the imf , such as salpeter s ( 1955 ) , from @xmath247 to 3 , results in only a 10% difference in the conversion between metallicity and number of lyc photons emitted .    when in the past this line of reasoning has been applied to measures of the igm metallicity at @xmath248 ( e.g. madau & shull 1996 ; miralda - escude & rees 1997 ) , it has been concluded that the star formation activity prior to that epoch probably produced sufficient photons to reionise the universe . with our new estimate of , much closer in time to what may have been the end of the process of reionisation , we are able to revisit this question more critically . we begin by calculating the igm metallicity by mass , @xmath249 , implied by our measure of : @xmath250 where @xmath251 ( pettini et al . 2008a ) is the contribution of baryons to the critical density , @xmath252 is the fraction of carbon which is triply ionised , and @xmath253 is the mass fraction of metals in carbon . for comparison , in the sun , @xmath254 and @xmath255 ( asplund , grevesse , & sauval 2005 ) ; here we assume that the same value of @xmath253 applies at high redshifts because : ( a ) the ratio of carbon to oxygen ( the major contributor to @xmath256 ) is approximately solar at low metallicities ( pettini et al . 2008b ; fabbian et al . 2009 ) ; and ( b ) any departures are in any case likely to result in only a small correction compared to other uncertainties in the following discussion . we also adopt the conservative limit @xmath257 , as done by songaila ( 2001 ) ; this is the maximum fractional abundance reached by civ under the most favourable ionisation balance conditions . with these parameters , our measured @xmath258 implies @xmath259    in recent years , much theoretical attention has been directed to estimating the likely properties of metal - poor early - type stars . schaerer ( 2002 ) pointed out that stellar luminosities at far - uv wavelengths are higher at lower metallicities , leading to a greater output of lyc photons associated with stellar nucleosynthesis . specifically , the energy emitted in hydrogen ionising photons ( per baryon ) is related to the average cosmic metallicity by : @xmath260 where @xmath261mev is the rest mass of the proton and @xmath262 is the stellar efficiency conversion factor . schaerer ( 2002 ) estimated @xmath263 for stars with @xmath264 , a factor of @xmath265 higher than at solar metallicities ( see also venkatesan & truran 2003 ) . for an average energy of 21ev per lyc photon ( schaerer 2002 ) , our determination of @xmath266 then implies that less than one ( @xmath267 ) lyc photon per baryon was emitted by early - type stars prior to @xmath13 . this background is clearly insufficient to keep the universe ionised . when we take into account that : ( a ) an unknown fraction , @xmath268 , of the emitted lyc photons will escape from the regions of star formation into intergalactic space , and ( b ) more than one intergalactic lyc photon per baryon is likely to be required to keep the clumpy igm ionised against radiative recombinations ( e.g. madau , haardt , & rees 1999 ; bolton & haehnelt 2007 ) , we reach the conclusion that our shortfall is by at least one order of magnitude . there are a number of possible solutions to this problem . the most obvious one is to recall that eq . ( [ eq : z_igm2 ] ) gives the _ lower limit _ to the igm metallicity , for two reasons . first , our accounting of  only includes high column density absorbers , with @xmath269@xmath109 . a steepening of the column density distribution , @xmath167 , at @xmath231 could hide significant amounts of metals in lower column density systems . however , the recent null result by becker et al . ( 2009 ) runs counter to this explanation . second , if @xmath270 , some of the tension would be relieved . for example , in the models considered by oppenheimer et al . ( 2009 ) most of the c is doubly - ionised at @xmath376 , and @xmath271 , a factor of five lower than the upper limit assumed in eq . ( [ eq : z_igm2 ] ) . on the other hand , there are limits to the extent to which the shortfall can be explained by ionisation effects alone . if the igm is not highly ionised at these redshifts , so that @xmath270 , we would also expect a non - negligible fraction of c to be singly ionised . unlike ciii , which is virtually impossible to observe at these redshifts because its resonance lines are either too weak or buried in the ly@xmath15 forest , cii has a well - placed strong transition at rest wavelength @xmath272which should provide , in conjunction with @xmath27(civ ) , some indication of the ionisation balance of c. for two of the civ absorbers in the present sample , at @xmath39 and 5.8288 in line to sdssj103027.01 + 052455.0 ( table  [ tab : abs ] ) , the corresponding cii@xmath273 lines are covered by the esi spectrum of pettini et al . ( 2003 ) . in neither case is cii absorption detected ; the corresponding upper limits are @xmath27(cii)/@xmath27(civ)@xmath274 at @xmath39 and @xmath27(cii)/@xmath27(civ)@xmath275 at @xmath276 . clearly these are high - ionisation absorbers for which it seems unlikely that civ is only a trace ion stage of carbon . in future , it will be possible to quantify better the ionisation state of the metal - bearing igm at these redshifts with observations targeted at other elements , such as si which may be observable in three ion stages : siii , siiii , and siiv . returning to @xmath249 , another reason why the value in eq . ( [ eq : z_igm2 ] ) may underestimate the cosmic mean metallicity is that it does not include carbon in stars . the ensuing upward correction however , is unlikely to be more than a factor of @xmath244 , unless current estimates ( e.g. bouwens et al . 2008 ) still miss a significant fraction of the cosmic star formation activity prior to @xmath13 as argued , for example , by faucher - gigure et al . it is also intriguing to note that schaerer ( 2002 ) proposed an efficiency factor as high as @xmath277 ( nearly five times higher than the value used here in eq . [ eq : e_z ] ) for metal - free stars . additionally , the number of lyc photons in the igm may be boosted by a population of faint qsos yet to be detected . possibly , all of these factors contribute and , given all the unknowns , one may argue that this kind of accounting exercise is premature . future work , aimed at improving the statistics of  absorption at high redshifts and at identifying the galaxies from which these metals may have originated , will undoubtedly place the above speculations on much firmer observational ground .","summary":"the early - type stars responsible for synthesising these metals would have emitted only about one lyman continuum photon per baryon prior to ; such a background is insufficient to keep the igm ionised and we speculate on possible factors which could make up the required shortfall .   ","abstract":"we present the results of the largest survey to date for intergalactic metals at redshifts , using near - ir spectra of nine qsos with emission redshifts . we detect three strong  doublets at.8 , two low ionisation systems at , and numerous mgii absorbers at.8 . we find , for the first time , a change in the comoving mass density of  ions as we look back to redshifts . at a mean , we deduce which implies a drop by a factor of compared to the value at , after accounting for the differing sensitivities of different surveys . the observed number of  doublets is also lower by a similar factor , compared to expectations for a non - evolving column density distribution of absorbers .    these results point to a rapid build - up of intergalactic  over a period of onlymyr ; such a build - up could reflect the accumulation of metals associated with the rising levels of star formation activity from indicated by galaxy counts , and/or an increasing degree of ionisation of the intergalactic medium ( igm ) , following the overlap of ionisation fronts from star - forming regions . if the value of we derive is typical of the igm at large , it would imply a metallicity . the early - type stars responsible for synthesising these metals would have emitted only about one lyman continuum photon per baryon prior to ; such a background is insufficient to keep the igm ionised and we speculate on possible factors which could make up the required shortfall .    [ firstpage ]    quasars : absorption lines , intergalactic medium , cosmology : observations"}
{"article_id":"0902.1991","section_id":"c","document":"we have conducted the largest survey to date for intergalactic metals at redshifts @xmath278 . our sample consists of near - ir spectra of nine high - redshift qsos covering a total absorption distance @xmath42 , seven times greater than the pilot observations by ryan - weber et al . our main results can be summarised as follows :    \\1 . we detect three definite and one possible  doublets ; the three definite cases all correspond to column densities of triply ionised carbon in excess of @xmath279@xmath109 . we detect two further  doublets in a tenth qso which is not included in the final sample as it shows evidence for mass ejection ( a bal qso ) ; in any case these two systems are probably associated with the qso environment rather than being truly intergalactic .    \\2 . from the three definite detections , we deduce a comoving mass density @xmath6 at a mean @xmath5 . this value represents a drop in @xmath11 by a factor of @xmath7 compared to @xmath280 at the @xmath211 significance level , after the different levels of completeness of optical and near - ir surveys are taken into account . if the column density distribution of  absorbers remained invariant at @xmath49 in its shape and normalisation as determined at @xmath222 , we would have expected to find @xmath221  doublets in our data , instead of only three , adding to the evidence for a decrease in the frequency of intergalactic  as we approach @xmath234 thus our data suggest a relatively rapid build - up of intergalactic  over a period of only @xmath9myr , from @xmath281 to @xmath282gyr after the big bang . such a build - up could reflect the earlier rise of cosmic star formation activity from @xmath10 indicated by galaxy counts and/or an increasing level of ionisation in the igm . numerical simulations of galaxy formation which include momentum - driven galactic outflows are consistent with our findings and suggest that both factors  a genuine build - up of metallicity and higher ionisation  contribute to the rise in  from @xmath13 to @xmath283 . _ if _ the value of  we have derived is representative of the igm at large , it corresponds to a metallicity @xmath284 . the accumulation of this mass of metals in the igm in turn implies that only about one lyman continuum photon per baryon had been emitted by early - type stars prior to @xmath13 . this background is clearly insufficient to keep the the universe ionised , suggesting that more carbon is present at these early epochs , in undetected ionisation stages , low column density systems , stars , or a combination of all three . all of these estimates are of necessity still rather uncertain . however , with the forthcoming availability of x - shooter on the vlt , as well as planned improvements in the performance of near - ir spectrographs on other large telescopes , it should be possible in the near future to make full use of metal absorption lines in qso spectra to trace early star formation and the consequent reionisation of the igm .","summary":"we present the results of the largest survey to date for intergalactic metals at redshifts , using near - ir spectra of nine qsos with emission redshifts . , we deduce which implies a drop by a factor of compared to the value at , after accounting for the differing sensitivities of different surveys . these results point to a rapid build - up of intergalactic  over a period of onlymyr ; such a build - up could reflect the accumulation of metals associated with the rising levels of star formation activity from indicated by galaxy counts , and/or an increasing degree of ionisation of the intergalactic medium ( igm ) , following the overlap of ionisation fronts from star - forming regions . if the value of we derive is typical of the igm at large , it would imply a metallicity .","abstract":"we present the results of the largest survey to date for intergalactic metals at redshifts , using near - ir spectra of nine qsos with emission redshifts . we detect three strong  doublets at.8 , two low ionisation systems at , and numerous mgii absorbers at.8 . we find , for the first time , a change in the comoving mass density of  ions as we look back to redshifts . at a mean , we deduce which implies a drop by a factor of compared to the value at , after accounting for the differing sensitivities of different surveys . the observed number of  doublets is also lower by a similar factor , compared to expectations for a non - evolving column density distribution of absorbers .    these results point to a rapid build - up of intergalactic  over a period of onlymyr ; such a build - up could reflect the accumulation of metals associated with the rising levels of star formation activity from indicated by galaxy counts , and/or an increasing degree of ionisation of the intergalactic medium ( igm ) , following the overlap of ionisation fronts from star - forming regions . if the value of we derive is typical of the igm at large , it would imply a metallicity . the early - type stars responsible for synthesising these metals would have emitted only about one lyman continuum photon per baryon prior to ; such a background is insufficient to keep the igm ionised and we speculate on possible factors which could make up the required shortfall .    [ firstpage ]    quasars : absorption lines , intergalactic medium , cosmology : observations"}
{"article_id":"1302.2935","section_id":"i","document":"smooth manifolds are some of the most important objects in mathematics . they contain a wealth of geometric information , such as tangent spaces , tangent bundles , differential forms , de  rham cohomology , etc . , and this information can be put to great use in proving theorems and making calculations . however , the category of smooth manifolds and smooth maps is not closed under many useful constructions , such as subspaces , quotients , function spaces , etc . on the other hand , various convenient categories of topological spaces are closed under these constructions , but the geometric information is missing . can we have the best of both worlds ? since the 1970 s , the category of manifolds has been enlarged in several different ways to a well - behaved category as described above , and these approaches are nicely summarized and compared in  @xcite . in this paper , we work with diffeological spaces , which were introduced by j.  souriau in his 1980 paper  @xcite , and in particular we study the natural topology that any diffeological space has . a diffeological space is a set @xmath3 along with a specified set of maps @xmath4 for each open set @xmath5 in @xmath6 and each @xmath7 , satisfying a presheaf condition , a sheaf condition , and a non - triviality condition ( see definition  [ de : diffeological - space ] ) . given a diffeological space @xmath3 , the @xmath0-topology on @xmath3 is the largest topology making all of the specified maps @xmath4 continuous . in this paper , we make the first detailed study of the @xmath0-topology . our results include theorems giving properties and characterizations of the @xmath0-topology as well as many examples which show the behaviour that can occur and which rule out some natural conjectures . our interest in these topics comes from several directions . first , it is known  @xcite that the topological spaces which arise as the @xmath0-topology of a diffeological space are precisely the @xmath1-generated spaces , which were introduced by jeff smith as a possible convenient category for homotopy theory and were studied by  @xcite . some of our results help to further understand which spaces are @xmath1-generated , and we include illustrative examples . second , for any diffeological spaces @xmath3 and @xmath8 , the set @xmath9 of smooth maps from @xmath3 to @xmath8 is itself a diffeological space in a natural way and thus can be endowed with the @xmath0-topology . since the topology arises completely canonically , it is instructive to compare it with other topologies that arise in geometry and analysis when @xmath3 and @xmath8 are taken to be smooth manifolds . a large part of this paper is devoted to this comparison , and again we give both theorems and illustrative examples .    finally , this paper arose from work on the homotopy theory of diffeological spaces , and can be viewed as the topological groundwork for this project . it is for this reason that we need to focus on an approach that produces a well - behaved category , rather than working with a theory of infinite - dimensional manifolds , such as the one throroughly developed in the book  @xcite . we will , however , make use of results from  @xcite , as many of the underlying ideas are related . here is an outline of the paper , with a summary of the main results :    in section  [ se : background ] , we review some basics of diffeological spaces . for example , we recall that the category of diffeological spaces is complete , cocomplete and cartesian closed , and that it contains the category of smooth manifolds as a full subcategory . moreover , like smooth manifolds , every diffeological space is formed by gluing together open subsets of @xmath6 , with the difference that @xmath10 can vary and that the gluings are not necessarily via diffeomorphisms .    in section [ se : d - topology ] , we study the @xmath0-topology of a diffeological space , which was introduced by iglesias - zemmour in  @xcite . we show that the @xmath0-topology is determined by the smooth curves ( theorem  [ th : curves ] ) , while diffeologies are not ( example  [ diffeology ] ) . we recall a result of  @xcite which says that the topological spaces arising as the @xmath0-topology of a diffeological space are exactly the @xmath1-generated spaces ( proposition  [ delta ] ) . we give a necessary condition and a sufficient condition for a space to be @xmath1-generated ( propositions  [ la ] and  [ countable ] ) and show that neither is necessary and sufficient ( proposition  [ pr : fc ] and example  [ lpc ] ) . we can associate two topologies to a subset of a diffeological space . we discuss some conditions under which the two topologies coincide ( lemmas  [ l1 ] and  [ l2 ] , proposition  [ pr : topologies - agree ] , and corollary  [ d - open ] ) . section  [ se : function - spaces ] contains our most substantial results . we compare the @xmath0-topology on function spaces between smooth manifolds with other well - known topologies . the results are ( 1 ) the @xmath0-topology is almost always strictly finer than the compact - open topology ( proposition  [ pr : d - vs - compact - open ] and example  [ compare ] ) ; ( 2 ) the @xmath0-topology is always finer than the weak topology ( proposition  [ weakvsd ] ) and always coarser than the strong topology ( theorem  [ th : d - vs - strong ] ) ; ( 3 ) we give a full characterization of the @xmath0-topology as the smallest @xmath1-generated topology containing the weak topology ( theorem  [ conj : d - top ] ) ; ( 4 ) as a consequence , we show that the weak topology is equal to the @xmath0-topology if and only if the weak topology is locally path - connected ( corollary  [ iff : weak = d ] ) ; ( 5 ) in particular , when the codomain is @xmath6 or the domain is compact , the @xmath0-topology coincides with the weak topology ( corollary  [ cor : n = r ] and corollary  [ m - cpt ] ) , but not always ( example  [ weak - neq - d ] ) . all smooth manifolds in this paper are assumed to be hausdorff , second countable and without boundary . we would like to thank andrew stacey and chris schommer - pries for very helpful conversations , and jeremy brazas for the idea behind example  [ lpc ] .","summary":"diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces . for each diffeological space , p.  iglesias - zemmour introduced a natural topology called the-topology . however , the-topology has not yet been studied seriously in the existing literature . in this paper , we develop the basic theory of the-topology for diffeological spaces . we explain that the topological spaces that arise as the-topology of a diffeological space are exactly the-generated spaces and give results and examples which help to determine when a space is-generated . our most substantial results show how the-topology on the function space between smooth manifolds compares to other well - known topologies .","abstract":"diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces . for each diffeological space , p.  iglesias - zemmour introduced a natural topology called the-topology . however , the-topology has not yet been studied seriously in the existing literature . in this paper , we develop the basic theory of the-topology for diffeological spaces . we explain that the topological spaces that arise as the-topology of a diffeological space are exactly the-generated spaces and give results and examples which help to determine when a space is-generated . our most substantial results show how the-topology on the function space between smooth manifolds compares to other well - known topologies ."}
{"article_id":"1102.4231","section_id":"i","document":"within the framework of quantum field theoretical models , it has been shown recently that the role of various combinatorial notions is a crucial one .    inside the area of theoretical physics , quantum field theory ( qft ) represents an important part ; its mathematical formalism was proven successful not only in elementary particle physics ( the celebrated standard model ) but also in condensed matter physics . like in other domains of theoretical physics ( exact solutions of statistical - mechanical problems , random matrix models , integrable systems and so on ) , also in qft a key role is played by combinatorics . thus , perturbative qft relies on graph theory , namely on ( feynman ) graphs which appear in the expansion with their combinatorial weights ; moreover , as we will present in this survey , graph polynomials can be naturally related to polynomials appearing in some representation of the feynman amplitudes in qft . furthermore , renormalization , which lies at the heart of qft , can be described through some appropriate combinatorial hopf algebras , as we will see in the sequel .    on the other hand , techniques of analytic combinatorics ( such as the mellin transform or the saddle point method ) are also used in qft for computing and analyzing quantities like feynman integrals ( which are associated to feynman graphs ) . it is worth emphasizing that , in the last years , both combinatorialists and theoretical physicist in general ( or field theorists in particular ) became more and more aware of this strong relation between their domains . this is a natural tendency , since the unfolding of new ideas in physics is often tied with the development of new combinatorial methods . we can thus speak nowadays of an emerging domain of combinatorial physics .    as already announced above , in this survey we focus on the appearance of combinatorial notions in qft , such as graph and map polynomials and combinatorial hopf algebras . thus , in graph theory the celebrated tutte polynomial ( see @xcite ) is known to characterize in a particularly elegant way a generic graph . on the other hand , the feynman integral of such a graph can be represented , through the parametric representations , using some polynomials in a set of parameters associated to the edges of the graph . in this survey we present the relation between the tutte polynomial ( or , more exactly , its multivariate formulation @xcite ) and the polynomials of this qft parametric representation @xcite .    on the other hand , we also present how the connes  kreimer hopf algebra of feynman graphs @xcite encodes in a powerful manner the combinatorial structure of perturbative renormalization in qft . we then generalize this framework and lift it to ribbon graphs ( also known as maps , see for example @xcite and references therein ) . at this level , the tutte polynomial can be replaced in a natural manner by the bollobs  riordan polynomial @xcite . from the qft point of view , the appropriate models are the non - commutative ones ( we present here the scalar @xmath1 model implemented on the moyal space ) . in this case also , a parametric representation generalizing in a highly non - trivial manner the commutative one can be defined @xcite . one can then relate the bollobs  riordan polynomial to the polynomials of the parametric representations of these qft models on the non - commutative moyal space @xcite . furthermore , a ribbon graph version of the connes  kreimer hopf algebra of feynman graphs can be defined @xcite . this algebra is proven to lie behind the renormalization of qft models on the non - commutative moyal space .","summary":"in this survey we present the appearance of some combinatorial notions in quantum field theory . we then generalize this to ribbon graphs and present the relation of the bollobs  riordan polynomial with the parametric representation of some field theory on the non - commutative moyal space . kreimer hopf algebra as the combinatorial backbone of the renormalization process in field theories . we then show how this generalizes to the scalar field theory implemented on the non - commutative moyal space . = cmr8 = cmti8 = cmbx8","abstract":"in this survey we present the appearance of some combinatorial notions in quantum field theory . we first focus on graph polynomials ( the tutte polynomial and its multivariate version ) and their relation with the parametric representation of the commutative field theory . we then generalize this to ribbon graphs and present the relation of the bollobs  riordan polynomial with the parametric representation of some field theory on the non - commutative moyal space . we also review the role played by the connes  kreimer hopf algebra as the combinatorial backbone of the renormalization process in field theories . we then show how this generalizes to the scalar field theory implemented on the non - commutative moyal space . finally , some perspectives for the further generalization of these tools to quantum gravity tensor models are briefly sketched .    = cmr8 = cmti8 = cmbx8"}
{"article_id":"1610.06505","section_id":"i","document":"manganites rmn@xmath0o@xmath1 ( r are rare earth ions , y and bi ) are typical representatives of multiferroics in which ferroelectric ( with @xmath8 k ) and magnetic ( with @xmath9 k ) orderings coexist  @xcite . it has been assumed until now that rmn@xmath0o@xmath1 has a centrosymmetric sp . . _ pbam _ which forbids the existence of electric polarization . the ferroelectric ordering along the @xmath10 axis at low temperatures is induced by charge and magnetic orders which break the central symmetry of the crystal due to the exchange - striction mechanism  @xcite . it has recently been shown  @xcite that the real rmn@xmath0o@xmath1 symmetry at room temperature is a noncentral symmetry which means that the electric polarization should exist at room temperature . the authors could not give preference to one of two possible space groups : _ p2 _ ( allowing polarization along the @xmath11 axis ) and _ pm _ ( allowing polarization in the @xmath12 plane ) on the basis of structural studies . by assuming from the physical considerations that the _ homogeneous _ electric polarization could exist at all temperatures only in one direction ( i.e. , along the @xmath10 axis ) , they preferred the sp . _ pm_. the authors  @xcite did not discuss the nature of this polarization . in  @xcite it was reported that the hysteresis loops of electric polarization and remanent polarization were detected in gdmn@xmath0o@xmath1 in a wide temperature range 5  330 k. we interpreted this polar state as a frozen superparaelectric state induced by _ local polar domains _ formed in the main crystal matrix due to phase separation and charge carriers self - organization . theoretically , the frozen superparaelectric state was considered in the system of isolated ferroelectric nanoscale domains in a dielectric matrix  @xcite . this paper presents a comparative study of the electric polarization hysteresis loops which were revealed in two crystals of the rmn@xmath0o@xmath1 family with @xmath2 and @xmath3 in temperature interval from 5 k up to 330 k. there are significant structural distortions in bimn@xmath00@xmath1 caused by bi ions due to the presence of alone pairs of 6s@xmath13 electrons  @xcite . the bi@xmath6 ions are nonmagnetic ones but they strongly distort the lattice , while strongly magnetic gd@xmath6 ions with the ground state ( @xmath14s@xmath15 ) interact weakly with the lattice . of particular interest is the correlation between the properties of phase separation domains and electrical polarizations in these two model crystals . magnetization , electric polarization , permittivity , and conductivity studies and also features of high - resolution x - ray diffraction scattering of rmn@xmath0o@xmath1 ( @xmath2 , @xmath3 ) are reported . a characteristic feature of rmn@xmath0o@xmath1 is the presence of equal amounts of manganese ions with different valences mn@xmath6 ( containing 3t@xmath16 , 1e@xmath17 electrons in the @xmath18 shell ) and mn@xmath7 ( with 3t@xmath16 , 0e@xmath17 electrons ) , which provides conditions for charge ordering . the mn@xmath7 ions have an octahedral oxygen environment and are arranged in the layers with @xmath19 and @xmath20 . the mn@xmath6 ions have a local non - central surrounding in the form of a pentagonal pyramid and are arranged in the layers with @xmath21 . the r@xmath6 ions have the environment similar to that of the mn@xmath6 ions and are arranged in the layers @xmath22  @xcite . charge ordering in rmn@xmath0o@xmath1 and the e@xmath17 electron transfer between mn@xmath6 -mn@xmath7 ion pairs ( double exchange  @xcite ) are key factors responsible for polar electric states of these multiferroics at all temperatures . the low - temperature ferroelectric ordering in rmn@xmath0o@xmath1 is caused by charge ordering of alternating mn@xmath6 - mn@xmath7 ion pairs with antiferromagnetically and ferromagnetically oriented spins along the @xmath10 axis . different values of indirect exchange between the antiferromagnetic mn@xmath6 - mn@xmath7 ion pairs and considerably stronger double exchange between the ferromagnetic pairs of these ions lead to the exchange striction that breaks the centrosymmetricity of the lattice , thus giving rise to the ferroelectric polarization along the @xmath10 axis at @xmath23  @xcite . the double exchange between mn@xmath6-mn@xmath7 ions induces phase separation in rmn@xmath0o@xmath1 which is similar to phase separation in lnamno@xmath24 ( a- sr , ba , ca ) manganites containing mn@xmath6 and mn@xmath7 ions as well . phase separation exists at all temperatures and makes the formation of local conductive domains containing mn@xmath6 - mn@xmath7 ion pairs with ferromagnetically oriented spins energetically favorable . the phase separation domains are located in a dielectric antiferromagnetic ( paramagnetic ) matrix of the original crystal . the size and geometry of the local phase separation domains are determined by a dynamic balance of interactions which leads to the attraction of charge carriers ( double exchange , the jahn - teller effect ) and coulomb repulsion  @xcite . the effect of phase separation domains on the rmn@xmath0o@xmath1 properties was studied from 5 k up to the temperatures above room temperature . at @xmath25 the phase separation domains manifested themselves as @xmath26 superlattices with alternating ferromagnetic layers containing different numbers of charge carriers . it was supposed that these superlattices were multiferroic domain walls ( with their own polarizations ) located between ferroelectric domains of the basic crystal matrix . a set of ferromagnetic resonances from individual superlattice layers was detected for a number of multiferroics rmn@xmath0o@xmath1 ( @xmath27 , @xmath28 , @xmath29 , @xmath30 , @xmath3 )  @xcite . in the paramagnetic and paraelectric temperature range , up to temperatures above room temperature , the polar nature of local phase separation domains was found to be responsible for dielectric properties and the features of the high - resolution x - ray diffraction spectra of rmn@xmath0o@xmath1 ( @xmath27 and @xmath28 ) single crystals  @xcite . the 2d superstructures of alternating layers of the initial rmn@xmath0o@xmath1 crystals and phase separation domains were revealed at sufficiently high temperatures . most distinctly these superstructures ( perpendicular to the c axis ) manifested themselves in the x - ray studies of eumn@xmath0o@xmath1 and eu@xmath31ce@xmath32mn@xmath0o@xmath1 at room temperature . the superstructure layer thicknesses were 900     and 700   , respectively  @xcite .","summary":"the electric polarization hysteresis loops and remanent polarization were revealed in multiferroics rmno with and at wide temperature interval from 5 k up to 330 k. until recently , the long - range ferroelectric order having an exchange - striction magnetic nature had been observed in rmno only at low temperatures (  35 k ) . the correlations between properties of the phase separation domains and polarization were revealed and studied . multiferroic , polarization hysteresis loop , phase separation , charge carrier self - organization    75.85.+t , 77.22.ej , 77.80.dj","abstract":"the electric polarization hysteresis loops and remanent polarization were revealed in multiferroics rmno with and at wide temperature interval from 5 k up to 330 k. until recently , the long - range ferroelectric order having an exchange - striction magnetic nature had been observed in rmno only at low temperatures (  35 k ) . we believe that the polarization we observed was caused by the frozen superparaelectric state which was formed by the restricted polar domains resulting from phase separation and charge carriers self - organization . at some sufficiently high temperatures the frozen superparaelectric state was destroyed , and the conventional superparaelectric state occurred . this happened when the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . the hysteresis loops were measured by the so - called pund method which allowed us to correctly subtract the contribution of conductivity from the measured polarization . the correlations between properties of the phase separation domains and polarization were revealed and studied . the high - temperature polarization also had a magnetic nature and was controlled by the magnetic field because the double exchange between pairs of mn ions with different valences ( mn and mn ) in rmno was the basic interaction resulting in phase separation .    multiferroic , polarization hysteresis loop , phase separation , charge carrier self - organization    75.85.+t , 77.22.ej , 77.80.dj"}
{"article_id":"1610.06505","section_id":"r","document":"single crystals of rmn@xmath0o@xmath1 were grown by the spontaneous crystallization technique described in  @xcite . the as - grown single crystals were in the form of 2  3 mm thick plates with areas of 3  5 mm@xmath13 . to measure the polarization , capacitors with a thickness of 0.3  0.6 mm and area of 3  4 mm@xmath13 were used . the electric polarization was measured by two methods , i.e. , the thermo - stimulated pyrocurrent method and the so - called positive - up negative - down ( pund ) method of hysteresis loops measuring @xcite . in the first case the polarization was measured by a keithly 6514 electrometer and the measurements were produced during sample heating with a constant temperature variation rate after the preliminary sample cooling in a polarizing electric field which was switched off at the lowest temperature . in the second case we employed the version of the pund method presented in @xcite which was adapted to our measurements ( see fig . 1 in @xcite ) . if the sample had a relatively high conductivity ( which is important for rmn@xmath0o@xmath1 containing restricted polar phase separation domains with local conductivities ) , the shape of the polarization  electric field ( p - e ) hysteresis loop was distorted and did not give correct information on the intrinsic polarization p. in the pund method only the hysteresis of p can be extracted by applying a series of voltage pulses to the sample . during successive positive p1-p2 and negative n1-n2 pulses , independent curves ( p1-p2 and n1-n2 ) of effective polarization p changes are registered . the pund method is based on the difference between polarization and conductivity responses to variations in the field e. the time intervals between p1-p2 and n1-n2 pulses should be chosen such that the intrinsic polarization p is still unrelaxed , while the conductivity relaxation is complete . in the conventional volume ferroelectrics with the domain structure those time intervals may be up to seconds . in our case the intrinsic p response was determined by the restricted polar phase separation domains which rather rapidly restored after the field e was switched off . the reason for this will be discussed below . o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b).,title=\"fig:\",scaledwidth=45.0% ] o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b).,title=\"fig:\",scaledwidth=45.0% ]    as a result , the time intervals between the p1-p2 and n1-n2 pulses were chosen so that the responses to the p1 and n1 pulses were irreversible ( due to the intrinsic polarization contribution ) and the conductivity responses to the p2 and n2 pulses were closed and reversible ( see fig .  [ fig1 ] in @xcite ) . this could be achieved if the time intervals between the p1-p2 and n1-n2 pulses did not exceed 0.8 ms . the p1 and n1 curves characterized the total polarization and conductivity contributions . to obtain the actual p - e loop , we subtracted the p2 and n2 curves from the p1-n1 curves . the durations of pulses in the p1-p2 and n1-n2 series were 2 ms and 4.5 ms , the intervals between the pulse series were 4 ms and 9 ms for gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 , respectively . the permittivity and conductivity were measured by a good will lcr-819 impedance meter in the frequency range 0.5  50 khz at 5  350 k. magnetic properties were investigated by ppms ( quantum design ) . the intensity distributions of bragg reflections were studied with a high - sensitivity 3-crystal x - ray diffractometer .","summary":"we believe that the polarization we observed was caused by the frozen superparaelectric state which was formed by the restricted polar domains resulting from phase separation and charge carriers self - organization . at some sufficiently high temperatures the frozen superparaelectric state the high - temperature polarization also had a magnetic nature and was controlled by the magnetic field because the double exchange between pairs of mn ions with different valences ( mn and mn ) in rmno was the basic interaction resulting in phase separation .   ","abstract":"the electric polarization hysteresis loops and remanent polarization were revealed in multiferroics rmno with and at wide temperature interval from 5 k up to 330 k. until recently , the long - range ferroelectric order having an exchange - striction magnetic nature had been observed in rmno only at low temperatures (  35 k ) . we believe that the polarization we observed was caused by the frozen superparaelectric state which was formed by the restricted polar domains resulting from phase separation and charge carriers self - organization . at some sufficiently high temperatures the frozen superparaelectric state was destroyed , and the conventional superparaelectric state occurred . this happened when the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . the hysteresis loops were measured by the so - called pund method which allowed us to correctly subtract the contribution of conductivity from the measured polarization . the correlations between properties of the phase separation domains and polarization were revealed and studied . the high - temperature polarization also had a magnetic nature and was controlled by the magnetic field because the double exchange between pairs of mn ions with different valences ( mn and mn ) in rmno was the basic interaction resulting in phase separation .    multiferroic , polarization hysteresis loop , phase separation , charge carrier self - organization    75.85.+t , 77.22.ej , 77.80.dj"}
{"article_id":"1610.06505","section_id":"r","document":"complicated magnetic structures with wave vector @xmath33 and a number of low - temperature magnetic phase transitions at @xmath34 at which incommensuration parameters @xmath35 and @xmath36 change in a step - like fashion are typically observed in rmn@xmath0o@xmath1 with different r ions  @xcite . as temperature decreases , an incommensurate magnetic phase is appeared near t@xmath37 . at a lower temperature this phase is transformed into a commensurate structure . as temperature further decreases , one more transition into the incommensurate phase is possible . ferroelectric ordering in rmn@xmath0o@xmath1 is typically occurs in the intermediate commensurate phase . magnetic structures of gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 differ from those commonly observed in rmn@xmath0o@xmath1 . in gdmn@xmath0o@xmath1 , a commensurate collinear antiferromagnetic structure with wave vector @xmath38 occurs in the temperature range 0  30 k @xcite . at these temperatures there is a ferroelectric ordering with @xmath39 k. in the temperature range 35 k@xmath40 k there is an incommensurate phase . in bimn@xmath0o@xmath1 the commensurate noncollinear antiferromagnetic structure with @xmath41 is observed at t@xmath42 k @xcite .     along the @xmath10 axis at @xmath43 for gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 ( in the inset).,scaledwidth=45.0% ] [ fig1 ] shows temperature dependence of magnetization in magnetic field @xmath44 koe along different axes of the gdmn@xmath0o@xmath1 ( fig . [ fig1]a ) and bimn@xmath0o@xmath1 ( fig .  [ fig1]b ) crystals studied . it can be seen that the magnetic moment in gdmn@xmath0o@xmath1 is much higher due to the contribution of gd@xmath6 ions with the @xmath45 spin which have their own ordering at @xmath46 k. on the background of magnetization of gd ions , the antiferromagnetism of manganese ions along the a axis ( with @xmath47 k ) manifests itself only slightly ( see the left inset in fig . [ fig1]a ) . the right inset in fig . [ fig1]a shows that the curie - weiss temperature for gdmn@xmath0o@xmath1 nearly coincides with t@xmath37 . this means that there is a distinct phase transition near t@xmath37 in gdmn@xmath0o@xmath1 ( the magnetic state is not frustrated ) . a quite different magnetic state is observed in bimn@xmath0o@xmath1 ( fig . [ fig1]b ) . the antiferromagnetism along the @xmath11 axis manifests itself only slightly , while it is pronounced along the @xmath48 axis . unlike in gdmn@xmath0o@xmath1 , but similar to rmn@xmath0o@xmath1 with other r ions , the curie - weiss temperature exceeds @xmath49 k in 6 - 7 times . this means that the magnetic state in bimn@xmath0o@xmath1 is highly frustrated , and spin correlations in local domains are observed at @xmath50 . specific magnetic and structural properties of bimn@xmath0o@xmath1 in the rmn@xmath0o@xmath1 family are caused by the presence of electron alone pairs in bi@xmath6 ions . high - resolution neutron powder diffraction studies @xcite show that bimn@xmath0o@xmath1 is characterized at room temperature by the orthorhombic sp . . _ pbam _ , similar to other rmn@xmath0o@xmath1 . however , mn@xmath7-o6 octahedra , mn@xmath6-o5 pyramids , and bi@xmath6-o units are more deformed as compared with those in other rmn@xmath0o@xmath1 . as a result , the mn - o distances and magnetic exchange bonds differ as well .    as will be shown below , differences in magnetic and structural states of gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 lead to different electric polarizations at all temperatures . let us consider at first the low - temperature polar states . [ fig2 ] shows dispersion - free anomalies of real permittivity @xmath51 along the b axis which are characteristic of the low - temperature ferroelectric phase transition . as one can see , the value of @xmath51 at the maximum in the vicinity of t@xmath52 in gdmn@xmath0o@xmath1 considerably exceeds the maximum in bimn@xmath0o@xmath1 . [ fig3 ] shows electric polarizations along the @xmath10 axis ( p@xmath53 ) in gdmn@xmath0o@xmath1 ( fig.[fig3]a ) and bimn@xmath0o@xmath1 ( fig.[fig3]b ) . the polarizations are measured by the pyrocurrent method on the assumption that p@xmath54 at t@xmath55 . the maximum polarization p@xmath53 ( in our case @xmath56 @xmath57c / cm@xmath13 ) for the rmn@xmath0o@xmath1 family is observed in gdmn@xmath0o@xmath1  @xcite . in bimn@xmath0o@xmath1 , polarization p@xmath53 is an order of magnitude lower and is closer to the values typically observed in other rmn@xmath0o@xmath1 @xcite .     and pyrocurrents along the @xmath10 axis at @xmath59 and @xmath60 for gdmn@xmath0o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b).,title=\"fig:\",scaledwidth=45.0% ]   and pyrocurrents along the @xmath10 axis at @xmath59 and @xmath60 for gdmn@xmath0o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b).,title=\"fig:\",scaledwidth=45.0% ]    note that a fully polarized state is often observed in structurally perfect ( according to x - ray diffraction ) rmn@xmath0o@xmath1 single crystals with different r ions in the absence of an applied external electric field e  @xcite . this indicates that this fully polarized p@xmath53 polarization is formed in the internal field . we suppose that this is a staggered - like field caused by charge ordering of mn@xmath6 - mn@xmath7 ion pairs along the @xmath10 axis , and the polarization has an exchange - striction nature . this situation is observed for both crystals we studied . in gdmn@xmath0o@xmath1 ( fig . [ fig3]a ) , the maximum polarization is detected in @xmath59 . a uniform external field @xmath61 which is much weaker than the internal staggered - like field , only slightly reduces polarization p@xmath53 and can not reverse its orientation ( fig . [ fig3]a ) . the application of a strong field @xmath62 ( comparable to the internal field ) enhances the transfer of e@xmath17 valence electrons between the mn@xmath6 -mn@xmath7 ion pairs along the @xmath10 axis , which leads to the electric breakdown of the crystal . therefore , measurements of the polarization hysteresis loops p@xmath53 ( which are the response to an applied external field e ) is not effective when the striction contribution to the gdmn@xmath0o@xmath1 polarization at @xmath63 is measured . o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ] o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ] o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ]    in bimn@xmath0o@xmath1 ( which are also structurally perfect single crystals ) , bi ions distorts the uniformityof the internal staggered - like field , thus reducing its value and , hence , the exchange - striction polarization p@xmath53 . in this case application of field @xmath61 changes the internal field to a greater extent and can even reverse the bimn@xmath0o@xmath1 polarization ( see fig .  [ as can be seen , the application of e in the same direction in which the polarization was observed at @xmath59 enhances the polarization by the value close to that detected in e of the opposite orientation ( fig . [ fig3]b ) . there is good reason to believe that the internal exchange - striction polarization is the polarization observed at @xmath59 . there are two additional contributions to the polarization of bimn@xmath0o@xmath1 in the case of application of field @xmath62 . there is the contribution originating from a weak change in the internal staggered - like - field and that due to the response of phase separation domains to the applied field e. note that the polarization measured by the pyrocurrent method includes the contribution of conductivities of phase separation domains . as noted above , it was shown in @xcite that electric polarization hysteresis loops in gdmn@xmath0o@xmath1 were observed in a wide temperature interval ( from the lowest up to room temperature ) . we put forward the hypothesis that this polarization was due to the frozen superparaelectric state of restricted polar phase separation domains formed in the initial crystal matrix . phase separation must exist in rmn@xmath0o@xmath1 with any r ions at all temperatures , but the phase separation domain states depend on the r ion type and temperature . thus , two electric polarizations having different natures ( the long - range ferroelectric order with polarization p@xmath53 caused by exchange striction and the polarization due to polar phase separation domains ) must coexist in rmn@xmath00@xmath1 along the b axis at @xmath23 . the previous subsection was concerned with the polarizations p@xmath53 at @xmath23 measured by the pyrocurrent method at @xmath59 in gdmn@xmath0o@xmath1 ( fig.[fig3]a ) and bimn@xmath0o@xmath1 ( fig . [ fig3]b ) . this polarization gave no contribution to the hysteresis loops which were responses to the applied field e. on the contrary , the polarization caused by phase separation domains could be determined only by measuring the hysteresis loops by the pund method that excluded the contribution of conductivity . by using these two methods , we could separate the contributions of the polarizations considered above at low temperatures . let us consider in more detail the hysteresis loops for bimn@xmath0o@xmath1 in a wide temperature interval and compare them with the loops for gdmb@xmath0o@xmath1 . [ fig4 ] shows the p - e hysteresis loops of bimn@xmath0o@xmath1 in e oriented along the @xmath48 , @xmath10 , and @xmath11 axes ( left panels in figs . [ fig4]a ,  [ fig4]b , and  [ fig4]c , respectively ) . the right panels in these figures demonstrate temperature dependences of the remanent polarization ( @xmath67 ) . o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ] o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ] o@xmath1 ( left panels ) at different temperatures at e@xmath64 ( a ) , e@xmath65 ( b ) , and e@xmath66 ( c ) . temperature dependences of remanent polarization are shown in right panels.,title=\"fig:\",scaledwidth=45.0% ]    figs . [ fig5]a ,  [ fig5]b , and  [ fig5]c present the p - e hysteresis loops and prem for gdmn@xmath0o@xmath1 . as one can see , the hysteresis loops are observed for both crystals along all three axes from 5 k up to some temperatures t@xmath68 which depend on the axis direction . the maximum @xmath67 polarizations are observed along the @xmath11 axis from 5 k up to @xmath69 k in bimn@xmath0o@xmath1 and up to @xmath70 k for gdmn@xmath0o@xmath1 . the minimum @xmath67 along the @xmath10 axis which exists up to @xmath71 k is observed for gdmn@xmath0o@xmath1 , while a twice higher @xmath67 along the @xmath10 axis for bimn@xmath0o@xmath1 manifests itself up to @xmath72 k. the @xmath67 along the @xmath48 axis are observed for gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 up to @xmath73 k and @xmath69 k , respectively . thus , @xmath67 and hysteresis loops for bimn@xmath0o@xmath1 and gdmn@xmath0o@xmath1 which demonstrate a strong anisotropy are revealed in the paramagnetic phase . it is important to note that the polarizations of both crystals occurred along all crystal axes and disappeared at different temperatures along these axes . this fact means that the polarizations measured in the hysteresis loops were not caused by the ferroelectric phase transition in the homogeneous ferroelectric crystal states . as noted above , we assumed that these polarizations were induced by the restricted polar phase separation domains . it turned out that these polarizations were significantly lower than the exchange - striction ferroelectric low - temperature polarization along the @xmath10 axis at @xmath23 . the remanent polarization @xmath67 along the @xmath10 axis ( fig . [ fig5]b ) in gdmn@xmath0o@xmath1 is two orders of magnitude lower than the exchange - striction contribution of the basic crystal matrix polarization @xmath74 at @xmath75 k measured by the pyrocurrent method in the same sample at @xmath59 ( fig .  [ fig3]a ) . the contribution of @xmath74 into the hysteresis loops manifests itself only in the form of maxima on the background of @xmath76 near @xmath77 when the internal staggered - like - field which gives rise to polarization @xmath74 begins to decrease and disappears and the @xmath74 fluctuations increase ( see fig . [ fig5]b ) . there is no exchange - striction polarization of the main matrix in the direction of the @xmath48 and @xmath11 axes at @xmath23 , and therefore contributions to the hysteresis loops come only from phase separation domains at all temperatures . the fact that @xmath67 is independent of temperature along all axes of gdmn@xmath0o@xmath1 in a wide temperature range ( for the @xmath10 axis this relates to the background value minus the maxima near @xmath77 ) indicates that the contribution into the polarization from phase separation domains in gdmn@xmath0o@xmath1 is anisotropic but temperature - independent . at @xmath78 the remanent polarizations rather abruptly disappear along different crystal axes . of interest is the fact that , unlike in gdmn@xmath0o@xmath1 , the @xmath67 values along all axes of the bimn@xmath0o@xmath1 crystal abruptly increase in the vicinity of @xmath79 k and then rapidly reduce to zero near the @xmath78 . such @xmath67 jumps near 125 k indicate that phase separation domain states in bimn@xmath0o@xmath1 should change in a step - like fashion near this temperature . the absence of such jumps in gdmn@xmath0o@xmath1 shows that most probably these jumps in bimn@xmath0o@xmath1 result from structural lattice distortions caused by the bi ions . the effect of the longitudinal magnetic field h on the hysteresis loops was also studied . as one can see from the right panels in fig . [ fig5 ] , the field @xmath80 t increases in gdmn@xmath0o@xmath1 both the remanent polarization and temperature @xmath78 along the @xmath10 axis and only @xmath78 along the @xmath48 and @xmath11 axes . characteristic activation barriers e@xmath81 must exist at the interfaces between phase separation domains and the main matrix of the crystal . information on e@xmath81 along different crystal axes can be obtained from frequency - temperature dependences of real permittivity @xmath51 and conductivity @xmath82 .     and conductivity @xmath82 ( in insets ) at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c).,title=\"fig:\",scaledwidth=45.0% ]   and conductivity @xmath82 ( in insets ) at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c).,title=\"fig:\",scaledwidth=45.0% ]   and conductivity @xmath82 ( in insets ) at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c).,title=\"fig:\",scaledwidth=45.0% ]    fig . [ fig6 ] shows the @xmath51(t ) and @xmath82(t ) dependences for bimn@xmath0o@xmath1 at different frequencies along the @xmath48 axis ( fig . [ fig6]a ) , @xmath10 axis ( fig . [ fig6]b ) , and @xmath11 axis ( fig . [ fig6]c ) . it is evident that the values of @xmath51 and @xmath82 along all axes of the crystal are nearly independent of temperature at @xmath83 k. near @xmath79 k a frequency - dependent step - like @xmath51 increase to some constant level ( most pronounced along the @xmath48 and @xmath10 axes ) begins . as temperature further grows , @xmath51 starts to increase sharply again . the frequency - dependent growth of @xmath82 also begins near 125 k , and two the different temperature intervals of @xmath82 increase are observed as well . note that the temperature independence of @xmath51 and @xmath82 at @xmath83 k and similar steps in the @xmath51(t ) and @xmath82(t ) dependences near 125 k correlate with the temperature dependences of @xmath67 in bimn@xmath0o@xmath1 along different crystal axes ( see fig . [ fig4 ] ) . indeed , near @xmath79 k @xmath67 increases in a step - like fashion along all axes of the crystal . the temperatures at which the second high - temperature growth in @xmath51 and @xmath82 start are close to @xmath78 for different crystal axes . the temperatures of @xmath51 jumps at different frequencies at @xmath84 k are well described by the arrhenius law , which allows one to estimate characteristic activation barriers @xmath85 at the phase separation domain boundaries in bimn@xmath0o@xmath1 . these values are close to @xmath86 ev along different crystal axes ( see fig .  [ fig6 ] ) . let us turn to a more detailed examination of the conductivity of the crystals . we deal with the real conductivity @xmath87 @xcite which is calculated from dielectric losses @xmath88 ( @xmath89 is the angular frequency , @xmath90 is the permittivity @xmath51 at @xmath91 ) . this conductivity depends on both the frequency and temperature . the low - frequency conductivities are dispersion - free ( percolation conductivity @xmath92 ) . the conductivity @xmath93 has a frequency dispersion : the higher the frequency , the higher the conductivity . the frequency dispersion of this type is typical of local conductivity ( i.e. , dielectric losses ) in restricted domains  @xcite . in our case , we attributed this local conductivity to phase separation domains . the percolation conductivity ( leakage ) is attributable to the initial crystal matrix . the relative local conductivity @xmath94 characterizes the ratio between the phase separation domain local conductivity and matrix leakage . [ fig7 ] shows @xmath95 for bimn@xmath0o@xmath1 along the @xmath48 , @xmath10 , and @xmath11 axes ( figs . [ fig7]a ,  [ fig7]b , and  [ fig7]c , respectively ) . along the @xmath10 axis only one , most intense , maximum in @xmath95 in the temperature interval 125  220 k is observed . below 100 k @xmath95 also exists , but at @xmath96 k it is transformed into leakage , and near 125 k it again becomes a local conductivity ( see the inset in fig . [ fig7]b ) . the activation barrier calculated from the shifts of the local conductivity maxima at @xmath97 k ( fig . [ fig7]b ) exceeds @xmath98 derived from the @xmath51 jumps only slightly ( figs .  [ fig6]b and  [ fig7]b ) . at @xmath99 k the conductivities along the @xmath48 and @xmath11 axes were low and could not be measured correctly by our device . there are two @xmath95 maxima along these axes at @xmath97 k , the first is in the same temperature interval 125  220 k as along the @xmath10 axis ; the second is in the temperature region 225  350 k. the presence of two maxima split in temperature along the @xmath48 and @xmath11 axes in bimn@xmath0o@xmath1 means that the leakage sharply increases in the temperature interval between the maxima . such behaviors of @xmath95 along the @xmath48 and @xmath11 axes correlate with the temperature behaviors of @xmath51 along these axes ( fig . [ fig4 ] ) . however , the activation barriers calculated from the shifts of the first maxima of @xmath95 are almost twice as high as the barriers derived from the @xmath51 jumps ( compare fig . [ fig6 ] and fig . [ fig7 ] ) .     at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c ) . inset shows the same dependences along the @xmath10 axis at @xmath100 k at a larger scale.,title=\"fig:\",scaledwidth=45.0% ]   at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c ) . inset shows the same dependences along the @xmath10 axis at @xmath100 k at a larger scale.,title=\"fig:\",scaledwidth=45.0% ]   at different frequencies for bimn@xmath0o@xmath1 along the @xmath48 axis ( a ) , @xmath10 axis ( b ) , and @xmath11 axis ( c ) . inset shows the same dependences along the @xmath10 axis at @xmath100 k at a larger scale.,title=\"fig:\",scaledwidth=45.0% ]    tte inset in fig . [ fig8 ] shows temperature dependences of conductivities of gdmn@xmath0o@xmath1 along the @xmath10 and @xmath11 axes at different frequencies . the conductivity along the @xmath48 axis is close to that along the @xmath11 axis . of interest is the fact that the frequency - dependent conductivity jumps along the @xmath48 and @xmath11 axes in gdmn@xmath0o@xmath1 also emerge near 125 k , like in bimn@xmath0o@xmath1 . the activation barrier @xmath85 in gdmn@xmath0o@xmath1 calculated from the conductivity jumps is @xmath101 ev . [ fig8 ] shows the temperature intervals in gdmn@xmath0o@xmath1 in which @xmath95 of the phase separation domains exceeds considerably the matrix leakage . conductivity @xmath95 along the @xmath10 axis manifests itself up to @xmath102 k. at @xmath97 k there is only the leakage which grows with temperature . at @xmath79 k @xmath95 along the @xmath48 and @xmath11 axes rises abruptly and exists up to room temperature without a noticeable change . the hysteresis loops and @xmath67 along all axes in both crystals are screened by leakage rather sharply at the temperatures @xmath78 at which the leakage and local conductivities become comparable . this means that the @xmath78 values correspond to the temperatures at which the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . differences between polar properties of phase separation domains in gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 are observed along all axes of the crystals at @xmath103 k. at @xmath100 k the ground states of phase separation domains are similar for both crystals , which means that these states are formed inside the mn subsystems under the barriers of any origin . near 125 k the leakage and local conductivities along the @xmath10 axes become comparable in both crystals . the itinerant electrons which appear along the @xmath10 axes at @xmath97 k are localized anew in deeper potential wells thus passing into @xmath95 of the phase separation domains . in gdmn@xmath0o@xmath1 these @xmath95 exceed leakage up to @xmath78 equal to 295 k and 325 k along the @xmath48 and @xmath11 axes , respectively ( see fig .  [ fig5 ] ) . in bimn@xmath0o@xmath1 @xmath95 of phase separation domains emerges at @xmath97 k along all crystal axes , including the @xmath10 axis , due to the effect of bi ions . the localization of itinerant electrons in potential wells leads to deepening of these wells and increases the activation barriers of phase separation domains . these @xmath85 barriers can be calculated from the shifts of the temperature maxima of @xmath95 at different frequencies . indeed , these barriers in bimn@xmath0o@xmath1 turned out to be twice as high as @xmath85 calculated from the @xmath51 jumps . the latter barriers correspond to the condition when the kinetic energy of the itinerant electrons emerging along the @xmath10 axis becomes comparable to @xmath85 calculated from the @xmath51 jumps . the values of @xmath78 in bimn@xmath0o@xmath1 along different axes correlate with the temperatures at which the conductivity at the lowest frequency ( leakage ) begins to increase sharply in the first @xmath95 maxima ( compare fig . [ fig4 ] and fig  [ fig7 ] ) .     for gdmn@xmath0o@xmath1 along all axes ( the @xmath48 axis  unfilled symbols , the @xmath10 axis  filled symbols , the @xmath11 axis  lines ) for different frequencies . the inset shows temperature dependences of conductivity along the @xmath10 and @xmath11 axes for different frequencies.,scaledwidth=45.0% ]    note that near @xmath104 k dispersion - free anomalies typical of the ferroelectric phase transition manifest themselves in gdmn@xmath0o@xmath1 on the background of @xmath95 and @xmath93 along the @xmath10 axis ( see fig . [ fig8 ] ) . this is due to the fact that a maximum in @xmath88 should be observed near @xmath77 , while in bimn@xmath0o@xmath1 a low polarization @xmath74 does not manifest itself on the background of @xmath95 ( fig .  [ fig7]b ) . both the intrinsic polarization and @xmath95 of restricted polar phase separation domains give contributions into the p1 and n1 curves in measurements of hysteresis loops for gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 at @xmath105 by the pund method , while @xmath95 contributes significantly to the p2 and n2 curves in the same temperature interval . at these temperatures @xmath67 emerges in these crystals . near @xmath78 at which @xmath67 tends to zero , the polarization and local conductivity contributions to the p1-p2 and n1-n2 curves start to decrease simultaneously . at the temperatures at which @xmath106 , these contributions are transformed into linear dependences on e. at @xmath107 the loop restores as an inverted loop , and the leakage contribution begins to dominate in it . the experimental evidence of the existence of restricted polar phase separation domains of gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 was obtained in the x - ray high - sensitivity diffraction study carried out at room temperature ( see figs . [ fig9]a and  [ fig9]b , respectively ) . the angular intensity distributions of * ( 004 ) * , * ( 060 ) * and * ( 600)*@xmath108 bragg reflections were detected in the 3-crystal regime with the @xmath109 scan . as a monochromator and an analyzer , germanium crystals in the * ( 004 ) * reflection were used , which allowed conditions of nearly dispersion - free high - resolution ( @xmath110 ) survey geometry to be realized . [ fig9]a shows a single diffraction maximum of * ( 060 ) * and two diffraction maxima of the * ( 004 ) * bragg reflections recorded from different planes of a single crystal of gdmn@xmath0o@xmath1 . these planes are perpendicular to the @xmath10 and @xmath11 axes , respectively . the * ( 004 ) * bragg reflection positions are characterized by slightly different interplanar spacings @xmath111 ( @xmath112  ) . these * ( 004 ) * reflections , which have comparable intensities and half - widths ( @xmath113 ) clearly point to the coexistence of two phases with slightly differing @xmath11 lattice parameters which differ in the third decimal place . the bragg peak along the @xmath10 axis with a similar half - width is not split , i.e. , it is identical to these two phases . the positions of all bragg peaks nearly coincide with those for gdmn@xmath0o@xmath1 with the generally accepted _ pbam _ symmetry . this means that two phases we detected are high - quality gdmn@xmath0o@xmath1 single crystal phases with similar large correlation lengths @xmath114 . the phase with a higher intensity of the * ( 004 ) * bragg peak can be attributed to the original matrix . the phase with a lower intensity of such a peak can be attributed to the phase separation domains . a similar picture of the angular intensity distributions of the * ( 004 ) * , * ( 060 ) * and * ( 600)*@xmath108 bragg reflections is also observed for bimn@xmath0o@xmath1 , but splitting into two peaks for the reflexes along all axes of the crystal is detected ( fig . [ fig9]b ) . it is natural to attribute this to lattice distortions caused by bi ions along all crystal axes . note that the structural quality of both crystals is similar . bragg reflections as functions of interplanar distances ( d @xmath115 ) in gdmn@xmath0o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b ) . parameters of gdmn@xmath0o@xmath1 lattice are @xmath116   ; @xmath117   ; @xmath118  .,title=\"fig:\",scaledwidth=45.0% ]   bragg reflections as functions of interplanar distances ( d @xmath115 ) in gdmn@xmath0o@xmath1 ( a ) and bimn@xmath0o@xmath1 ( b ) . parameters of gdmn@xmath0o@xmath1 lattice are @xmath116   ; @xmath117   ; @xmath118  .,title=\"fig:\",scaledwidth=45.0% ]      let us discuss the shape and structure of phase separation domains in gmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 . as noted above , the phase separation domains in the form of @xmath26 superlattices were observed below the temperatures of magnetic and ferroelectric orderings in a number of rmn@xmath0o@xmath1 with various @xmath119 ions , including @xmath2 and @xmath3  @xcite . a set of ferromagnetic resonances was detected from individual layers of superlattices . the intensity of these resonances sharply decreased when @xmath120 k was approached . since the phase separation domains should exist at all temperatures , this fact means that the structure of the phase separation domains must change at @xmath121 k. we manage to study the temperature evolution of feromagnetic resonances of layered superlattices at @xmath121 k only in eu@xmath31ce@xmath32mn@xmath0o@xmath1 , in which the phase separation domains were similar to those in eumn@xmath0o@xmath1 , but their concentration was much high  @xcite . in temperature interval @xmath122 k only one ferromagnetic resonance signal was observed in eu@xmath31ce@xmath32mn@xmath0o@xmath1 . this resonance corresponded to the low - temperature superlattice layer having the maximal barrier and conductivity  @xcite . near @xmath123 k an intensity of this resonance became indistinguishable due to growth of conductivity . at room temperature the structure of phase separation domains was installed in eu@xmath31ce@xmath32mn@xmath0o@xmath1 in x - ray diffraction study  @xcite . the two @xmath124 well defined bragg peaks were accompanied by the characteristic oscillation peaks independent on the interplanar spacings @xmath111 , which pointed to existence of the layered superstructure in this crystal . as shown in  @xcite , the layered superstructure consisting of the alternating original crystal eumn@xmath0o@xmath1 layers and conductive layers of phase separation emerged in eu@xmath31ce@xmath32mn@xmath0o@xmath1 at all temperatures above 40 k. no similar oscillation peaks on the background of the bragg reflexes were observed in x - ray studies of gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 at room temperature ( fig . [ fig9 ] ) , i.e. , there were no layered superstructures in these crystals . most likely the phase separation domains in gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 had the shape of nanoscale droplets at @xmath121 k. the possibility of different geometries of the phase separation domains in coulomb - frustrated systems , including manganites and high - temperature superconductors , was shown theoretically in  @xcite . the properties of the phase separation domains in the form of nanoscale droplets for manganites were discussed in @xcite .    now consider in more detail what are polar phase separation domains . there is a probability that @xmath125 electrons of some mn@xmath6 ions tunnel to mn@xmath7 ions in the original rmn@xmath0o@xmath1 matrix . these valence electrons and recharged mn@xmath6-mn@xmath7 ion pairs are accumulated in the restricted phase separation domains inside the original matrix because phase separation is energetically favorable  @xcite . since mn@xmath6 ions appear in the mn@xmath7 ion positions ( i.e. , in the octahedral oxygen surrounding ) , they become jahn - teller ions and give rise to local deformations of these octahedra . in turn , mn@xmath7 ions appear in the mn@xmath6 ion positions ( in noncentrosymmetrical pentagonal pyramids ) and local distortions arise near these ions as well . as a result , structural distortions caused by both these factors occur inside restricted phase separation domains . we believe that phase separation domains are noncentrosymmetric , and their sizes are large enough to give rise to ferroelectric single - domain states inside them .    the restricted polar phase separation domain states existing in gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 original matrices are analogs of the superparaelectric state formed by an ensemble of spherical ferroelectric nanoparticles in a dielectric matrix theoretically studied in  @xcite . it was shown in  @xcite that at low temperatures a homogeneous polarization could exist in these particles ( in our case restricted polar phase separation domains ) if their sizes @xmath119 were less than the correlation radius @xmath114 but larger than the critical radius @xmath126 of the size - driven ferroelectric - paraelectric phase transition . under these conditions all dipole moments inside particles are aligned due to correlation effects . surface screening of depolarization fields makes single - domain states energetically favorable . if @xmath127 , separate paraelectric dipoles are uncorrelated and represent local polar defects which can only increase the width of the bragg peak original matrix . the fact that the well - defined bragg reflections related to the restricted polar phase separation domains are observed in our study together with similar bragg peaks of the original matrix indicates that the conditions for the ferroelectric single - domain states of phase separation regions given in  @xcite are fulfilled . it was also found in  @xcite that a frozen superparaelectric phase could emerge for an ensemble of ferroelectric nanoparticles in a dielectric matrix . in this phase remanent polarization and hysteresis loop arose at the temperatures lower than the freezing temperature @xmath128 . @xmath128 was defined from the condition that the potential barriers of nanoparticle polarization reorientation became equal to the thermal activation energy @xmath129 . at @xmath130 the conventional superparaelectric state occurred for which there are no hysteresis loops and remanent polarization . it was also accepted in @xcite that the temperature of thermal destruction of intrinsic nanoparticle ferroelectricity was @xmath131 . so , the temperature behavior of the gdmn@xmath0o@xmath1 and bimn@xmath0o@xmath1 polarization is also analogous to that of the frozen superparaelectric state discussed in  @xcite . @xmath78 considered above can be regarded as @xmath128 . as noted above , the @xmath78 values correspond to the temperatures at which the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . the restricted phase separation domains still exist at @xmath107 due to energetic favorability of the phase separation caused by strong interactions . but the frozen superparaelectric state turns into the conventional superparaelectric one near @xmath78 . since @xmath132 hysteresis loops are measured under the field e applied along different axes , electric polarizations inside phase separation domains are induced along these axes . indeed , the application of field e along any crystal axis initiates a drift of valence @xmath125 electrons localized inside phase separation domains in this direction . these electrons recharge @xmath133 and @xmath134 ions inside the phase separation domains . as a result , the spatial distribution of the @xmath133 and @xmath134 ions and structural distortions inside phase separation domains are bound to change , thereby giving rise to the polarization along the e direction . thus , the actual symmetry of rmn@xmath0o@xmath1 at room temperature can be established only in polarization measurements in @xmath135 . we believe that the additional structural reflexes typical of the noncentral monoclinic structure reported in  @xcite can be related to the frozen superparaelectric state arising in rmn@xmath0o@xmath1 at @xmath136 . note that in the cases when temperatures @xmath78 are sufficiently high , the correlations between the phase separation domains can occur in the entire crystal volume . this situation was observed earlier in eu@xmath31ce@xmath32mn@xmath0o@xmath1 at room temperature  @xcite . as noted above , phase separation and charge carrier self - organization give rise to a dynamic equilibrium of the phase separation domain states with a balance between attraction ( double exchange , jahn - teller effect ) and coulomb repulsion of charge carriers  @xcite . the formation of the phase separation domains due to a balance between strong interactions leads to specific features in rmn@xmath0o@xmath1 properties . first , polar phase separation domains are bound to emerge up to high temperatures , thus giving rise to high - temperature polarization . second , changes in polar phase separation domains under varying e rapidly relax to the dynamic equilibrium states after e is switched off . these features manifested themselves in our experiments and necessitated the use of the pund method for measuring the polarization hysteresis loops which were discussed above . the application of magnetic field h increases the barriers at the phase separation domain boundaries due to the double exchange growth , thus increasing the @xmath78 temperatures in gdmn@xmath0o@xmath1 ( see the right panels in fig . [ fig5 ] ) . the field h oriented along the @xmath10 axis in gdmn@xmath0o@xmath1 also enhances the polarization induced by the restricted polar domains due to the increasing probability of charge transfer between @xmath137 ion pairs with the greatest distance between them ( see the caption to fig . [ fig9]a ) . it was found that application of magnetic field @xmath80 t to bimn@xmath0o@xmath1 had a much weaker effect on phase separation domain properties and polarization than in gdmn@xmath0o@xmath1 because of strong structural distortions of the crystal field by bi ions .","summary":"was destroyed , and the conventional superparaelectric state occurred . this happened when the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . the hysteresis loops were measured by the so - called pund method which allowed us to correctly subtract the contribution of conductivity from the measured polarization .","abstract":"the electric polarization hysteresis loops and remanent polarization were revealed in multiferroics rmno with and at wide temperature interval from 5 k up to 330 k. until recently , the long - range ferroelectric order having an exchange - striction magnetic nature had been observed in rmno only at low temperatures (  35 k ) . we believe that the polarization we observed was caused by the frozen superparaelectric state which was formed by the restricted polar domains resulting from phase separation and charge carriers self - organization . at some sufficiently high temperatures the frozen superparaelectric state was destroyed , and the conventional superparaelectric state occurred . this happened when the potential barriers of the restricted polar domain reorientations become equal to the kinetic energy of the itinerant electrons ( leakage ) . the hysteresis loops were measured by the so - called pund method which allowed us to correctly subtract the contribution of conductivity from the measured polarization . the correlations between properties of the phase separation domains and polarization were revealed and studied . the high - temperature polarization also had a magnetic nature and was controlled by the magnetic field because the double exchange between pairs of mn ions with different valences ( mn and mn ) in rmno was the basic interaction resulting in phase separation .    multiferroic , polarization hysteresis loop , phase separation , charge carrier self - organization    75.85.+t , 77.22.ej , 77.80.dj"}
{"article_id":"1003.3402","section_id":"i","document":"the inspiral and coalescence of binary black holes or neutron stars appears to be the most promising source for the detectors of gravitational waves , so that there has been much effort going into the development of numerical codes and analytic approximation methods to find the corresponding solutions of einstein s equations . one of the recent approaches assumes the existence of a helical killing vector @xmath0 ( see e.g. @xcite ) . the field is assumed stationary in a rotating frame where @xmath0 generates time translations but @xmath0 becomes null at the light cylinder and is spacelike outside . @xmath0 has the form @xmath1 where @xmath2 is timelike and @xmath3 is spacelike with circular orbits with parameter length @xmath4 ( except where @xmath5 ) ; @xmath6constant . the space - time is not stationary but it is still periodic where @xmath0 is spacelike . requiring the helical symmetry for a binary system implies equal amounts of outgoing and incoming radiation so that the space - time , containing energy radiated all times is not expected to be asymptotically flat . a corresponding solution in maxwell s theory for two opposite point charges moving on circular orbits was considered a long time ago by schild @xcite . the properties of the field were analyzed recently in the newman - penrose formalism in @xcite . the rather complicated periodicity properties of the solution became apparent as well as its asymptotic behaviour : at @xmath7 the advanced fields exhibit the standard bondi - type expansion and peeling , whereas the retarded fields do decay with @xmath8 but in an oscillatory manner like @xmath9 . hence for the retarded plus advanced solution no radiation field is asymptotically defined . naturally , one would like to go beyond the linearized theory . there are special exact , time - dependent , solutions known , for example , szekeres s dust solution , which has in general no killing vector , which can be matched to an exterior schwarzschild metric @xcite . one can construct oscillating spherical shells of dust particles moving with the same angular momentum , but in every tangential direction , or oscillating einstein clusters which are matched to the schwarzschild space - time outside @xcite . can there be periodic solutions representing  bound states \" of gravitational or electromagnetic waves so that the radiation field at infinity vanishes and the bondi mass remains constant ? there have been various attempts to prove that , while solutions of the vacuum einstein equations can be genuinely periodic in a suitable time - coordinate ( so _ not _ time - independent ) , these solutions can not be asymptotically flat . these started with @xcite and @xcite , with a summary in english in @xcite , and @xcite and more recently was considered in @xcite . the method in @xcite considers vacuum metrics which are everywhere nonsingular , weak and asymptotically - flat and which can be expanded in a series in some parameter , with the flat metric as the first term in the series . each term in the series is assumed to be periodic in a fixed minkowski time - coordinate and to satisfy the de donder gauge condition . the second and third terms , call them @xmath10 and @xmath11 respectively , are expanded as fourier series in the background time - coordinate and the einstein equations then imply that @xmath10 satisfies the source - free wave equation , and @xmath11 satisfies a wave equation whose source is a quadratic expression in @xmath10 . assuming that the solution for @xmath10 is everywhere regular , the author shows that there can not be an asymptotically - flat solution for @xmath11 unless @xmath10 vanishes . therefore the space - time is flat . in @xcite , a similar calculation when @xmath10 is regular only outside a certain radius leads to the conclusion that @xmath10 must be time - independent in order to have asymptotically - flat @xmath11 , and the space - time is stationary . in @xcite it was observed by integrating the einstein pseudotensor and matter energy - momentum tensor over a 4-dimensional volume that `` the mean value of power radiated by a periodic , asymptotically minkowskian gravitational field is equal to zero '' . the question of existence of periodic fields was left open . in @xcite the authors used the spin - coefficient formalism ( see e.g. @xcite , @xcite ) to study the system of conformal einstein equations of friedrich @xcite . a coordinate system is based on two families of null hypersurfaces , incoming from past null infinity @xmath7 and labelled by constant @xmath12 and outgoing near @xmath7 and labeled by constant @xmath13 . the authors define periodicity as meaning periodic in @xmath12 in these coordinates and are then able to prove that , at @xmath7 , the @xmath13-derivatives of all orders of all components of the metric are independent of @xmath12 . they conclude that if the metric is analytic in these coordinates , then it necessarily has a killing vector , which in these coordinates is @xmath14 , at least in a neighbourhood of @xmath7 . thus any analytic metric , periodic in their sense , has such a killing vector . while certainly correct , there is a problem with this conclusion in that , by construction , the killing vector is null wherever it is defined , and reduces at @xmath7 to a constant translation along the generators . these are strong conditions and in fact no killing vector in flat space has these properties ( any null killing vector is necessarily a null translation , and a null translation is zero along one generator of @xmath15 ) becomes @xmath16 on @xmath7 , which vanishes at @xmath17 . ] . thus flat space is not periodic according to the definition of @xcite and nor is any of the familiar stationary , asymptotically flat solutions , for example the schwarzschild solution , so that this definition of periodicity is ` too strong ' .    for convenience , we follow @xcite in working at @xmath7 rather than @xmath18 , though this is trivial to switch , but we shall make a weaker definition of ` periodic in time ' which will permit metrics stationary near @xmath7 and indeed will allow only these for analytic , asymptotically - flat vacuum or electrovac metrics . we follow the method of @xcite for both the vacuum and electrovac field equations , deferring other cases to a second article , but in a different coordinate and tetrad system . our coordinate and tetrad system is similar to the one used at @xmath15 in @xcite , and to prove the existence of a symmetry at the event horizon in @xcite and at a compact cauchy horizon in @xcite . we also differ from @xcite in the choice of conformal gauge . in @xcite the unphysical ricci scalar is set to zero by a choice of conformal factor obtained by solving a wave equation . however , the solution of the characteristic ivp for this wave equation as posed in @xcite will not in general be periodic , so that the rescaled , unphysical metric would not in general share the periodicity of the physical metric - in fact , in the particular case of the reissner - nordstrm solution this gauge choice is compatible with periodicity only for zero mass , as we show in appendix c. thus we assume that there is at least one conformal factor which is periodic and then modify this choice in the course of the calculation in order to simplify the spin coefficients . from this point on , our method is then essentially the same as in @xcite , though a little more complicated , and we arrive at the same conclusion , but now with a killing vector which is time - like in the interior , at least near to @xmath7 . the condition of time - like periodicity which we impose is as follows : a space - time is time - like periodic if there is a discrete isometry taking any point of the physical space - time to a point in its chronological future . to define time - like periodicity at @xmath7 for an asymptotically - flat space - time , we require this isometry to extend to an isometry of a neighbourhood of @xmath19 which preserves the generators of @xmath19 . in particular , we require the existence of at least one @xmath20 which conformally compactifies the space - time and preserves the periodicity . the isometry has to be a supertranslation @xcite , @xmath21 on @xmath19 , in terms of the usual coordinates @xmath22 on @xmath7 and we shall assume that @xmath23 . ( we could imagine allowing @xmath24 to vanish on some generators of @xmath7 , since as noted above periodicity along a null translation in flat space would appear like this at @xmath7 , but this would be null - periodicity rather than time - like periodicity . ) we could assume further that @xmath24 is actually a positive constant but this turns out not to be necessary , as we shall find that , for analytic space - times , this assumption of periodicity necessarily leads to a space - time metric with a killing vector which , in coordinates to be defined , is @xmath14 and is time - like near @xmath7 . our result is    [ one ] a weakly - asymptotically simple , vacuum or electrovac , time - periodic space - time which is analytic in a neighbourhood of @xmath7 in the coordinates introduced below necessarily has a killing vector which is time - like in the interior and extends to a translation on @xmath7 . thus there are no _ non - trivial _ time - periodic solutions satisfying these conditions , in the sense that they would necessarily be actually time - independent if time - periodic . in a later article , we shall prove the corresponding result for the einstein equations coupled to either a massless scalar field with the usual energy - momentum tensor , or a solution of the conformally - invariant wave equation with the energy - momentum tensor from p125 of @xcite ( sometimes called the ` new improved energy momentum tensor ' ) .    the method of proof requires the assumption of analyticity . it was shown in @xcite that there are vacuum solutions analytic near @xmath7 . however , one would like either to drop the assumption of analyticity , for example following the lead of @xcite or @xcite with a similar problem , or to prove that it follows from the assumptions of periodicity and asymptotic - flatness . it remains to be seen in what circumstances this can be done since , as noted above , there are non - analytic solutions with matter in periodic motion and matched to a ( static ) schwarzschild exterior . while this work is primarily motivated by an interest in the possibility or impossibility of helical motions , it is worth noting the connection with the question of the inheritance of symmetry . recall that , for a solution of einstein s field equations with matter , the matter is said to inherit the symmetry of the metric if any isometry of the metric is necessarily a symmetry of the matter . there are explicit solutions of the einstein - maxwell equations known for which an isometry of the metric is _ not _ a symmetry of the maxwell field @xcite but these solutions are not asymptotically - flat . in @xcite some other references may be found for explicit solutions with maxwell fields which do not share the symmetry of the metric . the same will be true for some robinson - trautman solutions with null electromagnetic field which may depend on time though the metric is static ( see @xcite ,  28.2 ) these solutions will very likely have wire singularities extending to infinity . from theorem [ one ] noninheritance can not happen with asymptotically - flat , analytic solutions :    [ two ] in any weakly - asymptotically simple , stationary electrovac space - time which is analytic in a neighbourhood of @xmath7 in the coordinates introduced below , the maxwell field is also stationary . one can raise the question of inheritance also for einstein - scalar field solutions but the answer is rather different : for a massive ( complex ) klein - gordon field there do exist solutions , the so - called ` boson stars ' , for which the metric is spherically - symmetric , asymptotically - flat and static but the scalar field has a phase linear in time ( see e.g. @xcite ) ; however these solutions are not analytic at infinity and , by a scaling argument , such solutions do not exist with massless scalar fields . in a later article , we shall obtain this result as a corollary of the result corresponding to theorem [ one ] . in that subsequent work we start from the conformal einstein field equations with a general energy - momentum tensor as a source and specialize them to scalar field cases .    in section [ confemeq ] we analyze the conformal einstein - maxwell equations . we first rewrite maxwell s equations in the unphysical space - time , then translate the physical bianchi identities and obtain differential equations for the unphysical weyl spinor and ricci spinor . in appendix a we summarize a number of quantities , their relations and behaviour under conformal transformations in the newman - penrose formalism ( @xcite ) ; these are extensively used in the main text and in appendices b and c. in particular , all conformal equations for the gravitational and electromagnetic field analyzed in terms of spinors in section [ confemeq ] are projected on the spin basis ( i.e. the null tetrad ) and written down in the newman - penrose formalism in appendix b. in section 3 a suitable coordinate system and a convenient newman - penrose null tetrad which gives special values to some of the newman - penrose spin - coefficients are introduced in the neighbourhood of @xmath7 . as noted above , these differ from those used by the authors of @xcite , and we shall show the differences explicitly in section 3 . in appendix c we demonstrate that in contrast to @xcite our choice of gauge admits simple static ( i.e. ` periodic ' ) space - times like flat space and the reissner - nordstrm metric . in section 4 we follow @xcite ( although in a different conformal gauge ) and study the problem in the np formalism in the unphysical space - time , with data on @xmath7 . assuming periodicity along @xmath7 we first discover that the only possibility is the independence of all geometric quantities of an affine parameter @xmath12 along @xmath7 . by induction we then prove that all derivatives of all geometric quantities , including the physical metric components , in the direction into the physical space - time must also be @xmath25independent . the proof of theorem [ one ] and corollary [ two ] then follows from the assumed analyticity . this paper arose from a collaboration after p. t. posted his work @xcite on the gr - qc arxive and j. b. informed him that he and his phd . student m. s. were already engaged in tackling the same problem @xcite .","summary":"by an argument similar to that of gibbons and stewart , but in a different coordinate system and less restrictive gauge , we show that any weakly - asymptotically - simple , analytic vacuum or electrovacuum solutions of the einstein equations which are periodic in time are necessarily stationary .     +     +     +","abstract":"by an argument similar to that of gibbons and stewart , but in a different coordinate system and less restrictive gauge , we show that any weakly - asymptotically - simple , analytic vacuum or electrovacuum solutions of the einstein equations which are periodic in time are necessarily stationary .     +     +     +"}
{"article_id":"1409.4723","section_id":"i","document":"this paper concerns the search for a recursive formula for how denominator vectors ( @xmath0-vectors ) change under mutation of _ initial _ seeds . it is widely expected ( see e.g. ( * ? ? ? * remark  7.7 ) ) that no satisfactory initial - seed - mutation recursion holds in general , and indeed we do not produce one . however , a very nice initial - seed - mutation recursion holds in a varied collection of cluster algebras ( including the case considered in ( * ? ? ? * remark  7.7 ) ) . this recursion turns out to be equivalent to a beautiful duality formula in the style of the @xmath1-vectors/@xmath2-vectors dualities of nakanishi and zelevinsky @xcite . the first thing one notices when looking for such a recursion is that , to understand how denominators change when the initial seed is mutated , one must know something about a related family of integer vectors . specifically , if @xmath3 is the initial cluster , then the _ negation _ of the @xmath0-vector of a cluster variable @xmath4 is the vector of lowest powers of the @xmath5 occurring in the expression for @xmath4 as a laurent polynomial in @xmath6 . we define the * _ @xmath7-vector _ * of @xmath4 to be the vector of _ highest _ powers of the @xmath5 occurring in @xmath4 . our initial - seed - mutation recursion for @xmath0-vectors is equivalent to a description of the @xmath7-vectors in a given cluster in terms of the @xmath0-vectors in the same cluster .    in many cases , one can establish all three formulas by reading off the duality directly from expressions for denominator vectors found in the literature @xcite . in particular , all of them hold in finite type , in rank two , and more intriguingly , in nontrivial examples arising from marked surfaces . we conjecture that the initial - seed - mutation recursion holds in the case of source - sink moves in arbitrary cluster algebras . we prove this conjecture for cluster algebras arising from surfaces . besides their usefulness in understanding denominator vectors , the @xmath7-vectors may be of independent interest . a major goal in the study of cluster algebras is to give explicit formulas for the cluster variables . work in this direction includes realizing cluster variables as `` lambda lengths '' in the surfaces case @xcite , combinatorial formulas in rank two @xcite , in some finite types @xcite , and for some surfaces @xcite , and interpretations in terms of the representation theory of quivers , beginning with @xcite . short of a complete description of a cluster variable , one might instead describe its newton polytope ( the convex hull of the exponent vectors of the laurent monomials occurring in its laurent expansion ) . however , as far as the authors are aware , there are no results describing newton polytopes in cases where general formulas for the cluster variables are not known . ( the newton polytope may also be interesting when an explicit formula for the cluster variable is available , as in @xcite . )    together , the @xmath0-vectors and @xmath7-vectors amount to coarse information about newton polytopes , namely their `` bounding boxes . '' given a polytope @xmath8 in @xmath9 , define the * _ tight bounding box _ * of @xmath8 to be the smallest box @xmath10\\times\\cdots\\times[a_n , b_n]$ ] containing @xmath8 . ( readers who pay attention to bounding boxes of graphics files will find the notion familiar . ) equivalently , for each @xmath11 , the values @xmath12 and @xmath13 are respectively the minimum and maximum of the @xmath14 coordinates of points in @xmath8 . it is convenient to describe the tight bounding box by specifying the vectors @xmath15 and @xmath16 . the tight bounding box of the newton polytope of a laurent polynomial @xmath17 in @xmath6 is @xmath10\\times\\cdots\\times[a_n , b_n]$ ] such that @xmath12 is the lowest power of @xmath5 occurring in any laurent monomial of @xmath17 , and @xmath13 is the highest power of @xmath5 occurring . thus when @xmath4 is a cluster variable written as a laurent polynomial in the initial cluster @xmath3 , the tight bounding box of the newton polytope of @xmath4 is given by the negation of the @xmath0-vector and by the @xmath7-vector .","summary":"cluster variables in a cluster algebra can be parametrized by two families of integer vectors :-vectors and-vectors . while-vectors satisfy two recursive formulas ( one for initial - seed - mutations and one for final - seed - mutations ) ,-vectors admit only a final - seed - mutation recursion .    we present an initial - seed - mutation formula for-vectors and give two rephrasings of this recursion : one as a duality formula for-vectors in the style of the-vectors/-vectors dualities of nakanishi and zelevinsky , and one as a formula expressing the highest powers in the laurent expansion of a cluster variable in terms of the-vectors of any cluster containing it . we prove that the initial - seed - mutation recursion holds in a varied collection of cluster algebras , but not in general . we conjecture further that the formula holds _ for source - sink moves on the initial seed _ in an arbitrary cluster algebra , and we prove this conjecture in the case of surfaces .","abstract":"cluster variables in a cluster algebra can be parametrized by two families of integer vectors :-vectors and-vectors . while-vectors satisfy two recursive formulas ( one for initial - seed - mutations and one for final - seed - mutations ) ,-vectors admit only a final - seed - mutation recursion .    we present an initial - seed - mutation formula for-vectors and give two rephrasings of this recursion : one as a duality formula for-vectors in the style of the-vectors/-vectors dualities of nakanishi and zelevinsky , and one as a formula expressing the highest powers in the laurent expansion of a cluster variable in terms of the-vectors of any cluster containing it . we prove that the initial - seed - mutation recursion holds in a varied collection of cluster algebras , but not in general . we conjecture further that the formula holds _ for source - sink moves on the initial seed _ in an arbitrary cluster algebra , and we prove this conjecture in the case of surfaces ."}
{"article_id":"1512.08072","section_id":"i","document":"extragalactic background light ( ebl ) is the cumulative light emitted by any radiation process between the reionization era and the present epoch . sources include nucleosynthesis , emission from heated dust , and exotic particle decay . in particular , near - infrared ( ir ) ebl is thought to contain the redshifted ultraviolet radiation , which may have contributed to the reionization of the universe . therefore , near - ir ebl can serve as an indicator in investigations of galaxy formation and evolution in the early universe .    in the absolute measurement of near - ir ebl , foreground emissions , such as zodiacal light ( zl ) , integrated starlight ( isl ) , and diffuse galactic light ( dgl ) , must be removed from the sky brightness . previously , near - ir ebl has been investigated using data obtained from space telescopes , such as the diffuse infrared background experiment ( dirbe ) aboard the cosmic background explorer ( _ cobe _ ) satellite ( e.g. , hauser et al . 1998 ; gorjian et al . 2000 ; cambrsy et al . 2001 ; levenson et al . 2007 ; levenson & wright 2008 ) , the infrared telescope in space ( _ irts _ ) ( matsumoto et al . 2005 ; matsumoto et al . 2015 ) , and _ akari _ ( tsumura et al . the literature has shown that particularly at 1@xmath10 , the residual intensity was @xmath115 times higher than the intensity of the integrated galaxy light ( igl ) derived from deep galaxy counts ( madau & pozzetti 2000 ; totani et al . in addition , sano et al . ( 2015 ) , hereafter paper i , reanalyzed the dirbe data and revealed that deviations of the residual emission from isotropy are less than 10% at @xmath8 and @xmath12 in the entire sky . another indirect estimation of ebl intensity has been derived by observation of the spectra of blazars emitting high - energy @xmath7-rays . since such @xmath7-rays are attenuated by interacting with ebl photons in the propagation of the intergalactic space , upper limits of ebl intensity can be derived by assuming the intrinsic spectra of blazars ( e.g. , guy et al . 2000 ; dwek & krennrich 2005 ; schroedter 2005 ; aharonian et al . 2006 ; albert et al . 2008 ; mazin & raue 2007 ; orr et al . 2011 ; meyer et al . in addition , the recent result of the high energy stereoscopic system ( h.e.s.s . ) experiment has offered direct constraints on ebl , rather than estimated upper limits ( abramowski et al . most of the @xmath7-ray constraints on ebl at 1@xmath10 are a few to several times lower than the derived residual emissions , indicating that not all of the excess brightness originates from extragalactic sources . several studies have estimated the contributions of exotic extragalactic sources other than igl to ebl , including population iii ( pop - iii ) stars ( e.g. , inoue et al . 2013 ; fernandez et al . 2013 ) , intrahalo light ( ihl ) ( cooray et al . 2012 ; zemcov et al . 2014 ) , direct collapse black holes ( yue et al . 2013 ) , and dark stars ( maurer et al . as suggested by paper i , the total contribution of all of these sources can not account for the observed excesses at @xmath8 and @xmath12 . this fact also supports the idea that a portion of the excess emission may originate from the local universe : the milky way and/or the solar system .    at around @xmath4 , the previously derived residual emissions are smaller than those at 1@xmath10 , approaching igl and @xmath7-ray upper limits ( gorjian et al . 2000 ; wright & reese 2000 ; levenson et al . 2007 ; levenson & wright 2008 ) . since the zl contribution is much more dominant in wavelengths longer than @xmath13 , residual intensity has only been derived as upper limits ( hauser et al . 1998 ; tsumura et al . 2013c ) , consistent with the derived igl level ( fazio et al . 2004 ) . dgl , one of the foregrounds of optical to near - ir ebl , is thought to consist of starlight scattered by interstellar dust grains and thermal emission from the grains heated by this starlight . dgl can be used to measure the properties of the interstellar environment , including the intensity of the interstellar radiation field ( isrf ) , the size distribution of the dust grains , and the mass ratio of the total grains to the interstellar medium ( ism ) . in the current interstellar dust models ( e.g. , li & draine 2001 ; draine & li 2007 ; compigne et al . 2011 ) , interstellar dust is assumed to be a mixture of silicate and graphitic grains , including polycyclic aromatic hydrocarbon ( pah ) .    at optical wavelengths , dgl has been quantitatively investigated as a component that linearly correlates with diffuse interstellar @xmath14 emission ( e.g. , matsuoka et al . 2011 ; brandt & draine 2012 ; ienaka et al . in contrast , the dgl in the near - ir has been difficult to measure because the optical depth is too low to enhance the dgl emission ( leinert et al . it was only recently that an analysis of the data obtained by the cosmic infrared background experiment ( ciber ) ( arai et al . 2015 ) and dirbe ( paper i ) found the dgl component in high galactic latitudes at 1@xmath10 .    in the previous analysis of the dirbe data , arendt et al . ( 1998 ) used only a faint source model based on wainscoat et al.s ( 1992 ) star - counts model for the isl evaluation and did not find the dgl components at @xmath8 and @xmath12 . in contrast , paper i reanalyzed the dirbe data with an improved isl evaluation using the two micron all - sky survey ( 2mass ) point source catalog ( psc ) data ( cutri et al . 2003 ; skrutskie et al . 2006 ) and found the high - latitude dgl component at @xmath8 and @xmath12 . this suggests that precise isl evaluation is required for the dgl measurement because the brightnesses of both components are expressed as similar functions of the galactic latitude in principle . combining the results with those in the optical wavelengths ( matsuoka et al . 2011 ; ienaka et al . 2013 ) , arai et al . ( 2015 ) and paper i reported a bluer dgl spectrum from the optical to @xmath15 wavelengths , which is close to the expected scattered spectrum of an interstellar dust model in which the smaller dust grains are dominant . typical intensities of the high - latitude dgl at these bands were found to be less than 10% of that of the residual emission ( paper i ) .    in the longer near - ir wavelengths , arendt et al . ( 1998 ) derived the dgl results at @xmath0 and @xmath16 from the dirbe data only at low - galactic ( @xmath17 ) and high - ecliptic latitudes ( @xmath18 ) to enhance the dust emission and avoid strong zl emission . because of its low precision in the isl evaluation , their results were derived not by direct correlation against diffuse @xmath14 emission but by the color - color method , which makes use of the color difference between isl and dgl . more importantly , they assumed that the dgl results in the low galactic latitudes , including the region close to the galactic plane , are the same as those in the high - latitude region of greater interest for dgl and ebl measurements . naturally , it is questionable whether the dgl results at low latitudes are applicable at high latitudes because dust properties , such as size distribution and composition of the grains , could be different between these regions . thereafter , the obtained dgl results have been used for the high - latitudes dgl contribution to the ebl measurements ( dwek & arendt 1998 ; gorjian et al . 2000 ) . interstellar dust grains heated by the isrf for the solar neighborhood , which is estimated by mathis et al . ( 1983 ) , are expected to radiate thermal emission at the @xmath0 and @xmath16 wavelength range ( e.g. , dwek et al . 1997 ; li & draine 2001 ; draine & li 2007 ; compigne et al . in contrast , tsumura et al . ( 2013b ) and matsumoto et al . ( 2015 ) recently reported no detection of dgl at high galactic latitudes ( @xmath19 ) in their analysis of the diffuse sky spectrum obtained with _ akari _ and _ irts _ , because of the low signal - to - noise ratio in their analyses of limited regions of the sky . if the isl estimation is improved from the previous dirbe analysis ( arendt et al . 1998 ) , we expect dirbe to be the most appropriate data to confirm the high - latitude dgl component since they provide us with all - sky maps of higher signal - to - noise ratio .      as described in paper i , it is beneficial to use a combination of all - sky maps obtained from dirbe and the deep point source catalog ( 2mass psc ) for isl evaluation , in order to analyze the diffuse sky emission components at @xmath8 and @xmath12 . to apply this strategy to the dirbe data in the @xmath0 and @xmath16 bands , we use the allwise source catalog based on the wide - field infrared survey explorer mission ( wise ; wright et al . the allwise source catalog provides accurate photometries and positions of over 747 million objects in the @xmath20 ( w1 ) , @xmath21 ( w2 ) , @xmath22 ( w3 ) , and @xmath23 ( w4 ) bandpasses . in the w1 and w2 bands , the allwise achieved @xmath24 sensitivities of @xmath25 and @xmath26mag in the vega magnitude , respectively . these are comparable to those of the 2mass psc  15.8 and @xmath27mag in the @xmath28 and @xmath29 bands , respectively . since no star - count catalog has been available at @xmath30 , previous studies have used the @xmath12 dirbe or 2mass data to estimate the isl contribution at @xmath30 ( dwek & arendt 1998 ; wright & reese 2000 ; levenson et al . in contrast , the present study directly derives the isl intensity at @xmath0 and @xmath16 using the allwise source catalog . using the dirbe data , the present study mainly describes reanalysis of dgl and the residual emission components at @xmath0 and @xmath16 at high galactic latitudes . as our results , we first found a direct linear correlation between the diffuse near - ir and interstellar @xmath31 emission at high latitudes ( @xmath3 ) , which allows us to compare our results with those predicted by dust models in the high - latitude region . at @xmath30 , the intensity of the residual emission was the same level as in the other studies within the uncertainty , marginally consistent with the igl level and @xmath7-ray constraints on ebl . the remainder of this paper is organized as follows . in section 2 , we provide an overview of the dirbe data used in this paper and describe the analysis , including the decomposition of each diffuse emission . in section 3 , we present the results of each emission component at @xmath0 and @xmath16 in the high - latitude region . we compare the dgl results with the predictions of interstellar dust models composed of silicate and carbonaceous grains including pahs . we also compare the derived residual emission components with other studies . a summary of this paper appears in section 4 .    in this paper , the intensities of the sky emissions are expressed in units of @xmath32 or @xmath33 . the conversion formula between these units is @xmath34\\ , { \\it i_{\\nu}}\\ , ( \\rm{mjy\\,sr^{-1}}).\\ ] ]","summary":"using all - sky maps obtained from _","abstract":"using all - sky maps obtained from _ cobe_/dirbe at and , we present a reanalysis of diffuse sky emissions such as zodiacal light ( zl ) , diffuse galactic light ( dgl ) , integrated starlight ( isl ) , and isotropic residual emission including the extragalactic background light ( ebl ) . our new analysis , which includes an improved estimate of isl using the wide - field infrared survey explorer ( wise ) data , enabled us to find the dgl signal in a direct linear correlation between diffuse near - infrared and emission at high galactic latitudes ( ) . at , the high - latitude dgl result is comparable to the low - latitude value derived from the previous dirbe analysis . in comparison with models of the dgl spectrum assuming a size distribution of dust grains composed of amorphous silicate , graphite , and polycyclic aromatic hydrocarbon ( pah ) , the measured dgl values at and  constrain the mass fraction of pah particles in the total dust species to be more than . this was consistent with the results of _ spitzer_/irac toward the lower galactic latitude regions . the derived residual emission of at is marginally consistent with the level of integrated galaxy light and the ebl constraints from the-ray observations . the residual emission at is not significantly detected due to the large uncertainty in the zl subtraction , same as previous studies . combined with our reanalysis of the dirbe data at and , the residual emission in the near - infrared exhibits the rayleigh - jeans spectrum ."}
{"article_id":"1512.08072","section_id":"r","document":"the parameters determined by the fitting and the corresponding statistical uncertainties are listed in the `` result '' and `` statistical '' rows in table 1 , respectively . owing to the sample size of tens of thousands of pixels , the statistical uncertainty of each component is very small . in figure 2 , we illustrate the fitting results with the determined parameters in both bands . each panel shows that each emission component is decomposed from the sky brightness , according to the assumed linear combination model ( equation ( 13 ) ) . filled circles and error bars in each panel , respectively , represent the weighted means and uncertainties of the points within an arbitrary x - direction bin . in the following discussion , these weighted means are used as representative values . in particular , panels ( b ) and ( b ) of figure 2 illustrate the direct linear correlation between the intensity of interstellar @xmath2 emission and that of the diffuse near - ir light , indicating the existence of a dgl component in high galactic latitudes . in table 2 , we present the average of the determined intensity of each component in the analyzed region , together with its standard deviation . in comparison with the emission components at @xmath149 , the zl accounts for more than @xmath150 of the sky brightness at @xmath151 on average . such a strong zl component can make the decomposition analysis at @xmath151 more difficult and cause more dispersion of the samples from the best - fit lines in the result of the faint dgl component ( panel ( b ) of figure 2 ) . in addition to the fitting in the entire high - latitude sky , we divide the region into six galactic longitude bins : @xmath152 , @xmath153 , @xmath154 , @xmath155 , @xmath156 , and @xmath157 . we then conduct the @xmath158 minimum analysis in each field to estimate the scatter of the parameters between each region . the determined parameters at each galactic longitude field at @xmath0 and @xmath1 are illustrated in figures 3 and 4 , respectively . the regional difference of each parameter may be caused by the simultaneous fit of each component , which is adopted in the present analysis . if the intensities of some components have similar spatial distributions in a region , part of the intensity of the component can be absorbed or given by that of other components . the degree of multicollinearity is different in each region , causing regional variation in the fitting results . this phenomenon is inevitable in the decomposition analysis of multiple components over the wide field of the sky . as a conservative uncertainty associated with the regional variation in each parameter , we calculate the standard deviation of the determined value in the six regions and list them in the row `` scatter '' in table 1 . owing to the much stronger zl component at @xmath151 , the `` scatter '' of each parameter is larger at @xmath151 than at @xmath149 . for the parameters @xmath159 , @xmath160 , and @xmath105 , the total uncertainties are expressed as the quadrature sum of the uncertainties of `` statistical '' and `` scatter '' in the row `` quadrature sum '' in table 1 , though the `` scatter '' component is dominant . the panels ( b ) and ( c ) of figure 3 show that all or most of the values at the six divided regions fall into one side of the all - sky value , though the values in the divided regions are naively expected to be distributed evenly around the all - sky value . these phenomena may be attributed to the intensity difference of each emission component . as shown in table 2 , even at @xmath149 , the typical intensity of the zl can be 10 to 100 times higher than that of the isl and dgl . in this situation , the small difference of the zl intensity between each region could cause the biased fitting results in the isl and dgl components . the scaling factor of the kelsall model , the parameter @xmath159 , is determined to be 10%15% larger than 1.0 in both bands ( table 1 ) , indicating that the kelsall model underestimates the zl brightness . this trend has also been reported by tsumura et al . ( 2013a ) and matsumoto et al . ( 2015 ) in their analysis of the _ akari _ and _ irts _ data , respectively . as suggested by paper i , the incompleteness of the kelsall model can contribute to such deviations . to determine the numerous physical parameters of zl , kelsall et al . ( 1998 ) used only part of the dirbe data to avoid excessive computational times . this approximation can lower the precision of the determined parameters in the kelsall model , such as phase function , albedo of interplanetary dust . the scaling factor of the isl , the parameter @xmath105 , is determined to be less than 1.0 ( table 1 ) . taking into account the contributions of stars fainter than the sensitivity limits of allwise , the parameter @xmath105 should be more than 1.0 . however , several studies have reported a similar trend in the correlation analysis of the dirbe data against the isl of the 2mass sources ( cambrsy et al . 2001 ; levenson et al . they reported that the parameter can be less than 1.0 by @xmath161 at @xmath9 . cambrsy et al . ( 2001 ) attributed this to the different methods of photometric calibration used by dirbe and 2mass ; that is , sirius was used as a reference for dirbe ( hauser et al . 1998 ) , but several faint stars were used for 2mass ( skrutskie et al . 2006 ) to avoid saturation . wise was calibrated by several stars fainter than vega ( wright et al . 2010 ) , similar to the 2mass calibration strategy . the small value of @xmath105 can be caused because the effect of photometric calibration difference between dirbe and wise is more dominant than the contribution of the isl of fainter stars . additionally , the very small value of @xmath162 at @xmath1 may be contributed by the multicollinearity effect between zl and isl due to the intense zl component and the very weak isl component ( table 2 ) . the derived typical isl intensities ( table 2 ) are consistent with the values of the faint source model used in the previous analysis of the dirbe data ( see figure 2 of hauser et al . ( 1998 ) ) . the determined parameters , @xmath75 ( dgl ) and @xmath110 ( residual emission ) , are discussed in the following two subsections .            note .  symbols in the column headings are defined in subsection 2.2 . + the analyzed region is @xmath114 at @xmath149 and @xmath114 , @xmath122 at @xmath151 .    note .  except for @xmath108 , each component is represented by its average and the standard deviation + of the samples in the analyzed region  @xmath114 at @xmath149 and @xmath114 , @xmath122 at @xmath151 . + the surrounding regions of bright sources ( @xmath163 ) are excluded in both bands . as illustrated in panels ( b ) and ( b ) of figure 2 , we first find the dgl signal at the high galactic latitude region at @xmath0 and @xmath1 in the correlation between diffuse near - ir and @xmath2 emission . figure 5 shows the current results for intensity ratios between dgl and diffuse @xmath2 emission in the optical to the near - ir wavelengths . as indicated by the blue and green curves in figure 5 , brandt & draine ( 2012 ) estimated the spectra of the starlight scattered by the plane - parallel - distributed dust grains , based on the different dust models of zubko et al . ( 2004 ) , hereafter zda04 , and weingertner & draine ( 2001 ) , hereafter wd01 , respectively , with the de - reddening correction of the original isrf estimation derived by mathis et al . ( 1983 ) , hereafter mmp83 , and the stellar population synthesis model of bruzual & charlot ( 2003 ) , hereafter bc03 . brandt & draine ( 2012 ) used the bc03 model with solar metallicity and a star formation rate of @xmath164 , where @xmath165 denotes the timescale in units of gyr . as summarized in chapter 23 of draine ( 2011 ) , both the zda04 and the wd01 models are composed of graphite , silicate , and pah materials . however , they differ in the size distributions of the grains . the half - mass radius , @xmath166 ( 50% of the total mass in grains with the radius @xmath167 ) , is @xmath168 and @xmath169 for the graphite and silicate grains , respectively , in zda04 , but is @xmath170 for both grains in wd01 , leading to a much greater mass in @xmath171 in wd01 . draine ( 2011 ) pointed out that the wd01 model better reproduces the observed extinction curve from ultraviolet to the near - ir wavelengths , as derived by fitzpatrick ( 1999 ) . in addition to the scattering component of dgl , the orange curves in figure 5 represent the expected spectra of the near - ir emission from interstellar dust , a mixture of amorphous silicate and carbonaceous grains including pah ( draine & li 2007 ; hereafter dl07 ) . as shown in figure 12 of dl07 , the increase in the pah abundance directly causes high - intensity dust emission in the near - ir . in figure 5 , we show the three dl07 models in which the mass fraction between pah particles and total dust , @xmath172 , is different , i.e. , @xmath173 , @xmath174 , or @xmath175 . to compare with the values obtained in the general interstellar fields , the scaling factor against the isrf intensity of mmp83 , @xmath176 , is set to @xmath177 ,  corresponding to the isrf intensity for the solar neighborhood . in the literature , the value of @xmath177 has been adopted in the general interstellar field throughout the sky ( e.g. , dwek et al . 1997 ; li & draine 2001 ; draine & li 2007 ; compigne et al . all model spectra in figure 5 show the distinct pah feature of the c - h stretching mode at @xmath178 . in dl07 , the intensity of the dust emission is calculated as @xmath179 , where @xmath180 denotes hydrogen column density . to convert @xmath180 to the diffuse @xmath2 intensity , we use the ratio of @xmath2 emission to h i column density derived from the dirbe data at high - latitude regions of @xmath181  18.6 @xmath182 ( arendt et al . 1998 ) . compared with the values of the dl07 spectra convolved with each dirbe band ( asterisks in figure 5 ) , the present result at @xmath4 falls between the model with @xmath183 and that with @xmath184 . at @xmath1 , the present result prefers the model with @xmath183 , without the large uncertainty caused by the regional variation in the decomposition analysis ( see subsection 3.1 ) . as shown in figure 16 of dl07 , the ir emission colors obtained by the _ spitzer_/irac ( infrared array camera ) observation toward several regions of the lower galactic latitudes ( flagey et al . 2006 ) are closer to that of the dl07 model with @xmath183 . compigne et al . ( 2011 ) also modeled the high - latitude dust emission with the pah parameter of @xmath185 . the dust emission intensity at 3@xmath186 is comparable between their model and the dl07 model of @xmath183 ; the difference between the two models fall within @xmath187 in that wavelength range ( see figure 6 of compigne et al . ( 2011 ) ) . combining the present values with these results , it is probable that @xmath172 is above @xmath5 in the high - latitude region .    in the previous analysis of dirbe data , arendt et al . ( 1998 ) derived the intensity ratios of dgl to @xmath2 emission only in low - latitude regions of @xmath188 ( filled black circles in figure 5 ) . at @xmath4 , their low - latitude result is comparable to the present high - latitude value . this indicates that the pah abundance do not greatly change throughout the general interstellar field in the milky way , except in the region of the galactic plane . at @xmath1 , the result of arendt et al . ( 1998 ) is two times higher than that of the model spectra ; li & draine ( 2001 ) thus suggested an additional opacity for the ultra - small grain component to explain this excess . however , such components may not be required by our result at @xmath1 , without the uncertainty of regional variation . the intensities of the dl07 models with @xmath183 are a few times lower than that obtained with _ akari _ ( tsumura et al . 2013b ; solid black curve in figure 5 ) in the continuum spectra . the low - latitude result of _ akari _ ( @xmath189 ) may cause such a difference . it is suspicious that @xmath177 can be adopted in the low - latitude region because of its higher isrf . unfortunately , tsumura et al . ( 2013b ) did not find the dgl feature in the high - latitude region , probably due to the low signal - to - noise ratio of the observation , same as in the reanalysis of the _ irts _ data ( matsumoto et al . 2015 ) .    to maintain consistency with the results at optical wavelengths ( matsuoka et al . 2011 ; ienaka et al . 2013 ) , paper i and arai et al . ( 2015 ) have both suggested a bluer dgl spectrum at 1@xmath67 , fitted to the twice - scaled zda04 model spectra ( blue curves in figure 5 ) . however , there is no firm reason to allow the scaling of the model to fit the observed results . in addition , the size distribution of the dust grains differs between the dl07 and zda04 models ; dl07 adopts the wd01 model , which better reproduces the observed extinction curve ( fitzpatrick 1999 ) . therefore , it may be premature to conclude that the scattering components of dgl have a bluer spectrum with a larger contribution of smaller dust grains . figure 5 shows that the original model spectra based on the wd01 model ( green curves ) can be fitted to the observed results of paper i and arai et al . ( 2015 ) without violating the present results at @xmath0 and @xmath1 . in this case , the observed results of matsuoka et al . ( 2011 ) are larger than the model spectra by a factor of 2 . to explain this discrepancy , the albedo of the dust grains in the optical wavelengths should be larger than the dgl model of brandt & draine ( 2012 ) without a change in the albedo in the near - ir . by solving the simple radiative transfer of light through the dust slab , ienaka et al . ( 2013 ) expressed the parameters @xmath160 as functions of albedo and optical depth ( see appendix of ienaka et al . according to the solution of their equation , only an @xmath187 increase in the visual albedo can enhance the parameter @xmath160 by a factor of 2 . this small change in the optical albedo in the model of brandt & draine ( 2012 ) may explain the excess values of matsuoka et al . ( 2011 ) .    for a further study of interstellar dust using dgl , both precise spectroscopic observations of dgl with high signal - to - noise ratios and dgl models which simultaneously reproduce scattering and thermal emission components will be needed .            for the residual emission components @xmath190 , we estimate the additional uncertainties associated with the absolute gain of dirbe , faint galaxies , and the zl model . hauser et al . ( 1998 ) reported uncertainties of @xmath43 and @xmath44 in the absolute gain of dirbe at @xmath0 and @xmath151 , respectively . the values of these uncertainties correspond to percentages of the derived parameter @xmath190 , and appear in the row `` gain '' in table 1 .    the allwise catalog may contain unresolved faint galaxies , which should be added to the uncertainty budget of the parameter @xmath190 . levenson et al . ( 2007 ) estimated the contribution of such galaxies at @xmath149 of @xmath191 , which corresponds to galaxies of @xmath192 in the 2mass psc . assuming this value is of the same order as the allwise sources , we adopt this as the uncertainty of faint galaxies at @xmath149 . generally , the spectrum of a galaxy does not drastically change between @xmath0 and @xmath151 . we then set the same value at @xmath151 . these uncertainties are listed in the `` galaxies '' row in table 1 .    as described in kelsall et al . ( 1998 ) , the uncertainty of the kelsall model is estimated as the intensity difference between the two zl models at the north galactic pole ( ngp ) where the difference is reported to be the largest . this uncertainty is @xmath193 and @xmath194 at @xmath0 and @xmath151 , respectively , listed in the row `` zl model '' in table 1 . the quadrature sum of the uncertainties of the parameter @xmath190 is presented in the row `` quadrature sum '' in table 1 . for the parameter @xmath190 , the uncertainties associated with the regional variation in the parameter and the kelsall model dominate over the other uncertainties .              to test the isotropy of the residual emission , figure 6 illustrates @xmath195 with the parameters @xmath190 being functions of the galactic latitude @xmath196 ( panels ( a ) and ( a ) ) and the ecliptic latitude @xmath197 ( panels ( b ) and ( b ) ) in both bands . other than in the region where @xmath198 , the residual emission shows similar trends at @xmath0 and @xmath151 as functions of galactic latitude ; it increases toward the low - galactic latitudes ( panels ( a ) and ( a ) ) . paper i found the same trend in the analysis of the residual emission at @xmath8 and @xmath199 with the 2mass data and suggested two explanations for this trend . one was the simply modeled isl term , @xmath200 , where @xmath201 denotes the integrated intensity of the 2mass sources below the detection limit . such a trend could be caused if the spatial distribution of intensity as a function of galactic latitude differs between @xmath201 and the isl of stars fainter than the detection limits of 2mass . another was the contribution of the faint stars that were not detected in the 2mass psc due to the masking effect of the nearby bright sources . such faint stars increase as the number density of the bright sources increases toward the lower - galactic latitudes . these explanations can be applied to the present study , which evaluates isl using the allwise sources in the same way as the 2mass psc in paper i.    in the region of @xmath198 , the residual emission shows the inverse behavior : it increases toward ngp . to investigate this phenomenon , we plot @xmath202 and @xmath203 with the residual emission in figure 7 . reasonably , the modeled galactic components @xmath203 increase toward the low - galactic latitudes . in contrast , @xmath202 shows the same feature as the residual emission in the @xmath198 region , indicating that the trend is caused by @xmath63 . the fact that such a feature is larger at @xmath151 than at @xmath149 is then reasonable because of the stronger zl component at @xmath151 . however , the reason why such a feature is seen only at @xmath198 is unclear . for one thing , kelsall et al . ( 1998 ) pointed out that the intensity differences between the different zl models are largest in the ngp region . such difficulty in the modeling of zl near the ngp region may be related to the trend at @xmath198 .    as a function of ecliptic latitude , the residual emission is relatively constant at @xmath149 , but is systematically larger toward the lower - ecliptic latitudes at @xmath151 ( panels ( b ) and ( b ) of figure 6 ) . this indicates the difficulty of modeling of zl at @xmath151 , where the zl intensity is much stronger than that at @xmath149 . in addition to the high intensity of the zl at @xmath151 , the incompleteness of the zl model in the band may contribute to the large scatter of the other components  dgl , isl , and the residual emission ( see figure 4 ) . in this situation , there seems to be room for improvement on the zl model , though it is generally difficult .    though the residual emissions show some amount of scatter as functions of @xmath196 and @xmath197 , they are within the typical scatter derived by the regional variation in the parameters @xmath190 ( see table 1 and subsection 3.1 ) , because such regional variation naturally includes the dependence of @xmath196 and @xmath197 . such scatter as functions of @xmath196 and @xmath197 is also comparable to the estimated systematic uncertainty of the kelsall model ( table 1 ) . for the isotropy measurement of the residual emissions , we therefore use the `` scatter '' value ( table 1 ) as the conservative values . in our analysis , the deviation of the residual emission from the isotropy is then less than @xmath204 of the residual intensity at @xmath149 . this deviation from the isotropy is larger than that of @xmath205 at @xmath8 and @xmath199 ( paper i ) , partly because the residual emission intensity at @xmath149 is more than two times smaller than those at @xmath8 and @xmath199 . we do not discuss the isotropy of the residual emission at @xmath151 due to the very large scatter .      in figure 8 , we compare the resultant residual emissions of paper i and the present study with those of previous studies . as illustrated in figure 5 , the present dgl result at @xmath149 in the high galactic latitudes is comparable to the results obtained at low - galactic latitudes ( arendt et al . 1998 ) within the uncertainty . this leads to the same level of residual emissions as in the previous studies adopting the dgl result derived by arendt et al . ( 1998 ) at @xmath149 ( gorjian et al . 2000 ) . at @xmath151 , the residual emission is not significantly detected due to large uncertainty associated with the zl subtraction , same as the previous studies ( hauser et al . 1998 ; tsumura et al . 2013c ) . the intensity of the residual emission changes according to the different zl models ; using the kelsall model or wright s ( 1998 ) model , several studies have reported large residual emissions at @xmath8 and @xmath199 ( gorjian et al . 2000 ; cambrsy et al . 2001 ; levenson et al . 2007 ; tsumura et al . 2013c ; matsumoto et al . 2015 ; paper i ) , which are @xmath206@xmath207 times the observed or modeled igl intensity ( e.g. , madau & pozzetti 2000 ; totani et al . 2001 ; stecker et al . 2006 ; mazin & raue 2007 ; franceschini et al . 2008 ; finke et al . 2010 ; domnguez et al . 2011 ) . because such large residual emissions also exceed most of the @xmath7-ray constraints of ebl ( e.g. , aharonian et al . 2006 ; abramowski et al . 2013 ) , it is difficult to regard them as being entirely of extragalactic origin . in addition , paper i suggested that igl , together with the contributions of all of the exotic extragalactic sources estimated so far , including pop - iii stars ( inoue et al . 2013 ; fernandez et al . 2013 ) , ihl ( zemcov et al . 2014 ) , direct collapse black holes ( yue et al . 2013 ) , and dark stars ( maurer et al . 2012 ) , can not account for the excess residual emission , especially at @xmath208 . therefore , it is probable that part of the excess emission comes from the local universe .    compared with the residual emissions at @xmath8 and @xmath199 , the present result at @xmath149 is relatively small , approaching the igl level and @xmath7-ray constraints . combined with the results of paper i , the spectrum of the near - ir residual isotropic emission has the rayleigh - jeans spectrum , consistent with the previous studies . in contrast , a large gap exists between the two results in the optical wavelengths : matsuoka et al . ( 2011 ) and bernstein ( 2007 ) . because the results of matsuoka et al . ( 2011 ) were obtained from the _ pioneer 10/11 _ observation beyond 3au from the earth , where the zl contribution is negligible , the residual emission may be regarded as the optical ebl intensity . if this is true , the intensity gap between matsuoka et al . ( 2011 ) and bernstein ( 2007 ) can be attributed to the unmodeled zl contribution . the present decomposition analysis , which deals with the integrated light of each emission component can not identify where the residual emission comes from . as mentioned above , part of the residual emission can arise from the local universe , such as the milky way or solar system due to the contradiction against the @xmath7-ray constraints . in their interpretation of the derived isotropic residual emissions at @xmath209 and @xmath210 , dwek et al . ( 1998 ) suggested that the galactic component can not produce the residual intensity because an unreasonably large gas and dust mass is needed . from this point of view , the `` isotropic dgl component '' , the counterpart of the isotropic far - ir emission from ism , is unlikely to contribute to the residual emission in the optical to near - ir wavelengths . recently , lehner et al . ( 2015 ) reported the presence of the massive circumgalactic medium around the andromeda galaxy . however , it is very unclear that such component also exists around the milky way and creates the isotropic emission . another possible origin of the residual emission may be within the solar system , including zl . as reported by dwek et al . ( 2005 ) , the spectrum of near - ir excess residual emission is similar to the zl spectrum . in addition , some isotropic components associated with zl can be added to the kelsall model because absolute measurement of zl is impossible from the orbit of the earth ( hauser et al . however , such isotropic zl components have not been observationally confirmed and it is suspicious that they would have the same spectrum as the currently measured zl . to reveal whether the residual emission components include the zl contribution , the exo - zodiacal infrared telescope ( exzit ) , one of the science instruments of the solar power sail spacecraft planned for launch in 2020s , will be useful ; this mission is planned to observe the universe in the near - ir wavelengths beyond the interplanetary dust region ( matsuura et al . exzit will reveal the three - dimensional structure of interplanetary dust and the absolute ebl intensity without the uncertainty of the zl model .","summary":"spitzer_/irac toward the lower galactic latitude regions . the residual emission at is not significantly detected due to the large uncertainty in the zl subtraction , same as previous studies .","abstract":"using all - sky maps obtained from _ cobe_/dirbe at and , we present a reanalysis of diffuse sky emissions such as zodiacal light ( zl ) , diffuse galactic light ( dgl ) , integrated starlight ( isl ) , and isotropic residual emission including the extragalactic background light ( ebl ) . our new analysis , which includes an improved estimate of isl using the wide - field infrared survey explorer ( wise ) data , enabled us to find the dgl signal in a direct linear correlation between diffuse near - infrared and emission at high galactic latitudes ( ) . at , the high - latitude dgl result is comparable to the low - latitude value derived from the previous dirbe analysis . in comparison with models of the dgl spectrum assuming a size distribution of dust grains composed of amorphous silicate , graphite , and polycyclic aromatic hydrocarbon ( pah ) , the measured dgl values at and  constrain the mass fraction of pah particles in the total dust species to be more than . this was consistent with the results of _ spitzer_/irac toward the lower galactic latitude regions . the derived residual emission of at is marginally consistent with the level of integrated galaxy light and the ebl constraints from the-ray observations . the residual emission at is not significantly detected due to the large uncertainty in the zl subtraction , same as previous studies . combined with our reanalysis of the dirbe data at and , the residual emission in the near - infrared exhibits the rayleigh - jeans spectrum ."}
{"article_id":"1512.08072","section_id":"i","document":"we reanalyze the diffuse sky brightness at 3.5 and @xmath1 using the _ cobe_/dirbe data in the high galactic latitude region , in which dgl evaluation has been controversial for ebl measurements due to the low optical depth to enhance the dgl intensity . since paper i succeeded in finding the dgl component at 1.25 and @xmath9 with the precise isl evaluation by 2mass , we adopt a similar method at 3.5 and @xmath1 using the allwise source catalog instead of 2mass . taking account of the dirbe beam shapes for the allwise sources below the sensitivity limit , we create the isl intensity maps at 3.5 and @xmath1 , same as paper i. we then assume that the sky brightness is expressed as a linear combination of zl , dgl , isl , and residual emission including the ebl components and decompose the four components by a @xmath158 minimum analysis . as a result , we first find the direct linear correlation between diffuse near - ir light and interstellar @xmath2 emission in the high - latitude region of @xmath3 , indicating the extraction of the dgl component . the high - latitude dgl result at @xmath4 is revealed to be comparable to the low - latitude value derived from the previous dirbe analysis ( arendt et al . 1998 ) . compared with the model of the dgl spectra that assumes a size distribution of the dust grains composed of amorphous silicate and graphite including pah particles ( dl07 ) , the present results at @xmath0 and @xmath1 constrained the mass ratio of pahs to the total dust grains to be above @xmath5 , which is consistent with the results of _ spitzer_/irac .    for the residual emission , we derive the weak result of @xmath6 at @xmath4 , consistent with other studies . compared with the results of the residual emissions at 1@xmath67 , this intensity at @xmath4 approaches the @xmath7-ray constrains on ebl and the igl level , showing that the residual emission intensity exhibits the rayleigh - jeans spectrum in the near - ir . in our analysis , the deviation of the residual emission from the isotropy was less than @xmath211 at @xmath4 . at @xmath1 , the uncertainty of the residual emission is large , but the result in this band is consistent with the upper limits derived by the previous studies .      we wish to thank t.  d. brandt and k. tsumura for providing their data . we are grateful to the referee , varoujan gorjian , for a number of useful comments that improved the paper . is supported by grant - in - aid for japan society for the promotion of science ( jsps ) fellows . this publication uses the _ cobe _ datasets developed by the national aeronautics and space administration ( nasa ) goddard space flight center under the guidance of the _ cobe _ science working group . this publication also makes use of data products from wise , which is a joint project between the university of california , los angeles , and the jet propulsion laboratory / california institute of technology . wise 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 a. , & scully , s.  t.  2006 , , 648 , 774 tokunaga , a.  t. , & vacca , w.  d.  2005 , , 117 , 421 totani , t. , yoshii , y. , iwamuro , f. , maihara , t. , & motohara , k.  2001 , , 550 , l137 tsumura , k. , matsumoto , t. , matsuura , s. , et al . 2013a , , 65 , 119 tsumura , k. , matsumoto , t. , matsuura , s. , et al . 2013b , , 65 , 120 tsumura , k. , matsumoto , t. , matsuura , s. , et al . 2013c , , 65 , 121 wainscoat , r.  j. , cohen , m. , volk , k. , walker , h.  j. , & schwartz , d.  e.  1992 , , 83 , 111 weingartner , j.  c. , & draine , b.  t.  2001 , , 548 , 296 wright , e.  l.  1998 , , 496 , 1 wright , e.  l. , & reese , e.  d.  2000 , , 545 , 43 wright , e.  l.  2001 , , 553 , 538 wright , e.  l. , eisenhardt , p.  r.  m. , mainzer , a.  k. , et al . 2010 , , 140 , 1868 yue , b. , ferrara , a. , salvaterra , r. , xu , y. , & chen , x.  2013 , , 433 , 1556 zemcov , m. , smidt , j. , arai , t. , et al . 2014 , science , 346 , 732 zubko , v. , dwek , e. , & arendt , r.  g.  2004 , , 152 , 211","summary":"cobe_/dirbe at and , we present a reanalysis of diffuse sky emissions such as zodiacal light ( zl ) , diffuse galactic light ( dgl ) , integrated starlight ( isl ) , and isotropic residual emission including the extragalactic background light ( ebl ) . our new analysis , which includes an improved estimate of isl using the wide - field infrared survey explorer ( wise ) data , enabled us to find the dgl signal in a direct linear correlation between diffuse near - infrared and emission at high galactic latitudes ( ) . at , the high - latitude dgl result is comparable to the low - latitude value derived from the previous dirbe analysis . in comparison with models of the dgl spectrum assuming a size distribution of dust grains composed of amorphous silicate , graphite , and polycyclic aromatic hydrocarbon ( pah ) , the measured dgl values at and  constrain the mass fraction of pah particles in the total dust species to be more than . this was consistent with the results of _ the derived residual emission of at is marginally consistent with the level of integrated galaxy light and the ebl constraints from the-ray observations . combined with our reanalysis of the dirbe data at and , the residual emission in the near - infrared exhibits the rayleigh - jeans spectrum .","abstract":"using all - sky maps obtained from _ cobe_/dirbe at and , we present a reanalysis of diffuse sky emissions such as zodiacal light ( zl ) , diffuse galactic light ( dgl ) , integrated starlight ( isl ) , and isotropic residual emission including the extragalactic background light ( ebl ) . our new analysis , which includes an improved estimate of isl using the wide - field infrared survey explorer ( wise ) data , enabled us to find the dgl signal in a direct linear correlation between diffuse near - infrared and emission at high galactic latitudes ( ) . at , the high - latitude dgl result is comparable to the low - latitude value derived from the previous dirbe analysis . in comparison with models of the dgl spectrum assuming a size distribution of dust grains composed of amorphous silicate , graphite , and polycyclic aromatic hydrocarbon ( pah ) , the measured dgl values at and  constrain the mass fraction of pah particles in the total dust species to be more than . this was consistent with the results of _ spitzer_/irac toward the lower galactic latitude regions . the derived residual emission of at is marginally consistent with the level of integrated galaxy light and the ebl constraints from the-ray observations . the residual emission at is not significantly detected due to the large uncertainty in the zl subtraction , same as previous studies . combined with our reanalysis of the dirbe data at and , the residual emission in the near - infrared exhibits the rayleigh - jeans spectrum ."}
{"article_id":"1309.0394","section_id":"i","document":"this paper aims to illustrate the unifying power of the notion of topos , due to grothendieck , in the context of cyclic homology . our main motivation originates from the recent discovery ( _ cf._@xcite ) of the role of cyclic homology of schemes for the cohomological interpretation of the archimedean local factors of l - functions of arithmetic varieties . this result raises naturally the question of a conceptual interpretation of cyclic homology of schemes . in @xcite it was shown that cyclic cohomology can be interpreted as ext - functor in the category of cyclic modules . these modules are defined as contravariant functors from the ( small ) cyclic category @xmath7 to the category of abelian groups . this development brings at the forefront the crucial role played by the cyclic category as an extension of the simplicial category @xmath8 by finite cyclic groups . moreover , in _ op.cit . _  it was also shown that the classifying space @xmath9 is equal to the classifying space of the topological group @xmath10 , and later it was discovered ( _ cf._@xcite ) that the geometric realization of the simplicial set underlying a cyclic set ( this latter understood as a contravariant functor @xmath11 to the category of sets ) inherits naturally an action of @xmath10 . the equality @xmath12 then leads to a deep analogy between cyclic cohomology and @xmath10-equivariant cohomology .    in this article we show that one obtains a conceptual understanding of the above @xmath10-action on the geometric realization of cyclic sets by extending that result to the framework of topos theory . the transition from a small category to its classifying space produces in general a substantial loss of information : the classifying space of @xmath8 is , for instance , a singleton . it is exactly at this point that the implementation of topos theory turns out to be useful to provide the correct environment that encloses both schemes and small categories while also furnishing the tools for the development of cohomology . in the words of grothendieck :     _ lide du _ topos _ englobe , dans une intuition topologique commune , aussi bien les traditionnels espaces ( topologiques ) , incarnant le monde de la grandeur continue , que les ( soi - disant ) `` espaces '' ( ou `` varits '' ) des gomtres algbristes abstraits impnitents , ainsi que dinnombrables autres types de structures , qui jusque - l avaient sembl rives irrmdiablement au `` monde arithmtique '' des agrgats `` discontinus '' ou `` discrets '' . _    the category @xmath13 of sheaves of sets on a topological space @xmath6 is a topos that captures all the relevant information on @xmath6 . for a small category @xmath14 , the associated category @xmath15 of contravariant functors @xmath16 is a topos . what is more , the notion of point is meaningful for any topos @xmath17 : a point is simply a geometric morphism @xmath18 from the topos of sets to @xmath17 . to each point of @xmath17 corresponds a contravariant functor @xmath19 which is the inverse image part of the geometric morphism @xmath20 and that preserves finite limits and arbitrary colimits . this picture generalizes the functor that associates to a sheaf of sets on a topological space @xmath6 the stalk at a point of @xmath6 . in particular , for the topos @xmath15 ( @xmath14 a small category ) , the points are described by _ flat , covariant _ functors @xmath21 . then the inverse image part of the geometric morphism associated to a point of @xmath22 determines a natural generalization of the notion of the geometric realization of a simplicial set . this latter notion is obtained , in the case @xmath23 , by considering the flat functor @xmath24 that associates to an integer @xmath25 the standard @xmath26-simplex . in general , the flatness of @xmath3 implies that the geometric realization functor @xmath27 into finite products in @xmath28 . this property combines with the fact that @xmath29 extends to the larger cyclic category @xmath30 to yield the natural action of the group @xmath10 on the geometric realization of a cyclic set .    in this paper we provide a far reaching generalization of this construction for the points of the topos of simplicial sets . given a point @xmath0 of the topos @xmath31 with associated flat functor @xmath32 , a _ cyclic structure _ on @xmath0 is defined to be an extension of @xmath3 from @xmath8 to @xmath30 . our main result states that cyclic structures are classified by the datum provided by a totally left - ordered group @xmath33 ( not necessarily abelian ) endowed with a central element @xmath34 such that the interval @xmath35\\subset g$ ] generates @xmath33 . it is well known ( _ cf._@xcite ) that the points of the topos @xmath36 correspond to intervals @xmath37 _ i.e. _  totally ordered sets with a minimal element @xmath38 and a maximal element @xmath39 . proposition [ propcp ] shows that if @xmath40 is a left - ordered group with a fixed central element @xmath34 , one obtains a natural cyclic structure on the point @xmath41 of @xmath42 associated to the interval @xmath43 $ ] . the converse of this statement constitutes the main result of this paper . more precisely one shows ( _ cf . _   theorem [ main ] ) the following    * theorem *  _ let @xmath0 be a point of the topos of simplicial sets and let @xmath37 be the associated interval . let @xmath44   be endowed with the lexicographic ordering , where the equivalence relation identifies @xmath45 , @xmath46 . then , a cyclic structure on @xmath0 corresponds to a group law on @xmath33 such that@xmath47   the order relation on @xmath33 is left invariant @xmath48  the following equalities hold @xmath49 _ the proof of the above theorem is rather involved and is developed in  [ mainsect ] . as an immediate corollary one obtains examples ( corollaries [ hom ] and [ hom1 ] ) of points @xmath50 of the topos @xmath31 with a prescribed number of cyclic structures . moreover , theorem [ thmgeom1 ] shows that under the hypothesis of the above theorem , there exists , for any cyclic set @xmath51 , a _ canonical _ right action of the quotient group @xmath52 , of @xmath33 by the central subgroup @xmath53 , on the  geometric realization \" @xmath54 corresponding to the point @xmath0 of the topos @xmath1 . in the last part of the paper ( _ cf . _   [ the last ] ) we discuss the subtlety that distinguishes the notion of cyclic structure on a point of @xmath1 as given here , from the definition of a point of the topos of cyclic sets ( called  abstract circle \" ) as in the unpublished note @xcite . by using _ _  we prove that the category of points of the topos of cyclic sets is _ equivalent _ to the category @xmath55 of archimedean sets whose objects are pairs @xmath56 made by a totally ordered set @xmath6 together with an automorphism @xmath57 of @xmath6 such that @xmath58 , @xmath59 and fulfilling the following archimedean property : for any given pair @xmath60 there exists @xmath61 such that @xmath62 . modulo the identification @xmath63 ( @xmath20 morphism in @xmath55 : see definition  [ last ] ) , one obtains the equivalence of @xmath55 with the category of abstract circles : _ cf . _ proposition  [ equivcat ] . to the inclusion of categories @xmath64 corresponds a geometric morphism of topoi and a related map between the corresponding points that associates to an interval @xmath37 the archimedean set @xmath65 as in theorem [ main ] , endowed with the translation @xmath66 . in this way , one derives a reformulation of theorem [ main ] by stating that the cyclic structures on a point of @xmath1 are classified by ( order compatible ) group structures on the associated point of the topos of cyclic sets . thus the notion of cyclic structure on a point of the topos of simplicial sets is a very subtle concept involving both groups and linear orders , not be confused with the definition of point of the topos of cyclic sets , that only involves linear order .","summary":"this gives a far reaching generalization of the well - known circle action on the geometric realization of cyclic sets .","abstract":"given a point of the topos of simplicial sets and the corresponding flat covariant functor , we determine the extensions of to the cyclic category . we show that to each such cyclic structure on a point of corresponds a group , that such groups can be noncommutative and that each is described as the quotient of a left - ordered group by the subgroup generated by a central element . moreover for any cyclic set the fiber ( or geometric realization ) of the underlying simplicial set of at inherits canonically the structure of a-space . this gives a far reaching generalization of the well - known circle action on the geometric realization of cyclic sets ."}
{"article_id":"0709.3960","section_id":"i","document":"ngc  4945 is a nearby , almost edge - on ( @xmath10 ) , disk galaxy ( type sb(s)cd or sab(s)cd ) that is a member of the centaurus group of galaxies @xcite . its distance , determined most accurately from the luminosity of stars at the tip of the red giant branch , is 3.82@xmath110.31  mpc @xcite . this value is consistent with previous more cruder estimates of the distance to ngc  4945 ( see the discussion in bergman et al . 1992 ) , and so henceforth we shall assume that 1  corresponds to 19  pc in ngc  4945 . the central region of ngc  4945 contains an active galactic nucleus ( agn ) revealed most unambiguously by its strong and variable hard x - ray emission @xcite . megamaser emission has been detected from the nucleus , likely distributed in a disk with radius of @xmath515  mas ( @xmath50.3  pc ) around the agn ( greenhill et al . the agn is classified as a seyfert 2 @xcite , consistent with findings that seyfert  2 but not seyfert  1 galaxies exhibit water megamasers ( e.g. , review by * ? ? ? surrounding the agn , there is an inclined circumnuclear starburst ring with a radius of @xmath525 ( @xmath550 pc ) seen most clearly in pa@xmath13 @xcite . the central region of ngc  4945 is among the strongest and most prolific extragalactic sources of molecular lines ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . for these reasons , ngc  4945 is a particularly attractive candidate for studying the nature of molecular gas at the center of an active galaxy , and the role this gas plays in fueling and perhaps also determining in part the observed properties of both the circumnuclear starburst and agn .    because of its southerly declination ( @xmath14 ) , studies of the molecular gas in ngc  4945 have been largely restricted to single - dish telescopes , in particular the 15-m swedish - eso submillimeter telescope ( sest ) . @xcite made the first map of the central region of this galaxy in the @xmath15 transition of @xmath1co at angular resolution of 43  ( measured at full - width to half - maximum , fwhm , henceforth used throughout when quoting sizes ) . they attributed the observed strong central concentration of molecular gas to a disk with a radius of @xmath518  ( 340  pc ) . with just a single pointing at the nucleus , @xcite obtained high - quality spectra of both @xmath1co and @xmath2co in the @xmath15 transition . they found that the observed line ratio as a function of velocity can be modeled as a homogenous ring in rigid - body rotation with an inner radius of @xmath58  ( @xmath5150  pc ) and an outer radius of @xmath515  ( @xmath5280  pc ) . @xcite mapped the central region of ngc  4945 in both the @xmath15 and @xmath0 transitions of @xmath1co at an angular resolution of 43  and 24  respectively . based on the measured position - velocity diagram along the major axis of ngc  4945 in both transitions , they inferred the presence of a ring with a radius of 8@xmath113  ( @xmath5150  pc ) in the @xmath0 and 15@xmath113  ( @xmath5280  pc ) in the @xmath15 transitions . they noted that this did not necessarily suggest the presence of two rings , but rather a radial variation in the excitation conditions and/or optical depth in a single ring with a given radial thickness . @xcite mapped the central region of ngc  4945 in the @xmath16 transition of @xmath1co at an angular resolution of 15 . in this transition , they found an intrinsic size for the central concentration of radius @xmath17 ( @xmath5100  pc ) along its major axis . although the position - velocity diagram is once again consistent with a ring but with an even smaller radius than in lower @xmath1co transitions , @xcite were careful to point out that other structures ( e.g. , disk , bar , spiral , or even two independent molecular concentrations ) are possible . all the abovementioned single - dish observations infer the presence of a molecular ring with size smaller than the respective angular resolutions of these observations . it is not clear how this molecular ring is related to the starburst ring , whether it comprises the reservoir for fueling the active nucleus , and whether it is related to the hypothetical circumnuclear molecular torus required by agn unification models @xcite . observations at higher angular resolutions are needed to spatially resolve and hence clarify the spatial - kinematic distribution of the molecular gas at the center of ngc  4945 . the first such observations were made quite recently by @xcite , who used the australia telescope compact array ( atca ) to map a central region of radius 17  ( 323  pc ) in the @xmath15 transitions of hcn , hco@xmath18 , and hnc at an angular resolution of @xmath19 ( @xmath20  pc ) . these lines trace molecular gas at about an order of magnitude higher density ( @xmath5@xmath21 ) than the abovementioned @xmath1co lines ( @xmath5@xmath22 ) . the hnc map , which best traces the overall spatial - kinematic distribution of the molecular gas , reveals an inclined rotating disk - like feature with a radius of @xmath23 ( @xmath580  pc ) along the major axis and position angle of @xmath24 , somewhat misaligned from the major axis of both the starburst ring and large - scale galactic disk at a position angle of @xmath5@xmath25 . based on the measured position - velocity diagram , @xcite argue that the hnc line traces a ring with an inner radius of 3  ( 57  pc ) . their maps , however , are affected by a lack of short baselines that result in an inability to detect structures larger than @xmath515  ( @xmath5285  pc ) . furthermore , line absorption against the strong central continuum source at their observing wavelength of 3.3  mm ( 90  ghz ) may compromise the detectability of the innermost features . here , we present the first interferometric observations of the central region of ngc  4945 in @xmath1co , as well as in @xmath2co and c@xmath3o , at their @xmath26 transitions . the angular resolution attained is much higher than previous single - dish co observations , and we properly resolve for the first time the central molecular gas concentration in co lines . our maps recover virtually all the emission detected in single - dish observations , and are not affected by line absorption against the central continuum source . we show that the co gas is distributed in an inclined disk exhibiting rigid - body rotation out to a radius of @xmath55  ( @xmath595  pc ) ; i.e. , the molecular disk extends beyond the circumnuclear starburst ring seen in pa@xmath13 . the rotation curve flattens beyond this radius , and the isovelocity contours exhibit an s - shaped asymmetry suggestive of a highly inclined bar as has been invoked to produce a similar asymmetry in both molecular and atomic hydrogen gas extending to much larger radii . we do not detect any central hole in the disk , placing an upper limit of 22 ( 42  pc ) on the radius of any such hole . instead , we detect for the first time a spatially - unresolved component at the center of the disk that is kinematically decoupled from the surrounding disk . this inner component exhibits a broad velocity width comparable with the overall range in velocities exhibited by the surrounding disk , and is a good candidate for the hypothesized circumnuclear molecular torus invoked by agn unification models @xcite .","summary":"we have mapped the central region of ngc  4945 in the transition ofco ,co , and co , as well as the continuum at 1.3  mm , at an angular resolution of with the submillimeter array . the relative proximity of ngc  4945 ( distance of only 3.8  mpc ) permits a detailed study of the circumnuclear molecular gas and dust in a galaxy exhibiting both an agn ( classified as a seyfert  2 ) and a circumnuclear starburst in an inclined ring with radius (  pc ) . we find that all three molecular lines trace an inclined rotating disk with major axis aligned with that of the starburst ring and large - scale galactic disk , and which exhibits solid - body rotation within a radius of  (  pc ) . the rotation curve flattens beyond this radius , and the isovelocity contours exhibit an s - shaped asymmetry suggestive of a highly inclined bar as has been invoked to produce a similar asymmetry observed on larger scales . we infer an inclination for the nuclear disk of , somewhat smaller than the inclination of the large - scale galactic disk of . this component has a higher density than its surroundings , and is a promising candidate for the circumnuclear molecular torus invoked by agn unification models .","abstract":"we have mapped the central region of ngc  4945 in the transition ofco ,co , and co , as well as the continuum at 1.3  mm , at an angular resolution of with the submillimeter array . the relative proximity of ngc  4945 ( distance of only 3.8  mpc ) permits a detailed study of the circumnuclear molecular gas and dust in a galaxy exhibiting both an agn ( classified as a seyfert  2 ) and a circumnuclear starburst in an inclined ring with radius (  pc ) . we infer the systemic velocity from channel maps and pv - diagrams . we find that all three molecular lines trace an inclined rotating disk with major axis aligned with that of the starburst ring and large - scale galactic disk , and which exhibits solid - body rotation within a radius of  (  pc ) . the rotation curve flattens beyond this radius , and the isovelocity contours exhibit an s - shaped asymmetry suggestive of a highly inclined bar as has been invoked to produce a similar asymmetry observed on larger scales . we infer an inclination for the nuclear disk of , somewhat smaller than the inclination of the large - scale galactic disk of . the continuum emission at 1.3  mm also extends beyond the starburst ring , and is dominated by thermal emission from dust . if it traces the same dust emitting in the far - infrared , then the bulk of this dust must be heated by star - formation activity rather than the agn . we discover a kinematically - decoupled component at the center of the disk with a radius smaller than ( 27  pc ) , but which spans approximately the same range of velocities as the surrounding disk . this component has a higher density than its surroundings , and is a promising candidate for the circumnuclear molecular torus invoked by agn unification models ."}
{"article_id":"0709.3960","section_id":"r","document":"in figure  [ continuum ] , we show a map of the 1.3-mm continuum emission superposed on a pa@xmath13 image of the central region of ngc  4945 taken from @xcite . the continuum source has a total flux density of @xmath39  jy , and is clearly resolved . gaussian fitting yields a deconvolved size ( at fwhm ) of @xmath40 @xmath41 ( @xmath42  pc ) with the major axis at a position angle ( pa ) of @xmath43 . the centroid of this source is located at @xmath44 and @xmath45 , which is 18 to the south - east of the nominal centroid of the h@xmath12o megamasers @xcite . the latter coincides within measurement uncertainties with the centroid of the central radio continuum source detected at cm - wavelengths @xcite , and presumably marks the location of the agn . the major axis of the 1.3-mm continuum source is not aligned with the major axis of either the starburst ring or larger - scale galactic disk , both of which have a @xmath46 . along the major axis of the pa@xmath13 starburst ring , the 1.3-mm continuum extends beyond the inner bright rim of the starburst ring at a radius of @xmath525 ( @xmath550  pc ) , and also beyond the detectable outer radius of this ring at @xmath55  ( @xmath5100  pc ) . on the south - eastern side of the ring , the 1.3-mm continuum clearly extends beyond the measured extent of the pa@xmath13 emission . the central region of ngc  4945 has been imaged in the continuum at centimeter wavelengths at angular resolutions comparable with that attained here . at 21  cm ( 1.4  ghz ) , the source has a deconvolved size of @xmath47 @xmath48 with major axis at @xmath49 , and a total flux density of @xmath50  jy @xcite . at 5  cm ( 6  ghz ) , the source has a smaller deconvolved size of @xmath51 ( @xmath52 ) at @xmath53 , and a total flux density of @xmath54  jy @xcite . the size of the continuum source at centimeter wavelengths is therefore much smaller than that measured at 1.3  mm . instead , the centimeter continuum source has a size comparable with the starburst ring , and its major axis is aligned with that of the starburst ring . the steep negative spectral index of this source indicates that nonthermal ( synchrotron ) emission dominates at centimeter wavelengths , and presumably arises from star - formation - related activity ( e.g. , supernovae ) in the starburst ring ( in addition to any unresolved emission from the agn ) . @xcite have imaged the central continuum source at 3.3  mm ( 90  ghz ) at an angular resolution comparable with that attained here . like us , they find an elongated source whose centroid is offset to the south - east of the h@xmath12o megamasers , and whose major axis is at @xmath55 . with a reported deconvolved source size of @xmath56 and peak flux density of 0.13  jy , the corresponding total flux density for a gaussian source is @xmath51.0  jy . extrapolating from 21  cm and 5  cm , the expected flux density at 3.5  mm is @xmath50.5  jy , only half that actually measured . extrapolating to 1.3  mm , the estimated contribution from nonthermal emission is @xmath50.3  jy , less than one quarter the flux density measured at this wavelength . even if we assume that nonthermal emission dominates at 3.3  mm , this emission would only contribute at most about half the total flux density measured at 1.3  mm . thus , we conclude that dust emission dominates at 1.3  mm ( and also contributes significantly at 3.3  mm ) , and that this explains the different dimensions and position angles of the source at millimeter and centimeter wavelengths . in @xmath57 , we discuss the implications of these results for the origin of the central far - ir emission from ngc  4945 .      to estimate the mass of molecular gas from the inferred dust emission at 1.3  mm ( assuming a gas to dust ratio of 100 ) , we first subtract the estimated cotribution from nonthermal emission ( @xmath50.3  jy ) from the total continuum emission ( @xmath51.3  jy ) . the gas mass is then given by + @xmath58 d[{\\rm mpc}]^2 \\lambda[{\\rm mm}]^2 } { t_d[{\\rm k } ] \\kappa_d(\\nu)[{\\rm \\ g^{-1 } \\ cm^2}]}\\ ] ] + @xcite , where the dust continuum flux density @xmath59 , distance @xmath60 , wavelength @xmath61 , and dust absorption coefficient @xmath62 . assuming a dust temperature @xmath63 as inferred from far - infrared measurements @xcite , we find that @xmath64  m@xmath65 . if we adopt a dust temperature corresponding to the peak brightness temperature measured in @xmath1co(2 - 1 ) of @xmath530  k (  [ subsec : lineemission ] ) , the gas mass is then @xmath66  m@xmath65 . as we shall show in @xmath67[co - mass ] , the gas mass inferred from dust is comparable with values inferred from the three observed co lines .        like the continuum emission , the @xmath1co(2 - 1 ) , @xmath2co(2 - 1 ) , and c@xmath3o(2 - 1 ) lines are strongly concentrated towards the center of ngc  4945 . figures  [ 12channel ] and [ 13channel ] show channel maps of the @xmath1co(2 - 1 ) and @xmath2co(2 - 1 ) emission smoothed to a velocity resolution of @xmath5@xmath68 , with the circumnuclear starburst ring seen in pa@xmath13 plotted as an ellipse . in figure  [ mom0 + 1-maps ] , we show the corresponding total intensity ( moment 0 ) as well as intensity - weighted mean - velocity ( moment 1 ) maps . an inspection of these maps reveals that the molecular emission originates ( primarily ) from a highly - inclined rotating disk extending beyond the pa@xmath13 starburst ring . gaussian fitting to the moment maps yields a deconvolved size ( at fwhm ) for the disk of @xmath69 ( @xmath52 ) ( @xmath5@xmath70  pc ) and major axis at pa@xmath71 in @xmath1co(2 - 1 ) , a size of @xmath72 ( @xmath52 ) ( @xmath5@xmath73  pc ) and pa@xmath74 in @xmath2co(2 - 1 ) , and a size of @xmath75 ( @xmath52 ) ( @xmath5@xmath76  pc ) and pa@xmath77 in c@xmath3o(2 - 1 ) . the derived position angle of the major axis in the more optically thin @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) lines is in good agreement with the position angle along which the velocity gradient of the disk reaches a maximum in these lines . the major axis of the disk ( mean @xmath78 ) is therefore well aligned with that of the starburst ring as well as the larger - scale galactic disk at a position angle of @xmath5@xmath25 . we see no evidence for the central hole in our data , suggesting that any central hole in this disk has a size smaller than the synthesized beam , which measures 44 along the major axis of the disk .    in all three molecular lines , the inner region of the disk within a radius of @xmath55  ( @xmath595  pc ) appears to exhibit simple circular rotation with the isovelocity contours perpendicular to major axis of the disk as can be seen in figure  [ mom0 + 1-maps ] . beyond this radius , however , the disk exhibits significant deviations from circular rotation as can be best seen in @xmath1co(2 - 1 ) . here , the isovelocity contours on the north - eastern side of the disk twist to the north , and on the south - western side twist to the south , producing a s - shaped asymmetry . in this outer region , the spatial structure of the disk closely resembles the distribution of the 1.3-mm continuum emission ( e.g. , the south - east extension ) , reinforcing our earlier argument that the continuum emission at 1.3  mm is likely dominated by dust .    the position - velocity ( pv- ) diagrams of all three molecular lines along the inferred major axis of the disk are shown in figure  [ pv - diagrams ] . the pv - diagrams along the major axis in @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) indicate ( primarily ) rigid - body rotation , while in @xmath1co(2 - 1 ) it shows additional complex emission with a broad velocity width at or near disk center . cuts along different position angles reveal that this `` excess '' emission is always present as a ( vertical ) strip in velocity at the origin of the pv - diagram , not just in @xmath1co(2 - 1 ) but also in @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) . for example , in figure  [ pv - diagrams ] we also show the pv - diagrams along the minor axis of the disk ( @xmath79 ) , as well as halfway between the major and minor axes of the disk ( @xmath80 ) , in all three molecular lines . armed with this knowledge , a closer inspection reveals that this feature can just be seen in the pv - diagrams along the minor axis of the disk in @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) . this feature therefore corresponds to a kinematically - decoupled component with a size smaller than the synthesized beam ( i.e. , projected radius as small as 14 or 27  pc ) located at the center of the disk . in the channel maps , this kinematically - decoupled feature appears as the ever - present emission towards the center of the disk even at the most blueshifted and redshifted velocities detectable . by contrast , in an inclined disk exhibiting only rigid - body rotation , the most blueshifted and redshifted velocities should originate from just the outermost regions of the disk along its major axis . we infer from both the channel maps and pv - diagrams a systemic velocity of @xmath5@xmath6 measured with respect to the local standard of rest . ( all velocities quoted here are relative to the local standard of rest , which is @xmath81 lower than the heliocentric velocity . ) by contrast , single - dish observations in @xmath1co(1 - 0 ) and @xmath1co(2 - 1 ) infer a significantly lower systemic velocity of @xmath5@xmath82 @xcite . the hnc observation of @xcite indicate a systemic velocity , as measured at the midpoint between the two strongest hnc peaks in the pv - diagram ( their fig . 11 ) , of @xmath5@xmath83 , about halfway between single - dish and our interferometric co measurements . the systemic velocity inferred from interferometric observations in atomic hydrogen ( hi ) gas @xcite , averaged over the entire galaxy , is @xmath84 , in agreement with the abovementioned value derived from single - dish co measurements . on the other hand , hi detected in absorption towards the centroid of the central continuum source has a velocity of @xmath5@xmath6 ( see fig .  5 of * ? * ) , similar to the systemic velocity inferred here . arcsecond imaging of hydrogen recombination lines near 8.6  ghz @xcite shows that the emission peaks at the location of the central radio continuum source ; these recombination lines have a systemic velocity of @xmath5@xmath85 , again close to that inferred here . we therefore conclude , based on observations that better trace gas closer to the center of the galaxy , that the systemic velocity of ngc  4945 is more likely about @xmath6 .      the @xmath1co(2 - 1 ) emission towards the center of ngc  4945 has been observed a number of times with the sest @xcite . these observations often give different line profiles and intensities , caused most likely by inaccuracies in telescope pointing . only the @xmath1co(2 - 1 ) line profiles measured by @xcite and @xcite appear similar , and which also agree with that measured here . in figure [ 12co - spec - overlay ] , we plot our spatially - integrated @xmath1co(2 - 1 ) line profile corrected for the primary beam of the sma and convolved to the primary beam of sest , together with the line profile measured by @xcite . the integrated line intensity ( in main beam brightness temperature ) we measure of @xmath86 is @xmath5@xmath87 of that measured by @xcite of @xmath88 ( as quoted in * ? ? ? the quoted uncertainties do not take into account any errors in flux calibration , and so we have likely recovered the bulk if not all of the @xmath1co(2 - 1 ) emission present in the same region .    the @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) emissions toward the center of ngc  4945 also have been observed a number of times with the sest @xcite . the @xmath2co(2 - 1 ) line profile we measure is similar in shape to that measured in @xmath1co(2 - 1 ) as shown in figure  [ 12co - spec - overlay ] , and also similar to the @xmath2co(2 - 1 ) line profiles measured by @xcite and @xcite but not @xcite . the integrated line intensity we measure of @xmath89 is similar to that measured by @xcite of @xmath90 ( which has a higher s / n ratio than that measured by * ? ? ? the c@xmath3o(2 - 1 ) line profile we measure is again similar in shape to that measured in @xmath1co(2 - 1 ) , but is different to those measured by either @xcite or @xcite . the line profile we measure is closest in shape to that measured by @xcite . the integrated line intensity we measure of @xmath91 also is similar to that measured by @xcite of @xmath92 . in table  1 , we summarize the integrated intensities that we measure for all three lines together with the values measured by @xcite , @xcite , and @xcite with the sest .      to estimate the mass of molecular gas traced in @xmath1co(2 - 1 ) , we first use the conversion factor between the brightness temperature of the @xmath1co(1 - 0 ) line and molecular hydrogen column density of @xmath93 as has been proposed to be appropriate in the central regions of galaxies ( e.g. , see * ? ? ? table  [ tab : sum - flux ] lists the brightness temperature of the @xmath1co(2 - 1 ) line if its emission as mapped with the sma had been observed by sest ( details in @xmath94 ) . in table [ tab : flux - mass ] , we list the actual measured brightness of the three observed lines . assuming a line ratio ( in main beam brightness temperature ) of @xmath1co(2 - 1 ) to @xmath1co(1 - 0 ) of @xmath95 ( from * ? ? ? * after correcting for the different beam sizes ) , we derive a molecular hydrogen column density of @xmath96  @xmath97 . given the measured source size as described in @xmath98 and listed also in table  [ tab : flux - mass ] , the corresponding mass in molecular hydrogen gas is therefore @xmath99  m@xmath65 . to compute the molecular gas mass from the @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) lines , we assume that this gas is in local thermal equilibrium ( lte ) . we adopt the abundance ratio [ @xmath1co]/[@xmath2co]@xmath100 and [ @xmath1co]/[c@xmath3o]@xmath101 as estimated by @xcite and @xcite . we assume an excitation temperature of @xmath530  k based on the peak brightness temperature measured for the @xmath1co(2 - 1 ) line ( i.e. , 16.5 jy / beam ) , and that the @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) lines are optically thin . in this way , we derive a column density from the @xmath2co(2 - 1 ) line of @xmath102 , and column density from the c@xmath3o(2 - 1 ) line of @xmath103 . their corresponding molecular hydrogen gas masses are @xmath104  m@xmath65  as traced in @xmath2co(2 - 1 ) and @xmath105  m@xmath65 as traced in c@xmath3o(2 - 1 ) . the estimated mass in molecular gas from all three lines agrees with each other , and are also roughly comparable with the value estimated from the dust continuum emission of @xmath5@xmath106  m@xmath65 ( @xmath107 ) . we also compute the approximate mass in molecular hydrogen gas within the region where the disk exhibits circular rotation ( i.e. , radius @xmath108 ) . table  [ tab : flux - mass - small ] lists the measured brightness temperature within a gaussian region of size @xmath109 and position angle of 44 centered on the disk . the inferred column density and corresponding mass in molecular hydrogen gas are @xmath110 and @xmath111  m@xmath65  as listed in table  [ tab : flux - mass - small ] . follow the same method mentioned above , and the emitting area of 10by 47 ( assume the inclination of the disk is @xmath112 ) . the gas mass derived from @xmath1co is @xmath113  m@xmath65 , and the gas mass derived from @xmath2co and c@xmath3o is @xmath114  m@xmath65 and @xmath115  m@xmath65 , respectively .      to search for any radial variations in density and temperature of the molecular gas , we computed line ratios ( in measured brightness temperature ) in @xmath1co/@xmath2co , @xmath1co / c@xmath3o , and @xmath2co / c@xmath3o along the major axis of the disk . the results are shown in figure  [ ratio - major ] . both the @xmath1co/@xmath2co and @xmath1co / c@xmath3o line ratios increase from the north - eastern ( redshifted ) side to the south - western ( blueshifted ) side of the disk , spanning the range 515 in @xmath1co/@xmath2co and 1330 in @xmath1co / c@xmath3o . on the other hand , the @xmath2co / c@xmath3o ratio remains roughly constant along the major axis of the disk , occupying a relatively narrow range between 2.2 and 3.0 .    to determine the line ratios of the inner spatially - unresolved but kinematically - decoupled component described in @xmath98 , we turn to the pv - diagram along the minor axis of the disk as shown in figure  [ ratio - pvmin ] . notice that the emission from this inner component away from the velocity range 520650@xmath116 , which straddles the systemic velocity , can be well separated from that of the surrounding disk . in this way , we compute for the inner component line ratios that span the range 1217 in @xmath1co/@xmath2co , 1726 in @xmath1co / c@xmath3o , and 1.21.5 in @xmath2co / c@xmath3o . by comparison , the corresponding line ratios along the minor axis at velocities in the range 520650@xmath116 , where emission from the inner component and surrounding disk can not be easily separated , are generally lower , spanning the range 815 for @xmath1co/@xmath2co , 1418 for @xmath1co / c@xmath3o , and 1.21.6 for @xmath2co / c@xmath3o . we have used the lvg approximation @xcite to compute the physical conditions of the molecular gas implied by the measured line ratios . the collision rates for co in the temperature range @xmath117@xmath118 k were taken from @xcite and @xmath119-@xmath120 k from @xcite . in these calculations , we adopted a relative abundance of @xmath121/[h_{2 } ] = 1 \\times 10^{-6}$ ] @xcite , and isotopic ratios @xmath122/[^{13}co ] = 50 $ ] and @xmath122/[c^{18}o ] = 200 $ ] @xcite . we assume that the emission in all lines are emitted from the same region ( i.e. , a one - zone model ) , and a velocity gradient @xmath123 given the measured linewidth and diameter for the @xmath2co emitting region of @xmath5285  km s@xmath124 and @xmath5270  pc respectively . the results for all three sets of line ratios are shown together in figure  [ line_ratios_disk - diagrams ] , and exhibit the following trends : ( 1 ) at temperatures @xmath125 , all three line ratios exhibit only a weak dependence on temperature , with lower ratios corresponding to higher densities ; ( 2 ) at temperatures @xmath126 , for a given line ratio the density increases with temperature , with smaller line ratios continuing to indicate higher densities ; and ( 3 ) the line ratios @xmath1co / c@xmath3o and @xmath2co / c@xmath3o tend to indicate a higher density than @xmath1co/@xmath2co . the measured line ratios therefore imply a decrease in gas density and column density from the north - eastern ( redshifted ) side to the south - western ( blueshifted ) side of the disk . our measurements do not place strong constraints on the gas temperature , but we note that the measured @xmath1co/@xmath2co line ratios are comparable with average values of @xmath5@xmath127 found in starburst galaxies @xcite and @xmath5@xmath128 in seyfert galaxies @xcite . if the similar line ratios indicate similar physical conditions , then the preferred solution is for temperatures @xmath129 and densities @xmath130 , typical values of the bulk properties for giant molecular clouds in our galaxy . in this regime , the gas density changes by a factor of just a few across the major axis of the disk . consistent with this idea , single - dish observations in multiple lines and transitions find a density of @xmath5(35)@xmath131  @xmath132 and temperature of @xmath5100  k @xcite for the bulk of the centrally unresolved molecular gas . at radii beyond @xmath510  ( @xmath5190  pc ) at or beyond the outer regions of the disk , where @xmath2co and c@xmath3o are not detectable at our sensitivity limits , the line ratios @xmath1co/@xmath2co and @xmath1co / c@xmath3o have lower limits that are larger than their measured values at smaller radii . this indicates that the co emitting outer region of the disk is dominated by relatively diffuse gas at densities of @xmath5@xmath133 . the inner kinematically - decoupled component exhibits a @xmath2co / c@xmath3o line ratio that is near unity ( 1.21.5 ) ; i.e. , the less opaque c@xmath3o line has nearly the same flux density as the @xmath2co line . the @xmath1co / c@xmath3o line ratio of 1418 also is relatively low compared with values in the range 4070 typically found in other galaxies ( see * ? ? ? * ; * ? ? ? * ) . at face value , this suggests that even the @xmath2co and c@xmath3o lines are nearly optically thick in the inner kinematically - decoupled component . alternatively , the c@xmath3o species may be unusually abundant within the inner component . we consider the second possibility first . @xmath3o enrichment can occur through its production from @xmath134n by he - burning in high - mass stars ( @xmath135 m@xmath136 ) , and subsequently dispersed in wolf - rayet phase or in type ii supernova explosions @xcite . such enrichment may have occurred during past circumnuclear starsburt activity in ngc  4945 , analogous to that currently seen as the p@xmath13 ring . such low line ratios are seen in at least one other star forming galaxy , ngc  6946 @xcite . on the other hand , not all star forming galaxies show such low line ratios ; e.g. , both m82 @xcite and ngc  253 @xcite exhibit @xmath1co / c@xmath3o or @xmath2co / c@xmath3o line ratios comparable with the mean observed in other galaxies . we turn back to the first possibility , which requires both the @xmath2co and c@xmath3o lines to be optically thick . to infer the required physical properties of the molecular gas , we use the same lvg approximation and the same assumptions as before for the surrounding disk , except that we now assume an order of magnitude higher velocity gradient as is more appropriate for the inner component . the results are shown in figure  [ line_ratios_inner_component - diagrams ] , which reveals that the physical properties of the gas derived from the @xmath1co/@xmath2co and @xmath1co / c@xmath3o line ratios are comparable but very different from those derived from the @xmath2co / c@xmath3o line ratio . our results imply that the one - zone model is not valid for the inner kinematically - decoupled component , and that the @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) lines trace a different denser region than the @xmath1co(2 - 1 ) line . this situation is not uncommon in galaxies , with the @xmath1co emission originating from more extended and diffuse gas and the @xmath2co or c@xmath3o emission from more compact and dense gas ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the physical properties of the molecular gas as inferred from the @xmath1co/@xmath2co and @xmath1co / c@xmath3o line ratios are comparable with those inferred in the surrounding disk , and presumably correspond to the more diffuse part of the inner component . on the other hand , the measured @xmath2co / c@xmath3o line ratio implies that even at temperatures as low as @xmath137  k , the gas density is @xmath5@xmath138@xmath139 . this is 12 orders of magnitude higher than the gas density in the surrounding disk , and presumably corresponds to the denser part of the inner component . the inferred gas density of the denser part increases towards higher temperatures , with densities about an order of magnitude higher still at @xmath140  k.","summary":"we infer the systemic velocity from channel maps and pv - diagrams . the continuum emission at 1.3  mm also extends beyond the starburst ring , and is dominated by thermal emission from dust . we discover a kinematically - decoupled component at the center of the disk with a radius smaller than ( 27  pc ) , but which spans approximately the same range of velocities as the surrounding disk .","abstract":"we have mapped the central region of ngc  4945 in the transition ofco ,co , and co , as well as the continuum at 1.3  mm , at an angular resolution of with the submillimeter array . the relative proximity of ngc  4945 ( distance of only 3.8  mpc ) permits a detailed study of the circumnuclear molecular gas and dust in a galaxy exhibiting both an agn ( classified as a seyfert  2 ) and a circumnuclear starburst in an inclined ring with radius (  pc ) . we infer the systemic velocity from channel maps and pv - diagrams . we find that all three molecular lines trace an inclined rotating disk with major axis aligned with that of the starburst ring and large - scale galactic disk , and which exhibits solid - body rotation within a radius of  (  pc ) . the rotation curve flattens beyond this radius , and the isovelocity contours exhibit an s - shaped asymmetry suggestive of a highly inclined bar as has been invoked to produce a similar asymmetry observed on larger scales . we infer an inclination for the nuclear disk of , somewhat smaller than the inclination of the large - scale galactic disk of . the continuum emission at 1.3  mm also extends beyond the starburst ring , and is dominated by thermal emission from dust . if it traces the same dust emitting in the far - infrared , then the bulk of this dust must be heated by star - formation activity rather than the agn . we discover a kinematically - decoupled component at the center of the disk with a radius smaller than ( 27  pc ) , but which spans approximately the same range of velocities as the surrounding disk . this component has a higher density than its surroundings , and is a promising candidate for the circumnuclear molecular torus invoked by agn unification models ."}
{"article_id":"0709.3960","section_id":"c","document":"ngc  4945 is one of the three brightest iras point sources beyond the magellanic clouds . it has a far - ir luminosity of @xmath5@xmath141 @xcite , which is comparable with that radiated at all other wavelengths combined . nearly all ( at least 80@xmath142 ) of the far - ir emission arises from a central region no larger than @xmath143 ( @xmath144 ) , which is comparable in size to the central continuum source that we detected at 1.3  mm . the far - ir emission from this central source is attributed to dust at a temperature of @xmath540  k.    as pointed out by @xcite , it is not clear whether the central dust - emitting region in ngc  4945 is heated by the agn or circumnuclear starburst . this situation reflects the general difficulty in deducing the nature of the source that heats dust in the nuclear region of active galaxies . in the case of ngc  4945 , our observation reveals that the central dust that emits at 1.3  mm ( size @xmath5190  pc along the major axis ) spans the entire observable extent and somewhat beyond the circumnuclear starburst ring . this spatially - extended dust is unlikely to be heated predominantly by the agn as the latter is embedded in obscuring material that prevents uv photons ( @xmath145  ev ) from penetrating beyond a distance of at most 15 ( @xmath530  pc ) from the center @xcite . even soft x - rays from the agn can only escape along a x - ray plume ( believed to be blown by a nuclear starburst ) that emerges north - west of center @xcite ; i.e. , the axis of the x - ray plume is orthogonal to the plane of the central molecular gas and dust disk . thus , if the dust emitting at 1.3  mm can be used as a proxy for that emitting at far - ir wavelengths , the bulk of this dust is likely heated by the circumnuclear starburst . observations at higher angular resolutions are required to search for any dust heated by the central agn and to study the very inner structure . our observation spatially resolves the central molecular gas concentration as traced in co into an inclined rotating disk . the radius of this disk , measured over the region where it exhibits rigid - body rotation , is @xmath55  ( @xmath595  pc ) , although the central co - emitting region extends beyond this radius . the overall radial size of the emitting region in @xmath1co(2 - 1 ) is 82 ( 156  pc ) , which is similar to that inferred from spatially - unresolved single - dish observations by @xcite . their pv - diagram along the major axis of ngc  4945 ( their fig . 3 ) shows two local intensity peaks at velocities of @xmath5@xmath146 and @xmath5@xmath147 separated by @xmath148 , interpreted as the two cross - sections of a highly - inclined ring . our pv - diagram ( fig .  [ pv - diagrams ] ) also shows two local intensity peaks near these velocities , specifically at @xmath149@xmath116  and @xmath150@xmath116 , separated ( as measured from their centroids ) by @xmath513 . these local intensity peaks in the pv - diagram correspond to the location where the rotation curve changes from rigid body to nearly flat , rather than tracing local spatial peaks corresponding to the two cross - sections of an inclined ring . our spatially - resolved observations show no evidence for a central hole ( or depression ) in @xmath1co(2 - 1 ) , nor in @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) , thus placing an upper limit of 22 ( 42  pc ) on the radius of any such hole . the central molecular concentration is therefore a disk or torus ( if it has a spatially - unresolved central hole ) rather than a ring . if it has a thickness much smaller than its observed dimensions , then the disk must have an inclination of @xmath112@xmath151 to the plane of the sky as measured in @xmath2co(2 - 1 ) , where the disk is least contaminated by surrounding features exhibiting non - circular rotation ( see @xmath152 and below ) . this is significantly different from the inclination of the large - scale galactic disk of @xmath5@xmath8 . observations in atomic hydrogen ( hi ) gas also indicate a small change in the inclination of the galactic disk with radius ( ott et al . 2001 ) .    as mentioned in @xmath153 , @xcite measured a size for the central molecular concentration in hcn(1 - 0 ) of @xmath154 ( @xmath155 ) and major axis at @xmath156 . this is only about half the size that we measured in @xmath1co(2 - 1 ) of @xmath69 ( @xmath52 ) . as in previous observations , @xcite attribute the observed hnc(1 - 0 ) emission to the two cross - sections of an edge - on ring or edge - thickened disk . instead , our results suggest that the hnc(1 - 0 ) emission originates from the inner region of the disk that we observe here in co. the critical density of molecular hydrogen gas for collisional excitation of hnc(1 - 0 ) is @xmath5@xmath21 , which is about an order of magnitude higher than that for @xmath1co(2 - 1 ) of @xmath5@xmath22 . the excitation temperatures of these two species , however , are comparable . the smaller size of the disk in hnc(1 - 0 ) compared with that in @xmath1co(2 - 1 ) therefore suggests a radial decrease in ( average ) density with radius . @xcite reached the same conclusions from a comparison of the line intensities and sizes for the central source in @xmath1co(1 - 0 ) , @xmath1co(2 - 1 ) , and @xmath1co(3 - 2 ) . in addition , the average gas density on the north - eastern side of the disk is a factor of a few higher than that on the south - western side ( @xmath157 ) .    the peaks in hnc(1 - 0 ) emission ( fig . 11 of * ? ? ? * ) span approximately the same range of radii as the pa@xmath13 starburst ring . we therefore associate this dense molecular gas with fueling the circumnuclear starburst . the disk that we observe in co extends beyond the starburst ring , and therefore traces more diffuse gas in the disk at densities @xmath5@xmath158 ( @xmath157 ) . with an estimated star - formation rate of @xmath5@xmath159 @xcite , compared with a mass in molecular gas for the disk of @xmath51@xmath160  m@xmath65 , the circumnuclear starburst must therefore be a transient phenomenon ( lasting no longer than @xmath5@xmath161@xmath162  yrs ) if the disk is not replenished from its surroundings . the dynamical mass of the disk within a radius of 5  ( 95  pc ) , where the disk exhibits circular rotation , is @xmath5@xmath163  m@xmath65 . using the method described in @xmath164 , we infer a molecular gas mass within this region of @xmath5@xmath165  m@xmath65 ( from c@xmath3o ) , which is about 13 times lower . the dynamical mass within a radius of 03 ( 5.7  pc ) of the central super massive black hole as inferred from h@xmath12o masers is @xmath166  m@xmath65  @xcite . the central region of the disk within a radius of 5  ( 95  pc ) must therefore be dominated in mass by stars or , less likely , by gas not in molecular form .      the s - shaped asymmetry in the isovelocity contours of the intensity - weighted @xmath1co(2 - 1 ) mean - velocity map ( fig . [ mom0 + 1-maps ] ) resembles that seen extending to much larger scales in both molecular and atomic hydrogen gas . @xcite have imaged the entire disk of ngc  4945 in both @xmath1co(2 - 1 ) and hi at comparable angular resolutions of @xmath524  with the sest and australia telescope compact array ( atca ) respectively . they reported a similar antisymmetric distortion in the isovelocity contours around the central concentration , extending outwards to 100200  in hi . @xcite attribute these distortions to a ( nearly edge - on ) bar . if correct , then this bar must extend inwards ( almost ) to the central disk , and may be responsible for channeling gas inwards to form this disk . the spatially - unresolved but kinematically - decoupled inner component described in @xmath98 spans approximately the same range of velocities as the surrounding disk . we have conducted the following check to make sure that this feature is not an artifact of the finite angular resolution of our observation . if within a radius of @xmath55  the central concentration can be described by just a disk in rigid - body rotation , then the pv - diagram along its minor axis should show only emission at those velocities within the synthesized beam . for a radial velocity gradient as measured from the pv - diagrams along the major axis in @xmath2co(2 - 1 ) and c@xmath3o(2 - 1 ) of @xmath5@xmath167 , and with a width for the synthesized beam along the major axis of 44 , the pv - diagram along the minor axis should therefore only show velocities of @xmath168@xmath169 . instead , irrespectiveof the position angle of the cut through the center of the disk , the inner feature spans velocities of @xmath170@xmath171 . the gas density of the inner component as inferred in @xmath157 is sufficiently high to excite emission in the @xmath15 transitions of hcn , hco@xmath18 , and hnc as observed by cunningham & whiteoak ( 2005 ) . indeed , their channel map in hnc ( which suffers least from line absorption against the central continuum source ) shows emission at or near the centroid of the disk even at the largest blueshifted and redshifted velocities of 370 km s@xmath124 and 750 km s@xmath124 . similarly , their pv - diagram in hnc along the major axis of the disk shows that , even at disk center , the emission spans a broad range of velocities comparable with the range observed for the inner kinematically - decoupled component . because cunningham & whiteoak ( 2005 ) do not show a pv - diagram along the minor axis of the disk , however , we can not be entirely sure that the inner component that we detected in co also was detected in hnc .    what is the nature of this inner kinematically - decoupled component ? the near - ir vibrational line of molecular hydrogen traces the walls of a conically - shaped cavity with roughly the same lateral size as the pa@xmath13 starburst ring , attributed to a superbubble blown by supernova - driven winds @xcite . the inner kinematically - decoupled feature may therefore correspond to the cooler component of the molecular outflow . if extending to the same height as the outflow seen in the near - ir vibrational line of molecular hydrogen ( @xmath536 ) , such an outflow would have been barely resolved in our observation ( with an angular resolution of 33  perpendicular to the major axis of the disk ) . as mentioned in @xmath157 , we infer a density for this inner kinematically - decoupled component that is 12 orders of magnitude higher than that of the surrounding disk . this is contrary to expectations if the inner component corresponds to molecular gas entrained from the disk or surrounding gas . a more attractive explanation is that this inner kinematically - decoupled component comprises a separate rotating disk . this may naturally explain the relatively high density of @xmath5@xmath172 ( @xmath157 ) inferred for the inner component . the range in velocities exhibited by the inner component is similar to that exhibited by the water masers around the agn spanning 440@xmath173 @xcite , suggesting a connection between the two . if it has a radius of 14 ( @xmath98 ) , the dynamical mass of such an inner disk would be @xmath5@xmath160  m@xmath65 ; if the actual radius is smaller , the corresponding dynamical mass would also be smaller . by comparison , the dynamical mass inferred from the h@xmath12o mega - masers is @xmath166  m@xmath65 , which is about two orders of magnitude smaller still . the column density of intervening neutral gas derived from x - ray absorption towards the agn is @xmath5@xmath174 @xcite . this is about two orders of magnitude higher than the column density of molecular hydrogen gas inferred for the central disk of @xmath5@xmath175 ( @xmath164 ) . if the bulk of the absorption originates from the large - scale galactic disk which in hi has a radius of @xmath511.4  kpc @xcite , then the average density in this disk is required to be @xmath5@xmath176 . this is about two orders of magnitude higher than the typical density in the interstellar medium of @xmath5@xmath177 , and so the bulk of the x - ray absorption is unlikely to originate from the galactic disk . instead , this x - ray absorption may originate from the inner kinematically - decoupled component . as mentioned in @xmath157 , the denser part of inner component has densities of at least @xmath5@xmath138@xmath139 . to produce the required column density in x - ray absorption , this part of the inner component would then have to span a radius of roughly @xmath520  pc , and hence have a mass of @xmath5@xmath178 . if at this radius the inner component has a rotational velocity of @xmath179 , corresponding to half the full range of velocities measured for this component , the enclosed dynamical mass within this radius would then be @xmath5@xmath178 , comparable to its estimated mass in molecular gas . the required properties of the denser part of the inner component necessary to produce the observed x - ray absorption are comparable with the size and rotational velocity ( and hence also enclosed dynamical mass ) of a highly inclined rotating disk in radio recombination lines imaged by @xcite . this disk has its major axis aligned with the large - scale galactic disk , and an ionized gas mass of @xmath180@xmath181 . if the denser part of the inner component corresponds to the same disk imaged in radio recombination lines , then this disk must be composed primarily of molecular gas . this dense inner component may therefore be the hypothesized circumnuclear molecular torus invoked by agn unification models . in the case of ngc  4945 , which harbours a seyfert  2 nucleus , the circumnuclear molecular torus is required by agn unification models to be viewed at a large inclination to its rotation axis , as appears to be the case for the disk imaged in radio recombination lines .","summary":"if it traces the same dust emitting in the far - infrared , then the bulk of this dust must be heated by star - formation activity rather than the agn .","abstract":"we have mapped the central region of ngc  4945 in the transition ofco ,co , and co , as well as the continuum at 1.3  mm , at an angular resolution of with the submillimeter array . the relative proximity of ngc  4945 ( distance of only 3.8  mpc ) permits a detailed study of the circumnuclear molecular gas and dust in a galaxy exhibiting both an agn ( classified as a seyfert  2 ) and a circumnuclear starburst in an inclined ring with radius (  pc ) . we infer the systemic velocity from channel maps and pv - diagrams . we find that all three molecular lines trace an inclined rotating disk with major axis aligned with that of the starburst ring and large - scale galactic disk , and which exhibits solid - body rotation within a radius of  (  pc ) . the rotation curve flattens beyond this radius , and the isovelocity contours exhibit an s - shaped asymmetry suggestive of a highly inclined bar as has been invoked to produce a similar asymmetry observed on larger scales . we infer an inclination for the nuclear disk of , somewhat smaller than the inclination of the large - scale galactic disk of . the continuum emission at 1.3  mm also extends beyond the starburst ring , and is dominated by thermal emission from dust . if it traces the same dust emitting in the far - infrared , then the bulk of this dust must be heated by star - formation activity rather than the agn . we discover a kinematically - decoupled component at the center of the disk with a radius smaller than ( 27  pc ) , but which spans approximately the same range of velocities as the surrounding disk . this component has a higher density than its surroundings , and is a promising candidate for the circumnuclear molecular torus invoked by agn unification models ."}
{"article_id":"1506.05999","section_id":"i","document":"turbulence is an ubiquitous phenomenon in space and astrophysical plasmas . although it is generally driven by violent events or instabilities at large scales , a further cascade is responsible for transferring energy via nonlinear coupling from the large injection scale to much smaller scales , through the ion and the electron characteristic regimes , where they are eventually dissipated . in - situ measurements in the solar wind represent a unique opportunity to study those processes , since they provide observations in a huge range of scales ( see for example reviews by @xcite ) . the estimated turbulent energy cascade rate ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) is comparable to the proton heating needed to explain the non adiabatic evolution of the solar wind plasma during its expansion ( e.g. , * ? ? ? * ; * ? ? ? this suggests that turbulence plays an active role in transferring energy from electromagnetic fields to particles and heats the solar wind plasma . however , the processes that ultimately lead to heating in a collisionless turbulent medium are still unknown .    supporting evidence of a turbulent cascade is provided by the observed energy spectra , which exhibit a power - law behavior over a large range of scales , spanning nearly four decades in frequency . the spectral index of magnetic and kinetic spectra varies with the temperature of the solar wind streams @xcite . the latter is in turn correlated with the stream speed and , although to a smaller extent , with the degree of alfvenicity , i.e. , the correlation between kinetic and magnetic fluctuations @xcite . however , on average , at fluid - like scales a typical kolmogorov power law with spectral index @xmath0 is usually observed for magnetic fluctuations , while kinetic energy spectra show a iroshnikov - kraichnan @xmath1 scaling @xcite . in particular , such scaling is found to be typical of regimes with balanced turbulence , i.e. , zero cross - helicity @xcite . in the same range of scales , a certain amount of residual energy , i.e. , an excess of magnetic to kinetic energy , is typically observed , following a well defined power - law scaling with an index of @xmath4 @xcite . the electric field spectrum is observed to follow the velocity spectrum , when measured in the solar wind frame @xcite , while density fluctuations exhibit a kolmogorov - like cascade .    in the vicinity of the ion inertial length scale , a break in the magnetic field power spectrum is observed @xcite . early observations of the spectrum of magnetic fluctuations in a restricted region above the break found a power - law scaling with a variable spectral index , ranging from @xmath4 to @xmath5 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , more recently , observations extended to smaller scales suggest a general convergence of the spectra towards a spectral index of @xmath3 @xcite , or towards a power - law scaling of @xmath6 , exponentially damped at sub - electron scales @xcite . magnetic fluctuations at sub proton scales are also characterized by a reduction of the magnetic variance anisotropy @xcite , and by an increase of the magnetic compressibility @xcite , suggesting a change in the nonlinear interactions ruling the cascade . this is partially confirmed by the measured increase of the intermittency at ion scales @xcite , although a clear behavior of the flatness at smaller , sub - ion , scales has not been identified yet . there are observational indications that , below the ion inertial length scale , the electric field spectrum decouples from the velocity field and flattens @xcite but , due to the high noise level , present data do not allow to determine the existence of a power - law scaling at sub - ion scales . density fluctuations show a plateau just before the ion scales , while they follow a power law between the ion and the electron scales , with the same spectral index as the one of the magnetic field spectrum @xcite . properties of turbulence have been extensively analyzed by means of direct numerical simulations ( dns ) , employing many different methods and models . although several features of the solar wind turbulence can be partially recovered , we are still far from a comprehensive picture . at large fluid - like scales , dns of incompressible mhd and reduced mhd ( rmhd ) return a spectral index for the total energy close to @xmath4 , @xmath0 , or @xmath1 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these spectral indices are associated to the different nature of the nonlinear interactions regulating the cascade and the cascade rate . moreover , within the inertial range , a transition between different regimes can occur @xcite . more sophisticated dns , including other physical processes like expansion effects @xcite , hall - mhd ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , reduced hall mhd @xcite , gyrokinetic @xcite , and hybrid particle - in - cell ( pic ) simulations @xcite , all produce spectral indices consistent with @xmath0 . anyway , the restricted width of the inertial range prevents firm conclusions .    as far as the small kinetic scales are concerned , dns including proton and electron physics return a qualitatively unified picture . at sub - proton scales , they reproduce an increase of the ratio of the electric to magnetic power , together with a flattening of the electric field spectrum ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and a transition to a steeper spectrum for the magnetic field power near the ion scales ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? . however , a unique spectral index can not be identified for the magnetic field spectrum at proton scales . early works in hall mhd @xcite , electron - mhd @xcite , and gyrokinetic @xcite reported a spectral index of @xmath7 for the magnetic field at sub - ion scales . more recently , steeper spectra have also been observed : a spectral index of @xmath3 in gyrokinetic @xcite and finite larmor radius ( flr)-landau fluid simulations @xcite , or a @xmath6 power law both in 3d electron - mhd @xcite and in strong kinetic - alfvn turbulence @xcite . magnetic spectral indices inbetween about @xmath8 and @xmath9 have also been observed in full pic simulations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? .    in situ measurements of the proton velocity distribution functions show the presence of an ubiquitous temperature anisotropy between the direction parallel and perpendicular to the mean magnetic field @xcite , and a non adiabatic evolution of the solar wind plasma during its expansion @xcite , thus suggesting , as already mentioned , an active role played by the turbulence in exchanging energy between fields and particles . hybrid pic simulations have shown an overall ( macroscopic ) collisionless proton heating , with signatures of a preferential proton heating in the perpendicular direction with respect to the ambient mean magnetic field ( e.  g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? vlasov - hybrid simulations suggest that non - maxwellian kinetic effects , such as temperature anisotropies , can be produced by the turbulence , mostly concentrated in regions near and around the peaks of the current density @xcite .    in our previous work @xcite ( named hereafter as ) , we presented results from a high - resolution hybrid ( fluid electrons , pic protons ) two - dimensional ( 2d ) simulations of turbulence . the spectra of various fluctuations ( magnetic , kinetic , density and electric field ) , along with the magnetic compressibility and the non - dimensional ratio of the density and the magnetic fluctuations , simultaneously matched several features observed in the solar wind . in particular , for the magnetic field we showed that high - resolution hybrid simulations , although limited to a 2d geometry , are able to capture the nonlinear dynamics at fluid - like mhd scales and at subproton scales , both within the same numerical domain . in this paper , we analyze in further detail the spectral properties of several fields , also showing their stability with time . moreover , we investigate the shape of the electric field spectrum , by estimating the separated contributions from different terms in the generalized ohm s law . finally , we study the proton temperature anisotropy and the proton heating , also quantifying the dependence from the resistivity coefficient and the number of particles - per - cell ( ppc ) employed in the simulations . the paper is organized as follows : in section  [ sec : setup ] , we describe the numerical setup employed , define the physical units and normalizations in the code , and provide the parameters of our initial conditions . in section  [ sec : results ] , we describe the results of the performed simulations . in section  [ sec : parameters ] , we validate such results , by investigating the importance of a careful choice of some relevant numerical parameters . finally , in section  [ sec : conclusions ] , we summarize the achievements of our simulations and discuss them in the framework of both observational and previous numerical and theoretical studies .","summary":"a transition is observed around proton scales . at sub - ion scales , both spectra steepen , with the former still following a power law with a spectral index of . a slope is observed in the density and parallel magnetic fluctuations , highlighting the presence of compressive effects at kinetic scales .","abstract":"we investigate properties of plasma turbulence from magneto - hydrodynamic ( mhd ) to sub - ion scales by means of two - dimensional , high - resolution hybrid particle - in - cell simulations . we impose an initial ambient magnetic field , perpendicular to the simulation box , and we add a spectrum of large - scale magnetic and kinetic fluctuations , with energy equipartition and vanishing correlation . once the turbulence is fully developed , we observe a mhd inertial range , where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power - law scaling with spectral indices of and , respectively . this behavior is extended over a full decade in wavevectors and is very stable in time . a transition is observed around proton scales . at sub - ion scales , both spectra steepen , with the former still following a power law with a spectral index of . a slope is observed in the density and parallel magnetic fluctuations , highlighting the presence of compressive effects at kinetic scales . the spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at mhd scales , and flattens at small scales . all these features , which we carefully tested against variations of many parameters , are in good agreement with solar wind observations . the turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions . while the parallel proton heating is found to be independent on the resistivity , the number of particles per cell and the resolution employed , the perpendicular proton temperature strongly depends on these parameters .   "}
{"article_id":"1506.05999","section_id":"r","document":"we performed nine different simulations . their main parameters are listed in table  [ tab : modelslist ] . a label is assigned to each run in the first column , while in the other columns we report , from left to right : the spatial resolution , @xmath42 ( @xmath66 ) , the length of the simulation box , @xmath43 , the value of the resistivity coefficient , @xmath44 , and the number of ppc . run a employs the best spatial resolution , @xmath67 , and the highest number of particles , i.e. , 8000 ppc , corresponding to more than @xmath68 particles in the whole simulation domain . the resistive coefficient has been fine - tuned and set to the value @xmath69 , in units of @xmath70 . in subection  [ subsec : runa ] and [ subsec : spectra ] we will provide a detailed and quantitative analysis of the data produced by this run . the remaining simulations were performed in order to validate these results and to investigate the effects of the number of ppc ( runs b - e , see table  [ tab : modelslist ] ) , the resistivity ( runs f - g ) , and the spatial resolution ( runs h - i ) . their results will be discussed later , in section  [ sec : parameters ] .      , and the rms out - of - plane vorticity , @xmath71 ( _ first panel _ ) ; the rms perpendicular @xmath72 and parallel @xmath73 magnetic fluctuations , and the rms perpendicular @xmath74 and parallel @xmath75 velocity fluctuations ( _ second panel _ ) ; the mean values of the normalized perpendicular and parallel proton temperatures , @xmath76 and @xmath77 , and of the proton temperature anisotropy , @xmath78 ( _ third panel _ ) ; the mean values of the normalized cross helicity , @xmath61 , and of the normalized residual energy , @xmath64 ( _ fourth panel _ ) . in all panels , a vertical black dotted line marks the time of the maximum turbulent activity , i.e. , @xmath79.,title=\"fig:\",scaledwidth=45.0% ] +        in fig . [ fig : time_evolutions ] , the time evolution of a few quantities is shown up to @xmath80 . the initial non - linear time associated to the maximum injection scale , i.e. , @xmath81 , can be estimated as @xmath82^{-1 } \\sim 20 \\,\\omega_p^{-1}$ ] , and corresponds to the minor ticks of the @xmath83 axis . the total length of the simulation is approximately 25 @xmath84 .    in the first panel , from top to bottom , we report the rms out - of - plane current density , @xmath85 , and the rms out - of - plane vorticity , @xmath71 . the current increases quite rapidly , attains its maximum value just before @xmath86 and then slowly decreases . since it represents a good indicator of the level of turbulent activity  @xcite , we choose to perform a detailed analysis at @xmath87 , when the turbulence is expected to be fully developed . a vertical black dotted line marks this time in all four panels . the vorticity also increases quite rapidly , reaching an earlier and lower maximum value , and then it decreases extremely slowly . the second panel of fig . [ fig : time_evolutions ] shows the rms perpendicular @xmath88 and parallel @xmath89 magnetic fluctuations ( red lines ) , and the rms perpendicular @xmath90 and parallel @xmath91 velocity fluctuations ( blue lines ) . perpendicular and parallel components are drawn with solid and dashed lines respectively . @xmath88 exhibits a small increase until @xmath92 , and then it decreases quite smoothly . on the other hand , @xmath90 decreases with a similar trend , but without showing any initial growth . this indicates that the turbulence is fed by the perpendicular components of both the magnetic and the velocity fluctuations , whose energy decreases slowly and sustains the cascade for the whole evolution . contextually , the parallel components of both the magnetic and the velocity fluctuations rapidly originate from compressive effects , remaining much smaller than their perpendicular counterparts throughout the simulation .    in the third panel of fig . [ fig : time_evolutions ] , we report the space - averaged parallel and perpendicular proton temperatures , normalized to the initial value @xmath93 , @xmath94 and @xmath95 respectively , together with the space - averaged proton temperature anisotropy , @xmath96 . we recall here that @xmath97 and @xmath98 are defined with respect to the local magnetic field . since @xmath99 is imposed at @xmath100 , @xmath101 and @xmath102 share the same initial value , @xmath93 . in the very first part of the evolution , the former shows a little and sudden decrease , after which both increase with almost the same rate . the parallel and perpendicular energy gains , at the end of the simulation , i.e. , at @xmath103 , are approximately 6% and 8% respectively . this small excess of perpendicular energy quickly arises within @xmath104 , and it is preserved throughout the simulation , with the temperature anisotropy reaching a value @xmath105 in correspondence of the maximum turbulent activity , and then remaining quite constant until the end of the simulation . a detailed discussion about the proton heating will be further provided in subsection  [ subsec : heating ] . lastly , in the bottom panel of fig . [ fig : time_evolutions ] , we show the space - averaged values of the normalized cross helicity , @xmath106 , and of the residual energy , @xmath62 , ( see eq .   and  ) . the former is very close to zero at the beginning of the simulation ( as a result of the initially imposed random phases spectra ) , and it tends to maintain this value until the end . the latter , instead , decreases from zero to about @xmath107 in very few non - linear times @xmath84 , showing a global excess of the magnetic energy over the kinetic energy . these asymptotic values are reached very quickly , as a consequence of the relaxation from the initial random relative orientation of the velocity and the magnetic fluctuations towards a strongly aligned state . despite the steady time evolution of their space - averaged values , both @xmath106 and @xmath62 appear very patchy when looking at the spatial distribution throughout the 2d computational domain ( not shown ) , exhibiting quite a wide excursion from @xmath108 to @xmath109 between different albeit close regions . along @xmath83 at @xmath110 , corresponding to @xmath111 , @xmath112 and @xmath113 ( from top to bottom ) . in each panel , a gaussian function with the same variance is plotted with a dashed line as a reference . bottom panel : excess kurtosis of the same quantity , computed at the same time.,title=\"fig:\",scaledwidth=48.0% ] +   along @xmath83 at @xmath110 , corresponding to @xmath111 , @xmath112 and @xmath113 ( from top to bottom ) . in each panel , a gaussian function with the same variance is plotted with a dashed line as a reference . bottom panel : excess kurtosis of the same quantity , computed at the same time.,title=\"fig:\",scaledwidth=48.0% ] +    summarizing the time evolution of all the above - mentioned quantities , we can divide the evolution of the system in three different stages :    1 .   a rapid re - adjustment and relaxation of the initial conditions , occurring within @xmath114 2 . the onset of a turbulent cascade , fed by the perpendicular magnetic and velocity fluctuations , involving larger and larger scales on times of the order of @xmath115 3 .   a deacaying phase with slow and smooth variations of all rms quantities , during which the turbulence is fully developed and further sustained until at least @xmath116 , corresponding to @xmath117 . [ fig : turbulence ] shows isocontours of six different quantities in the whole simulation domain , all computed at @xmath118 . in the upper - left panel , we report the magnitude of the perpendicular magnetic fluctuations , @xmath119 , showing the presence of coherent structures in the magnetic field , i.e. , vortices and magnetic islands , embedded in a much more chaotic environment where stretched and twisted shapes emerge . in the upper - right panel , the magnitude of the perpendicular velocity fluctuations , @xmath120 , is shown to exhibit qualitatively the same kind of structures , but with lower intensity and much lower gradients . in some regions , high values of @xmath120 correspond to high values of @xmath119 , while in other regions the opposite situation holds . in the middle - left panel , we show the out - of - plane current density , @xmath121 . many thin current sheets form , since the very first phase of the evolution , mostly around and in - between vortices . once formed , each current sheet is quickly disrupted into smaller and smaller pieces , contributing to the generation of smaller - scale structures . at the time of maximum turbulent activity , this results in the articulated pattern shown here . in the middle - right panel , the out - of - plane vorticity , @xmath122 , is shown . it exhibits a structure similar to @xmath123 , with many thin layers , whose shape is however much more defined and clean in respect to @xmath124 . peaks of @xmath125 and peaks of @xmath123 occupy approximately the same regions . in the bottom left panel , we report the proton temperature variation in respect to the initial proton temperature , @xmath126 , where @xmath127 is the average proton temperature measured at @xmath79 . regions where @xmath128 is locally both negative or positive are clearly present , and a resulting global proton temperature enhancement can be observed , as already inferred from fig . [ fig : time_evolutions ] . interestingly , areas where a proton temperature enhancement occurs are located in the vicinity of current sheets ( cf . , a more detailed analysis shows that strong currents exhibit a complex evolution , which involves splitting / dissociation and leads to a relevant proton energization .    in the bottom right panel , the proton temperature anisotropy , @xmath78 , we observe a wide excursion between very close areas , the perpendicular proton temperature @xmath102 ranging from about half and almost twice the parallel one . therefore , there is a strong local reshaping of particle distributions , leading to both perpendicular and parallel anisotropies @xcite . nevertheless , as inferable from fig .  [ fig : time_evolutions ] , the relative difference between @xmath129 and @xmath130 is about 2% at @xmath79 , meaning that globally no preferential enhancement along the perpendicular or parallel direction is achieved . the small - scale coherent structures which have emerged by the time of maximum turbulent activity , already observed in fig . [ fig : turbulence ] , can be related to the phenomenon of intermittency , since they are able to induce departures from self - similarity and enhanced dissipation . in order to look for intermittency in our data , we examine the non - gaussian behavior of the probability density function ( pdf ) of a mhd primitive variable . in particular , we compute the pdfs at @xmath79 by taking increments of one of the perpendicular magnetic field components , i.e. , @xmath131 , along the other perpendicular direction , i.e. , @xmath83 , for three different spatial separations , @xmath132 . in the three top panels of fig .  [ fig : pdfs_kurtosis ] , we show three pdfs , computed for @xmath133 , which is approximatively in the middle of the inertial range ( upper panel ) , @xmath134 , which is the scale corresponding to the ion spectral break ( middle panel ) and @xmath135 , which is well inside the kinetic range ( bottom panel ) . a gaussian function with the same variance is plotted with a dashed line in each panel as a reference . the distribution of magnetic fluctuations is clearly different at different scales : it is closer to a normal distribution at very large scales , it shows a significant deviation at intermediate scales , and it displays very extended tails at small scales . in order to quantify the level of intermittency , we compute the fourth central moment @xmath136 ( or kurtosis ) of the distributions . in the bottom panel of fig . [ fig : pdfs_kurtosis ] , we show the excess kurtosis @xmath137 , computed from the increments of @xmath131 along @xmath83 , as a function of @xmath138 , again at @xmath79 . this quantity is clearly very close to zero up to the injection scale , i.e. , @xmath139 , and the it steadily increases through the inertial range and down to sub - proton scales . ( red solid line ) and @xmath90 ( blue solid line ) , respectively . power laws with different spectral indices are additionally shown in black dashed lines as a reference.,scaledwidth=47.0% ]    , compensated by @xmath140 . each of them is the time average in the interval @xmath141 $ ] , where @xmath142 is the time reported in the legend . note that all of them have been suitably rescaled for the sake of clarity , so that they did not overlapped each other . horizontal dotted black lines are additionally shown . bottom panel : the same as in the upper panel but for the perpendicular velocity fluctuations , @xmath90 , compensated by @xmath143.,scaledwidth=47.0% ]      since the small - scale structures shown in fig . [ fig : turbulence ] exhibit random orientations , and therefore the two - dimensional spectra of all fluctuations can be assumed statistically isotropic , we can perform a quantitative analysis of the turbulent cascade by computing the omnidirectional spectra . these are defined as @xmath144 where @xmath145 are the fourier coefficients of a given quantity @xmath27 , and @xmath146 is the amplitude of the fluctuation @xmath27 at the scale @xmath147 .    in fig . [ fig : spectra ] , we show the spectra of the perpendicular magnetic and velocity fluctuations , drawn with red and blue solid lines respectively , at @xmath79 . we clearly observe two power - law ranges , separated by a smooth spectral break at a scale of the order of the the proton inertial length , @xmath148 . in , we showed the spectra of the total magnetic and velocity fluctuations , which exhibit a very similar behavior , since the perpendicular components are the dominant ones for both field . in particular , in the inertial range the spectrum of the perpendicular magnetic fluctuations follows a kolmogorov @xmath149 power - law scaling over a full decade in wavenumber , approximately between @xmath150 and @xmath151 . simultaneously , the perpendicular proton bulk velocity fluctuations exhibit a less steep slope , with an iroshnikov - kraichnan scaling of @xmath152 , over a little less than a decade , in the range @xmath153 . moreover , an excess of magnetic energy over kinetic energy is observed , coherently with the negative value of the normalized residual energy @xmath154 already shown in the bottom panel of fig . [ fig : time_evolutions ] .    at kinetic scales , the spectra of both fields steepen , due to the presence of both kinetic and dissipative ( resistive ) effects . the spectrum of @xmath74 quickly drops with an exponential trend above @xmath155 , until it clearly saturates to the noise level due to the finte number of ppc , corresponding to the spectrum at @xmath100 . the spectrum of the magnetic fluctuations , on the contrary , continue to follow a power - law scaling also at sub - proton scales , although with a steeper spectral index , of the order of @xmath9 . for @xmath156 , @xmath157 does not show an exponential damping , as one would expect for resistive dissipation , but a small increase instead , since the adopted resistive coefficient is slightly smaller than the optimal value . as discussed , the maximum level of turbulent activity occurs at @xmath158 , which is about ten times the initial nominal nonlinear time @xmath84 . this can be explained with the fact that at @xmath159 we inject energy through several modes within the range @xmath160 $ ] , where @xmath161 is the largest scale corresponding to the computational box size , i.e. , @xmath162 . the nominal nonlinear time @xmath163 is different for each mode , being longer for lower @xmath164-vectors . as the system evolves , the injection scale gets larger and larger and most of the initial modes are involved in the development of the turbulent cascade at @xmath79 . since modes with lower @xmath164s keep feeding energy at large scales even afterwards , we expect turbulence to be still sustained also at later times .    in fig . [ fig : spectra_comp ] we show the spectra of the perpendicular magnetic fluctuations , compensated by @xmath140 ( top panel ) , and the spectra of the perpendicular velocity fluctuations , compensated by @xmath143 ( bottom panel ) , computed at regular intervals of @xmath165 , from the maximum of turbulent activity to almost the end of the simulation . here , the spectrum at a given time @xmath142 is the time - average between five different spectra corresponding to @xmath142 , @xmath166 and @xmath167 . the power - law scaling for both the magnetic and the velocity fluctuations are very well maintained , over about the same range , at all times @xmath168 , indicating that the turbulence decays in a self - similar way . note that spectra corresponding to different times have been slightly shifted along the vertical axis , in order to avoid overlapping . ( grey line ) , of the density fluctuations , @xmath19 ( purple line ) , of the magnitude of the magnetic field , @xmath169 ( orange line ) , and of its parallel component , @xmath73 ( red dot - dashed line ) . power laws with different spectral indices are additionally drawn in black dashed lines , as a reference.,scaledwidth=48.0% ]    in fig . [ fig : spectra2 ] , we show the spectra of the magnitude of the magnetic field , @xmath169 ( orange ) , of its parallel component , @xmath73 ( red dot - dashed ) , of the density fluctuations , @xmath19 ( purple ) and of the total current density , @xmath170 ( grey ) . the density and the parallel magnetic fluctuations are strongly coupled beyond @xmath171 . in the mhd range , they exhibit a flat spectrum , which is approximately an order of magnitude smaller than the one of the perpendicular magnetic fluctuations . therefore , the large - scale activity has little contribution from compressible fluctuations  although they can still play a significant role in the dynamics of the out - of - plane components  and the magnetic compressibility , i.e. , the ratio of parallel to total magnetic fluctuations , is also negligible at small @xmath164s . both spectra steepen at sub - proton scales , following a clean power - law scaling with a spectral index of @xmath3 . note that their relative power level with respect to other fields spectra increases , with @xmath172 ( and also @xmath173 ) becoming comparable with the spectrum of the perpendicular component , @xmath72 ( cf . [ fig : spectra ] ) . the spectral shape of the current density , @xmath170 , can be understood by recalling that @xmath174 . a simple order - of - magnitude estimate of its perpendicular and parallel components gives @xmath175 and @xmath176 , respectively . therefore , in the inertial range , where the magnetic activity is dominated by the perpendicular fluctuations , the spectrum of @xmath170 is determined by its parallel component @xmath123 and this results in the observed spectral index of @xmath177 , since @xmath178 , with @xmath179 . on the contrary , as already discussed , @xmath172 and @xmath157 are comparable at sub - proton scales , both showing a power - law scaling , with spectral indices of @xmath3 and @xmath9 , respectively . the corresponding components , @xmath123 and @xmath180 , are of the same order and exhibit a similar scaling , therefore @xmath181 , and the corresponding scaling is in - between @xmath182 and @xmath183 . the change in the spectral slope of @xmath184 at @xmath185 provides a further evidence of a spectral break in the magnetic field spectrum at proton scales . ( green solid line ) and energy associated to the different terms of eq . ( the term containing the resistive coefficient is negligible ) . a power law with a spectral index of @xmath186 is also drawn with a dashed black line , as a reference . the shaded grey region marks the range where numerical effects strongly affect the shape of @xmath187.,scaledwidth=48.0% ]    , as in fig . [ fig : efield ] , for the case with @xmath188 ( @xmath189).,scaledwidth=48.0% ]    finally , the spectrum of the perpendicular electric fluctuations is reported in fig . [ fig : efield ] , as a green line . we choose to pay particular attention to the electric field for three main reasons . uppermost , it is expected to exhibit the most complex spectrum , since it contains the contributions of four terms having different relative importance in different ranges of scales . secondly , it is the quantity that is mostly affected by both numerical effects and particle properties , so its behavior needs to be analyzed carefully , especially at small scales . lastly , no consistent observational data about the properties of @xmath190 are available yet , so making predictions about the shape of its spectrum can be relevant for future analysis . we recall here that , starting from the vlasov - fluid equations and assuming that the electrons act as a massless , charge - neutralizing fluid , the electric field can be computed from the generalized ohm s law as @xmath191 in fig . [ fig : efield ] , together with @xmath187 obtained from numerical data , we also report the energy associated to the first three terms of eq .  , computed a - posteriori and drawn with cyan , magenta and black dot - dashed lines respectively ( the contribution from the resistive term is negligible at all scales , since the resistive coefficient @xmath44 is @xmath47 . ) at large scales , @xmath187 is clearly dominated by the mhd term , @xmath192 , which is essentially perpendicular to @xmath25 , since its leading contribution comes from @xmath193 ( @xmath194 and @xmath195 are both of the second - order in the fluctuations ) . therefore , @xmath187 follows strictly the spectrum of the perpendicular velocity fluctuations ( cf . [ fig : spectra ] ) . approximately at @xmath196 , these two spectra decouple , since the second and third terms of eq . start contributing . we can accurately analyze the hall term , @xmath197 , by considering its perpendicular and parallel components separately . the former is of the first - order in the fluctuations , being led by @xmath198 ( other contributions are quadratic in @xmath73 and @xmath72 , and therefore negligible ) . on the contrary , the latter is only of the second - order in the fluctuations , having the only contribution from @xmath199 . therefore , we expect the hall term to be negligible at large scales , where @xmath180 is small , and to exhibit a power - law behavior at small scales , with spectral index @xmath200 following from @xmath201 . indeed , this is what we observe in fig . [ fig : efield ] ( compare the magenta dot - dashed line with the reference dashed black line ) . the electron pressure gradient term , @xmath202 , has only perpendicular components by construction ( our 2d computational domain is perpendicular to @xmath25 ) . in the inertial range , it is of course negligible , the spectrum of the density fluctuations being essentially flat ( compare with fig . [ fig : spectra ] ) . on the contrary , at small scales , it is expected to give a contribution @xmath203 , which has exactly the same slope as the contribution from the hall term , since the spectra of the density fluctuations and of the parallel magnetic fluctuations have the same spectral index of @xmath3 at sub - proton scales . this is indeed what we observe in fig . [ fig : efield ] , where the contribution from the electron pressure gradient term is drawn with a black dot - dashed line . we would expect a similar behavior for @xmath187 at sub - proton scales , i.e. , a power law with a spectral index of @xmath200 , and we observe a hint of a similar scaling in the range @xmath204 . the spectrum of the electric field fluctuations is the most affected by numerical effects among all the considered spectra , since the computation of @xmath190 involves both other fields ( @xmath205 and @xmath40 ) and derivatives ( @xmath206 and @xmath207 ) , as shown by eq .  . we already noticed that @xmath208 suffers from an accumulation of energy at small scales , which is only a numerical artifact , and so does @xmath184 ( cf . [ fig : spectra2 ] ) . moreover , derivatives in the numerical code are computed as finite differences , thus they are not able to recover very precise quantities at very small scales . for all these reasons , we can not extract any robust information about the spectrum of the electric field at high wavevectors . in order to emphasize this , we choose to mark the `` non - safety area '' , which we estimate as @xmath209 , with a shaded gray region in fig . [ fig : efield ] .    under particular conditions , i.e. , @xmath210 , one can obtain a better defined scaling for the electric field . in this case , the electron pressure gradient term , @xmath202 , in the ohm s law is zero ( see eq .  ) . consequently , the level of the electric field spectrum at small scales is higher , since it is supported only by the hall term @xmath197 . this can be seen in fig . [ fig : efield_beta0 ] , where we show the same analysis of the electric field spectrum as in fig . [ fig : efield ] , but for a case with @xmath188 and all the other parameters set as in run a. the electric field spectrum is now the sum of only two main contributions , @xmath192 and @xmath197 . no qualitative changes are introduced with respect to the case with a finite electron temperature ; the former term dominates the spectrum at mhd scales , while the latter is responsible for the flattening of the electric field at ion scales . the important difference with respect to run a , is that @xmath187 displays now a well defined power - law slope with an index of @xmath186 , consistent with the expectation . we expect the same slope also for the finite @xmath211 case of run a , in the absence of the numerical limitations discussed above .","summary":"once the turbulence is fully developed , we observe a mhd inertial range , where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power - law scaling with spectral indices of and , respectively .","abstract":"we investigate properties of plasma turbulence from magneto - hydrodynamic ( mhd ) to sub - ion scales by means of two - dimensional , high - resolution hybrid particle - in - cell simulations . we impose an initial ambient magnetic field , perpendicular to the simulation box , and we add a spectrum of large - scale magnetic and kinetic fluctuations , with energy equipartition and vanishing correlation . once the turbulence is fully developed , we observe a mhd inertial range , where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power - law scaling with spectral indices of and , respectively . this behavior is extended over a full decade in wavevectors and is very stable in time . a transition is observed around proton scales . at sub - ion scales , both spectra steepen , with the former still following a power law with a spectral index of . a slope is observed in the density and parallel magnetic fluctuations , highlighting the presence of compressive effects at kinetic scales . the spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at mhd scales , and flattens at small scales . all these features , which we carefully tested against variations of many parameters , are in good agreement with solar wind observations . the turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions . while the parallel proton heating is found to be independent on the resistivity , the number of particles per cell and the resolution employed , the perpendicular proton temperature strongly depends on these parameters .   "}
{"article_id":"1506.05999","section_id":"i","document":"in this work , we have presented properties of turbulence in a magnetized collisionless plasma by means of two - dimensional hybrid pic simulations , extending the results of . remarkably , our simulations implement a high number of collocation points ( @xmath262 ) and a very high number of particles ( up to @xmath263 ppc ) , covering a large simulation domain ( not less than @xmath264 ) with a fine spatial resolution . this enables to self - consistently describe the evolution of turbulence over three orders of magnitude in wavevectors , and to fully capture its transition from fluid - like mhd scales to kinetic sub - ion scales , by using a single simulation ( see ) . the adopted initial conditions consist of balanced and equipartitioned magnetic and velocity fluctuations , i.e. , with zero cross helicity and zero residual energy . the onset of a turbulent cascade appears quite early during the simulations ( @xmath87 , corresponding to approximatively @xmath265 nonlinear times @xmath84 ) , i.  e. , when most of the initial modes have started to partake into the cascade . in physical space , the activity of turbulence is characterized by magnetic field coherent structures , vortices , and strong and localized current sheets at smaller scales . generation of coherent structures associated to intermittency is observed as turbulence evolves through mhd to sub - proton scales . pdfs of increments of a perpendicular component of the magnetic fluctuations at @xmath79 exhibit a deviation from the normal distribution at all scales . this is small in the inertial range , becoming larger in correspondence of the spectral break at @xmath266 , while at @xmath239 the pdf has a much leaner shape with long non - zero tails . the corresponding excess kurtosis confirms this behavior . it is very small around the injection scale , since part of the mhd range fluctuations still acts as an energy reservoir for turbulence at @xmath258 , while it increases through the inertial range . moreover , we observe a further increase at smaller scales . observational data give no firm results about the behavior of this quantity at different scales @xcite . nevertheless , when shown , all previous simulations observe an increase of the kourtosis at smaller scales ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? when looking at the spectra of the relevant quantities , two clear distinct turbulent regimes are observed . at larger scales , the magnetic field follows a kolmogorov @xmath0 power law , while the velocity has a spectral index of @xmath1 , which is characteristic of a iroshnikov - kraichnan turbulence . an excess of magnetic energy with respect to the kinetic energy is observed throughout the inertial range . the two different scalings for the magnetic and velocity fluctuations , often observed in the solar wind @xcite , are very stable in time . they appear at the maximum of the turbulent activity and persist throughout all the simulations , as the energy reservoir at large scales is able to sustain and maintain the cascade . in , we showed that such magnetic and velocity scaling are also combined with a spectral index of @xmath4 for the residual energy , in agreement with observations in the solar wind @xcite . incompressible mhd @xcite and reduced mhd @xcite only partially reproduce such scaling . in our simulations , the 2d geometry and the presence of compressibility may play a role in setting the different scaling .    a clear transition in the spectra is observed at scales @xmath267 , with a change in the spectral indices of all fields . in particular , the spectrum of the perpendicular magnetic fluctuations steepens at @xmath268 , following a power law with spectral index @xmath269 for another decade . the location of the break does not show any significant dependence on the number of particles , the spatial resolution and the resistivity adopted , provided that a sufficient number of grid points allows to cover approximatively a decade at sub - proton scales , i.e. , that the scale at which resistive dissipation acts is sufficiently separated from the region of the break . the parallel component of the magnetic field , together with the density , follows a similar but slightly shallower slope with a spectral index of @xmath270 , in very good agreement with observations @xcite and other simulations @xcite . as a result , magnetic fluctuations tend to become isotropic at small scales , resulting in an increase of the magnetic compressibility , as observed in the solar wind @xcite . the spectrum of the perpendicular velocity fluctuations quickly drops above @xmath271 , without any clear power - law trend . the observation of a spectral index of @xmath3 has been ascribed to the effect of the electron landau damping by previous studies @xcite , however , this can not be the case in our simulations , where the electron kinetics is not taken into account . alternatively , the presence of coherent structures , such as current sheets , can produce a steepening of the energy spectra ( e.g. , * ? ? ? * ; * ? ? ? the increase of intermittency at small scales , observed in our simulations , seems to confirm this path towards the dissipation . we have to note , however , that a @xmath6 power law for the magnetic energy and the density spectra ( not far from the @xmath272 found here ) has been also interpreted as related to the dimensionality ( 1d or 2d ) of the magnetic and the density intermittent structures , without invoking dissipation @xcite . the spectrum of the electric fluctuations is highly dominated by its perpendicular component . it is strongly coupled to the spectrum of the perpendicular velocity fluctuations at fluid scales , then it decouples and flattens , exceeding the spectrum of the perpendicular magnetic fluctuations and becoming dominant for @xmath273 . at large scales , the only contribution comes from the mhd term in eq .  , whose leading term is @xmath274[eq : e_perp ] this corresponds to a power - law scaling @xmath275 which is observed in the simulations , and is also consistent with observations @xcite . in our case , the main contributions at sub - proton scales come from the hall and the electron pressure gradient terms , since the spectrum of the velocity fluctuations is observed to drop exponentially at short wavelengths . the leading terms at these scales are , then , @xmath276 note that , in general , the sum of the two terms inside parentheses would not necessarily result in a power law for the electric field . however , since in our simulations both @xmath19 and @xmath73 are observed to scale with the same power law  thanks to the strong coupling between the plasma and the magnetic compressibility  then the expected spectral index for the electric field is : @xmath277[eq : e_subion ] although it is not possible to directly test this scaling for the electric field spectrum in run a , individual terms in eq . follow well the prediction ( see fig . [ fig : efield ] ) . moreover , we were able to show that when assuming @xmath210 ( i.e. , setting to zero the electron pressure gradient term in the ohm s law ) , then the electric field spectrum  hence dominated by the hall term  follows a @xmath278 scaling in the sub - proton range ( fig . [ fig : efield_beta0 ] ) , being only very slightly affected by numerical effects at very small scales ( @xmath279 ) .    as a result of the interaction of particles with the turbulent fluctuations and small scale structures , we observe an overall parallel and perpendicular heating with similar rates , so that the temperature of the plasma remains globally nearly isotropic . this behavior can be achieved only if a high enough number of particles is employed , and the resistivity is properly set in order to assure an accurate conservation of the total energy and a clear power - law behavior for the spectrum of the magnetic fluctuations at all scales . the parallel temperature , @xmath101 , is found to have a very robust evolution , being essentially independent of the resistivity , the number of particles , and the spatial resolution employed . on the contrary , the time evolution of @xmath102 is strongly determined by both the resistivity and the number of ppc : if too few particles are employed , or if the resistivity is too low , the perpendicular heating can be largely overestimated / unphysical . conversely , when a too strong value of the resistivity is implemented , the artificial damping of fluctuations at ion scales can produce a strong reduction of the perpendicular heating , thus generating an equally unphysical preferential parallel heating . this proves that no firm conclusions can be drawn about the perpendicular heating by turbulence in hybrid simulations , unless a careful and empirically fine - tuned choice of all parameters has been taken . note , however , that the fact that we do not observe a global preferential heating does not imply the absence of signatures of localized preferential deformations of the particle distribution functions , as suggested by the bottom right panel of fig . [ fig : turbulence ] , where strong temperature anisotropies ranging from @xmath280 to @xmath281 are observed . they seem to be concentrated in regions with stronger coherent structures , identified by the presence of current sheets and a significant level of vorticity . these results are in agreement with previous works based on the vlasov - hybrid approximation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? as the overall heating is rather weak , slow , and nearly isotropic , we can infer that the local formation of large proton temperature anisotropies is likely due to energy exchanges between the parallel and perpendicular directions , and/or to the spatial transport , rather than due to the heating . solar wind observations show a certain variability of the spectral properties . in particular , the position of the break at ion scales and the shape of the magnetic field spectrum around it seems to depend on the power of magnetic fluctuations @xcite and on the plasma beta @xcite . investigating such a dependence , by exploring the parameter space of the level of fluctuations and the plasma beta , will be the subject of a fortcoming paper . the authors wish to acknowledge valuable discussions with olga alexandrova , chris chen , giuseppe consolini , roland grappin , frank lffler , and marco velli . this project has received funding from the european union s seventh framework programme for research , technological development and demonstration under grant agreement no 284515 ( shock ) . website : http://project - shock.eu / home/. this research was conducted with high performance computing ( hpc ) resources provided by the louisiana state university ( allocations hpc@xmath282hyrel14 and hpc@xmath282hyrel15 ) and by cineca ( grant hp10cvcuf1 ) . p.h . acknowledges gacr grant 15 - 10057s . l.m . was funded by stfc grant st / k001051/1 . a.v . acknowledges the interuniversity attraction poles programme initiated by the belgian science policy office ( iap p7/08 charm ) .","summary":"we investigate properties of plasma turbulence from magneto - hydrodynamic ( mhd ) to sub - ion scales by means of two - dimensional , high - resolution hybrid particle - in - cell simulations . this behavior is extended over a full decade in wavevectors and is very stable in time . all these features , which we carefully tested against variations of many parameters , are in good agreement with solar wind observations . the turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions . while the parallel proton heating is found to be independent on the resistivity , the number of particles per cell and the resolution employed , the perpendicular proton temperature strongly depends on these parameters .   ","abstract":"we investigate properties of plasma turbulence from magneto - hydrodynamic ( mhd ) to sub - ion scales by means of two - dimensional , high - resolution hybrid particle - in - cell simulations . we impose an initial ambient magnetic field , perpendicular to the simulation box , and we add a spectrum of large - scale magnetic and kinetic fluctuations , with energy equipartition and vanishing correlation . once the turbulence is fully developed , we observe a mhd inertial range , where the spectra of the perpendicular magnetic field and the perpendicular proton bulk velocity fluctuations exhibit power - law scaling with spectral indices of and , respectively . this behavior is extended over a full decade in wavevectors and is very stable in time . a transition is observed around proton scales . at sub - ion scales , both spectra steepen , with the former still following a power law with a spectral index of . a slope is observed in the density and parallel magnetic fluctuations , highlighting the presence of compressive effects at kinetic scales . the spectrum of the perpendicular electric fluctuations follows that of the proton bulk velocity at mhd scales , and flattens at small scales . all these features , which we carefully tested against variations of many parameters , are in good agreement with solar wind observations . the turbulent cascade leads to on overall proton energization with similar heating rates in the parallel and perpendicular directions . while the parallel proton heating is found to be independent on the resistivity , the number of particles per cell and the resolution employed , the perpendicular proton temperature strongly depends on these parameters .   "}
{"article_id":"cond-mat0306204","section_id":"i","document":"modern studies of quantum magnetism in condensed matter physics go beyond explaining details of particular experiments on the cuprate superconductors , the heavy fermion materials , organic conductors , or related materials , and aim to develop general paradigms for understanding complex orders in strongly interacting many body systems @xcite . spinor atoms in optical lattices provide a novel realization of quantum magnetic systems that have several advantages compared to their condensed matter counterparts , including precise knowledge of the underlying microscopic models , the possibility to control parameters of the effective lattice hamiltonians , and the absence of disorder . degenerate alkali atoms are generally considered as a weakly interacting gas due to the smallness of the scattering length compared to the inter particle separation @xcite . the situation may change dramatically either when atomic scattering length is changed by means of feshbach resonance @xcite , or when an optical potential created by standing laser beams confines particles in the minima of the periodic potential and strongly enhances the effects of interactions . in the latter case existence of the nontrivial mott insulating state of atoms in optical lattices , separated from the superfluid phase by the quantum phase transition ( si transition ) , was demonstrated recently in experiments @xcite . low energy ( temperature ) properties of spinless bosonic atoms in a periodic optical potential are well described by the bose - hubbard hamiltonian @xcite @xmath1 parameters of ( [ bhhamiltonian ] ) may be controlled by varying the intensity of laser beams , so one can go from the regime in which the kinetic energy dominates ( weak periodic potential , @xmath2 ) , to the regime where the interaction energy is the most important part of the hamiltonian ( strong periodic potential , @xmath3 ) . for integer fillings ( number of atoms per lattice site ) , the two regimes have superfluid and mott insulating ground states , respectively , as can be obtained from the mean - field analysis of the bose - hubbard hamiltonian @xcite . in the superfluid phase , atoms are delocalized in the lattice , fluctuations in the number of atoms in each site are strong , and there is a phase coherence between different sites . in the insulating state , atoms are localized , fluctuations in the particle number at each site are suppressed , and there is a gap to all excitations . such an insulating state represents a correlated many body state of bosons , where strong interactions between atoms result in a new ground state of the system .    in conventional magnetic traps , spins of atoms are frozen so effectively that they behave like spinless particles . in contrast , optically trapped atoms have extra spin degrees of freedom which can exhibit different types of magnetic orderings . in particular , alkali atoms have a nuclear spin @xmath4 . lower energy hyperfine manifold has 3 magnetic sublevels and a total moment @xmath5 various properties of such condensate in a single trap were investigated @xcite . for example , for particles with antiferromagnetic interactions , such as @xmath6 , the exact ground state of an even number of particles in the absence of a magnetic field is a spin singlet described by a rather complicated correlated wave function @xcite . however , when the number of particles in the trap is large , the energy gap separating the singlet ground state from the higher energy excited states is extremely small , and for the experiments of ref . @xcite , the precession time of the classical mean - field ground state is of the order of the trap lifetime . so , experimental observation of the quantum spin phenomena in such systems is very difficult . to amplify quantum spin effects one would like to have a system with smaller number of particles and stronger interactions between atoms . hence it is natural to consider an idea of @xmath7 atoms in an optical lattice , in which one can have a small number of atoms per lattice site ( in experiments of ref . @xcite this number was around 1 - 3 ) and relatively strong interactions between atoms . in this paper we study bosonic @xmath7 atoms in optical lattices with spin symmetric confining potentials and antiferromagnetic interaction between atoms . we demonstrate that spin degrees of freedom result in a rich phase diagram by establishing the existence of several distinct insulating phases , which differ from each other by their spin correlations .    in the insulating state of bosons in an optical lattice fluctuations in the particle number on each site are suppressed but not frozen out completely . virtual tunnelling of atoms between neighboring lattice sites gives rise to effective spin exchange interactions that determine the spin structure of the insulating states ( spin exchange interactions for @xmath8 bosons in optical lattices were discussed previously in @xcite ) . we will show that in two and three dimensional lattices insulating states with an odd number of atoms per site are always nematic , whereas insulating states states at even fillings are either singlet or spin nematic @xcite , depending on the parameters of the model . in one dimensional systems even more exotic ground states should be realized , including the possibility of a spin singlet dimerized phase that breaks lattice translational symmetry @xcite . the 2d and 3d general phase diagram , including singlet , nematic and superfluid phases , is shown in fig . [ phasediag0 ] . the extended version of this diagram , including discussion of various transition lines , is presented in section [ globalphase diagram ] . it is useful to point out that the lattice model for spin-1 bosons , which we analyze here , is very general and may also be applicable to systems other than cold atoms in optical lattices . for example , triplet superconductors in strong coupling limit may be described by a similar hamiltonian , and some of the phases discussed in this article may correspond to non - bcs states of such superconductors @xcite . the paper is organized as follows . in section [ introtoformalism ] we provide derivation of the hubbard - type hamiltonian for spin-1 bosons in optical lattices starting from microscopic interactions between atoms , and describe some general properties of our model . in section [ nodd ] we derive an effective spin hamiltonian which is valid for any odd number of atoms per site , @xmath9 , in the limit of small tunnelling between sites . we demonstrate equivalence between our system and a heisenberg model for @xmath7 spins on a lattice with biquadratic interactions and argue that the ground state is a nematic in two and three dimensions and is a dimerized singlet in 1d . in section [ n2 ] we derive effective spin hamiltonian for a system with @xmath10 atoms per site , valid deep in the insulating regime , and use mean - field approximation to determine the phase boundaries between isotropic and nematic phases . in section [ nbig ] we derive effective spin hamiltonian for the limit of large number of particles per site @xmath11 and small tunnelling , and discuss isotropic - nematic transition for even @xmath9 . in section [ globalphase diagram ] we summarize our results and review the global phase diagram for spin-1 bosons in optical lattices . finally , in section [ experiment ] , we discuss approaches to experimental detection of singlet and nematic insulating phases of @xmath7 bosons . details of technical calculations are presented in appendices a - d .","summary":"we show that spin exchange interactions give rise to several distinct phases , which differ in their spin correlations . in two and three dimensional lattices ,","abstract":"we consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions , such as , in optical lattices . we show that spin exchange interactions give rise to several distinct phases , which differ in their spin correlations . in two and three dimensional lattices , insulating phases with an odd number of particles per site are always nematic . for insulating states with an even number of particles per site , there is always a spin singlet phase , and there may also be a first order transition into the nematic phase . the nematic phase breaks spin rotational symmetry but preserves time reversal symmetry , and has gapless spin wave excitations . the spin singlet phase does not break spin symmetry and has a gap to all excitations . in one dimensional lattices , insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized . we discuss signatures of various phases in bragg scattering and time of flight measurements .    by 2.0 in"}
{"article_id":"cond-mat0306204","section_id":"c","document":"in summary , we have considered mott insulating phases of spin-1 atoms with antiferromagnetic interactions in optical lattices . in the experimentally interesting limit @xmath443 , and deep inside the mott phases @xmath444 ( @xmath9 is the filling factor ) , we performed detailed calculations for the following cases : i ) odd number of particles per site and @xmath445 ; ii ) two particles per site and an arbitrary ratio of @xmath446 and @xmath48 ; iii ) large number of particles per site @xmath447 with an arbitrary ratio of @xmath99 and @xmath48 . based on this analysis we argued that in two and three dimensional lattices insulating phases with an odd number of particles per site are always nematic . for an even number of particles per site , there is either a spin singlet phase or a first order phase transition between spin singlet and nematic phases controlled by the depth of the optical lattice . the resulting global phase diagrams are shown in fig . [ phasediag2 ] and [ phasediag ] . we have considered excitations for singlet and nematic phases and have reviewed the effects of small magnetic field . for one dimensional lattices we have found dimerized singlet phases for insulating states with odd fillings . we also discussed different experimental techniques to identify the proposed phases . we thank e. altman , d. haldane , w. hofstetter , d. podolsky , s. sachdev , a. sorensen , d.w . wang , and f. zhou for useful discussions . this work was partially supported by the nsf career award dmr-0132874 , phy-0134776 , and by the sloan and packard foundations . when this work neared completion , we learned that similar results have been obtained by m. snoek and f. zhou@xcite .","summary":"we consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions , such as , in optical lattices . insulating phases with an odd number of particles per site are always nematic . for insulating states with an even number of particles per site , there is always a spin singlet phase , and there may also be a first order transition into the nematic phase .","abstract":"we consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions , such as , in optical lattices . we show that spin exchange interactions give rise to several distinct phases , which differ in their spin correlations . in two and three dimensional lattices , insulating phases with an odd number of particles per site are always nematic . for insulating states with an even number of particles per site , there is always a spin singlet phase , and there may also be a first order transition into the nematic phase . the nematic phase breaks spin rotational symmetry but preserves time reversal symmetry , and has gapless spin wave excitations . the spin singlet phase does not break spin symmetry and has a gap to all excitations . in one dimensional lattices , insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized . we discuss signatures of various phases in bragg scattering and time of flight measurements .    by 2.0 in"}
{"article_id":"astro-ph0512039","section_id":"i","document":"a universe dominated by normal mass should undergo deceleration as it expands . thus , the counter - intuitive discovery of an accelerating universe based on observations of type  ia supernovae @xcite is of profound significance for physics . evidently `` dark energy , '' in the form of einstein s cosmological constant or a more general scalar energy field , is the dominant mass / energy constituent of the universe today . these important implications depend critically on the quality of the light curves of the type  ia supernovae ( sne  ia , hereafter ) and the ability to k - correct , deredden , and normalize these to a standard luminosity . the evidence for an accelerating universe is based on a differential measurement between local and distant sne  ia ( at lookback times of 410 gyr ) . the local samples are very heterogeneous , and as more sne have been added , the full sample dispersion around the local hubble flow has increased from 0.12 @xcite to 0.18 mag @xcite in units of distance modulus . moreover , there are still legitimate concerns about possible systematic errors due to poorly understood photometric systems @xcite , reddening corrections @xcite , and evolutionary effects @xcite . a new and larger sample of nearby ( @xmath1 ) sne , where these sources of observational error have been duly accounted for , is urgently needed .    with that purpose in mind , we have initiated a five - year program , the carnegie supernova project ( hereafter csp ) , to obtain well - calibrated optical and near - infrared light curves as well as optical spectrophotometry of @xmath2250 type  ia and core - collapse sne . the csp is built upon the unique resources of the las campanas observatory ( lco ) in chile . we have guaranteed access to large numbers of nights on the swope 1  m and the dupont 2.5  m telescopes ( @xmath2300 per year in both telescopes together ) , which are equipped with high - performance ccd optical imagers , near - infrared ( nir ) cameras , and ccd optical spectrographs . in addition to providing densely sampled light curves covering the near - ultraviolet to the nir ( @xmath0 ) , we have the means to obtain optical spectrophotometry at approximately weekly intervals . the csp is a follow - up project and relies on sne discovered in the course of other surveys . a large fraction of our targets come from the lick observatory supernova search @xcite conducted with the katzman automatic imaging telescope ( kait ) , and from dedicated sn searches by amateur astronomers ( e.g. , tim puckett , tom boles , berto monard , koichi itagaki ) , which constitute a growing source of nearby sne . the targets selected for the follow - up observations by the csp are sne discovered before or near maximum light with @xmath3 and @xmath4 @xmath5 + 20@xmath6 . the primary goal of the csp is to establish a fundamental data set of optical and nir light curves in a well - defined and well - understood photometric system for all types of sne . a secondary goal is to obtain complementary optical spectrophotometry for these same sne . the data set for the type  ia events will allow us to improve extinction corrections and to investigate systematic effects possibly due to differences in age and metallicity . the data for the type  ii  sne will be used to establish and refine precise techniques for measuring luminosity distances employing the expanding photosphere method @xcite or the standardized candle method @xcite , thereby providing an independent check on the type  ia results . we will be able to explore the use of both sn types for studies of local galaxy flows and independently measure the convergence depth ( the distance at which the bulk flows smooth out into the so - called large - scale hubble flow ) . ultimately , the data set will serve as a reference for observations of distant sne that will be obtained in coming years in the course of the joint dark energy mission @xcite and those being obtained in the course of the high-@xmath7 sn surveys such as the cfht legacy project @xcite , essence @xcite , and our own high-@xmath7 component of the csp which seeks to measure rest - band @xmath8 magnitudes of sne  ia at @xmath9 using the magellan telescopes @xcite . the low-@xmath7 csp data set will also allow us to gain a deeper understanding of the physics of thermonuclear ( type  ia ) events and the different classes of core - collapse sne ( types  ii ,  ib ,  ic ) . for example , during the first csp observing campaign , we obtained excellent coverage of sn  2005bf , a peculiar , luminous type  ic event which peaked 35 days after explosion and which may represent a transition object between the sne associated with gamma - ray bursts and ordinary sne  ib @xcite . the purpose of this paper is to describe the low-@xmath7 csp experiment , to explain the general procedures for data acquisition and reduction , to summarize the results obtained during the first ( 20042005 ) low-@xmath7 csp observing campaign , and to present the data for a few representative sne . in @xmath10 [ inst ] we discuss the instrumentation , in @xmath10 [ obs ] we describe our observations , in @xmath10 [ red ] we explain the data reduction procedures , and in @xmath10 [ res ] we show representative light curves and spectra obtained thus far .","summary":"supernovae are essential to understanding the chemical evolution of the universe . type  ia supernovae also provide the most powerful observational tool currently available for studying the expansion history of the universe and the nature of dark energy . our basic knowledge of supernovae comes from the study of their photometric and spectroscopic properties . however , the presently available data sets of optical and near - infrared light curves of supernovae are rather small and/or heterogeneous , and employ photometric systems that are poorly characterized . similarly , there are relatively few supernovae whose spectral evolution has been well sampled , both in wavelength and phase , with precise spectrophotometric observations . we expect to obtain high - precision light curves and optical spectrophotometry for about 250 supernovae of all types . in this paper in addition , we present preliminary photometry and spectra obtained for a few representative supernovae during the first observing campaign .","abstract":"supernovae are essential to understanding the chemical evolution of the universe . type  ia supernovae also provide the most powerful observational tool currently available for studying the expansion history of the universe and the nature of dark energy . our basic knowledge of supernovae comes from the study of their photometric and spectroscopic properties . however , the presently available data sets of optical and near - infrared light curves of supernovae are rather small and/or heterogeneous , and employ photometric systems that are poorly characterized . similarly , there are relatively few supernovae whose spectral evolution has been well sampled , both in wavelength and phase , with precise spectrophotometric observations . the low - redshift portion of the carnegie supernova project ( csp ) seeks to remedy this situation by providing photometry and spectrophotometry of a large sample of supernovae taken on telescope / filter / detector systems that are well understood and well characterized . during a five - year program which began in september 2004 , we expect to obtain high - precision light curves and optical spectrophotometry for about 250 supernovae of all types . in this paper we provide a detailed description of the csp survey observing and data reduction methodology . in addition , we present preliminary photometry and spectra obtained for a few representative supernovae during the first observing campaign ."}
{"article_id":"astro-ph0512039","section_id":"r","document":"during the first low-@xmath7 csp campaign , we observed a total of 72 sne . however , only 38 of these ( 17 sne  ia , 12 sne  ii , and 9 sne  ibc ) eventually qualified for inclusion in our follow - up program . this number represents 76% of our nominal expectation of @xmath250 sne , with the difference being ascribed to natural variations in the year - to - year sn discovery rates .      during the first campaign , we obtained 7852 science optical images , and established photometric sequences around all of the 38 sne included in our follow - up observations . final light curves must await the eventual subtraction of template images , but we present here preliminary light curves obtained with the swope telescope of two sne that did not suffer significant contamination from their hosts . while we chose these sne for minimal contamination , the effect is bound to appear at some point when the sne became very faint . nevertheless , these examples illustrate the excellent photometric quality of the csp light curves . figure [ sn04eo_opt_fig ] shows the @xmath79 light curves of the type  ia  sn  2004eo . we observed this object for @xmath280 days starting @xmath210 days before maximum light with a cadence rarely achieved in previous studies . to estimate the precision of our photometry we fit a lgendre polynomial to the light curves with the lowest possible order but making sure to eliminate systematic residuals . in this case , the scatter around the fits amounts to 0.028 ( order 8) , 0.012 ( order 9 ) , 0.006 ( order 12 ) , 0.012 ( order 15 ) , 0.010 ( order 9 ) , and 0.008 ( order 10 ) mag in @xmath111 , and @xmath24 , respectively . these dispersions can be taken as an empirical and realistic estimate of the random error in a single observation .    in figure [ sn04fx_opt_fig ] we present optical light curves for the type  ii plateau sn  2004fx . a pre - discovery image on 2004 oct . 22 , where the sn was not visible , indicates that the sn was caught no later than 20 days after explosion . our first observations confirm that the sn was still quite blue at that point and that it grew progressively redder . we observed the sn on a weekly basis through the plateau phase for @xmath280 days , every other night for the next 20 days as it evolved faster , and less frequently again during the linear phase . the scatter in @xmath67 about a fourth - order lgendre polynomial is 0.10 mag , but this is dominated by the last few points where the statistical uncertainties are much greater . when the four points with the greatest residuals are removed , the scatter drops to 0.044 mag . in the other bands , the scatter during the plateau phase around an order 10 lgendre polynomial varies between 0.02 and 0.03 mag . during the late - time linear phase the dispersion around a linear fit varies between 0.03 and 0.10 mag in @xmath112 . part of this scatter is caused by variable amounts of galaxy contamination as the seeing varied during the observations . we expect the final light curves to be much more uniform at these late epochs .      during the first campaign , we obtained thousands of individual nir images . the reduction process produced 1449 calibrated mosaics . we established photometric sequences around all of the 24 sne included in our follow - up observations . our nir light curves are preliminary , awaiting the final template images and subtraction . the nir photometry is presented in the @xmath59 light curves for two representative cases . figure [ sn04ey_ir_fig ] presents the type  ia sn  2004ey , while figure [ sn04fx_ir_fig ] shows the type  ii sn  2004fx . in both cases , we show for comparison the @xmath28-band light curves from our own optical follow - up program . the light curves show the typical sampling achieved of one point every 57 days , with gaps of up to 15 days during lunar `` dark runs '' when wirc was not available at the 2.5  m dupont telescope . by exchanging time with other programs , we were able to improve the sampling of some light curves , especially in the cases of sne  ia around maximum light , to one point every 12 days . for sne  ii , we relaxed the frequency of observations to one point every @xmath210 days , enough to follow the slow plateau evolution . from the observations reduced independently for detectors # 2 and # 3 of wirc , we are able to estimate the precision of the measurements . in cases of high s / n , where photon uncertainties can be neglected , the deviation between the two points is @xmath20.020.03 mag in the @xmath113 bands , consistent with expectations . the distinctive secondary maximum of sne  ia is clearly seen in figure [ sn04ey_ir_fig ] , occurring about 20 days after first maximum . this secondary maximum is remarkably prominent in @xmath51 , even surpassing the brightness of the first maximum . the nir behavior of the type  ii  sn is characterized by a slow yet steady luminosity increase during the plateau phase , a feature previously seen in sn  1999em @xcite .      during the first csp campaign , we obtained a total of 213 optical spectra which are fully reduced . during this period we provided spectral classification in the iau circulars for 27 sne . figure [ sn04ef_z ] displays the spectroscopic evolution of the type  ia  sn  2004ef starting 8 days before maximum light for a period of 47 days . the telluric features are quite evident in these spectra because we did not obtain telluric standard observations for this sn . figure [ sn04fx_z ] shows the temporal evolution of the spectrum of the type  ii sn  2004fx . unlike the case for sn  2004ef , these spectra were divided by a telluric standard . most telluric features disappear and only small residuals can be seen at the strongest absorptions ( like the `` a band '' near 7,600   ) .","summary":"the low - redshift portion of the carnegie supernova project ( csp ) seeks to remedy this situation by providing photometry and spectrophotometry of a large sample of supernovae taken on telescope / filter / detector systems that are well understood and well characterized . during a five - year program which began in september 2004 ,","abstract":"supernovae are essential to understanding the chemical evolution of the universe . type  ia supernovae also provide the most powerful observational tool currently available for studying the expansion history of the universe and the nature of dark energy . our basic knowledge of supernovae comes from the study of their photometric and spectroscopic properties . however , the presently available data sets of optical and near - infrared light curves of supernovae are rather small and/or heterogeneous , and employ photometric systems that are poorly characterized . similarly , there are relatively few supernovae whose spectral evolution has been well sampled , both in wavelength and phase , with precise spectrophotometric observations . the low - redshift portion of the carnegie supernova project ( csp ) seeks to remedy this situation by providing photometry and spectrophotometry of a large sample of supernovae taken on telescope / filter / detector systems that are well understood and well characterized . during a five - year program which began in september 2004 , we expect to obtain high - precision light curves and optical spectrophotometry for about 250 supernovae of all types . in this paper we provide a detailed description of the csp survey observing and data reduction methodology . in addition , we present preliminary photometry and spectra obtained for a few representative supernovae during the first observing campaign ."}
{"article_id":"cond-mat0303179","section_id":"i","document":"exploring the use of individual molecules as active components in electronic devices  @xcite has been at the forefront of nanoelectronics research in recent years due to the potential advantage of ultrahigh density / speed and low - cost device fabrication through self - assembly / self - organization processes that such molecular - scale devices may bring  @xcite . numerous useful device characteristics including molecular rectifying diodes , negative differential resistance and field - effect transistors have been demonstrated using molecular - scale structures including small conjugated molecules  @xcite , single- and multi - wall carbon nanotubes  @xcite and macromolecules like dna  @xcite . a quantitative understanding of the physical mechanisms underlying the operation of such diverse molecular - scale devices has been and remains a major challenge in nanoelectronics research . the electrical characteristics of molecular devices are usually measured by sandwiching the molecules between two metallic electrodes  @xcite . the measured transport characteristics reflects both the nature of the metal - molecule interface and the properties of the molecular layer  @xcite . there are basically three electronic processes of interest in such metal - molecule - metal junctions : charge transfer between the metals and the molecules , the change of the electrostatic potential and the modification of the molecular geometry and electronic states . the nature of these processes under both zero and nonzero bias determines the electrical characteristics of the molecular junction . here it is natural to separate the problem into device at equilibrium and device out of equilibrium since : ( 1 ) the linear dc - transport property of the molecular device probes the equilibrium charge distribution of the molecular junction established by adsorption onto the electrodes ; ( 2 ) the nonlinear transport probes the charge response of the molecular junction to the applied electrical field established through a finite bias voltage . a microscopic theory of molecular electronics will therefore need to : ( 1 ) determine the appropriate geometry of the molecular junction ; ( 2 ) determine the self - consistent charge transfer and the resulting lineup of the molecular levels relative to the metal fermi - level and the modification of the molecular states upon formation of the metal - molecule - metal junction ; ( 3 ) determine the molecular screening of the applied electric field , the field - induced modification of molecular states ( the static stark effect ) and the non - equilibrium electron distribution when current is flowing ; ( 4 ) determine the current / conductance - voltage characteristics and their correlation with the molecular and device structures . none of these issues has been satisfactorily solved such that theory can be used in conjunction with experiment for an unambiguous identification of the device operation mechanism . the purpose of our work is to elucidate the above device electronic processes and their dependence on the given molecular and device structures under both equilibrium and nonequilibrium conditions within a well - defined theoretical model . specifically , we will investigate the different aspects of molecular transport due to the interplay between the electronic processes at the metal - molecule interface , the electronic processses in the molecule core and the molecular response to the applied electrical field when current is flowing . correspondingly , we focus our attention on the electron dynamics and calculate the device characteristics within the coherent transport regime . our emphasis is on the conceptual understanding and the chemical trends obtained from detailed microscopic calculation of simple but representaive molecular and device structures . our work can therefore be considered as a `` minimal '' quantitative microscopic model of single - molecule electronics . the ionic dynamics of the metal - molecule - metal junction can also be affected by the above electronic processes both at equilibrium and out of equilibrium , i.e. , the adsorption and bias / current - induced conformation change . neither aspect will be treated here . by confining ourselves to the coherent transport regime , we also neglect the effect of electron - vibrational coupling on transport  @xcite . solving the adsorption - induced conformation change requires an accurate knowledge of the surface lattice structure at the atomic - scale for devices under applied voltage . this is almost never known in typical molecular transport measurement . since one goal of such calculation is to provide the input nuclear configuration for transport calculation , our purpose can be served equally well by examining the effect that different adsorption and molecular geometries may have on the device characteristics , which will be treated in subsequent papers of the series . a rigorous solution of the bias / current - induced conformational change and the general solution of inelastic contribution to non - linear current due to electron - vibrational coupling is a challenging topics which requires solving the nonequilibrium dynamics of the coupled electron - nuclei systems  @xcite since the molecular potential energy surface is affected by the nonequilibrium electron dynamics and electron energy is dissipated in moving the atoms . by focusing on the electron dynamics in the molecular junction with fixed geometry , the present work will provide a reference for evaluating the importance of such additional complications and provide the necessary input for further investigation in situations where they are indeed critical .    in typical molecular junction measurement , conjugated molecules are attached to the metallic electrodes through appropriate end groups . in this paper we will consider current transport through two benene - based molecular radicals  phenylene dithiol ( pdt ) and biphenylene dithiol ( bpd)adsorbed symmetrically onto two semi - inifinite gold @xmath1111@xmath2 electrodes through the end sulfur atoms . these structures chosen are among the simplest possible but are still representative of current experimental work . for the device at equilibrium , we obtain the self - consistent charge transfer , the adsorption - induced change in the electrostatic potential , the lineup of the molecular level relative to the metal fermi - level and the modification of the individual molecular states due to the metal - molecule coupling . for the device out of equilibrium , we obtain the charge injection / redistribution within the metal - molecule - metal junction , the molecular screening of the applied field and the resulting voltage drop , the modification of the molecular states by the applied field , the non - equilibrium occupation of molecular orbitals , the current / conductance - voltage characteristics for the given contact geometry . the calculation we present is performed using a recently developed self - consistent matrix green s function ( scmgf ) method  @xcite which is based on the non - equilibrium generalization of the quasi - particle green s function theory  @xcite and uses a finite local - orbital basis set . by replacing the quasi - particle exchange - correlation self - energy  @xcite with the exchange - correlation potential within the density functional theory  @xcite , the well - established technique of self - consistent field theory of molecular electronic structure can then be utilized for transport calculations  @xcite . the real - space formulation of our approach allows us to provide an intuitive and coherent physical picture of the molecular tranport by analyzing the device elctronic processes both at the atomic - scale and on the basis of individual molecular orbitals . we view the molecules as comprised of chemically well - defined atomic groups and interpret their electrical characteristics in terms of the response of these atomic groups to the perturbation induced by the metal - molecule coupling and the applied electric field . we emphasize the insight obtained with such atomic - scale analysis and show the important effect of atomic - scale charge and potential inhomogeneity on device characteristics at the molecular scale , which may otherwise be obscured by the molecular - level analysis treating the molecules as a whole . in particular , two important conclusions come out of this work : ( 1 ) the adsorption - induced modification of molecular states is larger than the field - induced effect unless we go to large bias , so accurate modeling of the electronic processes at equilibrium is critical for determining the low - bias transport characteristics ; ( 2 ) the effect of both the metal - molecule coupling and the applied electric field in turning the individual molecular orbitals into effective conduction channels depends on the detailed charge and potential distribution across the metal - molecule - metal junction and may be different for different molecular orbitals . `` engineering '' the charge and potential inhomogeneity as commonly done in quantum semiconductor heterostructures will be equally important at the molecular scale . both aspects have been largely neglected in the past . we therefore hope the results obtained here will provide a useful guide regarding the nature of electron transport at the ultimate limit of device scaling and the prospect of device engineering through molecular design .","summary":"we view the molecules as `` heterostructures '' composed of chemically well - defined atomic groups , and analyze the device characteristics in terms of the charge and potential response of these atomic - groups to the perturbation induced by the metal - molecule coupling and the applied electrical field , which are modeled using a first - principles based self - consistent matrix green s function ( scmgf ) method . as the first example , we examine the devices formed by attaching two benzene - based molecular radicals  phenyl dithiol ( pdt ) and biphenyl dithiol ( bpd)symmetrically onto two semi - infinite gold electrodes through the end sulfur atoms . the charge transfer creates a potential barrier at the metal - molecule interface that modifies significantly the frontier molecular states depending on the corresponding electron density distribution . for both molecules , but as current flows , the electrons within the molecular junction redistribute substantially , with resistivity dipoles developing in the vicinity of potential barriers . only the delocalized-electrons in the benzene ring can effectively screen the applied electric field . the field - induced modification of the molecular states ( the static stark effect ) becomes significant as the bias voltage increases beyond the linear - transport region .","abstract":"we present the first in a series of microscopic studies of electrical transport through individual molecules with metallic contacts . we view the molecules as `` heterostructures '' composed of chemically well - defined atomic groups , and analyze the device characteristics in terms of the charge and potential response of these atomic - groups to the perturbation induced by the metal - molecule coupling and the applied electrical field , which are modeled using a first - principles based self - consistent matrix green s function ( scmgf ) method . as the first example , we examine the devices formed by attaching two benzene - based molecular radicals  phenyl dithiol ( pdt ) and biphenyl dithiol ( bpd)symmetrically onto two semi - infinite gold electrodes through the end sulfur atoms . we find that both molecules acquire a fractional number of electrons with similar magnitude and spatial distribution upon contact with the electrodes . the charge transfer creates a potential barrier at the metal - molecule interface that modifies significantly the frontier molecular states depending on the corresponding electron density distribution . for both molecules , the metal fermi - level is found to lie closer to the highest - occupied - molecular - orbital ( homo ) than to the lowest - unoccupied - molecular - orbital ( lumo ) . transmission in the homo - lumo gap for both molecules is due to the metal - induced gap states arising from the hybridization of the metal surface states with the occupied molecular states . applying a finite bias voltage leads to only minor net charge injection due to the symmetric device structure assumed in this work . but as current flows , the electrons within the molecular junction redistribute substantially , with resistivity dipoles developing in the vicinity of potential barriers . only the delocalized-electrons in the benzene ring can effectively screen the applied electric field . for the pdt molecule , the majority of the bias voltage drops at the metal - molecule interface . but for the bpd molecule , a significant amount of the voltage also drops in the molecule core . the field - induced modification of the molecular states ( the static stark effect ) becomes significant as the bias voltage increases beyond the linear - transport region . a bias - induced reduction of the homo - lumo gap is observed for both molecules at large bias . the stark effect is found to be stronger for the bpd molecule than the pdt molecule despite the longer length of the former . for both molecules , the peaks in the conductance are due to electron transmission through the occupied rather than the unoccupied molecular states . the calculation is done at room temperature , and we find the temperature dependence of the current - voltage characteristics of both molecules is negligible ."}
{"article_id":"cond-mat0303179","section_id":"c","document":"a common practice in the literature on molecular electronics is to characterize the molecular transport as `` electron transport '' if the conduction is mediated by tunneling through the unoccupied molecuar states , or as `` hole transport '' if the conduction is mediated by tunneling through the occupied molecular states , following the terminology commonly used in semiconductor / organic device and electron transfer research . here it is important to recognize their differences .    for bulk semiconductor devices , the concepts of `` electron '' or `` hole '' are associated with introducing shallow - impurity ( dopant ) atoms into the ideal lattice structure , which introduces electron intos the ( unoccupied ) conductand band or removes electrons from the ( filled ) valence band . the `` electron '' or `` hole '' thus introduced are mobile charge carriers with delocalized wavefunctions . the system as a whole remains charge neutral , since the charges associated with these carriers are compensated by the impurity ions left behind . therefore , the type of charge transport is an equilibrium property depending only on the type and amount of dopant atoms introduced . by contrast , for organic devices , the system is often not doped . charge transport occurs by injecting charge carriers into the system from the electrodes . the type of transport depends on the charging state of the molecule and the nonequilibrium injection of charge carriers into the neutral system . for both cases , the type of transport is determined by the change in the occupation of electron states through doping or contact injection , indpendent of the nature of charge transport itself ( band transport or polaron hopping ) . the situation for coherent molecular transport is quite different . for the symmetric molecular devices considered here , both the total number of electrons ( the charging state of the molecule ) and the occupation of the individual molecular orbitals change little with the applied bias . although a fractional amount of charge is transfered from the gold to the molecule upon electrode contact , the transfered charge is localized in the interfacial region and characterizes the changes in the interfacial bond . the change in the occupation of molecular states is fractional and gradual , either upon contact to the electrodes at equilibrium or upon application of a nonzero bias voltage out of equilibrium ( fig . ( [ xuefig4 - 2 - 1 ] ) ) . this is due to the quantum mechanical nature of the coherent tunneling transport , where we can not characterize the tunneling electron as being physically injected into the molecule and subsequently extracted out . therefore , it is more appropriate to characterize molecular transport through the resonant molecular states without associating it with specific transport types . the focus of the present series of work is on current transport through a single molecule in contact with two metallic electrodes . this corresponds closely to the molecular transport measurements using atomic - size break junctions  @xcite , where either one or several molecules are probed . however , many molecular transport experiments are performed on molecular monolayers where thousands or tens of thousands of molecules are probed by the contacts to the electrodes  @xcite . such experiments with monolayer configuration present a quite different situation from the single molecule configuration considered here . besides the additional complexity of inter - molecular interactions within the monolayer , the most important difference lies in the interface electrostatics . note that the same boundary condition for the electrostatic potential across the molecular junction applies to both the single molecule configuration and the monolayer configuration : deep inside the electrodes they approach the bulk value , which can be shifted rigidly with respect to each other by the applied bias voltage . for the single molecule configuration , the transfer of charge across the metal - molecule interface is confined in a small region , whose contribution to the electrostic potential decays to zero in regions far away from the molecule . but for the monolayer configuration , the electrostatic potential in regions far away from the molecule is the superposition of contributions from the transfered charge on a large number of molecules . to satisfy the same boundary condition of the electrostatic potential , the charge transfer per molecule in a molecular monolayer can be orders of magnitude smaller than that in the single molecule considered here  @xcite . this is the situation often met in organic electronics , where a monolayer of self - assembled molecules is used to modify the work function of the metallic contacts  @xcite . similar problems have also been considered in the electron transport through metal - carbon nanotube interfaces  @xcite . here it is important to recognize the different physics of the metal - molecule interface in single - molecule devices and monolayer devices , since it may have profound effects on the device functionalities achievable using molecular materials . we have presented a first - principles based microscopic study of current transport through individual molecules . the real - space formulation allows us to establish a clear connection between the transport characteristics and the molecular electronic structure perturbed by the metal - molecule coupling and the applied electric field . by separating the problem into equilibrium and non - equilibrium situations , we identify the critical electronic processes for understanding the linear and non - linear transport characteristics . at equilibrium , the critical problem is the charge transfer process upon formation of the metal - molecule - metal contact , which modifies the molecular states and determines the energy level lineup relative to the metal fermi - level . this is mainly an interface - related process and can be controlled by controlling the contact . out of equilibrium , the central problem is the molecular charge response and the consequent molecular screening of the applied electric field , which depends on both the molecule core and the nature of the metal - molecule contact and can be understood by viewing the molecules as `` heterostructures '' of chemically well - defined local groups and analyzing their electrical response to the applied electrical field  @xcite      author to whom correspondence should be addressed . email : ayxue@chem.nwu.edu a. aviram and m. a. ratner , chem . * 29 * , 277 ( 1974 ) . _ molecular electronics : science and technology _ , edited by a. aviram and m. ratner ( new york academy of sciences , new york , 1998 ) . c. joachim , j. k. gimzewski and a. aviram , nature * 408 * , 541 ( 2000 ) and references thererein . m. a. reed , c. zhou , c. j. muller , t. p. burgin and j. m. tour , science * 278 * , 252 ( 1997 ) ; 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laham , c. y. peng , a. nanayakkara , c. gonzalez , m. challacombe , p. m. w. gill , b. johnson , w. chen , m. w. wong , j. l. andres , c. gonzalez , m. head - gordon , e. s. replogle and j. a. pople \" , gaussian , inc .  , pittsburgh , pa , 1998 . v. heine , phys . a*138 * , 1689 ( 1965 ) . j. tersoff , phys . lett .  * 52 * , 465 ( 1984 ) ; j. tersoff , phys .  rev . b * 30 * , 4874 ( 1984 ) . w. mnch , rep . phys .  * 53 * , 221 ( 1990 ) . e. h. rhoderick and r. h. williams , _ metal - semiconductor contact _ , 2nd edition ( oxford university press , oxford , 1988 ) . i. h. campbell and d. l. smith , solid state phys .   * 55*,1 ( 2001 ) . p. k. h. ho , m. granstrm , r. h. friend and n. c. greenham , adv .  mat .  * 10 * , 769 ( 1998 ) . w. li et al .  , adv .  mat .  * 11 * , 730 ( 1999 ) . v. mujica , a. e. roitberg and m. a. ratner , j.  chem . 112 * , 6834 ( 2000 ) . r. landauer , ibm j.  res . develop . * 1 * , 223 ( 1957 ) ; * 32 * , 306 ( 1988 ) . a. wacker , phys .  rep . * 357 * , 1 ( 2002 ) . _ \" the force concept in chemistry _ , edited by b. m. deb ( van norstrand reinhold company , new york , 1981 ) . a. h. verbruggen , ibm j.  res . develop .   * 32 * , 93 ( 1988 ) . f. kassubek , c. a. stafford and h. grabert , phys . b * 59 * , 7560 ( 1999 ) . j. reichert et al .  , bf 88 , 176804 ( 2002 ) . j. g. kushmerick et al .  , bf 89 , 86802 ( 2002 ) . j. park et al .  , nature * 417 * , 722 ( 2002 ) . w. liang et al .  , nature * 417 * , 725 ( 2002 ) . cui et al .  , science * 294 * , 571 ( 2001 ) . a simple estimate can be given in the limit of an ideal ( infinite ) two - dimensional molecular monolayer . we assume the molecule - metal distance is @xmath83 and each molecule occupies a surface area of @xmath84 on average . replacing the charge distribution of the two - dimensional monolayer by an uniform charge sheet , a charge transfer of @xmath85 per molecule is enough to give an electrostatic potential drop of @xmath86 across the metal - monolayer junction . d. janes , private communication . f. lonard and j. tersoff , phys . lett .   * 83 * , 5174 ( 1999 ) . y. xue and m.a . ratner , to be published . since our emphasis in this work is in conceptual issues , we have not tried testing or optimizing the more technical aspects of the modeling work such as the choice of the exchange - correlation functionals and the optimum molecular basis sets . for example , the calculations reported in this work were performed using a quite restricted basis set for the metal atoms on the surface of the semi - infinite substrate . the metal atoms belonging to atomic - scale structures on top of the substrate and the molecule itself are treated using much better basis sets as in standard molecular calculations . it is clear that the description of the metallic substrate is inadequate . and obtaining a better balance in the basis set decription between the substrate atoms and the molecule is a difficult and important issue for further improving the accuracy of the modeling of molecular - scale devices within the negf formalism . such refinement may be needed for obtaining quantitative agreement with specific transport measurement . in particular , the calculated charger transfer from the gold surface to sulfur may be different depending on the basis sets ( plane waves or extended gaussian basis sets ) as well as the surface models ( semi - infinite crystal , cluster or supercell geometry ) chosen .","summary":"we present the first in a series of microscopic studies of electrical transport through individual molecules with metallic contacts .","abstract":"we present the first in a series of microscopic studies of electrical transport through individual molecules with metallic contacts . we view the molecules as `` heterostructures '' composed of chemically well - defined atomic groups , and analyze the device characteristics in terms of the charge and potential response of these atomic - groups to the perturbation induced by the metal - molecule coupling and the applied electrical field , which are modeled using a first - principles based self - consistent matrix green s function ( scmgf ) method . as the first example , we examine the devices formed by attaching two benzene - based molecular radicals  phenyl dithiol ( pdt ) and biphenyl dithiol ( bpd)symmetrically onto two semi - infinite gold electrodes through the end sulfur atoms . we find that both molecules acquire a fractional number of electrons with similar magnitude and spatial distribution upon contact with the electrodes . the charge transfer creates a potential barrier at the metal - molecule interface that modifies significantly the frontier molecular states depending on the corresponding electron density distribution . for both molecules , the metal fermi - level is found to lie closer to the highest - occupied - molecular - orbital ( homo ) than to the lowest - unoccupied - molecular - orbital ( lumo ) . transmission in the homo - lumo gap for both molecules is due to the metal - induced gap states arising from the hybridization of the metal surface states with the occupied molecular states . applying a finite bias voltage leads to only minor net charge injection due to the symmetric device structure assumed in this work . but as current flows , the electrons within the molecular junction redistribute substantially , with resistivity dipoles developing in the vicinity of potential barriers . only the delocalized-electrons in the benzene ring can effectively screen the applied electric field . for the pdt molecule , the majority of the bias voltage drops at the metal - molecule interface . but for the bpd molecule , a significant amount of the voltage also drops in the molecule core . the field - induced modification of the molecular states ( the static stark effect ) becomes significant as the bias voltage increases beyond the linear - transport region . a bias - induced reduction of the homo - lumo gap is observed for both molecules at large bias . the stark effect is found to be stronger for the bpd molecule than the pdt molecule despite the longer length of the former . for both molecules , the peaks in the conductance are due to electron transmission through the occupied rather than the unoccupied molecular states . the calculation is done at room temperature , and we find the temperature dependence of the current - voltage characteristics of both molecules is negligible ."}
{"article_id":"0902.0491","section_id":"i","document":"the oncoming limits of conventional downscaling of field - effect transistors have strengthened the need for innovative device architectures.@xcite in this context , the use of mechanical strains has become an attractive solution to improve the electrical performances by enhancing the carrier mobility.@xcite as a matter of fact , strain engineering techniques such as the growth of a contact etch stop layer ( cesl),@xcite or si channels strained by sige source and drain extensions are now widely spread in the semiconductor industry . more generally , the electronic properties of strained si@xmath4ge@xmath5 layers grown on si@xmath6ge@xmath7 buffers are attracting much attention.@xcite these heterostructures , that can be integrated into si - based electronics and photonics , indeed offer the opportunity to tune the band gap of the active layer . the modeling of the electrical properties of such devices requires a detailed description of the effects of strains on the band structure . over the past decades , the _ ab initio _ methods such as the density functional theory@xcite ( dft ) have provided comprehensive information about the deformation potentials of semiconductors.@xcite however , such _ ab initio _ methods require heavy computational resources and are not , therefore , suitable for the calculation of the transport properties of large systems . for that reason , the physics and electronic device community is actively developing more efficient semi - empirical approaches , such as the @xmath8,@xcite the empirical pseudopotential@xcite or the tight - binding@xcite ( tb ) methods , that can work out the electronic structure of strained semiconductors devices . among these semi - empirical approaches , the tb method has long proved successful in predicting the electronic properties of semiconductor nanostructures such as nanocrystals or nanowires . the use of an atomic orbitals basis set with interactions limited to a few nearest neighbors indeed allows the calculation of the wave functions of million atom systems.@xcite the tb method is also well suited to quantum transport calculations,@xcite and to the atomic scale description of , e.g. , impurities@xcite or electron - phonon coupling.@xcite in this respect , the first nearest neighbors @xmath0 model is one of the most accurate and efficient tb description of semiconductor materials.@xcite    the effects of strains are accounted for in tb models through the bond length dependence of the nearest neighbor parameters @xmath9 ( @xmath10 and @xmath11 being two orbitals on different atoms ) , which is usually fitted to a power law:@xcite @xmath12 where @xmath3 is the distance between the two atoms in the strained crystal and @xmath13 is the equilibrium distance . although some hydrostatic and uniaxial deformation potentials can be reproduced that way,@xcite much better accuracy can be achieved with the introduction of strain - dependent on - site parameters.@xcite indeed , hydrostatic strain shifts the average potential@xcite in the crystal , while uniaxial and shear strains split the @xmath2 or @xmath3 orbitals of a given atom . in their original @xmath0 parametrization , jancu _ et al._@xcite therefore introduced a term that lifts the degeneracy between the @xmath14 , @xmath15 , and @xmath16 orbitals under uniaxial @xmath17 strain . jancu and voisin later generalized this approach to uniaxial @xmath18 strain.@xcite these hamiltonians , however , feature the macroscopic strains @xmath19 , whose expression as a function of the atomic positions ( the basic input of the tb method ) is not univocal . et al._@xcite therefore introduced position - dependent orbital energies in the @xmath0 hamiltonian . they could reproduce that way the valence band deformation potentials @xmath20 and @xmath21 , but did not really improve on @xmath22 . this limitation is a consequence of the `` diagonal '' assumption made in that model . uniaxial @xmath23 strain indeed leaves , for example , the @xmath24 , @xmath25 and @xmath26 orbitals of a given atom equivalent . it however couples these orbitals off the diagonal of the hamiltonian .    in this paper , we discuss a model for the on - site matrix elements of the @xmath0 tb model , based on an explicit expression for the crystal field , assuming that the total potential is the sum of central , atomic contributions.@xcite it features off - diagonal couplings between different orbitals , and is able to reproduce the effects of arbitrary strains on the band energies and effective masses at all relevant k - points . it only involves a few additional parameters , is fully consistent with the symmetries of the crystal , and is free from any ambiguity that might arise from the introduction of the macroscopic strains @xmath19 in an atomistic description . we present this model in section [ sectionmodel ] , then discuss its properties in section [ sectiondiscussion ] . finally , we apply this model to silicon , germanium and their alloys , which are the most relevant materials for microelectronics , in section [ sectionapplications ] . we provide detailed comparisons with _ ab initio _ data on strained si , ge and sige , and discuss two important problems : the increase of the longitudinal effective mass under shear strains ( missing in previous tb models ) , and the description of random alloys .","summary":"this model features on - site , off - diagonal couplings between the , and orbitals , and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full brillouin zone . it introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions . we apply this model to silicon , germanium and their alloys as an illustration . in particular , we make a detailed comparison of tight - binding and _ ab initio _ data on strained si , ge and sige .","abstract":"we discuss a model for the on - site matrix elements of the tight - binding hamiltonian of a strained diamond or zinc - blende crystal or nanostructure . this model features on - site , off - diagonal couplings between the , and orbitals , and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full brillouin zone . it introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions . we apply this model to silicon , germanium and their alloys as an illustration . in particular , we make a detailed comparison of tight - binding and _ ab initio _ data on strained si , ge and sige ."}
{"article_id":"1608.03110","section_id":"i","document":"in astrophysical , space and laboratory plasmas , magnetic reconnection is a crucial mechanism of conversion of magnetic energy into plasma heating , bulk plasma motion and particle acceleration . in the past , mainly the fluid aspects of this process were analyzed theoretically and numerically , as well as observationally and experimentally@xcite . collisionless magnetic reconnection causes , however , also non - maxwellian velocity space distribution functions ( vdf ) which are beyond any fluid description . non - maxwellian vdfs are formed , first of all , by local plasma processes . but they also contain information about the particles history of their past interactions with turbulence , providing remote signatures of the latter . hence , measured vdfs can be used for the investigation of magnetic reconnection , e.g. , in the earth magnetosphere . in addition to ion - vdfs , already well investigated in the past , recently also electron vdfs ( evdfs ) are becoming increasingly well observed , e.g. by the multi - spacecraft mission mms with its unprecedent spatial and temporal resolution to measure evdfs@xcite . self - consistent kinetic simulations using vlasov- or particle - in - cell ( pic ) codes have to be carried out since hybrid , test particle or fluid approaches can not reveal evdfs self - consistently .    in the past , the formation of evdfs was investigated mainly for reconnection through current sheets ( css ) embedded in antiparallel asymptotic magnetic fields @xcite . these works identified and explained several evdfs structures in and close to the diffusion region of reconnection , as long as the feedback reaction via waves and plasma turbulence plays a minor role@xcite . this implies that most of the evdf features in antiparallel magnetic field reconnection can be explained even in terms of test particle trajectories in prescribed electromagnetic fields . one typical evdf shape is , for example , triangular evdfs@xcite . let @xmath3 be the direction of the initially antiparallel magnetic fields on both sides of the cs , @xmath4 the direction across the cs ( e.g. , of the density gradients in a harris - sheet equilibrium ) . then @xmath5 spans the reconnection plane and @xmath6 is the out - of - reconnection - plane ( current ) direction . triangular evdfs appear in the @xmath7 plane and have different striations or filamentary structures called `` beamlets '' . each `` beamlet '' corresponds to groups of particles that succeeded to bounce across the cs midplane ( @xmath8 , along @xmath3 ) the same number of times due to their meandering orbits@xcite . the `` beamlet '' with the maximum negative ( @xmath9 directed ) velocity @xmath10 corresponds to electrons with a larger number of reflections , which spent more time near the maximum reconnection electric field @xmath11 . their direction in the @xmath7 plane reflects the angle between the reconnecting magnetic field component @xmath12 and the out - of - plane component @xmath13 at the location where the electrons lose their gyrotropy . other structures in the vdfs are arcs and swirls . they are formed just outside the diffusion region , after the electrons are remagnetized . ring structures in the outflows jets form cup - like distributions in the 3d velocity space@xcite . the temporal evolution of evdfs structures was also studied @xcite . flat - top distributions were found in the exhaust region@xcite , formed due to pitch angle diffusion after large anisotropies are generated for small asymptotic electron plasma-@xmath14 ( @xmath15 being the ratio of the electron thermal pressure to the magnetic pressure ) . the latter can cause strong parallel ( to the magnetic field ) electric fields and double layers , i.e. sites of additional particle acceleration . flat - top distributions are formed due to the chaotic scattering of electrons that cross the neutral plane where they temporarily lose their gyrotropy@xcite . the resulting velocity space pitch angle scattering reduces the anisotropy . flat - top distributions were also observed in the earth s magnetosphere@xcite . similar investigations were used to analyze the formation of vdfs by finite guide - field ( @xmath16 ) reconnection . note that finite guide - field strengths correspond to a deviation from a 180@xmath17 angle between the asymptotic fields in antiparallel reconnection . the resulting shear angles of the asymptotic fields are given by @xmath18 $ ] for the normalized guide - field @xmath19 , where @xmath20 is the asymptotic reconnection magnetic field strength . already for small guide fields @xmath21 ( corresponding to @xmath22 ) , the triangular - like structures in the evdfs disappear@xcite due to the modification of the quasi - adiabatic motion@xcite . since the form of the evdfs changes as @xmath23 , relatively large mass ratios are needed to investigate the evdfs of finite guide - field reconnection@xcite . also , the structures outside the diffusion region ( rings , arcs ) disappear because the extended outflow jets along the separatrices , typical for antiparallel reconnection , vanish already for very small guide fields @xcite . in weak guide - field reconnection , electron trapping influences the formation of the evdfs causing anisotropic pitch angle distributions@xcite , as long as the adiabatic invariant @xmath24 is conserved . the density and magnetic field is asymmetrically distributed through the earth s magnetopause@xcite and finite guide - field reconnection applies . kinetic simulations of reconnection through such asymmetric current sheets revealed mainly crescent - shaped evdfs , which were explained as being due to a normal electrostatic field component generated by the pressure gradients through the cs@xcite . such crescent - shaped evdfs were mostly found at the stagnation points , where the ion and electron flows vanish at a location which just slightly deviates from its position in symmetric cs reconnection . crescent - shaped vdfs are , however , not a unique signature of asymmetric reconnection , they were obtained already in symmetric 1d cs fields for which they were verified by test particle calculations@xcite . these predictions are now being verified by mms spacecraft magnetopause observations @xcite . before discussing the evdfs formed by stronger guide - field reconnection , let us clarify a terminology . in guide - field reconnection , the plasma density is different at different separatrices@xcite : around two separatrices the plasma density is enhanced , while it drops near the other two separatrices , forming density `` cavities '' . we will call these two different near - separatrix regions `` high - density '' and `` low - density separatrix '' , respectively . evdfs in cs with strong guide fields ( @xmath25 , i.e. , @xmath26 ) , have been investigated , e.g. , by refs .  . they found parallel ( to the magnetic field ) electron beams , relating them to parallel bipolar electric fields formed in the cavities of the `` low - density separatrices '' . this is in contrast to the antiparallel case , where mainly the reconnection electric field near the x - line accelerates the electrons towards the exhaust region . especially in fully 3d configurations , the streaming instabilities due to the electron beams in the cavities of the `` low - density separatrices '' generate strong electrostatic turbulence ( see , e.g. , ref .  ) . similar turbulence is also generated in 2d configurations . but it is weaker and located away from the cs midplane , where a small projection of the parallel wavenumber onto the reconnection plane exists . the turbulence leads to thermalization of the beams via pitch - angle scattering forming flat - top distributions . the formation mechanisms of these vdfs in dependence on the guide - field strength is , however , still not clear , as well as their shapes in the exhaust region away from the x - line . the previous theoretical and numerical investigations were confirmed by the detection of particle beams in the earth s magnetosphere . in particular , measurements of ion beams in the magnetotail region known as plasma sheet boundary layer ( psbl . see , e.g. , refs .   and references therein ) , located between the dense plasma sheet and the low density tail lobe . electron beams were detected in the psbl less often , perhaps , due to the higher instrumental resolution required@xcite . but recent measurements by the mms mission are providing more opportunities@xcite . the psbl region exhibits a strong broadband electrostatic noise from around the lower hybrid frequency @xmath27@xcite up to the electron plasma frequency consisting of mostly perpendicular ( to the magnetic field ) propagating waves , a feature which is associated also with flat - top evdfs@xcite . waves around the lower hybrid frequency are also often detected in magnetic reconnection events in the earth s magnetotail@xcite . electron beams evolve into electron holes via streaming instabilities , as shown by several 3d guide - field reconnection simulations ( e.g. , ref .  ) , but also in 2d@xcite and reduced 1d setups ( see , e.g. , refs .   and references therein ) . electron holes have been observed in laboratory experiments@xcite , in the earth s magnetotail@xcite and in the magnetopause@xcite . note that electron holes and associated electrostatic turbulence do not only appear in guide - field reconnection ( as originally thought ) , but they were also found in antiparallel reconnection cases , as soon as the mass ratio and simulation box size were chosen large enough@xcite . based on the previous discussion , there is still the open question about the formation of evdfs in dependence on a strong guide - field strength , i.e. , for shear angles of the reconnecting fields much smaller than @xmath28 . for this part of the parameter space the consequences of instabilities , turbulence , particle trapping and scattering for the formation of the evdfs are not well known , yet . this is true , in particular , for the exhaust region of reconnection . to fill this gap in view of the coming mms observations we derive the potentially measurable non - maxwellian evdf signatures in dependence on the guide - field strength , taking into account the nonlinear interaction of the electrons with their self - generated turbulence . the remaining work is organized as follows . in sec . [ sec : setup ] , we describe the simulation setup and parameters used . in sec .  [ sec : results ] , we give a general overview of the evdfs obtained in the simulations ( sec . [ sec : evdfs ] ) , their distribution in phase space ( sec . [ sec : phasespace ] ) , the mechanism of beam formation ( sec .  [ sec : beamformation ] ) , the identification of the dominant beam instabilities and the turbulence generated by them ( sec . [ sec : beaminstabilities ] ) . finally , in sec . [ sec : conclusion ] , we summarize , discuss and give an overview of the expected properties of the evdfs in dependence on the most probable macroscopic plasma and field parameters , mainly on the guide - field component strength ( the opening shear angle ) of the reconnecting magnetic fields .","summary":", the evolution of the evdfs was investigated mainly for antiparallel or weak - guide - field reconnection . the shape of evdfs is , however , not well known yet for oblique ( or component- ) reconnection in dependence on a finite guide magnetic field component perpendicular to the reconnection plane . in view of the multi - spacecraft mission mms , we derive the non - maxwellian features of evdfs formed by collisionless magnetic reconnection starting from very weak ( ) up to very strong ( ) guide - field strengths , taking into account the feedback of the self - generated turbulence . for this sake , the obtained evdfs can be used for diagnosing collisionless reconnection by means of multi - spacecraft observations carried out by the mms mission .","abstract":"non - maxwellian electron velocity space distribution functions ( evdf ) are useful signatures of plasma conditions and non - local consequences of collisionless magnetic reconnection . in the past , the evolution of the evdfs was investigated mainly for antiparallel or weak - guide - field reconnection . the shape of evdfs is , however , not well known yet for oblique ( or component- ) reconnection in dependence on a finite guide magnetic field component perpendicular to the reconnection plane . in view of the multi - spacecraft mission mms , we derive the non - maxwellian features of evdfs formed by collisionless magnetic reconnection starting from very weak ( ) up to very strong ( ) guide - field strengths , taking into account the feedback of the self - generated turbulence . for this sake , we carry out 2.5d fully - kinetic particle - in - cell ( pic ) simulations using the acronym code . we obtained anisotropic evdfs and the distribution of electron beams propagating along the separatrices as well as in the exhaust region of reconnection . the beam evdfs are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field . the beams propagate in the direction opposite to the background plasma electron flows , providing a source of free energy for instabilities . in dependence on the guide - field strength , the relative drift speed of the electrons can exceed the threshold of streaming instabilities . we investigated the non - linear consequences of the resulting self - generated plasma turbulence for the formation and the final shaping of the evdfs . we found how , both near the separatrices and in the exhaust region of reconnection , the turbulence as well as its non - linear feedback to the evdfs depend on the guide - field strength . the influence of the self - generated plasma turbulence leads well beyond the limits of the quasi - linear approximation , phase space holes are created and strong isotropizing pitch - angle scattering takes place . the obtained evdfs can be used for diagnosing collisionless reconnection by means of multi - spacecraft observations carried out by the mms mission . + _ the following article has been submitted to physics of plasmas . after it is published , it will be found at http://scitation.aip.org/content/aip/journal/pop_"}
{"article_id":"1608.03110","section_id":"r","document":"due to the initial perturbation and all the available magnetic flux in the simulation box , reconnection saturates after @xmath61 . as was found before@xcite , the guide fields delays the onset of reconnection and lowers the reconnection rates , mostly due to the hall effect@xcite of magnetized electrons interacting with the ions . the resulting spatial structure of the out - of - plane current density @xmath62 , is shown in fig . [ fig : jz_bg ] for three guide - field cases ( @xmath63 ) . for each case , the corresponding moment of time is chosen just after the saturation stage , when the opening angle of the exhaust region and reconnection rates are similar . note that a strong plasma turbulence develops in the exhaust region for @xmath64 . turbulence does not develop , however , at the boundaries in the @xmath65direction . this is because the initial current carrying particles accumulate there following the reconnection outflow / exhaust . thus , this turbulent region resembles the psbl of the earth s magnetosphere . the plasma flow is more laminar in the smaller guide - field @xmath51 case ( fig . [ fig : jz_bg]b ) . turbulence does not develop at all for the smallest guide - field @xmath66 . the three values of @xmath63 represent well three different regimes of guide - field reconnection . note that in all these cases the electrons are strongly magnetized in the guide magnetic field , since the critical guide - field above which this happens is exactly ( see eq .  9 in ref .  ) @xmath67^{1/4}=0.26.\\ ] ] the resulting evdfs are shown in fig . [ fig : vdfs_bg ] for a characteristic point between the `` low - density separatrix '' and the exhaust region ( shown in fig .  [ fig : jz_bg ] ) . as the distributions in the plane @xmath68 and @xmath7 demonstrate , the evdfs deviate more from a maxwellian distribution for stronger guide fields . the reason for this deviation can be found by analyzing the turbulence developed inside the exhaust region . as one can see in fig . [ fig : vdfs_bg](c ) , a structure that resembles a double beam forms in the strong guide field case @xmath64 . the faster beam propagates in the direction opposite to the local magnetic field ( depicted as an red arrow ) , mainly in the @xmath69 direction , in agreement with previous works ( discussed in sec . [ sec : intro ] ) . the mean drift speed of the faster beam can be estimated as @xmath70 ( outwards from the x - line ) , while the slower beam propagating in the opposite direction has a drift speed of @xmath71 ( inwards to the x - line ) . the dip in velocity space between the two beams indicates a source of free energy and a later evolution into an phase space hole . note that the two beam components are anisotropic with @xmath72 which provides another source of free energy for instabilities . specifically , the faster beam has @xmath73 and @xmath74 , while the slower beam has @xmath75 and @xmath74 . the decay channel is likely through the electron whistler instability , possible even in low - plasma-@xmath15 conditions ( present here ) , generating parallel propagating waves ( see sec . 7.3.2 - 3 in ref .  ) .    in the moderately strong @xmath76 case ( fig . [ fig : vdfs_bg](b ) ) , the distribution is anisotropic along the magnetic field direction , with @xmath77>@xmath78 . there is no clear double beam structure , only a barely visible double peaked maxwellian with components much closer each other than for the @xmath64 case ( compare specially the evdfs in the plane @xmath79 ) . for the smallest guide - field @xmath66 ( fig . [ fig : vdfs_bg](a ) ) , the evdf is very close to an isotropic maxwellian , not developing a tail or plateau in the magnetic field direction . this is because the electrons spent less time being accelerated near the x - line by the reconnection electric field @xmath11 than for stronger guide - field cases . it is still possible to distinguish , however , a small `` bump '' oppositely directed to the local magnetic field , specially in the plane @xmath79 . the main consequence of these evdfs structures for both @xmath76 and @xmath66 cases is that both of them do not become unstable and do not generate any significant turbulence . electron beams , evolving later into structures similar to phase space holes , typically develop in the whole exhaust region between the separatrices for the case @xmath80 . this can be seen in phase space plots @xmath81 shown in fig . [ fig : phase_space ] for different guide fields , obtained as an @xmath82cut at @xmath83 ( in the exhaust region . see fig . [ fig : jz_bg ] ) . in all the cases , the `` high - density separatrix '' is represented as the leftmost peak with @xmath84 . a density cavity forms around the `` low - density separatrix '' ( rightmost dip with @xmath85 ) . the differences in the separatrices densities are more expressed the larger the guide fields strength is . the reason is that strong guide fields enhance acceleration of the plasma flows . these plasma flows are then scattered along the separatrices ( see , e.g. , chp . 8.4.1 of ref .  ) . for higher guide - field strengths , bipolar electrostatic fields occur along the `` low - density separatrix '' , as discussed in sec . [ sec : intro ] . the maximum speed in @xmath10 of the electrons in the `` high - density separatrix '' is enhanced , while the width of their distribution in @xmath4 becomes narrower ( strong density gradient ) .        note that for the guide - field case @xmath80 ( fig . [ fig : phase_space](c ) ) , the distribution of the plasma population in the `` high - density separatrix '' constitute one arc of a crescent - like ( parabolic ) shape in the phase space cut @xmath86 ( at @xmath87 ) . the other end of the arc is next to the `` low - density separatrix '' ( at @xmath88 ) . note that these arcs are asymmetrical or tilted , suggesting a relation with some simulations of beam - driven lower hybrid instability@xcite , that explained those phase space structures as a result of the wave steepening associated with this instability ( see discussion in sec .  [ sec : beaminstabilities ] ) . in most of the exhaust region , the mean drift speed of the electrons forming the upper arc or crescent - shaped population is @xmath89 , increasing towards the `` low - density separatrix '' . there is a second internal crescent - shaped distribution , with average drift speed of @xmath90 inside the exhaust region and boundaries between @xmath91 . therefore , throughout this region , the two crescent - shaped populations form the two beams ( drifting away mostly in the @xmath9direction ) similar to those seen in fig . [ fig : vdfs_bg](c ) ( taken at @xmath92 ) . the structures in between resemble phase space holes of size @xmath93 wide . for smaller guide fields ( e.g. , @xmath94 ) , the dip between the two beams is reduced . this is seen in fig . [ fig : phase_space](b ) as a reduction in the distance between the two crescent - shaped populations close to the cs center . for @xmath95 ( fig . [ fig : phase_space](a ) ) , the two crescent - shaped populations completely merge in the exhaust region , becoming completely stable . the different crescent - shaped populations in the phase space cut @xmath86 correspond to electrons which were accelerated at different times and distances from the x - line , as predicted theoretically by ref .   and simulated by ref .  . electrons accelerated earlier and closer to the x - line obtain a higher speed in the @xmath96 direction , being pushed inwards to the exhaust region at an earlier time . those high energetic electrons are located in the boundaries of the crescent - shaped distribution in the phase space plane @xmath86 ( closer to the separatrices ) , where they are accelerated first . near the midplane they are decelerated instead , resulting in the concave shape of the crescent in the phase space cut @xmath86 . this process is due to the conservation of the magnetic moment @xmath97 : since the in - plane @xmath98 magnetic field is weaker ( stronger ) near the cs midplane ( separatrices ) , the electron @xmath10 drift speed has to be smaller ( larger ) there . on the other hand , because the out - of - plane magnetic field @xmath13 is stronger ( weaker ) near the cs midplane ( separatrices ) , this invariance also implies that the electron in - plane @xmath99 drift speeds are larger ( smaller ) there ( results not shown here ) . the smaller the guide - field , the more crescent shaped distributions are formed ( see fig .  [ fig : phase_space](a ) ) . this is because electrons experience a greater acceleration near the x - line with maximum value of the reconnection electric field , but spend shorter time there compared to the case of stronger guide fields . as a result , electrons are trapped in magnetic field lines closer to each other than in stronger guide fields . a similar magnetic trapping effect was discussed by ref .  . they showed that electrons trapped in the reconnecting magnetic fields lines can be advected with the plasma inflow to the x - line . since magnetic moment in guide - field reconnection is always conserved , the electrons move to a local minimum of the magnetic field .      in order to reconstruct the acceleration of the electron beams , we selected all the electrons ( @xmath100 ) belonging to the evdf shown in fig . [ fig : vdfs_bg](c ) for the case @xmath80 at @xmath101 . then , we rerun the simulation outputting at a higher cadence the particle data , in order to trace the trajectories of the beam particles . we found that most of the electrons in the ( faster ) @xmath96 beam ( population i ) entered the vicinity of the x - line from a `` low - density separatrix '' ( fig .  [ fig : trajectories](a ) ) and become accelerated by the reconnection electric field . from there , they are expelled into the direction of the `` high - density separatrix '' . obviously , the electrons spend a longer time in the acceleration region the larger the guide - field is@xcite . for @xmath80 , this is visualized as a strong drop in @xmath10 between @xmath102 ( see fig . [ fig : time_histories](a ) ) . the longer acceleration time is , however , compensated by the smaller reconnection electric field these electron see . as a result , the overall acceleration and final drift speed in the beam are not significantly larger than for lower guide - field cases . on the other hand , after the electrons enter the exhaust region , their large @xmath96 speed is associated with an in - plane ( @xmath5 ) curved drift motion along the magnetic field lines . this drift is directed outwards from the x - line in the region between the `` high - density separatrix '' and the cs - midplane , and inwards to the x - line in the region between the `` low - density separatrix '' and the cs - midplane . as a result , the beam evdf of this population has a mean drift speed with negative @xmath103 and @xmath104 components for the location shown in fig . [ fig : jz_bg](c ) ( see also discussion of fig .  [ fig : vdfs_bg](c ) ) .    a typical electron trajectory with initially positive velocity @xmath105 ( population ii ) is shown in fig .  [ fig : trajectories](b ) ( for the evdf shown in the fig .  [ fig : vdfs_bg](c ) ) . their @xmath10 speed does not change significantly ( fig . [ fig : time_histories](b ) ) : they approach the x - line from the `` high - density separatrix '' , but do not encounter it as close as the ones entering via the `` low - density separatrix '' . most of them belonged originally to the background population . inside of the exhaust region , they have the opposite drift motion to those of the beam electrons with @xmath96 , i.e. : directed inwards to the x - line in the region between the `` high - density separatrix '' and the cs midplane , and outwards from the x - line in the region between the `` low - density separatrix '' and the cs - midplane . as a result , and different from the previous case , their beam evdf has a mean drift speed with positive @xmath106 and @xmath107 components for the location shown in fig . [ fig : jz_bg](c ) . the counterstreaming beam electrons cause an instability whose main source of free energy is the in - plane projection of the relative drift speed between them and the relative speed of each one with respect to the ions ( practically at @xmath108 compared with the electrons ) . the beam instability vanishes if the guide fields strength exceeds significantly @xmath109 . even though the beam in the negative @xmath96 direction is slightly faster in this limit ( due to the extra time spent in the acceleration region close to the x - line ) , its velocity projection in the @xmath5 plane is smaller due to the stronger magnetization . for small guide fields @xmath110 , on the other hand , there is no formation of electrons beams but rather a barely visible double peaked maxwellian , and therefore no significant source of free energy for instabilities ( see also discussion of fig . [ fig : phase_space ] ) . finally , there is a third electron population ( population iii ) illustrated by the trajectory shown in fig . [ fig : trajectories](c ) . these particles come from one of the `` high - density separatrices '' . their @xmath10 speed component is positive , being decelerated near the x - line , and then ejected into the `` low - density separatrix '' . inside the exhaust region , the electrons of these population are scattered due to conservation of magnetic moment ( close to a minimum of magnetic field ) , changing their curved drift motion ( fig . [ fig : time_histories](c ) ) from the characteristic direction of population ii ( with @xmath105 ) to those of the population i ( with @xmath96 ) . it might seem that the counterstreaming beams of populations i and ii can be at the same physical location only due to the returning electrons through the periodic @xmath3 boundaries ( since they are ejected through different separatrices from the x - line ) . but the beams with @xmath96 have also a significant contribution from population iii with electrons changing the direction of their @xmath10 speed , allowing a direct interaction between counterstreaming beams . we can make a crude estimation by detecting the number of traced electrons changing direction from @xmath105 to @xmath96 in the exhaust region , keeping the negative drift speed at the end of the considered time period . they are 2083 , but many of them with low @xmath10 should be discarded since they do not contribute significantly to the beam . by establishing a bottom threshold of minimum change in @xmath111 , we get 1741 , and for @xmath112 we get 852 . the beam population with @xmath96 has 5794 traced electrons ( while the beam population with @xmath105 has 6801 ) . therefore , the contribution of the population iii to the counterstreaming beam @xmath96 can be estimated to be between @xmath113 and @xmath114 . the rest should come from the returning electrons through the periodic boundaries . therefore , a significant proportion of the instability and turbulence reported for the @xmath80 case should always be seen , independent of any boundary condition .          for moderately strong guide fields ( @xmath115 ) , fast beams are accelerated causing turbulence due to streaming instabilities . as a result , structures resembling phase space holes are formed while pitch - angle scattering isotropize the originally anisotropic beam evdfs . the beam evdfs ( c.f . [ fig : vdfs_bg](c ) ) are , therefore , transient in their interaction with turbulence . plateaus formed in the evdfs fill the voids in the velocity - space between the beams , making them stable ( see fig .  [ fig : vdf_bg3_later ] ) . the strong electrostatic turbulence start after @xmath116 ( and close to the reconnection rate peak time ) , as one can see in the @xmath117 electric field spectrogram shown in fig . [ fig : probe_info](a ) . the magnetic fluctuation strength is lower than the electric one , as observed in the psbl of the earth s magnetosphere under low plasma-@xmath14 conditions@xcite . note that the electrostatic fluctuations reported here are seem different from the parallel ( and bipolar ) turbulence usually seen in the `` low - density separatrices '' ( cavities ) of guide - field reconnection due to streaming instabilities . the main reason is that they have mostly low frequencies ( see discussion later ) and are not constrained to the separatrix region , but fill most of the exhaust region . the instabilities generating electrostatic turbulence in the `` low - density separatrices '' of reconnection were found to be mostly of streaming - type , generating mostly high frequency waves at electron scales . in particular , two - streaming and buneman instabilities seem to be very ubiquitous , as shown by 2d pic simulations of magnetic reconnection with@xcite and without guide - field@xcite . shear flow instabilities like kelvin - helmholtz instability have also been reported@xcite(see more details in chp . 8.4.1 of ref .   and references therein ) . streaming instabilities due to electron beams have been observed in the psbl of the earth s magnetosphere , generating high frequency langmuir - like waves ( see , e.g. , and references therein ) , as well as in the magnetopause@xcite . we found evidence that the instability operating in our case might be due to a combination of buneman ( electron beams with ions ) and two - streaming ( between electron beams ) instability with parallel propagation ( see a general overview of these instabilities in ref .   and 3.2 and 8.5 of ref .  ) in addition to a ( beam - driven ) lower - hybrid instability with nearly perpendicular propagation@xcite , with the latter being probably the dominant one . note that most of the relative drift speed between the beams is in the out - of - plane @xmath6 direction because of the strong magnetization for the guide field @xmath80 . however , there is a small in - plane projection of that relative drift that allow the existence of parallel propagating waves and the mechanism behind all these instabilities in the reduced 2.5d geometry of our simulations . the main result of these instabilities is the generation of lower hybrid waves and turbulence . an alternative way of interpreting this is considering the in - plane drift speed of the electron beams as a transverse current perpendicular to the local magnetic field ( mostly along @xmath6 ) , generating a cross - streaming instability known as modified two - streaming instability mtsi ( see e.g. , refs .   and chp .  4.4 in ref .  ) . mtsi was proposed to be active in the diffusion region of magnetic reconnection@xcite . note that this can only be an effect of our simulation geometry . in any case , the features of this instability are very similar to those of the lower - hybrid instability , leading to the same kind of unstable waves and turbulence . in addition , other instabilities might also be active , like electron whistler , due to the initial anisotropy of the beams ( see sec . 7.3.2 - 3 in ref .  ) . we found four signatures of these streaming instabilities generating lower hybrid turbulence . first : the characteristic frequency of the electric field fluctuations is broadband with ( low ) frequencies up to the lower hybrid frequency @xmath118 ( see fig . [ fig : probe_info](a ) ) . for our parameters , this corresponds to @xmath119 . the most likely source of free energy for this wave activity is the lower - hybrid instability due to parallel propagating electron beams ( see fig . [ fig : vdfs_bg](c ) ) , possibly interacting also with the ion distribution ( practically at @xmath120 ) , agreeing in order of magnitude with theoretical predictions@xcite . note that monochromatic wave activity such as typically expected only from two - streaming / buneman instabilities generates electron trapping in coherent structures , with high frequency waves close to electron scales , not observed in our case . on the other hand , the obliquely propagating lower hybrid waves are incoherent , broadband , and able to scatter particles@xcite , which agree more with our simulations results . furthermore , the typical decay period of the electron beams is within the order of magnitude of the growth rate of these instabilities ( for similar parameters , ref . reported flattening of evdfs beams in @xmath121 in their pic simulations , which is about @xmath122 in our case ) . note that 3d pic simulations of guide - field reconnection have shown that waves in the lower hybrid range of frequencies can be generated by either the lower hybrid drift instability ( lhdi ) due to density gradients@xcite , or beam - driven lower hybrid instability caused by the nonlinear decay of two - streaming / buneman instabilities in the cavities of the `` low - density separatrix''@xcite . 2d simulations of magnetic reconnection without guide field have also found wave activity close to the lower hybrid frequency generated by the buneman instability@xcite , in scenarios where the relative streaming speed is relatively slow . this interplay between the nonlinear phase of the structures generated by the buneman instability and the subsequent generation of lower hybrid waves have also been reported in simulations specifically designed to study this instabilities@xcite . the second evidence for this streaming instability is its threshold or stabilization condition . for the following estimations , we should estimate first the typical relative drift speed between the electron beams . the field aligned speed between the two counterstreaming beams in fig . [ fig : vdfs_bg](c ) : @xmath123 , while the local magnetic field direction is given by the unitary vector @xmath124 . then , the magnitude of the projection of the field aligned speed onto the plane @xmath5 can be obtained by multiplying @xmath125 by the factor @xmath126 , resulting in @xmath127 ( note that @xmath128 ) . the relative drift speed with respect to the practically unmagnetized ions is about half of these values . this has to be compared with the parallel beam temperature , given by @xmath129 . the corresponding projection is @xmath130 . both temperatures ( field aligned or in - plane projection ) are much smaller than the relative electron beam drift speed , satisfying the criterion to trigger the beam - driven lower hybrid instability . the lower hybrid instability is stabilized for high plasma-@xmath14 conditions , because it requires negligible magnetic shear@xcite . the instability is allowed only for drift speeds @xmath131 such as @xmath132 . for an in - plane drift speed of @xmath133 , this ratio is @xmath134 , which is therefore well satisfied . for smaller guide fields , even if the same kind of electron beams would appear ( which is not the case ) , they would be stable since the higher plasma-@xmath14 would violate the previous condition . quasilinear@xcite and kinetic pic simulations@xcite have shown that the lower hybrid instability can be active in a wide range of parameters in which other parallel propagating instabilities ( such as buneman ) are stable . this might be the case when the evdfs have plateau - like structures between the beams , as it is in our case at some locations . the third evidence is that wave activity in the lower - hybrid frequency range causes parallel electron heating and perpendicular ion heating ( see , e.g. refs .  , and references therein ) this is because the lower hybrid waves have long parallel wavelengths ( resonating with electrons ) and short perpendicular wavelengths ( resonating with ions ) . indeed , lower hybrid waves are known to propagate nearly perpendicularly with @xmath135 ( see some additional features and approximations of the dispersion relation of these waves in ref .  ) . both features are recovered in our simulations results ( the ion distributions are not shown here ) . this characteristic heating due to lower hybrid waves was also observed in the psbl of the earth s magnetosphere@xcite , although due to kinetic alfvn waves ( kaws ) . the fourth evidence for the streaming instability is its phase speed and wave number . for that , fig . [ fig : probe_info](b ) shows the wavenumbers @xmath136 of the electric field @xmath117 fluctuations . the wavenumbers with higher spectral power show a broadband distribution ( as expected from lower hybrid activity@xcite ) in the range @xmath137 . the low end range can be misleading because the homogeneity assumption of linear theory breaks down at such large spatial scales ( closer to the cs halfwidth ) . this wavenumber ( @xmath136 ) contains both parallel and perpendicular fluctuations , but we can take it as @xmath138 for an estimations of the order of magnitude . therefore , the range of wave phase speeds is on the order of @xmath139 for @xmath140 . this implies that at least the waves within the lower phase speed range can resonate with the ( in - plane projected ) electron beams . note that the possibly also active anisotropy - driven electron - whistler instability perhaps also contributes to the turbulence as one can see at smaller scales than the size of the phase space structures ( in the upper range of unstable @xmath141 ) . note that these electrostatic structures seem different from the known electron holes located in the `` low - density separatrix '' region of guide - field reconnection . the latter are as large as eight times the electron skin depth @xmath142 , decreasing in units of @xmath143 for higher mass ratios , and mostly independent on the guide - field and mass ratio@xcite ( see also chp . 8.4.1 of ref .  ) . the size of the electrostatic structures in the exhaust region of reconnection discussed here are , however , inversely proportional to the guide - field . their sizes coincide with the electron holes previously reported only in the order of magnitude for the case @xmath80 . note that several other effects can hinder the applicability of linear theory to our case . this requires magnetized electrons with @xmath144 , relatively well satisfied in our case . but the approximation of homogeneous plasma , the neglect of electromagnetic effects , wave - wave coupling and the relative drift speed are either not well satisfied or vary in a wide parameter range . that is why all the previous estimations should be taken with caution .","summary":"the beams propagate in the direction opposite to the background plasma electron flows , providing a source of free energy for instabilities . in dependence on the guide - field strength , the relative drift speed of the electrons can exceed the threshold of streaming instabilities . the influence of the self - generated plasma turbulence leads well beyond the limits of the quasi - linear approximation , phase space holes are created and strong isotropizing pitch - angle scattering takes place . + _ the following article has been submitted to physics of plasmas . after it is published , it will be found at http://scitation.aip.org/content/aip/journal/pop_","abstract":"non - maxwellian electron velocity space distribution functions ( evdf ) are useful signatures of plasma conditions and non - local consequences of collisionless magnetic reconnection . in the past , the evolution of the evdfs was investigated mainly for antiparallel or weak - guide - field reconnection . the shape of evdfs is , however , not well known yet for oblique ( or component- ) reconnection in dependence on a finite guide magnetic field component perpendicular to the reconnection plane . in view of the multi - spacecraft mission mms , we derive the non - maxwellian features of evdfs formed by collisionless magnetic reconnection starting from very weak ( ) up to very strong ( ) guide - field strengths , taking into account the feedback of the self - generated turbulence . for this sake , we carry out 2.5d fully - kinetic particle - in - cell ( pic ) simulations using the acronym code . we obtained anisotropic evdfs and the distribution of electron beams propagating along the separatrices as well as in the exhaust region of reconnection . the beam evdfs are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field . the beams propagate in the direction opposite to the background plasma electron flows , providing a source of free energy for instabilities . in dependence on the guide - field strength , the relative drift speed of the electrons can exceed the threshold of streaming instabilities . we investigated the non - linear consequences of the resulting self - generated plasma turbulence for the formation and the final shaping of the evdfs . we found how , both near the separatrices and in the exhaust region of reconnection , the turbulence as well as its non - linear feedback to the evdfs depend on the guide - field strength . the influence of the self - generated plasma turbulence leads well beyond the limits of the quasi - linear approximation , phase space holes are created and strong isotropizing pitch - angle scattering takes place . the obtained evdfs can be used for diagnosing collisionless reconnection by means of multi - spacecraft observations carried out by the mms mission . + _ the following article has been submitted to physics of plasmas . after it is published , it will be found at http://scitation.aip.org/content/aip/journal/pop_"}
{"article_id":"1608.03110","section_id":"i","document":"our goal was to find characteristic signatures in the electron velocity space distributions ( evdfs ) formed by non - antiparallel ( component- , finite guide - field- ) magnetic reconnection in collisionless plasmas . using 2.5-dimensional pic code simulations , we self - consistently obtained the evdfs near the separatrices as well as in the exhaust ( outflow ) region of reconnection in dependence on the guide - field strength . to obtain the observable evdfs , we took into account the feedback of the non - linear interaction of the self - generated turbulence caused by the non - maxwellian evdfs with the electrons . guide - field reconnection generates , in addition to the electron beams along the separatrices , also unstable beams in the reconnection exhaust ( outflow ) region . these beams propagate mostly aligned with the local magnetic field , their evdfs are gyrotropic and anisotropic . they accumulate free energy not only due to their relative streaming , but also by their anisotropy with a higher temperature in the direction perpendicular to the local magnetic field . the different kinds of free energy are released via plasma instabilities , causing turbulence mainly in the lower - hybrid frequency range . we found that the beam electrons are not accelerated by parallel electric fields in the cavities of the `` low - density separatrix '' regions , but rather by the reconnection electric field . after being accelerated near the x - line , these electrons are ejected into the beams , depending on their incidence angle and speed , either to the `` high- '' or `` low - density separatrix '' regions . a large number of the beam electrons become trapped in the exhaust region . the resulting counter - streaming electron beams cause streaming instabilities .    for strong guide fields @xmath145 , the resulting streaming instability is evidenced by a strong electrostatic broadband turbulence near the lower hybrid frequency , which arises as soon as the relative drift speed between the beams exceeds the instability threshold . the phase speeds and wavenumbers of the unstable waves match the theoretical predictions of lower - hybrid streaming instabilities . as a result of their interaction with the self - generated turbulence , the beam electrons are pitch - angle scattered . hence , with time the evdfs become increasingly isotropic . furthermore , the gaps in the velocity space between the counterstreaming beams become filled and plateaus arise in the evdfs in association with phase space holes .    in case of small guide - fields ( @xmath146 ) , reconnection does not generate those beams . the reason is that the electron acceleration near the x - line is less efficient in this limit because the acceleration time near the x - line is too short . instead , a larger part of the released energy by reconnection enhances the outflow plasma bulk speed .    in the limit of very strong guide fields ( @xmath147 ) , on the other hand , the relative beam drift velocity is largest while the in - plane projection of the gained speed is smaller than in the strong guide - field regime @xmath145 . in this case , the guide - magnetic field component @xmath148 is much larger than the in - plane component @xmath98 . note that in a 2.5d setup , the beam energy can not be dissipated by waves propagating in the out - of - plane direction . in three - dimensions , the beam energy will probably be dissipated via out - of - plane directed turbulent electromagnetic fields . note that the formation of counter - streaming electron beams and the resulting turbulence in the reconnection exhaust is not just an artifact of the periodic boundary conditions . in fact , a significant contribution ( estimated to be @xmath149 ) comes from the reflection of streaming beam electrons in the exhaust / outflow region of reconnection , independent of the boundaries which these electrons do not reach . we confirmed this by running simulations with larger boxes in the exhaust / outflow direction . they revealed the same or even higher turbulence levels ( results not shown here ) . a system with periodic boundary conditions is also relevant for the understanding of acceleration at multiple x - points between the magnetic islands , as it is known to happen in strong guide - fields@xcite , in cascading reconnection @xcite and in plasmoid - unstable current sheets @xcite . note that we investigated the evdfs typical for non - antiparallel ( magnetic field ) reconnection through symmetric ( density ) current sheets . our predictions , therefore , neglect the effects arising in asymmetric current sheets like at the earth s magnetopause . previous simulations of asymmetric reconnection@xcite have shown , however , that the density asymmetry affects the evdfs mainly by additional particle acceleration in the electrostatic field generated by the pressure gradients across the current sheet@xcite . concerning the strength of the guide - fields , mms observations revealed already finite guide - field reconnection situations with @xmath150@xcite , @xmath94 @xcite and @xmath151 @xcite . close to the reconnection x - line , those authors already found anisotropic evdfs preferentially heated in the magnetic field direction . this qualitatively agrees well with our predictions ( detailed evdfs not shown here ) . the next task of the mms mission will be the investigation of magnetic reconnection the earth s magnetotail . there the reconnecting current sheets are symmetric . smaller ( @xmath95 ) @xcite as well as larger guide - fields@xcite can be expected . note that based on mass ratio scalings to larger mass ratios than the ones used in this study ( @xmath33 ) , evdfs like those discussed here will probably be obtained already for smaller guide - fields@xcite .      * * very small guide fields ; @xmath152 ( or @xmath153 ) * : + already for very small but finite guide fields strengths , most of the non - maxwellian evdfs typical for antiparallel reconnection ( triangular - like , crescent , rings , swirls , arc - shaped ) start to vanish . the details were already reviewed in a number of papers ( see sec . [ sec : intro ] ) . no distinguishable anisotropic heating takes place near the x - line . * * moderately small guide fields ; @xmath154 ( or @xmath155 ) * : + close to the x - line , the electrons become anisotropically heated with higher temperature in the magnetic field direction , forming a plateau in their evdf . therefore , the mean electron drift is in the direction opposite to the local magnetic field . the drift speed increases for larger guide fields strengths . the electron temperature in the direction parallel to the magnetic field @xmath156 is maximum for @xmath157 . meanwhile , the beam axes rotate in the planes containing the guide field direction depending on the strength of the local in - plane component of the reconnecting magnetic field . between the separatrices and the exhaust regions , the evdfs vary from anisotropic plateaus near the separatrices ( crescent shapes in the phase space @xmath86 : the velocity direction aligned with the guide field and the spatial direction across the current sheet midplane ) , to more isotropic , heated maxwellian evdfs in the exhaust ( see fig .  [ fig : phase_space](a ) ) . towards the outer layers of the exhaust and adjacent to the separatrices , the electron beam drift speed is reduced while it increases towards the current sheet midplane . + the anisotropic plateaus of the evdfs in the exhaust region are , however , different from the ones close to the x - point . for the guide field range @xmath158 , they contain a small `` bump '' in one end of the plateau . for stronger guide fields ( @xmath159 ) , after reaching a maximum thermal spread and anisotropy , the `` bump '' at the plateau completely splits off from the evdf `` core '' , forming two distinguishable beams . therefore , the maximum drift speed of the beams can be estimated to reach the `` parallel thermal spread '' defined as : @xmath160 ( three standard deviations from the mean ) , where @xmath161 is the parallel drift speed of the entire evdf in this regime ( i.e. : in the plateau close to the x - line and between the core and the bump in the exhaust region ) . this speed can be used as a rough measure of the efficiency of the acceleration process . altogether the thermal spread ranges from @xmath162 ( for @xmath163 ) up to @xmath164 ( for @xmath165 ) . from simulations for a number of different guide - field strengths ( results not shown here in detail ) , we obtained an exponential regression fitting for the thermal spread : @xmath166 , with @xmath167 , @xmath168 and @xmath169 . the factor @xmath170 increases for smaller asymptotic plasma@xmath171 and larger temperature ratios @xmath172 , while @xmath173 depends on the critical magnetization of the electrons in the guide - field ( @xmath174 , see eq .  ) . it becomes smaller ( less negative ) for smaller critical guide fields ( up to @xmath175 ) . * * large guide fields : @xmath176 ( or @xmath177 ) * : + for larger guide - fields , the evdfs closer to the x - line are almost completely gyrotropic but anisotropic , heated preferentially along the guide - field direction , as in the case @xmath178 . with an increasing guide - field strength , the parallel mean electron beam drift speed @xmath179 becomes more negative . the parallel temperature @xmath156 reaches a minimum for guide - fields close to @xmath80 , not changing even for stronger guide fields . the maximum parallel thermal spread is roughly the same as for @xmath180 : @xmath164 , with a very weak dependence on the guide - field strength . due to the interaction with self - generated turbulence , the evdfs in the exhaust region are complex and intermittent . after the reconnection rate reaches a maximum , beams can be seen throughout the whole exhaust region ( see fig .  [ fig : vdfs_bg ] ) . the larger @xmath2 is , the more anisotropic the beams become . due to the conservation of the magnetic moment ( see sec .  [ sec : beaminstabilities ] ) , the near - separatrix electron beams propagate either slightly faster or with the same @xmath181 as those obtained close to the x - line . as a result , the total energy of the beam electrons can be slightly higher . + note that the relative drift speed of the beams does not depend on the guide - field strength , while the velocity space dip between the beams is deeper for stronger @xmath2 . at time scales of the order of @xmath182 , phase space holes are formed as well as stable plateaus while the beam anisotropy is reduced . * * very large guide fields : @xmath183 ( or @xmath184 ) * : + in case of even stronger guide fields , the evdfs are similar to those formed in the large guide - field regime ( @xmath185 ) . but the lifetime of the beams is larger since they do not generate significant turbulence , phase space holes or plateaus . note that this changes when the beam energy can be dissipated via self - generated turbulence in the guide field direction . we acknowledge the developers of the acronym code ( verein zur frderung kinetischer plasmasimulationen e.v . ) . in particular , we are most grateful to patrick kilian for his helpful discussions and valuable comments .    118ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ]  + 12$12  & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty in  http://www.cambridge.org/us/academic/subjects/astronomy/astrophysics/reconnection-magnetic-fields-magnetohydrodynamics-and-collisionless-theory-and-observations[__ ] ,  ( ,  )  chap .  , pp . link:\\doibase 10.1103/revmodphys.82.603 [ * * ,   ( ) ] link:\\doibase 10.1146/annurev - astro-082708 - 101726 [ * * ,   ( ) ] link:\\doibase 10.3389/fphy.2013.00031 [ * * ,   ( ) ] link:\\doibase 10.1007/978 - 3 - 319 - 26432 - 5 [ _ _ ] ,  astrophysics and space science library ( ,  ) link:\\doibase 10.1007/s11214 - 015 - 0164 - 9 [ * * ,   ( ) ] link:\\doibase 10.1186/bf03353282 [ * * ,   ( ) ] link:\\doibase 10.1063/1.3263694 [ * * , ( ) ] link:\\doibase    10.1063/1.3521576 [ * * ,   ( ) ] link:\\doibase    10.1103/physrevlett.106.065002 [ * * ,   ( ) ] link:\\doibase 10.1063/1.4899043 [ * * , ( ) ] link:\\doibase 10.1002/2014gl060608 [ * * ,   ( ) ] link:\\doibase    10.1002/2015gl063601 [ * * ,   ( ) ] link:\\doibase    10.1063/1.4933055 [ * * ,   ( ) ] link:\\doibase    10.1063/1.4932337 [ * * ,   ( ) ] @noop ( ) ,   link:\\doibase 10.1029/jz070i017p04219 [ * * , ( ) ] link:\\doibase 10.1029/gl017i002p00127 [ * * ,   ( ) ] link:\\doibase 10.1029/91gl01905 [ * * ,   ( ) ] link:\\doibase 10.1016/0273 - 1177(95)00994 - 9 [ * * ,   ( ) ] link:\\doibase 10.5636/jgg.48.781 [ * * ,   ( ) ] link:\\doibase 10.1016/s0273 - 1177(97)00965 - 4 [ * * ,   ( ) ] link:\\doibase 10.1029/2005ja011542 [ * * , ( ) ] link:\\doibase 10.1029/ja094ia09p11821 [ * * , ( ) ] link:\\doibase    10.1029/2007ja012461 [ * * ,   ( ) ] link:\\doibase 10.1103/physrevlett.102.075003 [ * * ,   ( ) ] link:\\doibase    10.1063/1.4766895 [ * * ,   ( ) ] link:\\doibase    10.1002/2015ja021892 [ * * ,   ( ) ] link:\\doibase 10.1016/0273 - 1177(91)90030-n [ * * ,   ( ) ] link:\\doibase    10.1103/physrevlett.107.135001 [ * * ,   ( ) ] link:\\doibase 10.1029/2008ja013520 [ * * ,   ( ) ] link:\\doibase 10.1063/1.4811092 [ * * ,   ( ) ] link:\\doibase 10.1016/j.asr.2005.05.025 [ * * ,   ( ) ] link:\\doibase 10.1029/2007ja012930 [ * * ,   ( ) ] link:\\doibase    10.1007/s11214 - 014 - 0078-y [ * * ,   ( ) ] link:\\doibase 10.1002/2016gl067886 [ * * ,   ( ) ] link:\\doibase    10.1002/2016gl068243 [ * * ,   ( ) ] link:\\doibase 10.1002/2016gl069034 [ * * ,   ( ) ] link:\\doibase    10.1002/2016gl068373 [ * * ,   ( ) ] http://arxiv.org/abs/1607.05670 [ ( ) ] ,   link:\\doibase 10.1007/bf00167825 [ * * ,   ( ) ] link:\\doibase 10.1126/science.aaf2939 [ * * ,   ( ) ] link:\\doibase    10.1002/2016gl069212 [ * * ,   ( ) ] link:\\doibase 10.1063/1.871095 [ * * ,   ( ) ] link:\\doibase 10.1029/2002ja009699 [ * * ,   ( ) ] link:\\doibase    10.1126/science.1080333 [ * * ,   ( ) ] link:\\doibase 10.1029/2003ja009999 [ * * , ( ) ] link:\\doibase    10.1063/1.3467503 [ * * ,   ( ) ] link:\\doibase    10.1063/1.3697976 [ * * ,   ( ) ] link:\\doibase    10.1029/2011gl048572 [ * * ,   ( ) ] link:\\doibase    10.1017/s0022377814000944 [ * * ,   ( ) ] link:\\doibase 10.1029/2004ja010748 [ * * ,   ( ) ] link:\\doibase 10.1029/2004ja010519 [ * * ,   ( ) ] link:\\doibase 10.1063/1.1914309 [ * * , ( ) ] link:\\doibase 10.1103/physrevlett.94.095001 [ * * ,   ( ) ] link:\\doibase 10.1029/2006ja011793 [ * * , ( ) ] link:\\doibase    10.1002/2015ja021573 [ * * ,   ( ) ] link:\\doibase    10.1029/98gl00855 [ * * ,   ( ) ] \\doibase 10.1023/a:1005206701965 [ * * ,   ( ) ] link:\\doibase    10.1186/s40623 - 015 - 0256 - 5 [ * * ,   ( ) ] link:\\doibase 10.1002/2016gl068768 [ * * ,   ( ) ] link:\\doibase 10.1029/98ja01104 [ * * ,   ( ) ] link:\\doibase    10.1029/2010ja016324 [ * * ,   ( ) ] link:\\doibase    10.1002/2013ja019483 [ * * ,   ( ) ] link:\\doibase 10.1029/2008gl035608 [ * * ,   ( ) ] link:\\doibase 10.1016/j.jcp.2005.09.023 [ * * ,   ( ) ] \\doibase 10.1051/0004 - 6361:20078419 [ * * ,   ( ) ] link:\\doibase 10.1051/0004 - 6361/201117186 [ * * ,   ( ) ] link:\\doibase    10.1103/physrevlett.101.255003 [ * * ,   ( ) ] link:\\doibase 10.1103/physrevlett.105.165002 [ * * ,   ( ) ] link:\\doibase 10.1029/2005gl024650 [ * * ,   ( ) ] in link:\\doibase 10.1007/978 - 3 - 642 - 23869 - 7 [ _ _ ] ,   ( ,  ,  )  pp . link:\\doibase 10.1007/bf02733547 [ * * , ( ) ] link:\\doibase    10.1051/0004 - 6361/201321557 [ * * ,   ( ) ] link:\\doibase 10.1063/1.872088 [ * * ,   ( ) ] link:\\doibase 10.1063/1.1768552 [ * * ,   ( ) ] link:\\doibase 10.1063/1.1834592 [ * * ,   ( ) ] link:\\doibase 10.1029/2004ja010751 [ * * , ( ) ] http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/planetary-science-and-astrobiology/theory-space-plasma-microinstabilities[__ ] ( ,  ) link:\\doibase 10.1063/1.2409764 [ * * , ( ) ] link:\\doibase 10.1029/91gl00235 [ * * ,   ( ) ] link:\\doibase    10.1002/2014ja019978 [ * * ,   ( ) ] link:\\doibase 10.1007/s11214 - 011 - 9807 - 7 [ * * ,   ( ) ] link:\\doibase 10.1002/2014gl059893 [ * * ,   ( ) ] link:\\doibase 10.1029/2009ja014343 [ * * , ( ) ] link:\\doibase    10.1063/1.3698621 [ * * ,   ( ) ] link:\\doibase    10.1029/ja089ia10p08885 [ * * ,   ( ) ] link:\\doibase    10.1029/95ja03145 [ * * ,   ( ) ] link:\\doibase    10.1063/1.4896716 [ * * ,   ( ) ] link:\\doibase 10.1002/2016gl068992 [ * * ,   ( ) ] link:\\doibase    10.1029/2002ja009573 [ * * ,   ( ) ] link:\\doibase 10.1088/0029 - 5515/16/2/014 [ * * ,   ( ) ] link:\\doibase 10.1063/1.861501 [ * * , ( ) ] link:\\doibase 10.1029/ja090ia01p00377 [ * * ,   ( ) ] link:\\doibase 10.1063/1.2198212 [ * * , ( ) ] link:\\doibase 10.1063/1.1693881 [ * * , ( ) ] link:\\doibase    10.1063/1.864285 [ * * ,   ( ) ] link:\\doibase 10.1142/p020 [ _ _ ]  ( , ) link:\\doibase 10.1029/2002ja009810 [ * * , ( ) ] link:\\doibase    10.1063/1.1597494 [ * * ,   ( ) ] link:\\doibase 10.1103/physrevlett.102.145004 [ * * ,   ( ) ] link:\\doibase 10.1029/2010gl043608 [ * * ,   ( ) ] link:\\doibase 10.1063/1.873099 [ * * , ( ) ] link:\\doibase 10.1029/2000ja000001 [ * * ,   ( ) ] link:\\doibase 10.1063/1.3132628 [ * * ,   ( ) ] link:\\doibase 10.1029/2001ja900113 [ * * ,   ( ) ] link:\\doibase 10.1029/2006gl025957 [ * * ,   ( ) ] link:\\doibase 10.1088/0004 - 637x/737/1/24 [ * * ,   ( ) ] link:\\doibase 10.1088/0004 - 637x/730/1/47 [ * * ,   ( ) ] link:\\doibase    10.1088/0004 - 637x/815/1/6 [ * * ,   ( ) ] link:\\doibase 10.1063/1.2783986 [ * * ,   ( ) ] link:\\doibase 10.1063/1.3264103 [ * * ,   ( ) ] link:\\doibase 10.1088/0741 - 3335/58/1/014021 [ * * ,   ( ) ] link:\\doibase 10.1002/2016gl069787 [ * * ,   ( ) ] link:\\doibase    10.1002/2016gl069166 [ * * ,   ( ) ] link:\\doibase 10.1103/physrevlett.117.015001 [ * * ,   ( ) ] link:\\doibase 10.1029/2007ja012760 [ * * ,   ( ) ] link:\\doibase    10.1029/2011ja017402 [ * * ,   ( ) ]","summary":"non - maxwellian electron velocity space distribution functions ( evdf ) are useful signatures of plasma conditions and non - local consequences of collisionless magnetic reconnection . in the past we obtained anisotropic evdfs and the distribution of electron beams propagating along the separatrices as well as in the exhaust region of reconnection . the beam evdfs are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field . we investigated the non - linear consequences of the resulting self - generated plasma turbulence for the formation and the final shaping of the evdfs . we found how , both near the separatrices and in the exhaust region of reconnection , the turbulence as well as its non - linear feedback to the evdfs depend on the guide - field strength .","abstract":"non - maxwellian electron velocity space distribution functions ( evdf ) are useful signatures of plasma conditions and non - local consequences of collisionless magnetic reconnection . in the past , the evolution of the evdfs was investigated mainly for antiparallel or weak - guide - field reconnection . the shape of evdfs is , however , not well known yet for oblique ( or component- ) reconnection in dependence on a finite guide magnetic field component perpendicular to the reconnection plane . in view of the multi - spacecraft mission mms , we derive the non - maxwellian features of evdfs formed by collisionless magnetic reconnection starting from very weak ( ) up to very strong ( ) guide - field strengths , taking into account the feedback of the self - generated turbulence . for this sake , we carry out 2.5d fully - kinetic particle - in - cell ( pic ) simulations using the acronym code . we obtained anisotropic evdfs and the distribution of electron beams propagating along the separatrices as well as in the exhaust region of reconnection . the beam evdfs are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field . the beams propagate in the direction opposite to the background plasma electron flows , providing a source of free energy for instabilities . in dependence on the guide - field strength , the relative drift speed of the electrons can exceed the threshold of streaming instabilities . we investigated the non - linear consequences of the resulting self - generated plasma turbulence for the formation and the final shaping of the evdfs . we found how , both near the separatrices and in the exhaust region of reconnection , the turbulence as well as its non - linear feedback to the evdfs depend on the guide - field strength . the influence of the self - generated plasma turbulence leads well beyond the limits of the quasi - linear approximation , phase space holes are created and strong isotropizing pitch - angle scattering takes place . the obtained evdfs can be used for diagnosing collisionless reconnection by means of multi - spacecraft observations carried out by the mms mission . + _ the following article has been submitted to physics of plasmas . after it is published , it will be found at http://scitation.aip.org/content/aip/journal/pop_"}
{"article_id":"1603.09466","section_id":"i","document":"like high - energy physics , condensed matter is dominated by the idea of symmetry . any physical property which _ can not _ be traced back to a broken symmetry is therefore of enormous fundamental interest . in this context , the spin liquid phases found in frustrated magnets are a rich source of inspiration  @xcite . perhaps the most widely studied examples are the `` spin ice '' states in ho@xmath3ti@xmath3o@xmath4 and dy@xmath3ti@xmath3o@xmath4 , classical spin - liquids famous for their magnetic monopole excitations  @xcite . and there is now good reason to believe that a _ quantum _ spin - liquid phase , in which the magnetic monopoles are elevated to the role of `` elementary '' particles , could exist in spin - ice like materials where quantum effects play a larger role  . ( [ eq : hex1 ] ) ] , with symmetric off - diagonal exchange @xmath5 , and vanishing dzyaloshinskii - moriya interactions ( @xmath6 ) . there are four distinct ordered phases , illustrated in the insets of fig . [ fig : finite - temperature - phase - diagram ] . points correspond to published estimates of parameters for yb@xmath0ti@xmath0o@xmath1 [ ] , er@xmath0ti@xmath0o@xmath1 [ ] , and er@xmath0sn@xmath0o@xmath1 [ ] , setting @xmath6 . the white circle corresponds to the path through parameter space shown in fig . [ fig : finite - temperature - phase - diagram ] . ] the extraordinary physics of spin ice stems from the combination of the geometrical frustration inherent to the pyrochlore lattice on which the magnetic rare earth ions r@xmath7 reside , and the strongly anisotropic nature of the interactions between rare - earth ions @xcite . this mixture of geometrical frustration and strong spin anisotropy is common to many pyrochlore materials , and gives rise to a wide array of interesting physical behaviors @xcite . the spin ices belong to a wider family of rare - earth pyrochlore oxides r@xmath0m@xmath0o@xmath1 in which the magnetic ions have a doublet ground state , and highly - anisotropic interactions . the physical properties of these materials depend on the choice of rare - earth r@xmath7 and transition metal m@xmath8 , and are fabulously diverse . in addition to spin ices , this family includes a wide range of systems that order magnetically , spin glasses and systems where local moments couple to itinerant electrons  @xcite . materials of current interest include yb@xmath0ti@xmath0o@xmath1 , which exhibits striking `` rod - like '' features in neutron scattering  @xcite , and has been argued to undergo a higgs transition into a ferromagmetically ordered state  @xcite ; er@xmath0ti@xmath0o@xmath1 , which appears to offer an elegant worked example of ( quantum ) order by disorder  @xcite ; and er@xmath0sn@xmath0o@xmath1 , which has yet to been seen to order at _ any _ temperature  @xcite . alongside continuing investigations into these materials , the last few years has seen the synthesis of a steady stream of new rare earth pyrochlore oxides , exhibiting both ordered @xcite and disordered @xcite low temperature states . ( [ eq : hex1 ] ) ] , with @xmath5 , @xmath9 . coloured regions show the four ordered phases illustrated in fig . [ fig : finite - temperature - phase - diagram ] . white regions indicate where quantum fluctuations eliminate conventional magnetic order , within a linear spin - wave theory . parameters @xmath10 , @xmath11 are shown on a log - polar scale with @xmath12 . the white circle corresponds to the path through parameter space shown in fig . [ fig : finite - temperature - phase - diagram ] . ]        given this `` embarrassment of riches '' , it seems reasonable to ask whether there is _ any _ common framework which can connect the properties of different rare  earth pyrochlore oxides , place new materials in context , and help guide the search for novel magnetic states . in this article , we enlarge on the results in an earlier preprint  @xcite to develop a broad scenario for these materials , based on the concept of multiple  phase competition . we go on to show how this approach can be used to explain many of the interesting properties of yb@xmath0ti@xmath0o@xmath1 , er@xmath0ti@xmath0o@xmath1 and er@xmath0sn@xmath0o@xmath1 . our starting point is the most general model of nearest  neighbour interactions compatible with the symmetries of the pyrochlore lattice  @xcite @xmath13 where the sum on @xmath14 runs over the nearest  neighbour bonds of the pyrochlore lattice , @xmath15 describes the magnetic moment of the rare - earth ion , and the matrix @xmath16 is a function of four independent parameters . following the notation of ross _ et al . _ [ ] , we identify these as ( @xmath17 ) , `` ising '' ( @xmath18 ) , `` symmetric off - diagonal '' ( @xmath19 ) and `` dzyaloshinskii - moriya '' ( @xmath20 ) interactions . this model encompasses an extremely rich variety of different magnetic physics , including an exchange - based `` spin - ice '' ( @xmath17=@xmath21=@xmath22=@xmath23 ) , and the heisenberg antiferromagnet on a pyrochlore lattice ( @xmath17=@xmath24 , @xmath22=@xmath20=@xmath25 ) , both of which are believed to have spin - liquid ground states  @xcite . nonetheless , materials such as er@xmath0ti@xmath0o@xmath1 , which is extremely well - described by a nearest  neighbour exchange model  @xcite , _ do _ order magnetically  @xcite .    the phase diagram of @xmath26 [ eq .  ( [ eq : hex1 ] ) ] for a quantum spin1/2 has previously been studied using mean - field and spin  wave approximations , with many papers emphasising connections with spin ice @xcite . in this article we take a different approach , starting from an analysis of the way in which different spin configurations break the point - group symmetries of the pyrochlore lattice . we show that , for classical spins , the problem of finding the ground state of @xmath26  [ eq .  ( [ eq : hex1 ] ) ] can be neatly separated into two steps : i ) finding the ground state of a single tetrahedron and ii ) understanding how the spin - configuration on that tetrahedron can be used to tile the pyrochlore lattice . the first step , in turn , reduces to understanding how the different interactions in the model transform under the symmetries @xmath27 of a single tetrahedron . the second step , summarized in a simple set of `` lego  brick '' rules , enables us to encompass both ordered ground states , which break lattice symmetries , and spin - liquids , which do not . this approach , augmented by spin - wave calculations and extensive classical monte carlo simulations , makes it possible both to establish a complete phase diagram for @xmath26 [ eq . ( [ eq : hex1 ] ) ] as a function @xmath28 , and to link ground state properties to predictions for neutron - scattering experiments . in this article , taking our motivation from estimated parameters for yb@xmath0ti@xmath0o@xmath1 [ ] , er@xmath0ti@xmath0o@xmath1 [ ] and er@xmath0sn@xmath0o@xmath1 [ ] , we concentrate on ordered phases in the limit . here there is a competition between four different types of order  : a palmer  chalker @xcite phase ( @xmath29 ) , a non - collinear ferromagnet ( fm ) , a coplanar antiferromagnet ( @xmath30 ) , and a non - coplanar antiferromagnet ( @xmath31 ) . the way in which these phases relate to one another is illustrated in fig . [ fig : classical - phase - diagram ] , fig . [ fig : quantum - phase - diagram ] and fig . [ fig : finite - temperature - phase - diagram ] . crucially , the same symmetry - based approach used to find ordered ground states also permits us to explore the way in which these physically distinct states are connected by the `` accidental '' degeneracies arising at boundaries between phases with different symmetry . the enlarged ground - state manifolds at these phase boundaries have far - reaching consequences , once quantum and thermal fluctuations are taken into account . the common theme which emerges is of systems `` living on the edge ''  the physical properties of materials showing one type of magnetic order being dictated by the proximity of another , competing , ordered phase . thus , in yb@xmath0ti@xmath0o@xmath1 , we find ferromagnetic order proximate to competing , `` @xmath30 '' and `` @xmath31 '' phases , which manifest themselves in the `` rods '' seen in neutron scattering . meanwhile , in er@xmath0ti@xmath0o@xmath1 , we discover that the reason fluctuations select the well  established `` @xmath31 '' ground state  @xcite , is proximity to a neighboring palmer  chalker phase , as illustrated in fig . [ fig : figure - of - doom - lite ] . and in the case of er@xmath0sn@xmath0o@xmath1 , we find that fluctuations of palmer  chalker order predominate , but that all forms of magnetic order are strongly suppressed by the proximity of a degenerate ground - state manifold connected to a neighbouring `` @xmath31 '' phase . we note that the same approach of combining symmetry analysis and the `` lego  brick '' rules can also be used to systematically search for unconventional ordered states and new ( classical ) spin - liquid phases on the pyrochlore lattice . this is a theme which will be developed elsewhere @xcite . the remainder of the present article is structured as follows :    in section  [ section : model ] we introduce a general model of nearest  neighbour exchange interactions on a pyrochlore lattice and , restricting to classical spins , establish the conditions under which the model has a magnetically ordered ground state . we also provide a complete classification of possible ordered states in terms of the irreducible representations of the tetrahedral symmetry group @xmath32 .    in section  [ section : classical - ground - states ] we show that this symmetry analysis can be used to determine the classical ground state of @xmath26  [ eq .  ( [ eq : hex1 ] ) ] for arbitrary parameters @xmath28 . the nature of the ground states in the limit @xmath33 , which is of particular relevance to real materials , is explored in some detail , including analysis of the degenerate manifolds arising at the phase boundaries of the model .    in section  [ section : spin - wave - theory ] we explore the spin - wave excitations associated with these ordered phases . this enables us to make predictions for neutron scattering , and to develop a ground state phase diagrams for classical and semiclassical spins , focusing again on the limit @xmath5 and @xmath6 , as illustrated in fig . [ fig : classical - phase - diagram ] . it also enables us to identify regions of the phase diagram where strong quantum fluctuations are liable to eliminate classical order entirely , as illustrated in fig . [ fig : quantum - phase - diagram ] . in section  [ section : finite - temperature ] we use classical monte carlo simulation to explore the finite - temperature phase transitions which separate each of the ordered phases from the high - temperature paramagnet . the results of this analysis are summarized in fig . [ fig : finite - temperature - phase - diagram ] .    in section  [ section : living - on - the - edge ] we study the finite  temperature consequences of the enlarged ground  state manifolds arising at the boundary between different ordered phases . this is illustrated in fig . [ fig : figure - of - doom - lite ] . in sections  [ section : er2ti2o7 ] ,  [ section : yb2ti2o7 ] and  [ section : er2sn2o7 ] , we discuss the implications of these results for the rare - earth pyrochlore oxides er@xmath3ti@xmath3o@xmath4 , yb@xmath0ti@xmath0o@xmath1 and er@xmath3sn@xmath3o@xmath4 , respectively . other rare  earth pyrochlore magnets to which the theory might apply are discussed briefly in section  [ section : other - pyrochlores ] . we conclude in section  [ conclusions ] with a summary of our results , and an overview of some of the interesting open issues . technical details of calculations are reproduced in a short series of appendices at the end of the article  : appendix  [ appendix : local - coordinate - frame ] provides details of the local coordinate frame throughout the article , and the associated form of the @xmath34tensor . appendix  [ appendix : linear - spin - wave ] provides technical details of the linear spin  wave calculations described in section  [ section : spin - wave - theory ] . appendix  [ appendix : classical - mc ] provides technical details associated with the classical monte carlo simulations described in section  [ section : finite - temperature ] . as far as possible , we have endeavoured to make sections  [ section : er2ti2o7][section : other - pyrochlores ] , describing the application of the theory to experiments on rare  earth pyrochlores , self  contained . readers chiefly interested in these materials may safely omit the theoretical development in sections  [ section : classical - ground - states ] to  [ section : living - on - the - edge ] of the article .    ti@xmath0o@xmath1 . for @xmath35 , fluctuations select six states with non  coplanar antiferromagnetic order ( @xmath31 ) from a one  dimensional manifold of degenerate ground states . the entropic selection of these six states can be traced to an enlarged ground  state manifold found on the boundary with the palmer  chalker phase ( @xmath29 ) . plots show the probability distribution of the order parameter @xmath36 , as described in section  [ section : living - on - the - edge ] . ]","summary":"the family of magnetic rare  earth pyrochlore oxides rmo plays host to a diverse array of exotic phenomena , driven by the interplay between geometrical frustration and spin  orbit interaction , which leads to anisotropy in both magnetic moments and their interactions . in this article we establish a general , symmetry  based theory of pyrochlore magnets with anisotropic exchange interactions . starting from a very general model of nearest  neighbour exchange between kramers ions , we find four distinct classical ordered states , all with , competing with a variety of spin - liquids and unconventional forms of magnetic order . the finite  temperature phase diagram of this model is determined by monte carlo simulation , supported by classical spin - wave calculations . we pay particular attention to the region of parameter space relevant to the widely studied materials ertio , ybtio , and ersno . we find that many of the most interesting properties of these materials can be traced back to the `` accidental '' degeneracies where phases with different symmetries meet . these include the ordered ground state selection by fluctuations in ertio , the dimensional  reduction observed in ybtio , and the lack of reported magnetic order in ersno . we also discuss the application of this theory to other pyrochlore oxides","abstract":"the family of magnetic rare  earth pyrochlore oxides rmo plays host to a diverse array of exotic phenomena , driven by the interplay between geometrical frustration and spin  orbit interaction , which leads to anisotropy in both magnetic moments and their interactions . in this article we establish a general , symmetry  based theory of pyrochlore magnets with anisotropic exchange interactions . starting from a very general model of nearest  neighbour exchange between kramers ions , we find four distinct classical ordered states , all with , competing with a variety of spin - liquids and unconventional forms of magnetic order . the finite  temperature phase diagram of this model is determined by monte carlo simulation , supported by classical spin - wave calculations . we pay particular attention to the region of parameter space relevant to the widely studied materials ertio , ybtio , and ersno . we find that many of the most interesting properties of these materials can be traced back to the `` accidental '' degeneracies where phases with different symmetries meet . these include the ordered ground state selection by fluctuations in ertio , the dimensional  reduction observed in ybtio , and the lack of reported magnetic order in ersno . we also discuss the application of this theory to other pyrochlore oxides"}
{"article_id":"0802.4053","section_id":"i","document":"this paper is the third in a series investigating the use of `` counter - propagating wave methods '' ( cpwms)@xcite for solving the  equation exactly . cpwms are a particular variant of the more general multipolar decomposition methods , wherein the wavefunction @xmath1 is decomposed into two or more components , @xmath4 . thus , for a two - term , or `` bipolar '' decomposition , @xmath0 . this rather trivial - seeming procedure can be quite advantageous in the context of quantum trajectory methods ( qtms),@xcite i.e. trajectory - based numerical techniques for performing exact quantum dynamics calculations , based on bohmian mechanics.@xcite conventional qtms use a single - term or `` unipolar '' representation of the wavefunction from which all other quantities , such as the quantum trajectories themselves , are uniquely determined . multipolar decomposition , on the other hand , can lead to radically different qtm behavior for the individual @xmath4 components , owing to the fact that the bohmian equations of motion are non - linear.@xcite    as applied to wavepacket dynamics for reactive scattering systems , qtms suffer from a significant and well - known numerical drawback , which to date , precludes a completely robust application of these methods . namely , qtms are numerically unstable in the vicinity of amplitude nodes and `` quasi - nodes '' ( i.e. rapid oscillations),@xcite owing to singularities in the `` quantum potential , '' @xmath5 , which together with the classical potential , @xmath6 , determines the quantum trajectories . in the reactive scattering context , such behavior is always observed , due to interference between the incident and reflected waves . on the other hand , if the latter two contributions to the total @xmath1 were somehow separated , and associated with two different interference - free @xmath4 components , the node problem might well be circumvented . if , in addition , the @xmath4 component field functions were smooth and slowly - varying , far fewer qtm trajectories and time - steps might be required than for @xmath1 itself  although the latter could be reconstructed at any desired time simply via linear superposition of the components . these numerical advantages thus provide significant motivation for consideration of the bipolar approach . a much more detailed discussion may be found in the first two articles of this series , paper  i ( ref .  ) and paper  ii ( ref .  ) . the most obvious aspect of any bipolar decomposition , including those restricted along the lines of the preceding paragraph,@xcite is that it is not unique . the covering function method,@xcite for instance , treats @xmath1 as the difference between two very large - amplitude components , thus `` diluting '' the effects of interference . the one - dimensional ( 1d ) cpwm approach,@xcite on the other hand , regards the bipolar decomposition = _ + + _ - [ psitot ] as a superposition of right- and left - traveling counter - propagating waves , @xmath7 . for stationary states at least , the decomposition is defined such that the @xmath7 components correspond to semiclassical wkb approximations , @xmath8 , in the large - action limit . in addition to providing pedagogical value ( semiclassical and bohmian mechanics can not be so reconciled in a unipolar context ) , the semiclassical field functions are typically smooth and slowly - varying , i.e. the semiclassical - like cpwm components @xmath7 provide the desirable numerical advantages described in the preceding paragraph .    in paper i ( ref .  ) , a _ unique _ cpwm bipolar decomposition was determined for bound stationary eigenstates of arbitrary 1d hamiltonians . the resultant @xmath7 field functions are smooth and interference - free , and approach the wkb approximations in the large - action limit ( within the classically allowed region of space ) as desired . moreover , the quantum potentials @xmath9 become vanishingly small in this limit , so that the bipolar quantum trajectories approach classical trajectories , and only a small number are required for a numerical propagation , regardless of excitation energy , @xmath10 . in contrast , the unipolar @xmath1 exhibits _ motionless _ trajectories , and an arbitrarily increasing number of nodes in the large - action / energy limit . results were presented for both the harmonic and morse oscillator potentials .    in paper ii ( ref .  ) , the 1d cpwm ideas were modified somewhat for stationary scattering states of discontinuous potentials . although the cpwm decomposition of paper  i is uniquely specified for any arbitrary 1d eigenstate  bound or scattering  and in the bound case , always satisfies the correspondence principle , the non-@xmath11 nature of the scattering states is such that the paper  i decomposition generally does _ not _ satisfy correspondence globally . as discussed in sec . [ semiclassical ] , this requires that global modifications must be made in order to enable a correspondence between @xmath8 and @xmath7 . these are such as to lead to substantial differences between the density _ functions _ @xmath12 and @xmath13 , although the _ trajectories _ are identical . moreover , the resultant @xmath7 are found to correspond to the familiar `` incident , '' `` transmitted , '' and `` reflected '' waves of traditional scattering theory@xcite in the appropriate asymptotic limits . from the time - dependent standpoint , reflection was found to be due to trajectory _ hopping _ from one cpwm component to the other , as can be naturally understood using a simple ray optics analogy . the method was applied to several elementary discontinuous potential systems , including the square barrier / well .    in the present paper ( paper  iii ) , the ref . formulations are generalized to incorporate both continuous _ and _ discontinuous potential systems . once again , an analogy is drawn from semiclassical mechanics , albeit a `` sophisticated '' version@xcite less frequently considered ( sec . [ semiclassical ] ) . as in paper  ii , a time - dependent method based on ray optics is developed for computing stationary states of any desired energy and boundary conditions . for the most part , the discussion of the preceding paragraph still applies , but some additional key points should be emphasized . first , the bipolar decomposition now provides a sensible definition of `` incident , '' `` transmitted , '' and `` reflected '' waves _ throughout all space _ , not just asymptotically . second , the explicit hopping of trajectories from one cpwm component to the other is replaced with a _ coupling term _ in the time - evolution equations . third , the trajectories become _ completely classical_. finally , an alternative methodology is also developed , based on the use of _ constant velocity trajectories _ , which can be readily applied to barrier tunneling situations . the new methods are found to be remarkably efficient , accurate , and robust across a diverse range of 1d test potentials and system energies ( sec .  [ results ] ) . the paper is organized as follows . a derivation and discussion of the time - evolution equations for the cpwm bipolar components @xmath7 , both for classical and constant velocity trajectories , are presented in sec . [ theory ] and the appendices . [ numerical ] provides numerical details of the various bipolar algorithms used to compute stationary states . results are presented in sec . [ results ] for four benchmark applications : eckart barrier ; square barrier ; uphill ramp ; double - gaussian barrier . for the first three , these are compared with known analytic solutions . concluding remarks , including prospects for future development , may be found in sec . [ conclusion ] .","summary":"in a previous paper [ j. chem . phys . * 121 * 4501 ( 2004 ) ] a unique bipolar decomposition , was presented for stationary bound states of the one - dimensional  equation , such that the components and approach their semiclassical wkb analogs in the large action limit . phys . * ! ! ! * ! ! ! ! a constant velocity trajectory version is also developed .","abstract":"in a previous paper [ j. chem . phys . * 121 * 4501 ( 2004 ) ] a unique bipolar decomposition , was presented for stationary bound states of the one - dimensional  equation , such that the components and approach their semiclassical wkb analogs in the large action limit . the corresponding bipolar quantum trajectories , as defined in the usual bohmian mechanical formulation , are classical - like and well - behaved , even when has many nodes , or is wildly oscillatory . a modification for discontinuous potential stationary stattering states was presented in a second paper [ j. chem . phys . * ! ! ! * ! ! ! ! ( 2005 ) ] , whose generalization for continuous potentials is given here . the result is an _ exact _ quantum scattering methodology using _ classical _ trajectories . for additional convenience in handling the tunneling case , a constant velocity trajectory version is also developed ."}
{"article_id":"0802.4053","section_id":"i","document":"scattering applications are of paramount importance for chemical reactions , because all reactions may be regarded as scattering events . from a theoretical exact quantum perspective , therefore , multichannel scattering theory,@xcite both time - dependent and time - independent , will always play an essential role . at the same time however , trajectory - based methods also bring much to bear on dynamics , providing great insight into reactive processes , vis - a - vis the determination of which trajectories make it past the barrier to products vs. those that do not . quantum trajectory methods ( qtms ) therefore exhibit great potential promise as a chemical dynamics tool , combining a trajectory - based description with exact quantum dynamics . however , _ all _ reactive systems exhibit interference between the incident and reflected ( non - reactive ) waves , thus causing numerical instability problems for conventional unipolar qtms . cpwm bipolar decompositions offer a natural means of alleviating this interference difficulty , by splitting the reactant region @xmath1 into incident @xmath36 and reflected @xmath37 components , neither of which exhibits interference on its own . moreover , this splitting can be extended through the interaction region over to the product region , by which point @xmath36 has transformed smoothly into the transmitted wave , and @xmath37 has damped to zero .    as discussed in sec . [ theory ] and the appendices , the cpwm approach borrows conceptually from semiclassical scattering methods . indeed , for the first bipolar decomposition considered ( b , sec . [ classicaltraj ] ) the bipolar trajectories are simply equal to the classical trajectories themselves , and the correspondence principle is satisfied in precisely the usual wkb limit , @xmath41 . three features , however , contribute to render the present approach fundamentally different from basic wkb theory : ( 1 ) time - dependent formulation ; ( 2 ) coupling between @xmath36 and @xmath37 ; ( 3 ) universal , local reflection and transmission formulae ( see also paper  ii ) . point ( 3 ) is what determines point ( 2 ) , i.e. if only local transmission were considered without reflection , then the coupling would vanish and the basic wkb solutions would result . the combination of ( 1 ) and ( 3 ) provides a local physical understanding related to the ray optics picture in electromagnetic theory , and also gives rise to useful flux relations and numerical algorithms . regarding the second bipolar decomposition considered , i.e. the f , constant velocity scheme , this was motivated by practical concerns , but also by an alternative ray optics description ( sec . [ constanttraj ] ) . this can be related to the semiclassical approach of frman and frman , and in that context , also satisfies a generalized kind of correspondence principle . note that neither set of evolution equations [ ] involves a quantum potential ; instead , all quantum effects manifest through @xmath7 coupling . in both cases , the trajectories themselves are not `` context - sensitive,''@xcite in that they may be computed independently of the @xmath7 evolution . moreover , no spatial differentiation of the wavefunction is required , although there may be situations where explicit calculation of one spatial derivative is numerically advantageous ( sec . [ eckart ] ) . several other numerical modifications have also been introduced for convenience ( sec . [ algorithmic ] ) , resulting in a shift from an exact time - dependent  interpretation of the dynamics [ wherein the exact stationary state is `` revealed '' over time ( paper  ii ) ] to what may be regarded as more of a relaxation approach . be that as it may , the resulting algorithms offer a remarkably simple , efficient , and accurate means of performing reactive scattering calculations of all kinds in 1d ( sec .  [ results ] ) . indeed , the time - steps required for the benchmark molecule - like systems considered here are orders of magnitude larger than for typical fixed - grid calculations performed at a comparable level of accuracy . moreover , the converged bipolar solution density plots render the determination of global reflection and transmission probabilities , as well as probabilities for reaction intermediate states , quite straightforward .    in future publications we will continue to generalize the methodology described here and in paper  ii , for the type of multidimensional time - dependent wavepacket dynamics relevant to real chemical physics applications . as additional motivation for the present work , we now sketch how this might be achieved . first , it is necessary to generalize the stationary state results of this paper and paper  ii for arbitrary time - evolving wavepackets . this is done initially for the discontinuous step potential , and then generalized for arbitrary continuous potentials in a manner similar to appendix a. in fact , much of the groundwork is already laid , in that the time - dependent framework has already been introduced . the generalization to multidimensional systems is less straightforward but can certainly be achieved ( such calculations have already been performed , as will be reported in a future publication ) . conceptually at least , many direct chemical reactions can be described using a single scattering reaction coordinate , plus additional `` bound '' coordinates . it is natural to consider applying the current cpwm bifurcation to the former , and the paper  i bifurcation to each of the latter . however , the total number of wavefunction components would then be @xmath157 where @xmath158 is the number of degrees of freedom . on the other hand , for most time - dependent wavepacket calculations , node formation in @xmath1 is associated primarily with the reaction coordinate itself , due to wavepacket reflection off of the reaction profile barrier . thus , a natural approach would be to bifurcate _ only _ along the reaction coordinate . only two component wavefunctions result , regardless of @xmath158 . it remains to be seen whether such a procedure will render qtm calculations possible for actual molecular systems . nevertheless , it seems very likely that some such bipolar or multipolar approach will go a long way towards ameliorating the infamous node problem , which has thus far severely limited the effectiveness of qtms in the molecular arena . this work was supported by awards from the welch foundation ( d-1523 ) and research corporation . the authors would like to acknowledge robert e. wyatt and eric r. bittner for many stimulating discussions . david j. tannor and john c. tully are also acknowledged . jason mcafee is also acknowledged for his aid in converting this manuscript to an electronic format suitable for the arxiv preprint server .","summary":"( 2005 ) ] , whose generalization for continuous potentials is given here .","abstract":"in a previous paper [ j. chem . phys . * 121 * 4501 ( 2004 ) ] a unique bipolar decomposition , was presented for stationary bound states of the one - dimensional  equation , such that the components and approach their semiclassical wkb analogs in the large action limit . the corresponding bipolar quantum trajectories , as defined in the usual bohmian mechanical formulation , are classical - like and well - behaved , even when has many nodes , or is wildly oscillatory . a modification for discontinuous potential stationary stattering states was presented in a second paper [ j. chem . phys . * ! ! ! * ! ! ! ! ( 2005 ) ] , whose generalization for continuous potentials is given here . the result is an _ exact _ quantum scattering methodology using _ classical _ trajectories . for additional convenience in handling the tunneling case , a constant velocity trajectory version is also developed ."}
{"article_id":"0808.2145","section_id":"i","document":"the last two decades , an ever - increasing amount of research have been dedicated to understanding the electronic structure of so - called quantum dots@xcite : semiconductor structures confining from a few to several thousands electrons in spatial regions on the nanometre scale . in such calculations , one typically seeks a few of the lowest eigenenergies @xmath0 of the system hamiltonian @xmath1 and their corresponding eigenvectors @xmath2 , i.e. , @xmath3 one of the most popular methods is the ( full ) configuration interaction method ( ci ) , where the many - body wave function is expanded in a basis of eigenfunctions of the harmonic oscillator ( ho ) , and then necessarily truncated to give an approximation . in fact , the so - called curse of dimensionality implies that the number of degrees of freedom available per particle is severely limited . it is clear , that an understanding of the properties of such basis expansions is very important , as it is necessary for _ a priori _ error estimates of the calculations . unfortunately , this is a neglected topic in the physics literature .    in this article , we give a thorough analysis of the ( full ) configuration interaction ( ci ) method using ho expansions applied to parabolic quantum dots , and give practical convergence estimates . it generalizes and refines the findings of a recent study of one - dimensional systems,@xcite and is applicable to for example nuclear systems@xcite and quantum chemical calculations@xcite as well . we demonstrate the estimates with calculations in the @xmath4 dimensional case for @xmath5 electrons , paralleling computations in the literature@xcite . the main results are however somewhat discouraging . the expansion coefficients of typical eigenfunctions are shown to decay very slowly , limiting the accuracy of _ any _ practical method using ho basis functions . we therefore propose to use an effective two - body interaction to overcome , at least partially , the slow convergence rate . this is routinely used in nuclear physics@xcite where the inter - particle forces are of a completely different , and basically unknown , nature . for electronic systems , however , the interaction is well - known and simpler to analyze , but effective interactions of the present kind have not been applied , at least to the author s knowledge . the modified method is seen to have convergence rates of at least one order of magnitude higher than the original ci method . an important point here is that the complexity of the ci calculations is not altered , as no extra non - zero matrix elements are introduced . all one needs is a relatively simple one - time calculation to produce the effective interaction matrix elements . the ho eigenfunctions are popular for several reasons . many quantum systems , such as the quantum dot model considered here , are perturbed harmonic oscillators _ per se _ , so that the true eigenstates should be perturbations of the ho states . moreover , the ho has many beautiful properties , such as complete separability of the hamiltonian , invariance under orthogonal coordinate changes , and thus easily computed eigenfunctions , so that computing matrix elements of relevant operators becomes relatively simple . the ho eigenfunctions are defined on the _ whole _ of @xmath6 in which the particles live , so that truncation of the domain is unnecessary . indeed , this is one of the main problems with methods such as finite difference or finite element methods.@xcite on the other hand , the ho eigenfunctions are the _ only _ basis functions with all these properties . the article is organized as follows . in sec . [ sec : model ] we discuss the harmonic oscillator and the the parabolic quantum dot model , including exact solutions for the @xmath7 case . in sec . [ sec : series - new ] , we give results for the approximation properties of the hermite functions in @xmath8 dimensions , and thus also of many - body ho eigenfunctions . by approximation properties , we mean estimates on the error @xmath9 , where @xmath10 is any wave function and @xmath11 projects onto a finite subspace of ho eigenfunctions , i.e. , the model space . here , @xmath12 is in fact the best approximation in the norm . the estimates will depend on analytic properties of @xmath10 , i.e. , whether it is differentiable , and whether it falls of sufficiently fast at infinity . to our knowledge , these results are not previously published .    in sec . [ sec : ci ] , we discuss the full configuration interaction method , using the results obtained in sec . [ sec : series - new ] to obtain convergence estimates of the method as function of the model space size . we also briefly discuss the effective interaction utilized in the numerical calculations , which are presented in sec . [ sec : numeric ] . we conclude with a discussion of the results , its consequences , and an outlook on further directions of research in sec . [ sec : conclusion ] . we have also included an appendix with proofs of the formal propositions in sec . [ sec : series - new ] .","summary":"we give a thorough analysis of the convergence properties of the configuration - interaction method as applied to parabolic quantum dots among other systems , including _ a priori _ error estimates . we demonstrate a significant increase in accuracy of the configuration interaction method .","abstract":"we give a thorough analysis of the convergence properties of the configuration - interaction method as applied to parabolic quantum dots among other systems , including _ a priori _ error estimates . the method converges slowly in general , and in order to overcome this , we propose to use an effective two - body interaction well - known from nuclear physics . through numerical experiments we demonstrate a significant increase in accuracy of the configuration interaction method ."}
{"article_id":"0808.2145","section_id":"r","document":"[ sec : numeric ]      we now present numerical results using the full configuration - interaction method for @xmath7@xmath341 electrons in @xmath4 dimensions . we will use both the `` bare '' hamiltonian @xmath342 and the effective hamiltonian ( [ eq : eff - hamiltonian ] ) .    since the hamiltonian commutes with angular momentum @xmath343 , the latter taking on eigenvalues @xmath344 , the hamiltonian matrix is block diagonal . ( recall , that the fock - darwin orbitals @xmath72 are eigenstates of @xmath343 with eigenvalue @xmath13 , so each slater determinant has eigenvalue @xmath345 . ) moreover , the calculations are done in a basis of joint eigenfunctions for total electron spin @xmath346 and its projection @xmath229 , as opposed to the slater determinant basis used for convergence analysis . such basis functions are simply linear combinations of slater determinants within the same shell , and further reduce the dimensionality of the hamiltonian matrix.@xcite the eigenfunctions of @xmath1 are thus labeled with the total spin @xmath347 for even @xmath51 and @xmath348 for odd @xmath51 , as well as the total angular momentum @xmath349 . ( @xmath350 produce the same eigenvalues as @xmath351 , by symmetry . ) we thus split @xmath290 ( or @xmath291 ) into invariant subspaces @xmath352 ( @xmath353 ) and perform computations solely within these . the calculations were carried out with a code similar to that described by rontani _ _ in ref . table [ tab : code - comparison ] shows comparisons of the present code with that of table iv of ref .   for various parameters using the model space @xmath353 . table [ tab : code - comparison ] also shows the case @xmath116 , @xmath7 , @xmath354 , and @xmath86 , whose exact lowest eigenvalue is @xmath355 , cf . [ sec : bad - example ] . we note that there are some discrepancies between the results in the last digits of the results of ref .  . the spaces @xmath291 were identical in the two approaches , i.e. , the number of basis functions and the number of non - zero matrix elements produced are cross - checked and identical . we have checked that the code also reproduces the results of refs .  , using the @xmath352 spaces . our code is described in detail elsewhere@xcite where it is also demonstrated that it reproduces the eigenvalues of an analytically solvable @xmath51-particle system@xcite to machine precision . c|ccc|dd|dd|dd & & & & & & + @xmath51 & @xmath82 & @xmath351 & @xmath356 & & & & & & + 2 & 1 & 0 & 0 & 3.013626 & & 3.011020 & & 3.009236 & + & 2 & 0 & 0 & 3.733598 & 3.7338 & 3.731057 & 3.7312 & 3.729324 & 3.7295 + & & 1 & 2 & 4.143592 & 4.1437 & 4.142946 & 4.1431 & 4.142581 & 4.1427 + 3 & 2 & 1 & 1 & 8.175035 & 8.1755 & 8.169913 & & 8.166708 & 8.1671 + & 4 & 1 & 1 & 11.04480 & 11.046 & 11.04338 & & 11.04254 & 11.043 + & & 0 & 3 & 11.05428 & 11.055 & 11.05325 & & 11.05262 & 11.053 + 4 & 6 & 0 & 0 & 23.68944 & 23.691 & 23.65559 & & 23.64832 & 23.650 + & & 2 & 4 & 23.86769 & 23.870 & 23.80796 & & 23.80373 & 23.805 + 5 & 2 & 0 & 5 & 21.15093 & 21.15 & 21.13414 & 21.13 & 21.12992 & 21.13 + & 4 & 0 & 5 & 29.43528 & 29.44 & 29.30898 & 29.31 & 29.30251 & 29.30 +      for the remainder , we only use the energy cut spaces @xmath352 . figure [ fig : raw - plots ] shows the development of the lowest eigenvalue @xmath357 for @xmath358 , @xmath359 and @xmath86 as function of the shell truncation parameter @xmath50 , using both hamiltonians @xmath1 and @xmath320 . apparently , the effective interaction eigenvalues provide estimates for the ground state eigenvalues that are better than the bare interaction eigenvalues . this effect is attenuated with higher @xmath51 , due to the fact that the two - electron effective coulomb interaction does not take into account three- and many - body effects which become substantial for higher @xmath51 . eigenvalues for @xmath358 , @xmath86 , @xmath360 as function of @xmath50 for @xmath1 ( solid ) and @xmath320 ( dashed ) . @xmath361 and @xmath362 are represented by squares , circles and stars , resp . ] we take the @xmath320-eigenvalues as `` exact '' and graph the relative error in @xmath363 as function of @xmath50 on a logarithmic scale in fig . [ fig : loglog - error ] , in anticipation of the relation @xmath364 the graphs show straight lines for large @xmath50 , while for small @xmath50 there is a transient region of non - straight lines . for @xmath365 , however , @xmath84 is too large a value to reach the linear regime for the range of @xmath50 available , so in this case we chose to plot the corresponding error for the very small value @xmath366 , showing clear straight lines in the error . the slopes are more or less independent of @xmath82 , as observed in different calculations .    in fig . [ fig : loglog - error - eff ] we show the corresponding graphs when using the effective hamiltonian @xmath320 . we estimate the relative error as before , leading to artifacts for the largest values of @xmath50 due to the fact that there is a finite error in the best estimates for the eigenvalues . however , in all cases there are clear , linear regions , in which we estimate the slope @xmath367 . in all cases , the slope can be seen to decrease by at least @xmath368 compared to fig . [ fig : loglog - error ] , indicating that the effective interaction indeed accelerates the ci convergence by at least an order of magnitude . we also observe , that the relative errors are improved by an order of magnitude or more for the lowest values of @xmath50 shown , indicating the gain in accuracy when using small model spaces with the effective interaction . notice , that for symmetry reasons only even ( odd ) @xmath50 for even ( odd ) @xmath351 yields increases in basis size @xmath369 $ ] , so only these values are included in the plots .    to overcome the limitations of the two - body effective interaction for higher @xmath51 , an effective three - body interaction could be considered , and is hotly debated in the nuclear physics community . ( in nuclear physics , there are also more complicated three - body effective forces that need to be included.@xcite ) however , this will lead to a huge increase in memory consumption due to extra nonzero matrix elements . at the moment , there are no methods available that can generate the exact three - body effective interaction with sufficient precision . we stress , that the relative error decreases very slowly in general . it is a common misconception , that if a number of digits of @xmath363 is unchanged between @xmath50 and @xmath370 , then these digits have converged . this is not the case , as is easily seen from fig . [ fig : loglog - error ] . take for instance @xmath358 , @xmath354 and @xmath86 , and @xmath84 . for @xmath371 and @xmath372 we have @xmath373 and @xmath374 , respectively , which would give a relative error estimate of @xmath375 , while the correct relative error is @xmath376 . the slopes in fig . [ fig : loglog - error ] vary greatly , showing that the eigenfunctions indeed have varying global smoothness , as predicted in sec . [ sec : analytic - props ] . for @xmath377 , for example , @xmath378 , indicating that @xmath379 . it seems , that higher @xmath380 gives higher @xmath145 , as a rule of thumb . intuitively , this is because the pauli principle forces the wave function to be zero at coalesce points , thereby generating smoothness .","summary":"the method converges slowly in general , and in order to overcome this , we propose to use an effective two - body interaction well - known from nuclear physics . through numerical experiments","abstract":"we give a thorough analysis of the convergence properties of the configuration - interaction method as applied to parabolic quantum dots among other systems , including _ a priori _ error estimates . the method converges slowly in general , and in order to overcome this , we propose to use an effective two - body interaction well - known from nuclear physics . through numerical experiments we demonstrate a significant increase in accuracy of the configuration interaction method ."}
{"article_id":"0905.4803","section_id":"i","document":"spacetime was invented using classical concepts , such as positions of bodies and ticks of clocks . although classical spacetime serves remarkably well as a backdrop for precise description of microscopic quantum systems , such as atoms and even particle collisions , the concept of a spacetime event is not easily interpreted in the context of quantum mechanics . for one thing , the notion of a pointlike event does not take account of the particle / wave duality of quantum mechanics . for another , events themselves are not , even in principle , observable quantities , but are defined only by interactions of mass - energy .    a quantum model for measuring the invariant interval between spacelike events using light quanta and clocks can be constructed in a spacetime with one spacelike dimension@xcite . however , as described below , if there is a minimum fundamental wavelength , event positions defined by wave phases in two spacelike dimensions for example , reflections off a beamsplitter surface in a michelson interferometer are intrinsically uncertain , by the geometric mean of the minimum wavelength and the event separation . this paper describes how a new fundamental nonlocal quantum uncertainty of spacetime position associated with a minimum wavelength at the planck scale could be studied with experiments that make precise position measurements in two directions across macroscopic distances . it is well known that spacetime must adopt some new quantum character below the planck length , @xmath1 meters , or planck time , @xmath2 seconds . no spatially localized quantum particle states can exist in classical spacetime above the planck energy , because of gravity . a particle spatially localized within a planck volume lies within the schwarzschild radius for its energy , behind an event horizon where it can never be seen . the interpretation of spatial wavefunctions must be modified in some way at the planck scale , an effect that may appear as a minimum fundamental wavelength or maximum frequency@xcite . the planck frontier in field theory corresponds to a uv cutoff in 3 + 1d spacetime . however , a consistent theory of mass - energy and spacetime can not be achieved simply by imposing a filter on field modes at the planck scale in some frame . a planck length ruler in some frame will , in some other frame boosted along its length , appear shorter , violating the minimum - length restriction ; or well - separated particles in one frame will in some other frame be closer together and form a black hole . the reconciliation must be achieved by a new unified theory that includes new , unfamiliar transformation properties . moreover , it is recognized that a frequency cutoff entails a violation of lorentz covariance@xcite . the new effect discussed here violates lorentz invariance , but in a new way that would not have appeared in current experimental tests . remarkably precise insights about unification at the planck scale come from the theory of black hole evaporation , whereby a black hole converts to quantum particles in flat spacetime . in particular the entropy of a black hole , identified with the logarithm of the total number of degrees of freedom of radiated particles , is one quarter of the area of its event horizon in planck units . this idea has led to the conjecture@xcite that all of physics may be `` holographic '' , encoded in some way on two dimensional null surfaces or light sheets with the same information content per area as the null surface representing a black hole event horizon . however , there has been no experimental test of this conjecture . although there are candidates ( e.g. , @xcite ) for holographic theories of everything that incorporate a minimum length at the planck scale , it is not generally agreed how to apply them to macroscopic experiments operating in nearly - flat , nearly - classical spacetime .    in this paper we investigate the experimental consequences of a particular hypothesis about how spacetime emerges in a holographic world . relationships between observables at different locations obey a `` planck information flux '' limit : correlations between observables at two events are limited by the capacity of a planck wavelength null carrier wave between them . transverse positions then have an uncertainty described by a simple effective theory based on wave optics  @xcite . a new uncertainty arises because the wavefunction encoding the transverse component of position spreads by diffraction . just as in diffraction of classical waves , the resulting transverse position uncertainty of a system has a standard deviation of probability , @xmath3 after longitudinal propagation over a length @xmath4 , if this transverse information is encoded with minimum wavelength @xmath5 . a normalization of the minimum wavelength @xmath6 is derived from the black hole entropy - area relationship @xmath7 .    in this interpretation , families of paths that connect events and relationships of bodies in classical spacetime have roughly the same status as rays in optics : they are an approximate description of a configuration of a physical system of waves . rays have a fundamental indeterminacy imposed by diffraction limits ; the actual physical system , consisting of wave energy ( or in this application , position probability ) , is not sharply confined into rays . a time - averaged classical metric likewise does not capture all of the physical wavelike qualities . just as in wave optics , diffractive blurring and fluctuations of transverse correlations in such a system can occur on observable scales much larger than the wavelength ( in this application , the planck length ) , given a macroscopic propagation distance . the potentially observable new phenomenon associated with these ideas is a universal `` holographic noise '' : random fluctuations in the relative transverse spacetime positions of bodies widely separated in spacetime , as measured by the phase of null fields@xcite . the spectral density of this noise is given just by the planck time , with no parameters aside from numerical factors that depend on a particular experimental setup . the paraxial - wave effective theory presented here expresses these ideas quantitatively , and makes statistical predictions for the effective positions of optical elements and for the time series of signals in michelson interferometers . the predicted amplitude in equivalent strain units is smaller than the previous published estimate by a factor of @xmath0 . the remaining uncertainties in precise normalization are mainly connected with interpreting the connection of the fundamental wavelength of this effective theory with black hole entropy .    in principle , holographic noise has a precisely characterized frequency spectrum and an absolutely calibrated normalization from black hole physics , with no parameters . it also exhibits a new , distinctive spatial shear character , unlike metric perturbations that correspond to strain motions , like gravitational waves . finally , signals in two nearby interferometers with no physical connection are shown to be highly correlated . these distinctive signatures can be used to design an apparatus to provide convincing evidence for or against the effect , and to distinguish it from other physical sources of noise . estimates are given here for the spectral amplitude of correlated displacement as a function of separation of two interferometers . this new effect , although quantum - mechanical , does not correspond to quantum fluctuations of gravitons or gravitational radiation , metric fluctuations derived from noncommutative geometry , or indeed any perturbation of the metric . it is therefore distinct from previously conjectured fluctuations of a quantum - gravitational origin ( e.g. , @xcite ) , based on various hypotheses about quantum perturbations of a metric . holographic noise on macroscopic scales can be described as a new kind of coherent movement of mass - energy relative to an unperturbed classical metric a fluctuating departure from classical geodesic trajectories . the position of mass - energy , measured in the transverse direction relative to the separation between events , jitters randomly with time relative to nominal classical geodesics , in an observer - dependent way , on the planck diffraction scale . on the other hand , the equivalence principle still holds in a long time average sense , and with respect to different forms of energy . other current tests of lorentz invariance are not sensitive to this effect . for example , since the theory is built on null sheets , identical longitudinal propagation is predicted for all null particles and radiation , so no dispersion is predicted in arrival times of photons of different energies arriving from cosmological distances , consistent with current limits@xcite . the effect is suppressed for small length scales or long averaging times . on a subatomic scale of length and time @xmath8 , the holographic spreading over an averaging time @xmath9 is of order @xmath10 , below the range of current laboratory tests .","summary":"arguments based on general principles of quantum mechanics suggest that a minimum length or time associated with planck - scale unification may entail a new kind of observable uncertainty in the transverse position of macroscopically separated bodies . transverse positions vary randomly about classical geodesics in space and time by about the geometric mean of the planck scale and separation , on a timescale corresponding to their separation . the spectral amplitude of equivalent strain derived here is a factor of smaller than previously published estimates .","abstract":"arguments based on general principles of quantum mechanics suggest that a minimum length or time associated with planck - scale unification may entail a new kind of observable uncertainty in the transverse position of macroscopically separated bodies . transverse positions vary randomly about classical geodesics in space and time by about the geometric mean of the planck scale and separation , on a timescale corresponding to their separation . an effective theory based on a planck information flux limit , and normalized by the black hole entropy formula , is developed to predict measurable correlations , such as the statistical properties of noise in interferometer signals . a connection with holographic unification is illustrated by representing matrix theory position operators with a schrdinger wave equation , interpreted as a paraxial wave equation with a planck frequency carrier . solutions of this equation are used to derive formulas for the spectrum of beamsplitter position fluctuations and equivalent strain noise in a michelson interferometer , determined by the planck time , with no other parameters . the spectral amplitude of equivalent strain derived here is a factor of smaller than previously published estimates . signals in two nearly - collocated interferometers are predicted to be highly correlated , a feature that may provide convincing evidence for or against this interpretation of holography ."}
{"article_id":"cond-mat0105156","section_id":"i","document":"the influence of inhomogeneities and defects of different types on transmission properties of waveguides for both quantum and classical waves is a subject of long - term intensive research . most of theoretical studies have been restricted to flat surfaces . in practice , however , side boundaries of mesoscopic conductors are either inherently rough ( due to growth , fracture , etc . ) , or artificially patterned ( e.g. due to lithographic preparation ) . one way or the other , surface - corrugated conducting systems find widespread applications in technology and material science ( quantum conductors , optical fibers , etc . ) , and , hence , it is often necessary to know how the shape of the confining surface affects the charge or classical wave transport in different systems .    of peculiar interest for contemporary microelectronics , from both applied and theoretical viewpoints , are two - dimensional ( 2d ) conductors of mesoscopic size . nowadays there exists widely established opinion ( see , e.g. , refs .   and references therein ) that dynamic properties of pure - in - bulk quantum wires , in particular two - dimensional , are largely determined by scattering the electrons from randomly rough side boundaries of the conductor . this scattering mechanism is proven to be responsible for both relaxation processes in multi - mode conductors @xcite and for non - dissipative ( anderson ) localization of conduction electrons in narrow single - mode wires @xcite .    in studying the electron transport in 2d surface - corrugated systems two main problems are especially highlighted . one of them is relevant to adequate description of the electron scattering from statistically rough surfaces . the other , dynamic , problem is pertinent to proper consideration of the interference of multiply scattered quantum waves , which is essential for describing within the framework of a perturbation theory the effects resulting from non - dissipative localization of the electron states .    to resolve the first problem and make an adequate comparison with experimental data one needs a theory which relates transport properties of the conduction electrons to the shape of bounding surfaces of the conductor . since in random - inhomogeneous 2d wires fluctuations of both of the side boundaries can be considered as either mutually independent or correlative , subject to the preparation technology , it is important to trace the relation between the kinetic quantities and the statistics of boundary irregularities , as well as mutual correlation of the opposite boundaries .    in the previous paper @xcite we have studied the case of a single - mode 2d conductor with statistically identical rough side boundaries . the particular model considered in ref . @xcite of the wire with completely correlated boundaries ( ccb ) is equivalent to the deterministic waveguide system of constant width whose inhomogeneities consist in solely waveguide bends . it was shown that the electron dynamics in such conducting strips is governed by quite a different hamiltonian than that pertinent to the seemingly more general model of 2d conductor with one boundary which is rough and the other being ideally flat @xcite . a substantial distinction of the hamiltonians in ref . @xcite and ref . @xcite have resulted in qualitative functional distinction of the obtained scattering lengths . the results of refs . @xcite and @xcite have provided the grounds to propose that in those works the quantum wave scattering can be assumed to be associated with fundamentally different physical factors , namely with deviation of the boundaries from their `` ideal '' shape in ref . @xcite and fluctuation of their slopes in ref . @xcite . provided the supposition is true , when studying particle or classical wave transport in surface - corrugated waveguide systems one has to distinguish between two different non - interfering scattering mechanisms which we call by - height ( bh ) and by - slope ( bs ) scattering . however , it should be noted that quantum wave scattering was analyzed in refs . @xcite and @xcite for different waveguide geometries and with the use of substantially different methods . therefore , the conjecture stated in ref . @xcite about the relative significance of these scattering mechanisms needs to be additionally substantiated .    to avoid possible misunderstanding and support our idea of different scattering mechanisms pertaining to the imperfect boundaries of guiding systems , we examine the waveguide ( conductor ) geometry admitting of both bh and bs scattering simultaneously . we consider a 2d conducting strip with statistically symmetrical rough boundaries ( the abbreviation ssb will be used for such a strip , in contrast to the ccb strip considered in ref . @xcite ) , which is physically equivalent to the waveguide with a straight central line ( guiding axis ) and a randomly fluctuating width . it will be shown below that the suggested model of the waveguide corresponds qualitatively to a 2d wire with opposite side boundaries whose inter - correlation can be thought of as arbitrary . for the ssb model , as well as for the arbitrary 2d waveguide , the presence is typical of both bh and bs scattering mechanisms . it is noteworthy that these mechanisms compete with one another , depending on the roughness statistical parameters , even in the simplest case of boundary asperities being small in height and rather smooth . technically , specifying the scattering mechanisms is most straightforward by reducing the problem of the electron scattering from complicated boundaries of the conductor to the appropriate `` bulk '' problem specified by a complex hamiltonian but simple boundary conditions . analysis of the problem thus formulated can often be found much easier than of the problem with complicated boundary conditions . in some cases it can even be performed non - perturbatively . in this work , using such an approach , we managed to reasonably discriminate between bh and bs scattering mechanisms and analyze their competition in the electron - surface scattering . besides , solving the `` surface '' problem in `` bulk '' formulation enabled us to carefully trace such a fine _ spectral _ effect as the anderson localization of current carriers . note that the method for solving the problems of the by - surface scattering through reduction to the hamiltonian form is not quite original . it was employed , in particular , in refs . @xcite and @xcite where the coordinate transformation was used , which smooths out the rough surface to the flat one . in this paper , analogous reduction of a `` surface '' problem to the hamiltonian formulation is made by merely going over to the _ local mode representation_. this approach ensures the optimal choice of trial quantum states which serve as a basis for the perturbation theory . in our view , it is essential that the mode states _ a priori _ contain the information on lateral confinement of the system under consideration and , therefore , are more adjusted to perturbative treatment of transport problems in waveguide - like systems than the widely used isotropic plane - wave basis .","summary":"transport properties of narrow two - dimensional conducting wires in which the electron scattering is caused by side edges roughness have been studied . the method for calculating dynamic characteristics of such conductors fundamentally different _ by - height _ and _ by - slope _ scattering mechanisms associated with edge roughness are discriminated . the results for single - mode systems , previously obtained by conventional methods , are proven to correspond to the former mechanism only . yet the commonly ignored by - slope scattering is more likely dominant . the transmittance of ultra - quantum wires is calculated over all range of scattering parameters , from ballistic to localized transport of quasi - particles .","abstract":"transport properties of narrow two - dimensional conducting wires in which the electron scattering is caused by side edges roughness have been studied . the method for calculating dynamic characteristics of such conductors is proposed which is based on the two - scale representation of the mode wave functions at weak scattering . with this method , fundamentally different _ by - height _ and _ by - slope _ scattering mechanisms associated with edge roughness are discriminated . the results for single - mode systems , previously obtained by conventional methods , are proven to correspond to the former mechanism only . yet the commonly ignored by - slope scattering is more likely dominant . the electron extinction lengths relevant to this scattering differ substantially in functional structure from those pertinent to the by - height scattering . the transmittance of ultra - quantum wires is calculated over all range of scattering parameters , from ballistic to localized transport of quasi - particles . the obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter - correlation of the boundaries defects ."}
{"article_id":"cond-mat0105156","section_id":"c","document":"with general formula ( [ g - moments ] ) , write down the expressions for average resistance @xmath201 and average conductance @xmath202 . at @xmath203 the integrals in eq . ( [ g - moments ] ) can be calculated exactly , so the average resistance is equal to @xmath204 \\ . \\label{sopr}\\ ] ] at @xmath63 the integration can be performed asymptotically in the parameter @xmath205 , giving rise to the following expression : @xmath206 2^{-1}\\pi^{5/2}\\left(l / l_b\\right)^{-3/2 } \\exp\\left(-l/ 4l_b\\right ) \\qquad & \\mbox { if } \\qquad l / l_b\\gg 1 \\ . \\end{array } \\right . \\label{cond_assymp}\\ ] ] the results ( [ ln_g - av])([cond_assymp ] ) are completely in line with the concepts of the localization theory for one - dimensional disordered systems . obvious indications of the ballistic electron transport in short wires can be easily seen , @xmath207 at @xmath208 . also , no signs of diffusive motion of the electrons in long wires are present in any result . and conversely , in long wires , @xmath209 , the resistance ( [ sopr ] ) displays an exponential increase with a growing strip length , and the asymptotic ( [ cond_assymp ] ) shows an exponential decrease of the average conductance as the length @xmath1 exceeds the value of @xmath210 . that behaviour is characteristic for conduction electrons undergoing anderson localization . the inverse of the quadruple backscattering extinction length is equal to the lyapunov exponent for the electron wave function in the case of dimension unity@xcite , so that the quantity @xmath211 is conventionally called the ( one - dimensional ) localization length .    both of the formulas ( [ g - moments ] ) and ( [ ln_g - av ] ) , and , hence , ( [ sopr ] ) and ( [ cond_assymp ] ) , are universal in that they are applicable for any one - dimensional degenerate system subject to weak _ static _ disorder . only the particular dependence of scattering lengths @xmath212 and , consequently , the localization length @xmath213 is determined by the physical nature of disorder . in this paper , we have found that if the boundary roughness prove to be just the main cause of the disorder in a 2d single - mode conducting strip , the interpretation of scattering mechanism may be substantially different , depending on the interrelation between by - slope scattering lengths ( [ slope_scatt ] ) and by - height lengths ( [ l_fhl_bh ] ) . to make the correct comparison of the lengths the roughness statistics needs to be specified . we will make the comparison for two characteristic models consistent with the demand for analyticity of the random functions @xmath4 descriptive of boundaries of the conductor . specifically , we examine the case of asperities subject to gaussian ( exponential ) correlation statistics , @xmath214 , an those described by the lorentz ( power - type ) correlation function @xmath215^{-1}$ ] . for the gaussian roughness , from ( [ l_b(s ) ] ) and ( [ l_bh ] ) the estimates can be obtained    [ lbgauss ] @xmath216 \\exp\\left(-2k_1 ^ 2r_c^2\\right ) & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ , \\end{array }   \\right . \\label{lbhgauss}\\ ] ] @xmath217 ( k_1r_c)^4\\exp\\left(-k_1 ^ 2r_c^2\\right ) & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ . \\end{array }   \\right . \\qquad\\quad \\label{lbsgauss}\\ ] ]    if the hight correlation is lorentzian , the estimates change to the following ,    [ lblorentz ] @xmath218 \\exp\\left(-2k_1r_c\\right ) & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ , \\end{array }   \\right . \\label{lbhlorentz}\\ ] ] @xmath219 ( k_1r_c)^5\\exp\\left(-2k_1r_c\\right ) & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ . \\end{array }   \\right . \\qquad\\quad \\label{lbslorentz}\\ ] ]    based on estimates ( [ lbgauss ] ) and ( [ lblorentz ] ) , the relative intensity of bs and bh scattering can be estimated as follows ,    [ lh / lb ] @xmath220 ( r_c / d)^4\\exp\\left(k_1 ^ 2r_c^2\\right ) & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ , \\end{array }   \\right . \\qquad\\quad \\label{lh / lbgauss}\\ ] ] @xmath221 ( r_c / d)^5 & \\qquad\\rm{if}\\quad & r_c / d\\gg 1 \\ ( \\rm{i.e.}\\ k_1r_c\\gg 1 ) \\ . \\end{array }   \\right . \\label{lh / lblorentz}\\ ] ]    from these estimations it can be seen that in all of the limiting cases considered here the characteristic ratio @xmath222 is determined by the product of small rayleigh parameter @xmath223 and some scale parameter , though individual for different roughness correlation , which depends on the relation between the roughness correlation length and de - broglie wave length of the electrons . in the case of small - scale asperities , when @xmath224 ( or , which is the same , @xmath225 ) , regardless of the correlation model the relative intensity of bh and bs scattering is characterized by the parameter @xmath226 which varies over a rather wide range . this is because of bh and bs scattering being associated with independent physical origins . whereas scattering from the potential @xmath65 is governed by the height of the boundary roughness and thus is estimated mostly in terms of the parameter @xmath227 , eqs . ( [ lbhgauss ] ) and ( [ lbhlorentz ] ) , the bs scattering is mostly determined by the slope of the asperities , i.e. by gradients @xmath228 , and is , consequently , governed by the parameter @xmath229 , eqs . ( [ lbsgauss ] ) and ( [ lbslorentz ] ) .    it would be tiresome to discuss here in detail the interrelation between bh and bs scattering mechanisms assuming the asperities to be large - scale , when the parameter @xmath230 ( i.e. @xmath231 ) , since in this case the the result depends largely on the correlation model . we leave this particular analysis to an interested reader . it is noteworthy that in the event when the `` slope '' mechanism dominates the `` height '' mechanism , the `` surface '' scattering rate is proportional to the forth power of the rms height @xmath14 rather than to @xmath232 , which is customary in the diffraction theory@xcite . this fact must be taken into account when analyzing experiments aimed at reproducing the surface shape using the data on quantum , as well as classical , wave scattering in rough - bounded waveguide systems . apart from the identification of dominant scattering mechanism , specifying scattering lengths ( [ lbgauss ] ) and ( [ lblorentz ] ) for different statistical models of boundary roughness also allows for the criteria of validity of the obtained results in terms of essential physical parameters of the disordered systems . along with the presumption of smallness and smoothness of boundary asperities ( see eqs . ( [ small_height ] ) and ( [ small_slope ] ) ) the criteria are dictated by ( [ weak - scatt ] ) of weak scattering . in specifying those criteria , the smallest of the extinction lengths @xmath233 should be taken to substitute the length @xmath97 in ( [ weak - scatt ] ) since the inequality always holds true @xmath234 .    in conclusion , we make some remarks concerning the methodological side of the problem of wave scattering from rough waveguide surfaces . as far as we know , until the present time there has not been made any reasonable distinction between bh and bs scattering in such systems . only the existence in general of different competing mechanisms responsible for wave scattering from rough surfaces was indicated in ref . @xcite on the basis of the experimental results . accordingly , the relative function of these scattering mechanisms in dynamic processes in waveguide - like systems was not properly analyzed . meanwhile , in the course of this work we have made certain that application of linearized ( impedance - type ) boundary conditions to a single - mode waveguide is equivalent to retaining in eq . ( [ g11_main ] ) the approximate potential ( [ vh_if ] ) instead of its exact value ( [ vh ] ) , and also disregarding all `` slope '' potentials . however , omitting the latter potentials implies the neglect of bs scattering mechanism , that is proven to be not always justifiable . alternative small - slope approximation of refs . @xcite , being guided by a solely slope parameter of the rough surface , does not allow one to separate bh and bs scattering mechanisms as well .    in this work , the method has been suggested within the framework of which both of the above - mentioned scattering mechanisms appear quite naturally , being associated with different terms of the hamiltonian . we have demonstrated that at least in a single - mode waveguide the scattering caused even by mildly sloping boundary asperities can be attributed to either `` height '' or `` slope '' scattering mechanism , depending on the statistical properties of the roughness . the competition between these mechanisms is governed by physically different parameters . it is noteworthy that taking into account the bs mechanism is particularly essential if boundary asperities are classified as being large - scale . acknowledges support from conacyt .","summary":"the obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter - correlation of the boundaries defects .","abstract":"transport properties of narrow two - dimensional conducting wires in which the electron scattering is caused by side edges roughness have been studied . the method for calculating dynamic characteristics of such conductors is proposed which is based on the two - scale representation of the mode wave functions at weak scattering . with this method , fundamentally different _ by - height _ and _ by - slope _ scattering mechanisms associated with edge roughness are discriminated . the results for single - mode systems , previously obtained by conventional methods , are proven to correspond to the former mechanism only . yet the commonly ignored by - slope scattering is more likely dominant . the electron extinction lengths relevant to this scattering differ substantially in functional structure from those pertinent to the by - height scattering . the transmittance of ultra - quantum wires is calculated over all range of scattering parameters , from ballistic to localized transport of quasi - particles . the obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter - correlation of the boundaries defects ."}
{"article_id":"astro-ph0305510","section_id":"i","document":"thanks to the outstanding angular resolution of the x - ray telescopes aboard the _ chandra x - ray observatory _ , we are able to study the structure of pulsar - wind nebulae ( pwne ) , formed by relativistic outflows from pulsar magnetospheres . particularly detailed _ chandra _ images have been obtained for pwne around the crab pulsar ( mori et al . 2002 ; hester et al . 2002 ) , vela pulsar ( helfand , gotthelf , & halpern 2001 ; pavlov et al . 2001a ) , and psr b150958 ( gaensler et al . each of these images shows an approximately axially - symmetric pwn morphology , with an extended structure stretched along the symmetry axis . this suggests that such structures , usually called _ jets _ , are common to at least young pulsars . most likely , these jets are associated with collimated outflows of relativistic particles along the pulsar s rotation axes . investigations of pulsar jets allow one to understand the origin and properties of pulsar winds and their interaction with the ambient medium . moreover , since jets have been observed in many astrophysical objects ( e.g. , agns , galactic microquasars ) , studying pulsar jets may shed light on the mechanism of jet formation in these objects as well .    due to its proximity ( @xmath17 pc , from the annual parallax of the vela pulsar  caraveo et al .  2001 ; dodson et al . 2003a ) , the vela pwn is particularly well suited for studying the pulsar outflows . this pwn was discovered with _ ( harnden et al .  1985 ) and studied extensively with _ rosat _ and _ asca _ ( markwardt & gelman 1998 , and references therein ) . the _ einstein _ and _ rosat _ observations with the high resolution imagers ( hris ) have established the overall kidney - bean shape of the vela pwn , with a symmetry axis approximately co - aligned with the pulsar s proper motion . the first observations of the vela pwn with _ ( pavlov et al .  2000 ; helfand et al . 2001 ) have shown a detailed structure of the nebula , including inner and outer arcs , northwest and southeast jets , and bright knots in the southeast part of the pwn . furthermore , pavlov et al .  ( 2001a ) found that the nebula elements were variable in position , brightness , and , perhaps , spectrum . based on two observations with the _ chandra _ s advanced ccd imaging spectrometer ( acis ) , pavlov et al . ( 2001a ) noticed a long , curved extension of the northwest jet in approximately the same direction , well beyond the apparent termination point of the bright `` inner jet '' at its intersection with the outer arc . this dim `` outer jet '' ( dubbed `` filament '' in that paper ) had a brighter `` blob '' close to the jet s end , which showed particularly strong displacement between the two observations taken 7 months apart . to understand the nature of the variability of the vela pwn , we carried out a series of eight monitoring observations with the _ chandra _ acis . these observations have confirmed the dynamical structure of the pwn , with most dramatic changes occurring in the outer jet . moreover , we were able to detect an `` outer counter - jet '' , a much dimmer extension of the southeast ( counter-)jet , which is clearly seen only in the summed image , together with highly asymmetric diffuse emission . in the present paper , we concentrate mainly on the highly variable outer jet , which has been detected in ten acis observations and three observations with the high resolution camera ( hrc ) , deferring a detailed analysis of the other pwn elements to a future work . we describe the observations , their analyses , and observational results in  2 , and discuss possible interpretations in  3 . the summary of our results and concluding remarks are presented in  4 .","summary":"_ observations spread over years we found that this outer jet shows particularly strong variability , changing its shape and brightness .","abstract":"observations of the vela pulsar - wind nebula ( pwn ) with the _ chandra x - ray observatory _ have revealed a complex , variable pwn structure , including inner and outer arcs , a jet in the direction of the pulsar s proper motion , and a counter - jet in the opposite direction , embedded in diffuse nebular emission . the jet consists of a bright ,-long inner jet , between the pulsar and the outer arc , and a dim , curved outer jet that extends up to in approximately the same direction . from the analysis of thirteen _ chandra _ observations spread over years we found that this outer jet shows particularly strong variability , changing its shape and brightness . we observed bright blobs in the outer jet moving away from the pulsar with apparent speeds ( 0.3 and fading on time - scales of days to weeks . if the blobs are carried away by a flow along the jet , the observed variations suggest mildly relativistic flow velocities , about ( 0.3 . the spectrum of the outer jet fits a power - law model with a photon index . for a distance of 300 pc , the apparent average luminosity of the outer jet in the 18 kev band is about erg s , compared to from the whole pwn within from the pulsar . the x - ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons / positrons . this interpretation allows one to estimate the magnetic field ,  g , maximum energy of x - ray emitting electrons , ev , and energy injection rate , , for the outer jet . in the summed pwn image , we see a faint , strongly bent , extension of the outer jet . this bending could be caused by combined action of a wind within the supernova remnant , with a velocity of a few km s , along with the ram pressure due to the pulsar s proper motion . the more extreme bends closer to the pulsar , as well as the apparent side motions of the outer jet , can be associated with kink instabilities of a magnetically confined , pinched jet flow . another feature found in the summed image is a dim ,-long outer counter - jet , which also shows a power - law spectrum with.5 . southwest of the jet / counter - jet ( i.e. , approximately perpendicular to the direction of pulsar s proper motion ) , an extended region of diffuse emission is seen . relativistic particles responsible for this radiation are apparently supplied by the outer jet ."}
{"article_id":"astro-ph0305510","section_id":"c","document":"the detected variability of the outer jet is the most vivid demonstration of the dynamical behavior of the vela pwn . the observed changes of the overall shape of the outer jet over a time scale of weeks suggest apparent speeds up to ( 0.30.7)@xmath82 , which is comparable to the apparent speeds of the blobs moving along the outer jet away from the pulsar . the spectra of the outer jet , as well as those of the other pwn elements , fit well with a power - law model , indicating that this is radiation from ultrarelativistic particles . these observations allow one to assume that the outer jet is associated with a polar outflow of relativistic particles from the pulsar s magnetosphere . possible implications of our observational results are discussed below . the orientation of the jets is the most important item for explaining the observed dynamical behavior , evaluating the velocities , and calculating the energetics of these outflows . immediately after the first _ observations of the vela pwn , it was suggested that the bright ( inner ) jet and counter - jet are co - aligned with the rotational axis of the pulsar and , presumably , with the direction of pulsar s velocity ( pavlov et al .  2000 ; helfand et al . 2001 ) . as we have seen from figures 3 and 4 , the projection of the outer jet on the sky plane may strongly deviate from the ( straight ) extension of the projection of the inner jet / counter - jet . however , the outer jet projection was close to that line during the period of 2001 november 25 through 2002 january 13 , when the apparent velocities of the bright blobs were measured . assuming , by analogy with the jets in agns and galactic microquasars , that the apparent motion of blobs is associated with motion of matter along an approximately straight line ( e.g. , the three - dimensional velocities of the blobs coincide with the bulk flow velocity ) , one can constrain the true speed , @xmath83 , and the angle @xmath84 between the line of sight and the direction of motion . the apparent speed , @xmath85 , is related to the true speed by the equation @xmath86 . figure 10 shows the dependence @xmath87 for typical @xmath88 inferred from the observed motions of the blobs . for @xmath89 , the blobs can be approaching ( @xmath90 ) as well as receding ( @xmath91 ) . the range of minimum values of @xmath92 is @xmath93 ( at @xmath94 ) , while the range of maximum allowed @xmath84 ( at which @xmath95 ) , is @xmath96 . the latter values are smaller than the @xmath97 , inferred by helfand et al . ( 2001 ) under the assumption that the pwn arcs are dopler - brightened parts of a torus around the jet / counter - jet , and they are smaller then the @xmath98 suggested by pavlov ( 2000 ) assuming the arcs are doppler - brightened parts of ring - like shocks in relativistic conical outflows . if we adopt , e.g. , @xmath99 , then the maximum possible apparent speed ( at @xmath95 ) is @xmath100 , which is below the lower limits of @xmath101 and @xmath102 on the apparent speeds of blobs a and b at @xmath42 pc . thus , if any of the above - mentioned interpretaions of the arcs and the inner jet / counter - jet are correct , we have to conclude that the outer jet is tilted from the pulsar rotation axis towards the observer even if its projection onto the sky looks almost straight , like in panels 59 of figure 4 . moreover , we can not rule out the possibility that the outer jet in these observations is strongly bent in the plane perpendicular to the sky plane  e.g. , similar to the jet s sky projections in panels 1 , 2 or 13 . in this case the directions of the local flow velocities vary along the jet , which might explain the different apparent velocities of the blobs a and b. such bending opens up a possibility that the bright regions of the jet are merely due to the projection effect  the segments of a uniformly bright , bent jet , which are oriented along the line of sight , appear brighter because of the increased optical depth , and the brightness is further enhanced by the doppler boosting if the flow in these segments is streaming toward the observer . for instance , if the loop - like jet in panel 2 of figure 3 were a two - dimensional stucture , the southern segment of the loop would look like a bright blob if it were observed from the southwest direction . if this interpretation is correct , then the observed motions are caused by changing geometrical shape of the jet rather than the flow of locally bright material along the jet . an argument against such an interpretation is that the outer jet apparently terminates with a bright blob in at least 10 of 13 observations , and it is hard to believe that the end segment of a randomly bent jet is so often directed toward the observer . however , the extension of the jet beyond these bright blobs , as seen in the summed image of figure 1 ( see also  3.3 ) , suggests that this may still be the case .            another interesting fact related to the jet geometry is that the outer jet is consistently brighter than the outer counter - jet , with the ratio of surface brightnesses @xmath1039 ( the large uncertainty in the brightness ratio is due to the nonuniform backgrounds ) . if the two jets are energetically similar and , on average , are oriented along a straight line , then the outer jet is approaching while the outer counter - jet is receding , contrary to the receding inner jet and approaching inner counter - jet in the geometry assumed by pavlov et al . ( 2000 ) and helfand et al . ( 2001 ) . within this interpretation , the brightness ratio is @xmath104^{\\gamma + 2}$ ] , where @xmath54 is the photon index . for @xmath1039 and @xmath1051.4 , it gives @xmath1060.33 , @xmath107@xmath108 . furthermore , these values of @xmath109 are consistent with @xmath1100.7 , inferred from the blob s motion , if @xmath111 and @xmath112 ( see fig . 10 ) . to reconcile this result with the previously suggested orientation of the inner jets , one has to assume that the outer jet is tilted by a large angle ( @xmath113@xmath114 ) from the inner jet direction towards the observer , while the outer counter - jet is tilted by a similar angle away from the observer . contrary to the observed variable bendings of the outer jet , such tilts would have persisted for at least 5 years , since we confirm the existence of the brighter outer jet as far back as the 1997 _ rosat _ hri observation ( fig . it is not clear what could cause such persistent tilts . furthermore , it not clear why the outer jet and counter - jet are so much dimmer than their inner counterparts , and what causes the abrupt decrease of brightness in the outer jet and counter - jet , with bright knots at the junctions of the inner and outer parts . in particular , the transition from the inner jet to the outer jet apparently occurs at the intersection of the jet with the outer arc , which hints that the outer arc is not a part of a ring - like structure but an umbrella - like shell pierced by the jet ( kargaltsev et al . such a shell could be a bow shock created by the ( inner ) jet in the ambient medium , or it could form as a result of compression of the plasma outflow ( hence , amplification of the frozen - in magnetic field ) by the pulsar s motion in the ambient snr matter ( similar to that suggested by aschenbach & brinkmann 1975 for the crab pwn ) . another possible effect of the pulsar s motion is distortion of the ring - like structure(s ) ( e.g. , the post - shock region presumably associated with the inner arc ) by the ram pressure of the ambient matter , if the pulsar s rotational axis is not co - aligned with its velocity . in this case the leading part of the ring can be flattened by the ram pressure so that the assumption that the ring s sky projection is a perfect ellipse can result in wrong values for the inclination angles . finally , one could consider a possibility that the structures appearing as the bright inner jet and counter - jet are , in fact , merely traces of particle beams in conical outflows brightened by the doppler boosting ( e.g. , radhakrishnan & deshpande 2001 ; pavlov 2000 ) , while the outer jet and counter - jet are the `` true pulsar jets '' . such an assumption implies a quite different interpretation of the whole pwn . we will discuss these and other possible pwn models in a future paper currently , we can not unambiguously determine the orientation of the jets or the true velocities . however , from the observed variations of the shape of the outer jet , with mildly relativistic apparent velocities , we can conclude that the true velocities are neither ultrarelativistic nor nonrelativistic ; @xmath115 and @xmath116 can be adopted as conservative lower and upper limits . the power - law spectra of the outer jet and the other pwn elements can be interpreted as optically thin synchrotron emission from ultrarelativistic electrons ( and/or positrons ) with a power - law spectrum : @xmath117 , where @xmath118 is the lorentz factor , @xmath119 . the electron index @xmath120 is related to the photon index as @xmath121 , i.e. , @xmath1221.8 for @xmath1231.4 observed in the outer jet . a characteristic energy @xmath124 of the synchrotron photon depends on @xmath125 and magnetic field @xmath126 as @xmath127 kev , where @xmath128 , @xmath129 . if the minimum and maximum energies of the photon power - law spectrum are @xmath130 and @xmath131 , respectively , then the corresponding boundaries of the electron power - law spectrum are @xmath132^{1/2 } b_{-4}^{-1/2}$ ] and @xmath133^{1/2 } b_{-4}^{-1/2}$ ] , where the photon energies are in units of kev , @xmath134 is the doppler factor ( @xmath135 is the speed of the bulk motion ) , and @xmath136 and @xmath137 are dimensionless factors . the values of these factors are given in table ii of ginzburg & syrovatskii ( 1965 ; gs65 hereafter ) ; e.g. , @xmath138 and 1.8 , @xmath139 and 0.032 , for @xmath140 and 2.0 , respectively . we will use the well - known formulae for synchrotron radiation to estimate the magnetic field and energetics of the outer jet . since the bulk motions observed in the jet are only mildly relativistic ( @xmath141 is a plausible estimate ) , the doppler factor is not strongly different from unity ; moreover , its actual value is unknown because of the uncertain orientation of the jet . therefore , we will neglect the bulk motion of the jet s matter for most of the estimates below .    from the _ chandra _ acis observations , the power - law spectrum of the outer jet is seen in the energy range between @xmath142 kev and @xmath143 kev . since @xmath144 and @xmath145 , we can constrain the minimum and maximum energies of the electron power - law distribution : @xmath146 , @xmath147 . one can put a lower limit on the magnetic field in the outer jet using the condition that the larmor radius of most energetic electrons responsible for the x - ray emission , @xmath148 cm , does not exceed the jet radius , @xmath149 cm . this condition gives @xmath150 @xmath11 g . an upper limit on the magnetic field can be estimated from the fact that the spectrum of the outer jet maintains its power - law shape ( shows no appreciable spectral break ) at the observed energies @xmath151 kev up to the end of the outer jet . this means that the time of synchrotron losses , @xmath152 s , for the most energetic particles responsible for the observed x - ray spectrum [ @xmath153 is longer ( or comparable to ) the flow time , @xmath154 s , where @xmath155 cm . this gives @xmath156 @xmath11 g , i.e. , @xmath157300 @xmath11 g for plausible values of @xmath158 and @xmath92 . an independent estimate on the plasma parameters for the outer jet can be obtained from the brightness of the synchrotron radiation , assuming some value for the ratio @xmath159 of the magneic energy density , @xmath160 , to the energy density of relativistic particles , @xmath161 . we can not exclude the possibility that there are some relativistic ions in the jet , in addition to the synchrotron - emitting electrons ( e.g. , gallant & arons 1994 ) , so that @xmath162 , where @xmath163 is the ratio of the energy density of ions to the energy density of electrons , @xmath164 . making use of the standard formulae for synchrotron radiation ( e.g. , gs65 ; pacholczyk 1970 ) , one can express the magnetic field in terms of the observable parameters . for a tangled magnetic field ( randomly distributed along the line of sight ) , we obtain @xmath165 \\frac{\\mathcal{b}_{-7}}{\\bar{s}_{16}}\\right\\}^{2/7}\\,\\,\\mu{\\rm g}\\,,\\ ] ] where @xmath166 photons ( scm@xmath60kevarcsec@xmath60)@xmath7 is the average spectral surface brightness at @xmath168 kev , @xmath61 is the normalization of the photon spectral flux measured in area @xmath56 , @xmath169 cm is an average length of the radiating region along the line of sight , @xmath170 , @xmath171 , @xmath130 and @xmath131 are the lower and upper energies of the photon power - law spectrum ( in kev ) , and @xmath172 is a numerical coefficient given by eq . ( 3.32 ) and table ii of gs65 ( e.g. , @xmath173 and 0.117 for @xmath122 and 1.8 [ @xmath105 and 1.4 ] , respectively ) . the value of @xmath126 depends on several unknown parameters . particularly uncertain are the boundary energies of the photon power - law spectrum because of the lack of high - resolution observations outside the x - ray range . fortunately , the dependence on these energies is rather weak : @xmath174 for @xmath175 ( which implies @xmath176 ) , and @xmath177^{2/7}$ ] , for @xmath178 . for @xmath179 ( a typical spectral surface brightness at 1 kev  see fig . 9 ) , @xmath18010 ( the main reason of the uncertainty is the unknown spatial structure and orientation of the jet ) , and @xmath1811.4 , we obtain @xmath182^{-2/7 } \\la 200\\,\\mu{\\rm g}$ ] , for plausible ranges of @xmath131 and @xmath130 . it is usually assumed that @xmath183 ( equipartition condition ) , while the value of @xmath163 is rather uncertain . for the lower limit on the equipartition field not to exceed the upper limit estimated from ( the lack of ) synchrotron cooling , @xmath163 should not exceed @xmath184 . thus , given the uncertainty of the parameters , we can only state that the equipartion field is consistent with the above - estimated limits , and that a plausible estimate for a typical field in the jet is @xmath185 g , with an uncertainty of a factor of 3 . it should be noted that the local field values can differ from the average field . for instance , if the brightness of the blobs is due to an increased magnetic field , at fixed @xmath186 , then the field in the blobs is a factor of 1.4 higher than the average field in the jet . on the other hand , the higher brightness can be explained by the projection effect ( larger @xmath186 ) and the doppler boost ( @xmath187 in eq .  [ 1 ] if the bulk motion is taken into account ) . assuming equipartition , @xmath188 erg @xmath189 , we can estimate the total energy of relativistic particles , @xmath190 erg , where @xmath191 @xmath192 is the volume of the jet . for plausible values of the magnetic field and the volume ( @xmath1931 , depending on the shape and orientation of the jet ) , we obtain @xmath194@xmath195 erg . the energy injection rate and the energy flux can be estimated as @xmath196 erg s@xmath7 and @xmath197 erg cm@xmath34 s@xmath7 , respectively , where @xmath198 is the jet radius , and @xmath199 is the flow speed . this injection rate is a small fraction of the spin - down energy loss rate of the vela pulsar , @xmath200 . on the other hand , it greatly exceeds the observed x - ray luminosity of the jet , @xmath201 , which means that most of the injected energy is emitted outside the x - ray range or , more probably , carried out of the jet without substantial radiation losses . one can also estimate the electron ( positron ) injection rate , @xmath202^{-1}$ ] , where @xmath203 [ ( 2-p)[(\\gamma_m^{1-p } - \\gamma_m^{1-p})]^{-1}$ ] is the average electron lorentz factor for the power - law distribution . for the mean observed @xmath204 , we have @xmath205 if @xmath206 . unfortunately , the minimum and maximum electron energies can not be determined without multiwavelength observations of the jet , therefore we will scale @xmath207 to a possible ( but arbitrary ) value of @xmath208 , which gives @xmath209 s@xmath7 . this estimate corresponds to the mean electron number density @xmath210 @xmath189 . the numerical estimates for @xmath211 and @xmath212 strongly depend on the boundary energies of the electron power - law spectrum ; in particular , the estimates become 3 orders of magnitude larger if @xmath213 is low enough ( @xmath184 ) for the jet to be synchrotron - emitting in the radio band . it is interesting to compare the estimate for @xmath211 with the pair production rate expected for the vela pulsar : @xmath214 s@xmath7 , where @xmath215 is the goldreich - julian density , @xmath216 cm and @xmath217 s are the neutron star radius and spin period , @xmath218 g is the pulsar magnetic field , and @xmath219 is the pair multiplication coefficient ( its plausible value is @xmath220  see , e.g. , hibschman & arons 2001 ) . the ratio @xmath221 can be interpreted as the fraction of pairs escaping from the pulsar through the outer jet , assuming that no pairs are created in the jet itself . it is worth noting that the maximum lorentz factor for the pairs created in the pulsar magnetosphere does not exceed a few @xmath222 , for both the polar cap models ( harding , muslimov , & zhang 2002 , and references therein ) and the outer gap models ( e.g. , zhang & cheng 1997 ) . the maximum lorentz factor in the outer jet , @xmath223 , is substantially higher , which means that the pairs , created by the pulsar , have been additionally accelerated beyond the pulsar magnetosphere . if ions are pulled out of the neutron star surface layers , their outflow rate is constrained to the goldreich - julian value : @xmath224 s@xmath7 , while their characteristic energy may exceed that of electrons / positrons ( gallant & arons 1994 ) . although the ions can be further accelerated to even higher energies , the maximum ion energy in the jet can not exceed @xmath225 ev [ @xmath226 because the larmor radius of ions with higher energies is larger than the jet radius . assuming that the ion - to - electron number density ratio in the jet does not exceed that in the magnetosphere outflow , we can constrain the ion - to - electron energy density ratio : @xmath227 , at @xmath228 cm . this means that relativistic ions do not make a substantial contribution to the energetics of the outer jet . since the bulk velocities in the outer jet are only mildly relativistic , the bulk kinetic energy of relativistic particles is much lower than the energy of their random motion . however , we can not rule out the possibility that some nonrelativistic electron - ion plasma from the ambient snr medium is entrained into the jet via interaction with the jet s magnetic field . to estimate an upper limit on the maximum density of the nonrelativistic component and maximum kinetic energy of the outer jet , it seems reasonable to assume that the _ total _ energy injection rate , including the kinetic energy , into the outer jet can not exceed a fraction of @xmath229 of the total power , @xmath230 erg s@xmath7 , supplied by the pulsar , which implies @xmath231 erg . this condition requires densities of nonrelativistic particles ( ions or electrons ) , @xmath232 @xmath189 . thermal x - ray radiation from such a low - density plasma is orders of magnitude fainter than the observed radiation from the outer jet . the corresponding upper limits on the pressure and energy density of the nonrelativistc components depend on the unknown mean energy of nonrelativistic particles ; however , they do not exceed the pressure and energy density of relativistic particles and the magnetic field . furthermore , the density of this plasma is much lower than the density of the ambient medium . on the other hand , the bulk pressure , @xmath233 erg @xmath189 , can be higher than the pressure in the ambient medium , @xmath234 erg @xmath189 . we see from figures 3 and 4 that the outer jet is never straight , showing either gentle bends ( e.g. , panels 510 ) or a strongly curved structure ( panels 1 , 2 , and 13 ) . the varying curvature of the outer jet can be explained by its interaction with the ambient medium ( snr plasma ) and/or by a kink instability in the jet flow .    a strong argument for an external wind to cause jet s bending is provided by the deep image of the pwn ( fig . 1 ) that allows one to see an extension of the outer jet beyond the apparent termination points ( often associated with outermost blobs ) observed in the individual images . it shows that the outer jet does _ not _ terminate abruptly , but it rather smoothly bends clockwise ( towards west and then southwest ) by at least @xmath235 . such bending suggests a persistent _ northeast wind _ in the ambient medium ( approximately perpendicular to the direction of the pulsar s proper motion . such a wind could also explain the very asymmetric diffuse emission outside the bright pwn  the wind `` blows off '' relativistic electrons , produced in the bright pwn , towards the southwest . moreover , it could explain , in the same way , the fact that the surface brightness is substantially higher at the southwest side of the outer jet compared with the northeast  some high - energy particles are leaking from the jet and blown away by the wind . finally , an additional support for the wind comes from the radio image of the ( outer ) pwn ( lewis et al .  2002 ; dodson et al . this image shows two lobes , northeast and southwest of the x - ray bright pwn , with a much smaller northeast lobe confined by a brightened northeast boundary . the smaller size and the brightening can be explained by compression of the radio - emitting plasma by the external northeast wind . the bulk pressure of this wind can be crudely estimated as @xmath236 , where @xmath237 is the diameter of the jet , @xmath238 is the curvature radius of the bending , and @xmath239 is the thrust ( jet s momentum flux ) through the jet s transverse area @xmath240 ( e.g. , leahy 1991 ) . if the bulk kinetic pressure is much lower than the magnetic pressure within the jet , @xmath241 erg @xmath189 , then the main contribution to the thrust comes from the longitudinal component of the magnetic stress tensor that , in turn , depends on the geometry of the magnetic field . for instance , we obtain @xmath242 for a tangled magnetic field , which gives @xmath243 erg @xmath189 , for @xmath244 cm . this bulk pressure is much lower than the typical thermal pressure in the vela snr . it corresponds to the wind velocity @xmath245 km s@xmath7 , where @xmath246 is the ion ( proton ) number density in the wind . attempts at separating the wind s x - ray emission from the snr background did not yield conclusive results . assuming a low - density wind , @xmath247 @xmath189 , we obtain @xmath248 km s@xmath7  high but not improbable velocity . such a velocity is comparable with the pulsar s proper motion velocity , @xmath249 km s@xmath7 ( caraveo et al . 2001 ) , but the pulsar s motion itself can not initiate the observed bending because the pulsar moves in the direction of the unbent jet ( at least in the sky projection ) . however , once the jet is substantially bent from its original direction by the putative snr wind , the pulsar s motion with respect to the snr matter can bend it further , so that the jet can become directed backwards ( towards southeast ) . a hint of such a bend is indeed seen in figure 1 . moreover , the relativistic particles blown off the jet by the snr wind are being picked up by the head wind ( in the pulsar s reference frame ) and dragged in the direction opposite to the pulsar s proper motion , feeding the diffuse nebula . such a picture is supported by the spectral slope of the diffuse emission , @xmath250 , which is softer than the emission of the brighter outer jet ( @xmath251 ) , but harder than the emission of the pwn shell ( @xmath252 ) . thus , we can conclude that the outermost observable part of outer jet is likely bent by the combined action of the snr wind and the pulsar s proper motion , and the outer jet finally bends backward and get diffused southwest of the pulsar . so far we have discussed only the bending of the jet s `` end '' . explaining more extreme bends in the brighter part of the outer jet ( e.g. , the hook - like or loop - like structures in panels 1 , 2 , 4 , and 13 ) by the wind action is more problematic . although we see that these bends are convex in the direction of the snr wind suggested above , the relatively small size ( and strong curvature ) of these structures would require a strong nonuniformity and very high velocities of the wind . even a stronger argument is the observed variability of the bent structures , associated with almost relativistic velocities . therefore , we have to invoke another mechanism to explain these features , not related to external winds . a natural explanation is the kink instability of a magnetically confined , pinched flow . estimates of the instability growth times and wavelengths depend on the model of such a flow , particularly the distribution of currents and topology of the magnetic field . the flow model is also tightly connected with the interpretation of the whole pwn , particularly the inner jets and arcs . analysis of these models is beyond the scope of the present paper . therefore , we only briefly mention that the ( outer ) jet can be modeled as a plasma beam carrying a charge current of @xmath253 @xmath254 s@xmath7 ( @xmath255  see  3.2 ) , self - confined by a predominantly toroidal magnetic field ( z pinch ) . a similar model for pulsar jets was suggested by benford ( 1984 ) , while collimation and confinment of agn jets by magnetic field was reviewed by begelman , blandford & rees ( 1984 ) and other authors . growth times of mhd instabilities in such a flow are proportional to the alfven crossing time , @xmath256 ( e.g. , begelman 1998 ) . using the expression for the alfven velocity in the ultrarelativistic plasma , @xmath257^{-1/2}$ ] ( akhiezer et al .  1975 ) , we obtain @xmath258 at equipartition between the magnetic and particle energy densities , which gives @xmath259 days . this time is comparable to the time scales of strong bendings ( @xmath260 days ) , which can be associated with the kink instabilities , and time scales of blob brightening ( about a week ) , which can be associated with the sausage ( neck ) instabilities .","summary":"the x - ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons / positrons . this interpretation allows one to estimate the magnetic field , the more extreme bends closer to the pulsar , as well as the apparent side motions of the outer jet , can be associated with kink instabilities of a magnetically confined , pinched jet flow .","abstract":"observations of the vela pulsar - wind nebula ( pwn ) with the _ chandra x - ray observatory _ have revealed a complex , variable pwn structure , including inner and outer arcs , a jet in the direction of the pulsar s proper motion , and a counter - jet in the opposite direction , embedded in diffuse nebular emission . the jet consists of a bright ,-long inner jet , between the pulsar and the outer arc , and a dim , curved outer jet that extends up to in approximately the same direction . from the analysis of thirteen _ chandra _ observations spread over years we found that this outer jet shows particularly strong variability , changing its shape and brightness . we observed bright blobs in the outer jet moving away from the pulsar with apparent speeds ( 0.3 and fading on time - scales of days to weeks . if the blobs are carried away by a flow along the jet , the observed variations suggest mildly relativistic flow velocities , about ( 0.3 . the spectrum of the outer jet fits a power - law model with a photon index . for a distance of 300 pc , the apparent average luminosity of the outer jet in the 18 kev band is about erg s , compared to from the whole pwn within from the pulsar . the x - ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons / positrons . this interpretation allows one to estimate the magnetic field ,  g , maximum energy of x - ray emitting electrons , ev , and energy injection rate , , for the outer jet . in the summed pwn image , we see a faint , strongly bent , extension of the outer jet . this bending could be caused by combined action of a wind within the supernova remnant , with a velocity of a few km s , along with the ram pressure due to the pulsar s proper motion . the more extreme bends closer to the pulsar , as well as the apparent side motions of the outer jet , can be associated with kink instabilities of a magnetically confined , pinched jet flow . another feature found in the summed image is a dim ,-long outer counter - jet , which also shows a power - law spectrum with.5 . southwest of the jet / counter - jet ( i.e. , approximately perpendicular to the direction of pulsar s proper motion ) , an extended region of diffuse emission is seen . relativistic particles responsible for this radiation are apparently supplied by the outer jet ."}
{"article_id":"astro-ph0305510","section_id":"i","document":"the multiple _ chandra _ observations of the vela pwn have allowed us to investigate the dynamical outer jet and discover a dimmer outer counter - jet outside the bright pwn . our main results can be summarized as follows . the outer jet extends up to about 0.40.5 light years from the pulsar in the sky plane along the direction of the pulsar s proper motion . its shape and brightness are variable on time scales of days to weeks . the brightness is nonuniform along the jet , with brighter blobs moving away from the pulsar with apparent subrelativistic speeds . the variations observed suggest typical flow velocities of 0.30.7 of the speed of light . the outer jet is , on average , a factor of 7 brighter than the outer counter - jet . if the outer jet and outer counter - jet are intrinsically similar but streaming in opposite directions , then the difference in brightness means that the outer jet is approaching at an angle of @xmath261@xmath262 to the line - of sight while the outer counter - jet is receding . such an orientation apparently contradicts to the previously suggested models of the inner jets and the bright arcs . the synchrotron interpretation of the hard ( @xmath263 ) power - law spectrum of the outer jet requires highly relativistic electrons or positrons , with energies of up to @xmath264 tev , and a typical magnetic field of about 100 @xmath11 g . the outer jet s spectrum is perhaps slightly softer than those of the inner jet and counter - jet , but it does not change appreciably along the outer jet . if the outer jet is a mildly relativistic outflow of an ultrarelativistic electron / positron plasma , the energy injection rate is @xmath265 .    \\4 . outside the bright pwn , there is an asymmetric , dim outer diffuse nebula that is substantially brighter southwest of the jet / counter - jet line . its spectrum is softer than that of the outer jet , but it is harder than the spectrum of the brighter pwn shell . it is possible that the x - ray emitting particles in the dim nebula are supplied through the outer jet , whose end part turns southwest with respect to its average ( northwest ) direction in the sky plane . such a turn can be caused by a northeast snr wind with a speed of a few times 10 km s@xmath7 , which also helps feed the dim nebula . the width of the outer jet , @xmath266 cm , remains approximately the same along the jet in different observations , including those which show strong bends . this suggests an efficient confinement mechanism , perhaps associated with magnetic fields generated by electric currents in the pinched jet . the current required , @xmath267 , is an order of magnitude lower than the goldreich - julian current in the pulsar magnetosphere . the bright blobs and strong bends could be caused by the sausage and kink instabilities , respectively , in such a pinched jet . the excellent resolution of the _ chandra _ telescope and high sensitivity of its detectors allowed us to obtain the spectacular pictures of the vela pwn , including the faint outer jet , and , in particular , to prove the highly anisotropic and dynamical nature of the pulsar outflows . however , as has been often the case with new high - quality data , our results raise new questions and put under doubt the previous simplistic interpretations of pwne in general and the vela pwn in particular . the most unclear issue is the interpretation of the complicated morphology of the vela pwn , particularly the relationship of the outer jet and outer counter - jet with their inner counterparts , the true orientation of the jets , and the actual topology of its arcs . we do not even know the actual three - dimentional orientations of the inner and outer jets and counter - jets , nor do we understand the cause of their different brightness . we can only guess about the nature of the bright blobs moving along the outer jet , the mechanism(s ) of the jet confinement , and the origin of the jet bendings . at least some of these issues can be clarified by a series of deeper _ chandra _ observations of the vela pwn , taken with intervals of a few days , the now - established time scale of the pwn variations . in particular , such observations would allow one to search for the spectral changes along the outer jet and check if the spectra of the blobs are different from those of the rest of the jet . they could also help find blobs in the very dim outer counter - jet and measure their velocities , which would provide a clue to the geometry of the system . the interpretation of the vela pwn would be much easier if it were detected at other wavelengths , outside the x - ray range . so far , contrary to the much better studied crab pwn , the vela pwn has not been detected in the optical , mainly because of numerous relatively bright field stars and snr filaments in the pulsar vicinity ( mignani et al . 2003 ) . to get rid of their light and detect the pwn or put a stringent upper limit on its brightness , the field must be observed in polarized light . it would also be very important to obtain a deep radio image the field around the vela pulsar with arcsecond resolution ( cf . dodson et al . both the optical and radio observations would provide estimates on the lower frequencies of the synchrotron spectra ( hence , lower energies of relativistic electrons ) , the critical parameters for evaluating the magnetic fields and the energetics of the observed pwn elements . measuring polarizations of the optical and radio emission would be crucial to establish the directions of the magnetic field in the pwn elements and understand their nature . we thank leisa townsley and george chartas for the advice on acis data reduction and bing zhang for useful discussions of pulsar physics . support for this work was provided by the nasa through chandra awards go1 - 2071x and go2 - 3091x , issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of nasa under contract nas8 - 39073 . this work was also partially supported by nasa grant nag5 - 10865 . aschenbach , b. , & brinkmann , w. 1975 , a&a , 41 , 147 akhiezer , a.  i. , akhiezer , i.  a. , polovin , r.  v. , sitenko , a.  g. , & stepanov , k.  n. 1975 , plasma electrodynamics , ( oxford : pergamon ) , p.112 begelman , m.  c. 1998 , apj , 493 , 291 begelman , m.  c. , blandford , r.  d. , rees , m.  j. 1984 , rev . , 56 , 255 benford , g. 1984 , apj , 282 , 154 caraveo , p.  a. , de luca , a. , mignani , r.  p. , & bignami , g.  f. 2001 , apj , 561 , 930 dodson , r. , legge , d. , reynolds , j.  e. , & mcculloch , p.  m. 2003a , apj , submitted ( astro - ph/0302374 ) dodson , r. , lewis , d. , mcconnel , d. , & deshpande , a.  a. 2003b , mnras , submitted ( astro - ph/0302373 ) gaensler , b.  m. , arons , j. , caspi , v.  m. , pivovaroff , m.  j. , kawai , n. , & tamura , k. 2002 , apj , 569 , 878 gallant , y.  a. , & arons , j. 1994 , apj , 435 , 230 ginzburg , v.  l. , & syrovatskii , s.  i. 1965 , ara&a , 3 , 297 [ gs65 ] harding , a.  k. , muslimov , a.  g. , & zhang , b. 2002 , apj , 576 , 366 harnden , f.  r. , grant , p.  d. , seward , f.  d. , & kahn , s.  m. 1985 , apj , 299 , 828 helfand , d.  j. , gotthelf , e.  v. , & halpern , j.  p. 2001 , apj , 556 , 380 hester , j.  j. , mori , k. , burrows , d. , et al . 2002 , apj , 577 , l49 hibschman , j. , & arons , j. 2001 , apj , 560 , 871 kargaltsev , o. , pavlov , g.  g. , sanwal , d. , & garmire , g.  p. 2002 , in neutron stars in supernova remnants , eds . p .. o.  slane & b.  m.  gaensler , asp conf . , v.271 ( san francisco : asp ) , 181 leahy , j.  p. 1991 , in beams and jets in astrophysics , ed . a.  hughes ( cambridge : cambridge univ .  press ) , 147 lewis , d. , dodson , r. , mcconnel , d. , & deshpande , a. 2002 , in neutron stars in supernova remnants , eds . p .. o.  slane & b.  m.  gaensler , asp conf . ser . , v.271 ( san francisco : asp ) , 191 markwardt , c.  b. , & gelman , h. 1998 , mem . italiana , 69 , 927 mignani , r.  p. , de luca , a. , kargaltsev , o. , pavlov , g.  g. , zaggia , s. , caraveo , p.  a. , & becker , w. 2003 , apj , submitted mori , k. , hester , j.  j. , burrows , d.  n. , pavlov , g.  g. , & tsunemi , h. 2002 , in neutron stars in supernova remnants , asp conf . , v.  271 , eds . o.  slane & b.  m.  gaensler ( san francisco : asp ) , 157 pacholczyk , a.  g. 1970 , radio astrophysics ( san francisco : freeman ) pavlov , g.  g. 2000 , aas head meeting 32 , # 07.05 pavlov , g.  g. , sanwal , d. , garmire , g.  p. , zavlin , v.  e. , burwitz , v. , & dodson , r.  g. 2000 , aas meeting 196 , # 37.04 pavlov , g.  g. , kargaltsev , o.  y. , sanwal , d. , & garmire , g.  p. 2001a , apj , 554 , l189 pavlov , g.  g. , zavlin , v.  e. , sanwal , d. , burwitz , v , . & garmire , g.  p. 2001b , apj , 552 , l129 plucinsky , p.  p. , et al . 2002 , in astronomical telescopes and instrumentation 2002 , eds . j.  e.  trmper & h.  d.  tananbaum , spie conf . , in press ( astro - ph/0209161 ) radhakrishnan , v. , & deshpande , a. 2000 , a&a , 379 , 551 townsley , l.  k. , broos , p.  s. , garmire , g.  p. , & nousek , j.  a. 2000 , apj , 534 , l139 zhang , l. , & cheng , k.  s. 1997 , apj , 487 , 370","summary":"we observed bright blobs in the outer jet moving away from the pulsar with apparent speeds ( 0.3 and fading on time - scales of days to weeks . this bending could be caused by combined action of a wind within the supernova remnant , with a velocity of a few km s , along with the ram pressure due to the pulsar s proper motion . relativistic particles responsible for this radiation are apparently supplied by the outer jet .","abstract":"observations of the vela pulsar - wind nebula ( pwn ) with the _ chandra x - ray observatory _ have revealed a complex , variable pwn structure , including inner and outer arcs , a jet in the direction of the pulsar s proper motion , and a counter - jet in the opposite direction , embedded in diffuse nebular emission . the jet consists of a bright ,-long inner jet , between the pulsar and the outer arc , and a dim , curved outer jet that extends up to in approximately the same direction . from the analysis of thirteen _ chandra _ observations spread over years we found that this outer jet shows particularly strong variability , changing its shape and brightness . we observed bright blobs in the outer jet moving away from the pulsar with apparent speeds ( 0.3 and fading on time - scales of days to weeks . if the blobs are carried away by a flow along the jet , the observed variations suggest mildly relativistic flow velocities , about ( 0.3 . the spectrum of the outer jet fits a power - law model with a photon index . for a distance of 300 pc , the apparent average luminosity of the outer jet in the 18 kev band is about erg s , compared to from the whole pwn within from the pulsar . the x - ray emission of the outer jet can be interpreted as synchrotron radiation of ultrarelativistic electrons / positrons . this interpretation allows one to estimate the magnetic field ,  g , maximum energy of x - ray emitting electrons , ev , and energy injection rate , , for the outer jet . in the summed pwn image , we see a faint , strongly bent , extension of the outer jet . this bending could be caused by combined action of a wind within the supernova remnant , with a velocity of a few km s , along with the ram pressure due to the pulsar s proper motion . the more extreme bends closer to the pulsar , as well as the apparent side motions of the outer jet , can be associated with kink instabilities of a magnetically confined , pinched jet flow . another feature found in the summed image is a dim ,-long outer counter - jet , which also shows a power - law spectrum with.5 . southwest of the jet / counter - jet ( i.e. , approximately perpendicular to the direction of pulsar s proper motion ) , an extended region of diffuse emission is seen . relativistic particles responsible for this radiation are apparently supplied by the outer jet ."}
{"article_id":"0904.1148","section_id":"i","document":"in this paper , we consider the problem of estimating the intensity of a poisson process . from a practical point of view , various methodologies have already been proposed . see for instance rudemo @xcite who proposed kernel and data - driven histogram rules calibrated by cross - validation . thresholding algorithms have been performed by donoho @xcite who modified the universal thresholding procedure proposed in @xcite by using the anscombe transform or by kolaczyk @xcite whose procedure is based on the tails of the distribution of the noisy wavelet coefficients of the intensity . finally , let us cite model selection type estimators built by willett and nowak @xcite based on models spanned by piecewise polynomials . from the theoretical point of view , cavalier and koo @xcite derived minimax rates on besov balls by using wavelet thresholding . in the oracle approach , various optimal adaptive model selection rules have also been built by baraud and birg ' e @xcite , birg @xcite and reynaud - bouret @xcite . let us mention that these procedures are also minimax provided the intensity to be estimated is assumed to be supported by @xmath3 $ ] .    in a previous paper , refined classical wavelet thresholding algorithms by proposing local data - driven thresholds ( see @xcite ) . under very mild assumptions , procedure achieves optimal oracle inequalities and optimal minimax rates up to a logarithmic term . in particular , results are true even if the support of the intensity is unknown or infinite , which is rarely considered in the literature . in @xcite , we give many arguments to justify this unusual setting and we illustrate the influence of the support on minimax rates by showing how these rates deteriorate when the sparsity of the intensity decreases . so , algorithm , that is easily implementable , automatically adapts to the unknown regularity of the signal as usual , but also to the unknown support which is not classical . the main goal of this paper is to study the optimal calibration of the procedure studied in @xcite from both theoretical and practical points of view . for this purpose , the next subsection briefly describes this procedure ( section [ data - driven ] gives accurate definitions ) and section [ calissue ] presents the calibration issue . we observe a poisson process @xmath4 whose mean measure @xmath5 is finite on the real line @xmath6 and is absolutely continuous with respect to the lebesgue measure ( see section [ rappelpoisson ] where we recall classical facts on poisson processes ) . given @xmath7 a positive integer , we define the intensity of @xmath4 as the function @xmath8 that satisfies @xmath9 so , the total number of points of the process @xmath4 , denoted @xmath10 , satisfies @xmath11=n{\\ensuremath{\\vert\\!\\vert f \\vert\\!\\vert}}_1<\\infty.\\ ] ] in particular , @xmath10 is finite almost surely . in the sequel , @xmath8 will be held fixed and @xmath7 will go to @xmath12 . the introduction of @xmath7 could seem artificial , but it allows to present the following asymptotic theoretical results in a meaningful way since the mean of the number of points of @xmath4 goes to @xmath13 when @xmath14 . in addition , our framework is equivalent to the observation of a @xmath7-sample of a poisson process with common intensity @xmath8 with respect to the lebesgue measure . the goal of this paper is to estimate @xmath8 by the points of @xmath4 . first , we decompose the signal @xmath8 to be estimated as follows : @xmath15 where @xmath16 denotes a biorthogonal wavelet basis . in our paper , we mainly focus on the haar basis ( in this case , @xmath17 for any @xmath18 ) or on a special case of biorthogonal spline wavelet bases ( in this case , @xmath19 is piecewise constant and @xmath20 is regular ) . see section [ biorthogonal ] where we recall well - known facts on biorthogonal wavelet bases or cohen , daubechies and feauveau @xcite for a complete overview on such families . as usual in the wavelet setting , our goal is to estimate the wavelet coefficients @xmath21 by thresholding empirical wavelet coefficients @xmath22 defined as @xmath23 thresholding procedures have been introduced by donoho and johnstone @xcite . their main idea is that it is sufficient to keep a small amount of the coefficients to have a good estimation of the function @xmath8 . in our setting , the estimate of @xmath8 takes the form @xmath24 where @xmath25 is defined in ( [ gamman ] ) . the thresholding procedure is detailed and discussed in section [ data - driven ] . we just mention here the form of the data - driven threshold @xmath26 : @xmath27 where @xmath28 is a sharp estimate of @xmath29 defined in ( [ vtilde ] ) and @xmath30 a constant to be chosen . as explained in section [ data - driven ] , we have for most of the indices @xmath18 s playing a key role for estimation : @xmath31 in this case , @xmath26 has a form close to the universal threshold @xmath32 proposed by donoho and johnstone @xcite in the gaussian regression framework : @xmath33 where @xmath34 ( assumed to be known ) is the variance of each noisy wavelet coefficient . note , however , that our procedure depends on the so - called _ threshold parameter _ @xmath30 that has to be properly chosen . the next section which describes calibration issues in a general way discusses this question . the major concern of this paper is the study of the calibration of the threshold parameter @xmath30 : how should this parameter be chosen to obtain good results in both theory and practice ? as usual , it can be proved that @xmath35 achieves good theoretical performances in minimax or oracle points of view ( see @xcite or theorem [ inegoraclelavraie ] ) provided @xmath30 is large enough . such an assumption is very classical in the literature ( see for instance @xcite , @xcite , @xcite or @xcite ) . unfortunately , most of the time , the theoretical choice of the threshold parameter is not suitable for practical issues . more precisely , this choice is often too conservative . see for instance juditsky and lambert - lacroix @xcite who illustrate this statement in remark 5 of their paper : their threshold parameter , denoted @xmath18 , has to be larger than 14 to obtain theoretical results , but they suggest to use @xmath36 $ ] for practical issues . so , one of the main goals of this paper is to fill the gap between the optimal parameter choice provided by theoretical results on the one hand and by a simulation study on the other hand . only a few papers have been devoted to theoretical calibration of statistical procedures . in the model selection setting , the issue of calibration has been addressed by birg and massart @xcite . they considered penalized estimators in a gaussian homoscedastic regression framework with known variance and calibration of penalty constants is based on the following methodology . they showed that there exists a minimal penalty in the sense that taking smaller penalties leads to inconsistent estimation procedures . under some conditions , they further prove that the optimal penalty is twice the minimal penalty . this relationship characterizes the `` slope heuristic '' of birg and massart @xcite . such a method has been successfully applied for practical purposes in @xcite . baraud , giraud and huet @xcite ( respectively arlot and massart @xcite ) generalized these results when the variance is unknown ( respectively for non - gaussian or heteroscedastic data ) . these approaches constitute alternatives to popular cross - validation methods ( see @xcite or @xcite ) . for instance , @xmath37-fold cross - validation ( see @xcite ) is widely used to calibrate procedure parameters but its computational cost can be high . the starting point of our results is the oracle inequality stated in section [ data - driven ] : theorem [ inegoraclelavraie ] shows that the estimate @xmath35 achieves the oracle risk up to a logarithmic term . this result is true as soon as @xmath38 and @xmath39 . in particular , nothing is assumed with respect to the support of @xmath8 or @xmath40 : our result remains true if @xmath41 and if the support of @xmath8 is unknown or infinite . the oracle inequality of theorem [ inegoraclelavraie ] is refined in section [ study ] where @xmath8 is assumed to belong to a special class denoted @xmath42 whose signals have only a finite number of non - zero wavelet coefficients ( see theorem [ classfn ] ) . then , in the perspective of calibrating thresholding rules , we consider theoretical performances of @xmath35 with @xmath43 by using the haar basis . for the signal @xmath44}$ ] , theorem [ inegoraclelavraie ] shows that @xmath35 with @xmath45 achieves the rate @xmath46 . but the lower bound of theorem [ lower ] shows that the rate of @xmath35 with @xmath43 is larger than @xmath47 for @xmath48 . so , as in @xcite for instance , we prove the existence of a minimal threshold parameter : @xmath49 . of course , the next step concerns the existence of a maximal threshold parameter . this issue is answered by theorem [ uppth ] which studies the maximal ratio between the risk of @xmath35 and the oracle risk on @xmath42 . we derive a lower bound that shows that taking @xmath50 leads to worse rates constants : a bad choice . the optimal choice for @xmath0 is derived from a numerical study , keeping in mind that the theory points out the range @xmath2 $ ] . some simulations are provided for estimating various signals by considering either the haar basis or a particular biorthogonal spline wavelet basis ( see section [ simulations ] ) . our numerical results show that choosing @xmath0 larger than 1 but close to 1 is a fairly good choice , which corroborates theoretical results . actually , our simulation study suggests that theorem [ lower ] remains true for all signals of @xmath42 whatever the basis for decomposing signals is used . finally , we lead a comparative study with other competitive procedures . we show that the thresholding rule proposed in this paper outperforms universal thresholding ( when combined with the anscombe transform ) or kolaczyk s procedure . finally , the robustness of our procedure with respect to the support issue is emphasized and we show the harmful role played by large supports of signals when estimation is performed by other classical procedures . section [ data - driven ] defines the thresholding estimate @xmath35 and studies its properties under the oracle approach . in section [ study ] , we refine this study on the set of positive functions that can be decomposed on a finite combination of the basis . calibration of thresholds is discussed in section [ penaltyterm ] and section [ simulations ] illustrates our theoretical results by some simulations . section [ proofs ] is devoted to the proofs of the results . finally , section [ maintools ] recalls well - known facts on poisson processes and biorthogonal wavelet bases . now , let us consider our procedure . theorem [ inegoraclelavraie ] applied with the haar basis , @xmath51 and @xmath52 implies that if @xmath53 is used with @xmath45 to estimate @xmath54}$ ] then its risk satisfies @xmath55 where @xmath56 is a constant . the question is : what happens , from the theoretical point of view , when @xmath57 ? the following result answers this question for the case @xmath43 . let @xmath44}$ ] . if @xmath43 then there exists @xmath48 not dependent of @xmath7 such that @xmath58    the question for the case @xmath59 remains open . however , combining theorems [ inegoraclelavraie ] and [ lower ] , proves that from a theoretical point of view , it is a very bad idea to use a parameter @xmath0 smaller than @xmath60 since in this case we can not achieve the rate @xmath61 obtained when @xmath45 . this result is reinforced by the simulation study of section [ simulations ] , where we observe that performances of our estimate deteriorate for @xmath43 and the optimal values of @xmath30 for estimating @xmath54}$ ] are larger or equal to 1 . so , theoretical and practical conclusions for calibrating thresholds fit for this simple example . unfortunately , we are not able to generalize theorem [ lower ] for @xmath62 , or for other signals decomposed on general biorthogonal wavelet bases , but our simulation study suggests that theorem [ lower ] remains true in some situations ( see section [ simulations ] ) . actually , our numerical results show that choosing @xmath0 larger than 1 but close to 1 is a fairly good choice for all the encountered situations ( finite / infinite support , bounded / unbounded intensity , smooth / non - smooth functions ) .    finally , we investigate an upper bound for the optimal choice of @xmath30 . for this purpose , we consider a special class of intensity functions denoted @xmath63 . corollary [ classfn ] and theorem [ uppth ] of section [ penaltyterm ] provide upper and lower bounds of the maximal ratio on @xmath63 of the risk of @xmath64 by the oracle risk and prove that @xmath0 should not be too large .","summary":"in this paper , we deal with the problem of calibrating thresholding rules in the setting of poisson intensity estimation . by using sharp concentration inequalities , this result is proved under mild assumptions and we do not impose any condition on the support of the signal to be estimated . then , we lead a numerical study that shows that choosing larger than 1 but close to 1 is a fairly good choice . finally , we compare our procedure with classical ones revealing the harmful role of the support of functions when estimated by classical procedures .   ","abstract":"in this paper , we deal with the problem of calibrating thresholding rules in the setting of poisson intensity estimation . by using sharp concentration inequalities , oracle inequalities are derived and establish the optimality of our estimate up to a logarithmic term . this result is proved under mild assumptions and we do not impose any condition on the support of the signal to be estimated . our procedure is based on data - driven thresholds . as usual , they depend on a threshold parameter whose optimal value is hard to estimate from the data . our main concern is to provide some theoretical and numerical results to handle this issue . in particular , we establish the existence of a minimal threshold parameter from the theoretical point of view : taking deteriorates oracle performances of our procedure . in the same spirit , we establish the existence of a maximal threshold parameter and our theoretical results point out the optimal range $ ] . then , we lead a numerical study that shows that choosing larger than 1 but close to 1 is a fairly good choice . finally , we compare our procedure with classical ones revealing the harmful role of the support of functions when estimated by classical procedures .    * calibration of thresholding rules for poisson *    * intensity estimation *    * patricia reynaud - bouretand vincent rivoirard *    * keywords * adaptive estimation , calibration , oracle inequalities , poisson process , wavelet thresholding + * mathematics subject classification ( 2000 ) * 62g05 62g20"}
{"article_id":"1303.2884","section_id":"i","document":"the multiferroic materials ( or multiferroics ) , where ferroelectricity coexists with some long - range magnetic order , have attracted a great deal of attention.@xcite a very special class of multiferroics is improper ferroelectrics . in the latter case , the ferroelectric ( fe ) polarization not only coexists , but can be induced by the magnetic order . the improper ferroelectrics are expected to display a strong magneto - electric coupling , which is extremely important for practical applications . for instance , because of such coupling , the fe polarization can be efficiently controlled by the magnetic field , while the magnetization can be controlled by the electric field . from a technological point of view , the ultimate goal is to find materials with the large fe polarization , which would be coupled to the magnetic texture at maximally possible temperature ( meaning that the magnetic transition temperature should be also high ) . manganites , crystalizing in the orthorhombic @xmath0 and @xmath1 structure , are regarded as one of the key multiferroic materials . despite low magnetic transition temperature ( typically , less than 40 k ) and modest values of the fe polarization ( less than @xmath11 @xmath12c/@xmath13 ) , which have been achieved so far,@xcite they have all essential ingredients to be called improper ferroelectrics . namely , the appearance of ferroelectricity coincides with some complex magnetic ordering . moreover , the possibility of switching the electric polarization by the magnetic fields has been directly demonstrated experimentally.@xcite therefore , these materials are fundamentally important and are typically used as a playground for testing various theories and models of multiferroicity .    nevertheless , the theoretical understanding of improper ferroelectricity in these compounds is still rather controversial and there is no unique view on the origin of this effect . first , all multiferroic manganites are rather artificially divided in two groups :    * the systems with the twofold periodic @xmath3-type antiferromagnetic ( afm ) texture ( such as homno@xmath14 and ymno@xmath14 ) , where the fe activity is attributed to the nonrelativistic exchange striction,@xcite and * the rest of the systems , with more general magnetic periodicity , where the fe activity is believed to be due to the relativistic spin - orbit ( so ) interaction and the magnetic texture itself is ascribed to the spin spiral.@xcite the typical example of such systems is tbmno@xmath14 , which has nearly fourfold periodic magnetic texture . this point was rationalized in the previous publications of one of the authors ( ref .  ) , where it was argued that there is no conceptual difference between twofold periodic and other multiferroic manganiets . the relativistic so interaction plays an equally important role in both cases : as it deforms the @xmath3-type afm state in the direction of the spin spiral , it will also deform the spin spiral and form a more general spatially inhomogeneous magnetic state . thus , the ground state of multiferroic manganites will be neither the collinear @xmath3-state nor the homogeneous spin spiral . the relativistic so interaction is essential for producing this inhomogeneity . however , the fe polarization itself is a nonrelativistic quantity in the sense that , for a given inhomogeneous distribution of spins , the appearance of the fe polarization can be described by nonrelativistic theories . another group of controversies is related to the question : how to calculate the polarization and what is the main contribution to it ? most of model calculations rely on the purely ionic picture , where the noncentrosymmetric distribution of spins gives rise to noncentrosymmetric atomic displacements . then , the polarization is evaluated in the framework of the point charge model.@xcite on the other hand , all modern first - principles calculations of the fe polarization are based on the berry - phase theory.@xcite besides ionic polarization , the berry - phase theory prescribes the existence of an electronic term . the latter can be expressed through the wannier functions and is reduced to the ionic polarization only if the wannier functions are fully localized at the atomic sites . in this sense , the deviation from the ionic picture is a measure of itineracy of the system . moreover , unlike the ionic contribution , the electronic polarization can be finite even in the centrosymmetric crystal structure , provided that the inversion symmetry is broken by a magnetic order . thus , the berry - phase theory excellently suits for improper ferroelectrics . the first - principles calculations show that the electronic polarization can be as large as or even exceed the ionic contribution.@xcite nevertheless , the physical meaning of this effect is still rather obscure and the electronic polarization is largely ignored in model calculations of multiferroic manganites . the purpose of this work is to make a bridge between first - principle electronic structure calculations and models of the fe polarization . our main message is that the electronic polarization is important and can not be ignored . in the model calculations , it can be described by some `` superexchange type '' theories , similar to interatomic magnetic interactions.@xcite on the other hand , in the first - principles calculations , one should pay a special attention to the relative direction of the electronic and ionic polarization : because of additional approximations , results of theoretical structural optimization do not necessarily guarantee the correct answer to this question . our analysis will be based on results of two previous works ( refs .  ) , where    * a realistic low - energy model for the mn @xmath6 bands of manganites was constructed on the basis of first - principles electronic structure calculations in the local - density approximation ( lda ) ; * this model was applied for the search of the magnetic ground state of orthorhombic manganites ; * the model calculations were supplemented with the berry - phase theory for the analysis of the fe polarization and its dependence on the form of the magnetic ground state .    in this work we will further rationalize the story . first , we will show that the behavior of the fe polarization can be well described in the framework of the double exchange ( de ) theory.@xcite the definition of the de hamiltonian will be given in sec . [ sec : idea ] . particularly , we will show that with the proper definition of the de model , which should include effects of orbital polarization of coulombic origin , one can reproduce , even quantitatively , the values of fe polarization obtained in a more general mean - field hartree - fock ( hf ) calculations for the low - energy model . then , we will introduce an analytically solvable model for the @xmath2 electrons in the single zigzag chain ( sec . [ subsec : analytics ] ) and argue that , besides double exchange , the behavior of electronic polarization in realistic manganites always corresponds to the limit of large intra - atomic energy splitting @xmath5 between @xmath2 states ( sec .  [ subsec : parameters ] ) . it will allow us to further generalize our story and derive an analytical expression for the electronic polarization in an arbitrary twofold periodic magnetic texture , based on the perturbation theory expansion for the wannier functions in the first order of @xmath7 ( sec . [ subsec:5orbitals ] ) . the idea itself has some similarities with the superexchange theory of interatomic magnetic interactions.@xcite this analytical expression nicely explains the behavior of electronic polarization in the low - energy model as well as in the more general first - principles calculations . it also provides a good quantitative estimate for the polarization . in sec . [ subsec : problems ] , we will present a critical analysis of relative directions of electronic and ionic polarizations in the experimental and theoretically optimized @xmath1 structures of ymno@xmath14 . then , in sec . [ subsec : switching ] , we will explain how the electronic polarization can be manipulated by changing the magnetic texture . finally , in sec . [ sec : summary ] , we draw our conclusions .","summary":"we argue that many aspects of improper ferroelectric activity in manganites with the and orthorhombic structure can be rationalized by considering the limit of infinite intra - atomic splitting between the majority- and minority - spin states ( or the double exchange limit ) , which reduces the problem to the analysis of a spinless double exchange ( de ) hamiltonian . we apply this strategy to the low - energy model , derived from the first - principles electronic structure calculations , and combine it with the berry - phase theory of electric polarization . this property holds for all considered compounds even in the local - density approximation , which typically underestimates . we further utilize this property in order to derive an analytical expression for in a general two - fold periodic magnetic texture , based on the five - orbital model and the perturbation - theory expansion for the wannier functions in the first order of .","abstract":"we argue that many aspects of improper ferroelectric activity in manganites with the and orthorhombic structure can be rationalized by considering the limit of infinite intra - atomic splitting between the majority- and minority - spin states ( or the double exchange limit ) , which reduces the problem to the analysis of a spinless double exchange ( de ) hamiltonian . we apply this strategy to the low - energy model , derived from the first - principles electronic structure calculations , and combine it with the berry - phase theory of electric polarization . we start with the simplest two - orbital model , describing the behavior of the bands , and apply it to the-type antiferromagnetic ( afm ) phase , which in the de limit effectively breaks up into one - dimensional zigzag chains . we derive an analytical expression for the electronic polarization ( ) and explain how it depends on the orbital ordering and the energy splitting between states . then , we evaluate parameters of this model for the series of manganites . for these purposes we start from a more general five - orbital model for all mn bands and construct a new downfolded model for the bands . from the analysis of these parameters , we conclude that the behavior of in realistic manganites always corresponds to the limit of large . this property holds for all considered compounds even in the local - density approximation , which typically underestimates . we further utilize this property in order to derive an analytical expression for in a general two - fold periodic magnetic texture , based on the five - orbital model and the perturbation - theory expansion for the wannier functions in the first order of . this expression explains the functional dependence of on the relative directions of spins . furthermore , it suggests that is related to the asymmetry of the transfer integrals , which should simultaneously have symmetric and antisymmetric components . finally , we explain how the polarization can be switched between orthorhombic directions and by inverting the zigzag afm texture in every second plane . we argue that this property is generic and can be realized even in the twofold periodic texture ."}
{"article_id":"1303.2884","section_id":"r","document":"we start with the analysis of the @xmath3-type afm phase . as was pointed out above , in the de limit , the fe afm @xmath3-phase breaks up into one - dimensional fm zigzag chains . therefore , the key moment for understanding the origin of the fe activity in the @xmath3-phase is the analysis of isolated zigzag chain.@xcite in sec . [ subsec : analytics ] , we start such an analysis with the simplest but analytically solvable model for the @xmath2 electrons . in sec .  [ subsec : parameters ] we will derive parameters of such a model , starting from a more general five - orbital model , which was obtained from the first - principles calculations.@xcite from the analysis of this model we will conclude that the situation , realized in most of the electronic structure calculations ( even in ordinary lda ) , corresponds to the limit of large energy splitting @xmath5 between atomic @xmath2 states , which incorporates the effects of the jt distortion and ( optionally ) the on - site coulomb repulsion . then , by considering the large-@xmath5 limit , in sec . [ subsec:5orbitals ] we will derive an analytical expression for the fe polarization , which is based on the five - orbital model . this expression explains the functional dependence of @xmath4 on the relative directions of spins and the form of nearest - neighbor transfer integrals . in sec . [ subsec : problems ] we will analyze relative directions of electronic and ionic polarizations in the noncentrosymmetric @xmath1 structure and point out on the problem of structural optimization , which apparently exists in some of the first - principles calculations , where the directions of noncentrosymmetric atomic displacements are inconsistent with the type of the orbital ordering , realized in the fm zigzag chain . in sec . [ subsec : switching ] , we discuss the possibility of switching the fe polarization by changing the magnetic texture : we argue that , even in the twofold periodic texture , there is another type of the afm zigzag ordering , which leads to a finite fe polarization along the orthorhombic @xmath9 axis . however , the value of this polarization is expected to be small . the zigzag chain consists of the two groups of sites : the lower corner sites @xmath11 and the upper corner sites @xmath97 ( see fig . [ fig.modelchain ] ) . ( color online ) geometry of the zigzag chain for the square lattice and the occupied @xmath2 orbitals of the @xmath105@xmath31@xmath32 and @xmath106@xmath31@xmath32 type . cubic and orthorhombic axes are denoted as @xmath107 and @xmath10 , respectively . , height=188 ]    the orthorhombic translation @xmath8 transforms each group to itself ( the translated sites are denoted as @xmath108 and @xmath109 , respectively ) . it is assumed that the lattice distortion stabilizes some @xmath2 orbitals at the sites @xmath11 and @xmath97 , which will be denoted as @xmath110 and @xmath111 , respectively . the orthogonal to them @xmath2 orbitals are denoted as @xmath112 and @xmath113 , respectively . furthermore , it is assumed that there is a symmetry operation ( @xmath114 ) , which transforms the zigzag chain to itself and which consists of the @xmath103 rotation around the @xmath8 axis ( @xmath115 ) with consequent translation . @xmath114 will transform site @xmath11 to site @xmath97 , and vice versa . for the @xmath0 structure ( and with some appropriate choice of the origin ) , such symmetry operation is @xmath116@xmath95@xmath117 ( where the first part stands for the rotation , and the second part specifies the translation ) while for the @xmath1 structure , it is @xmath116@xmath95@xmath118 . it is important that both symmetry operations include the translation @xmath119 . then , it is convenient to work in the local basis , corresponding to the diagonal presentation of the @xmath2 level splitting , such that @xmath114 would transform the basis functions of the site @xmath11 to the ones of the site @xmath97 , and vice versa . our idea is that , although we have two different sites , with such choice of the basis functions , the hamiltonian becomes periodic with the period @xmath119 and the problem can be treated as if it would have only one site in the primitive cell . similar idea was used for the analysis of the ce afm state in the half - doped manganites.@xcite rather generally , these basis functions can be chosen in the form : latexmath:[\\ ] ] where @xmath245 is proportional to the sum of squares of the transfer integrals from the unoccupied orbital 5 at the site @xmath246 to the occupied orbitals @xmath11-@xmath98 at the site @xmath247 : @xmath262/\\delta^2 $ ] . these transfer integrals should be calculated in the ` crystal - field representation ' , that diagonalizes the site - diagonal part of the one - electron hamiltonian . the parameter @xmath5 is understood as the energy difference between the unoccupied orbital @xmath61 and the center of gravity of occupied orbitals 1 - 4 ( see fig . [ fig.cf ] ) . splitting of @xmath6 levels for the experimental @xmath0 phase of ymno@xmath14 . the values , obtained using bare lda parameters of the low - energy model are denoted as ` lda ' , and the ones obtained after adding the hartree - fock potential are denoted as ` @xmath95@xmath70 ' . @xmath5 is the energy splitting between the unoccupied orbital @xmath61 and the center of gravity of occupied orbitals @xmath11-@xmath98.,height=302 ]    thus , in this analysis , we neglect the splitting between the occupied orbitals , which is smaller than @xmath5 . then , in the @xmath0 structure , each mn site is located in the inversion center . therefore , @xmath245 in the bonds @xmath96-@xmath254 and @xmath96-@xmath97 ( as well as @xmath96-@xmath109 and @xmath96-@xmath98 ) are equivalent , and eq .  ( [ eqn : p31 ] ) can be further transformed to @xmath263 . \\label{eqn : p32}\\ ] ] similar analysis can be performed for another mn site in the primitive cell ( say , site @xmath254 in fig . [ fig.2dtexture ] ) . moreover , since the sites @xmath96 and @xmath254 are connected by the symmetry operation @xmath248@xmath95@xmath117 , using eq . ( [ eqn : p32 ] ) , one can immediately obtain that @xmath264.\\ ] ] then , the total polarization @xmath265@xmath95@xmath266 can be evaluated as @xmath267 \\boldsymbol{a}.\\ ] ] here , @xmath42 is the primitive cell volume , containing four mn sites ( two in each of the @xmath10 planes , located at @xmath87@xmath21 @xmath94 and @xmath268 , which is reflected in the additional prefactor @xmath97 in the above expression ) . finally , by applying the symmetry operation @xmath248@xmath95@xmath117 , the sites @xmath96 and @xmath98 can be transformed to the sites @xmath254 and @xmath96 , respectively . thus , @xmath4 can be expressed through the transfer integrals in only one nearest - neighbor ( nn ) bond @xmath96-@xmath254 ( or in any equivalent to it bond ) : @xmath269 where @xmath270 \\boldsymbol{a } \\label{eqn : pe}\\ ] ] is the electronic polarization in the @xmath3-type afm state . for an arbitrary direction of spin at the site @xmath11 , the angular dependence @xmath271 in eq . ( [ eqn : ptotal ] ) should be replaced by a more general expressions @xmath272 . ( [ eqn : ptotal ] ) and ( [ eqn : pe ] ) allow us to rationalize many aspects of the multiferroic activity in manganites with the twofold periodic magnetic texture , namely :    * @xmath4 is parallel to the orthorhombic @xmath8 axis ; * if @xmath273@xmath95@xmath274 , @xmath4 is proportional to @xmath275 , which nicely explains the functional dependence of @xmath276 in fig . [ fig.ecanting](b ) and in the first - principles calculations for the same magnetic geometry ( ref .  ) ; * @xmath4 vanishes in the homogeneous spin - spiral state ( @xmath277 and @xmath278 ) . this is a very natural result from the viewpoint of the de physics : in the spin - spiral texture , all @xmath279 are the same . therefore , all bonds remain equivalent , and the inversion symmetry of the de hamiltonian is not broken ; * since @xmath280 , @xmath281 can be also presented in the form @xmath282 where @xmath283 is the scalar product of the 4-dimensional vectors @xmath284 , constructed from symmetric ( @xmath95 ) and antisymmetric ( @xmath31 ) parts of the transfer integrals : @xmath285@xmath182@xmath286 . thus , in order to have finite @xmath4 , the matrix of transfer integrals should have both symmetric and antisymmetric components . let us evaluate @xmath287 , using eq . ( [ eqn : ptotale ] ) , for the experimental @xmath0 phase of ymno@xmath14 . in this case , the unit cell volume is @xmath288 @xmath289 and the orthorhombic lattice parameter is @xmath290 .@xcite then , for the bare lda band structure , we have : @xmath291 ev ( see fig .  [ fig.cf ] ) , @xmath292@xmath293 mev , and @xmath294@xmath295@xmath296@xmath297 mev ( all parameters of the low - energy model for ymno@xmath14 can be found in supplemental material of ref .  ) . by substituting all these values in eq . ( [ eqn : ptotale ] ) , we obtain @xmath298@xmath299 @xmath12c/@xmath13 , which agrees very well with the value of @xmath31@xmath300 @xmath12c/@xmath13 , obtained directly from the berry - phase formula [ eq . ( [ eqn : pksv ] ) ] , without additional approximations ( apart from the de limit ) . for the more realistic case , including the effect of the hf potential , we have : @xmath301 ev , @xmath302@xmath303 mev , and @xmath304@xmath305@xmath306 mev . then , eq .  ( [ eqn : ptotale ] ) yields @xmath298@xmath307 @xmath12c/@xmath13 , which is again consistent with the value of @xmath31@xmath308 @xmath12c/@xmath13 , obtained directly from the berry phase formula [ eq . ( [ eqn : pksv ] ) ] . moreover , the values of the scalar product @xmath283 appear to be very close when they are calculated with and without the hf potential : @xmath31@xmath309 and @xmath31@xmath310 ev@xmath311 , respectively . this result is very natural because the form of the crystal - field orbitals in orthorhombic manganites is mainly controlled by the jt distortion : the latter is large and thus ` decides ' which orbitals will be occupied and which will not . on the other hand , the effect of on - site coulomb interactions , being inversely proportional to @xmath70,@xcite is considerably smaller . thus , although the coulomb interactions contribute to the splitting between occupied and empty states ( see fig . [ fig.cf ] ) , they practically do not change the subspace of occupied orbitals . therefore , the construction @xmath283 , which is evaluated in the crystal - field representation , will not strongly depend on whether it is calculated with or without the hf potential . in such a situation , the absolute value of @xmath199 will be mainly controlled by the parameter @xmath5 in the denominator of eq . ( [ eqn : ptotale ] ) . furthermore , @xmath5 can be presented in the form : @xmath312 , where @xmath313 and @xmath314 take into account the effects of the bare jt distortion and the on - site coulomb interactions , respectively . in the example considered above , @xmath313 is the lda level splitting and @xmath314 is the additional splitting , caused by the hf potential ( see fig . [ fig.cf ] ) . then , if @xmath315 is the fe polarization in lda , the effect of on - site coulomb interactions on @xmath199 can be evaluated using the following scaling relation : @xmath316 which was observed in many lda@xmath95@xmath70 calculations , treating the on - site coulomb repulsion @xmath70 as an adjustable parameter.@xcite    finally , it is instructive to evaluate @xmath317 for the noncollinear magnetic ground state of ymno@xmath14 using eq . ( [ eqn : ptotal ] ) . this magnetic ground state was obtained in ref .   by solving mean - field hf equations with the relativistic so interaction . for the @xmath0 phase of ymno@xmath14 , it yields @xmath318 and @xmath319 . then , using the value @xmath298@xmath308 @xmath12c/@xmath13 , obtained in the de limit ( see fig .  [ fig.ecanting ] ) , @xmath320 can be estimated as @xmath31@xmath321 @xmath12c/@xmath13 , which is consistent reasonably well with @xmath322@xmath323 @xmath12c/@xmath13 , obtained for the noncollinear magnetic ground state of ymno@xmath14 without additional approximations.@xcite in fact , the main discrepancy is caused by the de limit for @xmath199 . for example , if one uses @xmath298@xmath324 @xmath12c/@xmath13 , obtained without the de approximation,@xcite and the angular dependence of @xmath4 , given by eq . ( [ eqn : ptotal ] ) , @xmath320 can be estimated as @xmath31@xmath325 @xmath12c/@xmath13 , which is much closer to @xmath322@xmath323 @xmath12c/@xmath13 . so far , we considered only electronic polarization , which was induced by the orbital ordering in the fm zigzag chains . in this section , we will discuss how this electronic part is related to the ionic polarization in the noncentrosymmetric @xmath1 structure . moreover , we will elucidate the microscopic origin of the `` order of magnitude difference '' , which typically exists between experimental and theoretical values of the fe polarization , reported for the orthorhombic manganites with twofold periodic magnetic texture . the problem is formulated as follows . the great advantage of the first - principles calculations is that they allow us to perform the structural optimization and to find theoretically the atomic displacements , which are caused by the exchange - striction effects in the @xmath3-type afm phase . if one does such structural optimization for the orthorhombic manganites and subsequently calculates the fe polarization , the latter will be of the order of several @xmath12c/@xmath13.@xcite the conclusion is rather generic and was obtained for several popular types of the exchange - correlation functionals , such as lsda ( ref .  ) , generalized gradient approximation ( gga , refs .  ) , and lda(gga)@xmath95@xmath70 ( refs .  ) . the experimental polarization is typically smaller than @xmath326 @xmath12c/@xmath13.@xcite on the other hand , if one takes the experimental @xmath1 structure and calculates the fe polarization , it will be at least of the same order of magnitude as the experimental one.@xcite the reason of such discrepancy is that , in the experimental @xmath1 structure , there is a large cancelation of electronic and ionic contributions to the fe polarization , while in the theoretically optimized structure , these two contributions have the same sign and the cancelation does not occur.@xcite    in this section , we will further clarify the situation . in orthorhombic manganites , there are three types of atomic displacements , which control the fe polarization :    * the jahn - teller distortion , which gives rise to the orbital ordering ; * the exchange striction , which specifies the type of the ordering in the fm zigzag chain and , therefore , the sign of the electronic polarization . note , that in the cenrosymmetric @xmath0 structure , the fm chains with the @xmath105@xmath31@xmath32/@xmath106@xmath31@xmath32 and @xmath106@xmath31@xmath32/@xmath105@xmath31@xmath32 type of the orbital ordering are equivalent as they build two degenerate magnetic states . this degeneracy is lifted in the @xmath1 phase by the exchange striction effects , which pick up only one type of the fm zigzag chains ( characterized by larger mn - mn distances ) . as soon as the fm chains are selected , the type of the orbital ordering is fixed , so as the sign of the electronic polarization . * the fe atomic displacements , which occur in response to the magnetic inversion symmetry breaking and control the sign of the ionic polarization . the goal of this section is to understand how these three types of the lattice distortions correlate with each other in the experimental and theoretically optimized @xmath1 structures of ymno@xmath14 . let us consider the ionic polarization and concentrate on the behavior of the oxygen sites , which are located in the @xmath10 plane and give the largest contribution to @xmath327.@xcite in principles , one can consider the contributions of other atomic sites , which do not alter the conclusions . then , @xmath327 can be presented in the following form : @xmath328 where @xmath40 are the atomic charges and @xmath39 are the atomic displacements away from the centrosymmetric positions . moreover , it is understood that around each mn site in the primitive cell , the summation runs over four oxygen sites , located in the nearest neighborhood of mn . since each oxygen is shared by two mn atoms , this leads to the additional prefactor @xmath329 . there are many possibilities for choosing the centrosymmetric reference point for evaluation of @xmath39 . the final result should not depend on this choice . for our purposes , it is convenient to choose @xmath330@xmath31@xmath331 ( in the other words , we assume that in the centrosymmetric structure , all oxygen sites `` fall '' on the central mn site ) . this can be done because mn sites do not contribute to the fe polarization of the ionic type along the orthorhombic @xmath8 axis.@xcite the reason is that , apart from a constant shift , the projections of mn sites onto the @xmath8 axis are either @xmath94 or @xmath208 ( modulo the lattice translation @xmath236 ) and , therefore , can be transformed to each other by the reflection @xmath332@xmath236 . the mn sites do contribute to the ionic polarization in the @xmath333 plane . however , all these contributions have antiferroelectric character and cancel out after summation over the primitive cell . thus , around each mn site , the evaluation of @xmath327 is reduced to the summation of @xmath39 over neighboring mn - o bonds with the perfactors given by eq . ( [ eqn : ionicp ] ) . such a construction is very convenient , because in the centrosymmetric @xmath0 structure , each mn site is located in the inversion center . therefore , the sum of @xmath39 over all neighboring mn - o bonds will be equal to zero . in the @xmath1 structure , however , such a construction will give us a finite vector , which can serve as a measure of noncentrosymmetric atomic displacements around each mn site . for our purposes , only the fe ( @xmath8 ) components of these vectors are important , while the @xmath221 and @xmath9 components are antiferroelectric and will cancel each other . using this construction and taking the ionic value @xmath54@xmath334 , the contribution of the planar oxygen sites to @xmath335 in the experimental @xmath1 structure can be estimated as @xmath336 @xmath12c/@xmath13 , which is totally consistent with the previous finding.@xcite    the distributions of such vectors , obtained for the experimental and theoretical structures of ymno@xmath14 , are shown in figs . [ fig.problems](a ) and [ fig.problems](c ) , respectively . ( color online ) directions of ionic contributions to the polarization , caused by ferroelectric displacements of oxygen atoms around each mn site in the @xmath10 plane of noncentrosymmetric @xmath1 phase of ymno@xmath14 ( a and c ) , and the orbital ordering , realized in the ferromagnetic zigzag chain ( b and d ) , as obtained for the experimental ( a and b ) and theoretically optimized structure ( c and d).,title=\"fig:\",height=188 ]   ( color online ) directions of ionic contributions to the polarization , caused by ferroelectric displacements of oxygen atoms around each mn site in the @xmath10 plane of noncentrosymmetric @xmath1 phase of ymno@xmath14 ( a and c ) , and the orbital ordering , realized in the ferromagnetic zigzag chain ( b and d ) , as obtained for the experimental ( a and b ) and theoretically optimized structure ( c and d).,title=\"fig:\",height=188 ]    as for the theoretically optimized structure , we use results of lda@xmath95@xmath70 calculations with @xmath70@xmath21 @xmath222 ev ( see ref .  ) . nevertheless , we would like to emphasize that very similar results were obtained in lsda and lda@xmath95@xmath70 with @xmath70@xmath21 @xmath219 ev.@xcite as is seen in fig . [ fig.problems ] , the fe displacements have the same direction in the experimental and theoretically optimized @xmath1 structure of ymno@xmath14 . this direction corresponds to the positive value of @xmath335 . corresponding orbital ordering , realized in the fm chains , is shown in figs . [ fig.problems](b ) and [ fig.problems](d ) , for the experimental and theoretical structure , respectively . for the experimental @xmath1 structure , the orbital ordering is of the @xmath105@xmath31@xmath32/@xmath106@xmath31@xmath32 type . therefore , the electronic polarization is negative , and there is a partial cancelation of the electronic and ionic terms , which explains a relatively small value of the experimental polarization.@xcite however , the theoretical optimization of the crystal structures , performed both in lsda and lda@xmath95@xmath70 , yields different type of the orbital ordering : @xmath106@xmath31@xmath32/@xmath105@xmath31@xmath32 instead of @xmath105@xmath31@xmath32/@xmath106@xmath31@xmath32 . therefore , the electronic polarization will be positive , and the cancelation does not occur . thus , the directions of fe displacements , obtained in lsda and lda@xmath95@xmath70 , are inconsistent with the type of the orbital ordering , realized in the fm zigzag chains . this seems to be a serious problem of the first - principles calculations and at the present stage it is not clear how it should be solved . on the computational side , many attention recently is paid to the screened hybrid functionals ( see , e.g. , ref .  ) . therefore , it would be interesting to see how these functionals will work for the structural optimization in multiferroic compounds , where the inversion symmetry is broken by the magnetic degrees of freedom . the first applications for homno@xmath14 seem to show that the problem persists : although the electronic polarization is decreased , mainly due to the increase of the on - site level splitting , it has the same sign as the ionic one and the total polarization is overestimated in comparison with the experiment.@xcite on the other hand , the directions of fe displacements can be controlled by the relativistic so interaction , which is typically ignored in the process of structural optimization . this point of view was proposed , for example , in ref .  . what is interesting about the multiferroic systems is that the value and the direction of the fe polarization depend on the magnetic texture and , by changing this texture , one can also change the vector of polarization . in this section , we will discuss how such a behavior can be realized in the twofold periodic magnetic texture . again , let us consider the centrosymmetric @xmath0 structure and assume that the inversion symmetry is broken exclusively by the magnetic order . in such a case , most of attention is focused on the @xmath3-type afm phase ( fig .  [ fig.ecanting ] ) , which breaks the inversion symmetry but preserves the symmetry operation @xmath116@xmath95@xmath117 . therefore , the fe polarization will be parallel to the @xmath8 axis . now , the question is whether there are other types of the magnetic texture , which would break the inversion symmetry . as an example , let us consider the magnetic texture in fig . [ fig.iecanting](a ) . ( color online ) ( a ) antiferromagnetic texture yielding finite ferroelectric polarization along the @xmath9 axis . ( b ) behavior of electronic polarization in ymno@xmath14 upon rotation of magnetic moments , as obtained in the double exchange model with the hartree - fock potential @xmath76 ( de @xmath95@xmath70 ) . in the rotated texture , the directions of spins at the sites @xmath11 and @xmath96 were fixed , while the spins at the sites @xmath97 and @xmath98 were rotated by the angle @xmath99 , as explained in panel ( c ) . the interlayer coupling was kept afm for the sites @xmath11 and @xmath96 and fm for the sites @xmath97 and @xmath98 . , height=377 ]    in the plane @xmath100 , it is identical to the @xmath3-type afm order , and can be transformed to itself by applying the symmetry operation @xmath116@xmath95@xmath117 around even magnetic sites @xmath97 and @xmath98 . alternatively , one can apply the symmetry operation @xmath337@xmath119@xmath31@xmath117 around odd magnetic sites @xmath11 and @xmath96 . in the @xmath3-phase , the same symmetry operations can be applied in the planes @xmath338@xmath268 and also will transform the plane @xmath339 to the equivalent to it plane @xmath340@xmath268 . the magnetic texture in fig . [ fig.iecanting](a ) is obtained by the additional inversion around odd magnetic sites in the plane @xmath339 , which interchanges the symmetry operations @xmath116@xmath95@xmath117 and @xmath337@xmath119@xmath31@xmath117 . thus , the plane @xmath339 can be transformed to itself by the symmetry operation @xmath116@xmath95@xmath117 around odd sites or by @xmath337@xmath119@xmath31@xmath117 around even sites . therefore , the symmetry operations @xmath116@xmath95@xmath117 and @xmath337@xmath119@xmath31@xmath117 , although preserved locally in each of the plane , are broken globally , because they can not simultaneously transform the planes @xmath341 and @xmath338@xmath268 to themselves .    instead , the magnetic texture in fig . [ fig.iecanting](a ) obeys the symmetry operation @xmath342 , which is another symmetry operation of the space group @xmath0 . therefore , the fe polarization in this phase will be parallel to the @xmath9 axis . according to the above arguments , each plane may carry a finite polarization parallel to the @xmath8 axis . however , since neighboring planes are connected by the symmetry operation @xmath342 , the contributions from different planes will cancel each other . the behavior of @xmath343 , obtained in the de model for ymno@xmath14 , is explained in fig . [ fig.iecanting](b ) . here , we again consider a continuous rotation of spins between two kinds of the afm domains via an intermediate spin - spiral phase , as explained in fig . [ fig.iecanting](c ) . in comparison with fig . [ fig.ecanting ] , the planes @xmath344 and @xmath345 are connected by the fm pathes between even magnetic sites . @xmath343 appears to be about two orders of magnitude weaker than @xmath346 in the @xmath3-phase ( fig .  [ fig.ecanting ] ) nevertheless , this result is very natural and can be easily understood by considering the perturbation theory arguments , similar to the ones in sec . [ subsec:5orbitals ] . namely , in order to obtain @xmath343 , we should consider the transfer integrals @xmath347 between all possible combinations of sites @xmath246 and @xmath247 along the @xmath9 axis . of course , the main contribution is expected from the nn sites . moreover , according to eq . ( [ eqn : ptotale ] ) , in order to contribute to @xmath343 , these transfer integrals should have both symmetric and antisymmetric components . however , due to the combination of @xmath342 and the inversion symmetry around the mn sites , the nn integrals between the planes @xmath344 and @xmath345 will satisfy the following property : @xmath348 , where the matrix transformation @xmath349 , corresponding to the @xmath103 rotation around the @xmath9 axis , changes the sign of some of the matrix elements of @xmath16 . therefore , in the crystal - field representation , one can always choose the phases of the basis orbitals such that the corresponding matrix of the transfer integrals @xmath347 would become totally symmetric . thus , the nn contributions to @xmath343 in the second order of @xmath7 will vanish , and @xmath343 has finite value due to either next - nn integrals , which are small ( all transfer integrals for ymno@xmath14 can be found in the supplemental material of ref .  ) or the higher - order effects with respect to @xmath7 , which are also small . this naturally explains the fact that @xmath343 is much smaller than @xmath346 . this finding resembles the behavior of multiferroic manganites with nearly fourfold periodic magnetic texture , for which the possibility of switching the electric polarization was demonstrated experimentally.@xcite for example , in tbmno@xmath14 the polarization is aligned along the orthorhombic @xmath9 axis . however , the external magnetic field applied along the @xmath221 axis will change the magnetic texture and align the polarization parallel to the @xmath8 axis.@xcite moreover , most of experimental data also confirm the fact that @xmath343 is smaller than @xmath346 . for example , such a behavior is typical for the eu@xmath350y@xmath351mno@xmath14 compounds , containing only nonmagnetic rare - earth elements , that excludes the influence of the @xmath352 magnetism on the fe polarization.@xcite the results of this section suggest that this behavior is more generic and can be anticipated in other regimes , including the twofold periodic magnetic systems . the origin of this phenomenon is related to the specific symmetry of the crystal structure ( in the case of orthorhombic manganites  the @xmath0 symmetry ) and how it is lowered by the magnetic ordering in the de limit . it should not be confused with the spin - spiral alignment , which does break the inversion symmetry of the de hamiltonian ( see sec .  [ subsec:5orbitals ] ) . in is interesting to note that the magnetic texture depicted in fig . [ fig.iecanting ] can be viewed as a `` defected @xmath3-type afm texture '' , where the `` defects '' are two fm bonds between the planes @xmath344 and @xmath345 . of course , such `` defects '' are energetically unfavorable and , after including the so interaction , this magnetic texture will change in order to minimize the fm coupling in the defected bonds . this will lead to the substantial deformation of the magnetic texture in fig . [ fig.iecanting](a ) . nevertheless , we would like to emphasize that the noncollinear magnetic texture with @xmath343 can be stabilized even after including the so interaction . the situation was discussed in ref .  .","summary":"we start with the simplest two - orbital model , describing the behavior of the bands , and apply it to the-type antiferromagnetic ( afm ) phase , which in the de limit effectively breaks up into one - dimensional zigzag chains . we derive an analytical expression for the electronic polarization ( ) and explain how it depends on the orbital ordering and the energy splitting between states . then , we evaluate parameters of this model for the series of manganites . for these purposes we start from a more general five - orbital model for all mn bands and construct a new downfolded model for the bands . from the analysis of these parameters , we conclude that the behavior of in realistic manganites always corresponds to the limit of large . this expression explains the functional dependence of on the relative directions of spins . we argue that this property is generic and can be realized even in the twofold periodic texture .","abstract":"we argue that many aspects of improper ferroelectric activity in manganites with the and orthorhombic structure can be rationalized by considering the limit of infinite intra - atomic splitting between the majority- and minority - spin states ( or the double exchange limit ) , which reduces the problem to the analysis of a spinless double exchange ( de ) hamiltonian . we apply this strategy to the low - energy model , derived from the first - principles electronic structure calculations , and combine it with the berry - phase theory of electric polarization . we start with the simplest two - orbital model , describing the behavior of the bands , and apply it to the-type antiferromagnetic ( afm ) phase , which in the de limit effectively breaks up into one - dimensional zigzag chains . we derive an analytical expression for the electronic polarization ( ) and explain how it depends on the orbital ordering and the energy splitting between states . then , we evaluate parameters of this model for the series of manganites . for these purposes we start from a more general five - orbital model for all mn bands and construct a new downfolded model for the bands . from the analysis of these parameters , we conclude that the behavior of in realistic manganites always corresponds to the limit of large . this property holds for all considered compounds even in the local - density approximation , which typically underestimates . we further utilize this property in order to derive an analytical expression for in a general two - fold periodic magnetic texture , based on the five - orbital model and the perturbation - theory expansion for the wannier functions in the first order of . this expression explains the functional dependence of on the relative directions of spins . furthermore , it suggests that is related to the asymmetry of the transfer integrals , which should simultaneously have symmetric and antisymmetric components . finally , we explain how the polarization can be switched between orthorhombic directions and by inverting the zigzag afm texture in every second plane . we argue that this property is generic and can be realized even in the twofold periodic texture ."}
{"article_id":"1303.2884","section_id":"i","document":"this work is a continuation of previous studies , devoted to multiferroic manganites , which crystallize in the orthorhombic @xmath0 and @xmath1 structure.@xcite our main motivation was to present a transparent physical picture , which would explain why and how the ferroelectric polarization is induced by some complex magnetic order . for these purposes we invoke the double exchange theory , which was formulated for the low - energy model , derived from the first - principles electronic structure calculations . as far as the polarization is concerned , the de theory is very robust and reproduces results of more general mean - field hartree - fock calculations at a good quantitative level . furthermore , the main advantage of the de theory is that it allows us to greatly simplify the problem and , in a number of cases , derive an analytical expression for the fe polarization . thus , we could clarify very basic aspects of the fe activity in manganites with twofold periodic magnetic texture .    in our analysis we started from the general berry - phase theory.@xcite in the case of improper ferroelectrics , the basic quantity to be considered is the electronic polarization , which incorporates the change of the electronic structure in response to the noncentrosymmetric alignment of spins . then , our main message is that , for the analysis of electronic polarization in realistic manganites , one can always use two physical limits . the first one is the limit of large intra - atomic splitting @xmath67 between the majority- and minority - spin states . the second one is the limit of large intra - atomic splitting @xmath5 between the majority - spin @xmath2 states . therefore , for the electronic polarization , one can always consider the perturbation theory expansion with respect to both @xmath353 and @xmath7 . this perturbation theory describes asymmetric transfer of some weight of the wannier functions to the neighboring sites , which gives rise to the polarization . there is some similarity with the theory of superexchange interactions , which deals with the virtual hoppings,@xcite and where the terms proportional to @xmath7 and @xmath353 account for the fm and afm contributions , respectively.@xcite therefore , the de limit @xmath67@xmath177@xmath178 would correspond to neglecting all afm contributions . it may not be a good approximation for interatomic magnetic interactions . nevertheless , the main difference for the electronic polarization is that it appears only in the second order with respect to @xmath7 and @xmath353 . the physically relevant picture corresponds to the situation where @xmath354 . then , due to the inequality @xmath355 , it is logical to keep the effects of the first order of @xmath353 in the analysis of superexchange interactions , but neglect the effects of the second order of @xmath353 in the analysis of electronic polarization . this again justifies the use of the de limit in the latter case . on the basis of this perturbation theory expansion , we were able to explain how the electronic polarization depends on the relative directions of spins in an arbitrary twofold periodic magnetic texture . particularly , the multiferroic effect in orthorhombic manganites is a nonlocal phenomenon in the sense that the inversion symmetry is broken by making some of the mn - mn bonds magnetically inequivalent . in the de model , this inequivalence is achieved by the additional modulation of transfer integrals by @xmath90 . then , one trivial conclusion is that there will be no magnetic inversion symmetry breaking in the spin - spiral phase , where all @xmath90 are the same . therefore , in order to make finite polarization , it is essential to deform the spin spiral . in orthorhombic manganites , such deformation is caused by the relativistic spin - orbit interaction.@xcite the second important precondition for the fe activity is the asymmetry of the transfer integrals , which should simultaneously have symmetric and antisymmetric components . we also pointed out on a serious problem in the structural optimization , which apparently exists in the first - principles calculations ( at least at the level of lda@xmath95@xmath70 and gga@xmath95@xmath70 approximations for the exchange - correlation functional without relativistic spin - orbit coupling ) and which typically results in the large overestimation of the value of fe polarization in comparison with experimental data.@xcite in this work , we were able to clarify the origin of this problem : in the theoretical structure , the directions of noncentrosymmetric atomic displacements are inconsistent with the type of the orbital ordering in the ferromagnetic zigzag chains , which controls the sign of the electronic polarization . as the result , the electronic and ionic contributions have the same sign in the theoretically optimized structure , while , according to the experimental crystal structure , they should have opposite signs and partially cancel each other .    finally , we explained how the electronic polarization can be switched between orthorhombic @xmath8 and @xmath9 directions by inverting the magnetic texture in every second @xmath10 plane . we also expect a gigantic change of the absolute value of the polarization itself , which is related to very different symmetry properties of the nearest - neighbor transfer integrals along the @xmath9 direction and in the @xmath10 plane of manganites .    in this work , our analysis was limited by twofold periodic magnetic textures , which illustrate the basic idea of the double exchange theory of ferroelectric polarization . the idea can be extended to the systems with more general magnetic periodicity : apart from the additional complexity of the magnetic texture , there is no fundamental difference between twofold and more general magnetic periodicity . in both cases , the basic property , which should be considered and which gives rise to the ferroelectric activity is the alternation of angles between spins in different mn - mn bonds .                                  c. zener , phys . rev . * 82 * 440 ( 1951 ) ; p. w. anderson and h. hasegawa , phys . rev . * 100 * 675 ( 1955 ) ; p .- g . de gennes , phys . rev . * 118 * 141 ( 1960 ) ; k. kubo and n. ohata , j. phys . * 33 * 21 ( 1972 ) .                        for @xmath5@xmath21@xmath94 , the integral ( [ eqn : pfinal ] ) can be evaluated analytically : note that @xmath356 , and use that @xmath357 can be further transformed to @xmath358 after replacing @xmath359 by @xmath31@xmath359 .","summary":"furthermore , it suggests that is related to the asymmetry of the transfer integrals , which should simultaneously have symmetric and antisymmetric components . finally , we explain how the polarization can be switched between orthorhombic directions and by inverting the zigzag afm texture in every second plane .","abstract":"we argue that many aspects of improper ferroelectric activity in manganites with the and orthorhombic structure can be rationalized by considering the limit of infinite intra - atomic splitting between the majority- and minority - spin states ( or the double exchange limit ) , which reduces the problem to the analysis of a spinless double exchange ( de ) hamiltonian . we apply this strategy to the low - energy model , derived from the first - principles electronic structure calculations , and combine it with the berry - phase theory of electric polarization . we start with the simplest two - orbital model , describing the behavior of the bands , and apply it to the-type antiferromagnetic ( afm ) phase , which in the de limit effectively breaks up into one - dimensional zigzag chains . we derive an analytical expression for the electronic polarization ( ) and explain how it depends on the orbital ordering and the energy splitting between states . then , we evaluate parameters of this model for the series of manganites . for these purposes we start from a more general five - orbital model for all mn bands and construct a new downfolded model for the bands . from the analysis of these parameters , we conclude that the behavior of in realistic manganites always corresponds to the limit of large . this property holds for all considered compounds even in the local - density approximation , which typically underestimates . we further utilize this property in order to derive an analytical expression for in a general two - fold periodic magnetic texture , based on the five - orbital model and the perturbation - theory expansion for the wannier functions in the first order of . this expression explains the functional dependence of on the relative directions of spins . furthermore , it suggests that is related to the asymmetry of the transfer integrals , which should simultaneously have symmetric and antisymmetric components . finally , we explain how the polarization can be switched between orthorhombic directions and by inverting the zigzag afm texture in every second plane . we argue that this property is generic and can be realized even in the twofold periodic texture ."}
{"article_id":"cond-mat0308495","section_id":"i","document":"monte carlo ( mc ) simulations are powerful numerical tools for high - precision studies of many - body systems , both in the classical and quantum regime . especially near second - order phase transitions , where physical length scales diverge , it is essential to simulate large systems , which has become possible due to significant algorithmic advances within the last 15 years .    in classical simulations , conventional mc algorithms sample the canonical partition function by making local configurational updates . while being straightforward , this approach turns out to slow down simulations near phase transitions and gives rise to long autocorrelation times in the measurement of the relevant physical observables . for classical spin - like systems , this critical slowing down can be overcome using cluster algorithms  @xcite , which update large clusters of spins in a single mc step . the generalization of these non - local update schemes to the case of quantum monte carlo ( qmc ) simulations was initiated by the development of the loop algorithm in the world - line representation  @xcite . this very efficient method has been used in many studies , where it allowed the simulation of large systems at very low temperatures . in the original formulation ( either in discrete  @xcite or continuous  @xcite imaginary time ) , the loop algorithm however has a major drawback : to work efficiently , its application is restricted to specific parameter regimes . in the case of quantum spin models for example , it suffers from severe slowing down upon turning on a magnetic field  @xcite . this problem can be circumvented by performing cluster constructions in an extended configuration space , which includes world line configurations with two open world line fragments  @xcite , representing physical operators inserted into a mc configuration . the resulting worm algorithm  @xcite proceeds by first creating a pair of open world line fragments ( a worm ) . one of these fragments is then moved through space - time , using local metropolis or heat bath updates until the two ends of the worm meet again . this algorithm thus consists of only local updates of worm ends in the extended configuration space , but can perform non - local changes in the mc configurations . the cluster generation process of the worm algorithm allows for self intersections and backtracking of the worm , which might undo previous changes . while not being as efficient as the loop algorithm in cases with spin - inversion or particle - hole symmetry , the great advantage of the worm algorithm is that it remains efficient in an extended parameter regime , e.g. in the presence of a magnetic field for spin models  @xcite . an alternative qmc approach , which is not based upon the world - line representation , is the stochastic series expansion ( sse )  @xcite , a generalization of handscomb s algorithm @xcite for the heisenberg model . while in the original implementation  @xcite local mc updates were used , sandvik later developed a cluster update , called the operator - loop update for the sse representation  @xcite , which allows for non - local changes of mc configurations . within this sse approach one can efficiently simulate models for which the world line loop algorithm suffers from a slowing down . furthermore , loop algorithms are recovered in models with spin - inversion or particle hole symmetry  @xcite . in fact the two approaches , world - line and sse qmc are closely related  @xcite . recently , it has been realized that the rules used to construct the operator - loops in the original implementation  @xcite , were just one possible choice and that one can consider generalized rules , which give rise to more efficient algorithms  @xcite . this new approach led to the construction of the `` directed loop '' update scheme by syljusen and sandvik , first for spin-@xmath0 systems  @xcite . later it was adapted to general spin-@xmath1 models by harada and kawashima through a coarse - grained picture of the loop algorithm  @xcite . using a holstein - primakov transformation of the large spin-@xmath1 algorithm , a coarse - grained loop algorithm for softcore bosonic models was also developed  @xcite . the improvements achieved using the directed loop approach have been demonstrated in various recent studies  @xcite . for a recent review of non - local updates in qmc , see ref .  @xcite .    in this work , we show that the equations which determine the directed loop construction allow for additional weight factors , which were not considered by syljusen and sandvik  @xcite or used in  @xcite . we explain how these weight factors naturally arise from a formulation of the directed loop construction within the extended configuration space . instead of viewing the worm ends as link discontinuities  @xcite we consider them to represent physical operators with in general non - unity matrix elements  @xcite . taking these natural weight factors into account , and numerically optimizing solutions to the generalized directed loop equations , we are able to construct algorithms which display larger regions in parameter space where the worm propagation is bounce free , i.e. a worm never backtracks . this numerical approach allows for the implementation of directed loop algorithms in a generic qmc simulation code , which is not restricted to specific models . in particular , it provides directed loop algorithms for spin-@xmath1 and softcore boson systems directly using the numerical solution , without coarse graining , or using the split - spin representation and holstein - primakov transformation  @xcite .    performing simulations and calculating autocorrelation times of different observables , we find that minimizing bounces does not necessarily imply more efficient algorithms . in certain cases , the generalized directed loop algorithm presented in this paper has superior performances to the standard directed loop scheme , but in other cases it does not . we identify the non - uniqueness of bounce minimized solutions as the source of this observation : in the general case there are many solutions to the directed loop equations with minimal bounces , which however do not lead to the same performance of the algorithm .    to further improve the algorithm , we thus propose various _ additional _ strategies , which select out certain solutions in the subset of those which minimize bounces . these additional strategies can also be used in the standard directed loop approach . calculating again autocorrelation times with these different strategies , we indeed find that the efficiency can be further improved largely . however , we find that the specific strategy that gives rise to the best performances depends on the specific hamiltonian and on the observable of interest . the conclusion we reach from these results is that in most cases short simulations on small systems are needed in order to identify the optimal strategy before performing production runs .    throughout this work , we use the sse qmc scheme  @xcite in order to present our framework , since it appears to be the more natural approach to many problems . however , the ideas presented here can as well be implemented within the path integral approach  @xcite . the outline of the paper is as follows : we review in section  [ sec : sse ] the sse method and the operator - loop update scheme . then we introduce the generalized directed loop equations in in section  [ sec : dir.loops ] . in section  [ sec : num ] we show how to numerically solve these equations in order to obtain directed loop schemes with minimized bounces using linear programming techniques . in section  [ sec : phased ] we present algorithmic phase diagrams obtained within the framework proposed here , and compare them with those obtained using previous directed loop schemes . we discuss in section  [ sec : auto ] results on autocorrelation times obtained from the simulation of the magnetization process of various quantum spin chains . our results indicate , that minimizing bounces alone does not necessary lead to reduced autocorrelations of physical observables . we therefore introduce in sec . [ sec : strat ] supplementary strategies in order to improve the performance of directed loop algorithms , and present autocorrelation times obtained using these additional strategies . we finally conclude in sec . [ sec : conc ] .","summary":"efficient quantum monte carlo update schemes called _ directed loops _ have recently been proposed , which improve the efficiency of simulations of quantum lattice models . this also allows for an extension of the directed loop scheme to general lattice models , such as high - spin or bosonic models . the generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes . we show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency ; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest .","abstract":"efficient quantum monte carlo update schemes called _ directed loops _ have recently been proposed , which improve the efficiency of simulations of quantum lattice models . we propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world - line segments . using linear programming techniques to solve the generalized equations , we look for optimal construction schemes for directed loops . this also allows for an extension of the directed loop scheme to general lattice models , such as high - spin or bosonic models . the resulting algorithms are bounce - free in larger regions of parameter space than the original directed loop algorithm . the generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes . in contrast to general expectations , we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables , because of the non - uniqueness of the bounce - free solutions . we therefore propose different general strategies to further minimize autocorrelations , which can be used as supplementary requirements in any directed loop scheme . we show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency ; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest ."}
{"article_id":"cond-mat0308495","section_id":"c","document":"in this paper we presented a generalized approach to the construction of directed loops in quantum monte carlo simulations . viewing the worms ends not as artificial discontinuities , but as physical operators with corresponding weights we arrived at generalizations of the directed loop equations . using linear programming techniques to solve these equations we can avoid the analytical calculations needed in previous approaches , and arrive at a generic qmc algorithm . the generalized directed loop equations allow bounce - free solutions in larger regions of parameter space , but measurements of autocorrelation times for several models showed that minimizing bounces is not always sufficient to obtain an efficient algorithm . we therefore proposed a different means of further optimizing directed loop algorithms inside the subspace of bounce - minimal solutions . additional strategies were presented , the use of which improves the performance up to an order of magnitude . however , the optimal strategy in general depends on both the model _ and _ the observable of interest . one therefore needs to perform preliminary simulations to find out which supplementary strategy is optimal for a given problem before turning to long calculations , in order to account for the physical phase realized in the specific parameter regime . a recent paper  @xcite discussed issues similar to the ones addressed here : can one obtain strategies that improve the efficiency of qmc algorithms beyond the directed loop scheme  ? in our understanding of their work , the authors of ref . @xcite propose to _ always _ keep a non - zero bounce probability to vertices with the largest weight . they then provide a precise form of the scattering matrices . in ref . @xcite , syljusen also proposed to keep a non - zero bounce probability for the vertex with the largest weight in situations where he did not find bounce - free solutions . the main difference between the approach of pollet _ et al . _ , and syljusen thus concerns the off - diagonal elements of the scattering matrix . as shown explicitly in sec . [ sec : strat ] , the off - diagonal matrix elements strongly affect the efficiency of the algorithm in a parameter- and observable - dependent way . this indicates that there will be no simple rule for the construction of the scattering matrices , which perform optimal in all cases . similar conclusions were reached in ref . a full sse code featuring the implementation of the generalized directed loop technique described in the present paper is available as part of the alps project  @xcite . we thank k. harada , n. kawashima , a. sandvik , e. srensen , o. syljusen and s. todo for fruitful discussions . the simulations were done using the alps libraries  @xcite and performed on the asgard beowulf cluster at eth zrich . this work is supported by the swiss national science foundation .","summary":"using linear programming techniques to solve the generalized equations , we look for optimal construction schemes for directed loops .","abstract":"efficient quantum monte carlo update schemes called _ directed loops _ have recently been proposed , which improve the efficiency of simulations of quantum lattice models . we propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world - line segments . using linear programming techniques to solve the generalized equations , we look for optimal construction schemes for directed loops . this also allows for an extension of the directed loop scheme to general lattice models , such as high - spin or bosonic models . the resulting algorithms are bounce - free in larger regions of parameter space than the original directed loop algorithm . the generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes . in contrast to general expectations , we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables , because of the non - uniqueness of the bounce - free solutions . we therefore propose different general strategies to further minimize autocorrelations , which can be used as supplementary requirements in any directed loop scheme . we show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency ; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest ."}
{"article_id":"1609.09376","section_id":"i","document":"in this lecture , we present the most important aspects of the antenna and receiver components of synthesis telescopes . due to the increased breadth of material , we can not cover all of the topics contained in the previous version of the summer school chapter on antennas @xcite , in particular the section on antenna polarization properties . instead , we review the basics of antennas while adding new details of interest to astronomers on the atacama large millimeter / submillimeter array ( alma ) and the karl g. jansky very large array ( vla ) dish reflectors . we follow with an overview of the heterodyne receiver systems and the receiver calibration techniques in use at these telescopes . figure  [ fig1 ] shows a simple block diagram of the major components required in an synthesis telescope . the role of the primary antenna elements of an interferometer is much the same as in any single element telescope : to track and capture radiation from a celestial object over a broad collecting area and focus and couple this signal into a receiver so that it can be detected , digitized and analyzed . at the output of the receiver feed , the signal is at the radio , or sky , frequency @xmath0 , typically with a significant bandwidth @xmath1 . the signal undergoes frequency translations and filtering as it propagates through the electronics system . in synthesis telescopes of recent design , the analog signal processing and digitization systems are located in the antennas , with the resulting digital data transmitted over fiber optic cables to the correlator building . in general , the receiver , intermediate frequency , transmission cables , lo , and baseband portions of the electronics system all have the requirement of good amplitude and phase stability . these requirements and others such as stable bandpass shape , low spurious signal generation , and good signal isolation are discussed in @xcite and in the alma and evla memo series .","summary":"the primary antenna elements and receivers are two of the most important components in a synthesis telescope . together they are responsible for locking onto an astronomical source in both direction and frequency , capturing its radiation , and converting it into signals suitable for digitization and correlation . the properties and performance of antennas and receivers can affect the quality of the synthesized images in a number of fundamental ways . in this lecture , their most relevant design and performance parameters are reviewed , with emphasis on the current alma and vla systems . we discuss in detail the shape of the primary beam and the components of aperture efficiency , and we present the basics of holography , pointing , and servo control . on receivers ,","abstract":"the primary antenna elements and receivers are two of the most important components in a synthesis telescope . together they are responsible for locking onto an astronomical source in both direction and frequency , capturing its radiation , and converting it into signals suitable for digitization and correlation . the properties and performance of antennas and receivers can affect the quality of the synthesized images in a number of fundamental ways . in this lecture , their most relevant design and performance parameters are reviewed , with emphasis on the current alma and vla systems . we discuss in detail the shape of the primary beam and the components of aperture efficiency , and we present the basics of holography , pointing , and servo control . on receivers , we outline the use of amplifiers and mixers both in the cryogenic front - end and in the room temperature back - end signal path . the essential properties of precision local oscillators ( los ) , phase lock loops ( plls ) , and lo modulation techniques are also described . we provide a demonstration of the method used during alma observations to measure the receiver and system sensitivity as a function of frequency . finally , we offer a brief derivation and numerical simulation of the radiometer equation ."}
{"article_id":"1604.02976","section_id":"i","document":"ultracold atoms in optical lattices offer an ideal platform for simulating certain problems of condensed matter physics and constitute many - body systems exhibiting a diversity of physical phenomena . in particular , the understanding of the non - equilibrium dynamics of strongly correlated many - body systems in optical lattices is currently one of the most challenging problems for both theory and experiment . this dynamics is typically triggered by an external periodic driving @xcite or an instantaneous change ( quench ) of a hamiltonian parameter @xcite . remarkable dynamical phenomena employing a periodic driving @xcite of the optical lattice include bloch - oscillations @xcite , the realization of the superfluid to mott insulator phase transition @xcite , topological states of matter @xcite , artificial gauge fields @xcite , the realization of ferromagnetic domains @xcite and even applications to quantum computation @xcite . on the other hand , quench dynamics enables us to explore among others the light - cone - effect in the spreading of correlations @xcite , the kibble - zurek mechanism @xcite or the question of thermalization @xcite . driving or quenches can also be used in order to generate energetically low - lying collective modes , such as the dipole @xcite or the breathing mode @xcite . in general , a sudden displacement or a periodic shaking of the external trap induces a dipole oscillation of the atomic cloud , while a quench on the frequency of the trap excites a breathing mode of the cloud . these modes constitute a main probe both for theoretical investigations , to understand and interpret the non - equilibrium dynamics , and for experiments , as they can be used in order to measure key quantities of trapped many - body systems @xcite . recently , increasing effort has been devoted to control the atomic motion in optical lattices by subjecting them to a time - periodic external driving @xcite and investigating the optimal driving protocol @xcite . in this direction , it is important to carefully explore and design the relevant driving protocol to transfer the energy to the desired final degrees of freedom . to trigger or even control a certain type of ( collective ) modes of the dynamics , widely used techniques in the literature constitute either the periodic driving of the lattice potential , e.g. a lattice shaking , or a quench of a parameter of the system , e.g. a lattice amplitude quench or an interaction quench . in the former case a tunable local dipole mode and a resonant intra - well dynamics were recently explored by shaking an optical lattice @xcite . on the other hand , in the latter case it has been shown @xcite that a sudden increase of the inter - particle repulsion in a non - driven lattice induces a rich inter - well as well as intra - well dynamics which can be coupled and consequently mixed for certain quench amplitudes . however , for decreasing repulsive forces @xcite the accessible inter - well tunneling channels are much fewer compared to the excited intra - well modes , and in particular no resonant dynamics can be observed . from the above analysis it becomes evident that a crucial ingredient for the design and further control of the dynamics is the choice of the driving protocol of the system : by using different driving schemes , different types of excited modes are induced , i.e. different energetical channels can be triggered . in this direction , an intriguing question is how a combination of periodic driving and interaction quenches can be used to steer the dynamics of the system and as a consequence the coupling of the inter - well and intra - well modes . such an investigation will , among others , permit us to gain a deeper understanding of the underlying microscopic mechanisms , and will allow us to activate certain energy channels by using specific driving protocols for the control of the different processes .    in the spirit of the above - posed question we investigate in the present work the quantum dynamics of interaction quenched few - boson ensembles trapped in periodically driven finite optical lattices . concerning the periodic driving , a vibration of the optical lattice is employed . this scheme , in contrast to shaking , induces out - of - phase dipole modes among the outer wells and a local breathing mode in the central well of the finite lattice . we cover the dynamics of the periodically driven lattice with varying driving frequency in the complete range from adiabatic to high frequency driving . in particular we observe for the intermediate driving frequency regime , being intractable by current state of the art analytical methods @xcite , a resonant - like behavior of the intra - well dynamics . this resonance is accompanied by a rich excitation spectrum and an enhanced inter - well tunneling as compared to adiabatic or high intensity driving and it is mainly of single particle character . indeed , it survives upon increasing interaction obtaining faint additional features the most remarkable being the co - tunneling of an atom pair @xcite . to induce a correlated many - body dynamics we employ an interaction quench on top of the driven lattice , thus opening energetically higher inter - well and intra - well channels . as a consequence the inter - well tunneling is amplified even for adiabatic driving and admixtures of excitations possessing breathing - like and dipole - like components are generated . remarkably enough , as a function of the quench amplitude , the system experiences multiple resonances between the inter- and intra - well dynamics . this observation indicates the high degree of controlability of the system especially for the excited modes under such a combination of driving protocols and it is arguably one of our central results . to the best of our knowledge , this multifold mode coupling behavior unraveled with a composite driving protocol has never been reported before . moreover , the position of the above mentioned resonances is tunable via the driving frequency allowing for further control of the mode coupling in optical lattices . finally , the realization of intensified loss of coherence caused either by the resonant driving or by a quench on top of the driving is an additional indicator for the observed phenomena . to obtain a comprehensive understanding of the microscopic properties of the strongly driven and interacting system , we focus on the few - body dynamics in small lattices ( specifically , four bosons in a triple well setup ) however , we provide strong evidence that our findings apply equally to larger lattice systems and particle numbers . all calculations to solve the underlying many - body schrdinger equation are performed by employing the multi - configuration time - dependent hartree method for bosons ( mctdhb ) @xcite , which is especially designed to treat the out - of - equilibrium quantum dynamics of interacting bosons under time - dependent modulations . this work is organized as follows . in sec.ii we explain our setup and introduce the multi - band expansion and the basic observables that we shall use in order to interpret the dynamics . sec.iii presents the effects resulting from an interaction quench of a driven triple well for filling factors larger than unity . sec.iv . presents the dynamics for filling factors smaller than unity . we summarize our findings and give an outlook in sec.v . in appendix a the non - equilibrium dynamics induced by a driven harmonic oscillator and simultaneously interaction quenched bosonic cloud is briefly outlined . appendix b briefly comments on the resonant response of the driven lattice and finally appendix c describes our computational method .","summary":"the dynamical behavior is investigated with varying driving frequency , revealing a resonant - like behavior of the intra - well dynamics . we observe then multiple resonances between the inter- and intra - well dynamics at different quench amplitudes , with the position of the resonances being tunable via the driving frequency . our results pave the way for future investigations on the use of combined driving protocols in order to excite different inter- and intra - well modes and to subsequently control them . + keywords : non - equilibrium dynamics ; periodically driven lattices ; interaction quench ; excited modes ; tunneling dynamics ; dipole mode ; breathing - mode .","abstract":"the out - of - equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one - dimensional optical lattices is investigated . it is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out - of - phase dipole - like modes , while in the central well the atomic cloud experiences a local breathing mode . the dynamical behavior is investigated with varying driving frequency , revealing a resonant - like behavior of the intra - well dynamics . an interaction quench in the periodically driven lattice gives rise to admixtures of different excitations in the outer wells , an enhanced breathing in the center and an amplification of the tunneling dynamics . we observe then multiple resonances between the inter- and intra - well dynamics at different quench amplitudes , with the position of the resonances being tunable via the driving frequency . our results pave the way for future investigations on the use of combined driving protocols in order to excite different inter- and intra - well modes and to subsequently control them . + keywords : non - equilibrium dynamics ; periodically driven lattices ; interaction quench ; excited modes ; tunneling dynamics ; dipole mode ; breathing - mode ."}
{"article_id":"1604.02976","section_id":"c","document":"in the present work , the few - body correlated non - equilibrium quantum dynamics of an interaction quenched bosonic cloud in an external periodically driven finite - size optical lattice has been investigated . the effect of an interaction quench on top of the driven lattice has been analyzed . we focus on large lattice depths and small driving amplitudes in order to limit the degree of excitations that could lead to the creation of the cradle motion @xcite or even to heating processes . starting from the ground state of a weakly interacting small atomic ensemble , we examine in detail the time evolution of the system in the periodically driven optical lattice by a simultaneous interaction quench . it has been shown that for the case of the periodically driven lattice one can induce out - of - phase local dipole modes in the outer wells , while a local breathing mode can be generated in the central well . this is in direct contrast with a shaken lattice , where only in - phase dipole modes are excited . a wide range of driving frequencies has been considered in order to unravel the range from adiabatic to high frequency driving . we observe that within the intermediate frequency regimes , being intractable by current analytical methods , the system can be driven to a far out - of - equilibrium state when compared to other driving frequency regions . in particular , a resonance of the intra - well dynamics occurs with enhanced tunneling dynamics , thus opening energetically higher - lying inter - well tunneling channels . a prominent signature of the resonant regions as well as the effect of the interaction is provided via the study of the time - dependence of the first order coherence , where intensified loss of coherence is observed . this loss of coherence constitutes an independent signature of the resonant regions , allowing to study it from another perspective and , potentially , to measure it in experiments . following an interaction quench on top of the periodically driven lattice for various driving frequencies , we can trigger more effectively the inter - well as well as the intra - well dynamics and steer the system towards strongly out - of - equilibrium regimes . here , the tunneling as well as the local breathing mode in the middle - well are amplified , while in the outer wells the atomic cloud experiences an admixture of a dipole and a breathing component . this admixture leads to simultaneous oscillations around the minimum of the well as well as a contraction and expansion in the course of the dynamics . our analysis shows that one can use the interaction quench to manipulate the tunneling frequency rendering the single - particle tunneling dominant even at resonance . concerning the on - site modes it is shown that an interaction quench can be used in order to manipulate their amplitude oscillations yielding also a strong influence on the excitation dynamics .    subsequently , the dynamics of the periodically driven lattice ( i.e. for a fixed driving frequency ) as a function of the quench amplitude has been studied . in particular , the tunneling contains three modes , the breathing possesses two frequency branches and the corresponding admixture three branches : one from the breathing component and two which refer to the dipole component . furthermore , five resonances between the inter - well tunneling dynamics and the intra - well dynamics have been revealed . the inter - well tunneling experiences a resonance with the breathing component of the central well , two resonances with the breathing component of the outer wells and two resonances with the dipole component of the outer wells . these resonances can further be manipulated via the frequency of the periodic driving . as a result , the combination of different driving protocols can excite different inter- and intra - well modes as well as manifest various energetically higher components of a mode . most importantly , the observed resonances between different inter- and intra - well modes demonstrate the richness of the system , while their dependence on various system parameters , e.g. the driving frequency shows the tunability of the system . the above - mentioned realization of multiple resonances constitutes arguably one of the central results of our investigation , which to the best of our knowledge has never been reported in such a setting . finally , let us comment on possible future extensions of the present work . our analysis reveals that a combination of different driving protocols can induce admixtures of excited modes which in the present case corespond to admixtures of dipole - like and breathing - like modes . in this direction , it would be a natural next step to find the optimal pulse of the interaction quench protocol in order to induce a perfectly shaped squeezed state . also the understanding and prediction of the long - time dynamics imposing the interaction quench on the driven lattice at different transient times is certainly of interest .","summary":"the out - of - equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one - dimensional optical lattices is investigated . it is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out - of - phase dipole - like modes , while in the central well the atomic cloud experiences a local breathing mode .","abstract":"the out - of - equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one - dimensional optical lattices is investigated . it is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out - of - phase dipole - like modes , while in the central well the atomic cloud experiences a local breathing mode . the dynamical behavior is investigated with varying driving frequency , revealing a resonant - like behavior of the intra - well dynamics . an interaction quench in the periodically driven lattice gives rise to admixtures of different excitations in the outer wells , an enhanced breathing in the center and an amplification of the tunneling dynamics . we observe then multiple resonances between the inter- and intra - well dynamics at different quench amplitudes , with the position of the resonances being tunable via the driving frequency . our results pave the way for future investigations on the use of combined driving protocols in order to excite different inter- and intra - well modes and to subsequently control them . + keywords : non - equilibrium dynamics ; periodically driven lattices ; interaction quench ; excited modes ; tunneling dynamics ; dipole mode ; breathing - mode ."}
{"article_id":"1411.2834","section_id":"i","document":"observational and theoretical studies of mixing and oscillations are typically concerned with neutral particle states . important examples are neutral meson mixing , the oscillations of standard model ( sm ) neutrinos  @xcite and leptogenesis through the mixing of sterile right - handed neutrinos ( rhns ) in the early universe  @xcite . in contrast , for charged particles in the sm at vanishing temperature , mass degeneracies between different states are not strong enough to produce observable phenomena of mixing and oscillations . this does however not preclude the fact that these effects are present in principle . moreover , it has been demonstrated that the mixing of lepton doublets ( which are gauged ) can be of importance for leptogenesis  @xcite : at high temperatures , the asymmetries are in general produced as superpositions of the lepton doublet flavour eigenstates of the sm . in the sm flavour basis , this can be described in terms of off - diagonal correlations in the two - point functions , or alternatively in effective density - matrix formulations in terms of correlations of charge densities of different flavours . at smaller temperatures , interactions mediated by sm yukawa couplings become faster than the hubble expansion , such that the flavour correlations decohere . in particular , the sm leptons receive thermal mass corrections as well as damping rates that lift the flavour degeneracy . by now , these effects have been investigated in detail . it turns out that due to the interplay with gauge interactions , the flavour oscillations that may be anticipated from the thermal masses are effectively frozen , while the decoherence proceeds mainly through the damping effects , _ i.e. _ the production and the decay of leptons in the plasma  @xcite . the appropriate treatment of these flavour correlations turns out to be of leading importance for the washout of the asymmetries from the out - of - equilibrium decays and inverse decays of the rhns .    the origin of the charge - parity ( @xmath0 ) asymmetry for leptogenesis is usually attributed to the rhns and their couplings  @xcite . in the standard calculation , when describing the production and the decay of the rhns through @xmath5-matrix elements , one can diagrammatically distinguish between vertex and wave - function terms . the presence of finite - temperature effects as well as the notorious problem of correctly counting real intermediate states in the boltzmann equations  @xcite have motivated the use of techniques other than the @xmath5-matrix approach : it has been demonstrated that the wave - function contribution can alternatively be calculated by solving kinetic equations ( that are kadanoff - baym type equations which descend from schwinger - dyson equations , see refs . @xcite on the underlying formalism ) for the rhns and their correlations , or equivalently , by solving for the evolution of their density matrix  @xcite . the vertex contributions to the decay asymmetry can be obtained within the kadanoff - baym framework as well , as it is shown in refs . we note at this point that it has more recently been argued that the asymmetry from the wave - function correction and the contribution from the kinetic equation are distinct contributions that should be added together  @xcite . however , it is shown in refs . @xcite that the kinetic equations derived from the two - particle irreducible effective action capture all contributions of relevance for the @xmath0 asymmetry at leading order , which also encompasses the wave - function corrections . the calculations for leptogenesis based on schwinger - dyson equations on the closed - time - path ( ctp ) can also be applied to leptogenesis from oscillations of light ( masses much below the temperature ) rhns  @xcite , also known as the ars scenario after the authors  of ref . @xcite . in this approach , we can interpret the @xmath0 violation as originating from cuts of the one - loop self energy of the rhns , that are dominantly thermal . it can be concluded that thermal effects can largely open the phase - space for @xmath0-violating cuts that are strongly suppressed for kinematic reasons at vanishing temperature . putting together the elements of flavour correlations for charged particles and of thermal cuts , we can identify new sources for the lepton asymmetry , in addition to the one from cuts in the rhn propagator . in models with multiple higgs doublets , higgs bosons may be the mixing particles  @xcite , whereas in minimal type - i see - saw scenarios ( with one higgs doublet ) , this role can be played by mixing sm lepton doublets  @xcite . yet , the rhns remain of pivotal importance because due to their weak coupling , they provide the deviation from thermal equilibrium that is necessary for any scenario of baryogenesis . while the set of free parameters of the type - i see - saw model will remain underconstrained by present observations and those of the foreseeable future , the parameter space in that scenario is still much smaller than in models with multiple higgs doublets . for our phenomenological study , we therefore choose to consider the mixing of lepton doublets in the see - saw scenario , that is given by the lagrangian @xmath6    in short , the scenario of baryogenesis from mixing lepton doublets can be described as follows  @xcite : flavour - off diagonal correlations from the mixing of active leptons @xmath7 ( where @xmath8 is the flavour index ) can induce the production of lepton flavour asymmetries , corresponding to diagonal entries of a traceless charge density matrix in flavour space . different washout rates for the particular flavours may then lead to a net asymmetry in total lepton number , _ i.e , _ a non - vanishing trace of the charge density matrix . now , since off - diagonal correlations due to mixing vanish in thermal equilibrium , the mixing of lepton doublets that we aim to describe consequently is an out - of - equilibrium phenomenon . it is thus natural to assume that initially , when the primordial plasma is close to thermal equilibrium , all correlations between the sm lepton flavours vanish . therefore , we are interested in possibilities of generating these dynamically . due to gauge interactions , the distribution functions of the sm particles should track their equilibrium forms very closely . moreover , gauge interactions are flavour - blind , so they can neither generate flavour correlations nor destroy these ( up to the indirect effects that we discuss below ) . sizeable off - diagonal correlations can however be induced through couplings to the rhns @xmath9 , the distributions of which can substantially deviate from equilibrium . the flavour correlations in the doublet leptons @xmath10 are suppressed however due to the sm yukawa couplings @xmath11 with the charged singlets @xmath12 and the higgs field @xmath13 , where @xmath14 , and where @xmath15 is the totally antisymmetric @xmath16 tensor . by field redefinitions , we can impose that @xmath11 and @xmath17 are diagonal , which is a common and convenient choice of basis that we adapt throughout this present paper . for simplicity , we therefore write @xmath18 .    in this paper , within section  [ sec : freezeout ] , we first review the scenario of ref .  @xcite . we improve on the previous discussion by introducing a diagrammatic representation of the mechanism . moreover , we carefully discuss the generation and the decoherence of lepton flavour correlations at different temperatures , paying particular attention to the fact that both effects take a finite time to fully establish . section  [ sec : surveys ] contains a survey of the parameter space of baryogenesis from mixing lepton doublets based on the lagrangian  ( [ lagrangian ] ) . under the assumption that only two rhns are present , we perform a comprehensive scan , given the present best - fit values on the light neutrino mass differences and mixing angles , such that we can identify the point in parameter space that allows for the lowest reheat temperature for which an asymmetry in accordance with observation can result . in addition , we show that for three rhns , substantially smaller temperatures can be viable , what requires however anomalously large yukawa couplings of the @xmath19- and the @xmath20-leptons and a cancellation in their contributions to the mass matrix of the light neutrinos . the analysis is however restricted to the strong washout regime , such that it remains an open question of interest whether favourable parametric regions also exist when at least one of the rhns induces only a weak washout . the concluding remarks are given in section  [ sec : conclusions ] .","summary":"mixing lepton doublets of the standard model can lead to lepton flavour asymmetries in the early universe . we present a diagrammatic representation of this recently identified source of violation and elaborate in detail on the correlations between the lepton flavours at different temperatures . for a model where two sterile right - handed neutrinos generate the light neutrino masses through the see - saw mechanism , the lower bound on reheat temperatures in accordance with substantially smaller values are viable . this requires however a tuning of the yukawa couplings , such that there are cancellations between the individual contributions to the masses of the light neutrinos .     tum - hep-967 - 14    * phenomenology of baryogenesis from lepton - doublet mixing *    bjrn  garbrecht and ignacio izaguirre + 0.2 cm _","abstract":"mixing lepton doublets of the standard model can lead to lepton flavour asymmetries in the early universe . we present a diagrammatic representation of this recently identified source of violation and elaborate in detail on the correlations between the lepton flavours at different temperatures . for a model where two sterile right - handed neutrinos generate the light neutrino masses through the see - saw mechanism , the lower bound on reheat temperatures in accordance with the observed baryon asymmetry turns out to be . with three right - handed neutrinos , substantially smaller values are viable . this requires however a tuning of the yukawa couplings , such that there are cancellations between the individual contributions to the masses of the light neutrinos .     tum - hep-967 - 14    * phenomenology of baryogenesis from lepton - doublet mixing *    bjrn  garbrecht and ignacio izaguirre + 0.2 cm _ physik department t70 , james - franck - strae , + technische universitt mnchen , 85748 garching , germany _ + .2 cm _max - planck - institut fr physik ( werner - heisenberg - institut ) , fhringer ring 6 , + 80805 mnchen , germany _ + 1.4 cm"}
{"article_id":"1211.1661","section_id":"i","document":"a _ graph _ @xmath0 consists of a _ _ vertex set  _ _ @xmath1 and an _ _ edge set  _ _ @xmath2 , where each edge corresponds to a pair @xmath3 of vertices . a graph in which each edge has a _ weight _ associated with it is called a _ network_. a graph @xmath4 is a _ subgraph _ of @xmath0 if @xmath5 and @xmath6 . a graph @xmath7 is a _ homeomorph _ of @xmath8 if @xmath7 can be obtained by subdividing edges of @xmath8 with new vertices . we say that a graph @xmath9 is a _ square of a graph _ @xmath0 if @xmath10 . a two - terminal directed acyclic graph ( _ st - dag _ ) has only one source and only one sink . we consider a _ labeled graph _ which has labels attached to its edges . each path between the source and the sink ( a _ sequential path _ ) in an st - dag can be presented by a product of all edge labels of the path . we define the sum of edge label products corresponding to all possible sequential paths of an st - dag @xmath7 as the _ canonical expression _ of @xmath7 . an algebraic expression is called an _ st - dag expression _ ( a _ factoring of an st - dag _ in @xcite ) if it is algebraically equivalent to the canonical expression of an st - dag . an st - dag expression consists of literals ( edge labels ) , and the operators @xmath11 ( disjoint union ) and @xmath12 ( concatenation , also denoted by juxtaposition ) . an expression of an st - dag @xmath7 will be hereafter denoted by @xmath13 . we define the total number of literals in an algebraic expression as the _ complexity of the algebraic expression_. an equivalent expression with the minimum complexity is called an _ optimal representation of the algebraic expression_.    a _ series - parallel _ _ graph _ is defined recursively so that a single edge is a series - parallel graph and a graph obtained by a parallel or a series composition of series - parallel graphs is series - parallel . as shown in @xcite and @xcite , a series - parallel graph expression has a representation in which each literal appears only once . this representation is an optimal representation of the series - parallel graph expression . for example , the canonical expression of the series - parallel graph presented in figure [ fig1 ] is @xmath14 . since it is a series - parallel graph , the expression can be reduced to @xmath15 , where each literal appears once . ( 5,3.5)(-5,0)(1,3)(3,0)4 ( 1,3)(1,0)3 ( 2.5,3.3)(0,0)@xmath16 ( 4,3)(5.5,5)(7,3 ) ( 7.085,3)(3,-2)0 ( 5.5,4.3)(0,0)@xmath17 ( 4,3)(5.5,1)(7,3 ) ( 7.085,3)(3,2)0 ( 5.5,2.3)(0,0)@xmath18 ( 7,3)(8.5,5)(10,3 ) ( 10.085,3)(3,-2)0 ( 8.5,4.3)(0,0)@xmath19 ( 7,3)(8.5,1)(10,3 ) ( 10.085,3)(3,2)0 ( 8.5,2.3)(0,0)@xmath20 ( 1,3)(4,-2)(7,3 ) ( 7.085,3)(4,3)0 ( 4,0.8)(0,0)@xmath21    a _ fibonacci graph _ @xcite has vertices @xmath22 and edges @xmath23@xmath24 . as shown in @xcite , an st - dag is series - parallel if and only if it does not contain a subgraph which is a homeomorph of the _ forbidden subgraph _ positioned between vertices @xmath25 and @xmath26 of the fibonacci graph illustrated in figure [ fig2 ] . thus , a fibonacci graph gives a generic example of non - series - parallel graphs . ( 5,2)(-0.9,-0.5)(0,0)(1.5,0)9 ( 0,-0.3)(0,0)1 ( 1.5,-0.3)(0,0)2 ( 3,-0.3)(0,0)3 ( 4.5,-0.3)(0,0)4 ( 7.5,-0.3)(0,0)n-3 ( 9,-0.3)(0,0)n-2 ( 10.5,-0.3)(0,0)n-1 ( 12,-0.3)(0,0)n ( 0,0)(1.5,0)8(1,0)1.5 ( 0.75,0.2)(0,0)@xmath27 ( 2.25,0.2)(0,0)@xmath28 ( 3.75,0.2)(0,0)@xmath29 ( 8.25,0.2)(0,0)@xmath30 ( 9.75,0.2)(0,0)@xmath31 ( 11.25,0.2)(0,0)@xmath32 ( 0,0)(1.5,2)(3,0 ) ( 1.5,0)(3,2)(4.5,0 ) ( 3,0)(4.5,2)(6,0 ) ( 4.5,0)(6,2)(7.5,0 ) ( 6,0)(7.5,2)(9,0 ) ( 7.5,0)(9,2)(10.5,0 ) ( 9,0)(10.5,2)(12,0 ) ( 3.085,0)(1.5,0)7(3,-2)0 ( 1.5,1.3)(0,0)@xmath33 ( 3,1.3)(0,0)@xmath34 ( 9,1.3)(0,0)@xmath35 ( 10.5,1.3)(0,0)@xmath36 ( 5.55,-0.2)(0.2,0)6    mutual relations between graphs and expressions are discussed in a number of works . specifically , @xcite , @xcite , and @xcite consider the correspondence between series - parallel graphs and read - once functions . a boolean function is defined as _ read - once _ if it may be computed by some formula in which no variable occurs more than once ( _ read - once formula _ ) . on the other hand , a series - parallel graph expression can be reduced to the representation in which each literal appears only once . hence , such a representation of a series - parallel graph expression can be considered as a read - once formula ( boolean operations are replaced by arithmetic ones ) . problems related to computations on graphs have applications in different areas .    specifically , many network problems , which are either intractable or have complicated solutions in the general case are solvable for series - parallel graphs . for example , some efficient algorithms for flow problems on series - parallel networks are presented in @xcite , @xcite , @xcite , @xcite . papers @xcite , @xcite , @xcite , @xcite consider sequencing and scheduling in relation to precedence series - parallel constraints . linear algorithms for reliability problems on series - parallel networks are presented in @xcite , @xcite . an expression of a homeomorph of the forbidden subgraph belonging to any non - series - parallel st - dag has no representation in which each literal appears once . for example , consider the subgraph positioned between vertices @xmath25 and @xmath26 of the fibonacci graph shown in figure [ fig2 ] . possible optimal representations of its expression are @xmath37 or @xmath38 . for this reason , an expression of a non - series - parallel st - dag can not be represented as a read - once formula . however , for arbitrary functions , which are not read - once , generating the optimum factored form is np - complete @xcite . the problem of factoring boolean functions into shorter , more compact formulae is one of the basic operations in algorithmic logic synthesis . in logic synthesis , one standard measure of the complexity of a logic circuit is the number of literals . computation time also depends on the number of literals . some algorithms developed in order to obtain good factored forms are described in @xcite , @xcite . a symbolic approach to scheduling of a robotic line is considered in @xcite . the method uses the max - algebra tools and allows the shortest - path problem to be interpreted as the computation of the st - dag expression . the complexity of this problem is determined by the complexity of the st - dag expression . for a robotic line represented by a fibonacci graph , the proposed algorithm generates the processing sequence in polynomial time . a method for automated composition of algebraic expressions in complex business process modeling based on acyclic directed graph reductions is introduced in @xcite . the method transforms business step dependencies described by users into digraphs and finally generates algebraic expressions . if a graph is not series - parallel , the algorithm checks potential structural conflicts whose presence complicates certain aspects , such as execution control and system scalability . in this case , the expression generation may require exponential time . a lot of problems have polynomial algorithms on _ planar graphs _ , i.e. , the graphs that can be drawn in the plane without any edges crossing . for example , some polynomial - time algorithms for the exact computation of network reliability applied to planar graphs are surveyed in @xcite . in @xcite a polynomial algorithm for the connectivity augmentation problem is presented . this problem has applications in upgrading telecommunication networks to be invulnerable to link or node failures . there are also many practical applications with a graph structure in which crossing edges are a nuisance , including design problems for circuits , subways , utility lines @xcite .    in our work we consider expressions with a minimum ( or , at least , a polynomial ) complexity as a key to generating efficient algorithms on distributed systems . in @xcite we presented an algorithm ,  which generates the expression of @xmath39 complexity for an @xmath40-vertex fibonacci graph .    in this paper we investigate a non - series - parallel st - dag called a _ square rhomboid _ ( figure [ rhom_fig12 ] ) . this graph looks like a planar approximation of the square of a _ rhomboid _ , which is a series composition of _ rhomb _ graphs . a square rhomboid consists of the same vertices as the corresponding rhomboid . however , edges labeled by letters @xmath16 , @xmath17 , and @xmath18 ( see figure [ rhom_fig12 ] ) are absent in a rhomboid . geometrically , a square rhomboid can be considered to be a gluing  of two fibonacci graphs , i.e. , it is the next harder one in a sequence of increasingly non - series - parallel graphs . ( 10,4)(-0.2,-1.7)(0,0)(3,0)7 ( 1.5,1.5)(3,0)6 ( 1.5,-1.5)(3,0)6 ( 0,0.35)(0,0)1 ( 3.02,0.35)(0,0)2 ( 15,0.5)(0,0)n-1 ( 18,0.35)(0,0)n ( 1.5,1.8)(0,0)1 ( 4.5,1.8)(0,0)2 ( 13.5,1.8)(0,0)n-2 ( 16.5,1.8)(0,0)n-1 ( 1.5,-1.8)(0,0)1 ( 4.5,-1.8)(0,0)2 ( 13.5,-1.8)(0,0)n-2 ( 16.5,-1.8)(0,0)n-1 ( 0,0)(3,0)6(1,1)1.5 ( 0,0)(3,0)6(1,-1)1.5 ( 1.5,1.5)(3,0)6(1,-1)1.5 ( 1.5,-1.5)(3,0)6(1,1)1.5 ( 0,0)(3,0)6(1,0)3 ( 1.5,1.5)(3,0)5(1,0)3 ( 1.5,-1.5)(3,0)5(1,0)3 ( 1.5,0.3)(0,0)@xmath33 ( 16.5,0.3)(0,0)@xmath41 ( 3,1.75)(0,0)@xmath42 ( 15,1.75)(0,0)@xmath43 ( 3,-1.75)(0,0)@xmath27 ( 15,-1.75)(0,0)@xmath31 ( 0.55,0.95)(0,0)@xmath44 ( 15.4,0.95)(0,0)@xmath45 ( 2.4,0.95)(0,0)@xmath46 ( 17.56,0.95)(0,0)@xmath47 ( 0.6,-0.95)(0,0)@xmath48 ( 15.4,-0.95)(0,0)@xmath49 ( 2.4,-0.95)(0,0)@xmath50 ( 17.56,-0.95)(0,0)@xmath51 ( 4,0.2)(0.2,0)6 ( 13,0.2)(0.2,0)6 ( 5.5,1.7)(0.2,0)6 ( 11.5,1.7)(0.2,0)6 ( 5.5,-1.7)(0.2,0)6 ( 11.5,-1.7)(0.2,0)6    the set of vertices of an @xmath52-vertex square rhomboid consists of @xmath53 _ middle _ ( _ basic _ ) , @xmath54 _ upper _ , and _ _  _ _ @xmath54 _ lower _ vertices . upper and lower vertices numbered @xmath55 will be denoted in formulae by @xmath56 and @xmath57 , respectively . the square rhomboid ( @xmath58 for brevity ) including @xmath40 basic vertices will be denoted by @xmath59 and will be called an @xmath58 of size @xmath40 . our intention in this paper is to simplify the expressions of square rhomboids and eventually find their optimal representations . with that end in view , we present an algorithm based on a _ decomposition method_.","summary":"the paper investigates relationship between algebraic expressions and graphs . we consider a digraph called a square rhomboid that is an example of non - series - parallel graphs . our intention is to simplify the expressions of square rhomboids and eventually find their shortest representations . with that end in view","abstract":"the paper investigates relationship between algebraic expressions and graphs . we consider a digraph called a square rhomboid that is an example of non - series - parallel graphs . our intention is to simplify the expressions of square rhomboids and eventually find their shortest representations . with that end in view , we describe the new algorithm for generating square rhomboid expressions , which improves on our previous algorithms ."}
{"article_id":"1211.1661","section_id":"m","document":"the method is based on revealing subgraphs in the initial graph . the resulting expression is produced by a special composition of subexpressions describing these subgraphs . ( 10,4)(-1.1,-2.5)(0,0)(3,0)7 ( 1.5,1.5)(3,0)6 ( 1.5,-1.5)(3,0)6 ( 0,0.35)(0,0)1 ( 3.02,0.35)(0,0)2 ( 6,0.35)(0,0)3 ( 9,0.35)(0,0)4 ( 12,0.35)(0,0)5 ( 15,0.35)(0,0)6 ( 18,0.35)(0,0)7 ( 1.5,1.8)(0,0)1 ( 4.5,1.8)(0,0)2 ( 7.5,1.8)(0,0)3 ( 10.5,1.8)(0,0)4 ( 13.5,1.8)(0,0)5 ( 16.5,1.8)(0,0)6 ( 1.5,-1.8)(0,0)1 ( 4.5,-1.8)(0,0)2 ( 7.5,-1.8)(0,0)3 ( 10.5,-1.8)(0,0)4 ( 13.5,-1.8)(0,0)5 ( 16.5,-1.8)(0,0)6 ( 0,0)(3,0)6(1,1)1.5 ( 0,0)(3,0)6(1,-1)1.5 ( 1.5,1.5)(3,0)6(1,-1)1.5 ( 1.5,-1.5)(3,0)6(1,1)1.5 ( 0,0)(3,0)6(1,0)3 ( 1.5,1.5)(3,0)5(1,0)3 ( 1.5,-1.5)(3,0)5(1,0)3 ( 1.5,0.3)(0,0)@xmath33 ( 4.5,0.3)(0,0)@xmath34 ( 7.5,0.3)(0,0)@xmath60 ( 10.5,0.3)(0,0)@xmath61 ( 13.5,0.3)(0,0)@xmath62 ( 16.5,0.3)(0,0)@xmath63 ( 3,1.75)(0,0)@xmath42 ( 6,1.75)(0,0)@xmath64 ( 8.7,1.75)(0,0)@xmath65 ( 12,1.75)(0,0)@xmath66 ( 15,1.75)(0,0)@xmath67 ( 3,-1.75)(0,0)@xmath27 ( 6,-1.75)(0,0)@xmath28 ( 8.7,-1.75)(0,0)@xmath29 ( 12,-1.75)(0,0)@xmath68 ( 15,-1.75)(0,0)@xmath69 ( 0.55,0.95)(0,0)@xmath44 ( 3.55,0.95)(0,0)@xmath70 ( 6.55,0.95)(0,0)@xmath71 ( 9.55,0.95)(0,0)@xmath72 ( 12.55,0.95)(0,0)@xmath73 ( 15.5,0.95)(0,0)@xmath74 ( 2.4,0.95)(0,0)@xmath46 ( 5.4,0.95)(0,0)@xmath75 ( 8.4,0.95)(0,0)@xmath76 ( 11.4,0.95)(0,0)@xmath77 ( 14.45,0.95)(0,0)@xmath78 ( 17.45,0.95)(0,0)@xmath79 ( 0.6,-0.95)(0,0)@xmath48 ( 3.6,-0.95)(0,0)@xmath80 ( 6.6,-0.95)(0,0)@xmath81 ( 9.6,-0.95)(0,0)@xmath82 ( 12.6,-0.95)(0,0)@xmath83 ( 15.6,-0.95)(0,0)@xmath84 ( 2.4,-0.95)(0,0)@xmath50 ( 5.4,-0.95)(0,0)@xmath85 ( 8.4,-0.95)(0,0)@xmath86 ( 11.4,-0.95)(0,0)@xmath87 ( 14.45,-0.95)(0,0)@xmath88 ( 17.45,-0.95)(0,0)@xmath89 ( 9,2.5)(9,0.55 ) ( 9,0.1)(9,-2.5 )    for a non - trivial @xmath58 subgraph with a source @xmath90 and a sink @xmath91 we choose any _ decomposition vertex _ @xmath92 ( @xmath93 ) located in the basic group of a subgraph . we conditionally split each @xmath58 through its decomposition vertex ( see the example in figure [ rhom_fig3 ] ) . two kinds of subgraphs are revealed in the graph in the course of decomposition . the first of them is an @xmath58 with a fewer number of vertices than the initial @xmath58 . the second one is an @xmath58 supplemented by two additional edges at one of four sides . possible varieties of this st - dag ( we call it a _ _  single - leaf square rhomboid _ _ and denote by @xmath94 ) which are subgraphs revealed from an @xmath58 in figure [ rhom_fig3 ] , are illustrated in figure [ rhom_fig4](a , b , c , d ) . let @xmath95 ( an @xmath94 of size @xmath40 ) denote an @xmath94 including @xmath40 basic vertices . we denote by @xmath96 a subexpression related to an @xmath58 subgraph with a source @xmath90 and a sink @xmath91 . we denote by @xmath97 , @xmath98 , @xmath99 , @xmath100 subexpressions related to @xmath94 subgraphs of figure [ rhom_fig4](a , b , c , d , respectively ) with a source @xmath90 and a sink @xmath101 , a source @xmath102 and a sink @xmath91 , a source @xmath90 and a sink @xmath103 , and a source @xmath104 and a sink @xmath91 . ( 10,3)(-1.3,-1)(-1,0)(0,0)(a ) ( 0,0)(3,0)3 ( 1.5,1.5)(3,0)3 ( 1.5,-1.5)(3,0)2 ( 0,0.35)(0,0)1 ( 3.02,0.35)(0,0)2 ( 6,0.35)(0,0)3 ( 1.5,1.8)(0,0)1 ( 4.3,1.8)(0,0)2 ( 7.5,1.8)(0,0)3 ( 1.5,-1.8)(0,0)1 ( 4.3,-1.8)(0,0)2 ( 0,0)(3,0)3(1,1)1.5 ( 0,0)(3,0)2(1,-1)1.5 ( 1.5,1.5)(3,0)2(1,-1)1.5 ( 1.5,-1.5)(3,0)2(1,1)1.5 ( 0,0)(3,0)2(1,0)3 ( 1.5,1.5)(3,0)2(1,0)3 ( 1.5,-1.5)(3,0)1(1,0)3 ( 1.5,0.3)(0,0)@xmath33 ( 4.2,0.3)(0,0)@xmath34 ( 3,1.75)(0,0)@xmath42 ( 6,1.75)(0,0)@xmath64 ( 3,-1.75)(0,0)@xmath27 ( 0.55,0.95)(0,0)@xmath44 ( 3.55,0.95)(0,0)@xmath70 ( 6.55,0.95)(0,0)@xmath71 ( 2.4,0.95)(0,0)@xmath46 ( 5.4,0.95)(0,0)@xmath75 ( 0.6,-0.95)(0,0)@xmath48 ( 3.6,-0.95)(0,0)@xmath80 ( 2.4,-0.95)(0,0)@xmath50 ( 5.4,-0.95)(0,0)@xmath85    ( 10,4.5)(-1.3,-0.85)(-1,0)(0,0)(c ) ( 0,0)(3,0)3 ( 1.5,1.5)(3,0)2 ( 1.5,-1.5)(3,0)3 ( 0,0.35)(0,0)1 ( 3.02,0.35)(0,0)2 ( 6,0.35)(0,0)3 ( 1.5,1.8)(0,0)1 ( 4.5,1.8)(0,0)2 ( 1.5,-1.8)(0,0)1 ( 4.5,-1.8)(0,0)2 ( 7.5,-1.8)(0,0)3 ( 0,0)(3,0)2(1,1)1.5 ( 0,0)(3,0)3(1,-1)1.5 ( 1.5,1.5)(3,0)2(1,-1)1.5 ( 1.5,-1.5)(3,0)2(1,1)1.5 ( 0,0)(3,0)2(1,0)3 ( 1.5,1.5)(3,0)1(1,0)3 ( 1.5,-1.5)(3,0)2(1,0)3 ( 1.5,0.3)(0,0)@xmath33 ( 4.5,0.3)(0,0)@xmath34 ( 3,1.75)(0,0)@xmath42 ( 3,-1.75)(0,0)@xmath27 ( 6,-1.75)(0,0)@xmath28 ( 0.55,0.95)(0,0)@xmath44 ( 3.55,0.95)(0,0)@xmath70 ( 2.4,0.95)(0,0)@xmath46 ( 5.4,0.95)(0,0)@xmath75 ( 0.6,-0.95)(0,0)@xmath48 ( 3.6,-0.95)(0,0)@xmath80 ( 6.6,-0.95)(0,0)@xmath81 ( 2.4,-0.95)(0,0)@xmath50 ( 5.4,-0.95)(0,0)@xmath85    ( 10,0)(-1.2,-1.5)(10.5,0)(0,0)(d ) ( 12,0)(3,0)3 ( 13.5,1.5)(3,0)2 ( 10.5,-1.5)(3,0)3 ( 12,0.35)(0,0)5 ( 15,0.35)(0,0)6 ( 18,0.35)(0,0)7 ( 13.5,1.8)(0,0)5 ( 16.5,1.8)(0,0)6 ( 10.3,-1.8)(0,0)4 ( 13.5,-1.8)(0,0)5 ( 16.5,-1.8)(0,0)6 ( 12,0)(3,0)2(1,1)1.5 ( 12,0)(3,0)2(1,-1)1.5 ( 13.5,1.5)(3,0)2(1,-1)1.5 ( 10.5,-1.5)(3,0)3(1,1)1.5 ( 12,0)(3,0)2(1,0)3 ( 13.5,1.5)(3,0)1(1,0)3 ( 10.5,-1.5)(3,0)2(1,0)3 ( 13.5,0.3)(0,0)@xmath62 ( 16.5,0.3)(0,0)@xmath63 ( 15,1.75)(0,0)@xmath67 ( 12,-1.75)(0,0)@xmath68 ( 15,-1.75)(0,0)@xmath69 ( 12.55,0.95)(0,0)@xmath73 ( 15.5,0.95)(0,0)@xmath74 ( 14.45,0.95)(0,0)@xmath78 ( 17.45,0.95)(0,0)@xmath79 ( 12.6,-0.95)(0,0)@xmath83 ( 15.6,-0.95)(0,0)@xmath84 ( 11.45,-0.95)(0,0)@xmath87 ( 14.45,-0.95)(0,0)@xmath88 ( 17.45,-0.95)(0,0)@xmath89    ( 10,0)(-1.2,-6.85)(10.5,0)(0,0)(b ) ( 12,0)(3,0)3 ( 10.5,1.5)(3,0)3 ( 13.5,-1.5)(3,0)2 ( 12,0.35)(0,0)5 ( 15,0.35)(0,0)6 ( 18,0.35)(0,0)7 ( 10.3,1.8)(0,0)4 ( 13.5,1.8)(0,0)5 ( 16.5,1.8)(0,0)6 ( 13.5,-1.8)(0,0)5 ( 16.5,-1.8)(0,0)6 ( 12,0)(3,0)2(1,1)1.5 ( 12,0)(3,0)2(1,-1)1.5 ( 10.5,1.5)(3,0)3(1,-1)1.5 ( 13.5,-1.5)(3,0)2(1,1)1.5 ( 12,0)(3,0)2(1,0)3 ( 10.5,1.5)(3,0)2(1,0)3 ( 13.5,-1.5)(3,0)1(1,0)3 ( 13.5,0.3)(0,0)@xmath62 ( 16.5,0.3)(0,0)@xmath63 ( 12,1.75)(0,0)@xmath66 ( 15,1.75)(0,0)@xmath67 ( 15,-1.75)(0,0)@xmath69 ( 12.55,0.95)(0,0)@xmath73 ( 15.5,0.95)(0,0)@xmath74 ( 11.4,0.95)(0,0)@xmath77 ( 14.45,0.95)(0,0)@xmath78 ( 17.45,0.95)(0,0)@xmath79 ( 12.6,-0.95)(0,0)@xmath83 ( 15.6,-0.95)(0,0)@xmath84 ( 14.45,-0.95)(0,0)@xmath88 ( 17.45,-0.95)(0,0)@xmath89    any path from vertex @xmath25 to vertex @xmath105 in fig . [ rhom_fig3 ] passes through decomposition vertex @xmath26 or through edge @xmath65 or through edge @xmath29 . therefore , @xmath96 is generated by the following recursive procedure ( _ decomposition procedure _ ) :    1 . [ mr1]@xmath106 @xmath107 2 .   [ mr2]@xmath106 @xmath108 3 . [ mr3]@xmath106 @xmath109 4 . [ mr4]@xmath110 + @xmath111    the expression related to a one - vertex @xmath58 is defined formally as @xmath25 ( line [ mr1 ] ) . line [ mr2 ] describes the expression of @xmath112 which is a trivial subgraph . the procedure @xmath113 in line [ mr3 ] chooses an arbitrary number @xmath92 on the interval @xmath114 so that @xmath93 . this number is a number of a decomposition vertex in a basic group of the @xmath58 subgraph positioned between vertices @xmath90 and @xmath91 . a current subgraph is decomposed into six new subgraphs in line [ mr4 ] . subgraphs described by subexpressions @xmath115 and @xmath116 include all paths from vertex @xmath90 to vertex @xmath91 passing through vertex @xmath92 . subgraphs described by subexpressions @xmath117 and @xmath118 include all paths from vertex @xmath90 to vertex @xmath91 passing via edge @xmath119 . subgraphs described by subexpressions @xmath120 and @xmath121 include all paths from vertex @xmath90 to vertex @xmath91 passing via edge @xmath122 . @xmath123 is the expression of the initial @xmath58 of size @xmath40 . hence , the decomposition procedure is initially invoked by substituting @xmath25 and @xmath40 instead of @xmath90 and @xmath91 , respectively . we now consider the algorithm that generates the algebraic expression for a square rhomboid using 1-vdm as its base .","summary":", we describe the new algorithm for generating square rhomboid expressions , which improves on our previous algorithms .","abstract":"the paper investigates relationship between algebraic expressions and graphs . we consider a digraph called a square rhomboid that is an example of non - series - parallel graphs . our intention is to simplify the expressions of square rhomboids and eventually find their shortest representations . with that end in view , we describe the new algorithm for generating square rhomboid expressions , which improves on our previous algorithms ."}
{"article_id":"astro-ph0311327","section_id":"i","document":"extragalactic novae are particularly appealing objects for studies of close binary evolution . they are _ the _ tracer of interacting close binary stars , visible to much greater distances than any other well studied standard candle except supernovae ( novae display m@xmath4 up to @xmath5 ) . by studying the novae in a nearby galaxy , one can gather a homogeneous sample of objects , all at the same distance , that is not plagued by the selection effects hampering an analysis of the cataclysmic variable ( cv ) population in our own galaxy . given the large fraction of all stars that exist in binaries , the effort to understand binary formation and evolution has wide reaching implications for understanding stellar populations . there are currently many unsolved problems in the theory of close binary formation and evolution that are difficult to tackle using cvs in our own galaxy because of the selection effects mentioned above . the prediction that the nova rate should correlate with the star formation history in the underlying stellar population @xcite is one example . this prediction is based on our understanding of how close binaries form and evolve , combined with our understanding of how the mass of a nova progenitor influences the nova outburst . massive white dwarfs come from massive progenitors . these massive white dwarfs erupt as novae frequently as they need only accrete a small amount of hydrogen from their companions to explode as novae . this , in turn , implies that stellar populations with a low star formation rate should have a correspondingly low nova rate , i.e. , early - type galaxies with older stellar populations should have a lower luminosity specific nova rate ( lsnr ) than late - type galaxies with ongoing star formation . efforts have been made to detect a trend in lsnr with galaxy type @xcite , but the random errors are too large to date for a meaningful comparison . typical extragalactic nova surveys are carried out using short runs , and significant assumptions must be made about the mean lifetimes of novae in order to derive nova rates @xcite . it is also rare that an extragalactic survey has been able to spatially cover an entire galaxy and avoid making some assumption about the distribution of novae with light to derive a galactic nova rate . the resulting errors in the nova rates are large , but systematic biases are far more pernicious .    in order to accurately compare nova rates with the underlying stellar population , we are pursuing a research program that uses the comprehensive time and spatial coverage afforded by a dedicated observatory . we have begun our program with m81 and used 5 continuous months of observing time to produce a survey that requires no assumptions about nova distribution or mean lifetime . not since @xcite surveyed the central parts of m31 has such extensive , continuous coverage of a galaxy for novae been attempted . our survey updates the 5 year photographic survey of m81 for novae reported by @xcite . they found 23 novae , evenly divided over the disk and central bulge . significant incompleteness must be present in that survey due to photographic saturation in the bright central regions of the galaxy and due to large gaps in their time coverage . the results we present below show that a comprehensive spatial and temporal survey is required to minimize the systematic effects of incompleteness .","summary":"we observed m81 nearly every clear night during this interval , covering the entire galaxy , and discovered 12 novae .","abstract":"we present the results of a preliminary h survey of m81 for novae conducted over a 5 month interval using the 5 field of view camera ( wfcam ) on the calypso telescope at kitt peak , az . we observed m81 nearly every clear night during this interval , covering the entire galaxy , and discovered 12 novae . our comprehensive time coverage allowed us to produce the most complete set of h light curves for novae in m81 to date . a raw nova rate for m81 gives 23 yr which , because of the nature of our survey , is a hard lower limit . an analysis of the completeness in our survey gives a corrected nova rate of 30 yr . this agrees well with the rate of 33 yr , derived from monte carlo simulations using nova light curves and survey frame limits . the spatial distribution of the novae we discovered follows the bulge light much better than the disk or total light according to kolmogorov - smirnov tests of their radial distributions . the asymmetry in the distribution of novae across the major axis line of m81 implies a bulge - to - disk nova ratio of 9 and supports the idea that novae originate primarily in older stellar populations ."}
{"article_id":"astro-ph0311327","section_id":"c","document":"\\1 ) the raw nova rate for m81 provides a hard lower limit at 23 yr@xmath1 . using a set of representative nova h@xmath0 light curves in random outburst simulations we derive a completeness corrected nova rate of 30 yr@xmath1 . monte carlo simulations using the same set of light curves provide our most reliable nova rate for m81 of 33@xmath2 yr@xmath1 . the high nova rate found here for m81 , with a survey technique that uses comprehensive time and spatial coverage , implies that the nova rates for other galaxies derived from surveys with incomplete spatial coverage and widely spaced epochs are , at best , rough values and may be serious underestimates . \\2 ) the lsnr for m81 is @xmath36 yr@xmath37^{-1}$ ] using our best nova rate and the 2mass k - band photometry for m81 . this raises the lsnr for m81 up by a factor of two from that published by @xcite , and implies that the lsnr for other galaxies could be systematically low by similar or greater amounts . a definitive comparison between galaxies of different hubble type must await the results of comprehensive nova surveys , such as presented here . \\3 ) the cumulative radial distribution of the novae matches the bulge light distribution significantly better than either the total or the disk light distribution , which is ruled out at a 99% confidence level . the btr value for m81 of 0.25 derived from the asymmetry in the spatial distribution of the apparent bulge novae across the major axis line , implies a bulge - to - disk nova ratio for m81 of @xmath3 9 , according to the models of @xcite for novae in m31 . both these facts lead to an association of the novae in m81 with the older bulge stellar population . \\4 ) the disk novae reported here , nova 3 and 10 , have decline rates that place them in the slow class of novae , but their maximum magnitudes were not determined . nova 6 is most likely a fast hybrid nova , is 16 from the nucleus of m81 , but can not be unambiguously assigned to either the bulge or the disk . more comprehensive light curves of both bulge and disk novae are required to test for differences in their average maximum magnitudes and decline rates . it is a pleasure to acknowledge the calypso observatory director , edgar smith , for his generous allocation of observing time , his support for , and continued interest in this project . we also gratefully acknowledge the support of our observing team , elaine halbedel and viktor malnushenko , whose observing abilities and dedication through numerous trials made this project possible . we thank robin ciardullo for a comprehensive and rapid referee s report with excellent suggestions . we also thank alan shafter for valuable comments on the paper . ms thanks ren racine for conversations and support regarding novae in m81 . this research has made use of the nasa/ ipac infrared science archive , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . arp , h.  c.  1956 , , 61 , 15 ciardullo , r. , ford , h. , & jacoby , g.  1983 , , 272 , 92 ciardullo , r. , ford , h. c. , neill , j. d. , jacoby , g. h. , & shafter , a. w. 1987 , apj , 318 , 520 ciardullo , r. , shafter , a.  w. , ford , h.  c. , neill , j.  d. , shara , m.  m. , & tomaney , a.  b.  1990 , , 356 , 472 della valle , m. , rosino , l. , bianchini , a. , & livio , m.  1994 , , 287 , 403 della valle , m.  & livio , m.  1998 , , 506 , 818 filippenko , a.  v.  & chornock , r.  2003 , , 8086 , 3 hatano , k. , branch , d. , fisher , a. , & starrfield , s.  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shafter , a.  w. 1992 , , 81 , 683 weisz , d.  & li , w.  2003 , , 8069 , 2 yungelson , l , livio , m. , & tutukov , a. 1997 , apj , 481 , 127      1n & 09 56 24.6 & 68 58 24 & 19 & 89 & 29.7 & 0 & disk + 1s & 09 56 24.1 & 68 53 44 & 18 & 87 & 29.0 & 0 & disk + 2n & 09 55 31.8 & 69 01 34 & 18 & 82 & 27.3 & 3 & bulge + 2s & 09 55 30.1 & 68 56 52 & 5 & 23 & 7.7 & 0 & disk + 3n & 09 54 39.9 & 69 03 12 & 17 & 79 & 26.3 & 1 & disk + 3s & 09 54 40.6 & 68 58 29 & 10 & 48 & 16.0 & 0 & disk + 4n & 09 56 25.2 & 69 07 35 & 18 & 80 & 26.7 & 0 & disk + 4s & 09 56 25.3 & 69 02 57 & 5 & 25 & 8.3 & 0 & disk + 5n & 09 55 31.1 & 69 10 58 & 6 & 29 & 9.7 & 0 & disk + 5s&09 55 31.7 & 69 06 14&15/21 & 68/94 & 22.7/31.3 & 7 & bulge + 6n & 09 54 39.1 & 69 12 32 & 8 & 36 & 12.0 & 0 & disk + 6s & 09 54 39.4 & 69 07 50 & 21 & 94 & 31.3 & 1 & disk +      1 & 09 55 39.2 & 69 04 22 & 5s & 11 & 42 & 84 + 2 & 09 55 21.5 & 69 05 60 & 5s & 9 & 140 & 141 + 3 & 09 54 53.6 & 69 06 49 & 6s & 5 & 274 & 317 + 4 & 09 55 35.3 & 69 03 34 & 2n & 2 & 24 & 24 + 5 & 09 55 28.5 & 69 05 10 & 5s & 10 & 79 & 85 + 6 & 09 55 48.5 & 69 03 05 & 2n & 3 & 96 & 123 + 7 & 09 55 40.5 & 69 03 49 & 2n & 6 & 40 & 66 + 8 & 09 55 46.7 & 69 04 07 & 5s & 8 & 73 & 140 + 9 & 09 55 26.5 & 69 04 44 & 5s & 4 & 61 & 61 + 10 & 09 55 04.4 & 69 03 24 & 3n & 4 & 157 & 304 + 11 & 09 55 34.8 & 69 05 34 & 5s & 14 & 99 & 144 + 12 & 09 55 47.4 & 69 04 44 & 5s & 16 & 91 & 183 +      1 & 641.80 & 18.02 & 0.17 & 18.5 + & 644.79 & 18.46 & 0.17 & 18.8 + & 653.88 & 18.16 & 0.13 & 18.8 + & 668.78 & 18.50 & 0.11 & 18.9 + & 679.64 & 18.33 & 0.15 & 18.7 + & 689.88 & & & 18.3 + & 693.76 & 18.93 & 0.15 & 19.0 + & 707.60 & 18.69 & 0.25 & 18.7 + & 709.78 & 18.88 & 0.14 & 19.3 + & 711.89 & 19.20 & 0.22 & 19.2 + & 720.78 & & & 18.9 + & 723.79 & 18.88 & 0.17 & 19.0 + & 728.63 & 18.97 & 0.21 & 19.0 + & 735.63 & & & 18.5 + & 753.79 & & & 18.7 + & 758.79 & & & 18.4 + & 769.69 & & & 19.3 +   + 2 & 641.80 & 18.28 & 0.12 & 18.9 + & 644.79 & 18.05 & 0.09 & 19.3 + & 653.88 & 18.26 & 0.10 & 19.5 + & 668.78 & 18.67 & 0.10 & 19.7 + & 679.64 & 18.62 & 0.13 & 19.3 + & 689.88 & 19.02 & 0.23 & 19.0 + & 693.76 & 19.27 & 0.14 & 19.7 + & 707.60 & 19.41 & 0.23 & 19.5 + & 709.78 & 19.38 & 0.16 & 19.7 + & 711.89 & & & 19.4 + & 720.78 & & & 19.7 +   + 3 & 642.76 & 18.05 & 0.08 & 19.5 + & 652.76 & 18.66 & 0.23 & 19.5 + & 657.74 & & & 18.5 + & 670.78 & 18.87 & 0.11 & 20.0 + & 680.71 & 19.37 & 0.29 & 19.5 + & 705.75 & & & 19.9 + & 707.91 & & & 19.5 + & 710.68 & & & 19.0 + & 718.79 & & & 19.0 + & 721.80 & 19.87 & 0.33 & 20.0 + & 724.89 & & & 19.5 + & 725.61 & & & 19.5 + & 728.79 & & & 20.0 +   + 4 & 639.84 & & & 19.2 + & 643.78 & 18.45 & 0.23 & 19.0 + & 653.77 & & & 18.5 + & 668.68 & 19.66 & 0.54 & 19.7 + & 671.88 & & & 19.5 +   + 5 & 668.78 & & & 19.5 + & 679.64 & 18.72 & 0.15 & 19.1 + & 689.88 & & & 18.7 + & 693.76 & 18.55 & 0.10 & 19.5 + & 707.60 & 18.57 & 0.15 & 18.8 + & 709.78 & 18.55 & 0.09 & 19.5 + & 711.89 & 18.88 & 0.14 & 19.2 + & 720.78 & 18.79 & 0.15 & 19.4 + & 723.79 & 18.29 & 0.09 & 19.4 + & 728.63 & 18.20 & 0.09 & 19.2 + & 735.63 & 18.37 & 0.13 & 18.7 + & 753.79 & 18.98 & 0.18 & 19.0 + & 758.79 & & & 18.9 +   + 6 & 671.88 & & & 20.2 + & 676.90 & ( 19 ) & & + & 679.90 & ( 17.8 ) & & + & 680.90 & ( 17.9 ) & & + & 687.99 & 17.34 & 0.07 & 18.7 + & 692.63 & 17.37 & 0.04 & 19.7 + & 706.84 & 19.20 & 0.17 & 19.7 + & 709.63 & & & 18.7 + & 711.72 & & & 19.5 +   + 7 & 692.63 & & & 19.7 + & 706.84 & 18.26 & 0.12 & 19.7 + & 709.63 & 17.42 & 0.08 & 18.7 + & 711.72 & 16.97 & 0.04 & 19.5 + & 720.62 & 17.66 & 0.09 & 19.5 + & 723.61 & 17.79 & 0.13 & 19.0 + & 734.79 & 18.82 & 0.14 & 20.2 + & 758.70 & & & 19.3 + & 765.65 & & & 19.7 +   + 8 & 693.76 & & & 19.5 + & 707.60 & 17.76 & 0.09 & 18.8 + & 709.78 & 17.79 & 0.05 & 19.5 + & 711.89 & 17.95 & 0.07 & 19.2 + & 720.78 & 18.46 & 0.13 & 19.4 + & 723.79 & 18.64 & 0.12 & 19.4 + & 728.63 & 18.91 & 0.17 & 19.2 + & 735.63 & & & 18.7 + & 753.79 & & & 19.0 + & 758.79 & & & 18.9 + & 769.69 & & & 19.5 +   + 9 & 693.76 & & & 19.5 + & 707.60 & 18.69 & 0.20 & 18.8 + & 709.78 & 18.74 & 0.12 & 19.5 + & 711.89 & 19.12 & 0.19 & 19.2 + & 720.78 & 19.36 & 0.29 & 19.4 + & 723.79 & & & 19.4 +   + 10 & 728.71 & & & 19.7 + & 735.85 & & & 18.5 + & 754.77 & 18.59 & 0.10 & 19.2 + & 759.65 & 18.92 & 0.12 & 19.7 + & 770.69 & 18.78 & 0.17 & 19.5 + & 778.74 & & & 19.2 + & 785.75 & 19.68 & 0.40 & 19.7 + & 796.63 & & & 18.7 +   + 11 & 758.79 & & & 18.9 + & 769.69 & 17.61 & 0.06 & 19.7 + & 777.66 & 17.47 & 0.08 & 18.9 + & 778.66 & 17.59 & 0.04 & 19.9 + & 783.65 & 17.98 & 0.11 & 19.5 + & 794.64 & 18.23 & 0.08 & 20.1 + & 797.64 & 18.47 & 0.12 & 19.5 + & 798.65 & 18.90 & 0.19 & 19.2 + & 800.64 & 18.21 & 0.24 & 18.5 + & 801.68 & 18.64 & 0.22 & 18.9 + & 802.68 & 18.61 & 0.19 & 19.5 + & 805.67 & & & 19.1 + & 807.67 & 18.72 & 0.17 & 19.2 + & 808.64 & 18.82 & 0.20 & 19.3 + & 809.67 & & & 18.5 + & 810.65 & & & 19.0 + & 811.66 & & & 18.7 + & 812.66 & & & 19.1 + & 813.66 & 18.74 & 0.16 & 19.3 + & 815.67 & 18.57 & 0.14 & 19.3 + & 816.67 & & & 18.9 +   + 12 & 783.65 & & & 19.5 + & 794.64 & 18.60 & 0.11 & 20.1 + & 797.64 & 18.18 & 0.10 & 19.5 + & 798.65 & 18.29 & 0.12 & 19.2 + & 800.64 & 18.25 & 0.29 & 18.5 + & 801.68 & 18.48 & 0.19 & 18.9 + & 802.68 & 18.08 & 0.11 & 19.5 + & 805.67 & 17.96 & 0.15 & 19.1 + & 807.67 & 17.90 & 0.10 & 19.2 + & 808.64 & 17.98 & 0.09 & 19.3 + & 809.67 & 17.90 & 0.14 & 18.5 + & 810.65 & 18.04 & 0.13 & 19.0 + & 811.66 & 17.91 & 0.11 & 18.7 + & 812.66 & 18.43 & 0.14 & 19.1 + & 813.66 & 18.54 & 0.14 & 19.3 + & 815.67 & 18.52 & 0.14 & 19.3 + & 816.67 & 18.70 & 0.21 & 18.9 +      1 & @xmath38 18.0 & 87 & & 87 & 11 & 0.010 + 2 & 18.0 & 68 & @xmath3 3 & 65 & 8 & 0.021 + 3 & @xmath38 18.0 & 79 & & 79 & 5 & 0.027 + 4 & @xmath38 18.4 & 25 & & 25 & 2 & 0.049 + 5 & 18.2 & 74 & @xmath3 49 & 25 & 3 & 0.031 + 6 & 17.3 & 19 & @xmath3 11 & 14 & 2 & 0.129 + 7 & 17.0 & 28 & @xmath3 5 & 23 & 4 & 0.078 + 8 & @xmath38 17.8 & 21 & & 21 & 6 & 0.058 + 9 & @xmath38 18.7 & 13 & & 13 & 4 & 0.058 + 10 & @xmath38 18.6 & 31 & & 31 & 4 & 0.022 + 11 & 17.5 & 46 & @xmath3 8 & 38 & 13 & 0.036 + 12 & 17.9 & 22 & @xmath3 13 & 9 & 9 & 0.087 +      1n & 430 & 444 & 19 & 76 + 1s & 669 & 685 & 18 & 80 + 2n & 141 & 199 & 18 & 80 + 2n & 24 & 24 & 18 & 48 + 2s & 423 & 591 & 5 & 41 + 3n & 289 & 550 & 17 & 78 + 3s & 431 & 841 & 10 & 79 + 4n & 355 & 716 & 18 & 78 + 4s & 285 & 464 & 5 & 30 + 5n & 424 & 564 & 6 & 40 + 5s & 140 & 182 & 21 & 89 + 5s & 79 & 85 & 21 & 85 + 5s & 42 & 84 & 21 & 72 + 6n & 593 & 595 & 8 & 50 + 6s & 372 & 431 & 21 & 79 +      5 & 18.2 & 79 & 0.031 + 7 & 17.0 & 80 & 0.078 + 12 & 17.9 & 74 & 0.087 + cfnjs 6 & 18.2 & 65 & 0.080 + cfnjs 20 & 19.8 & 54 & 0.0044 + cfnjs 26 & 17.6 & 82 & 0.029 + cfnjs 31 & 18.5 & 80 & 0.013 + n1992 - 07 & 19.0 & 71 & 0.0070 + n1995 - 06 & 18.9 & 78 & 0.015 + n1995 - 07 & 19.4 & 71 & 0.0090 + n1995 - 09 & 21.2 & 3.5 & 0.046 +      1n & 430 & 444 & 19 & 0 & 0@xmath39 + 1s & 669 & 685 & 18 & 0 & 0@xmath40 + 2n & 141 & 199 & 18 & 3 & 8@xmath41 + 2n & 24 & 24 & 18 & 3 & 14@xmath42 + 2s & 423 & 591 & 5 & 0 & 0@xmath43 + 3n & 289 & 550 & 17 & 1 & 2@xmath44 + 3s & 431 & 841 & 10 & 0 & 0@xmath40 + 4n & 355 & 716 & 18 & 0 & 0@xmath40 + 4s & 285 & 464 & 5 & 0 & 0@xmath45 + 5n & 424 & 564 & 6 & 0 & 0@xmath43 + 5s & 140 & 182 & 21 & 7 & 16@xmath46 + 5s & 79 & 85 & 21 & 7 & 17@xmath47 + 5s & 42 & 84 & 21 & 7 & 20@xmath48 + 6n & 593 & 595 & 8 & 0 & 0@xmath49 + 6s & 372 & 431 & 21 & 1 & 2@xmath44 +","summary":"the spatial distribution of the novae we discovered follows the bulge light much better than the disk or total light according to kolmogorov - smirnov tests of their radial distributions . the asymmetry in the distribution of novae across the major axis line of m81 implies a bulge - to - disk nova ratio of 9 and supports the idea that novae originate primarily in older stellar populations .","abstract":"we present the results of a preliminary h survey of m81 for novae conducted over a 5 month interval using the 5 field of view camera ( wfcam ) on the calypso telescope at kitt peak , az . we observed m81 nearly every clear night during this interval , covering the entire galaxy , and discovered 12 novae . our comprehensive time coverage allowed us to produce the most complete set of h light curves for novae in m81 to date . a raw nova rate for m81 gives 23 yr which , because of the nature of our survey , is a hard lower limit . an analysis of the completeness in our survey gives a corrected nova rate of 30 yr . this agrees well with the rate of 33 yr , derived from monte carlo simulations using nova light curves and survey frame limits . the spatial distribution of the novae we discovered follows the bulge light much better than the disk or total light according to kolmogorov - smirnov tests of their radial distributions . the asymmetry in the distribution of novae across the major axis line of m81 implies a bulge - to - disk nova ratio of 9 and supports the idea that novae originate primarily in older stellar populations ."}
{"article_id":"1408.1063","section_id":"i","document":"finding an optimal lower bound for the number of arithmetic progressions of length 3 in any subset of fixed cardinality in a set is extremely difficult , and finding this for the cyclic group would imply close to optimal bounds to szemerdi s theorem . in this paper we develop new methods that theoretically will achieve the optimal lower bound by putinar s positivstellensatz , and provide a relaxation scheme based on the lasserre hierarchy providing lower bounds to the number of arithmetic progressions . the methods are general and can be applied to any fixed density set . we apply the methods to find the first known lower bound for the number of arithmetic progressions in any subset @xmath0 of the cyclic group @xmath1 with a fixed density @xmath2 for any prime @xmath3 ( theorem [ thm : density ] ) , and investigate how much this can be improved using a similar certificate ( theorem [ thm : density2 ] and corollary [ cor : density ] ) . we discuss a possible way to improve the bounds further , which in theory could ultimately generalize szemerdi s theorem , in section [ sec : discussion ] . we provide sharper lower bounds with algebraic certificate for all primes @xmath4 ( theorem [ thm : smallprimes ] ) , and in section [ sec : numerical2 ] we discuss lower bounds found using a numerical certificate for all primes @xmath5 and the correct results up to @xmath6 found by searching through all different possibilities . we have provided tables of all these exact lower bounds in the appendix .","summary":"szemerdi s theorem is an existence statement , whereas the ultimate goal in combinatorics is always to make enumeration statements . in this article we develop new methods based on real algebraic geometry to obtain several quantitative statements on the number of arithmetic progressions in fixed density sets .","abstract":"additive combinatorics is built around the famous theorem by szemerdi which asserts existence of arithmetic progressions of any length among the integers . there exist several different proofs of the theorem based on very different techniques . szemerdi s theorem is an existence statement , whereas the ultimate goal in combinatorics is always to make enumeration statements . in this article we develop new methods based on real algebraic geometry to obtain several quantitative statements on the number of arithmetic progressions in fixed density sets . we further discuss the possibility of a generalization of szemerdi s theorem using methods from real algebraic geometry ."}
{"article_id":"1408.1063","section_id":"i","document":"this section provides a literature review on existence type theorems about arithmetic progressions . we start with some basic definitions and discuss many of the major contributions to the field .    for @xmath48 , let us define the _ ( upper ) density _ @xmath49    as an example , the density of the even positive integers is @xmath50 . formally we define arithmetic progressions for the integers and for finite groups in the following way :    an _ arithmetic progression of length @xmath51 _ in the positive integers is given by @xmath52 , where @xmath53 . an arithmetic progression of length @xmath51 in a finite group @xmath54 is a set of @xmath8 distinct elements @xmath55 , where @xmath56 and @xmath57 . to clarify , for example @xmath58 , @xmath59 , @xmath60 , @xmath61 , @xmath62 and @xmath63 should be considered as the same arithmetic progression as it is the same set of @xmath19 distinct elements , hence when we write @xmath64 only one representative for every arithmetic progression is used . it is interesting to study arithmetic progressions since it measures how structured a set is . a set is usually either very random in nature or has a structure similar to that of an arithmetic progression . in additive combinatorics one tries to answer questions about the length of the longest arithmetic progressions contained in very unstructured sets , how structured sets are contained in generalizations of arithmetic progressions and many similar questions . in the last century a lot of results in additive combinatorics have been proven using probabilistic methods , fourier - analytic methods , sum set estimates , graph theory , ergodic theory and algebraic methods . to answer questions about existence of arithmetic progression in subsets of the integers is one of the most difficult questions in additive combinatorics , and the question that has gotten the most attention . we refer to the book by tao and vu @xcite for an accessible introduction to the subject . van der waerden proved in 1927 @xcite that for any given positive integers @xmath30 and @xmath8 there is a number @xmath65 such that if the integers @xmath66 are colored in @xmath30 colors , then there exists a monochromatic arithmetic progression of length @xmath8 . this is one of the key results of ramsey theory . the smallest such @xmath65 will be denoted @xmath67 and is called the _ van der waerden number_. already for @xmath68 we have a huge gap between the lower bound @xmath69 for primes by berlekamp @xcite and the upper bound @xmath70 by gowers @xcite . finding bounds for van der waerden - like numbers is still an active area of research , recent contributions include @xcite . results about arithmetic progressions in fixed - density sets implies results about monochromatic arithmetic progressions in colorings and are thus more general . the first non - trivial result about existence of arithmetic progressions in sets is due to roth in 1953 . the proof is based on the hardy - littlewood circle method , and because of this result roth was awarded the fields medal in 1958 . if @xmath48 and @xmath71 , then it follows that we can find arithmetic progressions in @xmath0 of length @xmath19 .    in 1969 szemerdi strengthened roth result to existence of arithmetic progressions of length 4 @xcite and in 1975 he generalized it to arithmetic progressions of arbitrary length @xcite . in order to prove the result szemerdi developed the famous regularity lemma , which states that every large enough graph can be partitioned into subgraphs of about the same size so that the edges between the different subgraphs behave fairly randomly . for these and other combinatorial results he was awarded the abel prize in 2012 . if @xmath48 and @xmath71 , then it follows that we can find arbitrarily long arithmetic progressions in @xmath0 . we denote by @xmath72 the smallest positive integer such that for any @xmath73 it holds that any subset of @xmath74 of cardinality @xmath75 contains an arithmetic progression of length @xmath8 for @xmath76 . similarly we define @xmath77 to be the smallest density such that any subset of @xmath78 of cardinality @xmath79 contains an arithmetic progression of length @xmath8 for any @xmath80 . szemerdi s theorem implies the existence of an @xmath72 for any @xmath8 and @xmath81 but fails to provide any good bounds for this number . another proof of szemerdi s theorem using ergodic methods was mainly due to furstenberg in 1982 @xcite . the ergodic methods makes the proof easier , and they have implied several other results in additive combinatorics including a multi - dimensional version and a polynomial version of szemerdi s theorem , and the related density hales - jewett theorem . tao gave a quantitative version based on ergodic theory in 2006 @xcite , but no effective bound for @xmath72 has been found using ergodic methods . even though roth s theorem is old , there has been more recent progress on improving the quantitative bounds @xmath82 . most results are formulated bounding @xmath83 instead of @xmath82 , and so we follow this notation . roth s original proof showed that there is a constant @xmath84 such that @xmath85 . this was improved by heath - brown and szemerdi @xcite showing that there exist constants @xmath86 and @xmath87 such that @xmath88 and later by bourgain @xcite showing that @xmath89 for some constant @xmath84 . more recently bourgain @xcite improved the bound to @xmath90 , then sanders @xcite improved it to @xmath91 and then sanders @xcite improved it further to @xmath92 for some large enough constant @xmath84 . versions of roth s theorem for other groups have also been of interest lately . the result was generalized to hold for arbitrary abelian groups of odd order by meshulam in 1995 @xcite . a way to generalize roth s theorem is through generalizing the ( triangle ) removal lemma , which is related to szemerdi s regulaity lemma . green generalized the removal lemma to abelian groups @xcite , and krl , serra and vela generalized it to hold for all finite groups , with a version of roth s theorem for all finite groups as a consequence @xcite :    let @xmath54 be a finite group of odd order @xmath65 and @xmath0 a subset of its elements . if the number of solutions of the equation @xmath93 with @xmath94 is @xmath95 , then the size of @xmath0 is @xmath96 .    to get the result to also hold for non - abelian groups they had to avoid using fourier analysis . other results in additive combinatorics for non - abelian groups are the results by bergelson and hindman @xcite , gowers @xcite , tao @xcite , sanders @xcite and solymosi @xcite . the results have been established long after the commutative counterparts , and often with much weaker bounds . let @xmath97 denote @xmath98 , @xmath99 , and so on . in 1998 @xcite gowers showed that there exists an absolute constant @xmath84 such that @xmath100 , which was a major improvement on the previous best bound . the bound was improved by green and tao in 2009 @xcite to @xmath101 . in 2001 gowers provided the first effective upper bound for @xmath72 for @xmath102 using the fourier analytic machinery he had developed and been awarded the fields medal for in 1998 . [ thm : gowers ] let @xmath8 be a positive integer and let @xmath103 . then @xmath104    before stating our next theorem , let us state what ( gower s version of ) szemerdi s theorem implies about @xmath105,\\delta)$ ] . [ cor : limit ] it follows by theorem [ thm : gowers ] that @xmath106,\\delta ) > 0 \\ } = 0.\\ ] ] conversely , if there are lower bounds @xmath107,\\delta ) \\leq w(k,[n],\\delta)$ ] with the additional property that @xmath108,\\delta ) > 0 \\ } = 0\\ ] ] holds , then szemerdi s theorem would follow . we want to show that for any @xmath109 and @xmath110 there exists @xmath111 such that @xmath112,\\delta ) > 0 \\ } < \\epsilon\\ ] ] for all @xmath113 . by theorem [ thm : gowers ] we know that if we pick @xmath114 , then any subset @xmath115 with cardinality @xmath116 , where @xmath117 , contains an arithmetic progression of length @xmath8 , hence the desired inequality holds .    on the other hand , suppose @xmath108,\\epsilon ) > 0 \\ } = 0.\\ ] ] since @xmath107,\\epsilon ) \\leq w(k,[n],\\epsilon)$ ] it follows that @xmath106,\\epsilon ) > 0 \\ } = 0,\\ ] ] or in other words that for any @xmath109 there exists an @xmath118 such that for any @xmath119 it holds that @xmath115 with cardinality @xmath120 has an arithmetic progression of length @xmath8 . this is equivalent to that there are bounds for szmerdi s theorem on the form @xmath121 . another proof strategy for szemerdi s theorem relies on generalizing szemerdi s regularity lemma to hypergraphs , and was developed independently by gowers @xcite and nagle , rdl , schacht and skokan @xcite . all the results above on szemerdi s theorem require a positive upper density , but this condition might not be necessary . an open problem is how dense does a set have to be in order to contain arithmetic progressions . the following has been conjectured by erds and turn . let @xmath0 be a subset of the positive integers . @xmath0 contains arithmetic progressions of any length if @xmath122 diverges . the primes do not have positive density , but results on arithmetic progressions among them would follow from the erds - turn conjecture . existence of arithmetic progressions of length 3 among any positive proportion of the prime numbers was proven by green @xcite and quantitative improvements were made by helfgott and roton @xcite . the result for arithmetic progressions of arbitrary length was found using szemerdi s regularity lemma and properties about the distribution of primes by green and tao @xcite . there exist arbitrarily long arithmetic progressions among the prime numbers . so far we have only discussed results on upper bounds for @xmath77 , one can also try to find lower bounds . the lower bounds are still very far from the upper bounds , and surprisingly not much improvements have been done on the lower bounds for over 50 years . let @xmath84 be a large enough constant . the lower bound for @xmath123 due to behrend @xcite @xmath124 was the best bound for over 60 years until elkin @xcite recently improved it to @xmath125 for larger @xmath8 the we have the following bound by rankin @xcite : @xmath126 soon after elkin improved the bound for @xmath123 , obryant @xcite improved the bounds for @xmath123 and general @xmath8 further : for every @xmath127 and @xmath65 large enough @xmath128 and @xmath129{\\log_2 n } + \\frac{1}{2n } \\log_2 \\log_2 n},\\ ] ] where @xmath130 is an unspecified constant and @xmath131 . szemerdi s theorem roughly states that any subset @xmath132 of the integers , however random and unstructured it is , will contain very structured subsets if @xmath65 and @xmath133 are large enough . one can ask how long arithmetic progressions there are in more structured sets , such as for example @xmath134 and @xmath135 . in fact , the additional structure allows us to find much longer arithmetic progressions , for example we have the following result from bourgain @xcite on sums of sets :    let @xmath136 be a prime nuber and @xmath137 additive sets in @xmath1 with @xmath138 for some @xmath139 where @xmath140 is a large enough absolute constant . then @xmath141 contains an arithmetic progression of length at least @xmath142 for some constant @xmath143 . iterated sumsets have even more structure , and results include those of srkzy @xcite , lev @xcite , nathanson and rusza @xcite , and szemerdi and vu @xcite . we state a quite general and strong theorem from @xcite :    let @xmath144 . there exists constants @xmath145 such that for any @xmath146 and @xmath147 of cardinality @xmath148 and @xmath149 , @xmath150 contains a proper arithmetic progression of length @xmath151    the number of arithmetic progressions in a fixed density set is closely related to the number of monochromatic arithmetic progressions in coloring of a set . all results above can easily be translated in terms of colorings . a _ @xmath152-coloring _ of a set @xmath0 is a map @xmath153 splitting @xmath0 into @xmath152 color classes . if there exist arithmetic progressions in any set @xmath154 with positive upper density @xmath71 then there exist monochromatic arithmetic progressions in any @xmath152-coloring of the positive integers . suppose there exist arithmetic progressions in any set @xmath154 with positive upper density . let @xmath155 be a @xmath152-coloring of the positive integers . since @xmath152 is finite we have @xmath156 for any @xmath17 , and thus for some @xmath157 the color class @xmath158 has positive upper density . by assumption there are arithmetic progressions in @xmath159 , and thus of color @xmath157 . the ultimate goal in combinatorial problems is always to count the desired constellation . the existence results on arithmetic progressions provide very strong results on how many arithmetic progressions there are in certain limits , but provides no information about the amount of arithmetic progressions far from the limits . to make the statements precise , let us define the functions of interest :    let @xmath160,c)$ ] denote the minimal number of monochromatic arithmetic progressions of length @xmath8 in any @xmath152-coloring of @xmath9=\\{1,\\dots , n\\}$ ] . let @xmath161 denote the minimal number of monochromatic arithmetic progressions of length @xmath8 in any @xmath152-coloring of a finite group @xmath54 . let @xmath7,\\delta)$ ] denote the minimal number of arithmetic progressions of length @xmath8 in any subset @xmath162 of cardinality @xmath163 . let @xmath164 denote the minimal number of arithmetic progressions of length @xmath8 in any subset @xmath165 of cardinality @xmath166 . it would of course be desirable to find the exact values of these functions for any possible inputs @xmath8 , @xmath17 , @xmath152 , @xmath81 and @xmath54 , but it is not likely that they will ever be found because of how complicated the functions are . finding the exact functions would give us sharp upper bounds for szemerdi s theorem for all @xmath8 , which is known to be extremely difficult already for low values of @xmath8 . since there is little hope in finding the exact functions , we aim to find as good lower bounds to the functions as possible . good lower bounds provide a better understanding of arithmetic progressions , and if they are good enough they may additionally improve the current best existence bounds . we state all the best bounds known for various inputs that we have been able to find in the literature . upper bounds are also provided , and are usually achieved by colorings . * r(3,[n],2 ) * : upper and lower bound from @xcite . @xmath167,2 ) \\leq \\frac{117}{2192}n^2(1+o(1))\\ ] ]    * r(3,@xmath12,2 ) * : upper and lower bound from @xcite ( the special case @xmath168 found first in @xcite ) . @xmath169 where constants depends on @xmath170 : @xmath171    * r(3,@xmath172,2 ) * : upper and lower bound from @xcite . @xmath173 where constants depends on @xmath170 : @xmath171    * r(3,g,2 ) * : let @xmath54 be any finite group . let @xmath174 denote the set of elements of @xmath54 of order @xmath8 , @xmath175 and @xmath176 . denote the euler phi function @xmath177 . let @xmath178 . lower bound from @xcite : @xmath179    * r(4,@xmath12,2 ) * : wolf @xcite contributed with several bound on @xmath180 . the bounds were improved by lu and peng @xcite . note that the results in their paper differs by a factor 2 , this is because they count @xmath181 and @xmath182 as distinct arithmetic progressions . if @xmath3 is prime we have ( * ? ? ? * theorem 1.1 ) : @xmath183 for general @xmath17 we have ( * ? ? ? * theorem 1.2 and theorem 1.3 ) : @xmath184 where constants depends on @xmath185 : @xmath186 furthermore we have ( * ? ? ? * theorem 1.5 ) @xmath187 and the following conjecture ( * ? ? ? * conjecture 1.1 ) : @xmath188    * r(4,[n],2 ) * : upper bound from ( * ? ? * equation ( 12 ) ) : @xmath189,2 ) \\leq \\frac{1}{72}n^2(1+o(1)).\\ ] ]    * r(5,@xmath12,2 ) * : for odd @xmath17 we have ( * ? ? ? * theorem 1.4 ) : @xmath190 for even @xmath17 we have ( * ? ? ? * theorem 1.4 ) : @xmath191 furthermore we have ( * ? ? ? * theorem 1.5 ) @xmath192    * r(5,[n],2 ) * : upper bound from ( * ? ? ? * equation ( 13 ) ) : @xmath193,2 ) \\leq \\frac{1}{304}n^2(1+o(1)).\\ ] ]    * w(3,@xmath1,@xmath81 ) * let @xmath3 be prime . a lower bound is given by theorem [ thm : density ] : @xmath194    since @xmath195 is an arithmetic progression in @xmath196 if and only if @xmath197 for distinct @xmath198 there are many related problems where one tries to count the number of solutions to various linear equations . one example is schur triples , which are triples @xmath195 such that @xmath199 , have been studied in @xcite . other examples include sets with no solutions to @xmath200 studied in @xcite and monochromatic solution to equations in groups @xcite .","summary":"additive combinatorics is built around the famous theorem by szemerdi which asserts existence of arithmetic progressions of any length among the integers . there exist several different proofs of the theorem based on very different techniques .","abstract":"additive combinatorics is built around the famous theorem by szemerdi which asserts existence of arithmetic progressions of any length among the integers . there exist several different proofs of the theorem based on very different techniques . szemerdi s theorem is an existence statement , whereas the ultimate goal in combinatorics is always to make enumeration statements . in this article we develop new methods based on real algebraic geometry to obtain several quantitative statements on the number of arithmetic progressions in fixed density sets . we further discuss the possibility of a generalization of szemerdi s theorem using methods from real algebraic geometry ."}
{"article_id":"1408.1063","section_id":"m","document":"tools from real algebraic geometry are used to prove the main results of this paper . even though the main result can be understood without understanding polynomial optimization , it played a vital part when finding the certificates in the main theorems . only a few of the most important theorems will be presented . for a more extensive survey on the topic we refer to the excellent paper by laurent @xcite . for a longer review of how we applied and implemented methods from real algebraic geometry to the specific problem we refer to @xcite . we use polynomial optimization to count monochromatic arithmetic progressions , and so in this section we briefly review the topic . let @xmath201 be polynomials . a problem on the form @xmath202 is a polynomial optimization problem . one way to solve a polynomial optimization problem is by studying the related problem : @xmath203    let @xmath204 $ ] be polynomials . the _ quadratic module _ generated by @xmath205 is defined by : @xmath206    a quadratic module @xmath207 is _ archimedean _ if there is an @xmath208 such that @xmath209    [ thm : putinar ] let the set @xmath210 be compact . assume that the associated quadratic module @xmath207 is archimedean . if @xmath211 is strictly positive on @xmath212 , then it is possible to find sums of squares @xmath213 such that @xmath214 .    in other words , if the quadratic module of the polynomial constraints in the polynomial optimization problem is archimedean it is possible to solve the polynomial optimization problem using @xmath215 where @xmath216 is the actual parameter , and @xmath217 is a formal indeterminate . let @xmath218 be the optimal value of the related problem in which the degrees of the sums of squares are bounded : @xmath219 it is easy to see that @xmath220 for any @xmath221 . furthermore , the following important convergence result follows directly from putinar s positivstellensatz ( we present a simplified version of theorem 3.4 page 805 @xcite , and theorem 4.1 page 79 @xcite ) :    let @xmath222 $ ] , let @xmath223 be compact and assume that @xmath224 is archimedean . assume that @xmath225 and @xmath226 defined as above are finite and let @xmath218 denote the optimal value of the @xmath221th restriction defined above . then @xmath227 as @xmath228 . the family of relaxations @xmath218 is often referred to as the lasserre hierarchy . let @xmath229 denote the vector of all monomials of degree less than or equal to @xmath230 . @xmath231 is a sum of squares of degree @xmath232 if and only if it is possible to find a positive semidefinite matrix @xmath233 such that @xmath234 . it follows that @xmath218 can be obtained by @xmath235 we rewrite the problem in order to get it on the generic form of a semidefinite program . if we let @xmath236_\\alpha x^\\alpha$ ] , we see that @xmath237_0 = \\lambda , \\\\ & \\displaystyle [ f(x ) - v _ { \\lfloor \\frac{j}{2 } \\rfloor } ^tq_0v _ { \\lfloor \\frac{j}{2 } \\rfloor } + \\sum_{i=1}^m v _ { \\lfloor \\frac{j- \\deg(g_i)}{2 } \\rfloor}^tq_iv _ {   \\lfloor \\frac{j - \\deg(g_i)}{2 } \\rfloor } g_i(x)]_\\alpha = 0 \\\\ & \\textrm { for all } \\alpha , \\\\ & \\displaystyle   q_i \\succeq 0 \\textnormal { for } i = 0,1,\\dots , m . \\\\ \\end{array}\\ ] ] since @xmath238_\\alpha$ ] is a linear polynomial in the entries of the matrices @xmath239 this is indeed a semidefinite program . any numerical solution to the semidefinite program includes a certificate based on positive semidefinite matrices . the certificate can be translated into a sum of squares based certificate . the sum of squares based certificate attained additionally serves as a lower bound to the original polynomial optimization problem since @xmath240 . sum of squares based certificates are very easy to check by hand , which is one of the major advantages of this method . this subsection can be skipped for the reader who just wants to understand the final proofs as these methods were just necessary to find the numerical solutions that allowed us to find the final certificates . the main result we review in this section is theorem [ thm : schrijver ] as it is one of the strongest results when working on semidefinite programs with symmetries . we discuss the limitations of this theorem when applied to our specific problem in section [ sec : methodsdensity ] . because of these limitations we would barely gain anything by using theorem [ thm : schrijver ] instead of the easier lemma [ lem : groupaverage ] . although the lemma is a very basic result in representation theory , the numerical calculations done in this article would not have been possible without this lemma . let @xmath84 and @xmath241 be real symmetric matrices and let @xmath242 be real numbers . in this section the objective is to reduce the order of the matrices in the semidefinite programming problem @xmath243 when it is invariant under the actions of a group .    as in @xcite and @xcite , we use a @xmath244representation to reduce the dimension of the matrices . for a survey on @xmath244algebras we refer to the book by takesaki @xcite . the method we use as well as other efficient methods for invariant semidefinite programs are discussed in @xcite . other important recent contributions include @xcite . a _ matrix @xmath244-algebra _ is a collection of matrices that is closed under addition , scalar and matrix multiplication , and transposition . let @xmath54 be a finite group , which acts on a finite set @xmath245 and let @xmath246 be the group of all permutations of @xmath245 . let @xmath247 be a homomorphism @xmath248 that takes any element @xmath249 to a permutation @xmath250 of @xmath245 for which @xmath251 and @xmath252 . for every permutation @xmath253 we element - wise define the corresponding permutation matrix @xmath254 by @xmath255 for all @xmath256 . the span of these matrices is the following matrix @xmath244-algebra @xmath257 the matrices @xmath217 that commute with all permutation matrices are the _ invariant matrices _ of @xmath54 . the collection of all such matrices , @xmath258 is called the _ commutant _ of @xmath259 , and it is again a @xmath244-algebra . denote the dimension of the commutant by @xmath260 . let @xmath261 be the matrix of size @xmath262 of ones . the commutant has a basis of @xmath263-matrices @xmath264 such that @xmath265 . we form a new normalized basis by @xmath266 for which @xmath267 where @xmath268 is the kronecker delta . the _ multiplication parameters _ @xmath269 are then defined by @xmath270 for @xmath271 . we define @xmath272-matrices @xmath273 by @xmath274 for @xmath275 , which span @xmath276    the linear function @xmath277 defined by @xmath278 for @xmath279 is a bijection . the linear function additionally satisfies @xmath280 and @xmath281 for all @xmath282 . @xmath283 is positive semidefinite if and only if @xmath284 is positive semidefinite . [ cor : schrijver ]    the next lemma shows that we can find @xmath285 . it is then possible to use corollary [ cor : schrijver ] to reduce the order of the semidefinite constraint . [ lem : groupaverage ] there is a solution @xmath285 to a @xmath54-invariant semidefinite program @xmath286    let @xmath287 be @xmath262 matrices commuting with @xmath288 for all @xmath249 . if @xmath217 is an optimal solution to the optimization problem then the group average , @xmath289 , is also an optimal solution : it is feasible since @xmath290 where we have used that the well - known fact that the trace is invariant under change of basis . by the same argument @xmath291 , which implies that @xmath292 is optimal . it is easy to see that @xmath293 . all in all we get the following theorem :    [ thm : schrijver ] the semidefinite program @xmath294 has a solution @xmath295 that can be obtained by @xmath296    when @xmath230 is smaller than @xmath297 the theorem can be used to reduce the size of the linear matrix inequality , which in turn improves the computational efficiency . this allows us to solve many problems that would otherwise not be possible .","summary":"we further discuss the possibility of a generalization of szemerdi s theorem using methods from real algebraic geometry .","abstract":"additive combinatorics is built around the famous theorem by szemerdi which asserts existence of arithmetic progressions of any length among the integers . there exist several different proofs of the theorem based on very different techniques . szemerdi s theorem is an existence statement , whereas the ultimate goal in combinatorics is always to make enumeration statements . in this article we develop new methods based on real algebraic geometry to obtain several quantitative statements on the number of arithmetic progressions in fixed density sets . we further discuss the possibility of a generalization of szemerdi s theorem using methods from real algebraic geometry ."}
{"article_id":"1312.2761","section_id":"i","document":"models for accretion onto a black hole ( bh ) have been discussed now for more than 40 years . during the last 1015 years we have seen a dramatic increase in the amount of information on the bh x - ray binaries ( bhbs ) . spectral details ( iron lines and compton reflection ) , spectral transitions , and variability on various time scales has been studied in unprecedented details with the new generation x - ray telescopes such as _ rossi x - ray timing explorer ( rxte ) _ and _ xmm - newton_. excellent recent reviews are devoted to these advances @xcite . in addition to the x - ray data , we have seen an explosion of information coming from other wavelengths : radio , sub - mm , infrared , optical , uv , mev and nowadays even from the gev range . what is even more spectacular is that the properties of the bhs at these other wavebands are correlated with the x - ray flux and x - ray states . among the most impressive achievements we find the discovery of correlated fast variability in the optical / infrared ( oir ) band and in the x - rays @xcite with some hints actually coming already 30 years ago @xcite . this got theoreticians to scratch their heads and invent new models that often were in disagreement with previously established theories and contradicted many other available data .    here we discuss some of the recent discoveries . we would like to note that the time for theoretical ( phenomenological ) models based purely on spectral properties are long gone . in order to be considered seriously , any model has to address many observed facts together . this review consists of two parts . in the first one , we discuss the most recent reincarnation of the hot flow model , which now also considers the role of the non - thermal particles . in the second part , we discuss recent observational advances . we review the spectral data in various energy bands concentrating on the x - rays and the oir . then we discuss the observed temporal properties and correlated variability in different energy bands , as well as more complicated temporal - spectral statistics such as fourier resolved spectra . in this review we will concentrate on the hard state and interpret the observations in terms of the hot flow model .","summary":"however , this scenario is largely ad hoc and is in contradiction with many previously established facts . here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid ( thermal / non - thermal ) hot flow model satisfies most of the constraints .","abstract":"the general picture that emerged by the end of 1990s from a large set of optical and x - ray , spectral and timing data was that the x - rays are produced in the innermost hot part of the accretion flow , while the optical / infrared ( oir ) emission is mainly produced by the irradiated outer thin accretion disc . recent multiwavelength observations of galactic black hole transients show that the situation is not so simple . fast variability in the oir band , oir excesses above the thermal emission and a complicated interplay between the x - ray and the oir light curves imply that the oir emitting region is much more compact . one of the popular hypotheses is that the jet contributes to the oir emission and even is responsible for the bulk of the x - rays . however , this scenario is largely ad hoc and is in contradiction with many previously established facts . alternatively , the hot accretion flow , known to be consistent with the x - ray spectral and timing data , is also a viable candidate to produce the oir radiation . the hot - flow scenario naturally explains the power - law like oir spectra , fast oir variability and its complex relation to the x - rays if the hot flow contains non - thermal electrons ( even in energetically negligible quantities ) , which are required by the presence of the mev tail in cyg  x-1 . the presence of non - thermal electrons also lowers the equilibrium electron temperature in the hot flow model to kev , making it more consistent with observations . here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid ( thermal / non - thermal ) hot flow model satisfies most of the constraints ."}
{"article_id":"1312.2761","section_id":"i","document":"the purely thermal hot - flow model was shown to be consistent with many x - ray characteristics . however , that model fails to account for the mev tails and a number of oir properties . addition of a small , energetically - negligible non - thermal component to the electron distribution dramatically changes the prediction of the model . the hybrid hot - flow model is now successful in explaining the following facts :    1 . stability of spectra with photon index @xmath6@xmath181.61.8 and the cutoff at @xmath18100  kev in the hard state @xcite , 2 . concave x - ray spectrum @xcite , 3 .   low level of the x - ray and oir polarisation @xcite , 4 . presence of the mev tail in the hard state @xcite , 5 . softening of the x - ray spectrum with decreasing luminosity below @xmath1810@xmath92 @xcite , 6 . weakness of the cold accretion disc component in the hard state , 7 . correlation between the spectral index , the reflection amplitude , the width of the iron line and the frequency of the quasi - periodic oscillations , 8 .   hard x - ray lags with logarithmic energy dependence @xcite , 9 . non - thermal oir excesses and flat oir spectra @xcite , 10 . oir colours of the flares in the hard state ( poutanen et al . , in prep . ) , 11 . strong correlation between oir and x - ray emission and a complicated ccf shape @xcite , 12 . quasi - periodic oscillations at the same frequency in the x - ray and optical bands @xcite .    the model does not explain the radio points and the soft ir spectra . the jet is obviously a better model for those data . we , however , struggle to find any other observational fact that could be in conflict with the hybrid hot flow  truncated cold disc scenario . recently , the jet paradigm became popular and it was claimed that the jets are responsible not only for the radio emission from the bhbs , but also the oir and even the x - ray emission . unfortunately , that model is in contradiction with dozens of observed facts ( see * ? ? ? * and references therein ) , which are usually ignored by the model proponents . when new data appear , they often are rather puzzling and difficult to understand within the available paradigms . however , it would be beneficial for the community when introducing brand new models to check also whether those models satisfy other observational constraints .    in spite of a serious progress in understanding of the viscosity in accretion discs around bhs , there are still many open questions . if non - thermal particles are present in the hot flow , it is now time to understand what is their nature . how are they accelerated : in shocks or in magnetic reconnections events , or maybe via diffusive acceleration by mhd turbulence ? how are they related to the magneto - rotational instability that presumably drives the accretion ? we hope that the observational advances will soon be reflected in the advance of the theory . the work was partially supported by the academy of finland grant 268740 ( jp ) and the finnish doctoral program in astronomy and space physics ( av ) . we thank tomaso belloni , andrzej zdziarski , and feng yuan for valuable comments .","summary":"alternatively , the hot accretion flow , known to be consistent with the x - ray spectral and timing data , is also a viable candidate to produce the oir radiation .","abstract":"the general picture that emerged by the end of 1990s from a large set of optical and x - ray , spectral and timing data was that the x - rays are produced in the innermost hot part of the accretion flow , while the optical / infrared ( oir ) emission is mainly produced by the irradiated outer thin accretion disc . recent multiwavelength observations of galactic black hole transients show that the situation is not so simple . fast variability in the oir band , oir excesses above the thermal emission and a complicated interplay between the x - ray and the oir light curves imply that the oir emitting region is much more compact . one of the popular hypotheses is that the jet contributes to the oir emission and even is responsible for the bulk of the x - rays . however , this scenario is largely ad hoc and is in contradiction with many previously established facts . alternatively , the hot accretion flow , known to be consistent with the x - ray spectral and timing data , is also a viable candidate to produce the oir radiation . the hot - flow scenario naturally explains the power - law like oir spectra , fast oir variability and its complex relation to the x - rays if the hot flow contains non - thermal electrons ( even in energetically negligible quantities ) , which are required by the presence of the mev tail in cyg  x-1 . the presence of non - thermal electrons also lowers the equilibrium electron temperature in the hot flow model to kev , making it more consistent with observations . here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid ( thermal / non - thermal ) hot flow model satisfies most of the constraints ."}
{"article_id":"cond-mat9910181","section_id":"i","document":"conformal symmetry tends to emerge in pure ( homogeneous and rotationally invariant ) 2-d statistical mechanics models at their critical points . this high degree of symmetry severely constrains these theories , so that these critical points are well understood . many models , including the ising model , tricritical ising model , and tricritical three - state potts model , are part of a class of conformal field theories known as virasoro minimal models  @xcite . the ising model  @xcite , tricritical ising model  @xcite , and tricritical three - state potts model  @xcite have all been realized experimentally in adsorbed monolayer systems .    because physical systems always have impurities , it is important to consider the effect of quenched disorder on the critical behavior of these theories . when disorder is added to the bulk , random fields are usually relevant , but random bonds may or may not be ( see e.g. ref.s  @xcite ) . it is possible to show , for certain systems , that with the addition of disorder the system renormalizes into an infra - red fixed point . in fact , a rigorous theorem shows that when disorder in the order parameter is added to a system undergoing a first - order phase transition , the latent heat vanishes  @xcite , and a @xmath8 order transition can be expected . however , one generally does not know a priori whether the new critical point is disorder - dominated . a number of studies have reported cases in which the addition of quenched disorder to a pure 2-d model at its critical point resulted in another pure ( that is , non - random ) critical model  @xcite . other studies found quenched disorder to result in new disorder - dominated fixed points  @xcite . one can often see that a critical point is disorder - dominated by showing that various universal quantities are not self - averaging ( that measurements for a specific ` typical ' sample may differ substantially from those on an average one ) . one particularly interesting manifestation of this is multifractal behavior , which occurs when an infinite hierarchy of independent scaling dimensions are associated with a single operator  @xcite . ( see for example  @xcite for a relevant discussion . ) all the above studies have focused on the effects of adding quenched disorder to the bulk of a system . however , it is also interesting to consider the case where the 2-d model has a defect along which impurities have clustered . in this paper we consider the effects of adding quenched disorder only along a defect line , in each of the minimal models ; these models are labelled by an index @xmath9 , @xmath10 . each @xmath9 represents a different model : the ising model ( @xmath11 ) , tricritical ising model ( @xmath12 ) , tetracritical ising model ( @xmath13 ) , tricritical three - state potts model ( @xmath14 ) , etc . . . in section  [ sec - model ] we introduce our defect model , adding quenched disorder in the coupling to @xmath0 ( an operator in the kac table  @xcite ) using replicas . the physical meaning of this disorder varies from model to model , representing a random magnetic field for the ising model , but fluctuations in the ferromagnetic coupling ( or chemical potential ) in the tricritical ising model and tricritical three - state potts model . we find that the ising model renormalizes to a non - random model ( consisting of decoupled half - planes with free boundary conditions and no random magnetic field ) , while all other models renormalize to disorder - dominated fixed points . just as with bulk disorder , disorder on the defect can result in either a pure or disorder - dominated fixed point .    in section  [ sec - rg.d ] we calculate the renormalization group equation of the strength of the disorder @xmath15 , to 2-loop order by minimal subtraction  @xcite . we find that arbitrarily weak disorder grows , and flows to a new fixed point at which @xmath15 is of order @xmath16 . this justifies a @xmath16 expansion , where critical quantities are calculated perturbatively in @xmath16 . the `` boundary entropy ''  @xcite at the random fixed point is found to be @xmath17 , and larger than the entropy of the pure fixed point .    in section  [ sec - scaling ] the same scheme is used to find the moments of correlation functions of the operator @xmath0 along the defect . ( technical details associated with the irreducible representations of the symmetric group  @xcite are delegated to appendices  [ app - rgnm ] and  [ app - combo ] . ) it is found that the moments fall off as a sum of power laws , the dominant term decaying as    @xmath18    with    @xmath19    @xmath20 , so the operator @xmath0 exhibits multifractal behavior . this leads to a typical decay exponent  @xcite :    @xmath21    in section  [ sec - opfmoments ] we calculate one - point functions of the same operator off the defect line . the universal ( normalized ) amplitudes of the moments are found to be non - self - averaging , wheras the power law is self - averaging .    in section [ sec - ising ] , the ising model , which requires special considerations due to the presence of an additional marginal ( boundary ) operator , is analyzed . it is argued that when a random magnetic field is added along the defect line , the system renormalizes to two decoupled half - plane ising models with free boundary conditions and no disorder . we finally note that the manipulations needed to get the exponents in eq.([eq : mainres ] ) are similar to those needed to get the decay exponents of moments of two - point functions of @xmath22 , the energy operator , for the @xmath23-state potts model with _ bulk _ disorder in the bond strength . this model has been analyzed elsewhere by expanding about @xmath24 ( the ising model )  @xcite , and as a byproduct of our calculations here , we find in section  [ sec - scaling ] , eq.([eq : qspm.main]-[eq : qspm.typ ] ) , that    @xmath25    where    @xmath26    results of numerical transfer matrix calculations for the random bond q - state potts model can be found in  @xcite .","summary":"we analyze the effect of adding quenched disorder along a defect line in the 2d conformal minimal models using replicas . the disorder is realized by a random applied magnetic field in the ising model , by fluctuations in the ferromagnetic bond coupling in the tricritical ising model and tricritical three - state potts model ( the operator ) , etc .. we find that for the ising model , the defect renormalizes to two decoupled half - planes without disorder , but that for all other models , the defect renormalizes to a disorder - dominated fixed point . this leads to a typical decay exponent . the boundary entropy is larger than that of the pure system by order .    as a byproduct of our calculations","abstract":"we analyze the effect of adding quenched disorder along a defect line in the 2d conformal minimal models using replicas . the disorder is realized by a random applied magnetic field in the ising model , by fluctuations in the ferromagnetic bond coupling in the tricritical ising model and tricritical three - state potts model ( the operator ) , etc .. we find that for the ising model , the defect renormalizes to two decoupled half - planes without disorder , but that for all other models , the defect renormalizes to a disorder - dominated fixed point . its critical properties are studied with an expansion in for the virasoro minimal model . the decay exponents of the moment of the two - point function of along the defect are obtained to 2-loop order , exhibiting multifractal behavior . this leads to a typical decay exponent . one - point functions are seen to have a non - self - averaging amplitude . the boundary entropy is larger than that of the pure system by order .    as a byproduct of our calculations , we also obtain to 2-loop order the exponent of the moment of the energy operator in the q - state potts model with _ bulk _ bond disorder ."}
{"article_id":"cond-mat9910181","section_id":"c","document":"we have found a new universality class of disordered defect lines . the defect lines exist in various two - dimensional statistical mechanical models , such as the tricritical ising model and tricritical 3-state potts model . the large - distance behavior of these defect lines has been shown to be disorder - dominated . two - point functions along the defect exhibit multifractal behavior , and universal ( normalized ) amplitudes of one - point functions are non - self - averaging . we have also argued that when a random magnetic field is applied along a single line of the ising model , it causes the two sides of the defect to decouple , and to turn into two half - plane ising models with free boundary conditions and no disorder . results for the defect line in the @xmath2 virasoro minimal model were obtained by a @xmath16 expansion . however , the physically most interesting models are at low @xmath9 . for example , @xmath12 corresponds to the tricritical ising model , with a random bond strength ( or a random chemical potential ) along a line . our calculations show that this results in disorder - dominated long - distance behavior . it would be interesting to understand this model in a more fundamental and non - perturbative fashion . the random boundary / defect fixed points that we have found in this paper are , besides the bulk random bond @xmath23-state potts models , a rare case where detailed analytic information about random critical behavior is available . in particular , it would be most interesting to compare our results for the random defect lines in minimal models with future numerical results , such as those obtained by jacobsen and cardy for the bulk random potts models@xcite . as a byproduct of our calculations for the defect line , we have also obtained multifractal energy - energy correlations in the bulk random bond q - state potts model .    finally , we comment on the r.g . analysis performed under the assumption of broken replica symmetry . such a calculation was done in  @xcite for the q - state potts model with bulk disorder in the bond strength , where it was found that the replica symmetric disordered fixed point is unstable to a new fixed point with broken replica symmetry . however , numerical tests show that the potts model with random bonds is best described by the replica symmetric fixed point  @xcite . an identical analysis to that of  @xcite for the random defect problem that is the subject of the present paper shows that , again , the fixed point considered in this paper is unstable , and flows to a new stable fixed point with broken replica symmetry . thus , our random defect problem may provide further insights into the significance of the replica broken fixed point . * acknowledgements *    we thank tom davis for useful discussions . this work was supported in part by a regents fellowship of the university of california ( m.j . ) , and in part by the a.p . sloan foundation ( a.w.w.l . ) .","summary":"its critical properties are studied with an expansion in for the virasoro minimal model . one - point functions are seen to have a non - self - averaging amplitude .","abstract":"we analyze the effect of adding quenched disorder along a defect line in the 2d conformal minimal models using replicas . the disorder is realized by a random applied magnetic field in the ising model , by fluctuations in the ferromagnetic bond coupling in the tricritical ising model and tricritical three - state potts model ( the operator ) , etc .. we find that for the ising model , the defect renormalizes to two decoupled half - planes without disorder , but that for all other models , the defect renormalizes to a disorder - dominated fixed point . its critical properties are studied with an expansion in for the virasoro minimal model . the decay exponents of the moment of the two - point function of along the defect are obtained to 2-loop order , exhibiting multifractal behavior . this leads to a typical decay exponent . one - point functions are seen to have a non - self - averaging amplitude . the boundary entropy is larger than that of the pure system by order .    as a byproduct of our calculations , we also obtain to 2-loop order the exponent of the moment of the energy operator in the q - state potts model with _ bulk _ bond disorder ."}
{"article_id":"hep-th0312243","section_id":"i","document":"topological sigma models , first put forward by witten @xcite , have long fascinated a number of theoretical physicists and mathematicians . most remarkably , the task of summing up worldsheet instantons is nowadays elegantly formulated by the theory of gromov - witten invariants . explicit computations of them are still being actively pursued . it goes without saying that among many possible target spaces calabi - yau threefolds have played distinguished roles and are of lasting interest to string theorists . since the initial appreciation of the significance of d - branes there has been the lingering hope that the gromov - witten theory of calabi - yau threefolds might be completely rewritten in the language of bps d - branes . this contribution is intended for explaining the picture which , to my eye , looks particularly attractive in this regard . this is based on the general philosophy :    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the geometry of @xmath0-@xmath1 branes ( and _ not _ simply @xmath0-branes ) provides an alternative description of gromov - witten invariants of calabi - yau threefolds . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _    what we actually imagine is very simple and intuitive : in analogy with the ( generalized ) super kac - moody algebras we regard the string partition function as the inverse of  denominator function \" and interpret the bound state degeneracies of @xmath0-@xmath1 branes as the  super root multiplicities \" . the gromov - witten potentials are then extracted from the string partition function . in particular , the variable @xmath2 measuring @xmath1-charge is related to the genus expansion parameter @xmath3 of gromov - witten theory by @xmath4 . this sort of idea was formerly presented in @xcite when the calabi - yau threefold is elliptically fibered over a hirzebruch surface . there , an analogy to borcherds products @xcite was pursued . recall that borcherds products or their inverses arise in some cases as the denominator functions of generalized ( super ) kac - moody algebras . the first hint of the relevance of borcherds products to gromov - witten theory was given by harvey and moore @xcite . i will report further progress on the string partition functions of these elliptic calabi - yau threefolds elsewhere @xcite . so the first purpose of this work is simply to extend the @xmath0-@xmath1 picture of @xcite to general calabi - yau threefolds focusing on those aspects which are believed to be independent of any particular details of the threefolds . some time ago gopakumar and vafa @xcite proposed an alternative reformulation of gromov - witten theory of calabi - yau threefolds based on the space - time effective theory interpretation of gromov - witten potentials . this claim has been influential but at the same time very mysterious ( at least to the author ) . the second objective of this paper is to discuss how this proposal of gopakumar and vafa may actually reconcile with ours . quite recently , the relation between singular instantons of @xmath5 @xmath6 gauge theory and gromov - witten theory has been discussed @xcite in relation to the topological vertex formalism @xcite . this gauge theoretic approach ( donaldson - thomas theory ) is probably a dual viewpoint of our @xmath0-@xmath1 picture in the same way point - like instantons of @xmath7 @xmath6 gauge theory describe @xmath1-branes . so , as far as the ideology is concerned , these works seem to have some overlaps with @xcite and the present work . nevertheless , there is a marked difference in practice : they discuss the  sum side \" with a supply of explicit calculations for local toric calabi - yau threefolds using the localization technique whilst we discuss the  product side \" inspired from the examples of certain elliptic calabi - yau threefolds and the associated borcherds - like products @xcite@xcite . it will be very interesting ( and necessary ! ) to investigate the existence of  sum = product \" formulas connecting both sides for a general calabi - yau threefold . in fact , the topological vertex formalism of @xcite seems to allow an intuitive understanding in terms of @xmath0-branes and @xmath1-branes . [ comment ] for comments on this point . i am grateful to k. yoshioka for the collaboration in @xcite . i also thank a.  okounkov for kindly pointing out my nonsensical statement in the previous version of the manuscript and for explaining to me the marvelous proposal of him and his collaborators . . for a rational function @xmath8 of one variable @xmath2 we define @xmath9 as follows : @xmath10 is the laurent series of @xmath8 at @xmath11 and @xmath12 is that at @xmath13 . consider , for instance , @xmath14 for an integer @xmath15 . if @xmath16 then @xmath17 and @xmath18 coincide in @xmath19 $ ] . however , @xmath20\\,.\\ ] ]    a calabi - yau threefold @xmath21 is a complex 3-dimensional smooth projective variety with @xmath22 and @xmath23 . we assume that @xmath21 is polarized by some ample line bundle .","summary":"we discuss how the geometry of- branes may be related to gromov - witten theory of calabi - yau threefolds .","abstract":"we discuss how the geometry of- branes may be related to gromov - witten theory of calabi - yau threefolds ."}
{"article_id":"0910.1858","section_id":"i","document":"the asymmetric exclusion process ( asep ) is an important model from statistical mechanics which was introduced independently in the context of biology @xcite and in mathematics @xcite around 1970 . since then there has been a huge amount of activity on the asep and its variants for a number of reasons : although the definition of the model is quite simple , the asep is surprisingly rich . for example , it exhibits boundary - induced phase transitions , spontaneous symmetry breaking , and phase separation . furthermore , the asep is regarded as a primitive model for translation in protein synthesis @xcite , traffic flow @xcite , and formation of shocks @xcite ; it also appears in a kind of sequence alignment problem in computational biology @xcite . important mathematical techniques used to understand this model include the matrix ansatz of derrida , evans , hakim , and pasquier @xcite , and also the bethe ansatz @xcite . this paper concerns the asep on a one - dimensional lattice of @xmath0 sites with open boundaries . particles may enter from the left at rate @xmath7 and from the right at rate @xmath8 ; they may exit the system to the right at rate @xmath9 and to the left at rate @xmath10 . the probability of hopping left and right is @xmath11 and @xmath12 , respectively . , so we will often do so . ] dating back to at least 1982 , it was realized that there were connections between this model and combinatorics  for example , young diagrams appeared in @xcite , and catalan numbers arose in the analyses of the stationary distribution of the asep in @xcite . more recently , beginning with papers of brak and essam @xcite , and duchi and schaeffer @xcite , and followed by a number of works including @xcite , there has been a push to understand the roots of the combinatorial features of the asep . ideally , the goal is to find a combinatorial description of the stationary distribution : that is , to express each component of the stationary distribution as a generating function for a set of combinatorial objects . up to now , the best result in this direction was provided by @xcite , which addressed this question when @xmath6 in terms of permutation tableaux , combinatorial objects introduced in the context of total positivity on the grassmannian @xcite . there is a second reason why combinatorialists became intrigued by the asep . papers of sasamoto @xcite and subsequently uchiyama , sasamoto , and wadati @xcite linked the asep with open boundaries to orthogonal polynomials , in particular , to the askey - wilson polynomials . the askey - wilson polynomials are orthogonal polynomials that sit at the top of the hierarchy of ( basic ) hypergeometric orthogonal polynomials @xcite , in the sense that all other polynomials in this hierarchy are limiting cases or specializations of the askey - wilson polynomials . it is known that orthogonal polynomials have many combinatorial features : indeed , starting around the early 1980 s , mathematicians including flajolet @xcite , viennot @xcite , and foata @xcite , initiated a combinatorial approach to orthogonal polynomials . since then , combinatorial formulas have been given for the moments of ( the weight functions of ) many of the polynomials in the askey scheme , including @xmath5-hermite , chebyshev , @xmath5-laguerre , charlier , meixner , and al - salam - chihara polynomials , see e.g. @xcite . however , no such formula was known for the moments of the askey - wilson polynomials . therefore when the paper @xcite provided a close link between the moments of the askey - wilson polynomials and the stationary distribution of the asep , this gave the idea that a complete combinatorial understanding of the asep might also give rise to the combinatorics of the askey - wilson moments .    in this paper we give a complete solution to both of the above problems . namely , we introduce some new combinatorial objects , which we call _ staircase tableaux _ , and we prove that generating functions for staircase tableaux describe the stationary distribution of the asep , with all parameters general . we then use this result together with @xcite to give a combinatorial formula for the moments of the askey - wilson polynomials . the method of proof for our stationary distribution result builds upon important work of derrida , evans , hakim , and pasquier @xcite , who introduced a _ matrix ansatz _ as a tool for understanding its stationary distribution . briefly , the matrix ansatz says that if one can find matrices and vectors satisfying certain relations ( the _ dehp algebra _ ) , then each component of the stationary distribution of the asep can be expressed in terms of certain products of these matrices and vectors . knowing this ansatz , the strategy for proving our stationary distribution result which one would like to employ is the following : find matrices and vectors satisfying the dehp algebra , and show that appropriate products enumerate staircase tableaux . however , it has been known since 1996 ( * ? ? ? * section iv ) that when the parameters of the asep satisfy certain relations ( for example @xmath13 ) , there is no representation of the dehp algebra . therefore the above strategy can not succeed when all parameters of the asep are general . what we do instead is to introduce a slight generalization of the matrix ansatz ( see theorem [ ansatz2 ] ) , which is more flexible , albeit harder to use : instead of checking three identities , one must check three infinite families of identites . so our strategy is to find matrices and vectors such that appropriate products enumerate staircase tableaux , and prove that they satisfy the relations of the generalized matrix ansatz . this second step is quite involved , as our  matrices \" and  vectors \" are somewhat complicated ( they have four and two indices each , see section [ def - matrices ] ) , and there is no easy way to use induction to prove the three infinite families of identities . we believe that our new staircase tableaux deserve further study , because of their combinatorial interest and their potential connection to geometry . for example , staircase tableaux of size @xmath0 have cardinality @xmath14 , and hence are in bijection with doubly - signed permutations . in @xcite , we will prove this with an explicit bijection , and also develop connections to other combinatorial objects , including matchings , permutations , and trees . furthermore , because of the connection to the asep , we know that our staircase tableaux have some hidden symmetries which are not at all apparent from their definition . for instance , it is clear from the definition of the asep that the model remains unchanged if we reflect it over the @xmath15-axis , and exchange parameters @xmath1 and @xmath4 , @xmath3 and @xmath2 , and @xmath5 and @xmath16 . however , the corresponding bijection on the level of tableaux has so far eluded us . finally , staircase tableaux generalize permutation tableaux , which index certain cells in the non - negative part of the grassmannian @xcite ; it would be interesting to better understand the relationship between the tableaux , the asep , and the geometry , and potentially generalize it to staircase tableaux . it is worth mentioning that in recent years there has been an explosion of activity @xcite surrounding another version of the asep , in which particles hop not on a finite lattice but on @xmath17 . much of this interest was inspired by johansson s work @xcite , which reinterprets the tasep ( totally asymmetric exclusion process ) as a randomly growing young diagram . johansson then used the well - understood combinatorics of young diagrams and semi - standard tableaux to approach the problem of current fluctuations in the tasep . in light of this , one may hope that a better understanding of the combinatorics of staircase tableaux could lead to even more results on the asep with open boundaries . the structure of this paper is as follows . in section [ setup ] we define the asep ( with open boundaries ) , and in sections [ results ] and [ aw section ] we state our main results on the asep and on askey - wilson polynomials . in section [ newansatz ] we prove a generalized matrix ansatz , and in sections [ proof1 ] and [ awproof ] we prove our results on the asep and askey - wilson polynomials . section [ conc ] gives open problems , and the appendix describes how staircase tableaux generalize permutation tableaux and alternative tableaux @xcite . acknowledgments : we would like to thank i. gessel , r. stanley , and j. de gier for interesting remarks . we are also grateful to the referees for their thoughtful comments , which helped us to greatly improve the exposition .","summary":"introduced in the late 1960 s , the asymmetric exclusion process ( asep ) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one - dimensional lattice of sites . it has been cited as a model for traffic flow and protein synthesis . in the most general form of the asep with open boundaries , particles may enter and exit at the left with probabilities and , and they may exit and enter at the right with probabilities and . in the bulk , the probability of hopping left is times the probability of hopping right . the first main result of this paper is a combinatorial formula for the stationary distribution of the asep with all parameters general , in terms of a new class of tableaux which we call _ staircase tableaux_. this generalizes our previous work for the asep with parameters . using our first result and also results of uchiyama - sasamoto - wadati , we derive our second main result : a combinatorial formula for the moments of askey - wilson polynomials . since the early 1980 s there has been a great deal of work giving combinatorial formulas for moments of various other classical orthogonal polynomials ( e.g. hermite , charlier , laguerre , meixner ) . however , this is the first such formula for the askey - wilson polynomials , which are at the top of the hierarchy of classical orthogonal polynomials .","abstract":"introduced in the late 1960 s , the asymmetric exclusion process ( asep ) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one - dimensional lattice of sites . it has been cited as a model for traffic flow and protein synthesis . in the most general form of the asep with open boundaries , particles may enter and exit at the left with probabilities and , and they may exit and enter at the right with probabilities and . in the bulk , the probability of hopping left is times the probability of hopping right . the first main result of this paper is a combinatorial formula for the stationary distribution of the asep with all parameters general , in terms of a new class of tableaux which we call _ staircase tableaux_. this generalizes our previous work for the asep with parameters . using our first result and also results of uchiyama - sasamoto - wadati , we derive our second main result : a combinatorial formula for the moments of askey - wilson polynomials . since the early 1980 s there has been a great deal of work giving combinatorial formulas for moments of various other classical orthogonal polynomials ( e.g. hermite , charlier , laguerre , meixner ) . however , this is the first such formula for the askey - wilson polynomials , which are at the top of the hierarchy of classical orthogonal polynomials ."}
{"article_id":"hep-th0407090","section_id":"i","document":"in this paper we try to better understand and to analyze alternative theories of gravity depending on higher - order terms in the curvature invariant @xmath1 , in relation with some very interesting and possible cosmological application and , in particular , in relation with their capability to explain the cosmological acceleration of the universe , both in early times ( inflation ) and in present time universes . nevertheless we will focus our attention on the possible theoretical explanation of the present cosmological acceleration . + recent astronomical observations have shown that the universe is accelerating at present time ( see @xcite and @xcite for supernova observation results ; see @xcite for the observations about the anisotropy spectrum of the cosmic microwave background ( cmbr ) ; see @xcite for the results about the power spectrum of large - scale structure ) . physicists have thus to face the evidence of the acceleration of the universe and should give a coherent theoretical explanation to these experimental results : a problem which up to now seems to be still unsolved ! general relativity in interaction with a perfect - fluid like matter and the cosmological principle , providing the standard cosmological models , fail to give by their own a theoretical framework to explain the acceleration of the universe . we are thus forced to introduce some kind of _ dark matter or dark energy _ , which are responsible for the acceleration of the universe , or to modify general relativity such that acceleration is predicted ( see for example @xcite ) . + dark matter or dark energy models have been deeply investigated in relation with their capability of explaining the acceleration of the universe ( see @xcite and references therein ) , however up to now there are no satisfactory experimental evidences of the presence of the predicted amount of dark energy in the universe . the real nature of dark energy , which is required by general relativity in this cosmological context , is unknown but it is fairly well accepted that dark energy should behave like a fluid with a large negative pressure . the dark energy models with effective equation of state @xmath2 ( which determines the relation between pressure @xmath3 and density of matter @xmath4 ) smaller than @xmath5 are currently preferrable , owing to the experimental results of @xcite . + on the other side the simplest way of obtaining accelerated expansions within general relativity is to introduce a positive cosmological constant @xcite , an introduction which leads however to some theoretical and experimental problems and contradictions ( see for example @xcite and @xcite ) . we just want to stress here that models with a constant cosmological constant are not able to explain the evolution between different epochs of the universe , characterized by different values of acceleration ( deceleration ) . + the other possibility is to assume that we do not yet understand gravity at large scales , which means that general relativity should be modified or replaced by alternative gravitational theories of gravity when the curvature of spacetime is small ( see for example @xcite , @xcite , @xcite and references therein ) , providing modified friedmann equations . hints in this direction are suggested moreover from the quantization on curved spacetimes , when interactions among the quantum fields and the background geometry or the self interaction of the gravitational field are considered . it follows that the standard hilbert - einstein lagrangian has to be suitably modified by means of corrective terms , which are essential in order to remove divergences @xcite . these corrective terms result to be higher - order terms in the curvature invariants such as @xmath6 , @xmath7 , @xmath8 , @xmath9 , or non minimally coupled terms between scalar fields and the gravitational field . it is moreover interesting that such corrective terms to the standard hilbert - einstein lagrangian can be predicted in higher dimensions by some time - dependent compactification in string / m - theory ( see @xcite ) and corrective terms of this type arise surely in brane - world models with large spatial extra dimensions @xcite . as a matter of facts , if these brane models are the low energy limit of string theory , it is likely that the field equations include in particular the gauss - bonnet term , which in five dimensions is the only non - linear term in the curvature which yields second order field equations . in this framework gauss - bonnet corrections should be taken into account and cosmological models deriving from the gauss - bonnet have been recently studied ; see @xcite and references therein . + as an alternative to extra dimensions , it is also possible to explain the modification to friedmann equations ( which could provide a theoretical explanation for the acceleration of the universe ) by means of a modified theory of four dimensional gravity . the first attempts in this direction were performed by adding to the standard hilbert - einstein lagrangian analytical terms in the ricci scalar curvature invariant @xcite . a simple task to modify general relativity , when the curvature is very small , is hence to add to the lagrangian of the theory a piece which is proportional to the inverse of the scalar curvature @xmath10 or to replace the standard hilbert - einstein action by means of polynomial - like lagrangians , containing both positive and negative powers of the ricci scalar @xmath6 and logarithmic - like terms . such theories have been analyzed and studied both in the metric @xcite and the palatini formalisms @xcite , @xcite . it results that both in the metric and the palatini formalism they provide a possible theoretical explanation to the present time acceleration of the universe . moreover a mechanism ruling the present dark energy dominance transitting from values below @xmath11 to values above @xmath11 is actually preferable @xcite . ] ( due to the universe expansion ) and the present cosmic acceleration has been proposed in this framework ; see @xcite . + a discussion is open on the physical reliability of the palatini and/or the metric formalism @xcite and on the physical relevant frame both in the metric and the palatini formalism @xcite . up to now it appears that the aforementioned metric approach leads to results which are in contrast with the solar system experiments and also that the relevant fourth order field equations suffer serious instability problems @xcite . on the contrary the palatini formalism produces second order field equations which are not afflicted by instability problems and are in acceptable accordance with the results of the solar system experiments @xcite . a discussion is actually open on the accordance of the palatini formalism with the electron - electron scattering experiments @xcite . +   + the importance of modified theories of gravity depending on general analytical functions of the ricci scalar is also related with the possibility of avoiding singularities in these cosmological models @xcite and in the interpretation of black holes entropy in this context @xcite . recently , an explanation of the present day acceleration of the universe has been moreover formulated in the framework of non - symmetric gravitational theories @xcite and in modified theories depending on the determinant of the ricci tensor @xcite . +   + encouraged by recent developments of cosmological applications of alternative theories of gravity we consider in this paper ricci squared lagrangians in minimal interaction with matter , which have been deeply analyzed in @xcite in the vacuum case . as we already said before such lagrangians are deeply related with quantum field theory : to remove divergences one has to add counterterms to the lagrangian which depend not only on the ricci scalar but also on the ricci and the riemann tensors @xcite . it was proven in @xcite that ricci squared lagrangians provide second order field equations in the palatini formalism , such that the universality of einstein equations and the universality of the komar energy - momentum complex hold in vacuum . these remarkable results have important implications also in cosmological models . they imply that , in some sense , field equations for ricci squared lagrangians reproduce ( apart conformal transformations ) the standard einstein field equations in the vacuum case , while in the presence of matter this equivalence might be broken . the geometrical structure of the spacetime manifold is very rich and it is endowed with an anti - khlerian structure , deriving directly from the variational principle of ricci squared lagrangians ( see @xcite ) . spacetime turns out to have a bi - metric structure , or better a so - called _ metric compatible almost - product _ as well as an _ almost - complex structure with a norden metric_. the geometrical structure of spacetime is moreover characterized by a scalar - valued structural equation , which is simply obtained by contracting field equations with the metric @xcite and controls the solutions of field equations . lagrangians based on higher - order ricci scalars which led to higher - order metric compatible polynomial structures have been considered both in purely metric and palatini formalism in @xcite . + it was moreover shown in @xcite and @xcite that ricci squared theories in vacuum give field equations equivalent to einstein field equations with a cosmological constant , the value of which is fixed once the structural equations are solved and one particular solution of the structural equations is chosen . this fact is no longer true in the case of interaction with generic matter , where the solutions of the structural equation are dynamical ( the same happens in the case of non - linear lagrangians in the ricci scalar ; see @xcite and references therein ) . the equivalence with einstein field equations is hence broken and we obtain modified field equations , depending on the stress - energy tensor of matter involved in the theory . nevertheless , we remark that field equations are once again second order field equations in the metric field . + for cosmological applications we consider the physical metric @xmath12 to be a robertson - walker metric and the stress - energy tensor of matter to be a perfect fluid one . in this particular framework deriving from the cosmological principle we obtain that the levi - civita metric @xmath13 is _ conformal _ to the physical metric @xmath12 , apart for a rescaling factor of the cosmological time . from our construction it follows however that the signature of @xmath13 can be arbitrarily chosen ( it can be either riemannian , or lorentzian or kleinian , apart from some restrictions deriving from field equations ) . we are consequently able to introduce a generalized hubble constant and modified friedmann equations . a comparison with the @xmath14 theories is immediate . it is striking to notice that modified friedmann equations are once more first order field equations , which prevent the appearing of instabilities as it has already been shown in the case of ricci scalar theories in @xcite . this is an important consideration giving the palatini formalism a deeper physical significance , in view of cosmological applications . + an explicit example dealing with power lagrangians in the ricci squared invariant @xmath15 is analyzed in detail and the hubble constant is derived . it results that the deceleration parameter can be negative if particular values of @xmath16 are chosen . moreover we obtain values of @xmath2 that can be suitably fitted to the experimental results of @xcite . considerations are exposed about the _ frame changing _ , which means choosing @xmath13 to be a frw metric instead of @xmath12 . field equations and cosmological parameters are obtained and discussed also in that alternative ( _ jordan _ ) frame . +   + the paper is organized as follows : we start in section 2 by considering the case of @xmath14 lagrangians in a new matrix formalism , with the introduction of an operator @xmath17 modifying the einstein field equations @xcite . we pass in section 3 to the more complicated case of ricci squared @xmath18 lagrangians and we analyze the field equations and the structure of spacetime in the case of interaction with matter . we proceed in section 4 with cosmological applications and we obtain modified friedmann equations . in section 5 we discuss the relevant example of polynomial lagrangians in the ricci squared invariant . in section 6 we consider the theory in the alternative jordan frame , where @xmath13 is assumed to be a priori the frw physical metric .","summary":"alternative gravitational theories described by lagrangians depending on general functions of the ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at present time . in this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on ( other ) curvature invariants . we introduce ricci squared lagrangians in minimal interaction with matter ( perfect fluid ) ; we find modified einstein equations and consequently modified friedmann equations in the palatini formalism . the spacetime bi - metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation .","abstract":"alternative gravitational theories described by lagrangians depending on general functions of the ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at present time . in this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on ( other ) curvature invariants . we introduce ricci squared lagrangians in minimal interaction with matter ( perfect fluid ) ; we find modified einstein equations and consequently modified friedmann equations in the palatini formalism . it is striking that both ricci scalar and ricci squared theories are described in the same mathematical framework and both the generalized einstein equations and generalized friedmann equations have the same structure . in the framework of the cosmological principle , without the introduction of exotic forms of dark energy , we thus obtain modified equations providing values of in accordance with the experimental data . the spacetime bi - metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation ."}
{"article_id":"1510.03916","section_id":"i","document":"beyond the main - sequence of a stellar population , a star with an initial mass less than 8  evolves to the red giant phase at which it ejects most of its mass through a slow and dense wind ( @xmath8 ) . the intense mass loss process reaches its climax at the tip of the asymptotic giant branch ( agb ) with a rate of @xmath9 forming an extensive circumstellar envelope ( cse , @xmath10@xmath11 ) . such an evolutionary phase leads to the obscuration of the innermost envelope region near the stellar surface . consequently , information on the onset of dust formation and growth , the subsequent wind acceleration , the central engine governing the ( a)symmetric shapes of the entire cse , and the connection of these features with binary interactions and/or magnetic fields is very limited . the morphological diversity of the cses in evolved stellar phases is commonly assumed to be closely related to the possible binary nature of the system . in contrast to quasi - spherical shapes of cses at the agb , the majority of planetary nebulae ( pne ) or protoplanetary nebulae ( ppne ) bear bipolar or multipolar structures , often observed in ionized gas or dust scattered light ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? such bipolarity is a common feature of sources possessing accretion disks such as the protoplanetary jets coexisting with the accretion disks surrounding young stellar objects . in the outflowing cse of evolved giant stars , another gravitational potential ( e.g. , companion ) is hypothesized to assemble material in the form of circumstellar or circumbinary disk to feed the observed bipolar outflow . the accretion disks may form during the agb phase in _ close _ binary systems ( e.g. , * ? ? ? * ; * ? ? ? _ wide _ binary systems also induce , albeit less vigorous , asymmetry in the form of spiral patterns . it is now theoretically well understood that binary orbital motion leads to a spiral - shell pattern propagating over the entire cse ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the consequent wind anisotropy , caused by the binary orbital motion and the gravitational focusing of the wind material onto the companion , leads an overall flattened geometry of the cse @xcite . the binary - induced pattern and geometry of cse preserve the records of binary influence on the wind outflow . a well - defined spiral pattern of afgl 3068 found from dust scattered light and the binary separation inferred from near - infrared adaptive optics images @xcite were utilized to derive its binary stellar and orbital properties @xcite . the non - continuous shells within the cse of cit 6 , which appeared in a molecular line emission @xcite , were suggested to be a spiral - shell pattern when viewed with a large inclination from the orbital plane @xcite . such an interpretation may also be applicable to the multiple rings and arcs often found in the cses of agb stars and ppne , e.g. , irc+10216 @xcite and mira @xcite . in addition , within this framework , the wind properties derived from the circumstellar spiral pattern facilitated constraints on the mass loss history of r sculptoris @xcite . finally , the elliptical shapes of cses of agb stars in an optical imaging survey were suggested as a probe to infer that a significant fraction of agb stars may have hidden binary companions @xcite . in fact , substantial ppne may reveal evidence of the shape transition from outer rings and arcs formed in the cse during the previous agb phase to the inner region showing bipolar lobes developed by new vigorous ejections ( e.g. , egg nebula , * ? ? ? * ) . if the ring - like patterns originated from binary orbital motion , the typical dynamical timescales of the observed patterns ( 1001000 years ) correspond to the orbital periods of wide binary systems with the companions locating at a few tens to hundred au . such separations between binary stars are far larger than radius of wind acceleration zone so that the wind speed is sufficiently fast in the vicinity of the companion ( if it is in a circular orbit ) , precluding formation of an accretion disk and consequently a bipolar outflow . whether a _ wide _ binary can create a bipolar outflow has not been well studied . the onset of the asymmetric outflow , the role of a binary companion on it , and ultimately the mass loss process may be addressed by sub - arcsecond resolution observations toward the sources in this phase transition from the agb to ppn . the extreme carbon star cit 6 is an excellent target to study the role of a companion on the transition from a quasi - spherical shell - like structure ( over @xmath12 ) found in a molecular line emission map @xcite to a nascent bipolar structure ( @xmath13 ) observed in the near - infrared polarization image @xcite . the companion candidate revealed in optical images is @xmath14 away from the carbon star at a position angle ( pa , from north to east ) of @xmath15 @xcite . at a distance of 400pc ( * and references therein ) derived by using a period - luminosity relation from the pulsation period of the carbon star ( @xmath16yr ) , the projected binary separation corresponds to @xmath17au . the observed flux at 4500  suggests the candidate companion to be a main - sequence star of mass @xmath182  @xcite . on the other hand , the effective temperature @xmath19k @xcite and bolometric luminosity @xmath20 @xcite locate the carbon star cit 6 at the tip of agb of a star with an initial mass of @xmath21   ( current mass @xmath22 ) based on the stellar evolutionary model with solar metallicity using the code provided by @xcite . these photometric masses agree with the masses derived from a separate , parameter space analysis based on binary dynamics and the encoded circumstellar pattern @xcite . the circumstellar pattern of cit 6 was observed in the hc@xmath0n @xmath2=43 line emission at a high resolution of @xmath23 with the karl g.  jansky very large array ( jvla ) . the pattern was modeled with spherical shells , resulting in a necessary displacement of shell centroids along the radius and across the line velocity channels ( @xcite ; see also @xcite for various hc@xmath0n and hc@xmath24n lines of cit 6 ) . this departure from spherical symmetry is consistent with the spiral - shell model induced by a binary motion , and @xcite indeed presented a spiral - shell model reproducing the observed hc@xmath0n pattern in all channels . previously , @xcite speculated a spiral structure of cit 6 from another hc@xmath0n @xmath2=54 emission map at a lower resolution of @xmath25 , which is now resolved into a few windings of the modeled spiral - shell pattern . nevertheless , the pattern geometry was left incomplete , because the observed hc@xmath0n pattern is broken with an absence of emission to the west and in the central @xmath26 region . verifying the pattern shape with a chemically stable molecule such as @xmath1co is necessary to infer the companion of cit 6 , to examine the binary characteristics , and to obtain a clue of the kinematic connection of the spiral pattern to the observed near - infrared bipolar nebula in the innermost region where the hc@xmath0n emission was absent .    in this paper , we report the submillimeter array ( sma ) observations toward cit 6 in the @xmath1co @xmath2=21 and @xmath3co @xmath2=21 lines and the 226.2ghz and 350.6ghz continuum emission at sub - arcsecond resolutions . submillimeter telescope ( smt ) grid - mapping observations for the same lines are combined with the sma data to recover the extended cse emission . we describe the observations and calibrations in section[sec : obs ] . the results are presented in sections[sec : ove ] and [ sec : fin ] for the overall and fine structures in the cse of cit 6 , respectively . further discussion follows in section[sec : dis ] . we summarize our findings in section[sec : sum ] , and conclude in section[sec : ccs ] .","summary":"cit 6 is a carbon star in the transitional phase from the asymptotic giant branch ( agb ) to the protoplanetary nebulae ( ppn ) . hence , cit 6 is very attractive for studying the role of companions in the agb - ppn transition . theco channel maps reveal a spiral - shell pattern connecting the hcn segments in a continuous form , and an asymmetric outflow corresponding to the near - infrared bipolar nebula . an eccentric orbit binary is suggested for the presences of an anisotropic mass loss to the west and a double spiral pattern .","abstract":"cit 6 is a carbon star in the transitional phase from the asymptotic giant branch ( agb ) to the protoplanetary nebulae ( ppn ) . observational evidences of two point sources in the optical , circumstellar arc segments in an hcn line emission , and a bipolar nebula in near - infrared provide strong support for the presence of a binary companion . hence , cit 6 is very attractive for studying the role of companions in the agb - ppn transition . we have carried out high resolutionco=21 andco=21 observations of cit 6 with the submillimeter array combined with the submillimeter telescope ( single - dish ) data . theco channel maps reveal a spiral - shell pattern connecting the hcn segments in a continuous form , and an asymmetric outflow corresponding to the near - infrared bipolar nebula . rotation of theco channel peak position may be related to the inner spiral winding and/or the bipolar outflow . an eccentric orbit binary is suggested for the presences of an anisotropic mass loss to the west and a double spiral pattern . the lack of interarm emission to the west may indicate a feature corresponding to the periastron passage of a highly eccentric orbit of the binary . spatially - averaged radial and spectral profiles ofco=21 andco=21 are compared with simple spherical radiative transfer models , suggesting a change ofco/co abundance ratio from to inward in the cse of cit 6 . the millimeter continuum emission is decomposed into extended dust thermal emission ( spectral index ) and compact emission from radio photosphere ( spectral index ) ."}
{"article_id":"1510.03916","section_id":"c","document":"we have performed simple , one - dimensional , non - local thermodynamic equilibrium radiative transfer calculations using the sparx code to understand the overall distribution of the @xmath1co and @xmath3co molecules in the cse of cit 6 . since our focus here is on the overall cse distribution , the observed fine structures ( as described in section[sec : fin ] ) are ignored in the modeling ; see @xcite for a spiral - shell model for cit 6 , characterizing the hc@xmath0n @xmath2=43 pattern in channel maps . in figures[fig : spe ] and [ fig : pro ] , we present a simple model for an agb envelope expanding with a constant expansion velocity @xmath145 , a mass loss rate @xmath146 , a temperature distribution @xmath147 , a stochastic velocity of 1 , constant fractional abundances of molecules ( @xmath148 and @xmath149 ) , and a distance of 400pc . this model reproduces reasonably well the average radial profile of the observed @xmath1co @xmath2=21 ( figure[fig : pro ] , green curve ) and its spectra in different length scales ( figure[fig : spe ] , dashed line ) , providing some insights to physical conditions of the overall cse of cit 6 . the optical depth of the @xmath1co @xmath2=21 model at the systemic velocity is low ( @xmath150 ) at the center , increases to @xmath21 at @xmath101 , and decreases back to @xmath150 at @xmath151 . on the other hand , the expansion velocity channel has the large optical depth greater than 4 for almost all emitting regions with the peak value over 10 at @xmath152 . the over - predicted flux in figure[fig : spe](d ) may indicate that the @xmath1co abundance in the outermost region is lower than in the inner region possibly because of photodissociation due to interstellar ultraviolet photons . this interpretation is consistent with the radius at which the abundance drops to half of its photospheric value derived to be @xmath106 by e.g. , @xcite , based on @xcite .    the radial profile of @xmath3co @xmath2=21 , however , is not achieved by merely changing the _ single _ molecular fractional abundance with the same fixed mass loss rate and temperature profile as in @xmath1co model . the @xmath3co modeled and observed spectra are not too far off in the inner part ( figure[fig : spe](a)(b ) ) ; but the outer envelope of cit 6 contains significantly more @xmath3co emission compared to the model ( figure[fig : spe](c)(d ) ) . in fact , as seen in figure[fig : pro ] , the @xmath3co radial profile of cit 6 is relatively flatter and more attributed by extended component than in @xmath1co . the significant difference in slopes of the @xmath1co and @xmath3co radial profiles may imply a variation of their abundance ratio with radius . the @xmath1co/@xmath3co abundance ratio 50 in the presented model is somewhat larger than the value @xmath153 in the literature . our choice for the @xmath3co fractional abundance results from matching the brightness temperatures in the inner region closely the observed values , at the expense of the outer region . we have checked that the modeled @xmath3co spectra with a ratio @xmath4 can reproduce the smt single - dish observational data ( i.e. , for figure[fig : spe](c)(d ) ) , consistent with the earlier models by e.g. , @xcite , but resulting in a mismatch in the inner envelope . it may indicate that @xmath1co/@xmath3co abundance ratio varies with radius . considering both the @xmath1co @xmath2=21 and hc@xmath0n @xmath2=43 high resolution maps together , four to five windings of the spiral - shell pattern are found . in terms of their location , there are close agreements between the @xmath1co and hc@xmath0n patterns manifested in the channel maps ( figure[fig : chm ] ) and the p - v diagrams ( figure[fig : pvd ] ) . for example , to the west where the hc@xmath0n pattern is broken , the @xmath1co pattern is present and smoothly connects the hc@xmath0n segments from the north to the south . figure[fig : pvd](a ) and ( c ) show the @xmath1co and hc@xmath0n patterns along the pa of 10 , and their overlay in figure[fig : pvd](e ) demonstrates their coincidence . the local peak positions are marked by open circles ( blue for @xmath1co ; red for hc@xmath0n ) , illustrating their good match in the p - v diagram . in the bottom panels of figure[fig : pvd ] along the pa of 280 , the hc@xmath0n pattern in ( d ) is prominent in the outer shells , while the @xmath1co emission in ( b ) is centralized and the outer pattern fading away . however , their overlay in ( f ) again shows a good correlation .    albeit there is a good correlation in the pattern locations , some differences can be found between the @xmath1co @xmath2=21 and hc@xmath0n @xmath2=43 maps . the @xmath1co emission is omnipresent in the cse of cit 6 , while the hc@xmath0n line emission is absent toward the center and west sides ( see figure[fig : chm ] , e.g. , the panels for @xmath105 and 5 ) . the @xmath1co map exclusively reveals the first and second windings in the central 5  region , while their hc@xmath0n counterparts are missed . the p - v diagrams ( figure[fig : pvd](a)(b ) ) further exhibit the richness of the @xmath1co structure within the central 5 , where hc@xmath0n is lacking as shown in figure[fig : pvd](c)(d ) . the second and third @xmath1co windings appear broken in the hc@xmath0n map in the west side . the @xmath1co structures appearing at @xmath109 and @xmath103 in figure[fig : pvd](b ) are completely missed in the corresponding p - v diagram of hc@xmath0n , i.e. , figure[fig : pvd](d ) . to the west side where the hc@xmath0n @xmath2=43 emission was absent , the @xmath1co @xmath2=21 arm pattern appears but its radial profile is steeper than in any other directions . it implies that the west side is indeed special in both molecules , probably indicating anisotropic mass loss . nevertheless , the complete non - detection of the western part of spiral arm pattern in hc@xmath0n @xmath2=43 implies that the chemical effects on hc@xmath0n may be not negligible . the @xmath1co emission is seen in both the compressed spiral arm and the interarm region , whereas the hc@xmath0n emission seems to be mostly enhanced in the outer edge of the shock front as following . in the outer region where the hc@xmath0n pattern is prominent ( @xmath26 to 10 ) , the spiral - shell pattern appears better in hc@xmath0n with high arm - interarm contrasts . the hc@xmath0n pattern segments are narrow ( comparable to its synthesized beam size @xmath23 ) , while the @xmath1co arm pattern is broader and the arm - interarm contrasts are smaller . in addition , the hc@xmath0n emission peaks marked by red circles in figure[fig : pvd](e)(f ) tend to be located slightly outside of the @xmath1co emission peaks ( blue ) . all these features may indicate that hc@xmath0n is sufficiently excited at the edge of the spiral arm region tracing the shock front .    the critical density for a molecular line transition , at which the emission induced by molecular collisions dominates over spontaneous emission , gives an approximate lower limit on the gas density in the emitting region of such line transition . the critical density of @xmath1co @xmath2=21 is nearly independent of temperature ( @xmath154 ) , while that of hc@xmath0n @xmath2=43 is higher ( @xmath155 for @xmath156k ) and drops with temperature . it implies that the hc@xmath0n @xmath2=43 is a higher density tracer at the typical average temperatures of agb cses ( @xmath156k ) . in the radius range ( @xmath15710 ) where the hc@xmath0n pattern of cit 6 is observed , a low interarm number density @xmath158@xmath159 and gas temperature @xmath160k are expected @xcite . therefore the lack of hc@xmath0n line emission in the interarm region is reasonable . within the spiral arm , a number density of @xmath161@xmath162@xmath159 with a temperature of several hundreds kelvins is possible @xcite . hence , molecular collisions are sufficient for exciting hc@xmath0n @xmath2=43 , explaining the high arm - interarm contrast in the hc@xmath0n map . on the other hand , the critical density of @xmath1co @xmath2=21 is independent of gas temperature , making this emission well excited in both arm and interarm regions , and reducing the contrast between the arm and interarm regions . the systemic velocity channel interestingly shows a double spiral feature in the central @xmath163 region , as shown in figure[fig : dsp ] ( see also the middle panel of figure[fig : chm ] for a larger field ) , which was not generated in the previous hydrodynamic simulation assuming a constant wind velocity of 17  @xcite . a slower wind at the locus of the companion may facilitate generation of another spiral ( see e.g. , figure 3 of * ? ? ? * ) provided that the flow velocity is less than the escape velocity from the companion s gravitational potential . the inner double spirals are expected to merge together within one to two windings because of their different pattern propagation speeds . this merging seems to occur at around 4  in cit 6 , leaving the one - armed spiral pattern in the outer part of figure[fig : chm ] ( middle panel ) as traced in the hc@xmath0n and co line emissions .    however , the projected binary separation of @xmath17au @xcite is far beyond several stellar radii , where dust grains form and stellar radiation pressures on them accelerate the cse flow to the terminal velocity @xcite . we speculate that a highly eccentric orbit may allow the companion to pass the acceleration zone , possibly forming a double spiral in the inner part of the cse of cit 6 . an orbit with the periastron closer than the acceleration zone radius ( assuming 20au ) and the apocenter at @xmath164au requires an eccentricity @xmath165 .    for an eccentric orbit , the orbital speed of a mass - losing star is fastest at the periastron . therefore the accumulated mass ejection to this direction is lower than in other directions . the lack of @xmath1co interarm emission to the west ( along a pa of 270  in figure[fig : prf ] ) , closely resembles the column density map of a highly eccentric orbit model in ( * ? ? ? * see e.g. , the model with an eccentricity of 0.8 ) . the anisotropic mass loss due to the eccentric orbit alters the gas density particularly in the interarm region , which is similar to our finding from the @xmath1co brightness radial profiles . in this case , the periastron would be on the west side . @xcite further employed a concept of _ periodic _ mass loss enhancement triggered by a _ close _ fly - by companion in their piston model , creating a more complex pattern on the cse . if this strong tidal interaction model applies to cit 6 , the periastron , at which a larger mass loss could occur , would be on the opposite , east side leading to a higher average intensity . this situation is less likely for a wide binary like cit 6 , although the necessary binary separation for the strong tidal interaction between the stars is not well studied .","summary":"the lack of interarm emission to the west may indicate a feature corresponding to the periastron passage of a highly eccentric orbit of the binary .","abstract":"cit 6 is a carbon star in the transitional phase from the asymptotic giant branch ( agb ) to the protoplanetary nebulae ( ppn ) . observational evidences of two point sources in the optical , circumstellar arc segments in an hcn line emission , and a bipolar nebula in near - infrared provide strong support for the presence of a binary companion . hence , cit 6 is very attractive for studying the role of companions in the agb - ppn transition . we have carried out high resolutionco=21 andco=21 observations of cit 6 with the submillimeter array combined with the submillimeter telescope ( single - dish ) data . theco channel maps reveal a spiral - shell pattern connecting the hcn segments in a continuous form , and an asymmetric outflow corresponding to the near - infrared bipolar nebula . rotation of theco channel peak position may be related to the inner spiral winding and/or the bipolar outflow . an eccentric orbit binary is suggested for the presences of an anisotropic mass loss to the west and a double spiral pattern . the lack of interarm emission to the west may indicate a feature corresponding to the periastron passage of a highly eccentric orbit of the binary . spatially - averaged radial and spectral profiles ofco=21 andco=21 are compared with simple spherical radiative transfer models , suggesting a change ofco/co abundance ratio from to inward in the cse of cit 6 . the millimeter continuum emission is decomposed into extended dust thermal emission ( spectral index ) and compact emission from radio photosphere ( spectral index ) ."}
{"article_id":"1510.03916","section_id":"i","document":"we have observed cit 6 in all possible ( subcompact , compact , extended , and very extended ) array configurations of the sma from 2013 january to 2014 march , and combined with the smt mapping observations on 2015 january . our findings from the @xmath1co @xmath2=21 , @xmath3co @xmath2=21 , and continuum emission are summarized as follows :    * cit 6 s continuum position at the epoch 2013.1 is ( ra , dec)@xmath166 ( 10@xmath6316@xmath6402259 , @xmath6530341918 ) in j2000 , updating the proper motion measurement to be ( @xmath66 , @xmath67)masyr@xmath68 . on the other hand , the @xmath1co @xmath2=21 emission peak position rotates counterclockwise with the channel velocity , staying on the northwest side ( @xmath167mas ; @xmath168mas ) of the dust continuum emission center . the positional shift of molecular line emission peak in the proper motion direction is noticeable . * continuum emission at 226.2ghz from the sma observations best fits to a two - component model consisting of an unresolved source ( of flux 26.4mjy ) and an extended component with a size @xmath169 ( 34.5mjy ) . the unresolved continuum source is also observed at 350.6ghz and has a spectral index @xmath170 , consistent with thermal blackbody emission from a radio photosphere with a diameter of 8au and the temperature of 2000k . * the systemic lsr velocity of @xmath171 is defined as the middle velocity between the double peak spectral profile of the @xmath3co @xmath2=21 line in the innermost 1  region . with respect to the systemic velocity , the peaks are located at @xmath172 and its brightness temperature reaches zero at @xmath173 . the outer envelope has an additional @xmath85 component , brighter than the @xmath86 peak . * the @xmath1co @xmath2=21 emission spectral profile varies with integration radius ; a red - skewed double peak profile ( with a small blue - end bump ) over @xmath174 , a nearly flat - topped profile over @xmath90 , and a parabolic shaped profile from the single dish observations with a @xmath39-sized beam . it shows the optical depth change with radius ; i.e. , the innermost envelope is relatively optically thin and a significant fraction of 5  region becomes optically thick . * the spatially - averaged radial and spectral profiles of @xmath1co @xmath2=21 in all length scales are reasonably well reproduced by a simple spherical radiative transfer model . however , the fixed fractional abundance model fails in matching the overall radial distribution of the observed @xmath3co @xmath2=21 emission . this may suggest that the @xmath1co/@xmath3co abundance ratio varies in the cse of cit 6 from @xmath4 in the outer envelope to @xmath5 in the inner envelope . * the high resolution @xmath1co @xmath2=21 map ( from the sma ) reveals a spiral - shell pattern appearing as a 20% fluctuation of the average profile , due to the suggested binary orbital motion . this pattern is undetected in the @xmath3co @xmath2=21 emission likely due to sensitivity , as 20% of the observed @xmath3co maximum brightness corresponds to @xmath175 only . * the previously observed , arc - shaped pattern in the hc@xmath0n @xmath2=43 emission map turns out to be an incomplete form of the spiral - shell pattern appearing in the @xmath1co @xmath2=21 map . the hc@xmath0n segments ( broken to the west side and central 3  region ) are connected by the @xmath1co pattern . the hc@xmath0n @xmath2=43 line emission likely traces the shocked arm region with high arm - interarm contrasts . * a bipolar outflow of cit 6 is found for the first time in the @xmath1co @xmath2=21 channel map . the blue component ( at @xmath176 ) is separated from the agb envelope by a gap at @xmath86 , clearly seen in the p - v diagrams . the red counterpart ( at 19 ) is smaller than the blue component of the bipolar outflow , and points to a nearly perpendicular direction . * in the zoomed - in channel map and spectrum , the @xmath128 channels exhibit the strongest emission , indicating that the spectral asymmetry of the @xmath1co @xmath2=21 emission originates from the innermost region . in contrast , the source of the red - skewed profile of hc@xmath0n @xmath2=43 can be found from the broadly distributed outer shells at @xmath177 . * an eccentric binary orbit is hinted in the @xmath1co @xmath2=21 map by a double spiral feature at the systemic velocity and by the lack of interarm emission to the west , indicating the location of orbit periastron . the pattern spacing changes from @xmath178 between the outermost arms beyond @xmath117 to @xmath25 between the inner arms , characterizing an either reduced orbital period or slower wind flow .","summary":"we have carried out high resolutionco=21 andco=21 observations of cit 6 with the submillimeter array combined with the submillimeter telescope ( single - dish ) data . spatially - averaged radial and spectral profiles ofco=21 andco=21 are compared with simple spherical radiative transfer models , suggesting a change ofco/co abundance ratio from to inward in the cse of cit 6 . the millimeter continuum emission is decomposed into extended dust thermal emission ( spectral index ) and compact emission from radio photosphere ( spectral index ) .","abstract":"cit 6 is a carbon star in the transitional phase from the asymptotic giant branch ( agb ) to the protoplanetary nebulae ( ppn ) . observational evidences of two point sources in the optical , circumstellar arc segments in an hcn line emission , and a bipolar nebula in near - infrared provide strong support for the presence of a binary companion . hence , cit 6 is very attractive for studying the role of companions in the agb - ppn transition . we have carried out high resolutionco=21 andco=21 observations of cit 6 with the submillimeter array combined with the submillimeter telescope ( single - dish ) data . theco channel maps reveal a spiral - shell pattern connecting the hcn segments in a continuous form , and an asymmetric outflow corresponding to the near - infrared bipolar nebula . rotation of theco channel peak position may be related to the inner spiral winding and/or the bipolar outflow . an eccentric orbit binary is suggested for the presences of an anisotropic mass loss to the west and a double spiral pattern . the lack of interarm emission to the west may indicate a feature corresponding to the periastron passage of a highly eccentric orbit of the binary . spatially - averaged radial and spectral profiles ofco=21 andco=21 are compared with simple spherical radiative transfer models , suggesting a change ofco/co abundance ratio from to inward in the cse of cit 6 . the millimeter continuum emission is decomposed into extended dust thermal emission ( spectral index ) and compact emission from radio photosphere ( spectral index ) ."}
{"article_id":"gr-qc0210043","section_id":"i","document":"a number of large laser interferometers @xcite are approaching sensitivities to gravitational waves in the @xmath0 hz frequency band that could be sufficient for the detection of astrophysical events @xcite . the signals from these events will be buried deep in the instrumental noise , so that unambiguous detections will be possible only with highly efficient data processing algorithms . the focus of this article will be on transient sources of gravitational radiation , which will be defined as sources that have a relatively short duration ( milliseconds to tens of seconds ) and a bandwidth which overlaps at least partially with that of the interferometric detectors . a significant number of such transient sources have been theorized , with various levels of sophistication . for instance , the inspiral portion of coalescing compact binaries is well - understood ( by post - newtonian expansion techniques @xcite ) , as is the ring - down portion if a black hole results from the coalescence @xcite , but the merger portion is understood at best only qualitatively @xcite . as the mass of the binary increases , the signal - to - noise ratio of the merger portion dominates that of the inspiral and ringdown portions ; the coalescence of @xmath1 black hole binaries could be visible at large distances , provided that the merger waveform could be detected with sufficient efficiency @xcite . the collapse of the core of massive stars could also produce detectable signals @xcite ; depending on the type of progenitor , bar modes , r - modes , fragmentation instabilities or black hole ringdowns could be important sources of gravitational radiation . the details of the waveforms for most of these different mechanisms are far from known ; even in the best cases , only numerical simulations covering parts of the relevant physics are available in the literature @xcite . hence , as it can be seen from the preceding examples , the amount of information about the gravitational wave signal from various sources varies considerably , and this variability is obviously reflected in the efficiency of the algorithms that can be designed for each class of sources . only minimal assumptions about the signal will be made in this paper , and therefore the principal characteristic of the algorithm to be presented will be its robustness against poor modeling of the expected signal waveform . stated differently , this algorithm will be moderately sensitive to a very large class of signals , by opposition to being very sensitive to only a few specific signals . it will correspondingly be useful to search for transient sources that do not have waveforms that are precisely predicted , and to characterize the non - gaussian , transient component of the noise in the instruments . it is important when designing a detection algorithm to compare its efficacy to that of other designs ; the development process can stop when an algorithm that outperforms all others is discovered . various measures of this efficacy can be adopted , and various techniques to obtain the optimal algorithm be used , as it is discussed in section [ transient_detection ] . it is argued that the algorithm that is presented in this article , the tfclusters algorithm , has a structure which is close to that of the optimal detector for a large variety of signal classes . the tfclusters algorithm is explained in detail in section [ notation ] . to summarize , it consists of the following four steps :    ( i ) : :    the data @xmath2 from a gravitational wave detector are    transformed into a time - frequency representation with fixed time and    frequency resolutions @xmath3 and @xmath4 ,    respectively ; the instantaneous power at time @xmath5    and frequency @xmath6 , estimated from this    representation , is labeled @xmath7 . ( ii ) : :    a threshold @xmath8 is applied on the power , in order to    retain only pixels with @xmath9 . ( iii ) : :    clusters of pixels with power above threshold are formed by grouping    pixels sharing a common side ; clusters that do not conform to a fixed    set of rules on their size or distance to other clusters are    discarded . ( iv ) : :    a threshold on the sum of @xmath10 over    the surviving clusters is applied . data segments containing clusters    satisfying this threshold lead to the acceptance of the hypothesis    that they contain a signal .    in order to understand the operating characteristics of this algorithm , a simplified version [ without the clustering analysis , i.e. consisting only of steps ( i ) , ( ii ) and ( iv ) ] is shown in section [ optimality ] to maximize for all signals in @xmath11 the signal - to - noise ratio among all detectors that are based on the estimation of a lower bound of the signal power . this simplified algorithm is especially efficient for signals with a sparse representation in the time - frequency domain . since most signals are expected to have pixels that present a high degree of spatial correlation in the time - frequency domain , the clustering analysis of tfclusters is an interesting way to capitalize on that property to filter out a large portion of the noise , as it is shown in section [ clustering ] . an analytical method for computing the false alarm rate associated with tfclusters is developed , with the details for the clustering analysis being presented in section [ clustering_far ] . using the computer - generated enumeration of all the possible clusters of a certain size that can be formed , it is shown that large clusters are exponentially unlikely to occur when only noise is present . the rate of occurrence of pairs of clusters separated by a certain distance is computed in an analogous manner . one example of a complete analysis of the performances of tfclusters for a short , narrow - band signal , including the optimization of its efficiency at fixed false alarm rate , is presented in section [ clustering_pod ] . the efficiency of tfclusters is compared to that of the ( unrealistic ) ideal power detector ( which assumes a knowledge of the signal duration and central frequency ) as a function of the signal - to - noise ratio of the signal ; at fixed probability of detection , the reduction in signal - to - noise ratio for tfclusters is consistently less than about 30% . numerical simulations ( section [ simulations ] ) confirm that the analytical model for the false alarm rate is accurate in the regime of operation relevant to tfclusters , with errors on the predicted false alarm rates around 1% in most situations , and with maximum errors around 10% , due to the exclusion of higher - order terms in the theoretical modeling , or to unmodeled finite size effects .","summary":"clusters of such pixels that conform to a set of rules on their size and their proximity to other clusters are formed , and a final threshold is applied on the power integrated over all pixels in such clusters . is presented , and it is shown using a number of representative numerical simulations to be accurate at the 1% level for most values of the parameters , with maximal error around 10% .","abstract":"an efficient algorithm is presented for the identification of short bursts of gravitational radiation in the data from broad - band interferometric detectors . the algorithm consists of three steps : pixels of the time - frequency representation of the data that have power above a fixed threshold are first identified . clusters of such pixels that conform to a set of rules on their size and their proximity to other clusters are formed , and a final threshold is applied on the power integrated over all pixels in such clusters . formal arguments are given to support the conjecture that this algorithm is very efficient for a wide class of signals . a precise model for the false alarm rate of this algorithm is presented , and it is shown using a number of representative numerical simulations to be accurate at the 1% level for most values of the parameters , with maximal error around 10% ."}
{"article_id":"0812.3051","section_id":"i","document":"the nineteenth and twentieth centuries may be summarized as the centuries of non - relativistic classical science and relativistic quantum science respectively . judging by the scale of activity and progress in the field , the twenty - first century may well turn out to be the century of neural science . the hard problem of consciousness and its relationship to brain function is being systematically worn down using all the quantum technologies and theories developed over the last hundred years . central to this programme is the concept of the _ observer _ , the enigmatic ` _ _ i _ _ ' of _ i think therefore i am_. the problem is that , despite the many triumphs of quantum mechanics , the physics of the observer and observation is still not well understood . an important problem is that we are not sure what the correct way to model observers mathematically is . the _ exophysical _ perspective , which assumes that observers stand outside the space - time arena in which suos ( systems under observation ) exist , remains the dominant paradigm in all the sciences . reality is different however . the empirical facts are that actual observers are part of the physical universe and can be observed by other observers . as feynman wrote @xcite : ` _ _ ... we have an illusion that we can do any experiment that we want . we all , however , come from the same universe , have evolved with it , and do nt really have any real freedom . for we obey certain laws and have come from a certain past . _ _ ' this raises a question central to the interpretation of quantum mechanics : are observers just more complicated versions of suos , a view of reality known as the _ endophysical _ perspective , or are they fundamentally different altogether ? this question has been called the endo - versus - exo debate . another debate of central importance to the theory of observation involves the conflict between the classical world view and the quantum world view . the former postulates that suos and their properties exist independently of any observers or observation , whereas the latter can not make sense without them . regardless of how observers are defined and whether classical or quantum principles are involved , physicists generally believe that classical information in some form is extracted from suos in actual physics experiments . in all branches of science , their language reflects this belief . experimentalists talk of measuring an electron s spin or the mass of a new particle , and so on . whilst this point of view is of immense practical value , it may be a fundamental conceptual error . to quote heisenberg @xcite : ` _ _ the orbit _ _ [ of the electron ] _ comes into being only when we observe it_. ' it is difficult to think of any idea further from the classical world view than that one .    the conceptual issues in quantum mechanics such as wave - particle duality , quantum interference and non - locality gave the first indication that all might not be well with this perspective . we need only to look at the photon concept to appreciate some of the problems with the idea that photons are particles @xcite . developments in neuroscience are reinforcing the need to rethink the universality of the exophysical perspective . if large collections of neurons are seen to act in a coherent fashion more typical of observers than suos , then the boundaries between endo and exo physics will have been eroded . just when does a brain become an observer rather than an suo ? what seems to be missing is a dynamical theory of observation which regards observers and suos more on the same footing . in such a theory , observers would be subject to the same laws of physics as the suos that they were observing , just as feynman said in 1982 . such a theory would ideally be capable of accounting for the creation and annihilation of observers and their apparatus , because in the real world , nothing lasts forever . we are a long way from having such a theory of observation , but various authors have made some interesting comments on this topic @xcite . this paper outlines our current thoughts on the subject to date . these are based firmly on standard principles of quantum mechanics extended to cover the processes of observation . the most important idea is to discuss observation in terms of signal states of apparatus , referred to as _ labstates _ , rather than states of suos .","summary":"we introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus .","abstract":"we introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus . power sets of classical bits model the four classical states of elementary detectors , viz . the two normal yes / no signal states , the faulty or decommissioned state and the non - existence state . operators over power set registers are used to describe various physical scenarios such as the construction and decommissioning of physical devices in otherwise empty laboratories , the dynamics of signal states over those detectors , the extraction of information from those states , and multiple observers . we apply our quantum formalism to the elitzur - vaidman bomb - tester experiment and the hardy paradox experiment ."}
{"article_id":"astro-ph0206414","section_id":"i","document":"the cosmic ray ( cr ) energy spectrum extends up to @xmath1 ev . the presence of the highest - energy particles ( ultra high - energy crs , uhecrs ) poses an enigma , since many good arguments suggest that they should not be observed . this apparent contradiction has stimulated a variety of more exotic explanations of their existence . the enigma can only be solved by an experiment that can provide a much larger event statistics than the about 20 events with @xmath2 ev measured in the past 35 years . knowing the form of the energy spectrum of the cr particles , their arrival direction distribution over the whole sky , and possibly even their mass composition , would allow us to test some of the hypotheses about their origin and help to identify their sources . at present experimental results suggest that uhecrs are protons or nuclei , as for crs at much lower energies . however , many of the more exotic models of uhecr origin predict also photons and neutrinos .    the measurement of extensive air showers ( eas ) is presently the only way to study crs with energies above about 10@xmath3 ev . the properties of primary cosmic rays have to be deduced from the development of the shower in the atmosphere and from the particle ratios in the shower . the incident direction can easily be reconstructed from the arrival times of shower particles at different positions at the observation level and the primary energy is approximately reflected in the total number of secondary particles produced . the mass of the primary particle is more difficult to measure . it is reflected , in a subtle way , in the shower form , specifically the height of the shower maximum , and in the muon - to - electron ratio of the shower . the pierre auger observatory is conceived to measure crs with energies @xmath0 ev with good statistics over the whole sky @xcite . it will consist of two detector sites , one in the southern and one in the northern hemisphere . each site covers an area of 3000 km@xmath4 and combines two techniques to measure ( i ) the particle distribution at observation level with an array of water cherenkov detectors and ( ii ) the longitudinal shower development via optical imaging of the fluorescence light in the atmosphere during clear moonless nights ( @xmath5 10% of the total time ) . this hybrid detection provides a way to inter - calibrate both sub - systems and to control systematic uncertainties . the energy determination via the fluorescence light is basically calorimetric and therefore much less model - dependent than the energy reconstruction from particle densities at ground level . the southern site is presently under construction in argentina . the size of the site was chosen to register about 5000 events with energies @xmath6 ev and about 40 - 80 events above 10@xmath7 ev per year .    since experiments at energies @xmath8 ev can not be calibrated with a test beam the interpretation of eas measurements is performed by comparing experimental data with model predictions of the shower development in the atmosphere . therefore quantitative results rely on the model assumptions and on the quality of the simulation of particle interactions and transport in the atmosphere . the detailed shower development is far too complex to be fully described by a simple analytical model . therefore it is usually modeled by monte carlo ( mc ) simulation of transport and interaction of each individual shower particle , employing our present knowledge on interactions , decays and particle transport in matter . while the electromagnetic interaction ( responsible for electromagnetic sub - showers , ionization , cherenkov light production , ... ) and the weak interaction ( responsible for decays of unstable secondaries ) are well understood , the major uncertainties in eas simulation arise from the hadronic interaction models . with the present theoretical understanding of soft hadronic interactions , i.e. those with a small momentum transfer , one can not calculate interaction cross - sections or particle production from first principles . therefore , hadronic interaction models are usually a mixture of fundamental theoretical ideas and empirical parametrisations tuned to describe the experimental data at lower energies . the large extrapolation ( over 6 orders of magnitude in energy ) needed from experimental accelerator data to cr interactions is the second major source of uncertainty , and with an uncertain interaction model it is difficult to determine the energy spectrum and the composition of crs .    as a consequence of the better understanding of hadronic and nuclear interactions at high energies , and the increase in computing power , shower models have improved dramatically over recent years . also the understanding of the measuring process with a detector has markedly advanced . it is now possible to describe consistently experimental results over a wide range of energies and even to test hadronic models on the 20% level .    in this paper we review the physics and techniques of state - of - the - art modeling of extensive air showers , specifically those important for energies of @xmath9 ev or above . in sec . [ sec - had ] and [ sec - em ] we describe the modeling of hadronic and electromagnetic interactions , respectively . [ sec - neu ] summarizes briefly the simulation of showers induced by photons and neutrinos or other more exotic primary particles . statistical thinning techniques that allow simulation of showers at the highest energies in a finite time are discussed in sec . [ sec - thin ] . then two shower simulation programs are described and compared in sec . [ sec - programs ] . some simulation results are shown in sec . [ sec - results ] .","summary":"they are used to estimate the energy and mass of the primary particle . aiming at energies ev , the models have to be extrapolated far beyond the energies available at accelerators . on the other hand , hybrid measurement of ground particle densities and calorimetric shower energy , as will be provided by the pierre auger observatory , will strongly constrain shower models . while the main uncertainty of contemporary models comes from our poor knowledge of the ( soft ) hadronic interactions at high energies , also electromagnetic interactions , low - energy hadronic interactions and the particle transport influence details of the shower development . we review here the physics processes and some of the computational techniques of air shower models presently used for highest energies , and discuss the properties and limitations of the models .","abstract":"air shower simulation programs are essential tools for the analysis of data from cosmic ray experiments and for planning the layout of new detectors . they are used to estimate the energy and mass of the primary particle . unfortunately the model uncertainties translate directly into systematic errors in the energy and mass determination . aiming at energies ev , the models have to be extrapolated far beyond the energies available at accelerators . on the other hand , hybrid measurement of ground particle densities and calorimetric shower energy , as will be provided by the pierre auger observatory , will strongly constrain shower models . while the main uncertainty of contemporary models comes from our poor knowledge of the ( soft ) hadronic interactions at high energies , also electromagnetic interactions , low - energy hadronic interactions and the particle transport influence details of the shower development . we review here the physics processes and some of the computational techniques of air shower models presently used for highest energies , and discuss the properties and limitations of the models ."}
{"article_id":"astro-ph0206414","section_id":"i","document":"in the last decade much has changed in air shower simulations . through better understanding of the relevant hadronic interactions and the massive increase in computer performance very elaborate monte carlo models became feasible that track individual particles through atmosphere and detectors and simulate all their interactions with matter in great detail . predictions of air shower programs have become much more quantitative and describe the experimental data sufficiently well for data analysis and the design of new experiments . the weakest point in the simulations are the high - energy soft hadronic interactions , which are not well examined at accelerators so far , and the extrapolation to energies much beyond those available at accelerators . the most successful models are based on the gribov - regge theory of multi - pomeron exchange . there is a clear trend of convergence between different hadronic interaction models , due to objective improvement of the physics input . however , a level of systematic uncertainty of about 20% is likely to persist , since many of the input data , on which the models are built , appear to have uncertainties of this size . once observed , larger inconsistencies between data and simulations offer a possibility to improve the model assumptions . the calorimetric measurement of the shower energy via the fluorescence detectors in coincidence with the charged particle measurements in the auger experiment will assist with stringent tests of the shower models and promises the determination of an absolute energy scale as well as setting constraints on the shower models .    within the auger collaboration the two programs corsika and aires are used . they account for all processes necessary for air showers simulations up to 10@xmath118 ev . the programs complement each other in the sense that corsika uses more elaborate interaction models and aires is faster . corsika and aires agree to better than 20% for the basic shower parameters observed by the pierre auger observatory .","summary":"air shower simulation programs are essential tools for the analysis of data from cosmic ray experiments and for planning the layout of new detectors .","abstract":"air shower simulation programs are essential tools for the analysis of data from cosmic ray experiments and for planning the layout of new detectors . they are used to estimate the energy and mass of the primary particle . unfortunately the model uncertainties translate directly into systematic errors in the energy and mass determination . aiming at energies ev , the models have to be extrapolated far beyond the energies available at accelerators . on the other hand , hybrid measurement of ground particle densities and calorimetric shower energy , as will be provided by the pierre auger observatory , will strongly constrain shower models . while the main uncertainty of contemporary models comes from our poor knowledge of the ( soft ) hadronic interactions at high energies , also electromagnetic interactions , low - energy hadronic interactions and the particle transport influence details of the shower development . we review here the physics processes and some of the computational techniques of air shower models presently used for highest energies , and discuss the properties and limitations of the models ."}
{"article_id":"1304.2531","section_id":"i","document":"optimal quantization method appears first in @xcite where the author studies in particular the optimal quantization problem for the uniform distribution . it has become an important field of information theory since the early @xmath2 s . a common use of quantization is the conversion of a continuous signal into a discrete signal that assumes only a finite number of values . since then , optimal quantization is applied in many fields like in signal processing , in data analysys , in computer sciences and recently in numerical probability from the seminal work @xcite . its application to numerical probability relies on the possibility to discretize a random vector @xmath3 taking infinitely many values by a discrete random vector @xmath4 valued in a set of finite cardinality . this allows to approximate either expectations of the form @xmath5 or more significantly some conditional expectations like @xmath6 ( by quantizing both randoms variables @xmath3 and @xmath7 ) . optimal quantization is used to solve some problems emerging in quantitative finance as optimal stopping problems ( see @xcite ) , the pricing of swing options ( see @xcite ) , stochastic control problems ( see @xcite ) , nonlinear filtering problems ( see e.g. @xcite ) , the pricing of barrier options ( see @xcite ) .    in quantitative finance , several problems of interest amounts to the estimation of quantities of the form ( for a given borel function @xmath8 ) @xmath9 , \\quad t>0,\\ ] ] or involving terms like @xmath10 , \\quad   0<s < t,\\ ] ] related to a stochastic diffusion process @xmath11}$ ] solution to the stochastic differential equation @xmath12 where @xmath13 is a standard @xmath14-dimensional brownian motion starting at @xmath15 and where the functions @xmath16 \\times \\mathbb r^d \\rightarrow \\mathbb r^d$ ] and the matrix - valued diffusion coefficient function @xmath17 \\times \\mathbb r^d \\rightarrow \\mathbb r^{d \\times q}$ ] are borel measurable and satisfy some appropriate conditions which ensure the existence of a strong solution of the stochastic differential equation . since in general the solution of ( [ eqsignalintro ] ) is not explicit we have first to approximate the continuous paths of the process @xmath18}$ ] by a discretization scheme , typically , the euler scheme . given the ( regular ) time discretization mesh @xmath19 , @xmath20 , @xmath21 , the `` discrete time euler process '' @xmath22 , @xmath23 , associated to the previous diffusion process @xmath11}$ ] is recursively defined by @xmath24 then , once we have access to the discretization scheme of the stochastic process @xmath11}$ ] , the quantities ( [ eqpriceeurolikeoptionsc ] ) and ( [ eqnlfilterlikeoptionsc ] ) can be estimated by @xmath25\\ ] ] and @xmath26 , \\quad \\textrm{when   } t = t_{k+1 } \\textrm { and }   s = t_k.\\ ] ]    [ remconvereuler ] ( a ) for smooth functions @xmath27 or under hypoellipticity assumptions on @xmath28 ( see e.g. @xcite ) , the estimation of @xmath29 by @xmath30 induces the following weak error : @xmath31 with @xmath32 and where @xmath33 is the number of time discretization steps . \\(b ) also note that for every @xmath34 , @xmath35    the estimation of quantities like ( [ eqpriceeurolikeoptions ] ) or ( [ eqnlfilterlikeoptions ] ) can be performed using monte carlo simulations . nevertheless , an alternative to the monte carlo method can be to use cubature formulas produced by an optimal quantization approximation method , especially in small or medium dimension ( @xmath36 in the theory but in practice it may remain competitive with respect to the monte carlo method up to dimension @xmath37 , see @xcite ) . in fact , suppose that we have access to the optimal quantization or to some `` good '' ( in a sense to be specified further on ) quantizations @xmath38 ( we will sometimes denote @xmath39 by @xmath40 to simplify notations ) of the process @xmath41 on the grids @xmath42 of size @xmath43 ( which will be called an @xmath43-quantizer ) , for @xmath23 . suppose as well that we have access or have computed ( offline ) the associated weights @xmath44 , @xmath45 ; @xmath23 ( which are the distributions of the @xmath39 s ) , and the transition probabilities @xmath46 for every @xmath47 ; @xmath48 ; @xmath49 ( in other words , the conditional distributions @xmath50 ) . then , using optimal quantization method , the expressions ( [ eqpriceeurolikeoptions ] ) and ( [ eqnlfilterlikeoptions ] ) can be estimated by @xmath51   = \\sum_{i=1}^{n_n } f(x^{n}_i )   \\ , \\mathbb p \\big(\\widehat x_{t_n}^{\\gamma_n }    =   x^{n_n}_i \\big)\\ ] ] and @xmath52   = \\sum_{j=1}^{n_{k+1 } } \\widehat p_k^{ij } f(x^{k+1 } _ j ) , \\ ] ] respectively . the remaining question to be solved is then to know how to get the optimal or at least `` good '' grids @xmath53 , for every @xmath54 , their associated weights and transition probabilities . in a more general framework , as soon as the stochastic process @xmath41 ( or the underlying diffusion process @xmath55 ) can be simulated one may use stochastic gradient algorithm ( clvq ) or a randomized fixed point procedure ( lloyd ) to compute the ( hopfully almost ) optimal grids and their associated weights or transition probabilities . in the special case of the one dimensional setting we can often use the newton - raphson s algorithm in several situations of interest . this deterministic algorithm leads to more precise estimations and is dramatically faster than stochastic optimization methods .    to highlight the usefulness of our method , suppose for example that we aim to estimate the price of a put option with a maturity @xmath56 , strike @xmath57 and a present value @xmath58 in a local volatility model where the dynamics of the stock price process evolves following the stochastic differential equation ( called pseudo - cev in @xcite ) : @xmath59,\\ ] ] where @xmath60 and @xmath61 $ ] , @xmath62 , and @xmath63 stands for the interest rate in this situation the solution at time @xmath56 , @xmath64 , is not known analytically and if we want to estimate the quantity of interest : @xmath65 , where @xmath66 is the ( lipschitz continuous ) payoff function , we have first of all to discretize the process @xmath18}$ ] as @xmath67 , with @xmath68 ( using e.g. the euler scheme ) , and then estimate @xmath69 by optimal quantization . the only way to get the optimal grids and the associated weights in this situation is to perform stochastic algorithms like the clvq ( see e.g. @xcite ) or the lloyd s procedure ( see e.g. @xcite ) , even in the one dimensional framework . however , these methods may be very time consuming . in this framework ( as well as in the general local volatility model framework in dimension @xmath70 ) , our approach allows us to quantize the diffusion process in the pseudo - cev model using the newton - raphson algorithm to reduce dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to commonly proposed algorithms . it is important to notice that the companion weights and the probability transitions associated to the quantized process are obtained by a closed formula so that the method involves by no means monte carlo simulations . on the other hand , a comparison with monte carlo simulation for the pricing of european options in a local volatility model also shows that the proposed method is more efficient ( with respect to both computational precision and time complexity ) than the monte carlo method . let us be more precise about our proposed method in the general setting where the diffusion @xmath11}$ ] evolves following equation . let @xmath67 be the discrete euler process , with step @xmath71 , associated to the diffusion @xmath11}$ ] . our aim is in practice to compute the quadratic optimal quantizers @xmath72 associated with the @xmath73 s , for @xmath23 . such a sequence @xmath72 is defined for every @xmath23 by @xmath74 where for every @xmath54 , the function @xmath75 is called the distortion function associated to @xmath76 and is defined for every @xmath43-quantizer @xmath53 by @xmath77    now , by conditioning with respect to @xmath76 , we observe that we can connect the distortion function @xmath78 associated to @xmath79 with the distribution of @xmath76 by introducing the euler scheme operator as follows : @xmath80            \\end{aligned}\\ ] ] where @xmath81 is an @xmath82 sequence of @xmath83-distributed random vectors independent from @xmath84 and for every @xmath85 , the euler operator @xmath86 is defined by @xmath87 now , here is how we construct the algorithm . given the distribution of @xmath84 , we quantize @xmath84 and denote its quantization by @xmath88 . we want now to quantize @xmath89 , which distribution is unknown . keeping in mind equation ( [ eqdistasdistxtkintro ] ) and setting @xmath90 , we may approximate the distortion function @xmath91 by @xmath92 \\nonumber    =   \\mathbb e \\big [    d({\\cal e}_0(\\widehat x_{0}^{\\gamma_0 } , z_{1 } ) , \\gamma_{1})^2 \\big].\\ ] ] we then define the marginal quantization of @xmath89 by @xmath93 . this leads us to consider the sequence of marginal quantizations @xmath94 of @xmath95 , defined from the following recursion : @xmath96    from an analytical point of view , this approach raises some new challenging problems among which the estimation of the quadratic error bound @xmath97 , for every @xmath54 . we will show in particular that for any sequences of ( quadratic ) optimal quantizers @xmath53 for @xmath98 , for every @xmath99 , the quantization error @xmath100 is bounded by the cumulative quantization errors @xmath101 , for @xmath102 . owing to the non - asymptotic bound for the quantization errors @xmath101 , known as pierce s lemma ( which will be recalled further on ) we precisely show that for every @xmath103 , for any @xmath1040,1]$ ] , @xmath105 where @xmath106 is a positive real constant depending on the indicated parameters .    the paper is organized as follows . we recall first some basic facts about ( regular ) optimal quantization in section [ secoptiquant ] . the marginal quantization method is described in section [ sectmq ] . we give in this section the induced quantization error . in section [ sectioncommarquan ] , we illustrate how to get the optimal grids using newton - raphson s algorithm and show how to estimate the associated weights and transition probabilities . the last section , section [ sectnum ] , is devoted to numerical examples . we first compare the recursive marginal quantization of @xmath107 with its regular marginal quantization ( see section [ secoptiquant ] ) , where @xmath108}$ ] stands for the brownian motion and show the numerical performance of the marginal quantization method with respect to the regular quantization method . secondly , we use the marginal quantization method for the pricing of an european put option in a local volatility model ( as well as in the black - scholes model ) and compare the results with those obtained from the monte carlo method .    notations . we denote by @xmath109 , the set of @xmath110 real value matrices . if @xmath111 \\in { \\cal m}(d , q,\\mathbb r)$ ] , @xmath112 denotes its transpose and we define the norm @xmath113 , where @xmath114 stands for the trace of @xmath115 , for @xmath116 . for every @xmath117 , we will set @xmath118_{\\rm lip}= \\sup_{x\\neq y}\\frac{\\vert f(x)-f(y ) \\vert}{\\vert x - y \\vert}$ ] . for @xmath119 , @xmath120 .","summary":"we propose a new approach to quantize the marginals of the discrete euler diffusion process . the method is built recursively and involes the conditional distribution of the marginals of the discrete euler process . analytically , the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the euler process and the proposed quantizations . we show in particular that at every discretization step of the euler scheme , this error is bounded by the cumulative quantization errors induced by the euler operator , from times to time . for numerics , we then propose a close formula for the companion weights and the transition probabilities associated to the proposed quantizations . this allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework . numerical tests are carried out for the brownian motion and for the pricing of european options in a local volatility model . a comparison with the monte carlo simulations shows that the proposed method is more efficient ( w.r.t . both computational precision and time complexity ) than the monte carlo method .","abstract":"we propose a new approach to quantize the marginals of the discrete euler diffusion process . the method is built recursively and involes the conditional distribution of the marginals of the discrete euler process . analytically , the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the euler process and the proposed quantizations . we show in particular that at every discretization step of the euler scheme , this error is bounded by the cumulative quantization errors induced by the euler operator , from times to time . for numerics , we restrict our analysis to the one dimensional setting and show how to compute the optimal grids using a newton - raphson algorithm . we then propose a close formula for the companion weights and the transition probabilities associated to the proposed quantizations . this allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework . numerical tests are carried out for the brownian motion and for the pricing of european options in a local volatility model . a comparison with the monte carlo simulations shows that the proposed method is more efficient ( w.r.t . both computational precision and time complexity ) than the monte carlo method ."}
{"article_id":"astro-ph0212303","section_id":"i","document":"the abundance of deuterium in the interstellar medium ( ism ) is a strong constraint on chemical evolution scenarios . unlike most elements , the net cosmic abundance of deuterium is not enhanced by stellar processes or supernovae , so its abundance has been declining from the primordial value due to destruction by stellar processing . the primordial abundance of deuterium is itself an important quantity , as it can be used to measure @xmath16 , the universal ratio of baryons to photons , which can be compared to the predictions of big bang nucleosynthesis @xcite . one approach to finding the initial deuterium abundance is to measure it in high - redshift qso absorption - line systems , assuming that the clouds which give rise to these systems have undergone very little stellar processing @xcite . however , the large range in d / h values measured in these systems suggests that the gas in some of these clouds may in fact have undergone some stellar processing @xcite . it is therefore crucial to understand how chemical evolution affects the abundance of deuterium relative to other elements . several groups are measuring the abundance of deuterium and other elements along many sight lines in the galactic ism in order to establish the mean d / h ratio in the galactic disk , and to look for variations in the d / h ratio . these variations can shed light on the effects of star - formation history and mixing processes on the d / h ratio . the local d / h value can then be compared to regions that have undergone varying amounts of stellar processing ( _ e.g. , _ high velocity clouds , or intergalactic clouds ) , which will illuminate the effects of stellar processing on the d / h ratio in these systems . the _ copernicus _  satellite was used to measure the and lyman series absorption toward @xmath17 stars , and the results suggested a d / h ratio of 1.5@xmath1810@xmath19 , with a dispersion that may reflect real variations in the ism ( see vidal - madjar & gry 1984 for a review ) . several measurements of d / h in the local ism have been made with the _ hubble space telescope _ ( _ hst _ ) @xcite , though only the ly@xmath2 transitions of and could be analyzed , limiting the number of available sight lines to those with low enough columns that the absorption is not blended with the line but large enough columns that can be detected . three sight lines observed with the interstellar medium absorption profile spectrograph ( _ imaps _ ) spanned larger distances than the _ hst _  sight lines ( 250 to 500 pc versus @xmath20 100 pc ) , and like the _ copernicus _  results they showed evidence of variation in d / h with location @xcite . one of the science goals of the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) is to measure d / h in the milky way @xcite . _ fuse _  is uniquely suited to do this because it observes the spectral region from 905 to 1187   which includes all of the lyman transitions except ly@xmath2 . the ability to use multiple transitions means that _ fuse _  is able to measure @xmath15 ( ) along higher column density sight lines than missions that only observe ly@xmath2 ( _ e.g. , _ _ hst _ ) , and for many more sight lines than short term missions ( _ e.g. , _ _ imaps _ ) . moos et al . ( 2002 , and references therein ) reported results for the first set of seven sight lines ranging from 37 to 179 pc , five of which had both measurements ( from _ fuse _ ) and ( from _ hst _ ) . the results were consistent with a single value of d / h@xmath21 ( the uncertainty is @xmath22 in the mean ) . however , none of these sight lines extend as far as the three sight lines observed by _ imaps_. analysis of more extended sight lines is crucial for the verification and understanding of variations in the d / h ratio in the ism . in this paper we present _ fuse _  measurements of d / h toward two distant stars in the galactic disk : hd  195965 and hd  191877 . these stars are at distances greater than the _ imaps _  targets , extending the distance and range of @xmath15 ( ) for d / h measurements in the ism . information about these two sight lines is listed in table 1 . the _ fuse _ , stis , and ground - based observations and data reduction are described in   2 . section 3 describes some properties of the sight lines . in   4 we describe both the curve of growth and the absorption profile fitting analyses of the column density toward both stars . in   5 we discuss the determination of the and abundances along these sight lines , and in  6 we re - examine the column densities . section 7 contains a discussion of the results and conclusions .","summary":"we have carried out an investigation of the abundance of deuterium along two extended sight lines through the interstellar medium ( ism ) of the galactic disk . we use a combination of curve of growth analyses and line profile fitting to determine the abundance toward each object . we find d / h= ( ) , o / h= , and n / h= . toward hd  191877 the d / h and o / h values measured along these sight lines support the expectation that the ism is not well mixed on distances of pc .","abstract":"we have carried out an investigation of the abundance of deuterium along two extended sight lines through the interstellar medium ( ism ) of the galactic disk . the data include _ far ultraviolet spectroscopic explorer ( fuse ) _ observations of hd  195965 ( b1ib ) and hd  191877 ( b0v ) , as well as space telescope imaging spectrograph ( stis ) observations of hd  195965 . the distances to hd  195965 and hd  191877 , derived from spectroscopic parallax , are  pc and  pc , respectively , making these the longest galactic disk sight lines in which deuterium has been investigated with _ the _ fuse _  spectra contain all of the lyman series transitions ( and the corresponding d transitions ) except ly . the higher lyman lines clearly show the presence of deuterium . we use a combination of curve of growth analyses and line profile fitting to determine the abundance toward each object . we also present column densities for and toward both stars , and measured from ly absorption in the stis spectrum of hd  195965 . toward hd  195965 we find d / h= ( ) , o / h= , and n / h= . toward hd  191877 we find d / h= ( ) and n / h= . the column density toward hd  191877 is very uncertain . our preferred value gives o / h= , but we can not rule out o / h values as low as o / h= , so the o / h value for this sight line should be taken with caution . the d / h ratios along these sight lines are lower than the average value of ( ( in the mean ) found with _ fuse_for the local interstellar medium ( to 179 pc from the sun ) . these observations lend support to earlier detections of variation in d / h over distances greater than a few hundred pc . the o / h ratio toward hd  195965 is supersolar . this star is part of an ob association , so there may be local enrichment by nearby massive stars . the d / h and o / h values measured along these sight lines support the expectation that the ism is not well mixed on distances of pc . these observations demonstrate that although d / h studies through lyman absorption may become impractical at d pc and log() , d / h studies in the distance range from 500 to 2500 pc may be very useful for investigating mixing and chemical evolution in the ism ."}
{"article_id":"astro-ph0212303","section_id":"c","document":"the sight lines analyzed in this paper are the longest ones for which the column densities have been determined with _ fuse_. as such , they present the opportunity to look for variations in / , / , and / beyond the local ism sight lines presented by @xcite . table 8 contains column density ratios of various elements toward both stars , along with the mean values for the local ism from @xcite . in this section we discuss the behavior of these column density ratios beyond the local ism . the deuterium abundances along seven sight lines have been analyzed with _ fuse _ five of these had both and measurements , and the results were consistent with a constant value of d / h in the local ism . earlier _ copernicus _ observations showed evidence for variations in d / h at larger distances ( see vidal - madjar & gry 1984 for a review ) , evidence which was strengthened by subsequent _ imaps _ investigations @xcite . the main obstacle to verifying and understanding this variation is the paucity of suitable deuterium sight lines that probe distances @xmath101250 pc . figure 16 shows the d / h ratios for hd  195965 and hd  191877 plotted as a function of distance from the sun , along with five of the seven original _ fuse _  sight lines with reliable measurements , and several others from _ hst _ , _ imaps _ , and _ copernicus _  ( see moos et al the d / h ratios toward both stars are lower than the average value found for the original seven _ fuse _ sight lines . this contrasts with the lack of variation seen in the local ism . the new sight lines support the existence of variations in the d / h ratio at distances larger than a few hundred pc , as also suggested by _ imaps _ and_copernicus_.    in the simplest model of chemical evolution , stellar processing ( astration ) leads to a decline in the d / h ratio because d is easily destroyed in stars . thus , the d / h ratio is expected to vary among regions of the galaxy that have undergone different amounts of star formation in the past , provided that the gas in these regions has not mixed ( _ e.g. _ tosi et al . 1998 ; chiappini et al . 2002 ) . in a small volume like the local ism ( @xmath102 pc ) , @xcite showed that the time between supernova @xmath103 is roughly equal to the mixing time scale ( assumed to be the sound crossing time @xmath104 ) , suggesting that the gas in such a region is well - mixed . if a larger region is considered , say 1000 pc in radius to approximate the scales probed by hd  195965 and hd  191877 , the crossing time increases by a factor of 10 , while the time between supernovae decreases by a factor of 100 , so that @xmath105 . supernovae are not distributed randomly over this region but are spatially correlated in regions of star formation , meaning that substantial inhomogeneities will arise between star - forming regions and more quiescent regions . for these reasons it is not surprising to see variations over the distances probed by hd  195965 and hd  191877 . a more precise treatment of mixing in the ism was carried out by @xcite . using numerical simulations , they found that the mixing time scales were a few times 10@xmath106 years . chemical inhomogeneities in the ism are long - lived , so variations in d / h are expected over 1000  pc length scales . in fact , since the mixing time scales increase only slightly with length scale in their models , it is unlikely that the local ism ( _ e.g. , _ the original seven _ fuse _ sight lines ) would have a constant d / h value if any sources of inhomogeneities ( _ i.e. , _ supernovae ) have occurred within the past @xmath107 years . we have investigated several alternative explanations for the low d / h values . one possibility is that some of the d column is in high - velocity components which are outside of the velocity integration range used to determine @xmath15 ( ) @xcite . we have used the 1302.169    line in the stis spectrum of hd  195965 to rule this out for that sight line ( see   5 ) . note that @xmath108 of the column would have to be missed if the d / h ratio for the hd  191877 sight line were as high as the @xcite mean local ism value . figure 7 shows that this is not the case , although we can not rule out a much smaller systematic offset for hd  191877 . a second possibility is that a significant amount of d is locked up in hd molecules . to test this idea , we have measured the equivalent widths of several strong , isolated lyman series hd lines in the _ fuse_spectra : ( 3 - 0 )  r(0 )  1066.271   , ( 5 - 0 )  r(0 )  1042.847   , and ( 4 - 0 )  r(0 )  1054.288   . the column densities derived from the equivalent widths are @xmath109 @xmath56 for the hd  195965 sight line , and @xmath110 @xmath56 for the hd  191877 sight line . for both sight lines this is @xmath111% of the total d column density , much lower than the uncertainty in @xmath15 ( ) . the d / o and o / h ratios toward hd  195965 in table 8 are quite different from the average values in the local ism found by @xcite . this is a surprising result , since @xcite found very little variation in o / h in their survey , which covered distances and column densities similar to those of the sight lines in this paper . both the and column densities toward hd  195965 were determined through at least two independent methods , with very similar results . the was measured using both _ iue _  and stis data , and the was measured with a single - component cog which combined _ fuse _  and stis data , as well as independent estimates from the optically thin 1355.598    line and the damped 1302.169  line in the stis spectrum . both of these column densities are therefore quite firmly established , and we believe that it is very unlikely that there is a substantial systematic error in either quantity . hd  195965 appears to lie on a very high metallicity sight line , with supersolar o / h @xcite . this may be a region where the signature of stellar processed gas is still visible ( as is not the case for the local bubble ) . @xcite found that this star is in the cygnus ob7 association . if so , it may be in a peculiar region , perhaps in a metal - enriched cloud of ejecta from the star itself or a neighbor . since gas with high metallicity is thought to have undergone stellar processing , d / h in such gas is expected to be low . this expected anticorrelation between o / h ( or n / h ) and d / h was not seen in the first seven _ fuse _  sight lines , although it could have been masked by the small number of sight lines studied @xcite . figure 17 compares the o / h and d / h value for hd  195965 with those of the original seven _ fuse _ sight lines . unfortunately hd  195965 is the only point at high metallicity , so no firm conclusions can be drawn . however , it is possible that this sight line shows evidence of the expected anticorrelation in the ism ( see also steigman 2002 ) . note that an error in the column density toward hd  195965 would tend to move that point along a diagonal line with a positive slope , and thus could not produce the expected trend of decreasing d / h with rising o / h . the hd  191877 sight line lacks stis data , so we could not constrain the and abundances with multiple estimates . for these reasons we are less confident in the column densities found for the hd  191877 sight line . as discussed in   5 , the derived log @xmath15 ( ) is very uncertain , although our preferred value , found by coupling the @xmath47-values of and , is consistent with the _ fuse _  local ism ratio and the @xcite ratio . unfortunately , with the existing information , we can not make any strong conclusions about o / h toward hd  191877 . the n / h ratios toward hd  195965 and hd  191877 in table 8 are higher than the average values in the local ism found by @xcite . figure 18 shows a plot of n / h versus d / h along both sight lines , compared to the four _ fuse _  sight lines for which n / h was measured . the figure is very suggestive of an anticorrelation between d / h and n / h .    complicating the interpretation of this plot is the fact n / h ratio is susceptible to ionization effects , especially at low column densities which do not provide adequate shielded from ionizing photons , such as the column densities along the local ism sight lines @xcite . the dashed line in figure 18 shows the ism value of n / h found by @xcite . the sight lines used in that study had higher column densities than the _ fuse _  local ism sight lines , so the _ fuse _  sight lines are very likely underestimating n / h , because a significant fraction of n is ionized . the apparent trend in figure 18 may simply reflect the tendency for @xmath15()/@xmath15 ( ) to decrease with increasing @xmath15 ( ) . however , an anticorrelation between d and n abundances would be expected if d is destroyed in stars while n is produced ( _ e.g. _ steigman et al . 2002 ) . the overabundance of heavy elements accompanied by the underabundance of d seems to fit well within a simple chemical evolution scenario . while ionization effects probably play a role in the high n / h ratio on these sight lines , they may not be the only factor . a comprehensive n / h survey using _ fuse _ spectra is currently underway , and may shed light on this issue .    several sight lines do not follow the expected trend of low d / h accompanied by high n / h or o / h . @xcite found a low o / h ratio toward bd+28@xmath1124211 with _ fuse _ , while their d / h ratio is close to the local ism mean . @xcite found a low d / h toward @xmath113 orionis using _ imaps _ , but also a somewhat low n / h ratio . these deviations suggest that the simple picture of increasing heavy elements abundances with decreasing d / h is not complete . measuring d / h values in the milky way becomes increasingly difficult as @xmath15 ( ) increases , perhaps reaching a fundamental confusion limit . the cogs in figures 8 and 9 show that the high order lyman transitions are close to saturation . at higher column densities , these transitions will fall on the flat part of the cog and will not give precise column density information . even higher order transitions at shorter wavelengths , where the lines might not yet be saturated at higher column density , are not useful because the transitions begin to blend together . these facts make it unlikely that many galactic disk sight lines more distant than those studied here will be useful for d / h measurements . however , the sight lines analyzed in this paper demonstrate that d / h properties over the distance range from 500 to 2500 pc can be explored with _ fuse _ , even if these sight lines contain a significant amount of h@xmath52 . this first glimpse at d / h in this distance range suggests that it will be very useful for understanding mixing and chemical evolution in the ism . the chemical evolution model of @xcite predicts an increase in d / h with galactocentric radius , accompanied by a decrease in n / h and o / h , leading to a pronounced gradient in d / o and n / o . the gas in the outer parts of the galaxy has undergone less stellar processing , and in fact @xcite predict that the d / h ratios in the outer disk will approach the primordial value . the sight lines studied here have roughly the same galactocentric radii as the local ism sight lines of @xcite , so we can not test this model , but with _ fuse_observations of sight lines in the inner and outer galactic disk this may prove possible . we would like to thank ed jenkins , gary steigman , jeffrey linsky , cristina oliveira , and paule sonnentrucker for enlightening discussions . this work is based on data obtained for the guaranteed time team by the nasa - cnes - csa _ fuse _  mission operated by the johns hopkins university . financial support to u. s. participants has been provided by nasa contract nas5 - 32985 . french participants are supported by cnes . this work was partly supported by nasa guaranteed time observer funding to the stis science team under nasa contract nas5 - 30403 and is based upon observations obtained with the nasa / esa hubble space telescope , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . this work has made use of the profile fitting procedure owens.f developed by m. lemoine and the fuse french team . gh would like to thank sylvestre lacour and arielle moullet . dk thanks the staff at mcdonald observatory , especially david doss . abgrall , h. , roueff , e. , & drira , i.  2000 , , 141 , 297 de avillez , m. a. & mac low , m .- m . 2002 , apj , in press [ astro - ph/0209441 ] boesgaard , a.  m.  & steigman , g.  1985 , , 23 , 319 brown , t. , et al . 2002 , in the @xmath31 data handbook ( v4.0 ) , ed . b. mobasher , ( baltimore : stsci ) burles , s. , nollett , k.  m. , & turner , m.  s.  2001 , , 552 , l1 chiappini , c. , renda , a. , & matteucci , f. 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( pc ) & 69 & -249 + v ( mag ) & 6.98 & 6.26 + e(b - v ) & 0.25 & 0.18 + spectral type & b0v & b1ib + log [ n(hi ) ( @xmath56 ) ] ( _ iue _ ) & 20.90 @xmath53 0.09 & 20.90 @xmath53 0.10 +    lcccccc hd  195965 & fuse & p1028802 , p1028803 & 2000 nov 8,9 & 30000 & lwrs & @xmath115 + hd  195965 & fuse & p1028801 & 2000 jun 20 & 6400 & lwrs & @xmath115 + hd  195965 & stis / e140h & o6bg01010 & 2001 oct 9 & 415 & 0.1@xmath23@xmath18 0.03@xmath23 & @xmath116 + hd  195965 & iue & swp10843 & 1980 dec 20 & 1560 & small & @xmath117 + hd  191877 & fuse & p2051101 & 2001 jul 30 & 28100 & lwrs & @xmath115 + hd  191877 & fuse & p1028701 & 2000 jun 5 & 6100 & lwrs & @xmath115 + hd  191877 & iue & swp02837 & 1978 oct 2 & 2280 & small & @xmath117 +    ll d i 972.272 & h i ly@xmath118 , o i @xmath119 + d i 949.484 & h i ly@xmath113 , h@xmath52 lyman ( 14 - 0 ) p(2 ) @xmath120 , h@xmath52 werner ( 3 - 0 ) p(2 ) @xmath121 + d i 937.548 & h@xmath52 werner ( 4 - 0 ) p(4 ) @xmath122 , fe ii @xmath123 + d i 930.495 & o i @xmath124 , h@xmath52 werner ( 4 - 0 ) r(2 ) @xmath125 , h@xmath52 werner ( 4 - 0 ) q(1 ) @xmath126 +    lcccccc 919.102 & werner @xmath127 @xmath128 & 919.047 & 0.931 & lyman @xmath129 @xmath128 & 962.150 & 0.929 + 920.713 & werner @xmath127 @xmath130 & 920.830 & 0.0678 & lyman @xmath131 @xmath128 & 970.830 & 0.194 + 922.900 & lyman @xmath132 @xmath133 & 922.893 & -0.820 & lyman @xmath134 @xmath128 & 928.440 & -0.511 + 925.974 & none & & & & & +    lccc di 919.102 & 0.0425 & @xmath135 & @xmath136 + di 920.713 & 0.171 & @xmath137 & @xmath138 + di 922.900 & 0.312 & @xmath139 & @xmath140 + di 925.974 & 0.469 & @xmath141 & @xmath142 + oi 921.860 & 0.0402 & @xmath143 & @xmath144 + oi 922.220 & -0.646 & @xmath145 & @xmath146 + oi 936.630 & 0.527 & @xmath147 & @xmath148 + oi 1039.230 & 0.980 & @xmath149 & @xmath150 + oi 1039.230 & 0.980 & @xmath151 & @xmath152 + oi 1302.169 & 1.804 & @xmath153 & + oi 1355.598 & -2.803 & @xmath154 & + ni 951.079 & -0.911 & @xmath155 & @xmath156 + ni 951.295 & -1.766 & @xmath157 & @xmath158 + ni 953.415 & 1.100 & @xmath159 & @xmath160 + ni 953.655 & 1.377 & @xmath161 & @xmath162 + ni 959.494 & -1.321 & @xmath163 & @xmath164 + ni 1134.165 & 1.237 & @xmath165 & + ni 1134.165 & 1.237 & @xmath166 & + ni 1159.817 & -2.006 & @xmath167 & + ni 1160.937 & -2.553 & @xmath168 & +    lccc di 919.102 & 0.0425 & @xmath169 & @xmath170 + di 920.713 & 0.171 & @xmath171 & @xmath172 + di 922.900 & 0.312 & @xmath173 & @xmath174 + di 925.974 & 0.469 & @xmath175 & @xmath176 + oi 921.860 & 0.0402 & @xmath177 & @xmath178 + oi 922.220 & -0.646 & @xmath179 & @xmath180 + oi 925.446 & -0.490 & @xmath181 & @xmath182 + oi 936.630 & 0.527 & @xmath183 & @xmath184 + oi 1039.230 & 0.980 & @xmath185 & @xmath186 + oi 1039.230 & 0.980 & @xmath187 & @xmath187 + ni 951.079 & -0.911 & @xmath188 & @xmath189 + ni 951.295 & -1.766 & @xmath190 & @xmath191 + ni 953.415 & 1.100 & @xmath192 & @xmath192 + ni 953.655 & 1.377 & @xmath193 & @xmath194 + ni 959.494 & -2.006 & @xmath195 & @xmath196 + ni 1159.817 & -2.553 & @xmath197 & + ni 1134.165 & 1.237 & @xmath198 & + ni 1134.415 & 1.528 & @xmath199 & + ni 1134.980 & 1.693 & @xmath200 & +    lccccccc log n(d i ) & @xmath201 & @xmath202 & @xmath203 & @xmath204 & @xmath205 & @xmath206 + log n(h i ) & & @xmath207 & @xmath207 & & @xmath208 & @xmath208 + log n(o i ) & @xmath209 & @xmath90 & @xmath210 & @xmath85 & & @xmath85 + log n(n i ) & @xmath211 & @xmath212 & @xmath213 & @xmath214 & @xmath215 & @xmath216 +    lccc d / h & @xmath3 & @xmath7 & @xmath217 + d / o & @xmath218 & @xmath219 & @xmath220 + d / n & @xmath221 & @xmath222 & @xmath223 + o / h & @xmath5 & @xmath9 & @xmath224 + n / h & @xmath6 & @xmath8 & @xmath225 + o / n & @xmath226 & @xmath227 & @xmath228 +","summary":"we find d / h= ( ) and n / h= . the column density toward hd  191877 is very uncertain . the d / h ratios along these sight lines are lower than the average value of ( ( in the mean ) found with _ fuse_for the local interstellar medium ( to 179 pc from the sun ) . these observations lend support to earlier detections of variation in d / h over distances greater than a few hundred pc . the o / h ratio toward hd  195965 is supersolar . this star is part of an ob association , so there may be local enrichment by nearby massive stars . these observations demonstrate that although d / h studies through lyman absorption may become impractical at d pc and log() , d / h studies in the distance range from 500 to 2500 pc may be very useful for investigating mixing and chemical evolution in the ism .","abstract":"we have carried out an investigation of the abundance of deuterium along two extended sight lines through the interstellar medium ( ism ) of the galactic disk . the data include _ far ultraviolet spectroscopic explorer ( fuse ) _ observations of hd  195965 ( b1ib ) and hd  191877 ( b0v ) , as well as space telescope imaging spectrograph ( stis ) observations of hd  195965 . the distances to hd  195965 and hd  191877 , derived from spectroscopic parallax , are  pc and  pc , respectively , making these the longest galactic disk sight lines in which deuterium has been investigated with _ the _ fuse _  spectra contain all of the lyman series transitions ( and the corresponding d transitions ) except ly . the higher lyman lines clearly show the presence of deuterium . we use a combination of curve of growth analyses and line profile fitting to determine the abundance toward each object . we also present column densities for and toward both stars , and measured from ly absorption in the stis spectrum of hd  195965 . toward hd  195965 we find d / h= ( ) , o / h= , and n / h= . toward hd  191877 we find d / h= ( ) and n / h= . the column density toward hd  191877 is very uncertain . our preferred value gives o / h= , but we can not rule out o / h values as low as o / h= , so the o / h value for this sight line should be taken with caution . the d / h ratios along these sight lines are lower than the average value of ( ( in the mean ) found with _ fuse_for the local interstellar medium ( to 179 pc from the sun ) . these observations lend support to earlier detections of variation in d / h over distances greater than a few hundred pc . the o / h ratio toward hd  195965 is supersolar . this star is part of an ob association , so there may be local enrichment by nearby massive stars . the d / h and o / h values measured along these sight lines support the expectation that the ism is not well mixed on distances of pc . these observations demonstrate that although d / h studies through lyman absorption may become impractical at d pc and log() , d / h studies in the distance range from 500 to 2500 pc may be very useful for investigating mixing and chemical evolution in the ism ."}
{"article_id":"1003.5323","section_id":"i","document":"nearly 400 extrasolar planets have now been discovered using the radial velocity ( rv ) method . rv surveys currently have good statistical completeness only for planets with periods of less than ten years @xcite , due to the limited temporal baseline of the observations , and the need to observe for a complete orbital period to confirm the properties of a planet with confidence . the masses of discovered planets range from just a few earth masses @xcite up to around 20 jupiter masses ( m@xmath10 ) . we note that a 20 m@xmath10  object would be considered by many to be a brown dwarf rather than a planet , but that there is no broad consensus on how to define the upper mass limit for planets . for a good overview of rv planets to date , see @xcite or http://exoplanet.eu/catalog-rv.php . the large number of rv planets makes it possible to examine the statistics of extrasolar planet populations . several groups have fit approximate power law distributions in mass and semimajor axis to the set of known extrasolar planets ( see for example @xcite ) . necessarily , however , these power laws are not subject to observational constraints at orbital periods longer than 10 years  and it is at these orbital periods that we find giant planets in our own solar system . we can not obtain a good understanding of planets in general without information on long period extrasolar planets . nor can we see how our own solar system fits into the big picture of planet formation in the galaxy without a good census of planets in jupiter- and saturn - like orbits around other stars . repeatable detections of extrasolar planets ( as opposed to one - time microlensing detections ) have so far been made by transit detection ( e.g. @xcite ) , by rv variations @xcite , by astrometric wobble @xcite , or by direct imaging @xcite . of these methods , transits are efficient only for detecting close - in planets . as noted above , precision rv observations have not been going on long enough to detect more than a few planets with periods longer than ten years , but even as rv temporal baselines increase , long period planets will remain harder to detect due to their slow orbital velocities . the amplitude of a star s astrometric wobble increases with the radius of its planet s orbit , but decades - long observing programs are still needed to find long - period planets . direct imaging is the only method that allows us to characterize long - period extrasolar planets on a timescale of months rather than years or decades . direct imaging of extrasolar planets is technologically possible at present only in the infrared , based on the planets own thermal luminosity , not on reflected starlight . the enabling technology is adaptive optics ( ao ) , which allows 6 - 10 m ground - based telescopes to obtain diffraction limited ir images several times sharper than those from hst , despite earth s turbulent atmosphere . theoretical models of giant planets indicate that such telescopes should be capable of detecting self - luminous giant planets in large orbits around young , nearby stars . the stars should be young because the glow of giant planets comes from gravitational potential energy converted to heat in their formation and subsequent contraction : lacking any internal fusion , they cool and become fainter as they age .    several groups have published the results of ao imaging surveys for extrasolar planets around f , g , k , or m stars in the last five years ( see for example @xcite ; and @xcite ) . of these , most have used wavelengths in the 1.5 - 2.2 @xmath11 m range , corresponding to the astronomical @xmath12 and @xmath13 filters @xcite . they have targeted mainly very young stars . because young stars are rare , the median distance to stars in each of these surveys has been more than 20 pc . in contrast to those above , our survey concentrates on very nearby f , g , and k stars , with proximity prioritized more than youth in the sample selection . the median distance to our survey targets is only 11.2 pc . ours is also the first survey to include extensive observations in the @xmath1 band , and only the second to search solar - type stars in the @xmath0 band ( the first was @xcite ) . the distinctive focus on older , very nearby stars for a survey using longer wavelengths is natural : longer wavelengths are optimal for lower temperature planets which are most likely to be found in older systems , but which would be undetectable around all but the nearest stars . more information on our sample selection , observations , and data analysis can be found in our observations paper , @xcite , which also details our careful evaluation of our survey s sensitivity , including extensive tests in which fake planets were randomly placed in the raw data and then recovered by an experimenter who knew neither their positions nor their number . such tests are essential for establishing the true relationship between source significance ( i.e. 5@xmath14 , 10@xmath14 , etc . ) and survey completeness . our survey places constraints on a more mature population of planets than those that have focused on very young stars , and confirms that a paucity of giant planets at large separations from sun - like stars is robustly observed at a wide range of wavelengths .    in section [ sec : rv ] , we review power law fits to the distribution of known rv planets , including the normalization of the power laws . in section [ sec : tmod ] , we present the constraints our survey places on the distribution of extrasolar giant planets , based on extensive monte carlo simulations . in section [ sec : long ] we discuss the promising future of planet - search observations in the @xmath0 and especially the @xmath1 band , and in section [ sec : concl ] we conclude .","summary":"our survey concentrates more strongly than all others to date on very nearby f , g , and k stars , in that we have prioritized proximity higher than youth . our survey is also the first to include extensive observations in the band , which supplemented the primary observations . our observations show that giant planets in long - period orbits around sun - like stars are rare , confirming the results of shorter - wavelength surveys , and increasing the robustness of the conclusion .","abstract":"we have carried out an and band adaptive optics ( ao ) extrasolar planet imaging survey of 54 nearby , sunlike stars using the clio camera at the mmt . our survey concentrates more strongly than all others to date on very nearby f , g , and k stars , in that we have prioritized proximity higher than youth . our survey is also the first to include extensive observations in the band , which supplemented the primary observations . these longer wavelength bands are most useful for very nearby systems in which low temperature planets with red ir colors ( i.e. , ) could be detected . the survey detected no planets , but set interesting limits on planets and brown dwarfs in the star systems we investigated . we have interpreted our null result by means of extensive monte carlo simulations , and constrained the distributions of extrasolar planets in mass and semimajor axis . if planets are distributed according to a power law with , normalized to be consistent with radial velocity statistics , we find that a distribution with and , truncated at 110 au , is ruled out at the 90% confidence level . these particular values of and are significant because they represent the most planet - rich case consistent with current statistics from radial velocity observations . with 90% confidence no more than 8.1% of stars like those in our survey have systems with three widely spaced , massive planets like the a - star hr 8799 . our observations show that giant planets in long - period orbits around sun - like stars are rare , confirming the results of shorter - wavelength surveys , and increasing the robustness of the conclusion ."}
{"article_id":"1003.5323","section_id":"c","document":"we have surveyed unusually nearby , mature star systems for extrasolar planets in the @xmath0 and @xmath1 bands using the clio camera with the mmt ao system . by extensive use of blind sensitivity tests involving fake planets inserted into our raw data ( reported in detail in @xcite ) , we established a definitive significance vs. completeness relation for planets in our data , which we then used in monte carlo simulations to constrain planet distributions . we set interesting limits on the masses of planets and brown dwarfs in the star systems we surveyed , but we did not detect any planets . based on this null result , we place constraints on the power laws that may describe the distribution of extrasolar planets in mass and semimajor axis . we also place constraints on planet abundances independent of the distributions . if the distribution of planets is a power law with @xmath5 , the work of @xcite and @xcite indicates that the most optimistic ( i.e. planet - rich ) case permitted by the statistics of known rv planets correponds to about @xmath6 and @xmath7 . normalizing the distribution to be consistent with rv statistics , we find that these values of @xmath8 and @xmath9 are ruled out at the 90% confidence level , unless the semimajor axis distribution is truncated at a radius @xmath34 less than 110 au . though @xmath47 is not physically plausible , previous work has sometimes used it an example : for @xmath48 , corresponding to the best - fit value from @xcite , we rule out @xmath47 unless @xmath34 is less than 38 au . independent of distribution models , with 90% confidence no more than 50% of stars like those in our survey have a 5 m@xmath10  or more massive planet orbiting between 30 and 94 au , no more than 15% have a 10 m@xmath10  planet orbiting between 22 and 100 au , and no more than 25% have a 20 m@xmath10  object orbiting between 8 and 100 au . our constraints on planet abundances are similar to those placed by @xcite and @xcite , but less tight than those of @xcite and especially @xcite , the recent work of @xcite and @xcite also placed tighter constraints on exoplanet distributions than our survey . however , we have surveyed a more nearby , older set of stars than any previous survey , and have therefore placed constraints on a more mature population of planets . also , we have confirmed that a paucity of giant planets at large separations from sun - like stars is robustly observed at a wide range of wavelengths . the best current @xmath12 regime observations , those of @xcite , would attain sensitivity to lower mass planets than did our @xmath0 and @xmath1 band observations for all of our survey targets except those lying within 4 pc of the sun . however , as larger telescopes are built and longer exposures are attempted , the sensitivity of @xmath1 band observations may be expected to increase at least as fast as that of @xmath12 band observations ( in part because @xmath1 band detectors are currently a less mature technology ) . as shown in figures [ fig : hlm1 ] and [ fig : hlm2 ] , a modest increase from current sensitivity levels , even if paralleled by an equal increase in @xmath12 band sensitivity , would render the @xmath1 band the wavelength of choice for extrasolar planet searches around a large number of nearby stars .","summary":"we have carried out an and band adaptive optics ( ao ) extrasolar planet imaging survey of 54 nearby , sunlike stars using the clio camera at the mmt . the survey detected no planets , but set interesting limits on planets and brown dwarfs in the star systems we investigated . we have interpreted our null result by means of extensive monte carlo simulations , and constrained the distributions of extrasolar planets in mass and semimajor axis . if planets are distributed according to a power law with , normalized to be consistent with radial velocity statistics , we find that a distribution with and , truncated at 110 au , is ruled out at the 90% confidence level . these particular values of and are significant because they represent the most planet - rich case consistent with current statistics from radial velocity observations . with 90% confidence","abstract":"we have carried out an and band adaptive optics ( ao ) extrasolar planet imaging survey of 54 nearby , sunlike stars using the clio camera at the mmt . our survey concentrates more strongly than all others to date on very nearby f , g , and k stars , in that we have prioritized proximity higher than youth . our survey is also the first to include extensive observations in the band , which supplemented the primary observations . these longer wavelength bands are most useful for very nearby systems in which low temperature planets with red ir colors ( i.e. , ) could be detected . the survey detected no planets , but set interesting limits on planets and brown dwarfs in the star systems we investigated . we have interpreted our null result by means of extensive monte carlo simulations , and constrained the distributions of extrasolar planets in mass and semimajor axis . if planets are distributed according to a power law with , normalized to be consistent with radial velocity statistics , we find that a distribution with and , truncated at 110 au , is ruled out at the 90% confidence level . these particular values of and are significant because they represent the most planet - rich case consistent with current statistics from radial velocity observations . with 90% confidence no more than 8.1% of stars like those in our survey have systems with three widely spaced , massive planets like the a - star hr 8799 . our observations show that giant planets in long - period orbits around sun - like stars are rare , confirming the results of shorter - wavelength surveys , and increasing the robustness of the conclusion ."}
{"article_id":"math0304492","section_id":"i","document":"eulerian lattices provide an interesting , entirely combinatorial model for the combinatorics ( face lattices ) of convex polytopes . although the concepts have been around for a long time ( eulerian posets were formalized by stanley @xcite in 1982 , but the ideas may be traced back at least to klee s paper  @xcite from 1964 ) , there are surprisingly little systematic knowledge and development of eulerian _ lattices _ , despite a number of extensive recent studies of ( the flag vectors of ) eulerian _ posets _ ; cf . stanley  @xcite . a complete list of linear relations for the flag vectors of polytopes , spheres and lattices was given by bayer and billera in @xcite , where they proved their generalized dehn - sommerville relations . in this paper we present a combinatorial construction @xmath5 for eulerian lattices which specializes to the setting of `` strongly regular spheres . '' here the parameter @xmath6 is an integer between @xmath7 and @xmath8 , where @xmath9 is the length of the lattice , and denotes the dimension ( rank plus one ) of the elements that will correspond to coatoms of the new lattice . the @xmath5-construction may be more intuitive when applied to cellular spheres , but eulerian lattices provide a simple axiomatic setting in which we can most easily analyze the construction and derive its properties . thus we will start with lattices ( section  [ sec : eulerianlattices ] ) , and in a second step transfer the results to spheres and give a geometric interpretation of the construction ( section  [ sec : cellularspheres ] ) . in some cases this construction can be performed in the setting of convex polytopes , and then be used to construct interesting new classes of such ( section  [ sec : polytopes ] ) :    we provide the first infinite family of _ rational _ @xmath0-simplicial @xmath0-simple @xmath1-polytopes . we present for each @xmath10 an infinite family of @xmath3-simplicial @xmath0-simple @xmath4-polytopes . the first class solves a problem posed by eppstein , kuperberg and ziegler ( @xcite , compare also @xcite ) . they provided an infinite family of @xmath0-simplicial @xmath0-simple @xmath1-polytopes , but their construction is quite rigid and produces nonrational coordinates . in contrast , our construction will allow great flexibility for the actual choice of coordinates for a geometric realization of the polytopes in this family . thus we can also derive a number of consequences for the @xmath11-vector classification problem for @xmath1-dimensional polytopes ( section  [ sec : fvectors ] ) . the second class of polytopes solves a problem of grnbaum ( * ? ? ? * problem 9.7.7(iii ) ) and thus substantiates claims by perles and shephard @xcite and by kalai @xcite .    our construction contains the method of eppstein , kuperberg and ziegler as a special case : if we choose @xmath12 and apply @xmath13 to the face lattice of a simplicial @xmath1-polytope @xmath14 whose edges are tangent to the unit sphere , then we obtain the face lattice of a @xmath0-simplicial @xmath0-simple polytope which they call @xmath15 . thus the second class of examples displayed above is obtained by a generalization of the approach from @xcite to higher dimensions . in contrast , the construction of the first class relies on the analysis of the dual construction to @xmath13 , which we describe as `` vertex truncation '' in section  [ subsec : vt ] . the special case where @xmath14 is a regular polytope appears in the literature in the context of the construction of regular and `` uniform '' polytopes : here our vertex truncation can be seen as an instance of `` wythoff s construction '' as described by coxeter ( @xcite and @xcite ) , while a special case of the dual @xmath5-construction appears in gvay s work @xcite . _ acknowledgement . _ we would like to thank carsten lange , julian pfeifle and arnold wamer for several discussions and valuable hints .","summary":"we describe and analyze a new construction that produces new eulerian lattices from old ones . it specializes to a construction that produces new strongly regular cellular spheres ( whose face lattices are eulerian ) .    the construction does not always specialize to convex polytopes ; however , in a number of cases where we can realize it , it produces interesting classes of polytopes . we also construct for each an infinite family of-simplicial-simple-polytopes , thus solving a problem of grnbaum  .","abstract":"we describe and analyze a new construction that produces new eulerian lattices from old ones . it specializes to a construction that produces new strongly regular cellular spheres ( whose face lattices are eulerian ) .    the construction does not always specialize to convex polytopes ; however , in a number of cases where we can realize it , it produces interesting classes of polytopes . thus we produce an infinite family of rational-simplicial-simple-polytopes , as requested by eppstein , kuperberg and ziegler . we also construct for each an infinite family of-simplicial-simple-polytopes , thus solving a problem of grnbaum  ."}
{"article_id":"astro-ph9706120","section_id":"i","document":"approximately half of the heavy elements with mass number @xmath12 and all of the actinides in the solar system are believed to be produced in the @xmath1-process . the fundamental @xmath1-process theory of burbidge et al . ( 1957 ) and cameron ( 1957 ) successfully explains the gross features of the solar @xmath1-process abundance distribution , such as the existence of abundance peaks at @xmath13 , 130 , and 195 . on the other hand , it remains to be established where the @xmath1-process occurs and especially how many different kinds of @xmath1-process events contributed to the solar @xmath1-process abundances . major advances have been made in calculating @xmath1-process nucleosynthesis in supernovae ( see e.g. , woosley et al . 1994 ) and in using a wide range of model parameters to obtain yields that approximate the solar @xmath1-process abundances ( see e.g. , kratz et al . there has been a tendency to ascribe all the @xmath1-process nuclei to a single kind of @xmath1-process events ( but see goriely & arnould 1996 ) . however , most astrophysical models have difficulty in producing all the @xmath1-process abundance peaks from a single source , and the parametric studies certainly do not point to a single kind of @xmath1-process events .    with the recent progress in both observation and theory , there is a growing consensus that type ii supernovae are the most probable @xmath1-process site . the detection of @xmath1-process elements in the extremely metal - poor halo star cs 22892 - 052 by sneden et al . ( 1996 ) argues that the @xmath1-process is primary , already operating in the early history of the galaxy . studies of galactic chemical evolution ( mathews , bazan , & cowan 1992 ) show that the enrichment of the @xmath1-process elements in the galaxy is consistent with low mass type ii supernovae being the @xmath1-process site . furthermore , it has been proposed that the @xmath1-process occurs in the neutrino - heated ejecta from the hot protoneutron star produced in a type ii supernova ( woosley & baron 1992 ; woosley & hoffman 1992 ; meyer et al . 1992 ; woosley et al . while this so - called `` hot bubble '' @xmath1-process model has some deficiencies , especially the need for very high entropies that might be hard to obtain ( witti , janka , & takahashi 1994 ; takahashi , janka , & witti 1994 ; qian & woosley 1996 ; hoffman , woosley , & qian 1997 ) , it also has several attractive features . for example , the amount of ejecta from the hot bubble is consistent with the expected amount of @xmath1-process material from each supernova ( woosley et al . 1994 ) , and unlike the entropy , can be understood quite well in terms of a simple neutrino - driven wind model ( qian & woosley 1996 ) . in addition , it has been shown that the intense neutrino flux in this kind of @xmath1-process model can have important effects on the nucleosynthesis ( meyer 1995 ; fuller & meyer 1995 ; mclaughlin & fuller 1996 ; qian et al . 1997 ; haxton et al . 1997 ; mclaughlin & fuller 1997 ) . in particular , the typical neutrino fluences through the ejecta may lead to identifiable signatures in the @xmath1-process abundance pattern , thus providing a way to reveal the conditions at the @xmath1-process site ( qian et al . 1997 ; haxton et al . 1997 ) . regardless of the astrophysical site , two things are needed for an @xmath1-process to work : the neutrons and the seed nuclei to capture them . in fact , the potential of an astrophysical environment to be the @xmath1-process site can be gauged by a crucial quantity , the neutron - to - seed ratio . if one always starts from more or less the same seed nuclei , different neutron - to - seed ratios are required to produce the entire solar @xmath1-process nuclear abundance distribution . one can then ask whether different @xmath1-process nuclei are made in completely different astrophysical environments ( e.g. , type ii supernovae vs. neutron star coalescence ) or in similar environments but just with different neutron - to - seed ratios . because the @xmath1-process abundance distribution in cs 22892 - 052 agrees with that in the solar system quite well ( sneden et al . 1996 ) , and the solar @xmath1-process abundance distribution does not have sudden jumps as a function of the mass number @xmath14 , it may be more natural to expect that all @xmath1-process nuclei come from similar environments ( e.g. , the hot bubble regions in type ii supernovae ) . hereafter , we refer to the production of @xmath1-process nuclei in a specific environment with a certain distribution of neutron - to - seed ratios as an @xmath1-process `` event . '' the simplest scenario would be that all @xmath1-process nuclei are produced in a unique kind of @xmath1-process events with a generic abundance pattern . in that case , the solar @xmath1-process abundance distribution merely reflects the distribution of neutron - to - seed ratios characteristic of these unique @xmath1-process events .    however , wasserburg , busso , & gallino ( 1996 ) pointed out that the above minimal approach to account for the solar @xmath1-process abundance distribution is not consistent with the meteoritic abundance ratios @xmath5i/@xmath15i and @xmath6hf/@xmath16hf in the early solar system . these authors showed that the @xmath1-process events contributing to @xmath6hf were fully consistent with the uniform production of @xmath17th , @xmath18u , @xmath19u , and @xmath20pu up until the time when the solar system was formed . however , such a rather uniform production would grossly overproduce @xmath5i ( by a factor of @xmath21 ) and @xmath22pd ( by a factor of @xmath23 ) . consequently , they argued that there should be diverse sources for the @xmath1-process , one of which produced the @xmath1-process nuclei above @xmath24 and another producing those at lower @xmath14 with a smaller frequency .    in order to account for the solar @xmath1-process abundance distribution and to accommodate the meteoritic data on @xmath5i and @xmath6hf at the same time , we consider in this paper a minimal scenario where two kinds of @xmath1-process events contribute to the solar @xmath1-process abundances near and above @xmath3 . using simplified treatment of the @xmath1-process and taking into account other constraints , we show that the main features of the solar @xmath1-process abundance distribution from the peak at @xmath3 , through the peak at @xmath4 , and up to the region of the actinides can be reproduced by a reasonable superposition of these two kinds of @xmath1-process events . in  2 , we describe the hot bubble @xmath1-process model and our simplified @xmath1-process calculation in the context of this model . we also discuss the constraints on our @xmath1-process calculations from the observed solar @xmath1-process abundance distribution , the meteoritic data on @xmath5i and @xmath6hf , and considerations of various neutrino effects . in  3 , we present our results , and in  4 we discuss their implications for the nature and frequencies of the supernovae associated with these two kinds of @xmath1-process events .","summary":"it is shown that a semi - quantitative agreement with the gross solar-process abundance pattern from the peak at mass number , through the peak at , and up to the region of the actinides can be obtained by a superposition of two distinctive kinds of-process events . they would also make a significant amount of the nuclei between and 195 , includinghf , but very littlei . in order to match the solar-process abundance pattern and to satisfy thei andhf constraints , the events in case l , which would make the-process nuclei near and the bulk of those between and 195 ,","abstract":"we present a simplified analysis using equations for the charge flow , which include capture , for the production of-process nuclei in the context of the recent supernova hot bubble model . the role of capture in speeding up the charge flow , particularly at the closed neutron shells , is studied together with the-flow at freeze - out and the effect of neutrino - induced neutron emission on the abundance pattern after freeze - out . it is shown that a semi - quantitative agreement with the gross solar-process abundance pattern from the peak at mass number , through the peak at , and up to the region of the actinides can be obtained by a superposition of two distinctive kinds of-process events . these correspond to a low frequency case l and a high frequency case h , which takes into account the low abundance ofi and the high abundance ofhf in the early solar nebula . the lifetime ofhf ( yr ) associates the events in case h with the most common type ii supernovae . these events would be mainly responsible for the-process nuclei near and above . they would also make a significant amount of the nuclei between and 195 , includinghf , but very littlei . in order to match the solar-process abundance pattern and to satisfy thei andhf constraints , the events in case l , which would make the-process nuclei near and the bulk of those between and 195 , must occur times less frequently but eject times more-process material in each event .    assuming that all of the supernovae producing-process nuclei represent a similar overall process , we speculate that the usual neutron star remnants , and hence prolonged ejection of-process material , are associated with the events in case l. we further speculate that the more frequently occurring events in case h have ejection of other-process material terminated by black hole formation during the neutrino cooling phase of the protoneutron star . this suggests that there is now an inventory of black holes with masses and neutron stars resulting from supernovae in the galaxy . this-process model would have little effect on the estimates of the supernova contributions to the non--process nuclei ."}
{"article_id":"astro-ph9706120","section_id":"r","document":"as stated earlier , there are three parameters @xmath81 , @xmath82 , and @xmath83 in our simplified @xmath1-process calculation . before we present the results of our calculation , it is helpful to discuss the physics that relates the set of these three parameters to the progenitor abundance pattern at freeze - out in case h or l. obviously , in both cases the neutron - to - seed ratio @xmath83 is related to the average progenitor mass number @xmath123 at freeze - out through equation ( 8) . the mass number @xmath31 of a progenitor nucleus is approximately proportional to its charge @xmath27 , i.e. , @xmath124 , where the proportionality constant is @xmath1252.9 for the @xmath1-process path shown in fig . 1 . therefore , the average progenitor charge @xmath126 at freeze - out is @xmath127 from equations ( 8) and ( 17 ) we obtain @xmath128 and we assume @xmath129 in the following discussion . because only charge - changing reactions are involved in equations ( 3 ) and ( 4 ) , we can approximately view the @xmath1-process as a charge flow proceeding from @xmath130 to successively higher @xmath27 , accompanied by the capture of @xmath131 neutrons at each @xmath27 . when the neutrons run out at @xmath78 , the charges in the flow have an average value @xmath126 . without solving equations ( 3 ) and ( 4 ) for the charge flow , we can approximately calculate this average progenitor charge @xmath126 at freeze - out as @xmath132,\\ ] ] where @xmath133 is the average @xmath2-decay rate , and @xmath134 is the average initial @xmath0 capture rate [ proportional to @xmath81 ] , both appropriately taken for the progenitor nuclei involved in the calculation . equation ( 19 ) then relates @xmath81 , @xmath82 , and the freeze - out time @xmath136 to the progenitor abundance pattern at freeze - out in both cases h and l.    furthermore , @xmath81 , @xmath82 , and @xmath136 are subject to the neutrino fluence constraints in equations ( 15 ) and ( 16 ) for cases h and l , respectively . therefore , one can use either @xmath81 or @xmath82 as the only adjustable parameter in the two cases . once chosen , the other parameter , together with the freeze - out time @xmath136 , is determined by the average progenitor charge at freeze - out ( eq . [ 19 ] ) and the neutrino fluence constraint ( eq . [ 15 ] or [ 16 ] ) in each case .      for the convenience of presentation , we first give results for a reasonable value of @xmath137 , which corresponds to @xmath138 s@xmath48 for the progenitor nuclei with @xmath35 . the dependence of our results on @xmath81 will be examined in  3.3 . our best fit for case h is obtained for @xmath139 s and @xmath140 . the corresponding freeze - out time is @xmath141 s. the time evolution of the progenitor abundance pattern in case h is shown in fig . 2 as a series of snapshots . similarly , the best fit for case l is obtained for @xmath142 s and @xmath143 , with the corresponding freeze - out time @xmath144 s. the time evolution of the progenitor abundance pattern in case l is shown in fig . 3 . for a given @xmath81 , we find that case h is specified essentially by the constraint on @xmath5i production in equation ( 13 ) and the neutrino fluence constraint in equation ( 15 ) . with the freeze - out pattern obtained in case h , case l is specified by the solar @xmath1-process abundance ratios in equation ( 11 ) and the neutrino fluence constraint in equation ( 16 ) . the weighting parameter in equation ( 11 ) is found to be @xmath145 . with the above best - fit parameters , all the constraints discussed in  2.2 are satisfied . the abundance pattern obtained from the superposition of cases h and l is shown in fig . 4 . as explained previously , we can not compare this pattern with the solar @xmath1-process abundance distribution on a nucleus - by - nucleus basis , especially because we do not follow the transformation from the progenitor nuclei to the stable @xmath1-process nuclei after freeze - out . however , if we assume that the progenitor nuclei at the @xmath35 and 126 closed neutron shells approximately conserve their mass numbers during the transformation after freeze - out , the final abundances at these mass numbers ( regions i and iii ) shown in fig . 4 agree with the solar @xmath1-process abundances in the @xmath3 and 195 peaks quite well . while we can not obtain detailed abundances for the @xmath1-process nuclei in regions ii and iv mainly due to significant @xmath2-delayed neutron emission after freeze - out expected in these two regions , at least the sums of the abundances in these two regions , together with those in regions i and iii , agree with the solar @xmath1-process abundance pattern as required by our calculation . furthermore , we can show that the abundance ratio @xmath6hf/@xmath16hf in the early solar system is also consistent with the meteoritic data and with the scenario where the @xmath1-process events in both cases h and l occurred uniformly up until the solar system formation . as explained previously , the constraint on @xmath5i production requires that the last @xmath1-process event in case l contributing to the solar abundances occur @xmath100 yr before the solar system formation . because the lifetime of @xmath6hf is @xmath146 yr , the @xmath6hf made in this last @xmath1-process event in case l had already decayed to the stable @xmath6w when the solar system was formed . following wasserburg et al . ( 1996 ) , we take @xmath147 , where @xmath148 represents the @xmath1-process contribution to the solar abundance of @xmath6w . in the uniform production scenario we have @xmath149 where @xmath150 and @xmath151 stand for the final abundances of @xmath6hf in cases h and l , respectively . assuming @xmath152 ( cf . figs . 2 and 3 ) , we obtain @xmath153 , which corresponds to @xmath154 in good agreement with the meteoritic value @xmath155 . in fact , we can always obtain this agreement as long as @xmath156 and @xmath157 . we now examine the effect of @xmath0 capture on the charge flow . in our calculation equations ( 15 ) and ( 16 ) , which concern the neutrino fluence after freeze - out , impose much more stringent constraints on the @xmath0 flux than equation ( 14 ) , which concerns the approximate @xmath2-flow equilibrium at freeze - out . this result was found earlier by qian et al . ( 1997 ) . by the time the progenitor abundance pattern freezes out , the charge flow is carried dominantly by @xmath2-decay in both cases h and l. however , whereas equation ( 14 ) is satisfied for all five progenitor nuclei ( @xmath3969 ) in the @xmath38 peak in case h , it is satisfied only for three progenitor nuclei ( @xmath15848 ) in the @xmath35 peak in case l. this is because the bottle - neck in the charge flow due to the slow @xmath2-decay rates for the @xmath35 progenitor nuclei facilitates the establishment of an approximate @xmath2-flow equilibrium in the @xmath38 peak in case h , whereas no corresponding bottle - neck exists before the @xmath35 progenitor nuclei in case l. on the other hand , @xmath0 capture accelerates the charge flow quite noticeably in both cases h and l.    we recall that for given values of @xmath81 and @xmath82 , equation ( 19 ) determines the freeze - out time @xmath136 as a function of the average progenitor charge @xmath126 at freeze - out . here we give a more accurate way to evaluate this function . the time @xmath159 required for the charge flow to pass through the progenitor nucleus at charge @xmath27 is approximately determined by @xmath160\\right\\ } \\approx 1,\\ ] ] and @xmath161\\hat\\tau   \\left\\{1-\\exp\\left[-{\\delta t(z)\\over\\hat\\tau}\\right]\\right\\ } \\approx 1\\ ] ] for @xmath70 , where @xmath162 is the time required for the charge flow to proceed from @xmath130 up to @xmath27 . we assume that the freeze - out time @xmath136 is approximately given by @xmath163 \\approx\\sum_{z = z_s}^{\\bar z(t_{\\rm fo})-1}\\delta t(z),\\ ] ] with @xmath164 for @xmath165 . it is easy to see that equation ( 19 ) is obtained by replacing @xmath166 and @xmath167 for @xmath168 with @xmath133 and @xmath134 in equations ( 21 ) and ( 22 ) . using equations ( 21)(23 ) , we plot @xmath136 as a function of the average progenitor charge @xmath126 at freeze - out for @xmath137 , @xmath139 and 0.125 s , and for the case without neutrinos in fig . the time required to reach the same average progenitor charge at freeze - out is clearly longer without neutrinos than with neutrinos . the actual freeze - out times @xmath136 in cases h and l are indicated as filled circles in fig . the shortening of @xmath136 in both cases with respect to the case without neutrinos ( see  3.2 ) mainly results from the @xmath0-capture - induced acceleration of the charge flow at @xmath3649 , i.e. , at the progenitor nuclei with the @xmath35 closed neutron shell .    to conclude this subsection , we give a semi - analytic way to derive @xmath82 and @xmath83 in cases h and l for a given @xmath81 . as discussed in the beginning of  3 , the neutron - to - seed ratio @xmath83 is approximately given by the average progenitor charge @xmath126 at freeze - out via equation ( 18 ) . from the solar @xmath1-process abundance ratios in equation ( 11 ) and the constraint on @xmath5i production in equation ( 13 ) , we see that a large fraction of the progenitor abundances should be in region iii ( i ) at freeze - out in case h ( l ) . consequently , the average progenitor charge at freeze - out has to be @xmath16969 ( 4849 ) in case h ( l ) , which requires a neutron - to - seed ratio of @xmath17096 ( 4042 ) in good agreement with our numerical results . once @xmath126 is known , the freeze - out time @xmath136 can be calculated as a function of @xmath82 for a given @xmath81 using equations ( 21)(23 ) . the contours for @xmath171 , 49 , 68 , and 69 are shown as solid lines on the @xmath82-@xmath136 plot in fig . furthermore , the neutrino fluence constraint in equation ( 15 ) or ( 16 ) gives @xmath136 as another function of @xmath82 for a given @xmath81 . the contours for values of the neutrino fluence after freeze - out @xmath172 and 0.031 are shown as dashed lines in fig . the best - fit parameters for @xmath136 and @xmath82 in case h ( l ) should then lie on the dashed line for @xmath172 ( 0.031 ) and between the solid lines for @xmath173 ( 48 ) and 69 ( 49 ) . this is confirmed by our numerical results , which are indicated as filled circles in fig . we now consider the case without neutrinos , i.e. , @xmath174 . obviously , the neutrino fluence constraints in equations ( 15 ) and ( 16 ) can no longer be satisfied , and can only be treated as some upper limits on the neutrino fluence after freeze - out in this case . by leaving out neutrinos and the associated constraints in equations ( 15 ) and ( 16 ) , we also find freeze - out progenitor abundance patterns that can satisfy essentially all the other constraints discussed in  2.2 . these freeze - out progenitor abundance patterns corresponding to cases h@xmath175 and l@xmath175 are similar to those in cases h and l presented in  3.1 , but are obtained with slightly smaller neutron - to - seed ratios and considerably longer freeze - out times . the neutron - to - seed ratio in case h@xmath175 ( l@xmath175 ) is @xmath176 ( 44 ) with the corresponding freeze - out time @xmath177 ( 0.78 ) s. as shown in fig . 5 , approximately the same average progenitor charge at freeze - out is reached in cases h and h@xmath175 or in cases l and l@xmath175 . the weighting parameter in equation ( 11 ) is @xmath178 for case l@xmath175 with respect to case h@xmath175 in order to give the best fit to the gross solar @xmath1-process abundance pattern . the time evolution of the progenitor abundance pattern in the case without neutrinos is shown in fig . 7 .    here we notice some interesting differences between cases h@xmath175 ( l@xmath175 ) and h ( l ) . case h@xmath175 is essentially determined by the constraint on @xmath5i production in equation ( 13 ) . due to the slow @xmath2-decay rates for the progenitor nuclei with @xmath35 , a long @xmath136 is required to decrease the progenitor abundance at @xmath118 . however , once the charge flow passes the bottle - neck at @xmath35 , it reaches the progenitor nuclei at @xmath43 relatively fast . consequently , the @xmath1-process nuclei at @xmath43 are overproduced by about 40% in case h@xmath175 in order to satisfy the constraint on @xmath5i production in equation ( 13 ) . by comparison , the decaying @xmath0 flux in case h has the beneficial effect of accelerating the passage through the bottle - neck at @xmath35 at an earlier time without overproducing the @xmath1-process nuclei at @xmath43 at later times . furthermore , without neutrinos the approximate @xmath2-flow equilibrium constraint in equation ( 14 ) is satisfied only for two progenitor nuclei @xmath17948 ) in the @xmath35 peak in case l@xmath175 . therefore , while we can not conclude that neutrinos are required to satisfy all the constraints derived from the observed solar @xmath1-process abundance data , the cases with neutrinos seem to be more attractive .      we have presented the results for a fixed value of @xmath137 in  3.1 and for the case without neutrinos corresponding to @xmath174 in  3.2 . we now examine the dependence of our results on @xmath81 while taking into account all the constraints discussed in  2.2 . in other words , we want to find those cases that are similar to case h or l , but have different values of @xmath81 . as explained at the end of  3.1 , the solar @xmath1-process abundance ratios in equation ( 11 ) and the constraint on @xmath5i production in equation ( 13 ) require that the average progenitor charge at freeze - out be @xmath17369 ( 4849 ) in case h ( l ) . consequently , the neutron - to - seed ratio @xmath83 in those cases similar to case h ( l ) has to be close to 9496 ( 4042 ) . the other two parameters in our calculation , @xmath81 and @xmath82 , together with the freeze - out time @xmath136 , are constrained by the average progenitor charge @xmath126 at freeze - out and the neutrino fluence @xmath120 after freeze - out ( eq . [ 15 ] or [ 16 ] ) in each case . therefore , the combination of @xmath81 and @xmath82 in those cases similar to case h would most likely be located in the region between the contour lines for @xmath180=(68,0.015)$ ] and @xmath181 on the @xmath82 vs. @xmath81 plot . likewise , the combination of @xmath81 and @xmath82 in those cases similar to case l would most likely be located in the region between the contour lines for @xmath180=(48,0.031)$ ] and @xmath182 on the same plot . this plot is shown as fig . obviously , the parameter regions shown in fig . 8 include the best - fit parameters in cases h and l. we have checked a number of other combinations of @xmath81 and @xmath82 within these regions , and have confirmed that they give similar results to those discussed previously . in particular , the results corresponding to @xmath183 are very close to those in the case without neutrinos .    furthermore , although the parameter @xmath82 in case l is shorter than that in case h for the same @xmath81 , we can find a case l@xmath184 that has a smaller @xmath81 and a longer @xmath82 than both cases h and l ( see fig . 8) , and at the same time , gives a freeze - out progenitor abundance pattern essentially identical to that in case l. specifically , the parameters are @xmath185 [ corresponding to @xmath186 s@xmath48 for the progenitor nuclei with @xmath35 ] , @xmath188 s , and @xmath189 in case l@xmath184 . the corresponding freeze - out time is @xmath190 s. with the same weighting parameter @xmath145 in equation ( 11 ) , cases h and l@xmath184 give the same best - fit to the gross solar @xmath1-process abundance pattern as cases h and l. it follows that a range of @xmath81 and @xmath82 within the regions shown in fig . 8 can provide the yields in cases h and l.","summary":"we present a simplified analysis using equations for the charge flow , which include capture , for the production of-process nuclei in the context of the recent supernova hot bubble model . the role of capture in speeding up the charge flow , particularly at the closed neutron shells , is studied together with the-flow at freeze - out and the effect of neutrino - induced neutron emission on the abundance pattern after freeze - out . these correspond to a low frequency case l and a high frequency case h , which takes into account the low abundance ofi and the high abundance ofhf in the early solar nebula .","abstract":"we present a simplified analysis using equations for the charge flow , which include capture , for the production of-process nuclei in the context of the recent supernova hot bubble model . the role of capture in speeding up the charge flow , particularly at the closed neutron shells , is studied together with the-flow at freeze - out and the effect of neutrino - induced neutron emission on the abundance pattern after freeze - out . it is shown that a semi - quantitative agreement with the gross solar-process abundance pattern from the peak at mass number , through the peak at , and up to the region of the actinides can be obtained by a superposition of two distinctive kinds of-process events . these correspond to a low frequency case l and a high frequency case h , which takes into account the low abundance ofi and the high abundance ofhf in the early solar nebula . the lifetime ofhf ( yr ) associates the events in case h with the most common type ii supernovae . these events would be mainly responsible for the-process nuclei near and above . they would also make a significant amount of the nuclei between and 195 , includinghf , but very littlei . in order to match the solar-process abundance pattern and to satisfy thei andhf constraints , the events in case l , which would make the-process nuclei near and the bulk of those between and 195 , must occur times less frequently but eject times more-process material in each event .    assuming that all of the supernovae producing-process nuclei represent a similar overall process , we speculate that the usual neutron star remnants , and hence prolonged ejection of-process material , are associated with the events in case l. we further speculate that the more frequently occurring events in case h have ejection of other-process material terminated by black hole formation during the neutrino cooling phase of the protoneutron star . this suggests that there is now an inventory of black holes with masses and neutron stars resulting from supernovae in the galaxy . this-process model would have little effect on the estimates of the supernova contributions to the non--process nuclei ."}
{"article_id":"astro-ph9706120","section_id":"c","document":"we have found that the gross solar @xmath1-process abundance pattern near and above @xmath3 can be reproduced by a superposition of two kinds of supernova @xmath1-process events after taking into account the meteoritic data on @xmath5i and @xmath6hf . the first kind of events ( case h ) are mainly responsible for the @xmath1-process nuclei near and above @xmath4 . they also make a significant amount of the nuclei between @xmath3 and 195 , including @xmath6hf , but very little @xmath5i . the @xmath1-process nuclei near @xmath3 and the bulk of those between @xmath3 and 195 are made in the second kind of events ( case l ) . in each case , the @xmath1-process nucleosynthesis in a mass element expanding away from the protoneutron star is governed by the initial @xmath0 flux @xmath81 at the beginning of the @xmath1-process , the decay timescale @xmath82 of the @xmath0 flux , and the neutron - to - seed ratio @xmath83 . the parameter @xmath83 specifies the @xmath1-process nuclei mainly produced in each case . the other two parameters , @xmath81 and @xmath82 , are important in determining when all the neutrons are used up , i.e. , the freeze - out time @xmath136 . therefore , they determine the neutrino fluence @xmath120 after freeze - out , which may be responsible for the production of certain @xmath1-process nuclei through neutrino - induced neutron emission ( qian et al . 1997 ; haxton et al . in addition , the @xmath0 flux plays a significant , possibly even crucial role in decreasing the production of @xmath5i with respect to @xmath6hf in case h. in both cases h and l , the solar @xmath1-process abundance ratios in equation ( 11 ) and the constraint on @xmath5i production in equation ( 13 ) determine the average progenitor charge @xmath126 at freeze - out , and hence the neutron - to - seed ratio @xmath83 . for a given @xmath81 , the parameter @xmath82 , together with the freeze - out time @xmath136 , can be calculated from @xmath126 and the neutrino fluence constraint ( eq . [ 15 ] or [ 16 ] ) for each case , as shown in fig . the dependence of @xmath82 on @xmath81 is shown in fig . we wish to emphasize that the meteoritic constraint on coproduction of @xmath5i with @xmath6hf leads to well - defined parameters , especially the neutron - to - seed ratio , in case h. as illustrated by the case without neutrinos , it is difficult to suppress the production of @xmath5i , which has an @xmath35 progenitor nucleus with a long @xmath2-decay lifetime , and to avoid overproduction of the @xmath1-process nuclei at @xmath43 at the same time . when @xmath0 capture is included in the @xmath1-process calculation , this difficulty is noticeably alleviated . however , the parameters characterizing the @xmath0 flux are then subject to additional constraints . consequently , case h represents a particular kind of @xmath1-process events with possibly a very narrow range of neutron - to - seed ratios ( @xmath191 ) . on the other hand , although we have shown that the gross solar @xmath1-process abundance pattern near and above @xmath3 can be accounted for in the minimal scenario of two kinds of @xmath1-process events , the progenitor abundance pattern in case l can be regarded as some average over different events spanning a broader range of neutron - to - seed ratios ( e.g. , @xmath19250 ) , as long as these events occur infrequently enough to be consistent with the meteoritic data on @xmath5i and @xmath6hf . according to wasserburg et al . ( 1996 ) , the events in case h occur roughly once every @xmath61 yr , whereas those represented by case l occur roughly once every @xmath193 yr within a region of @xmath194 pc in size in the galaxy . the size of @xmath194 pc may be understood from the expansion of the supernova ejecta . for an explosion energy of @xmath195 erg , the initial velocity of the supernova ejecta is @xmath196 km s@xmath48 . in about a few @xmath197 yr , the supernova sweeps over a distance of about 6 pc and mixes with about the same amount of the interstellar medium as the total mass @xmath198 of the original ejecta . at times @xmath199 yr , the expansion ( commonly known as `` snow plowing '' ) under momentum conservation is described by @xmath200 where @xmath201 is the radius of the expansion front from the center of the supernova , @xmath202 is the expansion time since the supernova explosion , @xmath203 is the density of the interstellar medium , and @xmath204 is the mass of the hydrogen atom . if we ignore other means of mixing such as galactic rotation , clearly only those supernovae that could reach the position of the protosun within the lifetime of @xmath6hf ( @xmath7 yr ) were responsible for the @xmath6hf in the early solar system . from equation ( 24 ) , those supernovae occurred within @xmath205 pc from the position of the protosun for reasonable values of the relevant parameters . interestingly , within the lifetime of @xmath6hf , the number of supernovae in a region of @xmath205 pc in size is about one assuming a total galactic volume of @xmath206 kpc@xmath207 and a supernova frequency of @xmath208 in the whole galaxy . therefore , @xmath6hf can be replenished on a timescale of @xmath99 yr consistent with the meteoritic data if the supernova @xmath1-process events in case h occur with a frequency of @xmath209 in the whole galaxy , as also argued by wasserburg et al . ( 1996 ) . on the other hand , the meteoritic data require that the @xmath5i produced along with @xmath15i be replenished on a much longer timescale of @xmath100 yr . because the lifetimes of @xmath5i and @xmath6hf are very close , the regions enclosing the supernovae contributing to these two nuclei have about the same size . consequently , those supernova @xmath1-process events represented by case l must occur with a frequency of @xmath210 in the whole galaxy . the frequencies @xmath211 and @xmath212 , together with the corresponding amounts of @xmath1-process ejecta @xmath213 and @xmath214 in cases h and l , determine the superposition parameter @xmath103 in equation ( 11 ) . as found in  3 , we have @xmath2152 . so the amount of @xmath1-process material ejected in the less frequent case l is @xmath820 times more than that in the more frequent case h. this implies that the mass loss rate is much higher , or more likely , that the period for ejecting @xmath1-process material is much longer in case l than in case h.    following the preceding arguments for two distinct @xmath1-process sources , we propose the following @xmath1-process scenario assuming that all of the type ii supernovae producing @xmath1-process nuclei are of a generally similar nature . we suggest that material with higher neutron - to - seed ratios is ejected in the neutrino - driven winds at higher neutrino luminosities , i.e. , at earlier times during the neutrino cooling phase of the protoneutron star . in addition , the early @xmath1-process ejecta have a neutron - to - seed ratio of @xmath191 . the neutron - to - seed ratio then rapidly decreases to @xmath21650 . if neutrino emission were uninterrupted , the neutron - to - seed ratio would stay @xmath21650 , and the corresponding amount of material , all ejected , would be @xmath820 times more than the amount of material with @xmath191 . however , we consider that the continuous mass loss in the neutrino - driven winds is commonly terminated during the rapid transition from @xmath191 to @xmath21650 . this would occur in @xmath217% of the type ii supernovae , with only @xmath8% of them having prolonged continuous mass loss . depending on the initial core mass of the supernova progenitor , among other things , both neutrino emission and mass loss could be terminated by black hole formation during the neutrino cooling phase of the protoneutron star ( brown & bethe 1994 ) . in this scenario there would then be @xmath9 black holes with masses @xmath10 from the @xmath1-process events in case h and @xmath11 neutron stars from the less frequent @xmath1-process events represented by case l in the galaxy today .    in the above @xmath1-process scenario we have associated high neutron - to - seed ratios with high neutrino luminosities and low neutron - to - seed ratios with low neutrino luminosities . qualitatively , a shorter @xmath82 is expected for a higher neutrino luminosity ( qian & woosley 1996 ) . this can be achieved in the framework of the present model ( cf . cases h and l@xmath184 in fig . 8) . of course , a consistent set of the three parameters @xmath81 , @xmath82 , and @xmath83 at different times during the neutrino cooling phase of the protoneutron star can only be obtained in a detailed numerical study of type ii supernovae . we note that many other nuclear species are produced by the explosive nucleosynthesis ( e.g. , fe and si ) in type ii supernovae and by the hydrostatic burning ( e.g. , @xmath218o ) in the outer envelope during the presupernova evolution . the explosive nucleosynthesis is associated with the shock propagation through the envelope . the products from both the explosive nucleosynthesis and the hydrostatic burning are largely unaffected by the neutrinos from the protoneutron star [ except for the @xmath219-process discussed by woosley et al . ( 1990 ) ] or by the possible formation of a black hole during the neutrino cooling phase of the protoneutron star . therefore , the abundant non-@xmath1-process nuclei are ejected together with the @xmath1-process elements in a type ii supernova . the scenario given here would not significantly alter the usual supernova contributions to the non-@xmath1-process nuclei . furthermore , we note that neutrino - driven winds also develop after the accretion - induced collapse ( aic ) of a white dwarf into a neutron star ( woosley & baron 1992 ) . therefore , the aic events could also correspond to the infrequent @xmath1-process events represented by case l. however , because there is no envelope around the final neutron star in the aic events , the overall nucleosynthetic signature of such events is different from that of type ii supernovae . only the nuclear species produced in the neutrino - driven winds , especially the @xmath1-process nuclei , are ejected in the aic events .    finally , the diversity of @xmath1-process sources have some interesting consequences for galactic chemical evolution . at very low metallicities , only type ii supernovae could make fe , whereas both type ia and type ii supernovae contribute to fe at sufficiently high metallicities . therefore , if the @xmath1-process events in case h were mainly associated with type ii supernovae , the abundance ratio of the corresponding main @xmath1-process product with respect to fe would remain constant at low metallicities and decrease with increasing metallicity after type ia supernovae began to make fe . on the other hand , if the @xmath1-process events represented by case l were mainly associated with the aic events , the metallicity dependence for the abundance ratio of the corresponding main @xmath1-process product with respect to fe would be sensitive to the difference between the time at which such events first occurred and the onset of increase in metallicity due to type ia supernova .    the above suggestions regarding the nature of supernova @xmath1-process events are highly speculative . however , if the binary distribution of @xmath1-process sources with very different frequencies and very different mass contributions is correct , then some new supernova @xmath1-process models will be required along the general lines indicated here .    we want to thank gerry brown and sterl phinney for helpful discussions . this work was supported in part by the u. s. department of energy under grant no . de - fg03 - 88er-40397 , by nasa under grant no . nag5 - 4076 , and by division contribution no . 5827(973 ) . y .- qian was supported by the david w. morrisroe fellowship at caltech . brown , g. e. , & bethe , h. a. 1994 , , 423 , 659 burbidge , e. m. , burbidge , g. r. , fowler , w. a. , & hoyle , f. 1957 , rev . phys . , 29 , 547 cameron , a. g. w. 1957 , , 69 , 201 cameron , a. g. w. , cowan , j. j. , klapdor , h. v. , metzinger , j. , oda , t. , & truran , j. w. 1983 , , 91 , 221 fuller , g. m. , & meyer , b. s. 1995 , , 389 , 517 goriely , s. , & arnould , m. 1996 , , 312 , 327 haxton , w. c. , langanke , k. , qian , y .- z . , & vogel , p. 1997 , , 78 , 2694 hoffman , r. d. , woosley , s. e. , & qian , y .- z . 1997 , , 482 , kppeler , f. , beer , h. , & wisshak , k. 1989 , rep . phys . , 52 , 945 kratz , k .- , thielemann , f .- k . , hillebrandt , w. , mller , p. , harms , v. , whr , a. , & truran , j. w. 1988 , j. phys . g , 14 , s331 kratz , k .- , bitouzet , j .- p . , thielemann , f .- k . , mller , p. , & pfeiffer , b. 1993 , , 403 , 216 mathews , g. j. , bazan , g. , & cowan , j. j. 1992 , , 391 , 719 mclaughlin , g. c. , & fuller , g. m. 1996 , , 464 , l143 mclaughlin , g. c. , & fuller , g. m. 1997 , , submitted meyer , b. s. , howard , w. m. , mathews , g. j. , woosley , s. e. , & hoffman , r. d. 1992 , , 399 , 656 meyer , b. s. 1995 , , 449 , l55 mller , p. , nix , j. r. , & kratz , k .- 1996 , atomic data nucl . data tables , submitted qian , y .- z . , & woosley , s. e. 1996 , , 471 , 331 qian , y .- z . , haxton , w. c. , langanke , k. , & vogel , p. 1997 , , 55 , 1532 sneden , c. , mcwilliam , a. , preston , g. w. , cowan , j. j. , burris , d. l. , armosky , b. j. 1996 , , 467 , 819 takahashi , k. , witti , j. , & janka , h .- th . 1994 , , 286 , 857 wasserburg , g. j. , busso , m. , & gallino , r. 1996 , , 466 , l109 witti , j. , janka , h .- th . , & takahashi , k. 1994 , , 286 , 841 woosley , s. e. , hartmann , d. h. , hoffman , r. d. , & haxton , w. c. 1990 , , 356 , 272 woosley , s. e. , & baron , e. 1992 , , 391 , 228 woosley , s. e. , & hoffman , r. d. 1992 , , 395 , 202 woosley , s. e. , wilson , j. r. , mathews , g. j. , hoffman , r. d. , & meyer , b. s. 1994 , , 433 , 229","summary":"must occur times less frequently but eject times more-process material in each event .    this suggests that there is now an inventory of black holes with masses and neutron stars resulting from supernovae in the galaxy .","abstract":"we present a simplified analysis using equations for the charge flow , which include capture , for the production of-process nuclei in the context of the recent supernova hot bubble model . the role of capture in speeding up the charge flow , particularly at the closed neutron shells , is studied together with the-flow at freeze - out and the effect of neutrino - induced neutron emission on the abundance pattern after freeze - out . it is shown that a semi - quantitative agreement with the gross solar-process abundance pattern from the peak at mass number , through the peak at , and up to the region of the actinides can be obtained by a superposition of two distinctive kinds of-process events . these correspond to a low frequency case l and a high frequency case h , which takes into account the low abundance ofi and the high abundance ofhf in the early solar nebula . the lifetime ofhf ( yr ) associates the events in case h with the most common type ii supernovae . these events would be mainly responsible for the-process nuclei near and above . they would also make a significant amount of the nuclei between and 195 , includinghf , but very littlei . in order to match the solar-process abundance pattern and to satisfy thei andhf constraints , the events in case l , which would make the-process nuclei near and the bulk of those between and 195 , must occur times less frequently but eject times more-process material in each event .    assuming that all of the supernovae producing-process nuclei represent a similar overall process , we speculate that the usual neutron star remnants , and hence prolonged ejection of-process material , are associated with the events in case l. we further speculate that the more frequently occurring events in case h have ejection of other-process material terminated by black hole formation during the neutrino cooling phase of the protoneutron star . this suggests that there is now an inventory of black holes with masses and neutron stars resulting from supernovae in the galaxy . this-process model would have little effect on the estimates of the supernova contributions to the non--process nuclei ."}
{"article_id":"0912.2966","section_id":"i","document":"from as way back as the @xmath6 , it has been known that the orbit of the planet mercury exhibits a peculiar motion of its perihelion , specifically , the perihelion of mercury advances by @xmath7 @xmath8 . when newton s theory of gravitation is applied to try and explain this ( by making use of the oblateness of the planets because when the sun s gravitational force acts on the oblate - planets , the oblateness causes torque [ on the planets ] and this torque is thought to give rise to the anomalous motion of the planets ) ; it was found first by leverrier in @xmath9 see _ e.g. _ @xcite that it predicted a precession of @xmath10 @xmath8 which is larger than the observed @xcite . with the failure of newton s theory to explain this , it was proposed that a small undetected planet was the cause . careful scrutiny of the terrestrial heavens by telescopes and spaces probes reveals no such object  the meaning of which is that the cause may very well be a hitherto unknown gravitational phenomena  einstein was to demonstrate that this was the case , that there existed a hitherto unknown gravitational phenomena that is the cause of this peculiar motion .    with the herald of einstein s general theory of relativity ( gtr ) in @xmath11 , einstein immediately applied his gtr to this problem ; much to his elation which caused him heart palpitations  he obtained the unprecedented value of @xmath12 and this was ( and is still ) hailed as one of the greatest triumphs for the gtr and this lead to its quick acceptance . venus , the earth , and other planets show such peculiar motion of their perihelion . observations reveal a shift of @xmath13 and @xmath14 respectively ( see _ e.g. _ kenyon @xmath15 ) . einstein s theory is able to explain the perihelion shift of the other planets well , so much that it is now a well accepted paradigm that the perihelion shift of planetary orbits is a general relativistic phenomena . einstein s gtr explains the perihelion shift of planetary orbits as a result of the curvature of spacetime around the sun . it does not take into account the spin of the sun and at the same time it assumes all the planets lay on the same plane . the assumption that the planets lay on the same plane is in the gtr solution only taken as a first order approximation  in reality , planets do not lay on the same plane . in this reading we set forth what we believe is a new paradigm ; we have coined this paradigm the azimuthally symmetric theory _ of _ gravitation ( astg ) and this is derived from poisson s well accepted equation for empty space  namely @xmath0 . poisson s law is a differential form of newton s law _ of _ gravitation . we explain the perihelion shift of the orbits of planets as a consequence of the spin of the sun  _ i.e. _ solar spin . it is well known that the sun does exhibit some spin angular momentum  specifically , it [ the sun ] undergoes differential rotation . on the average , it spins on its spin axis about once in every @xmath16 _ days _ ( see _ e.g. _ @xcite ) . its spin axis makes an angle of about @xmath17 with the ecliptic plane . it is important that we state clearly here that by no means have we discovered a new theory or a set of new equations ; we have merely applied poisson s well known azimuthally symmetric solution to gravity for a spinning gravitating body . further , with regard to einstein s gtr  _ vis _ ; in its solution to the problem of the perihelion shift of planetary orbits , it [ the gtr ] assumes the traditional newtonian gravitational potential , namely : @xmath18 , where @xmath19 is newton s universal constant of gravitation , @xmath20 is the mass of the central gravitating body and @xmath21 is the radial distance from this gravitating body . einstein s gtr which is embodied in einstein s law of gravitation , namely :    @xmath22    is designed such that in the low energy limit and low spacetime curvature such as in the solar system , this equation reduces directly to poison s equation . in einstein s law above , @xmath23 is the ricci tensor , @xmath24 the ricci scalar , @xmath25 the metric of spacetime , @xmath26 is einstein s controversial cosmological constant which at best can be taken to be zero unless one is making computations of a cosmological nature where darkenergy is involved , and @xmath27 where @xmath28 is the speed of light in vacuum ; and poisson s equation is given by :    @xmath29    where @xmath30 is the density of matter and the operator @xmath31 written for spherical coordinate system ( see figure [ scoord ] for the coordinate setup ) is given by :    @xmath32    [ scoord ] , the zenith ( the angle from the north pole ; the colatitude ) denoted by @xmath33 , and the azimuth ( the angle in the equatorial plane ; the longitude ) by @xmath34.,title=\"fig : \" ]    as already been said , our solution or paradigm , hails directly from poisson s equation , which in itself is a first order approximate solution to einstein s gtr , albeit with the important difference that we have taken into account solar spin . this fact that our paradigm explains reasonably well  within the confines of its error margins ; the precession of planetary orbits as a consequence of solar spin and at the sametime the gtr explains this same phenomena well as a consequence of the curvature of spacetime raises the question * `` is the precession of the perihelion of solar orbits a result of ( 1 ) solar spin or ( 2 ) is it a result of the curvature of spacetime ? '' * if anything , this is the question that this reading seems to raise . an answer to it , will only come once the meaning of the astg is fully understood .    in the above we say the astg _ `` explains reasonably well  within the confines of its error margins '' _  what immediately comes to mind is that can a theory have error margins or is it not experiments that have error margins ? as will be seen , certain undetermined constants ( @xmath35 ) in the theory emerge and at present , one has to infer these from observations and it is here that the error margins of the astg come into play . further , we show , that _ in - principle _ , the astg does explain ( 1 ) the increase in the mean earth - sun distance , ( 2 ) the increase in the mean earth - moon distance _ etc _ , and these emerge as a consequence of the fact that from the astg , the orbital angular momentum is not a conserved quantity as is the case in newtonian s gravitational theory and einstein s gtr . that the orbital angular momentum is not a conserved quantity may lead one to think that the astg violets the law _ of _ conservation of angular momentum  no , this is not the case . the lost angular momentum is transferred to the spin of the orbiting body and as well as the sun .","summary":"we show that to second order approximation , this azimuthally symmetric gravitational field is capable of explaining at least two things ( 1 ) the observed perihelion shift of solar planets ( 2 ) that the _ mean earth - sun distance _ must be increasing  this resonates with the observations of two independent groups of astronomers ( ; ) who have measured that the _ mean earth - sun distance _ must be increasing at a rate of about ( ) to ( ) . in - principle , we are able to explain this result as a consequence of loss of orbital angular momentum  this loss of orbital angular momentum is a direct prediction of the theory . further , we show that the theory is able to explain at a satisfactory level the observed secular increase earth year ( ; ) . furthermore , we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least .    [ firstpage ]    astronomical unit , azimuthal symmetry , orbit , perihelion shift , solar spin","abstract":"from a purely none - general relativistic standpoint , we solve the empty space poisson equation ( ) for an azimuthally symmetric setting , _ i.e. _ , for a spinning gravitational system like the sun . we seek the general solution of the form . this general solution is constrained such that in the zeroth order approximation it reduces to newton s well known inverse square law of gravitation . for this general solution , it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body . we show that to second order approximation , this azimuthally symmetric gravitational field is capable of explaining at least two things ( 1 ) the observed perihelion shift of solar planets ( 2 ) that the _ mean earth - sun distance _ must be increasing  this resonates with the observations of two independent groups of astronomers ( ; ) who have measured that the _ mean earth - sun distance _ must be increasing at a rate of about ( ) to ( ) . in - principle , we are able to explain this result as a consequence of loss of orbital angular momentum  this loss of orbital angular momentum is a direct prediction of the theory . further , we show that the theory is able to explain at a satisfactory level the observed secular increase earth year ( ; ) . furthermore , we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least .    [ firstpage ]    astronomical unit , azimuthal symmetry , orbit , perihelion shift , solar spin"}
{"article_id":"0912.2966","section_id":"c","document":"we have considered poisson s equation for empty space and solved this for an azimuthally symmetric setting  we have coined the term azimuthally symmetric theory _ of _ gravitation ( astg ) for the emergent theory thereof . from the emergent solution , we have shown that the astg is capable of explaining certain observed ( and yet to be observed ) anomalies :      one of the draw - backs of the astg as it currently stands is that it is heavily dependent on observations ; _ for _ the values of @xmath35 need ( have ) to be determined from observations . without knowledge of the @xmath388 , one is unable to produce the hard numbers required to make any quantifications . clearly , a theory incapable of making any numerical quantifications is _ useless_. this must be averted . we shall make use of the solar values of the @xmath388 in shading some light into our current thinking on this , _ i.e. _ finding a general form for the constants @xmath35 ; in the subsequent paragraphs , we shall make what we believe is a _ reasonable suggestion _ and give our current envisage - ment on the general form for these constants . \\(1 ) first things first , _ if _ the constants @xmath35 where all independent of each other , then , the theory would clearly be horribly complicated . if we take as guide the principle _ of _ occam s razor which in most if not all cases , leads to the simplest theory , then , these constants must be dependent on each other somehow so as to reduce the labyrinth of complications thereof . the simplest imaginable such dependence is @xmath389 ; in this way , the entire system of constants @xmath35 is dependent on just the one constant @xmath144 . this idea that the system of constants be dependent on just one constant is drawn from the theory of polynomial functions where for a polynomial function @xmath390 , one can have `` well behaved '' polynomial functions for which the constants @xmath391 have a general form , _ i.e. _ , were they dependent on @xmath392 ; _ e.g. _ , @xmath393 . we envisage the function @xmath58 to be a `` well behaved '' function . by `` well behaved '' we simple mean its system of constants , @xmath35 , is critically dependent on @xmath47 just as the constants @xmath391 depend on @xmath392 . \\(2 ) second , we could like that on a practical level , only the second order approximation of the theory must suffice , this means the terms @xmath394 must be practically negligible . we have already shown herein that the second order approximation of the astg is able to explain a sizable amount of anomalous observations . with the astg written in its second order approximation and as will be shown in the second reading ( _ i.e. _ , a follow - up reading that we hope will be published in the present journal ) , one is able without much difficulties , to explain from this second order approximation , the emergence of molecular bipolar outflows in star forming systems , as a gravitational phenomena . if the other terms beyond the second order approximation become practically significant , one will have difficulties to explain outflows . so in a way , we are not going to pretend but clearly state that , we want  albeit with a priori and posteriori justification ; to fine tune the theory so that it is able to explain the emergence of bipolar . this is the strongest reason we want the terms for which @xmath394 to be so small such that in practice one can neglect them entirely . \\(3 ) third and most important , the only data point we have of these constants is the determined values for the sun , _ i.e. _ , @xmath395 and @xmath396 . if logic is to hold  as it must ; then , our suggestion , @xmath389 ; must be able to explain this . we find that the following proposal :      meets ( 1 ) , ( 2 ) and ( 3 ) . we shall assume this result until such a time evidence to the contrary is brought forth . checking on ( 3 ) we see that within the error margins @xmath398\\lambda_{1}^{\\tiny \\odot}$ ] . further checking on ( 2 ) ; from ( [ lambda ] ) we will have @xmath399 which is practically small ; the meaning of which is that all terms for which @xmath394 can in practice be neglected entirely .    if the above proposal proves itself to be correct , then , the resultant theory will have just one undetermined parameter @xmath144 . we are not going to try and deduce what this parameter depends on but simple hint at our current thinking . we believe this parameter must depend on the angular frequency of the spin of the gravitating body in question . if we can find the correct dependence , then , the astg will stand on it own thus positioning itself on the podium to make testable predictions . we have left the task to make this deduction an exercise for the follow - up reading . the fact the we have deduced the crucial parameters @xmath146 & @xmath147 from experience , means we have in the current reading done some reserve engineering . normally , a theory must give these values and make clear predictions , just as when einstein wrote down his equations and found that his theory predicted a factor @xmath260 difference when compared to newton s theory when it come to the bending of light by the sun and when applied to the sun - mercury system , it accounted very well for the then unexplained @xmath400 per century for the precession of the perihelion of the orbit of this planet ; it just came out right . there were no free parameters that needed fitting as is the case of the astg . as argued above , once a general form for the @xmath35 is found , this setback of the astg will be solved . because we were able to obtain the values @xmath146 & @xmath147 which lead acceptable values for the perihelion precession , means that the values @xmath401 & @xmath402 are not random but systematic . if the theory was all wrong , then , only luck would make the obtained values for @xmath401 & @xmath402 give values of @xmath146 & @xmath147 such that equation ( [ simul ] ) give in general , acceptable values for the precession of the perihelion of the planets .    with regard to the values obtained for the precession of the perihelion of solar planets , it can be said that , the values obtained from the astg as shown in column 10 ( table [ pshift ] ) when weighed against the observational values listed in column 10 ( of the same table ) are acceptable . given that we have taken into account the fact the orbits of these planets are not found laying in the same plane , this can hardly be a coincident or an accident since changing their inclination by just @xmath403 will alter the predicted values of the precession of their perihelion . @xcite states that the secular increase in the mean earth - sun distance can not be explained within the realm of classical physics . contrary to this , we believe and hold that herein  we have shown from within the provinces of classical physics that this result is explainable from within the domains and confines of classical physics . before the present , the reason why perhaps this observation appeared beyond the reach of classical physics is because classical physics has not really considered gravitation as an azimuthally symmetric phenomenon as has been done in present reading . this strongly suggests that the ideas presented herein need to be explored further for they contain a debris of the truth . one of the interesting outcome that was not explored in this reading for fear of digression is that the astg has a provision for spiral orbits ( equation [ sol1 ] and [ sol2 ] ) . these orbits occur when @xmath404 . this condition implies the existence of a region ( @xmath405 ) in which spiral orbits will occur . evaluating the inequality @xmath404 , leads to : @xmath406 , and from this , it is easy for one to deduce that spiral orbits are unlikely in the solar system since these will have to occur inside the sun because @xmath407 .    at this point as we approach the end of this reading , we feel strongly that we must address the question ; `` does the spin along the azimuthal axis of a gravitating body induce an azimuthal symmetry into the gravitational field for this spinning body ? '' to answer this , we must ask the question ; `` will a contracting none - spinning cloud of gas experience any bulge alone its equator ? '' first , we know that the equatorial bulge will occur on a plane perpendicular to the spin axis . since a none - spinning gas cloud is going to have to spin axis , there is going to be no spin axis about which the equatorial bulge will occur . if the material in the cloud is randomly and uniformly distributed , the cloud will exhibit a spherically symmetric distribution of mass and its gravitational field is expected to be spherically symmetric . a spherically spherically symmetric gravitational field is one that only has a radial dependence , _ i.e. _ @xmath408 . now , if the gas cloud is spinning , the centrifugal forces will cause there to exist a disk and the material distribution will have an azimuthal symmetry , _ i.e_. @xmath409 . should not this azimuthal symmetric distribution of matter induce an azimuthal gravitational field ? from poison s equation ( [ poison ] ) , @xmath409 implies @xmath1 ; should not this , _ i.e. _ @xmath1 , hold as - well for a body spinning gravitating body in a vacuum ? from this , clearly , a spinning gravitating body ought to exhibit an azimuthal symmetry . we have argued in the last paragraph of  ( 2 ) that the spin of a gravitating body breaks the existing spherical symmetry of the non - spinning body and the above argument is just adding more to this . it is from this that the subtitle and running head finds its justification . if the astg turns out to be correct  as we believe it will ; then , we have an important question to ask ;  what is the speed of light doing in a theory of gravitation because from ( [ bdef ] ) we see that the constants @xmath410 and @xmath411 are intimately tied - up together ? this is a similar if not a congruent question that has been asked by @xcite in their expository work on earth flyby anomalies ( afa ) . the empirical formula deduced to quantify efa contains in it the speed of light , @xmath411 , so in their exposition of the phenomena of afa , @xcite have asked the perdurable question `` what is the speed of light doing there ? '' . efa are thought to be a gravitational phenomena , so , what does the speed of light have to do with gravitation  _ really _ ? if there is an intimate relationship between the speed of light and gravitation , then , one will be forgiven to think this suggests a link between gravitation and the theory of light  the speed of light , @xmath411 , appears to be dire to the astg presented herein . why not another value but the speed of light , @xmath411 ? we shall leave these matters hanging in - limbo .    in relation to the question above , _ i.e. _ , `` what is the speed of light doing in a theory of gravitation '' , one notes that newtonian gravitation  which requires instantaneous interaction as a postulate ; does not imply the dependence of the gravitational potential on the azimuthal angle for a spinning body as is the case in the astg , because at any instant @xmath412 , the gravitating body appears spherically symmetric . here we have the speed of light @xmath411 coming in because of the azimuthal symmetry . does this speed of light @xmath411 link ( or not ) the propagation of the gravitational phenomena to the speed of light ? in the present , we can only pause this as a question , for we still have to do further work on these ideas .    in closing , allow me to say that we find it hard to call what has been presented herein as `` a new theory _ of _ gravitation '' . when one tells you they have come up with a new theory of gravitation , what immediately comes to mind is that they have discovered a new principle upon which gravitation can further be understood from the present understanding . the astg is not founded on any new physical principle but on the well known vintage equation of poisson . what we have done is simply taken the azimuthally symmetric equations of this equation and applied them to gravitation . based on this understanding , it is difficult to call it a new theory . , the azimuthally symmetric equations of poisson have brought new and exciting physics  perhaps only because of this , the title of this reading finds its qualification . * :* i am grateful to mkoma george  baba _ va _ panashe , and his wife  mai _ va _ panashe , for their kind hospitality they offered while working on this reading and to mr . isak d. davids & ms . m. christina eddington for proof reading the grammar and spelling . further , i am grateful to the anonymous reviewers  for their invaluable criticism that has helped in the refinement of the arguments presented . last and certainly not least , i am very grateful to my professor , d. johan van der walt and professor pienaar kobus , for the strength and courage that they have given me .    miura t. , arakida h. , kasai h. & shuichi kuramata , 2009 , secular increase of the astronomical unit : a possible explanation in terms of the total angular momentum conservation law , accepted for publication in publication of the astronomical society of japan : arxiv:0905.3008 . iorio l. , 2008b , solar system tests of some models of modified gravity proposed to explain galactic rotation curves without dark matter , scholarly research exchange , vol . 2008 , article i d 968393 , doi:10.3814/2008/968393 . standish e. m. , 2005 , the astronomical unit now , in transits of venus : new views of the solar system and galaxy , proceedings iau colloquium , ed . kurtz , d. w. , no . 196 , ( cambridge university press , cambridge ) , pp.163 - 179 .","summary":"from a purely none - general relativistic standpoint , we solve the empty space poisson equation ( ) for an azimuthally symmetric setting , _","abstract":"from a purely none - general relativistic standpoint , we solve the empty space poisson equation ( ) for an azimuthally symmetric setting , _ i.e. _ , for a spinning gravitational system like the sun . we seek the general solution of the form . this general solution is constrained such that in the zeroth order approximation it reduces to newton s well known inverse square law of gravitation . for this general solution , it is seen that it has implications on the orbits of test bodies in the gravitational field of this spinning body . we show that to second order approximation , this azimuthally symmetric gravitational field is capable of explaining at least two things ( 1 ) the observed perihelion shift of solar planets ( 2 ) that the _ mean earth - sun distance _ must be increasing  this resonates with the observations of two independent groups of astronomers ( ; ) who have measured that the _ mean earth - sun distance _ must be increasing at a rate of about ( ) to ( ) . in - principle , we are able to explain this result as a consequence of loss of orbital angular momentum  this loss of orbital angular momentum is a direct prediction of the theory . further , we show that the theory is able to explain at a satisfactory level the observed secular increase earth year ( ; ) . furthermore , we show that the theory makes a significant and testable prediction to the effect that the period of the solar spin must be decreasing at a rate of at least .    [ firstpage ]    astronomical unit , azimuthal symmetry , orbit , perihelion shift , solar spin"}
{"article_id":"1612.01885","section_id":"i","document":"although skyrmions have been proposed@xcite long ago , there has been a strong rise in interest in recent years spurred by experimental observations of skyrmionic phases in various magnetic thin - films@xcite . magnetic skyrmions are characterized by a topologically nontrivial mapping from a two - dimensional ( 2d ) magnetic system in real space into three - dimensional spin space . this mapping leads to a topological charge @xmath0 which characterizes the skyrmion and is given by @xmath1 where @xmath2 is the normalized magnetization vector field and @xmath3 and @xmath4 are the spatial coordinates of the 2d magnetic layer@xcite . magnetic skyrmions are attractive candidates for magnetic storage of classical information@xcite because they are topologically stable in the sense that no continuous local deformation in the magnetic texture can remove a skyrmion ( _ i.e. _ , change @xmath0 ) , and they can be manipulated at high speed with relatively low current densities@xcite . furthermore , because skyrmions coupled to conventional superconductors are known to support majorana fermions@xcite , they may be a route to topological quantum computation@xcite . the dynamics of any classical magnetic texture with fixed magnitude , @xmath2 , is governed by the landau - lifshitz - gilbert ( llg ) equation@xcite . the dynamic properties of skyrmions can be considerably simplified by considering the motion of the average magnetic texture@xcite , which reduces to an equation of motion for the skyrmion s center - of - mass coordinate , known as thiele s equation . this skyrmion coordinate behaves as a massless dirac - like particle under a magnus force proportional to @xmath0@xcite , and a possible damping is parameterized by a phenomenological velocity - dependent term that is induced by the coupling of the skyrmion motion to other degrees of freedom in the system such as electrons , phonons , magnons , etc . ; the microscopic details of this coupling are typically left unspecified . using this phenomenological approach , several generalized equations have been proposed@xcite for a rigid magnetic structure in the presence of external static as well as rapidly changing forces . the thermal diffusion of a driven skyrmion has been studied within the classical framework by a numerical solution of the stochastic llg equation@xcite , where random fields are included to model the effects of thermal fluctuations . however , for small skyrmions at the nanometer scale , the size of skyrmions in state - of - the - art experiments@xcite , quantum fluctuations are expected to become relevant@xcite and the classical llg equation is expected to break down . in a fully quantum mechanical treatment starting from the spin and other degrees of freedom present in the system the quantum dynamics of the skyrmion should emerge naturally , giving rise for instance to possible mass and dissipation terms linked to the underlying microscopics . the goal of this work is to provide such a quantum treatment of skyrmions in insulating magnetic films . thereby we will restrict ourselves to systems where only spin degrees of freedom are present and other sources such as phonons and itinerant electrons are assumed to be negligibly small ( due to low enough temperatures ) or entirely absent , respectively . by employing quantum field theory methods and the fadeev - popov techniques for collective coordinates  @xcite , applied to magnetic systems  @xcite , we will derive the quantum dynamics of the skyrmion in a systematic way , thereby going beyond the classical limit . within this formalism the skyrmion position , which parametrizes the classical static solution of the euler - lagrange equations , is promoted to a time - dependent dynamical variable and a finite perturbation theory in terms of fluctuations around the skyrmion configuration is performed . the interaction of the skyrmion with these magnon modes gives rise to dissipation and to a non - local damping kernel whose form we obtain in a closed form and can evaluate analytically in some regimes of physical interest . in particular , we are able to microscopically calculate the contribution to the damping in the thiele equation from the incoherent magnon modes which in general depends on the magnetic dispersion relation and thus on the details of the free energy of the system .    for asymptotic ( imaginary ) times , we find that the damping kernel becomes local in time and reduces to a simple mass term which we can calculate explicitly in the presence of non - uniform magnetic traps and spatially dependent exchange interactions for arbitrary temperatures . specifically , in the zero  temperature limit we find that local defects and magnetic traps which break translational symmetry induce a finite mass so that the skyrmion motion is no longer dirac  like but rather follows a quadratic dispersion law of a massive particle . as a striking consequence , we find that in quasi - one dimensional wire geometries the skyrmion acquires a finite mass . such geometries are provided for instance by anisotropic magnetic traps , similar to linear tracks used for magnetic memory and logic devices @xcite . surprisingly , this shows that skyrmions in quantum confined geometries exhibit a fundamentally different dynamical behaviour compared to the one in unconfined geometries . the paper is organized as follows . in sec . [ sec.quant ] we derive a coherent - state path integral for a generic magnetic texture , while in sec . [ sec : skyrmion mass ] , we utilize this functional integral approach to calculate the damping experienced by such a magnetic texture as a result of the coupling to magnon fluctuations , and we also demonstrate that this damping reduces to a simple mass term . in sec .  [ sec : chiral magnets ] , we apply our formalism to a chiral magnet and show in sec.[subsec : mass zero t ] , that only a spatially nonuniform perturbation to the magnetic texture induces a skyrmion mass at zero temperature . to complete the description we examine in sec.[subsec : mass finite t ] the skyrmion mass at finite temperatures . we conclude with a discussion and some general remarks in sec . [ sec : discussion ] and sec . [ sec : conclusions ] . technical details are deferred to several appendices .","summary":"we study the quantum propagation of a skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite temperature path integral formalism , using field theoretic tools . promoting the center of the skyrmion to a dynamic quantity , the fluctuations around the skyrmionic configuration give rise to a time  dependent damping of the skyrmion motion . from the frequency dependence of the damping kernel , we are able to identify the skyrmion mass , thus providing a microscopic description of the kinematic properties of skyrmions . when the free energy is translationally invariant we find the skyrmion mass is finite only at finite temperature . however , if defects are present or a magnetic trap is applied , the skyrmion mass acquires a finite value , even at vanishingly small temperature . we demonstrate that a skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasi  one dimensional confinement .","abstract":"we study the quantum propagation of a skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite temperature path integral formalism , using field theoretic tools . promoting the center of the skyrmion to a dynamic quantity , the fluctuations around the skyrmionic configuration give rise to a time  dependent damping of the skyrmion motion . from the frequency dependence of the damping kernel , we are able to identify the skyrmion mass , thus providing a microscopic description of the kinematic properties of skyrmions . when the free energy is translationally invariant we find the skyrmion mass is finite only at finite temperature . however , if defects are present or a magnetic trap is applied , the skyrmion mass acquires a finite value , even at vanishingly small temperature . we demonstrate that a skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasi  one dimensional confinement ."}
{"article_id":"astro-ph0512227","section_id":"i","document":"in this paper we have examined the unbound axial outflows ( jets ) that develop within grmhd accretion simulations . what is noteworthy in these models is that the jets develop as a natural result of the accretion process , rather than as a direct consequence of conditions imposed on the simulation . the jets have two major components : a matter - dominated outflow that moves at a modest velocity ( @xmath165 ) along the centrifugal barrier surrounding an evacuated axial funnel , and a highly - relativistic poynting flux dominated jet within the funnel . the funnel wall jet is accelerated and collimated by magnetic and gas pressure forces in the inner torus and the surrounding corona . the poynting flux jet results from the formation of a large scale radial magnetic field within the funnel . this field is spun by the rotating spacetime of the black hole , hence the energy for this jet component comes not directly from accretion but from the black hole s rotation , although the field mediating this energy extraction is a product of accretion . the energies in both components of the jet are a function of black hole spin ; greater spins yield greater energy . the total jet power can be a significant fraction of the accretion energy estimated by the product of the mass accretion rate and the specific binding energy of the last stable orbit . we next consider the broader implications of these results within the context of several of the standard theoretical categories for jets , namely jet acceleration , power , collimation , and the blandford - znajek mechanism . it has been expected for many years ( since blandford & znajek 1977 ) , that within the axial funnel the spacetime rotation enforced by spinning black holes can drive a significant electromagnetic outflow . our results are clearly in line with that expectation . the outflow - generation process within the accretion flow itself that has for many years received the greatest attention has been magnetocentrifugal acceleration , such as envisioned in the model of blandford & payne ( 1981 ) , but this mechanism does not appear to be important here .    on the other hand , the main driving force we identify for the funnel wall jet  a high - pressure corona squeezing material against an inner centrifugal wall  has received very little attention in the past . in consequence of this compression , the pressure at the base of the matter outflow is kept high enough to create an outward radial pressure gradient that provides the momentum for the outflow . it is also worth commenting that these forces act over a substantial radial range , from a few gravitational radii out to many tens .      to measure the relative power in the unbound outflow , we have compared the jet energy flux with the mass accretion rate into the hole over the last 70% of the simulation . the simulation has no radiative losses , so we can not say what the radiative efficiency of the accretion disk would be . the novikov - thorne efficiency provides a convenient standard of comparison . this nominal efficiency corresponds to the binding energy of the innermost stable circular orbit , although the actual radiative efficiency could well be different because of , for example , magnetic torques in the plunging region ( krolik 1999 ; gammie 1999 ) , or heat advection into the hole . judged by this measure , the energy carried off in the outflow is considerable . in two cases ( @xmath4 and 0.99 ) , the electromagnetic power at @xmath72 is , by itself , comparable to the novikov - thorne prediction of radiated power . in the other high spin cases , it is about a quarter of the novikov - thorne number . one should remember , however , that energy can be ( and often is ) exchanged between the fields and the matter , so these measures of the electromagnetic power in the outflow are quantitatively accurate _ only _ at the fiducial location where they are measured . because the rate of energy loss in the matter outflow is usually a few times as great as the electromagnetic contribution , the total is typically comparable to the classical prediction of radiated power . another way to gain a feel for the magnitude of the electromagnetic power in the outflow is via dimensional analysis . the poynting flux at the inner boundary is @xmath166 ( cf . [ eqn : bzpoynting ] ) ; but what determines the magnetic field strength ? indeed , this has been the key question examined by such works as ghosh & abramowicz ( 1997 ) and livio , ogilvie , & pringle ( 1999 ) . these authors argued that the strength of the field responsible for a blandford - znajek process must be set by the fields in the accretion flow , and this may limit the total jet power .    at radii in the disk well beyond the marginally stable region , angular momentum conservation ensures that @xmath167 if magnetic torques are the primary agent of accretion , while the competition between orbital shear and other stresses tends to make @xmath168 . in these simulations , in which @xmath169 is common to all , but the black hole spin varies , if we wish to analyze the spin - dependence of the poynting flux near the event horizon , it makes sense to examine the ratio of the magnetic field intensity to the mass accretion rate at that location . we find that the time- and surface area - averaged ratio @xmath170 grows rapidly with increasing black hole spin , very nearly @xmath171 ( fig . [ fig : bsqeff ] ) . some of this growth is attributable to mere compression , as the event horizon shrinks as the spin rate rises . however , the dependence is much stronger than anything simple geometry could explain . it appears that the strong frame - dragging associated with extreme kerr spacetimes leads to substantial field amplification as well . the rapid growth in electromagnetic power output with faster black hole rotation is predominantly due to this effect . one of the key issues in jet formation and propagation is the degree to which the jets are collimated . of course , jets are observed on far larger scales than we are modeling in these simulations , but the degree of collimation seen here is nevertheless of some interest . generally speaking , whatever collimation there is occurs in the inner regions of the flow , where the inner disk and hot corona provide confinement . relatively close to the black hole ( @xmath172 ) , the boundary between the magnetically - dominated poynting flux jet and the funnel wall outflow follows the shape of the centrifugal barrier . at larger distances , however , the matter flows almost straight outward , so that the funnel is nearly conical , while the contours of constant effective potential gradually move toward smaller polar angle ( fig . [ fig : momflux ] ) . the precise shape and collimation of the jet is somewhat uncertain because the outer boundary of the funnel - wall , matter - dominated funnel wall outflow is somewhat indistinct . we see a smooth transition as a function of polar angle between mildly relativistic outflowing unbound matter and slightly slower , but bound , coronal matter . on the other hand , the boundary between the low - density magnetically - dominated funnel interior and the higher - density funnel - wall outflow is sharp and clear . it is possible that magnetic forces might provide additional collimation on larger scales , but this remains to be seen in future simulations .      in the astrophysical literature , the general idea that energy can be conveyed from rotating black holes to the outside world via magnetic connections is often dubbed the  blandford - znajek mechanism \" because they were the first to discuss a specific version of this process . in our simulations , when all is said and done , the funnel interior is dominated by a magnetic field that would be purely radial but for the rotation created by its connection to the black hole s ergosphere . thus , any toroidal field in the funnel , and consequently any poynting flux , is due entirely to general relativistic dynamics peculiar to spinning black holes . in other words , the outward poynting flux must be due to a process that could fit under the general rubric of  blandford - znajek \" . on the other hand , we also find specific differences from the classical blandford - znajek model , specifically the particular idealized picture presented in their original paper ( blandford & znajek 1977 ) . for example , although the funnel region is magnetically - dominated , it is _ not _ in general in a state of force - free equilibrium . indeed , the very large fluctuations that continually occur in the outflow show that it is never in any state of equilibrium , force - free or otherwise . in addition , as originally shown in phinney ( 1983 ) , the collapse of all wave speeds to @xmath173 in the exact force - free limit means that to understand the dynamics properly requires retention of a finite inertia . moreover , whereas in the classical blandford - znajek model there was zero accretion ( the only function of nearby orbiting matter is to support the currents sustaining the magnetic field ) , in our picture the electromagnetic luminosity in the outflow takes place entirely as a byproduct of accretion . in the classical model the magnetic field was a relic of plasma inflow that took place in the distant past ; because there was no continuing accretion , the energy output could be attributed unambiguously to the black hole s rotation . in our simulation , the magnetic field is a direct result of on - going accretion . while the proximate energy source for the jet is the black hole s rotation , accretion replenishes both the black hole s mass and angular momentum , and whether the rotational energy of the black hole actually decreases depends on details such as the radiative efficiency and , possibly , the accretion of photons ( krolik 2001 ; cf . thorne 1974 ) . in our @xmath82 simulation , the net angular momentum accreted is so small that , for reasonable values of the radiative efficiency , the system is very near the edge of an actual decrease in rotational kinetic energy . even if the black hole s rotational energy does not decrease , there can nevertheless be a significant increase in the efficiency of accretion . we find that for rapidly rotating black holes the total power in the poynting flux jet can be comparable to the nominal accretion power . a number of other numerical studies of the generic blandford - znajek mechanism have been carried out recently . one type of simulation has been devoted to examining the idealized problem of a rotating black hole embedded in thin plasma containing a specified external magnetic field ( koide 2003 ; semenov et al . 2004 ; komissarov 2005 ) . these simulations focus on points of basic principle , such as the extent to which accretion of either matter or electromagnetic fields with negative energy - at - infinity plays a role . komissarov ( 2005 ) particularly notes that plasma effects within the ergosphere were significant early on in his simulation while the initial plasma is accreting into the hole , but that the long - term steady state mechanism resembles closely the classic blandford - znajek model . the simulations of mckinney & gammie ( 2004 ) were more similar in their focus to ours , as they too were principally concerned with the connection between continuing accretion and the electromagnetic power output of black holes . for this reason , their ( axi - symmetric ) simulations employed initial conditions resembling ours ( isolated initial gas torus containing field loops ) . they found good agreement with several aspects of the classical blandford - znajek model for slowly rotating holes , but growing differences as the spin of the hole increases and the field becomes less monopolar . that this should be so is not too surprising , as the specific predictions of the blandford - znajek model were developed on the basis of a perturbation expansion in @xmath0 . in regard to the global energy and angular momentum budgets , mckinney & gammmie s results qualitatively resemble ours . they also saw that as the hole loses energy and angular momentum electromagnetically , its total mass and angular momentum are replenished by accretion . likewise , they , too , found that the overall efficiency ( energy released to infinity per rest - mass accreted ) can be significantly enhanced by the energy carried off in the jet . mckinney ( 2005 ) expanded upon these results and proposed an analytic fitting function for the electromagnetic efficiency of the jet as a function of black hole rotation rate , suggesting that this efficiency scales @xmath174 , where @xmath175 is the rotation rate of the black hole . if the poynting flux were due simply to rotation of a magnetic dipole whose magnitude is independent of black hole rotation but @xmath176 , the efficiency would , of course , increase @xmath177 . the slightly faster dependence mckinney ( 2005 ) found suggests either that there is a mixture of a higher multipole component or that the magnitude of the magnetic dipole increases slowly with increasing black hole spin . the choice of this functional form was motivated by the hope that electromagnetic radiation in this case resembled classical dipole radiation , in which the luminosity is @xmath178 . whether this applies in the present context depends , of course , on whether dipole field geometry is a reasonable approximation and on whether the mean field strength at the horizon produced by a fixed accretion rate is independent of spin . unfortunately , for a variety of technical reasons it is difficult to compare quantitatively the results of different numerical simulations . without the inclusion of additional physics in the basic equations , there is no absolute density scale in the gas . although efficiencies are well - defined ( ratios of energies to masses within the simulation ) , one can not define an absolute accretion rate . even the comparison of efficiencies from one type of simulation to another poses problems . for example , two dimensional simulations tend to over - emphasize axisymmetric mri modes . as a result , they tend to have large accretion rates early on , followed by a rapid decline as the magnetic field and accompanying turbulence die out , as expected from the anti - dynamo theorem . thus , when computing the efficiency in a two dimensional simulation simulation , one must be careful about choosing an appropriate interval over which to average the accretion rate . a second problem is that , as discussed previously , energy can be exchanged between the electromagnetic and matter components of the outflow , so the purely electromagnetic power is a function of radius . to cross - compare different simulations , it is therefore important to use the same fiducial distance for evaluating the electromagnetic power . lastly , jet properties may depend on the vertical thickness of the accretion disk , a parameter determined by the initial temperature of the disk and the treatment of the energy equation in the simulation . the gross accretion rate in general scales @xmath179 , but we do not know how the magnetic field in the vicinity of the black hole scales with disk temperature . further simulational work will be required to determine such effects , although because the strength of the axial funnel field is determined by the accretion flow , it is a reasonable expectation that the jet power might scale with the accretion rate ( ghosh & abramowicz 1997 ) .    keeping these _ caveats _ in mind , we can compare our electromagnetic efficiency in the jet with the scaling relation proposed by mckinney ( 2005 ) by modifying his relation to use the rotation rate of our inner grid radius instead of the rotation rate of the horizon . the quantitative match between our data and mckinney s formula is not particularly good , although qualitatively we , too , see a strong increase in efficiency as black hole spin increases . our results are better described by the simple formula @xmath180 a form that describes both the high and lower spin models . of course , without any clear theory to predict the strength of the magnetic field on the event horizon relative to the mass accretion rate as a function of black hole rotation rate , one can not expect to find a general formula for total jet power .    finally , we would like to close this paper by pointing out that , although the blandford - znajek mechanism was originally thought of as a scheme for powering jets , outflows are not the only place where electromagnetic power from the black hole can go . in this paper we have concentrated on jet properties . however , preliminary analysis of the accretion flow in these simulations indicates that the poynting flux and electromagnetic angular momentum flux from the black hole into the disk can be comparable to those within the outflow . these fluxes and their consequences will be examined in subsequent work . balbus , s.  a. & hawley , j.  f. 1998 , rev . phys . , 70 , 1 blandford , r.  d. & znajek , r. 1977 , mnras , 179 , 433 blandford , r.  d. & payne , d. 1981 , mnras , 199 , 833 de villiers , j .- p . & hawley , j.  f. 2003 , apj , 589 , 458 de villiers , j .- p . , hawley , j.  f. , & krolik , j.  h. 2003 , apj , 599 , 1238 ( paper  i ) de villiers , j .- p . , hawley , j.  f. , krolik , j.  h. & hirose , s. 2005 , apj , 620 , 878 ( paper iii ) de villiers , j .- p . , staff , j. , & ouyed , r. , astro - ph 0502225 evans , c.  r. , & hawley , j.  f. , apj , 332 , 659 gammie , c.  f. 1999 , apj lett 522 , l57 gammie , c.  f. , mckinney , j.  c. , & tth , g. 2003 , apj , 589 , 444 ghosh , p. & abramowicz , m.  a. 1997 , mnras , 292 , 887 hirose , s. , krolik , j.  h. , de villiers , j.  p. , & hawley , j.  f. 2004 , apj , 606 , 1083 ( paper  ii ) kato , y. , mineshige , s. , & shibata , k. 2004 , apj , 605 , 307 koide , s. 2003 , phys rev d , 67 , 104010 komissarov , s.  s. 2004 , mnras , 350 , 1431 komissarov , s.  s. 2005 , mnras , 359 , 801 krolik , j.  h. 1999 , apj lett 515 , l73 krolik , j.  h. 2001 , in _ explosive phenomena in astrophysical compact objects _ , i. yi and m. rho , eds . ( aip : new york ) , p. 10 krolik , j.h . , hawley , j.f . & hirose , s. 2005 , apj 622 , 1008 ( paper iv ) livio , m. , ogilvie , g.  i. , & pringle , j.  e. 1999 , apj , 512 , 100 lynden - bell , d. 2003 , mnras 341 , 1360 mckinney , j.  c. 2005 , apj , 630 , l5 mckinney , j.  c. , & gammie , c.  f. 2004 , apj 611 , 977 novikov , i.d . & thorne , k.s . 1973 , in black holes : les astres occlus , eds . c. de witt & b. de witt ( new york : gordon & breach ) , 344 phinney , e.s . 2003 , unpublished cambridge university ph.d . thesis punsly , b. , & coroniti , f.  v. 1990 , apj , 354 , 583 semenov , v. , dyadechkin , s. , & punsly , b. 2004 , science , 305 , 978 shibata , k. & uchida , y. 1985 , pasj , 37 , 31 stone , j.  m. , & norman , m.  l. 1992a , apjs , 80 , 753 stone , j.  m. , & norman , m.  l. 1992b , apjs , 80 , 791 thorne , k.  s. 1974 , apj , 191 , 507    lrrrrrrr kdr & -0.9 & 1.44 & 1.503 & 10 . & -0.287 & 8.72 & 4.17 + kd0c & 0.0 & 2.00 & 2.104 & 10 . & 0.0 & 6.00 & 3.46 + kdib & 0.5 & 1.86 & 1.904 & 10 . & 0.127 & 4.23 & 2.90 + kdpg & 0.9 & 1.44 & 1.503 & 10 . & 0.289 & 2.32 & 2.10 + kdg & 0.93 & 1.37 & 1.458 & 6 . & 0.306 & 2.10 & 1.98 + kdh & 0.95 & 1.31 & 1.403 & 6 . & 0.326 & 1.94 & 1.89 + kdja & 0.99 & 1.14 & 1.203 & 6 . & 0.406 & 1.45 & 1.57 +    lrrrrr kdr & -0.90 & 195.6 & 22.1 & 0.77 & 0.035 + kd0c & 0.00 & 156.3 & 22.2 & 0.11 & 0.005 + kdib & 0.50 & 234.8 & 20.6 & 0.76 & 0.037 + kdpg & 0.90 & 290.5 & 19.2 & 1.71 & 0.089 + kdg & 0.93 & 319.0 & 21.8 & 1.72 & 0.079 + kdh & 0.95 & 339.2 & 20.3 & 1.72 & 0.085 + kdj & 0.99 & 382.5 & 15.5 & 3.66 & 0.237 +    lrrrrr kdr & -0.90 & -82.7 & -4.8 & 3.15 & -2.65 + kd0c & 0.00 & -72.4 & 1.4 & 0.31 & 0.14 + kdib & 0.50 & -57.0 & 2.6 & 1.40 & 2.10 + kdpg & 0.90 & -42.9 & 7.5 & 2.26 & 6.96 + kdg & 0.93 & -46.0 & 11.7 & 5.44 & 6.36 + kdh & 0.95 & -42.2 & 16.8 & 5.68 & 8.88 + kdj & 0.99 & -28.7 & 26.4 & 14.3 & 12.8 +    lrrrrrrrr kdr & -0.90 & -20.8 & 0.41 & 2.71 & 0.088 & 0.509 & 0.023 & 0.039 + kd0c & 0.00 & -20.6 & -0.02 & 0.16 & 0.0022 & 0.007 & @xmath181&0.057 + kdib & 0.50 & -21.7 & 0.10 & 2.06 & 0.063 & 0.129 & 0.0063 & 0.081 + kdpg & 0.90 & -21.8 & 0.88 & 5.89 & 0.22 & 0.892 & 0.046 & 0.155 + kdg & 0.93 & -19.8 & 1.37 & 3.13 & 0.065 & 0.824 & 0.038 & 0.173 + kdh & 0.95 & -16.9 & 2.79 & 4.26 & 0.13 & 1.46 & 0.072 & 0.190 + kdj & 0.99 & -9.9 & 6.86 & 9.94 & 0.41 & 3.28 & 0.21 & 0.264 +","summary":"we compute a series of three - dimensional general relativistic magnetohydrodynamic simulations of accretion flows in the kerr metric to investigate the properties of the unbound outflows that result . the overall strength of these outflows increases sharply with increasing black hole rotation rate , but a number of generic features are found in all cases . these fields carry an outward - going poynting flux whose immediate energy source is the rotating spacetime of the kerr black hole . when the spin parameter of the black hole exceeds , the energy carried to infinity by these outflows can be comparable to the nominal radiative efficiency predicted in the novikov - thorne model .","abstract":"we compute a series of three - dimensional general relativistic magnetohydrodynamic simulations of accretion flows in the kerr metric to investigate the properties of the unbound outflows that result . the overall strength of these outflows increases sharply with increasing black hole rotation rate , but a number of generic features are found in all cases . the mass in the outflow is concentrated in a hollow cone whose opening angle is largely determined by the effective potential for matter orbiting with angular momentum comparable to that of the innermost stable circular orbit . the dominant force accelerating the matter outward comes from the pressure of the accretion disk s corona . the principal element that shapes the outflow is therefore the centrifugal barrier preventing accreting matter from coming close to the rotation axis . inside the centrifugal barrier , the cone contains very little matter and is dominated by electromagnetic fields . the magnetic fieldlines inside the cone rotate at a rate tied closely to the rotation of the black hole , even when the black hole spins in a sense opposite to the rotation of the accretion flow . these fields carry an outward - going poynting flux whose immediate energy source is the rotating spacetime of the kerr black hole . when the spin parameter of the black hole exceeds , the energy carried to infinity by these outflows can be comparable to the nominal radiative efficiency predicted in the novikov - thorne model . similarly , the expelled angular momentum can be comparable to that accreted by the black hole . both the inner electromagnetic part and the outer matter part can contribute in significant fashion to the energy and angular momentum of the outflow ."}
{"article_id":"astro-ph0208153","section_id":"i","document":"the x - ray background ( xrb ) was discovered before the cosmic microwave background ( cmb ) , but only now is its origin being fully understood . the hard ( @xmath9 ) xrb has been nearly completely resolved into individual sources ; most of these are active galactic nuclei ( agn ) , but there is a minor contribution from the hot , intergalactic medium in rich clusters of galaxies ( rosati et al . 2002 ; cowie et al . 2002 ; & mushotzky et al . in addition , the spectra of these faint x - ray sources are consistent with that of the `` diffuse '' xrb . if current models of the luminosity functions and evolution of these sources are reasonably correct , then the xrb arises from sources in the redshift range @xmath10 , making them an important probe of density fluctuations intermediate between relatively nearby galaxy surveys ( @xmath11 ) and the cmb ( @xmath12 ) . while there have been several attempts to measure large scale , correlated fluctuations in the hard xrb , these have only yielded upper limits or , at best , marginal detections ( e.g. barcons et al . 2000 , treyer et al . 1998 and references cited therein ) . on small scales , a recent correlation analysis of 159 sources in the chandra deep field south survey detected significant correlations for separations out to @xmath13 ( giacconi et al . ( at the survey flux level , these sources comprise roughly two thirds of the hard xrb . ) on much larger scales , a recent analysis by scharf et al . ( 2000 ) claims a significant detection of large - scale harmonic structure in the xrb with spherical harmonic order @xmath14 corresponding to structures on angular scales of @xmath15 the auto - correlation results we describe here complement this analysis , indicating clustering on angular scales of @xmath16 to @xmath17 , corresponding to harmonic order of @xmath18 . however , all three detections have relatively low signal to noise and require independent confirmation . the dipole moment of the xrb has received particular attention , primarily because of its relation to the dipole in the cmb , which is likely due to the earth s motion with respect to the rest frame of the cmb . if this is the case , one expects a similar dipole in the xrb with an amplitude that is 3.4 times larger because of the difference in spectral indices of the two backgrounds ( boldt 1987 ) . in the x - ray literature , this dipole is widely known as the compton - getting effect ( compton & getting 1935 ) . in addition , it is quite likely that the xrb has an intrinsic dipole due to the asymmetric distribution in the local matter density that is responsible for the earth s peculiar motion in the first place . searches for both these dipoles have concentrated on the hard xrb , since at lower energies the x - ray sky is dominated by galactic structure . there have been several tentative detections of the x - ray dipole ( e.g. scharf et al . ( 2000 ) ) , but these have large uncertainties . a firm detection of an intrinsic dipole or even an upper limit on its presence would provide an important constraint on the inhomogeneity of the local distribution of matter via a less often used tracer of mass and a concomitant constraint on cosmological models ( e.g. , lahav , piran & treyer 1997 ) . this paper is organized as follows . in section  2 we describe the hard x - ray map used in the analysis , the determination of its effective beam size , and cuts made to remove the foreground contaminants . in section  3 , we describe the remaining large scale structures in the map and the determination of their amplitudes . the dipole is of particular interest , and is the topic of section  4 . the correlation function of the residual map and its implications for intrinsic correlations are discussed in section  5 . in section  6 , we compare our results to previous observations and discuss the cosmological implications of these results in  7 .","summary":"if current agn models of the hard xrb are reasonable and the cosmological constant - cold dark matter ( ) cosmology is correct , this clustering implies an x - ray bias factor of . combined with the absence of a correlation between the xrb and the cosmic microwave background ( cmb ) finally , we marginally detect the dipole moment of the diffuse xrb and find it to be consistent with the dipole due to our motion with respect to the mean rest frame of the xrb .","abstract":"a careful analysis of the full - sky map of the x - ray background ( xrb ) reveals clustering on the scale of several degrees . after removing the contribution due to beam smearing , the intrinsic clustering of the background is found to be consistent with an auto - correlation function of the form where is measured in degrees . if current agn models of the hard xrb are reasonable and the cosmological constant - cold dark matter ( ) cosmology is correct , this clustering implies an x - ray bias factor of . combined with the absence of a correlation between the xrb and the cosmic microwave background ( cmb ) , this clustering can be used to limit the presence of an integrated sachs - wolfe ( isw ) effect and thereby to constrain the value of the cosmological constant , ( 95% c.l . ) . this constraint is inconsistent with much of the parameter space currently favored by other observations . finally , we marginally detect the dipole moment of the diffuse xrb and find it to be consistent with the dipole due to our motion with respect to the mean rest frame of the xrb . the limit on the amplitude of any intrinsic dipole is at the 95 % c.l . when compared to the local bulk velocity , this limit implies a constraint on the matter density of the universe of ."}
{"article_id":"astro-ph0208153","section_id":"i","document":"a standard way to detect the clustering of sources ( or of the emission of these sources ) is to compute the auto - correlation function ( acf ) , defined by @xmath98 where the sum is over all pairs of pixels , @xmath99 , separated by an angle @xmath2 , @xmath66 is the intensity of the @xmath100 pixel , @xmath101 is the mean intensity , and @xmath102 is the number of pairs of pixels separated by @xmath2 . figure [ fig : acf ] shows the acf of the residual map after being corrected with the 8-parameter fit and for photon shot noise in the @xmath103 bin . the error bars are highly correlated and were determined from monte carlo trials in which the pixel intensity distribution was assumed to be gaussian with the same acf as in the figure . there is essentially no significant structure for @xmath104 once local structures have been removed , as is evident in figures [ fig : acf ] , [ fig : resid ] , and [ fig : intrin ] . it is clear from figure [ fig : acf ] that the residuals of map a possess significant correlated structure . it must be determined how much , if any , is due to clustering in the xrb and how much is simply due to smearing by the psf of the map . it is straightforward to show that an uncorrelated signal smeared by a gaussian psf , @xmath105 , results in an acf of the form @xmath106 where @xmath107 is the gaussian width of the psf in figure [ fig : psf ] ( @xmath108 ) the dashed curve in figure [ fig : acf ] is essentially this functional form , modified slightly to take into account the pixelization . in the plot , its amplitude has been forced to agree with @xmath103 data point , while a maximum likelihood fit results in an amplitude about 5% lower ( a consequence of the correlated noise ) . for @xmath109 , the acf of the data clearly exceeds that accountable by beam smearing and this excess is even more pronounced with the maximum likelihood fit . the reduced @xmath64 for the fit to the first eight data points ( @xmath110 ) is @xmath111 for six degrees of freedom which is another measure of the excess structure between 3 and 9 degrees . note , this is a two parameter fit since the photon shot noise ( which occurs only at @xmath103 ) is also one of the parameters . while it is apparent that there is some intrinsic correlation in the x - ray background , it can not be estimated by the residual to the above two parameter fit since that overestimates the contribution of beam smearing in order to minimize @xmath64 . instead , we also include in the fit a form for the intrinsic correlation and find its amplitude as well . since the signal to noise is too small to allow a detailed model of the intrinsic clustering , we chose to model it with a simple power - law @xmath112 . this form provides an acceptable fit to the acf of both radio and x - ray surveys on somewhat smaller angular scales ( cress & kamionkowski 1998 , soltan et al . 1996 , giacconi et al . this intrinsic correlation was then convolved with the psf and applied to the quadcube pixelization of the map ( e.g. , boughn 1998 ) . finally , it is important to take into account the effects of the 8-parameter fit used to remove the large - scale structure as discussed in  3 . if the x - ray background has intrinsic structure on the scale of many degrees , the 8-parameter fit will tend to remove it in order to minimize @xmath64 . since the model is composed of relatively large scale features , the greatest effect is expected for the largest angles . the significance of this effect was determined by generating monte carlo trials assuming a gaussian pixel intensity distribution with the same acf as in figure [ fig : acf ] . the 8-parameter model was then fit and each trial map was corrected accordingly . the acfs computed for these corrected maps indicate that , as expected , the value of the acf is significantly attenuated for larger angles . the attenuation factor for @xmath113 is already 0.55 and decreases rapidly for larger angles . the errors indicated in figure [ fig : acf ] were also determined from these monte carlo trials and , as mentioned above , are highly correlated . we model the auto - correlation function as a sum of three templates and fit for their best amplitude . much of the analysis parallels the discussion for the fits of large scale structure in the map , with the exception that here the number of bins is small enough that it is simple to calculate the maximum likelihood fit . again , we model the observed correlation function vector as @xmath114 , where @xmath115 is a @xmath116 matrix containing the templates for shot noise ( @xmath117 ) , beam smearing ( @xmath118 ) , and intrinsic correlations in the xrb ( @xmath119 ) . the amplitudes are given by the three element vector @xmath120 and the noise is described by the correlation matrix determined from monte carlo trials , @xmath121 . shot noise contributes only to the first bin ( zero separation ) of the acf and has amplitude given by its variance , @xmath117 . beam smearing contributes to the acf with a template that looks like the beam convolved with itself , so appears as a gaussian with a fwhm a factor of @xmath122 larger than that of the beam and has amplitude denoted as @xmath123 . finally , the intrinsic correlations are modelled as @xmath124 , which is then smoothed appropriately by the beam . its amplitude is denoted by its inferred correlation at zero separation , @xmath125 we fit using a range of indices , @xmath126 , which cover the range of theoretical models of the intrinsic correlation . both the psf template and the intrinsic template are modified to include the effects of the attenuation at large angles as discussed above .    minimizing @xmath64 with respect to the three fit parameters , @xmath120 , results in the maximum likelihood fit to the model if one assumes gaussian statistics . this assumption is reasonable by virtue of the central limit theorem since each data point consists of the combination of the signals from a great many pixels , each of which is approximately gaussian distributed . in the presence of correlated noise , @xmath64 is defined by @xmath127 it is straightforward to show that the value of the parameters that minimize @xmath64 are given by @xmath128 where @xmath129 because of the large attenuation of the acf at large angles , we chose to fit to only those data points with @xmath130 , i.e. , @xmath131 , even though there appears to be statistically significant structure out to @xmath132 . the results of the fit of the @xmath133 model to the acf of the residuals of map a are listed in table [ tab : acf ] and plotted in figure [ fig : acf ] . it is also straightforward to show that the correlation matrix of the fit parameters is given by , @xmath134 so the errors given in table [ tab : acf ] are given by @xmath135 and the normalized correlation coefficients by @xmath136 . the correlations are as expected , i.e. , @xmath119 and @xmath123 are highly correlated , while @xmath117 is relatively uncorrelated with the other two parameters .    from the results in table [ tab : acf ] it appears that intrinsic correlations in the x - ray background are detected at the 4 @xmath92 level for sources with flux levels below @xmath39 . of course , if we have not successfully eliminated sources with fluxes larger than this , then the clustering amplitude might well be artificially inflated . it was for this reason that we used the rass catalog to identify and remove additional sources with intensities @xmath137 , the result of which was map b ( see  2 ) . the fits to map b are also listed in table [ tab : acf ] . the clustering amplitude , @xmath119 , of the fits to this modified map were only @xmath138 less than that of map a , i.e. , considerably less than 1 @xmath92 . the @xmath64s of both fits are acceptable . these results are not very sensitive to the attenuation corrections . if they are removed from the model , the resulting amplitude of the fit clustering coefficient only decreases by @xmath139 , less than @xmath140 . it should be noted that the corrections were relatively small ( an average attenuation factor of 0.83 ranging from 1.0 at @xmath141 to 0.55 for @xmath113 ) and in all cases , the attenuation was less than the error bar of the corresponding data point . if data points with @xmath142 are included , the fits become more sensitive to the attenuation corrections which are , in turn , quite sensitive to the 8-parameter fit .     a & 7.71 @xmath143 0.15 & 8.63 @xmath143 0.59 & 2.64 @xmath143 0.65 & 2.3/5 & -0.19 & -0.04 & -0.83 + b & 7.57 @xmath143 0.15 & 8.22 @xmath143 0.59 & 2.33 @xmath143 0.65 & 3.6/5 & -0.19 & -0.04 & -0.83 +    fit model parameters for map a with 55% sky coverage and map b with 52% sky coverage after removing additional rosat sources ( see  2 ) . the intrinsic fluctuations are modelled as @xmath144 . figure [ fig : resid ] is a plot of the residuals of the fit to the acf of map a for @xmath145 and of the uncorrected acf from @xmath17 to @xmath146 . the vertical scale is the same as for figure [ fig : acf ] . the _ rms _ of these 140 data points is @xmath147 and it is clear that there is very little residual structure at levels exceeding this value . the observed correlation function for @xmath148 in figure [ fig : resid ] is entirely consistent with the noise levels determined from the monte carlo simulations : the _ rms _ of @xmath149 is 1.03 , indicating that there is no evidence for intrinsic fluctuations on these scales . we also take this as an indication that the errors are reasonably well characterized by the monte carlo calculation . the variance of the photon shot noise , @xmath150 , is consistent with that expected from photon counting statistics only ( jahoda 2001 ) . it should be noted that not only the shape but the amplitude of the beam smearing contribution , @xmath118 , can be computed from source counts as a function of @xmath26 flux . we will argue in  6 that , while our fitted value is consistent with current number counts , the latter are not yet accurate enough to correct the data . figure [ fig : intrin ] shows the model of the intrinsic clustering , @xmath119 , compared to the data with both the shot noise and psf component removed . the model curve is not plotted beyond @xmath113 since the attenuation factor due to the 8-parameter fit corrections are large and uncertain at larger angles . the amplitude of @xmath119 is sensitive to the exponent in the assumed power law for the intrinsic correlations . for example , the fit amplitude for a @xmath151 power law the amplitude is a factor of @xmath152 larger than for a @xmath153 power law . however , for a range of fits with @xmath154 , the values of @xmath155 at @xmath156 are all within @xmath157 of each other . therefore , we chose to normalize the x - ray acf at @xmath158 when comparing to cosmological models ( see  7.1 ) . the @xmath159 are reasonable for all these fits . the bottom line is that there is fairly strong evidence for intrinsic clustering on these angular scales at the level of @xmath160 ( see  6.1 ) . while the exponent is @xmath161 , it is not strongly constrained . the implications of the intrinsic clustering of the x - ray background will be discussed in  7 .","summary":", the intrinsic clustering of the background is found to be consistent with an auto - correlation function of the form where is measured in degrees . this constraint is inconsistent with much of the parameter space currently favored by other observations .","abstract":"a careful analysis of the full - sky map of the x - ray background ( xrb ) reveals clustering on the scale of several degrees . after removing the contribution due to beam smearing , the intrinsic clustering of the background is found to be consistent with an auto - correlation function of the form where is measured in degrees . if current agn models of the hard xrb are reasonable and the cosmological constant - cold dark matter ( ) cosmology is correct , this clustering implies an x - ray bias factor of . combined with the absence of a correlation between the xrb and the cosmic microwave background ( cmb ) , this clustering can be used to limit the presence of an integrated sachs - wolfe ( isw ) effect and thereby to constrain the value of the cosmological constant , ( 95% c.l . ) . this constraint is inconsistent with much of the parameter space currently favored by other observations . finally , we marginally detect the dipole moment of the diffuse xrb and find it to be consistent with the dipole due to our motion with respect to the mean rest frame of the xrb . the limit on the amplitude of any intrinsic dipole is at the 95 % c.l . when compared to the local bulk velocity , this limit implies a constraint on the matter density of the universe of ."}
{"article_id":"astro-ph0703193","section_id":"i","document":"in a recent paper @xcite reported interferometric observations of the mercury - manganese star  ( hd  145389 , hr  6023 , hip  79101 , @xmath3 , @xmath4 , spectral type b9:p(hgmn ) , @xmath5 ) , which is a binary star . this object belongs to a class of peculiar non - magnetic b - type stars that show abundance anomalies of several elements , some of which ( such as hg and mn ) can be enhanced by orders of magnitude @xcite . depletions of other elements are seen as well . these anomalies are thought to be produced by radiatively - driven diffusion and gravitational settling @xcite . the observations of @xcite spatially resolve the companion of  for the first time . the object had previously been known as a single - lined spectroscopic binary with a period of about 560 days @xcite and an eccentric orbit . their interferometric measurements with the navy prototype optical interferometer ( npoi ) allowed @xcite to measure the brightness of the companion and use it to estimate its spectral type . this , in turn , facilitated their detection of spectral lines of the secondary for the first time in spectra taken at the dominion astrophysical observatory . the secondary was also detected spectroscopically by @xcite . the system is therefore technically now double - lined , although as pointed out by @xcite the handful of secondary radial velocities they were able to measure with great difficulty do not provide a firm constraint on the velocity semiamplitude of that star . furthermore , they found that the combination of their high - precision interferometric orbit with the elements of the single - lined spectroscopic orbit reported by @xcite led to absolute masses for the components that are inconsistent with the spectral types . therefore , although the total mass of the binary is now fairly well known , the individual masses can not yet be determined dynamically . such basic properties of the stars are of considerable interest given the chemical peculiarities of this class of objects , which have been the subject of extensive studies of many different kinds ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . we were puzzled by this apparent inconsistency between the seemingly precise radial velocities and the astrometry , and we wondered whether other velocity measurements available in the literature might clarify the situation . in addition ,  was observed in the course of the _ hipparcos _ mission @xcite . those measurements clearly revealed the motion of the center of light due to the binary orbit , suggesting they could be used to good advantage in the determination of the individual masses . the motivation for this paper is therefore threefold : _ i ) _ to show how , in the absence of spectroscopy , the astrometric measurements from _ hipparcos _ can indeed be combined with the npoi observations of @xcite to yield reliable masses for both stars for the first time , purely astrometrically . this serves as an interesting example of the value of the _ hipparcos _ intermediate data for solving or improving binary orbits and inferring other stellar properties ; _ ii ) _ to readdress the issue of the @xcite velocities in light of the new solution . we show that those data are not really inconsistent with the astrometry , but do lack critical phase coverage and must be supplemented by other information in order to be useful ; _ iii ) _ to incorporate additional velocity measurements not previously used , in order to further strengthen the orbital solution . the final masses not only have much improved precision , but are consistent with the mass - luminosity relation as given by current stellar evolution models .","summary":"we re - examine and then incorporate existing radial - velocity measurements into the orbital solution , obtaining improved masses of  m and  m that are consistent with the theoretical mass - luminosity relation from recent stellar evolution models .","abstract":"the mercury - manganese star  is a well known spectroscopic binary that has been the subject of a recent study by , in which they resolved the companion using long - baseline interferometry . the total mass of the binary is now fairly well established , but the combination of the spectroscopy with the astrometry has not resulted in individual masses consistent with the spectral types of the components . the motion of the center of light of  was clearly detected by the _ hipparcos _ satellite . here we make use of the _ hipparcos _ intermediate data ( ` abscissa residuals ' ) and show that by combining them in an optimal fashion with the interferometry the individual masses can be obtained reliably using only astrometry . we re - examine and then incorporate existing radial - velocity measurements into the orbital solution , obtaining improved masses of  m and  m that are consistent with the theoretical mass - luminosity relation from recent stellar evolution models . these mass determinations provide important information for the understanding of the nature of this peculiar class of stars ."}
{"article_id":"astro-ph0703193","section_id":"c","document":"the orbital solutions in  [ sec : orbit ] and  [ sec : neworbit ] provide an interesting illustration of the usefulness of the _ hipparcos _ intermediate data as a valuable complement to other astrometric or spectroscopic observations . the abscissa residuals from the satellite mission are publicly available for many thousands of binary stars distributed over the entire sky , and although a number of studies have appeared over the past few years that do take advantage of them , this is largely still an underutilized resource . in the case of the hgmn star  the _ hipparcos _ measurements are key to establishing the individual masses of the components , the most fundamental of the stellar properties . we find good agreement between these masses and the magnitudes and colors of the system and current stellar evolution models , suggesting the bulk composition of the object is near solar . although the faint secondary has now been detected , both interferometrically and spectroscopically , an accurate measurement of its radial velocity over the orbital cycle should help considerably for reducing the mass uncertainties , which are currently at the 8% and 4% level for the primary and secondary , respectively . we thank the referee for a number of helpful comments on the original manuscript . this work was partially supported by nsf grant ast-0406183 and nasa s massif sim key project ( blf57 - 04 ) . this research has made use of the simbad database , operated at cds , strasbourg , france , and of nasa s astrophysics data system abstract service .","summary":"we make use of the _ hipparcos _ intermediate data ( ` abscissa residuals ' ) and show that by combining them in an optimal fashion with the interferometry the individual masses can be obtained reliably using only astrometry .","abstract":"the mercury - manganese star  is a well known spectroscopic binary that has been the subject of a recent study by , in which they resolved the companion using long - baseline interferometry . the total mass of the binary is now fairly well established , but the combination of the spectroscopy with the astrometry has not resulted in individual masses consistent with the spectral types of the components . the motion of the center of light of  was clearly detected by the _ hipparcos _ satellite . here we make use of the _ hipparcos _ intermediate data ( ` abscissa residuals ' ) and show that by combining them in an optimal fashion with the interferometry the individual masses can be obtained reliably using only astrometry . we re - examine and then incorporate existing radial - velocity measurements into the orbital solution , obtaining improved masses of  m and  m that are consistent with the theoretical mass - luminosity relation from recent stellar evolution models . these mass determinations provide important information for the understanding of the nature of this peculiar class of stars ."}
{"article_id":"1501.06549","section_id":"i","document":"the macroscopic transport of solutes in porous media depends critically on microscopic features such as the structure of the porous matrix and the nature of the interactions between the solid and liquid phases . on the other hand , the complexity of the microscopic problem means that in practice it is often desirable to obtain a macroscopic effective - medium equation from which the macroscopic transport can be obtained directly . this idea of upscaling is ubiquitous in many sciences . in particular , diffusive transport in heterogeneous media occurs in hydrogeology ( aquifers , groundwater @xcite ) , contaminant transport ( water filtration with membranes ) , lithium - ion batteries @xcite , and biological applications such as porous biofilms @xcite and intracellular transport @xcite . efforts to find the form of the macroscopic equation and estimate the effective properties of the medium date back at least to the 19th century , when maxwell gives an approximate expression for the effective conductivity of a heterogeneous medium comprising small ( i.e.  well - separated ) spheres of one material distributed in another @xcite . since then a great variety of approaches have been developed to obtain such upscaled equations @xcite . a usual starting point is to suppose that the solute undergoes a simple diffusion process in the void or fluid phase @xmath0 of the porous medium @xmath1 so that the evolution of the concentration of particles @xmath2 is described by    [ origin ] @xmath3 where @xmath4 is the solid - fluid interface and @xmath5 is the outward unit normal to @xmath0 . the fraction of space available to the diffusing species is the porosity @xmath6 ( the complement of @xmath0 ) then the volume fraction of solid is @xmath7 . when the microstructure is fine we would like to be able to use an effective transport equation such as @xmath8 , \\qquad { \\bf x } \\in \\omega \\equiv \\omega_v \\cup \\omega_s,\\ ] ] where @xmath9 is an effective diffusion coefficient , which will depend both on @xmath10 and the geometry of @xmath0 . here @xmath11 is the homogenized solute concentration ( whose definition will be made precise in the next section ) . note that @xmath11 is defined throughout the material , whereas @xmath12 is defined only in the fluid region . in general , the homogenization procedure will depend on both the porous medium structure and the transport processes within the medium . a large number of homogenization techniques have been developed over the years @xcite . these can be divided into two very broad categories , deterministic and stochastic techniques . deterministic techniques include techniques such as volume averaging @xcite , multiple scales @xcite and the generalized taylor   brenner method of moments @xcite . here the averaging relies on the separation of scales between the microstructure and the macroscopic material , and is a local spatial average . many techniques , included the method of multiple scales and the generalized taylor  aris  brenner method of moments , assume some periodicity in the microstructure . in this case , the microscopic lengthscale measures variations within a period cell and the macroscopic lengthscale measures variations within the macroscopic region of interest . more specifically , the method of multiple scales constructs a family of problems involving the ratio @xmath13 between these two lengthscales and uses asymptotic expansions in @xmath13 to study systematically the convergence as @xmath14 to a limit problem . since @xmath13 is assumed to be small , the resulting family of problems contains rapidly oscillating ( periodic ) coefficients . thanks to its systematic nature , this method has formed the basis of a whole field in mathematics known as mathematical homogenisation @xcite .    in terms of the example above , deterministic approaches upscale from to by assuming a particular given geometry of the solid matrix @xmath15 from which the effective coefficient @xmath9 can be computed . for example , it is common to consider either very simple periodic structures [ such as the array of spheres depicted in figure  [ fig : det_ran](a ) ] or to consider a disordered unit cell representative of the material as a whole , which is then extended periodically @xcite . in the case of a periodic array of spherical inclusions , @xmath9 can be computed exactly using rayleigh s multipole method @xcite , leading to an infinite system of algebraic equations . more complex microscopic structures can be dealt with via multiple scales ( see for example @xcite ) or volume averaging @xcite . although these two methods are based on different underlying principles , they result in the same averaged equations @xcite . these equations contain effective parameters ( such as @xmath9 ) which depend on the microscale and are evaluated using the solution of a _ cell problem _ in the periodic unit cell ( in multiple scales ) or the solution of a closure problem in a _ representative elementary volume _ ( in volume averaging ) . for a review of the application of the method of volume averaging in ordered and disordered porous media we refer the reader to @xcite . the assumption of periodicity can be seen as artificial or too idealistic when modelling real heterogeneous media . as a result , an obvious progression came in the form of homogenization techniques for random media , in an attempt to reflect the uncertainty caused by the high degree of heterogeneity as well as the lack of experimental data @xcite . in its simplest setting , this can be seen as replacing the periodicity assumption in the multiple scales method by stochastic periodicity ( or statistical homogeneity ) @xcite . in particular , this means that the problem now contains random coefficients rather than periodic ones , and the homogenization consists of taking an averaging window of size @xmath13 large enough so that ergodicity holds , that is , that a spatial average is equivalent to an ensemble average . a rigorous derivation of the limit problem as @xmath14 is quite challenging in general , but has been done in specific cases such as steady heat conduction @xcite or , in a discrete setting , in a random conductance model for a network of resistors @xcite . in natural porous media such as soils and aquifers , the problem to be upscaled is usually more challenging than the cases above , as often one must consider the coupled problems for groundwater flow and solute transport . stochastic approaches developed in the context of hydrology include the works of cushman @xcite , dagan @xcite , and gelhar @xcite . a common starting point is to take the hydraulic conductivity to be a random field , for example assuming it has a lognormal probability density function @xcite ( p.  164 ) . in particular , this implies that the stokes velocity and the solute concentration are random fields as well . the classical approach is to linearize both the flow and the transport equations and to then take ensemble averages of the resulting problem @xcite .    in terms of the particular problem , a natural stochastic approach is to suppose that the microstructure is random and statistically homogeneous , with the effective properties arising by taking an ensemble average over different realizations of the microstructure @xcite . for example , one could assume that the solid matrix @xmath15 is composed of spherical inclusions uniformly distributed in @xmath1 with a non - overlapping constraint [ see figure  [ fig : det_ran](b ) for one sample of such configuration ] . however , it is usually very difficult to estimate the effective properties from such a description , since doing so requires an infinite set of statistical correlation functions , which are generally never known @xcite . brown @xcite provided a series form of the effective constant @xmath9 ( for dielectric constants rather than diffusivities , but the problem is analogous ) and showed that the first correction term to @xmath10 depends only on the solid volume fraction @xmath16 , but that all other terms require knowledge of the statistical distribution of the solid matrix . thus the best estimate one can obtain knowing only @xmath16 and @xmath10 is equivalent to maxwell s formula , namely @xmath17 . in the current notation . thus , the expression reported in @xcite for example is @xmath18 . the two definitions result in the same macroscopic equation for homogeneous media , but not when the volume fraction varies on the macroscale , as we will see later . ] as a result , subsequent work by hashin and shtrikman @xcite focused on using variational methods to obtain lower and upper bounds on @xmath9 as a function of @xmath16 , independent of the statistics of the medium . prager @xcite developed a method to introduce two- and three - particle correlation functions into such bounds . a specific application of these variational principles in the case of a porous medium formed by uniformly distributed spheres without non - overlapping constraints was used by weissberg @xcite , who obtained the upper bound @xmath19 . in @xcite . ] fig1_1a ( -10,90)(a )    fig1_1b ( -10,90)(b )    it is not completely clear which of these approaches is preferable in any given situation , or how they compare to each other . as pointed out in @xcite , enforced periodic structures can have an important influence on the homogenized model in low - porosity systems . on the other hand , the variational approaches used by brown @xcite or weissberg @xcite are very general and do not require any constraints on scale or periodicity . they would be applicable also for so - called non - homogenizable media , in which there is no clear separation of scales between micro and macrostructures . one situation in which all the approaches discussed above need to be rethought is that in which there is macroscopic inhomogeneity in the material as well as microscopic inhomogeneity . such a situation would arise in a material in which there is a non - uniform porosity on the macroscale . it might be thought that since the porosity is varying slowly it is locally constant , and the standard formulae can be used albeit with a cell problem ( and hence diffusivity ) which varies on the slow scale . however , we will see that this is not the case . despite its acknowledged importance in many physical systems ( for example , in the design of membranes for water filtration , in groundwater flow systems @xcite , and in portland cement @xcite ) , non - uniform porosity has rarely been accounted for in models and the effect on diffusion is not well understood . one exception is @xcite , which uses the method of volume averaging in systems with gradients in porosity . worryingly , though , they find that the effective diffusivity , the porosity , and its gradient are highly dependent upon the location of the centroid of the representative elementary volume .    in this paper we derive the effective transport equation for diffusion in a porous medium with gradients in porosity . we consider two types of porous media , namely an ordered medium with quasi - periodic inclusions and a disordered medium composed of randomly ( but not uniformly ) distributed inclusions . the homogenization procedures for each of these media are fundamentally different . thus , the purpose of the paper is twofold : first , to study how macroscopic changes in the microstructure affect the homogenized equation and , second , to compare the two different approaches used to model diffusion in porous media . we consider a simple diffusion process in the void or liquid phase , where the solute has a constant diffusion coefficient @xmath10 . the solid phase is composed of spherical and non - overlapping inclusions , which are impenetrable by the solute ( that is , the diffusion coefficient is zero in the solid phase ) . for most of this paper we consider a fixed solid matrix ( although we later remove this assumption in the stochastic approach to consider moving obstructions ) . we obtain the effective diffusion coefficient as a function of the microstructure of the medium , and in particular the porosity . we find that a non - uniform porosity on the macroscale results in an advection term in the homogenized equation , as found by @xcite . this term accounts for the biasing of the motion of solute particles towards regions of high porosity . we also show that our two approaches , although very different , can be reconciled to give the same macroscopic equation in the limit of small solid volume fraction .    the article is organized as follows . in  [ sec : determ ] we consider a deterministic approach and we apply the method of multiple scales to derive the effective transport equation in ordered porous media . we show how the method can be adapted to non - uniform porosity and non - periodic structures , providing they are locally periodic . we then consider the same problem for stochastic porous media ( disordered and non - periodic ) in  [ sec : stoch ] , and derive an equivalent effective equation from the fokker  planck description of the microstructure . in  [ sec : comparision ] we present two numerical studies comparing the two approaches , both with each other and with the exact solution of the corresponding microscopic problems . finally , in  [ sec : discussion ] , we present our conclusions .","summary":"two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented . the first is a deterministic approach based on the method of multiple scales ; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions .","abstract":"the problem of diffusion in a porous medium with a spatially varying porosity is considered . the particular microstructure analyzed comprises a collection of impenetrable spheres , though the methods developed are general . two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented . the first is a deterministic approach based on the method of multiple scales ; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions . we compare the two approaches , and we show good agreement between them in a number of example configurations .    diffusion , porous media , hard spheres , multiple scales , variable porosity .    35b27 , 35q84 , 60j70 , 82c31"}
{"article_id":"1501.06549","section_id":"m","document":"in this section we compare the macroscopic models for diffusion in a porous medium of variable porosity which we derived via multiple scales in  [ sec : determ ] and using the fokker  planck approach in  [ sec : stoch ] . as we mentioned above , the fokker  planck approach can only be systematically reduced to a low - dimensional effective diffusion equation in the limit of small volume fraction . we observed in figure  [ fig:23d_diag ] that the multiple - scales - derived diffusion coefficient seems numerically to asymptote to the fokker  planck - derived diffusion coefficient in this limit . in the next section we show that this is indeed the case , by considering the asymptotic solution to the multiple - scales model in the limit of low obstacle volume fraction @xmath16 . we then compare our effective equations with each other and with direct numerical simulations in a variety of test problems . we consider the model in the limit of low volume fraction @xmath16 . this means that the local volume fraction @xmath221 is also small ( almost everywhere ) , corresponding to small relative obstacle radius @xmath222 . in this limit , the cell problem can be solved explicitly . since @xmath42 , and hence @xmath223 , are constants as far as the cell problem is concerned , we can look for an asymptotic solution to in terms of the small parameter @xmath223 . consider , say , the first component of the vector function @xmath224 , which satisfies    [ cellproblem_1 ] @xmath225    we use the method of matched asymptotic expansions , supposing that the unit cell @xmath226 can be divided into two regions : an inner region in which , and an outer region in which @xmath227 . in the inner region , we set @xmath228 and define @xmath229 to give    [ cellproblem_as2 ] @xmath230    with a matching condition as @xmath231 . expanding @xmath232 gives that the leading - order inner solution @xmath233 is simply a constant in @xmath234 , whence the leading - order outer solution is also constant . at first order in @xmath235 we find    [ cellproblem_as3 ] @xmath236    using polar ( @xmath108 ) or spherical ( @xmath110 ) coordinates , we look for a solution to of the form @xmath237 ( @xmath108 ) or @xmath238 ( @xmath110 ) , where @xmath239 when @xmath108 and @xmath240 when @xmath110 . we find that @xmath241}{(d-1)r^{d-1}},\\ ] ] for an unknown function @xmath242 . since the leading - order outer solution is constant in @xmath44 , matching gives @xmath243 . thus @xmath244 thus the first non - constant term in the outer expansion is @xmath245 . matching with the outer solution gives that @xmath246 as @xmath247 . we can now use this asymptotic behavior to determine the outer solution at this order . however , it is possible to determine the effective diffusion coefficient , which is our primary aim , with the information we already have . since the integrals we have to evaluate in are all derivatives with respect to some component of @xmath44 , by integrating with respect to this component first we turn the volume integral over the unit cell @xmath83 into surface integrals over the exterior periodic boundaries and the interior boundary with the solid obstacle . the contributions from the exterior boundaries cancel due to periodicity , while on the interior boundary we can use the asymptotic solution . the result is @xmath248 thus as @xmath249 , @xmath9 is a scalar multiple of the identity , equal to    @xmath250    since @xmath251 at leading order . as expected , this result agrees with the asymptotic value obtained with the fokker  planck approach .    the drift term in the multiple - scales homogenized equation is @xmath252 . using , we obtain @xmath253 this asymptotic value also agrees with the drift obtained in the reduced fokker  planck model ; see . finally we comment that the nature of the calculation above makes it clear that the configuration of the inclusions does not affect the diffusion coefficient at this order , since the dominant contribution comes from the solution of the cell problem in the inner region , which has no information about the position of the inclusion(s ) in the unit cell . the aim of this section is to compare the two models for diffusion in porous media against each other as well as against numerical simulations for the full problem and stochastic simulations of the particle system . first , we consider the mean squared displacement of particles diffusing in two homogeneous porous media with the same porosity , namely a deterministic structure with a square lattice of obstacles and a random structure with obstacle configurations drawn from a uniform distribution with non - overlapping constraints . second , we consider the spreading out of a localized initial concentration of particles in porous media with gradients in porosity . again we consider locally periodic structures accessible to the multiple - scales analysis and random structures with the same ( ensemble ) average porosity . all the simulations are made in a two - dimensional unit square domain @xmath1 with @xmath160 point mobile particles and @xmath27 hard - disk obstacles of constant radius @xmath35 . when the porous structure is random with probability law @xmath254 , a new configuration of obstacles is generated for every new run .      in this section we compare the diffusion coefficient computed from simulations of the discrete stochastic system to the effective diffusion coefficient obtained in the previous sections , either from multiple scales @xmath9 if the obstacles are placed in a regular structure , or from the fokker  planck description @xmath107 if the obstacles are randomly distributed with density @xmath254 . in particular , we consider two porous media with uniform porosity @xmath16 ( so that @xmath255 so that the drift is @xmath256 ) and the same number @xmath27 of obstacles : ( i ) a square lattice configuration , and ( ii ) a random uniform configuration of obstacles with non - overlapping constraints . the numerical value of the diffusion coefficient is obtained from the mean - square displacement , using the relation @xmath257 as @xmath258 . to evaluate the mean - square displacement , we run @xmath259 runs with @xmath260 mobile particles , and compute @xmath261 . here @xmath262 is the position of the @xmath77th particle in the @xmath263 realization at time @xmath163 . point particles , this is equivalent to averaging over particle trajectories and regenerating the solid matrix every @xmath160 realizations ) . ] our stochastic simulations are performed integrating eq . using an euler  maruyama scheme , with reflective boundary conditions between mobile particles and obstacles ( @xmath264 ) and periodic boundary conditions on the outer boundary ( @xmath265 ) . the reflective boundary conditions between the mobile point particles and the obstacles are implemented similar to as in @xcite , namely , the distance that a particle has travelled ( illegally ) inside an obstacle is reflected back into the domain @xmath0 . to do that , we compute the point on the obstacle boundary where the particle penetrated , and compute a particle  wall elastic collision on that point . the integration timestep @xmath266 must be chosen carefully so that virtually no collisions are missed . a convergence study is shown in the appendix and based on this , we have used @xmath267 in the results presented below .    we perform experiments with the periodic and random porous media at porosities @xmath268 and 30% . from figure  [ fig:23d_diag](a ) , we expect differences between the random and periodic porous media to become apparent from @xmath269 . the question is whether the discrepancy between @xmath9 and @xmath107 is real ( due to the structure ) or artificial ( due to the nature of the asymptotic approximation in obtaining @xmath107 ) . we plot the mean - square displacement @xmath270 against time in figure  [ fig : msd_simul](a ) for the square lattice ( solid lines with error bars ) and the random structure ( dashed lines with crosses and error bars ) . ( the error bars indicate the 95% confidence interval , or @xmath271sd values , of each data point , and are barely discernible . ) as expected , @xmath272 increases linearly with time , with a slope that decreases with @xmath16 . = .8 cm [ ] [ ] [ ] @xmath163 [ ] [ ] [ ] @xmath16 [ ] [ ] [ ] @xmath273 [ ] [ ] [ ] @xmath274 [ ] [ ] [ ] @xmath275 [ ] [ ] [ ] @xmath273 [ ] [ ] [ ] @xmath274 [ ] [ ] [ ] @xmath275 [ ] [ ] [ ] @xmath107 th . [ ] [ ] [ ] @xmath107 sim . [ ] [ ] [ ] @xmath9 th .   [ ] [ ] [ ] @xmath9 sim . [ ] [ ] [ ] @xmath272 [ ] [ ] [ ] @xmath276 [ ] [ ] [ ] ( a ) [ ] [ ] [ ] ( b ) [ ] [ ] [ ] simulation [ ] [ ] [ ] @xmath107 [ ] [ ] [ ] @xmath9 [ ] [ ] [ ] @xmath277   as a function of time @xmath163 for diffusion of point particles in the presence of obstacles . the obstacles are arranged on a square lattice ( error bars ) or uniformly distributed ( error bars with crosses ) and at volume fraction @xmath278 . the theoretical curves using @xmath9 ( eq . ) and @xmath107 ( eq . ) are shown with solid lines and dashed lines , respectively . ( b ) the same data replotted as @xmath279 , to demonstrate that by the final simulation time the numerical diffusion coefficient has converged . the data points inside the dashed black rectangle are used to compute the numerical value of diffusion . in both plots , the error bars indicate the 95% confidence interval . parameters used for the simulations are : @xmath260 , @xmath259 ( a new obstacle configuration was generated at every new run in the random case ) , @xmath267 , @xmath280 , and @xmath281 for @xmath282 respectively.,title=\"fig : \" ]   as a function of time @xmath163 for diffusion of point particles in the presence of obstacles . the obstacles are arranged on a square lattice ( error bars ) or uniformly distributed ( error bars with crosses ) and at volume fraction @xmath278 . the theoretical curves using @xmath9 ( eq . ) and @xmath107 ( eq . ) are shown with solid lines and dashed lines , respectively . ( b ) the same data replotted as @xmath279 , to demonstrate that by the final simulation time the numerical diffusion coefficient has converged . the data points inside the dashed black rectangle are used to compute the numerical value of diffusion . in both plots , the error bars indicate the 95% confidence interval . parameters used for the simulations are : @xmath260 , @xmath259 ( a new obstacle configuration was generated at every new run in the random case ) , @xmath267 , @xmath280 , and @xmath281 for @xmath282 respectively.,title=\"fig : \" ]    the diffusion coefficient is given by @xmath283 . to check that we have run the simulation for long enough and rule out any anomalous transient diffusion , in figure  [ fig : msd_simul](b ) we plot @xmath284 @xcite . this type of plot highlights any time dependence in the diffusion coefficient @xcite . we observe that , for all curves in figure  [ fig : msd_simul](b ) , the curves have slope 0 after the first @xmath285 and hence have converged . to evaluate the diffusion coefficient , we average over the last @xmath286 of each simulation ( data points marked with a dashed rectangle in figure  [ fig : msd_simul](b ) ) . from figure [ fig : msd_simul](b ) and the estimated values ( data not shown ) , we note that : ( i ) for the square lattice case , theory ( eq . , solid lines ) and simulation results ( solid error bars ) for @xmath9 agree very well , as expected since @xmath9 from is exact . ( ii ) the random media simulation results ( error bars with crosses ) agree well with the asymptotic value @xmath107 ( eq . , dashed lines ) for @xmath287 but there is a significant discrepancy for @xmath288 . ( iii ) the difference between the regular and random porous media is within the error bars for @xmath289 but becomes apparent for @xmath290 . interestingly , while the multiple - scales effective diffusion coefficient @xmath9 does a better job for the period medium ( as we might expect ) , the fokker  planck effective diffusion coefficient @xmath107 seems to do a slightly better job for the random medium . this was not at all obvious , since this coefficient is only the leading term in an expansion as @xmath291 ( while the multiple - scales coefficient is valid for all @xmath16 ) . it seems that , for a given obstacle volume fraction @xmath16 , random porous media may have a slightly lower diffusion coefficient than periodic ones . because @xmath107 is an asymptotic expansion , we can use the order of the next term to estimate the error . the next term in the asymptotic expansion of @xmath107 is @xmath292 @xcite , which gives 0.065 and 0.1459 for @xmath293 and 0.3 respectively . the discrepancies in figure  [ fig : msd_simul](b ) between the asymptotic values @xmath107 and the simulation results for @xmath293 and 0.3 are 0.0103 and 0.0257 , respectively . in other words , the effective diffusion @xmath107 does better than expected from the asymptotic error bounds .      for our second model comparison , we consider a porous medium with a non - uniform porosity . as before , we consider both a locally periodic array of obstacles of constant radius @xmath35 , and a random array of obstacles giving the same local porosity .    for the locally periodic structure we use the arrangement illustrated in figure  [ fig : trans](a ) . the obstacles have a fixed radius @xmath294 , and the average volume fraction of obstacle is . to generate a random periodic medium with the same ( ensemble ) average local porosity we need to determine the probability density function of obstacle position @xmath254 , which we have seen is related to the volume concentration of obstacles by @xmath295 this is easily found once we have determined the variable obstacle radius @xmath296 in the mapped multiple - scales domain ( shown in figure  [ fig : trans](b ) ) .    to determine @xmath296 , consider one representative cell @xmath297 centered at @xmath42 in the original domain @xmath1 . the cell @xmath298 is mapped to a square of side @xmath13 centered at @xmath151 in @xmath299 , which we denote @xmath300 . the area of @xmath298 is then @xmath301 since the volume fraction in the cell is conserved , we have @xmath302 thus knowing @xmath303 through allows us to determine both @xmath221 ( and therefore @xmath254 ) , and also @xmath304 which we need in order to solve the multiple - scales cell problem . in figure [ fig : random_s](a ) we plot the density @xmath254 corresponding to the configuration shown in figure  [ fig : trans](a ) . we see that the maximum local solid volume fraction is about 2.5 times the average solid volume fraction @xmath16 . in figure [ fig : random_s](a ) we show one realization of obstacles randomly drawn from the corresponding probability distribution , with a non - overlapping constraint . fig4_2a ( -5,75)(a )    fig4_2b ( -10,90)(b )    we suppose that at @xmath305 a drop of solute of radius @xmath35 is placed centered at @xmath306 . we have chosen @xmath307 such that the drop does not intersect with any of the obstacles , that is , @xmath308 for @xmath309 . thus the initial condition is @xmath310 for @xmath311 , and zero otherwise . of course , this initial condition does not satisfy the requirement of the multiple - scales method that it varies slowly with respect to the obstacle separation ; nevertheless we expect that it will quickly spread into a function which does .    in figure [ fig : gradient_ia ] we illustrate the time evolution of the solute density for four different models . in figure [ fig : gradient_ia](a ) we show the ( numerically calculated ) true solution for the locally periodic distribution of obstacles . in figure  [ fig : gradient_ia](c ) we show the ( numerically calculated ) true solution for one realization of the random configuration of obstacles , distributed according to the density function @xmath254 . in figure [ fig : gradient_ia](b ) we show the solution of the effective equation derived through the multiple - scales method , while in figure  [ fig : gradient_ia](d ) we show the solution of the ( intrinsic version of the ) effective equation derived through the fokker  planck approach . in each case we show the intrinsic average @xmath66 , since this allows direct comparison between the solutions of the effective equations and the solutions of the real problems . given the normalization condition on @xmath11 , and hence we identify the intrinsic average as @xmath312 , where @xmath313 . ] we see that , perhaps counterintuitively , the maximum of the solute concentration initially moves to the right , towards the region of low porosity . this is because the localized source spreads out in all directions , but spreads out more in the high porosity region . the increased diffusion in the high - porosity region lowers the concentration more , giving the impression that the solute is moving towards the low - porosity region . at least visually , the two effective models capture the behavior of the true solutions , both for the regular structure and even for a single realization of the random structure . to make the comparison a little easier , we show in figure  [ fig : cut_ui ] a slice along the line @xmath314 for the true locally periodic solution , the multiple - scales - derived solution , and the fokker  planck - derived solution . we see that the agreement is remarkably good . fig4_3a ( 0,98)(a )    fig4_3b ( 0,98)(b )    fig4_3c ( 0,98)(c )    fig4_3d ( 0,98)(d )    = .8 cm    [ l][][]@xmath163 [ ] [ ] [ ] @xmath153 [ ] [ ] [ ] mspde [ ] [ ] [ ] fppde [ ] [ ] [ ] msfull [ ] [ ] [ ] [ -90]@xmath66    while the intrinsic average @xmath66 is the natural variable to compare with a particular realization of the microstructure , the volume average @xmath11 is the natural variable to compare with an ensemble average over a random microstructure ( and is also usually the natural variable in an application of the effective equations ) . while @xmath66 converges to the uniform measure as time evolves ( as in figure  [ fig : gradient_ia ] ) , the volume average @xmath11 approaches a non - uniform density which is a multiple of the porosity . we show in figure  [ fig : gradient_va ] the evolution of the volume average @xmath11 for three models . in figure [ fig : gradient_va](a ) we show the solution of the effective equation derived through the multiple - scales method , while in figure  [ fig : gradient_va](c ) we show the solution of the effective equation derived through the fokker  planck approach . in figure [ fig : gradient_va](b ) we show average of the true solution over 100 realizations of the randomly distributed obstacles . again , visually , both models seem to do a good job of approximating the ensemble average . fig4_5a ( 0,98)(a )    fig4_5b ( 0,98)(b )    fig4_5c ( 0,98)(c )    in figure  [ fig : cuty ] we show the solutions in figure  [ fig : gradient_va ] along the strip @xmath315 $ ] for @xmath316 . in figure [ fig : cuty](a ) we show the solutions of the multiple - scales - derived and fokker  planck - derived effective equations , along with the average over 100 realizations of the true solution for a random distribution of obstacles ( as in figure  [ fig : gradient_va ] ) . in figure [ fig : cuty](b ) we show some of the individual realizations along with the ensemble average , to give an idea of the variance . = .8 cm    [ b][][]@xmath163 [ ] [ ] [ ] ( a ) [ ] [ ] [ ] ( b ) [ ] [ ] [ ] @xmath153 [ ] [ ] [ ] [ -90]@xmath11 [ ] [ ] [ ] [ -90]@xmath11","summary":"we compare the two approaches , and we show good agreement between them in a number of example configurations .    diffusion , porous media , hard spheres , multiple scales , variable porosity .    35b27 , 35q84 , 60j70 , 82c31","abstract":"the problem of diffusion in a porous medium with a spatially varying porosity is considered . the particular microstructure analyzed comprises a collection of impenetrable spheres , though the methods developed are general . two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented . the first is a deterministic approach based on the method of multiple scales ; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions . we compare the two approaches , and we show good agreement between them in a number of example configurations .    diffusion , porous media , hard spheres , multiple scales , variable porosity .    35b27 , 35q84 , 60j70 , 82c31"}
{"article_id":"1501.06549","section_id":"c","document":"we have investigated the problem of diffusion through a porous medium in which the porosity is non - uniform . transport through porous media is inherently a multiscale process , with properties determined by individual pores at the microscale while one is usually interested transport over much larger distances . to derive an effective macroscopic model , a common approach is to assume that all heterogeneities lie within the microscale and that , once these are averaged out , we are left with a homogeneous porous medium at the macroscale . it is tempting to suppose that , if the properties such as porosity do vary macroscopically , then all we have to do is carry out this procedure locally at each point ( that is , treat the material as though it were uniform with a porosity equal to the local porosity ) , so that the effective diffusivity becomes a function of macroscopic position . however , in this paper we have seen that this is not the case , and that a more careful analysis is needed . we have considered two different approaches to the upscaling problem , suitable for deterministic and random porous media respectively , and have generalized them to heterogeneous media . the result is a macroscopic advection  diffusion equation , with the advection term accounting for the macroscopic gradients in porosity . first , we have extended the method of multiple scales to account for non - uniform porosity ( via a microscopic cell geometry parametrized by the macroscopic variable ) and non - periodic structures ( providing they are locally periodic , that is , they can be mapped into periodic structures by a transformation depending only on the slow scale ) . the resulting equation is equivalent at leading order to the one presented in @xcite using a volume - averaging approach , although some formally higher - order terms are included in their unit cell problem ( which leads them to some worrying conclusions ; for example , the effective diffusivity depends on the location of the centroid in the unit cell ) . the multiple - scales method has the advantage of being a systematic asymptotic expansion ( for which higher - order terms could in principle be calculated ) which is able to handle any porosity . its disadvantage is that , even with our extensions , it requires the microstructure to be locally periodic . our examples have considered spherical obstacles that remained spherical when mapped to a periodic arrangement , which has greatly simplified parts of the presentation . however , the technique is more general . in particular if the diffusion tensor is anisotropic ( for example , if the inclusions were ellipsoids instead of spheres ) the technique demonstrates systematically that the principal directions of the diffusion tensor would be aligned with the local axes of the ellipsoids . one question that always arises when deriving effective equations with the method of multiple scales is how much of an error is introduced by treating the microstructure as periodic , when in reality it is unstructured . to address this question , we considered a second approach involving diffusion through a random distribution of spherical obstacles . in this case we again used a systematic asymptotic expansion , but this time in the limit of low volume fraction of obstacles . the macroscopic equation turns out to be a particular case of our model for the diffusion of binary mixtures of finite - sized particles @xcite , when the diffusivity of one of the species is set to zero . we compared the macroscopic models described above to each other and also to their microscopic counterparts . for the examples we considered both effective material models performed well , and the differences between the structured and unstructured media were small . for both deterministic and random media , the mean - square displacement @xmath272 analysis in figure  [ fig : msd_simul ] showed that the effective transport mechanism of the solute particle is still normal diffusion , that is , @xmath272 grows linearly in time , and it is only the diffusion coefficient that changes from one ( in the microscale ) to @xmath9 in the macroscale . however , depending on the timescale used in such analysis , one can observe _ transient _ anomalous diffusion ( the transient period can only just be seen in our simulations , see figure [ fig : msd_simul](b ) ) . in the context of porous media , if the ratio @xmath35 between pore scale and typical domain length is not sufficiently small , diffusion may occur in a lengthscale shorter than the crossover region between transient anomalous diffusion and normal diffusion @xcite . this transient behavior should not be confused with real _ stationary _ anomalous diffusion @xcite .","summary":"the problem of diffusion in a porous medium with a spatially varying porosity is considered .","abstract":"the problem of diffusion in a porous medium with a spatially varying porosity is considered . the particular microstructure analyzed comprises a collection of impenetrable spheres , though the methods developed are general . two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented . the first is a deterministic approach based on the method of multiple scales ; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions . we compare the two approaches , and we show good agreement between them in a number of example configurations .    diffusion , porous media , hard spheres , multiple scales , variable porosity .    35b27 , 35q84 , 60j70 , 82c31"}
{"article_id":"1405.3715","section_id":"i","document":"the celebrated banados - teitelboim - zanelli ( btz ) solution @xcite is the unique black hole of general relativity in three dimensions . for a number of years , such a black hole solution was deemed impossible , and for good reason . in three - dimensional general relativity , there are no local gravitational degrees of freedom : curvature is algebraically fixed by the matter content , which implies that in a true vacuum the spacetime can only be flat . with a nonvanishing cosmological constant , the field equations admit locally de sitter ( ds ) and anti - de sitter ( ads ) solutions , but still preclude solutions with nontrivial curvature . hence , one is led to believe that black hole solutions in three - dimensional einstein gravity are impossible . this argument is evaded by noting that it relies solely on local considerations . taking account of its global structure , a spacetime can contain a black hole in spite of being locally maximally symmetric . the btz solution is an example ; it is locally ads , but it is turned into a black hole spacetime by certain identifications of spacelike related events . ever since its discovery , the btz black hole has generated a considerable amount of attention , in large part due to its foreseen applications , particularly in addressing conceptual issues of quantum gravity that become more tractable in three dimensions . this unrelenting desire for a quantum theory of gravity has also inspired a number of interesting theoretical ideas . one of these is the suggestion that lorentz invariance may not be fundamental or exact , but is merely an emergent symmetry on sufficiently large distances or low energies . it has been suggested in ref . @xcite that giving up lorentz invariance by introducing a preferred foliation and terms that contain higher - order spatial derivatives can lead to significantly improved uv behavior . the corresponding gravity theory is dubbed hoava gravity and we will review its basic properties in the next section . one needs to rethink the notion of a black hole in the presence of lorentz violations . theories that do not respect local lorentz symmetry may propagate superluminal excitations that can penetrate the usual horizon . they may even have instantaneous ( infinitely fast ) modes , as is the case for hoava gravity . however , studies of four - dimensional black holes in this theory @xcite have revealed the existence of a new type of horizon , called the universal horizon , which act as a causal boundary for all modes , irrespective of how fast they propagate . this allows one to generalize and preserve the ( or some ) notion of a black hole in the framework of lorentz - violating gravity theories ( see ref . @xcite for a recent review ) .    in this paper , we focus on the infrared limit of three - dimensional hoava gravity @xcite and our main goal is to seek a lorentz - violating version of the btz black hole , i.e.  a black hole solution with ads asymptotics . we show that such a spacetime exists only if one tunes the parameters of the theory . we find the most general family of solutions for this sector , assuming stationarity and circular symmetry , so generically our solution represents a rotating black hole . remarkably , some of our solutions represent black holes even for a positive or vanishing cosmological constant .    our motivation for seeking black hole solutions in the three - dimensional version of hoava gravity is twofold . first , we hope that they will be useful as a playground for studying quantum field theory and quantum gravity effects in black hole spacetimes , as has been the case for the btz black hole . second , we hope that we will gain some insight into the causal structure of black holes in the presence of lorentz violations  at least the aspects that do not depend on the dimensionality . it is worth stressing that our solutions are explicit and exact , unlike their four - dimensional counterparts . indeed , the static , spherically symmetric solutions of ref . @xcite are numerical and those of ref . @xcite are numerical and valid in the small - coupling limit . explicit solutions in 4 dimensions are also known for specific , tuned choices of the parameters of the theory , but they are all static @xcite . the only rotating solutions currently known in four dimensions are not entirely explicit , and moreover , rely on the assumption of slow rotation @xcite . working in three dimensions allows us to avoid approximations or numerics .    throughout this paper , we adopt a mostly - minus spacetime signature and set @xmath0 . in what follows , we will be referring to any solution for which the metric that couples minimally to matter fields has a killing horizon as a black hole . we choose to do so because , for the matter fields , which we assume to be relativistic , the killing horizon will be an event horizon . hence , the spacetime will be a black hole in the conventional ( gr ) sense . it should be clear , however , that this is actually an abuse of terminology in the context of hoava gravity , as perturbations that reside in the gravity sector can propagate infinitely fast , as mentioned earlier , so one could have chosen to reserve the term black hole for solutions that have a universal horizon .","summary":"we study black holes in the infrared sector of three - dimensional hoava gravity . it is shown that black hole solutions with anti - de sitter asymptotics are admissible only in the sector of the theory in which the scalar degree of freedom propagates infinitely fast .","abstract":"we study black holes in the infrared sector of three - dimensional hoava gravity . it is shown that black hole solutions with anti - de sitter asymptotics are admissible only in the sector of the theory in which the scalar degree of freedom propagates infinitely fast . we derive the most general class of stationary , circularly symmetric , asymptotically anti - de sitter black hole solutions . we also show that the theory admits black hole solutions with de sitter and flat asymptotics , unlike three - dimensional general relativity . for all these cases , universal horizons may or may not exist depending on the choice of parameters . solutions with de sitter asymptotics can have universal horizons that lie beyond the de sitter horizon ."}
{"article_id":"1405.3715","section_id":"c","document":"our intention was to find an analogue of the btz black hole in three - dimensional hoava gravity . to this end we first considered whether ads space or ads asymptotics are admissible in this theory . using the reduced action approach we have shown that this is only true if @xmath103 . we subsequently focused on the @xmath103 sector of the theory . we have found the most general class of solutions in this sector , without imposing specific asymptotics . remarkably , the black hole solutions in this class do not have exclusively ads asymptotics , but there exist instead also black holes with ds and flat asymptotics , unlike general relativity . the black hole solutions we found have very interesting properties . they harbor a curvature singularity , unlike their gr counterparts . they can have an inner and an outer metric ( killing ) horizon and one or two ergosurfaces . what is perhaps their most interesting feature within the context of lorentz - violating gravity theories is that they can have universal horizons . rotation does not seem to play a key role in the existence of these horizons . depending on the configuration of the preferred foliation , there can be nonrotating black holes without universal horizons or rapidly rotating black holes with universal horizons . some of our solutions also feature the existence of cosmological universal horizons . these results demonstrate that the existence of universal horizons does not seem to depend on spherical symmetry or the number of spacetime dimensions and it is not specific to black hole spacetimes . at the same time , they also highlight the importance of the asymptotic behavior of the foliation for the existence of universal horizons . the @xmath103 sector of three - dimensional hoava gravity , to which the requirement of ads asymptotics has restricted us , is likely to be a special theory . at the perturbative level the scalar mode that the theory propagates appears to travel at infinite speed and , at the same time , the theory is expected to be strongly coupled @xcite . in four dimensions choosing @xmath103 leads to a physically ( but not mathematically ) inconsistent theory @xcite . nevertheless , we expect the black hole solutions we present here to be useful tools for applications such as quantum field theory near horizons in the presence of lorentz violations and black hole thermodynamics , so long as one remains cautious about the interpretation of the results . finally , the existence of black hole solutions with flat or ds asymptotics in the @xmath103 sector of the theory suggests that it is also likely for black hole solutions with these asymptotics to exist when @xmath323 . we shall explore this possibility in future work . the authors thank jishnu bhattacharyya and ted jacobson for fruitful discussions that helped shape this work . the research leading to these results has received funding from the european research council under the european union s seventh framework programme ( fp7/2007 - 2013)/erc grant agreement n. 306425 `` challenging general relativity '' .","summary":"we derive the most general class of stationary , circularly symmetric , asymptotically anti - de sitter black hole solutions . we also show that the theory admits black hole solutions with de sitter and flat asymptotics , unlike three - dimensional general relativity . for all these cases , universal horizons may or may not exist depending on the choice of parameters .","abstract":"we study black holes in the infrared sector of three - dimensional hoava gravity . it is shown that black hole solutions with anti - de sitter asymptotics are admissible only in the sector of the theory in which the scalar degree of freedom propagates infinitely fast . we derive the most general class of stationary , circularly symmetric , asymptotically anti - de sitter black hole solutions . we also show that the theory admits black hole solutions with de sitter and flat asymptotics , unlike three - dimensional general relativity . for all these cases , universal horizons may or may not exist depending on the choice of parameters . solutions with de sitter asymptotics can have universal horizons that lie beyond the de sitter horizon ."}
{"article_id":"hep-ph0412400","section_id":"i","document":"the radiative and electroweak penguin transitions @xmath8 and @xmath9 ( @xmath10 ) provide valuable insight into the nature of flavour - changing neutral currents . induced through quantum fluctuations in the standard model , they may be strongly influenced by new heavy particles . this has been studied extensively for inclusive @xmath11 decays over the past decade . some years ago the qcd factorization approach to exclusive @xmath12 decays  @xcite was extended to exclusive radiative  @xcite and electroweak penguin decays  @xcite , thus opening the possibility to perform detailed studies of isospin breaking and cp asymmetries in these decays , as well as to obtain more precise predictions for branching fractions and forward - backward asymmetries .    at the time when these papers were written , only the exclusive @xmath0 decays had been observed , and a next - to - leading order ( nlo ) analysis could be done only for @xmath13 and @xmath3 , the case of @xmath14 being excluded by the absence of the nlo ( 2-loop ) virtual correction to the @xmath15 transition . this missing piece of input has recently been computed @xcite , while the formal justification of the qcd factorization method in radiative decays has been pursued in @xcite . moreover , the @xmath12 factories have now put limits on the @xmath6 and @xmath2 branching fractions  @xcite , and have performed first measurements of @xmath3  @xcite including the lepton invariant mass spectrum and forward - backward asymmetry  @xcite . these theoretical and experimental advances motivate the following study of the observables of interest with a complete next - to - leading order calculation ( except for weak annihilation ) . the paper is organized as follows : in section  [ sec : theoryinput ] we give a brief introduction to the theoretical formalism . we specify the input parameters to the analysis and give the various contributions to the decay amplitudes in numerical form . the theoretical expectations for the relevant observables are summarized in section  [ sec : pheno ] . for both , @xmath16 and @xmath17 decays ( @xmath18 ) , we discuss branching fractions ( lepton invariant mass spectrum and partially integrated branching fractions for @xmath19 ) , isospin asymmetries ( difference between charged and neutral @xmath12 meson decay ) and direct cp asymmetries . for @xmath19 the forward - backward asymmetry is also included . in section  [ sec:3.5 ] we collect the constraints on the ckm unitarity triangle that can be obtained from the branching fractions , isospin and cp asymmetries in @xmath6 decays . the analysis of the radiative decays overlaps with recent work of ali et al . @xcite and bosch and buchalla  @xcite , and we compare our results to theirs in the appropriate places . we conclude in section  [ sec : conclude ] . the technical appendix  [ app : a ] contains the new decay amplitudes for @xmath4 related to the up - quark sector of the effective weak hamiltonian .","summary":"we consider branching fractions , isospin asymmetries and direct cp asymmetries . for the electroweak penguin decays , the lepton - invariant mass spectrum and forward - backward asymmetry is also included . radiative and electroweak penguin transitions in are mainly interesting in the search for new flavour - changing neutral current interactions , but in addition the decays provide constraints on the ckm parameters .","abstract":"we provide standard model expectations for the rare radiative decays , and , and the electroweak penguin decays and at the next - to - leading order ( nlo ) , extending our previous results to transitions . we consider branching fractions , isospin asymmetries and direct cp asymmetries . for the electroweak penguin decays , the lepton - invariant mass spectrum and forward - backward asymmetry is also included . radiative and electroweak penguin transitions in are mainly interesting in the search for new flavour - changing neutral current interactions , but in addition the decays provide constraints on the ckm parameters . the potential impact of these constraints is discussed .    pitha 04/19 + si - hep-2004 - 13 + hep - ph/0412400 + 20 december 2004    1.5 cm    , and .5 cm     +    2.5 cm"}
{"article_id":"hep-ph0412400","section_id":"c","document":"our analysis provides standard model expectations for the exclusive , radiative and electroweak penguin decays @xmath183 and @xmath360 ( @xmath361 ) , extending our previous work  @xcite to @xmath362 and @xmath363 transitions . the theoretical framework is complete at next - to - leading order in the strong coupling ( except for weak annihilation which is included only in leading order ) , and leading power in the heavy - quark expansion . we have also included @xmath67 power corrections , mainly from weak annihilation , which are important for the isospin asymmetries . the observables related to @xmath213 decays can provide interesting constraints on the ckm triangle as was also recently discussed in @xcite . the accuracy of these constraints is limited by hadronic uncertainties , mainly from the hadronic form factors describing the @xmath364 transition ( for branching fractions ) , @xmath365 transitions / weak annihilation ( for the isospin asymmetry ) , and from the scale and charm quark mass uncertainty ( for direct cp asymmetries ) . nevertheless , the simultaneous measurement of branching fractions , isospin- and cp asymmetries can be used for an independent determination of the apex @xmath366 of the ckm triangle , which is complementary to the standard fit . in particular , if @xmath367 is not observed with a branching fraction near the current upper limit @xmath368 , a tension with the standard fit arises . we compared our calculations for @xmath84 with the first experimental results on these decays . the central value of the belle data on the partially integrated lepton invariant mass spectrum is about a factor of 2 larger than the theoretical prediction . although the discrepancy is not significant within current uncertainties , it will be interesting to see how it develops . if the problem is theoretical , this may result in the curious situation that the comparison with data seems to favour a larger form factor @xmath162 , but a smaller tensor form factor @xmath180 . the present experimental accuracy for the measurement of the forward - backward lepton asymmetry in this decay mode is not yet competitive with the theoretical one . in the future , however , we expect significant constraints on the wilson coefficient @xmath33 in @xmath270 transitions as already discussed in @xcite . we performed the first next - to - leading order calculation of exclusive @xmath15 transitions . in the long run when detailed experimental information on these transitions will become available , the ckm matrix can be assumed to be known . hence the various observables related to @xmath369 decays provide information on the modulus and phase of the wilson coefficient @xmath33 in @xmath363 transitions or related coefficients in extended flavour models , which is of interest in the context of new - physics scenarios with non - minimal flavour violation . the theoretical uncertainty related to hadronic input is currently sizeable , but we may look forward to improved determinations of @xmath214 form factors , and perhaps , the mechanism of weak annihilation , on the time scales of interest . these improvements will add @xmath370 to the list of rare processes that play an essential role in the program to uncover the origin of flavour violation . 0.4cm*acknowledgements *    0.2 cm we would like to thank patrick koppenburg for helpful discussions , and stefan bosch for reading the manuscript . this work was supported by the dfg sonderforschungsbereich / transregio 9 `` computergesttzte theoretische teilchenphysik '' . m.b . would like to thank the int , seattle for its generous hospitality while part of the work was being done . d.s . acknowledges support of the dfg graduiertenkolleg `` elementarteilchenphysik an der tev - skala '' and would like to thank the cern theory group for hospitality .","summary":"we provide standard model expectations for the rare radiative decays , and , and the electroweak penguin decays and at the next - to - leading order ( nlo ) , extending our previous results to transitions .","abstract":"we provide standard model expectations for the rare radiative decays , and , and the electroweak penguin decays and at the next - to - leading order ( nlo ) , extending our previous results to transitions . we consider branching fractions , isospin asymmetries and direct cp asymmetries . for the electroweak penguin decays , the lepton - invariant mass spectrum and forward - backward asymmetry is also included . radiative and electroweak penguin transitions in are mainly interesting in the search for new flavour - changing neutral current interactions , but in addition the decays provide constraints on the ckm parameters . the potential impact of these constraints is discussed .    pitha 04/19 + si - hep-2004 - 13 + hep - ph/0412400 + 20 december 2004    1.5 cm    , and .5 cm     +    2.5 cm"}
{"article_id":"0905.0655","section_id":"i","document":"in the standard model of low - mass star formation , dense cores are the precursors of star formation @xcite . therefore , to understand the process of star formation , one needs to observe the physical conditions of these cores . embedded young stellar objects ( ysos ) are sometimes detected in these cores . these ysos are partially obscured by the dust within the cores . to accurately model their physical properties requires knowledge of the quantity of dust and its composition , since both affect the degree of attenuation , or extinction , of starlight . by studying the dust , one can learn about its chemistry and evolution . furthermore , the dust provides a direct measure of the column density and mass . molecular tracers can suffer depletion in dense regions , making mass estimates from them unreliable . in this paper we use _ spitzer _ and deep ground - based @xmath9 observations to probe the dust properties within four cores : l204c-2 , l1152 , l1155c-2 , and l1228 . two of our cores , l1152 and l1228 , have known protostars while the other two do not . our first goal in this paper is to examine the yso population of these cores and to look for faint previously unknown protostars in all four cores . second , we will compute the extinction law in each core and compare it to the predictions of three dust models to draw conclusions about the dust properties within the cores . this paper is organized as follows :  [ sec : observe ] describes our observations and data processing pipeline including source classification , the removal of misidentified background galaxies , and how we computed line - of - sight ( los ) extinctions to each star . in  [ sec : core - ext ] we use these los extinctions to create extinction maps for each core . [ sec : coreysos ] explores the yso content in our cores . in  [ sec : dust ] we compute the relative extinction as a function of wavelength , the extinction law , for each core . we also create maps of the @xmath4 maps of the difference between the observed and predicted extinction laws and compare to the extinction maps . finally , we summarize our results in  [ sec : conclude ] .","summary":"our goals are to study the yso population of these cores and to measure the mid - infrared extinction law . with we also compute the line - of - sight extinction law towards each background star .","abstract":"we present observations in eight wavebands from m of four dense cores : l204c-2 , l1152 , l1155c-2 , and l1228 . our goals are to study the yso population of these cores and to measure the mid - infrared extinction law . with our combined near - infrared and _ spitzer _ photometry , we classify each source in the cores as , among other things , background stars , galaxies , or embedded young stellar objects ( ysos ) . l1152 contains three ysos and l1228 has seven , but neither l204c-2 nor l1155c-2 appear to contain any ysos . we estimate an upper limit of to for any undiscovered ysos in our cores . we also compute the line - of - sight extinction law towards each background star . these measurements are averaged spatially , to create maps of the changes in the mid - infrared extinction law throughout our cores , and also in different ranges of extinction . from the maps we identify two small regions in l1152 and l1228 where the outflows in those cores appear to be destroying the larger dust grains , thus altering the extinction law in those regions . on average , however , our extinction law is relatively flat from to m for all ranges of extinction and in all four cores . from to m this law is consistent with a dust model that includes larger dust grains than the diffuse interstellar medium , which suggests grain growth has occurred in our cores . at m , our extinction law is higher than predicted by dust models . however , it is similar to other empirical measurements ."}
{"article_id":"0905.0655","section_id":"c","document":"in this paper we presented deep @xmath9 and _ spitzer _ photometry of four isolated cores : l204c-2 , l1152 , l1155c-2 , and l1228 . based on previous observations , two of these cores were classified as starred and two were classified as starless . our data support these original classifications . we detect 10 ysos , three within l1152 , seven within l1228 , and none within l204c-2 or l1155c-2 . seven of these ysos have not been previously discovered . among these , we are able to resolve the driving source of the hh200 outflow in l1228 into two sources separated by @xmath96 , but we were unable to identify which of the two sources is responsible for the outflow .    to put constraints on possible faint ysos in all four cores , we selected 634 sources with @xmath6 m detections @xmath99 which are either undetected or too faint at other wavelengths to be considered in our high reliability catalogs . we computed the median sed for these sources and integrated the sed to obtain a luminosity of @xmath167 to @xmath168 l@xmath101 with colors of a very young flat spectrum or class i yso @xcite . in addition to studying the yso content of these cores , we used the line - of - sight measurements of the extinction and the extinction law to create maps of the extinction and @xmath4 deviation from specific dust grain models . our extinction law is nearly flat for all ranges of extinction in all four cores . in the irac bands ( @xmath11 m ) this extinction law matches the predictions of the wd5.5 dust model , a model designed to simulate the grain growth that occurs in dense regions , and also agrees with the other authors results @xcite . in the densest regions of l1152 and l1155c-2 , the @xmath134 m extinction law is higher than the wd5.5 model . this could be evidence for water ice in these cores or a steeper near - infrared extinction law than the average value . at @xmath6 m , our data are consistent with the extinction law remaining constant as the total extinction increases . the observed extinction law is much higher than that predicted by dust grain models , but does confirm the similarly large value found by other authors @xcite .    from the @xmath4 maps we identified cavities in l1152 and l1228 where the extinction law is more consistent with the wd3.1 dust model . the molecular outflows in these cores produce shocks , which may be destroying the large dust grains , thus producing a dust distribution similar to wd3.1 these cavities are visible in our @xmath4 maps , but would be missed in averages over an entire core . it is critical to create new dust grain models which reproduce the observed flat extinction law , especially at @xmath6 m . in this paper we used the @xcite models to estimate the luminosities of our ysos . however , @xcite assumed an extinction law that is between wd3.1 and wd5.5 in the irac bands and predicts a @xmath6 m extinction that is about @xmath70 of our observed value . the best - fit yso parameters would undoubtedly change with a flatter extinction law . furthermore , it is important to understand the mid - infrared extinction law because future telescopes , such as the james webb space telescope , will operate at these wavelengths . we are grateful to neal evans for providing useful feedback on several drafts and also the anonymous referee whose comments greatly improved the quality of this paper . support for this work , utilizing data from the `` cores to disks '' spitzer legacy science program @xcite , was provided by nasa through contracts 1224608 , 1230782 , and 1230779 issued by the jet propulsion laboratory , california institute of technology , under nasa contract 1407 . additional support for n.l.c .  was provided by nasa through jpl contracts 1264793 and 1264492 . l.g.m .  was supported by nasa origins grant nag510611 . this research has made use of pyraf , a product of the space telescope science institute , which is operated by aura for nasa . we also used the simbad database which is operated at cds , strasbourg , france . 24    bally , j. , devine , d. , fesen , r.  a. , & lane , a.  p. 1995 , , 454 , 345    chapman , n.  l. , mundy , l.  g. , lai , s .- p . , & evans , ii , n.  j. 2009 , , in press    de geus , e.  j. , de zeeuw , p.  t. , & lub , j.  1989 , , 216 , 44    draine , b.  t. 2003 , , 41 , 241    elston , r. 1998 , in proc . 3354 , p. 404 - 413 , infrared astronomical instrumentation , albert m. fowler ; 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{"article_id":"1610.03000","section_id":"i","document":"we are interested in randomly branched polymers with repulsive , short - range interactions between monomers . our choice of units and notation is explained in sec .  [ sec : units ] , the employed lattice model and the various ensembles are defined in secs .  [ sec : latticemodel ] and [ sec : ensembles ] , respectively . in section [ sec : observables ] we define a range of observables , which can be used to quantify the connectivity and the spatial configuration of trees . known exact results for ideal trees without volume interactions are briefly summarized in section  [ sec : idealtrees ] , while section  [ sec : flory ] reviews predictions of flory theory for interacting trees . all our numerical results are obtained for trees embedded in @xmath0 dimensions , even though many theoretical expressions are conveniently expressed for general @xmath21 . we measure energy in units of @xmath22 , length in units of the kuhn length , @xmath23 , and mass in units of the number of kuhn segments . we use the letters @xmath2 and @xmath24 to denote the mass of a tree or a branch , respectively . with @xmath2 kuhn segments connecting the nodes of a tree , there are @xmath25 nodes in a tree . the symbols @xmath26 and @xmath9 are reserved for contour lengths of _ linear _ paths on the tree , while @xmath27 and @xmath28 denote contour distances from a fixed point , typically the tree center . spatial distances are denoted by the letters @xmath29 and @xmath30 . examples are the tree gyration radius , @xmath31 , spatial distances between nodes , @xmath32 , and the spatial distances , @xmath33 , of a node from the tree center of mass .      we mainly study lattice trees on the @xmath20-cubic lattice . the functionality of the nodes is restricted to the values @xmath34 ( a leaf or branch tip ) , @xmath35 ( linear chain section ) , and @xmath36 ( branch point ) . connected nodes occupy adjacent lattice sites . since our models do not include a bending energy , the lattice constant equals the kuhn length , @xmath23 , of linear paths across ideal trees . a tree conformation , @xmath37 , can be described by the set of node positions , @xmath38 , in the embedding space and a suitable representation of its connectivity graph , @xmath39 . we employ a data structure in the form of a linked list , which retains for each node , @xmath40 , its position , @xmath41 , functionality , @xmath42 , and the indices @xmath43 of the nodes to which it is connected .    for ideal trees , nodes do not interact and their asymptotic branching probability , @xmath44 , is controlled via a chemical potential for branch points , @xmath45 where @xmath46 is the total number of 3-functional nodes in the tree . all our results are obtained for a value of @xmath47  @xcite . interactions between nodes are accounted for via @xmath48 where @xmath49 is the total number of kuhn segments inside the elementary cell centered at the lattice site @xmath50 . the statistical ( boltzmann ) weight @xmath51 of a tree conformation depends on both , the tree s connectivity , @xmath39 , and its spatial conformation , @xmath52 . in the following , we employ a notation where probabilities , partition functions and expectation values carry a subscript denoting the hamiltonian governing the annealed degrees of freedom and , if necessary , a superscript , characterizing the ( distribution ) of quenched connectivities .      for trees with annealed connectivity , tree conformations are observed with a probability @xmath53 and ensemble averages of observables are given by @xmath54    the statistical weight of a particular tree connectivity in the annealed ensemble is given by integrating over the spatial degrees of freedom : @xmath55      as a first step , consider an ensemble of trees with annealed spatial degrees of freedom , @xmath52 , and a given , unique connectivity , @xmath39 . a conformation is observed with a probability @xmath56 and ensemble averages for observables are calculated from @xmath57    in general , ensembles of trees with quenched connectivity are characterised by a given probability , @xmath58 , for observing particular connectivities , @xmath39 . expectation values are calculated by averaging expectation values for particular connectivities , @xmath59 , over the distribution @xmath58 : @xmath60      the connectivity distribution , @xmath58 , of branched polymers is determined by the process , by which they are synthesised . trees with `` randomly quenched connectivity '' are generated , if the connectivity of annealed trees is quenched after they have been equilibrated under the influence of some hamiltonian , @xmath61 . the probability to observe a particular connectivity in the randomly quenched ensemble is then given by eq . ( [ eq : p g ] ) : @xmath62 expectation values for this ensemble have to be calculated from eq . ( [ eq : a quenched ] ) using the hamiltonian , @xmath63 , describing the environmental conditions at the time of observation . @xmath64 in this paper , we investigate self - avoiding trees with randomly quenched _ ideal _ connectivity . they are generated using @xmath65 ( eq . ( [ eq : hideal ] ) ) and subsequently studied in good solvent conditions using @xmath66 ( eq .  ( [ eq : hvolumeinteractions ] ) ) . note that eq . ( [ eq : a randomly quenched ] ) can be simplified , if the environmental conditions at the time of observation are equal to those at the time of the connectivity quench . this holds immediately after the quench , but might also apply at a later time , if the trees are ( re)equilibrated under the original conditions . in this case , expectation values are equal to those for trees with annealed connectivity : @xmath67        a tree is a branched structure free of loops . its connectivity can be characterized in a number of ways . locally , nodes connecting kuhn segments differ according to their functionality , @xmath68 . branch points have a functionality @xmath69 , for branch tips @xmath70 . the numbers of branch and end points are related via @xmath71 where @xmath72 is the total number of nodes in the tree with functionality @xmath68 . in particular , we have for trees with a maximal connectivity of @xmath36 : @xmath73 the large scale structure of a tree can be analyzed in terms of the ensemble of sub - trees generated by cutting bonds . removal of a bond splits a tree of weight @xmath2 into two smaller trees of weight @xmath74 and @xmath75 . we denote the corresponding probabilities for the sub - tree weight as @xmath76 . in particular , @xmath77 denoting the smaller of the two remaining trees as a `` branch '' , one can define a mean branch weight : @xmath78 which grows as a characteristic power of the tree weight , @xmath79 ( eq .  ( [ eq : epsilon ] ) ) . alternatively , the tree connectivity can be analyzed in terms of the statistics of minimal distances , @xmath80 , of two nodes @xmath81 along linear paths on the tree . introducing the probability to find two nodes at a particular contour distance , @xmath82 , with @xmath83 the corresponding average distance is given by , @xmath84 furthermore , defining the node in the middle of the longest path as the central node of a tree we also measure ( 1 ) the average distance , @xmath85 of nodes from the central node @xmath86 where @xmath87 is the corresponding probability distribution , and ( 2 ) the average length @xmath88 of the longest distance from the central node . for ensemble averages one expects ( eq .  ( [ eq : rho ] ) ) : @xmath89 with @xmath90  @xcite .    similarly , we characterize the statistics of branches by measuring the average branch weight , @xmath91 , as a function of the _ longest _ contour distance of nodes from the branch root , @xmath92 . finally , we consider the average weight of the `` core '' of tree , @xmath93 , made of segments whose distance from the central node does not exceed @xmath94 . the overall spatial extension of the tree is best described through the gyration radius and the distribution , @xmath95 , of the distances @xmath96 between nodes : @xmath97 alternatively , one can consider the distribution @xmath98 of the node positions , @xmath99 , relative to the tree center of mass , @xmath100 : @xmath101 for ensemble averages one expects @xmath102 ( eq . ( [ eq : nu ] ) ) . the spatial conformations of linear paths on the tree can be characterized using standard observables for linear polymers . the most general information is contained in the end - to - end distance distribution , @xmath103 of paths of length @xmath9 for trees of total mass @xmath2 . in particular , one can extract the mean - square end - to - end distance @xmath104 and , for a given contact distance @xmath105 , the end - to - end closure probability @xmath106 of such paths , which are expected to scale as ( eqs .  ( [ eq : nu_path ] ) and  ( [ eq : theta_path ] ) ) : @xmath107 and to be asymptotically independent of tree weight . by construction @xmath108 so that @xmath109    for non - interacting lattice trees with gaussian / random walk path statistics , @xmath110 so that @xmath111 at the same time , the kramers theorem  @xcite links the gyration radius to the branch weight statistics : @xmath112      daoud and joanny  @xcite calculated the partition function @xmath113 of ideal lattice trees of @xmath2 kuhn segments in the continuum approximation : @xmath114 where @xmath115 is the first modified bessel function of the first kind , @xmath44 the branching probability per node and @xmath116 . by employing the kramers theorem , @xmath117 from this expression , it is possible to derive the following asymptotic relations for the quantities introduced above . for the branch weight distribution , @xmath118 for the gyration radius @xmath119 in agreement with the original results of zimm and stockmeyer  @xcite . the average branch weight ( see definition , eq . ( [ eq : treebranchsize ] ) ) is given by @xmath120 showing that @xmath121 for ideal trees , and the average fraction of @xmath36 nodes is given by @xmath122      flory theories  @xcite are formulated as a balance of an entropic elastic term and an interaction energy , @xmath123 @xmath124 represents the standard two - body repulsion between segments , which dominates in good solvent . et al . _ @xcite proposed the following elastic free energy for annealed trees : @xmath125 the expression reduces to the entropic elasticity of a linear chain  @xcite , @xmath126 , for unbranched trees with quenched @xmath127 . the first term of eq . ( [ eq : fgutin ] ) is the usual elastic energy contribution for stretching a polymer of linear contour length @xmath26 at its ends . the second term is less obvious : it is calculated from the partition function of an ideal branched polymer of @xmath2 bonds with @xmath26 bonds between two arbitrary fixed ends  @xcite .    for trees with quenched connectivity , eq . ( [ eq : fgutin ] ) has to be evaluated for the given path length @xmath26 and then minimised with respect to @xmath29 . in particular , branched polymers with a given quenched connectivity , @xmath128 , and mass , @xmath2 , are expected to swell to a size of @xmath129 eqs . ( [ eq : nu_of_rho ] ) and ( [ eq : nupath_of_rho ] ) reduce to the classical flory result , @xmath130 , for linear chains with @xmath131 in @xmath132 dimensions . the result is exact , except in @xmath0 , where @xmath133  @xcite . for trees with _ quenched ideal _ connectivity , @xmath134 , one recovers in @xmath135 the isaacson and lubensky  @xcite prediction , @xmath136    for swollen randomly branching polymers with annealed connectivity , eq . ( [ eq : fgutin ] ) needs to be minimised with respect to both , @xmath29 and @xmath26 . in particular , gutin _ et al . _ @xcite found : @xmath137 in @xmath138 , the chain is predicted to be unbranched and fully stretched , @xmath139 . in @xmath140 the predicted values are in reasonable agreement with numerical results  @xcite , even though the prediction @xmath12 slightly exceeds the exact result @xmath13 in @xmath0 @xcite . in particular , in @xmath0 @xmath141 and @xmath142 . consequently , annealed and quenched trees belong to different universality classes  @xcite . notice , that the flory theory gives no prediction for the exponent @xmath1 of contact probabilities between tree nodes , eq . ( [ eq : theta_path ] ) .    in the following , we will compare these results to computer simulations of trees in the two different ensembles . the same ideas can also be applied to a tree melt : corresponding results will be presented and discussed in forthcoming publications  @xcite .","summary":"we show , then , that contact probabilities can be aptly characterized by introducing a novel critical exponent , , which accounts for how they decay as a function of the node - to - node path distance on the tree .","abstract":"we present computer simulations of three systems of randomly branching polymers in dimensions : ideal trees and self - avoiding trees with annealed and quenched connectivities . in all cases , we performed a detailed analysis of trees connectivities , spatial conformations and statistical properties of linear paths on trees , and compare the results to the corresponding predictions of flory theory . we confirm that , overall , the theory predicts correctly that trees with quenched ideal connectivity exhibit _ less _ overall swelling in good solvent than corresponding trees with annealed connectivity even though they are _ more strongly _ stretched on the path level . at the same time , we emphasize the inadequacy of the flory theory in predicting the behaviour of other , and equally relevant , observables like contact probabilities between tree nodes . we show , then , that contact probabilities can be aptly characterized by introducing a novel critical exponent , , which accounts for how they decay as a function of the node - to - node path distance on the tree ."}
{"article_id":"1610.03000","section_id":"i","document":"in the present article , we have reconsidered the conformational statistics of lattice trees with volume interactions  @xcite . in particular , we have carried out computer simulations for two classes of three - dimensional systems , namely self - avoiding lattice trees with annealed and quenched _ ideal _ connectivity ( sections  [ sec : amoebaalgo ] and  [ sec : mdmethods ] , respectively ) . the well understood case of ideal , non - interacting lattice trees  @xcite served as useful references . in all cases , we have performed a detailed analysis of the observed connectivities and of the conformational statistics ( sections  [ sec : burning ] and  [ sec : extractexps ] ) . in particular , we have determined ( section  [ sec : results ] ) values of suitable exponents describing the scaling behavior of : the average branch weight , @xmath234 , the average path length , @xmath221 , the tree and branch gyration radii , @xmath277 and , addressed here for the first time , the mean - square path extension , @xmath278 , and the path mean contact probability @xmath279 . the applicability of flory theory  @xcite was not a foregone conclusion . in the case of linear chains , the approach is notorious ( and appreciated ) for the nearly perfect cancellation of large errors in the estimation of _ both _ terms in eq . ( [ eq : fflory ] ) @xcite . this delicate balance might well have been destroyed for trees , where the flory energy needs to be simultaneously minimized with respect to @xmath26 and @xmath29 . a strong point is the ability  @xcite of the approach to treat trees with annealed and with randomly quenched connectivity within the same formalism . to reduce the number of unfavorable contacts , the latter can only swell in a manner analogous to linear chains  @xcite with @xmath280 , while the former have the additional option of increasing their overall size by adjusting the branching statistics , @xmath281 . our results confirm that annealed systems swell by the predicted  @xcite combination of modified branching and path stretching , and that trees with quenched ideal connectivity exhibit _ less _ overall swelling in good solvent than corresponding trees with annealed connectivity , even though they are _ more strongly _ stretched on the path level . our study also reveals some , not entirely unexpected , limitations of the available flory theory for trees . first , the underlying uncontrolled approximations are manifest in ( small ) deviations of predicted from observed or exactly known values for the exponents defined in eqs . ( [ eq : epsilon ] ) to ( [ eq : nu_path ] ) . secondly , and in analogy to the case of linear chains , flory theory fails more dramatically in predicting contact probabilities or entropies . in a forthcoming publication  @xcite , we will try to extend the description of interacting trees beyond flory theory by combining scaling arguments with the wealth of information available from the analysis of the computationally accessible distribution functions for the quantities , whose _ mean _ behaviour we have explored above . _ acknowledgements _  ar acknowledges grant prin 2010hxaw77 ( ministry of education , italy ) . re is grateful for the hospitality of the kavli institute for theoretical physics ( santa barbara , usa ) and support through the national science foundation under grant no . nsf phy11 - 25915 during his visit in 2011 , which motivated the present work . in particular , we have benefitted from long and stimulating exchanges with m. rubinstein and a. yu . grosberg on the theoretical background . this work was only possible thanks to generous grants of computer time by psmn ( ens - lyon ) and p2chpd ( ucb lyon 1 ) , in part through the equip@meso facilities of the flmsn . 10    m.  rubinstein and r.  h. colby . . oxford university press , new york , 2003 . w.  burchard . , 143:113 , 1999 . p.  bacova , l.  g.  d. hawke , d.  j. read , and a.  j. moreno . , 46:46334650 , 2013 .    j.  isaacson and t.  c. lubensky . , 41:l469l471 , 1980 . w.  a. seitz and d.  j. klein . , 75:51905193 , 1981 . j.  a. m.  s. duarte and h.  j. ruskin . , 42:15851590 , 1981 . g.  parisi and n.  sourlas . , 46:871874 , 1981 . m.  e. fisher . , 40:16101613 , 1978 . d.  a. kurtze and m.  e. fisher . , 20(7):27852796 , 1979 . a.  bovier , j.  frhlich , and u.  glaus . . north - holland , amsterdam , k. osterwalder and r. stora ( eds . ) , 1984 . a.  yu . grosberg . , 10:560565 , 2014 . a.  rosa and r.  everaers . , 112:118302 , 2014 . m. rubinstein ( 2012 ) , talk in leiden conference on `` genome mechanics at the nuclear scale '' , december 11 . a.  r. khokhlov and s.  k. nechaev . , 112a:156160 , 1985 . m.  rubinstein . , 57:30233026 , 1986 . s.  p. obukhov , m.  rubinstein , and t.  duke . , 73:12631266 , 1994 . a.  grosberg , y.  rabin , s.  havlin , and a.  neer . , 23:373378 , 1993 . a.  rosa and r.  everaers . , 4:e1000153 , 2008 . t.  vettorel , a.  y. grosberg , and k.  kremer . , 6:025013 , 2009 . leonid  a. mirny . , 19:3751 , 2011 . g . de gennes . . cornell university press , ithaca , 1979 . m.  doi and s.  f. edwards . . oxford university press , new york , 1986 . a.  yu . grosberg and a.  r. khokhlov . . aip press , new york , 1994 . b.  h. zimm and w.  h. stockmayer . , 17:13011314 , 1949 . a.  m. gutin , a.  yu . grosberg , and e.  i. shakhnovich . , 26:12931295 , 1993 . m.  daoud and j.  f. joanny . , 42:13591371 , 1981 .    p.  j. flory . . cornell university press , ithaca ( ny ) , 1953 . j.  des cloizeaux and g.  jannink . . oxford university press , oxford , 1989 . a. rosa and r. everaers . , accepted . r. everaers and a. yu . grosberg and m. rubinstein and a. rosa . , 2016 . r. everaers . , a. rosa and r. everaers . , 2016 . cui , sm and chen , zy . , 53:62386243 , 1996 . g . de gennes . , 6:715 , 1968 . e.  j. janse van rensburg and n.  madras . , 25:303333 , 1992 . hsu , w.  nadler , and p.  grassberger . , 38(4):775 , 2005 . a.  yu . grosberg and s.  k. nechaev . , 48:345003 , 2015 . j.  c. le  guillou and j.  zinn - justin . , 39:9598 , 1977 . s.  plimpton . , 117:119 , 1995 .    k.  kremer and g.  s. grest . , 92:50575086 , 1990 . h.  j. heermann , d.  c. hong , and h.  e. stanley . , 17:l261l266 , 1984 . dietrich stauffer and ammon aharony . . taylor & francis inc . , 1994 .    w.  h. press , s.  a. teukolsky , w.  t. vetterling , and b.  f. flannery . . cambridge university press , cambridge , 2 edition , 1992 . p.  j. flory . . interscience , new york , 1969 .    * supplementary data *","summary":"we present computer simulations of three systems of randomly branching polymers in dimensions : ideal trees and self - avoiding trees with annealed and quenched connectivities . in all cases , we performed a detailed analysis of trees connectivities , spatial conformations and statistical properties of linear paths on trees , and compare the results to the corresponding predictions of flory theory . we confirm that , overall , the theory predicts correctly that trees with quenched ideal connectivity exhibit _ less _ overall swelling in good solvent than corresponding trees with annealed connectivity even though they are _ more strongly _ stretched on the path level . at the same time , we emphasize the inadequacy of the flory theory in predicting the behaviour of other , and equally relevant , observables like contact probabilities between tree nodes .","abstract":"we present computer simulations of three systems of randomly branching polymers in dimensions : ideal trees and self - avoiding trees with annealed and quenched connectivities . in all cases , we performed a detailed analysis of trees connectivities , spatial conformations and statistical properties of linear paths on trees , and compare the results to the corresponding predictions of flory theory . we confirm that , overall , the theory predicts correctly that trees with quenched ideal connectivity exhibit _ less _ overall swelling in good solvent than corresponding trees with annealed connectivity even though they are _ more strongly _ stretched on the path level . at the same time , we emphasize the inadequacy of the flory theory in predicting the behaviour of other , and equally relevant , observables like contact probabilities between tree nodes . we show , then , that contact probabilities can be aptly characterized by introducing a novel critical exponent , , which accounts for how they decay as a function of the node - to - node path distance on the tree ."}
{"article_id":"hep-ph9408305","section_id":"i","document":"stimulated by recent  @xcite and planned  @xcite experiments with polarized electron and proton beams , spin - dependent distribution functions have received a lot of attention . due to increasing accuracy , measurements of higher - twist distributions seem feasible in the near future . they are particularly interesting , since they contain valuable information on quark - gluon correlations . the goal of this paper is to analyze the role of quark transverse momentum in the twist - three distributions @xmath5 and @xmath6 , or equivalently the linear combinations @xmath7 and @xmath8 .    at leading - order level , one may consider transverse - momentum - dependent distributions which can be measured in drell - yan ( dy ) scattering at small but fixed @xmath9  @xcite . in deep inelastic lepton - hadron scattering ( dis ) or in dy integrated over @xmath9 one measures the distributions integrated over transverse momentum ; these are the twist - two unpolarized momentum distribution @xmath10 and two twist - two spin - dependent distributions , the helicity distribution @xmath11 and the transverse spin distribution @xmath12 . at leading order it does not matter what the transverse momentum dependence is ; the observables ( i.e. , structure functions and asymmetries ) do not change if one assumes zero transverse momentum [ i.e. , @xmath13 distributions . at subleading @xmath3 , the situation is less simple . as was demonstrated in ref . @xcite , for instance , assuming free quarks without transverse momentum gives the non - physical result @xmath14 . thus , even though @xmath0 and @xmath1 do not depend explicitly on @xmath15 , assuming zero transverse momentum may considerably alter their shape ( in @xmath16 ) . we will make these statements more precise in due course . first , let us recall some facts about the transverse spin - dependent distribution @xmath5 @xcite . using operator - product - expansion ( ope ) techniques , one shows that @xmath5 can be decomposed in three pieces , a twist - two part depending on @xmath11 , also known as the wandzura - wilczek ( ww ) term  @xcite , a quark - mass part depending on @xmath12  @xcite , and an explicitly interaction - dependent part . the latter is the most interesting , since it is sensitive to off - shellness and confinement effects . instead of using the ope , we rederive the different terms , using nonlocal matrix elements only . in this approach the transverse momentum of quarks is an essential ingredient . the nonlocal matrix element that fixes the interaction - dependent part contains two good quark fields and one transverse gluon field , so that it can be given a clear parton interpretation  @xcite . of course , if moments are taken , one should recover the ope local matrix elements . in this formalism it is also straightforward to derive the burkhardt - cottingham ( bc ) sum rule @xmath17  @xcite , although one must make assumptions . the status of the bc sum rule is less rigorous than , for instance , the bjorken sum rule . it was claimed that in perturbation theory it is valid at least up to @xmath18  @xcite , although recently this claim was disputed  @xcite . the twist - three distribution function @xmath6  @xcite is less well - known . it does not occur in the inclusive dis cross section other than multiplied with a quark - mass factor ( like @xmath12 , it is chirally odd ) . nonetheless , one can analyze it using the ope - based techniques  @xcite . again one finds three parts ; a twist - two part depending on @xmath12 , a quark - mass part depending on @xmath11 , and an interaction - dependent part . the interaction dependent part can also be given a parton interpretation@xcite . using the same techniques as for @xmath0 , we derive within our approach these parts , expressing them in a finite number of nonlocal matrix elements . we derive a sum rule very similar to the bc sum rule , namely , @xmath19 .    in order to support our claim that explicit treatment of quark transverse momenta is important at twist - three , we consider @xmath9-averaged polarized dy scattering . jaffe and ji derived an @xmath3 asymmetry , @xmath4 , for longitudinally - transversely polarized dy scattering  @xcite . in their calculation they assumed zero quark transverse momentum . without this assumption we find modifications in the asymmetry . to estimate the difference between the two results we use bag - model distributions . the difference turns out to be considerable . this paper has the following structure . in sec . [ sec2 ] , we analyze the content of @xmath5 and @xmath6 , using lorentz symmetry , discrete symmetries and the qcd equations of motion . we decompose the distributions in the three different parts , and derive the sum rules . in sec . [ sec3 ] we calculate the polarized dis hadron tensor , emphasising the role of transverse momentum . in sec .  [ sec4 ] , the more involved but essentially similar hadronic tensor for polarized dy scattering is considered , from which follows the double - spin asymmetry .","summary":"we show how to derive the burkhardt - cottingham sum rule in this approach and derive a similar sum rule for the chiral - odd distribution . the effect of intrinsic transverse momentum in experimental observables is illustrated in the calculation of the double - spin asymmetry in drell - yan scattering .","abstract":"in a nonstandard way we split up the polarized quark distributions and into their twist - two , quark - mass , and interaction - dependent parts , emphasizing the sensitivity to quark intrinsic transverse momentum . we show how to derive the burkhardt - cottingham sum rule in this approach and derive a similar sum rule for the chiral - odd distribution . the effect of intrinsic transverse momentum in experimental observables is illustrated in the calculation of the double - spin asymmetry in drell - yan scattering ."}
{"article_id":"1609.03788","section_id":"c","document":"our analysis of the dynamic stark effect , the photon statistics , and the generation of bipartite entanglement is based on the evaluation of the emission properties of a laser - driven quantum system . traditional approaches employ a master equation in an adiabatic approximation or perform a perturbative expansion in the laser - driving strength . they are restricted to ( weak ) off - resonant driving . the resonant case studied here requires the use of the full input - output formalism and the full master equation in the floquet basis . essential is the careful distinction of the transitions between different floquet states and their fourier modes . studying a few emitters in a laser - driven cavity we show that the dynamic stark effect , i.e. , the shift of the quasienergies @xmath28 , first appears in the second order of the laser - driving strength @xmath15 . this result is in accordance with an analytical calculation of the quasienergies for a single emitter with interaction terms in rotating - wave approximation . calculating the emission spectra for multiple emitters beyond the rotating - wave approximation we verified the validity of the general proportionality @xmath162 , where @xmath11 is the emitter - cavity coupling strength . we thus expect that laser intensity depended spectroscopic measurements will provide the same result , e.g. , for the vacuum rabi splitting .    the stationary state of the emitter - cavity system without laser - excitation  but weakly coupled to an environment at temperature @xmath100is the thermal state . this state is modified if the laser intensity is finite . for @xmath122 , the populations of the floquet states are thermally distributed . increasing @xmath15 , the dynamic stark shift of the quasienergies leads to modified thermal populations . in addition , the energy impact from the laser causes further population transfers . the stationary state is thus no longer thermal . nevertheless , according to our results for the entanglement between two emitters ( that depends only on the stationary populations ) , significant changes of the stationary state appear for @xmath163 . the stationary state is thus quite robust against the laser - excitation . in contrast to the stationary state , the statistics of emitted photons is strongly influenced by the external laser . the changes of the glauber function for small laser intensity have to be explained by the specific form of the output operator that connects different floquet states and includes transitions between their fourier modes . the contribution from these resonant transition sequences , in combination with a possible population enhancement due to an energetically lower starting point of these sequences , is responsible for the tremendous effect on the photon statistics . hence , changing the driving strength can significantly modify the statistics of the emitted photons . in particular , thermal light emission at weak emitter - cavity coupling is replaced by the emission of photons with highly super - poissonian statistics . this work was supported by deutsche forschungsgemeinschaft through the collaborative research centers 652 ( project b5 ) and transregio 24 ( project b10 ) .","summary":"we show that the dynamic stark effect , i.e. , the shift of spectral lines , first appears in the second order of the laser intensity . for the glauber function","abstract":"we calculate the emission spectra , the glauber function , and the entanglement of formation for a few two - level emitters coupled to a single cavity mode and subject to an external laser - excitation . to evaluate these quantities we couple the system to environmental degrees of freedom which leads to dissipative dynamics . because of the periodic time - dependence of the system hamiltonian , the coefficients of the ( markovian ) master equation are constant if floquet states are used as the computational basis . studying the emission spectra we show that the dynamic stark effect , i.e. , the shift of spectral lines , first appears in the second order of the laser intensity . for the glauber function , we find clearly distinguished parameter regimes of super- and sub - poissonian light emission and explain the additional features appearing for finite laser intensity in terms of the quasienergy spectrum of the driven emitter - cavity system . finally , we analyze the temperature and emitter - cavity coupling regimes where entanglement among the emitters is generated , and show that the laser - excitation leads to a decrease of entanglement ."}
{"article_id":"1411.1522","section_id":"i","document":"the potential of the pure quartic oscillator is given by @xmath124 which leads to an effective hamiltonian of the form @xmath125 from this hamiltonian it is easy to get the equations of motion for the expectation values , @xmath126 and for the moments @xmath127 g^{a-1,b } \\nonumber\\\\&-&4 \\,a \\,\\lambda   \\left[3\\ ,   q^2\\ , g^{a-1,b+1}+3\\ , q \\ , g^{a-1,b+2}+g^{a-1,b+3}\\right ] \\nonumber\\\\ & + & a \\,\\hbar^2 \\,\\lambda \\,(a-2)\\ , ( a-1)\\ ,    [ q\\,g^{a-3,b}+g^{a-3,b+1}].\\end{aligned}\\ ] ] as can be seen , in this case all orders couple . more specifically , in the equation for a moment @xmath13 there appear moments of order two , three and of all orders from @xmath128 to @xmath129 . the centroid of a classical distribution will follow the same equations ( [ qquartic ] ) and ( [ pquartic ] ) , replacing moments @xmath13 by their classical counterparts , @xmath130 whereas the evolution of the classical moments will be given by @xmath131 c^{a-1,b } \\\\\\nonumber&-&4 \\,a \\,\\lambda   \\left[3\\ ,   q^2\\ , c^{a-1,b+1}+3\\ , q \\ , c^{a-1,b+2}+c^{a-1,b+3}\\right].\\end{aligned}\\ ] ] the explicit order coupling differs a little bit from the quantum case , since in this equation there are only moments of order two , three and of all orders between @xmath132 and @xmath129 .      in order to obtain the stationary states of the pure quartic oscillator , the infinite set of algebraic equations obtained by equaling to zero the right - hand side of eqs . ( [ qquartic][eq_quartic ] ) must be solved . furthermore , recursive relation ( [ recursive ] ) must also be obeyed . in this particular case , that relation takes the following form : @xmath133 with the energy given by the numerical value of the expectation value of the hamiltonian , @xmath134    in practice , due to the coupling of the system , it is necessary to introduce a cutoff in order to get a finite system and be able to solve it . in our case different cutoffs have been considered ( specifically @xmath14= 15 , 20 , 25 , and 30 ) and the mentioned system of equations , in combination with relation ( [ relat ] ) and the definition of the energy ( [ energy_quartic ] ) , has been analytically solved . the idea behind performing this computation for several cutoffs is to study the convergence of the solution , that is , to check whether the solution for the moments does not change when considering higher - order cutoffs .    in principle , there are two different solutions : one that corresponds to the classical stationary configuration ( and thus its equilibrium position is at the origin @xmath135 ) and another , for which the position must not be vanishing [ note that this is possible due to the moment terms that appear in the hamilton equation ( [ pquartic ] ) ] and does not have a classical point counterpart . nevertheless , for this latter case , the solution for some moments with both even indices turns out to be negative , which makes this solution invalid . therefore , and as one would expect from symmetry considerations , the expectation values of any stationary state of the quartic oscillator corresponds to the origin of the phase space ( @xmath100 ) . furthermore , it can be seen that all its corresponding moments @xmath13 are vanishing in case any of the indices @xmath136 or @xmath137 is an odd number . the remaining moments can be written in terms of the energy @xmath108 and the fluctuation of the position @xmath107 , or any other chosen moment . that is , there is not enough information in our system of equations to fix all moments and one of them is free . regarding the convergence of the solution , comparing the solution obtained with the cutoff @xmath138 with the one corresponding to @xmath139 , we see that the expression of all moments coincides up to order 8 , whereas the solution with @xmath138 and @xmath140 give the same expression for all moments up to order 12 . finally , solutions that correspond to @xmath138 and @xmath141 coincide up to order 14 . from here the existence of a clear convergence of the solution with the cutoff order is concluded . nevertheless , this convergence seems to be slower with higher orders . here the explicit expressions for all nonvanishing moments up to sixth order is provided : @xmath142 the classical moments @xmath27 , as always , take the same values as their quantum counterparts with the particularization @xmath22 . in these expressions the singular behavior of the limit @xmath143 is made explicit as the divergence of several moments . this fact does not allow to perform regular perturbative treatments of this system .    in summary , after imposing the stationarity condition on eqs . ( [ qquartic][eq_quartic ] ) and using the definition of the energy ( [ energy_quartic ] ) in combination with the recursive relation ( [ relat ] ) , the only information left in order to characterize completely any stationary state of the pure quartic oscillator is the energy @xmath108 and the fluctuation of the position @xmath107 . in addition to these equations already mentioned , there is still some information more than we can get by making use of the inequalities obtained in ref . @xcite . in the following , use will be made of those relations to constrain the values of @xmath107 and the energy @xmath108 . for instance , heisenberg uncertainty principle ( [ heisenberg ] ) provides a lower bound for the product between @xmath108 and @xmath107 : @xmath144 higher - order inequalities give more complicated relations , which must be fulfilled by the energy @xmath108 and the fluctuation of the position @xmath107 of any stationary state of this system .    for the particular case of the ground state a reasonable assumption is that , as happens for the harmonic oscillator , it saturates the above relation . this would give @xmath145 and let the energy of the ground state @xmath146 as the only unknown physical quantity in ( [ momentsquartic ] ) . introducing then these expressions of the moments of the ground state in terms of @xmath146 in the higher - order inequalities , an upper and lower bound for the energy is obtained . by considering inequalities that only contain moments up to fourth - order yields the following result : @xmath147 or , in decimal notation , @xmath148 which already provides a good constraint on the energy . furthermore , all inequalities that contain moments up to order six reduce to the following tighter interval of validity for the energy : @xmath149 or , writing these fractions as decimal numbers , @xmath150 this gives a very tight constraint on the energy of this bound state . nevertheless , the exact ( numerically computed ) energy of this state is available in the literature ( see e.g. @xcite ) : @xmath151 . , instead of @xmath152 . therefore a factor @xmath153{4}$ ] must be introduced to relate the energy eigenvalues given in those references with the one obtained by the notation of the present paper . ] this numerical value is very close but outside the derived interval . therefore , we can conclude that , even if the saturation of the heisenberg uncertainty is a reasonable assumption for the ground state that provides a good estimation of the ground energy , this assumption is not satisfied and the uncertainty relation is not completely saturated for the present model . this analysis shows the practical relevance of the inequalities that were derived in ref . @xcite as a complementary method to extract physical information from the system . certainly the inequalities will not give exact relations between different quantities , but intervals of validity can be extracted from them . finally , let us stress the importance of considering higher - order inequalities . note that the interval derived from fourth - order inequalities ( [ interval4 ] ) does indeed allow the exact ( numerical ) value of the ground energy , and thus in principle permits the saturation of the uncertainty relation . therefore , in this particular example inequalities up to fourth order allowed a property of the system , which is forbidden by the stronger condition derived from higher - order ones . the classical point trajectory of the pure quartic oscillator , that is , the solution to eqs . ( [ qquartic]-[pquartic ] ) neglecting all moments , can only be written in terms on hypergeometric functions . nevertheless , the orbits on the phase space are easily obtained by the conservation of the classical energy : @xmath154 . contrary to the harmonic oscillator , the period depends on the energy @xmath155 of the orbit , and it is not a constant for different orbits . for latter use , note that the maximum ( classical ) value of the position and the momentum can be directly related to the energy as @xmath156 and @xmath157 . in order to compare different solutions , below we will also make use of a ( squared ) euclidean distance on the phase space ( @xmath158 ) . the maximum distance from the origin of a given orbit is reached at ( @xmath159 ) . we are interested on analyzing the quantum and classical evolution of a distribution that , respectively , follows eqs . ( [ qquartic]-[eq_quartic ] ) and ( [ qquarticc]-[eq_quarticc ] ) . nonetheless , due to the complicated form of these evolution equations , the possibility of getting an analytical solution seems unlikely . hence , in order to analyze the dynamics of the system , it is necessary to resort to numerical methods . here a comment about notation is in order . when the meaning is not clear from the context , we will sometimes denote as @xmath160 the solution of the quantum distributional system ( [ qquartic]-[eq_quartic ] ) , @xmath161 the solution of the classical distributional system ( [ qquarticc]-[eq_quarticc ] ) , and finally @xmath162 the solution corresponding to the classical point trajectory , that is , the solution to eqs . ( [ qquartic]-[pquartic ] ) dropping all moments . the very same notation will be used for the different solutions of the momentum @xmath163 .    for a numerical resolution of the system , two choices have to be made . on the one hand , for practical reasons , a cutoff @xmath14 has to be considered in order to truncate the infinite system . on the other hand , it will be necessary to choose initial conditions for the state to be analyzed .    regarding the truncation of the system , the dynamical equations for different values of the cutoff will be considered . more precisely , both the quantum system ( [ qquartic]-[eq_quartic ] ) and the classical distributional system ( [ qquarticc]-[eq_quarticc ] ) for every order up to tenth order will be solved . in this way , it will be possible to check the convergence of the solution with the considered @xmath14 , as well as study differences between the classical and quantum moments .    concerning the initial conditions , since the movement of the system is oscillatory around the equilibrium point @xmath135 , a vanishing value for the initial expectation of the position @xmath164 will be considered without loss of generality . for the expectation of the momentum @xmath12 , in order to check the dependence of the properties of the system with the energy , we will make evolutions for several values , namely @xmath165 and @xmath166 . note that the initial classical ( point ) energy ( @xmath167 ) will not be conserved through evolution ; instead , the complete hamiltonian ( [ hamiltonian_quartic ] ) will be constant . nevertheless , due to the correspondence principle , the larger the classical energy , a somehow more classical behavior is expected to be found . this can already be inferred from the equations themselves : in the case that moments are negligible with respect to expectation values @xmath11 and @xmath12 , the centroid will approximately follow a classical point orbit on phase space .    as for the initial values of the fluctuations and higher - order moments , a peaked state given by a gaussian of width @xmath168 will be chosen . its corresponding moments @xmath13 are vanishing if any of the indices @xmath136 or @xmath137 are odd . the only nonvanishing moments take the following values @xcite : @xmath169 therefore , initially the fluctuation of the position and of the momentum are @xmath170 . in principle the initial conditions for the classical pair @xmath11 and @xmath12 should be chosen large in comparison with their fluctuations , so that we can be safely say that we are in a semiclassical region where this method is supposed to provide trustable results . nonetheless , in this case the system oscillates around @xmath135 and in the turning points the momentum vanishes @xmath87 . thus , for this case the condition of @xmath11 and @xmath12 being much larger than their corresponding fluctuations can not be a good measure of semiclassicality . we will check if , as already mentioned above , the classical ( point ) energy of the system does play such a role .    given this setting , we will be interested in analyzing several aspects of the system . @xmath171 the validity of this method based on the decomposition of the classical and quantum probability distributions in terms of moments . in particular the convergence of the system with the truncation order @xmath14 as well as other control methods , like the conservation of the full hamiltonian , will be analyzed . @xmath172 the dynamical behavior of the moments . @xmath173 the deviation , due to quantum effects , from the classical trajectory on the phase space @xmath174 the relative relevance of the two different quantum effects that have been discussed in sec . [ sec_formalism ] : the distributional ones and the noncommutativity or purely quantum ones . @xmath175 the validity of the correspondence principle . that is , do systems with a larger energy have somehow a more classical behavior than those with lower energy ?    regarding the first two question ( @xmath171 and @xmath172 ) all results that will be commented for the quantum moments apply also to the classical ones . furthermore , except for the last issue ( @xmath175 ) about the correspondence principle , the qualitative behavior of the system is the same for all considered values of initial momentum @xmath176 . hence , the results regarding the first four points ( @xmath171 to @xmath174 ) will be presented for the particular case of @xmath177 and , finally , the last point ( @xmath175 ) will be discussed by comparing results obtained for different initial values of the classical energy . in all numerical simulations @xmath178 and @xmath179 have been considered . @xmath171 the natural tendency of the both quantum and classical moments is to increase with time , since the dynamical states are deformed through evolution . this formalism is best suited for peaked states so , when higher - order moments become important , it is expected not to give trustable results . numerically this is seen in the fact that , after several periods , the system becomes unstable and thus the results are no longer trustable .    in order to check the validity of our results we have several indicators at hand : numerical convergence of the solution , conservation of the constants of motion ( in this case the full hamiltonian ) , convergence of the results with the order of the cutoff , and fulfillment of the inequalities derived in @xcite . the numerical convergence has been checked by the usual method : by computing several solutions with an increasing precision and confirming that the difference between them and the most precise one tends to zero . the full hamiltonian has also been verified to be conserved during the evolutions presented in this paper .    for the analysis of the convergence of the system with the truncation order , we define the squared euclidean distance between points on the phase space as @xmath180 ^ 2+[p_n(t ) - p_{n-1}(t)]^2 $ ] , with @xmath181 and @xmath182 being the solution of the system truncated at @xmath54th order . in particular @xmath183 and @xmath184 correspond to classical point orbits . this will serve as a measure of the departure of the solution at every order from the previous order . in fig . [ figconvergence ] the distance @xmath185 between consecutive solutions is drawn in a logarithmic scale for @xmath186 for the first three periods of the evolution . from this plot it is clear that , at least during a few periods , the convergence is very fast with the truncation order . we have not included the @xmath187 and @xmath188 , since their value is lower than @xmath189 , the estimated numerical error for the solutions shown in this plot , during the first three periods . it is interesting to note that , whereas the rest of the @xmath185 have a more complicated structure , @xmath190 ( shown by the thickest black line in fig . [ figconvergence ] ) follows a periodic pattern with a local minimum every quarter of a period . these points of minimum deviation from the classical orbit correspond to points with maximum momentum ( @xmath135 ) and to turning points ( @xmath87 ) . ^2+[p_n(t ) - p_{n-1}(t)]^2 $ ] is shown in a logarithmic plot for @xmath186 . the distance between the second - order and the classical point trajectory ( @xmath190 ) corresponds to the black ( thickest ) line . for the distance corresponding to higher orders ( @xmath185 ) , the following colors have been used : brown ( @xmath191 ) , green ( @xmath192 ) , red ( @xmath193 ) , blue ( @xmath194 ) , purple ( @xmath195 ) , and orange ( @xmath196 ) ; the thickness of the lines being decreasing with the order . the estimated numerical error of these solutions is around @xmath189 , thus higher orders are almost numerical error during the first two periods . note that , at any time , we get a very rapid and strong convergence with the considered order.,scaledwidth=48.0% ]     over its maximum value @xmath197 ( black continuous thick line ) with respect to to the time ( measured in terms of the period @xmath198 ) is shown . the rest of the lines correspond to some moments @xmath13 rescaled by a factor for illustrational purposes . more precisely , the red ( long - dashed ) line corresponds to @xmath199 , the green ( dot - dashed ) line to @xmath200 , the blue ( dotted ) line to @xmath201 , and the gray ( continuous thin ) line to @xmath202 . the behavior of the moments is oscillatory , with an increasing amplitude.,scaledwidth=48.0% ]    remarkably we have found that the inequalities are the first indicator to signalize the wrong behavior of the system . in the particular case with @xmath177 , the tenth - order solution obeys all inequalities that contain only moments up to fourth order during more than five periods . but some of the inequalities that contain moments of sixth order are violated soon after the fourth cycle . finally , some inequalities with eighth order moments are violated after around 2.53 cycles . in fact , it is expected that the values obtained for higher - order moments be less accurate than those for lower - order ones due to the truncation of the system . as already commented above , in the evolution equation of a moment @xmath13 , there appear moments from order @xmath128 to @xmath129 [ only from @xmath132 to @xmath129 for the classical moments ] . thus , when we perform the truncation , let us say , at order @xmath14 , we remove several terms from the equations of motion for moments of order @xmath203 and @xmath204 , whereas evolution equations for lower - order moments are considered in a complete form . therefore , moments of order @xmath203 and @xmath204 suffer the presence of the cutoff directly . on the other hand , lower - order moments only feel the presence of the cutoff indirectly , due to the coupling of the equations .    in summary , after the analysis explained in the last few paragraphs , it is quite safe to assert that the results derived during the first 2.5 cycles are completely trustable [ for @xmath177 ] . as can be seen , in most of the plots only two periods are shown . @xmath172 the fluctuations and higher - order moments are oscillatory functions that evolve increasing their amplitude . in fig . [ figqmoments ] the evolution of some moments , as well as of the expectation value of the position @xmath11 , is shown as an example . note that , for illustrational purposes , the moments have been multiplied by different factors and the position is divided by its ( classical ) maximum value @xmath197 . interestingly , moments @xmath107 and @xmath206 are almost vanishing at turning points , when the position takes its maximum value , and have a maximum soon after @xmath11 crosses its origin .    , @xmath12 , and @xmath207 ( divided by their maximum values ) is shown in combination with the operators @xmath208 and @xmath209 acting on them . the black ( thinnest ) line represents the evolutions of the quantity we are considering , for instance in the upper plot @xmath210 , the blue ( thickest ) line represents the distributional effects , in the mentioned plot @xmath211 , whereas the red line stands for the purely quantum effects , in the considered graphic @xmath212.,title=\"fig:\",scaledwidth=50.0% ] + , @xmath12 , and @xmath207 ( divided by their maximum values ) is shown in combination with the operators @xmath208 and @xmath209 acting on them . the black ( thinnest ) line represents the evolutions of the quantity we are considering , for instance in the upper plot @xmath210 , the blue ( thickest ) line represents the distributional effects , in the mentioned plot @xmath211 , whereas the red line stands for the purely quantum effects , in the considered graphic @xmath212.,title=\"fig:\",scaledwidth=50.0% ] + , @xmath12 , and @xmath207 ( divided by their maximum values ) is shown in combination with the operators @xmath208 and @xmath209 acting on them . the black ( thinnest ) line represents the evolutions of the quantity we are considering , for instance in the upper plot @xmath210 , the blue ( thickest ) line represents the distributional effects , in the mentioned plot @xmath211 , whereas the red line stands for the purely quantum effects , in the considered graphic @xmath212.,title=\"fig:\",scaledwidth=50.0% ]    @xmath173 and @xmath174 in order to analyze the deviation of the quantum and classical distributional trajectories from their corresponding classical point orbit , two operators , @xmath208 and @xmath209 , are defined as follows @xmath213 the same definitions apply for @xmath214 and @xmath215 . these operators are a measure of the two quantum effects that were defined in @xcite and have been discussed in sec . [ sec_formalism ] of the present paper . on the one hand , the operator @xmath208 will contain the strength of the distributional effects . on the other hand , @xmath209 will encode the intensity of purely quantum effects , whose origin is due to the @xmath0 factors that appear explicitly in the quantum equations of motion . in our numerical analysis @xmath161 and @xmath160 will be considered to be the solutions to the corresponding truncated system at order 10 . finally , the complete departure from the classical orbit will be given by the sum of both differences : @xmath216    figure [ figp010 ] shows the evolution of the system as well as the differences given by the operators @xmath208 and @xmath209 acting on different variables in terms of time . ( note that these differences are multiplied by certain enhancement factors for illustrational purposes . ) more precisely , in the upper plot of the mentioned figure the evolution of the position divided by its ( classical ) maximum @xmath210 , as well as the differences @xmath217 and @xmath212 , are shown . the middle plot represents the evolution of @xmath218 with its corresponding @xmath214 and @xmath215 . finally , in the lower graphic the squared euclidean distance from the origin of the phase space is plotted , as well as the deviations @xmath219 and @xmath220 . must be understood as @xmath221 . ] this distance has been divided by its maximum classical value which , as commented above , can be easily related to the initial conditions as @xmath222 . looking at the enhancement factors that have been introduced for the differences @xmath208 and @xmath209 so that objects that have been plotted appear approximately with the same order of magnitude , it is straightforward to see that for all quantities the departure from the classical point trajectory @xmath223 is mainly due to the distributional effects measured by @xmath208 . in particular , during the two cycles that are shown , the absolute maximum departure from the classical trajectory is of the order of @xmath224 for the position and @xmath225 for the momentum . combining this result , it is direct to obtain the maximum departure as measured by the squared euclidean distance on the phase space : @xmath226 ; which also can be obtained from the lower plot of fig . [ figp010 ] .    as already commented , and as one of the main results of this paper , in this model we have shown that the distributional effects are much more relevant than the purely quantum ones . let us analyze its relative importance : from the values that can be seen in fig . [ figp010 ] we have that @xmath227 . this ratio happens to be of the order of @xmath110 , which is a measure of the purely quantum effects in the equations of motion . nevertheless , as we will be shown below when considering initial conditions of higher energy , this is not generic . in fact , this is a property of the nonlinearity of the equations : the effects of a term of order @xmath110 on the equations of motion are not necessarily of the same order in the solution . finally , it is of interest to analyze the time evolution of the terms @xmath211 and @xmath228 . note that both are periodic functions , with approximately the same period as the classical system @xmath198 , with an amplitude that increases with time . in fact , @xmath211 and @xmath228 follow the same pattern , that is , they have qualitatively the same form , but with a phase difference of @xmath229 so that when one of them is at a maximum ( or at a minimum ) the other one is around zero . in the case of @xmath230 and @xmath231 , they are also periodic functions with period @xmath198 , follow the same pattern and @xmath229 dephased . the main difference between the pattern followed by @xmath211 and @xmath228 with respect to the one followed by @xmath230 and @xmath231 is that , whereas the formers have just a critical point between consecutive changes of sign , the latters oscillate twice ( producing three critical points ) between two of their zeros . the net result of all commented effects on the phase - space orbits can be seen in the lower plot of fig . [ figp010 ] . minimum departure from classical orbit occurs at turning points and when @xmath11 crosses the origin . in this plot it is possible to see again that @xmath208 and @xmath209 follow qualitatively the same pattern but , interestingly , they are ( almost ) not dephased ; the phase differences in position and in momentum compensate each other . in a more detailed level , it is possible to observe that critical points of @xmath232 and @xmath233 do not exactly coincide in time : there is a slight delay between them . in addition , from these plots it can also be inferred that the orbit followed by the expectation values of quantum states does not coincide at any point with its classical counterpart , since there is no time when all corrections vanish : @xmath234 .    . note that enhancement factors , by which differences between solutions are multiplied , differ from the previous case.,scaledwidth=50.0% ]    @xmath175 finally , regarding the correspondence principle , it is necessary to relate the results commented above for the case @xmath177 , with results obtained for larger values of the initial condition of the momentum . in particular , fig . [ figp0100 ] shows the plot equivalent to the last graphic of fig . [ figp010 ] for the initial value @xmath235 . as already commented above , the qualitative behavior of the system does not change . nonetheless , there are significant modifications in quantitative aspects that lead us to conclude that the behavior is more classical . first of all we notice that the larger the value of @xmath176 , the longer ( in terms of its period ) the system stays stable . this is due to the fact that the corrections due to the moments are relatively smaller and take longer to move the system significantly from its classical trajectory . more precisely , as can be seen in fig . [ figp0100 ] , the system has to be evolved during six cycles so that the departure from the classical trajectory , dominated by distributional effects , @xmath232 is of the same order of magnitude as the one obtained for the previous ( @xmath177 ) case with just two cycles . in addition , as another important result of this paper , we note that the relative importance between the two quantum effects , which can be measured by the quantity @xmath236 is smaller the larger the energy of the system . that is , from fig . [ figp0100 ] , we get @xmath237 for the case with larger energy ( @xmath235 ) , whereas @xmath238 for the previous less - energetic case with @xmath177 . the case @xmath239 has also been checked for which , after a little bit more than half a cycle , the following values are measured : @xmath240 and @xmath241 . these results give @xmath242 for the case @xmath239 . this result shows that the quantity @xmath243 defines a semiclassical behavior of a system when its value is small . nonetheless , when @xmath243 tends to zero there are still distributional effects present . this shows that , as commented in the introduction , the classical limit of a quantum state is an ensemble of classical trajectories described , in this context , by its corresponding classical moments .","summary":"in addition , as an example of anharmonic system , the pure quartic oscillator is analyzed . finally , dynamical states are also considered in order to study the differences between their classical and quantum evolution .","abstract":"in a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented . here the application of this formalism to the system of a particle moving on a potential is considered in order to derive physical implications about the classical limit of a quantum system . the complete set of harmonic potentials is considered , which includes the particle under a uniform force , as well as the harmonic and the inverse harmonic oscillators . in addition , as an example of anharmonic system , the pure quartic oscillator is analyzed . classical and quantum moments corresponding to stationary states of these systems are analytically obtained without solving any differential equation . finally , dynamical states are also considered in order to study the differences between their classical and quantum evolution ."}
{"article_id":"1411.1522","section_id":"c","document":"in this paper the formalism presented in ref . @xcite , to analyze the evolution of classical and quantum probability distributions , has been applied to the system of a particle on a potential . due to the kinetic term , the hamiltonian of this system is quadratic in the momentum , and its dependence on the position is completely encoded in the potential . the special properties of the harmonic hamiltonians , which are defined as those that are at most quadratic on the basic variables , makes them much easier to be analyzed . thus , the study has been divided in two different sectors . on the one hand , the complete set of harmonic hamiltonians has been studied ; and , on the other hand , for the anharmonic case an interesting example has been chosen : the pure quartic oscillator .    by choosing different functional forms of the potential , three physically different harmonic hamiltonians can be constructed . first , the system of a particle moving under a uniform force , which also includes the free particle when the value of this force is considered to be zero . second , the harmonic oscillator with a constant frequency @xmath109 . and finally the inverse harmonic oscillator , which can be understood as a harmonic oscillator with imaginary frequency . for all of them the moments corresponding to their stationary and dynamical states have been explicitly obtained . in this framework the stationary states correspond to fix points of the dynamical system , which is composed by the infinite set of equations of motions for expectation values and moments . therefore , in order to find these stationary moments , the algebraic system obtained by dropping all time derivatives must be solved . with this procedure , and contrary to the usual treatment of considering the time - independent schrdinger equation , the stationary moments can be obtained without solving any differential equation . more precisely , regarding the particle under a uniform force , it has been shown that even if the classical ( distributional ) case accepts a stationary state where the particle is at rest at any position and with arbitrary value of its corresponding ( high - order ) fluctuations , such a state is forbidden in the quantum system by the heisenberg uncertainty principle . for the harmonic oscillator , the moments corresponding to any stationary state have been obtained in terms of the frequency of the oscillator and the energy of the state . these relations are valid for any stationary state . the only ingredient that is not derived by the present formalism , and thus one needs to include by hand , are the eigenvalues of the energy . finally , it has been proven that the inverse harmonic oscillator can not have stationary states .    concerning the pure quartic oscillator , the moments corresponding to any stationary state have been derived by making use of the above technique . in this case , the system of equations is not complete and thus it does not fix the whole set of moments . hence , apart from the energy of the state , the fluctuation of the position has been left as a free parameter . furthermore , in order to constraint the values of these two parameters , use has been made of the high - order inequalities which were derived in @xcite . for the particular case of the ground state , a reasonable assumption is that the heisenberg uncertainty relation is saturated . this leads to a tight interval for the value of the ground energy ( [ interval6 ] ) . it turns out that the exact ( numerically computed ) value of this energy is not contained in this interval , but it is quite close . therefore one can assert that , even if the exact saturation of the heisenberg uncertainty relation provides a good approximation for the ground state of the pure quartic oscillator , it is not exactly obeyed . the above analysis shows the practical relevance of the inequalities that were derived in @xcite as a complementary method to extract physical information from the system . in particular , high - order inequalities are of relevance because the conditions they provide are stronger than the ones obtained from lower - order inequalities .    finally , a numerical computation of the dynamical states corresponding to the pure quartic oscillator has been performed . to that end , a gaussian in the position has been assumed as the initial state . in this setting , a number of interesting results have been obtained . first , the validity of the method has been analyzed . the present formalism is valid as long as the high - order moments that one drops with the cutoff are small . the natural tendency of the moments in this system is to oscillate with a growing amplitude and thus , from certain point on , this method will not give trustable results . in order to find the region of validity of the method , on the one hand , different cutoffs have been considered and the convergence of the solution with the cutoff order has been studied . on the other hand , the conservation of the hamiltonian , as well as the fulfillment of the high - order inequalities mentioned above , has been monitored during the evolution . with these control methods at hand , one can estimate when ( after how many cycles ) the formalism is not valid anymore . in particular , this `` validity time '' increases with the value of the initial classical energy . second , the departure of the centroid from its classical point trajectory has been analyzed , as well as the relative relevance of the two different quantum effects : the distributional and the purely quantum effects . it has been shown that , as one would expect , the former ones , which are also present in the evolution of a classical probability distribution , are much more relevant than the latter ones . nonetheless , the strength of the purely quantum effects in the equations of motion is of order @xmath110 . therefore , a change in the numerical value of the planck constant would tune the relative relevance of these effects . finally , the correspondence principle has also been verified in the sense that the larger the classical initial value of the energy is chosen , the smaller purely quantum effects are measured . in particular , the smallness of the quantity @xmath243 , as defined in ( [ gamma ] ) , gives a precise notion of semiclassicality . in fact the vanishing of @xmath243 would define a complete classical ( distributional ) behavior of the system . let us stress the fact that this classical behavior is distributional . in other words , and as commented already throughout the paper , the classical limit of a quantum state is not a unique orbit on the phase space but , instead , an ensemble of classical trajectories which are described by a probability distribution or , in the context of the present formalism , by its classical moments .    the author thanks carlos barcel , ral carballo - rubio , iaki garay , claus kiefer , manuel krmer , and hannes schenck for discussions and comments . special thanks to martin bojowald for interesting comments on a previous version of this manuscript . financial support from the alexander von humboldt foundation through a postdoctoral fellowship is gratefully acknowledged . this work is supported in part by projects it592 - 13 of the basque government and fis2012 - 34379 of the spanish ministry of economy and competitiveness .","summary":"in a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented . here the application of this formalism to the system of a particle moving on a potential is considered in order to derive physical implications about the classical limit of a quantum system .","abstract":"in a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented . here the application of this formalism to the system of a particle moving on a potential is considered in order to derive physical implications about the classical limit of a quantum system . the complete set of harmonic potentials is considered , which includes the particle under a uniform force , as well as the harmonic and the inverse harmonic oscillators . in addition , as an example of anharmonic system , the pure quartic oscillator is analyzed . classical and quantum moments corresponding to stationary states of these systems are analytically obtained without solving any differential equation . finally , dynamical states are also considered in order to study the differences between their classical and quantum evolution ."}
{"article_id":"astro-ph0207009","section_id":"i","document":"years after the serendipitous discovery of gamma - ray bursts ( grbs ) by the vela spacecraft ( klebesadel et al . 1973 ) , the nature of the progenitors responsible for generating the initial explosion remains uncertain , while an elegant set of ideas about the production and evolution of the afterglow has developed ( mszros & rees 1997 ; sari & piran 1997 ) . aside from recent breakthroughs in x - ray spectroscopy of grbs (  piro et al . 2000 ) a large fraction of the observational information about the environments of grbs derives from optical spectroscopy and imaging of the host galaxies . optical spectroscopy of the integrated light and calibrated emission lines has been used to derive the star - formation rate ( sfr ) for a number of the host galaxies ( see for instance bloom et al . 1998 ; djorgovski et al . 1998 ) . as a complement to spectroscopy , high - resolution optical imaging and astrometry have helped pinpoint two - dimensional locations for grbs with respect to the host galaxy . the distribution of these grb locations has yielded a number of statistical constraints in the progenitor scenarios (  bloom , kulkarni , & djorgovski 2000 ) . a promising technique that has been applied with less success so far is the study of time dependence in absorption lines from metal ions ( perna & loeb 1998 ; bttcher et al . 1999 ) or @xmath13 vibrational levels ( draine 2000 ) that might be excited by the uv radiation generated during the evolution of the burst . the detection of absorption - line variability could provide important clues about the physical dimensions of the photoionized region and the density in the immediate environment of the grb . absorption - line variability can be quantified by measuring changes in the equivalent widths as a function of time or by identifying the appearance of new absorption features . vreeswijk  et al . ( 2001 ) studied the time evolution of the mg ii doublet in the optical spectra of grb 990510 and grb 990712 but failed to find any significant changes . in this work we present a study of the time evolution of absorption systems in the optical spectrum of grb 010222 , and discuss possible implications for its progenitor environment the outline of the paper is as follows :  2 describes the optical spectroscopy ,  3 describes the absorption line identification and continuum fitting . in  4 we detail column density determinations , arguments in favor of the @xmath14 redshift for grb 010222 , kinematics of the host galaxy , and a study of time evolution of absorption lines . a description of the photoionization code and results is given in  5 and  6 . finally , the implications of our results and conclusions are presented in  7 and  8 .","summary":"the absence of time dependence in the absorption lines implies that high - density environments are disfavored .","abstract":"= 100 we present sequential optical spectra of the afterglow of grb 010222 obtained one day apart using the low resolution imaging spectrometer ( lris ) and the echellette spectrograph and imager ( esi ) on the keck telescopes . three low - ionization absorption systems are spectroscopically identified at , , and . the higher resolution esi spectrum reveals two distinct components in the highest redshift system at and . we interpret the system as an absorption feature of the disk of the host galaxy of grb 010222 . the best fitted power - law optical continuum and [ zn / cr ] ratio imply low dust content or a local gray dust component near the burst site . in addition , we do not detect strong signatures of vibrationally excited states of . if the grb took place in a superbubble or young stellar cluster , there are no outstanding signatures of an ionized absorber , either . analysis of the spectral time dependence at low resolution shows no significant evidence for absorption - line variability . this lack of variability is confronted with time - dependent photoionization simulations designed to apply the observed flux from grb 010222 to a variety of assumed atomic gas densities and cloud radii . the absence of time dependence in the absorption lines implies that high - density environments are disfavored . in particular , if the grb environment was dust free , its density was unlikely to exceed . if depletion of metals onto dust is similar to galactic values or less than solar abundances are present , then 2 is probably ruled out in the immediate vicinity of the burst ."}
{"article_id":"astro-ph0207009","section_id":"r","document":"since the depletion correction / abundance and therefore the total @xmath121 near the burst site is not well determined , we examined the time dependence of equivalent widths for two different hydrogen column densities . the first , log@xmath122 @xmath65 represents the inferred hi column ignoring any dust depletion correction and takes into account the possibility of complete circumburst dust destruction . the second , log@xmath123 @xmath65 is appropriate for standard milky way depletion onto dust or perhaps less than solar metal abundances . the latter is also consistent with measurements of the red wing of a possible ly@xmath68 feature ( salamanca et al . 2001 ) , and the bepposax afterglow results ( int zand et al . 2001 ) . in each case we chose four different combinations of number densities @xmath124 and @xmath111 to reproduce the simulated hydrogen column density @xmath125 . the parameters for each model are listed in table 5 . the denser , more compact models represent the conditions in dense molecular clouds which have been postulated as a potential ambient environment for the progenitors of grbs . on the other hand , the low density and extended environments are compatible with low density molecular clouds , young stellar clusters , and possibly galactic superbubbles ( scalo & wheeler 2001 ) . we considered it relevant to trace the time evolution of two particular absorption lines present in our spectra , mg i ( 2852.96  ) and mg ii ( 2796.35  ) . mg i is an appealing line given the possibility of encountering mg in its neutral form in regions of the galaxy shielded from photoionization . mg ii(2796.35  ) is of interest because of its detection in a number of grb spectra . an additional observational reason for choosing these particular lines to test our models is the consistency of the line flux measurements on the red side of the spectrum where the effects of differential refraction appear of less importance . in order to model our observations , we integrated to a maximum time @xmath126 hours after the grb , when the second lris spectrum was obtained . the equivalent width at different stages was estimated using equations ( 1 ) and ( 2 ) which return @xmath57 . throughout our calculations we have assumed a constant doppler parameter @xmath52 representative of the system ( see table 3 ) . this appears to be a fairly robust assumption since the time dependence for the lines is mainly a function of the photoionization equations . figure 6 illustrates the time evolution of the equivalent width for mg i ( 2852.96  ) and mg ii ( 2796.35  ) in a log@xmath127 @xmath65 environment . the times when the lris spectra were obtained are indicated . notice the distinct differences in the line evolution in each case . the denser , more compact models are ionized rather rapidly since most of the gas is close to the grb and gets impacted by a large flux . on the other hand , less dense models representative of thin galactic environments require longer for noticeable effects to take place . the @xmath128 @xmath8 , @xmath129 pc model appears to mark the line where our low - resolution spectroscopy would have been able to detect time dependence with this column density . denser environments than this appear to be disfavored according to our model . figure 7 shows the time dependence for a log@xmath130 @xmath65 environment . similarly compact , high density environments are photoionized rather quickly while extended , less dense ones would evolve with a shallower decline . the @xmath131 @xmath8 , @xmath132 cm model is close to our detection limit for this denser environment . the results in this case are more dependent on the choice of the inner radius @xmath104 because the scale of some of the models becomes comparable to @xmath104 . a different choice for the inner radius would either accelerate or delay the photoionization timescale , therefore , compact models with this column density are more tentative . however , it appears that very dense , compact environments would have been more highly ionized than is observed in our initial spectrum . one interpretation of x - ray and optical afterglow data from grb 010222 invokes a transition from a relativistic to a non - relativistic regime , and consequently the deceleration of the shock , to account for the break in the light curve ( in t zand et al . this scenario requires an environment with @xmath133 @xmath8 and size @xmath110 cm . although our simulations argue against the presence of a dense @xmath134 cm neutral gas slab between the two observations , we can not rule out the presence of a large density slab at the time of the burst itself . however our modelling also presents an alternative scenario for more extended @xmath135 absorption in the host galaxy rather than a single slab . recent modelling of the multiwavelength observations of grb 010222 , including the radio emission , finds that a jet model expanding into homogeneous external medium with density @xmath136 @xmath8 is consistent with the broadband data ( panaitescu & kumar 2001 ) . a jet and low - density interpretation is also required to satisfy the standard - energy output with beaming corrections of frail et al . ( 2001a ) . one final point in this discussion is the shape of the @xmath137-ray burst light curve and baryon contamination . a very dense nearby medium gives rise to high optical depth @xmath59 where baryons could prevent relativistic expansion . the overall effect could lead to `` dirty '' fireballs and smearing of the @xmath137-ray profile . instead the burst profile appears highly structured ( in t zand et al . 2001 ) . consider now the actual column density to this burst if the host galaxy has a dust - to - gas ratio similar to that of the milky way . a color excess of @xmath138  mag is estimated for log@xmath123 @xmath65 and assuming a galactic conversion @xmath139  @xmath65  mag@xmath18 ( savage & mathis 1979 ) . this is significantly larger than @xmath140  mag for a log@xmath122 @xmath65 environment . it is possible that the uv emission from the burst is responsible for destruction of neighboring dust in the high - density case ( galama & wijers 2001 ) , but further extinction at larger distances is expected along the line of sight unless the burst is near the earth - facing side of the host galaxy ( reichart & price 2002 ) . we must keep in mind , however , the possibility that we are probing different scales in two separate energy bands .","summary":"this lack of variability is confronted with time - dependent photoionization simulations designed to apply the observed flux from grb 010222 to a variety of assumed atomic gas densities and cloud radii .","abstract":"= 100 we present sequential optical spectra of the afterglow of grb 010222 obtained one day apart using the low resolution imaging spectrometer ( lris ) and the echellette spectrograph and imager ( esi ) on the keck telescopes . three low - ionization absorption systems are spectroscopically identified at , , and . the higher resolution esi spectrum reveals two distinct components in the highest redshift system at and . we interpret the system as an absorption feature of the disk of the host galaxy of grb 010222 . the best fitted power - law optical continuum and [ zn / cr ] ratio imply low dust content or a local gray dust component near the burst site . in addition , we do not detect strong signatures of vibrationally excited states of . if the grb took place in a superbubble or young stellar cluster , there are no outstanding signatures of an ionized absorber , either . analysis of the spectral time dependence at low resolution shows no significant evidence for absorption - line variability . this lack of variability is confronted with time - dependent photoionization simulations designed to apply the observed flux from grb 010222 to a variety of assumed atomic gas densities and cloud radii . the absence of time dependence in the absorption lines implies that high - density environments are disfavored . in particular , if the grb environment was dust free , its density was unlikely to exceed . if depletion of metals onto dust is similar to galactic values or less than solar abundances are present , then 2 is probably ruled out in the immediate vicinity of the burst ."}
{"article_id":"astro-ph0207009","section_id":"c","document":"the use of high - resolution spectroscopy has resolved the host galaxy of grb 010222 into multiple components . we conclude that the grb took place in a galactic disk that gives rise to the strongest absorption system . the power - law index of the optical continuum indicates that the dust content at the burst place is low or that the reddening follows a gray dust model . under these conditions the bulk of the x - ray excess ( in t zand et al . 2001 ) can be attributed to inverse compton scattering . low resolution spectroscopy obtained over the span of two days failed to reveal any significant evidence for time dependence of the observed absorption lines . signatures of strong @xmath5 absorption and/or fluorescence are also absent from our spectra . photoionization models constructed to test a range of initial conditions for this burst show that dense , compact media would be photoionized fairly quickly while less dense media with large radii evolve slower with time . we argue that prior to a grb , an environment partially ionized either by the progenitor or by nearby sources would prevent the full manifestation of predicted absorption - line evolution . the physical attributes of grb 010222 are consistent with a low - density molecular cloud , superbubble , or young stellar cluster as the possible environment of the grb .    in the future some consideration should be given to a prompt optical - uv flash like the one accompanying grb 990123 . the intensity of such an event could in principle lead to dust destruction , but it might also be responsible for the photoionization of a fraction of the neutral gas . the full effect of such a flash has been ignored in our models . preferentially , the observation of time - dependent absorption lines would work best in bursts occurring in the earth - facing side of the host galaxy and in compact regions . our analysis suggests that this technique applied with high - resolution spectroscopy could potentially distinguish the metallicity of progenitor environments . in that regard shortening the interval between burst localization and initial spectroscopy becomes crucial to exploring earlier , less photoionized times . the next generation of high - resolution imagers might directly resolve the environment of grbs in a relatively nearby host galaxy . a prospect raised by the observations of grb 010222 is the study of the properties of galactic dust at high - redshift using bursts as beacons to illuminate the dust nearby . further exploration of this issue is encouraged as spectroscopy is obtained for a larger sample of grbs . we would like to thank r. -p . kudritzki and f. bresolin for obtaining the first set of spectra as well as h. spinrad , d. stern , a. dey , a. bunker , and s. dawson for taking the second set of lris spectra . we also acknowledge eric gotthelf for allowing us to use his new alpha computer and robert uglesich for tips on optimization in fortran . this work was supported by the national science foundation under grant no . ast-00 - 71108 . jsb is supported as a fannie and john hertz fellow . cccccc si ii(1526.71  ) & 3782.12 & 1.4773 & 1.10@xmath149 & 1.51 @xmath50 0.13 & 1.72 @xmath50 0.47 + c iv(1548.20  ) & 3835.36 & 1.4773 & 1.91@xmath149 & 2.55 @xmath50 0.23 & 2.67 @xmath50 0.29 + + c iv(1550.78  ) & & & 9.52@xmath150 & & + fe ii(1608.45  ) & 3984.61 & 1.4773 & 6.19@xmath150 & 0.40 @xmath50 0.04 & 0.52 @xmath50 0.30 + al ii(1670.79  ) & 4138.77 & 1.4771 & 1.83 & 1.48 @xmath50 0.09 & 1.58 @xmath50 0.12 + si ii(1808.01  ) & 4478.51 & 1.4770 & 5.53@xmath151 & 0.60 @xmath50 0.08 & 0.81 @xmath50 0.15 + al iii(1854.72  ) & 4592.77 & 1.4763 & 5.60@xmath149 & 0.79 @xmath50 0.06 & 0.94 @xmath50 0.13 + fe ii(2382.77  ) & 4592.77 & 0.9275 & 3.01@xmath149 & 1.01 @xmath50 0.08 & 1.21 @xmath50 0.17 + al iii(1862.79  ) & 4614.50 & 1.4772 & 2.79@xmath149 & 0.69 @xmath50 0.08 & . . . + zn ii(2026.14  ) & 5018.95 & 1.4771 & 4.89@xmath149 & 0.71 @xmath50 0.07 & 1.03 @xmath50 0.13 + + mg i(2026.48  ) & & & 1.15@xmath149 & & + cr ii(2056.25  ) & 5093.54 & 1.4771 & 1.05@xmath149 & 0.3 @xmath50 0.04 & 0.45 @xmath50 0.08 + zn ii(2062.66  ) & 5109.62 & 1.4772 & 2.56@xmath149 & 0.7 @xmath50 0.04 & 0.52 @xmath50 0.09 + + cr ii(2062.23  ) & & & 7.80@xmath150 & & + fe ii(2382.77  ) & 5137.88 & 1.1563 & 3.01@xmath149 & 0.64 @xmath50 0.08 & 0.81 @xmath50 0.11 + mg ii(2796.35  ) & 5390.80 & 0.9278 & 6.12@xmath149 & 1.04 @xmath50 0.10 & 1.06 @xmath50 0.13 + mg ii(2803.53  ) & 5403.80 & 0.9275 & 3.05@xmath149 & 0.71 @xmath50 0.07 & 0.91 @xmath50 0.08 + mg i(2852.96  ) & 5493.01 & 0.9254 & 1.83 & 0.67 @xmath50 0.13 & 0.63 @xmath50 0.15 + fe ii(2600.17  ) & 5605.97 & 1.1560 & 2.24@xmath149 & 1.32 @xmath50 0.07 & 1.21 @xmath50 0.11 + fe ii(2344.21  ) & 5807.30 & 1.4773 & 1.10@xmath149 & 1.97 @xmath50 0.06 & 1.86 @xmath50 0.06 + fe ii(2374.46  ) & 5881.78 & 1.4771 & 3.26@xmath150 & 1.67 @xmath50 0.08 & 1.80 @xmath50 0.22 + fe ii(2382.77  ) & 5902.60 & 1.4772 & 3.01@xmath149 & 2.37 @xmath50 0.09 & 2.10 @xmath50 0.12 + mg ii(2796.35  ) & 6030.31 & 1.1565 & 6.12@xmath149 & 2.07 @xmath50 0.13 & 2.08 @xmath50 0.16 +    cccccc mg ii(2803.53  ) & 6044.97 & 1.1562 & 3.05@xmath149 & 1.77 @xmath50 0.14 & 1.79 @xmath50 0.15 + mn ii(2576.88  ) & 6383.63 & 1.4773 & 3.51@xmath149 & 0.62 @xmath50 0.07 & 0.50 @xmath50 0.10 + fe ii(2586.65  ) & 6407.39 & 1.4771 & 6.84@xmath150 & 1.53 @xmath50 0.08 & 1.5 @xmath50 0.15 + fe ii(2600.17  ) & 6441.14 & 1.4772 & 2.24@xmath149 & 2.48 @xmath50 0.08 & 2.2 @xmath50 0.13 + mg ii(2796.35  ) & 6926.28 & 1.4769 & 6.12@xmath149 & 3.06 @xmath50 0.04 & 3.00 @xmath50 0.11 + mg ii(2803.53  ) & 6944.62 & 1.4771 & 3.05@xmath149 & 2.88 @xmath50 0.04 & 2.90 @xmath50 0.09 + mg i(2852.96  ) & 7067.07 & 1.4771 & 1.83 & 1.22 @xmath50 0.05 & 1.31 @xmath50 0.09 +    ccccc al ii(1670.79  ) & 4138.41 & 1.47692 & 1.83 & 1.87 @xmath50 0.43 + si ii(1808.01  ) & 4478.18 & 1.47686 & 2.18@xmath151 & 0.76 @xmath50 0.1 + al iii(1854.72  ) & 4592.39 & 1.47606 & 5.60@xmath149 & 0.41 @xmath50 0.20 + fe ii(2382.77  ) & 4592.39 & 0.92733 & 3.01@xmath149 & 0.53 @xmath50 0.26 + al iii(1854.72  ) & 4594.04 & 1.47695 & 5.60@xmath149 & 0.80 @xmath50 0.18 + fe ii(2382.77  ) & 4594.04 & 0.92803 & 3.01@xmath149 & 1.03 @xmath50 0.23 + al iii(1862.79  ) & 4614.18 & 1.47703 & 2.79@xmath149 & 0.49 @xmath50 0.07 + fe ii(2600.17  ) & 5011.47 & 0.92736 & 2.24@xmath149 & 0.41 @xmath50 0.11 + zn ii(2026.14  ) & 5018.98 & 1.47711 & 4.89@xmath149 & 0.91 @xmath50 0.12 + + mg i(2026.48  ) & & & 1.15@xmath149 & + cr ii(2056.25  ) & 5093.10 & 1.47689 & 1.05@xmath149 & 0.44 @xmath50 0.08 + zn ii(2062.66  ) & 5108.62 & 1.47671 & 2.56@xmath149 & 0.69 @xmath50 0.16 + + cr ii(2062.23  ) & & & 7.80@xmath150 & + cr ii(2066.16  ) & 5117.54 & 1.47684 & 5.15@xmath150 & 0.27 @xmath50 0.12 + fe ii(2382.77  ) & 5138.48 & 1.15652 & 3.01@xmath149 & 1.12 @xmath50 0.11 + mg ii(2796.35  ) & 5389.83 & 0.92745 & 6.12@xmath149 & 0.96 @xmath50 0.14 + mg ii(2803.53  ) & 5404.04 & 0.92758 & 3.05@xmath149 & 1.08 @xmath50 0.16 + mg i(2852.96  ) & 5498.99 & 0.92747 & 1.83 & 0.51 @xmath50 0.21 + fe ii(2260.78  ) & 5597.47 & 1.47590 & 2.44@xmath151 & 0.10 @xmath50 0.08 + fe ii(2260.78  ) & 5599.68 & 1.47688 & 2.44@xmath151 & 0.42 @xmath50 0.16 + fe ii(2600.17  ) & 5606.38 & 1.15616 & 2.24@xmath149 & 1.15 @xmath50 0.16 +    ccccc fe ii(2344.21  ) & 5804.03 & 1.47590 & 1.10@xmath149 & 0.37 @xmath50 0.11 + fe ii(2344.21  ) & 5806.33 & 1.47688 & 1.10@xmath149 & 1.51 @xmath50 0.23 + fe ii(2374.46  ) & 5878.93 & 1.47590 & 3.26@xmath150 & 0.30 @xmath50 0.06 + fe ii(2374.46  ) & 5881.25 & 1.47688 & 3.26@xmath150 & 1.24 @xmath50 0.10 + fe ii(2382.77  ) & 5899.50 & 1.47590 & 3.01@xmath149 & 0.56 @xmath50 0.09 + fe ii(2382.77  ) & 5901.84 & 1.47688 & 3.01@xmath149 & 2.21 @xmath50 0.16 + mg ii(2796.35  ) & 6028.98 & 1.15602 & 6.12@xmath149 & 2.49 @xmath50 0.08 + mg ii(2803.53  ) & 6044.44 & 1.15601 & 3.05@xmath149 & 2.14 @xmath50 0.60 + mg i(2852.96  ) & 6152.90 & 1.15667 & 1.83 & 0.54 @xmath50 0.31 + mn ii(2576.88  ) & 6382.58 & 1.47686 & 3.51@xmath149 & 0.58 @xmath50 0.12 + fe ii(2586.65  ) & 6404.29 & 1.47590 & 6.84@xmath150 & 0.64 @xmath50 0.13 + fe ii(2586.65  ) & 6406.82 & 1.47688 & 6.84@xmath150 & 1.72 @xmath50 0.20 + mn ii(2594.50  ) & 6426.18 & 1.47685 & 2.71@xmath149 & 0.68 @xmath50 0.12 + fe ii(2600.17  ) & 6437.76 & 1.47590 & 2.24@xmath149 & 0.49 @xmath50 0.05 + fe ii(2600.17  ) & 6440.31 & 1.47688 & 2.24@xmath149 & 2.12 @xmath50 0.19 + mn ii(2606.46  ) & 6455.96 & 1.47691 & 1.93@xmath149 & 0.56 @xmath50 0.12 + mg ii(2796.35  ) & 6923.66 & 1.47596 & 6.12@xmath149 & 1.63 @xmath50 0.24 + mg ii(2796.35  ) & 6926.76 & 1.47707 & 6.12@xmath149 & 1.51 @xmath50 0.19 + mg ii(2803.53  ) & 6940.97 & 1.47580 & 3.05@xmath149 & 1.39 @xmath50 0.15 + mg ii(2803.53  ) & 6944.06 & 1.47690 & 3.05@xmath149 & 1.61 @xmath50 0.11 + mg i(2852.96  ) & 7063.74 & 1.47593 & 1.83 & 0.42 @xmath50 0.24 + mg i(2852.96  ) & 7066.33 & 1.47684 & 1.83 & 1.21 @xmath50 0.22 +    cccccccc mn@xmath62 & 2576.88 & 0.3508 & 22.8 & 14.00 @xmath50 0.44 & 20.47 @xmath50 0.44 & 21.92 @xmath50 0.44 & 0.50 + & 2594.50 & 0.2710 & 35.3 & 13.95 @xmath50 0.17 & 20.42 @xmath50 0.17 & 21.87 @xmath50 0.18 + & 2606.46 & 0.1927 & 29.6 & 14.00 @xmath50 0.20 & 20.47 @xmath50 0.20 & 21.92 @xmath50 0.21 + mg@xmath62 & 2803.53 & 3.05@xmath149 & . . & @xmath10 13.88 & @xmath10 18.30 & @xmath10 19.85 & @xmath69 2.65 + fe@xmath62 & 2382.77 & 3.01@xmath149 & . . & @xmath10 14.16 & @xmath10 18.65 & @xmath10 20.92 & @xmath69 2.3 +      cccc @xmath152 & 0.089 & 1000.0 & i + @xmath152 & 0.89 & 100.0 & ii + @xmath152 & 89 & 1.0 & iii + @xmath152 & @xmath153 & 6.48 @xmath11 @xmath154 & iv + @xmath155 & 3.2 & 1000.0 & v + @xmath155 & @xmath156 & 0.19 & vi + @xmath155 & @xmath157 & 6.48 @xmath11 @xmath154 & vii + @xmath155 & @xmath96 & 3.56 @xmath11 @xmath154 & viii +","summary":"the best fitted power - law optical continuum and [ zn / cr ] ratio imply low dust content or a local gray dust component near the burst site .","abstract":"= 100 we present sequential optical spectra of the afterglow of grb 010222 obtained one day apart using the low resolution imaging spectrometer ( lris ) and the echellette spectrograph and imager ( esi ) on the keck telescopes . three low - ionization absorption systems are spectroscopically identified at , , and . the higher resolution esi spectrum reveals two distinct components in the highest redshift system at and . we interpret the system as an absorption feature of the disk of the host galaxy of grb 010222 . the best fitted power - law optical continuum and [ zn / cr ] ratio imply low dust content or a local gray dust component near the burst site . in addition , we do not detect strong signatures of vibrationally excited states of . if the grb took place in a superbubble or young stellar cluster , there are no outstanding signatures of an ionized absorber , either . analysis of the spectral time dependence at low resolution shows no significant evidence for absorption - line variability . this lack of variability is confronted with time - dependent photoionization simulations designed to apply the observed flux from grb 010222 to a variety of assumed atomic gas densities and cloud radii . the absence of time dependence in the absorption lines implies that high - density environments are disfavored . in particular , if the grb environment was dust free , its density was unlikely to exceed . if depletion of metals onto dust is similar to galactic values or less than solar abundances are present , then 2 is probably ruled out in the immediate vicinity of the burst ."}
{"article_id":"cond-mat0509436","section_id":"i","document":"the competition between electrostatic and kinetic energy in a two dimensional electron gas is a problem which is simple to formulate ( what is the phase diagram of @xmath1 electrons on a surface @xmath2 at zero temperature ) yet difficult to tackle . one reason for this difficulty lies in the smallness of the difference in energy between different phases ( the fermi liquid which is stable at high density when the kinetic energy dominates  @xcite and the electrostatically favored ( wigner ) triangular crystal , stable at low density  @xcite ) . in the region of interest in this study , @xmath3 ( the dimensionless parameter @xmath4 controls the ratio of the electrostatic energy over the kinetic energy ) where there is a strong competition between the two kinds of energy , the difference of energy between the two phases is only of the order of @xmath5 of the total energy so that very accurate methods were needed to study this problem . to illustrate this point , we plot in the fig .  [ fig : intro ] the energy of these two phases as a function of @xmath6 ( @xmath7 being the electronic charge , @xmath8 the dielectric constant , @xmath9 the effective mass and @xmath10 the electronic density ) . at large distances , the physics is entirely controlled by electrostatic , and important amount of energy are involved . once we add a positive background to the system and make it globally neutral , we arrive at the energies plotted in the upper panel of fig . [ fig : intro ] : on the scale of the plot the liquid and crystal are completely indistinguishable . if we remove the madelung energy ( excess electrostatic energy of the uniform background with respect to the crystal ) , we still can not distinguish between the two phases ( middle panel of fig . [ fig : intro ] ) . it is only after we have removed the zero point fluctuation energy of the crystal that the curves become different and show a crossing at @xmath11 where the wigner crystallization has been believed to occur  @xcite ( lower panel of fig . [ fig : intro ] ) .    in a seminal article in 1989 , tanatar and ceperley  @xcite used a fixed node quantum monte carlo ( fn - qmc ) technique  @xcite to locate the critical value @xmath12 where the quantum melting of the wigner crystal occurs . their work was followed by more precise numerics  @xcite and a better description of the liquid phase  @xcite that included backflow corrections . + 0.05 cm   quantum monte - carlo energy as a function of @xmath13 for a system of @xmath14 electrons in @xmath15 sites for the liquid phase ( squares ) , solid phase ( diamonds ) and hybrid phase ( full circles ) . upper panel : total energy , the three phases are indistinguishable . middle panel : total energy minus the madelung ( electrostatic ) energy @xmath16 with @xmath17 . lower panel : total energy minus the madelung energy and the energy of the crystal s phonons @xmath18 with @xmath19 . the energies are given in mry . for holes in a gaas heterostructure , a rydberg corresponds roughly to 350 kelvin ( @xmath20 , @xmath21).,title=\"fig:\",width=302 ]    on the other hand there were indications that this scenario of a ( first order ) direct transition between the wigner crystal and the fermi liquid phase might miss some of the physics . for instance , the quantum melting of the bosonic wigner crystal  @xcite is found ( by similar qmc calculations ) to occur at @xmath22 so that for @xmath23 the fermionic statistics ( from which all the difficulties of the qmc calculations come , as we shall see ) is crucial to stabilize the crystal . also , the classical melting @xcite as a function of temperature does not occur in a one step process . the system first looses its translational order but retains some orientational order ( hexatic phase  @xcite ) while at a higher temperature , any order disappears . the possibility of an intermediate quantum hexatic phase was put forward in  @xcite . in fact , it was recently argued on rather general grounds that a direct first order transition is simply impossible in this system  @xcite but should occur through a serie of intermediate phases ( including bubbles or stripes of one phase in the other ) . the possibility of a supersolid phase analogous to the one proposed by andreev and lifshitz  @xcite has also been considered  @xcite . all these indications  @xcite lead us recently to revisit the melting of the wigner crystal in the framework of the fn - qmc calculations . we introduced a third phase called hybrid phase ( as it had the symmetry of the crystal but is otherwise delocalized ) and showed that it was more stable than both the liquid and crystal phase ( full circles in the lower panel of fig . [ fig : intro ] ) in the intermediate density range  @xcite giving a strong support to the more exotic scenarios .    to understand the status of our result however , it is of prime importance to understand the nature of the ( fixed node , fn ) approximation involved in the fn - qmc technique . in practice , the fn - qmc algorithm is fed with a wave - function called the _ guiding wave function _ ( gwf ) that has to be given explicitly , and that should be as close as possible to the ground state of the system . the fn - qmc algorithm projects the gwf onto the ( true ) ground state of the system . however , to avoid the notorious sign problem that arises in qmc simulations involving fermions , one approximation is introduced : the projection is done with the constraint that _ the sign of the wave function ( nodal structure ) remains unchanged _ at every point of the hilbert space . the method gives the best wave function for a given structure of the nodes of the gwf and is in this sense variational  @xcite . the physical meaning of the fn approximation is not completely obvious . implicit in the interpretation given above of the fn - qmc results is that a gwf is associated to a phase ( crystal , liquid or hybrid ) the stability of which can therefore be studied . however , this paradigm should not be taken too literally and will be revisited in this article .    after presenting our model and the fn - qmc method in section ii , we perform fn - qmc calculations on a small system of @xmath24 electrons ( section iii ) . as this system can be studied exactly , it is an interesting tool to study the nature of the fn approximation . we find that in addition to the fn results at large imaginary ( projection ) time , important information is embedded in the evolution of the results from the variational calculation to the full fn - qmc results . in section iv , we explain the construction of the hybrid gwf , and show that its nodal structure corresponds to delocalized waves . section v is devoted to a characterization of the physics associated with the hybrid gwf . this is done through a systematic study of various physical quantities , and in particular of their evolution between the variational and fn - qmc calculations . we find that the success of the hybrid gwf with respect to the crystal one is closely linked to its delocalized nature . section vi contains a detailed discussion of various technical aspects ( thermodynamic limit , lattice effects , mixed and unbiased estimates , ... ) the chief result of section vi is a precise determination of the critical value @xmath0 . at which the liquid - hybrid transition takes place ( in both the continuum and thermodynamic limit ) . in the discussion section vii , we discuss the implications of our results to the scenarii proposed in the literature .","summary":"the fermi liquid - wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum monte carlo calculations . recently , we proposed ( phys . rev . lett . * 94 * , 046801 ( 2005 ) ) that for intermediate densities , a hybrid phase ( with the symmetry of the crystal but otherwise liquid like properties ) is more stable than both the liquid and the crystal phase . here the liquid - hybrid transition takes place at . we find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature . we discuss the implications of our results for various transition scenarii ( quantum hexatic phase , supersolid , multiple exchange , microemulsions ) proposed in the literature .","abstract":"the fermi liquid - wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum monte carlo calculations . recently , we proposed ( phys . rev . lett . * 94 * , 046801 ( 2005 ) ) that for intermediate densities , a hybrid phase ( with the symmetry of the crystal but otherwise liquid like properties ) is more stable than both the liquid and the crystal phase . here we confirm this result both in the thermodynamic and continuum limit . the liquid - hybrid transition takes place at . we find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature . we discuss the implications of our results for various transition scenarii ( quantum hexatic phase , supersolid , multiple exchange , microemulsions ) proposed in the literature ."}
{"article_id":"cond-mat0509436","section_id":"m","document":"the system under consideration consists of @xmath1 spinless electrons on a rectangular @xmath25 grid with nearest neighbor hopping and long range coulomb repulsion . to avoid strong finite size effects on the electrostatic energy , the system is repeated periodically and fills the whole two dimensional plane . in practice , we use periodic boundary conditions for the hopping terms and the effective two - body interaction is obtained from the bare coulomb interaction using the ewald summation technique . the system hamiltonian reads  @xcite [ eq : model ] h =- t_r , rc_r^c_r + _ rr v(r - r ) n_r n_r + . where the operator @xmath26 ( @xmath27 ) creates ( destroys ) an electron on point @xmath28 with the standard anticommutation relation rules , the sum @xmath29 is done on the nearest neighbor points on the grid and @xmath30 is the corresponding hopping amplitude . the density operator reads @xmath31 . @xmath32 is the effective strength of the two body interaction @xmath33 which reads , v(r ) = _ l ( k_c |r + l| ) @xmath34 in the previous equation , @xmath35 is a ( irrelevant ) cut off . the vector @xmath36 takes discrete values @xmath37 with @xmath38 and @xmath39 integer numbers . the vector @xmath40 also takes discrete values , @xmath41 and @xmath42 . the complementary error function is defined as @xmath43 . in order to assure electrostatic neutrality we add a positive continuum background /n = 4 t + u v(0 ) -2 u /k_c - 2 u k_c/ where @xmath44 is the average number of electrons per site and @xmath45 with the restriction that the sum over @xmath36 does not includes the null vector . the presence of the grid can be understood either as a discretization of the continuum problem ( and the nearest neighbor hopping corresponds to the discretized laplacian ) or as a tight - binding approach to two dimensional electron systems where each site corresponds to an atomic orbital . in conventional 2d systems ( say gaas / gaalas heterostructures ) , densities range from @xmath46 down to @xmath47 . since the distance between nearest atoms is of the order of a few angstroms , this would lead to @xmath48 to @xmath49 electrons per site in our tight - biding picture . in this study , we will study systems with @xmath50 , @xmath51 and @xmath52 close to realistic values . the presence of the jellium ( which is merely a constant term and thus can not affect the physics ) allows us to make a quantitative contact with the literature in the continuum limit as @xmath53 . in this limit , the physics depends only on the @xmath13 parameter which reads , @xmath54 while the rydberg unit of energy is @xmath55 . in the following , unless specifically stated , we shall measure all energies @xmath56 in unit of @xmath57 ( i.e. energy per particle in unit of the fermi energy of the non - interacting problem . ) with this normalization , the energy of the system at @xmath58 in the thermodynamic @xmath59 and continuum @xmath60 limit is @xmath61 so that results in rydberg can be obtained by multiplying the energies ( in unit of @xmath57 ) by @xmath62 . we have added a very small disorder @xmath63 in order to lift the degeneracies of the non interacting problem . @xmath64 are independent and uniformly distributed inside @xmath65 $ ] . we choose @xmath66 corresponding to an extremely large ratio @xmath67 of the mean free path @xmath68 over fermi wave length @xmath69 . we explicitly checked that our result are insensitive to the presence of this disorder . the grid has been chosen to accommodate a ( almost ) triangular wigner crystal without distortion . hence we use systems of @xmath70 electrons ( @xmath71 ( @xmath71 even ) lines of @xmath72 particles ) in @xmath73 sites . the triangular crystal requires @xmath74 . in this work , we focus on @xmath75 and @xmath76 for which we find that the distortion is negligible . we aim to sample the ground state @xmath77 of @xmath78 and its corresponding ground state energy @xmath79 with the green function monte - carlo technique . the idea behind this method is to project an initial ( variational ) guiding wave - function @xmath80 on the exact ground state @xmath77 by applying the operator @xmath81 in a stochastic way . in practice , one works in the many particle basis @xmath82 and applies the function [ eq : green ] g_rr= _ rr - _ g(r)^-1_g(r ) where @xmath83 , @xmath84 is a ( small ) time step and @xmath85 is an unimportant offset of the energies ( that should be roughly set to the ground state energy of the system , here we took @xmath86 ) . in the absence of the @xmath87 , @xmath88 is a discretized version of the operator @xmath81 for a small ( imaginary ) time step @xmath84 . upon applying @xmath89 times @xmath88 on a vector @xmath90 , the @xmath91 on the left of eq.([eq : green ] ) are canceled by the @xmath92 on the right so that one obtains i_n=_rr ( g^n)_rr ^2_g(r)= _ g|e^-(h- ) n|_g from which one can extract the ground state energy ( as @xmath93 when @xmath94 ) . the stochastic implementation of this scheme is based on the green function monte carlo for lattice hamiltonians introduced in ref . to which we refer for more details . the algorithm to update the slater determinants used in the calculation of @xmath95 can be found in ref .  . by sampling directly the time spent by the walkers at one point of the hilbert space using the algorithm described in ref . we can use arbitrary small time steps @xmath84 without any loss in computing time and hence effectively work in continuum ( imaginary ) time . instead of using the standard branching technique , the control of the walkers population is done using a fixed number of walkers and the reconfiguration algorithm introduced by sorella  @xcite . this algorithm allows to avoid the bias introduced in the branching technique by artificially controlling the walker population . quantum averages of physical quantities @xmath96 are calculated using the forward walking technique  @xcite , and hence do not suffer from the bias of mixed estimates . so far the scheme is essentially exact . however , it suffers from the usual `` sign problem '' , the sign of @xmath97 fluctuates so that the statistical accuracy decreases exponentially with @xmath98 , and it is of little practical use . one way out of the sign problem is the fixed - node approximation where one forbids the sign of the wave function to change upon applying @xmath88 ( hence the name : the nodal surface where the wave - function changes of sign remains the same than the one of @xmath99 . the practical implementation of the fixed - node approximation on a grid is done@xcite by replacing @xmath78 by an effective hamiltonian @xmath100 that depends on the gwf . @xmath101 is equal to @xmath102 when @xmath103 . when @xmath104 , the link is cut @xmath105 and is replaced by an effective potential @xmath106 where @xmath107 is the heaviside function ( this corresponds to replace the value of the wave - function on those sites @xmath108 by the surmise @xmath91 ) . the fixed node approximation can be thought as a `` supervariational '' technique where the amplitude of the wave - function is optimized at every point of the hilbert space while its sign remain fixed . it can be proved indeed that the energies @xmath109 calculated with @xmath110 are larger than the true ground state energy @xmath79 but smaller than the variational energy associated with the guiding wave - function  @xcite . the fixed node approximation in a lattice looks _ a priori _ more drastic than in the continuum since we do impose the ratio of the wave - function across the nodal surface . however , for @xmath60 the fraction of `` nodal '' sites goes to zero and the technique becomes equivalent to the fixed node diffusive monte - carlo used in the continuum  @xcite .    as an illustration , we present in fig .  [ fig : rawdata ] a typical trace obtained for 32 particles at @xmath111 . @xmath112 corresponds to the variational energy @xmath113 . after an initial rapid decrease , the fn energy ( per particle ) @xmath114 decreases slowly as @xmath115 ( see inset ) and then saturates above an imaginary time @xmath116 . the energy is estimated by further averaging the result over @xmath98 for @xmath117 . the typical achieved accuracy allows us to determine @xmath114 with a precision better than @xmath118 . this remarquable precision ( here the relative accuracy is @xmath119 ) should be contrasted with the fact that important changes in the physics can lead to very tiny changes in energy . for instance the condensation energy in a superconductor is only a very small fraction @xmath120 ( @xmath121 superconducting gap , @xmath122 fermi energy ) of the total energy ( only electrons near the fermi surface form cooper pairs ) . the formation of a wigner crystal ( localized in real space ) from a fermi liquid ( localized in momentum space ) corresponds however to a complete reorganization of the system and the changes in energy , though small @xmath123 , can be measured with the gfmc technique . + 0.05 cm ( color online ) . typical curve of @xmath114 as a function of @xmath98 . system of 32 particles in @xmath124 sites at @xmath111 for a liquid gwf with @xmath125 . here , @xmath126 walkers were used , @xmath127 and @xmath128 . inset : same curve as a function of @xmath115 . the dashed lines are linear fits to guide the eye . , title=\"fig:\",width=302 ]      central in the fixed - node technique is the choice of the gwfs used in the calculations . here , the guiding wave - functions have the general form of a slater determinant multiplied by a jastrow function , _ g(r)= det  [ _ i(r_j)]_i < j j(| r_i - r_j| ) . the jastrow part takes coulomb interaction into account by introducing correlations between electrons . since it has no nodes , the fn results should not depend on its particular form ( as we explicitly checked ) . we use modified yukawa functions@xcite , j(r)= , where @xmath129 is the average distance between electrons . @xmath130 and @xmath131 are ( optimized ) variational parameters . to avoid the coulomb singularity when two electrons get close to each other , we impose the cusp condition  @xcite that reads @xmath132 for the modified yukawa . the slater determinant of one - body wave functions , @xmath133 $ ] enforces the antisymmetric nature of the fermionic wave function and is responsible for the nodal structure of the gwf . the gwf used in the literature for the study of the melting of the wigner crystal  @xcite are of two kind , adapted to the two limits of very low ( large ) @xmath13 :    * for the liquid state the gwf @xmath134 is constructed out of plane waves @xmath135 with a well defined fermi surface . @xmath134 is the exact ground state at @xmath58 . * for the crystal gwf @xmath136 , localized orbitals @xmath137 are used . here the @xmath138 with @xmath139 stand for the positions of the electrons in the classical crystal . @xmath136 provides the exact ground state in the continuum at large @xmath13 with the variational parameter @xmath140 . this gwf captures the two leading terms of the large @xmath13 expansion of the energy ( madelung and zero point fluctuation energy ) that reads , e = -c_1 r_s/2 + c_1/2 /2 + with @xmath17 and @xmath19 .    in this article , we will use the two previously mentioned gwf , and introduce a third ( hybrid ) one that somehow interpolates between the crystal ( real space ) and the liquid ( momentum space ) .","summary":"we confirm this result both in the thermodynamic and continuum limit .","abstract":"the fermi liquid - wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum monte carlo calculations . recently , we proposed ( phys . rev . lett . * 94 * , 046801 ( 2005 ) ) that for intermediate densities , a hybrid phase ( with the symmetry of the crystal but otherwise liquid like properties ) is more stable than both the liquid and the crystal phase . here we confirm this result both in the thermodynamic and continuum limit . the liquid - hybrid transition takes place at . we find that the stability of the hybrid phase with respect to the crystal one is tightly linked to its delocalized nature . we discuss the implications of our results for various transition scenarii ( quantum hexatic phase , supersolid , multiple exchange , microemulsions ) proposed in the literature ."}
{"article_id":"1211.2780","section_id":"i","document":"functional data analysis is a branch of statistics that has been studied frequently and developed over recent years . this type of data appears in many practical situations such as continuous phenomena . thus , the possible application fields that favor the use of functional data are broad and include the following : climatology , economics , linguistics , medicine , and so on . because the pioneering work of authors such as @xcite and @xcite , many developments have been investigated to build theories and methods regarding functional data ; for instance , how can the mean or the variance of functional data be defined ? what type of model can be considered with functional data ? these papers also emphasize the drawback of merely using multivariate methods with this type of data ; rather , they suggest considering these data as objects that belong to a specific functional space . the monographs of @xcite provide and overview of both the theoretical and practical aspects of functional data analysis . regression is one of the most studied functional models . in this model , the variable of interest @xmath0 is real and the covariate @xmath1 belongs to a functional space @xmath2 endowed with a semi - norm @xmath3 . thus , the regression model is written @xmath4    where @xmath5 is an operator and @xmath6 is the random error term . much research has investigated this model when the operator @xmath7 is supposed to be linear , which has contributed to the popularity of the so - called functional linear model . in this linear context , the operator @xmath7 is written as @xmath8 where @xmath9 denotes the inner product of the space @xmath2 and @xmath10 belongs to @xmath2 . thus , the goal is to estimate the unknown function @xmath10 . we refer the reader to @xcite and @xcite for different methods of estimating @xmath10 . another way to approach the ( [ regression ] ) model is to think in a nonparametric way . many authors have also investigated this direction . recent advances on the topic have been the subject of a bibliographical review in @xcite and monographs by @xcite , @xcite , thereby providing the theoretical and practical properties of a kernel estimator of the operator @xmath7 . specifically , if @xmath11 is a sample of independent and identically distributed couples with the same law as @xmath12 , then , this kernel estimator is defined for all @xmath13 by    @xmath14    where @xmath15 is a kernel and @xmath16 is a bandwidth . @xcite considered the asymptotic normality of in the dependent case , while @xcite obtained almost sure convergence . this nonparametric regression estimator raises several problems because the choice of the semi - norm @xmath17 of the space @xmath2 and the choice of the bandwidth ,  . with regard to bandwidth , many solutions have been considered when the covariate is real ( e.g. , cross validation ) . recently , @xcite studied an estimator using a sequence of bandwidths in the multivariate setting that allowed the computation of this estimator in a recursive way thereby generalizing previous research ( @xcite and @xcite ) . this estimator has acceptable theoretical properties ( from the point of view of the mean square error and almost sure convergence ) . it is also of practical interest : for instance , it presents a computational time gain when researchers want to predict new values of the variable of interest when new observations appear . this case is not true for the basic kernel estimator , which must be computed again using the whole sample . the purpose of the current study is to adapt the recursive estimator studied in @xcite to a case in which the covariate is functional . the remainder of the paper is organized as follows . section 2 defines the recursive estimator of the operator @xmath7 when the covariate @xmath1 is functional and presents the asymptotic properties of this estimator . section 3 evaluates the performance of our estimator using a simulation study and a real dataset . finally , the proofs of the theoretical results are presented in section 4 .","summary":"these results are established with rates and precise evaluation of the constant terms . _ keywords  : _ functional data , recursive kernel estimators , regression function , quadratic error , almost sure convergence , asymptotic normality . + _ msc  : _ 62g05 ,  62g07 ,  62g08 .","abstract":"the main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach . the mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived . these results are established with rates and precise evaluation of the constant terms . also , a central limit theorem for this class of estimators is established . the method is evaluated on simulations and real data set studies .    _ keywords  : _ functional data , recursive kernel estimators , regression function , quadratic error , almost sure convergence , asymptotic normality . + _ msc  : _ 62g05 ,  62g07 ,  62g08 ."}
{"article_id":"math0510487","section_id":"i","document":"let @xmath3 and  @xmath4 be two finite sets . we will call functions from @xmath3 to  @xmath4  * tableaux * ; we think of each tableau @xmath5 as a labeling of the points of  @xmath3 by elements of  @xmath4 . formally , we identify a tableau @xmath6 with its corresponding set @xmath7 of ordered pairs , whose projection to @xmath3 is bijective . we specify a subset @xmath1 of `` special '' tableaux . also , let @xmath8 be a relation containing every @xmath9 . there are obvious minimal and maximal choices of @xmath10 , namely @xmath11 and @xmath12 , but it will be convenient to not  restrict  @xmath10 . our motivating example is when @xmath3 is the set of boxes in partition  @xmath13 and @xmath14 , so a tableau @xmath15 is a young tableau of shape  @xmath13 and with entries bounded above by @xmath16 ( without any other demands on the labeling ) , and @xmath1 is the special subset of semistandard young tableaux . in a moment ( section  [ sub : youngtab ] ) , we will describe this case in detail . define the simplicial complex @xmath17 , which we call a * tableau complex * , as follows . consider the collection of subsets of  @xmath10 as a simplex under reverse inclusion ; thus the vertices are the complements @xmath18 rather than the elements @xmath19 . we view the faces of this simplex as * set - valued tableaux * , thought of as relations @xmath20 , in which every element @xmath21 is labeled by a set of elements @xmath22 . a set - valued tableau @xmath23 is a face of  @xmath24 whenever @xmath25 , meaning that @xmath26 for all  @xmath21 . ( this set - theoretic containment is always intended when we say that one set - valued tableau contains another , even when both are being considered as faces of a simplicial complex , where containment among faces goes the opposite way . ) the tableau complex is defined by its facets ( maximal faces ) , which we declare to be the tableaux @xmath9 . ( in this paper , the terms `` function '' and `` tableau '' , when unadorned by `` set - valued '' , mean single - valued functions in the usual sense . ) the face with no vertices , which we call the * empty face * , is the set - valued tableau  @xmath10 . consider the tableau complex in which @xmath27 and @xmath4 is the english alphabet , and where @xmath1 consists of all the english words in [ dh]e[al][dl ] . in detail , @xmath28 . for simplicity , in the following figure , at the vertices we indicate the _ unused _ letters of  @xmath10 . [ fig : deld ]    for example , the vertex common to `` hell '' , `` heal '' , `` head '' and `` held '' is @xmath29 . this complex is a @xmath30-ball , but if `` deld '' were a word , it would label the outer face , and this complex would be a @xmath30-sphere .    [ t : tabcomplex ] the following hold for an arbitrary tableau complex @xmath31 .    1 . @xmath32 is * pure * , meaning that its facets ( the tableaux @xmath33 ) all have the same dimension . the codimension of a face  @xmath24 in  @xmath32 is the number @xmath34 of its `` extra '' values . for example , faces of codimension  @xmath35 , which we call * ridges * , are set - valued tableaux taking two values for precisely one @xmath21 and taking one value at all other points of  @xmath3 . 3 .   each ridge is a face of at most two facets . in particular , if a tableau complex is shellable then it is homeomorphic to a ball or sphere . the link of a face in a tableau complex is again a tableau complex . all of these results are proved in section  [ sub : gen ] except the last ( the statement about links ) , which is proposition  [ prop : link ] . we shall see that abstractly , a tableau complex is a ( multicone on a ) top - dimensional subcomplex of a join of boundaries of simplices . tableau complexes can also be characterized , among pure complexes , by the extremal property given toward the end of section  [ sec : extremal ] . although tableau complexes are not generally ( shellable ) balls or spheres , we can give conditions that guarantee this conclusion . the next theorem thus defines the main class of tableau complexes of interest in this paper . except for the claim about interior faces , which is proposition  [ prop : boundary ] , it is a simpler - to - state special case of theorem  [ thm : posetball ] . [ t : posetball ] let @xmath3 be a poset , and @xmath4 totally ordered . let @xmath36 be a set of pairs @xmath37 in @xmath3 with @xmath38 . let @xmath1 be the set of tableaux @xmath39 such that    * if @xmath40 , then @xmath41 , and * if @xmath42 , then @xmath43 ;    thus @xmath1 consists of the order - preserving tableaux from @xmath3 to  @xmath4 that are strictly order - preserving on the pairs in  @xmath36 . let @xmath44 . then the tableau complex @xmath17 is    1 . homeomorphic to a ball or sphere ; 2 . vertex - decomposable , as defined in @xcite , and hence shellable ; and 3 .   a manifold with ( possibly empty ) boundary whose interior faces are those set - valued tableaux  @xmath24 such that every tableau @xmath45 lies in  @xmath1 . if @xmath4 is taken to be a set of natural numbers , then the tableaux in theorem  [ t : posetball ] are _ @xmath46-partitions _ @xcite , where @xmath47 . in our context , however , this point of view is misleading for a couple of reasons . first , the condition that @xmath4 be totally ordered can be relaxed in a natural way , as we will see during the proof . second , @xmath46-partitions naturally form a set that is infinite and possesses additive structure ; both of these properties are unnatural from the point of view of tableau complexes . more deeply , @xmath46-partitions correspond naturally to the basis elements of the stanley - reisner ring of a certain simplicial complex ( a grbner degeneration of the cone of @xmath46-partitions ) rather than to the facets . we give three formulae for the hilbert series of the stanley - reisner ring , the third one based on an explicit shelling of tableau complexes . for proofs , see section  [ sec : hilb ] , where the statements break the products over @xmath48 and @xmath49 further into products over  @xmath21 . [ t : kpoly ] let @xmath50 be a tableau complex , and recall that the vertices of  @xmath32 are set - valued tableaux @xmath51 .    1 .   [ c:1 ] the hilbert series , in variables @xmath52 is a vertex of  @xmath53 , equals @xmath54 , where the denominator product is over all vertices @xmath55 of  @xmath32 , and the numerator is the -polynomial @xmath56 the sum being over all set - valued tableaux @xmath57 such that @xmath45 for some @xmath9 . [ c:2 ] if @xmath32 is homeomorphic to a ball or a sphere , then writing @xmath58 and @xmath59 for the size of  @xmath3 , the -polynomial can be expressed an alternating sum @xmath60 over the set - valued tableaux @xmath57 such that every tableau @xmath45 satisfies @xmath9 . [ c:3 ] assume furthermore the hypotheses of theorem  [ t : posetball ] , and set @xmath61 . then there is a shelling for  @xmath32 such that the minimal new face when the facet @xmath9 is added during the shelling is an explicitly described set - valued tableau @xmath62 . consequently , @xmath63    as a result of theorem  [ t : kpoly].[c:3 ] , we get a positive combinatorial rule to compute the @xmath64-vector @xmath65 of @xmath32 : if @xmath66 , then @xmath67 counts the number of @xmath9 with @xmath68 . we now describe the prototypical example of a tableau complex , and an application to computing vexillary grothendieck polynomials , or equivalently , hilbert series formulae for vexillary determinantal varieties . let @xmath69 be an english partition , or equivalently , a young shape with its origin at its upper - left corner . a * set - valued young tableau * @xcite is a filling of the boxes of  @xmath13 , each with a nonempty finite set of natural numbers . the set in each box is typically expressed as a strictly increasing list . when the set in every box is a singleton , what results is an ( ordinary ) young tableaux . if @xmath70 denotes the number of entries in a set - valued tableau  @xmath71 , and @xmath72 is the number of boxes in the partition , then @xmath73 . moreover , @xmath74 only for tableaux . ( tableaux are assumed ordinary unless the term `` set - valued '' is written . ) a set - valued tableau @xmath71 is called * semistandard * if for every pair @xmath75 of boxes of @xmath71 ,    * each entry of @xmath76 is weakly less than each entry of @xmath77 whenever @xmath76 lies left of  @xmath77 , and * each entry of @xmath76 is strictly less than each entry of @xmath77 whenever @xmath76 lies above @xmath77 . one can speak of one set - valued tableau * containing * another ( of the same shape @xmath13 ) if for each box of  @xmath13 , the set of numbers in one set - valued tableau contains the corresponding set in the other . in these terms , for @xmath71 to be semistandard , one needs that every tableau contained in  @xmath71 is semistandard in the usual sense . more generally , we define a set - valued tableau to be * limit semistandard * if _ some _ tableau it contains is semistandard . for example , the first of the following set - valued tableaux is semistandard , the second is limit semistandard , and the third is neither : @xmath78 hereafter , we will not bother to write the commas in our examples ; no confusion will result because we only use numbers that are at most  @xmath79 . the * union * of two set - valued tableaux of the same shape @xmath13 simply assigns to each box of @xmath13 the union of the two sets associated to it . moreover , if either set - valued tableau is limit semistandard , so is the union . the intersection is not always defined , however , because of the requirement that every box of  @xmath13 be nonempty . in addition to the partition @xmath13 , fix a maximum entry value @xmath80 . define the * empty - face tableau * @xmath81 associated to @xmath13 and @xmath16 as the union of all the semistandard tableaux with shape @xmath13 and all entries at most @xmath16 . consider the partition  @xmath13 as a poset in which @xmath82 whenever and ; thus each box is less than the boxes southeast of it . writing @xmath83 = \\{1,\\ldots , n\\}$ ] , we get a tableau complex @xmath84}t{e_{\\lambda , n}}$ ] , in the sense of theorem  [ t : posetball ] : take @xmath36 to be the set of pairs in which one box sits atop another in  @xmath13 , so @xmath1 is the set of semistandard young tableaux on  @xmath13 with maximum value  @xmath16 . observing that @xmath84}t{e_{\\lambda , n}}$ ] depends only on  @xmath13 and  @xmath16 , we denote this * young tableau complex * by @xmath85 . see figure  [ fig:1ball ] for an example . the special case of theorem  [ t : posetball ] for young tableau complexes is as follows . the young tableau complex @xmath85 is homeomorphic to a shellable ball or sphere , and its interior faces are labeled by buch s semistandard set - valued young tableaux @xcite . [ exa:21 ] let @xmath86 and @xmath87 . then @xmath88 is a @xmath89-dimensional ball . it has one interior vertex , missing the @xmath30 in the upper left box . we draw the boundary @xmath30-sphere in figure  [ fig:2sphere ] .    when vertex - decomposing a young tableau complex  that is , writing it as the union of the star and the deletion of a single vertex  the two subcomplexes are * flagged * young tableau complexes , in which a vector @xmath90 bounds the sizes of the entries in the rows of  @xmath13 . this suggests that we ought to work in that level of generality ; see figure  [ fig:23ball ] . flagged young tableaux are used to compute the schubert polynomials for vexillary permutations @xcite , and one choice of vertex decomposition parallels the `` transition formula '' for their double grothendieck polynomials  @xcite . hence we are able to give set - valued - tableaux - based formulae for double grothendieck polynomials of vexillary permutations , via theorem  [ t : kpoly ] . the second formula in the following corollary , which appeared already in @xcite , is a common generalization of buch s and wachs s formulae , each of which specializes to the usual tableau formula for schur polynomials . the other two parts give new formulae for these polynomials . see section  [ sec : vex ] for proofs . let @xmath91 be a vexillary permutation with associated partition @xmath13 and flagging @xmath90 . each of the following is a formula for the double grothendieck polynomial @xmath92 .    1 . as a sum over the set @xmath93 of limit semistandard tableau associated to @xmath94 , @xmath95 where @xmath96 is the union of all semistandard tableaux @xmath97 , and @xmath98 is the difference of the row and column indices of the box  @xmath99 . 2 .   as a sum over the set @xmath100 of semistandard set - valued tableau associated to @xmath94 , @xmath101 3 .   as a sum over the set @xmath102 of semistandard young tableaux of shape @xmath13 flagged by  @xmath90 , @xmath103 where @xmath104 is the tableau obtained by adding to each box @xmath105 all numbers in @xmath106 either smaller than the entry of @xmath107 , or larger than that entry provided that replacing the entry with the larger number would not give a tableau in @xmath108 . the second of these formulae for vexillary double grothendieck polynomials was based on the algebraic geometry of matrix schubert varieties @xcite . it was that geometry that first motivated us to fit young tableaux into a simplicial complex .","summary":"we define a simplicial complex whose facets , all of the same dimension , correspond to these tableaux . such _ tableau complexes _ have many nice properties , and are frequently homeomorphic to balls , which we prove using vertex decompositions  .    in our motivating example , the facets are labeled by semistandard young tableaux , and the more general interior faces are labeled by buch s set - valued semistandard tableaux . one vertex decomposition of this `` young tableau complex '' parallels lascoux s transition formula for vexillary double grothendieck polynomials . , we present a common generalization of the formulae of wachs and buch , each of which implies the classical tableau formula for schur polynomials .","abstract":"let be finite sets and a set of functions from which we will call `` tableaux '' . we define a simplicial complex whose facets , all of the same dimension , correspond to these tableaux . such _ tableau complexes _ have many nice properties , and are frequently homeomorphic to balls , which we prove using vertex decompositions  .    in our motivating example , the facets are labeled by semistandard young tableaux , and the more general interior faces are labeled by buch s set - valued semistandard tableaux . one vertex decomposition of this `` young tableau complex '' parallels lascoux s transition formula for vexillary double grothendieck polynomials . consequently , we obtain formulae ( both old and new ) for these polynomials . in particular , we present a common generalization of the formulae of wachs and buch , each of which implies the classical tableau formula for schur polynomials ."}
{"article_id":"1201.4430","section_id":"i","document":"one of key issues toward a full understanding of the formation process of high - mass stars is to reveal their initial conditions . for this purpose , infrared dark clouds ( irdcs ) are thought to be good targets . irdcs are extinction features against the background mid - ir emission ( e.g. prault et al . 1996 ; egan et al . more than ten thousands of irdcs have been identified on the msx data ( simon et al . 2006 ) and the spitzer data ( peretto & fuller 2009 ) . by mapping observations with bolometer arrays , many massive clumps ( @xmath6100 @xmath7 ) have been found in irdcs ( e.g. rathborne et al . these massive clumps are known to be in various evolutionary stages of star formation . chambers et al . ( 2009 ) classified the massive clumps associated with irdcs into 4 groups on the basis of the 1.2 mm continuum data and the infrared data . according to their results , star formation has already occurred in these massive clumps , except for some candidates of high - mass starless clumps . it has been well established that chemical composition is a useful indicator of evolutionary stages for low - mass starless cores ( e.g. suzuki et al . 1992 ; benson et al . 1998 ) . we considered that such a chemical approach would also be useful for high - mass sources , and carried out systematic surveys of several molecular lines toward massive clumps associated with irdcs ( sakai et al . 2008 ; 2010 ) . as a result , we found that the ccs / n@xmath8h@xmath9 ratio of massive clumps is lower than that of young low - mass starless cores . this indicates that most of the massive clumps are chemically evolved than the young low - mass starless cores , since the ccs / n@xmath8h@xmath9 ratio is known to become lower for more evolved cores ( benson et al . in addition , we found that the sio and ch@xmath3oh abundances relative to h@xmath0co@xmath9 are enhanced in several massive clumps . since sio and ch@xmath3oh are known as `` shock tracers '' , these results suggest that the effect of shocks is more significant in the irdcs than in the hmpos . such shocks would be caused by an interaction between outflows and dense gas . recently , vasyunina et al . ( 2011 ) surveyed the lines of 13 molecules toward massive clumps in irdcs . they suggest that the chemical composition of the massive clumps in irdcs is similar to that of low - mass prestellar cores rather than that of hmpos . in addition , spectral line observations toward massive clumps have extensively been carried out for fundamental molecules ( teyssier et al . 2002 ; pillai et al . 2006 ; purcell et al . 2006 ; ragan et al . 2006 ; beuther & sridharan 2007 ; leurini et al . 2007a ) .    in spite of the above efforts , the initial conditions of high - mass star formation have not been established well . in this paper , we examine it on the basis of the deuterium fractionation in massive clumps . in cold molecular clouds , the deuterium atom is known to be fractionated into molecules except for hd ( i.e. the main reservoir of the deuterium atom ) through the following exothermic isotope - exchange reactions ; @xmath10 @xmath11 @xmath12 the h@xmath13 , ch@xmath13 , and c@xmath8h@xmath14 ions are related to the formation processes of various molecules , so that the deuterium fractionation is transferred to their daughter molecules . since the backward reaction rates of the above reactions are sensitive to the gas kinetic temperature , the equilibrium deuterium fractionation ratios of molecules depend on the temperature . furthermore , the deuterium fractionation is enhanced in the evolved stages of starless cores , because co , which is a main destroyer of h@xmath8d@xmath9 , is depleted onto dust grains below 20 k. such an enhancement was indeed confirmed toward some low - mass starless cores ( caselli et al . therefore , the deuterium fractionation ratio is regarded as a good indicator to trace the evolved starless core phase . in order to investigate the starless phase of high - mass star formation , fontani et al . ( 2011 ) focused on the n@xmath8d@xmath9 and n@xmath8h@xmath9 ratio . they observed the n@xmath8d@xmath9 ( @xmath1=21 ) and n@xmath8h@xmath9 ( @xmath1=10 , 32 ) lines toward 27 massive clumps including irdcs , high - mass protostellar objects , and ultra - compact hii regions , and suggested that the n@xmath8d@xmath9/n@xmath8h@xmath9 ratio is higher in high - mass starless core candidates . pillai et al . ( 2007 ) also observed the nh@xmath8d / nh@xmath3 ratio toward 32 pre / protocluster sources . they found moderately high deuterium fractionation ratios ( 0.0010.7 ) in the massive clumps .    in general , the deuterium fractionation can be affected by star formation activities . since the gas kinetic temperature around protostars becomes higher than that in cold cores , the equilibrium deuterium fractionation ratios are lower in star forming cores . however , the equilibrium condition would hardly be satisfied in actual star forming regions for the neutral species . rodgers & millar ( 1996 ) pointed out that the initial deuterium fractionation ratio remains over 10@xmath15 yr after the onset of star formation . if so , the deuterium fractionation ratios of `` star forming '' cores contain novel information on physical conditions and history of their starless core phase . by observing the deuterium fractionation ratios of the neutral species in high - mass star forming cores , we would be able to know their initial conditions before the birth of high - mass protostars . recently , candidates of high - mass starless cores have been found ( e.g. beuther et al . 2010 ) , whose detailed characterization will provide us with a clue to understand the necessary conditions for high - mass star formation . however a limited number of such sources has been known so far in the galaxy ( e.g. chambers et al . 2009 ) . furthermore , it is not guaranteed that massive stars will certainly form in such sources in the future . our approach is to derive the initial condition of high - mass star formation from the dnc / hnc ratio of `` star - forming '' cores , which is complimentary to the effort investigating the candidates of high - mass starless cores . based on this motivation , we have observed the dnc and hn@xmath0c lines toward irdcs and high - mass protostellar objects ( hmpos ; sridharan et al . 2002 ; beuther et al . we choose dnc and hn@xmath0c , because hirota et al . ( 2001 ) observed the dnc / hnc ratio toward low - mass cores with the nobeyama radio observatory ( nro ) 45 m telescope . the hnc line is sometimes optically thick , and hence we observed the hn@xmath0c line , which is generally optically thin . hence , we can critically compare the high - mass data with the low - mass data . in this paper , we also compare the observation results with the model calculation results , and discuss how the deuterium fractionation ratios vary after the onset of star formation .","summary":"we have observed the hnc=10 and dnc=10 lines toward 18 massive clumps , including infrared dark clouds ( irdcs ) and high - mass protostellar objects ( hmpos ) , by using the nobeyama radio observatory 45 m telescope . we suggest that the dnc / hnc ratio in star - forming cores depends on the physical conditions and history in their starless - core phase , such as its duration time and the gas kinetic temperature .","abstract":"we have observed the hnc=10 and dnc=10 lines toward 18 massive clumps , including infrared dark clouds ( irdcs ) and high - mass protostellar objects ( hmpos ) , by using the nobeyama radio observatory 45 m telescope . we have found that the hnc emission is stronger than the dnc emission toward all the observed sources . the averaged dnc / hnc ratio is indeed lower toward the observed high - mass sources ( 0.009.005 ) than toward the low - mass starless and star - forming cores ( 0.06 ) . the kinetic temperature derived from the nh ( , ) = ( 1 , 1 ) and ( 2 , 2 ) line intensities is higher toward the observed high - mass sources than toward the low - mass cores . however the dnc / hnc ratio of some irdcs involving the spitzer 24 m sources is found to be lower than that of hmpos , although the kinetic temperature of the irdcs is lower than that of the hmpos . this implies that the dnc / hnc ratio does not depend only on the current kinetic temperature . with the aid of chemical model simulations , we discuss how the dnc / hnc ratio decreases after the birth of protostars . we suggest that the dnc / hnc ratio in star - forming cores depends on the physical conditions and history in their starless - core phase , such as its duration time and the gas kinetic temperature ."}
{"article_id":"1201.4430","section_id":"c","document":"as mentioned in introduction , the equilibrium deuterium fractionation ratios would be affected by the gas kinetic temperature . to examine this , we estimate the kinetic temperature from the nh@xmath3 rotation temperature by using the equation ( 2 ) in walmsley & ungerechts ( 1983 ) . for discussion , we only use the nh@xmath3 data obtained by sakai et al . ( 2008 ) in order to minimize the systematic errors caused by the difference in angular resolution . we exclude i18089 - 1732 mm1 and i18264 - 1152 mm1 in the following discussion , because we do not have the nh3 data observed with the nro 45 m telescope . although the nh@xmath3 lines were observed toward these objects by sridharan et al . ( 2002 ) using the effelsberg 100 m telescope , the beam size ( 40@xmath44 ) is smaller than that of our nro 45 m observations by a factor of 2 . the kinetic temperature of i18089 - 1732 mm1 is much higher than the other sources . this may be partly related to the difference in the angular resolution .    in figure [ fig : f3 ] , we plot the @xmath26(dnc)/@xmath26(hnc ) ratio against the gas kinetic temperature for the observed sources . for comparison , we also plot the data of low - mass cores , which are reported by hirota et al . we only use the data of the low - mass cores toward which the gas kinetic temperature is reported ( jijina et al . 1999 and references therein ) . the temperature is systematically higher in the high - mass sources than in the low - mass sources . in figure [ fig : f3 ] , we can clearly see the difference in the dnc / hnc ratio between low- and high - mass star forming regions . the average value of the dnc / hnc ratio is 0.009 ( @xmath20.005 ) for the observed high - mass sources , while it is 0.06 ( @xmath20.03 ) for the low - mass sources . since the high - mass sources are generally more distant than the low - mass sources , the lower dnc / hnc ratio might be due to the lower spatial resolution for the high - mass sources . however , hirota et al . ( 2003 ) revealed the distribution of the dnc / hnc ratio toward the low - mass cores , and found that the dnc / hnc ratio is quite uniform within the cores with a scale of about 3@xmath45 from the edge to the center . even if the low - mass cores would be located at a distance of a few kpc , which is more distant than the low - mass cores typically by a factor of 10 , the high dnc / hnc ratio would be observed with our 20@xmath44 . we therefore think that the lower dnc / hnc ratios of the high - mass sources are not due to the distance effect . indeed , there is no correlation between the distance and the dnc / hnc ratio . in addition , we can see a trend that the @xmath26(dnc)/@xmath26(hnc ) ratios of the spitzer - dark sources are slightly higher than those of the other sources . the average value for the spitzer - dark sources is also higher than that for the other sources ( see table [ tab : t5 ] ) . this trend is similar to that reported by fontani et al . ( 2011 ) , where the @xmath26(n@xmath8d@xmath9)/@xmath26(n@xmath8h@xmath9 ) ratios of high - mass starless cores tend to be higher than that of the hmpos and uc hii regions . however , our observed spitzer dark sources have lower @xmath26(dnc)/@xmath26(hnc ) ratios than the low - mass cores . this is different from that found by fontani et al . ( 2011 ) , where the @xmath26(n@xmath8d@xmath9)/@xmath26(n@xmath8h@xmath9 ) ratio of several hmscs is comparable to that of low - mass starless cores . this difference may partly be due to a diversity of the deuterium fractionation in the high - mass starless core phase . indeed , the @xmath26(n@xmath8d@xmath9)/@xmath26(n@xmath8h@xmath9 ) ratios of some high - mass starless cores are as low as those of the hmpos and the uc hii regions even in the sample of fontani et al . in addition , tatematsu et al . ( 2010 ) found a starless core that has the low dnc / hnc ratio ( @xmath240.008 ) toward the orion a giant molecular cloud . on the other hand , the difference may be attributed to chemical reasons . if n@xmath8d@xmath9 and dnc is formed mainly from h@xmath8d@xmath9 and ch@xmath8d@xmath9 , respectively ( roueff et al . 2007 ) , for instance , the deuterium fractionation ratio is thought to be different between n@xmath8d@xmath9 and dnc . we need to observe every sources with the same molecular lines in order to confirm the diversity of the deuterium fractionation ratio in the starless phase .    in the present stage , it is still controversial whether the spitzer - dark sources are really in the starless phase of high - mass stars . the hn@xmath0c column density of our observed spitzer - dark sources is smaller than that of the other sources ( table [ tab : t5 ] ) , and is comparable to that of the low - mass cores ( hirota et al . in addition , the 1.2 mm peak flux of the spitzer - dark sources ( 37 to 115 mjy ) is lower than that of the spitzer - bright sources ( 110 to 424 mjy ) ( beuther et al . 2002 ; rathborne et al . it may be possible that the lower hnc abundance is due to the depletion onto dust grains , and that the lower mm - continuum emission is due to the low temperature . nevertheless , we can not rule out a possibility that the observed spitzer dark sources are smaller than the other sources and they are just low - mass star forming regions . on the other hand , the hnc column density is comparable between the spitzer - bright irdcs and hmpos , and hence , we may say that their masses are similar . thus , we think that comparison of the dnc / hnc ratio between the spitzer - bright irdcs and the hmpos is much more secure to investigate the evolution of the dnc / hnc ratio .      to investigate whether the lower dnc / hnc ratio of the high - mass sources is explained only by the difference of the gas kinetic temperature , we performed chemical model calculations . the chemical network used is the same as that reported by aikawa et al . this model includes the gas - phase reactions , grain - surface reactions , depletion onto dust grains , and desorption from dust grains . we assume a static geometry with a constant h@xmath8 density of 10@xmath46 @xmath47 for simplicity , and calculated the temporal variation of the molecular abundances for 10 k , 20 k , and 30 k. we assume the so - called low - metal values ( see table 1 of aikawa et al . 2001 ) as the elemental abundances . all the heavy elements are assumed to be initially in the atomic form and the hydrogen in the molecular form . the deuterium is assumed to be in the form of hd , with the fractional abundance of 3.0@xmath4810@xmath49 relative to h@xmath8 . we adopt the binding energy of co on the dust to be 1180 k. therefore , co still remains on the dust at the temperature of 20 k , and the sublimation temperature of co is about 21 k in this model . the results at 10@xmath46 yr and 10@xmath40 yr after starting chemical reactions from the initial condition are plotted in figure [ fig : f3 ] .    according to the model calculation , the dnc / hnc ratio does not change very much between 10 k and 20 k , while it considerably decreases at 30 k. roueff et al . ( 2007 ) also reported a similar result for dnc / hnc . in figure [ fig : f3 ] , the observed dnc / hnc ratios for the low - mass sources are consistent with the model calculation . on the other hand , the ratios observed for the massive clumps are lower than the model prediction . the discrepancy is particularly significant for the sources with the gas kinetic temperature around 20 k.    roueff et al . ( 2007 ) predicted that the d / h ratio for some molecules such as c@xmath8h@xmath14 could become , in general , higher in denser regions . however , they suggest from their model calculation that the equilibrium dnc / hnc ratio does not depend on the density in the low - metal abundance case . therefore , the differences of the h@xmath8 density would not explain the trend seen in figure [ fig : f3 ] . indeed , it is unlikely that the high - mass star forming regions are less dense than the low - mass star forming regions . it is known that existence of the ortho h@xmath8 molecule enhances the backward reaction of ( 1 ) , because the ortho h@xmath8 molecule in its lowest rotational state ( @xmath1=1 ) has the rotational energy of about 170 k ( gerlich et al . 2002 ; flower et al . hence , it decreases the deuterium fractionation ratio of h@xmath8d@xmath9 and those of various molecules . we ignored this effect in the chemical model calculation , because the ortho - to - para ratio of h@xmath8 is reported to be close to 0 for low - mass protostar sources ( flower et al . 2006 ; caselli et al . 2008 ; pagani et al . 2009 ; troscompt et al . if the ortho - to - para ratio of h@xmath8 is significantly higher in the massive clumps , the lower deuterium fractionation at 20 k could be explained . however , the fractionation ratio at higher temperatures would also have to decrease in this case , which contradicts with the ratios in hmpos ( figure 3 ) . although the ortho - to - para ratio of h@xmath8 may affect the deuterium fractionation ratio to some extent , we do not consider it in the following discussion for simplicity . another possibility for the discrepancy between the model and observational results is that the dnc and hn@xmath0c emissions would come from warmer regions than the nh@xmath3 ( 1 , 1 ) and ( 2 , 2 ) emissions . since the critical density of the dnc and hn@xmath0c lines ( @xmath2410@xmath40 @xmath41 ) is higher than that of the nh@xmath3 lines ( @xmath2410@xmath15 @xmath41 ) , the dnc and hn@xmath0c emissions trace denser regions . in the objects associated with the spitzer sources , the inner dense part is likely to be warmer due to various activities of newly born stars , and hence , the dnc and hnc emissions tend to trace such regions . the smaller beams size of the dnc and hnc observations in comparison with the nh@xmath3 observations may also contribute to this effect . if this is the case , the temperature estimated from the nh@xmath3 observation may be underestimated , and the data points around 20 k may have to be shifted to the higher temperature , giving a better agreement with the chemical model calculation . however , some massive clumps have relatively lower dnc / hnc ratio than the hmpos , although the gas kinetic temperature of the massive clumps is lower than that of the hmpos ( figure [ fig : f3 ] ) . for example , the dnc / hnc ratio of g034.43 + 00.24 mm3 ( 0.0029 ) is lower than that of i18151 - 1208 mm1 ( 0.0088 ) , while the kinetic temperature of g034.43 + 00.24 mm3 ( 19 k ) is lower than that of i18151 - 1208 mm1 ( 31 k ) . this trend is not explained only with the difference in the gas kinetic temperature .    in figure [ fig : f3 ] , the model results at 10@xmath46 and 10@xmath40 yr are shown . at 10@xmath46 yr , the deuterium fractionation ratio does not reach its steady state value , as seen in the difference of the ratio between 10@xmath46 and 10@xmath40 yr . this means that the deuterium fractionation ratio depends not only on the current temperature but also on the past physical history of the clump . hence , the time dependence effect has to be considered for the dnc / hnc ratio , as discussed in the next section . when we consider the evolution of molecular clouds from diffuse clouds into dense cores , the deuterium fractionation ratio of molecules gradually increases with time from the cosmic d / h ratio ( @xmath2410@xmath49 ) ; the deuterium fractionation is expected to be low in the early stage of molecular cloud evolution . in fact , hirota et al . ( 2001 ) found the low deuterium fractionation in a few young low - mass starless cores . in addition , crapsi et al . ( 2005 ) found that the deuterium fractionation ratio is higher in the cores closest to the onset of gravitational collapse among the sample of low - mass starless cores , and they suggest that the deuterium fractionation increases with the core evolution . the birth of protostars raises the temperature around them . the deuterium fractionation ratio then starts to decrease toward the equilibrium value at the new temperature . the timescale of this change is different from species to species , depending on the destruction timescale of each species . first , we consider the timescale for dnc / hnc . the main destruction pathways of dnc are as follows ; @xmath50 @xmath51 although the dissociative recombination of dnch@xmath9 can reproduce dnc , it competes with hcn + d and cn + d + h. thus , the abundance of dnc could decrease with the above reactions . the timescale of the above reactions ( 7 ) and ( 8) is comparable to each other , and depends on the abundances of hco@xmath9 and h@xmath13 . for instance , the timescale of the reaction with hco@xmath9 is represented as @xmath52 } \\sim 4 \\times 10^{12 } \\ ; { \\rm s } \\sim 10 ^ 5 \\ ; { \\rm yr},\\ ] ] in the case of the density of 10@xmath46 @xmath47 . since the hco@xmath9 abundance depends on the h@xmath8 density ( umebayashi & nakano , 1980 ) , the above timescale would have the weak power - low dependence on the density as @xmath53 . therefore , the dnc / hnc ratio can be preserved after the temperature rise . on the other hand , we note that the destruction timescale of molecular ions is much shorter than that of neutral molecules , because they can react with co and/or electron . for example , the main destruction pathway of n@xmath8d@xmath9 is the following reaction ; @xmath54 the destruction timescale of n@xmath8d@xmath9 is therefore given as @xmath55 } \\sim 10^{8 } \\ ; { \\rm s } \\sim 4 \\ ; { \\rm yr } .\\ ] ] the deuterium fractionation ratio of molecular ions immediately decreases after the onset of star formation , and reaches at the equilibrium value at the new temperature .      to investigate how the deuterium fractionation ratio changes after the temperature rise , we performed the following chemical model calculations . we simply assume a sudden temperature rise from 10 to 30 k at a given age , 1@xmath4810@xmath46 yr or 3@xmath4810@xmath46 yr , and calculate the temporal variation of chemical compositions after that . we plot the calculated dnc / hnc and n@xmath8d@xmath9/n@xmath8h@xmath9 ratios in figure [ fig : f4]a . we also plot the dnc / hnc and n@xmath8d@xmath9/n@xmath8h@xmath9 ratios for the cases without the temperature rise . as seen in figure [ fig : f4]a , the dnc / hnc and n@xmath8d@xmath9/n@xmath8h@xmath9 ratios slowly increases with time until the temperature rise , and they decrease after that . the decrease of the deuterium fractionation ratios originates from the above gas phase processes . although molecules are evaporated from dust grains after the temperature rise , the dnc / hnc ratio in the gas phase is not affected by this effect . hnc is not efficiently formed by grain - surface reactions , so that the dnc / hnc ratio in ice mantle is not significantly different from the ratio in the gas phase .    for clarity , we plot the dnc / hnc ratio after the temperature rise in figure [ fig : f4]b . in figure [ fig : f4]b , we can see that the dnc / hnc ratio gradually decreases with a timescale of several times 10@xmath15 yr , while the n@xmath8h@xmath9 ratio rapidly decreases with a timescale of several 10 yr . this is consistent with the rough estimate of the timescales mentioned before . more importantly , the dnc / hnc ratio after the temperature rise depends on the time when the temperature is raised . in other words , the dnc / hnc ratio in the star forming clumps depends on the initial dnc / hnc ratio before the onset of star formation . since the dynamical age of outflows of the hmpos are estimated to be several times 10@xmath1510@xmath46 yr ( beuther et al . 2002b ) , the initial dnc / hnc ratio is conserved in the massive clumps and hmpos to some extent . as mentioned in section 4.1 , some massive clumps with the spitzer sources have lower dnc / hnc ratio than the hmpos . this difference would reflect the difference of the deuterium fractionation ratio at the onset of star formation .    for comparison , we plot the average value of all of our observed sources in figure [ fig : f4 ] . the observed value is comparable to the constant temperature case of 30 k. on the other hand , the cases that the temperature rise from 10 k to 30 k at 10@xmath46 yr and 3@xmath4810@xmath46 yr can not reproduce the observed value , because the dnc / hnc ratio just before the temperature rise is preserved after the temperature rise . this indicates that the dnc / hnc ratio just before the onset of star formation should have been low for these sources . thus , we speculate that the dnc / hnc ratio just before the onset of star formation would be lower for the observed high - mass sources than for the low - mass cores . the lower dnc / hnc ratio implies that the cold starless phase of the observed sources is shorter than that of the low - mass cores , or that the initial temperature is warmer ( @xmath6 20 k ) than that of the low - mass cores ( @xmath2410 k ) . the timescale of high - mass starless phase is still controversial . from the statistical study , chambers et al . ( 2009 ) estimated the timescale of starless phase to be 3.7@xmath4810@xmath46 yr , while parsons et al . ( 2009 ) estimated it to be a few 10@xmath56 - 10@xmath15 yr . although our observed results seem to support the short timescale of the starless phase , we need more careful considerations . in fact , sakai et al . ( 2008 ) measured the ccs / n@xmath8h@xmath9 ratio toward the irdcs and hmpos , and obtained only the upper limits of the ccs / n@xmath8h@xmath9 ratio . from these results , they suggest that massive clumps in irdcs and hmpos are chemically more evolved than young low - mass dense cores . however , this argument is based on the single - dish observations , which may be affected by the limited angular resolution and sensitivity . if the dnc / hnc ratio reflects the timescale of starless core phase , we should see a correlation between the dnc / hnc ratio and the ccs / n@xmath8h@xmath9 ratio with high - sensitivity and high - angular resolution observations . in this relation , devine et al . ( 2011 ) have recently found the chemically young envelope toward the irdc g19.30 + 00.07 with the vla observations . existence of such a chemically young envelope may be related to the chemical youth of the clump . the initial temperature of high - mass star formation has not been established well either . the theoretical models of high - mass star formation generally assume the initial temperature from 10 to 30 k ( e.g. krumholz et al . 2009 ; peters et al . 2011 ) . however , this assumption is not based on the observational results . if the deuterium fractionation ratio would reflect the initial temperature , it will provide us with novel information for understanding the high - mass star formation , because the initial temperature affects the accretion rate and the gravitational instability causing clump fragmentation . discrimination of these two possibilities is not an easy task . a systematic observation of n@xmath8d@xmath9/n@xmath8h@xmath9 toward the same sources would be an important clue to this , as shown in figure [ fig : f4]a . the n@xmath8d@xmath9/n@xmath8h@xmath9 ratio is expected to be higher than the dnc / hnc ratio , if the clump temperature is 30 k from the starless - core phase ( see the curves for the constant temperature of 30 k ) .    for a future work , we are going to observe the dnc / hnc and n@xmath8d@xmath9/n@xmath8h@xmath9 ratios toward an irdc clump with the high - angular resolution by using alma . from this observation , we will obtain important information about the behavior of the deuterium fractionation in the high - mass star forming regions in more detail .","summary":"we have found that the hnc emission is stronger than the dnc emission toward all the observed sources . this implies that the dnc / hnc ratio does not depend only on the current kinetic temperature . with the aid of chemical model simulations ,","abstract":"we have observed the hnc=10 and dnc=10 lines toward 18 massive clumps , including infrared dark clouds ( irdcs ) and high - mass protostellar objects ( hmpos ) , by using the nobeyama radio observatory 45 m telescope . we have found that the hnc emission is stronger than the dnc emission toward all the observed sources . the averaged dnc / hnc ratio is indeed lower toward the observed high - mass sources ( 0.009.005 ) than toward the low - mass starless and star - forming cores ( 0.06 ) . the kinetic temperature derived from the nh ( , ) = ( 1 , 1 ) and ( 2 , 2 ) line intensities is higher toward the observed high - mass sources than toward the low - mass cores . however the dnc / hnc ratio of some irdcs involving the spitzer 24 m sources is found to be lower than that of hmpos , although the kinetic temperature of the irdcs is lower than that of the hmpos . this implies that the dnc / hnc ratio does not depend only on the current kinetic temperature . with the aid of chemical model simulations , we discuss how the dnc / hnc ratio decreases after the birth of protostars . we suggest that the dnc / hnc ratio in star - forming cores depends on the physical conditions and history in their starless - core phase , such as its duration time and the gas kinetic temperature ."}
{"article_id":"1201.4430","section_id":"i","document":"we conducted a survey of the hn@xmath0c @xmath1=10 and dnc @xmath1=10 lines toward the 18 massive clumps , and compared the results with the chemical model calculation . the main results are summarized as follows . * we detected the hn@xmath0c @xmath1=10 emission toward all the observed sources and the dnc @xmath1=10 emission toward 16 out of the 18 sources above the 3 @xmath22 confidence level at a velocity resolution of 0.08 km s@xmath23 . the intensities of the dnc line appear to be weaker than those of the hn@xmath0c line toward all the sources in contrast to the case for the low - mass star forming regions . * the dnc / hnc ratio averaged for the observed sources except for the two sources is found to be 0.009 ( @xmath20.005 ) , which is lower than that of the low - mass cores . the kinetic temperature derived from the nh@xmath3 ( @xmath1 , @xmath4 ) = ( 1 , 1 ) and ( 2 , 2 ) line intensities is higher toward the observed high - mass sources than toward the low - mass cores . however , the ratios observed for the massive clumps are lower than the model calculation , particularly for the sources with the gas kinetic temperature around 20 k. furthermore , we found that the dnc / hnc ratios of some massive clumps with the spitzer sources are lower than that of hmpos . these results suggest that the dnc / hnc ratio can not simply be explained by the current temperature of the clumps . * from the model calculations , it is found that the dnc / hnc ratio decreases with a timescale of several times 10@xmath15 yr after the birth of protostars , whereas the n@xmath8d@xmath9/n@xmath8h@xmath9 ratio decreases with a timescale of less than 100 yr . therefore , the dnc / hnc ratio of star forming clumps can reflect the initial dnc / hnc ratio just before the birth of protostars . we are grateful to the nro staff for excellent support in the 45 m observations . the 45 m radio telescope is operated by nobeyama radio observatory , a branch of national astronomical observatory of japan . this study is supported by grant - in - aid from ministry of education , culture , sports , science , and technologies ( 21740144 , 21224002 , 23740146 and 23540266 ) . aikawa , y. , ohashi , n. , inutsuka , s. , herbst , e. , takakuwa , s. 2001 , , 552 , 639 aikawa , y. , herbst , e. , roberts , h. , caselli , p. 2005 , , 620 , 330 benson , p. j. , caselli , p. , myers , p. c. 1998 , , 506 , 743 beuther , h. , schilke , p. , menten , k. m. , motte , f. , sridharan , t. k. , wyrowski , f. 2002a , , 566 , 945 beuther , h. , schilke , p. , sridharan , t. k. , menten , k. m. , walmsley , c. m. , wyrowski , f. 2002b , , 383 , 892 beuther , h. , sridharan , t. k. 2007 , , 668 , 348 beuther , h. , henning , th . , linz , h. , krause , o. , nielbock , m. , steinacker , j. 2010 , , 518 , l78 caselli , p. , walmsley , c. m. , tafalla , m. , dore , l. , myers , p. c. 1999 , , 523 , l165 caselli , p. , vastel , c. , ceccarelli , c. , van der tak , f. f. s. , crapsi , a. , bacmann , a. 2008 , , 492 , 703 chambers , e. t. , jackson , j. m. , rathborne , j. m. , simon , r. 2009 , , 181 , 360 crapsi , a. , caselli , p. , walmsley , c. m. , myers , p. c. , tafalla , m. , lee , c. w. , bourke , t. l. 2005 , , 619 , 379 devine , k. e. , chandler , c. j. , brogan , c. , churchwell , e. , indebetouw , r. , shirley , y. , borg , k. j. 2011 , , 733 , 44 egan , m. p. , shipman , r. f. , price , s. d. , carey , s. j. , clark , f. o. , cohen , m. 1998 , , 494 , l199 flower , d. r. , pineau des forets , g. , walmsley , c. m. 2006 , , 449 , 621 fontani , f. , caselli , p. , crapsi , a. , cesaroni , r. , molinari , s. , testi , l. , brand , j. 2006 , , 460 , 709 fontani , f. , palau , a. , caselli , p. , sanchez - 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blant , p. , wiesenfeld , l. 2009 , , 506 , 1243 umebayashi , t. , nakano , t. 1980 , , 32 , 405 vasyunina , t. , linz , h. , henning , th . , zinchenko , i. , beuther , h. , voronkov , m. 2011 , , 527 , 88 walmsley , c. m. , ungerechts , h. 1983 , , 122 , 164 wilson , t. l. , rood , r. 1994 , , 32 , 191    lrrrrrr + g015.05 + 00.07 mm1 & 18 17 50.4 & -15 53 38 & 24.7 & 2.5 & 6.1 & 1 + g015.31 - 00.16 mm3 & 18 18 45.3 & -15 41 58 & 30.8 & 3.0 & 5.6 & 1 + g024.08 + 00.04 mm3 & 18 35 02.2 & -07 45 25 & 51.9 & 3.6 & 5.5 & 1 + g024.08 + 00.04 mm4 & 18 35 02.6 & -07 45 56 & 52.0 & 3.6 & 5.4 & 1 + g034.43 + 00.24 mm9 & 18 53 18.4 & 01 28 14 & 59.0 & 1.6 & 7.3 & 1 +   + g019.27 + 00.07 mm1 & 18 25 58.5 & -12 03 59 & 26.8 & 2.3 & 6.4 & 1 + g022.35 + 00.41 mm1 & 18 30 24.4 & -09 10 34 & 52.7 & 3.7 & 5.2 & 1 + g023.60 + 00.00 mm2 & 18 34 21.1 & -08 18 07 & 53.3 & 3.7 & 5.3 & 1 + g034.43 + 00.24 mm3 & 18 53 20.4 & 01 28 23 & 59.7 & 1.6 & 7.3 & 1 + i18151 - 1208 mm2 & 18 17 50.4 & -12 07 55 & 29.7 & 2.6 & 6.1 & 2,3,4 + i18223 - 1243 mm3 & 18 25 08.3 & -12 45 28 & 45.7 & 3.7 & 5.2 & 2,3,4 + i18337 - 0743 mm3 & 18 36 18.2 & -07 41 01 & 56.4 & 3.8 & 5.3 & 2,3,4 +   + i18089 - 1732 mm1 & 18 11 51.5 & -17 31 29 & 33.1 & 3.6 & 5.1 & 2,3,4 + i18151 - 1208 mm1 & 18 17 58.0 & -12 07 27 & 33.2 & 2.8 & 5.9 & 2,3,4 + i18182 - 1433 mm1 & 18 21 09.2 & -14 31 57 & 60.0 & 4.6 & 4.3 & 2,3,4 + i18223 - 1243 mm1 & 18 25 10.5 & -12 42 26 & 45.3 & 3.6 & 5.2 & 2,3,4 + i18264 - 1152 mm1 & 18 29 14.6 & -11 50 22 & 43.7 & 3.4 & 5.4 & 2,3,4 + i18337 - 0743 mm1 & 18 36 41.0 & -07 39 20 & 58.4 & 3.9 & 5.2 & 2,3,4 + [ tab : t1 ]      lrrrr + g015.05 + 00.07 mm1 & 0.21(0.01 ) & 2.13(0.01 ) & 0.47(0.03 ) & 24.78(0.04 ) + g015.31 - 00.16 mm3 & 0.28(0.01 ) & 0.87(0.05 ) & 0.22(0.03 ) & 30.88(0.02 ) + g024.08 + 00.04 mm3 & 0.15(0.01 ) & 1.71(0.12 ) & 0.25(0.03 ) & 51.78(0.05 ) + g024.08 + 00.04 mm4 & 0.18(0.01 ) & 1.21(0.08 ) & 0.28(0.03 ) & 52.02(0.03 ) + g034.43 + 00.24 mm9 & 0.22(0.01 ) & 1.93(0.10 ) & 0.39(0.03 ) & 58.53(0.04 ) +   + g019.27 + 00.07 mm1 & 0.47(0.01 ) & 2.51(0.05 ) & 1.37(0.03 ) & 26.63(0.02 ) + g022.35 + 00.41 mm1 & 0.27(0.01 ) & 2.52(0.08 ) & 0.77(0.03 ) & 52.70(0.03 ) + g023.60 + 00.00 mm2 & 0.27(0.01 ) & 2.71(0.09 ) & 1.19(0.02 ) & 53.65(0.04 ) + g034.43 + 00.24 mm3 & 0.51(0.01 ) & 1.95(0.03 ) & 1.19(0.02 ) & 59.67(0.01 ) + i18151 - 1208 mm2 & 0.31(0.01 ) & 2.68(0.08 ) & 0.98(0.03 ) & 29.98(0.03 ) + i18223 - 1243 mm3 & 0.61(0.01 ) & 2.35(0.03 ) & 1.50(0.02 ) & 45.97(0.01 ) + i18337 - 0743 mm3 & 0.20(0.01 ) & 1.60(0.07 ) & 0.34(0.02 ) & 56.34(0.03 ) +   + i18089 - 1732 mm1 & 0.44(0.01 ) & 3.33(0.06 ) & 1.51(0.02 ) & 32.80(0.02 ) + i18151 - 1208 mm1 & 0.43(0.01 ) & 1.99(0.04 ) & 1.03(0.03 ) & 33.37(0.02 ) + i18182 - 1433 mm1 & 0.35(0.01 ) & 3.19(0.07 ) & 1.17(0.03 ) & 60.16(0.03 ) + i18223 - 1243 mm1 & 0.39(0.01 ) & 1.98(0.04 ) & 0.81(0.02 ) & 45.35(0.02 ) + i18264 - 1152 mm1 & 0.50(0.01 ) & 2.76(0.06 ) & 1.51(0.04 ) & 43.61(0.03 ) + i18337 - 0743 mm1 & 0.40(0.01 ) & 3.32(0.06 ) & 1.35(0.02 ) & 58.44(0.02 ) + [ tab : t3 ]    lrrrr + g015.05 + 00.07 mm1 & 0.12 ( 0.01 ) & 1.98 ( 0.26 ) & 0.25 ( 0.04 ) & 25.00 ( 0.11 ) + g015.31 - 00.16 mm3 & 0.13 ( 0.02 ) & 1.25 ( 0.20 ) & 0.18 ( 0.05 ) & 31.15 ( 0.09 ) + g024.08 + 00.04 mm3 &  &  & @xmath570.12 &  + g024.08 + 00.04 mm4 & 0.11 ( 0.01 ) & 1.75 ( 0.24 ) & 0.35 ( 0.04 ) & 51.71 ( 0.10 ) + g034.43 + 00.24 mm9 & 0.19 ( 0.01 ) & 2.21 ( 0.19 ) & 0.35 ( 0.05 ) & 58.55 ( 0.08 ) +   + g019.27 + 00.07 mm1 & 0.10 ( 0.01 ) & 2.22 ( 0.34 ) & 0.30 ( 0.05 ) & 25.97 ( 0.14 ) + g022.35 + 00.41 mm1 & 0.14 ( 0.01 ) & 2.76 ( 0.25 ) & 0.47 ( 0.04 ) & 52.60 ( 0.10 ) + g023.60 + 00.00 mm2 &  &  & @xmath570.32 &  + g034.43 + 00.24 mm3 & 0.18 ( 0.01 ) & 1.18 ( 0.11 ) & 0.21 ( 0.03 ) & 59.50 ( 0.05 ) + i18151 - 1208 mm2 & 0.17 ( 0.01 ) & 2.53 ( 0.20 ) & 0.59 ( 0.04 ) & 29.33 ( 0.08 ) + i18223 - 1243 mm3 & 0.23 ( 0.01 ) & 2.65 ( 0.11 ) & 0.73 ( 0.03 ) & 45.75 ( 0.05 ) + i18337 - 0743 mm3 & 0.11 ( 0.01 ) & 1.78 ( 0.19 ) & 0.13 ( 0.03 ) & 56.06 ( 0.08 ) +   + i18089 - 1732 mm1 & 0.09 ( 0.01 ) & 3.39 ( 0.42 ) & 0.31 ( 0.04 ) & 32.24 ( 0.18 ) + i18151 - 1208 mm1 & 0.22 ( 0.01 ) & 2.05 ( 0.14 ) & 0.45 ( 0.04 ) & 33.18 ( 0.06 ) + i18182 - 1433 mm1 & 0.16 ( 0.01 ) & 2.86 ( 0.20 ) & 0.47 ( 0.04 ) & 60.26 ( 0.09 ) + i18223 - 1243 mm1 & 0.19 ( 0.01 ) & 1.43 ( 0.10 ) & 0.43 ( 0.03 ) & 45.01 ( 0.04 ) + i18264 - 1152 mm1 & 0.39 ( 0.02 ) & 2.10 ( 0.10 ) & 0.91 ( 0.06 ) & 43.78 ( 0.04 ) + i18337 - 0743 mm1 & 0.14 ( 0.01 ) & 3.55 ( 0.23 ) & 0.52 ( 0.03 ) & 58.83 ( 0.10 ) + [ tab : t4 ]    lrrrrr + g015.05 + 00.07 mm1 & 0.55@xmath58 & 0.0111@xmath59 & 15.2@xmath60 & 19@xmath61 & 2.4 + g015.31 - 00.16 mm3 & 0.82@xmath62 & 0.0154@xmath63 & 12.6@xmath64 & 14@xmath65 & 1.0 + g024.08 + 00.04 mm3 & @xmath570.49 & @xmath570.0101 & 12.1@xmath66 & 14@xmath67 & 1.1 + g024.08 + 00.04 mm4 & 1.26@xmath68 & 0.0262@xmath69 & 12.9@xmath70 & 15@xmath71 & 1.3 + g034.43 + 00.24 mm9 & 0.92@xmath72 & 0.0147@xmath73 & 13.9@xmath70 & 16@xmath71 & 1.9 + average & 0.89(0.29 ) & 0.0169(0.0065 ) & 13.3(1.2 ) & 15.6(2.0 ) & 1.5(0.6 ) +   + g019.27 + 00.07 mm1 & 0.23@xmath74 & 0.0041@xmath75 & 15.4@xmath76 & 19@xmath77 & 6.9 + g022.35 + 00.41 mm1 & 0.62@xmath78 & 0.0134@xmath79 & 16.0@xmath80 & 20@xmath81 & 4.0 + g023.60 + 00.00 mm2 & @xmath570.38 & @xmath570.0081 & 16.0@xmath82 & 20@xmath77 & 4.4 + g034.43 + 00.24 mm3 & 0.18@xmath83 & 0.0029@xmath84 & 15.5@xmath85 & 19@xmath77 & 6.0 + i18151 - 1208 mm2 & 0.62@xmath86 & 0.0116@xmath87 & 17.8@xmath88 & 24@xmath61 & 5.4 + i18223 - 1243 mm3 & 0.50@xmath89 & 0.0107@xmath90 & 16.2@xmath82 & 20@xmath77 & 7.8 + i18337 - 0743 mm3 & 0.39@xmath91 & 0.0081@xmath59 & 15.0@xmath80 & 18@xmath81 & 1.7 + average & 0.42(0.19 ) & 0.0085(0.0042 ) & 16.0(0.9 ) & 20.1(1.7 ) & 5.2(2.0 ) +   + i18089 - 1732 mm1 & 0.21@xmath83 & 0.0047@xmath92 & 38 & 194 & 15 + i18151 - 1208 mm1 & 0.46@xmath93 & 0.0088@xmath94 & 20.8@xmath95 & 31@xmath96 & 6.4 + i18182 - 1433 mm1 & 0.42@xmath74 & 0.0105@xmath94 & 19.0@xmath88 & 26@xmath65 & 6.8 + i18223 - 1243 mm1 & 0.55@xmath97 & 0.0117@xmath87 & 17.5@xmath98 & 23@xmath65&4.5 + i18264 - 1152 mm1 & 0.62@xmath99 & 0.0128@xmath87 & 18 & 24 & 8.5 + i18337 - 0743 mm1 & 0.39@xmath83 & 0.0084@xmath75 & 17.1@xmath66 & 22@xmath77 & 7.3 + average & 0.44(0.13 ) & 0.0095(0.0029 ) & 21.7(8.1 ) & 53.4(69.0)&8.1(3.6 ) + [ tab : t5 ]","summary":"the averaged dnc / hnc ratio is indeed lower toward the observed high - mass sources ( 0.009.005 ) than toward the low - mass starless and star - forming cores ( 0.06 ) . the kinetic temperature derived from the nh ( , ) = ( 1 , 1 ) and ( 2 , 2 ) line intensities is higher toward the observed high - mass sources than toward the low - mass cores . however the dnc / hnc ratio of some irdcs involving the spitzer 24 m sources is found to be lower than that of hmpos , although the kinetic temperature of the irdcs is lower than that of the hmpos . we discuss how the dnc / hnc ratio decreases after the birth of protostars .","abstract":"we have observed the hnc=10 and dnc=10 lines toward 18 massive clumps , including infrared dark clouds ( irdcs ) and high - mass protostellar objects ( hmpos ) , by using the nobeyama radio observatory 45 m telescope . we have found that the hnc emission is stronger than the dnc emission toward all the observed sources . the averaged dnc / hnc ratio is indeed lower toward the observed high - mass sources ( 0.009.005 ) than toward the low - mass starless and star - forming cores ( 0.06 ) . the kinetic temperature derived from the nh ( , ) = ( 1 , 1 ) and ( 2 , 2 ) line intensities is higher toward the observed high - mass sources than toward the low - mass cores . however the dnc / hnc ratio of some irdcs involving the spitzer 24 m sources is found to be lower than that of hmpos , although the kinetic temperature of the irdcs is lower than that of the hmpos . this implies that the dnc / hnc ratio does not depend only on the current kinetic temperature . with the aid of chemical model simulations , we discuss how the dnc / hnc ratio decreases after the birth of protostars . we suggest that the dnc / hnc ratio in star - forming cores depends on the physical conditions and history in their starless - core phase , such as its duration time and the gas kinetic temperature ."}
{"article_id":"1605.02555","section_id":"i","document":"this paper is devoted to the systematic studies of the asymptotic solutions of advection equation with time - oscillating velocity field . we employ the two - timing method in the form introduced by @xcite , which allows us to produce the classification of an infinite number of distinguished limits and solutions . we have obtained several new versions of averaged equations for a passive scalar and have presented several examples . the main purpose of this paper is the introduction of a new systematic and general viewpoint on the hierarchy of distinguished limits , drifts , and pseudo - diffusion . this viewpoint can help to organize and to unify a number of results , including that of @xcite . we have chosen the advection equation as the simplest interesting example , with the hope that similar studies can be performed for other interesting equations . the two - timing method has been used by many authors , see @xcite , however our analysis goes well beyond the usual calculations of the main approximations in various special cases . our analytic calculations are rigorous and straightforward by their nature , however they include a large number of integration by parts and algebraic transformations ; the performing of such calculations represents a ` champion - type ' result by itself . the details of calculations are fully presented in the appendix . the key point of asymptotic theory for odes or pdes ( with two or more small parameters ) is the choice of asymptotic path in the space of these parameters . in other words , all available small parameters should be expressed through a single one ; it allows one to compare different terms in asymptotic series . the related literature is very diverse and short of exact mathematical formulations . usually , during the studies of a particular problem , some ` lucky ' asymptotic path is chosen on the basis that it gives the successful derivation of an averaged equation or successful calculation of the main term in asymptotic solution , see _ e.g. _ @xcite . such ` lucky ' asymptotic paths are called _ distinguished limits _ ( dl s ) , while related solutions are called _ distinguished limit solutions _ ( dls s ) . any studies of the multiplicity of distinguished paths ( as well as the multiplicity of averaged equations and related solutions ) and interrelations between them are always avoided . a different approach is given by @xcite , where the concept of ` strong ' , ` moderate ' , and ` weak ' oscillations is introduced . however , this approach overlooks some asymptotic solutions and could be seen as being ` too rigid ' ; therefore we propose its development in this paper . our asymptotic procedure is based on the simultaneous scaling ( with the use of strouhal number @xmath0 ) a slow time - scale and vibrational velocity amplitude . this procedure is flexible , self - consistent , covers broad classes of asymptotic solutions , and leads to a natural classification of solutions . the considered advection equation is a hyperbolic pde of the first order with time - oscillating coefficient , which represents the _ prescribed _ velocity field . we emphasize that the velocity field has no connection to any particular dynamics . indeed , the governing equations for a velocity can be chosen very differently : they could represent an inviscid or viscous fluid , a fluid with any rheology , liquid crystals , blood , elastic and plastic medium , _ etc . _ the advection equation can be also a part of the collisionless boltzmann equation or vlasov equation ( see _ e.g. _ @xcite ) . the introduction of dimensional variables into the advection equation and the use of the two - timing assumption leads us to the problem with _ two independent small scaling parameters that represent the ratio of two time - scales and amplitude of oscillations_. the given set of parameters produces the _ strouhal number @xmath0 as a basic large dimensionless parameter _ ; the appearance of @xmath0 means that the scaling is not unique . in agrement with the general _ ansatz _ of asymptotic theory we can use @xmath0 to vary all the characteristic scales ; in our approach we use @xmath0 to introduce the appropriate scales of velocity and slow time . the obtained dimensionless equation has been used for the identifying of distinguished limits . we have found the infinite sequence of the distinguished limits , which are corresponding to the successive degeneration of a drift velocity . the _ order _ of this degeneration is chosen to enumerate the distinguished limits . the derivation of averaged equations produce the successive approximations for a drift velocity as well as a qualitatively new ` diffusion - like ' term , which we call _ pseudo - diffusion_. remarkably , all the coefficients in the obtained averaged equations are universal ; they are the same in dls s of different orders and only ` moving ' to lower approximations with the increasing of the order of dls . as the next important step we discover _ one - parametric _ families of solutions ( infinite number of solutions corresponding to each dls ) , different parametric solutions contain different slow time - scales and different velocity amplitudes . our results are particularly striking for the case of purely periodic velocity oscillations . here we address an intriguing question : how to find the related slow time - scale while it does not appear in the coefficients of the equation ? our answer is : the slow time - scale is uniquely determined by the magnitude of a given velocity in terms of @xmath0 . for a given velocity we obtain the unique slow time - scale . we have established that the solutions corresponding to different orders of velocity are physically different even if they have the same functional form . the central notion which appears in this paper is a _ drift velocity_. our study can be seen as a general view on the studies of drift velocities with the emphasis at their different appearances in averaged equations ; it is complemented by an unexpected but inevitable appearance of pseudo - diffusion . we put the studies of drifts into the general context of the asymptotic theory , that has never been done before . in addition , there is a difference between the _ classical drift _ and _ eulerian drift_. the classical ( or lagrangian ) drift appears as an averaged velocity for fixed lagrangian coordinates ; hence the classical drift represents an average velocity of material particles . the classical drift , in its main approximation , is a well - studied phenomenon , see @xcite . in our consideration ( as well as in @xcite ) the average operation takes place for _ fixed eulerian coordinates _ , hence our drift represents an average velocity at a given eulerian position and we call it an _ eulerian drift_. the relation between the classical drift and eulerian drift represents an open question to study , while their leading terms ( in the amplitude series ) are certainly coincide . in our consideration of eulerian drift we explicitly show its different options , approximations , and appearances . we calculate first three approximations for the eulerian drift velocity that is especially useful in the cases of vanishing leading approximation . situation with _ pseudo - diffusion _ is more intriguing . first of all , the appearance of this ` diffusion - like ' term in averaged equations is surprising by itself . another surprise is the form of the pseudo - diffusion matrix which appears as a _ lie - derivative _ of an averaged _ quadratic displacement tensor_. for different flows , pseudo - diffusion can correspond to diffusion or ` anti - diffusion ' or to some intermediate cases . we make the first step in the understanding of the meaning of pseudo - diffusion by considering some simple example of rigid - body oscillations . we arrive to a surprising conclusion that the combination of the advection due to rigid - body oscillations and the eulerian averaging procedure can produce the evolution of the averaged field , which formally coincides with physical diffusion . we present five examples of flows aimed to illustrate different appearances of drift and pseudo - diffusion . these examples cover the general form of modulated oscillatory fields , stokes drift , a spherical ` acoustic ' wave , a class of velocity fields with vanishing main term of the drift , and a velocity field which provides a chaotic averaged ` lagrangian ' dynamics . it is important , that in this paper we do not use any additional assumptions , except the two - timing hypothesis itself . all the results appear from the straightforward and rigorous calculations and represent mathematical theorems , although they are not formulated explicitly in this way . hence , our results can be seen as the test on the validity and reliability of two - timing method . any failure to interpret our results physically or mathematically can be explained only by the insufficiency of two time - scales , that might mean that three time - scales ( or more ) are required . at the same time , following to a high mathematical rigour , we avoid any physical interpretations , while such interpretations could be needed in future .","summary":"the aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two - timing method . our results are :    \\(i ) the dimensionless advection equation contains _ two independent small parameters _ , which represent the ratio of two characteristic time - scales and the spatial amplitudes of oscillations ; the scaling of the variables and parameters contains strouhal number ;    \\(ii ) an infinite sequence of _ distinguished limits _ has been identified ; this sequence corresponds to the successive degenerations of a _ drift velocity _ ;    \\(iii ) we have derived the averaged and oscillatory equations for the first _ four distinguished limits _ ; derivations are performed up to the forth orders in small parameters ;    \\(v ) we have shown , that _ each distinguish limit solution _ generates an infinite number of _ parametric solutions _ ; these solutions differ from each other by the slow time - scale and the amplitude of prescribed velocity ;    \\(vi ) we have discovered the inevitable appearance of _ pseudo - diffusion _ , which appears as a lie derivative of the averaged tensor of quadratic displacements ; we have clarified the meaning of pseudo - diffusion using a simple example ;    \\(vii ) our main methodological result is the introduction of a logical order into the area and classification of an infinite number of asymptotic solutions ; we hope that it can help to study the similar problems for more complex systems ;    \\(viii ) since in our calculations we do not employ any additional assumptions , our study can be used as a test for the validity of the two - timing hypothesis ;    \\(ix ) the averaged equations for five different types of oscillating velocity fields have been considered as the examples of different drifts and pseudo - diffusion .","abstract":"the aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two - timing method . our results are :    \\(i ) the dimensionless advection equation contains _ two independent small parameters _ , which represent the ratio of two characteristic time - scales and the spatial amplitudes of oscillations ; the scaling of the variables and parameters contains strouhal number ;    \\(ii ) an infinite sequence of _ distinguished limits _ has been identified ; this sequence corresponds to the successive degenerations of a _ drift velocity _ ;    \\(iii ) we have derived the averaged and oscillatory equations for the first _ four distinguished limits _ ; derivations are performed up to the forth orders in small parameters ;    \\(v ) we have shown , that _ each distinguish limit solution _ generates an infinite number of _ parametric solutions _ ; these solutions differ from each other by the slow time - scale and the amplitude of prescribed velocity ;    \\(vi ) we have discovered the inevitable appearance of _ pseudo - diffusion _ , which appears as a lie derivative of the averaged tensor of quadratic displacements ; we have clarified the meaning of pseudo - diffusion using a simple example ;    \\(vii ) our main methodological result is the introduction of a logical order into the area and classification of an infinite number of asymptotic solutions ; we hope that it can help to study the similar problems for more complex systems ;    \\(viii ) since in our calculations we do not employ any additional assumptions , our study can be used as a test for the validity of the two - timing hypothesis ;    \\(ix ) the averaged equations for five different types of oscillating velocity fields have been considered as the examples of different drifts and pseudo - diffusion ."}
{"article_id":"astro-ph0606334","section_id":"i","document":"the quasar luminosity function ( qlf ) describes the space density of active galactic nuclei ( agn ) as a function of luminosity and redshift . the qlf encodes information on quantities like the black hole number density per unit mass , and the gas accretion efficiency . it therefore constrains physical models of agn and of super massive black hole formation . the optical ( b - band ) qlf at @xmath12 has been determined accurately for luminosities , corresponds to @xmath13 ergs s@xmath3 . ] exceeding @xmath14 from the 2df quasar survey ( which corresponds to absolute magnitudes @xmath15 , boyle et al . 2000 ; croom et al . 2004 ) . at higher redshifts the optical luminosity function of luminous quasars has been determined from quasars in the sloan digital sky survey @xcite at @xmath16 . in addition , deep _ chandra _ and _ xmm _ imaging has constrained the x - ray qlf at x - ray luminosities as low as @xmath17 ergs s@xmath3 @xcite . following @xcite , @xcite have used the x - ray qlf to constrain the b - band qlf down to fainter optical luminosities ( @xmath18 ) at @xmath19 . at these redshifts , no observational constraints exist on the optical qlf at fainter luminosities . however , the details of the existence and evolution of low luminosity agn is crucial for our understanding of the growth of low mass black holes , and of their role in the formation of super massive black holes .    in this paper we demonstrate how existing ly@xmath0 surveys may be used to constrain the b - band qlf at absolute magnitudes as low as @xmath20 . existing wide - field narrow - band surveys ( e.g. * ? ? ? * ) are optimised to detect ly@xmath0 line emission from high - redshift galaxies , and in order to maximise their detection rate , deeply image fields as large as 1 deg@xmath21 on the sky ( e.g. * ? ? ? the combination of wide field and deep images , together with concentration on a strong emission line , rather than continuum , allows these wide - field narrow - band surveys to put stringent constraints on the number density of agn with @xmath22 . constraints on even fainter agn are derived from deep spectroscopic surveys of regions around intermediate redshift clusters of galaxies , which offer an ultra - deep view into the high redshift universe ( z=4.5 - 6.7 ) through strong gravitational lensing ( with magnification factors of 10 - 1000 , santos et al , 2004 ) .    throughout this paper , the terms agn and quasar are interchangeable and refer to broad lined active galactic nuclei , also known as type i agn . the outline of this paper is as follows : in   [ sec : lum ] we relate the ly@xmath0 luminosity of a quasar to its b - band luminosity . in   [ sec : lya ] we summarise constraints on the number density of ly@xmath0 emitters at high redshift , and discuss the abundance of quasars among these sources . we show how this existing data constrains the faint end of the quasar luminosity function . in   [ sec : phys ] we calculate the observable ly@xmath0 properties of agn and use these to physically interpret our results . we also model the appearance of faint agn in the optical and x - ray bands . finally , in   [ sec : discuss ] we discuss the possible cosmological implications of our work , before presenting our conclusions in   [ sec : conclusion ] . we use the _ wmap _ cosmological parameters : @xmath23 = @xmath24 @xcite throughout the paper .","summary":"[ firstpage ]    cosmology : theory - quasars : general - galaxies : high redshift","abstract":"recent surveys have detected ly emission from at luminosities as low as erg s . there is good evidence that low numbers of agn are among observed faint ly emitters . combining these observations with an empirical relation between the intrinsic ly and b - band luminosities of agn , we obtain an upper limit on the number density of agn with absolute magnitudes $ ] at . these agn are up to two orders of magnitude fainter than those discovered in the chandra deep field , resulting in the faintest observational constraints to date at these redshifts . at , the powerlaw slope of the very faint end of the luminosity function of agn is shallower than the slope observed at lower redshifts , , at the 98% confidence level . in fact , we find marginal evidence that the luminosity function rises with luminosity , corresponding to a powerlaw slope , at magnitudes fainter than ( 75% confidence level ) . these results suggest either that accretion onto lower mass black holes is less efficient than onto their more massive counterparts , or that the number of black holes powering agn with is lower than expected from the relation by one - two orders of magnitude . extrapolating from reverberation - mapping studies suggests that these black holes would have . to facilitate the identification of agn among observed ly emitters , we derive observational properties of faint agn in the ly line , as well as in the x - ray and optical bands .    [ firstpage ]    cosmology : theory - quasars : general - galaxies : high redshift"}
{"article_id":"astro-ph0606334","section_id":"c","document":"recent ly@xmath0 surveys have detected ly@xmath0 emitting objects from redshifts as high as @xmath53 , and at luminosities as low as @xmath2 erg s@xmath3 ( e.g. * ? ? ? no evidence of agn activity exists among these several hundred ly@xmath0 emitters @xcite . wide field ly@xmath0 surveys are designed to deeply image wide fields on the sky , yielding survey volumes in a narrow shell of redshift space as large as @xmath334 mpc@xmath98 , while deep spectroscopic surveys of gravitationally lensed regions probe deeper into smaller volumes . the absence of agn within these fields can place a tight upper limit on the number density of agn with ly@xmath0 luminosities exceeding the surveys detection thresholds , @xmath335 .    in  [ sec : lum ] we have shown empirically that the ly@xmath0 luminosities of agn equal their b - band luminosities to within a factor of a few ( eq .  [ eq : key ] ) . as a result , deep ly@xmath0 surveys can be used to obtain upper limits on the number density of agn with b - band luminosities exceeding @xmath336 . when expressed in b - band solar luminosities , @xmath69 is @xmath337 ( which corresponds to an absolute magnitude of @xmath338 ) . in  [ sec : lyaagn ] we demonstrated that such agn are expected to be powered by black holes with masses in the range @xmath263 at @xmath1 .    we derive upper limits on agn number densities and constrain the quasar b - band luminosity function @xmath70 at a luminosity @xmath339 . the non - detection of agn among @xmath1 laes rules out the model predictions by wyithe & loeb ( 2003 ) , which succesfully reproduce the brighter end of the observed quasar luminosity function at @xmath340 , at @xmath179 confidence levels at all redshifts . at @xmath5 , we find that @xmath341log@xmath342log@xmath343 , the value observed at lower redshifts , for log@xmath317 \\lsim 11 $ ] at the @xmath344 confidence level ( fig  [ fig : dpdb ] ) . we find marginal evidence that at these luminosities , the luminosity function rises with luminosity , corresponding to a powerlaw slope @xmath345 ( 75% confidence level ) . in other words , the qlf may increase with @xmath36 at these faint luminosities , in contrast to observations of more luminous agn . these results represent the faintest observational constraints on the quasar luminosity function at these redshifts to date . we have found that models of the quasar luminosity function which are successful in reproducing the bright end of the quasar luminosity function predict more agn to be present than are observed , by up to two orders of magnitude ( fig . [ fig : lumfunc ] ) at @xmath346 . these results imply either that accretion onto lower mass black holes is less efficient than onto their more massive counterparts , or that the number of black holes powering agn with @xmath9 is lower than expected from the @xmath10 relation by one - two orders of magnitude . extrapolating from reverberation - mapping studies suggests that these black holes would have @xmath11 . our work has demonstrated the effectiveness of ly@xmath0 surveys in constraining the faint end of the quasar b - band luminosity function . deeper and larger surveys will allow for a better determination of its slope , and whether indeed the quasar luminosity function rises with luminosity for @xmath9 at @xmath5 , and at other redshifts . these constraints will offer new insights on the growth of low mass black holes and their relation to the known super massive black holes . to help identify agn among observed ly@xmath0 emitters , we have modeled the observable properties of the ly@xmath0 line for high redshift , faint agn . using the empirical kaspi - relations , we estimate that the observable ly@xmath0 line widths ( half width at half maximum ) of faint agn will be @xmath347 km s@xmath3 . for agn embedded in a neutral medium the peak of the ly@xmath0 line is redshifted up to @xmath348 km s@xmath3 relative to the true line center (   [ sec : lyaagn ] ) . to facilitate the identification of these faint agn , we have estimated their observable properties in the visible (   [ sec : broadagn ] , fig  [ fig : mab ] ) and x - ray bands (   [ sec : xray ] ) . we caution that selection criteria used in ly@xmath0 surveys to select candidate high redshift ly@xmath0 emitters currently introduce a bias against detecting agn with log@xmath317 \\gsim 11.3 $ ] (   [ sec : broadagn ] ) , corresponding to the faintest agn identified in the chandra deep fields . * acknowledgments * our research is supported by the australian research council . the authors would like to thank colin norman for helpful discussions and zoltn haiman for useful comments on an earlier version of the manuscript . a.  j. , cowie l.  l. , capak p. , alexander d.  m. , bauer f.  e. , brandt w.  n. , garmire g.  p. , hornschemeier a.  e. , 2003 , apjl , 584 , l61    r. , 2004 , mnras , 347 , 59    b.  j. , shanks t. , croom s.  m. , smith r.  j. , miller l. , loaring n. , heymans c. , 2000 , mnras , 317 , 1014    r. , haiman z. , 2000 , apjl , 542 , l75    s. , fall s.  m. , 1993 , apj , 415 , 580    cowie , l.  l. , barger , a.  j. , bautz , m.  w. , brandt , w.  n. , & garmire , g.  p.  2003 , apjl , 584 , l57    s.  m. , smith r.  j. , boyle b.  j. , shanks t. , miller l. , outram p.  j. , loaring n.  s. , 2004 , mnras , 349 , 1397    s. , rhoads j.  e. , malhotra s. , stern d. , dey a. , spinrad h. , jannuzi b.  t. , wang j. , landes e. , 2004 , apj , 617 , 707    dekel , a. , & silk , j.   1986 , apj , 303 , 39    m. , haiman z. , rees m.  j. , weinberg d.  h. , 2004 , apj , 601 , 666    dijkstra , m. , haiman , z. , & loeb , a.  2004b , apj , 613 , 646    ellis , r. , santos , m.  r. , kneib , j .- p . , & kuijken , k.  2001 , apjl , 560 , l119    fan , x. , et al . 2001 , aj , 121 , 54    fan , x. , et al .  2001b , aj , 122 , 2833    x. , narayanan v.  k. , strauss m.  a. , white r.  l. , becker r.  h. , pentericci l. , rix h .- w . , 2002 , aj , 123 , 1247    fan , x. , et al .  2005 , aj in press , arxiv : astro - 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two orders of magnitude . extrapolating from reverberation - mapping studies suggests that these black holes would have . to facilitate the identification of agn among observed ly emitters","abstract":"recent surveys have detected ly emission from at luminosities as low as erg s . there is good evidence that low numbers of agn are among observed faint ly emitters . combining these observations with an empirical relation between the intrinsic ly and b - band luminosities of agn , we obtain an upper limit on the number density of agn with absolute magnitudes $ ] at . these agn are up to two orders of magnitude fainter than those discovered in the chandra deep field , resulting in the faintest observational constraints to date at these redshifts . at , the powerlaw slope of the very faint end of the luminosity function of agn is shallower than the slope observed at lower redshifts , , at the 98% confidence level . in fact , we find marginal evidence that the luminosity function rises with luminosity , corresponding to a powerlaw slope , at magnitudes fainter than ( 75% confidence level ) . these results suggest either that accretion onto lower mass black holes is less efficient than onto their more massive counterparts , or that the number of black holes powering agn with is lower than expected from the relation by one - two orders of magnitude . extrapolating from reverberation - mapping studies suggests that these black holes would have . to facilitate the identification of agn among observed ly emitters , we derive observational properties of faint agn in the ly line , as well as in the x - ray and optical bands .    [ firstpage ]    cosmology : theory - quasars : general - galaxies : high redshift"}
{"article_id":"1508.07601","section_id":"i","document":"symmety in physics not only is the key to understanding phases of matter but also play a vital role in unifying seemingly different things and uncovering fundamental principles underlying them . in particular , unitary groups have been playing very important roles in quantum mechanics as the orthogonal groups in classical mechanics . for instance , su(3 ) is the fundamental symmetry underlying the quantum chromodynamics ( qcd ) of strong interactions . in traditional condensed - matter physics , however , high symmetry like su(@xmath0 ) is usually realized , aside from few exceptions , only in rather idealized situations and has been mainly used as mathematical convenience that makes problems tractable . for instance , in the large-@xmath0 approximations , we replace the physical symmetry su(2 ) with su(@xmath0 ) and use @xmath1 as the ( small ) control parameter of the approximation hoping that there is a smooth crossover down to @xmath2 . recent suggestions@xcite that su(@xmath0)-symmetric fermion systems could be simulated using the alkaline - earth atoms and their cousins ( @xmath3yb , @xmath4yb , @xmath5sr , etc . ) loaded in optical lattices opened a new era of su(@xmath0 ) physics @xcite ( see , e.g. , refs .   for recent reviews ) . for instance , the su(@xmath0 ) generalization of quantum magnetism is of direct relevance to the mott - insulating regime of these systems . the su(@xmath0 ) `` spin '' models provide us with examples of underconstrained systems that yield , on top of usual `` magnetically ordered '' states , various unconventional states , e.g. , deconfined criticalities@xcite , an algebraic spin liquid@xcite and a chiral spin liquid@xcite .    on the other hand , topological states of matter@xcite have been subjects of extensive research for the past decade . since the advent of topological insulators and superconductors@xcite , it has been widely realized that there exists a special class of `` topological '' phases that is stable _ only _ in the presence of certain symmetries@xcite . this class of topological phases is called `` symmetry - protected topological ( spt)''@xcite as it is topologically protected only when we impose symmetries on the system in question , and otherwise they reduce to trivial ones . the catalogue of possible topological phases depends crucially on the symmetry we impose and different lists of possible phases may be obtained for different protecting symmetries ( see , e.g. , ref .   for a catalogue of spt phases ) . one defining property of spt phases is the existence of gapless boundary excitations ( edge states ) that are intrinsically different from those in the gapped bulk . a modern mathematical way of observing the edge states would be to use the entanglement spectrum@xcite that is obtained solely from the ground - state wave function . in the following , we heavily use the entanglement spectrum in characterizing topological phases .    despite the recent effort@xcite in systematically enumerating possible spt phases in one dimension , not much is known , except for a few examples , about how to observe those phases in realistic settings . recently , it has been suggested@xcite that a class of spt phases is realized in the mott - insulating region of the alkaline - earth cold fermions , and this is one of the motivations of our study here . specifically , deep inside the mott phase at half - filling , the low - energy physics of a system of alkaline - earth fermions is described by an su(@xmath0 ) `` spin '' model ( see secs . [ sec : relation - to - ae ] and [ sec : strong - coupling ] ) whose ground state is expected to be in one of the topological phases predicted in ref .  . therefore the alkaline - earth fermions provide us with a unique arena for the realization of new spt phases in a very controlled manner . our goal is to clarify the nature of the ground state of the above su(@xmath0 ) spin hamiltonian in several complementary ways and demonstrate the use of non - local string order parameters to detect the phase . the outline of this paper is as follows . in sec . [ sec : model ] , we introduce the su(@xmath0 ) heisenberg model and sketch how it is derived as the effective hamiltonian for the mott - insulating phase of the alkaline - earth cold fermions on a one - dimensional optical lattice . a variant of the heisenberg model that gives useful insights about the topological properties of the original model is introduced as well . after briefly summarizing the minimal background of spt phases expected for our su(@xmath0 ) spin systems , we try , in sec . [ sec : spt ] , to characterize the topological properties of the ground state of the su(@xmath0 ) heisenberg model using its entanglement spectrum . by carefully investigating the structure of the spectrum obtained for @xmath6 , we present a strong evidence that the ground state of the su(4 ) heisenberg model is in one of the su(4 ) topological phases . in sec .  [ sec : string - orer - parameter ] , we present an alternative way of characterizing the su(@xmath0 ) spt phases using _ non - local _ string order parameters .    although the alkaline - earth fermions , that motivated our study , possess very precise su(@xmath0 ) symmetry , it would be interesting theoretically to consider the situations where the original su(@xmath0 ) symmetry gets lowered . we investigate this problem in sec . [ sec : symmetry - reduction ] to find that , depending on @xmath0 , the system remains topological even after the su(@xmath0 ) symmetry is relaxed . summary of the main results is given in sec . [ sec : summary ] .","summary":"in this paper , we investigate topological properties of the ground state of the su( ) heisenberg chain , which is argued to be relevant to the mott - insulating phase of alkaline - earth cold fermions in a one - dimensional optical lattice . by calculating the entanglement spectrum , we then discuss an alternative characterization of it with non - local string order parameters .","abstract":"in this paper , we investigate topological properties of the ground state of the su( ) heisenberg chain , which is argued to be relevant to the mott - insulating phase of alkaline - earth cold fermions in a one - dimensional optical lattice . by calculating the entanglement spectrum , we show that the ground state is in one of the topological phases protected by su( ) symmetry . we then discuss an alternative characterization of it with non - local string order parameters . we also consider how the reduction of the protecting symmetry affects the topological phase paying particular attention to the entanglement spectrum ."}
{"article_id":"1404.2080","section_id":"i","document":"in many physical systems , nonlinear interactions give rise to couplings between different dynamical scales . in the case of an electrically neutral fluid flow , the velocity field represents the dynamical quantity of interest and the couplings occur between different scales of motion . a similar picture exists for an electrically conductive fluid , where the interplay between velocity and the self - consistent magnetic field gives rise to alfvn waves . the nonlinear interaction can now be interpreted either as the couplings of velocity and magnetic scales or scattering of counter - propagating alfvn waves of different sizes . for kinetic systems , where the dynamical quantity is represented by a probability distribution function , defined in a six - dimensional phase space , the picture becomes more complicated . not only that spatial and velocity structures evolve differently , the dynamics can involve moments of the distribution function . these moments can be seen , to an extent , as preferential modes of the distribution function that mediate the nonlinear interactions . this situation is present , as well , for magnetized plasmas described kinetically using the gyrokinetic approximation . @xcite the gyrokinetic ( gk ) formalism , valid for a plasma evolving under the influence of a strong magnetic guide field and which obeys the gyrokinetic ordering , represents a self - consistent method of removing the fast gyration phase from the motion of charged particles and decreasing the distribution function phase space from six to five dimensions@xcite . the influence of the magnetic guide field on the system leads to the development of a spatial anisotropy . moreover , a similar anisotropy is also developed in velocity space . it should be understood that these anisotropic directions occur at the dynamical level of the equations and that the perpendicular velocity symmetry is taken into account explicitly by the gyrokinetic formalism . thus , any non - trivial geometry of the magnetic field ( non - slab , or in general possessing a non - diagonal metric ) will intrinsically complicate the development and saturation of gk turbulence , i.e. , the couplings between different dynamical scales .    for a turbulent gk state , the dynamics determine the type of structures that develop along each direction and influence the linear and nonlinear redistribution of energy in the system . as such , investigating the energy redistribution problem for a spectral form of the gk equations can lead to insight regarding the dynamics of the equations . while different approaches exist for the study of the dynamics introduced by the linear terms , the nonlinear terms drastically limit the available possibilities . to understand the dynamics introduced by the nonlinear term , the redistribution of free - energy ( a gk ideal invariant , i.e. , a global quantity that remains constant in time in the absence of source and sink effects ) is usually investigated . in the current work , we will only look at the redistribution of energy between perpendicular spatial scales , obtained as the integration of contributions along all other directions . while this represents a point of interest in the study of gk turbulence , it should always be remembered that the fundamental dynamics occur in a higher dimensional space that links spatial and velocity dynamics ( linear@xcite and nonlinear @xcite phase space mixing ) , as well as the perpendicular and parallel spatial scales ( the concept of critical balance @xcite ) . this is important , as investigating the energetic exchanges of the perpendicular spatial scales only captures part of the nonlinear dynamics . understanding the behavior of gk turbulence in the perpendicular directions is important for ( heat and particles ) transport studies , with relevance to the field of fusion research . the choice of this study to concentrate on the interaction of scales and not of modes@xcite is given in part by practical concerns . promising modeling techniques , like application of large eddy simulations ( les ) to gk turbulence @xcite , rely on the concept of scales , on their separation and on their local energetic interaction . furthermore , these concepts form the basis of our phenomenological understanding of the problem . to facilitate the analysis , a fourier mode decomposition of the distribution function in the perpendicular spatial directions is used . in general , well - suited decompositions are needed to give modes proper physical significance ( e.g. , using spherical harmonics for spherical symmetric problems ) . since a natural mode decomposition choice that would depend on the complex geometry is not known to us , we prefer to build our understanding on the phenomenological relevant concept of scales and not on the plane - wave modes . although the spectral modes enter in the nonlinear dynamics , it is the scales that posses phenomenological information and that can be measured experimentally . the presence of a complex magnetic geometry complicates further the link between dynamical relevant modes and the spatial scales , as perpendicular wavenumbers contribute to more than one perpendicular scale . from this perspective , contributions to perpendicular scales made by modes that possess special symmetries , like the zonal flow , are accounted for separately . while the separation is done at the mode level , the energetic interaction is still performed from the perspective of the scales . this aspect of the problem will be detailed in the current work . we apply this analysis to ion temperature gradient ( itg ) and electron temperature gradient ( etg ) turbulence . the mathematical difference between these two cases consists in the adiabatic response given by the electro - neutrality condition , which enters in the gk poisson equation . the two cases differ by an additional nonlinear term mediated by the electrostatic potential resulting from the flux - surface average contribution to the electro - neutrality condition . as such , in our analysis , we separate the flux - surface average contribution ( responsible for the generation of zonal flows ) of the electrostatic potential that appears for the itg case compared to the etg one .    considering the phenomenological interpretation of turbulence , as cascades of energy between scales , decomposing the net transfers into the forward ( positive ) and backward ( negative ) contributions allows us to better understand the nature of the energetic exchanges that take place . this analysis is particularly important for the development of more advanced les models for gk turbulence . furthermore , looking at the problem from the perspective of scale fluxes , including the scale locality of flux contributions @xcite ( measuring the contribution of an energy flux through a scale from scales progressively dissimilar in size ) , provides overall understanding of the gk turbulence problem . to ease the reading of the manuscript , we first introduce the gk equations in section  [ secii ] , presenting the difference between the itg and etg adiabatic responses and the impact made on the nonlinear term . we continue by presenting the scale decomposition in section  [ seciii ] , the transfers analysis in section  [ seciv ] , the scale flux analysis in section  [ secv ] and end with a discussion of the problem from a theoretical and modeling perspective .","summary":"turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities , either ion temperature gradient ( itg ) or electron temperature gradient ( etg ) . the analysis consists in decomposing the system into a series of scale structures , while accounting separately for contributions made by modes possessing special symmetries ( e.g. , the zonal flow modes ) .","abstract":"in magnetized plasma turbulence , the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free - energy exchanges . the plasmas considered here , with appropriate ion or electron adiabatic electro - neutrality responses , are described by the gyrokinetic formalism in a toroidal magnetic geometry . turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities , either ion temperature gradient ( itg ) or electron temperature gradient ( etg ) . the analysis consists in decomposing the system into a series of scale structures , while accounting separately for contributions made by modes possessing special symmetries ( e.g. , the zonal flow modes ) . the interaction of these scales is analyzed using the energy transfer functions , including a forward and backward decomposition , scale fluxes and locality functions . the comparison between the itg and etg cases shows that etg turbulence has a more pronounced classical turbulent behavior , exhibiting a stronger energy cascade , with implications for gyrokinetic turbulence modeling ."}
{"article_id":"1607.06168","section_id":"i","document":"traditionally network science has focused on static networks , whose links offer permanent connections between their nodes . yet , it is increasingly recognized that most natural and social systems are best described as _ temporal _ networks , acknowledging that their links exist only intermittently . for example , within cellular metabolic networks @xcite , the links correspond to brief chemical reactions ; in social networks @xcite friendship links are inferred from face - to - face or digital communications of short duration . such temporality @xcite has profound effects on most dynamical processes taking place on networks @xcite , slowing down synchronization and the diffusion of innovative information @xcite , impeding exploration and navigation @xcite , and raising barriers to accessibility @xcite . while in static networks such signal - carrying paths are permanently available , in temporal systems complete instantaneous paths between the inputs and the rest of the nodes are not guaranteed , potentially degrading our ability to control a system .","summary":"despite the traditional focus of network science on static networks , most networked systems of scientific interest are characterized by temporal links . by disrupting the paths , link temporality has been shown to frustrate many dynamical processes on networks , from information spreading to accessibility .","abstract":"despite the traditional focus of network science on static networks , most networked systems of scientific interest are characterized by temporal links . by disrupting the paths , link temporality has been shown to frustrate many dynamical processes on networks , from information spreading to accessibility . considering the ubiquity of temporal networks in nature , we must ask : are there any advantages of the networks temporality ? here we develop an analytical framework to explore the control properties of temporal networks , arriving at the counterintuitive conclusion that temporal networks , compared to their static ( _ i.e. _  aggregated ) counterparts , reach controllability faster , demand orders of magnitude less control energy , and the control trajectories , through which the system reaches its final states , are significantly more compact than those characterizing their static counterparts . the combination of analytical , numerical and empirical results demonstrates that temporality ensures a degree of flexibility that would be unattainable in static networks , significantly enhancing our ability to control them ."}
{"article_id":"cond-mat0602494","section_id":"i","document":"since born and von krmn , the construction of microscopic elastic models of crystals has formed an important part of solid - state physics , aimed to determine elastic constants and lattice dynamical properties ( born & von krmn 1912 ; born 1914 ) . imposing global translational and rotational invariance is a delicate matter , although the required relationship are well established ( born & huang 1954 ) . in fact , inconsistencies associated with rotational invariance in the earlier models were pointed out by lax ( 1965 ) and keating ( 1966@xmath0 ) . more recently , the importance of triangular lattices has emerged with the study of soft matter systems such as percolating gels ( feng & sen 1984 ; schwartz _ et al . _ 1985 ; arbabi & sahimi 1993 ) , membrane with crystalline order ( kantor & nelson 1987 ; seung & nelson 1988 ; gompper & kroll 1997 ) , biological membranes ( discher _ et al_.  1997 ; coughlin & stamenovic 2003 ) , red blood cell cytoskeleton ( saxton 1990 ; lim _ et al_.  2002 ; marcelli _ et al . _ 2005 ) , and finite element modeling ( gusev 2004 ) .    in this paper , we consider a triangular lattice embedded in three dimensions and we determine the most general expression of the harmonic elastic energy up to next - nearest neighbour interactions . we formulate a systematic procedure to generate all the energy terms allowed by symmetry . this procedure could be applied to other type of lattices . we show that in order to correctly ensure rotational invariance , it is necessary to consider the boundary of the lattice , as first suggested by lax ( 1965 ) . our central result , equation  ( [ fk ] ) , gives _ all _ the allowed energy terms , with no particular connection to mechanical elements such as springs , elastic wedges , etc . this contrasts with the above cited papers that postulate energy terms in a non exhaustive way . in particular , the most general energy contains a non - central nearest neighbour term ( with coefficient @xmath1 ) , which was believed to violate rotational invariance in percolating gels ( feng & sen 1984 ) on the grounds of keating s argumentation ( 1966@xmath0 ) . the situation is actually delicate since in a later paper , keating ( 1968 ) restricted the generality of some assertions of its earlier papers . our paper is organised as follows . in  2 we formulate the elastic energy of triangular lattices . in  2@xmath2 , we write down all the scalar energy terms quadratic in the displacements of the lattice vertices . in  2@xmath3 , we retain only the terms satisfying the six - fold symmetry of an infinite triangular lattice . in  2@xmath4 , we consider also the edges : we study the symmetries relative to them and we retain the allowed edge terms . in  2@xmath5 , we impose global translational and rotational invariance , taking explicitely into account the reduced symmetry of the boundary , and we retain the allowed terms . in  2@xmath6 , we collect all the contributions and we extract the resulting bulk terms . in  3 , we analyse and discuss the results obtained in  2 . in  3@xmath2 , we give a possible interpretation of our energy in terms of mechanical elements . in  3@xmath3 , we rewrite the energy into the generic expression ( [ fk ] ) , which constitutes our central result . in  3@xmath4 , we establish the connection between our model and its continuum version . finally , in  4 , we give a brief summary and we detail the origin of the rotational invariance problem .","summary":", this is relevant to biological physics ( e.g. , red blood cell cytoskeleton ) and soft matter ( e.g. , percolating gels , etc . ) . in order to correctly impose the rotational invariance of the bulk terms we find that some terms that were suspected in the litterature to violate rotational symmetry are in fact admissible .    [ first page ]","abstract":"triangular lattice , lattice elasticity , non - central forces , cytoskeleton we establish the most general form of the discrete elasticity of a 2d triangular lattice embedded in three dimensions , taking into account up to next - nearest neighbour interactions . besides crystalline system , this is relevant to biological physics ( e.g. , red blood cell cytoskeleton ) and soft matter ( e.g. , percolating gels , etc . ) . in order to correctly impose the rotational invariance of the bulk terms , it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice . we find that some terms that were suspected in the litterature to violate rotational symmetry are in fact admissible .    [ first page ]"}
{"article_id":"1611.08549","section_id":"i","document":"the percolation phase transition on finite graphs is one of the most intriguing and striking phenomena at the intersection of mathematical physics , combinatorics , and probability theory . the classical erds  rnyi random graph  @xmath0 is perhaps the most carefully studied reference model : as the edge probability  @xmath5 increases past the ` critical probability ' @xmath6 , the global structure changes radically , from only small components to a single giant component plus small ones . more precisely , using the parametrization @xmath7 , and for simplicity assuming @xmath8 , by the inspiring work of erds and rnyi  @xcite , bollobs  @xcite , uczak  @xcite , and aldous  @xcite , we nowadays distinguish three qualitatively different phases of  @xmath0 . in the subcritical phase @xmath9 , the @xmath10 largest components @xmath11 are typically all of comparable size : @xmath12 , the largest component typically dominates all other components : @xmath13 . in the critical window @xmath14 , the rescaled sizes latexmath:[$|c_1|/n^{2/3 } ,    distribution to non - degenerate random variables , i.e. , they are not concentrated .    in the language of mathematical physics , @xmath0 interpreted as percolation on the complete @xmath16-vertex graph is a mean - field model . hence , we expect that the percolation phase transition of many ` high dimensional ' finite graphs is similar , with the hypercube and various tori being examples of great interest ( see , e.g. ,  @xcite ) . to fix notation , we assume that @xmath17 is a given transitive @xmath16-vertex graph , and we write @xmath18 for the binomial random subgraph where each edge is included independently with probability  @xmath5 . as pointed out by nachmias and peres  @xcite , in this general percolation setting it is a challenging problem to find a good definition of the critical probability  @xmath19 , such that for a suitable critical window around @xmath19 , for example , the size of the largest component is not concentrated .    the folklore average degree heuristic @xmath20 is a natural first guess ( the graph @xmath17 is assumed to be transitive and thus regular , so the choice of the vertex  @xmath21 does not matter ) . for the hypercube with vertex set @xmath22 , and thus degree @xmath23 , ajtai , komls and szemerdi @xcite showed that there is a critical threshold @xmath24 ; this was sharpened by bollobs , kohayakawa , and uczak  @xcite , who raised the question whether the critical probability might be exactly @xmath25 . however , borgs , chayes , van der hofstad , slade and spencer  @xcite and van der hofstad and nachmias  @xcite have shown that there is critical window of width @xmath26 about a critical probability @xmath19 , which by van der hofstad and slade  @xcite satisfies @xmath27 ; since the width of the window is @xmath28 , the value @xmath25 is outside the critical window . a more sophisticated suggestion for the critical probability was pioneered by borgs , chayes , van der hofstad , slade and spencer  @xcite ( and used for the hypercube result just described ) . they essentially proposed to define  @xmath29 as the unique solution to the polynomial equation @xmath30 where the susceptibility @xmath31 denotes the expected size of the component  @xmath32 containing a fixed vertex  @xmath21 in  @xmath33 . ( this is a widely studied key parameter in percolation theory and random graph theory , see , e.g. , @xcite . since  @xmath17 is assumed to be transitive , the choice of  @xmath21 does not matter . ) the aforementioned technical definition is guided by erds  rnyi mean - field type behaviour . indeed , in the subcritical phase we expect that  @xmath32 closely mimics a subcritical branching process , which suggests that typically @xmath34 up to logarithmic corrections ( see , e.g. , section 1.2 in  @xcite or proposition  5.1 in  @xcite ) . furthermore , in the supercritical phase we expect that the largest component dominates all other components , which by transitivity suggests that @xmath35 . assuming that inside the critical window we can observe subcritical and supercritical features , it thus seems plausible that the critical probability should roughly satisfy @xmath36 , motivating the choice of equation  . borgs et al . @xcite showed that ( a minor variant of ) the discussed definition is very useful in combination with the so - called finite triangle condition : they recovered many erds  rnyi features under such generic mean - field assumptions ( see  @xcite for some more recent developments ) .    as pointed out by peres  @xcite , the suggestion of borgs et al . @xcite builds the mean - field scaling @xmath37 into the definition of the critical probability . it would be desirable to have a useful general definition that recovers this scaling for @xmath16-vertex mean - field graphs @xmath38 , rather than having separate definitions for each different scaling behaviour ( or , in mathematical physics jargon , for each ` universality class ' ) . with this aim in mind , nachmias and peres  @xcite suggested to define  @xmath29 as the value of  @xmath5 which maximizes the logarithmic derivative @xmath39 to motivate this definition , note that by the margulis  russo formula  @xcite the derivative @xmath40 intuitively counts the expected ( weighted ) number of edges of @xmath33 which can affect the size of  @xmath41 , see also section  [ sec : maxder ] . in other words , @xmath42 equals the probability where the addition of a random edge has maximum relative impact on the component size  @xmath41 . denoting the maximum value of   by  @xmath43 , warnke  @xcite conjectured that for mean - field graphs  @xmath17 the width of the critical window is of order  @xmath44 . this is motivated by the fact that @xmath45 entails that the susceptibility satisfies @xmath46 for @xmath47 .      in this paper we investigate , as a first test - case , the suggested definition of nachmias and peres  @xcite for the erds  rnyi random graph  @xmath0 i.e. , the case @xmath48 ( as proposed by peres  @xcite ) . here our first main result confirms that their definition of the critical probability  @xmath42 has the desired properties , i.e. , that for @xmath49 the logarithmic derivative @xmath50 satisfies the following :    its maximizer lies inside the critical window @xmath51 , and    the inverse of its maximum value coincides with the @xmath2width of the critical window . [ thm : main ] we have @xmath52    theorem  [ thm : main2 ] shows that   remains valid with @xmath53 replaced by @xmath2 .    having established the qualitative behaviour of the logarithmic derivative for @xmath0 , it is intriguing to investigate the finer scaling behaviour inside critical window . by symmetry considerations it might be tempting to believe that @xmath3 or @xmath4 could be the maximizer of @xmath54 , as speculated by  peres  @xcite . our second main result refutes this tantalizing belief , instead strengthening the general feeling that @xmath55 is no special point inside the critical window of form @xmath56 . [ thm : main2 ] given @xmath57 , for @xmath58 we have , as @xmath59 , @xmath60 where the infinitely differentiable function  @xmath61 is defined in  . moreover , if @xmath62 , then the convergence in  is uniform for @xmath63 in any compact interval @xmath64\\subset{{\\mathbb r}}$ ] . furthermore , @xmath65    the definition of the function  @xmath66 appearing in theorem  [ thm : main2 ] is quite involved , since it intuitively needs to capture the contribution of components with arbitrary numbers of cycles . it is easy to find asymptotics as @xmath67 ; we have @xmath68 as @xmath69 and @xmath70 as @xmath71 ; hence @xmath72 as @xmath69 and @xmath73 as @xmath71 ; furthermore , @xmath74 for all @xmath75 , see appendix  [ appagl ] for proofs . theorem  [ thm : main2 ] also extends to convergence of higher derivatives , see appendix  [ appahigher ] .    it would be interesting to know whether the logarithmic derivative  @xmath76 has a unique maximizer  @xmath77 , and whether it is unimodal . figure  [ fig : plots ] below ( which is obtained by numerical integrations ) suggests that this is the case , with  @xmath78 ( we conjecture  @xmath79 based on our limited precision numerical data ) . plot of the functions @xmath80 , @xmath76 and @xmath81 for @xmath82 $ ] , where  @xmath66 is as in theorem  [ thm : main2 ] . it provides some evidence for our belief that @xmath76 has a unique maximizer  @xmath83.,width=264 ]    the high - level structure of our proofs is as follows . for theorem  [ thm : main ] our starting point is the margulis  russo formula , which allows us to write @xmath84 in terms of sums involving the squared component sizes of  @xmath0 . using ideas from random graph theory we then estimate these sums , combining correlation inequalities and the ` symmetry rule ' ( also called ` discrete duality principle ' ) with results for the largest component and the susceptibility of @xmath0 , which eventually implies   ; see section  [ sec : maxder ] . for theorem  [ thm : main2 ] with @xmath85 , our starting point is the well - known fact that @xmath86 for some random variable  @xmath87 . using technical arguments we then justify taking expectations and derivatives , which in view of @xmath88 eventually establishes   with @xmath89 ; see section  [ sec : convergence ] . for inequality we show that  @xmath66 and its derivatives can be computed at  @xmath55 by series expansions ( exploiting recursive formulas for the area under a normalized brownian excursion ) . since these series converge exponentially , we can then numerically verify   by finite truncation ; see section  [ sec : zero ] .      in the present paper we discuss only the erds  rnyi random graph @xmath49 , i.e. , percolation on the complete @xmath16-vertex graph . in particular , theorem  [ thm : main ] shows that the definition of the critical probability  @xmath42 suggested by nachmias and peres  @xcite ` works ' in this case . it is an interesting open problem to establish analogous results for other finite graphs . for example , consider again the hypercube with vertex set @xmath22 discussed above , see @xcite . in the subcritical phase @xmath90 with @xmath91 , ( * ? ? ? * proposition  a.1 ) combined with ( * ? ? ? * theorem 1.3 and theorem  1.5 ) show that @xmath92 and @xmath93 , and thus @xmath94 in the supercritical phase @xmath95 with @xmath96 and @xmath97 , we have @xmath98 according to ( * ? ? ? * theorem  1.1 ) ; hence it is natural to conjecture that the logarithmic derivative satisfies @xmath99 in the supercritical phase too , and , moreover , that the logarithmic derivative has a maximum of order @xmath100 which is attained inside the critical window . proving this , however , remains a challenging problem . another important example would be random @xmath101-regular graphs with  @xmath102 .    moreover , it would be conceptually very interesting to start with the maximizer of   and then derive properties of the phase transition of  @xmath33 ( rather than , as in this paper , using known results for  @xmath103 to verify properties of the maximizer ) . it also seems highly desirable to better understand the critical probability  @xmath19 for finite transitive graphs  @xmath17 which do not exhibit the mean - field behavior of the complete graph  @xmath104 or the hypercube  @xmath22 . here the perhaps simplest example is percolation on the @xmath16-vertex cycle , @xmath105 , for which it is not difficult to check that there are three different phases : ( i )  for @xmath106 we typically have @xmath107 , ( ii )  for @xmath108 we typically have @xmath109 , and ( iii )  for  @xmath110 the rescaled sizes @xmath111 of the @xmath10 largest components are not concentrated . hence the critical window is parametrized by @xmath112 with @xmath113 . for @xmath114 it is routine to see that @xmath115 a short calculation shows that @xmath116 implies @xmath117 . furthermore , @xmath118 for @xmath110 , and @xmath119 otherwise . for the critical probability  @xmath42 of @xmath16-vertex cycles , it follows that the mean - field definition of borgs et al .  fails ( as expected , since cycles are not ` high dimensional ' ) . by contrast , the definition based on the maximizer of the logarithmic derivative of the susceptibility does correctly predict @xmath120 and the @xmath121width of the critical window , supporting the hope that this definition might work beyond the mean - field case .      for emphasis , we will often use @xmath122 and @xmath123 for probability and expectation with respect to @xmath0 . we let  @xmath124 denote the components of @xmath0 in order of decreasing sizes , @xmath125 ( resolving ties by taking the component with the smallest vertex label first , for definiteness ) . finally , convergence in distribution is denoted @xmath126 , and unspecified limits are as @xmath127 .","summary":"for percolation on finite transitive graphs , nachmias and peres suggested a characterization of the critical probability based on the logarithmic derivative of the susceptibility . as a first test - case , we study their suggestion for the erds  rnyi random graph  , and confirm that the logarithmic derivative has the desired properties : ( i )  its maximizer lies inside the critical window  , and ( ii )  the inverse of its maximum value coincides with thewidth of the critical window . we also prove that the maximizer is not located at or , refuting a speculation of  peres .","abstract":"for percolation on finite transitive graphs , nachmias and peres suggested a characterization of the critical probability based on the logarithmic derivative of the susceptibility . as a first test - case , we study their suggestion for the erds  rnyi random graph  , and confirm that the logarithmic derivative has the desired properties : ( i )  its maximizer lies inside the critical window  , and ( ii )  the inverse of its maximum value coincides with thewidth of the critical window . we also prove that the maximizer is not located at or , refuting a speculation of  peres ."}
{"article_id":"1203.1056","section_id":"i","document":"quiescent prominences are long - lived , partially - ionized , plasma condensations in the tenuous , million - degree hot , ionized solar corona @xcite . these partially - ionized condensations , at least , their optically - thin observable parts , are typically two orders of magnitude denser and cooler than the surrounding corona . as a macroscopic structure prior to an eruption , a prominence can be remarkably stable , persisting for days to weeks as a long , vertical slab , approximately @xmath2 wide , @xmath3 tall , @xmath4 long , seemingly suspended by magnetic fields to curve the full prominence length right above and along a magnetic neutral line on the photosphere . by prominence we shall henceforth be referring to this common type , the polar crown prominence being the canonical example ; see the above review articles for a comprehensive view of prominences of all varieties . figure 1 is a hinode / sot image taken in the ca ii 396.8 nm `` h - line '' spectral region showing the cool part of the prominence at a high spatial resolution , revealing its characteristic narrow , vertical , dense threads interspersed among narrow , dark lanes . this static image belies the remarkably dynamic nature of these interior structures . prominence movies from _ hinode _ and _ sdo / aia _ instruments have established that over internal scales of the order of @xmath5 and time scales of minutes , these structures are in a constant state of motion at less than free - fall speeds in a characteristic range of @xmath6 @xcite . the ever - present cool , dense threads are falling whereas the dark lanes among them are narrow streams of hot , tenuous plasma traveling upward at comparable speeds @xcite . vertical motions in both directions are actually present in both types of structures , but the high - resolution movies show a discernible average descent of the dense threads and a general bubbly rise of hot , tenuous plasmas . the latter may be the result of rapid heating to coronal temperatures associated with emerging magnetic fluxes that push into the overlying dense prominence material . this condition may be understood in terms of a nonlinear rayleigh - taylor hydromagnetic instability @xcite . such emergent - flux structures can be of considerable sizes that first form quasi - statically beneath a quiescent prominence before pushing their ways clear through the prominence without a macroscopic eruption @xcite .    a recent quantitative analysis of the motions of descending threads observed with _ sdo / aia _ indicates that over a 20 hour period , an order of magnitude more mass may be drained in this manner than found at any one time in a moderate - size , slowly evolving prominence @xcite . using the lower end of the range of observed prominence densities to compute , the drainage can remove some @xmath7 from the corona in a day , a mass comparable to that of a coronal mass ejection . of particular interest is that the drainage rate estimated from observation is changing in proportion to the slowly - changing , estimated total prominence mass during quasi - steady evolution . this observational result raises two questions . how does the observed significant mass drainage via cool threads relate to the replenishing mass - injection represented by the upward streams of hot , tenuous plasmas ? berger et al . ( 2011 ) propose that emerging magnetic flux drives a constant cycling of mass from the photosphere , in the form of tenuous hot plasma , into the coronal cavity overlying a quiescent prominence . this up - flow returns as the draining vertical threads , essentially establishing a novel form of magneto - thermal convection in the solar outer atmosphere . the other question relates to the embedded magnetic fields in these processes . spectral polarimetric observations have shown that quiescent prominence plasmas embed typically horizontal , local fields of the order of @xmath8 @xcite . these fields are sufficiently intense to dictate the structures of their prominences under a high degree of the frozen - in condition due to high electrical conductivity . in particular , a large amount of mass can be supported by fields of the observed intensities . yet more mass can drained through the prominence in less than a day than the amount trapped quasi - steadily in the prominence at any one time . how is the observed drainage reconcilable with the observed prominence field being generally horizontal if we accept the frozen - in condition ? an attractive hypothesis is that it is in the nature of prominence dynamics to develop such extreme physical conditions that the usual frozen - in condition breaks down spontaneously . this hypothesis is what we set out to investigate as a theoretical hydromagnetic possibility . the first paper of the series here treats the case of thermal collapse during plasma condensation producing cold , dense , poorly ionized plasmas within which the frozen - in condition can not be sustained . the second paper takes up a separate piece of physics , demonstrating that despite the high magnetic reynolds - numbers of the prominence interior , magnetic reconnection takes place readily via spontaneous formation and dissipation of electric current - sheets @xcite . the two papers provide a hydromagnetic basis to understand the observed restless interior of a prominence . specifically the first paper here treats the following theoretical problem . we construct a complete family of exact solutions describing a vertical kippenhahn - schlter ( ks ) plasma - slab supported against gravity in a bowed magnetic field in unbounded space , varying only in the direction perpendicular to the slab @xcite . we assume static force equilibrium under ( i ) the frozen - in condition and ( ii ) a steady balance among optically - thin radiation , heating , and thermal conduction directed along the field . these three energy processes take the theoretical forms studied by low & wu ( 1981 ) , representing an energy transport of a minimum physical complexity relevant to prominences . despite its one - dimensionality , the ks slab captures important properties of this complex system . the novel result of the study is that the set of everywhere - analytical solutions found in the earlier study is only a subset of measure zero of all the physically admissible equilibrium states of the ks slab . generally , force - balance and steady energy - transport can not both be met under the frozen - in condition without a fraction of the total mass of the slab having collapsed into a mathematical singularity representing an exceedingly cold , dense sheet at the center of the otherwise diffuse slab . the weight of that mass sheet is supported by a discrete lorentz force due to a discrete electric current in the sheet . this discrete current can be maintained only if the frozen - in condition is rigorously obeyed , that is , the electrical conductivity is infinite . the electrical conductivity in the solar atmosphere is large but finite , of course . in that case , an evolution to equilibrium must at first seek a state with an inevitable singularity when the frozen - in condition does apply to a very high degree . as the singularity develops , the small nonzero electrical resistivity unavoidably becomes significant at a point in time , resulting in current dissipation . a breakdown of the frozen - in condition thus occurs spontaneously . the general inevitability of mass - sheet singularity in the ks - slab is demonstrated in section 2 . the singular equilibrium solutions containing a mass sheet with a discrete current are analyzed in section 3 . the breakdown of the frozen - in condition is illustrated in section 4 , treating an exact solution for a steady , vertical resistive hydromagnetic flow and pointing out the need for a more realistic multi - fluid description . our results are summarized in section 5 to relate in general terms to the physics of prominences .","summary":"hinode _ and _ sdo / aia _ high - resolution observations . this first paper is a study of the static equilibrium of the kippenhahn - schlter diffuse plasma slab , suspended vertically in a bowed magnetic field , under the frozen - in condition and subject to a theoretical thermal balance among an optically - thin radiation , heating , and field - aligned thermal conduction . the everywhere - analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system . for most values of the total mass frozen into a given bowed field , force - balance and steady energy - transport can not both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness , within which the frozen - in condition must break down our hydromagnetic result suggests that the narrow , vertical prominence threads may be falling across magnetic fields , with optically - thick cores much denser and ionized to much lower degrees than conventionally considered . this implication is discussed in relation to ( i ) the recent _ sdo / aia _ observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors , ( ii ) the canonical range of determined from spectral - polarimetric observations of prominence magnetic fields over the years and ( iii ) the need for a more realistic multi - fluid treatment .","abstract":"this series of papers investigates the dynamic interior of a quiescent prominence revealed by recent _ hinode _ and _ sdo / aia _ high - resolution observations . this first paper is a study of the static equilibrium of the kippenhahn - schlter diffuse plasma slab , suspended vertically in a bowed magnetic field , under the frozen - in condition and subject to a theoretical thermal balance among an optically - thin radiation , heating , and field - aligned thermal conduction . the everywhere - analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system . for most values of the total mass frozen into a given bowed field , force - balance and steady energy - transport can not both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness , within which the frozen - in condition must break down . an exact , resistive hydromagnetic extension of the kippenhahn - schlter slab is also presented , resolving the mass - sheet singularity into a finite - thickness layer of steadily - falling dense fluid . our hydromagnetic result suggests that the narrow , vertical prominence threads may be falling across magnetic fields , with optically - thick cores much denser and ionized to much lower degrees than conventionally considered . this implication is discussed in relation to ( i ) the recent _ sdo / aia _ observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors , ( ii ) the canonical range of determined from spectral - polarimetric observations of prominence magnetic fields over the years and ( iii ) the need for a more realistic multi - fluid treatment ."}
{"article_id":"1203.1056","section_id":"c","document":"the vertical descent of prominence threads at less than free - fall speeds has been interpreted in several ways . the large - scale twisted field in the prominence cavity may be evolving with flux - tubes falling bodily together with their frozen - in plasmas as the result of intermittent magnetic reconnections occurring somewhere else along a flux - tube @xcite . van ballegooijen and cranmer ( 2010 ) proposed that the prominence plasma is flowing under the frozen - in condition in a 3d tangled global field that has a strong vertically - oriented component . in contrast , here we propose a spontaneous breakdown of the frozen - in condition to allow a resistive flow across a local horizontally - oriented field . what seems clear is that all these dynamical processes may occur simultaneously . our ks - slab model shows that the nonlinear coupling of force - balance with energy - balance under a rigorous imposition of the frozen - in condition must generally produce a cold , zero - thickness sheet of mass if static equilibrium is to be attained . this mass sheet contains a discrete electric current that generates the lorentz force supporting the weight of the sheet . in a real plasma of a high but finite electrical conductivity , this discrete current must dissipate resistively . in other words , the typically high degree of the frozen - in condition must physically break down within the mass sheet . in a time - dependent relaxation to such an equilibrium , a mass sheet would first develop during the time when the frozen - in condition applies approximately . then , in that developing mass sheet , the frozen - in condition soon breaks down to produce a downward resistive flow across the supporting field . yet , the frozen - in condition is not broken down permanently . the implied resistive heating in the sheet , fueled by gravitational potential energy released by the falling , poorly - ionized plasma , can bring back the frozen - in condition , but only to recreate the circumstance under which a thin , cold sheet is again inevitable . this recurrent spontaneous breakdowns of the frozen - in condition is a physically attractive hypothesis to explain the constantly restless interior of a quiescent prominence as revealed by _ sdo / aia _ and _ hinode _ observations . gravity , anisotropic lorentz force , optically - thin radiation , heating , and anisotropic thermal conduction all play essential roles in creating what seems quite general circumstances under which thin collapsed mass sheets must form . the particular optically - thin radiative loss and heating described by equations ( [ radiation ] ) and ( [ heating ] ) are artificial , but they capture basic properties sufficiently well for us to use the ks - slab to demonstrate the inevitability of mass - sheet singularity with mathematical rigor . our demonstration is surprisingly complete . the mass - sheet singularity in our ks - slab is resolvable into a sheet of finite width using an exact solution for a cross - field resistive flow to account for the breakdown of the frozen - in condition . both the static and time - dependent problems of this complex coupling are formidable , especially for 2d and 3d systems . direct numerical simulation holds the only hope for making progress but to be fruitful this approach must start with a physics - based hypothesis like the one presented here . much further work is needed to treat physically more realistic energy processes for applications directly to the prominence @xcite and other astrophysical systems , notably the interstellar medium @xcite . observation remains the spearhead in the investigation of quiescent prominences @xcite . presently not all the observed properties in prominences can be theoretically understood or understood in a unified way . for example , the sub - arcsecond threads , revealed by ground - based , high - resolution , static @xmath0 images of on - disk prominences , have remained difficult for theory to unify with the space observations of prominences at the solar limb from _ hinode _ and _ sdo / aia _ @xcite . these two views of prominence structures have also not been reconciled with the polarimetric observations of prominence and coronal magnetic fields @xcite . observations can pose good physical questions to be addressed theoretically in their own rights , without necessarily aiming at a comprehensive explanation of all the rich observations . in the face of many unanswered questions , our series of paper seeks to build up our intuition for seeing the complex observations in terms of the elementary physical principles . previous works of this kind have addressed magnetic support of the prominence weight under the frozen - in condition using 2d and 3d field models with energy transport greatly simplified or ignored for the sake of tractability @xcite . in complement , models of 1d sophisticated energy transport along field lines , prescribed to be fixed in space , made progress with insights into the condensation processes by suppressing the dynamical interaction of the field with energy transport@xcite . heasley and mihalas ( 1976 ) pioneered studying the coupling of radiative transfer to the equilibrium forces in a slab model . allowing for gravity and a heuristic approximation of the lorentz force , this interesting work encountered an inevitable presence of collapsed mass - sheets , perhaps a rudimentary form of the singularity we found in our ks - slab model ; see also anzer & heinzel ( 1999 ) .    collapsed mass sheet may be a common occurrence in the corona . all it takes is a failure to bring energy to where it is needed whenever a particular mode of energy transport becomes over constrained by the coupled requirement of balancing the forces in the gravitationally stratified fluid . let us conclude with the following intuitive physical picture that has emerged from our study .    in our ks - slab , there are two thermal - insulation mechanisms that can keep the prominence cool against the million - degree hot , thermally highly - conducting corona . the magnetic field is an insulator against thermal conduction across it . not so well recognized is the self - insulation of the prominence plasma along a flux tube . in a sheared u - shaped flux tube , the frozen - in mass is gravitationally stratified along the tube so as to progressively radiate away the two thermal fluxes conducted inward from the high - temperature upper parts of the tube in the corona . if the total mass is large enough , the steady state may be one in which these thermal fluxes are depleted before the bottom of the tube is reached . then the bottom contracts into a cold dense mass simply from want of heat . the degree of ionization of such a core would fall below a threshold whereupon the frozen - in condition must break down . the prominence / corona transition is similar to the corona / chromosphere transition of the solar atmosphere but that analogy is just imperfect . in the solar atmosphere , the bottom of the chromosphere never cools below about @xmath316 because the photosphere beneath it has no bottom and is heated actively by the solar luminosity coming through from below . if the prominence plasma sitting at the bottom of an u - shaped tube has no internal heat source and is self - insulating , it would simply cool to an equivalent of the solar photosphere with a very different property , one with such high density and low temperature as to break the frozen - in condition . this massive core would then flow resistively across the field into the adjacent flux tubes . no steady flow is expected , just a recurrent process of the breakdown alternating with restoration of the frozen - in condition by resistive heating .    in realistic 3d situations , the super - cooled core of a prominence plasma slips resistively out of its optically - thin chromospheric cladding into an adjacent flux tube . there it can either continue to slip resistively into other tubes further away or else become so ionized in the new hot environment as to be frozen into the new tube it has just occupied . a sufficiently massive super - cooled core can thus fall through the bottoms of successive u - tubes leaving behind in each of these tubes ionized plasmas at chromospheric temperatures , until the former runs out of mass to remain a collapsed core . a vertical thread of chromospheric plasma is naturally produced . the movie of such a process made at the cool chromospheric temperature would then show such a thread forming from out of nowhere with a general downward descent . the presence of u - shaped flux tubes is the pre - requisite of this process . although such massive , poorly ionized cores are time - dependent objects , this picture argues for the presence of prominence plasmas that are more massive , more dense , much colder , and less ionized than currently being contemplated . perhaps the canonical observation - based numbers describing the prominence , electron density of @xmath317 , temperature of @xmath318 , degree of ionization @xmath319% , are _ only _ the properties of the optically - thin , chromospheric cladding of the not yet observed , transient , optically - thick cores . the tangled - field models of van ballegooijen and cranmer ( 2010 ) readily give peak densities well in excess of the aforementioned canonical values . these models assume a moderate field of only 10 g , whereas even larger densities are implied for fields as high as 60 g given by polarimetric observations @xcite . our ks - slab suggests that even more extreme densities might occur commonly in prominences . we emphasize that upward and downward motions accompany this process . the unloading of a flux tube to give mass to the one below results in the former rising by its resultant overcompensating lorentz force . correspondingly , the mass - receiving tube below sinks heavily until the lorentz force of its stretched field can hold it swaying into position . here is an instance of a flux - tube of fluid rising or falling bodily , carrying its frozen - in magnetic flux along with it . our hypothesis suggests that the cavity magnetic field supporting the prominence is `` porous '' in spite of the high electrical conductivity . the observations of liu , berger & low ( 2011 ) thus have the significance as a quantitative statement of how porous that magnetic field can be , namely , that an order of magnitude more mass than retained by the prominence at any one time can pass resistively and agitatedly down the cavity field in a day .    in the second paper we will get a clearer picture of the role of the magnetic field in this process @xcite . the field actually is the dominant dynamical player , for it can , on its own , create and restore the frozen - in condition in a permanent restlessness @xcite . this mechanics may be basic to the proposal that the long - lived macroscopic prominence is a form of magneto - thermal convection in the corona proposed by berger et al . ( 2011 ) . we thank yuhong fan , michael goodman , phil judge and bruce lites for discussions . the national center atmospheric research is sponsored by the national science foundation . teb was supported by the solar - b fpp contract nnm07aa01c at lockheed martin . wl is supported by nasa sdo / aia contract nng04ea00c .","summary":"this series of papers investigates the dynamic interior of a quiescent prominence revealed by recent _","abstract":"this series of papers investigates the dynamic interior of a quiescent prominence revealed by recent _ hinode _ and _ sdo / aia _ high - resolution observations . this first paper is a study of the static equilibrium of the kippenhahn - schlter diffuse plasma slab , suspended vertically in a bowed magnetic field , under the frozen - in condition and subject to a theoretical thermal balance among an optically - thin radiation , heating , and field - aligned thermal conduction . the everywhere - analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system . for most values of the total mass frozen into a given bowed field , force - balance and steady energy - transport can not both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness , within which the frozen - in condition must break down . an exact , resistive hydromagnetic extension of the kippenhahn - schlter slab is also presented , resolving the mass - sheet singularity into a finite - thickness layer of steadily - falling dense fluid . our hydromagnetic result suggests that the narrow , vertical prominence threads may be falling across magnetic fields , with optically - thick cores much denser and ionized to much lower degrees than conventionally considered . this implication is discussed in relation to ( i ) the recent _ sdo / aia _ observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors , ( ii ) the canonical range of determined from spectral - polarimetric observations of prominence magnetic fields over the years and ( iii ) the need for a more realistic multi - fluid treatment ."}
{"article_id":"astro-ph9906164","section_id":"c","document":"the paper develops a theory of eccentric ( @xmath509 ) linearized perturbations of an axisymmetric disk galaxy residing in a spherical dark matter halo and with a spherical bulge component . the disk is represented by a large but finite number @xmath1 of rings with shifted centers _ and _ with perturbed azimuthal matter distributions . this description is appropriate for a disk with small ` thermal ' velocity spread @xmath68 where the matter is in approximately laminar circular motion . the spread for a thin disk has @xmath67 , but it is sufficent to give a toomre @xmath510 . earlier , baldwin _ et al . _ ( 1980 ) discussed asymmetries in disk galaxies in terms of shifted rings but without interactions between the rings and without azimuthal displacements of the ring matter . account is taken of the shift of the matter at the galaxy s center , which may include a massive black hole . the gravitational interactions between the rings and between the rings and the center is fully accounted for , but the halo and bulge components are treated as passive gravitational field sources . equations of motion are derived for the ring and the center , and from these we obtain the lagrangian for the rings@xmath2center system . for this system we derive an energy constant of the motion , and a total canonical angular momentum constant of the motion . we first discuss the nature of the precession of a single ring with the other rings fixed ; this case although not self - consistent is informative . there are four modes , analogs to the normal modes of a non - rotating system , and two have negative energy and two positive energy . negative energy modes are unstable in the presence of dissipation such as that due to dynamical friction . we go on to study the eccentric motion of a disk consisting of two rings of different radii but equal mass @xmath3 . above a threshold value of @xmath4 the two rings are unstable with instability due merging of positive and negative energy modes . this result is obtained by solving the eighth order polynomial for the frequencies of the eight modes . above a second , somewhat larger threshold value of @xmath4 , a second instability appears , and in this case the ring motion is such that the angular momentum of the inner ring decreases while that of the outer ring increases . for the unstable motion , the maximum of the azimuthal density enhancement of a ring occurs at an angle about @xmath340 from the direction of the radial shift . this allows the center of mass of the ring to move closer to the center of mass of the other ring and to the origin . we also analyze the eccentric motion of a disk of one ring interacting with a radially shifted central mass . this system has six modes , the frequencies of which are obtained by solving a sixth order polynomial . in this case , instability sets in above a threshold value of the central mass ( for a fixed ring mass ) , and it acts to increase the angular momentum of the central mass ( which therefore rotates in the direction of the disk matter ) , while decreasing the angular momentum of the ring . the instability is again due to the merging of positive and negative energy modes . we study the eccentric dynamics of a disk with an exponential surface density distribution represented by a large number @xmath403 of rings and a central mass @xmath511 which may include the mass of a black hole . the outer radius of the disk is @xmath512 kpc ; we have checked that this value has negligible affect on the reported results . in this case , we numerically integrate the equations of motion . a check on the validity of the integrations is provided by monitoring the mentioned total energy and total canonical angular momentum , which are found to be accurately constant in all presented results . the inner part of the disk @xmath513 kpc is found to be strongly unstable with @xmath440folding time @xmath514 myr for the conditions considered . the @xmath440folding time is somewhat longer if @xmath515 . angular momentum of the rings is transferred _ outward _ , _ and _ to the central mass if it is present . a _ trailing _ one - armed spiral wave is formed in the disk . this differs from the prediction of baldwin _ et al . _ ( 1980 ) of a leading one - armed spiral . the outer part of the disk @xmath516 is stable and in this region the angular momentum is transported by the wave . thus our results appear compatible with the theorem of goldreich and nicholson ( 1989 ) regarding angular momentum in _ stable _ rotating fluids . the instability found here appears qualitatively similar to that found by taga and iye ( 1998b ) for a fluid kuzmin disk with surface density @xmath517 with a point mass at the center where unstable trailing one - armed spiral waves are found . the present linear theory does not address the issue of saturation of growth of the eccentric motion . one possibility is that the strong instability of the inner rings of the disk leads to the destruction of this part of the disk . for this reason we have studied a disk with a modified exponential density distribution where the surface density of the inner part of the disk is reduced . however , the mass of the center of the galaxy was kept the same as in the case of an exponential disk , @xmath518 . in this case we find much slower , linear - as opposed to exponential - growth of the eccentric motion of the disk for times @xmath519 gyr . a trailing one - armed spiral wave forms in the disk and becomes more tightly wrapped as time increases . angular momentum is transferred outward . the motion of the central mass if present is small compared with that of the disk for @xmath519 gyr .    for long times @xmath501 gyr , the the azimuthal displacements and shifts of the inner rings start to become large compared with the values in the outer disk . at the same time , the radial shift of the center grows . this shift is significantly reduced if the mass of the center is changed from @xmath520 to @xmath521 . baldwin , j.e . , lynden - bell , d. & sancisi , r. 1980 , , 193 , 313    barnes , j.e . , & hut , p. 1989 , , 70 , 389    binney , j. , & tremaine , s. 1987 , galactic dynamics ( princeton : princeton university press )    briggs , f.h . 1990 , apj , 352 , 15    buta , r. , van driel , w. , braine , j. , combes , f. , wakamatsu , k. , sofue , y. , & tomita , a. 1995 . , 450 , 593    contopoulos , g. , & grosbl , p. 1986 , a&a , 155 , 11    contopoulos , g. , & grosbl , p. 1988 , a&a , 197 , 83    freeman , k.c . 1970 , , 160 , 811    frieman , e. , & rotenberg , m. 1960 , rev . phys . , 32 , 898    goldreich , p. , & nicholson , p.d . 1989 , , 342 , 1075    haynes , m.p . , hogg , d.e . , maddalena , r.j . , roberts , m.s . , & van zee , l. 1998a , , 115 , 62    ichimaru , s. 1973 , _ basic principles of plasma physics _ ( benjamin : reading , massachusetts ) , ch . 4    jog , c.j . 1997 , , 488 , 642    knapen , j.h . 1997 , , 286 , 403    kornreich , d.a . , haynes , m.p . , & lovelace , r.v.e . 1998 , aj , 116 , 2154    lauer , t.r . , faber , s.m . , groth , e.j . , shaya , e.j . , campbell , b. , code , a. , currie , d.g . , baum , w.a . , ewald , s.p . , hester , j.j . , holtzman , j.a . , kristian , j. , light , r.m . , ligynds , c.r . , oneil , e.j . , jr . , & westphal , j.a . 1993 , , 106 , 1436    levine , s.e . , & sparke , l.s . 1998 , , 496 , l13    lovelace , r.v.e . , jore , k.p . , & haynes , m.p . 1997 , , 475 , 83    lovelace , r.v.e . 1998 , a&a , 338 , 819    miller , r.h . , & smith , b.f . 1988 , in _ applied mathematics , fluid mechanics , and astrophysics : a symposium in honor of c.c . lin_. d.j . benney , f.h . shu , & c. yuan , eds . ( singapore : world scientific ) , p. 366 miller , r.h . , & smith , b.f . 1992 , , 393 , 508    richter , o .- g . & sancisi , r. 1994 . , 290 , l9    rix , h .- w . , & zaritsky , d. 1995 , , 447 , 82    rownd , b.k . , dickey , j.m . , & helou , g. 1994 , , 108 , 1638    schoenmakers , r.h.m . , franx , m. , & de zeeuw , p.t , 292 , 349    swaters , r.a . , schoenmakers , r.h.m . , sancisi , r. , & van albada , t.s . 1998 , , in press ( astro - ph/9811424 )    syer , d. , & tremaine , s. 1996 , , 281 , 925    taga , m. , & iye , m. 1998a , , 299 , 111    taga , m. , & iye , m. 1998b , , 299 , 1132    zaritsky , d. , & rix , h .- w . 1997 . , 477 , 118","summary":"a theory is developed for the dynamics of eccentric perturbations $ ] of a disk galaxy residing in a spherical dark matter halo and including a spherical bulge component . the disk is represented as a large number of rings with shifted centers _ and _ with perturbed azimuthal matter distributions . account is taken of the dynamics of the shift of the matter at the galaxy s center which may include a massive black hole . the gravitational interactions between the rings and between the rings and the center is fully accounted for , but the halo and bulge components are treated as passive gravitational field sources . equations of motion and a lagrangian are derived for the ringcenter system , and these lead to total energy and total angular momentum constants of the motion .    we first study the eccentric motion of a disk consisting of two rings of different radii but equal mass , . for small the two rings are stable , but for larger than a threshold value the rings are unstable with a dynamical time - scale growth . for sufficiently above this threshold , the instability acts to decrease the angular momentum of the inner ring , while increasing that of the outer ring . the instability results from the merging positive and negative energy modes with increasing . secondly , we analyze the eccentric motion of one ring interacting with a radially shifted central mass . in this case instability sets in above a threshold value of the central mass ( for a fixed ring mass ) , and it acts to increase the angular momentum of the central mass ( which therefore rotates in the direction of the disk matter ) , while decreasing the angular momentum of the ring .    thirdly , we study the eccentric dynamics of a disk with an exponential surface density distribution represented by a large number of rings . angular momentum of the rings is transferred outward _ and _ to the central mass if present , and a trailing one - armed spiral wave is formed in the disk . fourthly , we analyze a disk with a modified exponential density distribution where the density of the inner part of the disk is reduced . in this case we find much slower , linear growth of the eccentric motion . a trailing one - armed spiral wave forms in the disk and becomes more tightly wrapped as time increases . the motion of the central mass if present is small compared with that of the disk .   ","abstract":"a theory is developed for the dynamics of eccentric perturbations $ ] of a disk galaxy residing in a spherical dark matter halo and including a spherical bulge component . the disk is represented as a large number of rings with shifted centers _ and _ with perturbed azimuthal matter distributions . account is taken of the dynamics of the shift of the matter at the galaxy s center which may include a massive black hole . the gravitational interactions between the rings and between the rings and the center is fully accounted for , but the halo and bulge components are treated as passive gravitational field sources . equations of motion and a lagrangian are derived for the ringcenter system , and these lead to total energy and total angular momentum constants of the motion .    we first study the eccentric motion of a disk consisting of two rings of different radii but equal mass , . for small the two rings are stable , but for larger than a threshold value the rings are unstable with a dynamical time - scale growth . for sufficiently above this threshold , the instability acts to decrease the angular momentum of the inner ring , while increasing that of the outer ring . the instability results from the merging positive and negative energy modes with increasing . secondly , we analyze the eccentric motion of one ring interacting with a radially shifted central mass . in this case instability sets in above a threshold value of the central mass ( for a fixed ring mass ) , and it acts to increase the angular momentum of the central mass ( which therefore rotates in the direction of the disk matter ) , while decreasing the angular momentum of the ring .    thirdly , we study the eccentric dynamics of a disk with an exponential surface density distribution represented by a large number of rings . the inner part of the disk is found to be strongly unstable . angular momentum of the rings is transferred outward _ and _ to the central mass if present , and a trailing one - armed spiral wave is formed in the disk . fourthly , we analyze a disk with a modified exponential density distribution where the density of the inner part of the disk is reduced . in this case we find much slower , linear growth of the eccentric motion . a trailing one - armed spiral wave forms in the disk and becomes more tightly wrapped as time increases . the motion of the central mass if present is small compared with that of the disk .    epsf.def = cmmib10 at 10pt"}
{"article_id":"1106.6055","section_id":"i","document":"direct observations of distant galaxies remain the most straightforward way to probe the fundamental nature of the high - redshift universe . such observations can provide some much - needed constraints on numerical simulations , which may provide better answers to the question of how large scale structure forms and how star formation begins in dark matter halos . star formation in early galaxies is dependent upon the mechanism by which gas cools ; that mechanism itself is dependent upon the ionization state and metal enrichment of that gas which are not well constrained at high redshift . the ly@xmath0  emission line is a very useful tool for the detection of high - redshift galaxies , as the earliest stars in the universe should ionize surrounding hydrogen gas , which will then recombine to produce ly@xmath0  emission ( see @xcite ) . this ly@xmath0  line can be probed quite effectively at high redshifts via the use of narrowband filters , which focus on regions with low sky background and that are free of strong oh lines ( e.g. , @xcite ) . high - redshift objects should have essentially no flux blueward of rest - frame ly@xmath0  and none blueward of rest - frame 912  ; this is a result of the ly@xmath0  forest effect at high redshift , due to strong absorption by intervening clouds ( e.g.,@xcite . such narrowband surveys have proved quite successful so far ( e.g. , @xcite ) and have resulted in samples of galaxies over a range of redshifts , including the spectroscopic confirmation of a ly@xmath0  emitting galaxy at @xmath10 @xmath11 6.96 @xcite . even when these narrowband surveys do not successfully detect high-@xmath10 objects , such null results can be used to constrain the ly@xmath0  luminosity function ( e.g. , @xcite ) . the early universe is expected to be metal poor , but metals have been detected in the intergalactic medium ( igm ) at @xmath10 @xmath11 5.7 @xcite , and so the igm must have been enriched in metals by @xmath10 @xmath1 6 at the latest , with recent results tentatively indicating a metallicity downturn between @xmath10 @xmath1 5.7 and @xmath10 @xmath1 5 @xcite . additionally , the ly@xmath0  line is sensitive to igm obscuration at neutral hydrogen fractions ranging from low to high ( e.g. , @xmath12 ; @xcite ) , and thus observations of ly@xmath0  -emitting galaxies serve as a powerful probe of the reionization history of the universe ; the gunn - peterson test , for example , is only useful when the neutral gas fraction is @xmath131% @xcite . increasing the neutral hydrogen fraction in the igm increases the attenuation of ly@xmath0  emission from those galaxies @xcite . as this neutral fraction increases , the ly@xmath0  luminosity function will vary according to the amount of light being attenuated by the igm . previous estimates of the redshift of the epoch of reionization using constraints from studies of ly@xmath0  emitters do not concur with constraints derived from polarization observations of the cmb . the latter suggests that the redshift of reionization is @xmath14 @xmath11 10.5 @xmath15 1.2 , should reionization be an instantaneous process @xcite , whereas the former have indicated a significantly later end to the epoch . constraints on the ly@xmath0  luminosity function ( lf ) can assist in determination of the redshift at which reionization has been completed , owing to the resonant scattering of ly@xmath0  photons in a neutral igm . if the intrinsic number density of young galaxies remains constant over redshift , then a significant decline in the observed ly@xmath0  lf at a given redshift could indicate a change in igm phase . on the lower redshift end , malhotra & rhoads ( 2004 ) found no significant evolution of ly@xmath0  lf between 5.7 @xmath13 @xmath10 @xmath13 6.6 ; whereas at higher redshifts , an evolution of ly@xmath0  lf between 6.5 @xmath13 @xmath10 @xmath13 7 is suggested based on single detections @xcite . ouchi et al . ( 2008 ) found little evolution between @xmath10 @xmath1 3 and @xmath10 @xmath1 6 in the observed lfs , although they suggest a real evolution , with increase in intrinsic ly@xmath0  luminosity being canceled out by increase in igm absorption . curtis - lake et al . ( 2011 ) have recently identified ly@xmath0  emitters at a high rate over 6 @xmath13 @xmath10 @xmath13 6.5 in ukidss . ono et al . ( 2011 ) have measured a decrease in ly@xmath0  emission line detection fraction over 6 @xmath13 @xmath10 @xmath13 7 , as have schenker et al . ( 2011 ) over 6 @xmath13 @xmath10 @xmath13 8 and pentericci et al . ( 2011 ; following up work by fontana et al . ( 2010 ) ) over 6 @xmath13 @xmath10 @xmath13 7 ; these studies are uv - continuum - selected galaxies ( i.e. , lyman break galaxies ) rather than selected via ly@xmath0  emission line but share the same goal , and all conclude that the neutral hydrogen fraction of the igm is increasing over those epochs . the seven ly@xmath0  candidates found by hibon et al . ( 2010 ) at @xmath10 @xmath11 7.7 would indicate no evolution of the ly@xmath0  lf if they are found to be spectroscopically confirmed ( although soon to be published work suggests that at least five are not confirmed ; see clment et al . ( 2011 ) ) ; the four ly@xmath0  candidates found by tilvi et al . ( 2010 ) could either indicate mild or no evolution between 6.5 @xmath13 @xmath10 @xmath13 7.7 depending on the number of candidates which are confirmed . two lyman break galaxies at @xmath167.0 were recently spectroscopically confirmed by vanzella et al . ( 2011 ) , their luminosities fairly consistent with that of the well - known confirmed @xmath17 iye et al . ( 2006 ) ly@xmath0  emitter . at present , small number statistics severely affect our ability to draw definite conclusions on the ly@xmath0  luminosity function and properties of the igm . it is therefore essential to expand the sample of high - redshift candidates at epochs when the igm became metal - enriched and reionized , and thus shed light on the nature of the early universe . as redshift increases , galaxy sizes and luminosities decrease , and cosmological dimming must also be taken into account . because of this , detection of galaxies at @xmath10 @xmath18 7 can be quite difficult @xcite . thus it is essential to have a large survey volume in order to detect a sufficient number of high-@xmath10 objects . this conclusion is bolstered by the biased nature of galaxy formation and the non - uniformity of large - scale structure at high-@xmath10 @xcite . presently , most studies searching for high-@xmath10 galaxies have significant depth but small area ( e.g. , @xcite ) or have small volume but high magnification by virtue of cluster lensing @xcite , so all results are affected by cosmic variance . there is a need for surveys which probe both a deep and wide region in order to best constrain global properties of high-@xmath10 galaxies ; the present paper reports on a survey that tries to fill that role .    in this paper , we present the results from a search for ly@xmath0  emitting galaxies at @xmath10 @xmath11 7.7 in the cosmos field , utilizing custom - made ultra - narrowband filters which are tuned to avoid the oh sky lines and thus reach extremely low infrared sky backgrounds . the organization of this paper is as follows . in section [ obsdata ] , we discuss our observations and reduction of the data that we obtained , as well as photometric calibration . in section [ selection ] , we describe our method of candidate ly@xmath0 emitter selection and the basic properties of the resulting candidate ly@xmath0  emitters . in section [ contaminants ] , we discuss possible sources of contamination in our samples . in section [ mcsim ] , we estimate the number of ly@xmath0  emitting galaxies that we should expect to find in our survey through the use of a detailed monte carlo simulation . in section [ lylf ] , we present the ly@xmath0  luminosity function derived from our candidates and compare to previously derived ly@xmath0  lfs . finally , in section [ conc ] , we summarize our conclusions . this work shares authors , instrument , and technique with the work of tilvi et al . ( 2010 ) , and can thus be viewed as part of a series with that paper . throughout this work , we assume a standard flat @xmath19cdm cosmology with @xmath20 @xmath11 0.3 , @xmath21 @xmath11 0.7 , and @xmath22 @xmath11 0.71 , where @xmath20 , @xmath21 , and @xmath22 are the matter density , dark energy density , and hubble parameter ( in units of 100 km s@xmath8 mpc@xmath8 ) , respectively . all magnitudes listed are in the ab magnitude system .","summary":"the study of ly  emission in the high - redshift universe is a useful probe of the epoch of reionization , as the ly  line should be attenuated by the intergalactic medium ( igm ) at low to moderate neutral hydrogen fractions . here","abstract":"the study of ly  emission in the high - redshift universe is a useful probe of the epoch of reionization , as the ly  line should be attenuated by the intergalactic medium ( igm ) at low to moderate neutral hydrogen fractions . here we present the results of a deep and wide imaging search for ly  emitters in the cosmos field . we have used two ultra - narrowband filters ( filter width of -9  ) on the newfirm camera , installed on the mayall 4 m telescope at kitt peak national observatory , in order to isolate ly  emitters at 7.7 ; such ultra - narrowband imaging searches have proved to be excellent at detecting ly  emitters . we found 5 detections of four candidate ly  emitters in a survey volume of 2.8 x 10 mpc ( total survey area arcmin ) . each candidate has a line flux greater than 8 x 10 erg s . using these results to construct a luminosity function and comparing to previously established ly  luminosity functions at 5.7 and 6.5 , we find no conclusive evidence for evolution of the luminosity function between 5.7 and 7.7 . statistical monte carlo simulations suggest that half of these candidates are real 7.7 targets , and spectroscopic followup will be required to verify the redshift of these candidates . however , our results are consistent with no strong evolution in the neutral hydrogen fraction of the igm between 5.7 and 7.7 , even if only one or two of the 7.7 candidates are spectroscopically confirmed ."}
{"article_id":"1106.6055","section_id":"i","document":"we have utilized two custom - made unb filters , at wavelengths 1.056 and 1.063 @xmath23 m ( fwhm 7.4 and 8.1  , respectively ) on the newfirm camera at the kpno 4 m mayall telescope to perform a deep and wide search for @xmath10 @xmath11 7.7 ly@xmath0  emitters in the cosmos field . our study comprised a co - moving volume of 2.8 @xmath51 10@xmath4 mpc@xmath80 ( survey area @xmath1760 arcmin@xmath6 ) and probed down to a limiting flux of @xmath18 @xmath51 10@xmath7 erg s@xmath8 @xmath9 ( 50% completeness limit ) , which is comparable to or better than previous ly@xmath0  searches at similar redshifts . we used a very detailed selection procedure , making use of five different quantitative parameters as well as qualitative methods to ensure narrow - line detection and elimination of contaminants ( including 3 low-@xmath10 interlopers already known in the cosmos catalog ) . we were left with a total of four candidates ( three detected in the 1.056 @xmath23 m filter , one in the 1.063 @xmath23 m filter ) , each detected at 5 sigmas or higher , down to line fluxes of 8 @xmath51 10@xmath7 erg s@xmath8 @xmath9 . detailed monte carlo simulations would suggest that up to two of these candidates are real . if we assume only two real candidates , comparison of the resultant ly@xmath0  lf to the @xmath10 @xmath11 5.7 ouchi et al . ( 2008 ) and @xmath10 @xmath11 6.5 kashikawa et al . ( 2006 ) ly@xmath0  lfs would indicate that there has been no significant evolution of the ly@xmath0  lf between 5.7 @xmath13 @xmath10 @xmath13 7.7 . this result is consistent with the findings of tilvi et al . ( 2010 )  that work used the same instrument , equivalent field of view , reached similar flux limits , but was half the volume of our work , owing to our extra filter . to pin down the neutral hydrogen fraction at @xmath10 @xmath11 7.7 and thus the stage of the reionization process at that epoch , we will need more detailed ly@xmath0  lfs in order to accurately determine the characteristic luminosity , @xmath82 , of these objects . this will require a ) spectroscopic confirmations of these candidate high - redshift ly@xmath0  emitters , and b ) surveys encompassing more fields , as cosmic variance is likely to affect the number of emitters found in each region . the success of previous narrowband surveys at identifying ly@xmath0  emitters at lower redshift and the robustness of our current set of candidates mean that the future of such high-@xmath10 studies is quite promising . it is also encouraging to note that our results match well with surveys in different fields . the pursuit of surveys such as these , along with the advances that should be brought to the field by jwst and other new instruments , should provide a bright future for the study of the dark ages . + h.b.k . and s.v . were supported by the nsf through contracts ast 0606932 and 1009583 . h.b.k . would like to acknowledge m. coleman miller for helpful discussion of statistics and bayesian error calculation , and is very grateful to peter capak for assistance with the cosmos data catalog and discussion of cosmos psfs and aperture correction methods . monte carlo simulations were performed using the university of maryland s yorp computing cluster . the observations reported here were obtained at the kitt peak national observatory , national optical astronomy observatory , which is operated by the association of universities for research in astronomy ( aura ) , inc . , under cooperative agreement with the national science foundation . +    bahcall , j.  n. , & salpeter , e.  e.  1965 , , 142 , 1677 bertin , e. , & arnouts , s.  1996 , , 117 , 393 bertin , e. , mellier , y. , radovich , m. , missonnier , g. , didelon , p. , & morin , b.  2002 , astronomical data analysis software and systems xi , 281 , 228 bouwens , r.  j. , illingworth , g.  d. , blakeslee , j.  p. , & franx , m.  2006 , , 653 , 53 bouwens , r.  j. , et al . 2010 , , 725 , 1587 capak , p. , et al . 2011 , , 730 , 68 clment , b. , et al . 2011 , arxiv:1105.4235 cowie , l.  l. , & hu , e.  m.  1998 , , 115 , 1319 cuby , j .- g . , hibon , p. , lidman , c. , le fvre , o. , gilmozzi , r. , moorwood , a. , & van der werf , p.  2007 , , 461 , 911 curtis - 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10 & 35 & 2@xmath5110@xmath84 & 6 & stark+2007 + 8.8 & 6.3@xmath83 & 1.3@xmath5110@xmath84 & 0 & cuby+2007 + 8.96 & 1.12@xmath85 & 6@xmath5110@xmath84 & 0 & sobral+2009 +    ccccccc 1 & 10:00:46.94 & + 02:08:48.84 & 21.87 & 1.21@xmath5110@xmath84 & 8.34@xmath5110@xmath71 & 7.32 + 2 & 10:00:20.52 & + 02:18:50.04 & 22.25 & 8.55@xmath5110@xmath7 & 5.90@xmath5110@xmath71 & 5.17 + 3@xmath86 & 09:59:56.21 & + 02:10:09.84 & 22.31 & 8.09@xmath5110@xmath7 & 5.58@xmath5110@xmath71 & 4.89 + 4 & 10:00:48.79 & + 02:09:21.24 & 22.39 & 8.00@xmath5110@xmath7 & 5.52@xmath5110@xmath71 & 4.84 +","summary":"we present the results of a deep and wide imaging search for ly  emitters in the cosmos field . we have used two ultra - narrowband filters ( filter width of -9  ) on the newfirm camera , installed on the mayall 4 m telescope at kitt peak national observatory , in order to isolate ly  emitters at 7.7 ; such ultra - narrowband imaging searches have proved to be excellent at detecting ly  emitters . we found 5 detections of four candidate ly  emitters in a survey volume of 2.8 x 10 mpc ( total survey area arcmin ) . statistical monte carlo simulations suggest that half of these candidates are real 7.7 targets , and spectroscopic followup will be required to verify the redshift of these candidates .","abstract":"the study of ly  emission in the high - redshift universe is a useful probe of the epoch of reionization , as the ly  line should be attenuated by the intergalactic medium ( igm ) at low to moderate neutral hydrogen fractions . here we present the results of a deep and wide imaging search for ly  emitters in the cosmos field . we have used two ultra - narrowband filters ( filter width of -9  ) on the newfirm camera , installed on the mayall 4 m telescope at kitt peak national observatory , in order to isolate ly  emitters at 7.7 ; such ultra - narrowband imaging searches have proved to be excellent at detecting ly  emitters . we found 5 detections of four candidate ly  emitters in a survey volume of 2.8 x 10 mpc ( total survey area arcmin ) . each candidate has a line flux greater than 8 x 10 erg s . using these results to construct a luminosity function and comparing to previously established ly  luminosity functions at 5.7 and 6.5 , we find no conclusive evidence for evolution of the luminosity function between 5.7 and 7.7 . statistical monte carlo simulations suggest that half of these candidates are real 7.7 targets , and spectroscopic followup will be required to verify the redshift of these candidates . however , our results are consistent with no strong evolution in the neutral hydrogen fraction of the igm between 5.7 and 7.7 , even if only one or two of the 7.7 candidates are spectroscopically confirmed ."}
{"article_id":"astro-ph9809164","section_id":"i","document":"in this paper we investigate some of the difficulties in detecting the effects of neutrino flavor oscillations on the neutrino spectra from type ii supernovae . in particular , we examine what might be learned from different target materials in proposed , long - duration neutrino experiments such as the observatory for multiflavor neutrinos from supernovae ( omnis @xcite ) and the lead astronomical neutrino detector ( land @xcite ) . these detectors would record neutrons spalled from nuclei following inelastic neutrino excitations . while neutrons can be produced in either neutral or charge current interactions , the relative strength of these two contributions is sensitive to target thresholds and charge , and thus can be adjusted through the choice of target material .    in this way sensitivity to neutrino flavor can be achieved . for example , one expects a target with low z and a high charged - current threshold to be characterized by a low @xmath5,e@xmath6 ) cross section , and thus to produce neutrons primarily through neutral current interactions , particularly if the target is also characterized by a low neutron separation threshold . alternatively , a target with a high z , so that coulomb effects enhance the phase space for emitted electrons , and low @xmath5,e@xmath6 ) threshold should have a much stronger response to charge current interactions . the main purpose of this study is to explore what can be achieved with such target strategies , taking into account the considerable uncertainties that exist in our understanding of supernova @xmath0 , @xmath7 and heavy - flavor neutrino spectra . an observation of neutrino flavor transformation , or the demonstration that this phenomena does not occur over some range of neutrino masses and mixing angles , would have important consequences for both particle physics and astrophysics ( for a review see ref . neutrino flavor oscillations arise in extended models in which neutrinos are massive or have magnetic moments , and in which the flavor and mass eigenstates are not coincident . the strength of the flavor mixing can be greatly enhanced in matter , with two familiar examples being spin - flavor precession @xcite and the mikheyev - smirnov - wolfenstein ( msw ) @xcite mechanism , with the latter being the most popular proposed solution of the solar neutrino problem . the deficit of solar neutrinos relative to the predictions of the standard solar model can be explained by @xmath8 or @xmath9 flavor oscillations ( or by an oscillation to a sterile state @xmath10 ) . the favored msw solution for the sun suggests that the mass - squared difference between @xmath0 and the second neutrino involved in the oscillation is @xmath11m@xmath12 ev . if this second neutrino is the @xmath13 , then the seesaw mechanism @xcite predicts a mass hierarchy where the @xmath13 mass @xmath14 few @xmath15 ev and the @xmath16 mass is in or near the cosmologically interesting range , 1 to 100 ev @xcite . this is an attractive scenario as it allows the @xmath16 to be a source of hot dark matter . if neutrino oscillations are responsible for the solar neutrino problem , similar effects should arise for supernova neutrinos . very general arguments lead to a hierarchy of average energies for supernova neutrinos , @xmath17 . this pattern is established near the neutrinosphere ( roughly the surface of the neutron star ) , where the neutrinos decouple from the matter at a density of @xmath18 g @xmath19 . neutrino oscillations can alter this pattern in a distinctive way , producing a characteristic signature in terrestrial supernova detectors , given an msw neutrino mass level crossing outside the neutrinosphere . as the density at the neutrinosphere is 10 orders of magnitude greater than that of the solar core , such crossings occur for an extended range of @xmath20 , where @xmath21 and @xmath22 are the masses of the heavy and light neutrino eigenstates being mixed . the resulting values , @xmath23 ev@xmath24 @xmath25 @xmath26 m@xmath24 @xmath25 @xmath27 ev@xmath24 , encompasses not only the msw solutions discussed in connection with the solar neutrino problem , but also mixing that might be associated with cosmologically interesting tauon neutrino masses . neutrino flavor transformation can also have important consequences for supernova dynamics and nucleosynthesis . after collapse and core bounce , the energy spectra of neutrinos emitted from the neutrino sphere of the cooling proto - neutron star are approximately fermi - dirac , with small chemical potentials . although a crude equipartition of energy between neutrino species is imposed by the weak equilibrium that obtains in the core , the subsequent decoupling of the neutrinos from the matter at the neutrinosphere is flavor dependent and leads to the hierarchy of average energies noted above . the @xmath13 , @xmath28 , @xmath16 , and @xmath29 species decouple deepest in the core because they lack charged current reactions with nucleons and have smaller cross sections for scattering off electrons than the @xmath0 and @xmath30 species . the @xmath0s have the lowest average energy because they are the last to decouple : matter near the neutrinosphere is partially deleptonized and thus rich in neutrons , enhancing @xmath0 + n @xmath31 p + e@xmath6 . for example , in one study the @xmath13 , @xmath28 , @xmath16 , and @xmath29 have average energies @xmath32 , while the electron neutrinos and antineutrinos have energies @xmath33 and @xmath34 @xcite . neutrinos may be responsible for the revival of the supernova shock wave , which stalls in most numerical simulations at a radius of around 200 - 400 km above the surface of the protoneutron star shortly after core bounce , @xmath35 0.1 s. neutrino interactions in the nucleon gas left in the wake of the shock wave can deposit considerable energy , providing the push needed for a successful explosion . oscillations can enhance this effect : if a @xmath36 oscillation took place between the edge of the neutron star and the stalled shock at this epoch , the resulting more energetic @xmath0 flux increases the rate of neutrino heating @xcite . neutrino flavor oscillations can also alter supernova nucleosynthesis at later times @xmath37 @xcite . terrestrial experiments exploiting accelerator or reactor neutrino sources , such as lampf s liquid scintillator neutrino detector ( lsnd @xcite ) and the cern experiments nomad @xcite and chorus @xcite , are placing constraints on vacuum oscillations . to date , no evidence for @xmath38 mixing has been found at nomad or chorus . lsnd has attributed an excess of events above background to @xmath39 , although these events have also been interpreted as an upper limit @xcite . the karmen @xcite experiment , which is similar to lsnd in its sensitivity to @xmath26m@xmath24 and mixing angle , has not yet accumulated enough data to convincingly confirm or rule out the lsnd result . but perhaps the strongest indication of oscillations comes from the deficit of muons in the interactions of upward going atmospheric neutrinos , as recently reported by the superkamiokande collaboration @xcite . the solar neutrino problem , atmospheric neutrino anomaly , and lsnd results all suggest new physics , though all of these anomalies together are difficult to reconcile with a simple pattern of neutrino masses and mixing angles arising in theories with only three active neutrinos @xcite . important new constraints on neutrino properties can be extracted from observations of supernova neutrinos . one technique for measuring neutrino mass , independent of mixing angles , exploits the time delay and/or spreading in the neutrino signal ( see for example ref . the arrival time difference for @xmath0 and @xmath16 neutrinos with masses @xmath40 and @xmath41 , respectively , is @xmath42,\\ ] ] where @xmath43 and @xmath44 are the energies of the tauon and electron neutrinos , @xmath45 is the distance to the supernova in 10 kiloparsecs ( comparable to the galactic radius ) , and @xmath46 is measured in seconds . ( alternatively , one can rewrite eq . ( 1 ) for a single flavor , but with arrival times dependent on the neutrino energy . ) the result is a characteristic spreading of the neutrino pulse , with arrival times correlated with the neutrino energy and/or flavor . neutrino masses , or limits on masses , can be deduced by comparing an observed neutrino signal with the spectra and time - dependent luminosities arising in plausible supernova models . measurements made by kamiokande and imb at the time of sn1987a were argued to provide a limit on the @xmath30 mass . the analysis were limited by the small number of detected neutrino events and by uncertainties in modeling the supernova mechanism and associated neutrino emission @xcite . as a result , the deduced limits span a considerable range . clearly such astrophysical uncertainties will also affect future time - of - flight neutrino mass limits derived from new detectors like omnis and land . yet these detectors should have two important advantages . first , they promise a large number of neutrino events for a galactic supernova , possibly giving us a detailed time history of neutrino emission associated with the supernova . for example , it was recently argued that large event rates would allow experimentalists to map out the expected initial sharp rise in neutrino emission following core bounce , a feature in the neutrino cooling curve that could be exploited to significantly tighten mass limits @xcite . second , complimentary information from other new detectors , such as superkamiokande @xcite , will reduce the degree to which analyses must depend on poorly understood aspects of supernova models . the spectrum and flavor of supernova neutrinos will be more accurately characterized given a complement of detectors with different thresholds and flavor sensitivities . flavor specificity in time - of - flight measurements is quite important because competing laboratory limits on the @xmath16 and @xmath13 masses , 24 mev and 170 kev , respectively , are so poor . if neutrinos mix , supernovae could provide an important consistency check on models of neutrino masses and also possibly on time of flight derived neutrino masses . flavor oscillations , enhanced by matter effects , can lead to transformation between @xmath0 s and either the @xmath13 or @xmath16 , leading to an anomalously energetic @xmath0 spectrum . this departure from the usual hierarchy of average neutrino energies is a powerful test for new physics because it will occur for an extended range of @xmath26m@xmath24 and mixing angles . in fact , the neutrino mass level crossings become increasingly adiabatic for larger @xmath26m@xmath24 , with adiabatic flavor transformation occurring for mixing angles sin@xmath47 . thus the observation of an excess of supernova @xmath0 events provides an opportunity to probe neutrino phenomena that may be inaccessible otherwise . several detectors , both in operation and proposed , could detect neutrinos from a galactic supernova . ( a partial review can be found in @xcite . ) two of particular note are the light water cerenkov detector superkamiokande , which has an inner fiducial volume of 22.5 kilotons and has been in operation for approximately two years ; and the sudbury neutrino observatory @xcite , a heavy water cerenkov detector whose inner vessel will contain one kiloton of d@xmath48o . sno is currently in its commissioning phase and should be fully operational by the end of 1998 . in sno charged and neutral current reactions will produce distinct signals . the neutral current neutrino reaction d@xmath49np produces free neutrons . these will be detected either by their ( n,@xmath50 ) reactions on @xmath3cl , which will be introduced by dissolving salt in the water , or by their interactions in specially designed counters utilizing the @xmath51he(n , p ) reaction . the charged current reaction d(@xmath0,e@xmath6)pp produces energetic electrons that will be observed through cerenkov light . ( the absence of coincident neutrons distinguishes this reaction from d(@xmath30,e@xmath52)nn . ) a supernova neutrino burst altered by @xmath53 oscillations will produce an enhanced ( @xmath0,e@xmath6 ) signal , while leaving the rest unchanged . superkamiokande is of particular interest because of its size and its likely longevity : the collaboration hopes to operate the detector for three decades , a period approaching the timescale for galactic supernova . however the enormous event rate for ( @xmath30,e@xmath52 ) off free protons tends to obscure , in the case of flavor oscillations , the @xmath0 signal of interest . perhaps the best opportunity for measuring the @xmath0 s is through the reaction @xmath54o(@xmath0,e@xmath6 ) , which produces a back - angle enhancement in the electron distribution that will distort the known ( and nearly isotropic ) distribution from ( @xmath55,e@xmath52 ) @xcite . in contrast , the flavor oscillation effects on the forward - peaked events from @xmath56-electron scattering are very subtle and difficult to extract . this cross section is approximately linear in the neutrino energy and so there is no net change in the event rate due to flavor oscillations . the event rate is then proportional to the luminosity , which we noted earlier was approximately independent of flavor . note that this contrasts with semileptonic interactions , where cross sections scale as e@xmath57 or faster , depending on nuclear thresholds . yet there is a shift in the distribution of forward - peaked events towards higher energy from neutrino - electron scattering . this is because the @xmath0-electron cross section is approximately six times that the cross section for heavy flavor neutrinos . in turn , this effect may provide a signal for flavor oscillations @xcite . another interesting possibility , suggested quite recently @xcite , is the detection of the 5 - 10 mev @xmath50 rays produced in cascades following the neutral current breakup of @xmath54o . a supernova at a distance of 10 kpc would produce a few hundred such events from @xmath13 and @xmath16 interactions in superkamiokande . a tauon mass could then be extracted from analysis of the time evolution of the signal @xcite . one of the arguments for detectors such as omnis and land is that they could remain in operation over a long period of time , making the probability of observing a galactic supernova reasonably high . these detectors would record neutrons produced in the neutral current breakup of nuclei , @xmath58 where @xmath59 represents all neutrino and antineutrino species . here ( z , n ) denotes a nucleus with z protons and n neutrons . a similar signal can arise for the analogous charged current reactions @xmath60 and @xmath61    by itself , the observation of a neutron in omnis or land provides no information on the type of initiating neutrino reaction . the goals of this paper include calculating the cross sections and spallation probabilities for these detectors more carefully than has been attempted before ; exploring to what extent the use of multiple nuclear targets might enhance flavor sensitivity ; and exploring what can be learned by comparing the rates for one and two neutron spallation . ideally one would hope to find targets with very different relative sensitivities to @xmath0 and neutral current reactions . the success of such a strategy clearly depends on our ability to accurately calculate ( or measure ) the neutrino responses of the targets , and to estimate uncertainties in supernova flux predictions . in section [ sec : neutphys ] we discuss neutrino - induced neutron spallation in both high z and low z target materials , describing the underlying nuclear structure physics governing the responses . we also provide estimates of cross sections for four possible target materials , @xmath1be , @xmath2na , @xmath3cl and @xmath4pb . in section [ sec : detect ] we discuss strategies for determining whether the neutrino flux has been altered by oscillations . although our study is by no means exhaustive , it appears that the tactic of looking for changes in total spallation cross sections is rather challenging . it is very difficult , even using multiple targets , to achieve the necessary degree of sensitivity to the @xmath0 temperature . the primary difficultly is our uncertain knowledge of the spectrum of supernova neutrinos in the absence of oscillations . the one exception we found to this general rule is the two neutron spallation channel in @xmath4pb , which appear to provide an exquisitely sensitive @xmath0 thermometer . the underlying physics involves the first - forbidden contributions to the charged and neutral current channels which have not been considered previously . we suggest some experimental work that would help in characterizing the @xmath4pb response to neutrinos .","summary":"this is because matter enhanced neutrino oscillations can lead to an anomalously hot spectrum , and thus to enhanced charged current cross sections in terrestrial detectors . two recently proposed supernova neutrino observatories , omnis and land , will detect neutrons spalled from target nuclei by neutral and charged current neutrino interactions . as we find that strategies for detecting oscillations which use only neutron count rates are problematic at best , even if cross sections are determined by ancillary experiments . plausible uncertainties in supernova neutrino spectra tend to obscure rate enhancements due to oscillations . however , in the case ofpb , a signal emerges that is largely flavor specific and extraordinarily sensitive to the temperature , the emission of two neutrons . this signal and its flavor specificity are associated with the strength and location of the first - forbidden responses for neutral and charge current reactions , aspects of thepb neutrino cross section that have not been discussed previously . hadronic spin transfer experiments might be helpful in confirming some of the nuclear structure physics underlying our conclusions .","abstract":"the neutrinos from a type ii supernova provide perhaps our best opportunity to probe cosmologically interesting muon and/or tauon neutrino masses . this is because matter enhanced neutrino oscillations can lead to an anomalously hot spectrum , and thus to enhanced charged current cross sections in terrestrial detectors . two recently proposed supernova neutrino observatories , omnis and land , will detect neutrons spalled from target nuclei by neutral and charged current neutrino interactions . as this signal is not flavor specific , it is not immediately clear whether a convincing neutrino oscillation signal can be extracted from such experiments . to address this issue we examine the responses of a series of possible light and heavy mass targets ,be ,na ,cl , andpb . we find that strategies for detecting oscillations which use only neutron count rates are problematic at best , even if cross sections are determined by ancillary experiments . plausible uncertainties in supernova neutrino spectra tend to obscure rate enhancements due to oscillations . however , in the case ofpb , a signal emerges that is largely flavor specific and extraordinarily sensitive to the temperature , the emission of two neutrons . this signal and its flavor specificity are associated with the strength and location of the first - forbidden responses for neutral and charge current reactions , aspects of thepb neutrino cross section that have not been discussed previously . hadronic spin transfer experiments might be helpful in confirming some of the nuclear structure physics underlying our conclusions ."}
{"article_id":"astro-ph9809164","section_id":"r","document":"in this section we will discuss event rates and possible strategies for land , omnis , and similar neutron spallation supernova neutrino observatories . the calculations presented in the previous section were performed for specific isotopes of the materials that have been proposed for these targets . for example , @xmath4pb comprises slightly more than half of natural lead , while @xmath3cl and @xmath2na comprise 75% and 100% of natural chlorine and sodium , respectively . ( one of the proposed target material in omnis in salt . ) therefore a simplification we make is to treat these target materials as being composed of the principal isotopes . given that we are concerned with neutrino spectrum uncertainties that can change rates by factors of @xmath14 3 , more detailed modeling is difficult to justify . in the case of pb , the responses are governed by sum rules proportional to n - z or nz / a , quantities that vary little from a=208 to a=206 , for example . for chlorine one anticipates that our charged current allowed cross sections will be a bit low , given that the ignored isotope @xmath154cl has n - z=3 and is more neutron rich than @xmath3cl . interest has been expressed in @xmath1be because its neutron emission thresholds are so low @xcite . in some sense it can be viewed as a neutron target . its inclusion is also interesting as a theory benchmark , since full shell model calculations satisfying both the allowed and first - forbidden sum rules could be performed . there is general consistency among the first - forbidden responses in table i for @xmath1be , @xmath2na , and @xmath3cl , even though the last two were evaluated in the somewhat schematic goldhaber - teller model .    because of urgent issues such as a cosmologically interesting muon and/or tauon neutrino mass , proposed supernova neutrino observatories have as their goal the observation of at least the entire galaxy . thus a typical horizon for such detectors is on the order of the galactic radius , @xmath14 10 kpc . we begin by expressing the neutrino fluence at earth normed to such a galactic distance . the total number fluence of a given neutrino species ( e.g. , @xmath0 , @xmath155 , @xmath13 , etc . ) is @xmath156 assuming a total energy in neutrinos of 3 @xmath157 ergs , and an equipartition of energy among the six neutrino species , results consistent with most transport calculations ( see , e.g. , ref . @xcite ) . the exact distribution of energy among the neutrino species will be an additional source of error , but considerably smaller then that associated with the uncertain spectral distribution . the distance to the supernova , @xmath158 , is given here in units of 10 kiloparsecs . as a consequence of the equipartition of energy , a neutrino species characterized by a lower average energy will have a higher fluence than one with higher average energy . all of our detector event totals will be calculated with this standard fluence ; results for other distances and total explosion energies can be obtained by appropriately scaling to eq . [ eq : flux ] .    in table iii we present the resulting neutron ( and multiple neutron pb ) supernova events , summed over flavor , for one - tonne pb , nacl , and be targets , given our assumed normalized neutrino fluence of eq . [ eq : flux ] for a standard distance of 10 kpc . in the case of neutral current interactions , total inelastic cross sections of these targets ( that is , summed over all subsequent decay channels ) are not very different when quoted per target mass ( or per nucleon ) : values are within a factor of two of 1.2 @xmath159 cm@xmath24 per nucleon for e@xmath160 25 mev . this is consistent with naive expectations . the forbidden contributions are significant and scale , according to the thomas - reiche - kuhn sum rule , approximately as a. targets are distinguished , however , by the ease with which they emit neutrons . in the case of @xmath3cl and @xmath2na , the greater phase space for proton emission tends to dominate over coulomb effects , leading to neutral current neutron spallation probabilities of only @xmath14 10% . but @xmath4pb and @xmath1be are more favorable cases , the former because of inhibiting coulomb barriers and the latter because of an exceptionally low threshold for neutron emission . thus neutron emission is the dominant decay channel for pb and be , producing about an order of magnitude more signal than in a salt detector of equal mass . while the neutron yield is important in efforts to constrain neutrino masses kinematically , flavor specificity may be more crucial in @xmath161 oscillation tests . that is , does an anomalously hot @xmath0 spectrum produce a distinctive signal in a detector ? a salt detector , unfortunately , remains problematic . such an oscillation raises the charged current cross section from an insignificant level to a value comparable to the neutral current cross section summed over flavors . but the @xmath162 reaction moves one to the proton - rich side of the parent nucleus , yielding neutron spallation probabilities of at most a few percent . the net result is that the oscillation - induced change in total neutron events is quite modest , and would be obscured by existing uncertainties in heavy flavor spectra . to illustrate this point , in figure 1 we plot neutron events with and without oscillations . in each case there is a band of values corresponding to the range of spectrum choices used in tables i and ii , reflecting existing uncertainties in our knowledge of the neutrino spectra . as the bands , with and without oscillations , overlap substantially , it is clear that neutrino spectral uncertainties will obscure plausible oscillation - induced enhancements of the charged current events . the @xmath1be case is somewhat different . the neutron yields following @xmath162 are exceptionally small , regardless of oscillations . the reaction @xmath163 has a small cross section but a high neutron yield per reaction ; but even in the event of antineutrino oscillations , the effect on the total yield ( neutral and charged , summed over flavor ) is about 10% . thus @xmath1be is a relatively clean neutral current detector . this property of a @xmath1be target suggests the possibility of reducing spectral uncertainties by comparing ratios of rates for different nuclear targets . given that @xmath1be measures the neutral current response and has perhaps the most easily calculable cross section , it can be considered a monitor of the heavy flavor temperature : the neutral current rate is not altered by oscillations . thus , by comparing the event rate in a target with a strong charged current response to that of @xmath1be , one might hope to remove much of the uncertainty associated with unknown aspects of the @xmath16 and @xmath13 spectra . studies of ratios of events might also prove helpful if the distance to the supernova were not known . superficially this sounds quite attractive as the heavy flavor spectrum also determines the enhanced charged current response following oscillations .    to address this issue more quantitatively , we calculated the ratio of the nacl events to be events with and without oscillations . all neutron - producing channels are included , and the heavy flavor , @xmath0 , and @xmath155 spectra are allowed to vary over the ranges in tables i and ii . the resulting ranges for the ratios , which are narrower than those of figure 1 , are shown in figure 2 . while this strategy clearly has helped in reducing sensitivity to variation in the spectra , there remain additional uncertainties that affect the ratio , particularly cross section uncertainties . the extended cross section error bars shown in figure 2 result from combining a @xmath112 50% uncertainty in the cross section for each target material ( be and nacl ) . we regard such an uncertainty as an optimistic guess for what might be achievable , given additional work . it appears to us that a definitive claim of oscillations would be difficult to make in a salt detector , even given a normalizing target such as @xmath1be . the situation is much improved for a pb detector . the first effect apparent from table i is the exceptionally strong @xmath162 cross section , a result primarily of the coulomb enhancement of the cross section . as a result , transmutation of @xmath16 s to @xmath0 s would increase the number of neutron events by a factor of four , as mentioned previously . thus the comparisons in figures 1 and 2 are much more favorable . even more exciting , of course , in the flavor specificity provided by multiple neutron events . the results for multiple neutron events are shown separately in figures 1 and 2 . the enhancement resulting from a complete conversion of @xmath16 s to @xmath0 s is so large , a factor of 40 , that it could not be attributed to spectral uncertainties . we conclude that the ability to identify multiple neutron events with high efficiency in a pb detector could be of great importance . perhaps the most important nuclear structure assumption in the pb calculations is the placement of the spin - flip dipole strength for neutral current excitation at the position of the measured e1 resonance : this leads to the weak neutral current production of multiple neutrons . presumably the location of the dipole spin - flip strength could checked by spin transfer ( p , p ) measurements . if this strength were located substantially above the e1 giant resonance , our conclusions would have to be reexamined . these arguments for finding a signature for neutrino flavor transformation have been based on the assumption that the energy spectrum for one type of neutrino species ( the electron neutrino ) is completely transformed into that of another ( the mu or tau neutrino ) ; i.e. , that neutrino flavor evolution through resonances is adiabatic over a broad range of neutrino energies that includes high energies . for the msw mechanism this will only occur if the density gradient is sufficiently small in the resonance regions , where the transformation takes place . ignoring neutrino background effects ( that is , ignoring neutrino - neutrino neutral current forward exchange scattering contributions to the neutrino effective mass @xcite ) , this condition on the vacuum mixing angle for adiabatic evolution may be expressed as @xcite , @xmath164 where @xmath165 is the density scale height at the resonance position . here @xmath166 is the matter density of material at the resonance position . again , this expression for @xmath167 ignores neutrino background effects . the magnitude of the neutrino - neutrino forward scattering effects is discussed in ref.s @xcite . for a neutrino energy @xmath67 and mixing parameters @xmath168 and @xmath169 the resonance density is @xmath170 where @xmath171 is the electron fraction . the relevant densities in the supernova range from @xmath172 at the surface of the the neutron star to @xmath173 in the hydrogen envelope . therefore , for small mixing angle , flavor transformation can occur for a range of @xmath168 of @xmath174 to @xmath175 . the most stringent condition on the mixing angle comes from the outer edges of the supernova . taking densities from woosley et al . @xcite , at this location we find a condition on the mixing angle of @xmath176 , from eq . ( 25 ) . for higher densities , the adiabatic condition gives a less stringent limit . this range of masses and mixings that would be observable in a supernova includes the popular small - angle msw solution to the solar neutrino problem . this solution has a mass squared difference , @xmath177 , see for example @xcite , and can occur either through transformation between @xmath150 , @xmath178 or between @xmath179 . in the first case , a similar crossing would occur in the supernova at a similar density , if on the other hand , if this transformation occurs by @xmath178 , then the seesaw mechanism would predict a @xmath16 mass of 2 - 100 ev @xcite . this would necessitate a @xmath36 level crossing at high density @xmath181 , or around @xmath182 . there is then an additional @xmath178 crossing at lower density , given a standard mass hierarchy . although this latter scenario presents a more complicated picture of the neutrino transformations occurring in the supernova , the effect in terms of neutron count rates seen in the detector is exactly the same . therefore , either of these proposed msw solutions to the solar neutrino problem would imply the presence of matter enhanced neutrino oscillations in the post - core - bounce supernova . finding a signature of matter enhanced neutrino oscillations in a supernova neutrino detector would provide a completely independent check of this solar solution . and if the solar neutrino problem proved to have some other origin , the wider range of mass differences and mixing angles accessible to supernova neutrino experiments keeps possibilities open for new physics to emerge there . finally , we should stress that our primary focus in this paper has been on a specific issue , that of finding a signal for flavor oscillations , including those of the @xmath16 . the selection of one target material over another would have to take into account many other issues , e.g. , their comparative utility in testing the spreading of neutrino arrival times due to kinematic effects of neutrino masses . target materials will vary in cost , in ease of neutron detection , and in ambient backgrounds . our efforts have been directed toward improved event rate estimates and questions of flavor specificity , in the hope that this information will help experimentalists make optimal choices . d. b. cline _ et . _ , astrophysical letters and communications , * 27 * , 403 , 1990 . d. b. cline _ et . al . _ , phys . d * 50 * , 720 ( 1994 ) , p. f. smith , astroparticle physics , * 8 * 27 ( 1997 ) . c. k. hargrove _ et . al . _ , astroparticle physics , * 5 * , 183 ( 1996 ) . b. balantekin , proceedings of the jorge andre swieca summer school , campos de jordao , sao paulo , in press , ( 1997 ) . c. s. lim and w. j. marciano , phys . d. * 37 * , 1368 ( 1988 ) ; 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the next three are appropriate for @xmath155s with @xmath139 @xmath14 16 mev ; and the last three correspond to @xmath0s with @xmath144 11 . cross sections are given for each spectrum so that arbitrary oscillation scenarios can be explored . [ cols=\"^,^,^,^,^,^,^,^,^,^,^ \" , ]","summary":"the neutrinos from a type ii supernova provide perhaps our best opportunity to probe cosmologically interesting muon and/or tauon neutrino masses . this signal is not flavor specific , it is not immediately clear whether a convincing neutrino oscillation signal can be extracted from such experiments . to address this issue we examine the responses of a series of possible light and heavy mass targets ,be ,na ,cl , andpb .","abstract":"the neutrinos from a type ii supernova provide perhaps our best opportunity to probe cosmologically interesting muon and/or tauon neutrino masses . this is because matter enhanced neutrino oscillations can lead to an anomalously hot spectrum , and thus to enhanced charged current cross sections in terrestrial detectors . two recently proposed supernova neutrino observatories , omnis and land , will detect neutrons spalled from target nuclei by neutral and charged current neutrino interactions . as this signal is not flavor specific , it is not immediately clear whether a convincing neutrino oscillation signal can be extracted from such experiments . to address this issue we examine the responses of a series of possible light and heavy mass targets ,be ,na ,cl , andpb . we find that strategies for detecting oscillations which use only neutron count rates are problematic at best , even if cross sections are determined by ancillary experiments . plausible uncertainties in supernova neutrino spectra tend to obscure rate enhancements due to oscillations . however , in the case ofpb , a signal emerges that is largely flavor specific and extraordinarily sensitive to the temperature , the emission of two neutrons . this signal and its flavor specificity are associated with the strength and location of the first - forbidden responses for neutral and charge current reactions , aspects of thepb neutrino cross section that have not been discussed previously . hadronic spin transfer experiments might be helpful in confirming some of the nuclear structure physics underlying our conclusions ."}
{"article_id":"cond-mat9912097","section_id":"i","document":"interest in utilizing the `` colossal magnetoresistance '' ( cmr ) effect has resulted in enormous literature , which spans properties of manganites at numerous compositions , ceramic and crystals , crystalline films on different substrates , stoichiometric and not ( for extensive review see @xcite ) . nevertheless , until recently , it was somewhat difficult to establish systematic trends which govern the physical properties of these materials ( especially their low temperature behavior ) , to access peculiarities pertinent to the ground state and its dependence on composition . as for the overall behavior , especially for the high temperature properties , which are responsible for the cmr phenomena itself , the consensus is that the zener s double exchange ( de ) mechanism @xcite together with the jahn - teller ( jt ) effect for mn@xmath7 as suggested in @xcite produce the basis for their understanding . high temperature lattice deformations localize carriers by a formation of the jt or local polarons @xcite . with temperature decrease , de mechanism delocalizes carriers and result in simultaneous onset of metallic conductivity and half - metallic ferromagnetic state . the physical picture , is by all means correct , but the method , introduced in @xcite , is not sufficient for understanding delicate qualitative features , especially at the low temperatures .    as an important issue , we have to mention , is the evolution of ground state for the doped manganites from the insulating antiferromagnetic state of lamno@xmath2 to the pronounced metallic ferromagnetic one in la@xmath0sr@xmath8mno@xmath2 at @xmath9 .    it has been demonstrated first in our short paper @xcite that both the half - metallic state at finite concentrations and the insulating state of the parent lamno@xmath2 can be brought together by making use of a simple band model . parent lamno@xmath2 is considered in that scheme as a band insulator . as for the doping process , it has been shown in @xcite , that it leads to the percolative scenario , producing the well defined threshold concentration @xmath10 for the onset of low - temperature metallic conductivity .    in the presentation below we describe in more details and further elaborate the theory , proposed by gorkov and kresin , keeping in mind both some future applications and analysis of available experimental data at @xmath11 is also provided . it is shown that the two bands theory agrees reasonably well with the results of recent experiments , demonstrating applicability of the fermi liquid approach to the metallic manganites . the scheme serves as a theory unifying rather rich low temperature properties of manganites and is capable of some predictions regarding the evolution of physical parameters , the shape of the fermi surface etc . with concentration . the experimental data show also the consistency with our results in the metallic concentration range and trace remaining percolation features . the paper is written as follows . in sec . ii the main features are identified and accounted in hamiltonian . iii contains the energy spectrum and its dependence on a spin ordering or jt - deformations . properties of a stoichiometric compound lamno@xmath2 , treated as a band insulator , are considered in sec . growth of the percolative regime for the phase separation and the critical composition for onset of metallic conduction are discussed in sec . v. sec . vi contains a summary of major metallic properties calculated in the framework of the two band model , while in sec . vii a comparison with available experimental data is discussed . viii contains brief summary and conclusions .","summary":"the phase diagram and low temperature properties of the doped manganites abmno are discussed for the concentrations . the transition from insulating antiferromagnetic to metallic ferromagnetic state at is treated by means of percolation theory . the unifying description of insulating and metallic states is presented . the behavior of conductivity , spin wave excitations , etc . is analyzed and the comparison with experimental data is carried out .","abstract":"the phase diagram and low temperature properties of the doped manganites abmno are discussed for the concentrations . the transition from insulating antiferromagnetic to metallic ferromagnetic state at is treated by means of percolation theory . the unifying description of insulating and metallic states is presented . the undoped manganite is a band insulator consisting of ferromagnetic layers , which are coupled antiferromagnetically along the direction with a low nel temperature . the metallic phase can be described by the two - band fermi liquid picture . the behavior of conductivity , spin wave excitations , etc . is analyzed and the comparison with experimental data is carried out ."}
{"article_id":"cond-mat9912097","section_id":"c","document":"we have discussed above two major issues in doped manganites : 1 .  the concept of percolation , leading , as it was first predicted in @xcite , to the new understanding of the phenomena related to the phase separation , which takes place in these materials at low enough concentrations;2 .  the possibility to interpret some low temperature data in the habitual band ( or fermi liquid ) picture . the latter makes possible to suggest an unifying view which circumvent the often raised concerns regarding the role of strong interactions , importance of which is commonly expected in the transition metal oxides @xcite . the fermi liquid approach is a selfconsistent theory , which of course , may be broken at strong interactions . the only way to justify the fermi liquid approach is to see whether the experimental results do fit the theory predictions or not . as it was shown above , the theory works reasonably well at @xmath107 and at @xmath9 for @xmath359 , probably because the @xmath360 mechanism results in rather effective de - localization while the jt - effect partially takes care of the coulomb interaction . in the intermediate regime with respect to @xmath84 , the tendency towards the phase segregation turns out to have a percolative character and , therefore , theoretical analysis becomes much more complicated . the question whether the samples quality is an intrinsic property or may be further improved , seems to be of principle importance . experience with lsmo materials @xcite implies that attempts made to improve the crystals quality are worth of trying . already the lsmo samples with @xmath361 are encouraging , being reasonably close to the possibility of studying metallic manganites by methods traditional to the normal physics of metals , including the possibility of the de haas - van alphen studies in fields of the order of @xmath362 tesla . l.p.g . and v.z.k . gratefully acknowledge h.d . drew , t. egami , j. lynn , s. von molnar for numerous stimulating discussions . the work was supported ( l.p.g . and m.o.d . ) by the national high magnetic field laboratory through nsf cooperative agreement # dmr-9527035 and the state of florida . j. h. jung , k. h. kim , t. w. noh , e. j. choi , jaejun yu , phys . b * 57 * , r11043 ( 1998 ) ; y. okimoto , t. katsufuji , t. ishikawa , a. urushibara , t. arima and y. tokura , phys . rev . lett . * 75 * 109 ( 1995 ) and referencies therein .                                                                                           + * fig . 1 * in - plane staggered distortions inside the ferromagnetic layer . solid segmenets represent the elongations of octahedra . the new unit cell is shown as the dashed square . + * fig . 2 * the fermi level , e(x ) , dos , @xmath291 , the spin stiffness coefficient d(x ) and the drude conductivity , @xmath363 , plotted as a function of concentration , x , for the spectrum , given in @xcite . the shaded area shows the percolative regime where eqs . ( 37 - 46 ) are not applicable . + * fig . 3 * the fermi surface a ) x=0.2 ; b ) x=0.3 ; c ) x=0.5 .","summary":"the metallic phase can be described by the two - band fermi liquid picture .","abstract":"the phase diagram and low temperature properties of the doped manganites abmno are discussed for the concentrations . the transition from insulating antiferromagnetic to metallic ferromagnetic state at is treated by means of percolation theory . the unifying description of insulating and metallic states is presented . the undoped manganite is a band insulator consisting of ferromagnetic layers , which are coupled antiferromagnetically along the direction with a low nel temperature . the metallic phase can be described by the two - band fermi liquid picture . the behavior of conductivity , spin wave excitations , etc . is analyzed and the comparison with experimental data is carried out ."}
{"article_id":"1703.03137","section_id":"i","document":"turbulent thermal convection plays very important role in a range of phenomena in astrophysical and geophysical systems , where the underlying surfaces over which convective turbulence occurs are always rough . as an idealised model for the study of turbulent thermal convection in general , turbulent rayleigh - bnard convection ( rbc ) , where a fluid layer confined between two horizontally parallel plates heated from below and cooled from above , has been studied extensively in the past two decades ( for reviews , see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in terms of equations of motion , there are two control parameters in rbc , i.e. the rayleigh number @xmath8 and the prandtl number @xmath9 , where @xmath10 is the applied temperature difference across a fluid layer of height @xmath11 , @xmath12 is the gravitational acceleration constant and @xmath5 , @xmath13 and @xmath14 are respectively the thermal expansion coefficient , the thermal diffusivity and the kinematic viscosity of the working fluid . any laboratory convection experiments are confined , thus the aspect ratio @xmath15 and the container shape come into the problem . one of the central issues in the study of turbulent rbc is to determine how the response parameters , i.e. the nusselt number @xmath4 and the reynolds number @xmath6 , depend on the control parameters , where @xmath4 is a measurement of the system s heat transport efficiency and @xmath6 quantifies the turbulence intensity . the functional forms of @xmath16 and @xmath17 are usually expressed in terms of power laws : @xmath18 a comprehensive review on this issue can be found in @xcite . it is now generally accepted that there are multiple scalings in the @xmath19 phase space where the bulk flow is in a turbulent state according to the grossmann and lohse model for turbulent thermal convection @xcite .    besides its fundamental importance in geophysical and astrophysical problems , turbulent thermal convection over rough surfaces is found to be a more effective way to transport heat , which is also useful in practical applications . heat transport enhancement is observed when the top and bottom plates are rough and the thermal boundary layer ( bl ) is thinner than the roughness height @xcite . the enhancement is later found to be due to more thermal plumes being emitted from the tip of the roughness elements @xcite . although the heat transport is enhanced , the scaling relation between @xmath4 and @xmath7 is found to be insensitive to the plate morphology @xcite . several later experiments show that the scaling exponents also change in convection cells with rough plates ( rough cells hereafter ) when compared with observations in convection cells with smooth plates ( smooth cells hereafter ) . using glass spheres adhered to the bottom plate of the convection cell , the scaling exponent is found to depend on the distribution of the roughness height @xcite . for @xmath20 , a scaling exponent of @xmath21 is reported when grooved roughness is distributed on both the plates and sidewall of the convection cell @xcite . a change of the scaling exponent from 0.28 in a smooth cell to 0.35 in a rough cell is observed @xcite . the rough cell used in the experiments of @xcite had similar design with the ones used in @xcite and @xcite.these authors have suggested that the discrepancy between their experiments and those of @xcite and @xcite may be attributed to the different constructions and materials of the rough plates . in the earlier experiments , rough plates made of brass were attached on the surfaces the top and bottom smooth plates . while in the later experiment , the roughness elements were directly machined on a piece of copper . in addition to studying the global transport properties of the convection cell , the heat transport properties of individual plates with rough / smooth surfaces were also investigated @xcite . it is found that heat transport property of individual plate differs significantly and depends on the nature of the opposite plate of the same convection cell and the pertaining temperature boundary conditions . by determining the @xmath4 separately for the bottom rough plate and the top smooth plate , a scaling exponent of 1/2 for the rough plate and of 1/3 for the smooth plate are reported @xcite . the effects of roughness elements on the local dynamics of turbulent rbc are also studied . using flow visualization and near - wall temperature measurements , it is shown that the interaction of the large - scale circulation ( lsc ) and the secondary flow in the grooved region of the rough plate enhances plume emission which leads to the enhancement of heat transport @xcite . the study of local temperature fluctuations suggest that the enhancement of heat transport is determined by the dynamics in the near plate region @xcite . the effects of rough plates on the velocity bl have been investigated very recently @xcite , where it is found that the flow field is very different before and after the heat transport enhancement transition . direct numerical simulations ( dnss ) of turbulent rbc in rough cells also show that the scaling exponent increases @xcite . the scaling exponent @xmath5 increases to 0.37 in a rough cell with grooved walls at the top and bottom plates when compared with the smooth cell @xcite . the scaling exponent was also found to depend on the geometry of the roughness elements or  obstacles \" in a quasi-2-d dns @xcite . but the number of roughness elements in this study is very limited ( only 4  obstacles \" are used ) . in a 2-d study , using sinusoidal rough elements , the scaling exponent @xmath5 is also found to depend on the wavelength of the roughness elements @xcite . in a dns study of turbulent taylor - couette flow the scaling exponent is also found to increase with wall - roughness @xcite . these numerical studies imply the importance of roughness geometry on turbulent transport . however , the limited number of roughness element in a 3-d or a ( quasi- ) 2-d computation domain makes the comparison between the dns studies and experimental ones less straightforward . although there are quite a number of previous experiments studying the effect of roughness on turbulent rbc , to the best of our knowledge no experimental study has been made to systematically varying roughness geometry . this motivates the present study in which the effects of roughness geometry on turbulent rbc have been investigated by systematically varying the roughness geometry . a parameter @xmath0 which is defined as the height of a single roughness element over its base width is used to characterise the geometry of roughness elements . in addition to heat transport enhancement as found by previous studies , we find that the heat transport scaling in a rough cell with fixed roughness height @xmath22 may be classified into three regimes . the experiments further show that @xmath0 can be used as a tuning parameter to manipulate heat transport scaling in rough cells in the heat transport enhanced regime . the reynolds number and local temperature fluctuation scalings with @xmath7 also change with @xmath0 , suggesting that the geometry of roughness elements not only alters the global heat transport of the system but also influences the bulk turbulence and the dynamics of the lsc . the remainder of the paper is organised as follows : the experimental setup and measurement techniques are introduced in  [ sec_setup ] which is divided into four subsections . the construction of the convection cell is described in  [ subsec_cell ] . the properties of the working fluids used and the explored @xmath19 phase space are introduced in  [ subsec_fluid ] . the temperature measurement techniques are documented in  [ subsec_temp ] , and  [ subsec_piv ] introduces the measurement of the viscous bl using particle image velocimetry ( piv ) .  [ sec_results ] presents the experimental findings . the heat transport measurements for different values of @xmath0 are reported in  [ subsec : nu ] . the transitions between different heat transport regimes are discussed in  [ subsec_transition ] . the reynolds number and local temperature fluctuation measurements are presented in  [ subsec_re ] and  [ subsec_temp_fluc ] , respectively . a discussion of the proper parameter that characterises the system is reported in  [ subsec_con_para ] before we summarise and conclude our findings in  [ sec_con ] .","summary":"we present a systematic investigation of the effects of roughness geometry on turbulent rayleigh - bnard convection ( rbc ) over rough plates with pyramid - shaped and periodically distributed roughness elements . using a parameter defined as the height of a roughness element over its base width , the heat transport , , the heat transport enhances . this leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow , which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport .","abstract":"we present a systematic investigation of the effects of roughness geometry on turbulent rayleigh - bnard convection ( rbc ) over rough plates with pyramid - shaped and periodically distributed roughness elements . using a parameter defined as the height of a roughness element over its base width , the heat transport , the flow dynamics and local temperatures are measured for the rayleigh number range , and the prandtl number from 3.57 to 23.34 at four values of ( 0.5 , 1.0 , 1.9 , and 4.0 ) . it is found that the heat transport scaling , i.e. where is the nusselt number , may be classified into three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling is the same as that in a smooth cell . in regimes ii and iii , the heat transport enhances . when is increased from 0.5 to 4.0 , increases from 0.36 to 0.59 in regime ii , and it increases from 0.30 to 0.50 in regime iii . the experiment thus clearly demonstrates that the heat transport scaling in turbulent rbc can be manipulated using in the heat transport enhanced regime . previous studies suggest that the transition to heat transport enhanced regime , i.e. from regime i to regime ii , occurs when the thermal boundary layer ( bl ) thickness becomes smaller than the roughness height . direct measurements of the viscous bl in the present study suggest that the transition from regime ii to regime iii is likely a result of the viscous bl thickness becoming smaller than the roughness height . the scaling exponent of the reynolds number with respect to changes from 0.471 to 0.551 when is increased from 0.5 to 4.0 , suggesting a change of the dynamics of the large - scale circulation . interestingly , the transition from regime ii to regime iii in terms of the heat transport scaling is not reflected in the-scaling with . it is also found that increasing increases the clustering of thermal plumes which effectively increases the plumes lifetime . this leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow , which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport ."}
{"article_id":"1703.03137","section_id":"r","document":"( colour online ) photos of the bottom plate of a rough cell with @xmath23 . left : top view ; right : side view . the red heater connection wires can be seen on top of the left panel . plates with @xmath0 values of 0.5 , 1.9 and 4.0 have the same design . ] the experiments were carried out in four cylindrical convection cells . each of the convection cells consisted of top and bottom plates and a plexiglas sidewall . except for the geometry of roughness elements on the top and bottom plates , the constructions of the convection cells were otherwise identical . the sidewall was made of plexiglas tube with a wall - thickness of 4 mm . the convection cells had a diameter @xmath24 of 19.2 cm and a height @xmath11 of 20.3 cm measured from the base of the roughness elements . thus the aspect ratios @xmath25 of the convection cells were approximately unity . the top and bottom plates were made of 12 mm - thick copper except for the ones for rough cell with @xmath26 which were made of aluminium . the thermal conductivity of aluminium is 205 w/(m@xmath27c ) at temperature 25 @xmath27c , which is roughly half that of copper . the differences in heat transport properties in convection cells with plates made of copper and aluminium , i.e. the effects of finite conductivity of plates @xcite , have been shown to be minimal in the @xmath7 and @xmath2 range reported in the present studies @xcite . the pyramid - shaped roughness elements were directly machined on the top and bottom plates that were then plated with nickel to prevent oxidation . the roughness elements were arranged in a square lattice form ( see figure [ fig_pic ] ) , which was the same as those used previously @xcite . by keeping the height of roughness elements @xmath22 a constant at 8 mm and changing the base width @xmath28 of individual roughness elements from 16 mm to 2 mm , rough plates with roughness parameter @xmath0 , defined as the ratio of @xmath22 and @xmath28 , at 0.5 , 1.0 , 1.9 and 4.0 were used in the experiments . with the increase of @xmath0 , the number density @xmath29 ( in unit of number of roughness element per @xmath30 ) also increases , i.e. @xmath29 = 0.38 ( @xmath31 ) , 1.5 ( @xmath32 ) , 6.1 ( @xmath33 ) , and 24.5 ( @xmath34 ) . to clarify whether the number density or the @xmath0 is the key parameter that characterizes the system , another sets of rough plates with @xmath0 = 4.0 and a roughness height of 4 mm were used . the present study implies that @xmath0 is a more suitable parameter to characterise the geometry of the roughness elements and the response of the system , rather than the number density of the roughness elements . the top plate was cooled by passing temperature - controlled water from a water bath ( poly science , 9702 ) through a chamber fitted on its top . the cooling water entered the chamber through two inlets and left the chamber through two outlets . the arrangements of the inlets and outlets were such that the two inlets were along one diameter of the plate and the two outlets were along another diameter perpendicular to the inlets . temperature stability of the cooling water was better than 0.01 @xmath27c . a stirring blade driven by the inlet and outlet flows was installed inside the cooling chamber to ensure temperature uniformity across the top plate . the bottom plate was electrically heated by two rubber heaters connected in series and sandwiched in between the bottom plate and a copper plate with a thickness of 10 mm ( see , e.g. figure [ fig_pic ] ) . the heaters were connected to a dc power supply with a long term voltage stability of 99.99% ( sorensen , xfr300 - 4 ) . to ensure good thermal contact , a thin layer of thermally conductive paste was used between the heaters and the plates . the largest temperature difference within the same plate was about @xmath35 . it should be noted that under this arrangement , the temperature boundary condition for the top plate was constant temperature and that for the bottom plate was constant heat flux .    to prevent heat leakage and to minimise the influence of the environmental temperature fluctuation , the convection cells were wrapped with styrofoam with a thickness of 6 cm . a temperature regulated copper basin was placed beneath the convection cell to prevent heat leakage from the bottom plate of the convection cell by maintaining the same temperature at the top and bottom of the basin . the whole set up was put into a thermostat where the temperature was regulated to match the mean temperature @xmath36 of the top and bottom plate . the temperature stability of the thermostat was better than 0.1 @xmath27c .      only about one and a half decades of @xmath7 can be achieved in a single experimental setup using classical working fluid like water . to extend the @xmath7 range , two kinds of working fluids , namely deionized water and flourinert fc770 ( fc770 hereafter , 3 m inc . ) were used . water has been widely used in the study of turbulent convection , we will mention here only the properties of fc770 . the data listed below are given by the manufacturer ( 3 m inc . ) and are all obtained at the temperature @xmath37c . the fc770 has @xmath13 = 0.063 w/(m@xmath27c ) , @xmath5 = 0.00148/@xmath27c , @xmath38 m@xmath39/s , the specific heat @xmath40 1038 j/(kg@xmath27c ) , and the density @xmath41 = 1793 kg / m@xmath42 . the working fluid was filled into the convection cell through a hole attached with a stainless steel tube ( @xmath43 8 mm in diameter ) located at the centre of the top plate . the working fluids were degassed in the following way to ensure there was no bubble forming during a single run of the experiment , which typically lasts for three weeks . deionized water was boiled for a hour and then cooled down to room temperature before filling into the convection cell . for fc770 , it was first filled into the convection cell and degassed by keeping the temperature of the top and bottom plate , and thus the whole convection cell , at @xmath44c for 24 hours . then the temperature of the convection cell was lowed to @xmath45c which was the @xmath36 for all the experiments using fc770 , and the bubbles formed were totally removed . the explored @xmath7 and @xmath2 phase space at different values of @xmath0 is shown in figure [ fig_phasespace ] . except for @xmath46 which was investigated for a single @xmath2 ( 23.34 ) in the present studies , all the other values of @xmath0 were studied for the four values of @xmath2 , i.e. @xmath2 = 3.67 ( water , @xmath47 @xmath27c ) , @xmath2 = 4.34 ( water , @xmath48 @xmath27c ) , @xmath2 = 6.14 ( water , @xmath49 @xmath27c ) , and @xmath2 = 23.34 ( fc770 , @xmath50 @xmath27c ) . the experiments covered @xmath51 . the temperature difference applied across the convection cell using water as the working fluid for different values of @xmath0 were : 0.98 @xmath27c to 26.99 @xmath27c ( @xmath34 ) ; 0.47 @xmath27c to 20.16 @xmath27c ( @xmath33 ) and 0.89 @xmath27c to 24.75 @xmath27c ( @xmath32 ) . the temperature difference applied using fc770 as working fluid at different values of @xmath0 were : 1.40 @xmath27c to 22.14 @xmath27c ( @xmath34 ) ; 0.99 @xmath27c to 17.25 @xmath27c ( @xmath33 ) ; 1.11 @xmath27c to 27.63 @xmath27c ( @xmath32 ) and 0.96 @xmath27c to 29.66 @xmath27c ( @xmath31 ) . ( colour online ) @xmath19 phase space explored for different values of @xmath0 . the case for @xmath0 = 0.5 is only studied for @xmath5223.34 . all experiments were conducted in convection cells with roughness height @xmath22 = 8 mm , except for the ones corresponding to hexagons that were conducted in convection cell with @xmath22 = 4 mm.,scaledwidth=65.0% ]      temperature of the top plate was measured using four thermistors ( omega , model 44031 ) embedded at a distance of @xmath53 from the centre of the plate and uniformly in the azimuthal direction . four thermistors at the mirror location of the top plate embedded in the bottom plate with one additional thermistor at the centre were used to measure its temperature . the thermistors were calibrated individually and separately in a temperature controlled water bath . the temperature range of calibration was from 5 @xmath27c to 70 @xmath27c with a temperature accuracy better than 0.01 @xmath27c . the resistances of the thermistors were measured using a @xmath54 digital multimeter ( keithley , 2700 ) and were converted to temperature using the calibration curve . the sampling rate of the temperature measurement was 0.7 hz .    local temperatures at the cell centre and @xmath43 1 cm away from the sidewall were measured using two small thermistors with a bead diameter of @xmath55 mm and a time constant of 30 ms in liquid ( measurement specialities , model : g22k7mcd419 ) . these small thermistors had a temperature accuracy of 0.01 @xmath27c . they were guided into the convection cell using a stainless steel tube with an outer diameter of 1.1 mm and wall thickness of 0.2 mm ( goodfellow , stainless steel - aisi 304 tube ) . each of the small thermistors had an independent temperature measurement system specially designed to measure the temperature fluctuation . detailed design of the measurement system can be found in @xcite . briefly , the thermistor acted as one arm of a ac wheatstone electrical bridge . the resistance fluctuations of the thermistor induced by the temperature fluctuations in the convection cell were converted to the voltage fluctuations of the electrical bridge which were magnified using a lock - in amplifier ( stanford research system , sr830 ) . the output signal from the lock - in amplifier was then digitised and stored by a dynamic signal analyser ( hp , 35670a ) . the measured voltage was converted to resistance and then to temperature using the calibration curve of the thermistors . the sampling rate of the local temperature varied from 16 hz to 128 hz depending on @xmath7 and @xmath2 to ensure that the small scale temporal temperature fluctuations were fully resolved .    from the temperature measurements , the heat transport across the convection cell , i.e. the nusselt number @xmath56 , local temperatures , and the reynolds number @xmath57 were measured as a function of @xmath7 , @xmath2 and @xmath0 , where @xmath58 was the input heating power at the bottom plate , @xmath59 was the thermal conductivity of the working fluid and @xmath60 was the characteristic velocity of the lsc . each measurement lasted at least 12 hours after the system had reached a stable state to ensure that the system had explored all flow states . the dynamics of viscous boundary layer in the rough cell with @xmath23 was measured using a commercial particle image velocimetry ( piv ) system that had been documented elsewhere @xcite . the flow was seeded with particles with a diameter of 2 @xmath61 m and density matched with water . a 2d flow region with a size of 20 mm@xmath62 28 mm was measured within the lsc s circulation plane with @xmath63 denoting the direction along the circulation path of the lsc and @xmath64 denoting the direction pointing upwards at the centre of bottom plate ( see , e.g. figure [ fig_piv ] ) . the origin of the coordinate system was located at the centre of the plate . to minimise optical distortion of the particle images induced by the curved surface of the cell , a jacket filled with water with flat window was adhered to the convection cell . the optical arrangement was such that the measurement plane was within one groove of the rough plate and the images were acquired perpendicular to it . a mask with the shape exactly matching that of the plate geometry when viewing from the front was applied to the measured images to exclude the parts blocked by the roughness elements in the captured images . the velocity field was obtained by cross - correlating two consecutive images taken with a time separation that matches the velocity of the flow at different @xmath7 . the velocity map consisted of 63@xmath62 79 vectors in the @xmath65 and @xmath66 directions respectively . totally 26136 vector maps were acquired at a sampling rate of 2.2 hz , which lasts for @xmath67 hours . the velocity fluctuation map was obtained by subtracting the mean velocity map from each of the instantaneous velocity map . the measurements were done at @xmath68 and @xmath69 . to lock the direction of the lsc , the convection cell was tilted with respect to the vertical direction by @xmath70 .","summary":"the flow dynamics and local temperatures are measured for the rayleigh number range , and the prandtl number from 3.57 to 23.34 at four values of ( 0.5 , 1.0 , 1.9 , and 4.0 ) .","abstract":"we present a systematic investigation of the effects of roughness geometry on turbulent rayleigh - bnard convection ( rbc ) over rough plates with pyramid - shaped and periodically distributed roughness elements . using a parameter defined as the height of a roughness element over its base width , the heat transport , the flow dynamics and local temperatures are measured for the rayleigh number range , and the prandtl number from 3.57 to 23.34 at four values of ( 0.5 , 1.0 , 1.9 , and 4.0 ) . it is found that the heat transport scaling , i.e. where is the nusselt number , may be classified into three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling is the same as that in a smooth cell . in regimes ii and iii , the heat transport enhances . when is increased from 0.5 to 4.0 , increases from 0.36 to 0.59 in regime ii , and it increases from 0.30 to 0.50 in regime iii . the experiment thus clearly demonstrates that the heat transport scaling in turbulent rbc can be manipulated using in the heat transport enhanced regime . previous studies suggest that the transition to heat transport enhanced regime , i.e. from regime i to regime ii , occurs when the thermal boundary layer ( bl ) thickness becomes smaller than the roughness height . direct measurements of the viscous bl in the present study suggest that the transition from regime ii to regime iii is likely a result of the viscous bl thickness becoming smaller than the roughness height . the scaling exponent of the reynolds number with respect to changes from 0.471 to 0.551 when is increased from 0.5 to 4.0 , suggesting a change of the dynamics of the large - scale circulation . interestingly , the transition from regime ii to regime iii in terms of the heat transport scaling is not reflected in the-scaling with . it is also found that increasing increases the clustering of thermal plumes which effectively increases the plumes lifetime . this leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow , which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport ."}
{"article_id":"1703.03137","section_id":"r","document":"we show in this section that the heat transport in turbulent rbc over rough plates may be classified into three regimes based on the scaling law of @xmath4 vs. @xmath7 . in addition , the heat transport scaling in the enhanced regime ( regimes ii and iii ) can be manipulated by changing the roughness geometry . the transition from regime i to regime ii in a rough cell with @xmath22 = 4 mm and @xmath71 is discussed in section  [ regime_i_ii ] . the heat transport measurement with changing the geometry of roughness elements , i.e. for different values of @xmath0 , is presented in  [ regime_ii_iii ] together with the observation of regime ii and regime iii . ( colour online ) ( @xmath72 ) @xmath4 as a function of @xmath7 in a rough cell with a roughness elements height of 4 mm . the down - pointing triangles are taken from @xcite(@xmath73 ) , the hexagons are taken from @xcite(@xmath74 ) , the stars are taken from @xcite . ( @xmath75 ) the compensated plot of the same data in ( @xmath72 ) . ]    previously , @xcite find that the heat transport can not be altered in a rough cell if thermal bl thickness @xmath76 is larger than the height of the roughness elements . we call this regime i of convective turbulence in a rough cell . as @xmath76 decreases with increasing @xmath7 , it will eventually become smaller than the roughness height , i.e. @xmath77 . when this happens turbulent convection enters a new , heat transport enhanced regime , termed regime ii here . this regime has been observed by a number of previous experiments @xcite . we plot in figure [ fig_regime_i_ii](@xmath72 ) @xmath4 as a function of @xmath7 in a rough cells with @xmath78 mm and @xmath71 . for comparison , the data from @xcite in a smooth cell with @xmath79 , from @xcite in a smooth cell with @xmath80 and from @xcite in a smooth cell with @xmath81 are plotted respectively as down - pointing - triangles , hexagons and stars . figure [ fig_regime_i_ii](@xmath75 ) plots the corresponding data in a compensated form . it is seen that @xmath4 in the rough cells first overlaps nicely with those from the smooth cells for @xmath82 . with increasing @xmath7 , there is a gradual transition , where the heat transport enhances . within the transitional @xmath7 range @xmath83 , there is no well defined scaling law between @xmath4 and @xmath7 . for @xmath84 , the data shows a power - law relation , i.e. @xmath85 . these data clearly demonstrate the transition from regime i to regime ii . such a transition is also observed by @xcite in a rough cell with @xmath86 mm . using the relation @xmath87 ( which was valid only for the plate - wise averaged thermal bl thickness and for a smooth cell ) , we had @xmath88 mm at @xmath89 , which might be considered to be close to the roughness height of 4 mm in an order of magnitude sense and broadly consistent with the proposed interpretation by @xcite . we present measurements of @xmath4 as a function of @xmath7 in convection cells with a roughness height @xmath22 of 8 mm and different roughness geometries in this subsection . the roughness height was much larger than @xmath76 for the explored range of @xmath7 . therefore , regime i behaviour was not observed here . instead , we focus on regime ii and regime iii ( a new regime to be defined below ) . ( colour online ) left panel : @xmath4 as a function of @xmath7 in rough cells for ( @xmath72 ) @xmath71 ; ( @xmath90 ) @xmath26 ; ( @xmath12 ) @xmath23 and ( @xmath91 ) @xmath46 . the down - pointing triangles are from @xcite(@xmath73 ) , the hexagons are from @xcite(@xmath74 ) and the stars are from @xcite(@xmath73 ) . data at @xmath68 in ( @xmath92 are from @xcite ; @xmath4 at @xmath93 at @xmath34 and 1.9 are larger than those at @xmath94 at the same @xmath7 . for a better comparison , they are shifted downwards respectively by 1.5 and 1.34 and displayed using squares with cross . the solid lines are power law fits to the data larger and smaller than @xmath95 . right panel : the compensated plot of @xmath4 with the fitted @xmath7 scaling for @xmath7 larger and smaller than @xmath96 from the left panel . ]    figures [ fig1](@xmath97 ) show @xmath4 as a function of @xmath7 and @xmath2 in rough cells with @xmath98 and 0.5 , respectively . the solid lines in the figure are power law fit to each data set for @xmath7 larger and smaller than a critical rayleigh number @xmath99 . the same data from smooth cells as shown in figure [ fig_regime_i_ii ] are shown in these figures . the general conclusion that one can draw from these figures is that the heat transport is enhanced in rough cells . we first discuss the case with @xmath23 ( figure [ fig1](@xmath12 ) ) . within the precision of the experiments , data at different values of @xmath2 but the same @xmath7 collapse onto each other , suggesting that the @xmath2-dependence in the rough cell with @xmath23 is very weak in the present parameter range , which is consistent with observation in a smooth cell @xcite . detailed examination of the data shows that there is a transition of the @xmath100 scaling at @xmath101 . below and above @xmath102 , the data can be fitted by different scaling laws , i.e. @xmath103 and @xmath104 . the different scaling laws suggest that the heat transport enhancement regime in a rough cell can be further classified into two regimes for the @xmath2 range covered in the present experiments . we term the two regimes before and after @xmath102 as regime ii and regime iii . the data are compensated by the scaling exponents in regimes ii and iii and shown in figure [ fig1](@xmath105 ) . a gradual transition around @xmath95 is clearly seen . data at @xmath106 and 0.5 are plotted in figure [ fig1 ] ( @xmath107 ) . one interesting feature revealed in figure [ fig1](@xmath72 ) and ( @xmath90 ) is that the @xmath4 at @xmath93 is larger than that at @xmath108 when @xmath7 is the same . we note that this @xmath4-enhancement for fc770 ( @xmath93 ) , as compared to water ( @xmath108 ) , only occurs for the large @xmath0 cases . in fact , for the smallest value of @xmath0 ( @xmath109 ) there is a slight decrease in @xmath4 . this is quite surprising and unexpected , as in the case of a smooth cells , @xmath4 is peaked around @xmath110 @xcite . it is not clear why the heat transport enhancement in rough cells has this peculiar @xmath2-dependence , and furthermore this behaviour has a strong @xmath0 dependence , i.e. its 150% for @xmath71 , 134% for @xmath26 , 4% for @xmath23 , and -8% for @xmath46 . one possible reason leading to such a @xmath2-abnormality is that the lifetime of the thermal plumes at larger @xmath2 is larger compared to the small @xmath2 case . assuming that the thermal plumes have typical length scale comparable to the thermal bl thickness , the estimated thermal diffusion time scale , i.e. @xmath111 , for fc770 is 14.5 sec and that for water is 2.6 sec at @xmath112 . when normalised by the lsc turn - over time , the dimensionless plume lifetime for fc770 is 0.25 and that for water is 0.11 for @xmath71 . another likely reason is the stronger plume clustering effect in rough cells with larger @xmath0 as shown by the shadowgraph images in figure [ fig_shadow ] , which also has the effect of increasing plume lifetime or slowing the decay of plumes . while it is difficult to quantify the combined effect of these two factors , it appears that larger values of @xmath0 together with a larger @xmath2 result in a more efficient enhancement in the heat transport . for small @xmath0 and/or small @xmath2 , thermal plumes lose more heat to the surrounding fluid and therefore @xmath4 wo nt be enhanced as much . ( colour online ) the scaling exponent @xmath5 from power law fits to @xmath4 vs @xmath7 , i.e. @xmath3 , in regime ii ( circles ) and regime iii ( triangles ) as a function of @xmath0 . also plotted in the figure is the scaling exponent @xmath113 from power law fits to @xmath6 vs @xmath7 ( squares ) , i.e. @xmath114 , as a function of @xmath0 . the solids lines are empirical power law fits to the respective data sets : @xmath115 , @xmath116 and @xmath117.,scaledwidth=65.0% ]    to determine more accurately the scaling law of @xmath4 vs. @xmath7 , the data at @xmath93 in figure [ fig1](@xmath72 ) and ( @xmath90 ) are shifted downwards by a constant , i.e. 1.50 in ( @xmath72 ) and 1.34 in ( @xmath90 ) , to collapse data at different @xmath2 but the same @xmath7 . the transition of the heat transport scaling around @xmath102 is observed for all @xmath0 studied . the power law fits of @xmath118 in regimes ii and iii for different values of @xmath0 are summarised in table [ tab : table1 ] . it should be noted that the shifted high @xmath2 data were included in the fitting . since @xmath7 obtained using water as working fluid at @xmath108 and that using fc770 as working fluid at @xmath93 had an overlapping range of less than a half decade , i.e. from @xmath119 to @xmath120 , a determination of the @xmath2 dependence in regime iii was not possible in the present experiments . it is seen that the heat transport law is distinctively different in regime ii and regime iii . this can be seem more clearly from the compensated plot in the right panel next to figure [ fig1](@xmath121 .    the experimentally determined scaling exponent @xmath5 , i.e. @xmath3 , in both regime ii and regime iii increases significantly with @xmath0 . in regime ii , the @xmath5 increases from 0.36 to 0.59 when @xmath0 is increased from 0.5 to 4.0 ; and in regime iii , it increases from 0.30 to 0.50 . these data are plotted in figure [ fig3 ] . if a power law fit is attempted to these data within the limited range of @xmath0 , we obtain @xmath122 and @xmath123 which are shown as solid lines in the figure . within the error bar , the @xmath0-dependences of @xmath124 and @xmath125 are the same except that the pre - factor of @xmath124 is larger than @xmath125 . the results suggest that the scaling law of the heat transport in turbulent rbc over rough plates can be manipulated using @xmath0 . in this sense , the present experiments demonstrate clearly the importance of roughness geometry on turbulent heat transport . any realistic model for turbulent thermal convection in nature should take into account the effects of wall roughness . very recently , it is found that there is an upper bound for the heat transport in turbulent convection over rough plates , i.e. @xmath4 can not grow faster than @xmath126 in the limit of @xmath127 @xcite . with increasing @xmath7 , regime ii is just a transient , and regime iii is the dominated one . our experiments showed that at @xmath71 the scaling exponent already reached 0.50 , which was consistent with the upper bound derived @xcite . one interesting question is whether the scaling exponent will saturate to 0.50 with further increasing @xmath0 which is very challenging to achieve experimentally due to technical difficulties in machining the plates . dns studies may provide helpful insights into this aspect of the problem . ( colour online ) the heat transport enhancements in regime ii ( open symbols ) and regime iii ( solid symbols ) as a function of @xmath0.,scaledwidth=65.0% ]       cccc &    .[tab : table1 ] measured scaling law of the nusselt number @xmath4 and normalized temperature fluctuations @xmath128 in regime iii for different values of @xmath0 . [ cols=\"^ \" , ]      + 4.0 & @xmath129@xmath130 & @xmath131 & @xmath132@xmath133 + 1.9 & @xmath134@xmath135 & @xmath136 & @xmath137@xmath138 + 1.0 & @xmath139 @xmath140 & @xmath141 & @xmath142@xmath143 + 0.5 & @xmath144 @xmath145 & @xmath146&@xmath147@xmath148 +    we next study the @xmath0-dependence of the heat transport enhancement behaviour in regime ii and regime iii . figure [ fig_enhancement ] shows the heat transport enhancement in rough cells compared with that in a smooth cell . it is seen that the heat transport enhancement in regime ii ( open symbols in figure [ fig_enhancement ] ) first increases and then decreases with increasing @xmath0 . the situation is very different in regime iii ( solid symbols in figure [ fig_enhancement ] ) where it is found that the heat transport enhancement increases monotonically with increasing @xmath0 . a maximum heat transport enhancement of 637% is observed at @xmath71 . we note that in a dns study , @xcite show that the heat transport is enhanced more for slender roughness elements , i.e. larger @xmath0 , using only four roughness elements with a roughness height of 0.125h (  obstales \" in @xcite ) in a quasi-2-d convection cell . the observation in @xcite is qualitatively in agreement with what we find here , e.g. heat transport enhancement generally increases with @xmath0 ( see e.g. figure [ fig_enhancement ] ) .      to understand what may have happened at @xmath102 , i.e. the transition from regime ii to regime iii , we recall that there are two bls in turbulent rbc , i.e. the thermal bl and the viscous bl . the viscous bl is thicker than the thermal bl for @xmath149 . according to the grossmann - lohse model for turbulent rbc , bls play crucial role in determine the global heat transport @xcite . the transition seen in figure [ fig1 ] may be understood in terms of the viscous bl cross - over , i.e. the roughness elements not only strongly perturb the thermal bl , but also alter the viscous bl in regime iii . to verify this , we directly measured the dynamics of the viscous boundary layer in a rough cell with @xmath23 . ( colour online ) the instantaneous ( @xmath72 ) and time - averaged ( @xmath75 ) velocity fields measured near the bottom plate within the large - scale circulation plane ( @xmath150 , @xmath68 and @xmath23 ) . the velocity magnitude ( in units of mm / s ) is colour coded with the colour bar nearby each figure , and also represented by the length of the vectors . the velocity field is not accessible experimentally below the dashed lines . ] ( colour online)(@xmath72 ) typical time - averaged horizontal velocity @xmath60 and root - mean - square horizontal velocity @xmath151 profiles ( @xmath152 , @xmath23 and @xmath68 ) . the vertical dashed line indicates the location of the viscous boundary layer . ( @xmath75 ) normalized viscous boundary layer thickness @xmath153 vs @xmath7 . the dashed line marks the height of the roughness elements . the datum at the highest @xmath7 ( symbols with cross , @xmath154 ) shows different behaviours with other data points which we believe is an artefact due to the strong optical distortion of the images used for piv analysis . ] ( colour online ) @xmath4 as a function of @xmath6 measured in rough cells with different values of @xmath0 at ( @xmath72 ) @xmath93 ( @xmath75 ) @xmath155 ( @xmath156 ) @xmath68 and ( @xmath90 ) @xmath108 . ] an example of the instantaneous velocity map measured at @xmath157 and @xmath68 is shown in figure [ fig_piv](@xmath72 ) . the triangles outline the space occupied by the roughness elements schematically . the velocity magnitude is coded by both the colour and the length of the vectors . the instant velocity field shows that the mean flow is going from the right to the left and there are intermittent bursts of the flow velocity . figure [ fig_piv](@xmath75 ) depicts the time averaged velocity field with the velocity magnitude coded also in both colour and the length of the vectors . one may notice that the time - averaged maximum velocity magnitude is significantly reduced when compared with the instantaneous one as revealed by the scale bars . after averaging over time one sees that the mean velocity is uniform with respect to @xmath63 except very close to the plate , e.g. in between the roughness elements . a tiny counter - rotating vortex may be identified in the region -8 mm @xmath158 -5 mm and 0 mm @xmath159 4 mm . the mean velocity field varied weakly with @xmath63 ( figure [ fig_piv](@xmath75 ) ) . we thus averaged the mean velocity field along @xmath65direction to obtain the mean velocity and the root - mean - square ( rms ) velocity profiles . figure [ fig2](@xmath72 ) shows an example of the horizontal mean velocity profile @xmath160 and the profile of the rms velocity @xmath161 measured at @xmath150 and @xmath68 . a remarkable feature shown in figure [ fig2](@xmath72 ) is that the rms velocity is comparable to the mean velocity very close to the plate , and it s even larger than the mean velocity within the viscous bl . the origin of the enhanced velocity fluctuation is not clear but speculatively this should largely correlate with the intermittent bursts of thermal plumes . in contrast , the maximum rms velocity in a smooth cell is only about 30% of the maximum mean velocity and it is always smaller than the mean velocity within the boundary layer region @xcite .    the viscous boundary layer thickness was determined using the so - called slope method : the intersection between the extrapolation of the linear part of the velocity profile very close to the plate and the maximum mean horizontal velocity was defined as the thickness of the viscous boundary layer @xmath162 ( indicated by the vertical dashed line in figure [ fig2](@xmath72 ) ) @xcite . the @xmath7-dependence of the viscous bl thickness normalised by the height of the convection cell is plotted in figure [ fig2](@xmath75 ) . with increasing @xmath7 , @xmath163 becomes thinner and thinner . at @xmath164 , @xmath163 approximately equals to @xmath165 . this roughly corresponds to @xmath102 seen in the measured @xmath4 ( @xmath166 . this observation indicates that the transition of the heat transport law between regimes ii and iii may be caused by the viscous bl becoming smaller than the height of the roughness elements . after this viscous bl cross - over , the roughness elements strongly perturb both the thermal and the viscous bls . the thermal plumes emitted from the tip of pyramids can then be directly ejected into the bulk . for @xmath93 , the estimated viscous bl thickness at the smallest @xmath7 explored in the experiments ( @xmath167 ) was 0.04h @xcite , which was very close to the height of roughness element , implying that the measurements with @xmath93 were all in regime iii .    in the asymptotically large @xmath7 limit , the thickness of the bls is so small such that the roughness elements perturb both the thermal and the viscous bls . the system is in regime iii in this case wherein @xmath4 is very sensitive to the lsc , or equivalently to the reynolds number @xmath6 associated with the lsc ( to be defined in section [ subsec_re ] ) . we plot in figure [ fig_nu_re ] @xmath4 as a function of @xmath6 for ( @xmath72 ) @xmath2 = 23.34 , ( @xmath75 ) @xmath2 = 6.14 , ( @xmath156 ) @xmath2 = 4.34 , and ( @xmath90 ) @xmath2 = 3.57 . on one hand , figure [ fig_nu_re ] ( @xmath72 ) shows that @xmath4 increases with @xmath0 for all @xmath6 measured at @xmath93 , which are in the regime iii . on the other hand , @xmath4 at other @xmath2 where mostly within the regime ii shows weak dependence on @xmath6 . this is another evidence supporting that the viscous bl cross - over may also play important role in turbulent thermal convection with the presence of roughness elements . the self - organised large - scale circulation ( lsc , or `` wind of turbulence '' ) is one of the fascinating features of turbulent rbc . the flow dynamics of the lsc is characterised by the associated reynolds number @xmath6 . we study in this section how the roughness geometry alters the dynamics of the lsc by examining the @xmath6 dependence on both @xmath7 and @xmath2 . it has been well - known that there exits a well - defined low - frequency oscillation in turbulent rbc . the time scale of this oscillation is interpreted as the turnover time @xmath168 of the lsc ( see , e.g. @xcite and references therein ) . by choosing a typical length scale of the lsc , e.g. 4h , the reynolds number is calculated as : @xmath169 time - resolved temperature signals measured @xmath170 cm away from the sidewall were used to determine @xmath168 and thus the @xmath6 as a function of @xmath7 and @xmath2 when changing the roughness geometry , i.e. at different values of @xmath0 . the turnover time of the lsc was determined by locating the time position of the first peak of the temperature auto - correlation function @xmath171 , which is defined as : @xmath172[t(t)-\\langle t(t)\\rangle_t]\\rangle_t}{\\sigma_t^2}\\ ] ] where @xmath173 denoted time - averaging and @xmath174 is the rms temperature . an example of the autocorrelation function measured in convection cell with @xmath71 at @xmath175 and @xmath93 is depicted in figure [ fig_oscillation ] . clear oscillations can be seen from @xmath171 . fitting the data points nearby the first peak of @xmath171 with a six order polynomial , the time location of the first peak was determined and denoted as @xmath168 . the uncertainty of @xmath168 was from @xmath176 s to @xmath177 s with increasing @xmath7 . autocorrelation function of the temperature measured @xmath170 cm away from sidewall in a rough cell with @xmath71 at @xmath175 and @xmath93 . here @xmath168 is the turnover time of the lsc.,scaledwidth=65.0% ]     ( colour online ) reynolds number @xmath6 as a function of @xmath7 and @xmath2 in rough cells for ( @xmath72 ) @xmath71 , ( @xmath156 ) @xmath26 , ( @xmath178 ) @xmath23 and ( @xmath12 ) @xmath46 . to determine more precisely the scaling exponent of @xmath6 with respect to @xmath7 , data measured at @xmath179 and @xmath180 in ( @xmath181 ) are multiplied by a @xmath2-dependent constant @xmath182 to collapse with data at @xmath93 . the shifted data are shown in the main plot in the right panel ( @xmath183 ) with power law fit @xmath184 shown as solid lines . the insets in ( @xmath183 ) show the compensated plot @xmath185 with respect to @xmath2 with the solid lines representing power law fits to the data . see table [ tab : table1 ] for the fitted power laws . ] figure [ fig_re ] displays @xmath6 as a function of @xmath7 and @xmath2 in rough cells with @xmath71 ( @xmath186 ) , @xmath26 ( @xmath187 ) , @xmath23 ( @xmath188 ) and @xmath189 @xmath190 . let s first discuss the case for @xmath71 . the @xmath6 as a function of @xmath7 for @xmath191 and @xmath192 are plotted in figure [ fig_re](@xmath72 ) on a log - log scale . the @xmath6 exhibits power law dependence on @xmath7 at different @xmath2 , i.e. @xmath114 . to determine more precisely @xmath113 , data at @xmath2 = 3.57 , 4.34 and 6.14 were multiplied by a @xmath2-dependent constant to collapse them with data at @xmath93 onto a single line . the shifted data are shown in the main plot of figure [ fig_re](@xmath75 ) . a power law fits to the data over almost three decades of @xmath7 yielded : @xmath193 . the @xmath7-dependence of @xmath6 was then divided out by compensating the data in figure [ fig_re](@xmath72 ) with the so - determined power law , e.g. the inset of figure [ fig_re](@xmath75 ) . within a relatively limited range of @xmath2 , the data was also described by a power law , i.e. @xmath194 . the so - determined @xmath17 was :    @xmath195    applying the same procedure to data obtained in rough cells with @xmath26 ( figure [ fig_re](@xmath156 ) ) , @xmath23 ( figure [ fig_re](@xmath178 ) ) , and @xmath46 ( figure [ fig_re](@xmath12 ) ) , we determined the @xmath7 and @xmath2 dependence of @xmath6 for each values of @xmath0 , respectively . the scaling laws of @xmath196 for different values of @xmath0 are summarised in table [ tab : table1 ] .    on one hand , with @xmath0 increasing from 0.5 to 4.0 the scaling exponent @xmath113 , i.e. @xmath114 , increases from 0.472 to 0.551 , which is plotted as a function of @xmath0 in figure [ fig3 ] . the data may be described by an empirical power law within very limited range of @xmath0 , i.e. @xmath117 . on the other hand , the scaling exponent @xmath197 , i.e. @xmath198 , remains at the same value around @xmath199 within experimental uncertainty except for @xmath71 . whether there is a change of the @xmath2-dependence of @xmath6 in the rough cell with @xmath71 requires future investigation with a wider range of @xmath2 . the change of @xmath113 with @xmath0 suggests a change of the lsc dynamics when the geometry of the roughness elements is changed . it is thus interesting to study torsional and sloshing oscillations of the lsc dynamics in rough cells with different values of @xmath0 as those done in a smooth cell @xcite . this is beyond the scope of the present studies and will be investigated in the future . interestingly , the transition of the heat transport scaling law from regime ii to regime iii is not observed in the reynolds number measurement . ( colour online ) reynolds number @xmath6 as a function of @xmath200 for different values of @xmath0 with the solid line representing a power law fit to the data irrespective of @xmath0 . ( @xmath72 ) @xmath93 and @xmath201 ; ( @xmath75 ) @xmath202 and @xmath203 ; ( @xmath156 ) @xmath204 and @xmath205 ; ( @xmath90 ) @xmath108 and re=@xmath206 . ] it is found very recently that @xmath6 is insensitive to the plate morphology for a given input heat flux for @xmath207 and 0.5 @xcite , i.e. when @xmath6 is plotted against the flux rayleigh number @xmath200 , data at different values of @xmath0 collapse . we plot @xmath6 as a function of @xmath200 for different values of @xmath0 and @xmath2 in figure [ fig_reranu ] . the data at the same @xmath2 but different @xmath0 indeed overlap onto each other which is in agreement with the observation in @xcite , but now for a wider range of @xmath0 and @xmath2 . in addition , data at the same @xmath2 can be fitted by a power law , i.e. @xmath201 @xmath208 , @xmath209 @xmath210 , @xmath211 , and @xmath212 @xmath213 . the scaling exponents of these power laws fits are the same within experimental uncertainty but the magnitudes decrease with @xmath2 . ( colour online ) probability density functions ( pdfs ) of the standardised temperature measured ( @xmath72 ) at the cell centre and ( @xmath75 ) near sidewall for different values of @xmath0 ( @xmath214 and @xmath93 ) . the root - mean - square temperatures as a function of @xmath0 at the cell centre and sidewall are plotted in ( @xmath156 ) and ( @xmath90 ) , respectively . ]    since regime ii is a transitional state , we focus on temperature fluctuations measured in regime iii only . to simplify the analysis , we do nt take into account the effects of @xmath2 and limit the analysis to measurements done in fc770 only ( @xmath2=23.34 ) . the results may shed light upon the mechanism leading to the change of the heat transport scaling in rough cells with different roughness geometries in regime iii . the probability density function ( pdf ) of the standardised temperature @xmath215 measured at @xmath216 at four different values of @xmath0 at the cell centre and sidewall are displayed in figure [ fig_pdf_localtemp ] ( @xmath72 ) and ( @xmath75 ) respectively , where @xmath174 is the rms temperature that is shown as a function of @xmath0 in figure [ fig_pdf_localtemp ] ( @xmath156 ) and ( @xmath90 ) at the cell centre and sidewall . it is seen that the pdfs at different @xmath0 overlap onto each other very nicely at the cell centre , suggesting that the bulk turbulence shares the similar dynamics at different values of @xmath0 . a notable feature seen in figure [ fig_pdf_localtemp ] ( @xmath72 ) is that the pdfs are significantly skewed toward the negative side , i.e. more cold plumes are detected in the cell centre than hot ones . this feature hasnt been observed either by us or reported by others in smooth cells with the same boundary conditions , i.e. constant temperature at the top boundary and constant heat flux at the bottom boundary . thus , the reason for this phenomenon remains unknown to us at present . at sidewall , the shapes of the pdfs remain approximately invariant with @xmath0 except the case with @xmath46 . for measurements with @xmath46 the thermistor was so - positioned such that the upwelling hot plumes of the lsc were detected , while for the other cases the downwelling cold plumes of the lsc were detected . the positive tails of the pdfs overlap well onto each other while the negative tails , especially those larger than @xmath217 , change with @xmath0 . the rms temperature at the cell centre increases considerably with @xmath0 as can be seen from figure [ fig_pdf_localtemp](@xmath156 ) , and that at the sidewall first remains almost the same for @xmath0=0.5 and 1.0 and then increases with @xmath0 as well . as the large temperature fluctuations are caused by thermal plumes , this observation suggests a change of the plume dynamics with increasing @xmath0 . ( colour online ) @xmath0-dependence of the normalised root - mean - square temperature as a function of @xmath7 at ( @xmath72 ) the cell centre and ( @xmath75 ) the sidewall . the solid lines are power law fits to the individual data set with the scaling exponents displayed nearby each data set . the data are measured at @xmath93 . ] the rayleigh number dependence of normalised rms temperatures @xmath218 for different values of @xmath0 measured at the cell centre and near the sidewall are shown in figure [ fig_rms](@xmath72 ) and ( @xmath75 ) , respectively . with increasing @xmath0 , @xmath128 enhances considerably . the changes lie not only in the magnitudes but also the scaling exponents with @xmath7 . the scaling exponents of the power law fits , e.g. @xmath219 , are displayed nearby each data set in figure [ fig_rms](@xmath72 ) and ( @xmath75 ) and the scaling laws of each data set are summarised in table [ tab : table1 ] . the scaling exponent increases from -0.16 to -0.09 with @xmath0 increased from 0.5 to 4.0 in the cell centre . for comparison , @xcite obtained an exponent of -0.17 in the centre of a smooth cell for a comparable @xmath2 ( @xmath2 = 12.3 ) . with a possible @xmath2-dependence of the temperature fluctuation unknown at the present , the experimental results suggest that the @xmath7-dependence of the temperature fluctuation at the cell centre becomes stronger with increasing @xmath0 . near the sidewall , the scaling exponent increases from -0.23 to -0.08 in the @xmath0 range covered in the experiments , suggesting a weakened dependence of temperature fluctuation on @xmath0 at the sidewall . to the best of our knowledge , there has been no report on the smooth - cell value for this exponent in the similar @xmath2 range near sidewall . ( colour online ) probability density function of the temperature deviation from the mean @xmath220 normalised by the applied temperature between the top and bottom plate @xmath221 at ( @xmath72 ) the cell centre and ( @xmath75 ) the sidewall ( @xmath214 , @xmath93 ) . ]    to gain further insight into the dynamics of temperature fluctuations with increasing @xmath0 , we examine the pdfs of the normalised temperature deviation from the mean @xmath222 for different values of @xmath0 at @xmath214 at the cell centre and the sidewall respectively , as displayed in figure [ fig_sigma_t](@xmath72 ) and ( @xmath75 ) . the figure reveals that large events are becoming more probable with increasing @xmath0 at the same @xmath7 , i.e. hotter and colder plumes , suggesting that the effects of changing roughness geometry are to modify the dynamics of thermal plumes and make them more coherent and energetic ( therefore decay slower ) . this is also supported by the shadowgraph visualisation of the flow field , such as those presented in figure [ fig_shadow ] . these images are taken at @xmath223 and @xmath5223.34 . it is seen that , with increasing @xmath0 , both the density and the morphology of the thermal plumes change drastically . in the smooth cell there is a well - defined lsc with few thermal plumes passing through the cell centre ( figure [ fig_shadow](@xmath72 ) ) . in the rough cell with @xmath23 , more thermal plumes are passing through the cell centre ( figure [ fig_shadow](@xmath75 ) ) . in the rough cell with @xmath71 , thermal plumes occupy almost all the space in the convection cell ( figure [ fig_shadow](@xmath156 ) ) . furthermore , the plumes are now packed ( or clustered ) much more densely . this will result in their slower decay through thermal diffusion , which explains why it is now much more probable to find large temperature excursions in the cell centre ( figure [ fig_sigma_t](@xmath72 ) ) . shadowgraph images of the instantaneous flow fields in a rough cell with ( @xmath72 ) @xmath0=0.0 ( @xmath75 ) @xmath23 and ( @xmath156 ) @xmath71 . the images were taken at @xmath223 and @xmath93 . ] ( colour online ) ( @xmath72 ) the time averaged plume amplitude @xmath224 normalised by @xmath221 and ( @xmath75 ) the time averaged plume width @xmath225 normalised by the large - scale circulation turnover time @xmath168 as a function of @xmath7 extracted from the temperature time series measured at the sidewall at @xmath93 . the scaling of the power law fits are displayed nearby each data set . ]    to quantitatively understand the change of the dynamics of thermal plume , we extract time series of thermal plume amplitude @xmath226 and width @xmath28 using the time - resolved temperature data measured near sidewall . the detailed plume extraction method can be found in @xcite . the normalised time - averaged plume amplitude @xmath227 and normalised time - averaged plume width @xmath228 are shown in figure [ fig_plume](@xmath72 ) and ( @xmath75 ) respectively . figure [ fig_plume](@xmath72 ) reveals that with the increase of @xmath0 , the plume amplitude @xmath229 increases . the solid lines are power law fits to the data at different values of @xmath0 with the scaling exponents listed nearby each data set . the scaling exponent of plume amplitude increases from -0.386 to -0.266 with @xmath0 increasing from 0.5 to 4.0 . in contrast , the @xmath230dependence of the plume width remains almost the same with a scaling exponent around 0.25 for @xmath0 smaller than 4.0 . it should be noted that the scaling exponent of plume width for @xmath71 increases considerably ( 0.341 ) when compared with other values of @xmath0 , which may be correlated with the drastically changed plume dynamics and morphology in rough cell with @xmath71 . as the thermal plumes are main heat carriers in turbulent rbc , the experiments suggest that the change of plume dynamics may lead to the change of the scaling law of heat transport for different values of @xmath0 .      when varying @xmath0 the number density @xmath29 of roughness elements also varies , i.e. @xmath231 . in fact , the two parameters have one - to - one correspondence provided that the ratio of the roughness element height @xmath22 to the cell height @xmath11 and @xmath15 are fixed , which is the case for the present study . to figure out whether @xmath0 is the most relevant parameter that characterises the system , we carried out another experiment , in which @xmath0 was kept constant at 4.0 and the height of the roughness elements was halved . thus the number density of the roughness elements is increased by a factor of 4 . ( colour online ) ( @xmath72 ) @xmath4 as a function of @xmath7 and @xmath2 at fixed @xmath71 measured in rough cells with roughness height @xmath22 of 4 mm and 8 mm . the down - pointing triangles are from @xcite and the hexagons are from @xcite in smooth cells . the solid lines are power law fits to the respective data set . the power law fitting in cell with @xmath232 8 mm is extrapolated to @xmath233 . ( @xmath75 ) compensated plot of the same data in ( @xmath72 ) . ] ( colour online ) @xmath6 as a function of @xmath7 in rough cells with @xmath232 8 mm ( solid symbols ) and 4 mm ( open symbols ) at @xmath52 4.34 ( triangles ) and 23.34 ( squares ) , respectively . in both cells @xmath71 . the solid lines are power fits to each data set . for @xmath68 , @xmath234 ( @xmath235 mm ) @xmath236 ( @xmath2324 mm ) ; and for @xmath93 @xmath237 ( @xmath235 mm ) @xmath238 ( @xmath2324 mm ) . , scaledwidth=65.0% ]    we show in figure [ fig_nu4](@xmath72 ) @xmath4 as a function of @xmath7 for measurements in @xmath0 = 4.0 rough cells with @xmath235 mm and @xmath78 mm together with the same smooth cell data which have be shown in figure [ fig_regime_i_ii ] and figure [ fig1 ] . the estimated viscous boundary layer thickness at the highest @xmath7 reached in the experiment is 4.8 mm . thus , the measurements at @xmath93 and @xmath78 mm are in regime ii . a scaling exponent @xmath5 = 0.60 is observed in rough cell with @xmath78 mm in regime ii , which is consistent with 0.59 observed in regime ii of rough cell with @xmath239 8 mm , which is indicated by the two parallel lines in figure [ fig_nu4 ] . the similar @xmath7-dependence of @xmath4 in regime ii in rough cells with @xmath22 = 4 mm and 8 mm can be seen more clearly from the compensated plot in figure [ fig_nu4](@xmath75 ) . these observations suggest that @xmath0 is not only a suitable parameter describing the geometry of the pyramid - shaped roughness elements , but also a suitable parameter to characterise the response of turbulent rbc over rough plates with different roughness geometries . a noticeable feature from figure [ fig_nu4](@xmath72 ) is that the measured @xmath4 in the rough cell with @xmath239 8 mm is larger than that in the rough cell with @xmath239 4 mm in regime ii despite the fact that they have similar @xmath7-dependence . this may be explained by the measured reynolds number based on the circulation time of the lsc as plotted in figure [ fig_re4 ] . it is seen that @xmath6 in the rough cell with @xmath240 mm is larger than that in the rough cell with @xmath2324 mm , which is true for both @xmath241 4.34 and @xmath52 23.34 . the result suggests that a faster lsc can transport heat more efficiently cross the convection cell .","summary":"when is increased from 0.5 to 4.0 , increases from 0.36 to 0.59 in regime ii , and it increases from 0.30 to 0.50 in regime iii . it is also found that increasing increases the clustering of thermal plumes which effectively increases the plumes lifetime .","abstract":"we present a systematic investigation of the effects of roughness geometry on turbulent rayleigh - bnard convection ( rbc ) over rough plates with pyramid - shaped and periodically distributed roughness elements . using a parameter defined as the height of a roughness element over its base width , the heat transport , the flow dynamics and local temperatures are measured for the rayleigh number range , and the prandtl number from 3.57 to 23.34 at four values of ( 0.5 , 1.0 , 1.9 , and 4.0 ) . it is found that the heat transport scaling , i.e. where is the nusselt number , may be classified into three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling is the same as that in a smooth cell . in regimes ii and iii , the heat transport enhances . when is increased from 0.5 to 4.0 , increases from 0.36 to 0.59 in regime ii , and it increases from 0.30 to 0.50 in regime iii . the experiment thus clearly demonstrates that the heat transport scaling in turbulent rbc can be manipulated using in the heat transport enhanced regime . previous studies suggest that the transition to heat transport enhanced regime , i.e. from regime i to regime ii , occurs when the thermal boundary layer ( bl ) thickness becomes smaller than the roughness height . direct measurements of the viscous bl in the present study suggest that the transition from regime ii to regime iii is likely a result of the viscous bl thickness becoming smaller than the roughness height . the scaling exponent of the reynolds number with respect to changes from 0.471 to 0.551 when is increased from 0.5 to 4.0 , suggesting a change of the dynamics of the large - scale circulation . interestingly , the transition from regime ii to regime iii in terms of the heat transport scaling is not reflected in the-scaling with . it is also found that increasing increases the clustering of thermal plumes which effectively increases the plumes lifetime . this leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow , which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport ."}
{"article_id":"1703.03137","section_id":"c","document":"we studied systematically in this paper the effects of roughness geometry on the global heat transport , the flow dynamics and the local temperature fluctuations in turbulent rayleigh - bnard convection over rough plates . the experiments were carried out in rough cells with pyramid - shaped roughness elements directly machined on the top and bottom plates . we defined a parameter @xmath0 ( the height of the roughness element over its base width ) to characterise the geometry of the roughness element and to analyse the observed scaling behaviour of @xmath242 and @xmath17 , where @xmath7 and @xmath2 are respectively the rayleigh number and prandtl number , @xmath4 and @xmath6 are respectively the nusselt number and reynolds number . we varied @xmath0 from 0.5 to 4.0 by keeping the roughness height at a constant of 8 mm and changing the base width from 16 mm to 2 mm . in addition , a rough cell with @xmath2394 mm was used . the experiments covered rayleigh number @xmath243 and @xmath2 from 3.57 to 23.34 .    it is found that the heat transport is enhanced significantly by roughness elements , and the enhancement depends strongly on the roughness geometry . it is also found that the heat transport scaling , i.e. @xmath3 , may be classified in to three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling in a rough cell is the same as that in a smooth cell in this regime . in regimes ii and iii heat transport enhances . the scaling exponents @xmath5 of @xmath4 vs. @xmath7 increase from 0.36 to 0.59 with @xmath0 increased from 0.5 to 4.0 in regime ii . it increases from 0.30 to 0.50 in regime iii with @xmath0 increased from 0.5 to 4.0 . the experiment thus clearly demonstrated that the heat transport scaling in turbulent rbc could be manipulated using @xmath0 in regimes ii and iii . the transition from regime i to regime ii may be understood in terms of the thermal boundary layer thickness becoming smaller than the roughness height with increasing @xmath7 as suggested by a number of previous studies @xcite . the transition from regime ii to regime iii may be understood in terms of viscous boundary layer crossing , i.e. the viscous bl thickness becomes thinner than the height of the roughness elements , as shown by direct measurement of the viscous boundary layer profiles in the present study . when this happens , the thermal plumes emitted from the tip of the roughness can be directly ejected into the bulk flow . an unexpected @xmath2 effect in turbulent rbc over rough plates was also observed : larger heat transport enhancement was observed for larger values of @xmath0 and larger @xmath2 . this may be correlated with the strong clustering of thermal plumes as clearly seen from the shadowgraph visualization of the flow field ( figure [ fig_shadow ] ) . the reynolds number @xmath6 is measured based on the turnover time of the large - scale circulation evaluated near the sidewall of the cells . both the @xmath7 and @xmath2 dependence of @xmath6 were studied for different roughness geometries , i.e. @xmath244 . the scaling exponent @xmath113 increased from 0.472 to 0.551 with @xmath0 increasing from 0.5 to 4.0 . and @xmath197 remained at the same value around @xmath245 except for the case of @xmath71 ( @xmath246 ) . with a limited range of @xmath2 , a truly increased @xmath197 for @xmath71 was not for assertion . consistent with the observation in @xcite , it is found that @xmath6 is insensitive to the plate morphology for a fixed flux rayleigh number , i.e @xmath200 , but now with a wider range of @xmath2 and @xmath0 as compared with the experiment of @xcite . time - resolved local temperatures at the cell centre and sidewall were measured using two small thermistors . the probability density functions ( pdfs ) of the standardised temperature ( @xmath247 in the cell centre remain almost invariant with respect to @xmath0 . the measured local temperature fluctuations at both the cell centre and sidewall increase considerably with @xmath0 . the scaling exponent of the normalised rms temperature ( @xmath174/@xmath221 ) with @xmath7 increases from @xmath248 to @xmath249 at the cell centre and from @xmath250 to @xmath251 at the sidewall with @xmath0 increased from 0.5 to 4.0 . by extracting thermal plume amplitude and width using a method described in @xcite , it is found that both the plume amplitude and width increase with @xmath0 . the scaling exponent of plume amplitude increases from -0.386 to -0.266 with @xmath0 increasing from 0.5 to 4.0 . the scaling exponent for the plume width remains at the same value around 0.25 except for the case of @xmath71 which is -0.34 . as thermal plumes are the main heat carriers in turbulent rbc , the experiments suggested that that the change of thermal plume dynamics might be a possible reason leading to the change of the scaling laws between @xmath4 and @xmath7 in regime iii . the experiments demonstrated that the heat transport behaviour in turbulent thermal convection can be manipulated using a roughness parameter @xmath0 that characterises the geometry of the roughness elements . it further showed that the flow dynamics and local temperature fluctuations are also altered by roughness geometry . there are several open questions : what is the effects of @xmath0 on the dynamics of the large - scale circulation , e.g. twisting / sloshing oscillation , flow cessation / reversal ? how will the vertical mean and variance temperature profiles change with @xmath0 ? finally , we remark that the 0.5 scaling exponent observed for @xmath0 = 4.0 in regime iii reminds one of the kraichnan ultimate regime of turbulent convection @xcite . whether regime iii for @xmath252 4.0 really corresponds to the kraichnan regime needs further investigations . the place to look would be the boundary layer , i.e. a truly turbulent boundary layer should be the ultimate test for the kraichnan regime . a very recent dns study suggests roughness may be used as a route to trigger the transition to the ultimate state of turbulent convection @xcite . if this is indeed the case , then the dynamics of turbulent convection in the kraichnan regime may be studied in a rayleigh number range that is accessible using classical fluids like water in a table top experiment .","summary":"it is found that the heat transport scaling , i.e. where is the nusselt number , may be classified into three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling is the same as that in a smooth cell . in regimes ii and iii the experiment thus clearly demonstrates that the heat transport scaling in turbulent rbc can be manipulated using in the heat transport enhanced regime . previous studies suggest that the transition to heat transport enhanced regime , i.e. from regime i to regime ii , occurs when the thermal boundary layer ( bl ) thickness becomes smaller than the roughness height . direct measurements of the viscous bl in the present study suggest that the transition from regime ii to regime iii is likely a result of the viscous bl thickness becoming smaller than the roughness height . the scaling exponent of the reynolds number with respect to changes from 0.471 to 0.551 when is increased from 0.5 to 4.0 , suggesting a change of the dynamics of the large - scale circulation . interestingly , the transition from regime ii to regime iii in terms of the heat transport scaling is not reflected in the-scaling with .","abstract":"we present a systematic investigation of the effects of roughness geometry on turbulent rayleigh - bnard convection ( rbc ) over rough plates with pyramid - shaped and periodically distributed roughness elements . using a parameter defined as the height of a roughness element over its base width , the heat transport , the flow dynamics and local temperatures are measured for the rayleigh number range , and the prandtl number from 3.57 to 23.34 at four values of ( 0.5 , 1.0 , 1.9 , and 4.0 ) . it is found that the heat transport scaling , i.e. where is the nusselt number , may be classified into three regimes in turbulent rbc over rough plates . in regime i , the system is in a dynamically smooth state . the heat transport scaling is the same as that in a smooth cell . in regimes ii and iii , the heat transport enhances . when is increased from 0.5 to 4.0 , increases from 0.36 to 0.59 in regime ii , and it increases from 0.30 to 0.50 in regime iii . the experiment thus clearly demonstrates that the heat transport scaling in turbulent rbc can be manipulated using in the heat transport enhanced regime . previous studies suggest that the transition to heat transport enhanced regime , i.e. from regime i to regime ii , occurs when the thermal boundary layer ( bl ) thickness becomes smaller than the roughness height . direct measurements of the viscous bl in the present study suggest that the transition from regime ii to regime iii is likely a result of the viscous bl thickness becoming smaller than the roughness height . the scaling exponent of the reynolds number with respect to changes from 0.471 to 0.551 when is increased from 0.5 to 4.0 , suggesting a change of the dynamics of the large - scale circulation . interestingly , the transition from regime ii to regime iii in terms of the heat transport scaling is not reflected in the-scaling with . it is also found that increasing increases the clustering of thermal plumes which effectively increases the plumes lifetime . this leads to a great increase in the probability of observing large temperature fluctuations in the bulk flow , which corresponds to the formation of more coherent plumes or plume clusters that are ultimately responsible for the enhanced heat transport ."}
{"article_id":"0803.2087","section_id":"r","document":"initially , we performed test runs , to check whether the spherical or axial symmetry is conserved wherever it should be conserved , and whether the 2-d results of the axisymmetric calculations are reproduced in 3-d . having calculated both the models of spherical bondi accretion ( * s*-models ) , as well as the axisymmetric accretion with low angular momentum ( * l*-models ) , we found that : + ( a ) the results from the 2-d models are reproduced in the @xmath36 slices of the 3-d models ; in particular , the accretion rate @xmath37 and the flow pattern are the same ; + ( b ) the non - radial velocity components in the * s*-models , which analytically should be @xmath38 , can locally have non zero values , but both are orders of magnitude smaller than the local radial velocity and sound speed ( that ratio is of the order of @xmath39 ) ; + ( c ) the symmetry with respect to both the equatorial plane and rotation axis is conserved ( @xmath40 , where @xmath41 denotes density , energy , or velocity components ) in all models at early stages of the evolution , i.e. @xmath42 .    the * s*-models conserved their spherical symmetry in both 2-d and 3-d , throughout our runs . for * l*-models , as the system evolved , asymmetries began to arise with respect to the equatorial plane , in both 2-d and 3-d models . we note that this was already the case in pb03 simulations . the axisymmetry in the present reference 3-d model ( i.e. the model with axisymmetric initial conditions ) is conserved initially and at intermediate times of the system evolution ( however see the results below ) . the computations of an axisymmetric , 2.5-d model of an accretion flow with low angular momentum were presented in pb03 . we have recalculated this model in 3-d for the purpose of the present work . the simulations start from a spherically symmetric gas cloud around a black hole , with density and velocity distributions derived from the bondi solution . the matter located far from the black hole possesses a specific angular momentum that exceeds the critical value , @xmath43 , at the equatorial plane and is decreasing towards the polar regions ( cf . [ eq : phizero ] ) .    the time evolution of the system with the initial conditions described above proceeds as follows . after a transient episode of purely radial infall , when the rotating material reaches the vicinity of the black hole , a thick torus forms in the equatorial region . the gas settled in this region is supported against gravity by the gas pressure and rotation , and the rate of accretion on the black hole , @xmath37 , decreased down to about 30% of the bondi accretion rate ( in pb03 the exact value of @xmath37 was found to depend on the details of the angular momentum distribution ) . this is because the material accretes only through the polar funnels , while the torus is made of material that can not accrete . ( there is no transport due to viscosity ; however the non - axisymmetric shocks can result in some transport of the angular momentum ) . the gas which approached the centrifugal barrier at the equator , could either outflow radially , or try to turn towards one of the poles and accrete . consequently , meridional circulation movements are observed in the flow . the accretion rate onto bh varies in time . due to meridional circulations , the flow is not symmetric with respect to the equatorial plane ; however , the time averaged properties ( e.g. accretion rate ) and the shape of the torus did settle down to a steady state , as shown in pb03 . in the equator the flow is subsonic down to very small radii , while at the poles , at some distance from the center , the radial velocity exceeds the local speed of sound .    here , we repeated the calculations of pb03 in 3-d and ran new simulations on a relatively long time scale . most of our simulation runs lasted up to @xmath44 . for comparison , the sound crossing time at the @xmath28 is about @xmath45 , while at the radii corresponding to the dense tori formed in the innermost part of the flow ( see section [ sec : main ] ) , the sound crossing time is @xmath46 . figure [ fig : sonic3d ] shows the sonic surface , i.e. the isosurface where the mach number , @xmath47 is a unity . at the @xmath48 . for the zero - vorticity flow , the surface shape can be derived analytically , as it passes orthogonally through the velocity equipotential surfaces ( papaloizou & szuszkiewicz 1994 ) . in general , the shape of the surface can be more complex . as one can see in the figure , the sound waves are propagating outwards in the flow . the sonic surface for initially axisymmetric model is shown in the left panel , and for comparison in the right panel we also show the non - axisymmetric case ( model @xmath49 , to be described in sec . [ sec : main ] ) . we find that both qualitatively and quantitatively the initial results in 3-d axisymmetric case are the same as in 2.5-d . the main new feature of the torus in 3-d , which could not be studied in the pb03 simulation , is that in the very late stages of the evolution ( @xmath50 ) the axisymmetry breaks and the inner torus becomes tilted with respect to the equator , and in the end it starts precessing . this departure from the symmetry at later times is caused by the equatorial outflow and meridional circulations in the torus become suppressed , while the material tries to get through towards the black hole and accrete along one of the poles . at the same time , for some regions ( e.g. , @xmath51 ) the accretion occurs through the northern pole , at the opposite side ( @xmath52 ) and the flow chooses rather the southern pole . consequently , a torque is induced and the rotation axis of the torus changes in time . the precession of the torus is illustrated in figure [ fig : levol ] in terms of the total angular momentum , * @xmath53*@xmath54 , which is changing in time . this figure shows the motion of the innermost part of the flow , i.e. the torus , defined by the density threshold @xmath55 . initially , the dominant component is @xmath56 , while @xmath57 and @xmath58 are close to zero ( but fluctuating ) . it means that the torus rotates basically around the @xmath59 axis . after @xmath60 , @xmath57 and @xmath58 are non - zero , and the rotation axis tilts towards the 4@xmath61 quarter in the @xmath62 plane . at @xmath63 , @xmath58 starts decreasing while @xmath57 still decreases and @xmath56 is almost constant . it means that the torus is now precessing , i.e. the rotation axis moves counter - clockwise with respect to an observer along the + z axis . figure [ fig : levol ] also shows for comparison , the results for the torus precession in case of non - axisymmetric initial conditions ( model @xmath49 ) . this model will be discussed below in more detail ( sec . [ sec : main ] ) . the precession is also shown in figures [ fig : tilt ] and [ fig : twist ] ( see e.g. fragile et al . the tilt , defined as an angle between the angular momentum vector of the gas and the @xmath59 axis , is initially equal to zero for all radii . later during the simulation the tilt rises strongly in the inner parts of the flow . the tilt is equal to : @xmath64    in the figure [ fig : tilt ] we plot the tilt angle , @xmath65 , as a function of radius , for several time snapshots , starting from @xmath66 . the differential form of the torus precession is also visible in figure [ fig : twist ] , in which we plot the cumulative twist angle , @xmath67 , as a function of time . the twist angle is defined as a cumulative angle by which the angular momentum vector revolves in the @xmath62 plane , by the time @xmath68 : @xmath69 before the disk was tilted , it did not precess , and by definition the twist was zero . therefore the results in the figure are also plotted from time @xmath66 . the solid line is the twist averaged over the radius for the inner part of the flow ( @xmath70 ) , i.e. the torus , while the dashed line shows the twist averaged for the whole range of radii . clearly , the innermost torus precesses much stronger than the rest of the flow , and the maximum twist at the end of the simulation was @xmath71 .    to check whether the tilt and precession of the inner torus found in this simulation is a physical or rather numerical effect , we performed several further test simulations . first , we reversed the direction of the flow in the initial condition , i.e. we changed the sign of the azimuthal velocity @xmath16 . in this simulation , we also found that the torus tilts and starts precessing , at the same time ( @xmath72 ) . however , the tilt and precession are in the opposite directions as measured with respect to the grid , i.e. the initial tilt was @xmath73 and decreased to about @xmath74 , while the twist was negative . second , we checked how transient the effect of precession is . due to technical limitations , we were not able to run all the simulations for very long time , but we completed one run up to @xmath75 , for the model @xmath76 . in this model we found that the tilt angle increased from @xmath77 to @xmath78 , and the tilt spreaded to larger radii , so that not only the innermost parts of the flow precessed . however , at this very late phase , some of the ring - like structures of the largest density were broken into two separate parts , each of them of a `` c '' shape . therefore the precession may not be a long - term effect . we plan to investigate this in near future . third , we checked for the importance of the adopted physics of the model , in particular , the ratio of the sound speed to the free fall velocity . we calculated two models with much smaller bondi radius , @xmath79 and @xmath80 , which correspond to a much larger sound speed at infinity : respectively , 3.15 and 1.82 times larger than in all the other simulations . these models are denoted as @xmath81 and @xmath82 in table [ tab : models ] . the models could be run for much longer time in terms of @xmath83 , i.e. for @xmath84 and @xmath85 , respectively . however , in these models we did not find any signatures of tilt or precession . this is because here the mach numbers are never large : they are at most @xmath86 at the inner radius , whereas for the precessing torus the mach numbers reached the values as large as 4.7 - 6.0 . the small mach numbers in models @xmath81 and @xmath82 make the shocks smaller ; hence they do not amplify the asymmetries growing out of initial perturbations .    finally , we tested the role of the artificial viscosity , which might help to spread the shocks and avoid precession if it was a numerical artifact . the artificial viscosity was parametrized with the standard neumann - richtmeyer artificial viscosity coefficient _ qcon _ = 2.0 however , the results in this simulation were very similar to the original simulation . specifically , for time @xmath87 the maximum tilt angle was @xmath88 , while in the former case and @xmath89 in the latter .    from the above tests , we conclude that the precession in our initially axisymmetric model is rather a physical than numerical effect , and is connected with relatively large supersonic speeds of the flow achieved in our model . now we investigate how the non - axisymmetric initial distribution of the specific angular momentum affects the evolution of the flow . in particular , we check whether the rotationally supported torus forms and if a steady state can be achieved ( with or without torus precession ) . we start our simulation with the non - zero specific angular momentum enclosed in a conical region of a width @xmath30 ( see eq . [ eq : phizero ] ) . a naive prediction could be that the rotating gas will reach the innermost regions , spiral in , and after a few orbital cycles the material with large angular momentum would be mixed with the non - rotating gas . therefore a rotationally supported torus would form , regardless of @xmath30 . the only dependence on this parameter would be the moment when such a torus forms . however , as we show below , the numerical simulations lead us to a different result : depending on @xmath30 the rotating gas may not form a torus at all . we performed the runs for non - axisymmetric initial conditions for a range of @xmath30 . the models are summarized in table [ tab : models ] . the non - axisymmetric models are labeled with the letters @xmath49-@xmath90 , while the reference model is labeled as @xmath91 . as we mentioned in sec . [ sec : method ] and as the table shows , we tested the models with smaller ( 32 zones ) and larger ( 60 zones ) resolution in the @xmath33-direction . we checked , that the time averaged results for the accretion rate only very weakly depend on the resolution , however the amplitude of time variability of @xmath92 increases with resolution . below , we present these results for the largest adopted value of @xmath93 ( model @xmath49 ) . this parameter translates into a small non - axisymmetric perturbation in the initial conditions , i.e. small content of non - rotating material . in figures [ fig : torus1 ] , [ fig : torus1_large ] , [ fig : torus2 ] , [ fig : torus2lspec ] and [ fig : torus2lspec_large ] we show the color coded maps of the central region , as well as the zoomed - out . the maps show the density distribution and velocity field , as well as the specific angular momentum , plotted for several snapshots during the evolution : @xmath940 , 0.018 , 0.09 , 0.16 , 0.23 and 0.29 . note that the top - right panel in figure [ fig : torus1 ] , as well as all the top panels in figure [ fig : torus2lspec ] , i.e. for @xmath95 , are plotted on the scale 20 times larges compared to other panels , because in the inner region initially we assumed @xmath96 . [ fig : torus1 ] shows the density and specific angular momentum distribution in the central region ( up to 0.02 @xmath28 ) , plotted for the equatorial plane . the orientation of the plots in the @xmath62 plane is standard , i.e. the @xmath97 semi - axis corresponds to @xmath98 . the density distribution , initially spherical at @xmath99 ( top left panel ) changes in time , as the material which carries specific angular momentum approaches the center . at @xmath100 , the gas is rotating around the @xmath59-axis ( arrows over plotted on the density maps denote the direction of the velocity vectors with components @xmath101 and @xmath16 ) . the material is distributed axisymmetrically , and the specific angular momentum is rather large ( i.e. @xmath102 ) for most of the @xmath33 directions . a clump of gas with relatively smaller @xmath103 , which can be seen on the second right panel , is a remaining of the gas with @xmath96 initially present at the equator for @xmath104 ) . this clump is tracking the archimedean spiral ( see also e.g. lemaster et al . 2007 ) , and such a trajectory appears to be due to the pressure gradient force and rotation ( similarly to a cyclone ) .    at @xmath105 , the material with small @xmath103 is already mixed with the gas of high @xmath103 . the material rotates very fast in the equatorial plane , and a circular pattern of slightly larger and smaller specific angular momentum regions , visible on the third plot , form due to mixing . these motions are suppressed at @xmath106 . for some specific directions , namely @xmath107 and @xmath108 , the angular momentum near the inner radius becomes very small ( as indicated by the green spots in fig . [ fig : torus1 ] ) , and the density in these regions drops , indicating that the material falls radially to the black hole . the solid line in the angular momentum maps mark the contour at which @xmath109 . we note that at @xmath110 and @xmath111 , in the equatorial plane a substantial fraction of material has @xmath112 . this material is located at an extended region approximately along the diagonal of the plane ( i.e. @xmath113 and @xmath114 , as marked by the orange shade in fig . [ fig : torus1 ] ) . another region of even smaller angular momentum , @xmath115 , has a very limited radial extension close to the center , and is slightly elongated along the other diagonal ( i.e. @xmath116 and @xmath117 , as marked by the green shade in fig . [ fig : torus1 ] ) . for the same @xmath33 , but at larger distances , the specific angular momentum in the equatorial plane is very large , and exceeds @xmath118 .    in figure [ fig : torus1_large ] we show the distribution of @xmath103 on the larger scale . ( note also that the color scale is different than in fig . [ fig : torus1 ] . the red and green shades now mark the regions with @xmath119 ) . as the figure shows , more material with @xmath120 mixes in at late stages of evolution , @xmath105 sec .    from the figs . [ fig : torus1 ] and [ fig : torus1_large ] , we conclude that a torus starts forming in the innermost regions in the equatorial plane at @xmath100 , and it is rotationally supported for all the @xmath33 directions , because the low @xmath103 material is quickly mixed in . at @xmath105 , the distribution of density and specific angular momentum is almost axisymmetric , but only in the inner region . however as the zoom - out maps show , the gas with @xmath121 is mixing in and is distributed asymmetrically . the innermost symmetric configuration lasts until about @xmath106 , and after this time the torus position and shape changes . to investigate what really happens , we need to look at the flow from a different perspective . therefore , in figures [ fig : torus2 ] , [ fig : torus2lspec ] and [ fig : torus2lspec_large ] , we show the slices perpendicular to the equatorial plane . the maps show density and velocity field , as well as the specific angular momentum , as seen from @xmath122 , @xmath123 , @xmath124 and @xmath125 , at the same times as in figs.[fig : torus1 ] and [ fig : torus1_large ] . as shown in the figure [ fig : torus2 ] , at @xmath100 , the material is indeed accumulated near the equator , while at the poles the density is much lower . the axial symmetry is not perfect , since at @xmath126 the torus is geometrically thicker than at other @xmath33 directions , which corresponds to the location of the clump with smaller specific angular momentum ( c.f . , [ fig : torus1 ] ) . as indicated by the arrows ( velocity vectors with @xmath101 and @xmath15 components ) , an equatorial outflow occurs at most of the @xmath33 directions , however at @xmath126 this outflow is weaker , because of slower rotation .    at @xmath105 , the torus is relatively thin and located at the equator in every @xmath33 direction , while at the poles the density is very low . the gas accretes onto the center mostly through the poles , while at the equator the flow pattern is complex ( circulations , outflows ) . the flow complexity is reduced at @xmath106 , because the gas that flows into the equatorial region has less angular momentum and can directly accrete onto the black hole , finding its way along one of the poles . at @xmath122 and @xmath127 the gas turns towards the northern pole ( i.e. @xmath128 ) , while at @xmath126 and @xmath129 the flow turns towards the southern pole ( i.e. @xmath130 ) . a line which would mark the regions of the maximum density , is now tilted with respect to the equator by an angle of @xmath131 . this means that the torus which at @xmath105 , was almost symmetric with respect to the equatorial plane , is tilted after @xmath106 .    in figure [ fig : torus2lspec ] we show the maps of specific angular momentum , also perpendicularly to the equatorial plane and for the same @xmath33 directions as in fig . [ fig : torus2 ] . as the figure shows , the specific angular momentum distribution is symmetric with respect to the equatorial plane at @xmath105 , and nearly symmetric at @xmath106 . the axial symmetry is not perfect , however the regions of large angular momentum ( @xmath132 ) appear in every slice . at @xmath133 , the flow is no longer symmetric , and the regions with very large specific angular momentum appear either below the equator ( at @xmath122 and @xmath129 ) or above it ( at @xmath126 and @xmath127 ) . these regions correspond to a flatter torus , i.e. relatively thin on one side , while the gas which is not rotating fast makes the configuration geometrically thicker . we notice , that the lack of the top - bottom symmetry in density and @xmath103 maps at this phase of system evolution is a consequence of the earlier non - axisymmetry . this asymmetry was introduced to the velocity field in the initial conditions at large radii , and subsequently propagated to the inner radii and affected the density distribution there , as soon as the rotating gas reached there .    in figure [ fig : torus2lspec_large ] we show the distribution of the specific angular momentum in the zoom out . the flow is rotationally supported in the outer regions . the @xmath103 distribution in the flow is asymmetric at large scales ( there is significantly more material with large @xmath103 for the directions of @xmath122 and @xmath125 than for @xmath129 and @xmath124 ) . however , this is the case only in the inner region , i.e. the torus is tilted , while outer regions , even at late times , are rather symmetric with respect to the equatorial plane .    to visualize the 3-d configuration better , in figure [ fig : density3d330 ] we show the density isosurfaces in 3-d . the plots show 3 arbitrarily chosen contours of the constant density : 2000 , 1250 and 500 @xmath20 , which correspond to the gas densities very close to the inner radius , i.e. inside @xmath134 . the maps are plotted for 5 different time snapshots : @xmath100 , 0.09 , 0.16 , 0.23 and 0.29 . we do not show the density distribution at t=0 , because it is purely spherical . the orientation of the figures is almost edge - on , i.e. the @xmath59-axis is the rotation axis of the system , and @xmath62 plane is the equatorial plane . these density contours may be regarded as the shapes of the torus ( however one should keep in mind that the material with smaller / larger density is also present there ) . therefore , as the figure shows , the torus is closed already at @xmath100 . after @xmath106 , the configuration becomes tilted with respect to the equatorial plane , and at @xmath135 this tilt is the largest . after @xmath135 the torus starts precessing , and the precession period is very long ( by the end of the run , the ring precessed around the @xmath59-axis by less than @xmath123 ) . the torus precession was also shown in the right panel of the figure [ fig : levol ] ( sec . [ sec : reference ] ) . the changing values of @xmath57 , @xmath58 and @xmath56 , show that at @xmath136 the rotation axis , which is defined by the direction of * l * , starts to tilt towards the first quarter of the @xmath62 plane , and after @xmath137 the rotation axis moves counter - clockwise .    in figure [ fig : lspec3d330 ] we show the isosurfaces of the specific angular momentum in 3-d . the contours are for @xmath138 , 2.15 and 3.0 , and correspond to the zoomed - out regions shown in fig . [ fig : torus2lspec_large ] ( the radial extension of about 0.6 @xmath28 ) . as the figure shows , the material with various angular momentum is mixing in the innermost region at @xmath139 while at the outer parts initially the momentum is not mixed . at later times , the outer parts of the flow contain more and more mixed angular momentum layers , while in the innermost region the gas rotates slower than at the beginning , and the angular momentum distribution is smoother .    in figure [ fig : torus3 ] we show the maps of entropy , @xmath140 , radial to azimuthal velocity ratio , @xmath141 , angular velocity , @xmath142 , and velocity divergence , @xmath143 , as calculated close to the end of this simulation , at time @xmath144 . the maps show the inner region in the equatorial plane . close to the center , the angular velocity is the largest along the diagonal of the plane ( @xmath113 and @xmath145 ) , which corresponds to the cross - section line along which the torus crosses through the equatorial plane ( cf . [ fig : density3d330 ] ) . this line also corresponds to the largest entropy , as well as positive velocity divergence , while at the other diagonal there is smaller entropy and negative velocity divergence . this means that the fluid is compressible ( and supersonic ) . our analysis of the 3-d results shows the flow has a largest negative divergence close to the poles while the largest positive divergence is somewhat above and below the equator , i.e. on the surface of the torus , as well as at its cusp . from the poles , the gas flows radially onto the center with large supersonic velocities , i.e. @xmath146 . close to the equator , the flow is captured in the torus and the radial velocities are smaller , so @xmath147 . still , the gas rotates very fast , and the total mach number is large , @xmath148 , because of the contribution from the azimuthal velocity . the entropy in the flow should be constant along the streamlines , however may vary from one streamline to the other . the entropy gradient corresponds to a non - zero vorticity in the flow . the direction of vorticity arrows ( @xmath149 ) in the bottom - right panel indicate that the torus is rotating counter - clockwise . the direction of radial velocity arrows in the bottom - left panel confirms that the radial inflow occurs from the directions of the smallest angular velocity . the above considerations led us to the conclusion that qualitatively , the basic pattern of the torus evolution is uniform . it does only weakly depend on whether we assume the axisymmetric initial conditions , or if the initial distribution of angular momentum was perturbed ( provided that this perturbation was small enough to allow for the torus formation ) . the axisymmetry was explicitly assumed by pb03 throughout their 2-d simulations , as well as in our 3-d reference models in the initial conditions . the similarity of the torus behavior that we find here means that in both 3-d models @xmath91 and in the @xmath49 models , the rotationally supported tori form after time @xmath139 , than they exhibit strong equatorial outflows ( which stabilize them ) , then they become tilted with respect to the equatorial plane due to the asymmetric polar accretion , and finally start precessing . what differs in the models , is the moment when the outflow stops and when the torus becomes tilted , as well as the tilt angle ( it is about twice as large in model @xmath49 than in model @xmath91 at the end of our simulations ; see also fig . [ fig : levol ] ) . these two features ( i.e. tilt and precession ) can not be studied in the 2-d simulations , but are detected in the 3-d models . however , we note that the similarity between the @xmath91 and @xmath49 models is less pronounced when considering the details , e.g. , of the torus shape . the asymmetric torus can be thicker ( warped ) , or thinner , depending on @xmath33 . to investigate further the difference between @xmath91 and @xmath49 models and the role of non - axisymmetry , we calculated the angular momentum at the inner boundary , as a function of the angles @xmath32 and @xmath33 .    in the axisymmetric model @xmath91 , the specific angular momentum at @xmath22 depends only on @xmath32 by definition . after the torus is formed , the maximum value at the equator is @xmath150 , while the value averaged over the angle @xmath32 is @xmath151 . for the non - axisymmetric case ( in particular , model @xmath49 ) , the results depend also on the angle @xmath33 . therefore both the equatorial angular momentum , @xmath152 , and the @xmath32-averaged , @xmath153 , are scattered and do not have to match with the axisymmetric solution . in figure [ fig : phiscatter ] , the results for the axisymmetric model , are denoted by single points , while the non - axisymmetric solutions are represented by the horizontal lines to show the scatter in @xmath33 .    the level of non - axisymmetry is represented as the spread between the maximum and minimum values of @xmath103 at a given time . for the model @xmath49 , in the beginning of the torus evolution , i.e @xmath154 , the equatorial and averaged values of @xmath103 match well with the axisymmetric solutions and are only slightly scattered with @xmath33 . the equatorial value is much larger than the @xmath32-averaged , which means that the torus is located in the equatorial plane where @xmath103 is the largest . as the evolution proceeds , @xmath155 , the scatter with @xmath33 increases and the range of @xmath103 does not match the axially symmetric solution . however , the equatorial angular momentum is still much larger than the average . this means that the torus is located at the equatorial plane , but it is now asymmetric . after @xmath133 , the situation changes , and @xmath103 at the equator has a very large scatter , being either smaller or larger than the @xmath32-averaged value ( i.e. the solid and dashed lines overlap in the figure ) . the averaged angular momentum has also some scatter , but much smaller than the equatorial one . this indicates that the torus is not symmetric , and is tilted with respect to the equatorial plane . we performed similar analysis of other non - axisymmetric models , @xmath156-@xmath90 ( cf . table [ tab : models ] ) . for models @xmath156 and @xmath157 ( @xmath158 and @xmath159 ) , at the beginning of the simulation @xmath160 , the equatorial value of @xmath103 is always larger than the averaged , and the scatter with @xmath33 is smaller in model @xmath156 than that in model @xmath157 . this indicates that a rotationally supported torus is present in the equatorial plane . at later times , the equatorial @xmath103 becomes equal or smaller than average , and the scatter in both models @xmath156 and @xmath157 is quite substantial ( larger than in model @xmath49 ) . this implies that a torus , which possibly tried to form at the early phase , is broken ( i.e. not completely closed ) , as well as tilted from the equator . an example of such a broken torus configuration is shown in figure [ fig : fi240 ] .    for models @xmath161 and @xmath90 ( @xmath162 and @xmath163 ) , the scatter in both @xmath32-averaged and equatorial @xmath103 is very large and does not decrease with time ( up to @xmath164 ) . the averaged @xmath103 can be larger or smaller than the axisymmetric one , while the equatorial @xmath103 in these models is always smaller than that in the axisymmetric case , and locally ( i.e. for some @xmath33 angles ) can be smaller than the @xmath32- averaged . we conclude that in these models the torus does not form , the solution is not axisymmetric , and the gas with very small angular momentum can accrete onto the black hole through the equator . we note that in this sense the properties of these models are similar to those of the model @xmath49 in later times . however , when comparing the density distributions , in the models @xmath161 and @xmath90 the gas is always distributed much more uniformly , i.e. it does not concentrate neither close to the equator nor to any specific plane . in model @xmath49 , the gas density near the poles is always orders of magnitude lower than that at the equatorial plane , or the plane tilted to the equator by a small angle . this is not the case for models @xmath161 and @xmath90 , for which the torus does not form . for models @xmath156 and @xmath157 , the gas is concentrating near the equator , but only for some range of @xmath33-directions , i.e. the torus is not closed .    figure [ fig : mintime ] shows the time evolution of the accretion rate through the inner boundary , @xmath37 for the non - axisymmetric models . before the rotating material approaches the black hole ( @xmath165 ) , @xmath37 is equal to the bondi accretion rate for all models . once the gas starts rotating also in the innermost parts , the accretion rate drops reaching about 25% - 40% of the bondi rate for models @xmath49 , @xmath156 , @xmath157 and @xmath91 . this is because much more material gets captured in the rotating torus , and does not fall radially into the black hole . the model @xmath49 gives the lowest accretion rate with rather small and regular variability pattern , very close to that obtained in the reference model @xmath91 . figure [ fig : lintime ] presents the evolution of the angular momentum flux through the inner boundary : @xmath166 , in units of the critical angular momentum @xmath118 and renormalized by the value of the bondi accretion rate . at the beginning of the simulation , @xmath167 , since there is no rotation in the vicinity of the black hole . once the rotating matter reaches the inner boundary , the angular momentum starts accreting to the center . when the torus starts forming , the fast rotation near the center leads to a fast rise in @xmath168 . however , after several orbital cycles the outflow begins and the net radial velocity drops , as well as drops the density near the polar regions , therefore the @xmath168 is rather small during the torus evolution . note that the quantity plotted in the figure [ fig : lintime ] is not a flux of specific angular momentum , but the total one . this corresponds to the amount of angular momentum which may be transferred to the black hole and used to spin it up . however , as the figure shows , the total angular momentum which the black hole could gain during our simulation , is extremely low : @xmath169 , where @xmath170 . figure [ fig : lintime ] shows two trends in the magnitude of @xmath168 . for small @xmath30 ( models @xmath90 and @xmath161 ) , the rotation at inner boundary is very small , but the density is high both in the equator and in the polar regions ( still close to the spherical accretion ) . therefore , in model @xmath161 , with faster rotation , @xmath168 is larger . for large @xmath30 ( models @xmath49 , @xmath156 and @xmath157 ) , the material accumulates rather close to the equator , at least for some @xmath33 angles , while at the poles the density is small . therefore regardless of the fast rotation , these models give systematically smaller @xmath171 than those in the models @xmath90 and @xmath161 . also , this is why the model @xmath156 gives smaller @xmath172 than that in the model @xmath157 . model @xmath49 is the only one in which the torus is closed ( the gas rotates fast at the equator at every @xmath33 angle ) . this leads to a larger @xmath172 than that in model @xmath156 , which is again less affected by the density distribution .    in the models @xmath49 , @xmath156 and @xmath157 , the accretion rate and @xmath173 are variable . for model @xmath49 , a characteristic wave pattern can be seen in the specific angular momentum distribution in the equatorial plane ( see fig . [ fig : torus1 ] at @xmath174 ) . this behavior is reflected in the variable @xmath37 and @xmath168 , due to the variable radial velocity and nearly constant density at the inner boundary . at time @xmath175 , when the accretion rate stops varying rapidly , the corresponding waves in specific angular momentum map are smoothed out . the outflow of the gas at this time is suppressed , and the gas accretes onto the center through the poles . as a consequence , the mass flux and angular momentum flux through the inner boundary slightly increase , and the curves are smoother . the subsequent drop of both of these quantities at time @xmath176 is caused by the density decrease at the inner edge , when the torus is tilted with respect to the equatorial plane . the density at inner radius increases again at @xmath144 and the torus starts precessing .    the behavior of the flow in models @xmath156 and @xmath157 is more chaotic . the accretion rate and @xmath168 vary in time until the end of our simulations . also , no precession was detected , because in principle it would be hard to determine the boundaries of the structure which might be precessing . we can not use a density threshold to define a torus , because such a torus is not a closed ring in these two models .","summary":"the main new element of this study is that we used fully three dimensional ( 3-d ) numerical simulations . in particular , it may prevent the formation of a proper torus ( i.e. its closing , in the azimuthal direction ) . in such models , the mass accretion rate is only slightly less than the corresponding bondi rate .","abstract":"we report on the fourth phase of our study of slightly rotating accretion flows onto black holes . the main new element of this study is that we used fully three dimensional ( 3-d ) numerical simulations . we consider hydrodynamics of inviscid accretion flows . we assume a spherically symmetric density distribution at the outer boundary , but brake the flow symmetry by introducing a small , latitude - dependent angular momentum . we also consider cases where angular momentum at large radii is latitude- and azimuth - dependent . for the latitude - dependent angular momentum , 3-d simulations confirm axisymmetric results : the material that has too much angular momentum to be accreted forms a thick torus near the equator . consequently , accretion proceeds only through the polar funnel , and the mass accretion rate through the funnel is constrained by the size and shape of the torus , not by the outer conditions . in 3-d simulations , we found that the torus precesses , even for axisymmetric conditions at large radii . for the latitude and azimuth - dependent angular momentum , the non - rotating gas near the equator can also significantly affect the evolution of the rotating gas . in particular , it may prevent the formation of a proper torus ( i.e. its closing , in the azimuthal direction ) . in such models , the mass accretion rate is only slightly less than the corresponding bondi rate ."}
{"article_id":"0803.2087","section_id":"c","document":"this paper presented the fourth phase of our study of slightly rotating accretion flows onto black holes ( see pb03 , proga & begelman 2003b , and proga 2005 for the first , second and third phase ) . here we followed pb03 , but we considered 3-d not 2-d axisymmetric effects . as in pb03 we made a few simplifications . for example , we neglected the gravitational field due to the host galaxy , radiative heating and cooling , viscosity and mhd effects . perhaps the most important simplification we made is neglecting the transport of energy and angular momentum outward as needed to accrete matter with a specific angular momentum higher than @xmath118 . as shown proga & begelman ( 2003b ) for the axisymmetric case , magnetic fields , that can drive the transport , can dramatically alter the flow solution . still our hd results provide a useful exploratory study of accretion onto black holes as they have revealed unexpected properties and complexity of accretion flows even with simplified physics . to our best knowledge there have not been any mhd simulations of rotating flows where a closed torus was either assumed or failed to form . our results show that such flows are plausible ( see also loeb 2004 ) and motivate new simulations . in what follows we summarize and discuss our results . we have performed numerical 3-d hydrodynamical simulations of slightly rotating , inviscid accretion flows onto a black hole . as in pb03 , we attempt to mimic the boundary conditions of classic bondi accretion flows with the only modifications being the introduction of a small , latitude - dependent and also azimuth - dependent angular momentum at the outer boundary and a pseudo - newtonian gravitational potential . the adopted form of the distribution of @xmath103 the density distribution at infinity to approach spherical symmetry , because the centrifugal force is negligible .    for the latitude - dependent angular momentum , 3-d simulations confirm axisymmetric results . namely , the material that has too much angular momentum to be accreted forms a thick torus near the equator . therefore the geometry of the polar funnel , where material is accreted , and the mass accretion rate through it are constrained by the size and shape of the torus but by the outer conditions . however , in 3-d the torus precesses and is non - axisymmetric even for axisymmetric conditions at large radii . for the latitude- and azimuth - dependent angular momentum in the initial conditions , the non - rotating gas near the equator can significantly affect the evolution of the rotating gas . it can prevent closing , in the azimuthal direction , of the rotating gas and the proper torus does not form . in such cases , the mass accretion rate is only slightly less than bondi rates . simulations with none or a small amount of a non - rotating gas near the equator show that a torus forms and limits the accretion rate . however , a non - rotating gas near the equator can inhibit torus formation and the accretion rate will be close to the bondi rate . thus , our simulations show that in 3-d it may be even more difficult than in 2-d to explain the inactive mode of accretion . however , if the torus forms then our simulations show that the torus will precess . this precession may have important consequences in terms of reducing the mass accretion rate . namely , a precessing torus may produce a precessing jet / wind that will then affect a larger volume of the surrounding material than a non - precessing jet / wind . our simulations are in principle relevant to any type of a black hole , which accretes gas with some small angular momentum , because the results should scale with the black hole mass . note , that the parameters in our models were chosen so that the ratio of the bondi radius to the schwarzschild radius was equal to 10@xmath177 and the computational domain was between 1.5 @xmath25 and 1.2 r@xmath178 . in this context , one of the most interesting cases is that of the low luminosity active galaxies , and in particular the sgr a@xmath179 , for which the supermassive black hole of @xmath180 was identified in the center ( ghez et al . 2005 ) . the bondi accretion rate in the galaxy center inferred from the studies of stellar winds was estimated to be between @xmath181 and @xmath182 @xmath183yr@xmath184 , while the polarization studies suggest that the actual accretion rate is between @xmath185 and @xmath186 @xmath183yr@xmath184 from rosat observations ( quataert , narayan & reid 1999 ; baganoff et al . 2003 ; bower et al . although the values overlap , most of the authors agree that in sgr a@xmath179 the accretion rate onto the black hole is well below the bondi value . also , studies of other quiescent agn suggest that some modification of the bondi accretion is needed ( e.g. di matteo et al . 2000 ) .    the hydrodynamical studies of black hole accretion in sgr a@xmath179 which took into account a random distribution of stars were presented in coker & melia ( 1997 ) . the analytical estimates of the effective angular momentum of the accreting gas performed by mocibrodzka , das & czerny ( 2006 ) were based on the strengths of the stellar winds . recently , cuadra , nayakshin & martins ( 2006 ) modeled the wind accretion allowing the stars to move on the elliptical orbits . we show here that the accretion rate of less than 40% of the bondi value is possible also in models , where the rotationally supported torus does not close , and an asymmetric structure of material being almost spherical on one side of the black hole may persist as a kind of steady - state ( model with @xmath187 ) . only for very small input of the angular momentum gas , corresponding to the total @xmath188 , the accretion flow is still remains almost spherical and the accretion rate does not drop much below the bondi value . perhaps our most intriguing results we found , is the instability and precession of the torus . the precession occurs for the closed rotationally supported torus , which forms for large angular momentum input @xmath189 . in other words , we found that even a very small asymmetry in the angular momentum distribution ( not necessarily in the initial conditions ) will lead to the torus misplacement from the equatorial plane and its precession . this happens after a few tens of orbital cycles . for the models where the torus did not form due to a very large content of non rotating gas accreting in purely radial direction , the asymmetric condition makes the quasi - steady configuration very unstable , and rapid fluctuations of the global flow pattern occur on the timescales of a few dynamical cycles . the clumps of gas with large density become misplaced from the equator . for example , in the model with @xmath190 the misplacement reaches a few tens of degrees and changes in the flow configuration are extremely violent . the problem of the stability of accretion tori with respect to the axial perturbations was studied in a number of papers . the classical rayleigh condition for the torus stability ( sufficient only for axisymmetric modes ) is that the specific angular momentum should not decrease outwards ( see e.g. chandrasekhar 1961 ) . the kelvin - helmholtz instability occurs when two superimposed layers of fluid are in a relative motion . when the velocity shear exceeds a critical value , the resulting pressure gradient ( from bernoulli s law ) between the peaks and troughs of an interfacial wave overcomes the surface tension and gravity , and the mode grows exponentially . papaloizou & pringle ( 1984 ) studied the stability of the non - axisymmetric modes of the differentially rotating tori . in this first paper , they limited their considerations to the homentropic tori with constant specific angular momentum , and they found , that all such tori are unstable to the low order modes and the instability occurs on a dynamical timescale . these instabilities are found to be global , i.e. their presence can not be detected via the local analysis nor from the considerations of axisymmetric modes . in their second paper ( papaloizou & pringle 1985 ) , they considered the tori with non - constant specific angular momentum and they found that for low azimuthal number @xmath191 the instability is driven by a kelvin - helmholtz mechanism . the modes are stable in disks with angular velocity decreasing with radius as @xmath192 , if @xmath193 . for high @xmath191 , the modes regain their sonic character , and there exist sonic modes which are driven by both mechanisms . however , their analytical calculations were done in the limit of a keplerian disk ( @xmath194 ) . in our models , @xmath195 is about @xmath196 . in the innermost parts , the flow is supersonic and compressible . future work is needed to perform stability analysis for such flow properties .    from the point of view of numerical , multi - dimensional simulations , as it has been recently discussed by foglizzo , galletti & ruffert ( 2005 ) that it is not always obvious to determine whether the hydrodynamical instabilities are a physical or numerical effect . as shown by our simulations , and confirmed by the tests with smaller mach numbers ( models @xmath81 and @xmath82 ) , the instabilities that lead to the torus precession do not develop in a subsonic flow ( see also mocibrodzka & proga 2008 ) . the acoustic instability develops in the 3-d accretion when the mach number is large , and for @xmath197 , and it is found to be a physical instability in a strongly supersonic flow . we plan to verify this result for other values of @xmath198 , and perform more detailed resolution tests in the future work .    from the observational point of view , the precessing torus might be relevant to the interpretation of jet emitting sources , provided that the jet axis is always perpendicular to the disk surfaces . recent observations of radio jets show jet reorientation . one of possible explanation for this reorientation may be the jet precession , as was suggested e.g. , for the shape of the source 3c294 ( erlund et al . also , the morphology of the bal quasar 1045 + 352 indicates either a precessing jet or an ongoing merger process ( kunert - bajraszewska & marecki 2007 ) . in addition , the morphology of some of the vlba observed curved jets suggests jet precession because of relatively short timescales ( lister 2006 ) . we thank monika mocibrodzka and aneta siemiginowska for helpful discussions and comments . we thank the developers of zeus - mp for providing the code publicly available and for support . this work was supported by nasa under grant nng05gb68 g . this work was also supported by the national science foundation through teragrid resources provided by national center for supercomputing applications under grant ast070019n . 99 baganoff f.k . , et al . , 2003 , apj , 591 , 891 begelman , m.c . , & meier , d.l . 1982 , apj , 253 , 873 blandford r. , begelman m. , 1999 , mnras , 303 , l1 bondi h. , 1952 , mnras , 112 , 195 bower g.c . , falcke h. , wright m.c . , backer d.c . , 2005 , apj , 618 , l29 chandrasekhar , s. , hydrodynamic and hydromagnetic stability , 1961 , oxford university press catlett , c. et al . `` teragrid : analysis of organization , system architecture , and middleware enabling new types of applications , '' hpc and grids in action , ed . lucio grandinetti , ios press advances in parallel computing series , amsterdam , 2007 coker r.f . , melia f. , 1997 , apj , 488 , l149 cuadra , j. , nayakshin , s. , springel , v. , & di matteo , t. 2006 , mnras , 366 , 358 di matteo , t. , quataert e. , allen s.w . , narayan r. , fabian , a.c . , 2000 , mnras , 311 , 507 erlund , m.c . , fabian , a.c . , blundell , k.m . , celotti , a. , & crawford , c.s . , 2006 , mnras , 371 , 29 foglizzo t. , galletti p & ruffert m. , 2005 , a&a , 435 , 397 fragile p.c . , blaes o.m . , annios p. , salmonson j.d . , 2007 ( astro - 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ph/0706.3900 ) woosley , s.e . 1993 , apj , 405 , 273          ( see tab . [ tab : models ] ) , for 6 time snapshots , from top to bottom : @xmath199 = 0.0 , 0.018 , 0.09 , 0.16 , 0.23 and 0.29 . the maps show the central region ( only upper right map is zoomed - out ) in the equatorial plane ( @xmath200 ) : density and velocity field ( left ) and specific angular momentum ( right ) . the solid line marks the contour of @xmath201 . ] ( see tab . [ tab : models ] ) , plotted in the @xmath36 plane , at 4 slices of the @xmath33 angle : @xmath202 , @xmath123 , @xmath124 and @xmath125 . the maps show density and velocity fields in the central region . the corresponding times are , from top to bottom : @xmath199 = 0.0 , 0.018 , 0.09 , 0.16 , 0.23 and 0.29 . ] ( see tab . [ tab : models ] ) , plotted in the @xmath36 plane , at 4 slices of the @xmath33 angle : @xmath202 , @xmath123 , @xmath124 and @xmath125 , and at @xmath199 = 0.0 , 0.018 , 0.09 , 0.16 , 0.23 and 0.29 ( from top to bottom ) . the maps show the central region ( only first map is in zoomed - out ) . the solid line mark the contour of @xmath203 . ] = 0.018 , 0.09 , 0.16 , 0.23 and 0.29 , for model @xmath204 ( see tab . [ tab : models ] ) . the colors mark the surfaces of @xmath205 , 1250 and 2000 @xmath20 . the boxes are scaled to the density isocontour @xmath206 @xmath20 and show the central region of the radius about 0.004 @xmath28 . ] = 0.018 , 0.09 , 0.16 , 0.23 and 0.29 , for model @xmath204 ( see tab . [ tab : models ] ) . the colors mark the surfaces of @xmath207 , 2.15 and 3.0 . the boxes are scaled to the isocontour of @xmath207 and show the region of the radius about 0.6 @xmath28 . ] ( see tab . [ tab : models ] ) plotted in the equatorial plane , at @xmath199 = 0.29 . the maps show : angular velocity ( upper left ) , velocity divergence ( upper right ) , radial to azimuthal velocity ratio ( bottom left ) and entropy ( bottom right ) . the arrows denote the directions of velocity vectors with @xmath208 and @xmath16 components ( upper two panels ) , with only @xmath208 component ( bottom left panel ) or vorticity vectors with @xmath209 and @xmath210 components ( bottom right panel ) . ] = -8 cm , for one of the broken torus models , @xmath211 ( see tab . [ tab : models ] ) . the colors mark the surfaces of @xmath205 , 1250 and 2000 @xmath20 . the boxes are scaled to the density isocontour @xmath206 @xmath20 and show the central region of the radius about 0.004 @xmath28 . , title=\"fig : \" ]","summary":"we report on the fourth phase of our study of slightly rotating accretion flows onto black holes . we consider hydrodynamics of inviscid accretion flows . we assume a spherically symmetric density distribution at the outer boundary , but brake the flow symmetry by introducing a small , latitude - dependent angular momentum . we also consider cases where angular momentum at large radii is latitude- and azimuth - dependent . for the latitude - dependent angular momentum , 3-d simulations confirm axisymmetric results : the material that has too much angular momentum to be accreted forms a thick torus near the equator . consequently , accretion proceeds only through the polar funnel , and the mass accretion rate through the funnel is constrained by the size and shape of the torus , not by the outer conditions . in 3-d simulations , we found that the torus precesses , even for axisymmetric conditions at large radii . for the latitude and azimuth - dependent angular momentum , the non - rotating gas near the equator can also significantly affect the evolution of the rotating gas .","abstract":"we report on the fourth phase of our study of slightly rotating accretion flows onto black holes . the main new element of this study is that we used fully three dimensional ( 3-d ) numerical simulations . we consider hydrodynamics of inviscid accretion flows . we assume a spherically symmetric density distribution at the outer boundary , but brake the flow symmetry by introducing a small , latitude - dependent angular momentum . we also consider cases where angular momentum at large radii is latitude- and azimuth - dependent . for the latitude - dependent angular momentum , 3-d simulations confirm axisymmetric results : the material that has too much angular momentum to be accreted forms a thick torus near the equator . consequently , accretion proceeds only through the polar funnel , and the mass accretion rate through the funnel is constrained by the size and shape of the torus , not by the outer conditions . in 3-d simulations , we found that the torus precesses , even for axisymmetric conditions at large radii . for the latitude and azimuth - dependent angular momentum , the non - rotating gas near the equator can also significantly affect the evolution of the rotating gas . in particular , it may prevent the formation of a proper torus ( i.e. its closing , in the azimuthal direction ) . in such models , the mass accretion rate is only slightly less than the corresponding bondi rate ."}
{"article_id":"nucl-ex0103003","section_id":"i","document":"the beta - decay lifetime of the neutron is of interest in a number of contexts . it has a direct impact on cosmological modeling as an input to the calculation of the production of light elements during the big bang . the isotopic ratios measured in extragalactic gas clouds ( in which isotopic abundances are thought to have remained constant since the big bang ) can be compared to big bang nucleosynthesis calculations in order to place limits on the ratio of baryons to photons in the early universe . in the calculation of the expected @xmath3he/@xmath4h ratio , the dominant uncertainty is the lifetime of the neutron@xcite . beta decay of the neutron is both the simplest nuclear beta decay , and more generally , the simplest of the charged - current weak interactions in baryons . measurements of the weak interaction parameters can be obtained using neutron beta decay with fewer and simpler theoretical corrections than measurements using the beta decay of nuclei . the neutron beta decay rate is proportional to the quantity @xmath5 where @xmath6 and @xmath7 are the semileptonic vector and axial - vector coupling constants . to extract the coupling constants uniquely from neutron beta - decay measurements requires either an independent measurement of @xmath6 or @xmath7 or of the ( more experimentally accessible ) ratio @xmath8 . the technique of magnetic trapping offers the promise of significant improvements over previous measurements in the accuracy of the neutron lifetime ( @xmath9 ) . past measurements have relied on two techniques for measuring @xmath9 : beam and closed - sample type measurements . at present , both techniques appear to be systematically limited at the @xmath10 level .    in a beam measurement , a well collimated cold neutron beam passes continuously through a decay region of known volume . each neutron decay occurring in that volume is counted . at the end of the decay region , the flux of the neutron beam is measured with a 1/@xmath11 weighting , where @xmath11 is the velocity . the neutron lifetime is ideally given by the ratio of the number of decays per unit time to the number of neutrons in the decay region . in the most precise measurement to date using this method ( @xmath12  s @xcite ) , neutron decays were counted by detecting the decay protons and the beam flux was measured by detecting @xmath13-particles emitted in the @xmath14 reaction . of the 4.8  s uncertainty , 3.4  s is attributed to systematic effects in the measurement of the neutron flux . an improved version of this experiment ( presently running at the national institute of standards and technology , nist ) aims for an accuracy of less than two seconds@xcite .    in the closed - sample measurements , neutrons with energies lower than the interaction potential of the material ( i.e.  ultracold neutrons or ucn ) are loaded into a physical box and stored ( via total reflection of the neutrons from the material surfaces ) for a variable length of time before being counted . the neutron lifetime can be extracted from the dependence of the detected neutron population on the storage time . several storage techniques have been used to make measurements of the neutron lifetime . the most precise storage measurements yielded values of @xmath15  s@xcite , @xmath16  s@xcite and @xmath17  s@xcite . experiments using this storage technique to measure the neutron lifetime measure the total rate at which neutrons are lost from the storage vessel , both by beta decay and by any other loss mechanisms . the accuracy of the lifetime measurement is limited either by unknown loss mechanisms or by the uncertainty in corrections for large loss mechanisms which arise from the interactions between the stored neutrons and the walls of the storage vessel . most experiments use storage data to extrapolate to the ideal case of no wall losses . in ref . @xcite , the physical size of the storage vessel is varied , and the measurements are extrapolated to an infinite volume . in ref . @xcite , the storage time is measured as a function of ucn velocity , and an extrapolation is made to zero velocity , or an infinite time between collisions with the walls . the most recent measurement , @xcite , uses two different storage - vessel sizes with neutron detectors to measure the relative rate at which neutrons are scattered out of the storage vessel in the two configurations . a second storage technique uses the interaction of the magnetic moment of the neutron with magnetic field gradients . this technique was first discussed by vladimirski@xmath18 in 1961@xcite , just two years after zeldovich first discussed material storage@xcite . since that time there have been several experiments to store neutrons magnetically with varying degrees of success@xcite .    in the nestor ( neutron storage ring ) experiment , neutrons in a range of velocities from 6  m  s@xmath19 to 20  m  s@xmath19 were stored in a sextupole magnetic storage ring analogous to the storage rings used at particle accelerators@xcite . magnetic field gradients reflect neutrons at a glancing incidence , storing neutrons in certain trajectories . the storage ring technique relies on the stored neutrons to remain in these trajectories . neutron loss from these trajectories ( attributed to betatron oscillation ) limited this measurement . three - dimensional magnetic trapping was later attempted with a spherical hexapole trap@xcite . the lack of neutrons trapped in this experiment was attributed to upscattering of neutrons from the trap by phonons in their 1.2  k helium bath . another experiment used a large ( @xmath20  @xmath21 ) box with several current loops providing the magnetic field for confinement along the floor and walls ( the top was `` closed '' by gravity ) . despite its size it was never able to confine more than a few ( of order one ) neutrons at a time due to its a trap depth of @xmath22k@xcite .    the use of three - dimensional magnetic confinement to measure the neutron lifetime provides an environment that is free of the systematic effects that have limited previous lifetime measurements . the magnetic trapping technique is not sensitive to variations in the neutron flux ; each decay is recorded as a function of time and both the lifetime and initial number of neutrons can be extracted . magnetic trapping also eliminates wall interactions and betatron losses ; neutrons are not confined by physical walls and are energetically forbidden from leaving the trapping region . these advantages should allow for a significant improvement in the accuracy of the neutron lifetime . given a sufficient neutron flux it should be possible ( using estimates of known loss mechanisms discussed below ) to measure @xmath9 at the @xmath23 level . the method of measuring the neutron lifetime using magnetic trapping that is discussed in this paper was proposed in 1994@xcite .    in this work ultracold neutrons are produced , magnetically trapped , and detected as they decay . the experimental concepts are discussed in section  [ sect : idea ] . a description of the experimental apparatus is given in section  [ sect : app ] . the results are presented in section  [ sect : res ] , with a discussion of these results in section  [ sec : disc ] . the feasibility of using an improved version of this experiment to make a neutron lifetime measurement is discussed in section [ sect : conclusion ] . the techniques developed for this experiment have other potential fundamental physics applications , also discussed in section [ sect : conclusion ] , such as improved sensitivity in the search for the neutron s electric dipole moment@xcite or detection of low energy neutrinos@xcite .","summary":"three - dimensional magnetic confinement of neutrons is reported .","abstract":"three - dimensional magnetic confinement of neutrons is reported . neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light . this light is frequency downconverted to the visible and detected . results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime ."}
{"article_id":"nucl-ex0103003","section_id":"r","document":"neutrons have a magnetic moment , @xmath24 , and interact with a magnetic field , @xmath25 , by the dipole interaction : @xmath26 where the magnetic moment of the neutron is oriented anti - parallel to its spin ( @xmath27 ) . when the neutron spin is aligned parallel to the magnetic field the interaction energy is positive and regions of high magnetic field repel neutrons in the parallel spin state . these neutrons are denoted `` low - field seekers '' . static magnetic traps create a magnetic field minimum in free space to confine low - field - seeking particles . one such trap , known as an ioffe trap , conceptually ( and in our case schematically ) consists of four wires and two coils as shown in fig . [ fig : ioffe ] . this configuration has been used to confine ions and plasmas and more recently to trap neutral atoms@xcite . the four wires with alternating current direction provide a cylindrical quadrupole field . the two coils , coaxial with the same current sense , provide a non - zero field throughout the trapping region . our magnet is of this form and is described further in section  [ sect : app ] . the interaction potential given in eq . [ eq : magint ] also causes the component of the magnetic moment perpendicular to the field to precess around the local direction of the field with a frequency @xmath28 ( @xmath29  mhz at 1  t ) . if this precession is considerably faster than the change in the direction of the field seen by the neutron , that is if @xmath30 then the neutron spin will remain aligned with @xmath25 as it moves throughout the trap ( i.e.  the neutron spin state will not change relative to the field ) . under these conditions , one can essentially view the magnetic potential , @xmath31 , as depending only on the magnitude , not the direction , of the magnetic field . near regions in which the field approaches zero this condition is not fulfilled and trapped , low - field - seeking neutrons can invert their spin and be lost from the trap ( majorana spin - flip losses ) . provided @xmath32 is sufficiently large ( i.e.  no zero - field regions ) a neutron initially in the trapped state will remain in the trapped state as it moves throughout the trap .      to load neutrons into the trap their energy must be dissipated inside the trapping region . the `` superthermal '' process ( so called because it allows one to achieve phase space densities greater than that coming from a `` thermal '' liquid hydrogen or deuterium cold source ) is an efficient method to load the trap@xcite . the superthermal production of ucn in superfluid helium depends critically on the fact that cold neutrons can not scatter with individual helium atoms as they would in a gas , but must scatter with excitations ( phonons and rotons ) in the superfluid . the dispersion curve ( energy versus momentum ) for these excitations in superfluid helium@xcite is shown in fig . [ fig : disp ] with the energy of the free neutron ( @xmath33 ) overlaid for comparison . for a neutron to scatter to the vicinity of @xmath34 via the dominant single phonon scattering process , momentum and energy conservation limit the initial neutron momentum to values of @xmath35 . this results in the creation of a single 12  k phonon in the helium . similarly , a ucn with @xmath36  mk can only `` upscatter '' by absorbing a 12  k phonon ( ignoring multi - phonon processes for the moment ) . this fact allows one to treat the neutron interaction with the superfluid as a two level system with a 12  k energy difference between the two levels . and at @xmath37 , which corresponds to a neutron wavelength of 0.89  nm , or an energy of 12  k. ]    the one - phonon upscattering rate can be expressed as @xmath38 where @xmath39 is the boltzmann constant . for a fixed @xmath40 ( 12  k in our case ) , the upscattering rate can be made arbitrarily small since it decreases exponentially with the temperature @xmath41 of the helium bath . physically this corresponds to decreasing the population of phonons of energy @xmath40 . in practice , however , the rates of other ( multi - phonon ) scattering processes dominate the upscattering rate at low temperatures . the second - order process is denoted as two - phonon upscattering , although it applies equally to the scattering of a neutron by a single phonon , in which the phonon is not absorbed . the rate of the two - phonon upscattering scales as @xmath42@xcite and has been measured down to 500  mk @xcite . in a helium bath at a temperature of 1.16  k , the upscattering rate was @xmath43  s@xmath19 , corresponding to a storage time of 40  s. at our operating temperature of 250  mk , the upscattering rate should be 2000 times less than the beta - decay rate . minor modifications to the apparatus now allow the helium to be cooled below 100  mk , making the two - phonon upscattering rate negligible in performing a lifetime measurement . the use of superfluid helium to produce ucn has been demonstrated in several previous experiments@xcite and upscattering rates have been measured in refs . @xcite and @xcite . when a neutron decays in the trap , the recoiling electron scatters from atomic electrons of the helium , ionizing tens of thousands of helium atoms . the electron deposits 300  kev  cm@xmath19 in the helium with the range of a typical electron of order 1  cm@xcite . the helium ions tend to form diatomic molecular ions before recombining with electrons , leading to the creation of excited - state diatomic helium molecules . these molecules are created in both singlet and triplet states . when each helium molecule decays it emits a photon in the extreme ultraviolet ( euv ; @xmath45  nm ) . the singlet decays give a relatively intense pulse of light in a short time ; 4000  euv photons in less than 20  ns for a typical neutron decay@xcite . these singlet decays and are used to detect the neutrons decaying in the trap . the longer decay time for the triplet states renders them less useful for this purpose . the same number of photons emitted over 13  s@xcite makes it impossible to distinguish the triplet events from backgrounds . to detect the light pulse emerging from the singlet decays directly in the trap would require euv sensitive detectors that work at low temperatures ( @xmath46  mk ) , in liquid helium , and inside an intense magnetic field ( 1  t ) . the detectors would also be exposed to the cold neutron beam , or at least to neutrons scattering in the helium , and would need to tolerate this radiation without creating backgrounds . finally , there is limited space available inside the magnet bore . since it is extremely difficult to satisfy these detector requirements , the scintillation light is detected indirectly . the euv scintillation light is converted to blue / violet light inside the apparatus using a pure hydrocarbon , 1 - 1 - 4 - 4 tetraphenyl 1 - 3 butadiene ( tpb ) . tpb absorbs euv light and emits light in a spectrum ranging from 400  nm to 500  nm@xcite . this light can then be transported out of the trapping region and into detectors at room temperature . the detector insert is described in detail in section  [ sect : app ] . each experimental run consists of a loading phase in which the neutrons are loaded into the trap and an observation phase in which the trapped neutrons are detected as they decay . at the start of a run the magnetic field is on forming the magnetic trap which will confine the neutrons . the neutron beam is turned on and neutrons begin to scatter in the liquid helium , producing ucn which become confined in the trap . the ucn creation rate is proportional to the incident neutron flux and is constant during the loading phase . ucn are lost from the trap by beta decay in proportion to the number trapped . thus , neutrons accumulate in the trap with a time constant of the neutron lifetime or approximately 15  min . in the actual experiment , the trap is loaded for 22.5  min , yielding 78  % of the trapped ucn population that could be achieved with an infinite loading time . once the beam is turned off , the number of neutrons in the trap decreases due to beta decay . the photomultiplier tubes are turned on 10  s after the beam is turned off and neutron decays are detected for 1  h , giving a time - varying signal directly proportional to the decreasing number of neutrons in the trap . trapped neutrons are indicated by an exponentially decaying signal consistent with the neutron beta - decay lifetime , or a more rapid decay if there are additional trap losses . two classes of problems could prevent observation of this signal : spurious losses ( which cause the initial trapped population to be significantly lower due to losses during loading ) and background events ( which could give a much higher overall counting rate and obscure a trapped neutron signal ) . the next two subsections will treat these two issues . known loss mechanisms include one- and two - phonon upscattering ( which as discussed above is reduced by cooling the helium target ) , majorana spin - flips ( which are minimized by the non - zero - field character of the trap ) , and @xmath47he absorption . in addition , some neutrons with energies greater than the trap depth ( that is , sufficient to allow them to escape ) may be confined by the field for an extended period of time but escape from the trap before they decay . helium has two stable isotopes , @xmath47he and @xmath3he . while @xmath3he does not absorb neutrons , @xmath47he has an extremely high absorption cross - section . for ucn contained within a bath of @xmath3he with a small amount of @xmath47he present , the absorption rate is given by : @xmath48 where @xmath49 is the ratio of @xmath47he atoms to @xmath3he atoms , @xmath50 is the density of helium nuclei , @xmath51 is the thermal cross section for neutron capture onto @xmath47he and @xmath52 is the neutron velocity at room temperature . isotopically purified @xmath3he is available with @xmath53@xcite . at this limit , the absorption rate is @xmath54 , or ten thousand times less than the beta - decay rate . this gives a negligible shift in the trap lifetime . `` reversing '' this analysis allows the data presented in section  [ sect : res ] to yield a three standard deviation upper limit on the @xmath47he concentration of @xmath55 . a more accurate , independent measurement of @xmath49 using accelerator mass spectroscopy is presently being pursued . a `` marginally trapped '' neutron is one with an energy greater than the trap depth , but in a trajectory that keeps the neutron confined in the trapping region for a significant time . simulations have determined that the vast majority of these neutrons will be expelled from the trap within a few seconds@xcite . in addition , it has been shown through analytical calculations@xcite that by lowering the magnetic field to 30  % of its original value and then raising it back up , a trapped sample is achieved that has no neutrons stored with energies above the trap depth and about one - half of the original trapped neutrons . for this demonstration of trapping , this procedure is not necessary . background events are any events recorded by the data acquisition system that arise from sources other than decaying neutrons . the data acquisition system records an event when coincident pmt pulses above a set charge threshold occur on the two photomultipliers observing the trapping region . events which are coincident with the detection of light pulses from pmts observing plastic scintillator paddles placed below the primary detection cell are vetoed . hence the detection system is designed to reject several expected backgrounds . cosmic ray muons pass through materials at a rate of 1  @xmath56  min@xmath19@xcite and penetrate any reasonable shielding . they leave an ionization trail as they pass through , depositing roughly 2  mev  g@xmath19@xmath57 times the density of the material@xcite . pulses in the primary detection system due to cosmic ray muons are vetoed by the auxiliary paddles and do not produce background events . the requirement of coincidence between two pmts observing the trapping region suppresses background events caused by neutron induced luminescence of materials . the neutron absorbers used to shield the materials surrounding the trapping region from the neutrons ( primarily hexagonal boron nitride , hbn ) glow after exposure to neutrons with a magnitude decreasing slowly on a time scale comparable to an experimental run@xcite . this luminescence ( which was for some time the major obstacle to extracting the trapped neutron signal ) was attenuated by placing graphite between the hbn and the light collection system and by replacing the collimator and beam stop with b@xmath58c ( a material which has considerably less luminescence ) . to suppress this background , coincident detection in two pmts is employed . a signal is recorded when at least two photons are detected in each pmt within a 23  ns window . with this threshold , the efficiency for detecting neutron decays is 31  % . the system is also susceptible to background events from other sources . the passage of high - energy particles through any part of the trapping region or detection system is expected to cause scintillations in the primary pmts . other than cosmic ray muons which are vetoed , any particle that causes a detected scintillation will produce a background event . such particles include decay products from radioactive nuclei , either naturally occurring or created by neutron capture during the loading phase , and neutral particles ( gamma rays or fast neutrons ) created outside of the apparatus . unlike muons , gamma rays and fast neutrons tend to lose a significant fraction of their energy in each scattering event and can not be detected with veto detectors . to reduce background events from gamma rays , the apparatus is shielded with 10  cm of lead . backgrounds from decays of isotopes created by neutron absorption decay exponentially with their respective lifetimes . to minimize such backgrounds , the materials exposed to the neutron beam are carefully chosen such that their primary constituents have small neutron absorption cross sections ( or absorb neutrons to form a stable isotope , thus giving no background ) .    despite several successful methods of reducing backgrounds , a decaying signal with peak magnitude of roughly 0.2  s@xmath19 had to be extracted from a time - varying background signal of about 6  s@xmath19 initially , with a constant component of 2  s@xmath19 at longer times . this was accomplished by measuring the background directly , taking half of the runs with the magnetic trap initially turned off , and subtracting this background from the trapping runs .","summary":"neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime .","abstract":"three - dimensional magnetic confinement of neutrons is reported . neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light . this light is frequency downconverted to the visible and detected . results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime ."}
{"article_id":"nucl-ex0103003","section_id":"r","document":"the experiment resides at the end of cold neutron guide number six ( ng-6 ) in the guide hall of the nist center for neutron research ( ncnr)@xcite . neutrons are released from the 20  mw reactor and are moderated by d@xmath59o surrounding the reactor core and then by a liquid hydrogen cold source operating at a temperature of 20  k. neutrons partially thermalize with the hydrogen and exit towards the neutron guides . some fraction of these neutrons pass into the open end of ng-6 , a rectangular @xmath60ni - coated guide 60  m long , 15  cm tall and 6  cm wide . neutrons exiting the far end of ng-6 pass through a 6  cm diameter collimating aperture ( @xmath61 ) and then through filtering materials consisting of 10  cm of bismuth and 10  cm of beryllium . the single crystal bismuth attenuates the flux of gamma rays from upstream sources . the polycrystalline blocks of beryllium bragg - reflect neutrons with wavelengths less than 0.395  nm , removing them from the beam . the neutron beam exiting the filter has a measured capture flux of @xmath62  n  @xmath56s@xmath19@xcite .    immediately preceding the trapping region , a second aperture ( @xmath63 ) collimates the beam before it enters the trapping region . the collimators @xmath61 and @xmath63 are chosen such that any neutron passing through both collimators will be absorbed in the beamstop at the end of the trapping region unless it scatters in the helium . the wavelength spectrum of the beam is measured in a separate experiment by the time - of - flight method . the beam is collimated to a diameter of 400  @xmath64 m . a cadmium disc positioned directly behind the collimator and rotating at 67  hz blocks the beam except when either of a pair of slits 250  @xmath64 m wide passes in front of the collimator . neutrons passing through the slit are detected using a @xmath47he detector placed 69  cm behind the chopper . the output of the @xmath47he detector is recorded with a multi - channel scaler , with a 5  @xmath64s bin width . the scaler is triggered using a light emitting diode ( led ) and a photodiode detecting the passage of the slit approximately 180@xmath65 from the neutron beam . data from the time - of - flight spectrum is shown in fig . [ fig : tof_dat ] . two points in the spectrum are available to set the initial time , the beryllium edge , at 0.395  nm , and the narrow slice of the beam removed by an upstream monochromator in the neutron guide at 0.48  nm . both the unnormalized capture flux and 0.89  nm flux ( important for ucn production using scattering from liquid helium ) can be extracted . using the known capture flux for normalization , the flux at 0.89  nm is @xmath66 the error bars are one standard deviation and primarily correspond to uncertainties in the wavelength calibration . the ucn are confined in an ioffe - type superconducting magnetic trap@xcite . the magnet uses four racetrack - shaped coils to produce the quadrupole field . these consist of two different size coils and are assembled as shown in fig . [ fig : form ] . the two larger coils , with 777 turns each , are 69.1  cm long by 9.2  cm high , with a coil cross - section of 3.2  cm by 2.0  cm . the smaller coils , with 336 turns each , are 65.2  cm long by 5.3  cm high , with a cross section of 1.5  cm by 2.0  cm . the coils are placed onto the 6 - 4 eli grade titanium form and isolated using kapton and g-10 spacers . aluminum compression plates , machined to give a cylindrical outer surface , are attached to the form to provide compression of the coils . this cylindrical assembly is wrapped under 67  n of tension with 20 layers of kevlar to uniformly compress ( prestress ) the coils . to protect the kevlar , the magnet was first wrapped in a layer of tedlar then the kevlar , and then an outer layer of fiberglass with the wrappings embedded in epoxy . the quadrupole assembly had an outer diameter of 14.5  cm and an inner bore of 5.08  cm . the ends of the titanium form were machined to mate directly with the inner vacuum can of the cryostat . the solenoid assembly surrounds the quadrupole assembly and consists of two sets of solenoids . each set contains a primary solenoid which is flanked by a pair of smaller solenoids with opposite polarity . these cause the magnetic field of the primary solenoid to fall off more quickly with distance along its axis . the primary solenoids each consist of 1564  turns with an inner diameter of 14.7  cm , outer diameter of 18.2  cm and length of 5.15  cm . the two `` bucking '' coils placed 5.0  cm on each side of the primary coil are 365  turns with an inner diameter of 14.7  cm , outer diameter of 21.5  cm and length of 1.15  cm .    the magnitude of the quadrupole field increases linearly with radius with a gradient of 0.69  t  cm@xmath19 ( at 180  a ) . along the axis of the form , the field minimum ( 0.11  t at 180  a ) is provided by the solenoids . denoting this axis as the @xmath67-axis , the magnitude of the field along the @xmath68-axis is shown at @xmath69 in fig . [ fig : quadprof ] .    ) . ]    the solenoids each create a short high - field region closing off the ends of the trapping region . the field along the @xmath67-axis is shown at @xmath70 in fig . [ fig : solprof ] .    ) , showing the `` pinch '' resulting from each solenoid , closing the ends of the trap . ] the depth of the magnetic trap is defined as the difference between the lowest field point at which neutrons can be lost from the trap ( @xmath71 ) and the lowest field point in the trap ( @xmath72 ) . in our geometry , the solenoids were chosen to produce a peak field higher than the walls of the quadrupole . the trap depth is thus set by the quadrupole field at the inner edge of the detector insert ( see below ) . this occurs at a radius of 1.59  cm , corresponding to a trapping field of 1.15  t. subtracting the minimum field of 0.11  t gives a net trap depth of @xmath73  t.      cooling the helium target below 250  mk requires the use of a @xmath47he-@xmath3he dilution refrigerator which is connected to horizontally oriented magnetic trapping region . this required a custom - designed cryogenic dewar , consisting of a horizontal section to house the magnet and trapping region and a vertical section to house the refrigerator and is shown in fig . [ fig : dewar ] . the neutron beam enters from one end of the dewar and light from the neutron decays exits from the opposite end . the neutron entrance windows consist of two layers of different materials , one to make a vacuum seal and the other to block black - body radiation , with both having good neutron transmission properties . the vacuum windows are made from a clear fluoropolymer , teflon pfa . a simple compression seal , where the edges of a teflon disc are compressed between two metal flanges until the teflon begins to deform , provides the vacuum seal@xcite . the windows used at 250  mk ( where black - body absorbers are not needed ) are 250  @xmath64 m thick , 6.35  cm in diameter , leaving a 6.35  mm wide section compressed around the circumference of a window 5.08  cm in diameter . the other two windows at 300  k and 4  k are similar with a 7.62  cm diameter disc making a window 6.35  cm in diameter . to block blackbody radiation , a 50  @xmath64 m thick , 6.35  cm diameter beryllium disc ( grade pf-60 , brush wellman ) covered the teflon window at both the 4  k and 77  k end flanges . the light transmission windows , on the opposite end of the cryostat , are made from ultra - violet transmitting ( uvt ) acrylic ( polymethyl methacrylate or pmma ) and are sealed using epoxy , indium o - ring seals , or rubber o - rings . the isotopically pure @xmath3he and detector insert are contained within the inner vacuum can ( ivc ) and held fixed with respect to the magnet and neutron beam , while thermally anchored to the dilution refrigerator . the helium is contained within the ivc in a tube made of 70 - 30 cupronickel which extends through the magnet and into the end can of the dewar . there , a copper end cap is soft - soldered ( using 50/50 tin / lead solder with nokorode paste flux ) to each end of the tube to provide a sealing surface for either the teflon window or the light transmission window . the endcaps are thermally anchored to the copper heat link which extends to the dilution refrigerator . the cell is filled with isotopically purified @xmath3he by condensing it in from room temperature . the helium is stored as a low pressure room temperature in two 450  l electropolished stainless steel tanks . the storage volume is connected to the cell through stainless steel tubing and all - metal valves . two independent fill lines enter the dewar and each are thermally anchored at various points of the dilution refrigerator before they connect to the cell . the heat link and the fill lines are flexible near the t - section the cell and lower half of the heat link is supported directly from the ivc using kevlar braid . when the neutron beam is open to the trapping region , @xmath74  n  s@xmath19 enter the helium bath . at the end of the trapping region , those neutrons which have not scattered in the helium are absorbed in the beam dump . since the scattering cross section for cold neutrons in liquid helium@xcite decreases rapidly with wavelength , at 0.89  nm , only 6  % of the neutrons scatter , while at 0.45  nm , almost 40  % scatter . as a result , about 2@xmath75  n  s@xmath19 ( or a total of 3@xmath76 neutrons ) scatter into the walls when the beam is on , potentially producing backgrounds .    to minimize such backgrounds , neutron absorbing materials are placed such that scattered neutrons do not reach materials that can activate . several different materials are used , all of which contain either lithium or boron , materials which have high neutron absorption cross sections . a sketch of the shielding and windows on the beam entrance end of the dewar is shown in fig . [ fig : efbeam ] . the sensitivity to activation - induced backgrounds is greatest inside the detector insert and lightpipes . to minimize activation in the detection system , the materials inside the shielding are carefully chosen to contain elements which have minimal activation such as hydrogen , carbon and oxygen . surrounding these materials is a shield of hexagonal boron nitride ( hbn , grade ax05 , carborundum corporation ) to absorb the remaining neutrons . this shield consists of a series of interlocking hbn cylinders ( 5  cm long , with an outer diameter of 4.15  cm and a wall thickness of 1.5  mm ) . hbn has a neutron attenuation length of 56  @xmath64 m at 0.89  nm . the hbn is coated with a thin layer of colloidal graphite ( aerodag g , acheson industries ) to attenuate the luminescence ( see below ) . in addition , non - interlocking tubes of graphite ( 15  cm long with a wall thickness of 0.2  mm , grade axf-5q1 , poco graphite ) are inserted between the boron nitride tube and detection region . the detector insert is a uvt acrylic tube whose inner surface is coated with tpb - doped polystyrene ( mass fraction of 40  % tpb ) . this insert , shown in fig . [ fig : detection ] , together with a series of acrylic windows and lightpipes leading to a pair of pmts , forms a detection system allowing neutron decay events to be recorded as a function of time . each beta - decay event in the trapping region gives rise to a pulse of euv light in the helium . this light is downconverted to the visible by the tpb and transported past the opaque b@xmath58c beamstop by the acrylic tube ( 3.8  cm outer diameter , 3.1  mm wall thickness ) to a 3.8  cm diameter solid acrylic lightpipe . this lightpipe extends to the end of the helium - filled cell ( see fig .  [ fig : eflight ] ) . at the end of the cell , the light passes through a pair of uvt acrylic windows into a 7.6  cm diameter lightpipe which extends out of the dewar . the window on the cell is formed by epoxying ( stycast 1266 ) an acrylic window to an acrylic tube . the other end of the tube is epoxied to an thin ( 0.5  mm wall thickness ) aluminum cylinder ( `` snout '' ) which attaches to the cell body . the 3.8  cm lightpipe is epoxied to the window of the snout to prevent the detection insert from moving with respect to the cell . the 7.6  cm lightguide is heatsunk to the 77  k radiation shield using strips of aluminum foil as shown in the figure . outside the dewar , the light emerging from the 7.6  cm lightpipe is coupled into a pair of 5  cm diameter pmts using a series of optical elements ( fig . [ fig : pmts ] ) . the light is first `` condensed '' as it passes through the winston cone@xcite . the light exiting the winston cone is split into two 5  cm diameter lightpipes using a splitter which is made from two 5  cm diameter lightpipes machined at a @xmath77-angle and epoxied together , forming an ell . the corner is machined away leaving a flat elliptical surface with a 5  cm minor axis and a 7.1  cm major axis which is attached to the winston cone . the winston cone and the splitter are diamond turned , polished , and aluminized to maximize the light transmission . the assembly has an 80  % transmission efficiency from the 7.6  cm diameter lightpipe to the two ends of the splitter . all of the optical elements are contained within an aluminum housing which both blocks light and creates a space through which dry n@xmath59 gas is flowed to prevent helium contamination of the pmts .        the photomultipliers are burle model 8850 . the signal is read out at the anode as a discrete current pulse with the tubes biased using positive high voltage . a series of calibrations was performed using both alpha and beta sources to determine the efficiency for detecting neutron decay events . using a @xmath78sn beta line conversion source ( @xmath79  kev ) , the assembled detector insert and light collection system were tested using a single pmt at the end of the winston cone . the resulting spectrum is shown in fig .  [ fig : calib ] , with a typical pulse on average giving between 5.5 and 6.0 photoelectron signal . a series of tests using the higher energy @xmath80po alpha source ( @xmath81  mev ) gives the relative detection efficiency for euv light produced at different longitudinal positions along the cell . the efficiency varies from 75  % to 125  % ( relative to the efficiency at the center of the cell ) along the length and has an approximately linear dependence . a simple monte carlo is used to calculate our efficiency for detecting trapped neutrons . each event is modeled by taking a random position along the length of the cell and a random beta energy , weighted by the known shape of the beta spectrum . the results of the @xmath78sn calibration give an output of @xmath82 photoelectrons per mev of electron kinetic energy . the expected signal is corrected for the measured 80  % efficiency of the splitter and for the dependence of the signal on the position of the event in the cell . requiring coincidence between pulses in both pmts , each having an integrated area corresponding to two or more photoelectrons , results in the detection of @xmath83  % of neutron beta decays in the trapping region . a schematic of the data acquisition system is shown in fig . [ fig : daq ] . the anode signal from each of the two pmts looking at the decay region ( labeled i and j ) is fanned into three outputs . one output connects directly to a digital oscilloscope , while the other two , along with the four muon veto detectors , pass into a discriminator . the voltage thresholds for the pmt signals are set to trigger on each pulse which would give a charge - integrated signal of two or more photoelectrons ( denoted as i@xmath84 and j@xmath84 ) , as determined empirically . the muons are detected using three plastic scintillators ( @xmath85 ) which surround the lower half of the dewar and a fourth detector with slightly smaller dimensions that is placed over the pmts and connecting lightguides . the muon thresholds are set such that each detector produces about 1000  s@xmath19 . varying this threshold so as to change this counting rate by more than a factor of two had no effect on the 8  s@xmath19 muon coincidence rate with the detector insert , indicating that all true coincidences are being included at these threshold levels .        the outputs i@xmath84 and j@xmath84 are anded to produce a coincident i@xmath86 j@xmath84 signal 23  ns long . the inverted output of the 1.5 + coincidence signal is delayed and ored with the delayed combined muon signal to produce @xmath87 , or a coincidence between i@xmath84 and j@xmath84 , where no muon paddle has recorded a coincident muon . this signal is used to trigger the digital oscilloscope . in addition to the above , the trigger output signal from the oscilloscope is recorded . this signal is used in combination with the number of times that the coincidence circuit tried to trigger the oscilloscope to correct for the deadtime of the oscilloscope and to assign time information to each scope event . the counters are active for 98  % of the time , with a dead time of 20  ms during the read out by the computer . digitizing the pulses with an oscilloscope allows one to integrate the area of each pmt pulse and make a cut on the integrated pulse area instead of the peak voltage . the integrated charge gives a sharper distinction between one- and two - photoelectron events , increasing the signal - to - background discrimination efficiency . the first two input channels of the oscilloscope were connected to the amplified outputs of the two photomultiplier tubes i and j. the third , used to trigger the oscilloscope , is connected to the logic signal @xmath88 . for each event , the oscilloscope recorded data at 250 megasamples per second for 1  @xmath64s . after 100 trigger events were recorded , the scope was read out by the computer , giving a deadtime of nearly one second between sets of 100 triggers .","summary":"this light is frequency downconverted to the visible and detected .","abstract":"three - dimensional magnetic confinement of neutrons is reported . neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light . this light is frequency downconverted to the visible and detected . results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime ."}
{"article_id":"nucl-ex0103003","section_id":"r","document":"data were taken in a series of runs , each divided into three phases ( fig . [ fig : posplot ] ) . for the first 100  s , the neutron beam is off . this data are used for diagnostic purposes to detect shifts in the background event rate ( such as from neutron activation of materials in the trapping region with long lifetimes ) . in the loading phase , for the next 1350  s , the neutron beam is on and the trapped ucn population slowly increases , asymptotically approaching the theoretical maximum . during this phase the photomultiplier tubes are turned off and no events are recorded . in the last , or observation phase , data are recorded as the trapped neutron population decays for 3600  s through beta decay . data are recorded both in the form of scaler totals each second and sets of one hundred oscilloscope events . two types of runs were performed . in a `` trap - on '' run the magnetic trap is energized throughout the entire run . in a `` trap - off '' run the magnet is initially off but is brought up to full current during the last 50  s of the loading phase ( making conditions during the observation , phase identical between trap - on and trap - off runs ) . this results in a small number of trapped ucn in the trap - off runs , estimated to be at most 2  % of that in the trap - on runs . the non - trapping or trap - off data are subtracted from the trap - on data . s ) and the times at which the neutron beam is turned on ( @xmath89  s ) and off ( @xmath90  s ) . the run ends at @xmath91  s. ]    to verify that the difference in signal observed between trap - on and trap - off runs is due to the decay of trapped ucn and not from backgrounds , additional runs were necessary . trap - on and trap - off data were taken in the same manner but with other conditions changed so that no ucn should be trapped . specifically , data are taken with the temperature of the helium bath at 1.2  k , rather than at 250  mk ( denoted as `` warm runs '' ) and separately with the helium bath doped with enough @xmath47he ( @xmath92 ) to quickly absorb trapped ucn without significantly attenuating the neutron beam ( denoted as `` @xmath47he runs '' ) . the trapping data were acquired over the course of two reactor cycles . during the first reactor cycle , from 3/23/99 to 4/5/99 , a series of trapping runs was taken , followed by a set of warm runs , more trapping runs , and finally a set of @xmath47he runs . between reactor cycles the cell was pumped out and flushed several times with isotopically pure helium in order to cleanse the cell of residual @xmath47he from the @xmath47he runs . during the next reactor cycle , from 4/16/99 to 5/23/99 , a longer series ( about 18  days ) of trapping runs was taken , followed by a series ( about 20  days ) of @xmath47he runs .    in the first reactor cycle , the magnet operated at a current of 180  a , giving a trap depth of 0.75  mk . during the second cycle , a grounding problem developed in the magnet and it operated at a lower current of 120  a , resulting in a trap depth of only 0.5  mk . the number of trapped neutrons theoretically scales with magnetic field as @xmath93 , resulting in the number of trapped neutrons being a factor of @xmath94 smaller than in the first cycle . the background count rate remained the same , thus even with four times as many runs , the signal extracted from the second set of data is statistically equal to that from the first set .    353 pairs ( trap - on and trap - off ) of data runs were taken , 87 with a trap depth of 0.75  mk and 266 with a trap depth of 0.5  mk . for the 0.75  mk set , there are 32 pairs of trapping runs , 31 pairs of warm runs , and 24 pairs of @xmath47he runs . in the 0.5  mk set , there are 128 pairs of trapping runs and 136 pairs of @xmath47he runs . data are collected using two parallel systems : storage of events using an array of scalers and digitization of the event pulses using a digital oscilloscope as discussed above . the oscilloscope data is binned into 1  s bins and is corrected for deadtime during the oscilloscope readout . this deadtime is strongly dependent on the trigger rate , which is decreasing in time over the course of a run . the exact bin in the scaler data in which the oscilloscope is being read is known . any counts which occur in these bins are thrown out and the entire one second bin is declared as deadtime to avoid any bias . the data are then histogrammed into bins of fifty seconds where the deadtime is small and can be corrected by scaling the data by one over the live fraction . data from the first 50  s of observation in each run contain too much deadtime to be accurately corrected in this manner and instead are removed . the data of a given type ( trapping , warm or @xmath47he ; trap - on or trap - off ; 0.75  mk or 0.5  mk ) are pooled together in fifty second bins and deadtime corrected . these sets of data are compared , subtracting the pooled trap - off data from the pooled trap - on data , to look for a signal ( or lack thereof ) indicating the decay of trapped neutrons . the pooled data from the first reactor cycle are shown in fig . [ fig : cycle1pn ] . the average of the 32 trap - on runs and the 32 trap - off runs is shown starting 50  s after the beam was turned off . the difference between the two is also shown , with error bars ( purely statistical uncertainty ) . there are several significant features in the `` raw '' data from the trap - on and trap - off runs . after the neutron beam has been turned off , both signals approach a level of @xmath95  s@xmath19 . this component of the background is referred to as the `` flat '' background , since it is relatively constant over the course of a given run . at earlier times in the run , a time - varying background can be seen as well . each of these two components of the background arises from different sources . the flat background in the earliest runs of the cycle was 1.4  s@xmath19 , but rose quickly to 1.8  s@xmath19 by the second day , and averaged 2  s@xmath19 over the entire data set . this shift was due to the slow buildup , from neutron activation , of radioactive nuclei with lifetimes greater than one day . approximately 0.6  s@xmath19 of the flat background arises from such long - lifetime activation . the remaining 1.4  s@xmath19 of the flat background probably arises from both gamma rays penetrating the lead shielding around the cryostat and any long - lived radioactive isotopes ( such as uranium or thorium ) naturally occurring in the materials of the apparatus or shielding . without further measurements , the possibility that the majority of the present `` flat '' background comes from naturally occurring radioactive isotopes in our apparatus can not be ruled out . the time - varying component of the background could include the activation of shorter - lived isotopes , either main constituents of the apparatus or trace impurities in or near the detector . no single isotope appears to dominate this component of the background , as it did not fit well to a single exponential . any remnant of the luminescence signal ( discussed below ) will also decrease with time , though this signal should be eliminated by the multiphoton threshold and requirement of coincidence between two pmts . neutron absorption in the hbn ( and perhaps other materials ) creates color centers which relax by emitting light@xcite . this luminescence signal varies with time , temperature and magnetic field , and is therefore the most problematic of our backgrounds . cuts which were required to reduce the luminescence background also eliminate about two - thirds of the events arising from trapped neutrons . in addition , the temperature dependence of the luminescence makes the `` warm '' data , in which the helium was warmed to 1.2  k , potentially suspect ( although unlikely to be so ) . thus , because of the luminescence , data in which the helium were doped with @xmath47he was taken to confirm the presence of trapped neutrons .    since the luminescence most likely results from the recombination of electrons and holes in the boron nitride , it should emit single photons uncorrelated in time . neutron decays on the other hand result in several photons being detected in coincidence between the two pmts , providing an easy way to distinguish the neutron decay signal from the luminescence background . in practice , the rate of the luminescence signal is more than five orders of magnitude greater than the trapping signal . with a single - photon counting rate of 50,000  s@xmath19 in each pmt , the accidental coincidence rate ( with a coincidence window of 43  ns ) is 100  s@xmath19 , three orders of magnitude larger than the expected neutron decay signal . even the probability of three single photons arriving independently within the coincidence window is larger than the expected trapped neutron signal . the luminescence background can be reduced to a tolerable level ( assuming that the luminescence photons are always uncorrelated ) by requiring coincidence between four photons ( corresponding to less than two false coincidences in each 1  h run ) . recalling that a neutron decay in the center of the trapping region emitting a 330-kev electron will produce on average a signal of five photoelectrons , a 4 p.e . threshold is a strenuous constraint .    in practice , such a reduction in the luminescence background can not be obtained by setting a four - photoelectron threshold on a single photomultiplier tube because there is not a sharp distinction between a three- and a four - photoelectron event . even with a higher threshold , a single photoelectron event can result in a much larger `` afterpulse '' in the pmt@xcite . this afterpulse results from contamination of the pmt vacuum over time ( especially by helium , which diffuses through glass ) and occurs between 400  ns and 600  ns after the initial pulse . the size of the afterpulsing effect was studied by illuminating a pmt with light from an led ( light - emitting diode ) at low current ( and thus , producing predominantly uncorrelated single photons ) . from the pulse - height distribution , it is determined that between 2 % and 4 % of the presumably single photon pulses generated a multiple photon afterpulse . to eliminate these backgrounds , two separate photomultiplier tubes in coincidence are used , with a threshold of two photoelectrons on each . [ fig : differencedata ] shows the pooled background subtracted data ; i.e.  the difference between the pooled trap - on data and the pooled trap - off data , divided by the number of runs which were pooled together . the following models are simultaneously fit to the data : @xmath96 where @xmath97 is the experimental counting rate and the subscripts correspond to the first and second reactor cycle . the @xmath98 s correspond to the amplitude of the neutron decay signal , @xmath99 corresponds to the lifetime of the neutrons in the trap ( assumed to be the same in each reactor cycle ) and the @xmath100 s correspond to any residual offset between trap - on and trap - off runs , which could arise from small changes in the `` flat '' background rate over the course of many runs . the data from each cycle are binned into seventy 50  s bins , with the first starting 50  s after the beam is turned off . the five parameters , @xmath101 and @xmath99 are varied using a routine adapted from the grid fit algorithm described in ref.@xcite to minimize the chi - squared ( @xmath102 ) of the fit . the values of the fit parameters are those which yield the minimum @xmath102 , and the 68  % confidence interval for each parameter is given by the range over which the @xmath102 ( varying the other four parameters ) increases by one relative to the minimum ( varying all five parameters ) . the fit gives a minimum @xmath102 of 150.67 with 135 degrees of freedom at@xcite : @xmath103 note that @xmath104 and @xmath105 are significantly above zero , indicating trapped ucn are present in the trap . the data shown in fig .  [ fig : differencedata ] are evidence of an increase in the counting rate in runs in which the magnetic trap is turned on . however , from this evidence alone we can not definitely conclude that the increase represents an additional source of counts from trapped ucn as opposed to , for example , small , magnet - dependent changes in the rate of neutron - induced backgrounds . it has been assumed that the trap - on data contain both the neutron decay signal and background events , while the trap - off data contain no decay events , but the same backgrounds . if this assumption is true , then trap - on and trap - off data taken under conditions chosen to eliminate the trapped ucn without changing the backgrounds should be consistent with each other .    to keep the background rate the same in any different experimental configuration , the detector ( including the scintillation properties of the helium bath are concerned ) , must remain unchanged . similarly , the neutron beam , which causes all the time - varying backgrounds , must remain unchanged as well . two changes to the experimental configuration which meet these conditions and remove the trapped neutrons are warming the helium target to a temperature of 1.2  k and doping a small amount of @xmath47he ( @xmath106 ) into the isotopically purified @xmath3he .    in ref . @xcite , the upscattering rate for ucn stored in superfluid helium was measured to be @xmath107  s@xmath19 at 1.16  k , giving a ucn storage lifetime of 40  s at that temperature . during the loading phase , the continuous upscattering of ucn reduced the expected peak number of trapped ucn in our experiment from @xmath108 to @xmath109 , a factor of @xmath110 . with @xmath111 ( for the @xmath112  mk runs ) , this gives a maximum of 29 trapped ucn when the beam is turned off , or an initial beta - decay rate of 0.03  s@xmath19 , decreasing with a lifetime of 40  s , to under 0.01  s@xmath19 before the first analyzed data , 50  s after the beam is turned off . this is compared to an expected rate of 0.16  s@xmath19 at that time in the trapping data . since the luminescence background varies with temperature , as well as with magnetic field , the warm runs could conceivably produce a false negative . the @xmath47he technique does not have this feature , making it a more conclusive negative than the `` warm '' data .    for the @xmath47he runs , 10 pa - l of @xmath47he was introduced into the @xmath113  pa - l of @xmath3he filling the experimental cell , yielding a concentration @xmath114 . this concentration gives a ucn lifetime of 0.4  s and an absorption length of 400  m for 0.395  nm neutrons , the lowest wavelength neutrons passing through the beryllium filter . this attenuation is a factor of two shorter at 0.8  nm , on the tail of the spectrum . over the 1  m length of helium in the target , the @xmath47he should absorb less than 1  % of the beam . thus , any background arising from the cold neutrons in the beam , rather than from ucn remaining after the beam is turned off , should be changed by less than one percent . the data from the warm runs are shown in fig . [ fig : warmdata ] . there are no warm data from the second reactor cycle , so the data are fit only to @xmath104 and @xmath115 , with @xmath116  s held fixed . this two parameter fit gives a result of : @xmath117 with a @xmath102 of 76.1 for 68 degrees of freedom . this is consistent with the prediction of @xmath118  s@xmath19 . the data from the @xmath47he runs are shown in fig . [ fig : heliumdata ] . the data are fit to eq . [ eq : datafit ] with @xmath119  seconds . this four parameter fit gives the following results , with a minimum @xmath102 of 119.3 for 136 degrees of freedom : @xmath120 the amplitudes @xmath104 and @xmath105 are consistent with zero trapped ucn in the trapping region and inconsistent with the signal observed in the trapping data . the remaining constant offsets arise from the slow change in the `` flat '' background rate from run to run . he data for reactor cycle one ( * a * ) and two ( * b * ) . ]    a discussion of these results is given below .","summary":"results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions .","abstract":"three - dimensional magnetic confinement of neutrons is reported . neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light . this light is frequency downconverted to the visible and detected . results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime ."}
{"article_id":"nucl-ex0103003","section_id":"c","document":"having demonstrated magnetic trapping of ucn , we now consider the prospects for making a measurement of the neutron lifetime . first , the error bars on the measurement quoted in eq . [ fitvals ] may seem discouraging , compared to the weighted world average value of @xmath139  s@xcite . however , the uncertainty in the present data is due entirely to statistical fluctuations in the large backgrounds being subtracted and not from the number of trapped ucns . there is every reason to believe that a large reduction in at least the time - varying background is possible , since these backgrounds are created by neutrons of all wavelengths , while the trapped ucn are produced by neutrons in a narrow band around 0.89  nm . thus , a 0.89  nm nearly monochromatic beam should reduce these backgrounds by almost two orders of magnitude relative to the neutron signal . the flat background can be reduced by increasing the detection efficiency , allowing higher rejection thresholds to be set . presently , the efficiency is 31  % , mainly limited by the transport of the blue light down the tube surrounding the trapping region . an increase in the wall thickness of the tube will not only allow efficiencies @xmath140  % , but will allow the thresholds to be raised , thereby lowering the backgrounds . the detection efficiency may also be raised by using an optically transparent beamstop rather than the opaque b@xmath58c beamstop . lastly , the number of trapped ucn could be increased by building a magnetic trap either physically larger than that described here , `` deeper '' ( in terms of magnetic trap depth ) , or both . the number of trapped ucn is approximately proportional to the volume of the trap ( @xmath141 ) and to @xmath142 . in fact , collimation constraints in setups of our type make the ucn population depend slightly more strongly on @xmath143 and less so on @xmath144 . the present magnet has a bore of 5.08  cm and the diameter of the trap is 3  cm . in a larger - bore magnet , this ratio will substantially improve , giving a trap depth that is a larger fraction of the field at the bore of the magnet . an improvement of more than two orders of magnitude in the number of trapped ucn , giving a potential measurement at the 1  s level , is likely in the next few years . ultimately , this method of measuring the neutron lifetime is limited by losses of neutrons from the trap , which would give the appearance of a lifetime shorter than the actual beta - decay lifetime . ways in which neutrons could be lost from the trap , other than beta - decay , include : scattering by excitations in the liquid helium , absorption by @xmath47he , majorana spin - flip transitions and the marginal trapping of neutrons . scattering of trapped neutrons by excitations in the liquid helium can be reduced to below @xmath23 of the beta - decay rate by cooling the helium to below 150  mk @xcite . absorption by @xmath47he is reduced by using isotopically purified @xmath3he . at the level to which the supplied @xmath3he has been verified@xcite , a limit of @xmath145 of the beta - decay rate can be set . the actual purity is probably better and will be measured using accelerator mass spectrometry . majorana spin - flip transitions occur near zero - field regions and can be suppressed in an ioffe trap by the application of a bias field . marginally trapped neutrons can be eliminated by ramping the magnetic field down to 30% of its maximum value and then back up , resulting in a population of ucn all with energies less than the trap depth and thus all truly trapped . the beta - decay lifetime of a neutron in a bath of liquid helium could in principle differ from that of a neutron in vacuum due to either a change in the available phase space for the decay products or a change in the matrix element that governs the decay . small changes in the phase space factor arise from an increased or decreased amount of energy available to the decay products . for example , the minimum energy of the electron in helium is 1.3  ev@xcite . the net effect of this energy difference is to increase the neutron lifetime by at most @xmath146 . we estimate that all of the phase - space effects are less than @xmath23 . also , the matrix element for the decay could be influenced by the presence of the helium nuclei . the axial - vector coupling constant @xmath7 is known to vary by 26% compared to that of muon decay@xcite . we can estimate the effect of such a change by considering the range of the strong force ( @xmath147  m ) and the density of helium nuclei in the neutron s environment . the effect of the helium nuclei in the environment of the neutron should be @xmath148 . there is no reason to expect any of these effects , or the loss mechanisms mentioned above , will prevent a measurement of the neutron lifetime at the @xmath23 level , given sufficient statistics . in addition to the immediate use of trapped ucn in a measurement of the neutron lifetime , the techniques developed for this experiment are applicable to a wide range of future experiments . the detection of euv scintillations in liquid helium ( or neon ) using wavelength shifters has been proposed for use in a solar neutrino experiment@xcite . also , both the production and storage of ucn in a helium bath and the detection techniques described herein are relevant to a proposed experiment to measure the electric dipole moment ( edm ) of the neutron using polarized ucn in a bath of liquid helium@xcite . the apparatus described above could also be readily adapted for use as a relatively strong source of polarized ucn . this source of perfectly polarized ucn could be useful in the determination of correlation coefficients in neutron decay which can be combined with @xmath149 to test the standard model . a ucn beam could also be used as a probe for the investigation of condensed matter , because the ucn s wavelength is comparable to interesting correlation lengths in crystalline , polymeric and biological materials .","summary":"the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light .","abstract":"three - dimensional magnetic confinement of neutrons is reported . neutrons are loaded into an ioffe - type superconducting magnetic trap through inelastic scattering of cold neutrons withhe . scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay . the electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light . this light is frequency downconverted to the visible and detected . results are presented in which neutrons are magnetically trapped in each loading cycle , consistent with theoretical predictions . the lifetime of the observed signal ,  s , is consistent with the neutron beta - decay lifetime ."}
{"article_id":"0910.1714","section_id":"i","document":"spintronics is by now a well established field that aims to expand the potential of conventional electronics by exploiting the spin of electrons in addition to their charge @xcite . the field attracted widespread attention with the proposal of a spin - based field effect transistor by datta and das @xcite in 1990 . later , the discovery @xcite of exceptionally long spin dephasing times in bulk _ n_-gaas prompted numerous investigations of spin dynamics in gaas based systems . for double - sided quantum wells ( qw ) not doped or with a two - dimensional electron gas ( 2deg) various studies with optical techniques aimed at understanding the more complex dynamics of 2d electron spin ensembles . the dependence of spin dephasing times and electron g - factors on parameters such as confinement energy , carrier density and crystal orientation has been investigated @xcite . heterojunction systems , with a strongly asymmetric qw that contains a high - mobility 2deg , also have long attracted considerable interest . these systems provide the highest values for electron mobility . further , this material is of interest since the qw asymmetry results in a strong and tunable rashba spin - orbit coupling , that can cancel dresselhaus spin - orbit coupling @xcite , and this gives access to control over spin relaxation and dephasing @xcite . however , most of what is known about electron spin dynamics in these heterostructures was obtained using transport measurements @xcite . complementing this with magneto - optical pump - probe measurements brings the advantage that spin dynamics can be studied with ultra - high time resolution . we report here on using time - resolved magneto - optical kerr rotation ( trkr ) @xcite to study the dynamics of spin ensembles in such a heterojunction qw system that contains a high - mobility 2deg . initial trkr studies on such systems suggest that this may also provide an interesting platform for studying electron - electron interactions @xcite . however , it is not yet well established in which regimes the kerr response of 2deg electrons can be reliably isolated from other contributions to the kerr signal . the reason is that such multilayered gaas / algaas heterostructures have several gaas layers that have an identical value for the gap . this results in optical readout signals that contain contributions from ( photo - excited ) electron populations in several layers .    for our heterostructure , three different layers can contribute to the observed kerr signals from electron spins : the 2deg layer , the bulk epitaxial _ i_-gaas layer that forms the heterojunction and the _ i_-gaas substrate . the response of these three layers occurs at nearly the same photon energy , hindering discrimination of layers by tuning the laser photon energy when using very short pulses . we exploit , instead , that one can use differences in the g - factor to isolate the signal from each population . the g - factor depends on the electron kinetic energy @xmath0 ( with respect to the bottom of the conduction band ) , which can be approximated as @xmath1 where for bulk gaas @xcite @xmath2 and @xmath3 . for 2deg electrons these parameters were reported @xcite as @xmath4 and @xmath5 . due to band filling by ( photo)electrons , the g - factor thus shifts with an increase of the ( quasi-)fermi level as well . a related consequence is that the g - factors shifts towards less negative values with increasing the degree of confinement in a qw ( possibly with an increased shift from wavefunctions penetrating algaas barriers ) . however , it is not obvious that discrimination by g - factors can be applied without accounting for electron momentum relaxation and the intermixing of the populations in different layers @xcite during the evolution of spin dynamics . our measurement technique relies on using a pump pulse which inserts optically - oriented electron - spin populations well above the bottom of the conduction band , and subsequent momentum relaxation and diffusion of carriers can result in intractable kerr signals . nevertheless , our results show that one can define situations and regimes ( defined by pump intensity ) where the three spin populations can be studied without being hindered by these effects . 2.3@xmath6 ) . the applied magnetic field is oriented in the plane of the 2deg . the rotation angle @xmath7 of the linear probe polarization is measured as a function of the time delay between pump and probe pulses . ( b ) schematic of the conduction and valence bands of the heterojunction system that contains a 2deg ( not to scale ) . the composition of the different layers i - iv is detailed in the main text . at the interface between layers ii and iii the conduction bands of the two materials bend , forming a potential well in layer ii where the 2deg is formed.,width=264 ]    the g - factor of the 2deg is well separated from that of the bulk layers , and our results show that the 2deg population can be studied as a independent population when the density of photo - excited carriers does not exceed the 2deg electron density from doping . the g - factor for the two bulk layers , on the other hand , is the same so a different approach is needed to distinguish the signal originating from each . here we use that our heterostructure contains a barrier that blocks carrier diffusion between the two bulk _ i_-gaas layers . the effect of this is that the carrier density in the layer closest to the surface reaches a higher average value . the effective g - factor for the uppermost _ i_-gaas layer then acquires a less negative value ( eq . [ eq : gfactorvse ] ) than that of the underlying substrate . this can be applied in a regime where the density of photo - excited carriers exceeds the 2deg electron density from doping , and under these conditions the signal from the 2deg is suppressed by strong band filling in the 2deg layer .    in section  [ sec : methods ] of this article we discuss the experimental methods and sample materials that we used . results are presented and discussed in section  [ sec : results ] . there , we first compare the kerr response of our heterostructure to that of well - characterized @xcite bulk _ n_-gaas material that is probed under identical conditions in our setup , and we highlight the differences . next , we show that the response from the heterostructure can always be described as a superposition of signals from two independent electron populations , and we confirm that this is true for both the kerr signals and for time - resolved reflectance signals that give insight in carrier dynamics of the populations . measurements of spin dynamics are then analyzed in both the time and frequency domain , confirming that it is possible to treat the different electron populations as independent . in order to confirm that we correctly assign each of the observed g - factors to a particular population in the heterostructure we study how the g - factor , spin dephasing time , and carrier lifetime of each population depend on pump - photon density and temperature . section  [ sec : conclusion ] presents a summary of the main findings and conclusions .","summary":"the kerr signals from the gaas epilayer and the substrate can be distinguished when using a barrier between the two layers that blocks intermixing of the two electron populations . we support this interpretation by studying how the spin dynamics of each population has its unique dependence on temperature , and how they correlate with time - resolved reflectance signals .","abstract":"we present time - resolved kerr rotation measurements of electron spin dynamics in a gaas / algaas heterojunction system that contains a high - mobility two - dimensional electron gas ( 2deg ) . due to the complex layer structure of this material the kerr rotation signals contain information from electron spins in three different layers : the 2deg layer , a gaas epilayer in the heterostructure , and the underlying gaas substrate . the 2deg electrons can be observed at low pump intensities , using that they have a less negative g - factor than electrons in bulk gaas regions . at high pump intensities , the kerr signals from the gaas epilayer and the substrate can be distinguished when using a barrier between the two layers that blocks intermixing of the two electron populations . this allows for stronger pumping of the epilayer , which results in a shift of the effective g - factor . thus , three populations can be distinguished using differences in g - factor . we support this interpretation by studying how the spin dynamics of each population has its unique dependence on temperature , and how they correlate with time - resolved reflectance signals ."}
{"article_id":"0910.1714","section_id":"m","document":"in a semiconductor , a laser pulse can promote electrons from valence - band states to conduction - band states . in a iii - v semiconductor like gaas , such transitions obey well - defined selection rules . if the laser pulse is linearly polarized , the number of photo - excited electrons with their spin parallel to the beam s propagation direction equals the number of photo - excited electrons with their spin antiparallel to the beam s direction . if the laser pulse is circularly polarized , the number of photo - excited electrons with spin aligned along the beam s direction will exceed by 3 to 1 the number of electrons with spin aligned in the opposite direction ( and vice versa for the opposite light helicity ) @xcite . a circularly polarized laser pulse can therefore generate a non - equilibrium population of spin polarized electrons in the conduction band of gaas . this process is known as optical spin orientation .    in trkr experiments , optical spin orientation with an ultrashort pump pulse is followed by optical spin probing with a weaker laser pulse with linear polarization that is reflected on the sample . an unequal filling of the spin - up and spin - down conduction bands produced by the pump pulse gives rise to a transient difference in the absorption coefficient for right and left circularly polarized light ( rcp and lcp respectively ) . through kramers - kronig relation this also gives rise to a difference in the refractive index for rcp and lcp light . such a difference in the refractive index gives a rotation of the linear probe polarization upon reflection on an interface of the sample , given that the linear polarization is a superposition of rcp and lcp light . this process is known as kerr rotation , and the kerr rotation angle @xmath7 ( for probing with a certain photon energy ) is proportional to the expectation value for spin orientation parallel to the propagation direction of the incident probe beam . the kerr rotation is strongest when the probe photon energy is near resonance with transitions to the states with unequal spin filling , but its magnitude and sign depend on the detuning with respect to exact resonance @xcite , and interference effects and additional faraday rotations in systems with reflections from multiple interfaces @xcite . note that trkr signals thus predominantly reflect the properties of electrons at the quasi - fermi level of the photo - induced electron population . in addition to rotation , the reflected pulse may have obtained a certain degree of ellipticity , known in this case as kerr ellipticity . in our experiments we study the reflected probe with a polarization bridge with balanced photodetectors @xcite . the recorded signal is then proportional to the kerr rotation , while kerr ellipticity and reflectance changes give only third order corrections . figure  [ fig : schematic]a depicts the configuration of the experimental setup with pump and probe beams incident on the sample , and the rotated linear polarization of a reflected probe pulse . a trkr trace is obtained by plotting the kerr rotation angle @xmath7 of the reflected probe pulse as a function of the time delay between the pump and probe pulse ( see for example fig .  [ fig : bulkand2deg ] ) .    in the presence of an in - plane external magnetic field ( perpendicular to the initial orientation of the optically pumped spins ) , the injected spins precess around the field at the larmor frequency @xmath8 , @xmath9 where @xmath10 is the electron g - factor , @xmath11 is the bohr magneton , @xmath12 is the magnitude of the applied magnetic field , and @xmath13 is the reduced planck constant . in trkr traces this spin precession appears as oscillations of the kerr angle at the larmor frequency ( fig . [ fig : bulkand2deg]b ) . such traces can thus be used for determining the electron g - factor with eq . [ eq : larmorfreq ] . we characterize the transient nature of trkr traces with a kerr signal decay time @xmath14 . note that this can be shorter than the spin dephasing time @xmath15 for an electron ensemble . we restrict the use @xmath15 for the case that the number of optically oriented electrons in the probe volume is constant . when this number is decreasing in time at a rate @xmath16 due to processes as electron - hole recombination or diffusion out of the probe volume , the kerr signal decays according to @xmath17 ( an exception to this rule applies to electron doped systems , where kerr signals can live longer than the recombination time @xcite ) . we obtain @xmath14 from measuring trkr traces at @xmath18 or from studying the envelope of oscillatory signals at @xmath19 . in such trkr traces , hole spins only contribute to the signal at very short pump - probe delays ( up to @xmath20 ) , because ensembles of hole spins dephase very rapidly @xcite . thus , our trkr measurements predominantly represent electron spin dynamics .    200  ps ) in the kerr oscillations measured at 7 tesla on the 2deg sample ( plot d ) . comparing plots ( a ) and ( c ) also clearly shows a slow increase of the kerr signal for the 2deg sample for delays in the range 0 to 100  ps ( also present in the 7 tesla data ) . data taken with photon density of @xmath21 per pump pulse.,width=302 ]    the dynamics of photo - excited carriers can be studied independently from their spin polarization with time - resolved reflectance @xmath22 measurement . for these measurements , a pump pulse with linearly polarized light is used . in this way , no net spin polarization is generated . subsequently , a collinearly polarized probe pulse is incident on the sample . the pump - induced changes in sample reflectance are measured by comparing the intensity of the reflected probe pulse in the presence and absence of a preceding pump pulse . this method thus probes the presence of pump - induced electrons and holes at energies that are resonant with the probe photon energy , as a function of pump - probe delay . in time , photo - excited electrons and holes relax to the lowest available states , and electrons and holes recombine . this brings the sample reflectance back to its equilibrium value . figure  [ fig : schematic]b depicts the profile of the valence band and conduction band of the heterostructure that we studied . layer i is a ( 001 ) oriented @xmath23-gaas substrate . on this substrate a multilayer buffer consisting of ten periods of alternating gaas ( 5.2  nm ) and alas ( 10.6  nm ) layers was grown to smoothen the surface and to trap unintentional impurities . layer ii , the accumulation layer , consist of 933.0  nm of undoped gaas . a spacer layer ( iii ) is formed by 36.8  nm of undoped al@xmath24ga@xmath25as grown on top of the accumulation layer . the donor layer ( iv ) consists of 71.9  nm of si - doped al@xmath24ga@xmath25as with @xmath26 dopants/@xmath27 . the heterostructure is capped with 5.5  nm of @xmath28-gaas . the two algaas layers have a bandgap that is larger than all the photon energies that we used in our experiments . due to quantum confinement the @xmath29  nm gaas layers of the multilayer buffer and capping layer also only have optical transitions at energies above the photon energies that we use .    in this material a 2deg is formed since dopant electrons from the donor layer ( iv ) reduce their energy by relaxing into the conduction band of he narrow bandgap accumulation layer ( ii ) . these excess carriers are held at the interface by electrostatic attraction from the ionized donors . the conduction band of the accumulation layer is pulled below the fermi level only for a @xmath3015  nm wide layer near the interface , which results in the 2deg at this position ( estimate obtained from solving the coupled 1d poisson - schrdinger equations for the heterostructure @xcite ) . electron transport experiments on the 2deg at 4.2  k , after illumination , gave @xmath31 for electron mobility , and @xmath32 for the electron density . we obtained nearly identical values with optical studies on our 2deg material @xcite . n_-gaas reference material we used had a doping concentration of @xmath33 . several experiments on this material have shown that at this doping concentration very long spin dephasing times can be obtained with kerr studies , and the dependence of spin dephasing times on various experimental conditions has been characterized @xcite . the measurement setup comprises a magneto - optical flow cryostat , pulsed laser , polarization optics , and detection system . sample temperatures are varied between 4.2 k and 100 k in the flow cryostat . the cryostat is equipped with a superconducting magnet used to apply fields up to 7 tesla . the magnetic field is set parallel to the plane of the sample while the laser pulses are incident normal to the sample plane as shown in fig . [ fig : schematic]a . we used two different pulsed laser systems . most of the presented results were obtained with a cavity - dumped mode - locked ti : sapphire laser ( further named laser 1 ) with 15 fs pulses corresponding to a fixed spectrum extending from 740  nm to 880  nm , ( repetition rates ranging from 4  mhz to 80  mhz ) . this allows for wavelength tuning with 10  nm bandpass interference filters . the central wavelength for both pump and probe beam can thus be chosen independently . after filtering , the pulse spectrums have a significant amplitude in a 19  mev window . the filters are followed by prism compressors to ensure pulse durations with a full width at half maximum of approximately 120 fs at the sample . unless stated otherwise , we present measurements from using laser 1 with the pump and probe pulse wavelengths centered at 780  nm and 820  nm respectively . we reproduced most results in a setup with a tunable ti : sapphire laser ( further named laser 2 ) with @xmath30150  fs pulses at 80  mhz repetition rate . the spectrum of pulses is wider than fourier - transform limited , with significant amplitudes over a @xmath3015  mev window . with this laser pump and probe pulses were always centered at the same wavelength .    in each case , two beams derived from the laser are used as pump and probe with power ratio 24:1 or 4:1 . we checked that all our results were at intensities below the regime where saturation effects occur : kerr signals were always proportional to both the pump and probe intensity , and the probe was always non - invasive in the sense that the observed decay times did not depend on probe intensity . we report the intensity of pump pulses in units of photons/@xmath34 per pulse , because it has relevance with respect to the two - dimensional electron density from doping . note that this is the number of photons that is incident on the sample surface , and that the number is lower inside the sample due to reflection on each interface of the heterostructure . glan - thompson polarizers on both pump and probe beam lines are used to produce well defined polarizations . the pump - probe delay is varied using a retro - reflector mounted on a stepper - motor driven translation stage . the two beams are focused on the sample with a 25 cm focal length spherical mirror which gives spots with a diameter of approximately 150  @xmath35 full - width at base level .    in order to measure the transient kerr rotation of the sample , a photo - elastic modulator ( pem ) is used to modulate the polarization of the pump beam between rcp and lcp at a rate of 50 khz . besides improvement of signal - to - noise , this is crucial for avoiding dynamical nuclear polarization effects @xcite , and it rules out phase offsets in kerr signals from interference effects in case of reflections from multiple interfaces @xcite . the probe beam remains linearly polarized . the reflected probe is analyzed with a polarization bridge , which decomposes the probe beam into two orthogonal polarizations with a half - wave plate and a wollaston prism , and which detects both these components with a pair of balanced photodetectors . this bridge is tuned to give a zero difference signal from the two detectors for probe pulses with zero kerr rotation , and this difference signal is recorded with lock - in detection at the pem frequency . for measurements with overlapping pump and pulse spectrums , we employed a double modulation technique by adding an optical chopper in the probe beam ( at @xmath361  khz ) and recording a side band at @xmath37 from the 50 khz pem frequency . in both cases , the signal is proportional to the kerr rotation angle @xmath7 .    with this setup it is possible to measure transient reflectance ( @xmath38 ) and trkr under identical conditions . for @xmath38 measurements the pump and probe beams have parallel linear polarizations . the reflected probe beam is now sent directly to a single photodetector , while the pump beam is modulated using an optical chopper . modulations of the reflected probe intensity at the chopping frequency are then recorded with lock - in techniques . this gives a signal that is proportional to pump induced reflectance change of the sample .      before discussing the experimental data it is useful to discuss a hierarchy of timescales that is relevant for interpreting our results . the electron spin dynamics occurs at time scales of tens to hundreds of picoseconds . for example , the larmor precession period of electrons is of the order of 25  ps at 7  tesla , and we observe electron spin dephasing times for the 2deg in the range of 100  ps . the duration of the pump and probe pulses ( approximately 120 fs ) therefore provide sufficient time resolution to resolve all important spin dynamics . hole spins dephase within @xmath305 picoseconds @xcite . thus , the kerr signal after a few picoseconds contains information about electron spins only . most of the data shown uses delay steps of @xmath39  ps with delays up to 1 ns , which allows us to capture all relevant dynamics of electron spins . the timescales of other electron and hole relaxation processes are very diverse , ranging from a few tens of femtoseconds to nanoseconds . we typically use a pump pulse with the photon energy centered at 780  nm , pumping electrons in gaas layers at about 63  mev above the bottom of the conduction band . this leaves a non - equilibrium and non - thermal carrier distribution in the conduction and valence bands of the gaas layers . within the first hundreds of femtoseconds , conduction band electrons ( and valence band holes ) thermalize into a fermi - dirac distribution with a carrier temperature that is much higher than the lattice temperature . subsequently , electrons cool towards the lattice temperature . the initial cooling of electrons @xcite , with excess kinetic energy of more than 10  mev occurs very rapidly due to rapid momentum relaxation ( within 10  ps ) . once the excess kinetic energies drop below @xmath40  mev , further electron cooling slows down to a decay time of approximately 100  ps depending on electron density . note however , that we use probe pulses with about 19  mev spectral width , with the probe spectrum centered at 820  nm , just below the bottom of the conduction band of gaas . consequently , most electrons relax into the spectral window of the probe within 10  ps , and the final cooling stage in the time interval from 10 to 100  ps has little influence on our kerr and reflectance signals . thus , the fast carrier thermalization and initial cooling allows for pumping the sample with high - energy photons ( convenient for blocking of pump light that scatters into the probe channel by spectral filtering , and it ensures that the penetration depth of pump light for the top gaas layers is less than @xmath41 ) . right after a pump pulse , there will be a steep gradient in the photo - electron density along the direction of the pump over the length of the penetration depth . this equilibrates by electron diffusion along the beam direction . in the accumulation layer this takes place within the first 50  ps for high pump intensities , but may occur much slower @xcite for low pump intensities . for our spot sizes , electron diffusion into directions perpendicular to the laser beam propagation does not significantly change the electron density profile . other carrier processes that take place in timescales between 1  ps and 1  ns are exciton formation and carrier recombination . within the first hundred picoseconds electrons and holes form excitons . this implies a further reduction of the initial energy of the photo - excited electrons by a few mev , but this occurs within the spectral window of our probe , and these processes do therefore not strongly influence our @xmath38 and trkr traces . electron - hole recombination , on the other hand , is directly visible in @xmath38 measurements . obviously , recombination also results in loss of kerr signal , especially in undoped samples or under conditions where the photo - excited electron density exceeds the electron density due to doping @xcite . with time- and spectrally - resolved photoluminescence , we measured that the exciton recombination time for our 2deg sample at 4.2 k is greater than 2  ns in the accumulation layer , while it is approximately 360  ps for the substrate @xcite . both of these timescales become shorter with increasing pump intensity . as a function of temperature the 2deg recombination time increases , while it decreases for bulk gaas layers and @xmath28-gaas .","summary":"the kerr rotation signals contain information from electron spins in three different layers : the 2deg layer , a gaas epilayer in the heterostructure , and the underlying gaas substrate .","abstract":"we present time - resolved kerr rotation measurements of electron spin dynamics in a gaas / algaas heterojunction system that contains a high - mobility two - dimensional electron gas ( 2deg ) . due to the complex layer structure of this material the kerr rotation signals contain information from electron spins in three different layers : the 2deg layer , a gaas epilayer in the heterostructure , and the underlying gaas substrate . the 2deg electrons can be observed at low pump intensities , using that they have a less negative g - factor than electrons in bulk gaas regions . at high pump intensities , the kerr signals from the gaas epilayer and the substrate can be distinguished when using a barrier between the two layers that blocks intermixing of the two electron populations . this allows for stronger pumping of the epilayer , which results in a shift of the effective g - factor . thus , three populations can be distinguished using differences in g - factor . we support this interpretation by studying how the spin dynamics of each population has its unique dependence on temperature , and how they correlate with time - resolved reflectance signals ."}
{"article_id":"0910.1714","section_id":"r","document":"in order to highlight the kerr response that is characteristic for the heterostructure , we compare it to kerr measurements on the bulk _ n_-gaas sample that were obtained under identical conditions . figure  [ fig : bulkand2deg ] shows in the left column trkr signals from the bulk _ n_-gaas sample . its kerr signal at 0 tesla closely resembles a mono - exponential decay . the signal at 7 tesla shows oscillations at the larmor precession frequency for electrons in gaas ( g - factor is @xmath42 @xcite ) , with an envelope that shows again mono - exponential decay @xcite . the transient trkr signals from the heterostructure , on the other hand , are more complex . at 7 tesla ( fig . [ fig : bulkand2deg]d ) , the kerr response shows a node ( at @xmath30200  ps ) , indicating a beating between different precession frequencies . additionally , the envelope shows a slow increase in the delay range from 0 to 100  ps , which is also observed at 0 tesla ( fig . [ fig : bulkand2deg]c ) . the _ in - situ _ comparison with bulk @xmath28-gaas material is important for concluding that the observed beatings in trkr traces are characteristic for the heterostructure , given that beatings can also appear in kerr oscillations from @xmath28-gaas under certain measurement conditions @xcite .    the heterostructure data in figs . [ fig : bulkand2deg]c , d also show a very sharp spike at very short delays , with a decay time of about 3  ps . it is also present in several other trkr traces from the heterostructure that we will present and it was also observed with the @xmath28-gaas sample at weaker pump intensities . it is longer than the duration of pump - probe overlap , and therefore not an optically induced stark effect @xcite . instead , it occurs at a timescale that is consistent with hole spin dephasing , and hot - electron momentum relaxation . this part of the kerr signal is therefore possibly influenced by these effects . we further focus on the kerr signals at delays of 5  ps and longer , and do not include this spike in further analysis . ( see main text for details ) . plot ( g ) shows a fourier transform ( black line ) of the trkr data of plot ( a ) , showing to distinct precession frequencies ( with labels for populations a and b as in fig . [ fig : gfactorvsfluence ] ) . good fits to the spectrum can be obtained using a superposition of two lorentzians ( gray lines ) . data taken at 7 tesla and 4.2  k.,width=302 ]    figures  [ fig : trkrvsfluence]a - c show that the beatings and slow onset in the heterostructure kerr signals appear for a wide range of pump intensities . however , the exact appearance clearly depends on pump intensity . in what follows we will show that all three traces in figs . [ fig : trkrvsfluence]a - c can be described as the superposition of two oscillatory signals with mono - exponential decay remarkably well . each of the two contributions then results from a different electron population , each with its own decay time and effective g - factor . at the highest pump intensities ( fig . [ fig : trkrvsfluence]a ) , the signal is dominated by two bulk @xmath23-gaas electron populations , one in the in the substrate ( layer i in fig . [ fig : schematic]b ) and one in the accumulation layer ( ii ) . at the lowest pump intensity , ( fig . [ fig : trkrvsfluence]c ) the signal is dominated by a population in the 2deg quantum well , and a second one with bulk @xmath23-gaas characteristics .    figure  [ fig : trkrvsfluence]g shows the fourier transform of the trace in fig . [ fig : trkrvsfluence]a . the amplitude spectrum shows two distinct peaks . it can be fit very well with two lorentzians , and the same holds for the fourier transform of the traces in figs . [ fig : trkrvsfluence]b , c . this suggests that one can fit the traces in fig . [ fig : trkrvsfluence]a - c in the time - domain with a superposition of two mono - exponentially decaying cosine functions . that also builds on observations in @xmath28-gaas where trkr signals from single electron population with a single g - factor ( see also fig . [ fig : bulkand2deg]b ) can be described by a mono - exponentially decaying cosine function @xcite . for this fitting we use @xmath43 here @xmath44 is the pump - probe delay , @xmath45 @xmath46 and @xmath47 @xmath48 are , respectively , the kerr signal decay time and the kerr rotation amplitude for each population . similarly , @xmath49 and @xmath50 are the larmor frequencies and @xmath51 and @xmath52 are apparent initial phases @xcite for spin precession . for fitting we only use data for @xmath53  ps .    the fitting results of applying this to the experimental traces of fig .  [ fig : trkrvsfluence]a - c are presented in fig .  [ fig : trkrvsfluence]d - f . the excellent fits demonstrate that the total signal can be indeed described as being composed of two distinct contributions from two different populations . we find that we can obtain very good fits assuming two populations only for all pump intensities . a similar approach that assumes three populations does not improve the fits significantly . this is a remarkable result , given that the kerr response of our heterostructure does not necessarily split into two distinct contributions . the continuous character of the accumulation layer ( ii ) from quantum well to bulk epilayer , followed by a bulk substrate , could give more complex signals with signatures of relaxation processes and mixing effects between populations @xcite . we find that the sign of the amplitudes @xmath54 and @xmath55 of the two contributions is always opposite ( for @xmath56 and @xmath57 close to zero ) which corresponds to kerr rotations of opposite sign at @xmath58 . consequently , the slow signal increase at early delays and the beatings in our kerr oscillations have a common origin . the sign of the kerr response depends on detuning from resonance , but we predominantly probe slightly red - detuned for all populations . the opposite sign is therefore most likely from interference effects that play a role for the sign of kerr response with reflections from multiple interfaces @xcite . further evidence that these excellent fits in the time domain indeed reflect that the physics that underlies our kerr signals is that of two independent populations , each with a different but ( nearly @xcite ) constant g - factor , comes from fourier analysis of the traces . scenario s that include significant spreads or strongly drifting g - factors due to momentum relaxation can be ruled out based on the phase spectrum of fourier transformed trkr signals . in addition , direct measurements of the momentum - relaxation dynamics support this interpretation . traces from the 2deg sample at different pump - photon densities . data taken at 4.2 k and 0 tesla.,width=245 ]    we applied time - resolved reflectance measurements for these studies of the momentum - relaxation dynamics . it provides a direct measure for the momentum relaxation of electron populations into the spectral window of the probe and subsequent electron - hole recombination . figure  [ fig : transrefvsfluence ] shows @xmath38 as a function of pump - probe delay measured on the heterostructure sample using different pump intensities . at high pump - photon densities , @xmath38 first reaches a negative peak before decaying back to zero . at low pump - photon densities , the signal first shows a positive @xmath38 but at later delays @xmath38 obtains a negative value with only very slow decay back to zero .    also here we find that we can describe the full set of @xmath38 traces for @xmath59  ps as the sum of two mono - exponentially decaying responses of opposite sign : one response with positive @xmath38 that is short lived and another response with negative @xmath38 that is long lived . in addition , there is for each trace during @xmath60  ps an onset proportional to @xmath61 with a decay @xmath62  ps . this is consistent with the initial momentum relaxation of pumped electrons into the spectral window of the probe . for @xmath63 , we obtain excellent fits with an approach analogous to fitting trkr signals with eq . [ eq : fitfunction ] ( but with the cosine factors set to 1 ) . the difference in shape for traces recorded at different pump intensities is then predominantly due a shift in the relative weight of the two contributions .    at the lowest pump intensities , the signal is first dominated by a short lived ( @xmath64  ps ) positive contribution to @xmath38 . at later delays a longer lived ( 2 - 3  ns ) negative contribution dominates the signal . this is consistent with the photoluminescence results@xcite if we assign the positive short - lived contribution to the substrate , and the negative long - lived contribution to the 2deg layer . going to higher pump intensities , the relative weight of the negative contribution ( ratio @xmath65 , with @xmath55 the amplitude of the negative contribution ) increases from @xmath66 to @xmath29 . this is consistent with an increased importance for the accumulation layer ( ii ) that can be expected . in addition , the decay time for negative long - lived population decreases to @xmath39  ns . note , however , that at high pump intensity there is significant band - filling in the accumulation layer ( ii ) , so it should now be considered the recombination time for an electron population that is extended throughout this layer instead of a 2deg population . at the high pump intensities , the onset of the strong negative contribution ( with onset proportional to @xmath61 ) curves over into the weak positive contribution with a decay time of @xmath67360  ps , which makes it impossible to reliably fit this latter time scale for high - pump intensities . when increasing the temperature to 100 k , the life time of the negative contribution gradually shortens to @xmath30100  ps , while the life time of the positive contribution grows to @xmath308  ns . thus , we find that both trkr signals and @xmath38 signals can be described very accurately as the superimposed response of two different electron populations . moreover , the relative amplitudes @xmath54 and @xmath55 of populations that are observed with trkr correlate with those observed in @xmath38 signals ( further discussed at fig .  [ fig : gfactorvsfluence ] below ) . the fact that the signal or signal - envelope for each of the two contributions is well described by mono - exponential decay confirms that photo - excited electrons cool within about 10  ps to a temperature where all electrons are at energies within the spectral window of the probe . further cooling only causes small changes in the average value and spread of g - factors and are masked by the relatively short decay times of the kerr signals . further , we observe that for the substrate contribution to the signals , the decay times for the reflectance signals and kerr signals are comparable . this means that the loss of kerr signals is here for a significant part due to electron - hole recombination . ( solid diamonds , population a ) and @xmath68 ( open squares , population b ) . we ascribe these g - factors to electrons in the _ i_-gaas substrate ( layer i ) and electrons in the accumulation layer ( layer ii ) respectively . the gray lines through the data points of a en b are calculated g - factor values ( see main text for details ) . a third precession mode ( open circles , population c ) is observed at the lowest pump - photon densities and corresponds to electrons in the 2deg . data obtained under conditions as in fig .  [ fig : trkrvsfluence ] . the inset shows the calculated density of photo - excited electrons in the accumulation layer ( layer ii ) and in the substrate ( layer i ) as a function of depth from the top of the accumulation layer . the dashed vertical lines at 0.933 @xmath69 m show the position of the multilayer buffer . the gray line shows the calculated electron density immediately after photo excitation with a 780  nm pump pulse . the dashed black line ( solid black line ) shows the electron density 20  ps ( 50  ps ) after photo excitation.,width=302 ]    although the trkr traces from the heterostructure can always be fit assuming two spin populations , a total of three different spin populations show up in the trkr measurements when these are studied for a range of pump pulse intensities . from such data , we analyze the precession frequencies of the different spin populations , both with fourier analysis as in fig . [ fig : trkrvsfluence]g , and fitting in the time domain ( eq .  [ eq : fitfunction ] ) . figure  [ fig : gfactorvsfluence ] shows which g - factors are observed as a function of pump - pulse intensity . two spin populations show up at high pump - photon density ( labeled a and b ) a third population is only observed at low pump - photon density ( labeled c ) . the ratio of contributions @xmath70 , going over into @xmath71 , increases from @xmath72 to @xmath29 with increasing pump intensity . it thus closely follows the ratio @xmath73 discussed for fig . [ fig : transrefvsfluence ] . this provides the first evidence that signal contributions b and c come from the accumulation layer , and a from the substrate . in the next sections ( [ subsec : igaaskerr ] and [ subsec:2degkerr ] ) we further discuss the origin of these three spin populations . we also analyze the physics that results in the fact that these populations behave independently , and the spin dynamics of each population . the error bars indicate here the uncertainty in position for the two lorentzian peak shapes that we fit on the spectrums , and thus also give an indication for the kerr decay times for each contribution ( the smallest error bars corresponding to @xmath30250  ps , the largest to @xmath3070  ps ) . the value of the g - factor of each population gives a strong indication of the medium that the electrons populate . the g - factors of the different semiconductor materials that make up the heterostructure are well known . the g - factor of electrons in bulk gaas is approximately @xmath74 @xcite , and electrons in heterojunction 2degs and 15 to 20  nm wide gaas qws have a g - factor of about -0.36 @xcite . for electrons in the 5.5  nm wide gaas layers @xmath75 , and for @xcite bulk al@xmath24ga@xmath25as layers @xmath76 @xcite ( but electron populations in these latter two layers are not interacting with the photon energies that we use ) .    the value of the g - factor of population a is @xmath77 at all pump - photon densities . we therefore associate population a with electrons in bulk gaas . measurements of the temperature dependence of the g - factor of population a , discussed below , also indicate that these electrons populate a bulk layer of gaas . time - resolved kerr rotation measurements can not directly determine the sign of g - factors . however , the g - factor of gaas is known to be negative @xcite so we assign a negative value to the g - factor of population a.    the g - factor of population b shows a strong dependence on pump - photon density . at the highest pump - photon densities the g - factor of population b is @xmath68 ( while the signal contribution b is here about 5 times stronger than a with its kerr signal decay time as short as @xmath3070  ps , see also the broad peak in fig .  [ fig : trkrvsfluence]g ) . as the photon density is reduced , the g - factor of population b approaches the value of @xmath42 . this shows that this population also corresponds to electrons in bulk gaas , and we again assign a negative value to its g - factor . there are two bulk _ i_-gaas layers in the heterostructure : the accumulation layer ( ii , see fig . [ fig : schematic ] ) and the substrate ( i ) . the analysis in the next paragraphs demonstrates that population a corresponds to electrons in layer i , and that population b corresponds to electrons in layer ii . population c shows up in the trkr measurements only at low pump - photon densities , and corresponds to 2deg electrons , as will be further discussed in section  [ subsec:2degkerr ] .    at high pump - photon densities , the response from the two _ i_-gaas layers can be distinguished because different average electron densities are excited in each layer by the pump pulse , which results in different g - factors ( eq .  [ eq : gfactorvse ] ) . in the following discussion we will show how different average electron densities are obtained thanks to a pump beam with short penetration depth and the multilayer buffer between layer i and layer ii . at 4.2 k the absorption coefficient of 780  nm light in gaas gives a penetration depth of approximately 0.77  @xmath69 m @xcite . the density of photo - excited electrons that is present immediately after a pump pulse decays exponentially as a function of depth into the gaas layers over this length scale . thus , most of the incident pump photons are absorbed in the accumulation layer ( ii ) , giving a much higher concentration of photo - excited electrons in this layer than in the substrate ( i ) . the gray line in the inset in fig . [ fig : gfactorvsfluence ] shows the density of photo - excited electrons as a function of depth immediately after the absorption of a pump pulse . this strong gradient in the photo - electron density will rapidly equilibrate due to diffusion . the inset also shows the calculated electron density as a function of depth 20  ps and 50  ps later . we used here a bulk diffusion constant @xcite of 30  @xmath34/s , but the results of the model that we present below are quite independent from the exact value of diffusion constant that is used . in this calculation , the influence of the space - charge potential in the accumulation layer is ignored . this is justified at high pump - photon densities because the space - charge potential is screened by the photo - excited carriers . in addition , carrier - recombination effects are ignored since these occur at timescales longer than the considered diffusion times . note that the penetration depth for part of the probe spectrum ( centered at 820  nm ) is considerably longer than that of the pump , such that the kerr response of the deepest photo - excited electrons is not strongly attenuated with respect to electrons near the surface . in addition , the reflection on the multilayer buffer layer ensures that there is an enhanced kerr response for electrons in its direct vicinity .    the dashed vertical line in the inset in fig . [ fig : gfactorvsfluence ] at 0.933  @xmath69 m represents the position of the multilayer buffer , which acts as a barrier that blocks electron diffusion . the calculated electron density profiles at 20  ps and 50  ps show that the electron density , and thus the quasi - fermi level in the two layers , becomes discontinuous at the multilayer buffer . the accumulation layer reaches a much higher average electron density than the substrate ( see also top axis of fig .  [ fig : gfactorvsfluence ] for estimated values ) , and thereby a much higher value for the of the quasi - fermi level that is established after tens of picoseconds when most electrons are in the lowest available conduction band states ( besides spin relaxation ) due to cooling and diffusion . the average electron g - factor of a population that is observed in trkr signals depends on the quasi - fermi level as in eq . [ eq : gfactorvse ] . we used this to calculate the expected g - factors of electrons near the quasi - fermi level for the population in the accumulation layer ( ii ) and the substrate ( i ) , without any adjustable parameters @xcite . when calculating a photo - electron density from pump - photon density that is incident on the heterostructure surface we accounted for an estimate of the reflection on each interface in the heterostructure . these calculated g - factors are also plotted in fig . [ fig : gfactorvsfluence ] . the good agreement between the measured and calculated g - factors for populations a and b confirms that the two populations are indeed electrons in the accumulation layer and the substrate . the above discussion shows that the ability to distinguish the two populations relies on the short penetration depth for the pump pulse . our results did not change significantly when using 800  nm pump and 820  nm probe photons ( also showing that the initial rapid momentum relaxation does not result in significant spin dephasing ) . however , when using 820  nm photons for both pump and probe with laser 1 , we did no longer observe the beatings in our trkr oscillations . under these conditions , the relative contribution from the population in the substrate is much higher due to deeper penetration of pump light into gaas ( the penetration depth increases beyond 3  @xmath69 m when the wavelength increases beyond 820  nm @xcite ) . this prohibits an analysis of the contribution to the kerr signal from the top gaas layers of the heterostructure . we could , nevertheless , fully reproduce our results in a mono - color experiment , explored with the tunable laser 2 . also here , we had to ensure that the full spectrum of laser pulses had a short penetration depth . we could get results with a strong contribution from the accumulation layer to the kerr response ( both at high and low pump intensities ) by setting the central laser wavelength at least @xmath3020  mev above the bottom of the conduction band . momentum relaxation brings electrons again rapidly near the bottom of the conduction band , and probing then occurs predominantly with the low - energy wing of our pulse spectrum . when tuning the central wavelength above @xmath30810  nm , the kerr response was again fully dominated by electrons in the substrate . ( left column ) and @xmath78 ( right column ) in the heterostructure sample . electron populations a , b , and c ( see also fig .  [ fig : gfactorvsfluence ] ) are indicated by open squares , solid diamonds , and open circles respectively . the data points were obtained from fits with eq . [ eq : fitfunction ] to trkr measurements taken at 7 tesla.,width=302 ]    as an additional check for our interpretation in this regime with high pump - photon densities we studied how the kerr signals depend on temperature @xmath79 ( presented in fig . [ fig : fitparamvstemp ] ) and magnetic field @xmath12 ( only discussed ) . the kerr signal decay times for populations a and b as a function of temperature are presented in fig . [ fig : fitparamvstemp]a , and the corresponding g - factors in fig . [ fig : fitparamvstemp]b . these results were obtained from fitting eq . [ eq : fitfunction ] to trkr measurements taken at @xmath80 per pump pulse . the temperature dependence of the g - factors of populations a and b is in agreement with observations by oestreich _ et al . _ on gaas bulk samples @xcite , confirming that populations a and b correspond to electrons with bulk gaas characteristics . the g - factor of population b increases with temperature in a manner similar to population a. however , with increasing temperature the difference decreases . this is consistent with a broadening of the quasi - fermi level with temperature , which increases the average electron kinetic energy @xmath0 and ( by eq . [ eq : gfactorvse ] ) brings the g - factor values closer to zero . at the highest temperatures , the broadening of the quasi - fermi level starts to become larger than the difference in quasi - fermi level for populations a and b , which results in a smaller difference between the two g - factor values . the kerr signal decay times @xmath81 and @xmath82 of populations a and b show opposite trends as a function of temperature . at 4.2 k the decay time of population a is approximately 240 ps . as the temperature is raised this value decreases monotonically down to @xmath30120  ps . the signal decay time of population b , on the other hand , increases from @xmath3070  ps at 4.2  k to @xmath30140  ps at 100  k. we analyzed that several mechanism contribute to these kerr signal decay times , and full understanding goes beyond the scope of this article . instead , we will only discuss a few trends and typical values . the following three mechanism contribute to the kerr signal decay rates that we observe :    _ i _ ) electron - hole recombination . this directly contributes to loss of kerr signals at the electron - hole recombination rate . _ ii _ ) precessional dephasing due to a spread @xmath83 in g - factor values . at high pump - photon densities , band filling gives that the spin - oriented electrons have a spread in electron kinetic energy @xmath0 , which ( by eq . [ eq : gfactorvse ] ) directly results in a spread @xmath83 . this results in a dephasing rate @xcite @xmath84 . _ iii _ ) the dyakonov - perel ( dp ) spin dephasing mechanism @xcite , as a result of the cubic dresselhaus spin - orbit coupling in gaas : the spins of electrons in motion experience a @xmath85-vector dependent effective magnetic field . consequently , random momentum scattering ( at a rate @xmath86 ) randomizes spin states by precession . at low temperatures and high electron densities , this effect contributes to spin dephasing at a rate ( for a review see ref .  ) @xmath87 , where @xmath88 is the cubic dresselhaus constant , and @xmath89 the bulk ( photo-)electron density . the rate of this effect typically decreases with increasing magnetic field if @xmath90 is long enough to yield cyclotron motion . we estimate the dp rates with a numerical monte - carlo approach , that we described in detail in ref .  .    in our experiments , these contributions are often of similar magnitude , but the weights shift with temperature , field and electron density . at 4.2  k and 7  t , and for pumping at @xmath91 , the estimate for the precessional dephasing rate by @xmath92 gives about ( 1  ns)@xmath93 for population a , and ( 150  ps)@xmath93 for population b , thus not fully explaining the observed decay rates . in addition , both @xmath81 and @xmath82 gradually increase by a factor @xmath303 when lowering @xmath12 towards zero . this dependence is weaker than @xmath94 for both @xmath81 and @xmath82 , confirming that a spread in @xmath83 is not fully responsible for the observed decay . the electron - hole recombination time for population a is about @xmath95  ps at 4.2  k ( section  [ subsec : gaaskerr ] ) , and was observed to decrease to about 100  ps at 100  k. it thereby provides the dominant rate contributing to the decay of a , and also explains the temperature dependence of @xmath81 in fig . [ fig : fitparamvstemp]a . this is supported by the fact that the @xmath28-gaas reference sample ( measured under identical conditions ) shows here very similar decay times and temperature dependence as population a.    as said , the dependence of @xmath82 on temperature is opposite to that of @xmath81 . for population b ( in the accumulation layer ) , the electron - hole recombination time is much longer than for a ( section  [ subsec : gaaskerr ] ) , and increasing from @xmath301  ns to @xmath308  ns when increasing @xmath79 to 100  k. thus , electron - hole recombination barely contributes to the observed @xmath82 values . however , due to the much higher electron density for b , the dp mechanism now probably contributes significantly . the monte - carlo simulation ( for 0  k , 7  t , @xmath96  @xmath97 , and the typical value @xcite @xmath98 ) give a dp rate of ( 200  ps)@xmath93 if we assume a high mobility of @xmath99 ( giving @xmath100 ) . such high mobility values were indeed directly observed in transient grating experiments on our sample material @xcite at these high photon - electron densities , and due to the fact that population b is in a pure undoped layer of epitaxial quality . we can also explain the temperature dependence of b in fig . [ fig : fitparamvstemp]a when making this assumption . the observed momentum scattering rate @xmath101 increases by a factor @xmath3030 in proportion to @xmath79 in the range 10  k to 100  k @xcite due to acoustic phonon scattering @xcite . the shortening of @xmath90 towards 100  k thus results in a reduced dp dephasing rate with increasing temperature . a moderate increase of @xmath81 and constant behavior of @xmath82 when lowering the pump intensity is consistent with the rate contributions that we discussed here . figure  [ fig : gfactorvsfluence ] shows that population c with @xmath102 ( besides a population with @xmath103 ) can be observed when the pump - photon density drops below @xmath30@xmath104 per pulse . this crossover occurs around the 2deg electron density due to doping , and this provides another indication that population c resides in the 2deg quantum well . we assume again that the g - factor of this population is negative , and its value ( @xmath105 ) is then indeed consistent with the g - factor of electrons in heterojunction 2deg systems and 15 to 20  nm wide gaas qws @xcite . other electrons populations that could be considered to give rise to the signal of population c can be convincingly rejected based on the g - factor values that we discussed before ( section  [ subsec : igaaskerr ] ) . one can also rule out that population c corresponds to electrons or excitons trapped at impurities or defects in bulk gaas , since a g - factor of this value has not been observed before by us or by others in bulk gaas samples . we further remark that the g - factor values @xmath77 and @xmath106 rule out the interpretation that observing two populations at these low pump intensities results from simultaneous probing of electrons in two different subbands of the heterojunction qw . electrons in excited subbands have a g - factor that is closer to zero than the g - factor @xmath107 of electrons in the lowest subband @xcite . hence , the signal contribution with @xmath42 can not result from 2deg electrons . such an interpretation would also be inconsistent with the observed decay times for the two populations in both trkr traces and @xmath38 traces . instead , the population with @xmath42 must be due to electrons with bulk gaas characteristics around the multilayer buffer , and we label it again with a. however , for these low pump intensities we were not able to determine whether this signal contribution is dominated by electrons just above ( in layer ii ) or below ( in layer i ) the multilayer buffer ( further discussed below ) . we carried out two additional experiments which confirm that population c corresponds to 2deg electrons . in the first experiment , we performed trkr measurements on a heterostructure where the 2deg had been removed by wet etching to a depth of about 120  nm . on such material , one can still observe populations a and b at high pump - photon densities . at low pump - photon densities , however , population c is no longer observed , and kerr signals only contain a contribution with @xmath42 .    secondly , we took trkr data in an experiment where a microscope function@xcite was included in the setup with laser 1 . in these experiments we measured with pump and probe spots with a diameter of 1.6  @xmath69 m that could be focussed at different ( non - overlapping ) locations on the sample . we measured on heterostructure material that had been processed into an ensemble of parallel wires of 1.2  @xmath69 m width at a periodicity of 1.6  @xmath69 m . the wires were realized with electron - beam lithography and subsequent wet etching to a depth ( @xmath108  nm ) that removes doping layer ( and thereby the 2deg ) between wires . figure  [ fig : wiremicroscope ] shows results that were obtained with this kerr microscope . trkr signals that were obtained with the pump and probe spot separated by 4  @xmath69 m distance but focussed on the same wire show both population a and c ( beatings in fig . [ fig : wiremicroscope]b , and fourier analysis gives g - factors 0.34 and 0.43 ) . however , when repeating the measurement with the pump and probe separated by the same distance , but now separated along a direction orthogonal to the wires , the trkr signals only show population a ( no beatings in fig . [ fig : wiremicroscope]a , and fourier analysis gives only @xmath109 ) . this shows that population c must be in the accumulation layer , and that the signal contribution with @xmath109 is ( at least in the latter experiment ) dominated by electrons in the substrate , just below the multilayer buffer . when pumping on a wire , photo - electrons in the accumulation later ( ii ) can not escape from the wire : escape into a deeper layer is blocked by the multilayer buffer , while lateral escape is blocked by a @xmath110  ev barrier that results from upward bending of the conduction band below the etched tranches . consequently , no population can appear in the accumulation layer ( ii ) of neighboring wires . photo - electrons below the multilayer buffer , however , can diffuse to areas below neighboring wires . note that we can not conclude from this experiment that population a is in the substrate ( layer i ) in our experiments with the larger and overlapping pump and probe spots as well . with the microscope we probe only those electrons that have migrated away from the pump area , and we pumped at a slightly higher intensity .     wide strip of 2deg sample , obtained in a modified experimental setup where non - overlapping pump and probe spots of @xmath111 diameter were used . the trace in ( a ) is obtained with the pump focussed on the wire and the probe next to the wire with 4  @xmath69 pump - probe separation . the trace in ( b ) is obtained with both the pump and probe focussed on the wire , again with 4  @xmath35 pump - probe separation . data obtained at 4.2  k and 7  tesla , pump intensity of @xmath112 per pulse.,width=226 ]    in the experiments with large overlapping spots , the clean segregation into two distinct signal components nevertheless points to the interpretation that population a resides in the substrate ( and population c in the 2deg ) . this interpretation then assumes that all photo - electrons that are induced throughout the accumulation layer ( ii ) rapidly drift into heterojunction quantum well ( see fig . [ fig : schematic]b ) , and the segregation between signal components a and c then results from the fact that the multilayer buffer blocks this drift for photo - electrons in the substrate . however , salis _ et al . _ recently reported that the mobility of photo - electrons along the growth direction is surprisingly low at low pump - photon densities @xcite . this means that photo - electrons near the multilayer buffer in the accumulation layer ( ii ) do not migrate into the heterojunction quantum well within a few picoseconds . instead , these electrons then have a dwell - time for staying in the deeper half of layer ii that is in excess of the observed kerr signal decay times , and give a contribution to kerr signals with @xmath113 . this scenario is also consistent with the fact that the amplitude of signal contribution a is comparable to that of c ( unlike the results for the strong - pumping regime , where b gives a @xmath305 times stronger contribution than a , see the discussion in section  [ subsec : gaaskerr ] ) . when population a is in the substrate ( i ) , its signal is expected to be much weaker than the signal from c due to absorption throughout the accumulation layer and multiple reflections on the multilayer buffer ( at least in the mono - color experiment , discussed below ) . this analysis point to the conclusion that at low pump - photon densities signal contribution a is dominated by photo - electrons just above the multilayer buffer ( in layer ii ) . however , we can not fully rule a contribution from electrons below the multilayer buffer ( in layer i ) , since the low mobility values are not yet fully understood .    for both the experiment with large laser spots and the microscope , we could again only observe two populations when pumping well above the bottom of the conduction band for bulk gaas . with the pump wavelength longer than 808  nm , the kerr signals were dominated by a single population with @xmath42 . the population with @xmath106 could be observed in both the two - color ( laser  1 ) and monocolor ( laser  2 ) experiment when pumping with 808  nm or shorter pump wavelength ( see also the discussion in section  [ subsec : igaaskerr ] ) . however , different than for the experiments at high pump - photon densities , it is now not only a matter of having a short penetration depth for the pump . obtaining kerr signals with a strong contribution from 2deg electrons probably also requires direct pumping into 2deg subbands , and such transitions only obtain a significant matrix element when pumping at least @xmath3020  mev above the bottom of the conduction band for bulk gaas . this clearly must play a role when the drift of photo - electrons into the heterojunction quantum well is indeed a surprisingly slow process at low pump intensities @xcite . also for this low pump - photon density regime we studied how the kerr signals depend on temperature @xmath79 ( presented in fig . [ fig : fitparamvstemp ] ) and magnetic field @xmath12 ( only discussed ) . the kerr signal decay times for populations a and c as a function of temperature are presented in fig . [ fig : fitparamvstemp]c , and the corresponding g - factors in fig . [ fig : fitparamvstemp]d , as obtained from fitting eq . [ eq : fitfunction ] on trkr measurements taken at @xmath114 per pump pulse . the temperature dependence of the g - factor of population a follows again the trend that was reported for bulk gaas @xcite , and agrees with the high pump - photon density results when accounting for the lower photo - electron density . the trend for c shows a weaker temperature dependence , in agreement with a weaker dependence on @xmath0 for 2deg electrons ( eq .  [ eq : gfactorvse ] ) .    for the kerr signal decay times ( fig . [ fig : fitparamvstemp]c ) , we found evidence that at 4.2 k the decay rate for both population a and c is dominated by the dyakonov - perel ( dp ) spin dephasing mechanism . we conclude this from further experiments where our 2deg material was etched into 1.2  @xmath69 m wide wires . the decay times then show a clear dependence on the crystal orientation of the wire . this proves that the dp mechanism dominates , with spin - orbit fields that are highly anisotropic in @xmath85-space . this results from a rashba contribution @xcite to the spin - orbit fields that can cancel the dresselhaus contribution . the details of this study will appear in a future publication @xcite . for the 2deg population this conclusion agrees with earlier studies on high - mobility 2degs @xcite . the fact that the decay time for c shows almost no dependence on temperature , indicates that the dp mechanism remains dominant up to 100 k , and that in this low pump - intensity regime the 2deg mobility is not limited by scattering on acoustic phonons for all these temperatures . the kerr signal decay times for population a are around 40  k longer than the electron - hole recombination times for bulk ( as measured on bulk i - gaas ) . this provides another indication that population a resides in a layer around the multilayer buffer where electron - hole recombination is suppressed due to band bending . the increase of the decay time for a when increasing the temperature up to 40  k indicates a suppression of the dp mechanism due to more rapid momentum scattering . apparently , momentum scattering for this population is due to acoustic phonons . in the range 40  k to 100  k , the decay times shorten again . here , the thermal spread in electron kinetic energies @xmath0 becomes important , and results in a spread in g - factor values @xmath83 that increases the precessional dephasing rate .","summary":"the 2deg electrons can be observed at low pump intensities , using that they have a less negative g - factor than electrons in bulk gaas regions . at high pump intensities , thus , three populations can be distinguished using differences in g - factor .","abstract":"we present time - resolved kerr rotation measurements of electron spin dynamics in a gaas / algaas heterojunction system that contains a high - mobility two - dimensional electron gas ( 2deg ) . due to the complex layer structure of this material the kerr rotation signals contain information from electron spins in three different layers : the 2deg layer , a gaas epilayer in the heterostructure , and the underlying gaas substrate . the 2deg electrons can be observed at low pump intensities , using that they have a less negative g - factor than electrons in bulk gaas regions . at high pump intensities , the kerr signals from the gaas epilayer and the substrate can be distinguished when using a barrier between the two layers that blocks intermixing of the two electron populations . this allows for stronger pumping of the epilayer , which results in a shift of the effective g - factor . thus , three populations can be distinguished using differences in g - factor . we support this interpretation by studying how the spin dynamics of each population has its unique dependence on temperature , and how they correlate with time - resolved reflectance signals ."}
{"article_id":"0910.1714","section_id":"c","document":"we have characterized under what conditions it is possible to use time - resolved kerr rotation measurements for studies of electron spin dynamics of 2deg and epilayer ensembles in a gaas / algaas heterojunction system with a high - mobility 2deg . differences in g - factors of electrons in different layers of the heterostructure allow for discriminating the various populations , and for defining regimes where they behave as independent populations . this technique can be applied thanks to rapid momentum relaxation processes , which allows for pumping photo - electrons with an excess energy into the conduction band . at high pump - photon densities ( above the 2deg density from doping ) , this is crucial for having pump pulses with a short penetration depth , which ensures that kerr detection is mainly probing electron populations near the wafer surface . at low pump - densities , where 2deg spins can be observed , the excess pump - photon energy is also needed for directly pumping into subbands of the 2deg . furthermore , we find that having a barrier at about 1  @xmath69 m depth in the accumulation layer facilitates the segregation between kerr signals . at high pump - photon densities this directly blocks the intermixing of accumulation - layer and substrate populations , and this drives the difference in g - factor . here the accumulation layer can be studied as a bulk epilayer filled with electrons . further , since the kerr response is enhanced by reflection on each interface in the heterostructure , the multilayer buffer may also be important at low pump - photon densities for realizing a segregation between the kerr response from electrons in the heterojunction quantum well and electrons around the multilayer buffer . we analyzed that in our experiments several mechanism contribute to the dephasing of spin - oriented electron populations and the decay of kerr signals , and complete understanding requires further studies . our results here provide a basis for such further investigations , in particular for the spin dynamics of 2d electron ensembles in heterojunction quantum wells . an interesting direction is to explore whether confinement of such electron ensembles in micronscale device structures ( as large quantum dots and wires ) can be used to study spin dephasing anisotropy and suppression of spin dephasing due to confinement @xcite . in addition , continuing our work with a microscope function in the setup allows for studying spin dynamics of 2deg spins in transport channels with very high time resolution and micronscale spatial resolution @xcite . our results thereby provide a path to performing studies on heterojunction 2deg channels with tunable spin - orbit effects and electron density , which is interesting for work on the datta - das spin - transistor concept @xcite . notably , we showed that this can also be applied with non - overlapping pump and probe , giving access to exploring correlations between spin dynamics and spin transport . we thank bernard wolfs , ji liu , and thorsten last for help and useful discussions , and bernd beschoten for providing the bulk @xmath28-gaas sample . this work was financially supported by the dutch foundation for fundamental research on matter ( fom ) , the netherlands organization for scientific research ( nwo ) , and the german programs dfg - sfb 491 , dfg - spp 1285 and bmbf nanoquit .                                                                                                        for the @xmath28-gaas sample and bulk populations in the heterostructure sample , we observe g - factors close to @xmath115 . at the highest pump intensities , however , we observes values up to @xmath116 , as can be expected from band filling ( see . eq .  [ eq : gfactorvse ] ) . in addition , we observed for such high - pump - intensity traces that this effect diminishes over time scales of the electron - hole recombination times , resulting in weak g - factor drift during a trkr trace that brings the g - factor back towards @xmath42 . we did not include this in our fitting as with eq . [ eq : fitfunction ] , since it would give a much higher number of free parameters . however , this drift in - g - factor values only gave small shifts ( @xmath117 ) in the phase of kerr signals . we checked that the extracted @xmath14 values with our approach were not sigificantly different from fitting results where these effects were included . the decay time of the kerr signal for @xmath28-gaas is in this measurement substantially shorter than the long values observed in other studies @xcite . this is due to the high pump intensity , and in exact agreement with the reported dependence on pump intensity @xcite . with our setups we also observed kerr signal decay times well in excess of 5  ns when using lower pump intensities and low fields . we observe that using phases @xmath118 as free parameters is needed for obtaining good fits . we also observed this with the @xmath28-gaas reference material ( but not when pumping at low intensities close to the bottom of the conduction band ) . this contradicts with the expected direction of spin orientation parallel to the pump beam at @xmath58 . however , we only use data from delays @xmath53  ps for fitting , since holes contribute to the kerr signals up to @xmath119  ps . for @xmath120  ps there is also rapid relaxation of electron kinetic energy @xmath0 . since the effective g - factor has a value closer to zero for higher @xmath0 , early energy relaxation is consistent with apparent phase offsets for @xmath53  ps . however , full justification of using @xmath118 as free parameters requires further investigation .","summary":"we present time - resolved kerr rotation measurements of electron spin dynamics in a gaas / algaas heterojunction system that contains a high - mobility two - dimensional electron gas ( 2deg ) . due to the complex layer structure of this material this allows for stronger pumping of the epilayer , which results in a shift of the effective g - factor .","abstract":"we present time - resolved kerr rotation measurements of electron spin dynamics in a gaas / algaas heterojunction system that contains a high - mobility two - dimensional electron gas ( 2deg ) . due to the complex layer structure of this material the kerr rotation signals contain information from electron spins in three different layers : the 2deg layer , a gaas epilayer in the heterostructure , and the underlying gaas substrate . the 2deg electrons can be observed at low pump intensities , using that they have a less negative g - factor than electrons in bulk gaas regions . at high pump intensities , the kerr signals from the gaas epilayer and the substrate can be distinguished when using a barrier between the two layers that blocks intermixing of the two electron populations . this allows for stronger pumping of the epilayer , which results in a shift of the effective g - factor . thus , three populations can be distinguished using differences in g - factor . we support this interpretation by studying how the spin dynamics of each population has its unique dependence on temperature , and how they correlate with time - resolved reflectance signals ."}
{"article_id":"1612.05466","section_id":"i","document":"much of the work in the canon of physics has been derived under an assumption of isolation , where the system of interest has no interaction with its environment . often , particularly in the classical regime , this approximation has been successful in generating accurate predictions . there are however numerous systems whose behaviour can not be explained by their actions in a vacuum @xcite . in these cases stochastic terms are used , often as an _ a priori _ part of the model ( and without proper justification ) , to capture the effect of the environment . brownian motion is the most famous case of this technique in classical physics , but quantum physics and its applications have many examples where a similarly careful treatment of external effects is required @xcite . these systems can collectively be termed _ open dissipative quantum systems _ , and the problem of how to most accurately model them remains an active field of research . approaches to these systems can be split into two broad categories . the first method uses the paradigmatic example of a damped system , where the damping is an effective loss - mechanism that approximates the environment s effect and fluctuations are neglected . a typical example of this is the early work of kerner and stevens on sets of damped harmonic oscillators @xcite . the basis of this method in classical , phenomological equations means that it is capable of providing exact solutions for some simple systems , such as the damped harmonic oscillator . these solutions are however undermined by being fundamentally incompatible with quantum mechanics . this can be illustrated by the fact that there are no _ time - independent _ hamiltonians that can replicate the equation of motion for a damped oscillator ,    @xmath0    which has frequency @xmath1 and friction @xmath2 . while there exists a _ time - dependent _ hamiltonian that leads to this equation of motion @xcite , after quantisation the fundamental commutation relation becomes time - dependent @xcite . this unphysical result means that another approach to dissipative systems , to be detailed below , is the method of choice .    in this approach , pioneered by callen , welton , senitzky and lax , dissipative systems are modelled as a primary system ( the `` open system '' ) of interest coupled to an explicit secondary system ( the `` environment '' or `` heat bath '' ) which together describe the overall system being modeled ( the `` total system '' ) @xcite . in comparison to the first method , this model is lossless when considering the total system , and incorporates both the dissipation _ and _ fluctuations experienced by the open system as a consequence of its explicit coupling to the environment . combining this model with appropriate approximations ( e.g. weak coupling between the open system and environment ) allows quantum master equations to be derived , which retain the correct behaviour in the classical limit @xcite . the general scheme then is to treat the coupled systems as a single closed sytem which can be straightforwardly quantised . the environmental coordinates can then be eliminated in order to obtain an equation of motion for the primary system . in practice the functional form of the environment ( secondary system ) and its coupling must be chosen subject to several conditions . for example in the high - temperature classical limit we expect to recover a classical brownian motion . in addition , if the summation over environmental coordinates is to be exact , yet analytically tractable , the choice of environment is largely restricted to a set of harmonic oscillators , with a bilinear coupling to the open system . a particularly popular model is the caldeira - leggett ( cl ) hamiltonian @xcite :    @xmath3    this model couples the open system ( described by the coordinate @xmath4 to an environment of independent harmonic oscillators ( masses @xmath5 , frequencies @xmath6 , and displacement coordinates @xmath7 ) with each oscillator being coupled to the open system with a strength @xmath8 . the final term is a counter - term included to enforce translational invariance on the system and eliminate quasi - static effects @xcite . recently , a more general hamiltonian of the combined system ( the open system and harmonic environment ) was introduced @xcite which is only linear with respect to the environmental variables , but remains arbitrary with respect to the positions of atoms in the open system ( this model is detailed in section [ sec : model ] ) . in this hamiltonian interactions within the environment are not diagonalised . this is convenient because all parameters of the environment and its interaction with the open system can then be extracted by expanding the hamiltonian of the combined system in atomic displacements in the bath and keeping only harmonic terms , i.e. the open system can be considered as a part of the expansion of the total system . this rather general choice of total system hamiltonian enables one to derive classical equations of motion [ in the form of the generalised langevin equation ( gle ) ] for the atoms in the open system @xcite and propose an efficient numerical scheme for solving them @xcite . this method has been recently generalised to the fully quantum case @xcite where it was shown , using the method based on directly solving the liouville equation , that equations of motion for the observable positions of atoms in the open system have the gle form with friction memory and non - gaussian random force terms . although this method enables one to develop the general structure of the equations to be expected for the open system , this method lacks an exact mechanism for establishing the necessary expressions for the random force correlation functions .    in the study of quantum brownian motion , the path integral representation has been perhaps the most fruitful . some specific successful applications include tunnelling and decay rate calculations ( kramer s problem ) @xcite as well as recent first - principle derivations for the rate of processes in instanton theory @xcite . in particular the feynman - vernon influence functional formalism @xcite can be used to exactly calculate the effect of the environment on the open system using path integrals . approximations such as weak coupling between the primary system and environment are no longer necessary . path integrals also remove the need for an explicit quantisation of the system hamiltonian , as in this formalism quantum - mechanical propagators are represented as phase - weighted sums over trajectories , where the phase associated to each trajectory is proportional to the action of that path in the classical system @xcite . a useful consequence of this is that the classical limit is easily obtained @xcite , and the quantisation of the system is automatic when choosing this representation . finally , and probably most importantly , bath degrees of freedom can be integrated out exactly if the environment is harmonic and interacts with the open system via an expression that is at most up to the second order in its displacements . the key simplification of the feynman - vernon approach is that initially the density matrix of the total system @xmath9 can be partitioned ,    @xmath10    i.e. it can be expressed as a direct product of the initial density matrices of the open system @xmath11 and the environment @xmath12 , where each subsystem has equilibriated separately .    in the context of open , dissipative quantum systems , much work has been done using this formalism , expanding the methodology of the feynman - vernon influence functional for both exact and approximate results @xcite . using this model , quantum langevin equations for the reduced density matrix have been rigorously derived using path integrals @xcite . in special cases , further analytical results have also been obtained by kleinert @xcite and tsusaka @xcite . generalisations of these results to anharmonic baths produce approximate but more realistic models @xcite , while time - dependent heat exchange can also be exactly included @xcite . parallel to this is the work of stockburger , exactly deriving a stochastic liouville - von neumann ( sln ) equation , and applying it to two - level systems @xcite . approaches based on influence functionals have also found use in the real time numerical simulations of dissipative systems @xcite . with this corpus of techniques , path integrals ( and specifically influence functionals ) represent a powerful and flexible formalism that can be used to attack the problem of open quantum systems . so far , we have been discussing methods based on initially partitioning the total system . the initial condition of eq . ( [ eq : fv_direct_prod ] ) is however unphysical , as it is impossible in a real experiment to `` prepare '' a quantum system with the interaction between the open system and environment switched off , prior to any perturbation being applied . as a result , the transient behaviour we predict for perturbations away from a partitioned initial condition will always be spurious due to the artificial equilibriation of each system if we wish to extract the exact transient dynamics of an open system we must therefore use a more realistic , non - partitioned initial condition . fortunately , the influence functional formalism has the capacity to naturally generalise the initial conditions of the overall system and environment , rendering the assumption of a partitioned initial state unnecessary . this possibility was first noted by smith and caldeira @xcite , before being properly explored by grabert , ingold and schramm @xcite , who derived the time dependent expression for the reduced density matrix of an open system where all path integrals associated with the environment are fully eliminated . in this partition - free case , the limits on our ability to describe the reduced dynamics via a liouville operator have been derived by karrlein and grabert @xcite . in this work however , no differential equation for the reduced density matrix was derived , and the authors still used a simplified cl hamiltonian . we also note that a differential equation for the _ equilibrium _ reduced density matrix for the cl hamiltonian was obtained using path integrals in ref . @xcite and is consistent with our results .    in this paper , we derive , using the path integral formalism , a set of stochastic differential equations for the reduced density matrix of an open system which describe its dynamics _ exactly_. the derived equation does not have the gle form obtained previously in ref . indeed , it does not have a clearly defined friction term and the stochastic fields it contains are gaussian . nevertheless , our hamiltonian is identical to the one used in ref . @xcite , which is more general than the cl hamiltonian . using it , we obtain a system of first order stochastic differential equations over real and imaginary time that exactly describe the evolution of the state of a dissipative quantum system for partition - free initial conditions . these equations , which we term the extended stochastic liouville equation ( esln ) , represent both a synthesis and extension of the work outlined above , allowing for a simple and exact closed form description of an arbitrary open system evolving from realistic initial conditions . the derivation of the esln , ( and therefore the paper itself ) will be organised as follows :    section [ sec : model ] details the model employed , and the class of applicable initial conditions . in section [ sec : influence_functional ] the path integral representation for the density matrix of the primary system will be introduced , along with the influence functional and its explicit evaluation . in section [ sec : the - two - time - hubbard - stratonovich ] the two - time hubbard - stratonovich transformation is applied to the influence functional found in the previous section , introducing the corresponding complex gaussian stochastic fields . section [ sec : the - extended - stochastics ] presents the path integral describing the reduced density matrix of the primary system and the operator esln equations of motion that it implies , which represents the central result of this work . these equations account for both the generalised hamiltonian and partition - free initial conditions . finally , section [ sec : discussion ] concludes the paper with a discussion of the esln , its connection to previous results and the potential for numerical implementations .","summary":"allows us to derive a set of exact differential equations for the reduced density matrix of an open system , termed the extended stochastic liouville - von neumann equation . this provides a simple , yet exact , closed - form description for the evolution of open systems from equilibriated initial conditions . the applicability of this model and the potential for numerical implementations are also discussed .","abstract":"we present a partition - free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment . the influence functional formalism combined with a two - time hubbard - stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system , termed the extended stochastic liouville - von neumann equation . our approach generalises previous work based on caldeira - leggett models and a partitioned initial density matrix . this provides a simple , yet exact , closed - form description for the evolution of open systems from equilibriated initial conditions . the applicability of this model and the potential for numerical implementations are also discussed ."}
{"article_id":"1612.05466","section_id":"c","document":"having derived the esln , we should ask how it differs from previous work . the hamiltonian we have used is a generalisation of the caldeira - leggett model , allowing for a solution in either real or frequency space . the form of the interaction has also been generalised , but is still limited by the essential need for an interaction to be linear in environmental oscillator displacements . in fact , our hamiltonian emerges naturally from an arbitrary total system hamiltonian by expanding atomic displacements of the environment up to the second order . therefore , it can be directly applied to realistic systems . the fundamental result of our paper is the removal of the unphysical partitioned initial condition which implied that the open system and the bath were initially isolated . following previous procedures to accommodate a more physical partition - free approach , we applied the special variant of the hubbard - stratonovich transformation that allowed the initial condition to be determined via an auxiliary differential equation . this allows the esln to make exact predictions for the transient behaviour of the primary system when it is perturbed from equilibrium . additionally , when the total system is in equilibrium , the imaginary time differential equation allows for the exact calculation of the _ reduced equilibrium density matrix_. this is important , as the stationary distribution of dissipative systems with finite couplings has been shown to deviate from that expected under partitioned conditions @xcite . the true distribution is described by the `` hamiltonian of mean force '' , and eqs . ( [ eq : initial_density_operator ] ) and ( [ eq : eom_for_initial_density ] ) provide a route to the exact calculation of the stationary distribution . indeed , the imaginary time evolution has been independently derived by moix _ @xcite as an exact description of an open system in interactive equilibrium with its environment . this formulation of the equilibrium density matrix has been used by tanimura to develop hierarchical equations of motion for fermionic systems @xcite under the assumption that the environment spectral density is ohmic . the esln represents a unification and generalisation of the differential equations derived by stockburger @xcite and moix _ et al . _ @xcite , resulting in additional and highly non - trivial constraints on the correlations between the real and imaginary time noises . the connection between these two pieces of work was not previously apparent , but has emerged naturally from the simultaneous generalisation of the model hamiltonian and the initial total density matrix . this is the esln s principal advantage , and allows for a simpler and more general closed form description of the evolution of the reduced density matrix , as compared to hierarchical equations of motion @xcite . we also note that our approach can easily be generalised to several environments , e.g. , for heat transport problems along similar lines to ref . @xcite . extracting numerical results from the esln depends on the feasibility of generating noises that satisfy the correlations outlined in section [ sec : the - two - time - hubbard - stratonovich ] . real time noises of the same type can already be efficiently calculated @xcite , and the outlook for extending this to include the imaginary time noise is promising . looking forward , a first application of the esln is therefore likely to be a calculation of the time evolution of the density matrix for a simple system coupled to a harmonic bath , and the comparison between approximate partitioned and exact partition - free methods . the class of problems that this model may be applied to are rather broad . this includes a two - level spin boson system , coupled to a bath with an arbitrary spectrum @xcite , or the heat exchange between an arbitrary system and a bath with ohmic dissipation @xcite . it is possible that this generalisation may also be applied to numerical schemes for anharmonic bath models @xcite , and influence functional simulations of complex systems @xcite . to summarise , the influence functional formalism has been used to generate two stochastic differential equations that together describe the exact evolution of an open system that begins in coupled equilibrium with its harmonic environment . the results presented here are an extension to existing frameworks for thermodynamic analysis in the quantum regime , as well as offering a method for accessing the equilibrium states of arbitrary dissipative systems .","summary":"we present a partition - free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment . the influence functional formalism combined with a two - time hubbard - stratonovich transformation","abstract":"we present a partition - free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment . the influence functional formalism combined with a two - time hubbard - stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system , termed the extended stochastic liouville - von neumann equation . our approach generalises previous work based on caldeira - leggett models and a partitioned initial density matrix . this provides a simple , yet exact , closed - form description for the evolution of open systems from equilibriated initial conditions . the applicability of this model and the potential for numerical implementations are also discussed ."}
{"article_id":"cond-mat0504231","section_id":"i","document":"the transition temperature of a thin superconducting film in contact with a normal metal is reduced . this is known as the superconducting proximity effect ( spe ) . the double layer sn or a multi layer ( sn)@xmath4 can consist ( i ) of a superconductor s and normal conductor n or ( ii ) of two superconductors with different transition temperatures ( the one with the lower @xmath5 is generally denoted as n ) . its systematic experimental investigation started in 1960 s by the hilsch group in goettingen @xcite , @xcite and stimulated a number of further experimental investigations @xcite , @xcite , @xcite , @xcite . for the dirty case ( mean free path of the conduction electrons is much smaller than the coherence length ) werthamer @xcite derived a set of implicit equations for the transition temperature of double layers consisting of two superconductors . after some modification according to de gennes boundary condition @xcite between the superconductors , the wertheimer theory described the experimental results for double layers of two superconductors quite well ( see for example @xcite , @xcite , @xcite ) . the wertheimer theory is restricted to short mean free path , ( using the diffusion approximation ) and uses what is now called the single mode approximation ( the gap function is approaximated by a @xmath6-dependence ) . theoretical results for the clean case where the mean free path @xmath0 is larger than the bcs coherence length @xmath7 are more difficult and the case where @xmath8 and the film thicknesses are of the same order of magnitude are much more challenging .    in recent years the superconducting proximity effect has experienced a renewed interest . a large number of papers studied the spe theoretically @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and experimentally @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite particularly during the last 10 years . the studies have been extended to double layers of a superconductor and a ferromagnet ( sf ) @xcite , @xcite , @xcite . recently our group revisited the superconducting proximity effect using it as an experimental tool @xcite , @xcite . one interesting information the spe provides is the transparency of the interface between the two metal films for the conduction electrons . the reduction of @xmath5 in the superconducting component of the sn double layer depends on the rate at which electrons can cross the interface between s and n. this interface transparency is of interest in a number of other disciplines and applications in solid state physics .    when our group tried to compare the experimental results for the transition temperature with theoretical predictions we found that only a few recent theoretical investigations calculated the transition temperature of sn double layers @xcite , @xcite , @xcite . these papers considered the extreme cases , either the clean limit for infinitely large mean free path @xcite  or the dirty limit @xcite where the mean free path is much shorter than the bcs coherence length . reference @xcite considered superconductor - ferromagnet double layers in the `` dirty limit '' . it includes the case of an sn double layer by setting the exchange energy in the ferromagnet equal to zero . a multi - mode expansion of the order parameter is used in the superconductor . this yields a complex set of equations which contain the transition temperature implicitely . their single mode approximation is similar to wertheimers result .    since our experiments used films with short and large mean free paths the author prefered to develop a numerical procedure which is capable of calculating the transition temperature of arbitrary sequences of superconductors and normal conductors in a wide range of the mean free path . this calculation uses a simple interpretation of the gap equation which was stimulated by degennes work @xcite . below i will sketch the ( simple ) numerical procedure . in chapter ii the theoretical background is reviewed and the numerical procedure discussed in detail . in chapter iii some of the numerical results are presented . in the discussion of chapter iv i will point out a discrepancy between all experiments i am aware of which study the change of @xmath5 of a superconducting film when covered with a thin normal conducting film , i.e. the normalized intial slope @xmath9 , where @xmath10 and @xmath11 are the thickness and transition tmperature of the superconductor and @xmath12 is the initial slope of the @xmath5-reduction for zero thickness @xmath13 of the normal conductor .","summary":"surprisingly the coefficient in these experiments is of the order or less than 2 while the ( weak coupling ) theory predicts a value of about 4.5 . this agrees much better with the few experimental results that are available .   ","abstract":"a numerical method is developed to calculate the transition temperature of double or multi - layers consisting of films of super- and normal conductors . the approach is based on a dynamic interpretation of gorkov s linear gap equation and is very flexible . the mean free path of the different metals , transmission through the interface , ratio of specular reflection to diffusive scattering at the surfaces , and fraction of diffusive scattering at the interface can be included . furthermore it is possible to vary the mean free path and the bcs interaction in the vicinity of the interface . the numerical results show that the normalized initial slope of an sn double layer is independent of almost all film parameters except the ratio of the density of states , . there are only very few experimental investigations of this initial slope and they consist of pb / nn double layers ( nn stands for a normal metal ) . surprisingly the coefficient in these experiments is of the order or less than 2 while the ( weak coupling ) theory predicts a value of about 4.5 . this discrepancy has not been recognized in the past . the autor suggests that it is due to strong coupling behavior of pb in the double layers . the strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for . this agrees much better with the few experimental results that are available .    pacs : 74.45.+r , 74.62.-c , 74.20.fg"}
{"article_id":"cond-mat0504231","section_id":"r","document":"there are numerous parameters in the superconducting proximity effect : the coherence lengths @xmath116 ( for the superconductor this is the bcs @xmath7 if one uses the transition temperature in @xmath117 , the mean free path @xmath118 and the film thickness @xmath119 for each film . in addition one has the interface and the boundaries . any barrier between the two metals will reduce the transfer through the interface . furthermore one can have additional scattering at the interface between the two films due to a mismatch of the two lattices . the two surfaces with the vacuum can reflect or scatter the incident electrons or anything in between . all these scattering parameters influcence the propagation of the electrons and therefore the transition temperature of the double layer . in the numerical calculation all these parameters can be included if they are known or used as fit parameters .      in the majority of experiments the onset of superconductivity is measured for a double layer of a thick normal conducting film which is covered with a superconducting film of increasing thickness . therefore the first plotted numerical result represents a double layer of an infinitely thick normal conductor which is covered with a superconductor of increasing thickness . among the large number of possible parameters the following choice is made : ( i ) the electronic properties ( @xmath120,v@xmath121 of the normal metal and the superconductor are identical , ( ii ) the mean free path of the normal conductor is infinite , ( iii ) the thickness of the normal conductor is infinite , ( iv ) the interface is perfectly transparent , ( v ) for the mean free path of the superconductor the following values are chosen : @xmath122 @xmath123 , @xmath124 . the results are shown in fig.3a . the parameter @xmath125 is defined as @xmath126 . the curves of the transition temperature versus thickness of the superconductor show the typical behavior ; they approach @xmath11 for large @xmath10 and show a steep decline at a critical thickness @xmath127 . the value of the critical thickness decreases strongly with decreasing mean free path @xmath128 of the superconductor . it might be surprising that even a mean free path @xmath129 shifts the @xmath5-@xmath10 curve considerably to smaller thicknesses . for the smallest mean free path of @xmath130 the critical thickness is about @xmath131 . in fig.3b @xmath5 is plotted versus the reduced thickness @xmath132 . the points lie almost on an universal curve , particularly those for smaller @xmath128 . @xmath133{cc}% % tcimacro{\\frame{itbpfu}{3.2777in}{2.4259in}{0in}{\\qcb{fig.3 : the reduced % transition temperature $ t_c / t_s$ for an ns double layer where $ d_n=\\infty$ , % $ l_n=\\infty$ as a function of thickness $ d_s/\\xi$ ( $ \\xi$=bcs coherence of s ) % a ) for different mean free paths $ l_n$ of s , the parameter $ \\alpha = l_s/\\xi$.}% % } { } { nnssxx1a.eps}{\\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 3.2777 in ;   height 2.4259 in ;   depth 0 in ;   original - width 4.1046 in ; % original - height 3.032 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx1a.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{3.2777in}{\\begin{center } \\includegraphics [ height=2.4259 in , width=3.2777 in ] % { nnssxx1a.eps}% \\\\ fig.3 : the reduced transition temperature $ t_c / t_s$ for an ns double layer where $ d_n=\\infty$ , $ l_n=\\infty$ as a function of thickness $ d_s/\\xi$ ( $ % \\xi$=bcs coherence of s ) a ) for different mean free paths $ l_n$ of s , the parameter $ \\alpha = l_s/\\xi$. \\end{center}}}% % endexpansion & % tcimacro{\\frame{itbpfu}{3.0585in}{2.347in}{0in}{\\qcb{fig.3b : the same plot as % a ) with the s thickness scaled with the critical thickness $ d_cr.$}}% % { } { nnssxx1b.eps}{\\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 3.0585 in ;   height 2.347 in ;   depth 0 in ;   original - width 3.9435 in ; % original - height 3.0195 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx1b.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{3.0585in}{\\begin{center } \\includegraphics [ height=2.347 in , width=3.0585 in ] % { nnssxx1b.eps}% \\\\ fig.3b : the same plot as a ) with the s thickness scaled with the critical thickness $ d_cr.$ \\end{center}}}% % endexpansion \\end{array}\\ ] ]      in the next step the actual dependence of the gap function on position is of interest . in fig.4a - d this gap function @xmath134 is plotted as a function of @xmath135 . we choose double layers where @xmath5 lies in the steep decline of the @xmath5 curves in fig.3 at about @xmath136 . fig.4a shows @xmath137 for the superconductor with @xmath138 ( since the amplitude of @xmath134 approaches zero at the transition temperature the value @xmath139 at the maximum is of no phyisical significance ) . since the gap function has a horizontal slope at the free surface a comparison with a cosine function @xmath140 is useful . the resulting fits are shown in fig.4a - d . fig.4a for @xmath141 shows an almost perfect quarter of a cosine function with @xmath142 which is as close to @xmath143 as it can be . for @xmath144 the shape of the gap curve is still quite close to a cosine function but the factor has the value @xmath145 . for @xmath146 the shape of the gap curve shows already clear deviations from a cosine curve and the coefficient is @xmath147 . finally in the clean limit the gap function curves stronger for small @xmath148 than the cosine curve and the coefficient is @xmath149 for the shown fit . this behavior is interesting because in a number of theoretical papers the gap function is expanded into a series ( see for example ref . @xcite where a series consisting of @xmath150 and @xmath151 is used , @xmath152 is the superconducting diffusion length and @xmath153,@xmath154 are coefficients defined in that work ) . @xmath133{cc}% % tcimacro{\\frame{itbpf}{2.6642in}{2.2283in}{0in}{}{}{nnssxx2a.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.6642 in ;   height 2.2283 in ;   depth 0 in ;   original - width 3.8373 in ; % original - height 3.2046 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx2a.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\includegraphics [ height=2.2283 in , width=2.6642 in ] % { nnssxx2a.eps}% } % % endexpansion & % tcimacro{\\frame{itbpf}{2.8667in}{2.0988in}{0in}{}{}{nnssxx2b.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.8667 in ;   height 2.0988 in ;   depth 0 in ;   original - width 4.0224 in ; % original - height 2.9373 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx2b.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\includegraphics [ height=2.0988 in , width=2.8667 in ] % { nnssxx2b.eps}% } % % endexpansion \\\\% % tcimacro{\\frame{itbpf}{2.7729in}{2.2806in}{0in}{}{}{nnssxx2c.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.7729 in ;   height 2.2806 in ;   depth 0 in ;   original - width 4.117 in ; % original - height 3.3806 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx2c.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\includegraphics [ height=2.2806 in , width=2.7729 in ] % { nnssxx2c.eps}% } % % endexpansion & % tcimacro{\\frame{itbpf}{2.851in}{2.0108in}{0in}{}{}{nnssxx2d.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.851 in ;   height 2.0108 in ;   depth 0 in ;   original - width 4.0639 in ; % original - height 2.8584 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx2d.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\includegraphics [ height=2.0108 in , width=2.851 in ] % { nnssxx2d.eps}% } % % endexpansion \\end{array}\\ ] ] @xmath155{l}% fig.4a - d : the gap function $ ] ( z ) @xmath156z / d_s@xmath157d_s@xmath158d_cr@xmath159l_s/_0@xmath160    the simple form of the gap function in the case of @xmath141 makes it very obvious why the very disordered superconductors ( often discriminatingly called dirty superconductors ) are much easier to describe . this becomes still more obvious if one compares the shape of the gap function at different @xmath161 values ( which means , of course , using different thicknesses of the superconductor ) . in fig.5a the ( normalized ) gap functions for @xmath161  values of about 0.3 and 0.9 are shown as a function of @xmath162 . they lie perfectly on the same quarter of a cosine function . this is very different for the clean limit where the shape depends strongly on the temperature.@xmath133{cc}% % tcimacro{\\frame{itbpfu}{2.8427in}{2.2665in}{0in}{\\qcb{fig.5a , b : the gap % function $ \\delta\\left (   z\\right )   $ is plotted versus the position $ z / d_s$ for % two ns double layers , each at two different $ d_s$ ( resulting in different % t$_c$ of about 0.3 and 0.9 $ t_s$. ) a ) dirty limit $ l_s/\\xi$=0.01.}}% % { } { nnssxx3a.eps}{\\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.8427 in ;   height 2.2665 in ;   depth 0 in ;   original - width 3.8082 in ; % original - height 3.032 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' nnssxx3a.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{2.8427in}{\\begin{center } \\includegraphics [ height=2.2665 in , width=2.8427 in ] % { nnssxx3a.eps}% \\\\ fig.5a , b : the gap function $ \\delta\\left (   z\\right )   $ is plotted versus the position $ z / d_s$ for two ns double layers , each at two different $ d_s$ ( resulting in different t$_c$ of about 0.3 and 0.9 $ t_s$. ) a ) dirty limit $ l_s/\\xi$=0.01 . \\end{center}}}% % endexpansion & % tcimacro{\\frame{itbpfu}{2.831in}{2.2839in}{0in}{\\qcb { b ) clean limit % $ l_s=\\infty$.}}{}{nnssxx3b.eps}{\\special { language \" scientific word \" ; % type \" graphic \" ;   maintain - aspect - ratio true ;   display \" usedef \" ; % valid_file \" f \" ;   width 2.831 in ;   height 2.2839 in ;   depth 0 in ; % original - width 3.9967 in ;   original - height 3.2188 in ;   cropleft \" 0 \" ; % croptop \" 1 \" ;   cropright \" 1 \" ;   cropbottom \" 0 \" ; % filename ' nnssxx3b.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{2.831in}{\\begin{center } \\includegraphics [ height=2.2839 in , width=2.831 in ] % { nnssxx3b.eps}% \\\\ b ) clean limit $ l_s=\\infty$. \\end{center}}}% % endexpansion \\end{array}\\ ] ]      since in the dirty limit the gap function approached such a simple form for a superconductor in contact with an infinite clean normal metal it is worth to check the situation when both metals are dirty . this is the case which most theoretical papers investigate . @xmath133{cc}% % tcimacro{\\frame{itbpfu}{3.2453in}{2.6227in}{0in}{\\qcb{fig.6a , b : the function % $ \\delta/\\left (   nv\\right )   $ for an s$_\\text{1}$s$_\\text{2}$ double layer , % $ t_c1=t_s2/2 $ ( details in text and figures ) . both films are in the dirty % limit . text and figures ) . both films are in the dirty limit . in a ) the % transmission coefficient from s$_2 $ to s$_1 $ is $ t=1.0 $ whil in b ) $ t=0.8 $ .}% % } { } { sxssxx1a.eps}{\\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 3.2453 in ;   height 2.6227 in ;   depth 0 in ;   original - width 3.8912 in ; % original - height 3.1399 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' sxssxx1a.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{3.2453in}{\\begin{center } \\includegraphics [ height=2.6227 in , width=3.2453 in ] % { sxssxx1a.eps}% \\\\ fig.6a , b : the function $ \\delta/\\left (   nv\\right )   $ for an s$_\\text{1}% $ s$_\\text{2}$ double layer , $ t_c1=t_s2/2 $ ( details in text and figures ) . both films are in the dirty limit . text and figures ) . both films are in the dirty limit . in a ) the transmission coefficient from s$_2 $ to s$_1 $ is $ t=1.0 $ whil in b ) $ t=0.8 $ . \\end{center}}}% % endexpansion & % tcimacro{\\frame{itbpf}{3.1656in}{2.8269in}{0in}{}{}{sxssxx1b.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 3.1656 in ;   height 2.8269 in ;   depth 0 in ;   original - width 3.7443 in ; % original - height 3.3391 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' sxssxx1b.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{3.1656in}{\\begin{center } \\includegraphics [ height=2.8269 in , width=3.1656 in ] % { sxssxx1b.eps}% \\end{center}}}% % endexpansion \\end{array}\\ ] ]    in fig.6a @xmath163 is plotted for a double layer of two superconductors with different transition temperatures of @xmath164 and @xmath165 . in addition the density of states for superconductor n ( with the lower transition temperature ) is larger by a factor of 1.5 than for superconductor s. therefore the superconducting coherence lengths @xmath166 and @xmath167 are different ( the additional factor of two stems from the ratio of the transition temperatures ) . the difference in the density of states and the fermi velocity of the two metals yields a ratio of the two transmission coefficients at the interface @xmath168 . the thickness of each film is @xmath169 . in fig.6a the mean free paths are chosen in both films to be @xmath170 . for the corresponding superconducting diffusion lengths @xmath171 one finds @xmath172 and @xmath173 . according to de gennes the function @xmath174 should be continuous at the interface . as can be easily recognized from the plot in fig.6a this condition is well fulfilled . werthamer @xcite expressed the z dependence of the gap function @xmath175 in the two superconductors as @xmath176{lll}% $ \\cosh\\left (   k_{n}\\left (   d_{n}+z\\right )   \\right )   $ & in the superconductor with $ t_{n}$ in the range $ -d_{n}<z<0 $ & \\\\ $ \\cos\\left (   k_{s}\\left (   d_{s}-z\\right )   \\right )   $ & in the superconductor with $ t_{s}$ in the range $ 0<z < d_{s}$ & \\end{tabular}\\ ] ] fig.6a shows for @xmath177 a fit to the function @xmath178 and for @xmath179 to the function @xmath180 . the fitted curves lie within the trace of the points . the fitted values for the parameters are @xmath181 , @xmath182 and @xmath183 . this yields for the value of @xmath163 on the left and the right side of the interface : @xmath184 and @xmath185 . the corresponding slopes on the left and right side of the interface are : @xmath186 and @xmath187 . according to de gennes the derivative @xmath188 should be continuous at the interface for the dirty limit . using the input data of the two superconductors @xmath189 and @xmath190 one obtains for the ratio of the slopes @xmath191 . the simulated @xmath89 yields a slope ratio at the interface of @xmath192 . so the de gennes condition is verified with an accuracy of about 10% .    in a second simulation the transmission through the interface is reduced by a factor 2 . it is quite remarkable that this changes the transition temperature only from @xmath193 by just @xmath194 to @xmath195 . in fig.6b the function @xmath163 is plotted for the double layer as a function of @xmath79 . one recognizes that now @xmath163 is no longer continuous at the interface . the functional form in n and s can still be well fitted by a hyperbolic cosine and a cosine function . ( the fitted curves lie within the width of the numercal points ) .      when one condenses the normal metal on top of the superconductor then the transition temperature of the double layer decreases . here the focus is on the question how the intial slope at @xmath196 depends on various parameters , such as the mean free path in the superconductor and the normal conductor and the transparency of the interface . the dependence of the initial slope on the mean free path is shown in fig.7a , b . in both figures the thickness of the superconductor is equal to the bcs coherence length @xmath197the transition temperature @xmath161 is plotted versus the thickness of the normal conductor . in fig.7a the mean free paths in both films are equal and vary between @xmath198 @xmath123 and @xmath199 . in fig.7b four different combinations of @xmath200 are chosen . from the top to the bottom @xmath201 is equal to @xmath202 , @xmath203 , @xmath204 and @xmath205 . for all curves the initial slope is identical . ( in all the numerical calculations which were discussed so far the two density of states are assumed equal @xmath206 . ) @xmath133{cc}% % tcimacro{\\frame{itbpfu}{3.0959in}{2.2524in}{0in}{\\qcb{fig.7a , b : $ t_c$ for an % sn double layers as a function of $ d_n/\\xi$. the thickness of the % superconductor is equal to the bcs coherence length $ \\xi$. ( $ n_s = n_n$ ) . a ) the % mean free paths $ l_s = l_n$ are parameters.}}{}{ssnnxx1a.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 3.0959 in ;   height 2.2524 in ;   depth 0 in ;   original - width 4.0108 in ; % original - height 2.9116 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' ssnnxx1a.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{3.0959in}{\\begin{center } \\includegraphics [ height=2.2524 in , width=3.0959 in ] % { ssnnxx1a.eps}% \\\\ fig.7a , b : $ t_c$ for an sn double layers as a function of $ d_n/\\xi$. the thickness of the superconductor is equal to the bcs coherence length $ \\xi$. ( $ n_s = n_n$ ) . a ) the mean free paths $ l_s = l_n$ are parameters . \\end{center}}}% % endexpansion & % tcimacro{\\frame{itbpfu}{2.7314in}{2.2698in}{0in}{\\qcb{b ) different % combinations of the mean free paths are used as parameters.}}{}{ssnnxx1b.eps}% % { \\special { language \" scientific word \" ;   type \" graphic \" ; % maintain - aspect - ratio true ;   display \" usedef \" ;   valid_file \" f \" ; % width 2.7314 in ;   height 2.2698 in ;   depth 0 in ;   original - width 3.7028 in ; % original - height 3.0726 in ;   cropleft \" 0 \" ;   croptop \" 1 \" ;   cropright \" 1 \" ; % cropbottom \" 0 \" ;   filename ' ssnnxx1b.eps';file-properties \" xnpeu\";}}}% % beginexpansion { \\parbox[b]{2.7314in}{\\begin{center } \\includegraphics [ height=2.2698 in , width=2.7314 in ] % { ssnnxx1b.eps}% \\\\ b ) different combinations of the mean free paths are used as parameters . \\end{center}}}% % endexpansion \\end{array}\\ ] ]    in fig.8 the dependence of the initial slope on the thickness of the superconducting first layer is tested . the graph shows the dependence of @xmath161 for a small range of the thickness @xmath13 of the normal conductor to emphasize the initial range . @xmath207{3.1474in}{\\begin{center } \\includegraphics [ height=2.5122 in , width=3.1474 in ] % { ssnnxx2a.eps}% \\\\ fig.8 : $ t_c$ for sn double layers as a function of $ d_n/\\xi$. the parameter $ d_s$ is the thickness of the superconductor$.$ ( $ n_s = n_n$ , $ l_s = l_n=\\xi/10 $ ) . \\end{center}}}% % endexpansion\\ ] ] in table i the normalized initial slope is collected . ( the numerical points had to fitted with a polynomial to extract the slope from the numerical results ) . up to a thickness of @xmath208 the @xmath209 is constant within about @xmath210 . for larger @xmath10 it decreases slightly . but since the value of @xmath211 becomes quite small this thickness range is not well suited for the experimental determination of the slope . the main result is that the normalized initial slope is essentially independent of the thickness of the superconductor . @xmath212{|l|l|}\\hline $ \\dfrac{\\mathbf{d}_{s}}{\\xi}$ & $ \\dfrac{d_{s}}{t_{s}}\\dfrac{dt_{c}}{dd_{n}}% $ \\\\\\hline 0.25 & 4.35\\\\\\hline $ 0.5 $ & 4.34\\\\\\hline 0.75 & 4.31\\\\\\hline 1.0 & 4.26\\\\\\hline 1.5 & 4.13\\\\\\hline 2.0 & 4.02\\\\\\hline \\end{tabular } \\\\ & \\begin{tabular } [ c]{l}% table i : normalized initial slope for different\\\\ thicknesses $ d_{s}$ of the superconductor \\end{tabular}\\end{aligned}\\ ] ]    finally fig.9 shows that the initial slope does not depend on the transmission through the interface . in this calculation the density of states in both metals is chosen to be equal @xmath206 and the mean free paths are @xmath213 . the transmission coefficient is varied between 0.2 and 1.0 . the resulting @xmath5-@xmath13 curves show the same initial slope . @xmath214{3.2088in}{\\begin{center } \\includegraphics [ height=2.7048 in , width=3.2088 in ] % { ssnnxx2b.eps}% \\\\ fig.9 : $ t_c$ for an sn double layers as a function of $ d_n/\\xi$. the parameter $ t$ is the transparency of the interface$.$($n_s = n_n,$ $ d_s=\\xi$ , $ % l_s = l_n=\\xi/10 $ ) . \\end{center}}}% % endexpansion\\ ] ]","summary":"there are only very few experimental investigations of this initial slope and they consist of pb / nn double layers ( nn stands for a normal metal ) . pacs : 74.45.+r , 74.62.-c , 74.20.fg","abstract":"a numerical method is developed to calculate the transition temperature of double or multi - layers consisting of films of super- and normal conductors . the approach is based on a dynamic interpretation of gorkov s linear gap equation and is very flexible . the mean free path of the different metals , transmission through the interface , ratio of specular reflection to diffusive scattering at the surfaces , and fraction of diffusive scattering at the interface can be included . furthermore it is possible to vary the mean free path and the bcs interaction in the vicinity of the interface . the numerical results show that the normalized initial slope of an sn double layer is independent of almost all film parameters except the ratio of the density of states , . there are only very few experimental investigations of this initial slope and they consist of pb / nn double layers ( nn stands for a normal metal ) . surprisingly the coefficient in these experiments is of the order or less than 2 while the ( weak coupling ) theory predicts a value of about 4.5 . this discrepancy has not been recognized in the past . the autor suggests that it is due to strong coupling behavior of pb in the double layers . the strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for . this agrees much better with the few experimental results that are available .    pacs : 74.45.+r , 74.62.-c , 74.20.fg"}
{"article_id":"cond-mat0504231","section_id":"c","document":"the intention of this paper was to develop a convenient numerical procedure for the superconducting proximity effect so that graduate students could instantly compare their experimental results with the theory . one importat result of this investigation is the fact that the ( normalized ) initial slope of an sn double layer is independent of most film parameters except the density of states ratio and the effective bcs interaction . @xmath215    in the case of a weak coupling superconductor @xmath3 is given by the cooper limit , i.e. @xmath216 , the inverse of the bcs interaction . if the debye temperature is not several orders of magnitude larger than @xmath11 then one has to determine @xmath3 in equation ( [ slp ] ) numerically . using @xmath217  for pb then the prefactor is about 4.5 . ( this is actually the value for a wide range of the debye temperature between @xmath218 and @xmath219 ) . recently our group investigated the proximity effect between the superconductor pb and several alkali metals @xcite . it was a great surprise that the experimental initial slope of these sn double layers could not be explained with the density of states from the literature . instead the experimental @xmath220 was too small by more than a factor of two . table ii gives some of the data of the sn double layers . ( the thickness of the normal metal was the smallest thickness in a full curve.)@xmath212{cccccc}% \\textbf{metals } & $ \\mathbf{d}_{s}$ $ ( nm)$ & $ \\mathbf{d}_{n}$ $ ( nm)$ & $ \\mathbf{s}_{sn}|_{\\exp}$ & $ \\mathbf{n}_{\\mathbf{n}}\\mathbf{/n}_{\\mathbf{s}}$ & \\textbf{ratio}\\\\ pb / k & 12.9 & 2.04 & 0.423 & 0.223 & 1.90\\\\ pb / na & 13.9 & 2.18 & 0.546 & 0.300 & 1.82\\\\ pb / ag & 17.9 & 2.10 & 0.625 & 0.335 & 1.86\\\\ &   &   &   &   & \\end{tabular } \\\\ & \\begin{tabular } [ c]{l}% table ii : the normalized initial slope of sn double layers with pb as\\\\ superconductor and different normal metals . the columns 2 - 6 give the\\\\ thickness of the superconductor , the normal conductor , the experimental\\\\ initial slope , the ratio of the density of states and the ratio $ \\mathbf{s}% _ { sn}|_{\\exp}/\\left (   n_{n}/n_{s}\\right )   $ . \\end{tabular}\\end{aligned}\\ ] ]    we searched the literature for other measurements of sn double layers and their initial slope . it turned out that there are very few measurements of sn layers . ( at this stage we excluded transition metals because they show two - band superconductivity and it is not obvious how the different superconducting bands couple to the normal conductor ) . there were essentially two groups of publications which had measured sn double layers which contained information about the intial slope . the first group of papers was by hilsch et al.@xcite , @xcite who investigated quench condensed pbcu layers . the second work was by minnigerode @xcite who also investigated pbcu layers but prepared the layers at room temperature . particularly the second paper gives detailed tables of thicknesses of the two components and transition temperatures . the results of these papers are collected in table iii . the first column gives the components of the sn double layer , the second and third columns the thicknesses of the superconductor and normal metal . the fourth column contains the experimental normalized slope and the fifth gives the ratio @xmath221 . the last column contains the ratio of the experimental ( normalized ) slope to the density of states ratio . again the experimental normalized slopes are much smaller than the theory predicts.@xmath133{c}% \\begin{tabular } [ c]{cccccc}% \\textbf{metals } & $ \\mathbf{d}_{s}$ $ ( nm)$ & $ \\mathbf{d}_{n}$ $ ( nm)$ & $ \\mathbf{s}_{sn}|_{\\exp}$ & $ \\mathbf{n}_{\\mathbf{n}}\\mathbf{/n}_{\\mathbf{s}}$ & \\textbf{ratio}\\\\ pb / cu$^{1}$ & 10.0 & 10.0 & 0.542 & 0.448 & 1.21\\\\ pb / cu$^{1}$ & 15.0 & 10.0 & 0.500 & 0.448 & 1.12\\\\ pb / cu$^{2}$ & 22.9 & 3.30 & 1.110 & 0.448 & 2.48\\\\ pb / cu$^{2}$ & 24.3 & 3.90 & 0.935 & 0.448 & 2.08\\\\ pb / cu$^{2}$ & 32.9 & 4.10 & 0.883 & 0.448 & 1.97\\\\ pb / cu$^{2}$ & 27.2 & 13.10 & 0.683 & 0.448 & ( 1.52)\\\\ pb / cu$^{2}$ & 28,0 & 26.40 & 0.842 & 0.448 & ( 1.88)\\\\ pb / cu$^{2}$ & 33.4 & 17.70 & 0.608 & 0.448 & ( 1.36 ) \\end{tabular } \\\\% \\begin{tabular } [ c]{l}% table iii : the normalized initial slope of pbcu double layers , data$^{1}$ from\\\\ ref . \\cite{h31 } are quench condensed\\ and data$^{2}$ from ref . \\cite{m45 } are\\\\ condensed at room temperature . the columns 2 - 6 give the thickness of\\\\ the superconductor , the normal conductor , the experimental initial slope,\\\\ the ratio of the density of states and the ratio $ \\mathbf{s}_{sn}|_{\\exp } /\\left (   n_{n}/n_{s}\\right )   $ . \\end{tabular } \\end{array } \\text{\\ \\ \\ } % \\ ] ]    it is rather amazing that this fundamental discrepancy between experiment and theory has not been realized . what is the reason for this disagreement ? the authors best guess at the present time is that the use of the weak coupling theory of superconductitivity is not adaquate for the double layers containing the supercondutor pb . the superconductor pb is a convenient component of an sn double layer because it has a rather large @xmath5 and is easy to condense . however , pb is a strong coupling superconductor . the fermi sphere of free electrons is modified by the electron - phonon interaction . an electron @xmath222 which lies below the fermi energy within the debye energy @xmath223 can emit a virtual phonon and perform a transition into a state @xmath224 above the fermi energy . as a consequence the states below @xmath225 have an occupation less than 1 and the states above @xmath225 have an occupation larger than 0 , even at zero temperature . at @xmath226 the occupation does not jump from one to zero , but has a smaller step of @xmath227 , where @xmath228 is the electron - phonon enhancement factor . the parameter @xmath229 can be calculated with the eliashberg function @xmath230 which desribes the probability of an electron to emit or absorb a phonon of energy @xmath231 . ( a nice treatment of the electron - phonon physics can by found in the book by grimvall @xcite ) . if one moves now an electron from the fermi energy to a k - value above the fermi energy then it changes the occupation of the k - state only by @xmath232 . the change in kinetic energy is therefore reduced by the same factor ; the energy states lie closer together by the factor @xmath228 . as a consequence the density of states is enhanced by @xmath228 and the fermi velocity reduced by @xmath227 . this enhancement is restricted to a small region in the vicinity of the fermi energy . the new density of states @xmath233 and fermi velocity @xmath234 are called the renormalized density of states and fermi velocity and marked with a star . the fermi wave number @xmath225 does not change and both changes in @xmath42 and @xmath58 can be expressed by a change of the mass @xmath235 ( therefore the name mass enhancement ) . many properties of the electron gas and the strong coupling superconductor can be reasonably well calculated in a renormalized strong coupling description . for the superconductivity this means that one applies the weak coupling bcs theory using renormalized density of states and fermi velocity . the error for pb is generally less than 20% as the ratio of @xmath236 instead of 3.5 demonstrates . ( for other parameters see @xcite ) .    in strong coupling superconductors the effective interaction @xmath237 is replaced by @xmath238 where @xmath229 describes the strength of the electron - phonon interaction and @xmath239 is the coulomb pseudo - potential . in the literature one find @xmath229-values for pb which vary between 0.8 and  1.6 @xcite . depending how much the strong coupling theory modifies the expression for the initial slope it could alter dramatically the theoretical prediction for the initial slope . in the appendix we show that a renormalized strong coupling theory would yield an initial slope of @xmath240 . this appears to alter the theoretical value for the initial slope . the difficulty is that the weak coupling treatment just a replaces @xmath241 by @xmath242 . this means that for the transition temperature one obtains the equivalent condition @xmath243 this does not alter the situation and yields , as observed by morel and anderson @xcite , a too small value of @xmath244 for @xmath229 . an obvious proposal would be to solve the superconducting proximity effect for strong coupling superconductors . this means to develop and solve a series equations for the energy and position dependent gap function @xmath245 which has the equations @xmath246[gap2c ] ) and ( [ scge ] ) as limiting cases . this is a very demanding job which goes beyond the scope of the present paper and has to be left for future investigations . however , we can check whether this extension is a promissing one . for this purpose we consider the analogy to the cooper limit for strong superconductors . let us consider a double layer composed of ( very ) thin films of a strong coupling superconductor and a normal metal . the super- and normal conductor have @xmath229 values @xmath92 and @xmath247 . both have the same value for the renormalized coulomb repulsion @xmath239 . for sufficiently thin films the electrons in the double layer travel so quickly from the superconductor to the normal metal and vice versa that they average over the properties of the two metals . we have essentially a new superconductor with a new averaged electron - phonon interaction @xmath248 ( in complete analogy to cooper s arguement ) @xmath249 now we apply the strong coupling gap equation ( [ scge ] ) to this artificial strong coupling superconductor .    for the superconductor we chose pb , but somewhat simplify its properties slightly . for the eliashberg function we use a simple square law for @xmath250@xmath251@xmath20 and express the prefactor in terms of the electron - phonon parameter @xmath229 . @xmath252 we use for the debye temperature @xmath253  and for the coulomb parameter @xmath254 . next we calculate @xmath255 for @xmath256@xmath257 these parameters are inserted into equation ( [ scge ] ) in the appendix and yield the dependence of @xmath5 on @xmath229 . in fig.10 this dependence is plotted , @xmath5 as a function of @xmath229 for @xmath258 @xmath259 and @xmath260 . the transition temperature of pb , @xmath261 , corresponds to value of @xmath262 . @xmath263{3.7584in}{\\begin{center } \\includegraphics [ height=3.1216 in , width=3.7584 in ] % { supra_sc1a.eps}% \\\\ fig.10 : the dependence of $ t_c $ on the electron - phonon parameter $ \\lambda$ using the ( linear ) strong coupling gap equation . \\end{center}}}% % endexpansion\\ ] ]    from fig.10 one obtains @xmath264 . at @xmath265 this slope has the value @xmath266 . within the thin film approximation for @xmath229 one finds for the initial slope of @xmath5 in a thin double layer : @xmath267 or @xmath268    if we take @xmath269 and use @xmath270 then we find @xmath271    the strong coupling treatment ( in the thin film limit ) reduces the prefactor in the intial slope to 1.7 . this is a very satisfactory result . the strong coupling theory yields the correct intial slope . on the other hand it is also disappointing . it means that the superconducting proximity effect with superconductors such as pb one can not be solved with the weak coupling theory . furthermore it means that the simulation developed here ( as all other theoretical treatments the author is aware of ) can only be applied to weak coupling superconductors such as al . but i beleave that this disappointment is more than compensated by the knowledge that the use of strong coupling superconductors gives an additional window to the study of strong coupling effects .","summary":"the numerical results show that the normalized initial slope of an sn double layer is independent of almost all film parameters except the ratio of the density of states , . this discrepancy has not been recognized in the past . the strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for .","abstract":"a numerical method is developed to calculate the transition temperature of double or multi - layers consisting of films of super- and normal conductors . the approach is based on a dynamic interpretation of gorkov s linear gap equation and is very flexible . the mean free path of the different metals , transmission through the interface , ratio of specular reflection to diffusive scattering at the surfaces , and fraction of diffusive scattering at the interface can be included . furthermore it is possible to vary the mean free path and the bcs interaction in the vicinity of the interface . the numerical results show that the normalized initial slope of an sn double layer is independent of almost all film parameters except the ratio of the density of states , . there are only very few experimental investigations of this initial slope and they consist of pb / nn double layers ( nn stands for a normal metal ) . surprisingly the coefficient in these experiments is of the order or less than 2 while the ( weak coupling ) theory predicts a value of about 4.5 . this discrepancy has not been recognized in the past . the autor suggests that it is due to strong coupling behavior of pb in the double layers . the strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for . this agrees much better with the few experimental results that are available .    pacs : 74.45.+r , 74.62.-c , 74.20.fg"}
{"article_id":"cond-mat0504231","section_id":"c","document":"this paper derives the transition temperature of a double or multi layer of a superconductor and a normal conductor numerically . the equivalence in the propagation of the superconducting pair amplitude and a single electron in gorkov s linear gap equation is used . the single electrons act as messengers who carry the information about the superconducting gap ( @xmath272 ) from one position - time @xmath273 to another position - time @xmath274 . this message which decays thermally with time as @xmath275 , is integrated at @xmath276 over all start position - times @xmath277 and , after multiplication with the bcs interaction @xmath278  yields the new gap function @xmath14 . at the transition temperature the procedure has to be self - consistent , i.e. the initial and final gap function have to be identical . the propagation of the single electrons is then quasi - classically simulated . the frame work of the calculation is the weak coupling theory of superconductivity . this numerical procedure to calculate the transition temperature of double or multi - layers consisting of thin films of superconductors and normal conductors is very flexible . the following parameters can be taken from the experiment or fitted during the calculation :    * mean free path of the different metals * transmission through the interface * ratio of specular reflection to diffusive scattering at the surfaces * fraction of diffusive scattering at the interface . furthermore it is possible    * to vary the mean free path along the thickness of the films * to vary the bcs interaction @xmath1 at the interface . the few examples which were presented in chapter iii demonstrate why the dirty case is so much simpler than the clean one . they also show that even for small thickness of the normal metal the gap parameter in the superconductor is not quite constant . still the initial slope for an sn double layer follows the prediction of the cooper limit . an important outcome of the numerical simulation is result that the normalized initial slope of an sn double layer as a function of @xmath13 at @xmath196 does not depend on    * the mean free path of the two metal * the thickness of the superconductor * a ( not to large ) barrier between the two metal . this slope is essentially given by @xmath279    for the extreme weak coupling superconductor the value of @xmath3 is @xmath280 . if one applies the numeric procedure to double layers with pb as the superconducting component then one obtains @xmath281 . this is in strong disagreement with the results of the few experiments which allow the evaluation of the initial slope . their values for @xmath3 lie in the range of @xmath282 . the author believes that the discrepancy is due to the strong coupling properties of the pb . an analysis of the strong coupling gap equation in the thin - film limit confirms this supposition . it yields the value of about @xmath283 for a ( simplified ) pb film in contact with a normal metal which is characterized by @xmath284 and @xmath254 .","summary":"a numerical method is developed to calculate the transition temperature of double or multi - layers consisting of films of super- and normal conductors . the approach is based on a dynamic interpretation of gorkov s linear gap equation and is very flexible . the mean free path of the different metals , transmission through the interface , ratio of specular reflection to diffusive scattering at the surfaces , and fraction of diffusive scattering at the interface can be included . furthermore it is possible to vary the mean free path and the bcs interaction in the vicinity of the interface . the autor suggests that it is due to strong coupling behavior of pb in the double layers .","abstract":"a numerical method is developed to calculate the transition temperature of double or multi - layers consisting of films of super- and normal conductors . the approach is based on a dynamic interpretation of gorkov s linear gap equation and is very flexible . the mean free path of the different metals , transmission through the interface , ratio of specular reflection to diffusive scattering at the surfaces , and fraction of diffusive scattering at the interface can be included . furthermore it is possible to vary the mean free path and the bcs interaction in the vicinity of the interface . the numerical results show that the normalized initial slope of an sn double layer is independent of almost all film parameters except the ratio of the density of states , . there are only very few experimental investigations of this initial slope and they consist of pb / nn double layers ( nn stands for a normal metal ) . surprisingly the coefficient in these experiments is of the order or less than 2 while the ( weak coupling ) theory predicts a value of about 4.5 . this discrepancy has not been recognized in the past . the autor suggests that it is due to strong coupling behavior of pb in the double layers . the strong coupling gap equation is evaluated in the thin film limit and yields the value of 1.6 for . this agrees much better with the few experimental results that are available .    pacs : 74.45.+r , 74.62.-c , 74.20.fg"}
{"article_id":"1401.7904","section_id":"i","document":"geometric integrators are numerical methods that preserve geometric structures and properties of the flow of a differential equation . structure - preserving integrators have attracted considerable interest due to their excellent numerical behavior , especially for long - time integration of equations possessing geometric properties ( see @xcite , @xcite , @xcite ) .    an important class of structure - preserving integrators are _ variational integrators _ ( see @xcite ) . this type of numerical schemes is based on discrete variational principles and provides a natural framework for the discretization of lagrangian systems , including forced , dissipative , or constrained ones . variational integrators were introduced in the context of finite - dimensional mechanical systems , but were later generalized to lagrangian field theories ( see @xcite ) and applied in many computations , for example in elasticity ( @xcite ) , electrodynamics ( @xcite ) , or fluid dynamics ( @xcite ) . theoretical aspects of variational integration are well understood in the case when the lagrangian describing the considered system is regular , that is , when the corresponding legendre transform is ( at least locally ) invertible . however , the corresponding theory for degenerate lagrangian systems is less developed . the analysis of degenerate systems becomes a little more cumbersome , because the euler - lagrange equations may cease to be second order , or may not even make any sense at all . in the latter case one needs to determine if there exists a submanifold of the configuration bundle @xmath0 on which consistent equations of motion can be derived this can be accomplished by applying the dirac theory of constraints or the pre - symplectic constraint algorithm ( see @xcite , @xcite ) . a particularly simple case of degeneracy occurs when the lagrangian is linear in velocities . in that case , the dynamics of the system is defined on the configuration manifold @xmath1 itself , rather than its tangent bundle @xmath0 , provided that some regularity conditions are satisfied . such systems arise in many physical applications , including interacting point vortices in the plane ( see @xcite , @xcite , @xcite ) , or partial differential equations such as the nonlinear schrdinger ( @xcite ) , kdv ( @xcite , @xcite ) or camassa - holm equations ( @xcite , @xcite ) . in section  [ sec : numerical experiments ] we show how certain poisson systems can be recast as lagrangian systems whose lagrangians are linear in velocities . therefore , our approach offers a new perspective on geometric integration of poisson systems , which often arise as semi - discretizations of integrable nonlinear partial differential equations , e.g. , the toda or volterra lattice equations , and play an important role in the modeling of many physical phenomena ( see @xcite , @xcite , @xcite ) . this paper is organized as follows . in section  [ sec : geometric setup ] we introduce a proper geometric setup and discuss the properties of systems that are linear in velocities . in section  [ sec : veselov discretization and discrete mechanics ] we analyze the general properties of variational integrators and point out how the relevant theory differs from the non - degenerate case . in section [ sec : variational partitioned runge - kutta methods ] we introduce variational partitioned runge - kutta methods and discuss their relation to numerical integration of differential - algebraic systems . in section  [ sec : numerical experiments ] we present the results of our numerical experiments for kepler s problem , a system of two interacting vortices , and the lotka - volterra model . we summarize our work and discuss possible extensions in section  [ sec : summary ] .","summary":"we analyze the geometry underlying such systems and develop the appropriate theory for variational integration . we also construct variational runge - kutta methods and analyze their properties . we verify our results through numerical experiments for various dynamical systems .","abstract":"in this paper we construct higher - order variational integrators for a class of degenerate systems described by lagrangians that are linear in velocities . we analyze the geometry underlying such systems and develop the appropriate theory for variational integration . our main observation is that the evolution takes place on the primary constraint and the hamiltonian equations of motion can be formulated as an index-1 differential - algebraic system . we also construct variational runge - kutta methods and analyze their properties . the general properties of runge - kutta methods depend on the velocity part of the lagrangian . if the velocity part is also linear in the position coordinate , then we show that non - partitioned variational runge - kutta methods are equivalent to integration of the corresponding first - order euler - lagrange equations , which have the form of a poisson system with a constant structure matrix , and the classical properties of the runge - kutta method are retained . if the velocity part is nonlinear in the position coordinate , we observe a reduction of the order of convergence , which is typical of numerical integration of daes . we verify our results through numerical experiments for various dynamical systems ."}
{"article_id":"1401.7904","section_id":"m","document":"to construct higher - order variational integrators one may consider a class of partitioned runge - kutta ( prk ) methods . variational partitioned runge - kutta ( vprk ) methods for regular lagrangians are described in @xcite and @xcite . in this section we show how vprk methods can be applied to systems described by lagrangians such as . as in the case of regular lagrangians , we will construct an @xmath251-stage variational partitioned runge - kutta integrator for the lagrangian by considering the discrete lagrangian    @xmath252    where the internal stages @xmath253 , @xmath254 , @xmath255 , satisfy the relation    @xmath256    and are chosen so that the right - hand side of is extremized under the constraint    @xmath257    a variational integrator is then obtained by forming the corresponding discrete euler - lagrange equations . the @xmath251-stage variational partitioned runge - kutta method based on the discrete lagrangian with the coefficients @xmath258 and @xmath259 is equivalent to the following partitioned runge - kutta method applied to the hamiltonian dae :    [ eq : prk for dae ] @xmath260^t \\dot q_i - dh(q_i ) , } \\qquad \\qquad \\qquad i=1,\\ldots , s,\\\\ \\label{eq : prk for dae 2 } \\dot p^i & =   [ d\\alpha(q_i)]^t \\dot q_i - dh(q_i ) , \\qquad \\qquad \\qquad \\ ! i=1,\\ldots , s , \\\\ \\label{eq : prk for dae 3 } q_i & = q + h \\sum_{j=1}^s a_{ij } \\dot q_j , \\phantom{-dh(q_i ) , } \\qquad \\qquad \\qquad i=1,\\ldots , s , \\\\ \\label{eq : prk for dae 4 } p^i & = p + h \\sum_{j=1}^s \\bar a_{ij } \\dot p_j ,   \\phantom{-dh(q_i ) , } \\qquad \\qquad \\qquad \\ , i=1,\\ldots , s,\\\\ \\label{eq : prk for dae 5 } \\bar q & = q + h \\sum_{j=1}^s b_j \\dot q_j,\\\\ \\label{eq : prk for dae 6 } \\bar p & = p + h \\sum_{j=1}^s b_j \\dot p_j,\\end{aligned}\\ ] ]    where the coefficients satisfy the condition    @xmath261    and @xmath262 denote the current values of position and momentum , @xmath263 denote the respective values at the next time step , @xmath264 , @xmath265 , and @xmath253 , @xmath254 , @xmath266 , @xmath267 are the internal stages , with @xmath268 , and similarly for the others . see theorem  vi.6.4 in @xcite or theorem  2.6.1 in @xcite . the proof is essentially identical . the only qualitative difference is the fact that in our case the lagrangian is degenerate , so the corresponding hamiltonian system is in fact the index-1 differential - algebraic system rather than a typical system of ordinary differential equations . +    [ [ existence - and - uniqueness - of - the - numerical - solution . ] ] existence and uniqueness of the numerical solution . + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +    given @xmath3 and @xmath269 , one can use equations   to compute the new position @xmath118 and momentum @xmath270 . first , one needs to solve - for the internal stages @xmath253 , @xmath254 , @xmath266 , and @xmath267 . this is a system of @xmath271 equations for @xmath271 variables , but one has to make sure these equations are independent , so that a unique solution exists . one may be tempted to calculate the jacobian of this system for @xmath272 , and then use the implicit function theorem . however , even if we start with consistent initial values @xmath273 , the numerical solution @xmath274 for @xmath275 will only approximately satisfy the algebraic constraint ; so @xmath276 and @xmath277 can not be assumed to be the solution of - for @xmath272 , and consequently , the implicit function theorem will not yield a useful result . let us therefore regard @xmath3 and @xmath269 as @xmath117-dependent , as they result from the previous iterations of the method with the timestep @xmath117 . if the method is convergent , it is reasonable to expect that @xmath278 is small and converges to zero as @xmath117 is refined . the following approach was inspired by theorem  4.1 in @xcite . [ thm : existence of the numerical solution for prk ] let @xmath279 and @xmath45 be smooth in an @xmath117-independent neighborhood @xmath280 of @xmath3 and let the matrix    @xmath281    be invertible with the inverse bounded in @xmath282 , i.e. , there exists @xmath222 such that    @xmath283    where @xmath284 , @xmath285 , @xmath286 is the @xmath287 identity matrix , and @xmath288 denotes the block diagonal matrix    @xmath289    suppose also that @xmath262 satisfy    @xmath290    then there exists @xmath223 such that the nonlinear system - has a solution for @xmath226 . the solution is locally unique and satisfies    @xmath291    substitute and in and to obtain    @xmath292    for @xmath255 , where for notational convenience we left the @xmath253 s as arguments of @xmath45 , @xmath293 and @xmath294 , but we keep in mind they are defined by , so that is a nonlinear system for @xmath254 and @xmath267 . let us consider the homotopy    @xmath295    for @xmath255 . it is easy to see that for @xmath296 the system has the solution @xmath297 and @xmath298 , and for @xmath299 it is equivalent to . let us treat @xmath254 and @xmath267 as functions of @xmath300 , and differentiate with respect to this parameter . the resulting ode system can be written as    [ eq : ode system for dot qi and dot pi ] @xmath301    where for compactness we introduced the following notations : @xmath302 , similarly for @xmath303 ; @xmath304 is the @xmath251-dimensional vector of ones ; @xmath305 , and similarly , @xmath306 denotes the block diagonal matrix    @xmath307    with @xmath308 , where @xmath309 denotes the hessian matrix of the respective function , and summation over @xmath310 is implied . the system is further simplified if we substitute in . this way we obtain an ode system for the variables @xmath311 of the form    @xmath312 \\frac{d \\dot q}{d\\tau } = \\nonumber \\\\ & ( \\mathcal{\\bar{a } } \\mathbbm{1}_s)\\otimes dh(q ) - \\frac{1}{h}\\mathbbm{1}_s\\otimes\\big(p-\\alpha(q)\\big).\\end{aligned}\\ ] ]    since @xmath45 is smooth , we have    @xmath313_{ij } = a_{ij } d\\alpha(q_i ) = a_{ij } d\\alpha(q_j ) + o(\\delta ) = \\big [ ( \\mathcal{a}\\otimes i_n ) \\{d\\alpha\\ } \\big]_{ij } + o(\\delta),\\ ] ]    where @xmath314 for @xmath315 assumed small , but independent of @xmath117 . moreover , since @xmath45 and @xmath279 are smooth , the term @xmath306 , as a function of @xmath311 , is bounded in a neighborhood of 0 . therefore , we can write as    @xmath316 \\frac{d \\dot q}{d\\tau } = ( \\mathcal{\\bar{a } } \\mathbbm{1}_s)\\otimes dh(q ) - \\frac{1}{h}\\mathbbm{1}_s\\otimes\\big(p-\\alpha(q)\\big).\\end{aligned}\\ ] ]    by , for sufficiently small @xmath117 and @xmath315 , the matrix @xmath317 has a bounded inverse , provided that @xmath318 remain in @xmath280 . therefore , the ode with the initial condition @xmath319 has a unique solution @xmath320 on a non - empty interval @xmath321 , which can be extended until any of the corresponding @xmath322 leaves @xmath280 . let us argue that for a sufficiently small @xmath117 we have @xmath323 . given and , the ode implies that    @xmath324    therefore , we have    @xmath325    and further    @xmath326    for @xmath327 . this implies that all @xmath322 remain in @xmath280 for @xmath328 if @xmath117 is sufficiently small . consequently , the ode has a solution on the interval @xmath329 $ ] . then @xmath330 and @xmath331 satisfy the estimates , and are a solution to the nonlinear system - . the corresponding @xmath267 and @xmath266 can be computed using and , and the remaining estimates can be proved using the fact that @xmath45 and @xmath279 are smooth . this completes the proof of the existence of a numerical solution to - .    in order to prove local uniqueness , we substitute the second equation of in the first one to obtain a nonlinear system for @xmath254 , namely    @xmath332    for @xmath255 , where we again left the @xmath253 s for notational convenience . suppose there exists another solution @xmath333 that satisfies the estimates , and denote @xmath334 . based on the assumptions , we have @xmath335 , i.e. , it is at least bounded as @xmath336 . we will show that for sufficiently small @xmath117 we in fact have @xmath337 . since @xmath338 satisfy , we have    @xmath339    for @xmath255 . subtract from , and linearize around @xmath254 . based on the fact that @xmath335 , and using the notation introduced before , we get    @xmath340 \\delta \\dot q + o(h^2 \\|\\delta \\dot q \\|).\\ ] ]    by a similar argument as before , for sufficiently small @xmath117 the matrix @xmath341 $ ] has a bounded inverse , therefore implies @xmath342 , that is ,    @xmath343    for some constant @xmath344 . note that for @xmath345 we have @xmath346 , and therefore @xmath347 , which completes the proof of the local uniqueness of a numerical solution to - .    . [ [ remarks . ] ] remarks . + + + + + + + +    the condition may be tedious to verify , especially if one uses a runge - kutta method with many stages . however , this condition is significantly simplified in the following special cases :    1 .   for a non - partitioned runge - kutta method we have @xmath348 , and the condition is satisfied if @xmath349 is invertible , and the mass matrix @xmath350 , as defined in section  [ sec : equations of motion ] , is invertible in @xmath280 and its inverse is bounded . if @xmath351 is antisymmetric , then the condition is satisfied if @xmath352 is invertible , and the matrix @xmath353 is invertible in @xmath280 and its inverse is bounded . an interesting special case is obtained if we have , in some local chart on @xmath1 , @xmath355 for some constant matrix @xmath356 . without loss of generality assume that @xmath356 is invertible and antisymmetric . the lagrangian then takes the form    @xmath357    the euler - lagrange equations become    @xmath358    and the hamiltonian dae system is    @xmath359    let us consider a special case of the method with @xmath360 , i.e. , a non - partitioned runge - kutta method . applying it to we get    [ eq : prk for dae for linear alpha ] @xmath361 since @xmath356 is antisymmetric and invertible , then by theorem  [ thm : existence of the numerical solution for prk ] the scheme yields a unique numerical solution to if the runge - kutta matrix @xmath362 is invertible . [ thm : equivalence with a rk for the ode ] suppose @xmath362 is invertible and @xmath363 . then the method is equivalent to the same runge - kutta method applied to . substitute and in , and use the fact @xmath363 to obtain    @xmath364    since @xmath349 is invertible , this implies    @xmath365    substituting this in yields    @xmath366    together with and , this gives a runge - kutta method for . moreover , substituting and @xmath363 in , and using , one has    @xmath367    that is , @xmath368 satisfy the algebraic constraint . +    [ thm : invariance of the primary constraint ] the numerical flow on @xmath17 defined by leaves the primary constraint @xmath39 invariant , i.e. , if @xmath369 , then @xmath370 . if the coefficients of the method satisfy the condition , then is a variational integrator and the associated discrete hamiltonian map @xmath229 is symplectic on @xmath17 , as explained in section  [ sec : discrete mechanics ] . given corollary  [ thm : invariance of the primary constraint ] , we further have :    [ thm : symplecticity on the primary constraint ] if the coefficients @xmath258 and @xmath259 in satisfy the condition , then the discrete hamiltonian map @xmath229 associated with is symplectic on the primary constraint @xmath39 , that is , @xmath371 . [ [ convergence . ] ] convergence . + + + + + + + + + + + +    various runge - kutta methods and their classical orders of convergence , that is , orders of convergence when applied to ( non - stiff ) ordinary differential equations , are discussed in many textbooks on numerical analysis , for instance @xcite and @xcite . when applied to differential - algebraic equations , the order of convergence of a runge - kutta method may be reduced ( see @xcite , @xcite , @xcite ) . however , in the case of theorem  [ thm : equivalence with a rk for the ode ] implies that the classical order of convergence of non - partitioned runge - kutta methods is retained . [ thm : retention of the classical order of convergence ] a runge - kutta method with the coefficients @xmath258 and @xmath259 applied to the dae system retains its classical order of convergence . let @xmath220 be the classical order of the considered runge - kutta method , @xmath369 an initial condition , @xmath372 the exact solution to such that @xmath373 , and @xmath274 the numerical solution obtained by applying the method iteratively @xmath374 times with @xmath375 . theorem  [ thm : equivalence with a rk for the ode ] states that the method is equivalent to applying the same runge - kutta method to the ode system . hence , we obtain convergence of order @xmath220 in the @xmath3 variable , that is , for a fixed time @xmath376 and an integer @xmath377 such that @xmath378 , we have the estimate    @xmath379    for some constant @xmath222 ( cf . definition  [ thm : definition of the order of convergence ] ) . by corollary  [ thm : invariance of the primary constraint ] we know that @xmath380 , so we have the estimate    @xmath381    which completes the proof , since @xmath382 . +    of particular interest to us are runge - kutta methods that satisfy the condition , for instance symplectic diagonally - implicit runge - kutta methods ( dirk ) or gauss collocation methods ( see @xcite ) . the @xmath251-stage gauss method is of classical order @xmath383 , therefore we have :    [ thm : order of convergence of gauss methods ] the @xmath251-stage gauss collocation method applied to the dae system is convergent of order @xmath383 . as mentioned in section  [ sec : variational error analysis ] , the midpoint rule is a 1-stage gauss method , therefore it retains its classical second order of convergence . [ [ backward - error - analysis . ] ] backward error analysis . + + + + + + + + + + + + + + + + + + + + + + + +    the system can be rewritten as the poisson system    @xmath384    with the structure matrix @xmath385 ( see @xcite , @xcite ) . the flow @xmath76 for this equation is a _ poisson map _ , that is , it satisfies the property    @xmath386^{t } = \\lambda^{-1},\\ ] ]    which is in fact equivalent to the symplecticity property or written in local coordinates on @xmath1 or @xmath39 , respectively . let @xmath387 represent the numerical flow defined by some numerical algorithm applied to . we say this flow is a _ poisson integrator _ if    @xmath388^{t } = \\lambda^{-1}.\\ ] ]    the left - hand side of can be regarded as a quadratic invariant of . by theorem [ thm : equivalence with a rk for the ode ] the method is equivalent to applying the same runge - kutta method to . if its coefficients also satisfy the condition , then it can be shown that the method preserves quadratic invariants ( see theorem  iv.2.2 in @xcite ) . therefore , we have :    [ thm : r - k methods as poisson integrators ] if @xmath362 is invertible , the coefficients @xmath258 and @xmath259 satisfy the condition , and @xmath363 , then the method is a poisson integrator for .    the true power of symplectic integrators for hamiltonian equations is revealed through their backward error analysis : a symplectic integrator for a hamiltonian system with the hamiltonian @xmath389 defines the _ exact _ flow for a nearby hamiltonian system , whose hamiltonian can be expressed as the asymptotic series    @xmath390    owing to this fact , under some additional assumptions , symplectic numerical schemes nearly conserve the original hamiltonian @xmath389 over exponentially long time intervals ( see @xcite for details ) . a similar result holds for poisson integrators for poisson systems : a poisson integrator defines the exact flow for a nearby poisson system , whose structure matrix is the same and whose hamiltonian has the asymptotic expansion ( see theorem  ix.3.6 in @xcite ) . therefore , we expect the non - partitioned runge - kutta schemes satisfying the condition to demonstrate good preservation of the original hamiltonian @xmath279 . see section  [ sec : numerical experiments ] for numerical examples . partitioned runge - kutta methods do not seem to have special properties when applied to systems with linear @xmath354 , therefore we describe them in the general case in section  [ sec : nonlinear alpha ] . when the coordinates @xmath354 are nonlinear functions of @xmath3 , then the runge - kutta methods discussed in section  [ sec : linear alpha ] lose some of their properties : a theorem similar to theorem  [ thm : equivalence with a rk for the ode ] can not be proved , most of the runge - kutta methods ( whether non - partitioned or partitioned ) do not preserve the algebraic constraint @xmath391 , i.e. , the numerical solution does not stay on the primary constraint @xmath39 , and therefore their order of convergence is reduced , unless they are _ stiffly accurate_.      let us again consider non - partitioned methods with @xmath360 . convergence results for some classical runge - kutta schemes of interest can be obtained by transforming into a semi - explicit index-2 dae system . let us briefly review this approach . more details can be found in @xcite and @xcite . the system can be written as the quasi - linear dae    @xmath392    where @xmath393 and    @xmath394^t & -i_n \\\\ 0 & 0 \\\\ \\end{matrix } \\right ) , \\qquad\\qquad\\qquad f(y ) = \\left ( \\begin{matrix } dh(q ) \\\\ p-\\alpha(q ) \\\\ \\end{matrix } \\right),\\ ] ]    where @xmath286 denotes the @xmath287 identity matrix . let us introduce a slack variable @xmath395 and rewrite as the index-2 dae system    [ eq : index 2 dae form ] @xmath396    this system is of index 2 , because it has @xmath397 dependent variables , but only @xmath398 differential equations , and some components of the algebraic equations have to be differentiated twice with respect to time in order to derive the missing differential equations for @xmath395 . note that @xmath399 is a singular matrix of constant rank @xmath400 , therefore it can be decomposed ( using gauss elimination or the singular value decomposition ) as    @xmath401    for some non - singular matrices @xmath402 and @xmath403 . since @xmath404 is assumed to be smooth , one can choose @xmath94 and @xmath405 so that they are also smooth ( at least in a neighborhood of @xmath406 ) . premultiplying both sides of by @xmath407 turns the dae into    [ eq : index 2 dae block form ] @xmath408    where we introduced the block structure @xmath409 , @xmath410 , and    @xmath411    since @xmath403 is invertible , we can assume without loss of generality that the block @xmath412 is invertible , too ( one can always permute the columns of @xmath403 otherwise ) . let us compute @xmath413 from and substitute it in . the resulting system ,    [ eq : index 2 dae final block form ] @xmath414    has the form of a semi - explicit index-2 dae    @xmath415    provided that    @xmath416    has a bounded inverse . it is an elementary exercise to show that the partitioned runge - kutta method is invariant under the presented transformation , that is , it defines a numerically equivalent partitioned runge - kutta method for . runge - kutta methods for semi - explicit index-2 daes have been studied and some convergence results are available . convergence estimates for the @xmath406 component of can be readily applied to the solution of .    as in section [ sec : linear alpha ] , of particular interest to us are variational runge - kutta methods , i.e. , methods satisfying the condition , for example gauss collocation methods ( see @xcite , @xcite ) . however , in the case when @xmath404 is a nonlinear function , the solution generated by the gauss methods does not stay on the primary constraint @xmath39 and this affects their rate of convergence , as will be shown below . for comparison , we will also consider the radau iia methods ( see @xcite ) , which , although not variational / symplectic , are _ stiffly accurate _ , that is , their coefficients satisfy @xmath417 for @xmath418 , so the numerical value of the solution at the new time step is equal to the value of the last internal stage , and therefore the numerical solution stays on the submanifold @xmath39 . we cite the following convergence rates for the @xmath406 component of after @xcite and @xcite :    * @xmath251-stage gauss method  convergent of order @xmath419 , * @xmath251-stage radau iia method  convergent of order @xmath420 .    with the exception of the midpoint rule ( @xmath421 ) , we see that the order of convergence of the gauss methods is reduced . on the other hand , the radau iia methods retain their classical order @xmath420 . [ [ symplecticity . ] ] symplecticity . + + + + + + + + + + + + + +    since the gauss methods satisfy the condition , they generate a flow which preserves the canonical symplectic form @xmath57 on @xmath17 , as explained in section  [ sec : discrete mechanics ] . however , since the primary constraint @xmath39 is not invariant under this flow , a result analogous to corollary  [ thm : symplecticity on the primary constraint ] does not hold , i.e. , the flow is not symplectic on @xmath39 .      in section  [ sec : numerical experiments ] we present numerical results for the lobatto iiia - iiib methods ( see @xcite ) . their numerical performance appears rather unattractive , therefore our theoretical results regarding partitioned runge - kutta methods are less complete . below we summarize the experimental orders of convergence of the lobatto  iiia - iiib schemes that we observed in our numerical computations ( see figure  [ fig : convergence plots for kepler s problem ] , figure  [ fig : convergence plot for point vortices ] , and figure  [ fig : convergence plot for the lotka - volterra model ] ) :    * @xmath422-stage lobatto  iiia - iiib  inconsistent , * @xmath423-stage lobatto  iiia - iiib  convergent of order 2 , * @xmath424-stage lobatto  iiia - iiib  convergent of order 2 .    comments regarding the symplecticity of these schemes are the same as for the gauss methods mentioned above in section  [ sec : runge - kutta methods ] .","summary":"the general properties of runge - kutta methods depend on the velocity part of the lagrangian . if the velocity part is also linear in the position coordinate , then we show that non - partitioned variational runge - kutta methods are equivalent to integration of the corresponding first - order euler - lagrange equations , which have the form of a poisson system with a constant structure matrix , and the classical properties of the runge - kutta method are retained . if the velocity part is nonlinear in the position coordinate , we observe a reduction of the order of convergence , which is typical of numerical integration of daes .","abstract":"in this paper we construct higher - order variational integrators for a class of degenerate systems described by lagrangians that are linear in velocities . we analyze the geometry underlying such systems and develop the appropriate theory for variational integration . our main observation is that the evolution takes place on the primary constraint and the hamiltonian equations of motion can be formulated as an index-1 differential - algebraic system . we also construct variational runge - kutta methods and analyze their properties . the general properties of runge - kutta methods depend on the velocity part of the lagrangian . if the velocity part is also linear in the position coordinate , then we show that non - partitioned variational runge - kutta methods are equivalent to integration of the corresponding first - order euler - lagrange equations , which have the form of a poisson system with a constant structure matrix , and the classical properties of the runge - kutta method are retained . if the velocity part is nonlinear in the position coordinate , we observe a reduction of the order of convergence , which is typical of numerical integration of daes . we verify our results through numerical experiments for various dynamical systems ."}
{"article_id":"1401.7904","section_id":"i","document":"we analyzed a class of degenerate systems described by lagrangians that are linear in velocities , and presented a way to construct appropriate higher - order variational integrators . we pointed out how the theory underlying variational integration is different from the non - degenerate case and we made a connection with numerical integration of differential - algebraic equations . we also performed numerical experiments for several example models . our work can be extended in several ways . in section  [ sec : lotka - volterra model ] we presented our numerical results for the lotka - volterra model , which is an example of a system for which the coordinate functions @xmath354 are nonlinear . the 1- and 3-stage gauss methods performed exceptionally well and preserved the hamiltonian over a very long integration time . it would be interesting to perform a backward error ( or similar ) analysis to check if this behavior is generic . if confirmed , our variational approach could provide a new way to construct geometric integrators for a broader class of poisson systems .    it would also be interesting to further consider _ constrained _ systems with lagrangians that are linear in velocities and construct associated higher - order variational integrators . this would allow to generalize the space - adaptive methods presented in @xcite , @xcite to degenerate field theories , such as the nonlinear schrdinger , kdv or camassa - holm equations .","summary":"in this paper we construct higher - order variational integrators for a class of degenerate systems described by lagrangians that are linear in velocities .","abstract":"in this paper we construct higher - order variational integrators for a class of degenerate systems described by lagrangians that are linear in velocities . we analyze the geometry underlying such systems and develop the appropriate theory for variational integration . our main observation is that the evolution takes place on the primary constraint and the hamiltonian equations of motion can be formulated as an index-1 differential - algebraic system . we also construct variational runge - kutta methods and analyze their properties . the general properties of runge - kutta methods depend on the velocity part of the lagrangian . if the velocity part is also linear in the position coordinate , then we show that non - partitioned variational runge - kutta methods are equivalent to integration of the corresponding first - order euler - lagrange equations , which have the form of a poisson system with a constant structure matrix , and the classical properties of the runge - kutta method are retained . if the velocity part is nonlinear in the position coordinate , we observe a reduction of the order of convergence , which is typical of numerical integration of daes . we verify our results through numerical experiments for various dynamical systems ."}
{"article_id":"1207.3928","section_id":"i","document":"there are several automated tools for inferring the properties of the stellar populations contributing to the integrated galaxy spectra . the list includes moped @xcite , starlight @xcite , steckmap @xcite , vespa @xcite , or ulyss , as well as the use of line indices like the lick indices @xcite . similarly , there are semi - automatic procedures to deduce the properties of the gas ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , including the so - called strong - line ratio methods . these tools are ( and will be ) fundamental for understanding the galaxy formation and evolution , but the blind use of the codes results quite unsatisfactory from a physical stand point . one obtains a precise quantitative description of the stellar populations contributing to the integrated spectra , but ignores the reason why the code has chosen them rather than other potential alternatives . the educated eye of an astronomer is often far more telling from a physical point of view . unfortunately , the know - how of qualitatively interpreting a spectrum is learned after a long experience of working in the field . the information on which particular spectral feature informs of which particular physical property is scattered among a large number of technical publications , difficult to identify and to deal with for a newcomer . this paper aims at providing a step - by - step guide to qualitative interpretation of galaxy spectra . moreover , it will be compared with up - to - date numerical techniques to show that both qualitative and quantitative results are in excellent agreement . the work was originally planned as a mere academic exercise to understand the nature of the classes resulting from the k - means classification of all the galaxy spectra in the sloan digital sky survey data release 7 ( sdss - dr7 , * ? ? ? we wanted to translate the spectral shapes into physical units like stellar ages and metallicities , so that this information can be used to tailor class - based searches , or when interpreting spectra ( e.g. , * ? ? ? * ) . however , the exercise is of interest beyond the original scope . the simple decision tree we use is suitable to characterize any galaxy spectrum . we know of its generality because it allows to separate and characterize the 28 automated spectroscopic k - means - based ( ask ) classes @xcite which , by construction , are proxies that condense the properties of the some one - million sdss spectra @xcite . the ask class characterization represents a significant part of the paper , that are discussed in detail as an illustration of the procedure . as we stress above , our qualitative analysis may have several other applications , e.g. , ( 1 ) to gain physical insight when interpreting quantitative star formation histories ( sfhs ) derived from modern automated tools , ( 2 ) for quick - look galaxy classification ( not only in the local universe , but also at moderate - high redshifts , since the hubble expansion shifts the uv - visible spectrum to the near ir ) , ( 3 ) for interpreting noisy spectra where eyeball inspection is often better than detailed inversion , ( 4 ) as reference for identifying unusual galaxies , or ( 5 ) for educational purposes to develop physical intuition . the paper is organized as follows . section  [ ask_class ] introduces the ask spectral classification of galaxy spectra whose templates serve as reference point . section  [ list_features ] lists and discusses spectral features commonly used when interpreting galaxy spectra . they are employed to set up the recipe introduced in sect . [ decision_tree ] , which is abridged in a schematic shown in fig . [ decision ] . the recipe ( or algorithm ) is used in sect . [ qualitative_classes ] to disclose the physical properties of all the ask classes . the results of such qualitative analysis are compared with state - of - the - art quantitative analyses in sects . [ starlight ] and [ quantitative_lines ]  sect . [ starlight ] deals with the comparison of stellar components , whereas sect . [ quantitative_lines ] refers to the gas components . section  [ additional_results ] discusses several additional properties of the ask templates , whereas sect . [ conclusions ] summarizes the proposed qualitative analysis .","summary":", it is put forward as an instrument for quick - look analysis , and for gaining physical insight when interpreting the outputs provided by automated tools . though the recipe is of general application , it was developed for understanding the nature of the automatic spectroscopic k - means based ( ask ) template spectra . they resulted from the classification of all the galaxy spectra in the sloan digital sky survey data release 7 ( sdss - dr7 ) , thus being a comprehensive representation of the galaxy spectra in the local universe . using the recipe a number of byproducts follow from the analysis .","abstract":"we describe a simple step - by - step guide to qualitative interpretation of galaxy spectra ( fig .  [ decision ] ) . rather than an alternative to existing automated tools , it is put forward as an instrument for quick - look analysis , and for gaining physical insight when interpreting the outputs provided by automated tools . though the recipe is of general application , it was developed for understanding the nature of the automatic spectroscopic k - means based ( ask ) template spectra . they resulted from the classification of all the galaxy spectra in the sloan digital sky survey data release 7 ( sdss - dr7 ) , thus being a comprehensive representation of the galaxy spectra in the local universe . using the recipe , we give a description of the properties of the gas and the stars that characterize the ask classes , from those corresponding to passively evolving galaxies , to hii galaxies undergoing a galaxy - wide starburst . the qualitative analysis is found to be in excellent agreement with quantitative analyses of the same spectra . we compare the mean ages of the stellar populations with those inferred using the code starlight.we also examine the estimated gas - phase metallicity with the metallicities obtained using electron - temperature based methods . a number of byproducts follow from the analysis . there is a tight correlation between the age of the stellar population and the metallicity of the gas , which is stronger than the correlations between galaxy mass and stellar age , and galaxy mass and gas metallicity . the galaxy spectra are known to follow a 1-dimensional sequence , and we identify the luminosity - weighted mean stellar age as the affine parameter that describes the sequence . all ask classes happen to have a significant fraction of old stars , although spectrum - wise they are outshined by the youngest populations . old stars are metal rich or metal poor depending on whether they reside in passive galaxies or in star - forming galaxies ."}
{"article_id":"1207.3928","section_id":"r","document":"figure  [ scatterplot]a shows the index used to determine the gas metallicity , @xmath55}\\lambda6583/{\\rm h}\\alpha$ ] , vs the index used to characterize the age of the stellar populations , sai . it is clear that the two indices are correlated , indicating that the templates with the lowest oxygen content also have the youngest stellar populations . this is explicitly shown in fig . [ scatterplot]b , which presents the same kind of relationship but using quantitative determinations of ages and gas - phase metallicities . ( the two last points deviating from the linear relationship will be ignored since the trend they represent is not present in fig .  [ scatterplot]a , and they have particularly weak [ oiii]@xmath124363 lines , with the uncertainties that this entails  see item # [ line4363 ] in sect . [ list_features ] . ) the correlation is similar to that found by @xcite . the physical origin of the relationship is unclear . it may be a side - effect of the galaxy mass ( a phenomenon often referred to as downsizing ; see , e.g. , * ? ? ? first , the mass - metallicity relationship implies that low - mass galaxies are less metallic ( e.g. , * ? ? ? second , the mass - age relationship ( e.g. , * ? ? ? * ) implies that low - mass galaxies also have younger stellar populations . finally , the bluest ask classes contain more dwarf galaxies @xcite , therefore , they are less metallic and with younger stars , giving as a side - effect the observed correlation . even though this explanation is feasible , the relationship between gas - metallicity and stellar - age shown in figs . [ scatterplot ] is so clean that it looks fundamental rather than derived from the combined effect of two other relationships . this conjecture is supported by the scatter plots in fig . [ mass_age ] , that include the two variables involved in fig . [ scatterplot]b plus the galaxy mass . assigning masses to the ask templates is not without ambiguity , since the spectra of the individual galaxies were normalized before averaging ( sect . [ ask_class ] ) . however , we computed the mean and standard deviation among the masses of all the galaxies in each ask class , and those are the masses assigned to the classes in figs . [ mass_age ] . one can see that the templates follow a mass - metallicity relationship ( fig . [ mass_age]b ) and a mass - age relationship ( fig .  [ mass_age]a ) , but both are less tight than the metallicity - age relationship in fig .  [ scatterplot]b , which seems to be the primary relationship .    } \\lambda6583/{\\rm h}\\alpha$ ] , vs the index used to characterize the age of the stellar populations , sai . they are correlated . ( b ) same representation as ( a ) but using quantitative determinations of gas metallicity and age . the age of the point corresponding to ask  15 ( i.e. , the youngest class with the lowest oxygen content ) is just an upper limit , which we include to show that the relationship continues to the youngest targets . ] b. ( b ) scatter plot of the mass of the galaxies in a class versus the gas - phase metallicity . the error bars have the same meaning as in panel ( a ) . ]    in short , the properties of the gas and the stars are not independent but tightly correlated in real galaxies . galaxy mass does not seem to be the only factor driving such correlation . galaxy spectra seem to follow a 1d sequence , with a secondary branch for agns @xcite . in other words , an independent parameter ( affine parameter ) characterizes most properties of galaxy spectra , from the red passive ones to those actively forming stars . the actual nature of the affine parameter is unknown , but the results in this paper suggest it to be the mean age of the stellar population . the ask templates can be naturally ordered by mean stellar age ( or by sai , in our parlance ) , and the order thus obtained turns out to be extremely similar to the one obtained using minimal spanning trees by @xcite . the latter represents a non - trivial exercise to find the location of the templates in the 1637-dimensional space where the ask classification was carried out ( i.e. , a space where each galaxy is a point , and the 1637 coordinates represent the flux at particular wavelengths ) . they are organized in a 1d sequence with the same order given by the luminosity - weighted mean stellar age . we take the agreement between the two orderings as a strong suggestion that stellar age is the affine parameter . note that the emission line spectrum is prominent in blue galaxies and so it plays a major role in shaping the galaxy spectra . that fact that the spectrum of a galaxy is ( mostly ) dictated by the age of the stellar population implies that the emission lines and the absorption lines are not independent . this is indeed the conclusion reached in the previous paragraph through a totally different argument . we argued in sect . [ ask_class ] that the ask classes are representative of all local galaxies since they condense the properties of some one million galaxies of the local universe . even though we endorse the statement , it must be clarified . ask templates are representative of the most common galaxies , however , some important but uncommon galaxies are not included . in particular , the most massive galaxies that dominate the centers of galaxy clusters ( brightest cluster galaxies and cd galaxies ) are not properly described . these massive red galaxies have old stellar populations so they are classified as ask  0 and ask  2 .however , they represent a small fraction of all the galaxies in these classes , so that their contribution to the average ( template ) spectra of ask  0 and 2 is negligible . the same may happen with other kinds of rare objects like bl lac , objects with extreme star formation rates ( e.g. , * ? ? ? * ) , extremely metal poor galaxies ( e.g. , * ? ? ? * ) , and others . the fact that some objects may escape the simplified schematic in sect . [ decision_tree ] do not invalidate the analysis  it will be useful to indicate that these objects are unusual .    the comparison between figs . [ sfh_ask ] and [ sfh_ask_light ] evidences a fact that is well documented in the literature , but which still results somewhat surprising . most galaxies formed a significant fraction of their stellar mass long ago when the universe was just a few gyr old , even those forming stars today ( e.g. , * ? ? ? ? * ; * ? ? ? this fact is obviously true for ask classes representing passively evolving red galaxies ( see ask  0 in fig .  [ sfh_ask ] ) , but it also holds true for young ask classes  see the important contribution of old stellar populations to the ask  20 sfh in fig . [ sfh_ask ] , even though its luminosity - weighted mean age is just 4.5  myr ( table  [ table_summary ] ) . when the mass contribution is transformed to light contribution ( fig . [ sfh_ask_light ] ) , it becomes clear how newborn stars outshine the older populations , that are heavily underrepresented in the composite galaxy spectrum . if a galaxy happens to undergo a significant starburst , spectrum - wise it looks young . there is a conspicuous difference between the old stellar populations present in passively evolving galaxies and in star - forming galaxies . the metallicity of the old stars is high in passive galaxies and very low in starbursts ( compare the sfhs of ask  0 and ask  20 in the first column of fig . [ sfh_ask ] ) . the dominance of old metal rich stellar populations in red galaxies is well known , so does the fact that the old stars in dwarf galaxies of the local group have extremely low metallicity ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ?","summary":"there is a tight correlation between the age of the stellar population and the metallicity of the gas , which is stronger than the correlations between galaxy mass and stellar age , and galaxy mass and gas metallicity .","abstract":"we describe a simple step - by - step guide to qualitative interpretation of galaxy spectra ( fig .  [ decision ] ) . rather than an alternative to existing automated tools , it is put forward as an instrument for quick - look analysis , and for gaining physical insight when interpreting the outputs provided by automated tools . though the recipe is of general application , it was developed for understanding the nature of the automatic spectroscopic k - means based ( ask ) template spectra . they resulted from the classification of all the galaxy spectra in the sloan digital sky survey data release 7 ( sdss - dr7 ) , thus being a comprehensive representation of the galaxy spectra in the local universe . using the recipe , we give a description of the properties of the gas and the stars that characterize the ask classes , from those corresponding to passively evolving galaxies , to hii galaxies undergoing a galaxy - wide starburst . the qualitative analysis is found to be in excellent agreement with quantitative analyses of the same spectra . we compare the mean ages of the stellar populations with those inferred using the code starlight.we also examine the estimated gas - phase metallicity with the metallicities obtained using electron - temperature based methods . a number of byproducts follow from the analysis . there is a tight correlation between the age of the stellar population and the metallicity of the gas , which is stronger than the correlations between galaxy mass and stellar age , and galaxy mass and gas metallicity . the galaxy spectra are known to follow a 1-dimensional sequence , and we identify the luminosity - weighted mean stellar age as the affine parameter that describes the sequence . all ask classes happen to have a significant fraction of old stars , although spectrum - wise they are outshined by the youngest populations . old stars are metal rich or metal poor depending on whether they reside in passive galaxies or in star - forming galaxies ."}
{"article_id":"1207.3928","section_id":"c","document":"as argued in the introduction , we have sophisticated computer codes for inferring the properties of the stellar populations contributing to the observed galaxy spectra . similarly , tools are available for qualitative diagnostics of the physical properties of the galaxy gas . they have been developed by specialist groups , and then kindly offered to a much broader community . technicalities often complicate the interpretation of the results , therefore , there is a natural tendency to apply these sophisticated tools in black - box fashion , which turns out to be quite unsatisfactory for a physical stand point . one obtains a detailed description of the stars and gas producing the observed galaxy spectra , but overlooks the reasons why the computer code has preferred them rather than other alternatives . we provide a simple step - by - step guide to qualitative interpretation of galaxy spectra . it is not precise , and has not been planed as an alternative to the existing tools . however , it allows a quick - look that yields the main properties of the spectra in a intuitive fashion . this may be of interest in various applications , e.g. , to provide physical insight when using sophisticated tools , or to interpret noisy spectra . moreover , the results of the qualitative analysis agree with those inferred using up - to - date computer codes .    the step - by - step guide is described in sect . [ decision_tree ] , and it has been summarized as a simple questionary in fig .  [ decision ] . emission and absorption lines are analyzed separately , which give rise to a classification with one entry for the gas and another for the stars . ( in real galaxies , however , the properties of gas and stars are tightly correlated ; see sect . [ additional_results ] . ) the analysis has been systematically applied to the set of ask template spectra that resulted from the classification of all galaxy spectra in sdss - dr7 ( see sect . [ ask_class ] ) . their physical properties are summarized in table  [ table_summary ] . with the caveats pointed out in sect . [ additional_results ] , the ask classes represent a comprehensive set of galaxy spectra , that go all the way from passively evolving red galaxies ( e.g. , ask  0 ) to hii galaxies , dominated by massive newborn stars having no absorption lines ( e.g. , ask 15 ) . since it works for this set , the analysis should work for most galaxies . the qualitative analysis is found to be in excellent agreement with quantitative numerical codes . we show how the index for stellar - age ( sai ) follows an almost one - to - one correlation with the mean stellar age assigned by the code starlight ( fig . [ age_vs_age ] ) . similarly , we found how the proxy for gas metallicity is in good agreement with the ( oxygen ) metallicity inferred by applying the direct method to the emission lines of the ask templates ( fig . [ pplike ] ) . the ask templates are freely available ( see footnote #  [ my_foot ] ) and , together with their physical properties listed in table  [ table_summary ] , they can be used as benchmarks so that any other galaxy spectrum can be analyzed by reference to them . thanks are due to c. ramos almeida and e. prez - montero for discussions and help with references . this work has been funded by the spanish micin project _ estallidos _ , aya  2010 - 21887-c04 - 04 . et and rt acknowledge also financial support by the mexican research council ( conacyt ) , through grants cb-2005 - 01 - 49847 , 2007 - 01 - 84746 and 2008 - 103365-f . we are members of the consolider - ingenio 2010 program , grant micinn csd2006 - 00070 : first science with gtc . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss is managed by the astrophysical research consortium for the participating institutions ( for details , see the sdss web site at http://www.sdss.org/ ) . the starlight project is supported by the brazilian agencies cnpq , capes and fapesp and by the france - brazil capes / cofecub program .","summary":"we describe a simple step - by - step guide to qualitative interpretation of galaxy spectra ( fig .  [ decision ] ) . rather than an alternative to existing automated tools , we give a description of the properties of the gas and the stars that characterize the ask classes , from those corresponding to passively evolving galaxies , to hii galaxies undergoing a galaxy - wide starburst . the qualitative analysis is found to be in excellent agreement with quantitative analyses of the same spectra .","abstract":"we describe a simple step - by - step guide to qualitative interpretation of galaxy spectra ( fig .  [ decision ] ) . rather than an alternative to existing automated tools , it is put forward as an instrument for quick - look analysis , and for gaining physical insight when interpreting the outputs provided by automated tools . though the recipe is of general application , it was developed for understanding the nature of the automatic spectroscopic k - means based ( ask ) template spectra . they resulted from the classification of all the galaxy spectra in the sloan digital sky survey data release 7 ( sdss - dr7 ) , thus being a comprehensive representation of the galaxy spectra in the local universe . using the recipe , we give a description of the properties of the gas and the stars that characterize the ask classes , from those corresponding to passively evolving galaxies , to hii galaxies undergoing a galaxy - wide starburst . the qualitative analysis is found to be in excellent agreement with quantitative analyses of the same spectra . we compare the mean ages of the stellar populations with those inferred using the code starlight.we also examine the estimated gas - phase metallicity with the metallicities obtained using electron - temperature based methods . a number of byproducts follow from the analysis . there is a tight correlation between the age of the stellar population and the metallicity of the gas , which is stronger than the correlations between galaxy mass and stellar age , and galaxy mass and gas metallicity . the galaxy spectra are known to follow a 1-dimensional sequence , and we identify the luminosity - weighted mean stellar age as the affine parameter that describes the sequence . all ask classes happen to have a significant fraction of old stars , although spectrum - wise they are outshined by the youngest populations . old stars are metal rich or metal poor depending on whether they reside in passive galaxies or in star - forming galaxies ."}
{"article_id":"nlin0610075","section_id":"i","document":"the theory of integrable partial differential equations has many deep links to the differential geometry of curves and surfaces . for instance the famous sine - gordon ( sg ) and modified korteveg - de vries ( mkdv ) soliton equations along with their common hierarchy of symmetries , conservation laws , and associated recursion operators all can be encoded in geometric flows of non - stretching curves in euclidean plane geometry @xcite by looking at the induced flow equation of the curvature invariant of such curves . a similar encoding is known to hold @xcite in spherical geometry . recent work @xcite has significantly generalized this geometric origin of fundamental soliton equations to encompass vector versions of mkdv and sg equations by considering non - stretching curve flows in riemannian symmetric spaces of the form @xmath5 for @xmath6 . ( here @xmath3 represents the isometry group of @xmath7 , and @xmath8 acts as a gauge group for the frame bundle of @xmath7 , such that @xmath9 is an invariant subgroup under an involutive automorphism of @xmath3 . ) such spaces @xcite are exhausted by the groups @xmath10 and describe curved @xmath3-invariant geometries that are a natural generalization of euclidean spaces . in particular , for @xmath11 , the local isomorphism @xmath12 implies both of these spaces are isometric to the standard 2-sphere geometry , @xmath13 .    as main results in @xcite , it was shown firstly that there is a geometric encoding of @xmath14-invariant bi - hamiltonian operators in the cartan structure equations for torsion and curvature of a moving parallel frame and its associated frame connection @xmath15-form for non - stretching curves in the spaces @xmath2 viewed as klein geometries @xcite . the group @xmath14 here arises as the isotropy subgroup in the gauge group @xmath8 preserving the parallel property of the moving frame . secondly , this bi - hamiltonian structure generates a hierarchy of integrable flows of curves in which the frame components of the principal normal along the curve satisfy @xmath14-invariant vector soliton equations related by a hereditary recursion operator . these normal components in a parallel moving frame have the geometrical meaning of curvature covariants of curves relative to the isotropy group @xmath14 . thirdly , the two isometry groups @xmath10 were shown to give different hierarchies whose @xmath14-invariant vector evolution equations of lowest - order are precisely the two known vector versions of integrable mkdv equations found in the symmetry - integrability classifications presented in @xcite . in addition these hierarchies were shown to also contain @xmath14-invariant vector hyperbolic equations given by two different vector versions of integrable sg equations that are known from a recent generalization of symmetry - integrability classifications to the hyperbolic case @xcite . finally , the geometric curve flows corresponding to these vector sg and mkdv equations in both hierarchies were found to be described by wave maps and mkdv analogs of schrodinger maps into the curved spaces @xmath16 , @xmath17 . the present paper extends the same analysis to give a geometric origin for @xmath4-invariant vector soliton equations and their bi - hamiltonian integrability structure from considering flows of non - stretching curves in the lie groups @xmath18 . a main idea will be to view these lie groups as klein geometries carrying the structure of a riemannian symmetric space @xcite given by @xmath19 for @xmath6 ( with @xmath3 thus representing both the isometry group of @xmath7 as well as the gauge group for the frame bundle of @xmath7 ) . note for @xmath11 both these spaces locally describe a 3-sphere geometry , @xmath20 .    in this setting the parallel moving frame formulation of non - stretching curves developed in @xcite for the riemannian symmetric spaces @xmath16 , @xmath17 can be applied directly to the lie groups @xmath21 , @xmath22 themselves , where the isotropy subgroup @xmath23 of such frames is replaced by @xmath24 and @xmath25 in the two respective cases . as a result , it will be shown that the frame structure equations geometrically encode @xmath4-invariant bi - hamiltonian operators that generate a hierarchy of integrable flows of curves in both spaces @xmath10 . moreover , the frame components of the principal normal along the curves in the two hierarchies will be seen to satisfy @xmath4-invariant vector soliton equations that exhaust the two known vector versions of integrable nls equations and corresponding complex vector versions of integrable mkdv equations , as well as the two known complex vector versions of integrable sg equations , found respectively in the symmetry - integrability classifications stated in @xcite and @xcite . lastly , the geometric curve flows arising from these vector sg , nls , and mkdv equations in both hierarchies will be shown to consist of chiral wave maps , chiral variants of schrodinger maps and their mkdv analogs , into the curved spaces @xmath21 , @xmath22 . taken together , the results here and in @xcite geometrically account for the existence and the bi - hamiltonian integrability structure of all known vector generalizations of nls , mkdv , sg soliton equations . related work @xcite has obtained geometric derivations of the kdv equation and other scalar soliton equations along with their hereditary integrability structure from non - stretching curve flows in planar klein geometries ( which are group - theoretic generalizations of the euclidean plane such that the euclidean group is replaced by a different isometry group acting locally and effectively on @xmath26 ) . previous results on integrable vector nls and mkdv equations geometrically associated to lie groups in the riemannian case appeared in @xcite . earlier work on deriving vector sg equations from riemannian symmetric spaces and lie groups can be found in @xcite . the basic idea of studying curve flows via parallel moving frames appears in @xcite .","summary":"the derivation uses a parallel frame and connection along the curves , involving the klein geometry of the group . this is shown to yield the two known-invariant vector generalizations of both the nonlinear schrdinger ( nls ) equation and the complex modified korteweg - de vries ( mkdv ) equation , as well as-invariant vector generalizations of the sine - gordon ( sg ) equation found in recent symmetry - integrability classifications of hyperbolic vector equations . the curve flows themselves are described in explicit form by chiral wave maps , chiral variants of schrdinger maps , and mkdv analogs .   ","abstract":"a bi - hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non - stretching curves in the lie groups , , generalizing previous work on integrable curve flows in riemannian symmetric spaces . the derivation uses a parallel frame and connection along the curves , involving the klein geometry of the group . this is shown to yield the two known-invariant vector generalizations of both the nonlinear schrdinger ( nls ) equation and the complex modified korteweg - de vries ( mkdv ) equation , as well as-invariant vector generalizations of the sine - gordon ( sg ) equation found in recent symmetry - integrability classifications of hyperbolic vector equations . the curve flows themselves are described in explicit form by chiral wave maps , chiral variants of schrdinger maps , and mkdv analogs .    # 1#2([#1 ] ) and  ( [ # 2 ] ) # 1#2([#1 ] ) to  ( [ # 2 ] ) # 1#2([#1])([#2 ] )    # 1ref .     # 1#2^_#1_^#2 # 1#2_^#1^_#2 # 1#2^#1_#2 # 1_#1 # 1^#1    # 1    # 1    # 1#2e # 1e_x # 1e_t # 1e # 1e_x # 1#2 # 1e # 1#2 # 1#2_x # 1#2_t # 1^g # 1 v#1#2v # 1 # 1#2r # 1#2 # 1 # 1d # 1d^-1 # 1#1^t # 1#1^ # 1r # 1c # 1#2h # 1d ii # 1#2 c#1#2c # 1#2c    bi - hamiltonian , soliton equation , recursion operator , lie group , curve flow , wave map , schrdinger map , mkdv map     37k05,37k10,37k25,35q53,53c35"}
{"article_id":"nlin0610075","section_id":"c","document":"the lie groups @xmath21 and @xmath22 each contain a hierarchy of integrable bi - hamiltonian curve flows described by a chiral schrdinger map equation for the @xmath222 flow , a chiral mkdv map equation for the @xmath227 flow , and a chiral wave map equation for the @xmath248 flow coming from the kernel of the recursion operator of each hierarchy . the principal normal components in a parallel frame along these flows in each lie group satisfy @xmath4-invariant soliton equations respectively given by a vector nls equation , a complex vector mkdv equation , and a hyperbolic vector equation related to a complex vector sg equation . these two lie groups are singled out as exhausting the isometry groups @xmath3 that arise for compact riemannian symmetric spaces of the type @xmath2 as known from cartan s classification @xcite . moreover , since @xmath0 is locally isomorphic to @xmath75 when ( and only when ) @xmath11 , the integrable hierarchies of curve flows in the spaces @xmath317 therefore coincide precisely in the scalar case , with the @xmath270 flows reducing to @xmath318-invariant scalar soliton equations consisting of the nls equation @xmath319 and complex versions of mkdv and sg equations @xmath320 and @xmath321 ( up to rescalings of @xmath322 and @xmath261 ) .    the present results thus account for the existence of the two unitarily - invariant vector generalizations of the nls equation and the complex mkdv and sg equations that are known from symmetry - integrability classifications @xcite . moreover , their bi - hamiltonian integrability structure as summarized by the operators @xmath323 is shown to be geometrically encoded in the frame structure equations for the corresponding curve flows in the two lie groups @xmath18 . this encoding utilizes a parallel moving frame formulation based on earlier work @xcite studying integrable curve flows in the riemannian symmetric spaces @xmath2 . indeed , the bi - hamiltonian operator structure derived in @xcite for curve flows in @xmath2 can be recovered from @xmath324 and @xmath249 if the connection variables @xmath176 and @xmath178 are restricted to be real while the flow - direction variable @xmath302 is restricted to be imaginary , in which case the @xmath248 flow and all even - flows reduce to the hierarchy of flows in @xmath2 . more particularly , the operator @xmath325 acts as a vector nls / mkdv recursion operator which is ( up to a sign ) a complex version of the vector mkdv recursion operator coming from @xmath2 .    finally , there is a broad generalization @xcite of these results yielding hierarchies of group - invariant soliton equations associated to integrable curve flows described by geometric map equations in all semisimple lie groups and riemannian symmetric spaces .","summary":"a bi - hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non - stretching curves in the lie groups , , generalizing previous work on integrable curve flows in riemannian symmetric spaces .","abstract":"a bi - hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non - stretching curves in the lie groups , , generalizing previous work on integrable curve flows in riemannian symmetric spaces . the derivation uses a parallel frame and connection along the curves , involving the klein geometry of the group . this is shown to yield the two known-invariant vector generalizations of both the nonlinear schrdinger ( nls ) equation and the complex modified korteweg - de vries ( mkdv ) equation , as well as-invariant vector generalizations of the sine - gordon ( sg ) equation found in recent symmetry - integrability classifications of hyperbolic vector equations . the curve flows themselves are described in explicit form by chiral wave maps , chiral variants of schrdinger maps , and mkdv analogs .    # 1#2([#1 ] ) and  ( [ # 2 ] ) # 1#2([#1 ] ) to  ( [ # 2 ] ) # 1#2([#1])([#2 ] )    # 1ref .     # 1#2^_#1_^#2 # 1#2_^#1^_#2 # 1#2^#1_#2 # 1_#1 # 1^#1    # 1    # 1    # 1#2e # 1e_x # 1e_t # 1e # 1e_x # 1#2 # 1e # 1#2 # 1#2_x # 1#2_t # 1^g # 1 v#1#2v # 1 # 1#2r # 1#2 # 1 # 1d # 1d^-1 # 1#1^t # 1#1^ # 1r # 1c # 1#2h # 1d ii # 1#2 c#1#2c # 1#2c    bi - hamiltonian , soliton equation , recursion operator , lie group , curve flow , wave map , schrdinger map , mkdv map     37k05,37k10,37k25,35q53,53c35"}
{"article_id":"1305.5028","section_id":"i","document":"the cut locus @xmath2 of a point @xmath3 in a riemannian or finsler manifold is , roughly speaking , the set of all other points for which there are multiple minimizing geodesics connecting them from @xmath3 . of course , in some special cases , it may contain additional points where the minimizing geodesic is unique .    the notion of cut locus was introduced and studied for the first time by h. poincar in 1905 for the riemannian case . later on , in the case of a two dimensional analytical sphere , s. b. myers has proved in 1935 that the cut locus of a point is a finite tree ( @xcite ) in both riemannian and finslerian cases . moreover , in the case of an analytic riemannian manifold , m. buchner has shown the triangulability of @xmath2 ( @xcite ) , and has determined its local structure for the low dimensional case ( @xcite ) in 1977 and 1978 , respectively .    despite of the vast literature existing for the riemannian case , the investigations of the cut locus of a finsler manifolds are scarce ( see @xcite , @xcite , @xcite ) . recently , it was shown that the cut locus of a closed subset @xmath4 of a finsler surface has the structure of a local tree being a union of rectifiable jordan arcs ( @xcite ) . even though the results are similar to the riemannian case , showing that there is nothing special about the metric structure to be riemannian , one should pay always attention to the fact that , unlike its riemannian correspondent , the finslerian distance is not symmetric , so the proofs and arguments are quite different .    returning to the riemannian case , in the case of an arbitrary metric , the cut locus of a point can have a very complicated structure . for example , h. gluck and d. singer have constructed a @xmath5 riemannian manifold that has a point whose cut locus is not triangulable ( @xcite ) . there is a closed relationship between the complexity of the cut locus and the regularity of the metric , regardless it is riemannian or finslerian . indeed , if the metric has a certain degree of regularity , then the cut locus of a point may enjoy a simple structure . however , if the metric loses its regularity , the cut locus might become a very complicated set , for example a fractal . recall that , roughly speaking , a fractal is a set whose hausdorff dimension is not an integer ( see @xcite for alternative definitions and examples ) , fact that make fractals typical examples of what we call complicated sets \" . let us mention that the cut locus of any point on a @xmath5 riemannian manifold can not be a fractal ( see @xcite ) . however , there is a @xmath6 riemannian metric on the two dimensional sphere @xmath7 and a point @xmath8 such that the total length of @xmath2 is infinite ( see @xcite ) . motivated by all these , in the present paper , we are going to study the following two questions :    _ _    1 . there exists riemannian metrics having points whose cut locus is a fractal ? 2 . there are more general metric structures , for example finsler metrics , with the same property ? the answer to both questions above is affirmative . indeed , in the present paper we construct an at least @xmath1 differrentiable , @xmath9 , riemannian metric on a topological sphere @xmath10 , provided the dimension @xmath11 is high enough , namely , we prove    [ theorem a ] for any integer @xmath9 there is an at least @xmath1-differentiable riemannian metric on the @xmath12-dimensional sphere @xmath13 and a point @xmath3 in @xmath13 such that the hausdorff dimension of @xmath2 is a real number between 1 and 2 , where @xmath14 . moreover , we show that there is a finsler metric of randers type on this sphere with the same property . indeed , if we use the same notations as in theorem [ theorem a ] , we have    [ theorem b ] for any integer @xmath9 , under the influence of a suitable magnetic field @xmath15 defined on @xmath13 , there is an at least @xmath1-differentiable non - riemannian finsler metric of randers type on @xmath13 such that the cut locus of the point @xmath3 with respect to this finsler metric coincides with @xmath2 .","summary":"the present paper shows that for a given integer it is possible to construct an at least-differentiable riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal .","abstract":"the present paper shows that for a given integer it is possible to construct an at least-differentiable riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal . moreover , we show that this construction can be extended to the case of finsler sphere as well ."}
{"article_id":"cond-mat9904353","section_id":"i","document":"since the recent experimental observation of bose - einstein condensation in dilute atomic gases @xcite , much interest has been raised about the coherence properties of the condensates . considerable attention has been devoted to the matter of the relative phase between two condensates : how this phase manifests itself in an interference experiment @xcite , how it can be established by measurement @xcite , and how it evolves in presence of atomic interactions @xcite and in presence of particle losses @xcite . as it was proved in recent experiments performed at jila , binary mixtures of condensates represent an ideal system to study the phase coherence properties of bose - einstein condensates @xcite . in these experiments two condensates in two different internal atomic states are created with a well defined relative phase . after a time @xmath0 during which the condensates evolve in the trapping potentials , one mixes coherently the two internal atomic states which makes the two condensates interfere ; from the spatial interference pattern one gets the relative phase of the two condensates . by repeating the whole experimental process , one has access to the distribution of the relative phase after an evolution time @xmath0 , so that one can investigate phase decoherence as function of time . the interaction between the two condensates in the jila experiment gives rise to a rich spatial separation dynamics between the two condensates @xcite , which complicates the theoretical study of the relative phase dynamics . as a consequence previous theoretical treatments of the phase decoherence processes , dealing essentially with steady state condensates , as in @xcite , can not _ a priori _ be applied to the experimental situation .    a treatment of the phase coherence of two interacting , non stationary , condensates can be found in @xcite , with two important differences as compared to the present situation of interest : ( 1 ) in @xcite the condensates are subject to a continuous coherent coupling of amplitude @xmath1 ; results are obtained from a perturbative expansion in powers of @xmath2 and can not be simply extended to the present @xmath3 case . ( 2 ) in @xcite all the coupling constants @xmath4 between the two internal atomic states @xmath5 and @xmath6 are assumed to be equal .    in this paper we propose a formalism to study the relative phase dynamics of interacting and dynamically evolving bose - einstein condensates initially at zero temperature . we present the general method in section [ sec : gen - method ] . it consists in expanding the initial state on fock states , and in evolving each fock state in the hartree - fock approximation . we determine the time dependence of the phase collapse for a binary mixture of condensates , due to ( 1 ) fluctuations in the relative number of particles between the condensates , intrinsic to the initial state with well defined relative phase , and ( 2 ) fluctuations in the total number of particles . in the next two sections we apply this general formalism to two limiting cases that can be treated analytically .    the first case , in section [ sec : breath - together ] , considers a particular solution of the non - linear schrdinger equations for the condensates wavefunctions ; in this solution the two condensates remain spatially superimposed as they breathe in phase , provided that dynamical stability conditions ( that we determine ) are satisfied . we find that phase decoherence can be highly reduced with respect to non mutually interacting condensates when the three coupling constants @xmath7 between atoms in the two internal states @xmath8 are close to each other .    in section [ sec : closeg s ] , we therefore study in a more general case ( not restricted to the breathe - together solution ) the dynamics of the relative phase for a mixture of condensates for close coupling constants . our treatment requires also in this case the absence of demixing instability , a point that we discuss in detail . finally we discuss the case of the jila experiment in section [ sec : jila ] . this case , that corresponds to close coupling constants in a regime of demixing instability , is more difficult to analyze . the predicted phase collapse time depends on the fluctuations of the total number of particles ; it is on the order of 0.4 second for gaussian fluctuations of 8% .","summary":"we investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving bose - einstein condensates in traps . our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles . analytical results are presented for the breathe - together solution , an extension of previously known scaling solution to the case of a binary mixture of condensates . when the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other , a dramatic increase of the phase coherence time is predicted . + pacs numbers : 03.75.fi , 05.30.jp","abstract":"we investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving bose - einstein condensates in traps . our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles . analytical results are presented for the breathe - together solution , an extension of previously known scaling solution to the case of a binary mixture of condensates . when the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other , a dramatic increase of the phase coherence time is predicted . numerical results are presented for the parameters of the recent jila experiments . + pacs numbers : 03.75.fi , 05.30.jp"}
{"article_id":"cond-mat9904353","section_id":"c","document":"in the jila experiment the values of the three coupling constants between the atoms are known with good precision ; they are in the ratio @xcite : @xmath280 no breathe - together solution exists in this case , as @xmath281 lies within @xmath13 and @xmath282 . experimentally half of the particles are in the state @xmath5 so that @xmath283 , and the mean total number of particles is @xmath284 . although the coupling constants are close , the linearized treatment presented in section [ sec : closeg s ] does not apply either , because condition eq.([eq : seconde_cond ] ) is violated . it is actually found experimentally that the two condensates evolve far from the initial state , with formation of a crater in the @xmath5 condensate while the @xmath6 condensate becomes more confined at the center of the trap ; eventually the condensates separate in some random direction @xcite .    to avoid the crater formation and trigger the spatial separation of the two condensates in a reproducible direction a small spatial shift is applied to the trapping potential of one of the two states . the two condensates separate , with a relative motion exhibiting strongly damped oscillations @xcite . the system then reaches a steady state that still exhibits phase coherence , up to times on the order of @xmath285 ms after the phase state preparation @xcite . we have already studied in @xcite the damping of the relative motion between the condensates , by numerical integration of the coupled gross - pitaevskii equations eq.([eq : gpe ] ) . the agreement with the experimental results of @xcite is qualitatively good , although the damping in the theory is weaker and incomplete , small oscillations of the condensate wavefunctions remaining undamped even at long times . we have applied the formalism of section [ sec : gen - method ] by numerically integrating the gross - pitaevskii equations for the parameters of the jila experiment . the coefficients @xmath286 , now complicated functions of time and space , are obtained by evolving wavefunctions with slightly different numbers of atoms in @xmath5 and @xmath6 . in order to facilitate the comparison with the experiments , in which the @xmath287-integrated atomic density @xmath288 in the internal state @xmath5 is measured after the @xmath29 pulse applied at time @xmath0 , we calculated the following contrast : @xmath289 where the interference term eq.([eq : inter_n ] ) is averaged over a gaussian distribution of the total number of particles with a standard deviation @xmath50 . a direct comparison with the experiment would require the inclusion of the 22 ms ballistic expansion , not included in the present numerical calculations . our numerical result for @xmath290 at the center of the trap for the species @xmath5 , @xmath291 , is presented in fig.[fig : jilaa ] , for gaussian fluctuations in the total number of particles @xmath292 corresponding to the jila experiment @xcite , together with the pure gross - pitaevskii prediction @xmath293 obtained by setting all the @xmath64 s to 0 . the gross - pitaevskii prediction oscillates around @xmath294 . on the contrary the result of the more complete calculation including fluctuations in the relative and total number of particles exhibits a damping of the contrast , that we have fitted by convenience with the formula @xmath295 ; we obtain @xmath296 and @xmath297s . note the oscillatory aspect of the curves in fig.[fig : jilaa ] . more understanding of the structure of the condensate wavefunctions given by eq.([eq : gpe ] ) is required as this point : as detailed in @xcite @xmath298 is a sum of a smooth part , performing oscillations with frequencies expected to be close to eigenfrequencies of the steady state condensates @xcite , and of a noisy quasi - stochastic part . the slow oscillatory structure evident on @xmath293 comes from this smooth oscillating part of the wavefunctions . we have also considered the ideal case of a well defined total number of particles . the numerical prediction for the contrast @xmath290 in this case corresponds to a very long lived phase coherence : after a time of 1 second , the contrast is still very close to the pure gross - pitaevskii prediction . as the wavefunctions at long times perform mainly oscillations around the steady state we have also tried a much simpler steady state calculation ( see subsection [ subsec : sta ] ) . during the collapse time the contrast @xmath290 is a gaussian in time eq.([eq : gaus_court ] ) , with an initial value @xmath299 and with a half - width @xmath88 at the relative height @xmath72 . we plot in fig.[fig : jilab ] the variation of @xmath88 as function of the standard deviation @xmath50 . as we find @xmath300 s@xmath301 and @xmath302 s@xmath301 , one has @xmath303 , so that relatively high values of @xmath50 are required to observe a significant effect of the fluctuations of the total number of particles on phase decoherence . for @xmath304 the phase decoherence time is @xmath305 second , close to the result of the time - dependent calculation of fig.[fig : jilaa ] . note that for such a high value of @xmath306 the decay of the phase contrast in eq.([eq : gaus_court ] ) is essentially due to the first exponential factor accounting for the smearing of the phase by fluctuations of the total number of particles , the spreading of the phase for a fixed number of particles being very small ( @xmath307 ) . we now briefly consider the issue of losses of particles . an intrinsic source of losses in the jila experiment are the inelastic collisions between @xmath5 atoms and @xmath6 atoms , resulting in the simultaneous loss of two particles . we estimate the mean number @xmath308 of lost particles from the rate constant @xmath309 for binary inelastic collisions between the states @xmath310 and @xmath311 @xcite and from a numerical calculation of the overlap integral @xmath312 . for the jila parameters we find @xmath313 at time @xmath305 second . one could then naively expect the effect of losses on phase coherence to be comparable with the effect of fluctuations of @xmath12 .    to test this naive expectation we use the following simple model , inspired by the two - mode model developed in @xcite , and focusing on the effect of the losses on the drift velocity @xmath74 of the relative phase of the two condensates given in eq.([eq : vdrift ] ) . imagine that the system has initially @xmath51 condensate atoms and that @xmath314 binary inelastic collisions have taken place at times @xmath315 between time @xmath316 and time @xmath213 . the shift of the relative phase during @xmath213 is then given by : @xmath317 as we do in @xcite we assume a constant mean number of collisions @xmath131 per unit of time and we average the phase factor @xmath318 multiplying the interference term @xmath81 over the probability distribution of the times @xmath319 and of the number of loss events @xmath314 , @xmath320 to obtain : @xmath321\\right\\ } \\\\ & \\simeq &   \\exp \\left[-{2\\over 3}\\langle k\\rangle\\chi_s^2\\right ] \\ \\ \\ \\ \\mbox{for } \\ |\\chi_s| \\ll 1 \\label{eq : perte_court}\\end{aligned}\\ ] ] where @xmath322 is the mean number of lost particles during @xmath213 . at time @xmath323 second the corresponding modulus of the averaged phase factor is on the order of @xmath324 $ ] , very close to one : particle losses have a negligible effect on the phase coherence at the considered time @xmath88 , even if @xmath308 and @xmath50 have the same order of magnitude . actually an inspection of the @xmath214 dependent factor in eq.([eq : gaus_court ] ) and of eq.([eq : perte_court ] ) reveals that these equations have the same structure ; replacing in eq.([eq : gaus_court ] ) the variance @xmath325 of the total number of particles by the variance @xmath326 of the number of loss events ( @xmath327 as @xmath314 obeys a poisson law ) one recovers eq.([eq : perte_court ] ) up to a numerical factor inside the exponential . for equally large values of @xmath50 and @xmath328 the effect of losses on phase coherence is less important than that of fluctuations of @xmath12 because @xmath329 . we have also investigated another source of losses , the collisions of condensate atoms with the background gas of the cell . assuming a lifetime of the particles in the cell of 250 seconds as in @xcite we find as well that this loss mechanism has a negligible effect on the phase coherence for a time @xmath305 second .","summary":"numerical results are presented for the parameters of the recent jila experiments .","abstract":"we investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving bose - einstein condensates in traps . our treatment naturally includes the additional decoherence effect due to fluctuations in the total number of particles . analytical results are presented for the breathe - together solution , an extension of previously known scaling solution to the case of a binary mixture of condensates . when the three coupling constants describing the elastic interactions among the atoms in the two states are close to each other , a dramatic increase of the phase coherence time is predicted . numerical results are presented for the parameters of the recent jila experiments . + pacs numbers : 03.75.fi , 05.30.jp"}
{"article_id":"0805.1706","section_id":"i","document":"our goal in this paper is to present a practical extension of the evans function shooting method to computing the stability of _ multi - dimensional _ travelling wave solutions to parabolic nonlinear systems . the problem is thus to solve the linear spectral equations for small perturbations of the travelling wave . hence we need to determine the values of the spectral parameter for which solutions _ match _ longitudinal far - field zero boundary conditions and , in more than one spatial dimension , the transverse boundary conditions . these are the _ eigenvalues_. there are two main approaches to solving such eigenvalue problems . * _ projection : _ project the spectral equations onto a finite dimensional basis , which by construction satisfies the boundary conditions . then solve the resulting matrix eigenvalue problem . * _ shooting : _ start with a specific value of the spectral parameter and the correct boundary conditions at one end . shoot / integrate towards the far end . examine how close this solution is to satisfying the boundary conditions at the far end . re - adjust the spectral parameter accordingly . repeat the shooting procedure until the solution _ matches _ the far boundary conditions . the projection method can be applied to travelling waves of any dimension . its main disadvantage is that to increase accuracy or include adaptation is costly and complicated as we have to re - project onto the finer or adapted basis . further , from the set of eigenvalues that are produced by the resulting large algebraic eigenvalue problem , care must be taken to distinguish two subsets as follows . in the limit of vanishing discretization scale , one subset corresponds to isolated eigenvalues of finite multiplicity , while the other subset converges to the absolute or essential spectrum , depending on the boundary conditions ( see sandstede and scheel  @xcite ) . the latter subset can be detected by changing the truncated domain size and observing which eigenvalues drift in the complex spectral parameter plane . in contrast , for the shooting method , it is much easier to fine - tune accuracy and adaptivity , and zeros of the matching condition are isolated eigenvalues of finite multiplicity ( we do not have to worry about spurious eigenvalues as described above ) . its disadvantage though is that by its very description it is a one - dimensional method .    when implementing the shooting method , a wronskian - like determinant measuring the discrepancy in the boundary _ matching condition _ in the spectral problem is typically used to locate eigenvalues in the complex spectral parameter plane . this is known as the evans function or miss - distance function  see alexander , gardner and jones  @xcite or greenberg and marletta  @xcite . it is a function of the spectral parameter whose zeros correspond to eigenvalues , i.e.  a _ match_. in practice , we match at a point roughly centred at the front . further for parabolic systems it is typically analytic in the right - half complex parameter plane and the argument principle allows us to globally determine the existence of zeros and therefore unstable eigenvalues by integrating the evans function along suitably chosen contours .    the one - dimensional label of the evans function has started to be overturned and in particular deng and nii  @xcite , gesztesy , latushkin and makarov  @xcite , and gesztesy , latushkin and zumbrun  @xcite have extended the evans function theoretically to multi - dimensions . importantly from a computational perspective , humpherys and zumbrun  @xcite outlined a computational method crucial to its numerical evaluation in the multi - dimensional scenario . their method overcame a restriction on the order of the system that could be investigated numerically using shooting , in particular using exterior product spaces . it is based on continuous orhogonalization and is related to integrating along the underlying grassmannian manifold whilst evolving the coordinate representation for the grassmannian . more recently ledoux , malham and thmmler  @xcite provided an alternative ( though related ) approach to that of humpherys and zumbrun . this approach is based on chosen coordinatizations of the grassmannian manifold and integrating the resulting riccati systems .    the main idea of this paper is to determine the stability of multi - dimensional travelling waves by essentially combining the two main approaches in the natural way : we project the spectral problem transversely and shoot longitudinally . the basic details are as follows . 1 .   transverse to the direction of propagation of the travelling wave we project onto a finite fourier basis . this generates a large , linear , one - dimensional system of equations for the longitudinal fourier coefficients . we construct the stable and unstable solution subspaces associated with the longitudinal far - field zero boundary conditions by integrating with given grassmannian coordinatizations ( chosen differently for each subspace ) . the evans function is the determinant of the matrix of vectors spanning both subspaces and measures their linear dependence . we evaluate it at an intermediate longitudinal point . we compare the construction of the stable and unstable solution subspaces by integrating the spectral problem using the continuous orthogonalization method of humpherys and zumbrun . we also compare these with standard projection methods that project the spectral problem onto a finite multi - dimensional basis satisfying the boundary conditions and solve the resulting large algebraic eigenvalue problem .    the parabolic nonlinear systems that we will consider here are of the form @xmath0 on the cylindrical domain @xmath1 . here @xmath2 is a vector of component fields and @xmath3 represents a nonlinear coupling reaction term . the diagonal matrix @xmath4 encodes the positive constant diffusion coefficients . we suppose we have dirichlet boundary conditions in the infinite longitudinal direction @xmath5 and periodic boundary conditions in the transverse direction @xmath6 . we assume also , that we are in a reference frame travelling in the longitudinal direction with velocity @xmath7 . though we assume only two spatial dimensions our subsequent analysis in the rest of this paper is straightforwardly extended to higher dimensional domains which are transversely periodic . we also suppose we have a travelling wave solution @xmath8 of velocity @xmath7 satisfying the boundary conditions , whose stability is the object of our scrutiny .    as a specific application we consider a cubic autocatalysis reaction - diffusion system that admits wrinkled cellular travelling fronts . they appear as solutions bifurcating from planar travelling wave solutions as the autocatalytic diffusion parameter is increased . the initiation of this first bifurcation is known as the cellular instability and has been studied in some detail in the reaction kinetics and combustion literature ; see for example horvth , petrov , scott and showalter  @xcite or terman  @xcite . however our main interest here is the stability of these cellular fronts themselves . it has been shown by direct numerical simulation of the reaction - diffusion system that the cellular fronts become unstable as the autocatalyst diffusion parameter is increased further  see for example horvth , petrov , scott and showalter  @xcite and malevanets , careta and kapral  @xcite . we apply our multi - dimensional evans function shooting method to this problem and we reveal the explicit form of the spectrum associated with such fronts . we compare our shooting methods with standard direct projection methods obtaining high accuracy concurrency . we confirm the literature on these instabilities and establish the shooting method as an effective and accurate alternative to standard direct projection methods . our paper is structured as follows . in section  [ sec : evans ] we review grassmannian and stiefel manifolds . we show how to construct the stable and unstable solution subspaces of the spectral problem using a given grassmannian coordinatization and define the evans function using coordinatizations for each subspace . we show how to project the spectral problem onto a finite dimensional transverse basis in detail in section  [ sec : proj ] . a large portion of numerical effort is devoted to accurately constructing the multi - dimensional fronts whose stability we wish to study , and in section  [ sec : comp ] we detail the technique we used to do this . in section  [ sec : auto ] we outline our main application  the cubic autocatalysis problem  and review the known travelling wave solutions and stability properties . we then bring to bear our full range of numerical techniques to the cubic autocatalysis problem in section  [ sec : numerics ] , comparing their accuracy . in section  [ sec : conclu ] we provide some concluding remarks and outline future directions of investigation .","summary":"we present a numerical method for computing the pure - point spectrum associated with the linear stability of multi - dimensional travelling fronts to parabolic nonlinear systems . our method is based on the evans function shooting approach . transverse to the direction of propagation we project the spectral equations onto a finite fourier basis . this generates a large , linear , one - dimensional system of equations for the longitudinal fourier coefficients . we construct the stable and unstable solution subspaces associated with the longitudinal far - field zero boundary conditions , retaining only the information required for matching , by integrating the riccati equations associated with the underlying grassmannian manifolds . we compare our shooting approach with the continuous orthogonalization method of humpherys and zumbrun . we then also compare these with standard projection methods that directly project the spectral problem onto a finite multi - dimensional basis satisfying the boundary conditions .    multi - dimensional stability , parabolic systems , evans function    65l15 , 65l10","abstract":"we present a numerical method for computing the pure - point spectrum associated with the linear stability of multi - dimensional travelling fronts to parabolic nonlinear systems . our method is based on the evans function shooting approach . transverse to the direction of propagation we project the spectral equations onto a finite fourier basis . this generates a large , linear , one - dimensional system of equations for the longitudinal fourier coefficients . we construct the stable and unstable solution subspaces associated with the longitudinal far - field zero boundary conditions , retaining only the information required for matching , by integrating the riccati equations associated with the underlying grassmannian manifolds . the evans function is then the matching condition measuring the linear dependence of the stable and unstable subspaces and thus determines eigenvalues . as a model application , we study the stability of two - dimensional wrinkled front solutions to a cubic autocatalysis model system . we compare our shooting approach with the continuous orthogonalization method of humpherys and zumbrun . we then also compare these with standard projection methods that directly project the spectral problem onto a finite multi - dimensional basis satisfying the boundary conditions .    multi - dimensional stability , parabolic systems , evans function    65l15 , 65l10"}
{"article_id":"1211.6557","section_id":"i","document":"one of the best known discrete integrable system is the billiard inside ellipsoids . all the segments ( or their continuations ) of a billiard trajectory inside an ellipsoid of @xmath0 are tangent to @xmath1 quadrics of the pencil of confocal quadrics determined by the ellipsoid  @xcite . this situation is fairly exceptional . quadrics are the only smooth hypersurfaces of @xmath0 , @xmath2 , that have caustics  @xcite . caustic _ is a smooth hypersurface with the property that a billiard trajectory , once tangent to it , stays tangent after every reflection . caustics are a geometric manifestation of the integrability of billiards inside ellipsoids . periodic trajectories are the most distinctive trajectories , so their study is the first task . there exist two remarkable results about periodic billiard trajectories inside ellipsoids : the _ generalized poncelet theorem _ and the _ generalized cayley conditions_.    a classical geometric theorem of poncelet  @xcite implies that if a billiard trajectory inside an ellipse is periodic , then all the trajectories sharing its caustic are also periodic . its generalization to the spatial case was proved by darboux  @xcite . the extension of this result to arbitrary dimensions can be found in  @xcite . the generalized poncelet theorem can be stated as follows . if a billiard trajectory inside an ellipsoid is closed after @xmath3 bounces and has length @xmath4 , then all trajectories sharing the same caustics are also closed after @xmath3 bounces and have length @xmath4 . thus , a natural question arises . what caustics do give rise to periodic trajectories ? the planar case was solved by cayley  @xcite in the xix century . dragovi and radnovi  @xcite found some _ generalized cayley conditions _ for billiards inside ellipsoids fifteen years ago . they have also stated similar conditions in other billiard frameworks ; see  @xcite .    for simplicity , let us focus on the spatial case . let @xmath5 be the triaxial ellipsoid with ellipsoidal parameters @xmath6 . any billiard trajectory inside @xmath7 has as caustics two elements of the family of confocal quadrics @xmath8 we restrict our attention to nonsingular trajectories . that is , trajectories with two different caustics which are ellipsoids : @xmath9 , hyperboloids of one sheet : @xmath10 , or hyperboloids of two sheets : @xmath11 . the singular values @xmath12 are discarded . there exist some restrictions on the caustics @xmath13 and @xmath14 . it is known that eh1 , h1h1 , eh2 , and h1h2 are the only feasible caustic types ; see  @xcite . the meaning of these notations is evident . the generalized cayley condition in this context can be expressed as follows . the billiard trajectories inside the triaxial ellipsoid @xmath7 sharing the caustics @xmath13 and @xmath14 are periodic with _ elliptic period _ @xmath15 if and only if @xmath16 where @xmath17 . we claim that most results related to generalized cayley conditions become simpler when expressed in terms of the inverse quantities @xmath18 , @xmath19 , @xmath20 , @xmath21 , and @xmath22 . proposition  [ pro : c_n_n ] is a paradigmatic example . the elliptic period is defined in section  [ sec : preliminaries ] . roughly speaking , the difference between the period @xmath3 and the elliptic period @xmath23 of the periodic billiard trajectories sharing two given caustics is that _ all _ those trajectories close in cartesian ( respectively , elliptic ) coordinates after exactly @xmath3 ( respectively , @xmath23 ) bounces . we will see that either @xmath24 or @xmath25 . the previous matrix formulation is very nice from a theoretical point of view , but it has strong limitations from a computational point of view . we will see in section  [ sec : practical ] that it can be written as a system of two homogeneous symmetric polynomial equations with rational coefficients of degrees @xmath26 and @xmath27 in the variables @xmath18 , @xmath19 , @xmath20 , @xmath21 , and @xmath22 . thus , both degrees grow _ quadratically _ with the elliptic period @xmath23 , which turns this approach into a tough challenge . in particular , to our knowledge , the caustic parameters @xmath28 and @xmath29 have never been explicitly expressed in terms of the ellipsoidal parameters @xmath30 , @xmath31 , and @xmath32 for any @xmath15 . we will rewrite this matrix formulation as a computationally more appealing one which gives rise to ( non - symmetric ) homogeneous polynomial equations whose degrees are smaller than the elliptic period @xmath23 . we will find the following remarkable algebraic relations between caustic and ellipsoidal parameters using the new formulation . the billiard trajectories inside the ellipsoid @xmath7 sharing the caustics @xmath13 and @xmath14 are periodic with :    * elliptic period @xmath33 if the roots of @xmath34 are the caustic parameters ; * elliptic period @xmath35 if there exists @xmath36 such that the roots of @xmath37 are the ellipsoidal parameters ; and * elliptic period @xmath38 if the roots of @xmath39 are double ones . let us compare both formulations in the third case . on the one hand , the two homogeneous symmetric polynomial equations obtained from the matrix formulation have degrees 23 and 24 in the variables @xmath18 , @xmath19 , @xmath20 , @xmath21 , and @xmath22 . on the other hand , @xmath39 is a polynomial of degree four in a single variable . clearly , the polynomial formulation leads to a much simpler problem . nevertheless , it should be stressed that the matrix formulation determines _ all _ periodic billiard trajectories with elliptic period @xmath38 . on the contrary , we find just a _ subset _ of such trajectories using the polynomial @xmath39 . another natural question about periodic billiard trajectories is the following one . which are the triaxial ellipsoids of @xmath40 that display periodic billiard trajectories with a fixed caustic type and a fixed ( elliptic ) period ? a numerical approach to that question was considered in  @xcite , where the authors computed several bifurcations in the space of ellipsoidal parameters . we will find the algebraic relations that define the bifurcations associated to small elliptic periods . for instance , we will see that there exist periodic billiard trajectories with elliptic period @xmath41 and caustic type eh1 if and only if @xmath42 .    for brevity , we will not depict billiard trajectories inside triaxial ellipsoids of @xmath40 . the reader interested in 3d graphical visualizations is referred to  @xcite , where several periodic billiard trajectories with small periods are displayed from different perspectives . we complete this introduction with a note on the organization of the article . in section  [ sec : preliminaries ] we review briefly some well - known results about billiards inside ellipsoids , recalling the matrix formulation of the generalized cayley conditions obtained by dragovi and radnovi . we also introduce the concept of elliptic period . the practical limitations of the matrix formulation are exposed in section  [ sec : practical ] . next , we present the polynomial formulation in section  [ sec : polynomial ] . in section  [ sec : minimal ] we carry out a detailed analysis for minimal elliptic periods , whereas the study of more general elliptic periods is postponed to section  [ sec : general ] . the previous results are adapted to billiards inside ellipses of @xmath43 and inside triaxial ellipsoids of @xmath40 in sections  [ sec : planar ] and  [ sec : spatial ] , respectively .","summary":"all the segments ( or their continuations ) of a billiard trajectory inside an ellipsoid of are tangent to quadrics of the pencil of confocal quadrics determined by the ellipsoid . the quadrics associated to periodic billiard trajectories verify certain algebraic conditions . we find several remarkable algebraic relations between caustic parameters and ellipsoidal parameters that give rise to nonsingular periodic trajectories .    billiard , integrable system , periodic trajectory , cayley condition 37j20 , 37j35 , 37j45 , 70h06 , 14h99","abstract":"all the segments ( or their continuations ) of a billiard trajectory inside an ellipsoid of are tangent to quadrics of the pencil of confocal quadrics determined by the ellipsoid . the quadrics associated to periodic billiard trajectories verify certain algebraic conditions . cayley found them in the planar case . dragovi and radnovi generalized them to any dimension . we rewrite the original matrix formulation of these _ generalized cayley conditions _ as a simpler polynomial one . we find several remarkable algebraic relations between caustic parameters and ellipsoidal parameters that give rise to nonsingular periodic trajectories .    billiard , integrable system , periodic trajectory , cayley condition 37j20 , 37j35 , 37j45 , 70h06 , 14h99"}
{"article_id":"1211.6557","section_id":"i","document":"we adapt the previous setting of billiards inside ellipsoids of @xmath0 to the planar case @xmath141 . to follow traditional conventions in the literature , we write the ellipse as @xmath506 any nonsingular billiard trajectory inside @xmath7 is tangent to one confocal caustic @xmath507 where @xmath508 , with @xmath509 and @xmath510 . the names of the connected components of @xmath511 come from the fact that @xmath50 is a confocal ellipse for @xmath512 and a confocal hyperbola for @xmath513 . the singular cases @xmath514 and @xmath515 correspond to the @xmath516-axis and @xmath517-axis , respectively . we say that the _ caustic type _ of a billiard trajectory is e or h , when its caustic is an ellipse or a hyperbola ( compare with definition  [ defi : caustictype ] ) . we also distinguish between e - caustics and h - caustics . we recall some concepts related to periodic trajectories of billiards inside ellipses . these results can be found , for instance , in  @xcite . to begin with , we introduce the function @xmath518 given by the quotient of elliptic integrals @xmath519 it is called the _ rotation number _ and characterizes the caustic parameters that give rise to periodic trajectories . to be precise , the billiard trajectories with caustic @xmath50 are periodic if and only if @xmath520 for some integers @xmath521 , which are the _ winding numbers_. on the one hand , @xmath3 is the period , on the other hand , @xmath522 is twice the number of turns around the ellipse @xmath50 for e - caustics , and the number of crossings of the @xmath517-axis for h - caustics . thus , @xmath522 is always even . besides , all periodic trajectories with h - caustics have even period . ( compare with theorem  [ thm : windingnumbers ] . ) the winding numbers @xmath523 , rotation number @xmath524 , signature @xmath525 , caustic type ( e or h ) , and caustic parameter @xmath526 of all nonsingular periodic billiard trajectories inside the ellipse  ( [ eq : ellipse ] ) with elliptic period @xmath527 are listed in table  [ tab : planar ] . the ellipses where such trajectories take place are also listed . .[tab : planar]algebraic formulas for the caustic parameter corresponding to nonsingular periodic billiard trajectories with elliptic period @xmath527 in the planar case . [ cols=\"^,^,^,^,^,^,^,^\",options=\"header \" , ]     if @xmath30 , @xmath31 , and @xmath32 are the ellipsoidal parameters , and @xmath28 and @xmath29 are the caustic parameters , we set @xmath528 , where @xmath529 . we also set @xmath120 . let @xmath530 , with @xmath531 and @xmath532 , be the decomposition defined in corollary  [ cor : jk ] when @xmath533 . from proposition [ pro : c_n_n ] we know that @xmath534    in the rest of the proof , we study each caustic type separately .    _ caustic type eh1 . _ in this case @xmath535 , so @xmath536 thus the formula for @xmath28 follows from relation @xmath537 , whereas the formula for @xmath29 follows from relation @xmath538 . next , we look for ellipsoidal parameters such that the caustic parameters computed using these two formulas are placed in the right intervals : @xmath539 and @xmath540 .    to begin with , we note that @xmath541 , since @xmath542 . besides , @xmath543 on the other hand , if @xmath539 , then @xmath544 so @xmath545 . finally , @xmath546 therefore , @xmath539 and @xmath540 if and only if @xmath42 . _ caustic type h1h1 . _ if @xmath533 , then the caustic type  ( [ eq : caustictype ] ) is @xmath77 or , equivalently , h1h1 . hence , the study for the caustic type h1h1 was already carried out in theorem  [ thm : main ] . suffice it to note that the polynomial @xmath547 has two real simple roots if and only if its discriminant @xmath548 is positive . this discriminant is a second - degree polynomial in @xmath32 whose roots are @xmath549 we note that @xmath550 . thus , using that @xmath6 , we get @xmath551 .    _ caustic type eh2 . _ in this case @xmath552 , so @xmath553 using relations @xmath554 , with @xmath555 , we know that @xmath556 hence , @xmath21 and @xmath22 are the roots of the polynomial @xmath557 thus , using the change of variables @xmath558 , we get that @xmath28 and @xmath29 are the roots of @xmath559 we look for ellipsoidal parameters such that @xmath560 has a root in @xmath561 and a root in @xmath562 . the root in @xmath561 always exists , since @xmath563 and @xmath564 . besides , @xmath565 and @xmath566 , so @xmath560 has a root in @xmath562 if and only if @xmath567 or , equivalently , if and only if @xmath568 and @xmath569 . we have used that @xmath6 in the last equivalence .    _ caustic type h1h2 . _ in this case @xmath570 , so @xmath571 thus the formula for @xmath29 follows from relation @xmath537 , whereas the formula for @xmath28 follows from relation @xmath538 . next , we look for conditions on the ellipsoidal parameters such that the caustic parameters computed from the previous formulas are placed in the right intervals : @xmath572 and @xmath573 .    to begin with , we note that @xmath574 , because @xmath575 . besides , @xmath576 on the other hand , using that @xmath6 , we get that @xmath577 thus , @xmath539 and @xmath573 if and only if @xmath578 and @xmath579 . let us look for the winding numbers of the trajectories described in the previous proposition . the winding numbers @xmath3 , @xmath522 , and @xmath580 describe how the periodic billiard trajectories fold in @xmath40 . the following results can be found in  ( * ? ? ? * table 1 ) . first , @xmath3 is the period . second , @xmath522 is the number of @xmath581-crossings and @xmath580 is twice the number of turns around the @xmath303-axis for eh1-caustics ; @xmath522 is twice the number of turns around the @xmath516-axis and @xmath580 is the number of @xmath582-crossings for eh2-caustics ; @xmath522 is the number of tangential touches with each hyperboloid of one sheet caustic and @xmath580 is twice the number of turns around the @xmath303-axis for h1h1-caustics ; @xmath522 is the number of @xmath583-crossings and @xmath580 is the number of @xmath582-crossings for h1h2-caustics . besides , all periodic trajectories with h1h1-caustics or h1h2-caustics have even period . several periodic billiard trajectories with elliptic period @xmath41 were depicted in  ( * ? ? ? * table xv and table xvii ) . we conclude by direct inspection of those pictures that the nonsingular periodic billiard trajectories inside a triaxial ellipsoid with elliptic period @xmath41 have winding numbers @xmath584 this agrees with the formulas  ( [ eq : windingnumbers_c_n_n ] ) given in theorem  [ thm : main ] . we emphasize that those formulas were not rigorously proved , because their `` proof '' was based on conjecture  [ con : windingnumbers ] . next , we establish the algebraic formulas for the caustic parameters of other nonsingular periodic billiard trajectories . we begin with a technical lemma about four - degree polynomials . [ lem : technical ] let @xmath585 for some @xmath586 . let @xmath587 , @xmath588 , and @xmath589 be the three roots of @xmath590 . then @xmath591    if we set @xmath592 and @xmath593 , then @xmath594 on the one hand , if @xmath595 , then @xmath596 for all @xmath597 , which implies that @xmath598 . on the other hand , if @xmath599 , then @xmath600 for all @xmath597 , which implies that @xmath601 . finally , if @xmath602 , then @xmath603 for all @xmath604 , which implies that @xmath605 . we can now answer some questions about the nonsingular periodic billiard trajectories found in the second item of theorem  [ thm : samples ] , although the study is restricted to the spatial case . [ pro : c43_h1h1 ] there exist periodic billiard trajectories inside the triaxial ellipsoid  ( [ eq : ellipsoid_3d ] ) with elliptic period @xmath606 , signature @xmath607 , and caustic type h1h1 if and only if @xmath608 besides , the caustic parameters @xmath28 and @xmath29 of such periodic billiard trajectories are the roots of the quadratic polynomial @xmath609 , where @xmath610 and @xmath611 is the only root of the cubic polynomial @xmath612 in the interval @xmath613 .    if @xmath607 , the decompositions presented in definition  [ defi : decompositions ] are @xmath614 , @xmath615 , @xmath616 , and @xmath617 . thus , @xmath618 holds if and only if there exists some @xmath619 such that the following two equivalent properties hold :    a.   [ item : decompositions - first ] @xmath620 . b.   [ item : decompositions - second ] @xmath621 , for @xmath622 . if the caustic type is h1h1 , then @xmath623 , so @xmath624 let @xmath625 for @xmath626 . we set @xmath627 . then @xmath628 and @xmath629 is a root of @xmath630 . hence , @xmath611 is a root of the cubic polynomial @xmath631 we note that @xmath632 , @xmath633 , @xmath634 , and @xmath635 . this shows that @xmath199 has just one root in the interval @xmath613 .    from property  ( [ item : decompositions - second ] ) above , we deduce that the sums @xmath636 verify relations  ( [ eq : sl ] ) . besides , @xmath21 and @xmath22 are the roots of @xmath637 , so that @xmath28 and @xmath29 are the roots of the quadratic polynomial @xmath609 . we look for ellipsoidal parameters such that the previous periodic trajectories exist . from property  ( [ item : decompositions - first ] ) above , we deduce that such ellipsoidal parameters exist if and only the graph @xmath638 intersects the horizontal line @xmath639 at two different points @xmath640 or , equivalently , if and only if @xmath641 , where @xmath642 are the three ordered roots of the derivative of the polynomial @xmath643 . but @xmath644 according to lemma  [ lem : technical ] . as we have explained before , the period and winding numbers of any nonsingular periodic billiard trajectory can be determined by direct inspection of its corresponding figure . a periodic billiard trajectory with elliptic period @xmath35 and caustic type h1h1 whose caustic parameters verify the relations given in proposition  [ pro : c43_h1h1 ] is displayed in  ( * ? ? ? * figure 13 ) . that trajectory has ( cartesian ) period @xmath645 and winding numbers @xmath646 hence , @xmath647 , so the elliptic winding numbers are @xmath648 , @xmath649 , and @xmath650 . this result reinforces conjecture  [ con : tau ] . besides , these nonsingular four - periodic billiard trajectories with caustic type h1h1 are quite interesting , because they display the minimal period among all nonsingular periodic billiard trajectories ; see  ( * ? ? ? * theorem 1 ) . we end the study at this point . we just mention that there exist similar results when the signature or the caustic type do not coincide with the ones given in proposition  [ pro : c43_h1h1 ] . analogously , the case @xmath651 can be dealt with using the same techniques , although the final formulas become more complicated . for instance , it can be easily checked that the caustic parameters @xmath28 and @xmath29 of the billiard trajectories with elliptic period @xmath651 and signature @xmath652 verify the homogeneous symmetric polynomial equations @xmath653 where @xmath654 for @xmath655 . each of the other signatures @xmath656 gives rise to similar homogeneous although not symmetric polynomial equations of degrees three and four in the variables @xmath18 , @xmath19 , @xmath20 , @xmath21 and @xmath22 . we left the details to the reader . finally , we remember that the original matrix formulation of the generalized cayley condition @xmath657 gives rise to two homogeneous symmetric polynomial equations of degrees 23 and 24 in those five variables , as explained in section  [ sec : practical ] . this confirms , once again , that the polynomial formulation offers great computational advantages over the matrix formulation .","summary":"we rewrite the original matrix formulation of these _ generalized cayley conditions _ as a simpler polynomial one .","abstract":"all the segments ( or their continuations ) of a billiard trajectory inside an ellipsoid of are tangent to quadrics of the pencil of confocal quadrics determined by the ellipsoid . the quadrics associated to periodic billiard trajectories verify certain algebraic conditions . cayley found them in the planar case . dragovi and radnovi generalized them to any dimension . we rewrite the original matrix formulation of these _ generalized cayley conditions _ as a simpler polynomial one . we find several remarkable algebraic relations between caustic parameters and ellipsoidal parameters that give rise to nonsingular periodic trajectories .    billiard , integrable system , periodic trajectory , cayley condition 37j20 , 37j35 , 37j45 , 70h06 , 14h99"}
{"article_id":"gr-qc9707050","section_id":"i","document":"an important task in numerical relativity is locating black holes in numerically generated spacetimes , both for technical purposes and for extracting physical information . a black hole is a region of spacetime out of which no null geodesics escape to infinity . the boundary of the black hole , the event horizon , is formed by those outward - going , future - directed null geodesics which neither fall into the singularity nor escape to null infinity . the event horizon contains important geometric information about the spacetime . it is a global construction and can in principle only be determined when the entire spacetime is known . in practice , one can obtain a good approximation to the event horizon within a finite spacetime region , once the black hole has settled down to a stationary state . by definition , the event horizon repels future - directed null geodesics , but attracts past ones . one can then evolve past - directed null geodesics back through the spacetime , and find the event horizon as the surface to which they are attracted @xcite . locating black holes is crucial in numerical relativity also for a technical reason : spacetime slicings which avoid black holes rapidly become singular . instead one would like to excise a spacetime region just inside the event horizon from the numerical domain during the numerical evolution , using the fact that it can not influence events outside the black hole . during the time evolution , however , one does not yet know where the event horizon is . instead one needs to use the poor man s event horizon , the apparent horizon . an apparent horizon ( ah ) is defined within a single time slice , or spacelike hypersurface @xmath1 , namely as a smooth embedded 2-surface whose outgoing normal null geodesics have zero expansion . there may be one such surface enclosing another one , in which case the outermost one is the apparent horizon . if one combines the apparent horizon on each time slice into a 3-dimensional surface , this world tube will depend on the slicing , and can be discontinuous . nevertheless one can show that if an apparent horizon exists on a given time slice , it must be inside a black hole @xcite . the converse is not true : there are slicings of black hole spacetimes without any apparent horizons @xcite . for numerical purposes one simply hopes that this case is unusual and that the apparent horizon gives a reasonable indication of the event horizon . a wide variety of numerical algorithms for finding ahs have been explored or suggested . for the purpose of excising the black hole region , one needs to find the apparent horizon frequently , perhaps at each time step . when two black holes collide , a new ah enveloping the two separate ones appears suddenly . therefore the main requirements are speed and finding the ah from scratch , without a good initial guess . precision is less important for black hole excision , although a safe error estimate is , so that one can be sure not to excise too much and inject unphysical boundary conditions .    in spherical symmetry , the ah problem reduces to an algebraic equation . in axisymmetry , it reduces to an ordinary differential equation with periodic boundary conditions . in this paper we shall be concerned exclusively with the 3-dimensional problem without any symmetries , either continuous or discrete , where one deals with a highly nonlinear elliptic problem on a closed 2-surface . in practice this will always be the 2-sphere , or several disconnected 2-spheres @xcite , which can be treated separately . all 3d ah finder algorithms proposed so far can be classified according to a few key choices , which can be made independently one from another . how are candidate ahs represented ? one can parameterize an embedded 2-surface either by introducing coordinates on it , or as a level set of a function on the 3-dimensional slice in which it is embedded . how is the curvature of the candidate ah calculated ? one can discretize the necessary spatial derivatives by finite differencing , finite elements , or pseudo - spectral methods . a third fundamental choice is between solving the elliptic problem directly , or converting it into a parabolic problem , in which the solution of the elliptic problem is approached during an evolution in an unphysical time parameter . the distinction between these last two approaches is not sharp in practice . on the one hand one always solves a nonlinear elliptic problem by iteration . on the other , numerical implementation of any parabolic approach requires an implicit `` time '' step for stability , thus posing a new elliptic problem that becomes equivalent to the original one in the limit of an infinitely large time step . we now discuss previous ah finders in terms of these choices . nakamura , koshima and oohara @xcite represent the ah in spherical coordinates as @xmath2 . we note that this requires the surface to be a 2-sphere , and star - shaped ( convex ) around the point @xmath3 . the shape function @xmath4 is expanded in spherical harmonics . this spectral decomposition is used to calculate the derivatives of @xmath5 in formulating the elliptic problem . the orthonormality and completeness of the spherical harmonics is used to subtract the linear elliptic operator @xmath6 from the nonlinear elliptic problem and invert it . this gives rise to an iteration prescription . we shall see that this iteration can also be described as the discretization in unphysical time of a parabolic problem . it remains unclear from @xcite by what method the spectral decomposition back and forth is carried out for cauchy data which are only known in numerical form and on a grid . the nakamura _ _ algorithm has been independently coded and tested , and extended in various directions by kemball and bishop @xcite . they report exponential convergence , good robustness , and high precision unless the point @xmath3 is close to the ah . tod @xcite has proposed a geometrically defined flow under which a trial 2-surface evolves to the ah . for time - symmetric slices , the ah problem reduces to that of finding a minimal surface , and tod s prescription to mean curvature flow . this is well - known to converge to minimal surfaces . on non time - symmetric slices , only lower order terms are added to the problem , so that one may hope that tod s flow also converges for such data in practice . tod s algorithm is parabolic , without specifying how the surface is represented or differenced . tod s algorithm has been implemented numerically by bernstein @xcite using finite differencing in coordinates introduced on the surface . he discusses stable extrinsic algorithms for parabolic problems , and reports good results in axisymmetry using one of them , but technical problems to do with finite differencing on the sphere in the general case . pasch @xcite has implemented mean curvature flow representing the test surface as a level set . this allows for a change of topology during the evolution . he has successfully tested the algorithm using brill - lindquist data for 1 , 2 or 3 black holes , using a fast implicit time evolution package , and finite differencing on a cartesian grid in the embedding space . thornburg @xcite attacks the elliptic problem directly using finite differencing on a square @xmath7 grid , and newton s method to solve the discretized equations . he calculates the jacobian required for newton s method by first linearizing the differential equations , then finite differencing the result . this is more efficient than numerical differentiation . he finds high precision results , but a nonlinear instability in high - frequency modes . huq @xcite has extended newton s method to data without symmetries in cartesian - type coordinates . the ncsa / washu algorithm @xcite uses the parameterization @xmath2 , and a spectral decomposition to parameterize @xmath5 and calculate its derivatives . the discretized elliptic problem is solved by applying a standard minimization algorithm to the sum of @xmath8 over all surface points . the spectral basis is not required to be orthonormal for this purpose . _ @xcite have implemented the ncsa / washu algorithm independently , with the difference that they use the true spherical harmonics as a basis . both algorithms locate points on the 2-surface on a square @xmath7 grid , interpolating data from the 3-dimensional cartesian grid used in the 3 + 1 time evolution .    in this paper we review different previous algorithms in one common , fully covariant notation . this analysis suggests to us a new algorithm which combines essential ideas of the algorithms of tod and nakamura _ et al . _ from our analysis we expect this algorithm to be as fast as that of nakamura _ et al . _ ( and therefore much faster than existing implementations of tod s algorithm ) , while being as robust in practice as that of tod . we describe the details of a numerical implementation of this algorithm , and some initial tests . the results are encouraging . the paper is organized as follows . in section ii we set up the mathematical formalism of the problem . we begin by deriving the differential equation that determines an apparent horizon in ii.a . in ii.b we discuss different ways of parameterizing apparent horizon candidates , that is , smooth embedded 2-surfaces , and in ii.c we provide tools for spectral methods on the 2-sphere . in section iii we review various algorithms for finding ahs , namely the pseudo - spectral algorithm of nakamura _ et al . _ @xcite , jacobi s method , and the generalized mean curvature flow suggested by tod @xcite . we then build on this review by presenting a family of algorithm which contains the previous algorithms as limiting cases , and suggesting that in the middle of the family there are algorithms that perform better than the limiting members . in section iv we describe a numerical implementation of our proposed algorithm . in section v we test its performance in finding apparent horizons in brill - lindquist and kerr data given in cartesian coordinates on a grid .","summary":"we describe a family of algorithms which includes the pseudo - spectral apparent horizon finder of nakamura et al . and the curvature flow method proposed by tod as special cases .","abstract":"we review the problem of finding an apparent horizon in cauchy data in three space dimensions without symmetries . we describe a family of algorithms which includes the pseudo - spectral apparent horizon finder of nakamura et al . and the curvature flow method proposed by tod as special cases . we suggest that other algorithms in the family may combine the speed of the former with the robustness of the latter . a numerical implementation for cauchy data given on a grid in cartesian coordinates is described , and tested on brill - lindquist and kerr initial data . the new algorithm appears faster and more robust than previous ones .   "}
{"article_id":"gr-qc9707050","section_id":"c","document":"numerical general relativity requires a fast and robust algorithm for finding apparent horizons in cauchy data without symmetries in three dimensions given on a grid . in this paper we have described a new apparent horizon finder algorithm which appears to be as fast but more robust than its best predecessor . we began from a general classification of possible approaches to the problem . any approach which poses the problem as a nonlinear elliptic equation on a topological two - sphere and then attacks that equation directly will fail unless provided with a very good initial guess , because the problem is nonlocal in nature . while we have disregarded such approaches here , they will be ideal as a second stage whenever the apparent horizon needs to be determined to high precision . we concluded that for robustness the best algorithm is probably the ( generalized ) mean curvature flow suggested by tod @xcite , where an arbitrary initial surface evolves in an unphysical `` time '' towards the apparent horizon , turning the problem from an elliptic into a parabolic one . the algorithm is guaranteed to converge at least for time - symmetric ( @xmath147 ) data , and we have argued that it must be at least very robust also for @xmath325 data . unfortunately , numerical implementations of this algorithm face a numerical stability problem common to all parabolic equations , which make them slow , and increasingly so with increasing resolution , in practice . this stability or speed problem is not present in the algorithm of nakamura _ et al . _ ( nko ) @xcite . it is motivated by a standard way of solving nonlinear elliptic problems numerically , namely subtracting a simple linear elliptic operator from the nonlinear one , inverting it by pseudo - spectral methods and iterating . here we have thrown more light on how nko works , by making explicit the background metric it introduces , and by characterizing the iteration procedure as a specific finite differencing , in unphysical time , of a parabolic problem . this parabolic problem itself is the singular limit of a certain family of flows which are governed by a mixture of the physical geometry of the cauchy data and an unphysical background geometry . tod s flow is a different limiting case of that family , one in which no background metric appears . once we have recognized the existence of a continuum of possible algorithms between tod and nko , it is plausible that an algorithm somewhere in the middle of the continuum may be better than the extremes . by trial and error , we have determined the optimal member of the family of algorithms . this intermediate algorithm evolves the high - frequency components ( the fine details ) of the trial ah essentially like the nko algorithm , but it evolves the low frequency components ( the rough shape ) by a variant of generalized mean curvature flow . we therefore call it `` fast flow '' . we have given details of a numerical implementation of the pseudo - spectral methods which are needed for implementing both the original nko and our new algorithm . such details have not been published before . it should be stressed that the formal analysis of the algorithm in sect . iii is independent from its implementation in sect . iv , and there may be different and more efficient implementations .      by construction , the new algorithm is as fast as that of nko : the iteration steps are very similar , and there is the same small number of them . nko , however , updates @xmath100 ( the overall radius of the trial ah ) by a special procedure . according to how this is done @xcite , the additional overhead may be large . more importantly , the separate update of @xmath100 has the potential to reduce the robustness of nko : eqn . ( [ a00 ] ) may have several solutions , in which case all should be investigated , or none , in which case minima should be investigated instead @xcite . this requires some decision - taking , which will be hard to automate , or instead an infinitely branching search . we have also argued that zeros of eqn . ( [ a00 ] ) are hard to find . either nko or fast flow should be far more tolerant of initial guesses than the elliptic methods . the method of choice for robustness and elegance is clearly tod s mean curvature flow . the only question here is speed . we have argued that as a parabolic method this would be slow in the possible implementations known to us , but a quantitative comparison with the implementation of pasch @xcite would be interesting . the only existing algorithm directly accessible to the author is that of the ncsa / washu group @xcite . direct comparisons are planned in future realistic applications . the new algorithm seems to be more robust , though : it made the transition from two ahs to a single one in the family of brill - lindquist data summarized in table 1 without external input . this ability will be crucial for applying ah boundary conditions in the merger of two black holes when the computer code is on its own during a very large run . the ncsa / washu code has not been tested on a similar sequence of analytic initial data , but in some situations involving evolved black holes it presently requires some care in finding the correct horizon@xcite . m. huq , a finite difference method for locating apparent horizons in 3d cartesian coordinates , talk at the numerical relativity workshop at pennsylvania state university , 7 - 8 october 1993 ( unpublished ) . llddd surface parameters & grid size & @xmath327 & @xmath328 & @xmath329 + @xmath330 & 16 & 0.053 & 0.159 & 0.284 + & 32 & 0.016 & 0.037 & 0.069 + & 64 & 0.011 & 0.026 & 0.040 + @xmath330 , @xmath331 & 32 & 0.039 & 0.069 & 0.178 + & 64 & 0.047 & 0.047 & 0.053 + @xmath330 , @xmath332 & 32 & 0.052 & 0.087 & 0.274 + & 64 & 0.050 & 0.056 & 0.075 +    drrr offset & iterations & @xmath333 & @xmath334 + 0.0 & 10 & @xmath335 & @xmath336 + 0.1 & 10 & @xmath335 & @xmath336 + 0.2 & 11 & @xmath337 & @xmath338 + 0.3 & 12 & @xmath339 & @xmath337 + 0.4 & 10 & @xmath340 & @xmath341 +    drr separation & inner @xmath342 & outer @xmath342 + 0.0 & only one surface & @xmath343 + 0.4 & @xmath344 & @xmath345 + 0.8 & @xmath346 & @xmath345 + 1.2 & @xmath347 & @xmath348 + 1.4 & @xmath349 & @xmath350 + 1.6 & @xmath351 & no convergence ( @xmath352 ) + 1.8 & @xmath353 & no convergence ( @xmath354 ) + 2.0 & @xmath355 & ( not attempted ) +","summary":"we review the problem of finding an apparent horizon in cauchy data in three space dimensions without symmetries . the new algorithm appears faster and more robust than previous ones .   ","abstract":"we review the problem of finding an apparent horizon in cauchy data in three space dimensions without symmetries . we describe a family of algorithms which includes the pseudo - spectral apparent horizon finder of nakamura et al . and the curvature flow method proposed by tod as special cases . we suggest that other algorithms in the family may combine the speed of the former with the robustness of the latter . a numerical implementation for cauchy data given on a grid in cartesian coordinates is described , and tested on brill - lindquist and kerr initial data . the new algorithm appears faster and more robust than previous ones .   "}
{"article_id":"cs0512055","section_id":"i","document":"given a logic program @xmath0 , can we determine that @xmath0 terminates for certain queries ? this is the well - known termination problem in logic programming . it is undecidable in general . two different ways have been explored in the literature to attack this problem . the first way is to perform termination analysis at compile time , thus referred to as a _ static _ approach @xcite , while the other is to characterize and test termination of a logic program by applying a loop checking technique , thus referred to as a _ dynamic _ approach @xcite . loop checking is a technique for detecting and cutting infinite derivations at run time @xcite . static termination analysis has been extensively studied in the literature @xcite ( see @xcite for a survey ) . however , although a number of loop checking mechanisms have been proposed @xcite , it is only in @xcite that the idea of using a loop checking technique for termination analysis is formally presented . the intuition behind a dynamic approach is as follows . given a complete loop checking mechanism ( that cuts any infinite derivations ) and a set of queries , we run the program for each query while performing loop checking . if the query evaluation terminates without cutting any derivations , the program terminates for any query , otherwise it is potentially non - terminating for some queries .    in this paper , we are concerned with dynamic termination approaches . the core of such an approach is a characterization of infinite sldnf - derivations , as any loop checking mechanism relies on it . in @xcite , the first such characterization is established for general logic programs . however , this characterization applies only to concrete queries and can not handle moded queries . a moded query contains ( abstract ) atoms like @xmath1 where @xmath2 is a term ( i.e. , a constant , variable or function ) and @xmath3 is an input mode . an _ input mode _ stands for an arbitrary ground ( i.e.  variable - free ) term . moded queries are commonly used in termination analysis of logic programs , where to prove that a logic program terminates for a moded query @xmath1 is to prove that the program terminates for any ( concrete ) query @xmath4 where @xmath5 is a ground term . consider the following logic program :    @xmath6 = @xmath7 @xmath8 = @xmath9 ` @xmath10 + @xmath11 . ` @xmath12    for any concrete query @xmath13 , evaluating @xmath13 over @xmath14 will terminate . however , we can not evaluate a moded query @xmath15 while applying a loop checking mechanism to infer that @xmath14 terminates for @xmath15 .    in this paper , we present a dynamic approach to characterizing and testing termination of logic programs for moded queries . for a logic program @xmath0 and a moded query @xmath16 , the first issue we address is how to formulate an sldnf - derivation for @xmath16 . we will introduce a framework called a _ moded - query forest _ , which consists of all ( generalized ) sldnf - trees rooted at a ground instance of @xmath16 . an sldnf - derivation for @xmath16 is defined over the moded - query forest such that @xmath0 terminates for @xmath16 if and only if the moded - query forest contains no infinite sldnf - derivations . a moded - query forest may have an infinite number of sldnf - trees , so it is infeasible to test termination of a logic program by traversing the moded - query forest . we will introduce a compact approximation for a moded - query forest , called a _ moded generalized sldnf - tree_. the key idea is to treat an input mode as a special variable like a skolem constant . as a result , top - down derivations for a moded query can be constructed in the same way as the ones for a concrete query . a characterization of termination of a logic program for moded queries is then established in terms of some novel properties of a moded generalized sldnf - tree .    the paper is organized as follows . section [ pre ] reviews some basic concepts including generalized sldnf - trees . section [ sec2 ] establishes a characterization for logic programs with moded queries . section [ sec4 ] develops an algorithm for testing termination of logic programs for moded queries . section [ related - work ] describes some closely related work , and section [ conclusion ] concludes .","summary":", we present a novel dynamic approach to termination analysis for general logic programs with moded queries . we address several interesting questions , including how to formulate an sldnf - derivation for a moded query , how to characterize an infinite sldnf - derivation with a moded query , and how to apply a loop checking mechanism to cut infinite sldnf - derivations for the purpose of termination analysis . * keywords : * logic programming , moded queries , termination analysis , loop checking .","abstract":"the termination problem of a logic program can be addressed in either a static or a dynamic way . a static approach performs termination analysis at compile time , while a dynamic approach characterizes and tests termination of a logic program by applying a loop checking technique . in this paper , we present a novel dynamic approach to termination analysis for general logic programs with moded queries . we address several interesting questions , including how to formulate an sldnf - derivation for a moded query , how to characterize an infinite sldnf - derivation with a moded query , and how to apply a loop checking mechanism to cut infinite sldnf - derivations for the purpose of termination analysis . the proposed approach is very powerful and useful . it can be used ( 1 ) to test if a logic program terminates for a given concrete or moded query , ( 2 ) to test if a logic program terminates for all concrete or moded queries , and ( 3 ) to find all ( most general ) concrete / moded queries that are most likely terminating ( or non - terminating ) .    * keywords : * logic programming , moded queries , termination analysis , loop checking ."}
{"article_id":"cs0512055","section_id":"l","document":"termination of a logic program can be addressed in either a static or a dynamic way . static termination analysis builds from the source code of a logic program some well - founded termination conditions / constraints in terms of level mappings , interargument size relations and/or instantiation dependencies @xcite . in contrast , a dynamic termination approach characterizes and tests termination of a logic program by applying a loop checking technique . it directly makes use of some essential dynamic characteristics of infinite derivations , such as repetition of variant subgoals and recursive increase in term size , which are hard to capture in a static way ( for example , it is difficult to apply static termination analysis to prove that @xmath323 terminates for a moded query @xmath15 and that @xmath274 terminates for @xmath324 but does not terminate for @xmath293 ) . this paper develops a new dynamic approach with a characterization and a testing algorithm for moded queries . to the best of our knowledge , no similar work has been reported in the literature . the core of a dynamic termination approach is a characterization of infinite derivations . in @xcite , the first such characterization is established for general logic programs . however , it applies only to concrete queries and can not handle moded queries . a dynamic termination approach uses a loop checking mechanism ( a loop check ) to implement a characterization of infinite derivations . representative loop checks include va - check @xcite , os - check @xcite , and vaf - checks @xcite . all apply to positive logic programs . in particular , va - check applies to function - free logic programs , where an infinite derivation is characterized by a sequence of selected _ variant subgoals_. os - check identifies an infinite derivation with a sequence of selected subgoals with the same predicate symbol _ whose sizes do not decrease_. vaf - checks take a sequence of selected _ expanded variant subgoals _ as major characteristics of an infinite derivation . expanded variant subgoals are variant subgoals except that some terms may grow bigger . in this paper , a new loop check mechanism , lp - check ( with heuristic 1 ) , is introduced in which an infinite derivation is identified with a sequence of _ loop goals_. lp - check is more effective than va - check , os - check and vaf - checks , none of which can handle the logic program @xmath274 . most importantly , enhancing lp - check with condition ( c ) leads to the first loop check for moded queries .","summary":"the termination problem of a logic program can be addressed in either a static or a dynamic way . a static approach performs termination analysis at compile time , while a dynamic approach characterizes and tests termination of a logic program by applying a loop checking technique . in this paper","abstract":"the termination problem of a logic program can be addressed in either a static or a dynamic way . a static approach performs termination analysis at compile time , while a dynamic approach characterizes and tests termination of a logic program by applying a loop checking technique . in this paper , we present a novel dynamic approach to termination analysis for general logic programs with moded queries . we address several interesting questions , including how to formulate an sldnf - derivation for a moded query , how to characterize an infinite sldnf - derivation with a moded query , and how to apply a loop checking mechanism to cut infinite sldnf - derivations for the purpose of termination analysis . the proposed approach is very powerful and useful . it can be used ( 1 ) to test if a logic program terminates for a given concrete or moded query , ( 2 ) to test if a logic program terminates for all concrete or moded queries , and ( 3 ) to find all ( most general ) concrete / moded queries that are most likely terminating ( or non - terminating ) .    * keywords : * logic programming , moded queries , termination analysis , loop checking ."}
{"article_id":"cs0512055","section_id":"c","document":"we have presented a dynamic approach to characterizing and testing termination of a general logic program . the approach is very powerful and useful . it can be used ( 1 ) to test if a logic program terminates for a given concrete or moded query , ( 2 ) to test if a logic program terminates for all concrete or moded queries , and ( 3 ) to find all ( most general ) concrete / moded queries that are most likely terminating ( or non - terminating ) . for any concrete / moded query , the algorithm yields an answer _ terminating _ , _ most likely terminating _ , _ non - terminating _ or _ most likely non - terminating_. for a great majority of representative logic programs we collected in the literature , an answer _ most likely terminating _ ( resp . _ most likely non - terminating _ ) implies terminating ( resp . non - terminating ) . the algorithm can be incorporated into prolog as a debugging tool , which would provide the user with valuable debugging information for him / her to understand the causes of non - termination . a conspicuous advantage of a dynamic termination approach over static termination analysis is that it tests termination on the fly ( i.e. by evaluating some queries ) , thus capturing essential characteristics of infinite derivations . this makes a dynamic approach able to guess if a partial derivation is most likely to extend towards an infinite one . although static termination analysis has been extensively studied over the last few decades , exploration of dynamic termination approaches is just at the beginning . we expect to see more prosperous research in this direction . many problems are open , including extensions to typed queries @xcite and to logic programs with tabling @xcite . our ongoing work aims to develop a dynamic termination analyser and make a comparative study with existing static termination analysers . it is also promising future work to combine static and dynamic approaches for a hybrid termination analyser . a. brodsky and y. sagiv , inference of inequality constraints in logic programs , in : _ proc . of the tenth acm sigact - sigmod - sigart symposium on principles of database systems _ , denver , usa , acm press , 1991 , pp . 227 - 240 . m. bruynooghe , m. codish , j. gallagher , s. genaim , and w. vanhoof , termination analysis of logic programs through combination of type - based norms , _ acm transactions on programming languages and systems _ , to appear . d. chan , constructive negation based on the completed database , in : r. a. kowalski and k. a. bowen ( eds . ) , _ proc . of the fifth international conference and symposium on logic programming _ , seattle , usa , mit press , 1988 , pp . 111 - 125 . s. decorte , d. de schreye and m. fabris , automatic inference of norms : a missing link in automatic termination analysis , in : d. miller ( ed . ) , _ proc . of the 1993 international symposium on logic programming _ , vancouver , canada , mit press , 1993 , pp . 420 - 436 . n. lindenstrauss and y. sagiv , automatic termination analysis of logic programs , in : l. naish ( ed . ) _ proc . of the fourteenth international conference on logic programming _ , leuven , belgium . mit press , 1997 , pp . 63 - 77 . f. mesnard and u. neumerkel , applying static analysis techniques for inferring termination conditions of logic programs , _ the 8th international symposium on static analysis _ , paris , france , 2001 , pp . 93 - 110 . l. plmer , termination proofs for logic programs based on predicate inequalities , in : d. h. d. warren and p. szeredi ( eds . ) , _ proceedings of the seventh international conference on logic programming _ , mit press , cambridge , ma , 1990 , pp . 634 - 648 .","summary":"the proposed approach is very powerful and useful . it can be used ( 1 ) to test if a logic program terminates for a given concrete or moded query , ( 2 ) to test if a logic program terminates for all concrete or moded queries , and ( 3 ) to find all ( most general ) concrete / moded queries that are most likely terminating ( or non - terminating ) .   ","abstract":"the termination problem of a logic program can be addressed in either a static or a dynamic way . a static approach performs termination analysis at compile time , while a dynamic approach characterizes and tests termination of a logic program by applying a loop checking technique . in this paper , we present a novel dynamic approach to termination analysis for general logic programs with moded queries . we address several interesting questions , including how to formulate an sldnf - derivation for a moded query , how to characterize an infinite sldnf - derivation with a moded query , and how to apply a loop checking mechanism to cut infinite sldnf - derivations for the purpose of termination analysis . the proposed approach is very powerful and useful . it can be used ( 1 ) to test if a logic program terminates for a given concrete or moded query , ( 2 ) to test if a logic program terminates for all concrete or moded queries , and ( 3 ) to find all ( most general ) concrete / moded queries that are most likely terminating ( or non - terminating ) .    * keywords : * logic programming , moded queries , termination analysis , loop checking ."}
{"article_id":"1205.2592","section_id":"i","document":"a pure spin current consists of flows of opposite spins in opposite directions with the same amplitude . it bears neither net charge current nor net spin polarization . spin currents are a key element in spintronics.@xcite    detection of spin currents is important for characterization and applications in future spintronics technologies.@xcite while a polarized spin current may be detected by the conventional faraday / kerr rotation spectroscopy@xcite or through ferromagnetic filters,@xcite a pure spin current , without a direct electromagnetic induction , is much less traceable . still , pure spin currents have been detected in a few pioneering experiments in which they were converted into signals detectable by conventional techniques . for example , the spin - polarized electrons or excitons accumulated at the sample edges where a spin current is terminated may be detected by the faraday / kerr rotation,@xcite polarized light emission,@xcite and polarization - selective absorption.@xcite or the inverse spin hall effect@xcite can be used to covert a spin current into charge / voltage signals for electric measurement.@xcite all such measurements , however , disturb the spin currents to some extent and are indirect . we are motivated to find a non - destructive way to directly measure a pure spin current.@xcite    a basic symmetry principle states that whenever there is a current breaking the fundamental symmetries of a system , an interaction may arise between the current and another current of the same symmetry - breaking type so that the fundamental symmetries are retained.@xcite a classic example is the ampre effect and the rsted effect where a charge current is coupled to another charge current or a magnet . a straightforward analogue suggests that a pure spin current may be coupled to another spin current . such an idea stimulated the proposal of direct measurement of a pure spin current in a direct - gap semiconductor by a polarized light beam.@xcite a polarized light beam can be regarded as such a `` photon spin current''@xcite by mapping the photon polarization into a spin-1/2 in the jones vector representation@xcite @xmath0 where the right / left circular polarization @xmath1 corresponds to the spin up / down state @xmath2 quantized along the light propagation direction . the effective interaction between a pure spin current and a polarized light causes a phase delay which depends on the light polarization and wavevector . the observable result is a circular birefringence effect which is similar to the faraday rotation but involves no net magnetization nor time - reversal symmetry breaking . since faraday s disocvery in 1845,@xcite the circular birefringence effect of spin currents is the first example of faraday rotation without time - reversal symmetry breaking . we dub this effect as _ spin current faraday effect_.    at this point , we should mention a recent remarkable experiment realizing the direct in - situ detection of a spin current through the doppler effect of a spin - wave.@xcite in fact , the observed doppler effect and our predicted optical birefringence effect are fundamentally related to each other . the former is the frequency shift of the spin wave , while the latter is the phase shift of the light accumulated by a frequency shift over a coupling time . the frequency shift is measured in the near - field as in the experiment , while the phase shift should be measured in the far field by light polarization detection . fundamentally , both are due to the effective coupling between a pure spin current and another `` probe spin current '' , either a spin wave or a polarized light , mediated by virtual excitations in the systems .    the effective light - spin current interaction is induced in a semiconductor by virtual excitations of electron - hole pairs . the specific form of the phenomenological coupling depends on the microscopic mechanisms.@xcite since the light polarization essentially couples only to the orbital motion of electrons , the spin - orbit interaction is needed to establish the effective coupling . as there is inherent spin - orbit coupling in the valence bands due to the relativity effect , the rashba or dresselhaus effect due to the spatial inversion asymmetries@xcite is not a necessity , thus the system can bear the inversion symmetry . the optical birefringence effect of spin currents@xcite is usually very weak , because a tiny light wave vector @xmath3 is involved in the coupling to the velocity @xmath4 of the pure spin currents . however , if the velocity of spin currents couples to another optical field , @xmath5 the coupling will be much enhanced . this means we can use the second optical field to drive the spins , which may result in the nonlinear optics of the pure spin current . in fact , such an analogy stimulated the prediction of the second - order nonlinear optical effects of pure spin currents,@xcite which was soon verified by experiments.@xcite    in refs .   and we have sketched the main ideas based on symmetry arguments and given the key expressions in a special model neglecting the energy band anisotropy . in this paper , we will investigate in a more comprehensive way the linear and second - order nonlinear optical effects of pure spin currents , including a systematic symmetry analysis of all relevant physical quantities , and a detailed derivation for the effective hamiltonian as well as the second - order nonlinear optical susceptibility . the microscopic derivation confirms the qualitative results obtained by the symmetry analysis . in particular , both the symmetry analysis and the microscopic calculation lead to the conclusion that the linear birefringence effect ( similar to the voigt effect in magneto - optics ) always vanishes and only the circular birefringence effect exists , and the energy band anisotropy induces only a relatively small quantitative modification of the results . the absence of the voigt effect is fundamentally related to the lack of the @xmath6 state in the physical spin of photons [ not the pseudo - spin in eq . ( [ jonesvector ] ) ] . the microscopic mechanism of both linear and second - order nonlinear effects can be understood in a unified physical picture .    in this paper , we assume that the host semiconductor system has the inversion symmetry . we note that in compound semiconductors such as gaas the inversion symmetry is broken , which , though a small effect , is critical to some schemes of spin current generation.@xcite in our present scheme , however , the small inversion asymmetry in compound semiconductors is not important . for conditions used in our microscopic calculation , the spin splitting resulting from the dresselhaus effect due to the bulk inversion asymmetry ( the dresselhaus splitting is @xmath7  mev in gaas with doping density @xmath8  @xmath9 ) , much less than the detuning of the light from the interband transitions  @xcite that mediate the effective interaction , so we can neglect the bulk inversion asymmetry in the measurement process even though it could be of vital importance in generating the spin current . also , in this paper , we consider only bulk materials , so the structure inversion asymmetry plays no role , though it is the basis of the rashba effect . without considering the dresselhaus and rashba effects due to inversion asymmetries , we avoid the subtlety in the definition of a spin current.@xcite the effect of inversion asymmetries on the interaction between the polarized light beams and a spin current , of course , is worth further study , but we prefer leaving this question open in this paper .    the paper is organized as follows . [ sec_symmetry ] presents a systematic symmetry analysis for the coupling system to give a qualitative understanding of the linear and circular birefringence effects and the second - order nonlinear optical effect of pure spin currents . [ sec_calculation ] gives the theoretical model and microscopic derivations for both the linear and the second - order nonlinear optical effects , and also explains the physical pictures for the microscopic mechanism of optical effects of spin currents . [ sec_discussion ] presents the numerical results and discussions of the experiment scheme . [ sec_conclusion ] concludes this paper .","summary":"this interaction is rooted in the intrinsic spin - orbit coupling in valence bands and does not rely on the rashba or dresselhaus effect . the light - spin current interaction results in an optical birefringence effect of the spin current . the symmetry analysis indicates that in a semiconductor with inversion symmetry , the linear birefringence effect vanishes and only the circular birefringence effect exists . the circular birefringence effect is similar to the faraday rotation in magneto - optics but involves no net magnetization nor breaking the time - reversal symmetry . these findings form a basis of measuring a pure spin current where and when it flows with the standard optical spectroscopy , which may provide a toolbox to explore a wealth of physics connecting the spintronics and photonics .","abstract":"a spin current has novel linear and second - order nonlinear optical effects due to its symmetry properties . with the symmetry analysis and the eight - band microscopic calculation we have systematically investigated the interaction between a spin current and a polarized light beam ( or the `` photon spin current '' ) in direct - gap semiconductors . this interaction is rooted in the intrinsic spin - orbit coupling in valence bands and does not rely on the rashba or dresselhaus effect . the light - spin current interaction results in an optical birefringence effect of the spin current . the symmetry analysis indicates that in a semiconductor with inversion symmetry , the linear birefringence effect vanishes and only the circular birefringence effect exists . the circular birefringence effect is similar to the faraday rotation in magneto - optics but involves no net magnetization nor breaking the time - reversal symmetry . moreover , a spin current can induce the second - order nonlinear optical processes due to the inversion - symmetry breaking . these findings form a basis of measuring a pure spin current where and when it flows with the standard optical spectroscopy , which may provide a toolbox to explore a wealth of physics connecting the spintronics and photonics ."}
{"article_id":"0802.2338","section_id":"i","document":"given @xmath1 a smooth algebraic surface of degree @xmath2 , one can obtain information on @xmath3 by considering it as a branched cover of @xmath0 . it is well  known that for @xmath4 a generic projection , the branch locus is a plane curve @xmath5 which is , in general , singular , and its singularities are nodes and cusps . let @xmath6 be a generic affine portion of @xmath7 . it was proven in @xcite that if the braid monodromy factorizations ( bmf ) of the branch loci of two surfaces @xmath8 and @xmath9 are hurwitz - equivalent , then the surfaces are diffeomorphic . moreover , if the factorizations are not hurwitz - equivalent , then @xmath8 and @xmath9 are not projectively deformation equivalent . therefore , the bmt invariant ( the equivalence class of a bmf ) is really in the  middle \" , i.e. , between the diffeomorphism equivalence and the projectively deformation equivalence . we need to find an algorithm that decides whether two bmfs are equivalent . in general , it was shown in @xcite that there is no finite algorithm which determines whether two positive factorizations are hurwitz- equivalent . however , @xcite did not examine the particular case of the bmfs . therefore , we have to extract the information contained in the braid monodromy factorization via the introduction of more manageable ( but less powerful ) invariants . two discrete invariants are induced from the bmf of the branch curve  @xmath10 : the fundamental group of the complement of the branch curve ( see @xcite,@xcite,@xcite,@xcite ) and its subquotient : the fundamental group of the galois cover of @xmath3 ( see @xcite,@xcite,@xcite ) . we say that two surfaces are fundamental group equivalent ( fge ) if their fundamental groups of the complement of the branch curve are isomorphic .    in this article we present two surfaces , which are embeddings of a k3 surface with respect to two different linear systems ; therefore they are diffeomorphic . due to the nature of the particular linear systems , these embedded surfaces are not projectively deformation equivalent . it is also known that any two k3 surfaces can be abstractly deformed one into the other . thus one can raise the questions : are the surfaces fge ? are the fundamental groups of the corresponding galois covers isomorphic ? here we prove that although the latter groups are isomorphic , the surfaces are not fge . therefore , these surfaces are also not bmt  equivalent , which means that the surfaces are not in the same component of the hilbert scheme of linearly embedded k3 surfaces . * acknowledgments * : we are very grateful to ciro ciliberto , for pointing out the degeneration used for the  magician \" k3 surface and for other helpful discussions . we also wish to thank meirav amram for her fruitful remarks .","summary":"in this paper we present an example of two polarized k3 surfaces which are not fundamental group equivalent ( their fundamental groups of the complement of the branch curves are not isomorphic ; denoted by fge ) but the fundamental groups of their related galois covers are isomorphic . for each surface , we consider a generic projection to and a degenerations of the surface into a union of planes - the  pillow \" degeneration for the non - prime surface and the  magician \" degeneration for the prime surface . we compute the braid monodromy factorization ( bmf ) of the branch curve of each projected surface , using the related degenerations . by these factorizations , we compute the above fundamental groups . it is known that the two surfaces are not in the same component of the hilbert scheme of linearly embedded k3 surfaces . here we prove that furthermore they are not fge equivalent , and thus they are not of the same braid monodromy type ( bmt ) ( which implies that they are not a projective deformation of each other ) .   ","abstract":"in this paper we present an example of two polarized k3 surfaces which are not fundamental group equivalent ( their fundamental groups of the complement of the branch curves are not isomorphic ; denoted by fge ) but the fundamental groups of their related galois covers are isomorphic . for each surface , we consider a generic projection to and a degenerations of the surface into a union of planes - the  pillow \" degeneration for the non - prime surface and the  magician \" degeneration for the prime surface . we compute the braid monodromy factorization ( bmf ) of the branch curve of each projected surface , using the related degenerations . by these factorizations , we compute the above fundamental groups . it is known that the two surfaces are not in the same component of the hilbert scheme of linearly embedded k3 surfaces . here we prove that furthermore they are not fge equivalent , and thus they are not of the same braid monodromy type ( bmt ) ( which implies that they are not a projective deformation of each other ) .    [ section ] [ section ] [ section ] [ section ]    [ section ]"}
{"article_id":"1411.2889","section_id":"i","document":"let @xmath0 be a finitely generated group and let @xmath4 be a linear algebraic group defined over @xmath5 . the set of homomorphisms @xmath6 coincides with the real points of the _ representation variety _ @xmath7 hom@xmath8 . ( we note here that by a _ variety _ we mean an affine scheme of finite type over @xmath5 . in particular , we do not assume that it is irreducible or reduced ) . let @xmath9 denote the zariski closure of the set of representations @xmath10 with zariski - dense image . the main goal of the paper is to show that the dimension of @xmath11 is roughly of the order @xmath12 , where @xmath13 is the ( indefinite ) special orthogonal group @xmath2 with signature @xmath3 . before stating our main result , we provide a very brief discussion of a recent work in this direction . in a recent work , liebeck and shalev @xcite studied the representations of cocompact oriented fuchsian groups of genus @xmath14 and cocompact nonoriented fuchsian groups of genus @xmath15 in semisimple linear algebraic groups ; this study is based on the results from the theory of finite quotients of fuchsian groups . an explicit formula for the dimension of @xmath16 is given in the case where @xmath4 is a connected simple algebraic group over an algebraically closed field of _ arbitrary characteristic_. on the other hand , based on the deformation theory of weil @xcite , larsen and lubotzky @xcite studied the representation variety of cocompact oriented fuchsian groups @xmath0 of genus @xmath17 in almost - simple real algebraic groups . ( from now onward , we mean by fuchisan group a cocompact oriented fuchsian group of genus @xmath18 ) . an estimate of the dimension of @xmath11 , is given in the following cases :    1 . @xmath0 is any fuchsian group and @xmath4 is @xmath19 , @xmath20 , any split simple real algebraic group . @xmath0 is a @xmath21-dense fuchsian group and @xmath4 is any compact simple real algebraic group . we note here , a fuchsian group @xmath0 is said to be @xmath22-dense , where @xmath22 is an almost simple algebraic group , if there exists a homomorphism @xmath23 with dense image and @xmath24 is injective for all finite cyclic subgroups of @xmath0 ( * ? ? ? * definition 1.1 ) . the dimension of @xmath11 in these cases turns out to be roughly of the order @xmath12 , where @xmath25 is the euler characteristic of @xmath0 . the main goal of this paper is to show that a similar estimate of the dimension of @xmath26 holds , where @xmath2 is the indefinite special orthogonal group with signature @xmath3 . note that when @xmath27 , or @xmath28 , or @xmath29 the group @xmath2 is split ; as mentioned earlier , the estimates in these cases are treated by larsen and lubotzky @xcite . the main result of this paper deals with the remaining cases , that is when @xmath30 , @xmath31 , and @xmath32 ; in these cases @xmath2 is nonsplit and noncompact . before stating the main result we recall some notation . a cocompact oriented fuchsian group @xmath0 admits a presentation of the following kind : consider non - negative integers @xmath33 and @xmath34 and integers @xmath35 greater than or equal to @xmath36 , such that the euler characteristic @xmath37 is negative . for some choice of @xmath33 , @xmath34 , and @xmath38 , @xmath0 has a presentation @xmath39\\ldots[y_g , z_g ] \\rangle . \\end{split}\\ ] ]    now we state the main theorem of the paper . [ intro - thm-2 ] for every fuchsian group @xmath0 and for every special orthogonal group @xmath2 , where @xmath30 , @xmath32 and @xmath40 sufficiently large , @xmath41 where the implicit constant depends only on @xmath0 . the proof of the theorem is based on the deformation theory of weil @xcite and the work of larsen and lubotzky @xcite . while the upper bound follows almost immediately from the work of larsen and lubotzky , establishing a lower bound is difficult . a brief sketch of the proof follows . let @xmath0 be a fuchsian group with the presentation given by ( [ pre ] ) , and let @xmath4 be any linear algebraic group . the zariski tangent space at any point @xmath42 is given by the space of @xmath43-cocycles @xmath44 , where @xmath45 is the adjoint representation of @xmath4 in its lie algebra @xmath46 . let @xmath47 be the coadjoint representation of @xmath0 . the dimension of @xmath44 is given by the following formula @xcite : @xmath48 where @xmath49 denotes the @xmath0-invariant vectors under the coadjoint representation of @xmath0 . based on this formula , if @xmath50 is a representation with zariski - dense image in @xmath13 , an upper bound on @xmath51 , is given by ( * ? ? ? * proposition 2.1 ) @xmath52 as each irreducible component @xmath53 of @xmath11 contains a point @xmath54 with zariski dense image in @xmath13 , the dimension of @xmath55 is bounded above by the dimension of @xmath56 . the upper bound of @xmath57 follows .    on the other hand , to establish the lower bound , we construct a representation with zariski - dense image in @xmath58 . as it turns out , @xmath59 is a nonsingular point in @xmath60 , therefore it belongs to a unique irreducible component @xmath53 of @xmath60 . the main emphasis of this paper is to show that that there exists an open neighborhood of @xmath59 ( in the real topology ) , that does _ not _ contain representations of the following types :    1 . representations which stabilize some @xmath61-dimensional subspace where @xmath62 or which stabilize a @xmath63-dimensional _ isotropic _ subspace of @xmath64 , where @xmath65 denotes the natural representation of @xmath2 . representations @xmath66 such that the semisimple rank of the zariski - closure of @xmath67 is strictly less than the semisimple rank of @xmath58 . sieving representations of the former type is based on the theory of symmetric bilinear forms , and is easy . sieving representations of the latter type is based on the theory of semisimple algebraic groups , and requires some work . in the end , we have the following result :    [ intro - neigh ] let @xmath0 be a finitely generated group and let @xmath68 be a representation of @xmath0 in @xmath2 with zariski - dense image in @xmath58 . suppose @xmath69 , @xmath32 , and @xmath40 sufficiently large . then , there exists an open neighborhood of @xmath59 in @xmath60 ( in the real topology ) , such that each point @xmath54 in the neighborhood satisfies precisely one of the following conditions :    a.   the zariski closure of @xmath67 is @xmath2 . b.   the zariski closure of @xmath67 is conjugate to @xmath58 . now , using the deformation theory of weil @xcite , we show that the representations of the type @xmath70 in the open neighborhood given by theorem [ intro - neigh ] constitute a proper closed subvariety , whence the representations of type @xmath71 constitutes a zariski dense subset of the irreducible component @xmath53 . it follows that @xmath53 is contained in @xmath26 ( recall @xmath26 is the zariski - closure of the set of representations @xmath72 with zariski - dense image ) ; hence @xmath73 is bounded below by @xmath74 which in turn can be estimated by estimating the dimension of the zariski - tangent space at @xmath59 given by ( [ tas ] ) . along the way to proving theorem [ intro - neigh ] we prove the following result which may be of independent interest . [ intro - maximal - avoidance]_(maximal subgroup avoidance ) _ let @xmath0 be a finitely generated group . let @xmath4 be a semisimple subgroup of the special linear group @xmath75 . let @xmath76 be a semisimple subgroup of @xmath4 and let @xmath77 be a representation of @xmath0 such that the zariski - closure of @xmath78 is @xmath76 . let @xmath79 represent a finite set of conjugacy classes of proper reductive subgroups of @xmath4 . suppose @xmath80 for all @xmath81 . then there exists @xmath82 such that @xmath83 for all @xmath84 and @xmath85 . also , we shall present a proof of a generalisation of jordan s theorem on finite groups in @xmath86 . [ intro - larsen ] for all positive integers @xmath87 there exists a constant @xmath88 such that every closed reductive subgroup @xmath22 of @xmath89 , has an open subgroup @xmath90 of index @xmath91 such that @xmath92\\ ] ] where @xmath93 denotes the identity component of @xmath22 . the paper is organized as follows . in  [ term ] we introduce some terminology and notation that shall be adopted throughout the paper . in  [ sem - sim ] we prove a lemma on the finiteness of number of maxmal proper closed subgroups of a reductive group ; this lemma will be used in  [ word - maps ] . in  [ word - maps ] we consider word maps on semisimple algebraic groups and prove proposition [ intro - maximal - avoidance ] that is useful in establishing a certain uniform criterion on the subgroups of reductive groups . in  [ jordan ] we provide a proof of proposition [ intro - larsen ] ; the statement and the proof is due to michael larsen . in  [ deformation - point ] we begin the analysis of the representation variety @xmath60 and prove theorem [ intro - neigh ] . in  [ main - thm ] we prove the main result . in  [ final - rmk ] we comment on the possibility of extending these results to include other types of noncompact nonsplit real algebraic groups .","summary":"we estimate the dimension of the variety of homomorphisms from to with zariski dense image , where is a fuchsian group , and is the indefinite special orthogonal group with signature .","abstract":"we estimate the dimension of the variety of homomorphisms from to with zariski dense image , where is a fuchsian group , and is the indefinite special orthogonal group with signature ."}
{"article_id":"1209.0730","section_id":"i","document":"question of generating random bits from a source of biased coins dates back to von neumann @xcite who observed that when one focuses on a pair of coin tosses , the events ht and th have the same probability ( h is for ` head ' and t is for ` tail ' ) of being generated ; hence , ht produces the output symbol @xmath1 and th produces the output symbol @xmath2 . the other two possible events , namely , hh and tt , are ignored , namely , they do not produce any output symbols . however , von neumann s algorithm is not optimal in terms of the number of random bits that are generated . this problem was solved , specifically , given a fixed number of biased coin tosses with unknown probability , it is well known how to generate random bits with asymptotically optimal efficiency , namely , the expected number of unbiased random bits generated per coin toss is asymptotically equal to the entropy of the biased coin @xcite . however , these solutions , including elias s algorithm and peres s algorithm , can generate random bits only after receiving the complete input sequence ( or a fixed number of input bits ) , and the number of random bits generated is a random variable . we consider the setup of generating a  stream \" of random bits ; that is , whenever random bits are required , the algorithm reads new coin tosses and generates random bits dynamically . our new streaming algorithm is more efficient ( in the number of input bits , memory and time ) for producing the required number of random bits and is a better choice for implementation in practical systems . we notice that von neumann scheme is the one which is able to generate a stream of random bits , but its efficiency is far from optimal . our goal is to modify this scheme such that it can achieve the information - theoretic upper bound on efficiency . specifically , we would like to construct a function @xmath3 which satisfies the following conditions :    * @xmath4 generates a stream . for any two sequences of coin tosses @xmath5 , @xmath6 is a prefix of @xmath7 . * @xmath4 generates random bits . let @xmath8 be the sequence of coin tosses inducing @xmath9 bits ; that is , @xmath10 but for any strict prefix @xmath11 of @xmath12 , @xmath13 . then the first @xmath9 bits of @xmath14 are independent and unbiased . * @xmath4 has asymptotically optimal efficiency . that is , for any @xmath15 , @xmath16}{k}\\rightarrow\\frac{1}{h(p)}\\ ] ] as @xmath17 , where @xmath18 is the entropy of the biased coin @xcite . we note that the von neumann scheme uses only @xmath19 states , i.e. , a symbol in @xmath20 , for storing state information . for example , the output bit is @xmath1 if and only if the current state is h and the input symbol is t. in this case , the new state is @xmath21 . similarly , the output bit is @xmath2 if and only if the current state is t and the input symbol is h. in this case , the new state is @xmath21 . our approach for generalizing von neumann s scheme is by increasing the memory ( or state ) of our algorithm such that we do not lose information that might be useful for generating future random bits . we represent the state information as a binary tree , called status tree , in which each node is labeled by a symbol in @xmath22 . when a source symbol ( a coin toss ) is received , we modify the status tree based on certain simple rules and generate random bits in a dynamic way . this is the key idea in our algorithm ; we call this approach the random - stream algorithm . in some sense , the random - stream algorithm is the streaming version of peres s algorithm . we show that this algorithm satisfies all three conditions above , namely , it can generate a stream of random bits with asymptotically optimal efficiency . in practice , we can reduce the space size by limiting the depth of the status tree . we will demonstrate that as the depth of the status tree increases , the efficiency of the algorithm quickly converges to the information - theoretic upper bound . an extension of the question is to generate random bits or random - bit streams from an arbitrary markov chain with unknown transition probabilities . this problem was first studied by samuelson @xcite , and his algorithm was later improved by blum @xcite . recently , we proposed the first known algorithm that runs in expected linear time and achieves the information - theoretic upper bound on efficiency @xcite . in this paper , we briefly introduce the techniques of generating random - bit streams from markov chains . the rest of the paper is organized as follows . section [ stream_section_stream ] presents our key result , the random - stream algorithm that generates random bit streams from arbitrary biased coins and achieves the information - theoretic upper bound on efficiency . in section [ stream_section_generalization ] , we generalize the random - stream algorithm to generate random bit streams from a source of a larger alphabet . an extension for markov chains is provided in section [ stream_section_markov ] , followed by the concluding remarks .","summary":"generating random bits from a source of biased coins ( the biased is unknown ) is a classical question that was originally studied by von neumann . there are a number of known algorithms that have asymptotically optimal information efficiency , namely , the expected number of generated random bits per input bit is asymptotically close to the entropy of the source . however , only the original von neumann algorithm has a ` streaming property ' - it operates on a single input bit at a time and it generates random bits when possible , alas , it does not have an optimal information efficiency .    the main contribution of this paper is an algorithm that generates random bit streams from biased coins , uses bounded space and runs in expected linear time . as the size of the allotted space increases , the algorithm approaches the information - theoretic upper bound on efficiency .","abstract":"generating random bits from a source of biased coins ( the biased is unknown ) is a classical question that was originally studied by von neumann . there are a number of known algorithms that have asymptotically optimal information efficiency , namely , the expected number of generated random bits per input bit is asymptotically close to the entropy of the source . however , only the original von neumann algorithm has a ` streaming property ' - it operates on a single input bit at a time and it generates random bits when possible , alas , it does not have an optimal information efficiency .    the main contribution of this paper is an algorithm that generates random bit streams from biased coins , uses bounded space and runs in expected linear time . as the size of the allotted space increases , the algorithm approaches the information - theoretic upper bound on efficiency . in addition , we discuss how to extend this algorithm to generate random bit streams from-sided dice or correlated sources such as markov chains .    random number generation , biased coins , markov chains , streams ."}
{"article_id":"1601.03060","section_id":"i","document":"when faced with noisy and incomplete sensory information , humans and other animals often behave near - optimally @xcite . optimal behavior requires that the brain compute posterior distributions over task - relevant variables , which often involves complex operations such as multiplying probability distributions or marginalizing over latent variables . how do neural circuits implement such operations ? a prominent framework addressing this question is the probabilistic population coding ( ppc ) framework , according to which the population activity on a single trial encodes a probability distribution rather than a single estimate and computations with probability distributions can be carried out by suitable operations on the corresponding neural responses @xcite . for example , ma et al . @xcite showed that if neural variability belongs to a particular class of probability distributions , the posterior distribution in cue combination tasks can be computed with a linear combination of the input responses . moreover , in this scheme , the form of neural variability is preserved between the input and the output , leading to an elegantly modular code . in more complex tasks , linear operations are insufficient and it has been argued that multiplication and division of neural responses are necessary for optimal inference @xcite .    upon closer look , however , these previous implementations of ppc suffer from several shortcomings . first , the networks in these studies were either fully manually designed , or partially manually designed and partially trained with large amounts of probabilistic data to optimize explicitly probabilistic objectives , e.g. minimization of kullback - leibler ( kl ) divergence . therefore , this literature does not address the important question of learning : how can probabilistic inference be learned from a realistic amount and type of data with minimal manual design of the networks ? second , although there are some commonalities between the neural operations required to implement probabilistic inference in different tasks , these operations generally differ from task to task . for instance , it has been argued that some form of divisive normalization of neural responses is necessary in tasks that involve marginalization @xcite . however , the specific form of divisive normalization that individual neurons have to perform differs substantially from task to task . therefore , it is unclear if probabilistic inference can be implemented in _ generic _ neural networks , whose neurons all perform the same type of neurally plausible operation . third , in these studies , the number of neurons used for performing probabilistic inference scales unfavorably with the size of the input population ( linearly in the case of cue combination , but at least quadratically in all other tasks ) . therefore , the question of whether these tasks can be implemented more efficiently remains open .    in this paper , we address these issues . we show that generic neural networks trained with non - probabilistic error - based feedback perform near - optimal probabilistic inference in tasks with both categorical and continuous outputs . generic neural networks of the type we use in this paper have a long history @xcite , and have recently been linked directly to cortical responses @xcite . our main contribution is to connect generic neural networks to near - optimal probabilistic inference in common psychophysical tasks . for these tasks , we analyze the network generalization performance , the efficiency of the networks in terms of the number of neurons needed to a achieve a given level of performance , the nature of the emergent probabilistic population code and the mechanistic insights that can be gleaned from the trained networks . we also investigate whether the time - course of error - based learning in generic neural networks is realistic for non - linguistic animals learning to perform a probabilistic inference task .","summary":"animals perform near - optimal probabilistic inference in a wide range of psychophysical tasks . we show that generic neural networks trained with non - probabilistic feedback using a simple error - based learning rule perform near - optimal probabilistic inference in nine common psychophysical tasks . in a probabilistic categorization task , error - based learning in a generic network simultaneously accounts for a monkey s learning curve and for the evolution of qualitative aspects of its choice behavior . in all tasks , the number of neurons required for a given level of performance grows sub - linearly with the size of the input population , a substantial improvement on previous implementations of probabilistic inference using hand - crafted neurons . the tractability of the investigated tasks allows us to mechanistically understand the nature of this code .","abstract":"animals perform near - optimal probabilistic inference in a wide range of psychophysical tasks . probabilistic inference requires trial - to - trial representation of the uncertainties associated with task variables and subsequent use of this representation . previous work has implemented such computation using neural networks with hand - crafted and task - dependent operations . we show that generic neural networks trained with non - probabilistic feedback using a simple error - based learning rule perform near - optimal probabilistic inference in nine common psychophysical tasks . in a probabilistic categorization task , error - based learning in a generic network simultaneously accounts for a monkey s learning curve and for the evolution of qualitative aspects of its choice behavior . in all tasks , the number of neurons required for a given level of performance grows sub - linearly with the size of the input population , a substantial improvement on previous implementations of probabilistic inference using hand - crafted neurons . the trained networks develop a novel sparsity - based probabilistic population code in a task - dependent manner . the tractability of the investigated tasks allows us to mechanistically understand the nature of this code . our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error - based learning rules and that these types of networks can be used as simple plausible neural models of probabilistic inference ."}
{"article_id":"1601.03060","section_id":"r","document":"* tasks . * we trained generic feedforward or recurrent neural networks on nine probabilistic psychophysical tasks that are commonly studied in the experimental and computational literature . the main tasks were : ( a ) linear cue combination @xcite , ( b ) coordinate transformations @xcite , ( c ) kalman filtering @xcite , ( d ) causal inference @xcite , ( e ) stimulus demixing @xcite , ( f ) binary categorization @xcite , ( g ) visual search with heterogeneous distractors @xcite ( see _ methods _ for task details ) . we also trained generic networks on two additional `` modular '' tasks to be discussed below . * networks . * the networks all received noisy sensory information about the stimulus or the stimuli in the form of a neural population with poisson variability . the hidden units of the networks were modeled as rectified linear units ( relus ) . relus are commonly used in neural networks due to their demonstrated advantage over alternative non - linearities in gradient - based learning algorithms @xcite . linear ( sigmoidal ) output units were used in tasks with continuous ( categorical ) outputs . schematic diagrams of the networks used for the main tasks considered in this paper are shown in figure  [ diagrams_fig ] . differences between the network architectures are due entirely to differences in the input and output requirements of different tasks : different tasks have different numbers of inputs or outputs and the outputs are continuous or categorical in different tasks . other than these task - dictated differences , the networks are truly generic in the sense that they are composed of neurons that perform the same type of biologically plausible operations in all tasks .    networks were trained to minimize mean squared error or cross - entropy in tasks with continuous or categorical outputs , respectively . importantly , the networks were provided only with the actual stimulus values or the correct class labels as feedback in each trial . thus , they did not receive any explicitly probabilistic feedback , nor were they explicitly trained to perform probabilistic inference . we manipulated sensory reliability trial - by - trial via gain variables @xmath0 multiplying the responses of the input populations , with higher gains corresponding to more reliable sensory information . in each task , networks were tested with a wide range of gains or gain combinations ( in tasks with more than a single stimulus ) . to test the generalization capacity of the networks , we trained them with a limited range of gains or gain combinations , as well as with the full range of test gains or gain combinations . the latter unrestricted training regime is called the `` all @xmath1 '' condition , whereas the former limited training regime is called the `` restricted @xmath1 '' condition in what follows . the specific gain ranges and gain combinations used in each task are indicated below ( _ methods _ ) . * generic neural networks trained with error - based learning rules implement probabilistic inference in standard psychophysical tasks . * the performance of well - trained networks is shown in figure  [ performance_all_fig]c and d for both `` all @xmath1 '' ( black ) and `` restricted @xmath1 '' ( red ) training conditions in all tasks ( complete learning curves of the networks are shown in supplementary figure  [ all_tasks_fig ] ) . for continuous tasks , performance is measured in terms of fractional rmse defined as @xmath2 where @xmath3 is the root mean - squared error ( rmse ) of the trained network , @xmath4 is the rmse of the posterior mean estimate . for categorical tasks , performance is measured in terms of fractional information loss defined as the average kl - divergence between the actual posterior and the network s output normalized by the mutual information between the class labels and the neural responses @xcite . with this measure , a network that exactly reproduces the posterior achieves 0% information loss , whereas a network that produces random responses according to the prior probabilities of the classes has 100% information loss .    to make sure that optimal performance in our tasks can not be easily mimicked by heuristic , non - probabilistic models , we also calculated the performance of non - probabilistic reference models that did not take the reliabilities of the inputs into account ( figure  [ performance_all_fig]c - d , blue ) . the large performance gaps between these non - probabilistic models and the optimal model suggest that approaching optimal performance in our tasks requires performing truly probabilistic inference , i.e. taking the reliabilities of the inputs into account . in categorical tasks , the output nodes of the networks approximate the posterior probabilities of the classes given the inputs ( figure  [ performance_all_fig]b , d ) . theoretical guarantees ensure that this property holds under general conditions with a wide range of loss functions @xcite ( _ discussion _ ) . * encoding of posterior width in the hidden layers . * for continuous tasks , training with mean squared error loss guarantees asymptotic convergence to the posterior mean . do the networks also represent information about the posterior uncertainty in their hidden layers or do they discard this information ? representation of posterior uncertainty is evident in the kalman filtering task where accurate encoding of the posterior mean at a particular moment already requires the encoding of the posterior mean and the posterior width at the previous moment and the optimal integration of these with the current sensory information in the recurrent activity of the network . for the linear cue combination and coordinate transformation tasks , to test for the representation of posterior uncertainty in the hidden layer , we plugged the trained hidden layers into a network incorporating an additional input population and fixed their parameters ( figure  [ modular_fig]a ) . the rest of the network was then trained on a linear cue combination task with three input populations ( a similar modular task was designed in @xcite ) . if the fixed hidden layers do not encode the posterior width for the first two inputs , the combined network can not perform the three - input cue combination task optimally . however , the combined networks were able to perform the three - input cue combination task with little information loss despite receiving information about the first two inputs only through the fixed hidden layers ( figure  [ modular_fig]b - c ) . this suggests that although the initial networks were trained to minimize mean squared error , and hence were asymptotically guaranteed to reproduce the posterior means only , information about the posterior widths was , to a large extent , preserved in the hidden layer . the precise format in which posterior uncertainty is represented in the hidden layer activity will be discussed below . the combined coordinate transformation - cue combination ( ct+cc ) network also illustrates the generic nature of the representations learned by the hidden layers of our networks : the hidden layer of a network trained on the coordinate transformation task can be combined , without modification , with an additional input population to perform a different task , i.e. cue combination in this example .        * generalization to untrained stimulus conditions . * truly bayesian computation requires that the components of the bayesian computation , i.e. sensory likelihoods and the prior , be individually meaningful to the brain @xcite . thus , if we replace a particular likelihood for another , the system should continue to perform near - optimally . we tested for a limited form of such `` bayesian transfer '' by examining whether the trained networks generalize to unseen values or combinations of sensory reliability ( `` restricted @xmath1 '' conditions ) . as shown in figure  [ performance_all_fig]c and d ( red bars ) , the networks were able to generalize well beyond the training conditions in all tasks . an example is shown in figure  [ generalization_fig]a for the cue combination task . in this example , we trained a network with only two gain combinations , @xmath5 and @xmath6 , and tested it on all gain combinations of the form @xmath7 where @xmath8 with up to five - fold gain differences between the two input populations ( note that these gains are higher than those used in the main simulations to make the optimal combination rule approximately linear ) . to demonstrate that the trained networks performed qualitatively correct probabilistic inference , we set up cue conflict conditions similar to the cue conflict conditions in psychophysical studies @xcite , where we presented slightly different stimuli to the two input populations and manipulated the degree of conflict between the cues . the weights assigned to the first cue as a function of the gain ratio , @xmath9 , are shown in figure  [ generalization_fig]a both for the network and for the optimal rule . the network achieved low generalization error ( fractional rmse : 10.9% ) even after as few as 50 training examples in the impoverished training condition and performed qualitatively correct probabilistic inference in the untrained conditions . in particular , the network correctly adjusted the weights assigned to the two cues even as the ratio of their reliabilities varied over a 25-fold range ( figure  [ generalization_fig]a ) . the successful generalization performance of the neural networks is a result of two factors . first , the target function is approximately invariant to gain manipulations that differ between the training and test conditions . in cue combination , for instance , the target function is approximately invariant to the scaling of the input populations by arbitrary gains @xmath10 and @xmath11 ( equation  [ cue_comb_eq ] ) . the second factor is the network s inductive biases , i.e. how it tends to behave outside the training domain . these inductive biases depend on the details of the network architecture @xcite .    * alternative representations of stimulus reliability in the input populations . * thus far , we have assumed that sensory reliability has a purely multiplicative effect on the responses of input neurons . although this assumption likely holds for the effect of contrast on orientation selectivity in visual cortex @xcite , it is known to be violated for the effect of motion coherence on direction selectivity @xcite and for the effect of contrast on speed selectivity @xcite , and is unlikely to hold in the general case . the importance of this observation is that the poisson - like ppc approach proposed in @xcite can not easily handle cases where `` nuisance variables '' such as contrast or coherence do not have a purely multiplicative effect on neural responses . by contrast , our approach does not make any assumptions about the representation of stimulus reliability in the input populations . we demonstrated this in two cases ( figure  [ generalization_fig]b - c ) : ( i ) cue combination with tuning functions of the form reported in @xcite where stimulus coherence affects both the gain and the baseline of the responses ( figure  [ generalization_fig]b , left ) and ( ii ) cue combination with tuning functions of the form reported in @xcite for speed where both the peak response and the preferred speed depend on stimulus contrast ( figure  [ generalization_fig]b , right ) . thus , our networks can perform near - optimal inference regardless of the specific form in which stimulus reliability is encoded in the input populations . * sparsity - based representation of posterior uncertainty . * we now discuss how posterior uncertainty is represented in the hidden layers of the trained networks . we first note that in tasks with continuous output variables , the optimal solution is invariant to a multiplicative scaling @xmath0 of the input responses ( _ methods _ , equations  [ cue_comb_eq]-[kalman_last_eq ] ) . in such gain - invariant ( or approximately gain - invariant ) tasks , posterior uncertainty is represented in the sparsity of hidden layer activity . to understand the mechanism through which this sparsity - based representation arises , we investigated the conditions under which the network s output would be invariant to input gain scalings . we first derived an approximate analytical expression for the mean response of a typical hidden unit @xmath12 , as a function of the input gain @xmath0 , the mean input @xmath13 to the hidden unit for unit gain , and the mean @xmath14 and the standard deviation @xmath15 of the biases of the hidden units ( _ methods _ ) . to minimize the dependence of the mean hidden unit response on @xmath0 , we introduced the following measure of the total sensitivity of @xmath12 to variations in @xmath0 : @xmath16 where the prime represents the derivative with respect to @xmath0 , and numerically minimized @xmath17 with respect to @xmath13 , @xmath14 and @xmath15 , subject to the constraint that the mean response across different gains be equal to a positive constant @xmath18 . @xmath17 was minimized for a negative mean input @xmath13 , positive @xmath14 and a large @xmath15 value ( black star in figure  [ sparsity_fig]a ) . as an approximate rule , decreasing @xmath13 and increasing @xmath14 or @xmath15 lead to smaller @xmath17 values . because the input responses are always non - negative , the only way @xmath13 can be negative in our networks is if the mean input - to - hidden layer weight is negative . the negativity of the mean input @xmath13 implies that as the gain @xmath0 increases , the distribution of the total input to the unit shifts to the left ( figure  [ sparsity_fig]b , top ) , causing a larger proportion of the distribution to remain below the threshold ( represented by the dashed line in figure  [ sparsity_fig]b ) , hence decreasing the probability that the neuron will have a non - zero response ( figure  [ sparsity_fig]c , top ) . this mechanism causes the sparsification of the hidden unit responses with increasing @xmath0 and is particularly effective when the mean bias , @xmath14 , is large and positive . because increasing @xmath0 also increases the variance of the total input to the unit , the mean response for those inputs that do cross the threshold increases ( figure  [ sparsity_fig]d , top ) . as a result , the mean response of the neuron , which is a product of these two terms , remains roughly constant ( figure  [ sparsity_fig]e , top ) . we demonstrate this sparsification mechanism for a network trained on the coordinate transformation task in figure  [ sparsity_fig]f - i . because the coordinate transformation task is approximately gain - invariant ( _ methods _ , equation  [ ct_eq ] ) , the input - to - hidden layer weight distribution in the trained network was skewed toward negative values ( figure  [ sparsity_fig]f ) and the mean bias of the hidden units , @xmath14 , was positive ( figure  [ sparsity_fig]g ) , as predicted from our simple mean - field model . consequently , we found a strong positive correlation between the sparsity of hidden layer responses and the mean input response ( @xmath19 ; figure  [ sparsity_fig]i ) , but no correlation between the mean hidden layer response and the mean input response ( @xmath20 ; figure  [ sparsity_fig]h ) . the same type of analysis applies to the categorical tasks as well . however , the difference is that for some of our tasks with categorical outputs , in the optimal solution , the net input to the output unit had a strong dependence on @xmath0 . for example , in causal inference , the input to the sigmoidal output unit scales approximately linearly with @xmath0 ( equation  [ causal_inference_eq ] ) . similarly , in visual search , both global and local log - likelihood ratios have a strong dependence on @xmath0 ( through @xmath21 in equations  [ vs_global_eq]-[vs_local_eq ] ) . we emphasize that the distinction between @xmath0-dependence and @xmath0-invariance is not categorical : different tasks can have varying degrees of @xmath0-invariance or @xmath0-dependence and parameter choices in the same task can affect its @xmath0-dependence .    in the bottom panel of figure  [ sparsity_fig]b - e , predictions from the mean - field model are shown for a parameter combination where both @xmath13 and @xmath14 are small and slightly negative ( represented by the magenta dot in figure  [ sparsity_fig]a ) . this parameter combination roughly characterizes the trained networks in the causal inference task ( figure  [ sparsity_fig]j - m ) . in this case , because both @xmath13 and @xmath14 are close to 0 , the probability of non - zero responses as a function of @xmath0 stays roughly constant ( figure  [ sparsity_fig]c , bottom ) , causing the mean response to increase with @xmath0 ( figure  [ sparsity_fig]e , bottom ) .    based on our simple mean - field model , we therefore predicted that for those tasks where the net input to the output unit is approximately @xmath0-invariant , there should be a positive correlation between the sparsity of hidden unit responses and the input gain and no ( or only a weak ) correlation between the mean hidden unit response and the input gain . on the other hand , in tasks such as causal inference , where the net input to the output unit has a strong @xmath0-dependence , we predicted a positive correlation between the mean hidden unit response and the input gain and no ( or only a weak ) correlation between the sparsity of hidden unit responses and the input gain . we tested these predictions on our trained networks and confirmed that they were indeed correct ( figure  [ params_fig]a - b ) . for causal inference , visual search and stimulus demixing tasks , the correlation between the mean input and the sparsity of hidden layer responses was weak ( figure  [ params_fig]f ) , whereas for the remaining tasks , it was strong and positive . the opposite pattern was seen for the correlation between the mean input and the mean hidden layer response ( figure  [ params_fig]a ) . in @xmath0-dependent tasks such as causal inference , posterior uncertainty is thus represented largely in the mean hidden layer activity ; whereas in approximately @xmath0-invariant tasks such as coordinate transformation , it is represented largely in the sparsity of hidden layer activity . the sparsity - based representation of posterior uncertainty in @xmath0-invariant tasks was again driven by large negative mean input - to - hidden layer weights and large positive mean biases ( figure  [ params_fig]c - d ) . the difference between these two types of tasks ( @xmath0-invariant and @xmath0-dependent ) was also reflected in the tuning functions that developed in the hidden layer of the networks . for approximately @xmath0-invariant tasks such as coordinate transformation , increasing the input gain @xmath0 sharpens the tuning of the hidden units ( figure  [ tuning_functions_fig]a ) , whereas for @xmath0-dependent tasks such as causal inference , input gain acts more like a multiplicative factor scaling the tuning functions without changing their shape ( figure  [ tuning_functions_fig]b ) . we finally note that these results are decoder dependent . in the continuous tasks , for example , if we use a divisively normalized decoder instead of a linear read - out , posterior uncertainty is encoded in the mean hidden layer response , rather than in the sparsity of hidden layer responses ( supplementary figure  [ supp_relunorm_fig ] ) . ( plotted in log units ) as a function of the parameters @xmath13 , @xmath14 and @xmath15 for the constraint surface corresponding to @xmath22 . the optimal parameter values within the shown range are represented by the black star . the green and magenta dots roughly correspond to the parameter statistics in the trained coordinate transformation and causal inference networks , respectively . ( b ) for the parameter combination corresponding to the green dot , the mean input @xmath13 is negative and the mean bias @xmath14 is positive . increasing the gain @xmath0 thus shifts the input distribution to the left : compare the black and red lines for input distributions with a small and a large gain , respectively . the means of the input distributions are indicated by small dots underneath . ( c ) this , in turn , decreases the probability of non - zero responses , but ( d ) increases the mean of the non - zero responses ; hence ( e ) the mean response of the hidden units , being a product of the two , stays approximately constant as the gain is varied . in the bottom panel of ( b - e ) , the results are also shown for a different parameter combination represented by the magenta dot in ( a ) . this parameter combination roughly characterizes the trained networks in the causal inference task . ( f ) for a network trained in the coordinate transformation task , distributions of the input - to - hidden layer weights , @xmath23 ; ( g ) the biases of the hidden units , @xmath24 ; ( h ) scatter plot of the mean input @xmath25 vs. the mean hidden unit activity @xmath26 ; ( i ) the scatter plot of the mean input vs. the kurtosis of hidden unit activity @xmath27 . ( j - m ) similar to ( f - i ) , but for a network trained in the causal inference task.,scaledwidth=100.0% ]         ( averaged over @xmath28 ) and the second row shows the tuning functions with respect to @xmath28 . increasing the gain sharpens the tuning curves in the coordinate transformation task , whereas it has a more multiplicative effect in the causal inference task.,scaledwidth=100.0% ]    * random networks . * to investigate the architectural constraints on the networks capable of performing near - optimal probabilistic inference , we considered an alternative architecture , in which the input - to - hidden layer weights and the biases of the hidden units were set randomly and left untrained ; only the hidden - to - output layer weights and the biases of the output units were trained ( figure  [ random_recurrent_fig]a ) . such random networks can be plausible models of some neural systems @xcite . given the same amount of computational resources , these networks performed substantially worse than the fully trained networks ( figure  [ random_recurrent_fig]b ) . a well - known theoretical result can explain the inefficiency of random networks @xcite : the approximation error of neural networks with adjustable hidden units scales as @xmath29 with @xmath30 denoting the number of hidden units , whereas for networks with fixed hidden units , as in our random networks , the scaling is much worse : @xmath31 where @xmath32 is the dimensionality of the problem , suggesting that they need exponentially more neurons than fully trained networks in order to achieve the same level of performance .    * making the networks biologically more plausible : recurrent ei networks . * so far , we have only considered feedforward networks with undifferentiated neurons . to investigate whether introducing more biological realism would severely constrain the capacity of the networks to perform near - optimal probabilistic inference , following the approach proposed in @xcite , we trained fully recurrent networks with separate excitatory and inhibitory populations that respected dale s law : excitatory neurons projecting only positive weights , inhibitory neurons only negative weights . the input populations were also divided into excitatory and inhibitory sub - populations that obeyed dale s law ( figure  [ random_recurrent_fig]c ) . the performance of these recurrent ei networks were slightly worse than , but not substantially different from , the corresponding fully - trained feedforward networks ( figure  [ random_recurrent_fig]d ) . moreover , the networks re - coded stimulus reliability in a similar manner to the feedforward networks ( supplementary figure  [ supp_recurrent_ei_fig ] ) , suggesting that the main results reported for feedforward networks are robust to the incorporation of more biological realism into our networks .    -axis is cut off at 100% . ( c ) schematic diagram of a recurrent ei network that obeys dale s law : inhibitory connections are represented by the red arrows and excitatory connections by the blue arrows ; inhibitory neurons are represented by lighter colors , excitatory neurons by darker colors . both input and hidden layers are divided into excitatory - inhibitory sub - populations at a 4-to-1 ratio . inputs to the network were presented over 10 time steps . ( d ) performance of recurrent ei networks.,scaledwidth=100.0% ]    * error - based learning in generic neural networks accounts for the evolution of behavioral choice and accuracy in a binary categorization task . * the dependence of the networks performance on the number of training trials ( figure  [ all_tasks_fig ] ) suggests a possible explanation for deviations from optimal inference sometimes observed in experimental studies : i.e. insufficient training in the task . testing this hypothesis rigorously is complicated by possible prior exposure of the subjects to similar stimuli or tasks under natural conditions . among the tasks considered in this paper , the binary categorization task minimizes such concerns , because it involves classifying stimuli into arbitrary categories . moreover , in this task , the behavior of both human and monkey observers were best explained by heuristic models that were quantitatively suboptimal , but qualitatively consistent with the optimal inference model @xcite . therefore , we sought to test the insufficient - training hypothesis for suboptimal inference in this task . the stimulus distributions for the two categories and the decision boundaries predicted by the optimal ( opt ) and three suboptimal models ( fix , lin , quad ) are shown in figure  [ qamar_fig]a - b . different suboptimal models make different assumptions about the dependence of the decision boundary on the sensory noise , @xmath33 ( figure  [ qamar_fig]b ) . in particular , the fix model assumes that the decision boundary is independent of @xmath33 , whereas lin and quad models assume that the decision boundary is a linear or quadratic function of @xmath33 , respectively @xcite . the learning curve of a monkey subject who performed a large number of trials in this task ( monkey l in @xcite ) is shown in figure  [ qamar_fig ] together with the performance of a neural network that received the same sequence of trials as the subject . the input noise of the network was matched to the sensory noise estimated for the subject and the learning rate of the network was optimized to fit the learning curve of the subject . the neural network was trained online , updating its parameters after each trial , in an analogous manner to how the monkey subject learns the task . besides providing a good fit to the learning curve of the subject ( figure  [ qamar_fig]c ) , the neural networks also correctly predicted the progression of the models that best fit the subject s data , i.e. early on in the training the quad model , then the lin model ( figure  [ qamar_fig]d ) . when we performed the same type of analysis on human subjects data , human observers consistently outperformed the networks and the networks failed to reproduce the learning curves of the subjects ( figure  [ qamar_fig]e ) . there might be several possible non - exclusive explanations for this finding . first , prior to the experiment , human observers were told about the task , including what examples from each category looked like . this type of knowledge would be difficult to capture with error - based learning alone and might have given human observers a head - start in the task . second , human observers might have benefited from possible prior familiarity with similar tasks or stimuli . third , human observers might be endowed with more powerful computational architectures than simple generic neural networks that allow them to learn faster and generalize better @xcite .    * low computational complexity of standard psychophysical tasks and the efficiency of generic networks . * for each of our tasks , we empirically determined the minimum number of hidden units , @xmath34 , required to achieve a given level of performance ( 15% information loss for visual search , 10% fractional rmse or information loss for the other tasks ) as a function of the total number of input units , @xmath32 , in our generic networks . an example is shown in figure  [ nhu_fig]a for the causal inference task with @xmath35 and @xmath36 . the scaling of @xmath34 with @xmath32 was better than @xmath37 , i.e. sub - linear , in all our tasks ( figure  [ nhu_fig]b ) . previous theoretical work suggests that this result can be explained by the smoothness properties of the target functions and the efficiency of the generic neural networks with adjustable hidden units . in particular , barron @xcite showed that the optimal number of hidden units in a generic neural network with a single layer of adjustable hidden units scales as @xmath38 with @xmath32 , where @xmath39 is a measure of the smoothness of the target function , with more smooth functions having lower @xmath39 values . as an example , in @xcite , it was shown that for the @xmath32-dimensional standard gaussian function , @xmath39 can be upper - bounded by @xmath40 , leading to an estimate of @xmath41 hidden units in terms of @xmath32 . for some of our tasks ( e.g. binary categorization ; figure  [ nhu_fig]b ) , the scaling of @xmath34 with @xmath32 was approximately constant over the range of @xmath32 values tested , suggesting smoothness properties similar to a @xmath32-dimensional standard gaussian . for the other tasks , the scaling was slightly worse , but still sub - linear in every case : in the worst case of coordinate transformation , linear regression of @xmath42 on @xmath43 yields a slope of @xmath44 ( @xmath45 ) . we can gain some intuition about the relatively benign smoothness properties of our tasks by looking at the analytic expressions for the corresponding target functions ( equations  [ cue_comb_eq]-[vs_local_eq ] ) : although the inputs are high dimensional , the solutions can usually be expressed as smooth functions of a small number of one - dimensional linear projections of the inputs . the efficiency of our generic networks contrasts sharply with the inefficiency of the manually crafted networks in earlier ppc studies @xcite : except for the linear cue combination task , these hand - crafted networks used a quadratic expansion which requires at least @xmath46 hidden units . moreover , unlike generic neural networks , these networks with hand - crafted hidden units are not guaranteed to work well in the general case , if , for example , the target function is not expressible in terms of a quadratic expansion . stacking the quadratic expansions hierarchically to make the networks more expressive would make the scaling of the number of hidden units with @xmath32 even worse ( e.g. @xcite ) . the fundamental weakness of these hand - crafted networks is the same as that of the random networks reviewed above : they essentially use a fixed basis set theoretically guaranteed to have much worse approximation properties than the adjustable basis of hidden units used in our generic networks @xcite .    , the minimum number of hidden units required to reach within 10% of optimal performance ( 15% for visual search ) , @xmath34 , is estimated ( shown by the arrows ) . an example is shown here for the causal inference task with @xmath35 and @xmath36 input units , respectively . ( b ) @xmath34 plotted as a function of the total number of input units , @xmath32 , in different tasks . solid lines show linear fits . in these simulations , the number of training trials for each task was set to the maximum number of training trials shown in supplementary figure  [ all_tasks_fig].,scaledwidth=100.0% ]","summary":"probabilistic inference requires trial - to - trial representation of the uncertainties associated with task variables and subsequent use of this representation . previous work has implemented such computation using neural networks with hand - crafted and task - dependent operations . the trained networks develop a novel sparsity - based probabilistic population code in a task - dependent manner .","abstract":"animals perform near - optimal probabilistic inference in a wide range of psychophysical tasks . probabilistic inference requires trial - to - trial representation of the uncertainties associated with task variables and subsequent use of this representation . previous work has implemented such computation using neural networks with hand - crafted and task - dependent operations . we show that generic neural networks trained with non - probabilistic feedback using a simple error - based learning rule perform near - optimal probabilistic inference in nine common psychophysical tasks . in a probabilistic categorization task , error - based learning in a generic network simultaneously accounts for a monkey s learning curve and for the evolution of qualitative aspects of its choice behavior . in all tasks , the number of neurons required for a given level of performance grows sub - linearly with the size of the input population , a substantial improvement on previous implementations of probabilistic inference using hand - crafted neurons . the trained networks develop a novel sparsity - based probabilistic population code in a task - dependent manner . the tractability of the investigated tasks allows us to mechanistically understand the nature of this code . our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error - based learning rules and that these types of networks can be used as simple plausible neural models of probabilistic inference ."}
{"article_id":"1601.03060","section_id":"c","document":"we have shown that small generic neural networks trained with a standard error - based learning rule , but without any explicitly probabilistic feedback or training objective , implement probabilistic inference in simple psychophysical tasks and generalize successfully beyond the conditions they are trained in .    for tasks with continuous outputs , we trained our networks to minimize the squared error loss function , which is minimized by the posterior mean estimate . given the universal approximation guarantees for multilayer neural networks with rectified linear hidden units @xcite , it is not surprising that our networks can approximate the posterior mean given enough hidden units and training data . however , the findings that near - optimal performance can be achieved even in small networks trained with a relatively small number of training examples and that the networks can generalize successfully beyond the training data they receive depend on the particular problems we studied , in particular , on their low - dimensional nature and their smoothness properties , hence are not predicted by the universal approximation results . moreover , representing the posterior mean is necessary , but not sufficient for general probabilistic computation : it is also necessary to represent uncertainty on a trial - by - trial basis . using modular tasks , we showed that the networks implicitly represent uncertainty as well . this finding also holds when the networks are trained with absolute error loss ( supplementary figure  [ supp_alt_objectives_fig]a ) .    for tasks with categorical outputs , the output layer of a multilayer neural network is asymptotically guaranteed to converge to the posterior probabilities of the classes under a broad class of loss functions @xcite , including cross - entropy and mean squared error ( supplementary figure  [ supp_alt_objectives_fig]b ) . for the particular problems we studied , our results again show empirically that this convergence can be achieved relatively fast and does not require large networks . our tasks all assumed psychophysically realistic levels of sensory noise . at these noise levels , simple heuristic non - probabilistic models that did not take trial - to - trial uncertainty into account are unable to mimic the performance of optimal probabilistic models . random networks with only trainable readout weights performed poorly in our tasks . this can be understood as a consequence of the poor approximation properties of such networks @xcite . on the other hand , making our networks biologically more plausible by making them fully recurrent and introducing separate excitatory and inhibitory populations throughout the network that respect dale s law in their connectivity pattern did not significantly impair the performance of the networks . * relationship to previous work . * our work is consistent with the probabilistic population coding framework according to which , by virtue of the variability of their responses , neural populations encode probability distributions rather than single estimates and computations with probability distributions can be carried out by suitable operations on the corresponding neural responses @xcite . however , our work disagrees with the existing literature on the implementation of such computations . we show that these computations do not require any special neural operations or network architectures than the very generic ones that researchers have been using for decades in the neural network community @xcite .    the recent literature on probabilistic population coding respects the principle that poisson - like neural variability be preserved between the input and output of a network , because this leads to a fully modular code that can be decoded with the same type of decoder throughout the network @xcite . to obtain actual networks , these studies then postulate a literal , one - to - one correspondence between the required neural computations that must be computed at the population level and the computations individual neurons perform . this literal interpretation leads to inefficient neural architectures containing intermediate neurons that are artificially restricted to summing or multiplying the activities of at most two input neurons and that perform substantially different operations in different tasks ( e.g. linear summation , multiplication or different forms of divisive normalization ) @xcite . our generic networks are not necessarily inconsistent with the principle of the preservation of poisson - like variability between the input and output of a network . our categorical networks already satisfy this principle , and our continuous networks satisfy it if , instead of a purely linear decoder , we use a linear decoder that is then normalized by the total activity in the hidden layer ( supplementary figure  [ supp_relunorm_fig ] ) . however , our results show that it is unnecessary and inefficient to postulate a direct correspondence between population - level and individual - neuron computations : standard neural networks with rectified linear hidden units that perform the same type of operation independent of the task implement population - level computations required for optimal probabilistic inference far more efficiently . * experimental predictions . * our results lead to several experimentally testable predictions . first , for gain - invariant tasks , we predict a novel sparsity - based coding of posterior uncertainty in cortical areas close to the behavioral readout . stimulus manipulations that increase sensory reliability such as an increase in contrast of the stimulus would be expected to increase the sparseness of the population activity in these areas . another straightforward consequence of this relationship would be a positive correlation between the performance of the animal in the task and the population sparsity of neurons recorded from the same areas . second , for gain - dependent tasks such as causal inference , we predict a different coding of posterior uncertainty based on the mean activity in areas close to the readout . moreover , based on our mean - field model of the mechanism underlying these two types of codes , we expect a trade - off between them : the stronger the correlation between sparsity and posterior uncertainty , the weaker the relationship between the mean activity and posterior uncertainty and vice versa . this can be tested with population recordings from multiple areas in multiple tasks . third , at the level of single cells , we predict tuning curve sharpening with increased input gain in tasks where a sparsity - based coding of reliability is predicted ( figure  [ tuning_functions_fig]a ) . such tuning curve sharpening has indeed been observed in cortical areas mt @xcite , mst @xcite and mstd @xcite . on the other hand , we expect the input gain to act more like a multiplicative factor in tasks where a mean activity based coding of reliability is predicted ( figure  [ tuning_functions_fig]b ) . sparse and reliable neural responses have been observed under natural stimulation conditions @xcite . inhibitory currents have been shown to be crucial in generating such sparse and reliable responses @xcite , reminiscent of the negative mean input requirement in our mean - field model of the sparsity - based coding of posterior uncertainty ( figure  [ sparsity_fig]b ) .    * limitations . * our networks are highly idealized models of real neural circuits . although we validated our basic results using biologically more realistic recurrent excitatory - inhibitory networks ( figure  [ random_recurrent_fig]c - d ) , even these networks are simplistic models that ignore much of the complexity of real neural circuits . for example , real neural circuits involve several morphologically and physiologically distinct cell types with different connectivity patterns and with potentially distinct functions @xcite . real neurons also implement a diverse set of complicated non - linearities , unlike the simple rectification non - linearity we assumed in our networks . it remains to be determined what possible functional roles this diversity plays in neural circuits . however , even seemingly drastic simplifications can , in some cases , teach us important insights about the brain . for example , cortical networks are usually highly recurrent , thus modeling them as feed - forward networks might seem like a useless simplification . however , networks with feedback connections can sometimes behave effectively like a feedforward network @xcite . as another example , feedforward networks also currently provide the best characterization of the neural responses in higher visual cortical areas @xcite , even though these areas are known to involve abundant feedback connections both within the same area and between different areas . therefore , insights gained from understanding simplified models can be quite relevant for understanding real cortical circuits . second , our networks were trained with the backpropagation algorithm , which is usually considered to be biologically unrealistic due to its non - locality . although the backpropagation algorithm in its standard form we have implemented is indeed biologically unrealistic , biologically plausible approximations to backpropagation have been put forward recently @xcite . therefore , it is quite likely that one need not compromise the power of backpropagation in order to attain biologically plausibility . third , the stimuli that we used were far from naturalistic . however , the computations required in our tasks capture the essential aspects of the computations that would be required in similar tasks with natural stimuli . using simple stimuli allows for the parametric characterization of behavior and makes the derivation of the optimal solution more tractable . we have shown here that new insights can be obtained by combining analytically derived optimal solutions with neural networks . for example , understanding the novel sparsity - based representation of posterior uncertainty in the hidden layers of the networks in some tasks but not in others relied on the analysis of the optimal solutions in different tasks .    finally , as exemplified by the inability of error - based learning to account for the performance of human observers in the binary categorization task , we do not expect error - based learning in generic neural networks to fully account for all aspects of the performance of human observers , and possibly non - human observers as well , even in simple tasks . relatively mundane manipulations such as changing the target or the distractors , or the number of distractors in a visual search task , changing the duration of a delay interval in a short - term memory task require wholesale re - training of generic neural networks , which seems to be inconsistent with the way human observers , and possibly non - human observers , can effortlessly generalize over such variables . more powerful architectures that combine a neural network controller with an external memory can both learn faster and generalize better @xcite , offering a promising direction for modeling the generalization patterns of observers in simple psychophysical tasks .","summary":"our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error - based learning rules and that these types of networks can be used as simple plausible neural models of probabilistic inference .","abstract":"animals perform near - optimal probabilistic inference in a wide range of psychophysical tasks . probabilistic inference requires trial - to - trial representation of the uncertainties associated with task variables and subsequent use of this representation . previous work has implemented such computation using neural networks with hand - crafted and task - dependent operations . we show that generic neural networks trained with non - probabilistic feedback using a simple error - based learning rule perform near - optimal probabilistic inference in nine common psychophysical tasks . in a probabilistic categorization task , error - based learning in a generic network simultaneously accounts for a monkey s learning curve and for the evolution of qualitative aspects of its choice behavior . in all tasks , the number of neurons required for a given level of performance grows sub - linearly with the size of the input population , a substantial improvement on previous implementations of probabilistic inference using hand - crafted neurons . the trained networks develop a novel sparsity - based probabilistic population code in a task - dependent manner . the tractability of the investigated tasks allows us to mechanistically understand the nature of this code . our results suggest that probabilistic inference emerges naturally in generic neural networks trained with error - based learning rules and that these types of networks can be used as simple plausible neural models of probabilistic inference ."}
{"article_id":"1103.2308","section_id":"i","document":"carbon nanotubes ( cnts ) have been the focus of intense study in the last decades as they exhibit remarkable properties that make them good candidates for molecular electronic devices . @xcite lately their application as building blocks in spintronics has also been addressed . @xcite nonetheless the importance of spin - orbit coupling in these systems has been for a long time underestimated . the spin - orbit interaction ( soi ) was believed to be very weak , due to the low atomic number @xmath0 of carbon . as a result spin degenerate states were assumed . only recently it was proven experimentally  @xcite that in the spectrum of ultraclean cnts the effects of this coupling between spin and orbital degrees of freedom are clearly visible . this observation is in agreement with previous theoretical predictions  @xcite which argued that soi could be significant in cnts owing to their curvature . understanding the effects of this coupling on the spectrum of cnts is essential for the successful manipulation of the different degrees of freedom of these systems . signatures of spin - orbit coupling in the magnetic field dependence of the spectrum have been further identified in measurements  @xcite of relaxation and dephasing times in a cnt quantum dot and more recently in magnetoconductance experiments  @xcite performed on open cnt - wires , showing a double - peak feature caused by a spin splitting of the conduction bands due to the soi . the observed spin - orbit energy splitting is compatible with previous experimental and theoretical values  @xcite and further supports the relevance of spin - orbit effects in these systems . moreover new transport measurements  @xcite in cnt quantum dots with magnetic fields both parallel and perpendicular to the nanotube serve to analyze the influence of soi also in the cotunneling regime . the application of a parallel magnetic field modulates the distribution of the electronic spectrum of nanotubes ,  @xcite as has been confirmed experimentally in several optical and transport measurements . @xcite further theoretical studies  @xcite reveal that the transport properties are directly related to the magnetic - field modulated density of states . the soi -modified band structure and its implications on the electronic properties of cnts in a magnetic field has been in the focus of extensive theoretical work  @xcite . however , at present only few theoretical works exist  @xcite which investigate quantum transport through cnts including magnetic field , curvature and soi effects . in this paper we analyze the transport properties of finite - size carbon nanotubes in a parallel magnetic field in the regime of strong nanotube - lead coupling , using a tight - binding hamiltonian for the nanotube system and green function techniques . @xcite a magnetic field parallel to the tube axis is included via the aharonov - bohm phase and zeeman effect , and we take into account the spin - orbit coupling , which is responsible for the appearance of a spin - splitting and of spin - flip processes . the spin - splitting may allow for preparation of states with controlled spin and valley ( the so - called isospin ) degrees of freedom . the inclusion of the soi and the magnetic field leads furthermore to the breaking of the electron - hole symmetry , as we notice in our analysis of these systems . without an electron - hole symmetry spin - up and spin - down states may cross the fermi energy at different magnetic fluxes giving rise to peaks in the magnetoconductance corresponding to spin - polarized currents around the fermi energy similar to those experimentally observed in ref .   and as identified in the present work .    for zigzag and chiral nanotubes the finite size of the systems leads to a localization of the states in the magnetic field with a consequent suppression of current . @xcite we show that , as a consequence of the soi , this localization starts at a threshold value of the magnetic field which is different for the two spin species . this value can be further tuned with the chirality , radius or length of the tube , allowing for controlled polarized states . furthermore we find that numerical transport calculations in finite - size cnts are to a very good extent reproduced by using an analytical model hamiltonian in the reciprocal space . the proper boundary conditions are crucial for the understanding of finite - size effects . the analytical approach provides as well a fundamental insight into the nature of the states taking part in the transport processes . part of the discussion on localization was presented in abridged form in ref .  . the scope of the present work is to analyze various consequences of soi on the transport characteristics of cnts strongly coupled to leads . the paper is organized as follows . in sec . [ sec_theory ] we introduce the tight - binding approach that we use for modelling our system , where we keep the interactions to nearest neighbors only because , despite its simplicity , this approximation is known to provide a good agreement with experiments . @xcite our original tight - binding hamiltonian is modified to consecutively include the effects of an applied axial magnetic field , the curvature of the nanotube and the spin - orbit coupling . starting from this generalized tight - binding model for the real - space description of the cnts , an effective hamiltonian for the @xmath1 bands is obtained , which is formally the same as the one derived previously by other groups . @xcite this hamiltonian will allow us in sec . [ sec_model : dispersion_bc ] to make predictions for the energy spectrum when taking into account the boundary conditions to be satisfied at the cnt ends . finally the transport calculations are shown and discussed in sec . [ sec_numerical_transp]-[sec_numerical_pol ] . an analysis of the contribution to the cnt conductance properties of the different effects under consideration is carried out in sec . [ sec_numerical_transp ] , followed by a comparison of numerical and analytical results and an examination of the localization in the magnetic field of previously extended states in sec . [ sec_numerical_loc ] . the great potential of these cnt systems for their use in spintronics is demonstrated in sec . [ sec_numerical_pol ] , where the spin - polarized currents at small bias voltages are investigated . a summary of the main results is found in sec . [ sec_concl ] .","summary":"the transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated . upon including spin - orbit coupling and curvature effects , two main phenomena are analyzed which crucially depend on the tube s chirality : i ) finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states .","abstract":"the transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated . upon including spin - orbit coupling and curvature effects , two main phenomena are analyzed which crucially depend on the tube s chirality : i ) finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states . this phenomenon occurs due to the magnetic - field dependent open boundary conditions obeyed by the carbon nanotube s wave functions . the transport is fully suppressed above threshold values of the magnetic field which depend on the nanotube chirality , length and on the spin - orbit coupling . ii ) reversible spin polarized currents can be obtained upon tuning the magnetic field , exploiting the curvature - induced spin - orbit splitting ."}
{"article_id":"1103.2308","section_id":"c","document":"we have calculated the energy spectrum and transport properties of finite carbon nanotubes under a parallel magnetic field , including spin - orbit interactions . the spin - orbit coupling was treated following the approach of ando ,  @xcite but the spin quantization axis has been chosen parallel to the magnetic field to conveniently incorporate its effects . the mixing of the @xmath1 and @xmath63 orbitals , due to the curvature of the nanotube , is automatically taken into account by this approach . we derived an analytical formula for the energy spectrum of these systems , which provides a very good matching to the numerical calculations in its limits of validity , _ i.e.  _ for large enough radii to justify the approximations made . for radii of about 0.4 nm the agreement is already over 90% . this analytical formula can be applied to finite - size systems if the proper boundary conditions are imposed . the very good results of this approach allow us to use it as a powerful tool to gain insight into the numerical results , as we can identify the composition of the states in the energy spectrum without the highly costly numerical calculation of the eigenstates . we can furthermore vary the length of the central system at no computational cost . the analysis of the transport properties ( _ e.g .  _ the @xmath186 characteristics ) shows a mechanism of localization in chiral and zigzag nanotubes in a parallel magnetic field . the magnetic field modifies the boundary conditions , causing hitherto extended states to localize near the ends of the tubes . this localization is gradual and initially the states involved are still conducting . but at a critical value of the magnetic field , which depends on the nanotube chirality and length , the localization is complete and the transport is then suppressed . furthermore the soi together with the zeeman effect introduces a spin - splitting that breaks the electron - hole symmetry and allows the separation of polarized states . by exploiting this effect we achieve spin polarized currents across the system . the magnetic field can thus be used as a tool for controlling the spin and isospin of the current through the cnt . this work was partially funded by the _ deutsche forschungsgemeinschaft _ under the program grk1570 .","summary":"the transport is fully suppressed above threshold values of the magnetic field which depend on the nanotube chirality , length and on the spin - orbit coupling .","abstract":"the transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated . upon including spin - orbit coupling and curvature effects , two main phenomena are analyzed which crucially depend on the tube s chirality : i ) finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states . this phenomenon occurs due to the magnetic - field dependent open boundary conditions obeyed by the carbon nanotube s wave functions . the transport is fully suppressed above threshold values of the magnetic field which depend on the nanotube chirality , length and on the spin - orbit coupling . ii ) reversible spin polarized currents can be obtained upon tuning the magnetic field , exploiting the curvature - induced spin - orbit splitting ."}
{"article_id":"1103.0328","section_id":"i","document":"infrared dark clouds ( irdcs ) are dense , cold molecular clouds seen in silhouette against 8  @xmath3 m  galactic plane pah emission . dust is relatively transparent to 8  @xmath3 m  emission , so only the densest parts of molecular clouds ( a@xmath10 @xmath11 ) are opaque at this wavelength @xcite . since massive stars and their associated clusters form in massive and dense concentrations of dust and gas , it follows that the initial conditions of massive star formation are probably found in the highest density regions of molecular clouds . the glimpse team imaged about two - thirds of the inner galactic plane @xmath12 using the _ spitzer space telescope ( sst ) _ infrared array camera ( irac ) at 3.6 , 4.5 , 5.8 , and 8  @xmath3 m  with better than @xmath13 resolution @xcite . the glimpse images contain thousands of irdcs @xcite with structure on size scales @xmath14 to as small as the irac resolution ( see figure  [ 3col19 ] ) . because they are prominent in silhouette , irdcs are generally expected to lie at the near kinematic distance . preliminary studies show that irdcs are cold ( @xmath15  k ) and dense ( @xmath16  @xmath17 ) , and many have masses @xmath18  m@xmath8 @xcite . @xcite detected high deuteration in irdc clumps , evidence of very low temperatures . however , the details of the kinematics , chemistry , and star formation within irdcs are not well understood . high resolution observations of irdcs are needed to provide information on scales small enough to differentiate between cloud properties in quiescent and star forming regions , a distinction crucial to refining models of the earliest stages of massive star formation @xcite .    here we report results of a detailed study of an irdc at radio wavelengths using the very large array ( vla ) of the national radio astronomy observatory . irdc g19.30 + 0.07 ( @xmath19(j2000)=18@xmath2025@xmath2156@xmath22 , @xmath23(j2000)=@xmath2412@xmath250430 , v@xmath26  km  s@xmath27 ) is a filamentary irdc with a length of @xmath28  and a width of @xmath9 . using a flat galactic rotation curve with r@xmath29  kpc and v@xmath30  km  s@xmath27 , the kinematic distance to g19.30 + 0.07 is @xmath31  kpc . we have determined the physical and chemical properties of g19.30 + 0.07 using ammonia ( nh@xmath0 ) ( 1,1 ) , ( 2,2 ) , and dicarbon sulfide ( ccs ) ( @xmath1 ) transitions ( upper level energies ( @xmath32 ) of 23.8  k , 65.0  k , and 1.6  k respectively ) with an angular resolution roughly a factor of seven higher than previously reported for this irdc , 6compared to @xmath33  @xcite . to relate the gas properties to star formation , continuum observations at 8.4 ghz have been carried out to search for ionized gas associated with hiiregions in the irdc . nh@xmath34 and ccs are important molecules for investigating irdcs : both are typically considered to be high - density tracers ( @xmath35  @xmath17 ) , and the relative strengths of nh@xmath0 inversion lines can be used to estimate the temperature and column density of the gas @xcite . furthermore , [ ccs]/[nh@xmath0 ] relative abundances may provide information about chemical evolution @xcite . chemical models have mainly been developed from observations of low mass star forming regions ; this study examines whether such models might also apply in irdcs near young star forming clumps . the main goal of this paper is to examine the physical and chemical properties of the irdc g19.30 + 0.07 and explore the relationship between these properties and signs of star formation . the high spatial and spectral resolution of this study permits us to distinguish between multiple velocity components in the irdc , map the temperature and density distributions in the irdc at 6  resolution , and examine the relative distribution of two gas species in the irdc . this is one of the first irdc studies to explore the role of multiple cloud components , distinguished by small offsets in velocity , within an irdc . furthermore , evidence for star formation and outflows in g19.30 + 0.07 enables us to examine the relationship between irdc properties and star formation . this paper is structured as follows : in  2 , we present details of our vla observations and data reduction . in  3 , we present results of the nh@xmath0 , ccs , and continuum observations . in  4 we examine the gas kinematics and present the derived temperature , density , and mass distributions , as well as relative abundances of nh@xmath0 and ccs in the irdc . in  5 we discuss the relationship between physical and chemical properties , kinematics , and star formation within the irdc . conclusions are given in  6 .","summary":"this spatial distribution is consistent with theories of evolution for chemically young low - mass cores , in which ccs has not yet been processed to other species and/or depleted in high - density regions .","abstract":"we present very large array observations of ammonia ( nh ) ( 1,1 ) , ( 2,2 ) , and ccs ( ) emission toward the infrared dark cloud ( irdc ) g19.30 + 0.07 at  ghz . the nh emission closely follows the 8  m  extinction . the nh ( 1,1 ) and ( 2,2 ) lines provide diagnostics of the temperature and density structure within the irdc , with typical rotation temperatures of to 20  k and nh column densities of  . the estimated total mass of g19.30 + 0.07 is  m . the cloud comprises four compact nh clumps of mass to 160  m . two coincide with 24 memission , indicating heating by protostars , and show evidence of outflow in the nh emission . we report a water maser associated with a third clump ; the fourth clump is apparently starless . a non - detection of 8.4  ghz emission suggests that the irdc contains no bright hiiregions , and places a limit on the spectral type of an embedded zams star to early - b or later . from the nh emission we find g19.30 + 0.07 is composed of three distinct velocity components , or  subclouds . \" one velocity component contains the two 24  m  sources and the starless clump , another contains the clump with the water maser , while the third velocity component is diffuse , with no significant high - density peaks . the spatial distribution of nh and ccs emission from g19.30 + 0.07 is highly anti - correlated , with the nh predominantly in the high - density clumps , and the ccs tracing lower - density envelopes around those clumps . this spatial distribution is consistent with theories of evolution for chemically young low - mass cores , in which ccs has not yet been processed to other species and/or depleted in high - density regions ."}
{"article_id":"1103.0328","section_id":"r","document":"the nh@xmath0 ( 1,1 ) main line emission , integrated over 24.1 to 30.3  km  s@xmath27 , is shown overlaid on an infrared 3-color spitzer image of g19.30 + 0.07 in fig . [ 3col19 ] . the three colors in fig . [ 3col19 ] are glimpse 4.5  @xmath3 m  ( blue ) and 8  @xmath3 m  ( green ) emission and mipsgal @xcite 24  @xmath3 m  emission ( red ) . [ 3col19 ] shows that the nh@xmath0 ( 1,1 ) emission is spatially well correlated with the 8  @xmath3 m  extinction . nh@xmath0 ( 2,2 ) emission was also detected throughout the irdc , although due to the fainter line emission the ( 2,2 ) emission was not as well defined near the irdc boundaries . the rms noise in the nh@xmath0 ( 1,1 ) integrated intensity image is 5  mjy  beam@xmath27  km  s@xmath27 .    in our discussions of irdc structure , we use the guidelines described by @xcite : _ clouds _ have masses of @xmath45 to 10@xmath46  m@xmath8 and radii of @xmath47 to 10  pc , _ clumps _ have masses of @xmath48 to 10@xmath49  m@xmath8 and radii of @xmath50 to 1  pc , and _ cores _ have masses of @xmath47 to 10@xmath51  m@xmath8 and radii of @xmath52 to 0.1  pc . clumps produce star clusters , and cores produce individual stars . a 20  fwhm gaussian unsharp mask was used to identify the compact structure in g19.30 + 0.07 . the selection criteria for nh@xmath0 clumps were peaks having structure @xmath53 with integrated intensities @xmath54  jy  beam@xmath27  km  s@xmath27  in the masked image . g19.30 + 0.07 contains four apparent nh@xmath0 clumps , labeled in fig . [ 3col19 ] as c1 , c2 , c3 , and c4 . c1 and c2 coincide with 24  @xmath3 m  emission and have previously been studied at mm wavelengths with @xmath55 resolution @xcite . c3 is not associated with any 24  @xmath3 m  emission ; however , a h@xmath43o maser is located nearby ( see  3.4 ) . c4 is an nh@xmath0 emission peak not associated with any ir emission or masers . the 24  @xmath3 m  source s1 ( fig . [ 3col19 ] ) is not coincident with a peak in the nh@xmath0 emission . there is a h@xmath43o maser with velocity 19  km  s@xmath27  @xcite spatially coincident with s1 . this maser s velocity is slightly offset from the velocity of g19.30 + 0.07 , @xmath56  km  s@xmath27 . while it is possible that the maser is associated with an unrelated object along the line of sight , the probability of two dense cores capable of forming a h@xmath43o maser along the line of sight to s1 is small . it is more probable that the velocity offset between the maser and the irdc is caused by motion within the irdc related to star formation activity @xcite . multiple velocity components and broad line - wing structures are evident in the nh@xmath0 emission , as shown in figure  [ profile ] . double - line profiles indicate locations in the cloud where there are two overlapping kinematic components . the double - line profile features can not be attributed to self - absorption : as demonstrated in fig . [ profile]b , the double - line profile structure is seen in the more optically thin ( 2,2 ) emission as well as the ( 1,1 ) emission . furthermore , the double - line profiles are not correlated with nh@xmath0 high optical depth ( see  4.2 ) . finally , the individual components of the double - line profiles can be traced continuously from regions with single - line profiles at the same velocity ; it is in overlap regions that they appear double , as illustrated by the profiles shown in fig . [ profile ] . there are three distinct velocity components over the entire g19.30 + 0.07 dark cloud , which we will henceforth refer to as  subclouds . \" the spatial extents of these subclouds are derived from fits to the nh@xmath0 line profiles , as described in  4.1 . the subcloud positions relative to the 8  @xmath3memission are shown in fig .  [ profile ] .      where both ccs and nh@xmath0 emission is detected their velocities match very well . however , in many locations there is emission from one molecule and not the other . figure  [ ccs ] shows the distribution of the ccs and the nh@xmath0 ( 1,1 ) main line emission along with representative ccs profiles ; peaks in the ccs emission have been labeled as p1-p5 . the ccs in fig . [ ccs ] is integrated over four channels ( 1.2  km  s@xmath27 ) centered on the velocities of the subclouds as determined from the nh@xmath0 emission . the nh@xmath0 emission in figure  [ ccs ] has been smoothed to match the resolution of the ccs emission ( @xmath39 ) and integrated over the same velocity ranges . the rms noise in the ccs integrated intensity images is 1.3  mjy  beam@xmath27  km  s@xmath27 . no 8.4  ghz continuum emission is detected from g19.30 + 0.07 . the rms noise in the field is 0.025  mjy  beam@xmath27 . a 5@xmath57 ( 0.125  mjy ) upper limit on any free - free continuum emission implies an upper limit on the uv photon flux of @xmath58  s@xmath27 @xcite . however , it is unlikely that all of the emitted uv photons go into ionization of h and he . the uv flux could be reduced by absorption by an accretion disk or dust surrounding the protostar . thus , the uv flux limit is likely an underestimate of @xmath59 . furthermore , early - stage hii  regions can be small , dense , and optically thick , and consequently have low radio continuum flux densities . further discussion of the protostellar mass limit implied by the uv flux limit is given in  5.3 .      from our re - reduction and analysis of the @xcite h@xmath43o maser data we have detected two regions of maser emission . a previously unreported maser with a peak flux density of 1.58  jy was detected at @xmath19(j2000)=18@xmath2025@xmath2151.95@xmath22 , @xmath23(j2000)=@xmath2412@xmath6005140 at an lsr velocity of 28.8  km  s@xmath27 . this maser is located within the c3 ammonia clump ( fig . [ 3col19 ] ) , and is the first reported evidence of star formation associated with this clump . the second h@xmath43o maser , first reported in @xcite , has a peak flux density and velocity of 0.51  jy and 19.0  km  s@xmath27 , respectively , at a position of @xmath19(j2000)=18@xmath2025@xmath2158.64@xmath22 , @xmath23(j2000)=@xmath2412@xmath6004215 . this maser is located close to the 24  @xmath3 m  source s1 . the reported peak flux densities have been corrected for primary beam attenuation .","summary":"the nh emission closely follows the 8  m  extinction . the cloud comprises four compact nh clumps of mass to 160  m . two coincide with 24 memission , indicating heating by protostars , and show evidence of outflow in the nh emission . we report a water maser associated with a third clump ; the fourth clump is apparently starless .","abstract":"we present very large array observations of ammonia ( nh ) ( 1,1 ) , ( 2,2 ) , and ccs ( ) emission toward the infrared dark cloud ( irdc ) g19.30 + 0.07 at  ghz . the nh emission closely follows the 8  m  extinction . the nh ( 1,1 ) and ( 2,2 ) lines provide diagnostics of the temperature and density structure within the irdc , with typical rotation temperatures of to 20  k and nh column densities of  . the estimated total mass of g19.30 + 0.07 is  m . the cloud comprises four compact nh clumps of mass to 160  m . two coincide with 24 memission , indicating heating by protostars , and show evidence of outflow in the nh emission . we report a water maser associated with a third clump ; the fourth clump is apparently starless . a non - detection of 8.4  ghz emission suggests that the irdc contains no bright hiiregions , and places a limit on the spectral type of an embedded zams star to early - b or later . from the nh emission we find g19.30 + 0.07 is composed of three distinct velocity components , or  subclouds . \" one velocity component contains the two 24  m  sources and the starless clump , another contains the clump with the water maser , while the third velocity component is diffuse , with no significant high - density peaks . the spatial distribution of nh and ccs emission from g19.30 + 0.07 is highly anti - correlated , with the nh predominantly in the high - density clumps , and the ccs tracing lower - density envelopes around those clumps . this spatial distribution is consistent with theories of evolution for chemically young low - mass cores , in which ccs has not yet been processed to other species and/or depleted in high - density regions ."}
{"article_id":"1103.0328","section_id":"c","document":"we examined the stability of c1 , c2 , c3 , and c4 by comparing their gas mass to their virial masses . the virial mass ( @xmath149 ) is the mass at which thermal plus turbulent gas pressure balances gravitational forces in the clumps , i.e. , the gravitational and kinetic energy are in equipartition . the ratio of virial mass and clump mass ( @xmath150 ) is a basic indicator of whether the clumps are gravitationally bound and likely to collapse : if @xmath151 , the clump contains enough mass to collapse under gravity . this balance analysis assumes negligible contributions to clump stability from additional forces such as magnetic fields and clump rotation , neither of which are known for the clumps in g19.30 + 0.07 . additionally , clump confinement by external pressure @xcite has not been included . we calculated @xmath149 from the clump radius ( @xmath152 , determined in  4.4 ) and the nh@xmath0 fwhm linewidth ( @xmath105 ) using    @xmath153    the nh@xmath0 ( 1,1 ) fwhm linewidth was measured at the density peak of the clumps . values of @xmath105 , @xmath149 , and @xmath150 are listed in table  [ clumps ] . the clumps all have @xmath154 , inconsistent with indications of star formation that imply the clumps are undergoing gravitational collapse . however , equation 8 assumes virial equilibrium . if the clumps have already collapsed and harbor outflows the conditions of virial equilibrium are violated , and the linewidths will not accurately predict the thermal and turbulent motion supporting the clumps . indeed , clumps c1 , c2 , and c3 show evidence of outflow through either broad nh@xmath0 linewidths or h@xmath43o masers . clump c4 has @xmath155 ; this high ratio may be a result of increased linewidths toward c4 caused by the outflow originating from c2 ( see  4.1 ) . it is also worth noting that where the cores are optically thick the @xmath105 may be overestimated , which would lead to a greater overestimate of virial mass ( which is proportional to @xmath156 ) than of clump mass ( which is proportional to @xmath105 ) . the virial masses of c1 and c2 reported by @xcite are 893 and 823 @xmath157 , significantly larger than our @xmath149 values . @xcite used larger clump radii and higher linewidths in their virial mass calculations because of the lower resolution of their study ( 40 ) . our higher resolution shows most of the mass is contained within a smaller radius than previously thought . furthermore , we were able to resolve velocity gradients in the emission near the clumps ( fig . [ velcombo ] ) . the larger beam used by @xcite would have confused this emission , contributing to their larger linewidth measurements . chemical evolution models comparing ccs and nh@xmath0 distributions have mainly been developed from observations of low mass star forming regions and the environs of hii  regions ; we now examine whether such models might also apply in irdcs . chemical models such as those of @xcite , @xcite , and @xcite predict that ccs traces chemically young gas in lower density , quiescent envelopes of molecular clouds , while nh@xmath0 traces dense , evolved clumps . time - dependent gas - phase modeling suggests that for low - mass star - forming clumps the [ ccs]/[nh@xmath0 ] abundance ratio is a measure of the age of clumps , i.e. , a `` chemical clock '' : ccs abundance peaks in chemically young gas and decreases as the ccs components are reprocessed into molecules with stronger binding energies , such as co. @xcite and @xcite propose ccs is reprocessed on timescales of @xmath158  years , while de gregorio - monsalvo et al . ( 2005 , 2006 ) concluded that ccs has a lifetime of @xmath159 years after the onset of star formation . freeze - out onto dust grains likely plays a significant role in chemical changes during clump evolution . dust grain chemistry is particularly important for explaining the high abundances of nh@xmath0 observed in dense clumps @xcite . when co freezes out onto dust grains the abundance of nh@xmath0 is enhanced , because gas - phase co destroys nh@xmath0 parent molecules @xcite . furthermore , the abundance of hydrogenated molecules , including nh@xmath0 , may be enhanced as ices evaporate off dust grains @xcite near hot clumps in star - forming regions . freeze - out of ccs onto dust grains may also be responsible for low ccs abundances in gas clumps where @xmath160  @xmath17  @xcite . dust grain chemistry also explains how the chemical clock may be reset . @xcite propose collisions in gas with properties similar to irdc subclouds can trigger mhd waves and/or grain impacts that provide sufficient energy for thermal desorption of molecules from grain surfaces , leading to the presence of early - time molecules like ccs . the critical densities of the nh@xmath0 ( 1,1 ) and ccs ( @xmath1 ) emission lines differ by almost two orders of magnitude , @xmath161  @xmath17for nh@xmath0 @xcite and @xmath75  @xmath17  for ccs @xcite , which can complicate the interpretation of molecular distribution . however , despite its higher critical density , we detect ccs emission in the lower density envelopes around the high - density nh@xmath0 clumps rather than toward the center of the dense clumps , suggesting their spatial distributions are the result of chemical evolution in the irdc rather than a density effect . previous studies of the chemistry in g19.30 + 0.07 have been limited by poor resolution . prior to this investigation , @xcite observed g19.30 + 0.07 in nh@xmath0 emission using the effelsberg 100  m telescope with 40  resolution , but lacked the resolution needed to comment on small - scale structure . @xcite observed n@xmath43h@xmath162(10 ) , hc@xmath0n(54 ) , ccs(4@xmath03@xmath43 ) , ch@xmath0oh(76 ) , and nh@xmath0 ( 1,1 ) , ( 2,2 ) , and ( 3,3 ) emission towards the clumps in g19.30 + 0.07 with the nro 45-m telescope ( hpbw @xmath138  for ccs and @xmath163for nh@xmath0 ) . @xcite report abundances suggesting the clumps in g19.30 + 0.07 are more chemically evolved than low - mass starless cores . the high spatial resolution data we present here improve upon these findings by showing how morphology , temperature , and density structure in the irdc impact the distributions of the nh@xmath0 and ccs . [ ccs ] shows the integrated ccs emission in each of the subclouds and compares it to the nh@xmath0 integrated emission . although ccs emission is associated with the subclouds at 25.7  km  s@xmath27 , 26.7  km  s@xmath27 , and 28.4  km  s@xmath27 , the spatial distribution of the ccs and nh@xmath0 emission are not coincident . enhancements in the ccs with clump - like morphology are labeled as p1 to p5 in fig . [ ccs ] ; no evidence of nh@xmath0 clumps exist at these locations . typical ccs column densities ranged from @xmath133  @xmath6  to @xmath164  @xmath6 . we examined the [ ccs]/[nh@xmath0 ] column density ratio in areas with detectable emission from at least one of the molecules . in ccs peaks lacking detectable nh@xmath0 emission we assign an nh@xmath0 column density upper limit of @xmath113  @xmath6 . where nh@xmath0 but not ccs was detected we assign a ccs column density upper limit of @xmath133  @xmath6 . at clumps c1 , c2 , c3 , and c4 the [ ccs]/[nh@xmath0 ] ratio is @xmath165 , slightly higher than the upper limit determined by @xcite , and consistent with active , star forming clumps @xcite . at ccs emission peaks , [ ccs]/[nh@xmath0 ] ratios are @xmath166 , consistent with results from @xcite , who found [ ccs]/[nh@xmath0 ]  @xmath167 in low - mass starless clumps . a map of the column density ratios is shown in figure [ ratio ] .    comparing fig . [ ratio ] with fig . [ ccs ] shows that p1 is associated with the [ ccs]/[nh@xmath0 ] peak and located in the subcloud located at 25.7  km  s@xmath27 , the only subcloud lacking evidence of star formation . the ccs morphology and [ ccs]/[nh@xmath0 ] ratio in this subcloud are consistent with a chemically young clump in a stage too early to present evidence of star formation @xcite . the ccs peaks p2 , p4 , and p5 are located at subcloud interfaces , and p3 is spatially coincident with the outflow from c2 . the spatial coincidence of these ccs peaks with subcloud - subcloud and outflow - subcloud interfaces indicates collisions may be resetting the chemical clock of the gas at these locations , consistent with the @xcite model . one major caveat must be considered in the analysis of ccs emission . ccs ( @xmath1 ) is a low - lying energy state transition ( upper energy level only 1.6  k above ground ) , so it is difficult to know whether enhanced ccs emission is due to excitation effects or increased abundance . using the results of @xcite we were able to roughly constrain the ccs excitation temperature to @xmath142  k. however , the ccs ( @xmath168 ) observations were low resolution and only provided a column density upper limit . additional transitions of ccs must be measured at comparable resolution to this study to more accurately determine the ccs excitation temperature . sensitive interferometric observations at millimeter wavelengths could explore whether the abundance measurements in the ground state are consistent with abundances measured from higher energy transitions . we draw the following conclusions from the ccs detections : ( 1 ) ccs and nh@xmath0 are present in each of the three subclouds comprising g19.30 + 0.07 , but each molecule traces different parts of the subclouds ; ( 2 ) ccs appears to trace the boundaries of the irdc while nh@xmath0 peaks in the inner parts of the irdc , consistent with ccs enhancement in low - density envelopes and nh@xmath0 enhancement in denser clumps , in spite of the fact that the ccs transition has the higher critical density . this emphasizes that nh@xmath0 does not give the full picture of the dense gas in star - forming regions ; ( 3 ) in some cases , ccs appears to have clump - like morphology . the [ ccs]/[nh@xmath0 ] peak at p1 is located in the only subcloud lacking evidence of star formation . this supports the hypothesis that ccs cores may represent the very earliest stages of core formation ; ( 4 ) ccs peaks at subcloud - subcloud or outflow - subcloud interfaces may indicate collisions are resetting the chemical clock in some parts of the irdc ; and ( 5 ) further investigations at higher - energy transitions are needed to distinguish excitation and abundance effects in ccs emission . although early studies of g19.30 + 0.07 did not find any evidence of star formation @xcite , recent investigations , including this one , indicate substantial active star formation in this irdc . the observed evidence for star formation is : ( 1 ) archival mipsgal 24  @xmath3mobservations showing areas of hot dust associated with c1 , c2 , and s1 ; ( 2 ) structure in the nh@xmath0 spectral line observations consistent with outflows originating from c1 and c2 ; ( 3 ) h@xmath43o masers coincident with c3 and s1 ( fig . [ 3col19 ] ) . no 8.4  ghz continuum emission was detected in the irdc . a 5@xmath57 detection limit of 0.125  mjy  beam@xmath27 sets the upper limit of the uv photon flux at @xmath169  s@xmath27 , implying a stellar type of b3 or later @xcite . however , if the protostar is accreting material , much of the stellar uv radiation will be absorbed close to the star @xcite . also , in an irdc it is likely that some uv photons are absorbed by dust . thus , stars with types hotter than b3 could be present in g19.30 + 0.07 but be undetected by our measurements . in fact , orion source i , an early - b star with mass @xmath170  m@xmath8 @xcite , has an 8.4  ghz flux density of @xmath171  mjy @xcite at a distance of @xmath146  pc @xcite . if orion source i were located at the distance of g19.30 + 0.07 , 2.4  pc , its flux density would be only @xmath172  mjy , below the detection limit of this study . clump masses of @xmath173  m@xmath8 and the presence of outflows suggest that c1 and c2 may be protoclusters . using the initial mass function from @xcite and assuming a 50% star forming efficiency , these clumps would form stars up to masses of @xmath174  m@xmath8 . the smaller nh@xmath0 clump and h@xmath43o maser without accompanying 24  @xmath3memission at c3 suggest c3 likely contains protostars that are either lower - mass or younger than those in c1 and c2 . the 24  @xmath3 m  emission toward s1 suggests the presence of at least one protostar , consistent with the h@xmath43o maser coincident with s1 . it may be s1 is more evolved than c1 and c2 , and has destroyed or dispersed any dense gas associated with its formation . however , no shell of dispersed nh@xmath0 is detected around s1 . assuming the linewing structure discussed in  4.2 indicates outflows , the outflow masses provide insight into the masses of the stars contained in c1 and c2 . the column densities in the outflows were determined as in equations 6 and 7 , using the integrated emission from the nh@xmath0 ( 2,2 ) line - wings and assuming a @xmath129 of 10  k for nh@xmath0 . the column densities were summed over the outflow area to determine the masses of the outflows . the red and blue outflow components of c1 each contain @xmath175  m@xmath8 and the components in c2 each contain @xmath176  m@xmath8 , suggesting intermediate or high mass protostar progenitors . however , we note that nh@xmath0 only traces high density gas , so observations of the low - density gas are needed to better constrain the total outflow masses . various models attempt to explain the formation of massive stars , but recent work suggests accretion in turbulent clumps is the likely creation mechanism @xcite . @xcite present an evolutionary sequence of massive stars starting from high mass starless clumps : low- and intermediate - mass protostars form within the massive starless clumps and accrete matter until becoming a massive protostellar object , which develops into a massive star and clears the natal gas from its environment . c1 and c2 may be examples of clumps containing the embedded accreting protostars proposed in this model .    based on the results from this single irdc , the role that subclouds play in massive protostar and protocluster development is still unclear . they may indicate an early stage of fragmentation , cloud formation / collision , or a superposition along the line of sight . the subclouds appear distinct , but if less dense gas below our detection limits connects the subclouds , they may all be part of a larger structure . further work is needed to understand the role of subclouds in irdcs . understanding the role of irdcs in star formation requires a survey of their properties . we have examined one irdc in great detail , but is g19.30 + 0.07 a typical irdc , and how general are our findings ? our results are consistent with previous studies that indicate g19.30 + 0.07 has temperatures and densities typical for an irdc @xcite . the high resolution of this study compared to previous work has revealed new irdc features . notably , the kinematics have been analyzed in detail . we find that the irdc is composed of three subclouds , each of which has a slightly different velocity . the universality of multiple subclouds in irdcs and the role they play in protocluster evolution requires further investigation .","summary":"we present very large array observations of ammonia ( nh ) ( 1,1 ) , ( 2,2 ) , and ccs ( ) emission toward the infrared dark cloud ( irdc ) g19.30 + 0.07 at  ghz . the spatial distribution of nh and ccs emission from g19.30 + 0.07 is highly anti - correlated , with the nh predominantly in the high - density clumps , and the ccs tracing lower - density envelopes around those clumps .","abstract":"we present very large array observations of ammonia ( nh ) ( 1,1 ) , ( 2,2 ) , and ccs ( ) emission toward the infrared dark cloud ( irdc ) g19.30 + 0.07 at  ghz . the nh emission closely follows the 8  m  extinction . the nh ( 1,1 ) and ( 2,2 ) lines provide diagnostics of the temperature and density structure within the irdc , with typical rotation temperatures of to 20  k and nh column densities of  . the estimated total mass of g19.30 + 0.07 is  m . the cloud comprises four compact nh clumps of mass to 160  m . two coincide with 24 memission , indicating heating by protostars , and show evidence of outflow in the nh emission . we report a water maser associated with a third clump ; the fourth clump is apparently starless . a non - detection of 8.4  ghz emission suggests that the irdc contains no bright hiiregions , and places a limit on the spectral type of an embedded zams star to early - b or later . from the nh emission we find g19.30 + 0.07 is composed of three distinct velocity components , or  subclouds . \" one velocity component contains the two 24  m  sources and the starless clump , another contains the clump with the water maser , while the third velocity component is diffuse , with no significant high - density peaks . the spatial distribution of nh and ccs emission from g19.30 + 0.07 is highly anti - correlated , with the nh predominantly in the high - density clumps , and the ccs tracing lower - density envelopes around those clumps . this spatial distribution is consistent with theories of evolution for chemically young low - mass cores , in which ccs has not yet been processed to other species and/or depleted in high - density regions ."}
{"article_id":"1410.4373","section_id":"i","document":"the current development of mobile and wireless technologies enables direct _ ad hoc _ communication between various kinds of mobile entities , such as vehicles , smartphones , terrestrian robots , flying robots , or satellites . in all these contexts , the set of communication links depends on distances between entities , thus the network topology changes continuously as the entities move . not only changes are frequent , but in general they even make the network partitionned . clearly , the usual assumption of connectivity does not hold here , although another form of connectivity is often available over time and space ( temporal connectivity ) . also , the classical view of a network whose dynamics corresponds to _ failures _ is no longer suitable in these scenarios , where dynamics is the norm rather than the exception . this induces a shift in paradigm that strongly impacts algorithms . in fact , it even impacts the problems themselves . what does it mean , for instance , to elect a leader in such a network ? is the objective to distinguish a unique global leader , whose leadership then takes place over time and space , or is it to _ maintain _ a leader in each connected component , so that the decisions concerning each component are taken quickly and locally . the same remark holds for spanning trees . should an algorithm construct a unique , global tree whose logical edges survive intermittence , or should it build and maintain a _ forest _ of trees that strive to cover collectively all components in each instant ? both viewpoints make sense , and so far , were little studied in distributed computing ( see e.g.  @xcite for temporal trees , @xcite for maintained trees ) . we focus on the second interpretation , which reflects a variety of scenarios where the expected output of the algorithm should relate to the _ immediate _ configuration ( _ e.g. _ direct social networking , swarming of flying robots , vehicles platooning on the road ) . a particular feature of this type of algorithms is that they never terminate . more significantly , in highly dynamic networks , they are not even expected to stabilize to an optimal state ( here , a single tree per component ) , unless the changes stop , which never happens . this precludes , in particular , all approaches whereby the computation of a new solution requires the previous computation to have completed . this paper is an attempt to understand what can still be computed ( and guaranteed ) when no assumptions are made on the network dynamics : neither on the rate of change , nor on their simultaneity , nor on global connectivity . in other words , the topology is controlled by an almighty adversary . in this seemingly chaotic context , we present an algorithm that strives to maintain as few trees per components as possible , while always guaranteeing some properties . several works have addressed the spanning tree problem in dynamic networks , with different goals and assumptions . burman and kutten  @xcite and kravchik and kutten  @xcite consider a self - stabilizing approach where the legal state corresponds to having a ( single ) minimum spanning tree and the faults are topological changes . the strategy consists in recomputing the entire tree whenever changes occur . this general approach , sometimes called the `` blast away '' approach , is meaningful if stable periods of time exist , which is not assumed here . many spanning tree algorithms rely on random walks for their elegance and simplicity , as well as for the inherent localized paradigm they offer . in particular , approaches that involve multiple coalescing random walks allow for uniform initialization ( each node starts with the same state ) and topology independence ( same strategy whatever the graph ) . pionneering studies involving such processes include bar - ilan and zernik  @xcite ( for the problem of election and spanning tree ) , israeli and jalfon  @xcite ( mutual exclusion ) , and chapter 14 of aldous and fill  @xcite ( for general analysis ) . the principle of using coalescing random walks to build spanning trees in mildly dynamic networks was used by baala et al . @xcite and abbas et al . @xcite , where tokens are annexing territories gradually by capturing each other . regarding dynamicity , both algorithms require the nodes to know an upper bound on the cover time of the random walk , in order to regenerate a token if they are not visited during a long - enough period of time . besides the strength of this assumption ( akin to knowing the number of nodes @xmath0 , or the size of components in our case ) , the efficiency of the timeout approach decreases dramatically with the rate of topological changes . in particular , if they are more frequent than the cover time ( itself in @xmath1 ) , then the tree is constantly fragmented into `` dead '' pieces that lack a root , and thus a leader . another algorithm based on random walks is proposed by bernard et al . @xcite . here , the tree is constantly redefined as the token moves ( in a way that reminds the snake game ) . since the token moves only over present edges , those edges that have disappeared are naturally cleaned out of the tree as the walk proceeds . hence , the algorithm can tolerate failure of the tree edges . however it still suffers from detecting the disappearance of tokens using timeouts based on the cover time , which as we have seen , suits only slow dynamics .    a recent work by awerbuch et al . @xcite addresses the maintenance of _ minimum _ spanning trees in dynamic networks . the paper shows that a solution to the problem can be updated after a topological change using @xmath2 messages ( and same time ) , while the @xmath3 messages of the `` blast away '' approach was thought to be optimal . ( this demonstrates , incidentally , the revelance of _ updating _ a solution rather than recomputing it from scratch in the case of minimum spanning trees . ) the algorithm has good properties for highly dynamic networks . for instance , it considers as natural the fact that components may split or merge perpetually . furthermore , it tolerates new topological events while an ongoing update operation is executing . in this case , update operations are enqueued and consistently executed one after the other . while this mechanism allows for an arbitrary number of topological events _ at times _ , it still requires that such burst of changes are only episodical and that the network remains eventually stable for ( at least ) a linear amount of time in the number of nodes , in order for the update operations to complete and thus the logical tree to be consistent with physical reality . all the aforementioned algorithms either assume that _ global update _ operations ( e.g. wave mechanisms ) can be performed contemporaneously , or at least eventually , or that some node can collect _ global information _ about the tree structure . as far as dynamics is concerned , this forbids arbitrary and ever going changes to occur in the network . a purely localized scheme was proposed by casteigts et al . @xcite for the maintenance of a ( non - minimum ) spanning forest in unrestricted dynamic networks , using a coarse grain interaction model inspired from graph relabeling systems  @xcite . it can be described informally as follows . initially every node hosts a token and is the _ root _ of its own individual tree . whenever two roots arrive at the endpoints of a same edge ( see merging rule on figure  [ fig : scheme ] ) , one of them destroys its tokens and selects the other as parent ( _ i.e. _ the trees are merged ) . the rest of the time , each token executes a random walk within its own tree in the search for other merging opportunities ( circulation rule ) . tree relations are flipped accordingly . the fact that the random walk is _ confined _ to the underlying tree is crucial and different from all algorithms discussed above , in which they were free to roam everywhere without restriction . this simple feature induces very attractive properties for highly dynamic networks . in particular , whenever an edge of the tree disappears , the child side of that edge knows instantly that no token remains on its whole subtree . it can thus regenerate a token ( _ i.e. _ become root ) _ instantly _ , without global concertation nor further information collection . as a result , both merging and splitting of trees are managed in a purely localized fashion .    at an abstract graph level , this very simple scheme guarantees that the network remains covered by a spanning forest at any time , in which 1 ) no cycle can ever appear , 2 ) maximal subtrees are always directed rooted trees ( with a token at the root ) , and 3 ) every node always belongs to such a tree , whatever the chaos of topological changes . on the other hand , it is not expected to reach an optimal state where a single tree covers each connected component . even if the network were to stabilize , convergence to the optimum ( though easy to be made certain ) would not be expected to occur fast . whether this general principle could be implemented in a message passing model remained an open question . this paper provides an implementation of the spanning forest principle in the synchronous message - passing model . due to the loss of atomicity and exclusivity in the interaction , the algorithm turns out to be much more sophisticated than its original counterpart . while still reflecting the very same high - level principle , it faces new problems that require conceptual differences . in particular , the original model prevented a node from both selecting a parent and being selected as parent simultaneously , making it easier to avoid cycle creations . one of the ingredients in the new algorithm to circumvent this problem is an original technique ( which we refer to as the _ unique score _ technique ) that consists of maintaining , network - wide , a set of score variables that always remain a permutation of the set of nodes ids . this mechanism allows us to break symmetry and avoid the formation of cycles in a context where ids alone could not . the paper is organized as follows . in section [ sec : model ] , we present the model and notations that we use throughout the paper . then section  [ sec : algorithm ] presents the algorithm , whose correctness analysis is outlined in section  [ sec : correctness ] and detailed in section  [ sec : detailed - proofs ] . section  [ sec : simulation ] presents experimental results that validate our algorithm .","summary":"highly dynamic networks are characterized by frequent changes in the availability of communication links . many of these networks are in general partitioned into several components that keep splitting and merging continuously and unpredictably . we present an algorithm that strives to maintain a forest of spanning trees in such networks , without any kind of assumption on the rate of changes . while the high - level principles of the coarse - grain variant are preserved , the new algorithm turns out to be significantly more complex . in particular , it involves a new technique that consists of maintaining a distributed permutation of the set of all nodes ids throughout the execution . the algorithm also inherits the properties of its original variant : it relies on purely localized decisions , for which no global information is ever collected at the nodes , and yet it maintains a number of critical properties whatever the frequency and scale of the changes . in particular , the network remains always covered by a spanning forest in which 1 ) no cycle can ever appear , 2 ) every node belongs to a tree , and 3 ) after an arbitrary number of edge disappearance , all maximal subtrees immediately restore exactly one token ( at their root ) . these properties are ensured whatever the dynamics , even if it keeps going for an arbitrary long period of time . optimality is not the focus here , however the number of tree per components  the metric of interest here  eventually converges to one if the network stops changing ( which is never expected to happen , though ) . the algorithm correctness is proven and its behavior is tested through experimentation .","abstract":"highly dynamic networks are characterized by frequent changes in the availability of communication links . many of these networks are in general partitioned into several components that keep splitting and merging continuously and unpredictably . we present an algorithm that strives to maintain a forest of spanning trees in such networks , without any kind of assumption on the rate of changes . our algorithm is the adaptation of a coarse - grain interaction algorithm ( casteigts et al . , 2013 ) to the synchronous message passing model ( for dynamic networks ) . while the high - level principles of the coarse - grain variant are preserved , the new algorithm turns out to be significantly more complex . in particular , it involves a new technique that consists of maintaining a distributed permutation of the set of all nodes ids throughout the execution . the algorithm also inherits the properties of its original variant : it relies on purely localized decisions , for which no global information is ever collected at the nodes , and yet it maintains a number of critical properties whatever the frequency and scale of the changes . in particular , the network remains always covered by a spanning forest in which 1 ) no cycle can ever appear , 2 ) every node belongs to a tree , and 3 ) after an arbitrary number of edge disappearance , all maximal subtrees immediately restore exactly one token ( at their root ) . these properties are ensured whatever the dynamics , even if it keeps going for an arbitrary long period of time . optimality is not the focus here , however the number of tree per components  the metric of interest here  eventually converges to one if the network stops changing ( which is never expected to happen , though ) . the algorithm correctness is proven and its behavior is tested through experimentation ."}
{"article_id":"1310.4374","section_id":"i","document":"many problems in physics , chemistry and materials science lead to a free - space finite `` particle '' sum of @xmath0 functions , @xmath1 , centered at locations @xmath2 @xmath3 , where @xmath4 is a rectangular box @xmath5 centered at the origin of the reference frame @xmath6 for evaluation at @xmath0 locations @xmath7 , this sum has a quadratic cost . there are efficient and arbitrarily accurate approximation algorithms for this summation ( e.g. , the fast multipole method , fmm @xcite ) . often , an extension to this sum for @xmath8 must be computed in which periodic boundary conditions are enforced on box boundaries , resulting in the potential @xmath9 . this can be evaluated by replacing the sum ( [ r2 ] ) with the infinite sum @xmath10 for some functions @xmath1 , such as those representing the field of an electrostatic charge , this infinite sum may be divergent or conditionally convergent . in this case certain side conditions may be needed to compute a physically relevant sum . usually such infinite sums are performed using fourier - transform based ewald summation @xcite , which is accelerated via the fft . this method is described briefly in appendix d. accounting for all pairwise interactions the method can achieve @xmath11 complexity , for @xmath0 particles in the box @xmath12 which is periodically replicated over the full space @xcite . because of the technique used for grid - to - particle interpolation these methods are usually low - order . a high - order accurate gaussian interpolation based ewald summation algorithm was recently presented in @xcite . another scalable algorithm , which can be employed for computation of periodic sums ( [ 2 ] ) is the fmm . a criticism of fmm algorithms has been that they are relatively harder to implement , combining the need for efficient data structures , careful analysis and computation of special functions , and mixed memory access patterns . nevertheless , several open - source and commercial packages implementing the fmm for standard kernels in free space have become available . the fmm is used less often in practice to compute periodic sums , even though several methods to handle periodic boundary conditions using extensions to the basic fmm have been proposed , starting from the first publication of the algorithm @xcite . some authors ( e.g. @xcite ) claim that the overhead in the fmm for computation of periodic sums can be negligibly small . this is true under a few conditions , but not in others . this is discussed in detail in a section entitled discussion . analysis of the fmm and its plane - wave variant , which is better - suited tor large @xmath0 and parallel architectures than the smooth particle mesh ewald algorithm , is presented in @xcite . however , all these methods require constructing a new and different algorithm  a periodic variant , for which optimized implementations are not in general available . furthermore , some of these algorithms may not extend easily to non - cubic domains . it can be mentioned in this context that any fmm has a so - called break - even point , @xmath13 , such that at @xmath14 brute force summation ( [ r2 ] ) is faster than the fmm computation . the value of @xmath13 depends on the method used , implementation , required accuracy ( the fmm is an approximate algorithm ) , and hardware . it may vary in a range @xmath15 , which is of the order of @xmath0 for some practical problems ( e.g. for some molecular dynamics simulations ) . in such cases , the use of periodic fmm just for the purpose of computing of infinite sums ( [ 2 ] ) even if the overhead for periodization will be zero is questionable if some other periodization method , which can use finite brute force summation algorithms is available . special purpose hardware such as graphics processors or heterogeneous cpu / gpu architectures also allow the fast computation of finite sums , either via brute force summation @xcite , or via the mapping of the fmm onto these architectures @xcite . yokota et al . @xcite favorably compare a large scale fmm - based vortex element computations with a direct numerical simulation via periodic pseudospectral methods . their simulations could have been faster and more accurate  the fmm was executed on a finite system composed of 3@xmath16 images , which while not being truly periodic also makes using the fmm significantly more expensive . the problem this paper seeks to address is : _ given a black - box fast summation algorithm ( fsa ) for computing finite sums with a given kernel _ @xmath17 that is available to the user , _ is it possible to compute the same sum with periodic boundary conditions without any modification of the fsa ? _ we provide a positive answer to this question . our algorithm has the same cost as the fsa , and can be computed to any user specified accuracy @xmath18 , and does not use the fft . the basic idea of the method is to divide the sum ( [ 2 ] ) in to two parts . one part computes a finite sum of particles that lie within a sphere centered at the box . this is computed using the available fsa . the other part , is an approximation of the field within the box due to all particles outside the sphere . the field due to these sources can be represented within the box in terms of local expansions . such local expansions have also been proposed in other attempts to extend the fmm to periodic systems , but are there derived by explicit translation of multipole expansions from outside the box of interest into it . in our method , we propose to determine the coefficients directly from the periodicity conditions on the potential , which results in solution of a relatively small overdetermined function - fitting problem , easily solved via standard algorithms  e.g. , rank - revealing @xmath19 decomposition . this step is in the spirit of the `` kernel - independent '' fmm methods @xcite . in this context we should mention ref . even though it is dedicated to the helmholtz equation in two dimensions , a method for `` periodization '' of free - space solutions similar in spirit to that presented here was proposed and tested . moreover , the cited paper contains an additional `` periodization '' method based on boundary integrals , which can be tried for different kernels and space dimensionality ( also see @xcite , where periodization along one dimension is performed ) . we present this `` periodization '' approach in a general setting , but focus computational examples on the evaluation of the electrostatic potential @xmath20 and its gradient @xmath21 at @xmath22 evaluation points @xmath23 @xmath24 due to @xmath0 charged particles of charge @xmath25 placed in @xmath26 , and subject to periodic boundary conditions on @xmath27 . this reduces to computing the infinite , conditionally convergent , sum ( [ r2 ] ) , with kernel function @xmath1 : @xmath28 and the net charge in each box being zero . of course , in practical applications , such as in molecular dynamics , there will be other computations beyond the sum necessary to stabilize the overall computations . this paper does not consider these , focusing on the electrostatic sum at a single time step . the periodization method could be easily applied to other kernels for which a `` fast summation algorithm '' ( fsa ) is available . as long as the periodic sum makes sense , and the kernel @xmath1 can be expanded over some local basis , the proposed method should work . conditions similar to the charge neutrality in ( [ 1 ] ) may be necessary . the proposed method can also be applied for 2d problems , though we present it in 3d . also , the periodic extension of the computational domain ( box ) may be performed only along one or two coordinates , for which ewald summation may have problems .","summary":"in a number of problems in computational physics , a finite sum of kernel functions centered at particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries . even though the finite sum can be efficiently computed via fast summation algorithms , such as the fast multipole method ( fmm ) , the periodized extension is usually treated via a different algorithm , ewald summation , accelerated via the fast fourier transform ( fft ) . a different approach to compute this periodized sum just using a blackbox finite fast summation algorithm the method splits the periodized sum in to two parts . several technical details and efficient algorithms for auxiliary computations are provided , as are numerical comparisons .      j.  g. leishman , monitor dr .  d. smith ) ; by nsf award 1250187 ( pi : prof .  b.  balachandran ) ; by grant g34.31.0040 ( pi : prof . ","abstract":"in a number of problems in computational physics , a finite sum of kernel functions centered at particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries . even though the finite sum can be efficiently computed via fast summation algorithms , such as the fast multipole method ( fmm ) , the periodized extension is usually treated via a different algorithm , ewald summation , accelerated via the fast fourier transform ( fft ) . a different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper . the method splits the periodized sum in to two parts . the first , comprising the contribution of all points outside a large sphere enclosing the box , and some of its neighbors , is approximated inside the box by a collection of kernel functions ( `` sources '' ) placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions . the second part , comprising the part inside the sphere , and including the box and its immediate neighborhood , is treated via available summation algorithms . the coefficients of the sources are determined by least squares collocation of the periodicity condition of the total potential , imposed on a circumspherical surface for the box . while the method is presented in general , details are worked out for the case of evaluating electrostatic potentials and forces . results show that when used with the fmm , the periodized sum can be computed to any specified accuracy , at an additional cost of the order of the free - space fmm . several technical details and efficient algorithms for auxiliary computations are provided , as are numerical comparisons .      periodic sums ; fast multipole method ; ewald summation ; gpu computing ; kernel independent methods ; molecular dynamics ; long - range interactions      work partially supported by the following sources : afosr under muri grant w911nf0410176 ( pi prof .  j.  g. leishman , monitor dr .  d. smith ) ; by nsf award 1250187 ( pi : prof .  b.  balachandran ) ; by grant g34.31.0040 ( pi : prof .  i.  akhatov ) of the russian ministry of education & science . ; and by fantalgo , llc ."}
{"article_id":"1310.4374","section_id":"m","document":"the box on which the periodic sum is to be computed is denoted @xmath12 . let @xmath29 be a ball of radius @xmath30 centered at the center of the box @xmath4 and containing it . let @xmath31 be another ball with the same center and radius @xmath32 ( see fig . [ fig1 ] ) . we denote as @xmath33 a finite region which includes the ball @xmath34 ( the minimal @xmath35 is the ball @xmath34 ) . we decompose the infinite sum as @xmath36 where @xmath37 is to be computed using the fsa ( assumed to be the fmm in the sequel ) to the specified accuracy @xmath38 while @xmath39 is computed by some other method at least to the same accuracy . the sources in the infinite domain are indexed as @xmath40 , @xmath41 for appropriate vectors @xmath42 @xmath43 ( see eq . ( [ 2 ] ) ) .    to apply the fmm to the kernel function @xmath44 it should be possible to approximate it via a convergent series over a set of local basis functions @xmath45 . this means that for any source point @xmath46 we have the factorization @xmath47 where @xmath48 is the number of terms retained in the infinite series , @xmath49 are the expansion coefficients , and @xmath50 is the truncation error depending on @xmath51 and @xmath52 . the basis functions can be some standard choices , or , as in the kernel independent fmm @xcite , can be taken to be a collection of kernel functions , centered outside the region of approximation @xmath53 where @xmath54 are a collection of sources located outside ball @xmath31 . this method has the flavor of `` equivalent - source '' methods . since the function @xmath1 depends only on the distance between its argument , it is a `` radial basis function '' , or rbf @xcite . while any approximation scheme may be used , the use of kernel @xmath1 as rbf is dictated by the fact that this kernel satisfies the underlying equation ( e.g. the laplace equation ) , so the approximation to the field via the sum of such rbfs also satisfies the equation ( if it is linear and space invariant ) . substituting eq . ( [ 4 ] ) into the expression for @xmath55 from eq . ( [ 3 ] ) , we obtain @xmath56 a necessary condition for our method is convergence of both infinite sums @xmath57 and @xmath58 . the problem of computation of @xmath59 has been reduced to that of determination of @xmath48 fitting coefficients @xmath60 . these can be determined via least - squares collocation as follows . consider a set of @xmath61 check points , @xmath62 . a point @xmath63 has two properties : first,@xmath64 , and , second , that there exists @xmath65 such that point @xmath66 ( see fig . [ fig1 ] ) . this means that @xmath67 in terms of decomposition ( [ 3 ] ) and representation of the far field ( [ 6 ] ) this system can be rewritten as @xmath68 where @xmath69 we have @xmath70 linear equations in @xmath48 unknowns @xmath71 . as we are not constrained with the size of the set of the set points , @xmath61 can be selected to provide a substantial oversampling , so minimization of functional @xmath72 should take care about the `` noise '' introduced into the approximation due to @xmath73 . the least square minimization procedure is well known and formally it results in solution @xmath74 where @xmath75 and @xmath76 are organized as column vectors of size @xmath48 and @xmath70 , respectively and @xmath77 is the @xmath78 matrix , which is the pseudoinverse of @xmath79 , and superscript @xmath80 denotes transposition . note that this notation is formal , and is not the way the least - squares problem is solved in practice . rather a stable algorithm such as the rank - revealing qr decomposition @xcite is used , while it is strongly recommended to precompute and store matrix decompositions in the `` set '' part of the algorithm to reduce the cost of the `` get '' part . the known coefficients @xmath81 allow computation of @xmath55 and can be added to the @xmath82 obtained via the fsa . however , some technical details need to be specified . in the next section we provide analysis and details for the important case of the coulombic kernel ( [ 2 ] ) . a similar collocation of kernel based rbf expansions at a relatively small amount of the check points is also used in the `` kernel independent '' fmm @xcite with basis functions ( [ 5 ] ) . there , the collocation is at the level of the boxes in the fmm octree data structure , and fitting takes the place of expansions and translations . here , we collocate the differences of the overall solution at a set of check points @xmath83 and at their periodic images @xmath84 , at the level of the overall domain to determine the expansion coefficients for @xmath85 .      selection of an optimal set of check points @xmath86 is not trivial . a good check point set should yield a well conditioned solution , and sample the solution well spatially . a simple way which does not yield such a well conditioned set is to select the points @xmath87 on the boundary of box @xmath4 . this is because the corresponding periodic point @xmath88 will then also be located on the box boundary on the face opposite to @xmath89 . in this case the distances from the box center to @xmath89 and to @xmath90 will be the same , so both points will be located on a sphere of radius @xmath91 . if the basis is based on spherical functions , then several of these will take the same value for symmetrical points on the sphere , and the fitting equations may be rank deficient .    to avoid this degeneracy , the set @xmath92 was chosen from points on the surface of ball @xmath93 . three distributions were tried ( see fig . ( [ checkpoints ] ) : i ) random uniformly distributed points , ii ) gaussian nodes ( zeros of the legendre polynomial along @xmath94 , @xmath95 , see @xcite ) and equispaced with respect to @xmath96 ) , and , iii ) the almost uniform distribution of points over the sphere obtained by solving the so - called thomson problem of the equilibrium position of mutually repelling electrons constrained to be on the surface of the sphere @xcite , see @xcite . methods ii ) and iii ) show better results than the random distribution , as shown in section 3 . further , we fond that using the thomson points for the interpolation in eq . [ 5 ] provides good accuracy . the algorithm has two parts . in a first preliminary set - up step , denoted `` set '' , the check points are determined , and the matrix decompositions necessary to compute the least squares fit with the matrix @xmath79 in eq . ( [ 10 ] ) are precomputed . in simulations where the domain @xmath12 is fixed and the particles move , as in molecular dynamics , this matrix does not change , and the cost of the `` set '' step is amortized over the entire simulation . the second part of the algorithm , denoted `` get , '' computes the right hand side and solution of the fitting equations via an inexpensive step such as backsubstitution . the accuracy depends on the choice of basis functions , and the parameters @xmath48,@xmath70 , and @xmath97 . in the next section we provide both a theoretical and an empirical study for the case of the coulombic kernel ( green s function of laplace s equation ) .      1 .   set the circumsphere radius @xmath98 . based on the required accuracy determine @xmath99 , @xmath48 , and @xmath100 . 2 .   generate @xmath70 check points distributed over the surface of the ball @xmath101 , @xmath102 , @xmath103 denote this point set as @xmath104 . 3 .   for each point @xmath105 @xmath106 find a point @xmath107 , such that two cartesian coordinates of @xmath84 are the same as those of the respective coordinates of @xmath89 , while the other coordinate , @xmath108 is shifted by @xmath109 with respect to @xmath110 . denote @xmath111 @xmath112 4 . form the @xmath113 fitting matrix @xmath114 , @xmath115 , @xmath106 @xmath116 where @xmath117 are the basis functions at the checkpoints . compute matrix decomposition of @xmath79 necessary to solve the least squares problem . ( optional ) precompute other parameters which do not depend on the source distribution . if the summation needs certain auxiliary computations to ensure convergence , do those steps . for the coulomb kernels this may involve computation of the integrals of the basis functions over the box @xmath4 .      1 .   periodically extend the source box @xmath12 to cover the ball @xmath118 of radius @xmath97 . the newly generated sources and charges will have coordinates @xmath119 for the values of the periodization vector @xmath120 from set @xmath43 ( see eq . ( [ 2 ] ) ) and charges @xmath121 denote the set of all sources as @xmath122 . these constitute @xmath123 . 2 .   find the set of @xmath13 sources @xmath124 by removing sources from the set @xmath125 that are outside the sphere @xmath34 , and satisfy @xmath126 @xmath127 3 . using the fsa compute @xmath82 for a given set of evaluation points @xmath128 residing in @xmath129 and belonging to sets @xmath104 and @xmath111 , i.e. for points from the set @xmath130 if gradient computations are needed , compute @xmath131 at @xmath132 4 . form the right hand side of the periodization equation @xmath133 @xmath134 @xmath135 , @xmath136 organized in a column vector . 5 .   using the matrix decompositions in the `` set '' step solve the fitting equations for the @xmath48 expansion coefficients @xmath137 this step can formally be written as @xmath138 @xmath139 6 . ( optional ) compute the constant shift or other modification of the far field potential , if needed . evaluate @xmath140 , and if gradient computation is needed , @xmath141 , at @xmath142 . get the periodized solution of the problem , @xmath143 @xmath144 and if gradient computation is needed , @xmath145 @xmath146 @xmath147 @xmath142 .    in molecular dynamics and other n - body simulations the source and evaluation points are the same , so @xmath148    in step 5 for the laplacian kernel and spherical basis functions @xmath149 . in this case optional step 6 provides @xmath150 ( see eqs ( [ pfx1])-([pfx4 ] ) ) . otherwise set @xmath151 . step 2 reduces @xmath152 to the ball @xmath34 , which is not necessary , but is efficient . evaluation of the kernel at a single point requires @xmath153 operations . so , @xmath154 operations are needed to evaluate all basis functions . the complexity , @xmath155 , is also achieved when basis functions at a point can be computed recursively ( as for the spherical basis functions ) . with @xmath156 we can estimate the complexity of the `` set '' part of the algorithm as @xmath157 = o\\left ( p^{3}\\right ) ,   \\label{c1}\\ ] ] where we assumed that computation of the matrix decomposition ( e.g. , via qr ) @xmath158 operations , as @xmath159 . the term in the square brackets is the cost of the optional step for the laplace kernel and spherical basis functions , using the method presented in appendix b.    for the `` get '' part of the algorithm , assuming that @xmath160 and @xmath161 we have @xmath162 + o\\left ( pn\\right ) + o(n)=o\\left ( pn\\right ) + c^{(fsa ) } , \\label{c2}\\ ] ] where @xmath163 is the cost of the finite summation algorithm and the cost of the optional step of the algorithm is put in the square brackets ( see appendix c for this step for the laplacian kernel ) . this cost for the brute force summation is @xmath164 , while if the fmm is used as the fsa it can be estimated as follows .    in the fmm , generation of the data structure for @xmath165 points is @xmath166 which for deep trees , @xmath167 , results in formal @xmath11 complexity . however , in practice the depth of the trees in three dimensions is relatively small ( e.g. @xmath168 ) for sizes @xmath169 and even at larger @xmath170 this cost is much smaller than the cost of the run part of the fmm . moreover , the translation time in the fmm usually dominates over the time of generation and evaluation of expansions of complexity @xmath171 , where @xmath172 is the size of the expansions in the fmm . for optimal @xmath170 the fmm using @xmath173 methods for translations in three dimensions scale as @xmath174 or @xmath175 , where @xmath176 for well studied kernels such as those for the laplace and helmholtz equations ( in the latter case additional @xmath177 , @xmath178 factors appear in the algorithm complexity , which we drop in the present estimate ) . optimized kernel independent fmm has complexity @xmath171 . this can be summarized as @xmath179    note that for the laplacian kernel in three dimensions truncation numbers @xmath180 and @xmath181 should increase as @xmath182 for a fixed absolute @xmath183-norm error ( see error bounds below ) , while they are constant for the relative @xmath184-norm errors .","summary":"is presented in this paper . i.  akhatov ) of the russian ministry of education & science . ; and by fantalgo , llc .","abstract":"in a number of problems in computational physics , a finite sum of kernel functions centered at particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries . even though the finite sum can be efficiently computed via fast summation algorithms , such as the fast multipole method ( fmm ) , the periodized extension is usually treated via a different algorithm , ewald summation , accelerated via the fast fourier transform ( fft ) . a different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper . the method splits the periodized sum in to two parts . the first , comprising the contribution of all points outside a large sphere enclosing the box , and some of its neighbors , is approximated inside the box by a collection of kernel functions ( `` sources '' ) placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions . the second part , comprising the part inside the sphere , and including the box and its immediate neighborhood , is treated via available summation algorithms . the coefficients of the sources are determined by least squares collocation of the periodicity condition of the total potential , imposed on a circumspherical surface for the box . while the method is presented in general , details are worked out for the case of evaluating electrostatic potentials and forces . results show that when used with the fmm , the periodized sum can be computed to any specified accuracy , at an additional cost of the order of the free - space fmm . several technical details and efficient algorithms for auxiliary computations are provided , as are numerical comparisons .      periodic sums ; fast multipole method ; ewald summation ; gpu computing ; kernel independent methods ; molecular dynamics ; long - range interactions      work partially supported by the following sources : afosr under muri grant w911nf0410176 ( pi prof .  j.  g. leishman , monitor dr .  d. smith ) ; by nsf award 1250187 ( pi : prof .  b.  balachandran ) ; by grant g34.31.0040 ( pi : prof .  i.  akhatov ) of the russian ministry of education & science . ; and by fantalgo , llc ."}
{"article_id":"1310.4374","section_id":"c","document":"by proposing a method for computation of periodic sums we do not mind to compete with or diminish the role of the existing methods , such as based on ewald summation or the fmm for periodic functions for well - studied kernels . we realize that a variety of problems with periodic boundary conditions and practical concerns of researchers may require some solutions different from the existing approaches , as any of them , including the present one has some advantages and disadvantages . such problems are not limited with laplacian kernels . however , development of specialized approaches which usually are more efficient than generic approaches ( kernel - independent fmm is an example ) , also have some cost and availablity of a method which turns an available fsa to its periodic version without any intervention to the basic fsa algorith , in our opinion , is useful . the `` cons '' and `` pros '' of the fft vs fmm were discussed in the literature , including performance and scaling at large @xmath0 ( e.g. @xcite ) and application to solution of molecular dynamics problems ( e.g. @xcite ) . particularly , some difficulties for the use of the fmm for the md simulations were reported as a long term energy drift was observed in some computations using four or six term expansion in the fmm @xcite ( perhaps , @xmath325 or @xmath326 , which provides @xmath327 and 36 terms of expansion , respectively)@xmath328 of course , the number of terms should be evaluated carefully and the fmm and other errors should be consistent with the integration schemes used ( particularly , the fmm errors in gradients are higher than in the potential @xcite ) . in this context , we can mention that in the present algorithm one can enforce some conditions ( such as setting the mean of the potential to zero , similarly to the ewald scheme ) , which is normally is not controlled in the fmm - based algorithms . it can be more stable or not in terms of the energy drift if applied to the md simulations , but this requires an additional study , which , certainly , goes beyond the scope of the present work , where not only the md applications are envisioned . another advantage of not requiring the fft may arise for very large problems , which have to be implemented on distributed architectures , where the communication costs of the fmm are smaller than the fft . as far as comparing the present approach with an fmm algorithm implemented using periodic kernel functions is considered , we perform this comparison on three sizes of problems : with small @xmath329(say , @xmath330 ) , moderate @xmath0 ( say , @xmath331 ) and large @xmath0 ( say , @xmath332 ) . the first class may not require the fmm at all , as direct sums may be done faster and be more accurate , and the present algorithm can work efficiently and accurately ( choosing proper @xmath218 ) with direct sums . the second and the third types of the problems require a fast summation algorithm such as the fmm . in this case some authors claim that the overheads for solution of periodic problems are negligibly small compared to solution of the non - periodic problem . for example , @xcite claims that periodization of requires only 0.1% of the total computational time . this statement _ does not mean _ that the periodic version of the sum is 1.001 times slower than the solution of the non - periodic sum , as was remarked on an early draft of this paper . indeed , in @xcite ( page 1084 and table v ) it is stated `` _ the time spent on dealing with periodicity ranged from about 0.3 to 2.6 times of that of the free boundary computations , depending on the values of @xmath218 and @xmath70 and the type of the fmm . _ '' ( here @xmath333 in our notation ) . this shows that actual measured time ratios , such as reported in fig . [ timeratio ] , were in the range 1.3 to 3.6 . the overhead comes from the fact that the periodic fmm is the fmm executed in the extended domain , which is not the original cell @xmath12 , but in @xmath12 with its 26 neighbors , which is @xmath334 in our notation , see fig . the difference between the present and periodic fmms is that , first , the periodic fmm saves on generation of multipole expansions and multipole - to - multipole translations for the replicated domains , which is not implemented in the present algorithm , and , second , that for the present fmm some relatively small amount of receivers ( `` check points '' ) are added . discussions of the fmm costs and simplifications in appendix a and around eqs ( [ o3 ] ) and ( [ lt1 ] ) show that asymptotically as @xmath335 the second modification brings a negligible overhead , while the overhead due to the first modification is non - zero , and in practice can be several percents for cubic @xmath12 to tens of percents for non - cubic @xmath12 ( due to the geometric factor @xmath250 ) , which is the price of use of the fmm as a black box fsa .    at @xmath336 the costs of the periodic and non - periodic fmms are the same . the difference in costs of periodic and non - periodic fmms comes from two factors  the difference in the multipole - to - local translations and direct summations for the boxes near the boundaries of @xmath4 , due to the difference in the neighborhoods . we carefully counted these numbers accounting for the boundary effects , and found that for levels @xmath337 and @xmath338 ( midsize problems ) used in @xcite , the ratios of numbers of translations in periodic and non - periodic fmms is 1.96 and 1.38 , while the ratios of the numbers of direct summations is 1.30 and 1.14 , respectively . at levels @xmath339 and @xmath326 one can expect time ratios in a range 1.05 - 1.20 . one of the features of the present algorithm , which may be of practical interest , is the capability to obtain periodic solutions for non - cubic domains easily , which can be an issue for some other algorithms . these were illustrated in table [ table5 ] . performance for moderate box aspect ratio is comparable to the cubic case . for high aspect ratios , the algorithm works , but some issues , which could be the subject of future study must be noted . there is a substantial increase in the amount of sources added because of the enclosure of the whole domain in a sphere . because of this , both the memory needed and the computational time are relatively large , while still scaled as expected . possible ways to address this would be to devise more check point sets located not on a sphere , but on surface that are more conformal to the boundaries , and also a reduction of the size of domain @xmath12 . the latter can be achieved in a few ways including distribution of rbf centers not too far from the boundaries of @xmath4 or to use basis functions , which are better suited for boxes of high aspect ratios than the spherical basis functions .","summary":"periodic sums ; fast multipole method ; ewald summation ; gpu computing ; kernel independent methods ; molecular dynamics ; long - range interactions      work partially supported by the following sources : afosr under muri grant w911nf0410176 ( pi prof . ","abstract":"in a number of problems in computational physics , a finite sum of kernel functions centered at particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries . even though the finite sum can be efficiently computed via fast summation algorithms , such as the fast multipole method ( fmm ) , the periodized extension is usually treated via a different algorithm , ewald summation , accelerated via the fast fourier transform ( fft ) . a different approach to compute this periodized sum just using a blackbox finite fast summation algorithm is presented in this paper . the method splits the periodized sum in to two parts . the first , comprising the contribution of all points outside a large sphere enclosing the box , and some of its neighbors , is approximated inside the box by a collection of kernel functions ( `` sources '' ) placed on the surface of the sphere or using an expansion in terms of spectrally convergent local basis functions . the second part , comprising the part inside the sphere , and including the box and its immediate neighborhood , is treated via available summation algorithms . the coefficients of the sources are determined by least squares collocation of the periodicity condition of the total potential , imposed on a circumspherical surface for the box . while the method is presented in general , details are worked out for the case of evaluating electrostatic potentials and forces . results show that when used with the fmm , the periodized sum can be computed to any specified accuracy , at an additional cost of the order of the free - space fmm . several technical details and efficient algorithms for auxiliary computations are provided , as are numerical comparisons .      periodic sums ; fast multipole method ; ewald summation ; gpu computing ; kernel independent methods ; molecular dynamics ; long - range interactions      work partially supported by the following sources : afosr under muri grant w911nf0410176 ( pi prof .  j.  g. leishman , monitor dr .  d. smith ) ; by nsf award 1250187 ( pi : prof .  b.  balachandran ) ; by grant g34.31.0040 ( pi : prof .  i.  akhatov ) of the russian ministry of education & science . ; and by fantalgo , llc ."}
{"article_id":"1406.3259","section_id":"i","document":"_ high - throughput quantum - mechanics _ ( htqm ) computation of materials properties by _ ab initio _ methods has become the foundation of an effective approach to materials design , discovery and characterization @xcite . this data - driven approach to materials science currently presents the most promising path to the development of advanced technological materials that could solve or mitigate important social and economic challenges of the 21st century @xcite . in order for this approach to be successful , however , one needs the confluence of three key factors : * i. * improved computational methods and tools ; * ii . * greater computational power ; and * iii . * heightened awareness of the power of extensive databases in science@xcite . while the last two are driven by technological advances in computing and research and development needs , the development of improved computational tools appropriate for htqm frameworks is a grand challenge that is still in need of considerable advances . most htqm infrastructures rely on the predictive capability of density functional theory ( dft ) , the method of choice for the first principles study of materials properties . however , despite the enormous success of dft in describing many physical properties of real systems , its limitations in describing correctly the electronic band structure of insulators are well known . the method is limited by the presence of an unknown correlation term that represents the difference between the true energy of the many - body system of the electrons and the approximate energy that we can compute . the common approximations based on a nearly - homogeneous - electron - gas treatment of the electron density , the local - density ( lda ) and generalized - gradient approximation ( gga ) , are extremely successful in the description of many physical properties of materials , but dramatically underestimate the electron energy gap in insulators and semiconductors and thus fail to satisfactorily describe the electronic properties of these systems . higher order levels of theory that are able to predict with great accuracy the energy gaps exist ( the @xmath1 approximation@xcite and dynamical mean - field theory@xcite , among others ) but they are computationally expensive and unsuitable for extensive high - throughput materials characterization @xcite , even when machine learning methods are employed to simplify the complexity of the task especially when seeking for new materials systems @xcite . in order to address the energy gap problem at a lower computational cost the two most common corrections to traditional local and non - local approximations to dft are `` hybrid functionals '' and dft+@xmath2 . both approaches aim to reduce at some level the self - interaction error @xcite and introduce the derivative discontinuity in the exchange - correlation functional@xcite responsible for the underestimation of the energy gap@xcite . hybrid functionals are based on the idea of computing the exact exchange energy from the kohn - sham wavefunctions and to mix it with the ( semi)local approximation of exchange energy of dft@xcite . the method is very successful in predicting the energy gap with good accuracy and points to the importance of introducing some degree of exact exchange in traditional dft for a proper description of the electronic structure . however , the level of mixing is not determined from first principles , so the method suffers of some level of empiricism and , even after the introduction of range separated functionals suitable for periodic system calculations@xcite , it is more computationally demanding than lda or gga . the treatment of systems with strongly localized(correlated ) electrons is another outstanding issue that limits the predictive power of ( semi)local approximations to dft for systems where localization is important , such as transition metal insulators , and directly impacts the energy gap problem . the dft+@xmath2 method introduced by liechtenstein and anisimov @xcite aims at preserving the information of orbital localization from being averaged out as in lda or gga in order to improve the description of the band structure with a very modest increase in computational effort . since in this paper we are mainly concerned with an extension of this approach , let us discuss its guiding principles in some detail .    within the dft+@xmath2 ansatz , localized states @xmath3 largely retain their atomic nature and , therefore , can be expanded in term of an atomic - orbital basis set @xmath4 . the coulomb and exchange energy associated with these states is explicitly evaluated using the hartree - fock ( hf ) framework via electron repulsion integrals ( eri , also know as two - electron integrals ) with a screened ( renormalized ) coulomb interaction @xmath5 and added to the original dft energy after the removal of double counting terms in the energy expansion , in a spirit similar to the hybrid functionals approach . the hf coulomb and exchange energy of the localized states is given by @xcite : @xmath6 where @xmath7 is the spin density matrix @xmath7 of the atomic orbitals @xmath8 . this equation can be simplified via the introduction of the phenomenological parameters @xmath9 and @xmath10 that describe the on - site hubbard - like interactions as expressed by dudarev _ @xcite : @xmath11 here , @xmath12 is the spin occupation number of the atomic orbital @xmath8 . from the equations above , it clearly follows that the new parameters , @xmath9 and @xmath10 , contain the information of all the eris in an averaged scenario . in physical terms , @xmath9 is the strong correlation experienced between localized electrons  only subtly coupled to the sea of extended states in which they live . thus , the most akin definition of @xmath9 ( for the non - spin - polarized case ) is the average @xcite : @xmath13 where @xmath14 is the total number of localized states @xmath3 , and @xmath15 for @xmath16 orbitals , respectively . the exchange contribution , @xmath10 , is given by a similar average @xcite . although the physical picture is clear , an unambiguous procedure for computing @xmath17 from _ ab - initio _ does not exist . two factors need to be further clarified in eq . [ eq : d2 ] : _ i _ ) the screened ( renormalized ) coulomb interaction @xmath5 arising from the `` subtle coupling '' to the background extended states ; and _ ii _ ) the actual orbitals @xmath3 used to represent the `` localized electrons '' .    amongst the most common _ ab - initio _ methods to compute @xmath9 are the constrained random - phase approximation ( crpa ) @xcite and the linear - response constrained dft ( or clda ) @xcite . the former computes the screened coulomb interaction as the bare coulomb interaction renormalized by the inverse dielectric function , which is calculated using the random phase approximation . the latter circumvents the ambiguity of @xmath5 by indirectly determining @xmath9 as the second derivative of the total energy with respect to constrained variations of the atomic charge @xmath18 of the chosen hubbard center @xmath19 , @xmath20 . @xmath21 is the total energy of a supercell large enough to converge to the bulk environment for the atom @xmath19 . it is assumed that the charge perturbation on atom @xmath19 does not disturb the local environment . in dft with linear - combination - of - atomic - orbital ( lcao ) basis , this is enforced by suppressing the hopping integrals to prevent charge rehybridization or transfer with its environment @xcite and in the case of plane - wave dft by subtracting a correcting term from @xmath22 as given in ref .  . this method has been widely used for open - shell systems ; nonetheless , the numerical reliability becomes challenging for closed - shell systems where the localized bands are completely full , thus exhibiting very small response to the linear perturbation @xcite .    regarding the representation of the @xmath23 states , _ @xmath24 or @xmath25 electrons of transition metals , localized orbitals obtained either from the linear - muffin - tin - orbital ( lmto ) method @xcite or from the @xmath26-order muffin - tin - orbital ( @xmath27mto ) method @xcite can be used with both the clda and crpa to obtain @xmath9 . recently , maximally localized wannier functions ( mlwf ) , an invariant choice suitable for plane - wave calculations , have also been employed @xcite . by construction , these functions are associated with a given angular momentum ( @xmath28 ) and the direct correspondence makes them convenient to represent the localized @xmath24 or @xmath25 electrons . ultimately , pinpointing a single localized state within the solid is arbitrary  any of these options are equally valid . in principle , the options should be equivalent for very localized states ; nonetheless , the physical significance and construction becomes more ambiguous when bands corresponding to localized states are not fully disentangled @xcite . despite attempting the computation of the same physical entity , the clda and crpa methods do not yield the same value of @xmath9 @xcite . considering the number of assumptions taken in numerical implementations , the outcome is unsurprising . in this article , we introduce an alternative _ ab - initio _ method to compute @xmath9 and @xmath10 , which parallels the calculation of the hf energy for molecules and solids and follows closely the original definition of anisimov _ et al . _ [ eq : liechtenstein ] ) : the gapito - urtarolo - uongiorno ardelli ( ) pseudo - hybrid hubbard density functional . in the hubbard energy of dft+@xmath2 is calculated via the direct evaluation of the local coulomb ( @xmath9 ) and exchange ( @xmath10 ) integrals in which the screening of the bare coulomb interaction is replaced by a renormalization of the density matrix . through this procedure , the values of @xmath9 and @xmath10 are thus functionals of the electron density and depend directly on the chemical environment and crystalline field , introducing an effective procedure of giving the proper description of mott insulators and other strongly correlated transition - metal oxides . as a first application , we discuss the electronic properties of a series of transition metal oxides that show good agreement with hybrid functionals , the @xmath1 approximation and experimental results at a fraction of the computational cost . in particular , we will demonstrate that the  functional satisfies the rather ambitious criteria outlined by pickett _ et al . _ in one of the first seminal articles on lda@xmath29 @xcite : _ i _ ) reduces to ( lda)pbe when ( lda)pbe is known to be good ; _ ii _ ) the energy is given as a functional of the density ; _ iii _ ) the method specifies how to obtain the local orbital in question ; _ iv _ ) the definition of @xmath9 and @xmath10 is provided unambiguously . and _ v _ ) the method predicts antiferromagnetic insulators when appropriate . the article is organized as follows : the methodology is discussed in section  [ sec : method ] . the application of the method for four prototypical transition - metal oxides is presented in section  [ sec : results ] , and the results are compared against available experimental and theoretical data . section  [ sec : discussion ] discusses the important features of the method and suggests extensions of potential significance to the goal of discovering novel functional materials . conclusions are summarized in section  [ sec : conclusions ] .","summary":"htqm infrastructures rely on the predictive capability of density functional theory ( dft ) , the method of choice for the first principles study of materials properties . however , dft suffers of approximations that result in a somewhat inaccurate description of the electronic band structure of semiconductors and insulators . in this article","abstract":"the accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high - throughput quantum - mechanics ( htqm ) frameworks for accelerated materials discovery . htqm infrastructures rely on the predictive capability of density functional theory ( dft ) , the method of choice for the first principles study of materials properties . however , dft suffers of approximations that result in a somewhat inaccurate description of the electronic band structure of semiconductors and insulators . in this article we introduce , a pseudo - hybrid hubbard density functional that yields an improved prediction of the band structure of insulators such as transition - metal oxides , as shown for tio , mno , nio and zno , with only a _ negligible _ increase in computational cost ."}
{"article_id":"1406.3259","section_id":"m","document":"the foundations of the approach for evaluating the on - site coulomb and exchange parameters are :    _ i _ ) @xmath9 and @xmath10 are on - site quantities derived from the energy in the hartree - fock method . the hf theory considers pair - wise interactions of only two electrons at the time and therefore it misses the concept of screening . because of this approximation , the hf theory is known to be inappropriate in describing delocalized metallic systems ; however , it is qualitatively sound for molecules and insulators ( especially in the strong localization regime)@xcite . the on - site energies are derived from the hf energies following the ansatz of mosey and carter @xcite in which the occupied molecular orbitals ( mo ) , needed for the computation of the hf energy , are considered populated only in the subspace @xmath30 . _ ii _ ) no localized orbitals @xmath23 need to be explicitly computed . as in the hartree - fock method , all the mos , or crystalline wavefunctions for the case of solids , are used . this eliminates the indeterminacy in finding the subset of mos that better corresponds to the localized states , which can lead to a wide fluctuations of the calculated @xmath9 @xcite . during the calculation of the on - site hf energies , the localized orbitals are implicitly taken as a linear combinations the basis functions of interest , @xmath30 , with the expansion coefficients included in the renormalized density matrix coming directly from the solution of the kohn - sham equations projected onto the localized basis of choice ( see below ) ;    _ iii _ ) a plane - wave basis set is the natural choice for dft calculations of periodic systems , but on - site hf energies are more efficiently computed in a localized basis set . electron - repulsion integrals are evaluated using pseudo - atomic - orbitals ( pao ) expressed as linear combination of gaussian - type functions , that we define as the pao-3 g minimal basis set . this is possible by the projection procedure that we have recently developed @xcite , which seamlessly maps the plane - wave electronic structure onto a localized atomic - orbital basis set ( see appendix a ) . however , it is important to note that the construction of @xmath9 and @xmath10 outlined below is completely general and can be applied to any choice of basis , localized or otherwise .    _ @xmath31 is a true functional of the electron density in the spirit of the hohenberg - kohn theorems . this leads to the definition of the pseudo - hybrid hubbard density functional . the enormous quantity of electron repulsion integrals , eris , needed in the calculation of the hf exchange energy is the fundamental bottleneck in the use of hybrid dft functionals . in dft calculations based on lcao ( pao ) basis sets , the problem is made more tractable when the paos are expressed as linear combinations of gaussian - type functions , as it is commonly done in commercial packages such as gaussian09 @xcite and crystal06 @xcite . the electron repulsion integrals used in eq . [ eq : liechtenstein ] are defined as four paos interacting under the bare coulomb interaction @xmath32 as : @xmath33    the real - space evaluation of these integrals is not directly possible when using a plane - wave basis set , which is the preferred choice for periodic systems . for this reason , we employ the auxiliary space of paos naturally included in the definition of the pseudo - potentials . given that the radial and angular part of the pao basis functions , @xmath34 , are separable , they can be directly fitted using linear combinations of spherical - harmonic gaussian functions . for efficiency , the latter functions are then further expanded as linear combination of cartesian gaussians defining the pao-3 g minimal basis set . ( see appendix  [ sec : fitting ] for more technical details on these transformations ) . once expressed in the pao-3 g basis set , the eris can be efficiently evaluated using any optimized quantum - chemistry library . we use the c routines included in the open - source quantum - chemistry package pyquante . richard p. muller , pyquante 1.6.4 : python quantum chemistry ` http://pyquante.sourceforge.net/ ` ]      the knowledge of the eris and the molecular ( or crystal ) orbitals allows the calculation of the hf coulomb and exchange energies @xmath35 . for isolated systems ( molecules or clusters ) and in the restricted case :    @xmath36 \\nonumber \\\\   & = \\sum_{\\mu\\nu\\kappa\\lambda } p_{\\mu\\nu}p_{\\kappa\\lambda}[2(\\mu \\nu | \\kappa \\lambda ) - ( \\mu\\lambda|\\kappa\\nu ) ] . \\end{aligned}\\ ] ]    here @xmath37 are occupied molecular orbitals expanded in the paos basis ; @xmath38 is the charge of @xmath39 and @xmath40 is the overlap integral between the paos @xmath41 and @xmath42 . the last line of eq . [ eq : hf ] is expressed in the basis of atomic orbitals @xmath41 with the density matrix @xmath43 . the expression of the coulomb and exchange hf energies for a periodic system is analogous to the molecular case ( see pisani _ et al . _ @xcite ) : @xmath44,\\ ] ] where @xmath45 , @xmath46 and @xmath47 are lattice vectors and @xmath48 refers to the primitive unit cell . however , the mapping of the crystalline wavefunctions @xmath49 in a local basis ( i.e. the expansion coefficients @xmath50 ) is not readily available when using a plane - wave basis to solve for the electronic structure of the material as it is common for solids . we circumvent this problem by projecting the plane - wave solution into the chosen auxiliary space of paos following the method described in ref . [ ] . this projection procedure is a noniterative scheme to represent the electronic ground state of a periodic system using an atomic - orbital basis , up to a predictable number of electronic states , and with controllable accuracy by filtering out high - kinetic - energy plane waves components . see appendix  [ sec : hm_dm ] for a summary of this procedure to calculate the expansion coefficients @xmath50 and the real - space density matrices of the solid , @xmath51 . the energy functional for the dft+@xmath2 method is given by : @xmath52 where @xmath53 is the dft energy calculated using a lda or gga functional . the energy correction @xmath54 is given either in the original anisimov - liechtenstein @xcite or in the simplified dudarev@xcite formulation as :    @xmath55 - e_{\\textrm{dc } } , \\\\ e^{\\textrm{dudarev}}_{u }   = \\frac{\\bar{u}-\\bar{j}}{2}\\sum\\limits_{i}\\sum_{m,\\sigma}\\left [ n^{i\\sigma}_{mm } -\\sum\\limits_{m'}n^{i\\sigma}_{mm ' } n^{i\\sigma}_{m'm } \\right ] , \\label{eq : e_u_dudarev}\\end{gathered}\\ ] ]    with @xmath56 defined in eq . [ eq : liechtenstein ] for a given atom @xmath19 . @xmath57 corrects for a possible double counting of the localized - states interaction energy already captured ( in an averaged way ) in @xmath53 . the second formulation defines an effective on - site coulomb interaction @xmath58 ( henceforth referred simply as @xmath2 ) . it should be noticed that numerical implementations of the anisimov dft+@xmath2 functional ( eq .  [ eq : liechtenstein ] ) , for instance in quantum espresso @xcite or vasp @xcite , do not compute the eris explicitly . they are evaluated from tabulated slater integrals , which ultimately depend on the provided values of @xmath9 and @xmath10 , or from phenomenological considerations ( e.g. ref .  [ ] ) .    on the contrary , we evaluate @xmath9 and @xmath10 by computing directly the on - site coulomb and exchange energies on the chosen hubbard center , from the coulomb and exchange hartree - fock energies of the solid . the following assumptions are used . ( _ i _ ) we follow a central ansatz , introduced by mosey _ @xcite for the case of cluster calculations , that defines a `` renormalized '' occupation number @xmath59 for each mo @xmath39 : @xmath60 which is the mulliken charge of the basis @xmath61 . the set @xmath61 includes all the atomic orbitals in the unit cell that have the same quantum numbers as the orbitals @xmath30 of the hubbard center of interest . correspondingly , we define a renormalized density matrix as : @xmath62 the renormalized occupations can be interpreted as weighting factors that specify the on - site occupation of each electronic state .    the expressions in eqs . [ eq : focc ] and [ eq : fdm ] are applicable to isolated systems ( molecules and clusters ) . solid - state systems are calculated in reciprocal @xmath63-space that inherently apply periodic - boundary conditions , thus , surface effects are avoided . periodic plane waves are the basis of choice for the solution of solid - state systems . the @xmath63-space electronic - structure information of the material can be projected into a pao basis directly from the plane - wave dft solution . we take advantage of this to compute the reduced density matrices and occupation number , needed to calculate @xmath9 and @xmath10 , as follows    [ eq : rfocc ] @xmath64    here , @xmath65 is the total number of @xmath63-vectors in the @xmath66 brillouin zone . see appendix  [ sec : hm_dm ] for more details . @xmath31 , the on - site hf energy associated to the basis @xmath30 , is obtained from eq . [ eq : hf ] by restricting the summation indexes to @xmath30 . in the periodic case , it is reduced from eq . [ eq : hfsolid ] considering the central unit cell only , i.e. lattice vectors @xmath67 . combining ( _ i _ ) and , we obtain in the general spin - unrestricted case : @xmath68 ( mm'|m''m ' '' ) \\nonumber \\\\   & + \\frac{1}{2 } \\sum_{\\{m\\ } } [ \\bar{p}^{\\alpha}_{mm'}\\bar{p}^{\\alpha}_{m''m ' '' } + \\bar{p}^{\\beta}_{mm'}\\bar{p}^{\\beta}_{m''m ' '' } ] ( mm'''|m''m ' ) . \\end{aligned}\\ ] ]    in this notation , each primed and unprimed index @xmath69 runs over all the set @xmath30 . clearly , the above equation is equivalent to anisimov s original dft+@xmath2 functional ( eq .  [ eq : liechtenstein ] ) once we replace @xmath70 with the renormalized density matrix @xmath71 . however , while eq . [ eq : liechtenstein ] requires the knowledge of a subjective screened coulomb interaction @xmath5 , eq . [ eq : hf3 ] uses the bare coulomb interaction . although screening is not considered in the hf theory , the direct parallel between both equations shows that the renormalization of the density matrix effectively introduces a degree of screening .    the comparison of eqs . [ eq : dudarev ] with [ eq : hf3 ] leads to the definitions of @xmath9 and @xmath10 as density dependent quantities in the functional :    @xmath73(mm'|m''m ' '' ) } { \\sum_{m \\neq m'}n^{\\alpha}_{m}n^{\\alpha}_{m ' } + \\sum_{\\{m\\}}n^{\\alpha}_{m } n^{\\beta}_{m ' } + \\sum_{\\{m\\}}n^{\\beta}_{m } n^{\\alpha}_{m ' } + \\sum_{m \\neq m'}n^{\\beta}_{m}n^{\\beta}_{m'}},\\ ] ]    @xmath74(mm'''|m''m ' ) } { \\sum_{m \\neq m'}n^{\\alpha}_{m}n^{\\alpha}_{m ' } + \\sum_{m \\neq m'}n^{\\beta}_{m}n^{\\beta}_{m'}}.\\ ] ]    there are essential and relevant differences between eqs . [ eq : param_u ] and [ eq : param_j ] and the similar framework of mosey _ et al . _ @xcite : _ i _ ) our on - site energy requires the computation of a smaller number of electron - repulsion integrals , namely only those involving the @xmath30 set ( i.e. @xmath75 integrals for the @xmath24 shell ) . this directly parallels the original definition of anisimov , in sharp contrast with the methodology of mosey _ et al . _ requiring eris between all basis functions contained in the cluster ; _ ii _ ) we consider the larger set @xmath61 of localized orbitals ( instead of @xmath30 ) in the calculation of the reduced occupation number given in eq . [ eq : focc ] ; _ iii _ ) in the mosey _ @xcite approach the atom of interest is embedded in a cluster of volume large enough to yield local convergence to bulk conditions , thus requiring calculations on clusters of increasing volume to ensure convergence , which can become extremely computationally expensive ; _ iv _ ) finally , we never solve the full hartree - fock problem for the solid ( roothaan s equations ) but project the dft kohn - sham wavefunctions on the minimal pao-3 g basis set , thus implicitly including in the renormalized density matrix all the local screening effects that come from the mean field solution on the local set .","summary":"the accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high - throughput quantum - mechanics ( htqm ) frameworks for accelerated materials discovery .","abstract":"the accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high - throughput quantum - mechanics ( htqm ) frameworks for accelerated materials discovery . htqm infrastructures rely on the predictive capability of density functional theory ( dft ) , the method of choice for the first principles study of materials properties . however , dft suffers of approximations that result in a somewhat inaccurate description of the electronic band structure of semiconductors and insulators . in this article we introduce , a pseudo - hybrid hubbard density functional that yields an improved prediction of the band structure of insulators such as transition - metal oxides , as shown for tio , mno , nio and zno , with only a _ negligible _ increase in computational cost ."}
{"article_id":"1406.3259","section_id":"c","document":"in conclusion , we have introduced , a pseudo - hybrid density functional that incorporates the hubbard correction of dft@xmath29 as a natural function of the electron density and chemical environment . the values of @xmath9 and @xmath10 are functionals of the electron density and provide a variational way of obtaining the proper description of insulators such as transition - metal oxides . although a more extensive validation of this functional is needed , the first results of our tests show improved agreement to higher levels of theory ( hybrid functionals , the _ gw _ approximation ) and to experimental measurements for the electronic properties of tmos at a fraction of the computational cost . this is an essential requirement for the design efficient algorithms for electronic structure simulations of realistic material systems and massive high - throughput investigations @xcite . we thank drs . r. j. mathar , n. j. mosey , a. n. andriotis , c. rdl , a. ferretti , a. calzolari , p. gopal , l. liyanage , h. shi , m. fornari , g. hart , o. levy , c. toher , d. irving , and b. himmetoglu for various technical discussions that have contributed to the results reported in this article . this work was supported by onr - muri under contract n00014 - 13 - 1 - 0635 and the duke university center for materials genomics . s.c . acknowledges partial support by nist ( # 70nanb12h163 ) and doe ( de - ac02 - 05ch11231 , bes program under grant # edcbee ) . we also acknowledge the texas advanced computing center ( tacc ) at the university of texas austin for providing hpc resources , and the cray corporation for computational assistance .","summary":"we introduce , a pseudo - hybrid hubbard density functional that yields an improved prediction of the band structure of insulators such as transition - metal oxides , as shown for tio , mno , nio and zno , with only a _ negligible _ increase in computational cost .","abstract":"the accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high - throughput quantum - mechanics ( htqm ) frameworks for accelerated materials discovery . htqm infrastructures rely on the predictive capability of density functional theory ( dft ) , the method of choice for the first principles study of materials properties . however , dft suffers of approximations that result in a somewhat inaccurate description of the electronic band structure of semiconductors and insulators . in this article we introduce , a pseudo - hybrid hubbard density functional that yields an improved prediction of the band structure of insulators such as transition - metal oxides , as shown for tio , mno , nio and zno , with only a _ negligible _ increase in computational cost ."}
{"article_id":"1407.1313","section_id":"i","document":"the study of exoplanets has matured greatly in the past decade . the _ kepler _ survey has enriched the body of known exoplanets with thousands of newly discovered objects @xcite . meanwhile , the improved capabilities of both space- and ground - based telescopes have enabled the collection of high - precision photometry for the brightest of these planets . the majority of the observations carried out to date have focused on the class of gas giant planets known as hot jupiters , which typically have orbital periods of a few days and atmospheric temperatures ranging between 1000 and 3000  k. these planets are some of the most favorable targets for detailed study , as they have relatively frequent and deep eclipses ( e.g. , * ? ? ? * ) .    by observing the secondary eclipse , which occurs when the planet passes behind its host star , we can deduce the shape of the planet s infrared emission spectrum and thereby study the properties of its dayside atmosphere ( e.g. , * ? ? ? * ; * ? ? ? the strong thermal emission of hot jupiters makes them ideal targets for this type of analysis , and measurements of the secondary eclipse in multiple wavelength bands are commonly used to construct low - resolution emission spectra at infrared wavelengths ( e.g. , * ? ? ? * ; * ? ? ? * ) . by comparing these observations with theoretical atmospheric models , we can constrain the planet s atmospheric pressure - temperature profile , chemistry , albedo , and global circulation patterns ( see * ? ? ? * for a recent review ) . infrared secondary eclipses have been measured for more than fifty exoplanets to date , of which the majority were obtained using the _ spitzer space telescope _ ( e.g. , * ? ? ? * ; * ? ? ? although the telescope s cryogen was exhausted in 2009 , _ spitzer _ s infrared array camera ( irac ; * ? ? * ) continues to operate in the 3.6 and 4.5  @xmath0 m bands . hot jupiters on eccentric orbits are of particular interest for atmospheric studies . in contrast to hot jupiters that lie on circular orbits and are therefore likely tidally - locked , these eccentric bodies experience diurnal forcing due to their nonsynchronous rotation as well as significant variations in the incident stellar flux throughout an orbit , leading to time - variable atmospheric forcing @xcite . the response of the planet s atmosphere reflects a balance between the time - varying stellar irradiation , the gravity wave propagation timescale , and the radiative time scale ( e.g. , * ? ? ? these mechanisms can lead to thermal gradients in the planet s atmosphere , as well as temporal variations in those gradients . unlike the circular case , phase curve observations of eccentric exoplanets can not uniquely distinguish between flux variations due to the planet s rotation and variations due to the changing irradiation experienced by the planet . observations of the secondary eclipse ingress and egress break this degeneracy by providing a near - instantaneous picture of the planet s dayside temperature distribution . specifically , the apparent offset of the center of eclipse phase due to a zonally - advected hot spot @xcite , along with deviations in the eclipse light curve morphology from a uniform disk model during ingress and egress @xcite , can be used to construct a two - dimensional map of the planet s dayside brightness distribution and constrain important properties of the atmosphere . the only successful secondary eclipse mapping observation to date is of the circular hot jupiter hd 189733b and was carried out independently by @xcite and @xcite using the 8  @xmath0 m band on _ spitzer_.    recent general circulation models for eccentric hot jupiters have shown that while the dayside atmospheric brightness of these planets may exhibit some spatial and temporal variability@xcite , the phase curves of these planets should be relatively constant from one orbit to the next @xcite . the presence or absence of long - term variability has important implications for atmospheric studies of these planets . it is common practice to combine data at different wavelengths from separate epochs years apart and assume that these data offer a consistent picture of the dayside emission spectrum . by comparing many individual secondary eclipse observations over a long time baseline , we can directly constrain the magnitude of orbit - to - orbit variations in the planet s atmospheric circulation .    in this paper , we analyze twelve secondary eclipse and two transit observations of the eccentric hot jupiter xo-3b obtained in _ spitzer _ s 4.5  @xmath0 m micron band . this planet has a mass of @xmath4 @xcite and orbits its host star ( spectral type f5v , @xmath5 , @xmath6  k , and @xmath7 ; * ? ? ? * ; * ? ? ? * ) with a period of 3.19  days and an orbital semi - major axis of @xmath8  au @xcite . with an orbital eccentricity of @xmath9 @xcite , the stellar flux received by this planet varies by a factor of 3.2 between periapse and apoapse . @xcite reported secondary eclipse depths for this planet in the 3.6 , 4.5 , 5.8 , and 8.0 micron spitzer bands , but these data were taken in stellar mode and as a result have a lower cadence and precision than the now - standard staring mode observations . here , we present twelve additional secondary eclipse and two transit observations with a total baseline of almost three years . the paper is organized as follows : the observations and methodology for extracting photometry are described in section  [ sec : obs ] . in section  [ sec : analysis ] , we present the best - fit eclipse parameters for individual secondary eclipse and transit observations as well as the combined eclipse light curve . we then use our results to obtain an updated orbital ephemeris and discuss the implications of our results for the planet s atmospheric dynamics in section  [ sec : dis ] .","summary":"we report secondary eclipse photometry of the hot jupiter xo-3b in the 4.5  m band taken with the infrared array camera ( irac ) on the _ spitzer space telescope_. we measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses . _ observations .","abstract":"we report secondary eclipse photometry of the hot jupiter xo-3b in the 4.5  m band taken with the infrared array camera ( irac ) on the _ spitzer space telescope_. we measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses . we fit these data simultaneously with two transits observed in the same band in order to obtain a global best - fit secondary eclipse depth of and a center of eclipse phase of . we assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05% . the new secondary eclipse observations extend the total baseline from one and a half years to nearly three years , allowing us to place an upper limit on the periastron precession rate of  degrees / day  the tightest constraint to date on the periastron precession rate of a hot jupiter . we use the new transit observations to calculate improved estimates for the system properties , including an updated orbital ephemeris . we also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit - to - orbit variability of an eccentric hot jupiter and demonstrate the consistency of multiple - epoch _ spitzer _ observations ."}
{"article_id":"1407.1313","section_id":"c","document":"fitting all twelve secondary eclipse and two transit observations simultaneously reduces the relative scatter in the binned residuals of the cumulative light curve ( figure  [ total ] ) to below the 0.05@xmath30 level , which enables us to better discern any deviations from a spatially - uniform dayside brightness distribution at the time of secondary eclipse . at the same time , the large number of visits allows us to assess the orbit - to - orbit variability of the planet s atmosphere and to calculate improved estimates of the orbital parameters and ephemeris . we discuss each of these aspects separately below .      in our global fit , we allowed the orbital inclination @xmath24 and scaled semi - major axis @xmath33 to vary as free parameters . these two quantities are important for secondary eclipse mapping because they are the primary determinants of the eclipse / transit duration as well as the length of ingress and egress , and small variations in their values can produce residuals during ingress and egress that mimic the expected signals from a planet with a dayside brightness distribution that is not spatially uniform . conversely , setting the inclination and scaled semi - major axis as free parameters may cause our optimization routine to partially `` fit away '' any deviation in the light curve due to a genuine spatially - uniform dayside brightness . we examine the effect of allowing inclination and scaled semi - major axis values to vary freely by utilizing a mcmc routine with 200,000 steps to calculate the best - fit values and @xmath133 uncertainties of the global eclipse parameters as well as @xmath24 and @xmath33 , for cases where we fit ( a ) the twelve secondary eclipses alone and ( b ) all the secondary eclipses and transits together , as was done in the global fit in section  [ subsec : fits ] . for the first case , we obtain @xmath134  degrees and @xmath135 ; for the second case , we obtain @xmath136  degrees and @xmath137 . we see that these values are consistent at the @xmath138 level ; the marginalized posterior probability distribution for inclination and scaled semi - major axis are shown in figure  [ prob ] with the @xmath133 and @xmath139 contours marked . it is evident that the inclusion of the transits in the cumulative fit places a much stronger constraint on the inclination and scaled semi - major axis , which underlines the advantage of including the two transits in our cumulative fit in section  [ subsec : fits ] . meanwhile , the consistency between the distributions of inclination and scaled semi - major axis for the cases with and without the transits demonstrates that the twelve eclipses alone do appreciably constrain the value of these two parameters . indeed , the values of the global eclipse depth and center of eclipse phase computed from the mcmc fits with and without transits included are consistent to well within @xmath133 .     and @xmath139 contours are denoted by the dotted lines and solid lines , respectively.,width=351 ]    we calculate an updated ephemeris for the xo-3 system using the transit times listed in table  [ tab : values ] , combined with all previously published values @xcite . we define the zeroth epoch as that of the first _ transit observation ( transit 1 in this paper ) and carry out a linear fit to all of the measured transit times . our new observations extend the previous baseline by almost a factor of two , and as a result we derive a new , more precise estimate of the planet s orbital period and zeroth epoch midtransit time : @xmath140 the observed minus calculated transit times using these updated ephemeris values are plotted in figure  [ octransits ]    , including the two most recent transit times calculated in this paper ( blue diamonds).,width=351 ]        we obtain a second , independent estimate of the orbital period by fitting the secondary eclipse times calculated in @xcite as well as this paper and arrive at a best - fit value of @xmath141  days . this period differs from the best - fit transit period by 2.1@xmath29 . the observed minus calculated secondary eclipse times are plotted in figure  [ oceclipses ] , where the zeroth epoch is defined here as the seventh eclipse analyzed in this work . we can derive limits on the periastron precession rate from the two different estimates of the orbital period . we use the formalism in @xcite to convert the updated estimates for orbital eccentricity and pericenter longitude into a zeroth epoch center of eclipse time . next , we introduce a @xmath142 term and calculate the predicted center of eclipse times at each of the other epochs of eclipse observations , which we then fit with a line to obtain a new value of the eclipse period . we limit the value of @xmath142 so that the resulting estimates of the eclipse period do not differ from the transit period calculated above by more than 3@xmath29 and obtain the following constraint on the periastron precession rate : @xmath143 for comparison , the expected periastron precession rate from general relativity and tides for the xo-3 system are @xmath144 and @xmath145  deg./day , respectively @xcite . the most stringent limit we can place on the periastron precession rate is still roughly a factor of ten larger than the largest expected precession rate from theory . in order to reduce the derived limits to values comparable with the theoretical periastron precession rates , we would need to reduce the uncertainty in the eclipse period by roughly a factor of ten , which can be achieved by obtaining more secondary eclipse measurements of xo-3b over a sufficiently long time baseline . to assess this possibility , we envisioned a future campaign of eleven secondary eclipse observations with _ spitzer _ , spaced apart in a manner identical to that of the eleven most recent observations analyzed in this work ( pid : 90032 ) . assuming that the timing of the future secondary eclipse observations match the predictions of our previously - calculated eclipse ephemeris and have uncertainties comparable with those in our data , we shifted the simulated future observations forward in time and calculated the new predicted uncertainty in orbital period . from this , we showed that a total baseline of about 15 years ( versus the current baseline of roughly three years ) is needed to detect the presence of periastron precession due to general relativity or tides . lrr[t ! ]    @xmath146 & 3.19153247 @xmath147 & days + @xmath148 & 2456419.04365 @xmath149 & @xmath150 + @xmath151 & 0.2769 @xmath152 & + @xmath153 & 347.2 @xmath154 & degrees + @xmath155 & 1478 @xmath156 & m s@xmath57 + @xmath157 & -203 @xmath158 & m s@xmath57 + @xmath159 & 972 @xmath160 & m s@xmath57 + @xmath161 & -202 @xmath162 & m s@xmath57 + @xmath163 & 185 @xmath164 & m s@xmath57 + @xmath165 & -402 @xmath166 & m s@xmath57 + @xmath167 & -0.023 @xmath168 & m s@xmath57day@xmath57 + jitter & 45.6 @xmath169 & m s@xmath57 + @xmath170 & 0.27005 @xmath171 & + @xmath172 & -0.0612 @xmath173 & + [ tab : rv ]    the measured center of eclipse times and updated transit ephemeris can be combined with the radial velocity measurements analyzed in @xcite to arrive at an updated estimate of the orbital eccentricity and pericenter longitude . using the methodology of that paper , we obtain @xmath174 and @xmath175  degrees . these values are consistent with the eccentricity and pericenter longitude estimates reported in @xcite ( @xmath176 and @xmath177  degrees ) . the updated values reduce the uncertainty in the eccentricity value by about a factor of two . the full results of our radial velocity fits are shown in table  [ tab : rv ] and figure  [ fig : rv ] . in addition to a new estimate of the orbital period ( @xmath146 ) and center of transit time ( @xmath148 ) , we obtain values for the semi - amplitude of the planet s radial velocity ( @xmath155 ) , the relative radial velocity zero points for data collected by each of the different spectrographs from which radial velocity measurements of the system have been obtained ( @xmath178 ) , the slope ( @xmath167 ) of the best - fit radial velocity acceleration , as well as the radial velocity jitter . a complete description of the methodology used in our radial velocity fits can be found in @xcite .        . there is no significant linear acceleration detected in the data . bottom panel : phased radial velocity curve . [ fig : rv ]      examining the combined light curve and associated residual series in figure  [ total ] , we do not discern any anomalous signal in the residuals during ingress and egress above the level of the noise ( @xmath15@xmath179 ) . therefore , we place an upper limit of 0.05% on the relative magnitude of any deviation from a spatially - uniform surface brightness . we generate model secondary eclipse light curves using a one - dimensional semi - analytic model developed in @xcite and compare the observed upper limit on dayside brightness variations with the model - predicted signals in the residuals during ingress and egress .     and @xmath180 , the case of offset hotspot corresponds to @xmath181  days and @xmath182 , and the case of zonally - uniform brightness corresponds to @xmath183  days and @xmath182.,width=321 ]    the atmospheric model takes as inputs the radiative timescale @xmath184 and the rotational frequency of the planet s atmosphere @xmath185 in units of the periastron orbital angular frequency . we generate simulated light curves for models with ( a ) @xmath186 ( radiative equilibrium ; wind velocities are not important in this case and @xmath185 is set to 0 ) , ( b ) @xmath181  days and @xmath182 , which entails super - rotating winds and a hotspot that is offset from the substellar point , and ( c ) @xmath183  days and @xmath182 , which entails a zonally - uniform brightness . figure  [ models ] shows the predicted residuals during ingress and egress from the simulated light curves . in order to determine the expected residuals during ingress and egress when fitting the simulated light curves with our uniform disk brightness eclipse model , we consider the case where we fix the center of eclipse time to the model value as well as the case where we let the center of eclipse time vary as a free parameter . in both cases , we allow the eclipse depth to vary and use a third - order polynomial to model the out - of - eclipse flux . the resulting residuals are shown in figure  [ comparison ] .     and atmospheric rotation speed @xmath185 to our spatially - uniform disk brightness eclipse model , where the center of eclipse is fixed to the model value . bottom : same as above , but with the center of eclipse time as a free parameter.,width=351 ]    the magnitude of the residual signal during ingress and egress is reduced in both cases . in the case where the eclipse time is fixed , the least - squares algorithm adjusts the eclipse depth to partially compensate for the relatively large deviations from spatially - uniform brightness , resulting in a slight reduction in the magnitude of the expected residuals and non - zero residuals during eclipse . in the case where the eclipse time is allowed to vary , there is an additional reduction that most strongly affects the residuals from the model with large anti - symmetric residual signals during ingress and egress ( i.e. , @xmath181  days and @xmath182 ) . as discussed in @xcite , anti - symmetric residuals during ingress and egress can be `` fit away '' by adjusting the center of eclipse phase . in our cumulative fit of the twelve secondary eclipses , we have imprecise knowledge of the orbital parameters and must allow the eclipse phase to vary as a free parameter . as a result , the maximum expected relative magnitude of the residual signal during ingress and egress is @xmath15@xmath187 , much less than the noise level . therefore , we can not place meaningful constraints on the radiative timescale and wind speeds of xo-3b from these data . when fitting the secondary eclipse to the model light curve , we included the phase constant @xmath55 as a free parameter to describe variation in the observed out - of - eclipse flux due to the shape of the planet s phase curve in the region of the secondary eclipse . the global best - fit value , @xmath188 , is distinct from a flat phase curve slope at the @xmath189 level . it is generally difficult to estimate the slope of the phase curve from individual secondary eclipse observations , as this slope is degenerate with the change in flux due to the long - term position drift of the telescope . this is evident from the large scatter in phase constant values around the global best - fit value ( see figure  [ params ] ) . however , by using all twelve secondary eclipse observations in the combined fit , we are able to break this degeneracy and obtain a unique estimate of the phase curve slope in the region of the secondary eclipse . the observed increase in the planet s brightness is likely due to an increase in the atmospheric temperature due to increasing stellar irradiation experienced by the planet during secondary eclipse . another possible contributing factor may be changes in the apparent atmospheric brightness due to planetary rotation , which may be caused by an offset hotspot situated to the west of the substellar point during secondary eclipse . such an offset hotspot can be generated by either westward winds or the presence of clouds east of the substellar point . recent atmospheric circulation models do not readily produce westward winds that would lead to a westward offset of the hotspot at infrared wavelengths @xcite . while non - uniform clouds have been inferred from visible observations of kepler-7b @xcite , the significantly higher temperature and surface gravity of xo-3b place the equilibrium cloud decks at pressure levels greater than those probed by the 4.5-micron bandpass . yet another possibility is non - uniform atmospheric chemical composition across the planet . in particular , variations in the abundance of co@xmath190 in the atmosphere of hot jupiters has been shown to induce changes in the 4.5-micron flux from one side to the other , though the effect on the variation of emergent flux with phase is largely dampened by longitudinal homogenization of chemical abundances through circulation @xcite . therefore , while all of these mechanisms may contribute to the brightening of xo-3b at the time of secondary eclipse , it is expected that the overall warming of the planet due to decreasing planet - star distance is the dominant factor . a full - orbit phase curve analysis of xo-3b is contained in a parallel study ( cowan et al . 2014 , in prep . ) . we can use the detection of brightening during eclipse as an independent constraint on the atmospheric properties . in particular , long radiative timescales tend to keep the planet from warming up as it approaches periastron . the increasing flux at superior conjunction , which occurs shortly before periastron , therefore indicates a relatively short radiative timescale . we generate simulated phase curves using the model in @xcite for a range of @xmath184 and @xmath185 values . the positive global phase constant rules out radiative timescales longer than one day . this is consistent with the results of a phase curve analysis of another eccentric hot jupiter , hat - p-2b , which constrain the radiative timescale to @xmath191  hours @xcite . confidence limits ( dashed lines ) . the single early epoch measurement is from a partial phase curve observation on ut 2012 april 5 - 8 and was collected as part of a different observation program than the other eleven secondary eclipses.,width=351 ]      we next consider whether or not the planet displays any evidence for orbit - to - orbit variability in its dayside brightness . recent work by @xcite has suggested that measurable variations in the eclipse depth of a planet might result from orbit - to - orbit variations in the abundance of condensable species such as tio or silicates . in figure [ params ] , the best - fit eclipse parameters and uncertainties for the twelve individual eclipses are compared with the global best - fit eclipse parameters and uncertainties . the individual eclipse parameter values are largely consistent with the global values , and there is no apparent time - correlated variation in their values across the twelve eclipses . we find an average deviation in the individual eclipse depths for xo-3b at 4.5  @xmath0 m on the order of 5% , which is roughly consistent with the measurement uncertainty . in @xcite , the eclipse depth at 4.5  @xmath0 m was calculated to be @xmath192 , which is consistent with our global eclipse depth at the 2.1@xmath29 level . the agreement of individual eclipse depths measured at many different epochs suggests that any variability in the eclipse depth that is due to variability in xo-3b s global circulation patterns is likely small ( @xmath193% ) . recent three - dimensional ( 3d ) atmospheric circulation models that only consider radiative , dynamical , and equilibrium chemical processes find fairly low levels ( @xmath194% ) of orbit - to - orbit variability in the atmospheres of circular @xcite and eccentric @xcite exoplanets alike . there are only two planets with comparable observational limits on their orbit - to - orbit variability : hd 189733b , a hot jupiter on a circular orbit , and gj 436b , which is a warm neptune with a relatively modest orbital eccentricity ( @xmath195 ; * ? ? ? while the effects of condensation and/or turbulent mixing in the atmosphere of xo-3b may lead to some orbit - to - orbit variation in the eclipse depths , the relatively low level of variability evident in our data suggest that these processes do not appear to significantly alter the atmosphere s thermal structure on orbit - to - orbit ( and longer ) timescales at the pressure levels probed by the 4.5  @xmath0 m bandpass . these same data can also be used to evaluate the reliability of the reported uncertainties in secondary eclipse depths measured by the _ spitzer space telescope_. @xcite argue that errors in the eclipse parameters calculated from _ spitzer _ data may be significantly underestimated , a statement which has major implications for the ability to use secondary eclipse photometry to deduce characteristics of exoplanet atmospheres . in particular , @xcite argue that individual secondary eclipse measurements do not fully account for detector systematics , which may lead to poor reproducibility of individual eclipse depth measurements and result in apparently inconsistent values for the eclipse depth from one study to the next . the 2.1@xmath29 discrepancy between our global best - fit eclipse depth and the depth measured from the single 4.5  @xmath0 m observation in @xcite is consistent with this purported tendency to underestimate the uncertainties of single - eclipse depths . however , the notable self - consistency of the individual depth measurements for the twelve secondary eclipses analyzed in our work ( figure  [ params ] ) indicates that our technique of extracting photometry from the observations does adequately account for instrumental effects . therefore , we expect that the reported uncertainties in the parameter values from both individual eclipse fits and the combined fit are an accurate representation of the measurement uncertainties . this is the first time that such an extensive data set has been collected in the short - wavelength ( 3.6 and 4.5 micron ) _ spitzer _ channels , which are characterized by larger systematic effects due to the intrapixel sensitivity variations than the longer wavelength 5.8 and 8.0 micron channels . previous multiple - visit studies of hd 189733b and gj 436b were both at 8.0 microns and were thus not sufficient to definitively assess the validity of the arguments in @xcite .","summary":"the new secondary eclipse observations extend the total baseline from one and a half years to nearly three years , allowing us to place an upper limit on the periastron precession rate of  degrees / day  the tightest constraint to date on the periastron precession rate of a hot jupiter .","abstract":"we report secondary eclipse photometry of the hot jupiter xo-3b in the 4.5  m band taken with the infrared array camera ( irac ) on the _ spitzer space telescope_. we measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses . we fit these data simultaneously with two transits observed in the same band in order to obtain a global best - fit secondary eclipse depth of and a center of eclipse phase of . we assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05% . the new secondary eclipse observations extend the total baseline from one and a half years to nearly three years , allowing us to place an upper limit on the periastron precession rate of  degrees / day  the tightest constraint to date on the periastron precession rate of a hot jupiter . we use the new transit observations to calculate improved estimates for the system properties , including an updated orbital ephemeris . we also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit - to - orbit variability of an eccentric hot jupiter and demonstrate the consistency of multiple - epoch _ spitzer _ observations ."}
{"article_id":"1407.1313","section_id":"c","document":"in this paper , we analyzed twelve secondary eclipse observations of the hot jupiter xo-3b in the 4.5  @xmath0 m _ spitzer _ band . after correcting for the intrapixel sensitivity effect , we fit each photometric time series with a uniform disk model light curve and measured the best - fit eclipse depths and center of eclipse times . we included two transits observed in the same band and fit all of the data simultaneously to obtain a global best - fit secondary eclipse depth of @xmath196 and a center of eclipse phase of @xmath197 , as well as updated values for orbital inclination ( @xmath198  degrees ) , planet - to - star radius ratio ( @xmath199 ) , and scaled orbital semi - major axis ( @xmath200 ) . we combined the two transits analyzed in this work with all previously - published values and derived a more precise estimate of xo-3b s orbital period ( @xmath201  days ) . by comparing the transit period with one derived from the secondary eclipse times , we were able to constrain the orbital periastron precession of the planet to between @xmath202 and @xmath3  degrees per day . in addition , we incorporated the measured center of eclipse times and updated transit ephemeris in a radial velocity analysis to arrive at updated orbital eccentricity and pericenter longitude values of @xmath174 and @xmath175  degrees , respectively . the best - fit eclipse depths and center of eclipse times for individual secondary eclipse observations were found to be consistent with the corresponding global values . the lack of any discernible time - correlated variation in the eclipse depth values is indicative of a low level ( @xmath203 ) of orbit - to - orbit variability in the planet s atmospheric brightness and is consistent with recent three - dimensional atmospheric circulation models @xcite . furthermore , the self - consistency of the individual best - fit eclipse parameter values derived from data collected over a span of more than three years demonstrates the reliability of multiple - epoch _ data and our ability to adequately account for instrumental effects . our cumulative fit reduced the relative scatter in the binned residuals from the best - fit solution to less than 0.05% , and we did not observe any signals in the residual series during ingress and egress above the noise level . we therefore conclude that any deviations from a spatially - uniform surface brightness on the planet s dayside must have a relative magnitude of less than 0.05% . while the maximum expected residual signals during ingress and egress from plausible atmospheric models are smaller than the noise level achieved in our observations , our 4@xmath29 detection of brightening at the time of eclipse enabled us to constrain the atmospheric radiative time scale of xo-3b to @xmath204  day . more stringent constraints on xo-3b s orbital eccentricity from radial velocity fits could eventually yield predictions for the center of eclipse times that are precise enough to circumvent the problem encountered in our analysis , where the magnitude of the expected residual signal during ingress and egress was reduced by about an order of magnitude when we allowed the secondary eclipse time to vary in the fits . meanwhile , an analysis of the available full - orbit phase curve of xo-3b could be combined with the results presented here to construct a more detailed picture of the planet s atmospheric properties . lastly , a similarly - 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ir secondary eclipse photometry of two hot jupiters : wasp-48b and hat - p-23b . _ apj _ , 781:0 109 , 2014 . a.  p ' al , g.  ' a. bakos , g.  torres , r.  w. noyes , d.  a. fischer , j.  a. johnson , g.  w. henry , r.  p. butler , g.  w. marcy , a.  w. howard , b.  sip \" ocz , d.  w. latham , and g.  a. esquerdo . refined stellar , orbital and planetary parameters for the eccentric hat - p-2 planetary system . _ mnras _ , 401:0 2665 , 2010 . a.  p. showman , j.  j. fortney , y.  lian , m.  s. marley , r.  s. freedman , h.  a. knuston , and d.  charbonneau . atmospheric circulation of hot jupiters : coupled radiative - dynamical general circulation model simulations of hd 189733b and hd 209458b . _ apj _ , 699:0 564 , 2009 . k.  o. todorov , d.  deming , h.  a. knutson , a.  burrows , j.  j. fortney , n.  k. lewis , n.  b. cowan , e.  agol , j .- m . desert , p.  b. sada , d.  charbonneau , g.  laughlin , j.  langton , and a.  p. showman . _ warm spitzer _ photometry of three hot jupiters : hat - p-3b , hat - p-4b and hat - p-12b . _ apj _ , 770:0 102 , 2013 . j.  n. winn , m.  j. holman , g.  torres , p.  mccullough , c.  johns - krull , d.  w. latham , a.  shporer , t.  mazeh , e.  garcia - melendo , c.  foote , g.  esquerdo , and m.  everett . the transit light curve project . ix . evidence for a smaller radius of the exoplanet xo-3b . _ apj _ , 683:0 1076 , 2008 . j.  n. winn , j.  a. johnson , d.  fabrycky , a.  w. howard , g.  w. marcy , n.  narita , i.  j. crossfield , y.  suto , e.  l. turner , g.  esquerdo , and m.  j. holman . on the spin - orbit misalignment of the xo-3 exoplanetary system . _ apj _ , 700:0 302 , 2009 .","summary":"we fit these data simultaneously with two transits observed in the same band in order to obtain a global best - fit secondary eclipse depth of and a center of eclipse phase of .","abstract":"we report secondary eclipse photometry of the hot jupiter xo-3b in the 4.5  m band taken with the infrared array camera ( irac ) on the _ spitzer space telescope_. we measure individual eclipse depths and center of eclipse times for a total of twelve secondary eclipses . we fit these data simultaneously with two transits observed in the same band in order to obtain a global best - fit secondary eclipse depth of and a center of eclipse phase of . we assess the relative magnitude of variations in the dayside brightness of the planet by measuring the size of the residuals during ingress and egress from fitting the combined eclipse light curve with a uniform disk model and place an upper limit of 0.05% . the new secondary eclipse observations extend the total baseline from one and a half years to nearly three years , allowing us to place an upper limit on the periastron precession rate of  degrees / day  the tightest constraint to date on the periastron precession rate of a hot jupiter . we use the new transit observations to calculate improved estimates for the system properties , including an updated orbital ephemeris . we also use the large number of secondary eclipses to obtain the most stringent limits to date on the orbit - to - orbit variability of an eccentric hot jupiter and demonstrate the consistency of multiple - epoch _ spitzer _ observations ."}
{"article_id":"cond-mat0307118","section_id":"i","document":"the interplay between frustration and quantum fluctuations in antiferromagnetic ( af ) spin-1/2 systems in two dimensions ( d ) has attracted much experimental and theoretical attention in past years . in particular , many studies have been devoted to identify the possible phases which may appear at @xmath5 after the destabilization of a collinear af nel phase by quantum fluctuations when increasing frustration in @xmath6 invariant spin models . large-@xmath7 approaches predict then a valence bond crystal ( vbc ) phase , with long range order ( lro ) of singlet entities ( dimers , plaquettes of resonnating dimers ... ) and thus breaking translational symmetry and/or others space symmetries , if the transition out of the nel phase is continuous  @xcite . numerical results obtained from exact diagonalization ( ed ) studies support this prediction for several models : the @xmath8 model on the honeycomb lattice  @xcite and some models where the spins sit on a square lattice such as the crossed chain model  @xcite and the quadrumerized shastry - sutherland model  @xcite .    [ h ! ] +    [ h ] +    [ h ] +    yet , for the much studied @xmath1 model on the square lattice with a next - nearest - neighbor frustrating coupling @xmath9 in addition to the nearest - neighbor coupling @xmath10 ( see fig . [ fig_exchanges ] where the @xmath1 model corresponds to @xmath11 ) , the validity of this scenario remain unclear  @xcite . its classical ground - state has @xmath12 nel lro for @xmath13 and is the degenerate manifold corresponding to two decoupled nel states on interpenetrating square lattices for @xmath14 . there is a large consensus that @xmath12 nel lro ( see fig .  [ types_neel ] ) survives to quantum fluctuations for @xmath15 and quantum fluctuations select either a @xmath16 or a @xmath17 nel state in the manifold of classical ground - states for @xmath18 , whereas , in the intermediate range @xmath19 between these two gapless states , there is a phase without nel lro gapped to spin excitations . the transition out of the @xmath12 nel phase is second order while the transition out of the @xmath16 nel phase has been predicted to be of first order  @xcite but may be close to second order  @xcite .    whether this intermediate phase has vbc lro or is some resonnating valence bond ( rvb ) phase which do not break any space symmetries , i.e. a spin - liquid , is debated . earliest investigations , from ed calculations on samples up to @xmath20 spins , have shown enhanced columnar dimer - dimer correlations in this intermediate region , but the finite - size scaling of the order parameter for the columnar vbc lro of dimers , shown in fig . [ types_vbc](a ) , were not conclusive  @xcite . dimer series expansions , however , were in favor of vbc lro : earliest studies favored columnar lro  @xcite while latter calculations have lead to propose the occurence of two different vbc phases : the columnar dimer phase for @xmath21 and a columnar dimer phase with plaquette type modulation , as shown in fig . [ types_vbc](c ) , for @xmath22 , separated by a second order transition  @xcite . on the other hand , studies based on the green function monte carlo method , for systems of sizes larger than those which may be investigated by ed calculations , first favored either a plaquette lro  @xcite , as shown in fig . [ types_vbc](b ) , or a columnar dimer lro with plaquette type modulation  @xcite , similar to one of ref  @xcite , for @xmath23 . besides , it was concluded in ref  @xcite that the finite size scaling of the susceptibility to columnar dimer lro from both monte carlo and ed calculations would exclude columnar dimer lro at @xmath24 . however , latter calculations  @xcite , by the same group which favored the plaquette lro  @xcite , have lead to conclude in favor of the occurence of a spin - liquid phase for @xmath25 whereas it was pointed out that the ocurrence of the plaquette lro will be unlikely in view of the spatial symmetries of the low lying singlets in the ed spectra . in their latest study these authors suggest either a spin - liquid or , possibly , the columnar state but with a weak order parameter@xcite yet , as the monte carlo calculations and the series expansions start from some trial state which may bias the results and involve approximations which are not fully under control , while ed calculations which were performed on samples having different lattice symmetries and display irregular finite size scaling , the nature of the ground - state in the intermediate region remain an open question . in this paper , motivated by a recent paper of nersesyan and tsvelik  @xcite , refered as ( nt ) in the following , we attempt to shed light on this issue from ed calculations on a spatially anisotropic version of the @xmath1 model with two different nearest neighbor couplings . the hamiltonian of this @xmath0 model ( named the confederate flag model by nt ) reads : @xmath26 %   ---------                   \\,j\\,{\\bf s}_{l , m}.{\\bf s}_{l+1,m } \\,+\\ ,                   \\,j'\\,{\\bf s}_{l , m}.{\\bf s}_{l , m+1 } \\,+\\ , \\nonumber \\\\                 & \\,j_2\\ , ( { \\bf s}_{l , m}.{\\bf s}_{l+1,m+1 } \\,+\\ ,                             { \\bf s}_{l , m}.{\\bf s}_{l+1,m-1 } ) \\ , ] \\label{eq - heis}\\end{aligned}\\ ] ] which may also be viewed as an array of @xmath27 spin chains of lenght @xmath28 , if @xmath29 . the exchange @xmath30 ( see fig .  [ fig_exchanges ] ) couples first - neighbor ( horizontal ) pairs of spins along the chains , exchange @xmath31 first - neighbor spins in the ( vertical ) transverse direction and exchange @xmath9 second - neighbor pairs on the diagonals of the square plaquettes . all exchanges are assumed positive , describing af couplings . for @xmath32 one recovers the @xmath1 model . mostly interested with the limit @xmath33 , we shall also focus on the case @xmath34 . the classical ground - state of the @xmath0 model is rather similar to the one of the @xmath1 model . when @xmath29 , one has @xmath12 nel lro if @xmath35 , @xmath16 nel lro if @xmath36 and the ( horizontal ) @xmath30 chains are decoupled if @xmath37 . for @xmath38 , one has @xmath12 nel lro if @xmath39 , @xmath17 nel lro if @xmath40 whereas the ( vertical ) @xmath31 chains are decoupled if @xmath41 . this hamiltonian has been much studied in past years for a finite number of chains , the so - called @xmath27-leg ladders , generally in the case of open boundary conditions in the transverse direction ( for @xmath42 since if @xmath43 open and periodic boundary conditions are equivalent ) . numerical studies  @xcite based on the density matrix renormalization group ( dmrg ) method or monte carlo approaches have shown that the @xmath27-leg unfrustrated ladders ( @xmath44 ) display a behavior analogeous to a @xmath45-spin chain  @xcite , being fully gapped if @xmath27 is even and gapless if @xmath27 is odd . so @xmath12 nel lro only occurs in the limit @xmath46 . the effect of frustration has been especially investigated theoretically and numerically for the @xmath47-leg ladder ( see ref  @xcite and references therein ) . these studies have concluded that one has two phases separated by a transition line which has been found to coincide with the line of maximum frustration where the energy per spin reaches its maximum , noted @xmath48 in the following for all values of the number of chains . this line starts as @xmath49 for @xmath50 and bend slightly with increasing @xmath31 so that @xmath51 at @xmath52  @xcite ( as the dashed line in fig . [ phase_diag ] ) . if @xmath53 one has the haldane phase , where the two spins on a rung tend to be in a triplet state , so named as it contains the point @xmath54 whose low - energy spectrum is similar to that of a spin-1 heisenberg chain . if @xmath55 on has the so called singlet phase , so called as it contains the case @xmath56 with @xmath44 , where the ground - state consists of singlets on each rung . as shown by white  @xcite the singlet phase is also an haldane phase with diagonally situated next - nearest neigbor spins coupling to form an effective @xmath57 . both phases have a topological order , breaking a hidden @xmath58 symmetry , which can be measured by non - local string order parameters , similar to the string order parameter of the @xmath57 heisenberg chain . the two phases are fully gapped like the @xmath57 chain  @xcite , and have a non degenerate singlet ground - state . these ground - states become degenerate on the transition line @xmath48 . the nature of the transition has been debated . in a dmrg study  @xcite it was predicted that the transition line would be gapless for @xmath9 lower than @xmath59 . but more recent dmrg calculations  @xcite have concluded that a gap subsits between the two - fold degenerate ground - state and the excited states for all @xmath60 . so the transition is 1th order on the whole line @xmath48 in agreement with bosonization results in the limit of vanishing interchain coupling  @xcite . the elementary excitations then consist of gapped deconfined spin-1/2 spinons which may be viewed as kinks interpolating between the two ground - states  @xcite . note that these results imply that the classical behavior of independent chains on the line @xmath37 is then destabilized by quantum fluctuations . the single heisenberg chain is gapless . the spectrum of two independent chains too . the existence of a finite gap excludes such a behavior . a dmrg study of the three - leg frustrated ladder with open boundary conditions in the transverse direction  @xcite has shown that this system exhibit two phases separated by a transition line also coincident with the line of maximum frustration @xmath48 and which is a curve quasi identical to the one found for the 2-leg ladders . the phases are analogeous to those of the 2-leg ladders . the small @xmath9 phase , which is the phase of the unfrustrated ladder , show a tendency of the three spins on a vertical line to pair in a state of minimum spin whereas they tend to pair in a state of maximum spin in the large @xmath9 phase , which is equivalent to the spin-3/2 chain . on the transition line a bosonization study at weak interchain coupling @xcite has predicted that the ground - state is a chiral spin - liquid . recently nt , using an approach based on the bosonization method , investigated the crossover from finite @xmath27 to @xmath46 in the @xmath0 model on the line @xmath61 , in the limit of small interchain coupling ( @xmath62 ) and predicted that the classical behavior of independent chains is unstable to a special rvb ( spin - liquid ) state which may be a realization of the chiral @xmath63-flux rvb state  @xcite . its ground - state has a @xmath64 degeneracy , for @xmath27 even and transverse periodic boundary conditions , associated to the breaking of a local @xmath65 symmetry , present in the bosonised version of the model , corresponding to the invariance under independent translations by one lattice spacing along individual chains . each ground - state may be caracterized by different values of a set of non - local order parameters . these non - local order parameters correlate spins on two adjacent chains whereas different pairs of chains are uncorrelated . the elementary excitations consist of deconfined spin-1/2 spinons interpolating between different ground - states . these excitations are either gapless , as predicted for some values of the number of chains , such as @xmath66 , or gapped , as for the @xmath47-leg ladder ( @xmath43 ) . [ h ]    two questions then arise . first , does the state predicted by nt extends outside the range of small interchain coupling . second , what is the nature of the behavior in its vicinity , in particular for the case of an infinite number of chains . below we report results of ed calculations of @xmath67 spins for @xmath68 to shed light on these questions and more generally the phase diagram of the @xmath0 model . we shall consider only the case of an even number of chains . the ed calculations have been carried out on samples of @xmath67 spins in @xmath27 chains of lenghts @xmath28 with periodic boundary conditions both along and perpendicular to the chains : samples of 4 chains with @xmath69 spins and 6 chains with @xmath70 spins . additional calculations were also performed for the @xmath43 ladder for @xmath71 in order to compare with the @xmath72 results . contrary to the samples considered in previous ed calculations for the @xmath1 model , all samples have translation vectors parallel to the basis vectors of the square lattice which leads to a regular evolution of the properties with increasing @xmath28 and @xmath27 . examination of the ed spectra indicates that the model will display two nel phases , with magnetic wave - vectors @xmath12 and @xmath16 , separated by a magnetically disordered intermediate region , in the limit @xmath73 with both @xmath74 and @xmath46 , as shown in fig . [ phase_diag ] . at variance with a study based on the drmg method  @xcite , which appeared very recently on a preprint server , our results provide indications that the classical behavior of independent chain is destabilized by quantum fluctations and the rvb state of nt may occur along a curve coincident with the line of maximum frustration @xmath48 , located in this intermediate region , up to large interchain coupling . they also indicate that the intermediate region of the @xmath75 phase diagram ( see fig . [ phase_diag ] ) , on both sides of this line , has columnar vbc lro , which may extend up to @xmath4 and could already appear for @xmath27 even @xmath76 .    in sec.ii we describe the evolution of the energy per spin vs @xmath9 and @xmath31 and the location of the curve @xmath48 . the properties of the model in the regions of @xmath12 nel lro , @xmath16 nel lro and in the intermediate region are presented in sec . iii , iv and v , respectively . vi gives a summary of the our results and discuss briefly the possible behavior of the model for ferromagnetic @xmath9 and @xmath31 . [ h ]    [ h ]","summary":"the phase diagram of a spin-1/2 model is investigated by means of exact diagonalizations on finite samples . this model is a generalization of the model on the square lattice with two different nearest - neighbor couplings and may be also viewed as an array of coupled heisenberg chains . the results suggest that the resonnating valence bond state predicted by nersesyan and tsvelik [ phys . rev . b * 67 * , 024422 ( 2003 ) ] for is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum . ( ) +    pacs numbers : 75.10.jm ; 75.50.ee ; 75.40.-s","abstract":"the phase diagram of a spin-1/2 model is investigated by means of exact diagonalizations on finite samples . this model is a generalization of the model on the square lattice with two different nearest - neighbor couplings and may be also viewed as an array of coupled heisenberg chains . the results suggest that the resonnating valence bond state predicted by nersesyan and tsvelik [ phys . rev . b * 67 * , 024422 ( 2003 ) ] for is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum . this line is likely bordered on both sides by a columnar dimer long range order . this columnar order could extends for which correspond to the model .    ( ) +    pacs numbers : 75.10.jm ; 75.50.ee ; 75.40.-s"}
{"article_id":"cond-mat0307118","section_id":"i","document":"exact diagonalization calculations provide support that the rvb behavior predicted by nersesyan and tsvelik in the @xmath0 model at @xmath275 may be realized and extends along a curve coincident with the line of maximum frustration @xmath85 where it subsists up to large interchain coupling for an even number @xmath27 of chains of lenght @xmath74 . the line @xmath85 is the analogue of the transition line @xmath61 in the classical model on which the chains decouples . the independent chain behavior appears destabilized by quantum fluctuations . the line @xmath85 is located in an intermediate region of the phase diagram where the present results suggest that the ground - state displays a columnar @xmath16 valence bond long range order . this region of columnar order will have a finite width as soon as @xmath194 and extends on both sides of @xmath85 up to a value of @xmath31 close but smaller than @xmath30 for finite @xmath27 , that increase with @xmath27 and approach @xmath32 for @xmath131 . it separates two phases that are fully gapped haldane like phases for finite @xmath27 and evolves respectivelly to the @xmath12 and @xmath16 nel phases for @xmath46 . the haldane like phases have probably a topological order . its nature for @xmath42 deserves further investigation . the occurence of a columnar order for @xmath31 smaller than @xmath30 , next to the nel phase , agrees with the scenario deduced from large-@xmath7 approaches that valence bond crystal order is expected after the destabilization of a collinear af nel phase . it is possible that the columnar order may extend for @xmath4 if @xmath131 and that this scenario may be realized also in the @xmath1 model which corresponds to @xmath32 . the behavior of the @xmath0 model in the intermediate region for @xmath4 requires nonetheless further study to confirm this hypothesis . the exact diagonalization method is limited to systems of small sizes . the extrapolations to the infinite lenght limit are affected by uncertainities . indeed , some one dimensional systems requires data at very large lenghts to allow a reliable extrapolation to the infinite lenght limit . for certain systems there may be a crossover in the scaling behavior of the gaps at a very large lenght as shown for instance in ref . @xcite where some gaps do not decrease monotonicaly with the lenght beyond a certain lenght . for the present model we have assumed a monotonicaly decreasing smooth evolution of the gaps with increasing lenght . the assumption appears reasonable in view of the data available at large lenghts in the case of two chains ( the 2-leg ladder ) . yet , a small change in the evolution of the gaps at very large lengths is not to be excluded for those gaps that appear to extrapolate to vanishing or quasi vanishing values . the scaling behavior of the gaps to the low lying excited states as a function of the number of chains deserves further studies . in particular , calculations using an approach that can deal with very large systems , like possibly the dmrg method , would be worth to firmly establish wether the gaps that have been conjectured to extrapolate to zero really vanish or are just small but finite in the thermodynamic limit and thus check the exact degeneracy of the ground state on the line of maximum frustration . this study was limited to the case of af couplings . yet , the @xmath0 model with af intrachain coupling ( @xmath276 ) , but interchain couplings ( @xmath277 ) that are either or both ferromagnetic ( fm ) is also of interest  @xcite . indeed , fm couplings may be relevant to modelize certain 2-leg ladder materials  @xcite and might be introduced to describe some @xmath27-leg compounds . classically , the ground - state of the @xmath0 model remains af for @xmath278 and @xmath279 ( if @xmath79 ) . it is the @xmath12 nel state for @xmath280 , the @xmath16 nel state for @xmath281 , and the @xmath30 chains stay decoupled for @xmath61 . the spin-1/2 , 2-leg ladder ( with fm @xmath31 and/or @xmath9 ) has been studied by bosonization  @xcite and drmg  @xcite calculations . these studies showed that the singlet and haldane phases extends for @xmath282 , separated by a transition line which is the continuation of the boundary line for @xmath283 . this transition line is also the line of the points of maximum frustration @xmath85 . the transition line , however , does not deviate from the classical boundary line @xmath61 and the transition appears to be 2nd order for @xmath284 , instead of 1th order for @xmath283 . in the bosonization approach , the interchain interaction , derived at 1th order , proportional to @xmath285 which now turn to be @xmath286 , is then irrelevant and does not open a gap . the system is predicted to be critical and to consist of independent chains  @xcite . a similar change of sign of the interchain interactions appears in the bosonization approach of nt if @xmath287 for the 4-leg ladder . the same critical behavior could occur on the transition line in the 4-leg ladder and perhaps for @xmath27-leg ladders ( @xmath42 even ) . preliminary calculations indicate that the curve @xmath85 also remains on the classical boundary line for @xmath80 , where the model might be critical , perhaps down to @xmath288 . the model may exhibit `` sliding luttinger spin - liquid '' behavior as proposed for the crossed chain model  @xcite , at least for not too strong interchain interactions . on the line @xmath61 , the lowest energies @xmath198 in spin sector @xmath98 evolves linearly with @xmath98 . for @xmath46 , there may be also an intermediate region with a spin - liquid state around this line in between the nel phases , where @xmath289 . this issues deserve further study . acknowledgments : i thank patrick azaria , philippe lecheminant and claire lhuillier for fruitful discussions . i thank the aspen center for physics , where this work was continued , for hospitality . computations were performed at the centre de calcul pour la recherche de luniversit pierre et marie curie and at the institut de dveloppement des recherches en informatique scientifique du cnrs under contract 981052 .                                                                                    at 2nd order appears an additional contribution to the interchain interaction that could open a gap . however , this gap would be likely very small , probably much smaller than in the case of af interchain coupling and difficult to see numerically .","summary":"this line is likely bordered on both sides by a columnar dimer long range order . this columnar order could extends for which correspond to the model .   ","abstract":"the phase diagram of a spin-1/2 model is investigated by means of exact diagonalizations on finite samples . this model is a generalization of the model on the square lattice with two different nearest - neighbor couplings and may be also viewed as an array of coupled heisenberg chains . the results suggest that the resonnating valence bond state predicted by nersesyan and tsvelik [ phys . rev . b * 67 * , 024422 ( 2003 ) ] for is realized and extends beyond the limit of small interchain coupling along a curve nearly coincident with the line where the energy per spin is maximum . this line is likely bordered on both sides by a columnar dimer long range order . this columnar order could extends for which correspond to the model .    ( ) +    pacs numbers : 75.10.jm ; 75.50.ee ; 75.40.-s"}
{"article_id":"1202.4840","section_id":"i","document":"type iin supernovae ( sne  iin ) , a designation first proposed by @xcite , are characterized by spectra with a narrow h@xmath7 emission line superimposed on a broad emission component @xcite that lacks a broad p - cygni absorption feature @xcite . most sne  iin are core collapse events that are due to shock interaction of the ejecta with the circumstellar material ( csm ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , although some thermonuclear explosions are thought to detonate in a hydrogen - rich environment producing sne  iin - like events ( cf . * ; * ? ? ? * ; * ? ? ? as the shock interacts and heats the dense csm , there is a rapid increase in the production of uv photons . sne  iin are a very heterogeneous group ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ranging from the most luminous sne ( e.g. sn  2006gy with @xmath8 and sn  2008am with @xmath9 ; * ? ? ? * ; * ? ? ? * ) to some of the fainter ( e.g. sne  1997bs and 2008s with @xmath10 and @xmath11 , respectively ; * ? ? ? * ; * ? ? ? the nature of the fainter objects , such as sne  1997bs and 2008s , is unclear @xcite . many argue that they are non - terminal outbursts as opposed to core collapse objects ( e.g. * ? ? ? * ) and have been designated  supernova impostors \" @xcite . the great eruption of @xmath12  car is frequently cited as a galactic analogue . however , this may be misleading since the great eruption of @xmath12  car was an unusual event and none of the extragalactic impostors resemble it in terms of kinetic energy and duration ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? although some impostors are clearly non - terminal events ( e.g. @xmath12  car , p - cygni , sn  2000ch ) , it is not clear that this is the case for all fainter outbursts ( cf . * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * but see humphreys et  al.2011 ) . for the brighter sne  iin , there is mounting evidence that the progenitor is a massive , luminous star that retains its hydrogen - shell until shortly before explosion and that the terminal mass loss event is strongly correlated with the death of the star @xcite .    with the emergence of dedicated supernovae ( sne ) follow - up programs and telescopes ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , sne  iin are now being studied more frequently in both the optical and near - ir ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? uv studies , on the other - hand , have seriously lagged behind the redder wavelengths , even though the uv is a promising probe of these interesting objects . unlike other classes of sne , sne  iin are very bright in the uv and can be found in @xmath13 optical surveys while type  ia sne have much redder spectra @xcite . their intrinsic brightness and long - lived emission also aid in spectroscopically confirming such distant sne @xcite . since they are associated with massive stars and because of their intrinsic uv brightness , sne  iin are potentially strong probes of star formation and galaxy evolution out to relatively large redshifts ( @xmath13 ; * ? ? ? previous to 2005 , only three sne  iin had been observed in the uv ( sne  1988z , 1994y , and 1998s ; * ? ? ? * ) , and only a handful since . however , none of these sne were observed early enough to detect the rise in the uv light curve ( despite the rapid follow - up after discovery in the case of _ swift _ uvot observed sne  iin ) . recently , the sn  iin ptf09uj was caught on the rise ( @xmath11.8mag in @xmath14days based on two uv detections ; * ? ? ? this rapid uv rise was attributed to the supernova ( sn ) shock breaking through a dense csm .    in this paper , we describe sn  2011ht , where the rise in the uv was captured in far greater detail , with over 10 uv observations before peak . unlike ptf09uj , the rise to peak for sn  2011ht was large ( @xmath17mag ) and slow ( @xmath140days ) . in section 2 , we present the uv to optical photometric and spectroscopic observations , x - ray observations , pre - explosion images , and the host galaxy properties . in section 3 , we review the uv / optical light curves , blackbody fits , and spectral properties . in section 4 , we discuss our results including a comparison to other sn impostors and sne  iin , as well as model interpretations . in section 5 , we summarize our conclusions .","summary":"we present very early uv to optical photometric and spectroscopic observations of the peculiar type iin supernova ( sn ) 2011ht in ugc  5460 . the uv observations of the rise to peak are only the second ever recorded for a type iin sn and are by far the most complete . the sn , first classified as a sn impostor , slowly rose to a peak of in days . merged x - ray observations reveal aergs .","abstract":"we present very early uv to optical photometric and spectroscopic observations of the peculiar type iin supernova ( sn ) 2011ht in ugc  5460 . the uv observations of the rise to peak are only the second ever recorded for a type iin sn and are by far the most complete . the sn , first classified as a sn impostor , slowly rose to a peak of in days . in contrast to the magnitude increase in the-band light curve from the first observation until peak , the uv flux increased by magnitudes . the optical spectra are dominated by strong , balmer emission with narrow peaks ( fwhmkms ) , very broad asymmetric wings ( fwhmkms ) , and blue shifted absorption (kms ) superposed on a strong blue continuum . the uv spectra are dominated by , , , and absorption lines broadened bykms . merged x - ray observations reveal aergs . some properties of sn  2011ht are similar to sn impostors , while others are comparable to type iin sne . early spectra showed features typical of luminous blue variables at maximum and during giant eruptions . however , the broad emission profiles coupled with the strong uv flux have not been observed in previous sn impostors . the absolute magnitude and energetics (  ergs in the first 112 days ) are reminiscent of normal type iin sn , but the spectra are of a dense wind . we suggest that the mechanism for creating this unusual profile could be a shock interacting with a shell of material that was ejected a year before the discovery of the sn ."}
{"article_id":"1202.4840","section_id":"r","document":"in the initial uvot observations the source is detected at 21.01mag in the @xmath17 filter , 19.07mag in the @xmath19 , 17.74mag in the @xmath20-band ,- band filter is bluer than when used on the ground because it is unaffected by atmospheric absorption . ] and @xmath116.8mag in the @xmath21 and @xmath2 filters . only an upper limit was found for the @xmath18 filter . the peak magnitudes are @xmath93 , @xmath94 , @xmath95 , and @xmath95 in the uv ( @xmath17 , @xmath18 , @xmath19 ) , @xmath20 , @xmath21 , and @xmath2 filters , respectively . the peak occurred @xmath143days after discovery in the uv and @xmath20 bands , and after @xmath155days in the @xmath21 and @xmath2 bands . the initial rise in the light curves ( the first 20days ) is quite sharp , particularly in the uv ( @xmath96 , @xmath97 , @xmath98 , @xmath99 , @xmath100 , and @xmath101magday@xmath4 ) , followed by a slower rise to peak ( over the next @xmath12030days ; @xmath102 , @xmath103 , @xmath104 , @xmath105 , @xmath106 , and @xmath107magday@xmath4 ) . the initial asas - sn observations began @xmath123 days after discovery . the rise in the light curve is 0.05magday@xmath4 , consistent with the average of the 0.07 and 0.017 uvot @xmath108 rise times . after peak , all photometric bands are observed to fade , although the uv fades more rapidly ( @xmath109 , @xmath110 , @xmath111 , @xmath112 , @xmath113 , and @xmath114magday@xmath4 ) . the @xmath115 for the uv and @xmath24 bands is @xmath10.2 and 0.04 , respectively . the color evolution is peculiar because it evolves from red to blue at early times ( figure  [ fig - lc ] : _ bottom _ ) , followed by a more normal , slow reddening after the peak . this is best summarized by examining the evolution of the luminosity and temperature , which we can approximate well because of the wavelength coverage provided by the uvot . we fit the spectral energy distributions ( seds ) as blackbodies , allowing for galactic extinction ( e(@xmath116@xmath32)=0.01 ; * ? ? ? * ) as well as additional extinction in the host with a range of reddening laws ( mw , lmc , smc ) and @xmath19 filters suffer from a red leak that can lead to complications in the analysis of red spectra @xcite . the early spectra of sn  2011ht are very blue , and we account for the red leaks in the filter response functions used for the model seds . ] . our best fit host reddening value is zero , but values up to @xmath10.2 are consistent with the data . if we only fit the peak , where the @xmath117 is best , we obtain values of e(@xmath116@xmath32)=0.062 ( mw ) and 0.041 ( smc / lmc ) . we adopt the e(@xmath116@xmath32)=0.062 mw model for our standard reddening estimate . in figure [ fig - sed ] we compare a blackbody with e(@xmath116@xmath32)=0 , 0.041 , and 0.062 to the combined arc / dis and uvot / uvg ( epoch 2 ) spectrum . the blackbody approximates the sed reasonably well in the optical , but the fluxes overestimate somewhat the uv due to line blanketing . we also estimate a pseudo - bolometric luminosity . we use count rate to flux conversions for the best fit blackbody temperatures interpolated from blackbody values in @xcite , and then arrive at an average monochromatic flux density for each filter . the flux density is then integrated over the filter bandpass using trapezoidal integration . figure  [ fig - bol ] shows that these two estimates of the luminosity agree reasonably well , with the agreement improving as the temperature increases and there is proportionately less unobserved optical / near - ir emission . the bolometric light curve peaks at @xmath110@xmath118@xmath119 , roughly @xmath143days after discovery . the total energy emitted by the sn in the first 112 days is @xmath120ergs . for comparison purposes , this is @xmath1100@xmath121 greater - than the energy in the eruption of the 2008  n300 transient @xcite and @xmath1100@xmath121 less - than the radiated output of sn  2006gy @xcite . figure  [ fig - bb ] shows the evolution of the blackbody fits in temperature ( @xmath122 ) , radius ( @xmath123 ) , and luminosity ( @xmath124 ) along with the fit residuals . the fits are worse at early times , but we see a general trend that as the temperature increases the luminosity increases and the black body radius shrinks and then remains fairly constant until peak . after peak , @xmath122 and @xmath124 begin declining , while @xmath123 begins increasing . the estimates of @xmath122 , @xmath123 , and @xmath124 for each epoch are reported in table  [ tab5 ] . a close examination of the uvot / uvg spectra ( figure  [ fig - spect ] ) reveals absorption lines of and potential lines of , , , and . the uv spectrum below 1900  shows significant absorption features which differ between the two spectra taken 11days apart . the most likely explanation is a combination of noise in the early spectrum and physical changes in the state and velocity of the circumstellar matter . only the longer exposure of the later spectrum can be trusted below 1900 . the spectra also show broadened hydrogen lines of h@xmath125 , h@xmath126 , and h@xmath127 . the uv is dominated by lines of , most notably the uv1 , uv2 and uv62 multiplets . a comparison with the sn  1998s spectrum from @xcite reveals that several sets of absorption lines match the sn  2011ht lines , namely ( @xmath128 ) and ( @xmath129 , @xmath130 , and @xmath131 ; figure  [ fig - gclose ] ) . an 11  shift of the uvot spectrum ( which is within the wavelength accuracy of the instrument ) was applied based on the line identifications , so it is possible that the overall blueshift seen in the optical is masked .    at @xmath132 there is a possible resonance line of , but this is more likely the ( @xmath133 ) resonance line that is broadened by a velocity of @xmath11880kms@xmath4 . the @xmath134 , and @xmath135 lines are not resonance lines , but are probably the result of a cascade from . the line broadening of the two lines indicates velocities of 1220 and 1474kms@xmath4 , respectively . we attribute the line found at @xmath136  to @xmath137 , @xmath138 , @xmath139 triplet of . the c  iii ] ( @xmath140 ) line is seen at @xmath11904 . the resonance lines at @xmath141 and @xmath142   are present , while we also see the ( @xmath143 ) line whose lower level is the upper level of the @xmath142  line . similar to the lines this could be due to recombination of the levels or due to high temperature collisional excitation . the width of the uv lines is difficult to determine since there are so many faint lines confusing the measurements . a fwhm between 2533  is our best estimate , which equates to a velocity of about 1670kms@xmath4 . the early optical spectra are dominated by strong asymmetric ( the red side having greater flux ) balmer emission lines with narrow peaks , very broad wings , and p - cygni profiles . using the mods1 spectrum we have measured velocities with respect to the various rest frame peak emission and absorption lines ( table  [ tab4 ] ) . from the h@xmath7 p - cygni profile , we measure blueshifted velocities ( with respect to the velocity of the galaxy ) of 261 and 778kms@xmath4 in emission and absorption , respectively . we also measure the width of the narrow h@xmath7 line to be fwhm@xmath144kms@xmath4 while the broad wings are fwhm@xmath145kms@xmath4 . the h@xmath7 profile remains fairly consistent over the five epochs ( see figure  [ fig - halpha ] ) . the velocity in absorption decreases in the higher balmer lines ( see table  [ tab4 ] ) , and the absorption lines become stronger as the emission weakens ( figure  [ fig - balmer ] ) . h@xmath12 has no obvious emission altering the absorption profile , so we measure the absorption velocity to be 646  kms@xmath4 . paschen lines are easily identified on the red end of the spectrum . they show weak emission combined with blue shifted absorption . there are two very strong emission lines ( @xmath146 and @xmath147 ) , both of which show very broad wings . the @xmath147 line has an absorption feature similar to the hydrogen lines , but the absorption is absent from the @xmath146 line ( figure  [ fig - hei ] ) . the other lines are weak . normally ( @xmath148 ) is a very strong line , but it lies on the red wing of h@xmath7 and is difficult to analyze . the emission and absorption in the other lines ( @xmath149 , @xmath150 , @xmath151 , @xmath152 , and @xmath153 ) are weaker , with the latter two lines having the weakest emission . redward of h@xmath126 is a peculiar continuum where the ( @xmath151 ) line weakly appears in emission . this could be the result of thomson scattering . the absorption triplet at @xmath154 ( @xmath155 , @xmath156 , and @xmath157 ) is strong and has a velocity of 618  kms@xmath4 , similar to the h and absorption features . there are also three weak absorption lines between 3900 and 4000 . the line measured at 3939.6  is most likely  k with a velocity of @xmath158  kms@xmath4 .    in the last spectrum taken with the het / lrs , the strong , broad emission lines at @xmath147 and @xmath146 have disappeared . the other lines ( @xmath150 and @xmath149 ) are still present with weak p - cygni profiles . several lines have appeared in both absorption and emission . the strong absorption and p - cygni emission is ( @xmath159 multiplet 42 ) with the next absorption line probably being ( 42 ) at @xmath160 . there are four absorption / emission lines from 52005340  all from multiplet 49 . the absorption is still present and strong .","summary":"in contrast to the magnitude increase in the-band light curve from the first observation until peak , the uv flux increased by magnitudes . the optical spectra are dominated by strong , balmer emission with narrow peaks ( fwhmkms ) , very broad asymmetric wings ( fwhmkms ) , and blue shifted absorption (kms ) superposed on a strong blue continuum . the uv spectra are dominated by , , , and absorption lines broadened bykms . however , the broad emission profiles coupled with the strong uv flux have not been observed in previous sn impostors . the absolute magnitude and energetics (  ergs in the first 112 days )","abstract":"we present very early uv to optical photometric and spectroscopic observations of the peculiar type iin supernova ( sn ) 2011ht in ugc  5460 . the uv observations of the rise to peak are only the second ever recorded for a type iin sn and are by far the most complete . the sn , first classified as a sn impostor , slowly rose to a peak of in days . in contrast to the magnitude increase in the-band light curve from the first observation until peak , the uv flux increased by magnitudes . the optical spectra are dominated by strong , balmer emission with narrow peaks ( fwhmkms ) , very broad asymmetric wings ( fwhmkms ) , and blue shifted absorption (kms ) superposed on a strong blue continuum . the uv spectra are dominated by , , , and absorption lines broadened bykms . merged x - ray observations reveal aergs . some properties of sn  2011ht are similar to sn impostors , while others are comparable to type iin sne . early spectra showed features typical of luminous blue variables at maximum and during giant eruptions . however , the broad emission profiles coupled with the strong uv flux have not been observed in previous sn impostors . the absolute magnitude and energetics (  ergs in the first 112 days ) are reminiscent of normal type iin sn , but the spectra are of a dense wind . we suggest that the mechanism for creating this unusual profile could be a shock interacting with a shell of material that was ejected a year before the discovery of the sn ."}
{"article_id":"1202.4840","section_id":"c","document":"some of the properties of sn  2011ht are similar to sn impostors ( e.g. the emission line structures ) , while others are comparable to true sne  iin ( e.g. the luminosity )  sn  2011ht has the luminosity of a normal core - collapse sne ( see figure  [ fig - photocomp ] ) , but the spectrum of a dense wind ( see figure  [ fig - spectracomp ] ) . the spectrum originally showed hydrogen and the triplet in emission with p - cygni profiles , as well as narrow absorption lines of @xcite , typical of lbvs at maximum and during giant eruptions . the steep , blue continuum , strong uv flux , and the properties of the lines are not characteristic of dense winds . the uv decay slope of the sn  2011ht light curve is reminiscent of sn  2007pk @xcite . the broad asymmetric ( to the red ) wings in sn  2011ht are suggestive of thomson scattering . the sn impostors , sne  1999bw and 2001ac , showed strong , narrow balmer lines ( fwhm@xmath161 and 290kms@xmath4 , respectively ) characteristic of lbvs , with broad wings ( fwhm@xmath162 and 3000kms@xmath4 , respectively ) . the cause of these wings is not clear , but they have been attributed to either electron scattering , fast moving ejecta , or a combination of both @xcite . the cause of the broad wings in sne is not always clear either . for sn  1998s , the broad component has been attributed both to the ejecta @xcite and to scattering on thermal electrons @xcite . in sn  1999w , @xcite attributed the broad wings to a combination of cool shocked gas and thomson scattering , while @xcite argued they were primarily the result of electron scattering in the ejecta . even with detailed models it can be difficult to reach a conclusive interpretation . further complicating this picture is that some sne  iin initially reveal a thomson scattering profile but evolve to a shocked profile @xcite . if we suppose both the presence of thomson scattering in a pre - existing circumstellar medium ( csm ) in order to produce the line structures , and that the transient is a true sn based on its energetics , then we would expect a shock wave to be propagating through the csm with observable effects . significantly modifying the line structures requires @xmath163 on the scale of the apparent photosphere ( figure  [ fig - bb ] ) , and we use this to normalize the model by @xmath164 where the thomson opacity is @xmath165 and we identify the absorption feature of the spectra with the wind speed ( @xmath166 ) . the shell extends from @xmath167 to @xmath168 with a thickness @xmath169 . the term @xmath170 for a thick shell . producing significant levels of thomson scattering on these large scales requires a very dense wind , similar to that of an lbv in eruption @xcite . we can then estimate the h@xmath7 luminosity assuming it is due to recombination outside radius @xmath167 ( and ignoring @xmath168 ) as @xmath171 where @xmath172  ev , @xmath173  @xmath174/s is the h@xmath7 rate , and @xmath175 is the mean molecular weight . for the estimated h@xmath7 line flux of @xmath176  ergs  @xmath55  s@xmath4 ( @xmath177 ) in the mods spectrum , the line formation radius will be consistent with the photometric radius for @xmath163 , roughly as needed to broaden the lines with thomson scattering . a shock propagating through such a medium releases a significant amount of energy , with a shock luminosity of @xmath178 ( e.g. * ? ? ? * ) , where we have set the shock velocity to 2000kms@xmath4 , an intermediate velocity between the narrow and broad components . while this energy can be lost to re - accelerating the expansion of the flow , on these physical scales it will tend to be radiated . the natural shock temperature is @xmath179  kev . if the optical depth of the wind is low , the x - rays from the shock can not be thermalized and simply escape . averaging over the x - ray epochs from 11 november to 17 january ( days 43 - 110 ) gives a detection with @xmath180 . these can be reconciled by having a low optical depth , @xmath181 corresponding to a mass loss rate of a few @xmath182  year@xmath4 . a possible difficulty is that at the low shock densities implied by this optical depth , one would be directly observing the shock and would expect to see the characteristic emission lines associated with fast shocks ( e.g. the late time spectra of sn  1980k ; * ? ? ? * ) , although they would be heavily diluted by the large ratio between the shock and photospheric luminosities . the alternative is to make the medium dense enough so that the x - rays are absorbed before they escape ( see the recent discussion in * ? ? ? * ) . at the densities and temperatures we expect to see in the shell , the material is likely to be incompletely ionized , which means that the optical opacity ( dominated by electron scattering ) will be low compared to the x - ray opacity ( e.g. figure  [ fig - opac ] ) . in these conditions , @xmath183 and , if we require @xmath184 to fit the line profiles , the high x - ray optical depth will be sufficient to severely limit the softer x - rays to which _ swift _ is most sensitive . there is an upper bound of @xmath185 where @xmath186 begins to exceed the bolometric luminosity of the transient . if we follow the argument of @xcite and try to produce all the luminosity from an embedded shock , the energy available to heat the medium is @xmath187 , where @xmath188 is how long it takes the energy to escape . we equate this with the radiative energy @xmath189 to estimate a temperature @xmath190 thermalizing the shock photons to limit the x - ray transmittance places constraints on the ionization state of the atoms . to explain the line profiles , we require @xmath191 . but the optical depth can not be too high , or the photon diffusion time becomes too long and the shock breaks out before the radiation . this also implies that @xmath185 . the mass associated with the shell is then @xmath192 where we have used @xmath193  @xmath194  g@xmath4 for a largely ionized medium , but in can be lower if the h / he are able to partially recombine ( see figure  [ fig - opac ] ) . theses masses and mass loss rates in these high luminosity models are typical of other type  iin sne ( e.g. * ? ? ? * ) and are in the range of lbvs in eruption ( e.g. * ? ? ? there is one additional attractive feature of surrounding an explosive transient with a discontinuous shell of material . namely , it might be able to explain the large photospheric radius and low temperature of the first few epochs ( see figure  [ fig - bb ] ) . when the shock breaks out of the surface of the star , it produces a luminosity uv / x - ray spike in excess of @xmath195 in a brief burst . the duration depends on the structure of the star , wind profile and the photon energy , but the bulk of the breakout emission occurs well within 10,000s ( e.g. * ? ? ? * ; * ? ? ? * ) . in a shell geometry , this short radiation spike rapidly crosses to the shell and then photoionizes it before escaping . but if the radiation interacts in the shell , it is spread over the diffusion time @xmath196  days , which is relatively well - matched to the duration and apparent photospheric scales of the initial phase . the problem is that the required luminosity is at the high end of what we might expect from shock breakout . this can be explored further once the nature of this transient is fully understood .","summary":"some properties of sn  2011ht are similar to sn impostors , while others are comparable to type iin sne . early spectra showed features typical of luminous blue variables at maximum and during giant eruptions . are reminiscent of normal type iin sn , but the spectra are of a dense wind .","abstract":"we present very early uv to optical photometric and spectroscopic observations of the peculiar type iin supernova ( sn ) 2011ht in ugc  5460 . the uv observations of the rise to peak are only the second ever recorded for a type iin sn and are by far the most complete . the sn , first classified as a sn impostor , slowly rose to a peak of in days . in contrast to the magnitude increase in the-band light curve from the first observation until peak , the uv flux increased by magnitudes . the optical spectra are dominated by strong , balmer emission with narrow peaks ( fwhmkms ) , very broad asymmetric wings ( fwhmkms ) , and blue shifted absorption (kms ) superposed on a strong blue continuum . the uv spectra are dominated by , , , and absorption lines broadened bykms . merged x - ray observations reveal aergs . some properties of sn  2011ht are similar to sn impostors , while others are comparable to type iin sne . early spectra showed features typical of luminous blue variables at maximum and during giant eruptions . however , the broad emission profiles coupled with the strong uv flux have not been observed in previous sn impostors . the absolute magnitude and energetics (  ergs in the first 112 days ) are reminiscent of normal type iin sn , but the spectra are of a dense wind . we suggest that the mechanism for creating this unusual profile could be a shock interacting with a shell of material that was ejected a year before the discovery of the sn ."}
{"article_id":"0807.4802","section_id":"i","document":"rational algebraic curves and surfaces can be described in several different ways , the most common being parametric and implicit representations . parametric representations describe the geometric object as the image of a rational map , whereas implicit representations describe it as the set of points verifying a certain algebraic condition , e.g. as the zeros of a polynomial equation . both representations have a wide range of applications in computer aided geometric design ( cagd ) , and depending on the problem one needs to solve , one or the other might be better suited . to give a simple example , the parametric description is better for drawing a surface , as it allows to rapidly generate points on the surface , which can then be interpolated , whereas an implicit representation is better adapted for testing if a given point lies on the surface , since one only needs to check whether the point verifies the algebraic condition that defines the surface . it is thus interesting to be able to pass from the parametric representation to the implicit equation . this is a classical problem and there are numerous approaches to its solution , see @xcite and @xcite for good historical overviews . however , it turns out that the implicitization problem is computationally difficult . a promising alternative suggested in @xcite is to compute a so - called _ matrix representation _ instead , which is easier to compute but still shares some of the advantages of the implicit equation . here is the definition . let @xmath4 be a hypersurface . a matrix @xmath5 with entries in the polynomial ring @xmath6 $ ] is called a _ representation matrix _ of @xmath7 if it is generically of full rank and if the rank of @xmath5 evaluated in a point of @xmath8 drops if and only if the point lies on @xmath7 . it follows immediately that a matrix @xmath5 represents @xmath7 if and only if the greatest common divisor of all its minors of maximal size is a power of the homogeneous implicit equation @xmath9 $ ] of @xmath7 . one major ingredient in the construction of such matrices are syzygies . the theory of syzygies has been developed in the theoretical context of commutative algebra at the beginning of the 20th century by mathematicians such as david hilbert . however , it was only in the 1990s that the cagd and geometric modeling community discovered that the concept of syzygies is useful in their field . initially unaware of the connections to commutative algebra , @xcite , @xcite , @xcite , and numerous other authors labeled this approach the method of `` moving curves '' ( or `` moving surfaces '' ) and showed how it can be used to express the implicit equation as a determinant . in the case of a planar rational curve @xmath10 given by a parametrization of the form @xmath11 , @xmath12 , where @xmath13 $ ] are coprime polynomials of degree @xmath14 and @xmath15 is a field , a linear syzygy ( or moving line ) is a linear relation on the polynomials @xmath16 , i.e. a linear form @xmath17 in the variables @xmath18 and with polynomial coefficients @xmath19 $ ] such that @xmath20 . we denote by @xmath21 the set of all those linear syzygies forms and for any integer @xmath22 the graded part @xmath23 of syzygies of degree at most @xmath22 . actually , to be precise , one should homogenize the @xmath24 with respect to a new variable and consider @xmath21 as a graded module here . it is obvious that @xmath23 is a finite - dimensional @xmath15-vector space and one can easily obtain a basis @xmath25 by solving a linear system . we define the matrix @xmath26 of coefficients of the @xmath27 with respect to a @xmath15-basis of @xmath28_\\nu$ ] as @xmath29 that is , the coefficients of the syzygies @xmath27 form the columns of the matrix . note that the entries of this matrix are linear forms in the variables @xmath30 with coefficients in the field @xmath15 . let @xmath31 denote the homogeneous implicit equation of the curve and @xmath32 the degree of the parametrization as a rational map . intuitively , @xmath32 measures how many times the curve is traced . it is known that for @xmath33 , the matrix @xmath26 is a representation matrix ; more precisely : if @xmath34 , then @xmath26 is a square matrix , such that @xmath35 . also , if @xmath36 , then @xmath26 is a non - square matrix with more columns than rows , such that the greatest common divisor of its minors of maximal size equals @xmath37 .    in other words , one can always represent the curve as a square matrix of linear syzygies . in principle , one could now actually calculate the implicit equation . however , it might be advantageous to avoid the costly determinant computation and work directly with the matrix instead , as it has the advantage of making the well - developed theory and tools of linear algebra applicable to solve geometric problems . for instance , testing whether a point @xmath38 lies on the curve only requires computing the rank of @xmath26 evaluated in @xmath38 . other interesting results using square matrix representations directly to solve geometric problems are presented , for example , in @xcite or @xcite , in which intersection problems are treated by means of eigenvalue techniques .    it is a natural question whether this kind of matrix representation can be generalized to rational surfaces defined as the image of a map @xmath39 where @xmath40 $ ] are coprime polynomials of degree @xmath14 . in order to put the problem in the context of graded modules , one first has to consider an associated projective map @xmath41 where @xmath1 is a 2-dimensional projective toric variety ( for example @xmath2 or @xmath42 ) with coordinate ring @xmath43 and the @xmath44 are homogenized versions of their affine counterparts @xmath24 . in other words , @xmath1 is a suitable compactification of the affine space @xmath45 @xcite . in this case , a linear syzygy ( or moving plane ) of the parametrization @xmath46 is a linear relation on the @xmath47 , i.e. a linear form @xmath48 in the variables @xmath49 with @xmath50 $ ] such that @xmath51 exactly in the same way as for curves , one can set up the matrix @xmath26 of coefficients of the syzygies in a certain degree @xmath22 , but unlike in the curve case , it is in general not possible to choose a degree @xmath22 such that @xmath26 is a square matrix representation of the surface . in recent years , two main approaches have been proposed to deal with this problem :    * one allows the use of quadratic syzygies ( or higher - order syzygies ) in addition to the linear syzygies in order to be able to construct square matrices . * one only uses linear syzygies as in the curve case and obtains non - square representation matrices .    the first approach using linear and quadratic syzygies ( or moving planes and quadrics ) has been treated in @xcite for base - point - free homogeneous parametrizations , i.e. @xmath52 , and @xcite does the same in the presence of base points . in @xcite , square matrix representations of bihomogeneous parametrizations , i.e. @xmath3 , are constructed with linear and quadratic syzygies , whereas @xcite gives such a construction for parametrizations over toric varieties of dimension 2 . the methods using quadratic syzygies usually require additional conditions on the parametrization and the choice of the quadratic syzygies is often not canonical .    the second approach , even though it does not produce square matrices , has certain advantages , in particular in the sparse setting that we present . in previous publications , this approach with linear syzygies , which relies on the use of the so - called approximation complexes has been developed in the case @xmath52 , see for example @xcite , @xcite , and @xcite , and in @xcite for bihomogeneous parametrizations of degree @xmath53 . however , for a given affine parametrization @xmath54 , these two varieties are not necessarily the best choice of a compactification of affine space , since they do not always reflect well the combinatorial structure of the polynomials @xmath55 . in this paper we will extend the method to a much larger class of varieties , namely toric varieties of dimension 2 , and we will see that this generalization allows us to choose a `` good '' toric compactification of @xmath45 depending on the polynomials @xmath55 , which makes the method applicable in cases where it failed over @xmath2 or @xmath42 and we will also see that it is significantly more efficient and leads to much smaller representation matrices .    the main idea of our method is similar to the one in @xcite . we use a ( general ) toric embedding to consider our domain as a 2-dimensional toric variety contained in a higher - dimensional projective space , which we present in section  [ sec : setting ] . contrary to the cited paper , this natural domain will not be in general a hypersurface and its coordinate ring will usually not be gorenstein , which means that we have to give new proofs for some of the results in which this property was used . in section  [ approxt ] we proceed to establish the necessary homological tools and in particular to derive bounds on local cohomology in theorem  [ locosymalgt ] , our main technical result . after that , we will see in section  [ sec : equation ] that we can deduce the validity of the approach from previous results to produce an efficient representation matrix for the implicit equation ( see corollary  [ cor : main ] ) . the particular case of bihomogeneous parametrizations of any bidegree is illustrated in section  [ segret ] . we then show the advantages of our method through several examples in section  [ sec : examples ] . after some concluding remarks which summarize the scope of the paper in section  [ sec : final ] , an implementation in macaulay2 @xcite for the important special case @xmath3 is included as an appendix .","summary":", we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed .","abstract":"in this paper we show that a surface in parametrized over a 2-dimensional toric variety can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection . this constitutes a direct generalization of the corresponding result over established in and . exploiting the sparse structure of the parametrization , we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed . we also treat the important case in detail and give numerous examples .        matrix representation , rational surface , syzygy , approximation complex , implicitization , toric variety"}
{"article_id":"astro-ph0111369","section_id":"i","document":"the standard model for powerful jets associated with extragalactic radio sources @xcite assumes that the energy radiated in the radio lobes of such sources is produced in the active nuclei of their host galaxies , the central engine being a supermassive black hole surrounded by an accretion disc . the accretion process fuels a couple of twin supersonic jets which transport away bulk kinetic energy from the neighbourhood of the central black hole to the lobes , from scales of the schwarzschild radius of the supermassive black hole @xmath1 cm , to kiloparsec scales . this bulk kinetic energy is dissipated by shocks within the beam and ( mostly ) at the jet terminal shocks where electrons are accelerated and radiate via synchrotron and inverse compton mechanisms . typical lifetimes and kinetic powers of powerful radio sources are @xmath2y and @xmath3erg s@xmath4 , respectively @xcite .    among the problems that still remain open even after more than 30 years of research is the composition of extragalactic jets . within the standard model @xcite jets are made of a relativistic plasma that contains relativistic electrons and thermal protons ( @xmath5-plasma ) . on the other side , based on equipartition arguments kundt & gopal - krishna claim that extragalactic jets consist of beams of extremely relativistic electrons and positrons ( @xmath6-plasma ) with almost no ions . ultimately , the composition of jets is tightly related to their formation mechanisms . as discussed by celotti & blandford , electromagnetically dominated outflows , as those generated by the extraction of spin energy of the black hole , will become pair dominated jets with a low baryonic pollution . jets generated from the accretion disk by hydromagnetic winds will be made of baryonic plasma . probably , both processes are operating simultaneously in nature . sol , pelletier & asseo propose a _ two - flow _ model where the jet consists of a beam of relativistic particles ( pair plasma ) surrounded by a newtonian or mildly relativistic ( @xmath5-plasma ) wind accelerated from the disk . it is also possible that @xmath5-jets become pair - loaded later on , by interactions with high energy photons from the disk corona  begelman , blandford & rees  or by proton - proton collisions at parsec scale  anyakoha , okeke & okoye . observations show that a number of jets are highly polarised . this is a further argument in favour of jets made of e@xmath7 pairs as there is no internal faraday rotation or depolarisation ( the rotation produced by the electrons is compensated by that of the positrons ) , while an @xmath5-plasma gives rise to these effects . if jets were dominated by @xmath5-plasmas , observational limits on the degree of faraday rotation and depolarisation imply thermal electron densities @xmath8@xmath9  walker , benson & unwin  or a minimum energy cut - off for the electrons @xmath10mev @xcite . this suggests a lack of thermal ( cold ) matter , at least , in the most polarised sources . however , as the upper bounds on the thermal electron density derived from the depolarisation argument depend on the magnetic field structure , they might be underestimated if there are field reversals within the vlbi beam . finally , the detection of circular polarisation at parsec scales in several radio sources @xcite suggests that , in general , extragalactic radio sources are mainly composed of @xmath6-plasma . the argument is based on the fact that circular polarisation is produced by faraday conversion , which requires that the energy distribution of the jet emitting particles extends to very low energies . this in turn indicates that @xmath6-pairs are an important component of the jet plasma . sikora & madejski conclude that x - ray observations of blazars associated with ovv quasars impose strong constraints on the e@xmath7 pair content of jets of radio - loud quasars . according to these authors , pure electron - positron pair jets can be excluded because they may produce too much soft x - rays , while pure electron - proton jets may emit too few non - thermal x - ray radiation . therefore , only jets may be viable where the number density of electron - positron pairs is much larger than the proton number density , but small enough for protons still being dynamically more important . hirotani find that parsec - scale jets can not be dominated by baryons , if the electron density determined by the amount of synchrotron self - absorption necessary for an optically thick jet component , is of the same order as the one derived from the kinetic luminosity .    for jets composed of a pair plasma additional questions arise . how can they maintain their stability , as for a given particle density they are lighter and hence less stable than jets made of an electron - proton plasma can they transport enough energy to fuel the observed kiloparsec scale radio lobes ? concerning the stability of electron - positron plasma flows , sol demonstrate that the _ two - flow _ model is stable against excitation of electrostatic waves as long as the magnetic field is larger than a critical value @xmath11 . in their _ two - flow _ model , the relativistic beam is responsible for the vlbi jet and the observed superluminal motion , while the slower wind gives rise to the kiloparsec scale jet . achatz & schlickeiser also consider the stability of @xmath6-plasmas against the excitation of electromagnetic waves when the magnetic field exceeds @xmath11 . they find that the plasma may be stable over large distances provided plasma waves are damped thermally . the problem of the energy supply to large scales with a limited number of particles is turned around by celotti . she argues that the jets of low power radio sources mainly consist of @xmath6-plasma , while those of powerful radio - loud quasars are made of @xmath5-plasma . however , measurements of the circular polarisation of vlba - jets of several frii sources by wardle favour @xmath6-jets also in powerful sources ( at least , at parsec scales ) . another important and not yet solved question concerns the impact of the composition on the morphology and dynamics of jets from sub - parsec to kiloparsec scales . observations indicate that jets are relativistic at parsec scales  laing  , then decelerate until they become sub - relativistic or mildly relativistic  bridle  at kiloparsec scales with advance speeds of the terminal hotspots in the range @xmath12 to @xmath13 @xcite , where @xmath14 is the speed of light . at large scales the observed morphologies and deceleration of powerful radio sources is governed by interaction with the external medium . several theoretical models have considered the gross features of kiloparsec scale jets , their long term evolution . begelman & cioffi  bc89 hereafter  consider a simple model to describe the evolution of the cocoon . self - similar expansion is suggested by falle . komissarov & falle explore the large - scale flow caused by classical and relativistic jets in a uniform external medium . they find that jets with finite initial opening angles are recollimated by the high pressure in the cocoon and that the flow becomes approximately self - similar at large times . numerical investigations have also addressed the kiloparsec scale regime . two - dimensional newtonian hydrodynamic simulations of axisymmetric light jets were performed by cioffi & blondin in order to understand the evolution of the cocoon , and were compared with the simple analytic theory of bc89 . the grid resolution is quite high ( 15 zones per jet radius ) , but the simulations do only cover a relatively short period of the cocoon s evolution . the newtonian simulations of hooda , mangalam & wiita cover the evolution of axisymmetric extragalactic jets up to @xmath15y . their simulations include isothermal atmospheres with a density stratification given by a power - law , surrounded by an even hotter , but less dense intra - cluster medium where the jets accelerate and collimate . hooda & wiita extended the results of hooda to three - dimensions , but their simulations cover only a distance of 35 ( initial ) jet radii , and thus are too short to shed light on the long term evolution of real sources . mart , mller & ibez ( 1998 )  mmi98 hereafter  studied the long term evolution of powerful extragalactic jets on the basis of relativistic hydrodynamic simulations ( up to an evolutionary time of @xmath16y with a relatively low numerical resolution ) . the results are compared and interpreted with a simple generalisation of the model of bc89 . they find an evolution divided into two epochs . after a transient initial stage , the jet s evolution is dominated by a strong deceleration . the jet advance speed becomes as small as @xmath17 due to the degradation of the beam flow by means of internal shocks and the broadening of the beam cross section near the hotspot . the present work extends the investigations of mmi98 to much later evolutionary times and also addresses the question whether the content of thermal matter in powerful kiloparsec jets does influence their morphology , dynamics and emission properties . like mmi98 we assume that the dynamics of the jets is dominated by the thermal plasma  sikora & madejski  and , thus , a hydrodynamic approach is appropriate . for this purpose we have performed long - term simulations of axisymmetric , relativistic jets of extremely different composition , jets made of a pure leptonic or baryonic plasma , propagating into a uniform environment .","summary":"we study the influence of the matter content of extragalactic jets on their morphology , dynamics and emission properties . for this purpose we consider jets of extremely different compositions including pure leptonic and baryonic plasmas . our work is based on two - dimensional relativistic hydrodynamic simulations of the long - term evolution of powerful extragalactic jets propagating into a homogeneous environment . # 1ann . suppl . * pure appl . math . * . grav . * . fluid mech . * # 1 * # 1nature * # 1 * # 1mon . not . roy . astronom . soc . * theor . . suppl . * mod . # 1 * # 1siam j. numer . anal . * # 1 * # 1siam j. sci . comput . * # 1 *    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    hydrodynamics  relativity  plasmas  ism : jets and outflows  radiation mechanisms : thermal  galaxies : jets .","abstract":"we study the influence of the matter content of extragalactic jets on their morphology , dynamics and emission properties . for this purpose we consider jets of extremely different compositions including pure leptonic and baryonic plasmas . our work is based on two - dimensional relativistic hydrodynamic simulations of the long - term evolution of powerful extragalactic jets propagating into a homogeneous environment . the equation of state used in the simulations accounts for an arbitrary mixture of electrons , protons and electron - positron pairs . using the hydrodynamic models we have also computed synthetic radio maps and the thermal bremsstrahlung x - ray emission from their cavities .    although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets , we find that both the morphology and the dynamic behaviour are almost independent on the assumed composition of the jets . their evolution proceeds in two distinct epochs . during the first one multidimensional effects are unimportant and the jets propagate ballistically . the second epoch starts when the first larger vortices are produced near the jet head causing the beam cross section to increase and the jet to decelerate . the evolution of the cocoon and cavity is in agreement with a simple theoretical model . the beam velocities are relativistic ( ) at kiloparsec scales supporting the idea that the x - ray emission of several extragalactic jets may be due to relativistically boosted cmb photons . the radio emission of all models is dominated by the contribution of the hot spots . all models exhibit a depression in the x - rays surface brightness of the cavity interior in agreement with recent observations .    # 1ann . rev . . astrophys . * # 1 * # 1ann . rev . fluid mech . * # 1 * # 1astron . astrophys . * # 1 * # 1astron . astrophys . suppl . * # 1 * # 1astronom . j. * # 1 * # 1astrophys . j. * # 1 * # 1astrophys . j. suppl . * # 1 * # 1astrophys . j. lett . * # 1 * # 1comm . pure appl . math . * # 1 * # 1comput . . commun . * # 1 * # 1comput . phys . rep . * # 1 * # 1class . . grav . * # 1 * # 1j . comp . phys . * # 1 * # 1j . fluid mech . * # 1 * # 1nature * # 1 * # 1mon . not . roy . astronom . soc . * # 1 * # 1phis . review d * # 1 * # 1prog . theor . phys . * # 1 * # 1prog . theor . . suppl . * # 1 * # 1rev . mod . phys . * # 1 * # 1siam j. numer . anal . * # 1 * # 1siam j. sci . comput . * # 1 *    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    hydrodynamics  relativity  plasmas  ism : jets and outflows  radiation mechanisms : thermal  galaxies : jets ."}
{"article_id":"astro-ph0111369","section_id":"i","document":"we have performed the longest and best resolved large - scale simulations of relativistic jets up to date . the simulations extend up to an evolutionary age of @xmath191y which is only a few times smaller than the ages of typical powerful radio sources . the simulated jets differ in their density , temperature and composition , but have similar gross properties ( kinetic luminosity and thrust ) . hence , they may represent a relatively early stage of the observed extragalactic jets and their radio lobes . we have considered three models including a hot and a cold jet made of a pure ( leptonic ) electron - positron plasma ( models lh and lc ) and one baryonic model bc consisting of an electron - proton plasma . the leptonic hot model lh has a factor of 100 lower density ( @xmath97 ) than the other two models ( @xmath86 ) . although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets , we find that both the morphology and the dynamic behaviour are almost independent on the assumed composition of the jets . only the leptonic hot model lh behaves differently because of its very light beam . this reflects the well known influence of the density parameter @xmath32 according to which light jets are less stable than heavy ones . model lh suffers from considerable mass entrainment into the beam , which eventually leads to the disruption of the beam . the instability grows on a time scale of a few million years , the evolution of model lh is inconsistent with the sizes and ages of the jets of typical powerful radio sources . in addition , the initial conditions chosen for model lh are quite extreme , and most likely can not be found in actual jets .    in all models two evolutionary epochs can be distinguished . during the first epoch multidimensional effects are not yet important and the jet propagates with a velocity close to the 1d estimate . the mach disk is only slightly disturbed , the shedding of vortices is negligible , and both the hotspot pressure and the jet velocity are nearly constant . the aspect ratios of the cocoon and of the cavity increase with time , while the average cavity pressure decreases . the second epoch starts when the first larger vortices are produced near the jet head . the beam cross section increases and the jet decelerates progressively . the deceleration is repeatedly interrupted by short acceleration phases caused by the temporary replacement of the mach disk by a conical shock . the velocity increase during the acceleration phases can exceed 100% . the evolution of the cocoon and cavity aspect ratios of all models is in agreement with an extended version of the simple theoretical model proposed by begelmann & cioffi ( bc89 ) for the inflation of the cocoon . the cavity aspect ratio of the simulated models is too large according to current observations , the simulated jets are too elongated . this situation may change when the simulations are either extended even further in time or when the assumption of axisymmetry is relaxed . however , both approaches would require prohibitive amounts of computational resources and axisymmetry is , in general , a good approximation to study extragalactic jets . the size and shape of the cocoon depends on @xmath32 , on the ratio of the densities in the jet and in the ambient medium . according to our definition of the cocoon  the region containing material with a beam particle fraction @xmath192  we find that a light jet ( model lh ) has a very thin cocoon restricted to a narrow layer girding the beam . jets with heavier beams ( models bc and lc ) possess more extended cocoons , more similar to those of observed jets . the differences in the cocoon sizes become particularly evident when comparing the synthetic radio maps that we have computed for all models . the cocoon aspect ratio found for the leptonic hot model lh is unrealistically large , which provides another argument against its realization in nature ( see above ) . the propagation velocities and the hotspot pressures of our jets agree very well with the analytical and observed values . the strength of the equipartition magnetic field comfortably matches the expectations for a young powerful radio source ( whose magnetic fields are thought to be stronger than those of evolved radio sources ) . the beam velocities of the models are relativistic ( @xmath0 ) at kiloparsec scales . provided this is not an artefact caused by the assumed axisymmetry , the results strongly support the ideas of tavecchio and celotti that the x - ray emission of several extragalactic jets may be due to relativistically boosted cmb photons . the radio emission of all models is dominated by the contribution of the hotspots . the two cold models ( bc and lc ) have very similar radio - morphologies with a continuous beam connecting the inlet with the hotspot . this is different from model lh where the synthetic radio maps show a discontinuous and knotty beam even at a viewing angle of @xmath193 ( where the effects of doppler boosting are still small ) . we find that the thermal bremsstrahlung emission is strongly suppressed at very high energies ( @xmath194mev ) in the leptonic cold model because the average temperature of its cavity ( @xmath195k ) is much lower than that of the two other models ( @xmath196k ) . the baryonic and the leptonic hot model both show a gradual transition in the characteristics of their thermal bremsstrahlung emission . at low energies the emission is dominated by the shell , while the interior of the cavity dominates at high energies . all models exhibit a depression in the x - rays surface brightness of the cavity interior in agreement with recent observations @xcite . these observations also show a lack of strong x - ray emission from the boundaries of the radio lobes of hydraa . this does not contradict our results as hydraa is a fri source , while we have been simulating powerful radio sources . in a powerful source the bow shock is a strong shock and , hence , it may produce substantial x - ray emission . fri sources flare into the external medium and , most probably , they do not have strong bow shocks .","summary":"although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets , we find that both the morphology and the dynamic behaviour are almost independent on the assumed composition of the jets . the second epoch starts when the first larger vortices are produced near the jet head causing the beam cross section to increase and the jet to decelerate . the evolution of the cocoon and cavity is in agreement with a simple theoretical model . the beam velocities are relativistic ( ) at kiloparsec scales supporting the idea that the x - ray emission of several extragalactic jets may be due to relativistically boosted cmb photons . the radio emission of all models is dominated by the contribution of the hot spots . all models exhibit a depression in the x - rays surface brightness of the cavity interior in agreement with recent observations .   ","abstract":"we study the influence of the matter content of extragalactic jets on their morphology , dynamics and emission properties . for this purpose we consider jets of extremely different compositions including pure leptonic and baryonic plasmas . our work is based on two - dimensional relativistic hydrodynamic simulations of the long - term evolution of powerful extragalactic jets propagating into a homogeneous environment . the equation of state used in the simulations accounts for an arbitrary mixture of electrons , protons and electron - positron pairs . using the hydrodynamic models we have also computed synthetic radio maps and the thermal bremsstrahlung x - ray emission from their cavities .    although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets , we find that both the morphology and the dynamic behaviour are almost independent on the assumed composition of the jets . their evolution proceeds in two distinct epochs . during the first one multidimensional effects are unimportant and the jets propagate ballistically . the second epoch starts when the first larger vortices are produced near the jet head causing the beam cross section to increase and the jet to decelerate . the evolution of the cocoon and cavity is in agreement with a simple theoretical model . the beam velocities are relativistic ( ) at kiloparsec scales supporting the idea that the x - ray emission of several extragalactic jets may be due to relativistically boosted cmb photons . the radio emission of all models is dominated by the contribution of the hot spots . all models exhibit a depression in the x - rays surface brightness of the cavity interior in agreement with recent observations .    # 1ann . rev . . astrophys . * # 1 * # 1ann . rev . fluid mech . * # 1 * # 1astron . astrophys . * # 1 * # 1astron . astrophys . suppl . * # 1 * # 1astronom . j. * # 1 * # 1astrophys . j. * # 1 * # 1astrophys . j. suppl . * # 1 * # 1astrophys . j. lett . * # 1 * # 1comm . pure appl . math . * # 1 * # 1comput . . commun . * # 1 * # 1comput . phys . rep . * # 1 * # 1class . . grav . * # 1 * # 1j . comp . phys . * # 1 * # 1j . fluid mech . * # 1 * # 1nature * # 1 * # 1mon . not . roy . astronom . soc . * # 1 * # 1phis . review d * # 1 * # 1prog . theor . phys . * # 1 * # 1prog . theor . . suppl . * # 1 * # 1rev . mod . phys . * # 1 * # 1siam j. numer . anal . * # 1 * # 1siam j. sci . comput . * # 1 *    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    hydrodynamics  relativity  plasmas  ism : jets and outflows  radiation mechanisms : thermal  galaxies : jets ."}
{"article_id":"1305.2162","section_id":"i","document":"very high energy ( vhe ; 30 gev30 tev ) photons do not travel unimpeded through cosmological distances in the universe . a flux attenuation is expected due to photon - photon pair production with the lower energy photons of the extragalactic background light ( ebl ) in the ultraviolet , optical , and infrared ( ir ; @xcite ) . the ebl is the radiation emitted by star formation processes ( star light and star light absorbed / re - emitted by dust ) plus a small contribution from active galactic nuclei ( agns ) integrated over redshift over all the cosmic star - formation history ( @xcite ) . due to the properties of the interaction , a vhe photon of a given energy interacts mainly with an ebl photon within a well defined and narrow wavelength range . therefore , a signature of the ebl spectral distribution is expected in the observed vhe spectra of extragalactic sources ( @xcite ) . an interesting feature in the observed vhe spectra of extragalactic sources as a consequence of ebl absorption is given by the cosmic @xmath0-ray horizon ( cgrh ) , which has not been clearly observed yet . the cgrh is by definition the energy , @xmath1 , at which the optical depth of the photon - photon pair production becomes unity as a function of redshift . therefore , it gives an estimate of how far vhe photons can travel through the universe . due to the exponential behavior of the flux attenuation , an alternative definition is the energy at which the intrinsic spectrum is attenuated by the ebl by a factor of @xmath2 ( see @xcite ) . ( the intrinsic source spectrum is the one that we would observe if there were no effect from the ebl , also known as the ebl - corrected spectrum . )    an extreme category of agns , known as blazars , has been shown to be the best target for extragalactic vhe detections . they are characterized by having their energetic @xmath0-ray jets pointing towards us . in fact , most of the extragalactic sources already detected by imaging atmospheric cherenkov telescopes ( iacts ) such as h.e.s.s . , magic , and veritas ( @xcite , respectively ) are blazars . the observations of broadband spectral energy distributions ( seds ) of blazars show that they are characterized by a double - peaked shape and that their emission covers all the electromagnetic spectrum from radio up to the most energetic @xmath0-rays . the synchrotron / synchrotron self - compton ( ssc ) model provides a successful explanation for this behavior for most cases ( @xcite ) . in this framework a population of ultra - relativistic electrons causes the lower energy peak by synchrotron emission , while the second peak is then accounted for by inverse compton production of @xmath0-rays from the same population of high energy electrons and photons in the low energy peak . the direct observation of the cgrh in the vhe spectra of blazars remains elusive . this is due to two main observational difficulties . first , the lack of knowledge of the intrinsic spectra at vhe . extensive multiwavelength campaigns from radio up to @xmath0-rays are needed in order to predict the unattenuated vhe emission from the synchrotron / ssc model with enough precision . these campaigns should preferably be simultaneous due to the short - time flux variability of blazars ( @xcite ) . in this situation , the typical procedure in the literature to estimate the intrinsic vhe spectrum is either to assume a limit for the hardness of the slope @xmath3 with @xmath4 ( @xcite ) or to extrapolate the _ fermi_-large area telescope ( lat ) spectrum up to higher energies ( @xcite ) . second , it has been possible only in recent years to detect a considerable number of blazars in the gev energy range to allow us a statistical analysis . a large sample is necessary to reject intrinsic behaviors in the sources that mimic the effect of the cgrh . this improvement has been made thanks to the large data sets provided by the _ fermi _ satellite ( @xcite ) and the iacts . the only estimations of the cgrh so far are ebl - model - dependent lower limits from vhe observations of blazars ( @xcite ) , lower limits from _ fermi_-lat observations of blazars ( @xcite ) , and the predictions from ebl models ( @xcite , hereafter d11 ; @xcite ) . ( a table with a classification and description of the ingredients of these ebl models can be found in the proceeding by @xcite . ) indeed , an independent observation of the cgrh will also provide a completely independent and new test to the modeling of the ebl and consequently constraints on galaxy evolution . furthermore , the cgrh measurement also can be useful to estimate the cosmological parameters with a novel and independent methodology ( @xcite ; domnguez & prada , submitted ) . the detection of the cgrh is a primary scientific goal of the _ fermi _ @xmath0-ray telescope ( @xcite ) . this paper is organized as follows . section  [ sec : data ] describes the blazar catalog used in our analysis . the methodology is explained in section  [ sec : methodology ] . section  [ sec : results ] shows the results obtained from our analysis and in section  [ sec : discussion ] the results are discussed . finally , a brief summary of the main results is presented in section  [ sec : summary ] .    throughout this paper a standard @xmath5cdm cosmology is assumed , with @xmath6 , @xmath7 , and @xmath8  km  s@xmath9  mpc@xmath9 ( @xcite ) .","summary":"the cgrh is a fundamental quantity in cosmology . it gives an estimate of the opacity of the universe to very high energy ( vhe )-ray photons due to photon - photon pair production with the ebl . the only estimations of the cgrh to date are predictions from ebl models and lower limits from-ray observations of cosmological blazars and-ray bursts . here [ firstpage ]","abstract":"the first statistically significant detection of the cosmic-ray horizon ( cgrh ) that is independent of any extragalactic background light ( ebl ) model is presented . the cgrh is a fundamental quantity in cosmology . it gives an estimate of the opacity of the universe to very high energy ( vhe )-ray photons due to photon - photon pair production with the ebl . the only estimations of the cgrh to date are predictions from ebl models and lower limits from-ray observations of cosmological blazars and-ray bursts . here , we present homogeneous synchrotron / synchrotron self - compton ( ssc ) models of the spectral energy distributions of 15 blazars based on ( almost ) simultaneous observations from radio up to the highest energy-rays taken with the _ fermi _ satellite . these synchrotron / ssc models predict the unattenuated vhe fluxes , which are compared with the observations by imaging atmospheric cherenkov telescopes . this comparison provides an estimate of the optical depth of the ebl , which allows a derivation of the cgrh through a maximum likelihood analysis that is ebl - model independent . we find that the observed cgrh is compatible with the current knowledge of the ebl .    [ firstpage ]"}
{"article_id":"1305.2162","section_id":"m","document":"our methodology consists of finding the best - fitting homogeneous synchrotron / ssc models from multiwavelength data as simultaneous as possible from radio to the highest - energy @xmath0-rays detected by the _ fermi_-lat for the blazars in our catalog . these models predict the unattenuated vhe fluxes , which are compared with detections by iacts . the ratios between the unattenuated and detected vhe fluxes give an estimate of the ebl optical depth . by means of a maximum likelihood technique that is independent of any ebl model and that is based only on a few physically motivated assumptions , we then derive the cgrh for each blazar .      for every blazar in our sample , we built a quasi - simultaneous sed based on the data collected by @xcite and on the lat data from the second _ fermi_-lat agn catalog ( @xcite ) and the hard source catalog ( ackermann et al . , in preparation ) . these data are shown in the insets of figure  [ fig : e0fits ] . in many cases , these seds are not constructed from strictly simultaneous data . however , since we preferentially choose seds that are for a low state , we expect that the effects of variability are minimal in the @xmath0-ray energy range . we then fit the unique multiwavelength data of each source with a synchrotron / ssc model using a @xmath16 minimization technique . the model and fitting technique are fully described in finke , dermer & bttcher ( 2008 , see also @xcite ) . this model includes photoabsorption by photons internal to the blob . since bl lac objects and their presumed misaligned counterparts , fr  i radio galaxies usually lack optically thick dust tori ( @xcite ) we do not include photoabsorption from this radiation source , although it could in principle be important . we note that for 1es  1959 + 650 , there is evidence for an optically thick dust component ( @xcite ) . however , we did not obtain positive results with this source , as discussed in section  [ sec : discussion ] below . the fitting technique is double nested , with the _ inner loop _ fitting the synchrotron component with a particular electron distribution . in this paper , we use a broken power - law for the electron distribution with an exponential cutoff at high energies , that is , at @xmath17 . in some cases ( mrk  421 , 1es  2344 + 514 , pks  2005@xmath18489 , h  2356@xmath18309 , 1es  218 + 304 , and 1es  1101@xmath18232 ) we found that a single power - law with exponential cutoff was sufficient to provide good fits . our fits have as free parameters the electron indices @xmath19 , @xmath20 ; the minimum , maximum , and break electron lorentz factors , @xmath21 , @xmath17 , and @xmath22 , respectively ; and the overall normalization . often @xmath21 and @xmath17 were kept constant during the fit . the _ outer loop _ fit the ssc model the high energy data , and has three free parameters : the doppler factor , @xmath23 ; the magnetic field strength , @xmath24 ; and the minimum variability timescale , @xmath25 . we assume that the bulk lorentz factor @xmath26 . in the fits , @xmath25 was kept constant , with only @xmath23 and @xmath24 as free parameters . we discuss in more detail our choices of @xmath25 below . in the fits , we specifically leave off the iact data ; we only fit the ir through the lat @xmath0-rays . we use any radio points as upper limits , since this emission is likely from another region of the jet . we leave out the iact data because for this fit , we are fitting data which are unaffected by ebl attenuation . in some of the more distant sources , the highest energy lat point ( at energy @xmath27  gev ) can suffer significant attenuation . therefore , we remove this data point for sources at @xmath28 . this choice is supported by a variety of observational evidences ( see @xcite ) . once we have the resulting model curve from our fit that includes the extrapolation to vhe energies ( the overall model is shown with a black line in the insets of figure  [ fig : e0fits ] ) , we use this as the unattenuated / intrinsic spectrum for the source . we compare it with the flux observed from the iact detection to calculate the absorption optical depth ,    @xmath29    for photons observed in an energy bin centered at energy @xmath30 and a source at redshift @xmath31 . here @xmath32 is the observed differential flux and @xmath33 is the intrinsic flux at the energies given by the iact detection the fluxes given by the synchrotron / ssc model evaluated at the energies sampled by the iact . the uncertainties in @xmath34 come directly from the uncertainties in the iact observations . the @xmath35 data are shown with blue crosses in figure  [ fig : e0fits ] . the method used here for measuring @xmath36 is similar to the one described by @xcite .    for the synchrotron / ssc model , the radius of the spherical emitting region , @xmath37 is determined from the minimum variability timescale , @xmath25 , which is in turn constrained by the observed variability timescale through light travel time arguments so that @xmath38 ( @xcite ) . for consistency , we used the same @xmath25 for all of our blazars , @xmath39  s and @xmath40  s. as we see in section  [ sec : results ] , the choice of variability time makes very little difference to the model curve , although it has a large effect on the model fit parameters , which are not the focus of this paper . thus we are confident that the choice of @xmath25 has little effect on our resulting measurement of @xmath36 . however , although the two ssc models are similar they predict different vhe fluxes , which allows us to include the uncertainty in the variability timescale in our analysis . it should be noted that several sources have been observed to have extremely rapid ( @xmath41  s ) variability timescales ( @xcite ) . these rapid flares are quite rare , and since we have chosen seds from blazars in a quiescent state , we think these short timescales ( and the small emitting regions they imply ) are unlikely . furthermore , we have fit several of our objects with @xmath42  s and found the resulting doppler factors to be extremely high , @xmath43 a few hundred , and in two cases ( 1es  1101@xmath18232 and 3c  66a ) as high as 1000 . we believe these high doppler factors to be unreasonably high . +   +   +     +   +   +     +   +   +     +   +   +     +   +   +     +      we assume that @xmath35 ( as obtained from equation  [ eq : tau ] ) may be described by a third - order polynomial in @xmath44 ,    @xmath45    where @xmath30 is in units of tev . lower order polynomials are not sufficient to describe the optical depth . higher order polynomials introduce too many degrees of freedom and increase the computational time without increasing the precision of our analysis . this shape of the opacity ( which is the integral of the ebl spectral intensity and the pair - production cross section ; see @xcite ) is expected in the vhe range for two main reasons . first , the ebl sed must have a smooth shape as a consequence of the galaxy seds that produce the ebl and second because of the continuity of the cross - section of the pair - production interactions ( @xcite ) . a maximum likelihood method that scans the parameter space is adopted to compute the likelihood of the estimated data given the different polynomials @xmath35 ( blue crosses in figure  [ fig : e0fits ] ) for each blazar . the four parameters of the third order polynomial are explored by studying their probability density distributions . at this point , three physically motivated assumptions are made . first , that @xmath46 at @xmath47  tev ; since ebl attenuation is expected to be significantly low at these energies . second , that @xmath48  ul(@xmath49 ) , where ul is an upper limit calculated in the present work from the ebl upper limits presented in @xcite ; in particular @xmath50  ul(@xmath31 ) at @xmath51  tev . in @xcite two upper limits are presented coming from a realistic and a weaker assumption on the blazar emission that is called _ extreme _ and that provides the higher upper limits . extreme _ case is used in our analysis since we want to keep our methodology conservative . third , we impose that @xmath34 should increase monotonically with energy . these assumptions will be discussed in more detail in section  [ sec : discussion ] . the @xmath1 value derived from each blazar , for both slow and fast variability timescales , is then estimated from the most likely polynomial in the four dimensional parameter space ( these @xmath1 values are given in each inset of figure  [ fig : e0fits ] and also in table  [ tab2 ] ) . the uncertainty is estimated by using a standard jackknife analysis ( @xcite ) . the final ( combined ) @xmath1 for each blazar is then calculated as the geometric mean value for the two variability timescales values for a given source may initially be spread over a wide energy range . ] we stress that the uncertainties in this value includes the uncertainties derived from the two ssc modelings ( physically the uncertainty in the minimum time variability @xmath25 ) , which are bracketed by the two different predictions of the vhe fluxes . the lower and upper uncertainties of the combined @xmath1 are taken from the @xmath52 and @xmath53 of the state with the lowest and highest @xmath1 , respectively . we stress that these uncertainties are more conservative than @xmath14 .","summary":"the first statistically significant detection of the cosmic-ray horizon ( cgrh ) that is independent of any extragalactic background light ( ebl ) model is presented . , we present homogeneous synchrotron / synchrotron self - compton ( ssc ) models of the spectral energy distributions of 15 blazars based on ( almost ) simultaneous observations from radio up to the highest energy-rays taken with the _ fermi _ satellite . these synchrotron / ssc models predict the unattenuated vhe fluxes , which are compared with the observations by imaging atmospheric cherenkov telescopes . this comparison provides an estimate of the optical depth of the ebl , which allows a derivation of the cgrh through a maximum likelihood analysis that is ebl - model independent .","abstract":"the first statistically significant detection of the cosmic-ray horizon ( cgrh ) that is independent of any extragalactic background light ( ebl ) model is presented . the cgrh is a fundamental quantity in cosmology . it gives an estimate of the opacity of the universe to very high energy ( vhe )-ray photons due to photon - photon pair production with the ebl . the only estimations of the cgrh to date are predictions from ebl models and lower limits from-ray observations of cosmological blazars and-ray bursts . here , we present homogeneous synchrotron / synchrotron self - compton ( ssc ) models of the spectral energy distributions of 15 blazars based on ( almost ) simultaneous observations from radio up to the highest energy-rays taken with the _ fermi _ satellite . these synchrotron / ssc models predict the unattenuated vhe fluxes , which are compared with the observations by imaging atmospheric cherenkov telescopes . this comparison provides an estimate of the optical depth of the ebl , which allows a derivation of the cgrh through a maximum likelihood analysis that is ebl - model independent . we find that the observed cgrh is compatible with the current knowledge of the ebl .    [ firstpage ]"}
{"article_id":"1305.2162","section_id":"c","document":"in this work , we present an estimation of the cgrh based on a multiwavelength compilation of blazars that includes the most recent _ fermi_-lat data . we stress that our estimation of the cgrh is derived with only a few physically - motivated constraints . these results represent a major improvement with respect to previous works . these previous works provide only lower limits for the cgrh such as the ebl - model dependent limits estimated by @xcite ( that are based on a modified parameterization of the ebl models presented by @xcite ) . other cgrh limits are presented by @xcite using only _ fermi_-lat observations .    the _ fermi_-lat hard - source catalog ( ackermann et al . , in preparation ) is included in our analysis . the inclusion of this data set in our multiwavelength blazar catalog is essential for the right estimation of the cgrh since these measurements help to resolve the shape of the inverse compton peak . the optical depth is calculated using equation  [ eq : tau ] , which describes the ratio between the intrinsic flux from the synchrotron / ssc models and the observed flux by iacts . then , these data are fitted to polynomials of third order imposing some constraints . we also require an increasing and monotonic behavior of the polynomials . polynomials of order lower than three would not reproduce the expected optical depth shape while larger order polynomials would introduce unnecessary parameters into the fits . the constraints are all physically motivated and ebl - model independent . as we said before , the first condition is that @xmath58 at @xmath47  tev , which means that the attenuation is rather weak at those low energies . the second constraint is that @xmath59  ul(@xmath31 ) at @xmath51  tev , where ul are the opacities calculated from the ebl upper limit in the local universe found in @xcite . the upper limits of their so - called _ extreme _ case are used in our analysis . this _ extreme _ case represents the least constraining assumption on the blazar spectra since it allows us a wider range of spectral indices ( this results in a rather conservative hypothesis for our analysis ) . for this same reason , we prefer to use as conservative upper limits the results by @xcite rather than the newer results by @xcite that are based on a more constraining spectral condition . the ebl evolution is expected to affect the optical depth calculated at higher redshifts . to account for this effect we evolve conservatively the ebl upper limits at all wavelengths as @xmath60 ( in the co - moving frame ) when calculating the optical depths from these ebl limits from @xcite . we note that this is a robust limit given the fact that the maximum evolution ( which is dependent on the wavelength ) is @xmath61 in a realistic model such as d11 for @xmath62 ( the redshift range of our blazar catalog ) . the third constraint that we apply for our fits is to require only monotonically increasing functions for @xmath35 as a function of @xmath44 . this condition is also expected for any realistic ebl spectral intensity , which comes from galaxy emission , given the increasing behavior of the pair - production interaction with energy . interestingly , we see in figure  [ fig : e0fits ] that in most cases the iact observations are indeed detecting the flux decrement given by the cgrh feature ( the cherenkov observations span from negative to positive values of @xmath35 ) .        we find that the cgrh derived from 9 out of 11 blazars where our maximum likelihood methodology can be applied , is compatible with the expected value from the d11 model . the estimations from other ebl models such as @xcite , @xcite ( model @xmath63 ) , and @xcite are in agreement within uncertainties with the ebl model by d11 . we note that the fit of 1es  1101@xmath18232 has only one degree of freedom , see table  [ tab1 ] . the uncertainties of the two lowest redshift blazars ( mkn  501 and mkn  421 ) are systematically higher because the optical depth for these cases becomes unity at energies larger than the energies observed by the cherenkov telescopes . therefore , in these cases @xmath57 is given by an extrapolation of the polynomials rather than an interpolation between observed energies ( see fig .  [ fig : e0fits ] ) leading to greater uncertainty . for the case of 1es  2344 + 514 with fast flux variability timescale , a value of @xmath1 in agreement with the estimation by the d11 ebl model is derived . however , for this case the uncertainties are larger than @xmath1 and therefore no useful constraint can be derived . for the case of 1es  2344 + 514 with slow flux variability timescale , the ssc predicted flux is lower than the flux given iact data . for h  1426 + 428 , both flux variability timescales give uncertainties in the measurement of @xmath1 larger than @xmath1 and therefore no constraint can be derived . in both cases the synchrotron / ssc model does not seem to correctly fit the multiwavelength data . our maximum likelihood procedure can not be applied to any flux state on four blazars ( 1es  1959 + 650 , w  comae , h  2356@xmath18309 and 1es  1011 + 496 ) . there are different explanations for this fact . some blazars have shown flux variability on the scale of minutes ( @xcite ) and the iacts tend to detect the sources in higher - flux states . in most cases , the lat data are not simultaneous with the iact and other multiwavelength data . we have tried to alleviate this problem by choosing seds that are based on a low , non flaring state , where the variability seems to be small . in this way the effects of variability from epoch to epoch have been minimized . we compare the long - term light curves in x - rays using the quick - look results from the all sky monitor ( asm ) aboard the rossi x - ray timing explorer ( rxte ) with the time range of the iact observation for those four blazars where our maximum likelihood procedure could not be applied ( see the appendix for more details ) . clearly 1es  1011 + 496 was indeed detected by the iacts in flaring states . the situation for 1es  1959 + 650 is not clear . and the light curve of the h  2356@xmath18309 observation was rather irregular . we could not find x - ray data for w  comae in the asm database but this source was clearly detected in tev in a strong flare ( @xcite ) . the synchrotron / ssc model is the standard model for fitting high - peaked tev bl lac objects , and does seem to provide a good fit to their broadband seds ( @xcite ) . however , there are some alternatives . high - peaked bl lac objects are not thought to have a significant contribution to the @xmath0-ray flux from scattering external photon sources , but there are some exceptions , such as the eponymous bl lac ( @xcite ) . it has also been suggested that for some sources , a lepto - hadronic model provides a better fit , such as 1es  0414 + 009 ( @xcite ) . non - variable tev emission unrelated to the rest of the broadband sed could originate from compton - scattering of the cosmic microwave background ( cmb ) by an extended jet ( @xcite ) , which would certainly complicate their modeling . another way of creating non - variable tev emission unrelated to the sed , which would also avoid much of the ebl attenuation , would be if the agn produces a significant number of cosmic rays , which during propagation interact with the cmb and ebl to produce the observed @xmath0-rays ( @xcite ) . finally , even if the synchrotron / ssc model is valid for the tev blazars considered here , it is possible that the electron - positron pairs created by the vhe @xmath0-ray interactions with ebl photons can compton - scatter the cmb , producing @xmath0-rays observable by the lat ( @xcite ) . this would complicate the modeling process , since it would add other , poorly - constrained parameters ( @xcite ) . nonetheless , the simple synchrotron / ssc is a very attractive model , due to its success at fitting a large number of objects , and its relatively small number of free parameters . the existence of axion - like particles could also allow the @xmath0-rays to avoid the photoabsorption process , changing the expected vhe spectrum ( @xcite ) . a detailed broadband modeling including all these non - standard considerations is out of the scope of this work .    in summary , we built a catalog of 15 blazars from zhang et al . ( 2012 ) by requiring a good multiwavelength spectral coverage and tev detections . after fitting a synchrotron / ssc model to each source , there were four blazars where the tev detection was at higher fluxes than the flux extrapolation from the models . as described above , the long - term x - ray data from rxte were checked on the dates of the tev observations for these blazars showing a hint that h  2356@xmath18309 and 1es  1011 + 496 were flaring in x - ray and therefore probably in the tev range as well . the situation is not clear for 1es  1959 + 650 . however , as described above potential problems with the synchrotron / ssc model can not be ruled out . there are two other blazars ( h  1426 + 428 , 1es  2344 + 514 ) for which the uncertainties that we derive for @xmath1 are too high to set any constrain . this is due to large uncertainties in the tev measurements and/or the low number of tev spectral points , which do not allow a reliable @xmath1 estimation . the agreement between the cgrh observation presented in this work and the expected values from d11 indicates that these possibilities described above might not be relevant for many blazars . furthermore , figure  [ fig : morecgrh ] gives more information on the optical - depth shape derived from our methodology . this figure shows that the energies at which the optical depths are 0.5 , 1 ( the standard definition of cgrh ) , 2 and 3 are still compatible with the d11 model . the uncertainties are generally higher at @xmath34 different from 1 due to the fact that the cherenkov detections do not span the energy range needed in order to derive a better estimation of those energies . as seen in figure  [ fig : e0fits ] , the polynomials cut the horizontal lines of constant optical depths generally in wider energy ranges for @xmath34 values different from 1 ( @xmath55 ) . the agreement between the observed cgrh and the expected cgrh from d11 is also consistent with 3c  66a being located at a redshift slightly lower than @xmath64 with 99% confidence . ] and pg  1553 + 113 at @xmath65 . an independent confirmation of these redshifts will give support to both the current ebl knowledge and our methodology to derive the cgrh . by assuming an ebl model , it is possible to estimate redshifts using ebl attenuation in a realistic way considering the overall sed of the blazars ( see the proceeding by @xcite ) . however , we note that some previous estimation of the redshift is necessary in order to fit the synchrotron / ssc models ( @xcite ) . @xcite claimed that recent ebl models such as d11 are incompatible with iacts observations at more than @xmath66 . they based their conclusions in an analysis of @xmath67 blazars using two different methods that they call _ method  1 _ and _ method  2_. their more constraining results are derived from method  2 ( see section  3.2 in @xcite ) . this approach is based on the expected difference between spectral indexes when the vhe spectrum is fitted by a broken power law . this spectral difference is attributed to ebl attenuation , setting limits on the intensity of the local ebl . we consider their results inconclusive . their method  2 relies on the assumption that the vhe spectra may be well fitted by broken power laws . we performed f - tests on all the fits of their blazar sample to test whether broken power laws ( fitted by two different spectral indexes ) could be actually considered better fits to the observed vhe spectra than simple power laws ( fitted by a single spectral index ) of the fit due to the inclusion of an additional parameter in the model exceeds the value that can be attributed to random fluctuations in the data ; see @xcite . ] the f - tests performed for every one of their spectra show that for only 2 out of 12 cases ( rgb  j0152 + 017 and 1es  1101 - 232 ) the spectra can be considered fitted better by broken power laws than simple power laws . their results from method  1 ( see section  3.1 in @xcite ) are inconclusive as well . this method relies on the assumption that the vhe intrinsic spectrum is described by a power - law extrapolation of the _ fermi_-lat data points . as we see in the synchrotron / ssc fits of figure  [ fig : e0fits ] , this is not a realistic assumption due to the shape of the inverse compton peak . furthermore , we show in the present work that a more sophisticated ssc - based analysis is compatible with the current ebl knowledge . some authors have treated the _ fermi_-lat spectrum , extrapolated into the vhe regime , as an upper limit on the intrinsic spectrum , and used this to compute upper limits on @xmath36 ( @xcite ) . this provides only upper limits on @xmath36 rather than measurements , as we derive here . however , their techniques involve fewer assumptions about the blazar emission model and variability of the sed ( see the discussion above ) . thus , the two techniques are complementary . recently , @xcite and @xcite claimed the detection of an imprint of the ebl in the blazar spectra . @xcite base their analysis on _ fermi_-lat data from @xmath68 to 1.6 , whereas @xcite use h.e.s.s . data from blazars located at @xmath69 . these works do not give any results in terms of the cgrh but we are able to estimate it from their results . we find that the results presented in our analysis are compatible with the results from these two independent works , which supports our conclusions .    from our results , we can conclude that the ebl data from direct detection by @xcite , @xcite , and @xcite are likely contaminated by zodiacal light . this possibility has indirectly been proposed previously by several authors such as @xcite , @xcite , and @xcite using ebl upper limits but we confirm these results using a more robust approach .","summary":"we find that the observed cgrh is compatible with the current knowledge of the ebl .   ","abstract":"the first statistically significant detection of the cosmic-ray horizon ( cgrh ) that is independent of any extragalactic background light ( ebl ) model is presented . the cgrh is a fundamental quantity in cosmology . it gives an estimate of the opacity of the universe to very high energy ( vhe )-ray photons due to photon - photon pair production with the ebl . the only estimations of the cgrh to date are predictions from ebl models and lower limits from-ray observations of cosmological blazars and-ray bursts . here , we present homogeneous synchrotron / synchrotron self - compton ( ssc ) models of the spectral energy distributions of 15 blazars based on ( almost ) simultaneous observations from radio up to the highest energy-rays taken with the _ fermi _ satellite . these synchrotron / ssc models predict the unattenuated vhe fluxes , which are compared with the observations by imaging atmospheric cherenkov telescopes . this comparison provides an estimate of the optical depth of the ebl , which allows a derivation of the cgrh through a maximum likelihood analysis that is ebl - model independent . we find that the observed cgrh is compatible with the current knowledge of the ebl .    [ firstpage ]"}
{"article_id":"math0610828","section_id":"i","document":"let @xmath0 be a functor and @xmath4 , @xmath5 two classes of morphisms containing identities and stable under composition , such that @xmath6 . this induces the situation @xmath7 where @xmath8 and @xmath9 are localisation functors . in this note , we offer an answer to the following question . give sufficient conditions for @xmath10 to be an equivalence of categories . this answer , theorem [ t0 ] , is in the spirit of quillen s theorem a ( * ? ? ? a ) that we recall for motivation : in the above situation , forgetting @xmath11 and @xmath12 , if for all @xmath13 the category @xmath14 ( see  [ comma ] ) is @xmath15-connected , then @xmath3 is a weak equivalence .      in ( * ? ? ? 3.8 ) , we proved that @xmath16 is an equivalence of categories when @xmath17 is the category of smooth varieties over a field of characteristic @xmath18 , @xmath19 is its full subcategory consisting of smooth projective varieties , and we take for @xmath11 and @xmath12 either birational morphisms or  stable birational morphisms \" ( i.e. dominant morphisms such that the corresponding function field extension is purely transcendental ) . when we started revising @xcite , it turned out that we needed similar localisation theorems in other situations . at this stage it was becoming desirable to understand these localisation theorems more abstractly , and indeed we got two non - overlapping , technical ( and very ugly ) statements . the first author then discussed these results with georges maltsiniotis , and they arrived at corollary [ c2 ] below . using proposition [ p1 ] below , one can easily see that the hypotheses of corollary [ c2 ] are verified in the case of theorem 3.8 of @xcite . however , they are not verified in some of the other geometric situations mentioned above .     catching \" the latter situations led to theorem [ t0 ] . thus we had two sets of abstract hypotheses implying that @xmath10 is an equivalence of categories :    * hypotheses ( 0 ) , ( 1 ) and ( 2 ) of theorem [ t0 ] . * hypotheses ( 0 ) and ( 1 ) of corollary [ c2 ] ;    to crown all , maltsiniotis gave us an argument showing that @xmath20 : this is the content of theorem [ t1 ] a ) and the proof we give is essentially his . in the same period , jol riou proved a localisation theorem of a similar nature ( theorem [ riou ] ) . it turns out that hypotheses ( 0 ) , ( 1 ) and ( 2 ) are implied by riou s hypotheses ( and actually by less ) : see theorem [ p3 ] .    after stating and proving the main theorem , theorem [ t0 ] , we prove a  relativisation \" theorem , theorem [ t1 ] which leads to corollary [ c2 ] mentioned above . we then give a number of conditions which imply the hypotheses of theorem [ t0 ] in  [ 5 ] . in  [ 6 ] we show that the fact that @xmath10 is an equivalence of categories in is stable under adjoining products and coproducts . we then give some algebro - geometric applications ( hyperenvelopes , cubical hyperresolutions ... ) in  [ 7 ] , and finally , in  [ 8 ] , the birational applications we alluded to : those will be used to simplify the exposition of the revision @xcite of @xcite .    even though maltsiniotis did not wish to appear as a coauthor of this note , we want to stress his essential contributions in bringing the results here to their present form . let us also mention that hypotheses ( 0 ) , ( 1 ) and ( 2 ) imply much more than theorem [ t0 ] : they actually yield the existence of an  absolute \" derived functor ( in the sense of quillen ( * ? ? ? 1 ) ) associated to any functor @xmath21 such that @xmath22 is invertible . this will be developed in a forthcoming work of maltsiniotis and the first author , where a different proof of theorem [ t0 ] will be given @xcite ; see already  [ kan ] here for a weaker result . in @xcite , we also hope to lift theorem [ t0 ] to the  dwyer - kan localisation \" @xcite by suitably reinforcing its hypotheses . finally , we wish to thank the referee for a very helpful comment regarding theorem [ p3 ] ( see lemma [ inftycon ] ) .","summary":"these conditions are in the spirit of quillen s theorem a. we give some applications in algebaic and birational geometry .","abstract":"given a functor carrying a class of morphisms into a class , we give sufficient conditions in order that induces an equivalence on the localised categories . these conditions are in the spirit of quillen s theorem a. we give some applications in algebaic and birational geometry ."}
{"article_id":"1701.08825","section_id":"i","document":"the _ parameter space _ of complex degree @xmath0 polynomials is by definition the space of affine conjugacy classes of these polynomials . equivalently , one can talk about the space of all _ monic central polynomials _ of degree @xmath0 , i.e. polynomials of the form @xmath1 . any polynomial is affinely conjugate to a monic central polynomial . an important set is the _ connectedness locus _ @xmath2 consisting of classes of all degree @xmath0 polynomials @xmath3 , whose julia sets @xmath4 ( equivalently , whose _ filled julia sets _ @xmath5 ) are connected . general properties of the connectedness locus @xmath2 have been studied for quite some time . for instance , it is known that @xmath2 is a compact cellular set in the parameter space of complex degree @xmath0 polynomials ( this was proven in @xcite in the cubic case and in @xcite for higher degrees , see also @xcite ; by definition , following m. brown @xcite , a subset of a euclidean space @xmath6 is _ cellular _ if its complement in the sphere @xmath7 is an open topological cell ) .    for @xmath8 , a monic centered polynomial takes the form @xmath9 , and the parameter space of quadratic polynomials can be identified with the plane of complex parameters @xmath10 . clearly , @xmath11 has a unique critical point @xmath12 and a unique critical value @xmath10 in @xmath13 . thus , we can say that polynomials @xmath11 are parameterized by their critical values . the quadratic connectedness locus is the famous _ mandelbrot set _ @xmath14 , identified with the set of complex numbers @xmath10 not escaping to infinity under iterations of the polynomial @xmath11 . the mandelbrot set @xmath14 has a complicated self - similar structure . the `` pinched disk '' model for @xmath14 is due to douady and thurston @xcite . to describe their approach to the problem of modeling @xmath14 , we first describe _ laminational _ models of polynomial julia sets ( we follow @xcite ) and then use them to interpret results of @xcite . we assume basic knowledge of complex dynamics ( a detailed description is given later ) . let @xmath15 be the unit circle in @xmath13 , consisting of all complex numbers of modulus one . we write @xmath16 for the restriction of the map @xmath17 . we identify @xmath15 with @xmath18 by the mapping taking an _ angle _ @xmath19 to the point @xmath20 . under this identification , we have @xmath21 . we will write @xmath22 for the open unit disk @xmath23 .    given a complex polynomial @xmath3 , we let @xmath24 denote the set @xmath25 . this set is called the _ basin of attraction of infinity _ of @xmath3 . clearly , @xmath26 . if the julia set @xmath4 is locally connected , then it is connected , and the riemann map @xmath27 can be continuously extended to a map @xmath28 . this gives rise to a map @xmath29 , which semiconjugates @xmath30 with @xmath31 . define an equivalence relation @xmath32 on @xmath15 so that @xmath33 if and only if @xmath34 . then @xmath35 and @xmath4 are homeomorphic , and the homeomorphism in question conjugates the map @xmath36 induced on @xmath35 by @xmath37 , and @xmath31 . it is not hard to see that the convex hulls of @xmath32-classes are disjoint in @xmath38 . a productive idea is to consider equivalences relations @xmath39 whose properties are similar to those of @xmath32 . these properties will be stated precisely below . such equivalence relations are called _ laminational equivalence relations ( of degree @xmath0 _ ; if @xmath8 they are said to be _ quadratic _ , and if @xmath40 they are said to be _ cubic_. the maps @xmath41 induced by @xmath37 are called _ topological polynomials _ of degree @xmath0 ; again , if @xmath8 they are called _ quadratic _ and if @xmath40 they are called _ cubic_. for brevity , in what follows we will talk about `` @xmath39-classes '' instead of `` classes of equivalence of @xmath39 '' .    an important geometric interpretation of a laminational equivalence relation @xmath39 is as follows . for any @xmath39-class @xmath42 , take its convex hull @xmath43 . consider the edges of all such convex hulls ; add all points of @xmath15 to this collection of chords . the obtained collection of ( possibly , degenerate ) chords in the unit disk is denoted by @xmath44 and is called a _ geodesic lamination ( generated by @xmath39)_. for brevity in what follows we sometimes write `` lamination '' instead of `` geodesic lamination '' . clearly , @xmath44 is a closed family of chords . let @xmath45 denote the straight line segment connecting points @xmath46 , @xmath47 . we will never use this notation for pairs of points not in @xmath15 . recall also that points in @xmath15 are identified with their angles . thus , @xmath48 always means the chord of @xmath15 connecting the points with angles @xmath12 and @xmath49 ( not a half - radius of the unit disk originating at the center ) . for any chord @xmath50 in the closed unit disk @xmath38 set @xmath51 . for any @xmath39-class @xmath42 and , more generally , for any closed set @xmath52 , we set @xmath53 . recall the construction of douady and thurston . suppose that a quadratic polynomial @xmath54 has locally connected julia set . we will write @xmath55 for the convex hull of the @xmath56-class corresponding to the critical value @xmath10 . a fundamental theorem of thurston is that @xmath57 implies that @xmath55 and @xmath58 are disjoint in @xmath38 . consider the collection of all @xmath55 and take its closure . the thus obtained collection of chords and inscribed polygons defines a geodesic lamination @xmath59 introduced by thurston in @xcite and called the _ quadratic minor lamination _ ; moreover , it induces an equivalence relation @xmath60 on @xmath15 @xcite . the corresponding quotient space @xmath61 is a combinatorial model for the boundary of @xmath14 . it is called the _ combinatorial mandelbrot set_. conjecturally , the combinatorial mandelbrot set is homeomorphic to the boundary of @xmath14 . this conjecture is equivalent to the famous mlc conjecture : the mandelbrot set is locally connected . when defining the combinatorial mandelbrot set , we used a partial association between parameter values @xmath10 and laminational equivalence relations @xmath56 . in order to talk about @xmath56 , we had to assume that @xmath62 was locally connected . recall that a _ dendrite _ is a locally connected continuum that does not contain jordan curves . recall also , that a map from a continuum to a continuum is called _ monotone _ if under this map point - preimages ( _ fibers _ ) are connected . [ d : dendr - poly ] a complex polynomial @xmath3 is said to be _ dendritic _ if it has connected julia set and all cycles repelling . a topological polynomial is said to be _ dendritic _ if its julia set is a dendrite . in that case the corresponding laminational equivalence relation and the associated geodesic lamination are also said to be _ it is known that there are dendritic polynomials with non - locally connected julia sets . nevertheless , by @xcite , for _ every _ dendritic polynomial @xmath3 of degree @xmath0 , there is a monotone semiconjugacy @xmath63 between @xmath64 and a certain topological polynomial @xmath36 such that the map @xmath63 is one - to - one on all periodic and pre - periodic points of @xmath3 . moreover , by @xcite the map @xmath63 is unique and can be defined in a purely topological way . call a monotone map @xmath65 of a connected polynomial julia set @xmath66 onto a locally connected continuum @xmath67 the _ finest monotone map of @xmath4 onto a locally connected continuum _ if , for any monotone @xmath68 with @xmath69 locally connected , there is a monotone map @xmath70 with @xmath71 . then it is proven in @xcite that for _ any polynomial _ the finest monotone map on a connected polynomial julia set semiconjugates @xmath31 to the corresponding topological polynomial @xmath36 on its topological julia set @xmath72 generated by the laminational equivalence relation possibly with infinite classes @xmath32 , and that in the dendritic case this semiconjugacy coincides with the map @xmath63 constructed by kiwi in @xcite . clearly , this shows that @xmath63 is unique . thus , @xmath3 gives rise to a corresponding laminational equivalence relation @xmath32 even if @xmath4 is not locally connected . if @xmath9 is a quadratic dendritic polynomial , then @xmath55 is defined , and is a finite - sided polygon inscribed into @xmath15 , or a chord , or a point . a parameter value @xmath10 is said to be _ quadratic dendritic _ if @xmath54 is dendritic . the fundamental results of thurston @xcite imply , in particular , that @xmath55 and @xmath58 are either the same or disjoint , for all pairs @xmath10 , @xmath73 of dendritic parameter values . moreover , the mapping @xmath74 is _ upper semi - continuous _ ( if a sequence of dendritic parameters @xmath75 converges to a dendritic parameter @xmath10 , then the limit set of the corresponding convex sets @xmath76 is a subset of @xmath55 ) . we call @xmath55 the _ tag associated to @xmath10_.    now , consider the union of all tags of quadratic dendritic polynomials . this union is naturally partitioned into individual tags ( distinct tags are pairwise disjoint ! ) . thus the space of tags can be equipped with the quotient space topology induced from the union of tags . on the other hand , take the set of quadratic dendritic parameters . each such parameter @xmath10 maps to the polygon @xmath55 , i.e. to the tag associated to @xmath10 . thus each quadratic dendritic parameter maps to the corresponding point of the space of tags . this provides for a combinatorial ( or laminational ) model for the set of quadratic dendritic polynomials ( or their parameters ) .    in this paper , we extend these results to cubic dendritic polynomials . recall that monic centered quadratic polynomials are parameterized by their critical values . a combinatorial analog of this parameterization is the association between topological polynomials and their tags . tags of quadratic topological polynomials are post - critical objects of the corresponding laminational equivalences . monic centered cubic polynomials can be parameterized by a critical value and a co - critical point . recall that the _ co - critical _ point @xmath77 of a cubic polynomial @xmath3 corresponding to a simple critical point @xmath78 of @xmath3 is defined as a point different from @xmath78 but having the same image under @xmath3 as @xmath78 . if @xmath78 is a multiple critical point of @xmath3 , then we set @xmath79 . in any case we have @xmath80 . let @xmath10 and @xmath0 be the two critical points of @xmath3 ( if @xmath3 has a multiple critical point , then @xmath81 ) . set @xmath82 and @xmath83 . assuming that @xmath3 is monic and central , we can parameterize @xmath3 by @xmath46 and @xmath84 : @xmath85 for @xmath3 in this form , we have @xmath86 , @xmath87 . similarly to parameterizing cubic polynomials by pairs @xmath88 , we will use the so - called _ mixed tags _ to parameterize topological cubic dendritic polynomials .    consider a cubic dendritic polynomial @xmath3 . by the above there exists a laminational equivalence relation @xmath32 and a monotone semiconjugacy @xmath89 between @xmath90 and the topological polynomial @xmath36 . given a point @xmath91 , we associate with it the convex hull @xmath92 of the @xmath32-equivalence class represented by the point @xmath93 . if @xmath3 is fixed , we may write @xmath94 instead of @xmath92 . the set @xmath94 is a convex polygon with finitely many vertices , a chord , or a point ; it should be viewed as a combinatorial object corresponding to @xmath95 . for any points @xmath96 , the sets @xmath94 and @xmath97 either coincide or are disjoint .    by definition , a _ @xmath98critically@xmath99 marked _ ( cf @xcite ) cubic polynomial is a triple @xmath100 , where @xmath3 is a cubic polynomial with critical points @xmath10 and @xmath0 . if @xmath3 has only one ( double ) critical point , then @xmath81 , otherwise @xmath101 . in particular , if @xmath101 , then the triple @xmath100 and the triple @xmath102 are viewed as two distinct critically marked cubic polynomials . when the order of the critical points is fixed , we will sometimes write @xmath3 instead of @xmath100 . critically marked polynomials do not have to be dendritic ( in fact , the notion is used by milnor and poirier @xcite for hyperbolic polynomials , i.e. , in the situation diametrically opposite to that of dendritic polynomials ) . however in this paper whenever we talk about critically marked polynomials we mean that they are dendritic . let @xmath103 be the space of all critically marked cubic dendritic polynomials . with every marked dendritic polynomial @xmath100 , we associate the corresponding _ mixed tag _ @xmath104 here @xmath105 is the co - critical point corresponding to the critical point @xmath10 .    a similar construction can be implemented for any cubic dendritic laminational equivalence relation @xmath39 . let @xmath106 and @xmath107 denote the convex hulls of its critical classes . then either @xmath108 is the unique critical @xmath39-class or @xmath109 are disjoint . the sets @xmath106 and @xmath107 are called _ critical objects _ of @xmath39 . by a _ @xmath98critically@xmath99 marked cubic laminational equivalence relation _ we mean a triple @xmath110 ; in that case we always assume that @xmath39 is dendritic . if @xmath109 , then we define @xmath111 as the convex hull of the unique @xmath39-class that is distinct from the class @xmath112 but has the same @xmath113-image . if @xmath108 , then we set @xmath114 . the set @xmath115 is called the _ co - critical set of @xmath106_. for a marked laminational equivalence relation @xmath110 , define its _ mixed tag _ as @xmath116 we endow the family of products of compact subsets of @xmath38 with the product topology on @xmath117 . it is easy to see that the map @xmath118 is continuous as a map defined on a subset of @xmath117 . evidently , the map @xmath118 preserves inclusions . the subscript @xmath119 in @xmath118 indicates that @xmath118 acts on marked laminational equivalence relations unlike the map @xmath120 that acts on polynomials . these two maps are closely related though : for any marked dendritic cubic polynomial @xmath100 and the corresponding marked laminational equivalence relation @xmath121 , we have @xmath122 . consider the collection of the sets @xmath123 over all @xmath124 . by @xcite , for any dendritic laminational equivalence relation @xmath39 , there exists a dendritic complex polynomial @xmath3 with @xmath125 . thus , equivalently , we can talk about the collection of mixed tags of all dendritic laminations @xmath44 . in theorem  [ t : tagusc ] we show that the mixed tags @xmath123 are pairwise disjoint or equal . let us denote this collection of sets be @xmath126 ( for _ cubic mixed lamination of dendritic polynomials _ ) . note , that @xmath126 can be viewed as ( non - closed ) `` lamination '' in @xmath127 whose elements are products of points , leaves or gaps . one can consider @xmath126 as the higher - dimensional analog of thurston s @xmath59 restricted to dendritic polynomials . theorem  [ t : tagusc ] , in addition , establishes the fact that the collection of sets @xmath126 is upper semi - continuous . let the _ union _ of all sets in @xmath126 be denoted by @xmath128 . it follows that the quotient space of @xmath129 , obtained by collapsing all elements of @xmath126 to points , is a separable metric space which we denote by @xmath130 . denote by @xmath131 the corresponding quotient map . mixed tags of critically marked polynomials from @xmath103 are disjoint or coincide . the map @xmath132 is continuous . hence @xmath130 is a combinatorial model for @xmath133 . this theorem can be viewed as a partial generalization of thurston s results @xcite to cubic polynomials . it is also a first step towards defining a combinatorial model for @xmath134 . lavaurs @xcite proved that @xmath134 is not locally connected . epstein and yampolsky @xcite proved that the bifurcation locus in the space of real cubic polynomials is not locally connected either . this makes the problem of defining a combinatorial model of @xmath134 very delicate . there is no hope that a combinatorial model would lead to a precise topological model . schleicher @xcite constructed a geodesic lamination modeling the space of _ unicritical _ polynomials , that is , polynomials with a unique multiple critical point . we have heard of an unpublished old work of d. ahmadi and m. rees , in which cubic geodesic laminations were studied , however we have not seen it . the present paper is based on the results obtained in @xcite . these results are applicable to invariant laminations of any degree . the paper is organized as follows . in section [ s : basicdef ] , we discuss basic properties of geodesic laminations and laminational equivalence relations . in section [ s : long ] , we recall the results of @xcite adapting them to the cubic case . finally , section [ s : cudebi ] is dedicated to the proof of the main result .","summary":"complex 1-variable polynomials with connected julia sets and only repelling periodic points are called _ dendritic_. by results of kiwi , any dendritic polynomial is semi - conjugate to a topological polynomial whose topological julia set is a dendrite . we construct a continuous map of the space of all cubic dendritic polynomials onto a laminational model that is a quotient space of a subset of the closed bidisk . this construction generalizes the `` pinched disk '' model of the mandelbrot set due to douady and thurston . it can be viewed as a step towards constructing a model of the cubic connectedness locus .","abstract":"complex 1-variable polynomials with connected julia sets and only repelling periodic points are called _ dendritic_. by results of kiwi , any dendritic polynomial is semi - conjugate to a topological polynomial whose topological julia set is a dendrite . we construct a continuous map of the space of all cubic dendritic polynomials onto a laminational model that is a quotient space of a subset of the closed bidisk . this construction generalizes the `` pinched disk '' model of the mandelbrot set due to douady and thurston . it can be viewed as a step towards constructing a model of the cubic connectedness locus ."}
{"article_id":"1405.3186","section_id":"i","document":"the herschel space observatory @xcite is the fourth `` cornerstone '' mission in the esa horizon 2000 science programme . it has been the first large aperture space far  infrared ( fir)/sub  mm observatory , performing photometry and spectroscopy in the 55672@xmath0 m wavelength range . the observatory consisted of a telescope with a large ( 3.5 m ) monolithic low emissivity passively cooled mirror and three focal plane science instruments enclosed in a large heii cryostat : the pacs instrument @xcite , consisting of _ ( a ) _ a dual - band photometer , comprising a `` blue photometer '' with two filters mounted in a wheel , allowing to select a range centred at either 70@xmath0 m or 100@xmath0 m and a `` red photometer '' covering a spectral range centred at 160@xmath0 m ; and _ ( b ) _ an integral field spectrometer in the range . the photometric bands covered the same field - of - view ( fov ) , while the fov of the spectrometer was offset from the photometer . the spire instrument @xcite consisted of a three - band imaging photometer and an imaging fourier transform spectrometer . as for the pacs instrument , the photometer and spectrometer did not operate simultaneously . the three photometer arrays provided broad - band photometry in bands centred at 250 , 350 and 500  @xmath0 m with a common fov , and the spectrometer was also offset from the photometer . finally , the hifi instrument @xcite was a high - resolution heterodyne spectrometer with a continuous coverage from 480 to 1250  ghz in five bands , plus two bands providing a coverage of the 14101910  ghz range . both polarisations of the astronomical signal were detected for maximum sensitivity . to cover a wide frequency range with high sensitivity , hifi was designed to have 7 mixer bands and 14 local oscillator sub - bands ( two frequency sections per band ) . figure [ herschel_fov ] shows the position of the instruments apertures within the herschel fov . the herschel spacecraft ( s / c ) had a modular design , comprising the extended payload module ( eplm ) and the service module ( svm ) . the eplm consisted of the payload module described above , the sunshade and solar array and payload associated equipment . the svm housed `` warm '' payload electronics and provided services such as power , attitude and orbit control , the on - board data handling and command execution , communications , and safety . the herschel s / c was stabilised in three - axes . the attitude was commanded by means of reaction wheels and controlled using star trackers and gyroscopes , as described in section [ sec : acms ] . the s / c pointing modes were based either on stare pointings ( fine pointing mode ) or moving pointings at constant rate ( line scan mode ) . raster maps are `` grids '' of stare pointings at regular spacings ; scan maps are sequences of line scans at regular spacing . allowed scan angular speed ranged from 0.1arcsec / s to 1arcmin / s . in addition , the herschel spacecraft could track moving solar system targets at rates up to 10arcsec / min . the s / c slewed between different pointing positions at rates up to 7arcmin / s . the pointing calibration tasks were aimed , on the one hand , to provide an accurate alignment of the different fields of view of each instrument and instrument mode described above with respect to the telescope and the s / c attitude reference frame , and on the other , to characterise the performance of the various pointing modes . this paper describes these activities and is structured as follows : in section [ sec : acms ] , we discuss the basic elements of the attitude control and measurement system ( acms ) and the route of telemetry ( tm ) data from the spacecraft to the herschel science centre ( hsc ) at the european space astronomy centre ( esac ) . section [ sec : products ] is devoted to the pointing - related products generated at the hsc : the pointing product , the acms tm product and the spacecraft / instrument alignment matrices ( siam ) product . section [ sec : calib_params ] deals with the main calibration parameters of the herschel spacecraft pointing system and historical description of the evolution of the indicators of its performance , that in general met or surpassed the requirements set . however , given a clear scientific motivation for further improvement ( see section [ sec : calib_params ] ) , an outstanding effort has been done and is still being invested : in section [ sec : pointing_improvement ] , the work carried out within the ground segment centres to improve the s / c pointing measurements is described . on - going and future developments towards a final refinement of the herschel astrometry are also described .","summary":"we present the activities carried out to calibrate and characterise the performance of the elements of attitude control and measurement on board the herschel spacecraft . the main calibration parameters and the evolution of the indicators of the pointing performance are described , from the initial values derived from the observations carried out in the performance verification phase to those attained in the last year and half of mission , an absolute pointing error around or even below 1arcsec , a spatial relative pointing error of some 1arcsec and a pointing stability below 0.2arsec . the actions carried out at the ground segment to improve the spacecraft pointing measurements are outlined . on - going and future developments towards a final refinement of the herschel astrometry are also summarised . a brief description of the different components of the attitude control and measurement system ( both in the space and in the ground segments ) is also given for reference .","abstract":"we present the activities carried out to calibrate and characterise the performance of the elements of attitude control and measurement on board the herschel spacecraft . the main calibration parameters and the evolution of the indicators of the pointing performance are described , from the initial values derived from the observations carried out in the performance verification phase to those attained in the last year and half of mission , an absolute pointing error around or even below 1arcsec , a spatial relative pointing error of some 1arcsec and a pointing stability below 0.2arsec . the actions carried out at the ground segment to improve the spacecraft pointing measurements are outlined . on - going and future developments towards a final refinement of the herschel astrometry are also summarised . a brief description of the different components of the attitude control and measurement system ( both in the space and in the ground segments ) is also given for reference . we stress the importance of the cooperation between the different actors ( scientists , flight dynamics and systems engineers , attitude control and measurement hardware designers , star - tracker manufacturers , etc . ) to attain the final level of performance ."}
{"article_id":"1405.5758","section_id":"i","document":"in this contribution we consider linear elliptic problems with a heterogenous and highly variable diffusion coefficient @xmath0 as arisen often in hydrology or in material sciences . in the following , we are looking for @xmath1 which solves @xmath2 in a weak sense . here , we denote    * @xmath3 , @xmath4 , a bounded lipschitz domain with a piecewise polygonal boundary , * @xmath5 a source term , and * @xmath6 a symmetric matrix - valued function with uniform spectral bounds @xmath7 , @xmath8\\quad\\text{for almost all } x\\in \\omega.\\ ] ] we call the ratio @xmath9 the _ contrast _ of @xmath0 . under assumptions ( a1)-(a3 ) and by the lax - milgram theorem , there exists a unique weak solution @xmath10 to @xmath11 where @xmath12    the problematic term in the equation is the diffusion matrix @xmath0 , which is known to exhibit very fast variations on a very fine scale ( i.e. it has a multiscale character ) . these variations can be highly heterogenous and unstructured , which is why it is often necessary to resolve them globally by an underlying computational grid that matches the said heterogeneity . using standard finite element methods , this results in high dimensional solution spaces and hence an enormous computational demand , which often can not be handled even by today s computing technology . consequently , there is a need for alternative methods , so called multiscale methods , which can either operate below linear computational complexity by using local representative elements ( cf . @xcite ) or which can split the original problem into very localized subproblems that cover @xmath13 but that can be solved cheaply and independent from each other ( cf . @xcite ) .    in this paper , we focus on a rather recent approach called localized orthogonal decomposition ( lod ) that was introduced by mlqvist and peterseim @xcite and further generalized in @xcite . we consider a coarse space @xmath14 , which is low - dimensional but possibly inadequate for finding a reliable galerkin approximation to the multiscale solution of problem ( [ exact - solution ] ) . the idea of the method is to start from this coarse space and to update the corresponding set of basis functions step - by - step to improve the approximation properties of the space . in a summarized form , this can be described in four steps : 1 ) define a ( quasi ) interpolation operator @xmath15 from @xmath16 onto @xmath14 , 2 ) information in the kernel of the interpolation operator is considered to be negligible ( having a small @xmath17-norm ) , 3 ) hence define the space of negligible information by the kernel of this interpolation , i.e. @xmath18kern@xmath19 , and 4 ) find the orthogonal complement of @xmath20 with respect to a scalar product @xmath21 , where @xmath21 describes a discretization of the problem to solve . in many cases , it can be shown , that this ( low dimensional ) orthogonal complement space has very accurate approximation properties with respect to the exact solution . typically , the computation of the orthogonal decomposition is localized to small patches in order to reduce the computational complexity . so far , the concept of the lod has been successfully applied to nonlinear elliptic problems @xcite , eigenvalue problems @xcite and the nonlinear schrdinger equation @xcite . furthermore , it was combined with a discontinuous galerkin method @xcite and extended to the setting of partition of unity methods @xcite .    in this work , we are concerned with analyzing the lod framework in petrov - galerkin formulation , i.e. for the case that the discrete trial and test spaces are not identical . we show that an lod method in petrov - galerkin formulations still preserves the convergence rates of the original formulation of the method . at the same time , the new method can exhibit significant advantages , such as decreased computational complexity and mass conservation properties . in this paper , we discuss these advantages in detail ; we give examples for realizations and present numerical experiments . in particular , we apply the proposed framework to design a locally conservative multiscale solver for the simulation of two - phase flow models as governed by the buckley - leverett equation . we remark that employing petrov - galerkin variational frameworks in the construction and analysis of multiscale methods for solving elliptic problems in heterogeneous media has been investigated in the past , see for example @xcite and @xcite . the rest of the paper is organized as follows . section  [ sec : disc ] lays out the setting and notation for the formulation of the multiscale methods that includes the description of two - grid discretization and the localized orthogonal decomposition ( lod ) . in section  [ sec : methods ] , we present the multiscale methods based on the lod framework , starting from the usual galerkin variational equation and concentrating further on the petrov - galerkin variational equation that is the main contribution of the paper . we establish in this section that the petrov - galerkin lod ( pg - lod ) exhibits the same convergence behavior as the usual galerkin lod ( g - lod ) . furthermore , we draw a contrast in the aspect of practical implementation that makes up a strong advantage of pg - lod in relative comparison to g - lod . the other advantage of the pg - lod which can not be achieved with g - lod is the ability to produce a locally conservative flux field at the elemental level when discontinuous finite element is utilized . we also discuss in this section an application of the pg - lod for solving the pressure equation in the simulation of two - phase flow models to demonstrate this particular advantage . section  [ section : numerical : experiments ] gives two sets of numerical experiment : one that confirms the theoretical finding and the other demonstrating the application of pg - lod in the two - phase flow simulation . we present the proofs of the theoretical findings in section  [ section : proofs : pg : lod ] .","summary":"the multiscale space can then be used to obtain accurate galerkin approximations . as a model problem we consider the poisson equation . we also prove inf - sup stability of a pg continuous and a discontinuous galerkin finite element multiscale method . furthermore , we demonstrate that the petrov - galerkin method can decrease the computational complexity significantly , allowing for more efficient solution algorithms . as another application of the framework , we show how the petrov - galerkin framework can be used to construct a locally mass conservative solver for two - phase flow simulation that employs the buckley - leverett equation . to achieve this , we couple a pg discontinuous galerkin finite element method with an upwind scheme for a hyperbolic conservation law .    on multiscale methods in petrov - galerkin formulation +    daniel elfverson , victor ginting , patrick henning +    [ [ keywords ] ] keywords + + + + + + + +    finite element , multiscale method , numerical homogenization , petrov - galerkin method , conservation law , buckley - leverett equation","abstract":"in this work we investigate the advantages of multiscale methods in petrov - galerkin ( pg ) formulation in a general framework . the framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multiscale space with good approximation properties and a high dimensional remainder space , which only contains negligible fine scale information . the multiscale space can then be used to obtain accurate galerkin approximations . as a model problem we consider the poisson equation . we prove that a petrov - galerkin formulation does not suffer from a significant loss of accuracy , and still preserve the convergence order of the original multiscale method . we also prove inf - sup stability of a pg continuous and a discontinuous galerkin finite element multiscale method . furthermore , we demonstrate that the petrov - galerkin method can decrease the computational complexity significantly , allowing for more efficient solution algorithms . as another application of the framework , we show how the petrov - galerkin framework can be used to construct a locally mass conservative solver for two - phase flow simulation that employs the buckley - leverett equation . to achieve this , we couple a pg discontinuous galerkin finite element method with an upwind scheme for a hyperbolic conservation law .    on multiscale methods in petrov - galerkin formulation +    daniel elfverson , victor ginting , patrick henning +    [ [ keywords ] ] keywords + + + + + + + +    finite element , multiscale method , numerical homogenization , petrov - galerkin method , conservation law , buckley - leverett equation"}
{"article_id":"1405.5758","section_id":"m","document":"in this section , we state the lod in galerkin and in petrov - galerkin formulation along with their respective a priori error estimates and the inf - sup stability . in the last part of this section , we give two explicit examples and discuss the advantages of the petrov - galerkin formulation . subsequently we use the notation @xmath92 to abbreviate @xmath93 , where @xmath94 is a constant that is independent of the mesh sizes @xmath31 and @xmath25 ; and which is independent of the possibly rapid oscillations in @xmath0 .    in order to state proper a priori error estimates , we describe the notion of patch size and how the size of @xmath69 affects the final approximation . all the stated theorems on the error estimates of the lod methods are proved in section  [ section : proofs : pg : lod ] .    [ category - k]let @xmath95 be fixed . we define patches @xmath69 that consist of the element @xmath70 and @xmath96-layers of coarse element around it . for all @xmath97 , we define element patches in the coarse mesh @xmath22 by @xmath98    the above concept of patch sizes and patch shapes can be also generalized . see for instance @xcite for a lod that is purely based on partitions of unity . using definition [ category - k ] , we make an abstract assumption on the decay of the local correctors @xmath99 for @xmath100 :    * let @xmath101 be the _ optimal _ local corrector using @xmath88 that is defined according to ( [ local - corrector - problem ] ) and let @xmath102 . let @xmath95 and for all @xmath68 let @xmath103 as in definition [ category - k ] . then there exists @xmath104 and a generic constant @xmath105 that can depend on the contrast , but not on @xmath31 , @xmath25 or the variations of @xmath0 such that for all @xmath100 , @xmath106 where , @xmath107 denotes the global corrector given by ( [ global - corrector ] ) for @xmath103 . assumption ( a8 ) quantifies the decay of local correctors , by stating that the solutions of the local corrector problems decay exponentially to zero outside of @xmath70 . this is central for all a priori error estimates . for continuous galerkin methods , we can obtain the optimal order @xmath108 for the exponent in . this means , that the @xmath109-term fully vanishes . however , depending on the localization strategy ( i.e. how @xmath107 is computed ) it is also possible that @xmath110 takes the value @xmath111 and that hence a pollution term of order @xmath109 arises ( see ( * ? ? ? * remark 3.8 ) for a discussion ) . for discontinuous galerkin methods , the optimal known order is @xmath112 . however , even for this case it is known that the @xmath109-term is rapidly overtaken by the decay , leading purely to slightly larger patch sizes ( see e.g. @xcite ) . this method was originally proposed in @xcite : find @xmath113 that satisfies @xmath114    [ t : a - priori - local]@xmath115 assume ( a1)-(a8 ) . given a positive @xmath116 , let for all @xmath117 the patch @xmath103 be defined as in ( [ def - patch - u - k ] ) and let @xmath118 be as governed by . let @xmath38 be the fine scale reference solution governed by ( [ fine - grid ] ) . then , the following a priori error estimate holds true @xmath119 where @xmath105 and @xmath120 are the generic constants in ( a8 ) . the term @xmath121 describes the coarse part ( resulting from @xmath14 ) of @xmath122 and thus is numerically homogenized ( the oscillations are averaged out ) . in this sense , we can say that @xmath122 is an @xmath123-approximation of @xmath33 and @xmath121 an @xmath17-approximation of @xmath33 , respectively . furthermore , because @xmath124 converges with exponential order to zero , the error @xmath125 is typically dominated by the first term of order o@xmath126 . this was observed in various numerical experiments in different works , c.f . @xcite . in particular , a specific choice @xmath127 leads to a o@xmath126 convergence for the total @xmath123-error , see also @xcite .      in a straightforward manner , we can now state the lod in petrov - galerkin formulation : find @xmath128 that satisfies @xmath129    a unique solution of ( [ lod - problem - eq - pg ] ) is guaranteed by the inf - sup stability . in practice , inf - sup stability is clearly observable in numerical experiments ( see section [ section : numerical : experiments ] ) . analytically we can make the following observations . [ quasi - orth ] the inf - sup stability of the lod in petrov - galerkin formulation is a natural property to expect , since we have quasi - orthogonality in @xmath21 of the spaces @xmath86 and @xmath60 . this can be verified by a simple computation . let @xmath130 , let @xmath131 and let @xmath132 the optimal corrector as in assumption ( a8 ) , then @xmath133 with generic constants @xmath105 and @xmath134 as in ( a8 ) . this means that @xmath135 converges exponentially in @xmath96 to zero , and it is identical to zero for all sufficiently large @xmath96 ( because then @xmath136 ) . writing the pg - lod bilinear form as @xmath137 we see that it is only a small perturbation of the symmetric ( coercive ) g - lod version , where the difference can be bounded by the quasi - orthogonality . even though the quasi - orthogonality _ suggests _ inf - sup stability , the given assumptions ( a1)-(a8 ) do not seem to be sufficient for rigorously proving it . here , it seems necessary to leave the abstract setting and to prove the inf - sup stability result for the various lod realizations separately . for simplification , we therefore make the inf - sup stability to be an additional assumption ( see ( a9 ) below ) . later we give an example how to prove this assumption for a certain realization of the method . we also note that the inf - sup stability can be always verified numerically ( for a given @xmath96 ) by investigating the system matrix @xmath138 given by the entries @xmath139 for @xmath140 where @xmath141 denotes the dimension of @xmath14 and where @xmath142 denotes a basis of @xmath14 . to check the inf - sup stability we must compute the eigenvalues of @xmath138 . if their real parts are all strictly positive , we have inf - sup stability and the inf - sup constant is identical to the smallest real part of an eigenvalue . standard approaches for computing the eigenvalues of a non - symmetric matrix are the arnoldi method , the jacobi - davidson method and the non - symmetric lanczos algorithm ( cf . @xcite for a comprehensive overview ) . since @xmath141 is moderately small , the cost for applying one of the methods are still feasible . * we assume that the lod in petrov - galerkin formulation is inf - sup stable in the following sense : there exists a sequence of constants @xmath143 and a generic limit @xmath144 ( independent of @xmath31 , @xmath25 , @xmath96 or the oscillations of @xmath0 ) such that @xmath143 converges with _ exponential speed _ to @xmath145 , i.e. there exist constants @xmath146 ( possibly depending on @xmath31 , but not on @xmath25 , @xmath96 or the oscillations of @xmath0 ) and a generic @xmath147 such that @xmath148 . furthermore it holds @xmath149 for all sufficiently large @xmath150 and @xmath151 for all @xmath152 and @xmath153 . the following result states that the approximation quality of the lod in petrov - galerkin formulation is of the same order as for the galerkin lod , up to a possible pollution term depending on @xmath45 , but which still converges exponentially to zero . [ t : a - priori - local - pg]@xmath115 assume ( a1)-(a9 ) . given a positive @xmath116 , let for all @xmath117 the patch @xmath103 be defined as in ( [ def - patch - u - k ] ) and large enough so that the inf - sup constant in ( a9 ) fulfills @xmath154 for some @xmath155 and let @xmath156 be the unique solution of ( [ lod - problem - eq - pg ] ) . let @xmath38 be the fine scale reference solution governed by ( [ fine - grid ] ) . then , the following a priori error estimate holds true @xmath157 where @xmath105 and @xmath158 are the generic constants from assumption ( a8 ) and @xmath45 as in ( a5 ) . the previous subsection showed that the petrov - galerkin formulation of the lod does not suffer from a loss in accuracy with respect to the symmetric formulation . in this subsection , we give the specific example of the lod for the continuous galerkin finite element method . in particular , we discuss the advantage of the pg formulation over the symmetric formulation . let us first introduce the specific setting and the corresponding argument about the validity of ( a4)-(a9 ) on this setting . in addition to the assumptions that we made on the shape regular partitions @xmath22 and @xmath24 in section [ subsection : two - grid : disc ] , we assume that @xmath22 and @xmath24 are either triangular or quadrilateral meshes . accordingly , for @xmath159 we denote @xmath160 and define @xmath161 if @xmath24 is a triangulation and @xmath162 if it is a quadrilation . the coarse space @xmath49 is defined in the same fashion and since @xmath24 is a refinement of @xmath22 , assumption ( a6 ) is obviously fulfilled . for simplicity , we also assume that the coarse mesh @xmath22 is quasi - uniform ( which is the typical choice in applications ) . the bilinear form @xmath21 is defined by the standard energy scalar product on @xmath16 that belongs to the elliptic problem to solve , i.e. @xmath163 accordingly , we set @xmath164 for @xmath165 . hence , assumptions ( a5 ) and ( a6 ) are fulfilled and the solution @xmath38 of ( [ fine - grid ] ) is nothing but the standard continuous galerkin finite element solution on the fine grid @xmath24 . next , we specify @xmath166 in ( a7 ) . for this purpose , let @xmath167 be the nodal basis function associated with the coarse grid node @xmath168 , i.e. , @xmath169 . let @xmath15 be the weighted clment - type quasi - interpolation operator as defined in @xcite : @xmath170 first we note that it was shown in @xcite that @xmath58 is an isomorphism ( but not a projection , i.e. @xmath171 ) . hence , @xmath172 exists . this is one of the properties in ( a7 ) . the @xmath17- and @xmath123-stability of @xmath15 , as well as corresponding approximation properties , were proved in @xcite . it only remains to check the @xmath123-stability of @xmath172 . unfortunately , this property is not trivial to fulfill . first , we note that it was shown in @xcite that the mapping @xmath173 is nothing but the @xmath17-projection @xmath174 ( see also remark [ remark - on - l2-projection ] below ) . consequently , the question of @xmath123-stability of @xmath172 is equivalent to the question of @xmath123-stability of the @xmath17-projection . this result is well - established for quasi uniform grids ( cf . @xcite ) as assumed at the beginning of this section . however it is still open for arbitrary refinements . the most recent results on this issue can be found in @xcite , where the desired @xmath123-stability was shown for certain types of adaptively refined meshes . to avoid complicated mesh assumptions in this paper , we simply assume @xmath22 to be quasi - uniform . this is not very restrictive since adaptive refinements should typically take place on the fine mesh @xmath24 . alternatively , in light of @xcite , we could also directly assume that the @xmath17-projection on @xmath14 is @xmath123-stable to allow more general coarse meshes . it remains to specify @xmath77 , which we define by @xmath175 let us for simplicity denote @xmath176 . the decay assumption ( a8 ) was essentially proved in ( * ? ? ? * lemma 3.6 ) , which established the existence of a generic constant @xmath105 with the properties as in ( a8 ) such that @xmath177 for all @xmath100 . on the other hand we have by @xmath178 and equation ( [ local - corrector - problem ] ) that @xmath179 hence , by plugging this result into : @xmath180 which proves that assumption ( a8 ) holds even with @xmath108 . the remaining assumption ( a9 ) is less obvious and requires a proof . we give this proof for the continuous galerkin pg - lod in section [ section : proofs : pg : lod ] . we summarize the result in the following lemma . [ inf - sup - stability - pg - lod ] for all @xmath68 let @xmath181 for @xmath182 . then there exist generic constants @xmath183 ( independent of @xmath31 , @xmath25 , @xmath96 or the oscillations of @xmath0 ) and @xmath184 as in assumption ( a8 ) , so that it holds @xmath185 for @xmath186 and @xmath187 where @xmath188 , i.e. the space of all functions from @xmath60 that are zero on the boundary of the coarse grid elements . observe that @xmath143 converges with exponential speed to @xmath189 . furthermore we have @xmath190 ( because @xmath191 ) and also @xmath192 for all sufficiently large @xmath193 . let @xmath181 for @xmath182 with @xmath194 , then the cg - lod in petrov - galerkin formulation is inf - sup stable for sufficiently small @xmath31 . in particular , there exists a unique solution of problem ( [ lod - problem - eq - pg ] ) . lemma [ inf - sup - stability - pg - lod ] does not allow to conclude to inf - sup stability for the regime @xmath195 . however , even though this regime is not of practical relevance , it is interesting to note that we could not observe a violation of the inf - sup stability for any value of @xmath96 and in any numerical experiment that we set up so far .    since assumptions ( a1)-(a9 ) are fulfilled for this setting , theorems [ t : a - priori - local ] and [ t : a - priori - local - pg ] hold true for the arising method . furthermore , we have @xmath108 and @xmath196 in the estimates , meaning that the @xmath109-pollution in front of the decay term vanishes . we can summarize the result in the following conclusion .    assume the ( continuous galerkin ) setting of this subsection and let @xmath156 denote a petrov - galerkin solution of ( [ lod - problem - eq - pg ] ) . if @xmath197 for @xmath198 , then it holds @xmath199 in particular , the bound is independent of @xmath45 . the central disadvantage of the galerkin lod is that it requires a communication between solutions of different patches . consider for instance the assembly of the system matrix that belongs to problem ( [ lod - problem - eq ] ) . here it is necessary to compute entries of the type @xmath200 which particularly involves the computation of the term @xmath201 where @xmath202 denote two coarse nodal basis functions and @xmath203 and @xmath204 its corresponding supports . the efficient computation of ( [ problematic - term ] ) requires information about the intersection area of any two patches @xmath69 and @xmath205 . even if @xmath70 and @xmath206 are not adjacent or close to each other , the intersection of the corresponding patches can be complicated and non - empty . the drawback becomes obvious : first , these intersection areas must be determined , stored and handled in an efficient way and second , the number of relevant entries of the stiffness matrix ( i.e. the non - zeros ) increases considerably . note that this also leads to a restriction in the parallelization capabilities , in the sense that the assembly of the stiffness matrix can only be started if the correctors @xmath207 are already computed . another disadvantage is that the assembly of the right hand side vector associated with @xmath208 in ( [ lod - problem - eq ] ) is much more expensive since it involves the computation of entries @xmath209 . first , the integration area is @xmath210 instead of typically @xmath203 . this increases the computational costs . at the same time , it is also hard to assemble these entries by performing ( typically more efficient ) element - wise computations ( for which each coarse element has to be visited only once ) . second , @xmath209 involves a quadrature rule of high order , since @xmath207 is rapidly oscillating . these oscillations must be resolved by the quadrature rule , even if @xmath211 is a purely macroscopic function that can be handled exactly by a low order quadrature . hence , the costs for computing @xmath209 depend indirectly on the oscillations of @xmath0 . finally , if the lod shall be applied to a sequence of problems of type ( [ exact - solution ] ) , which only differ in the source term @xmath211 ( or a boundary condition ) , the system matrix can be fully reused , but the complications that come with the right hand side have to be addressed each time again . the petrov - galerkin formulation of the lod clearly solves these problems without suffering from a loss in accuracy . in particular :    * the pg - lod does not require any communication between two different patches and the resulting stiffness matrix is sparser than the one for the symmetric lod . in particular , the entries of the system matrix @xmath212 can be computed with the following algorithm : + + [ algorithm - computing - stiffness - pg - lod ] +    ' '' '' +   + let @xmath212 denote the empty system matrix with entries @xmath213 . +    ' '' '' +   + algorithm : assemblesystemmatrix ( @xmath22 , @xmath24 , @xmath96 ) +    ' '' '' +   + in parallel +    ' '' '' +   + observe that it is possible to directly add the local terms @xmath214 to the system matrix @xmath212 , i.e. the assembling of the matrix is parallelized in a straightforward way and does not rely on the availability of other results . * replacing the source term @xmath211 in ( [ exact - solution ] ) , only involves the re - computation of the terms @xmath215 for coarse nodal basis functions @xmath216 , i.e. the same costs as for the standard fe method on the coarse scale . furthermore , the choice of the quadrature rule relies purely on @xmath211 , but not on the oscillations of @xmath0 .    besides the previously mentioned advantages , there is still a memory consuming issue left : the storage of the local correctors @xmath217 . these local correctors need to be saved in order to express the final approximation @xmath218 which is spanned by the multiscale basis functions @xmath219 . as long as we are interested in a good @xmath123-approximation of the solution , this problem seems to be unavoidable . however , in many applications we can even overcome this difficulty by exploiting another very big advantage of the pg - lod : theorem [ t : a - priori - local - pg ] predicts that alone the coarse part of @xmath218 , denoted by @xmath220 , already exhibits very good @xmath17-approximation properties , i.e. if @xmath194 we have essentially @xmath221 in contrast to @xmath218 , the representation of @xmath222 does only require the classical coarse finite element basis functions . hence , we can use the algorithm presented earlier , with the difference that we can immediately delete @xmath223 after updating the stiffness matrix . observe that even if computations have to be repeated for different source terms @xmath211 , this stiffness matrix can be reused again and again . also , if a user is interested in the fine scale behavior in a local region ( but the @xmath223 were already dropped ) , it is still possible to quickly re - compute the desired local corrector for the region .    as an application , consider for instance the case that the problem @xmath224 describes the diffusion of a pollutant in groundwater . here , @xmath1 describes the concentration of the pollutant , @xmath0 the ( rapidly varying ) hydraulic conductivity and @xmath211 a source term describing the injection of the pollutant . in such a scenario , there is typically not much interest in finding a good approximation of the ( locally fluctuating ) gradient @xmath225 , but rather in the macroscopic behavior of pollutant @xmath1 , i.e. in purely finding a good @xmath17-approximation that allows to conclude where the pollutant spreads . a similar scenario is the investigation of the properties of a composite material , where @xmath0 describes the heterogenous material and @xmath211 some external force . again , the interest is in finding an accurate @xmath17-approximation . besides , the corresponding simulations are typically performed for a variety of different source terms @xmath211 , investigating different scenarios . in this case , the pg - lod yields reliable approximations with very low costs , independent of the structure of @xmath0 . [ remark - on - l2-projection]assume the setting of this subsection . in @xcite it was shown that @xmath226 for all @xmath227 and @xmath228 , i.e. @xmath14 and @xmath60 are @xmath17-orthogonal . this implies that @xmath229 with @xmath230 denoting the @xmath17-projection on @xmath14 . to verify this , let @xmath52 be arbitrary . then due to @xmath231 we can write @xmath232 ( with @xmath53 and @xmath131 ) and observe for all @xmath100 @xmath233 hence , @xmath234 with @xmath235 .    [ homogenization - setting]assume the setting of this subsection and let @xmath230 denote the @xmath17-projection on @xmath14 as in remark [ remark - on - l2-projection ] . we consider now a typical homogenization setting with @xmath236 being a sequence of positive parameters that converges to zero . let @xmath237^d$ ] denote the unique cube in @xmath238 and let @xmath239 for a function @xmath240 that is @xmath241-periodic in the second argument ( hence @xmath242 is rapidly oscillating with frequency @xmath243 ) . the corresponding exact solution of problem ( [ exact - solution ] ) shall be denoted by @xmath244 . it is well known ( c.f . @xcite ) that @xmath245 converges weakly in @xmath123 ( but not strongly ) to some unique function @xmath246 . furthermore , if @xmath247 it holds @xmath248 . with theorem [ t : a - priori - local - pg ] together with remark [ remark - on - l2-projection ] and standard error estimates for fe problems , we hence obtain : @xmath249 for @xmath235 . homogenization problems are typical problems , where one is often purely interested in the @xmath17-approximation of the exact solution @xmath245 , meaning one is interested in the homogenized solution @xmath250 . as discussed in this section , the pg - lod can have significant advantages over the ( symmetric ) g - lod with respect to computational costs , efficiency and memory demand . in subsection [ num - experiment - cg - pg - lod ] we additionally present a numerical experiment to demonstrate that the approximations produced by the pg - lod are in fact very close to the ones produced by ( symmetric ) g - lod , i.e. not only of the same order as predicted by the theorems , but also of the same quality . the above results suggest that the advantages can become even more pronounced for certain types of nonlinear problems . for instance , consider a well - posed problem of the type @xmath251 for a nonlinear function @xmath252 . here , it is intuitively reasonable to construct @xmath107 as before using only the linear elliptic part of the problem . this is a preprocessing step that is done once and can be immediately deleted stiffness matrix is calculated and saved . then we solve for @xmath253 that satisfies @xmath254 clearly , typical iterative solvers can be utilized to solve this variational problem . this iteration is inexpensive because it is done in @xmath14 and the preconstructed stiffness matrix can be fully reused within every iteration and since the other contributions are independent of @xmath255 . performing iterations on the coarse space for solving nonlinear problems within the framework of multiscale finite element ( msfems ) has been investigated ( see for example @xcite and @xcite ) .      in this subsection , we apply the results of section [ subsection - pg - lod ] to a lod method that is based on a discontinuous galerkin approach . the dg - lod was originally proposed in @xcite and fits into the framework proposed in section [ subsection : lod - framework ] . first , we show that the setting fulfills assumptions ( a4)-(a8 ) and after we discuss the advantage of the pg dg - lod over the symmetric dg - lod . for simplification , we assume that @xmath0 is piecewise constant with respect to the fine mesh @xmath24 so that all of the subsequent traces are well - defined .    again , we make the same assumptions on the partitions @xmath22 and @xmath24 as in section [ subsection : two - grid : disc ] and additionally assume that @xmath22 and @xmath24 are either triangular or quadrilateral meshes . the corresponding total sets of edges ( or faces for @xmath256 ) are denoted by @xmath257 ( for @xmath24 ) , where @xmath258 and @xmath259 denotes the set of interior and boundary edges , respectively . furthermore , for @xmath159 we denote the spaces of discontinuous functions with total , respectively partial , polynomial degree equal to or less than @xmath111 by @xmath260 and define @xmath261 if @xmath24 is a triangulation and @xmath262 if it is a quadrilation . the coarse space @xmath49 is defined in the same fashion with @xmath22 instead of @xmath24 . note that these spaces are no subspaces of @xmath263 as in the previous example . for this purpose , we define @xmath264 to be the @xmath24-piecewise gradient ( i.e. @xmath265 for @xmath52 and @xmath266 ) . for every edge / face @xmath267 there are two adjacent elements @xmath268 with @xmath269 . we define the jump and average operators across @xmath270 by @xmath271 & : = ( v\\vert t^-   - v\\vert t^+)\\quad\\text{and}\\quad\\ { a \\nabla v \\cdot n \\ } : = \\frac{1}{2 } ( ( a \\nabla v)\\vert t^- + ( a \\nabla v)\\vert t^+ ) \\cdot n,\\end{aligned}\\ ] ] where @xmath272 be the unit normal on @xmath273 that points from @xmath274 to @xmath275 , and on @xmath276 by @xmath271 & : = w\\vert t\\quad\\text{and}\\quad \\ { a \\nabla v \\cdot n \\ } : =   ( a \\nabla v)\\vert t   \\cdot n\\end{aligned}\\ ] ] where @xmath272 is the outwards unit normal of @xmath277 ( and @xmath13 ) . observe that flipping the roles of @xmath274 and @xmath275 leads to the same terms in the bilinear form defined below .    with that , we can define the typical bilinear form that characterizes the discontinuous galerkin method : @xmath278 ) _ { l^2(e ) } + ( \\ { a \\nabla w_h \\cdot n \\ } ,   [ v_h ] ) _ { l^2(e ) } \\right ) + \\sum_{e \\in { \\mathcal{e}}_h } \\frac{\\sigma}{h_e } ( [ v_h ] ,   [ w_h ] ) _ { l^2(e)}.\\end{aligned}\\ ] ] here , @xmath279 is a penalty parameter that is chosen sufficiently large and @xmath280 . the coarse bilinear form @xmath35 is defined analogously with coarse scale quantities . it is well known , that @xmath21 ( respectively @xmath35 ) is a scalar product on @xmath32 ( respectively @xmath14 ) . consequently ( a4 ) is fulfilled . as a norm on @xmath32 that fulfills assumption ( a5 ) , we can pick @xmath281 to be a norm on @xmath14 . in this case we obtain the constant @xmath282 . assumption ( a6 ) is obviously fulfilled .    as the operator in assumption ( a7 ) we pick the @xmath17-projection on @xmath14 , i.e. for @xmath52 we have @xmath283 in ( * ? ? ? * lemma 5 ) it was proved that the operator fulfills the desired approximation and stability properties . since @xmath15 is a projection , we have @xmath284 and hence obviously also @xmath285-stability of the inverse on @xmath14 . the localized bilinear form @xmath75 in ( [ localization - of - a_h - to - a_h - t ] ) is defined by @xmath286 where @xmath287 in @xmath70 and @xmath288 otherwise , is the element indicator function . obviously we have for all @xmath289 that @xmath290    in @xcite the dg - lod is presented in a slightly different way , in the sense that there exists no general corrector operator @xmath255 . instead , basis function correctors are introduced . however , it is easily checkable that each of these basis function correctors is nothing but the corrector operator , defined via ( [ local - corrector - problem ] ) , applied to an original coarse basis function . therefore , the correctors given by ( [ local - corrector - problem ] ) are just an extension of the definition to arbitrary coarse functions . hence , both methods coincide and are just presented in a different way . next , we discuss ( a8 ) . this property was shown in ( * ? ? ? * lemma 11 and 12 ) , however not explicitly for the setting that we established in definition [ localization - of - solution - space ] . it was only shown for @xmath291 , where @xmath292 denotes a basis function on @xmath70 associated with the @xmath293th node . however , the proofs in @xcite directly generalize to the local correctors @xmath99 given by equation . more precisely , following the proofs in @xcite it becomes evident that the availability of the required decay property ( a8 ) purely relies on the fact , that the right hand side in the local problems is only locally supported ( with a support that remains fixed , even if the patch size decreases ) . therefore ( a8 ) can be proved analogously . finally , assumption ( a9 ) is not easy to verify . it is obviously fulfilled for the case @xmath88 , but the generalized result is harder to verify . the following result holds under some restrictions on the meshes @xmath22 and @xmath24 . [ inf - sup - stability - dg - pg - lod ] assume that @xmath22 is quasi - uniform and that there exists an exponent @xmath294 with @xmath295 such that for all @xmath78 @xmath296 ( i.e. if @xmath24 is also quasi - uniform we assume @xmath297 ) . if @xmath182 is such that @xmath298 then , for sufficiently small @xmath31 , there exist generic positive constants @xmath183 such that @xmath299 hence , we have inf - sup stability for sufficiently small @xmath31 .    the proof is given in section [ section : proofs : pg : lod ] . we note that the inf - sup stability can be observed numerically already under weaker assumptions ( see section [ section : numerical : experiments ] ) and that it is in general a reasonable thing to expect as discussed in remark [ quasi - orth ] .    in conclusion , the discontinuous galerkin lod in petrov - galerkin formulation fulfills the assumptions of our framework ( up to a discussion on ( a9 ) ) . the advantages that we discussed in the previous subsection for the petrov - galerkin continuous finite element method in terms of memory and efficiency remains true . however , for the pg dg - lod there is a very important additional advantage . it is known that the classical dg method has the feature of local mass conservation with respect to the elements of the underlying mesh . this can be easily checked by testing with the indicator function of an element @xmath70 in the variational formulation of the method . the local mass conservation is a highly desired property for various flow and transport problems . however , the dg - lod does not preserve this property , since the indicator function of an element ( whether coarse or fine ) is not in the space @xmath86 . this problem is solved in the pg dg - lod , where we can test with any element from @xmath14 and in particular with the indicator function of a coarse element . hence , in contrast to the symmetric dg - lod , the pg dg - lod is locally mass conservative with respect to coarse elements @xmath68 . this allows for example the coupling of the pg dg - lod for an elliptic problem with the solver for a hyperbolic conservation law , which was not possible before without relinquishing the mass conservation . we discuss this further in the next subsection .      in this subsection , we investigate an application of the petrov - galerkin dg - lod in the simulation of two - phase flow as governed by the buckley - leverett equation . specifically , the lod framework is utilized to solve the pressure equation , which is an elliptic boundary value problem , and is coupled with a solver for a hyperbolic conservation law . the buckley - leverett equation can be used to model two - phase flow in a porous medium . generally , the flow of two immiscible and incompressible fluids is driven by the law of mass balance for the two fluids : @xmath300 \\quad \\mbox{for } \\alpha = w , n.\\end{aligned}\\ ] ] here , @xmath13 is a computational domain , @xmath301 $ ] a time interval , the unknowns @xmath302 $ ] describe the saturations of a wetting and a non - wetting fluid and @xmath303 and @xmath304 are the corresponding fluxes . furthermore , @xmath305 describes the porosity and @xmath306 and @xmath307 are two source terms . darcy s law relates the fluxes with the two unknown pressures @xmath308 and @xmath309 by @xmath310 here , @xmath206 denotes the hydraulic conductivity , @xmath311 and @xmath312 the relative permeabilities depending on the saturations , @xmath313 and @xmath314 the viscosities , @xmath315 and @xmath316 the densities and @xmath317 the gravity vector . the saturations are coupled via @xmath318 and a relation between the two pressures is typically given by the capillary pressure relation @xmath319 for a monotonically decreasing capillary pressure curve @xmath320 . in this case , we obtain the full two - phase flow system , which consists of two strongly coupled , possibly degenerate parabolic equations . however , if we neglect the gravity and the capillary pressure ( i.e. assume that @xmath321 ) , the system reduces to the so called buckley - leverett system with an elliptic pressure equation and an hyperbolic equation for the saturation : @xmath322 where we have @xmath323 , @xmath324 , the total mobility @xmath325 , the flux @xmath326 and the flux function @xmath327 . the total source is given by @xmath328 . observe that ( [ bl - system ] ) is obtained from ( [ tpf - system ] ) by summing up the equations for the saturations , using @xmath329 . an application for which neglecting the capillary pressure is typically justified are oil recovery processes . here , a replacement fluid , such as water or liquid carbon dioxide , is injected with very high rates into a reservoir to move oil towards a production well . however , often oil is trapped at interfaces of a low and a high conductivity region . this oil would become inaccessible which is why detailed simulations are required before the replacement fluid can be actually injected . depending on how the mobilities are chosen , the hyperbolic buckley - leverett problem can have one or more weak solutions ( c.f . one approach for solving the problem numerically is to use an operator splitting technique as proposed in @xcite , which is more well - known as the _ ( im)plicit ( p)ressure ( e)xplicit ( s)aturation _ , i.e. , impes . here , the hyperbolic buckley - leverett problem is treated with an explicit time stepping method where the flux velocity @xmath330 is kept constant for a certain time interval and then updated by solving the elliptic problem with the saturation from the previous time step ( see figure  [ fig : os - impes ] for an illustration ) . alternatively , depending on the type of the flux function @xmath211 , the hyperbolic problem can be also solved implicitly with a suitable numerical scheme for conservation laws ( c.f . @xcite ) where the flux @xmath330 arising from the darcy equation is , as in the previous case , only updated every fixed number of time steps . observe that the difficulties produced by the multiscale character of the problem are primarily related to the elliptic part of the problem . once the darcy problem is solved to update the flux velocity , the grid for solving the hyperbolic problem can be significantly coarsened . the reason is that @xmath331 is possibly still rapidly oscillating , but the relative amplitude of the oscillations is expected to remain small . in other words , just like for standard elliptic homogenization problems , @xmath330 behaves like an upscaled quantity @xmath332 with effective / homogenized functions @xmath333 , @xmath334 and @xmath335 . any realization of the lod involves to solve a number of local problems that help us to construct the low dimensional space @xmath86 . one might consider to update this space every time that the darcy problem has to be solved with a new saturation . however , since @xmath336 is essentially macroscopic , it is generally sufficient to construct the space only once for @xmath337 and reuse the result for every time step . this makes solving the elliptic multiscale problem much cheaper after the multiscale space is assembled . a justification for this reusing of the basis can be e.g. found in @xcite where it was shown that oscillations coming from advective terms can be often neglected in the construction of a multiscale basis . under certain assumptions , the relative permeability @xmath336 can in fact be interpreted as a pure enforcement by an additional advection term .","summary":"we prove that a petrov - galerkin formulation does not suffer from a significant loss of accuracy , and still preserve the convergence order of the original multiscale method .","abstract":"in this work we investigate the advantages of multiscale methods in petrov - galerkin ( pg ) formulation in a general framework . the framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multiscale space with good approximation properties and a high dimensional remainder space , which only contains negligible fine scale information . the multiscale space can then be used to obtain accurate galerkin approximations . as a model problem we consider the poisson equation . we prove that a petrov - galerkin formulation does not suffer from a significant loss of accuracy , and still preserve the convergence order of the original multiscale method . we also prove inf - sup stability of a pg continuous and a discontinuous galerkin finite element multiscale method . furthermore , we demonstrate that the petrov - galerkin method can decrease the computational complexity significantly , allowing for more efficient solution algorithms . as another application of the framework , we show how the petrov - galerkin framework can be used to construct a locally mass conservative solver for two - phase flow simulation that employs the buckley - leverett equation . to achieve this , we couple a pg discontinuous galerkin finite element method with an upwind scheme for a hyperbolic conservation law .    on multiscale methods in petrov - galerkin formulation +    daniel elfverson , victor ginting , patrick henning +    [ [ keywords ] ] keywords + + + + + + + +    finite element , multiscale method , numerical homogenization , petrov - galerkin method , conservation law , buckley - leverett equation"}
{"article_id":"hep-ph0009318","section_id":"c","document":"extraction of parton densities is one of the main goals of high - energy physics . it was proposed some time ago how to use semi - inclusive production of charged pions to determine both unpolarized and polarized parton densities in the nucleons . recently this idea was put into practice in both cases . such analyses assume implicitly the validity of the quark - parton model . in a recent work of two of us @xcite we have shown a breaking of the parton model in inclusive dis at photon virtuality @xmath14 as large as 5 - 7 gev@xmath10 which is bigger than commonly perceived . the modern experiments analyzing semi - inclusive production of pions are performed in a similar range of @xmath14 . in general the situation in semi - inclusive reactions can be even more complex and subtle . in the present analysis we have made a first attempt to determine the nonleading mechanisms . we have estimated a few effects beyond the quark - parton model which may influence the extraction of the @xmath0 asymmetry from semi - inclusive production of pions in dis .    based on the analysis of hadronic data we have found that the interaction of the resolved hadron - like photon with the nucleon may lead to an artificial enhancement of the measured @xmath0 asymmetry in the region of small @xmath12 . next , we have investigated the elastic production of @xmath79 mesons by a virtual photon on the proton and neutron targets based on two different models . unequal cross sections for proton and neutron targets also lead to an artificial modification of the @xmath0 asymmetry extracted based on qpm formulae . the effect found is opposite to the effect due to the resolved photon component . these two effects cancel only in a narrow range of @xmath4 . the net effect turned out to be @xmath4-dependent invalidating somewhat averaging in @xmath4 as done recently in @xcite . we suggest that instead of averaging over a broad range of @xmath4 one could try to select the region of @xmath4 ( @xmath12- and @xmath14-dependent ) where the influence of nonpartonic effects is small . unfortunately this can only be done at the expense of lowering the statistics considerably . an optimal choice of kinematical cuts in @xmath12 , @xmath14 and @xmath4 requires a more detailed study . clearly , increasing of @xmath14 looks helpful . this could be realized by hermes or by an as yet unproposed experiment for compass at cern . nuclear effects , even small ones , may also cloud the extraction of the true @xmath0 asymmetry . to our knowledge there is no reliable estimate of such effects for semi - inclusive production of pions . although in the light of the present analysis the precise direct extraction of @xmath0 is rather difficult , the semi - inclusive data can be used for tests of parton distributions , in particular the difference between @xmath216 and @xmath217 , provided nonpartonic and nuclear effects are understood and included in the analysis . finally we would like to point out that some of the effects discussed in the present paper may also influence the extraction of the polarized quark distributions from semi - inclusive production of pions in dis . this will be a subject of a separate analysis .","summary":"we investigate unambiguities in the extraction of the asymmetry from semi - inclusive production of pions in dis . the role of several effects beyond the quark - parton model ( qpm ) which lead to and and may therefore cloud such an extraction is studied .","abstract":"we investigate unambiguities in the extraction of the asymmetry from semi - inclusive production of pions in dis . the role of several effects beyond the quark - parton model ( qpm ) which lead to and and may therefore cloud such an extraction is studied . the results are discussed in the context of the recent hermes data . we find that the interaction of the resolved photon with the nucleon significantly modifies the observed asymmetry . the exclusive elastic production of mesons plays a similar role for the large- data sample . our estimate shows a rather small effect of the spectator mechanism . nuclear effects in the deuteron also look potentially important but are difficult to estimate quantitatively .    throughout the paper we make in addition several general remarks concerning semi - inclusive and exclusive production of mesons ."}
{"article_id":"0911.2287","section_id":"i","document":"in his work on log - concavity of multiplicities , e.g. @xcite , @xcite , a. okounkov introduced a procedure to associate convex bodies to linear systems on projective varieties . this construction was systematically studied by r. lazarsfeld and m. musta in the case of big line bundles in @xcite . the construction of these _ okounkov bodies _ depends on a fixed flag of subvarieties and produces a convex compact set for each cartier divisor on a projective variety . the okounkov body of a divisor encodes asymptotic invariants of the divisor s linear system , and it is determined solely by the divisor s numerical equivalence class . moreover , these bodies vary as fibers of a linear map defined on a closed convex cone as one moves in the space of numerical equivalence classes of divisors on the variety . as a consequence , one can expect to obtain results about line bundles by applying methods from convex geometry to the study of these okounkov bodies . let us consider an @xmath2-dimensional projective variety @xmath3 over an algebraically closed field , endowed with a flag @xmath4 , where @xmath5 is an @xmath6-dimensional subvariety that is nonsingular at the point @xmath7 . in @xcite , lazarsfeld and musta established the following : + * ( a ) * for each big rational numerical divisor class @xmath8 on x , okounkov s construction yields a convex compact set @xmath9 in @xmath10 , now called the _ okounkov body _ of @xmath8 , whose euclidean volume satisfies @xmath11 the quantity @xmath12 on the right is the _ volume _ of the rational class @xmath8 , which is defined by extending the definition of the volume of an integral cartier divisor @xmath13 on @xmath3 , namely , @xmath14 we recall that the volume is an interesting invariant of big divisors which plays an important role in several recent developments in higher dimensional geometry . for basic properties of volumes we refer to @xcite . + * ( b ) * moreover , there exists a closed convex cone @xmath15 characterized by the property that in the diagram @xmath16 \\ar@{^{(}->}[rr ] & & \\ { \\bf{r}}^{n } \\times n^{1 } ( x)_{{\\bf{r } } } \\ar@/^/[ld ] \\ \\\\ & n^1(x)_{{\\bf{r } } } ,   } \\ ] ] the fiber @xmath17 of @xmath18 over any big class @xmath19 is @xmath9 . this is illustrated schematically in figure 1 . @xmath18 is called the _ global okounkov body _ of @xmath3 . lazarsfeld and musta have used this theory to reprove and generalize results about volumes of divisors , including fujita s approximation theorem . using @xmath20 , they can additionally give alternative proofs of properties of the volume function @xmath21 , defined in the set of big classes of @xmath22-divisors . for example , it follows that @xmath23 is of class @xmath24 and satisfies the log - concavity relation @xmath25 for any two big classes @xmath26 . it is worth mentioning that in @xcite , k. kaveh and a. khovanskii use a similar procedure to associate convex bodies to finite dimensional subspaces of the function field @xmath27 of a variety @xmath3 . in their work , they use the bridge between convex and algebraic geometry provided by their construction to obtain results in both areas . the explicit description of okounkov bodies in concrete examples can be rather difficult . one easy case is that of smooth projective toric varieties . if @xmath13 is an invariant divisor on such a variety , and if the flag consists of invariant subvarieties , then it is shown in @xcite that the okounkov body of @xmath13 is the polytope @xmath28 that one usually associates to @xmath13 in toric geometry , up to a suitable translation .    in this paper , we are interested in describing the okounkov bodies of the divisors on the projectivization @xmath1 of a toric vector bundle @xmath0 on the smooth projective toric variety @xmath3 . such vector bundles were described by a. klyachko in @xcite in terms of certain filtrations of a suitable vector space , and they have been the focus of some recent activity , e.g. @xcite , @xcite , @xcite . as we will see , these filtrations can be used to compute the sections of all line bundles on @xmath1 . for our main result , we restrict to the case of rank two toric vector bundles , where the klyachko filtrations are considerably simpler . using the data from the filtrations , we construct a flag of torus invariant subvarieties on @xmath1 and produce finitely many linear inequalities defining the global okounkov body of @xmath1 with respect to this flag . in particular , we see that this is a rational polyhedral cone . as an application we show that the cox ring of @xmath1 is finitely generated , giving an alternative proof in a special case of a result of knop ( see @xcite and @xcite ) . this article is organized as follows . in  [ section.notation ] we review okounkov s construction and klyachko s description of toric vector bundles . next , in  [ section.filtrations ] we describe the klyachko filtrations for tensor products and schur functors of toric vector bundles of arbitrary rank . this allows us to compute the global sections of any line bundle on @xmath1 , a fact of independent interest . the main point in the description of okounkov bodies is the computation of the vanishing orders of all sections of certain line bundles along the subvarieties in a fixed flag . in  [ section.vanishing.orders ] we construct a flag of invariant subvarieties @xmath29 in @xmath1 , and show that in this setting it is enough to compute the vanishing orders of a special collection of isotypical sections with respect to the torus action . finally , in  [ section.okounkov.body ] we describe the global okounkov body of @xmath1 with respect to the flag @xmath29 and prove that the variety @xmath1 is a mori dream space . in the last section , we give some examples to illustrate our main result . i would like to thank w. fulton , m. hering , r. lazarsfeld and s. payne , from whom i learned some of the topics relevant to this article . i express my gratitude to the anonymous referee for his / her careful reading of this paper and his / her useful suggestions . i would especially like to thank m. musta for many insightful conversations and for his comments on earlier versions of this manuscript .","summary":"the global okounkov body of a projective variety is a closed convex cone that encodes asymptotic information about every big line bundle on the variety . in the case of a rank two toric vector bundle on a smooth projective toric variety , we use its klyachko filtrations to give an explicit description of the global okounkov body of . in particular , we show that this is a rational polyhedral cone and that is a mori dream space .   ","abstract":"the global okounkov body of a projective variety is a closed convex cone that encodes asymptotic information about every big line bundle on the variety . in the case of a rank two toric vector bundle on a smooth projective toric variety , we use its klyachko filtrations to give an explicit description of the global okounkov body of . in particular , we show that this is a rational polyhedral cone and that is a mori dream space .    okounkov bodies , toric vector bundles , klyachko filtrations , toric varieties , cox rings , mori dream spaces ."}
{"article_id":"astro-ph0109257","section_id":"i","document":"i zw 18 remains the most metal - poor blue compact dwarf ( bcd ) galaxy known since its discovery by sargent & searle ( 1970 ) . later spectroscopic observations by searle & sargent ( 1972 ) , lequeux et al . ( 1979 ) , french ( 1980 ) , kinman & davidson ( 1981 ) , pagel et al . ( 1992 ) , skillman & kennicutt ( 1993 ) , martin ( 1996 ) , izotov & thuan ( 1998 ) , vlchez & iglesias - pramo ( 1998 ) , izotov & thuan ( 1999 ) and izotov et al . ( 1999 ) have confirmed its low metallicity with an oxygen abundance of only @xmath5 1/50 the solar value . zwicky ( 1966 ) described i zw 18 as a double system of compact galaxies , which are in fact two bright knots of star formation with an angular separation of 58 . these two star - forming regions ( fig . [ fig1 ] ) are referred to as the brighter northwest ( nw ) and fainter southeast ( se ) components . later studies by davidson , kinman & friedman ( 1989 ) and dufour & hester ( 1990 ) have revealed a more complex optical morphology with additional diffuse features . the most prominent diffuse feature , hereafter i zw 18c ( fig . [ fig1 ] ) , is a blue irregular star - forming region @xmath5 22  northwest of the nw component . dufour , esteban & castaeda ( 1996a ) , izotov & thuan ( 1998 ) and van zee et al . ( 1998 ) have shown i zw 18c to have a systemic radial velocity equal to that of the ionized gas in the nw and se components , thus establishing its physical association to i  zw  18 . furthermore , van zee et al . ( 1998 ) have shown that i zw 18c is embedded in a common h i envelope with the nw and se components . many studies have been focused on the evolutionary state of i zw 18 . searle & sargent ( 1972 ) and hunter & thronson ( 1995 ) have suggested that it may be a young galaxy , recently undergoing its first burst of star formation . the latter authors concluded from _ hubble space telescope _ ( _ hst _ ) images that the colors of the diffuse unresolved component surrounding the se and nw regions are consistent with a population of b and early a stars , i.e. with no evidence for older stars . ongoing massive star formation in i  zw  18 is implied by the discovery of a population of wolf - rayet stars in the nw component ( izotov et al . 1997a ; legrand et al . 1997 ) .    from the analysis of color - magnitude diagram ( cmd ) based on _ hst _ images , dufour et al . ( 1996b ) concluded that star formation in i zw 18 began at least 30  50 myr ago and continuing to the present . martin ( 1996 ) and dufour et al . ( 1996b ) have discussed the properties of expanding superbubbles of ionized gas driven by supernova explosions and have inferred dynamical ages of 15  27 myr and 13  15 myr respectively . recently , aloisi , tosi & greggio ( 1999 ) have discussed the star formation history in i zw 18 using the same _ hst _ wfpc2 archival data ( i.e. those by hunter & thronson ( 1995 ) and dufour et al . ( 1996b ) ) . they compared observed cmds and luminosity functions with synthetic ones and concluded that there were two episodes of star formation in i zw 18 , the first one occuring over the last 0.5  1 gyr , an age more than 10 times larger than that derived by dufour et al . ( 1996b ) , and the second one with more intense activity taking place between 15 and 20 myr ago . no star formation has occurred within the last 15 myr . stlin ( 2000 ) from _ hst _ nicmos @xmath10 and @xmath11 observations concluded that a 1  5 gyr old stellar population is present . the component i zw 18c has not been studied in such detail mainly because of its faintness . its flux - calibrated optical spectra ( izotov & thuan 1998 ; van zee et al . 1998 ) reveal a blue continuum with weak balmer absorption features and faint h@xmath0 and h@xmath1 in emission . such spectral features suggest that the h ii region is probably ionized by a population of early b stars . dufour et al . ( 1996b ) found in a @xmath12 vs. @xmath13 cmd analysis of i zw 18c a well - defined upper stellar main sequence indicating an age of the blue stars of @xmath5 40 myr . however , numerous faint red stars were also present in the cmd , implying an age of 100  300 myr . those authors concluded that i zw 18c consists of an older stellar population with an age of several hundred myr , but which has experienced recently a modest starburst in its southeastern half as evidenced by the presence of blue stars and h@xmath0 emission . aloisi et al . ( 1999 ) estimated an age for i zw 18c not exceeding 0.2 gyr . we use here high signal - to - noise 4.5 m mmt , 4 m kpno and keck ii spectroscopy to study the evolutionary status of i zw 18c . we also discuss the nature of the extended emission in the outermost regions of i zw 18 . our motivation for this study is the following . until now , age estimates for the stellar populations in i zw 18c are based solely on _ hst _ cmds . while in principle cmd studies are powerful tools for studying stellar populations , they critically depend on the adopted distance to the galaxy and the interstellar extinction , which are a priori unknown . we use here distance - independent techniques based on spectroscopic observations to derive the age of the stellar populations in i zw 18c .    concerning the outermost regions of i zw 18 , while gaseous emission is an important contributor to the total light in the vicinity of the star - forming regions , there was no evidence for extended stellar emission at distances as far as 20  from the h ii regions ( e.g. , dufour et al . 1996b ; izotov et al . however , in some recent papers ( e.g. , legrand 2000 ; legrand et al . 2000 ; kunth & stlin 2000 ) such an old extended stellar population has been postulated . we use deep mmt and keck ii spectroscopic observations to clarify the origin of the extended emission and estimate the contribution of the ionized gas to it . the observations and data reduction are described in sect . the properties of the stellar population in i zw 18c are discussed in sect . 3 . in sect . 4 we discuss the properties of the outlying regions of i zw 18 . our results are summarized in sect .","summary":"we use all available observational constraints for i zw 18c , including those obtained from _ hubble space telescope _ color - magnitude diagrams , to argue that the distance to i zw 18 should be as high as 15 mpc .","abstract":"long - slit keck ii , 4 m kitt peak , and 4.5 m mmt spectrophotometric data are used to investigate the stellar population and the evolutionary status of i zw 18c , the faint c component of the nearby blue compact dwarf galaxy i  zw  18 . hydrogen h and h emission lines are detected in the spectra of i zw 18c , implying that ionizing massive stars are present . high signal - to - noise keck ii spectra of different regions in i zw 18c reveal h , h and higher order hydrogen lines in absorption . several techniques are used to constrain the age of the stellar population in i zw 18c . ages derived from two different methods , one based on the equivalent widths of the h , h emission lines and the other on h , h absorption lines are consistent with a 15 myr instantaneous burst model . we find that a small extinction in the range = 0.20  0.65 mag is needed to fit the observed spectral energy distribution of i zw 18c with that model . in the case of constant star formation , all observed properties are consistent with stars forming continuously between 10 myr and 100 myr ago . we use all available observational constraints for i zw 18c , including those obtained from _ hubble space telescope _ color - magnitude diagrams , to argue that the distance to i zw 18 should be as high as 15 mpc . the deep spectra also reveal extended ionized gas emission around i zw 18 . h emission is detected as far as 30  from it . to a surface brightness limit of 27 mag arcsec we find no observational evidence for extended stellar emission in the outermost regions , at distances 15   from i zw 18 ."}
{"article_id":"astro-ph0109257","section_id":"c","document":"we use spectroscopic and photometric data to constrain the age of the stellar population in the c component of i zw 18 ( @xmath51 i zw 18c ) and to study the origin of the extended emission around i zw 18 . we have arrived at the following main conclusions :    \\1 . deep 4 m kpno , mmt and keck ii spectra of i zw 18c show h@xmath1 and h@xmath0 hydrogen lines in emission , and h@xmath3 and h@xmath2 hydrogen lines in absorption . using their equivalent widths we derive an age of the stellar population of @xmath5 15 myr if an instantaneous burst is assumed . if star formation is continuous , then the equivalent widths are best reproduced by a short star formation episode continuously occurring between @xmath5 10 myr and @xmath5 25 myr ago . uncertainties in the observations and models may extend this range to between @xmath5 10 myr and @xmath6 100 myr ago . spectral energy distributions of the central ( c ) and eastern ( e ) regions of i zw 18c are used to derive extinction . the equivalent widths of the hydrogen emission and absorption lines and the spectral energy distributions are modeled by a 15 myr single stellar population if the extinction coefficient @xmath35(h@xmath1 ) = 0.1  0.3 , corresponding to @xmath4 = 0.20  0.65 mag .    \\3 . with the usually assumed distance of @xmath5 10 mpc the stellar population age derived from _ color - magnitude diagrams is too large as compared to the young age derived from the spectroscopic data . one possible source of the difference is interstellar extinction . furthermore , to have agreement between the cmds and the ionization state of i zw 18c , the distance to the bcd should be increased to @xmath5 15 mpc . concerning the extended emission around i zw 18 , keck ii spectra show h@xmath0 emission as far as 30  from the main body . the equivalent widths of emission lines are particularly strong in the extended envelope ( @xmath30(h@xmath1 ) = 471 ) , implying a dominant contribution of the ionized gas emission in the outermost regions of i zw 18 . within the large uncertainties of the continuum level , the emission at @xmath5 15  from i zw 18 is consistent with pure ionized gas emission . we do not find evidence for an old extended low - surface - brightness stellar component in the outlying regions of i zw 18 down to the surface brightness level @xmath7 @xmath5 27 mag arcsec@xmath8 , contrary to suggestions by kunth & stlin ( 2000 ) . it will be very difficult to detect the extended stellar emission at @xmath7 @xmath5 28 mag arcsec@xmath8 postulated by legrand ( 2000 ) , because of the important ionized gas emission at large distances . and n.g.g . thank the universitts  sternwarte of gttingen for warm hospitality . we are grateful to d. schaerer for making available his stellar evolutionary synthesis models in electronic form and for valuable comments on the manuscript . y.i.i . thanks the gttingen academy of sciences for a gauss professorship . we acknowledge the financial support of the volkswagen foundation grant no . i/72919 ( y.i.i . , n.g.g . , p.p . and k.j.f . ) , of dfg grant 436 ukr 17/1/00 ( n.g.g . ) , deutsche agentur fr raumfahrtangelegenheiten ( dara ) gmbh grants 50  or  9407  6 and 50  or  9907  7 ( k.j.f . and p.p . ) , and of the national science foundation grants ast-9616863 ( t.x.t . and y.i.i . ) and ast-9803072 ( c.b.f . ) . stlin , g. , bergvall , n. , & rnnback , j. 1996 . in d. kunth , b. guiderdoni , m. heydari - malayeri , t. x. thuan ( eds . ) . the interplay between massive star formation , the ism and galaxy formation . gif - sur - yvette : edition frontires , p. 605 lcrccrccrccr h@xmath1 & 0.69@xmath480.05 & 5.6@xmath480.3 & & & & & 0.76@xmath480.28 & 5.6@xmath482.1&&1.50@xmath480.28 & 6.7@xmath482.1 + h@xmath0&3.08@xmath480.06&49.7@xmath481.0&&0.61@xmath480.03&21.1@xmath481.1 & & 2.78@xmath480.26&51.8@xmath484.9&&5.72@xmath480.26&62.5@xmath484.9 +      lrrcrrrrcrrr @xmath13 & 19.20 & & & & & + @xmath40 & 0.50&0.72&&0.83&0.77&0.59&0.40&&0.81&0.75&0.37 + @xmath37 & 0.00&0.20&&0.17&0.15&0.08&0.01&&0.18&0.12 & 0.02 + @xmath39 & 0.10&0.17&&0.10&0.08 & 0.04 & 0.13&&0.16 & 0.08 & 0.21 + @xmath52 & & & & 0.15&0.10 & 0.25 & 0.47&&0.25 & 0.29 & 0.67 +    lccr 3727  [ o ii ] & 0.361@xmath480.038 & 0.374@xmath480.040&53 + 3868  [ ne iii ] & 0.139@xmath480.040 & 0.143@xmath480.042&20 + 3889  he i + h8 & 0.178@xmath480.026 & 0.196@xmath480.034&31 + 3968  [ ne iii ] + h7 & 0.212@xmath480.026 & 0.230@xmath480.034&39 + 4101  h@xmath3 & 0.254@xmath480.028 & 0.271@xmath480.034&49 + 4340  h@xmath2 & 0.455@xmath480.036 & 0.470@xmath480.041&106 + 4363  [ o iii ] & 0.040@xmath480.016 & 0.040@xmath480.016&13 + 4471  he i & 0.034@xmath480.014 & 0.034@xmath480.014&9 + 4686  he ii & 0.019@xmath480.011 & 0.019@xmath480.011&7 + 4861  h@xmath1 & 1.000@xmath480.060 & 1.000@xmath480.061&292 + 4959  [ o iii ] & 0.460@xmath480.036 & 0.454@xmath480.036&179 + 5007  [ o iii ] & 1.417@xmath480.079 & 1.399@xmath480.079&551 + 5876  he i & 0.069@xmath480.014 & 0.067@xmath480.014&40 + 6563  h@xmath0 & 2.902@xmath480.140 & 2.755@xmath480.146&1683 + 6678  he i & 0.038@xmath480.012 & 0.036@xmath480.012&21 + 6717  [ s ii ] & 0.051@xmath480.012 & 0.048@xmath480.011&25 + 6731  [ s ii ] & 0.023@xmath480.009 & 0.022@xmath480.008&15 +   + @xmath35(h@xmath1 ) & + @xmath53(h@xmath1 ) & + @xmath30(abs )   &    lc @xmath43(o iii)(k ) & 18200@xmath484000 + @xmath43(o ii)(k ) & 15100@xmath483200 + @xmath43(s iii)(k ) & 16800@xmath483400 + @xmath44(s ii)(@xmath54 ) & 10@xmath4810 +   + o@xmath55/h@xmath55(@xmath1510@xmath56 ) & 0.316@xmath480.174 + o@xmath57/h@xmath55(@xmath1510@xmath56 ) & 0.964@xmath480.504 + o@xmath58/h@xmath55(@xmath1510@xmath56 ) & 0.020@xmath480.016 + o / h(@xmath1510@xmath56 ) & 1.301@xmath480.533 + 12 + log(o / h ) & 7.114@xmath480.178 +   + ne@xmath57/h@xmath55(@xmath1510@xmath56 ) & 0.206@xmath480.125 + icf(ne ) & 1.35   + log(ne / o ) & 0.670@xmath480.365     lrcr 3889 h@xmath59+he i & 0.73@xmath480.29&0.183 & 54 + 4101 h@xmath3 & 0.91@xmath480.31&0.228 & 87 + 4340 h@xmath2 & 1.56@xmath480.38&0.392 & 125 + 4861 h@xmath1 & 3.98@xmath480.96&1.000 & 471 + 4959 [ o iii ] & 0.59@xmath480.25&0.148 & 69 + 5007 [ o iii ] & 1.94@xmath480.42&0.487 & 229 + 6563 h@xmath0 & 11.55@xmath480.89&2.902&1396","summary":"long - slit keck ii , 4 m kitt peak , and 4.5 m mmt spectrophotometric data are used to investigate the stellar population and the evolutionary status of i zw 18c , the faint c component of the nearby blue compact dwarf galaxy i  zw  18 . high signal - to - noise keck ii spectra of different regions in i zw 18c reveal h , h and higher order hydrogen lines in absorption . several techniques are used to constrain the age of the stellar population in i zw 18c . ages derived from two different methods , one based on the equivalent widths of the h , h emission lines and the other on h , h absorption lines are consistent with a 15 myr instantaneous burst model . we find that a small extinction in the range = 0.20  0.65 mag is needed to fit the observed spectral energy distribution of i zw 18c with that model . in the case of constant star formation , all observed properties are consistent with stars forming continuously between 10 myr and 100 myr ago . we find no observational evidence for extended stellar emission in the outermost regions , at distances 15   from i zw 18 .","abstract":"long - slit keck ii , 4 m kitt peak , and 4.5 m mmt spectrophotometric data are used to investigate the stellar population and the evolutionary status of i zw 18c , the faint c component of the nearby blue compact dwarf galaxy i  zw  18 . hydrogen h and h emission lines are detected in the spectra of i zw 18c , implying that ionizing massive stars are present . high signal - to - noise keck ii spectra of different regions in i zw 18c reveal h , h and higher order hydrogen lines in absorption . several techniques are used to constrain the age of the stellar population in i zw 18c . ages derived from two different methods , one based on the equivalent widths of the h , h emission lines and the other on h , h absorption lines are consistent with a 15 myr instantaneous burst model . we find that a small extinction in the range = 0.20  0.65 mag is needed to fit the observed spectral energy distribution of i zw 18c with that model . in the case of constant star formation , all observed properties are consistent with stars forming continuously between 10 myr and 100 myr ago . we use all available observational constraints for i zw 18c , including those obtained from _ hubble space telescope _ color - magnitude diagrams , to argue that the distance to i zw 18 should be as high as 15 mpc . the deep spectra also reveal extended ionized gas emission around i zw 18 . h emission is detected as far as 30  from it . to a surface brightness limit of 27 mag arcsec we find no observational evidence for extended stellar emission in the outermost regions , at distances 15   from i zw 18 ."}
{"article_id":"1512.00009","section_id":"i","document":"the discovery of thousands of exoplanet systems from _ kepler _ and other missions has confirmed the ubiquity and diversity of planetary systems in our galaxy . the dominant physical processes that lead to the observed configurations of exoplanet systems , however , remain unclear . a central question , for both high and low - mass planets , is whether what we see reflects the in situ growth of planets from a population of planetesimals , or is instead determined largely by migration at a later stage . answering this question robustly requires determining , from protoplanetary disk initial conditions , where and when planetesimals form .    in the  bottom - up \" model for planet formation , planets are built through several key stages , beginning with the coagulation of small particles into larger particles and particle aggregates , the formation of planetesimals from these solids , and the growth of planetesimals from accretion into larger bodies that become terrestrial planets and the cores of gas giants . in the first step , the collisions of particles through brownian and turbulent motions lead to their growth into larger bodies . this process is efficient at producing solids of sizes @xmath7 mm ( e.g. , * ? ? ? ? * ; * ? ? ? recent work has shown that it may be possible for solids to grow to @xmath7cm - m sizes as they drift through radially varying turbulence @xcite , though interior to the snow line , such growth is difficult and solids likely remain stunted at mm sizes @xcite . the propensity of these solids to grow in size only goes so far , however , and forming larger bodies of km size scales or larger ( i.e. , planetesimal scales ) faces two theoretical difficulties . first , if particles grow to sufficiently large sizes ( @xmath7 meter sizes at 1 au ) , they experience a significant head - wind from the sub - keplerian rotating gas , which causes them to lose angular momentum and rapidly spiral into the star @xcite . several mechanisms have been invoked to counteract this drift . for example , pressure bumps due to zonal flows @xcite , ice lines ( @xcite ; but see @xcite and @xcite ) , and abrupt transitions in ionization fraction @xcite may stop or slow this radial drift and may even be required given observations showing the presence of these particles at large disk radii ( e.g. , * ? ? ? * ) . however , even if these particle traps are efficient at slowing radial drift , particles still can not easily grow beyond mm - cm sizes . a combination of laboratory experiments ( primarily on silicates ) and modeling shows that particles within this size range do not easily stick together , and instead fragment or bounce @xcite . whether this is also the case for icy particles is less clear ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? a promising route toward surpassing these difficulties involves instabilities of aerodynamically coupled systems of gas and solid particles . as the gas removes angular momentum from the particles via a headwind , the particles experience inward radial drift . however , the back - reaction of the particle momentum on the gas causes particle over - densities to experience less gas drag as these over - densities act to boost the gas and reduce their own headwind . therefore , regions of higher particle density will experience slower radial drift , leading to a pile up of solids at various radii . this mechanism is the essence of what is known as the streaming instability @xcite . the streaming instability has been studied analytically in the linear regime @xcite and in the non - linear regime via numerical simulations ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the initial growth of the instability does not involve self - gravity , and in this limit , two and three - dimensional calculations have been used to quantify the strength of clumping as a function of the physical @xcite , and numerical parameters , e.g. , resolution @xcite . in particular , @xcite and @xcite carried out numerical calculations of the streaming instability without self - gravity and found that the instability generally leads to efficient particle clumping when the dimensionless stopping time ( i.e. , the stopping time multiplied by the orbital frequency ) is @xmath8 and the height - integrated solid - to - gas ratio is super - solar . furthermore , the instability occurs for a wide range in background gas pressure gradients , but for a given metallicity , it favors smaller gradients @xcite . three - dimensional calculations that include the mutual gravitational forces between particles have been used to study how planetesimals form @xcite . while many characteristics of planetesimal formation have yet to be fully explored , these studies have generally shown that planetesimals with masses consistent with dwarf planets and planetesimals in the main asteroid belt and kuiper belt can form after the streaming instability generates sufficiently strong clumps that self - gravity can take over ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these studies have established the streaming instability as the leading candidate mechanism for the efficient formation of planetesimals . many critical questions , however , remain open . these include whether the streaming instability  in isolation , or in concert with large - scale structures such as zonal flows @xcite  can form planetesimals in the inner disk , where the dimensionless stopping time of mm - sized particles @xmath9 . furthermore , the dependence of the initial planetesimal mass and size distributions on physical properties , such as @xmath10 , the metallicity , and gas - phase turbulence is an open issue . indeed , characterizing these distributions is of substantial importance to explaining properties of both the main asteroid belt and the kuiper belt planetesimal populations . to - date , simulations of the streaming instability in the presence of particle self - gravity @xcite have revealed a shallower planetesimal size distribution than what is inferred from main belt and kuiper belt observations @xcite . however , an extensive systematic survey of the dependence of this distribution on physical parameters has yet to be carried out . purely numerical issues are also of interest . the relative strengths and weakness of different numerical schemes are well - characterized in a variety of situations , including low and high - mach number turbulence , but much less is known in the more complex situation where we have multiple phases , aerodynamic coupling and self - gravity . all previous simulations of planetesimal formation that have included self - gravity have used high - order finite difference methods ( implemented in the pencil code ) . here , we instead combine particle self - gravity with a higher order godunov hydrodynamic scheme ( implemented in the athena code ; * ? ? ? * ) to study planetesimal formation and again address the dependence of planetesimal mass and size distributions on numerical effects .    in this paper , the first of a series , we describe our implementation of particle self - gravity within the athena code , and present results from a baseline set of 3d simulations . our primary focus is on independently verifying ( and in some cases extending ) prior numerical simulations of streaming - initiated planetesimal formation , and hence we start with parameter choices that match those in the existing literature . we specifically address the convergence of the initial planetesimal mass function with numerical resolution , and the effect of varying the strength of self - gravity as compared to tidal shear . we also study whether the results depend on _ when _ in the simulation particle self - gravity is turned on , given that it is common ( and computationally expedient ) to do so at a relatively late time when the non - self - gravitating streaming instability is already strongly non - linear . there has been some study of the impact of this approximation @xcite , but a detailed investigation of the effects of pre - gravity conditions on the outcome of planetesimal formation has not yet been performed . the outline of the paper is as follows . our methodology is described in detail in section  [ method ] , which includes a description of the numerical algorithm and the implementation of particle self - gravity , two test problems to check this implementation , and a description of our streaming instability calculations . in section  [ results ] , we present our results from each set of calculations , and we discuss these results in section  [ discussion ] . we wrap up with a summary and conclusions in section  [ conclusions ] . l|cccccccc si64-g0.05 & @xmath11 & @xmath12 & 300,000 & 0.3 & 0.02 & 0.05 & 400 &  + si128-g0.05 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 170 & fiducial run + si256-g0.05 & @xmath11 & @xmath14 & 19,200,000 & 0.3 & 0.02 & 0.05 & 150 &  + si512-g0.05 & @xmath11 & @xmath15 & 153,600,000 & 0.3 & 0.02 & 0.05 & 110 &  +   +   + si128-g0.02 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 170 &  + si128-g0.02_tm20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 150 & restarted @xmath16 earlier + si128-g0.02_tm10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 160 & restarted @xmath17 earlier + si128-g0.02_tp10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 180 & restarted @xmath17 later + si128-g0.02_tp20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 190 & restarted @xmath16 later + si128-g0.05 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 170 & fiducial run + si128-g0.05_tm20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 150 & restarted @xmath16 earlier + si128-g0.05_tm10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 160 & restarted @xmath17 earlier + si128-g0.05_tp10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 180 & restarted @xmath17 later + si128-g0.05_tp20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 190 & restarted @xmath16 later + si128-g0.1 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.1 & 170 &  + si128-g0.1_tm20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.02 & 150 & restarted @xmath16 earlier + si128-g0.1_tm10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.1 & 160 & restarted @xmath17 earlier + si128-g0.1_tp10 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.1 & 180 & restarted @xmath17 later + si128-g0.1_tp20 & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.1 & 190 & restarted @xmath16 later +   +   + si128-g0.05-no_clump & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 0 &  + si128-g0.05-low_clump & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 40 &  + si128-g0.05-med_clump & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 170 & same as fiducial run + si128-g0.05-high_clump & @xmath11 & @xmath13 & 2,400,000 & 0.3 & 0.02 & 0.05 & 240 &  +","summary":", we find that ( when a direct comparison is possible ) the athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques . in particular , the gravitational collapse of streaming - initiated clumps leads to an initial planetesimal mass function that is well - represented by a power - law , , with , which equates to a differential size distribution , with . likewise , the power - law slope appears indifferent to changes in the relative strength of self - gravity and tidal shear , and to the time when ( for reasons of numerical economy ) self - gravity is turned on , though the strength of these claims is limited by small number statistics . for a typically assumed radial distribution of minimum mass solar nebula solids ( assumed here to have dimensionless stopping time ) , our results support the hypothesis that bodies on the scale of large asteroids or kuiper belt objects could have formed as the high - mass tail of a primordial planetesimal population","abstract":"we study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over - densities generated via the streaming instability . to carry out these studies , we implement and test a particle - mesh self - gravity module for the athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self - gravitating solid particles . upon employment of our algorithm to planetesimal formation simulations , we find that ( when a direct comparison is possible ) the athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques . in particular , the gravitational collapse of streaming - initiated clumps leads to an initial planetesimal mass function that is well - represented by a power - law , , with , which equates to a differential size distribution , with . we find no significant trends with resolution from a convergence study of up to grid zones and particles . likewise , the power - law slope appears indifferent to changes in the relative strength of self - gravity and tidal shear , and to the time when ( for reasons of numerical economy ) self - gravity is turned on , though the strength of these claims is limited by small number statistics . for a typically assumed radial distribution of minimum mass solar nebula solids ( assumed here to have dimensionless stopping time ) , our results support the hypothesis that bodies on the scale of large asteroids or kuiper belt objects could have formed as the high - mass tail of a primordial planetesimal population"}
{"article_id":"1512.00009","section_id":"m","document":"in this section , we explain our methodology . we first describe the algorithmic details of athena in the shearing box approximation with the inclusion of aerodynamic coupling between the gas and the particles and the mutual gravitational attraction between particles solved via a fast fourier transform ( fft ) method . we then present tests of our particle self - gravity module , followed by a description of our set up , parameters , and diagnostics for the local , streaming instability simulations that we carry out in this paper . our simulations use athena , a second - order accurate godunov flux - conservative code for solving the equations of hydrodynamics and magnetohydrodynamics . the simulations we have carried out here neglect magnetic fields , and we use the hydrodynamics module of athena . we use the athena configuration that includes the dimensionally unsplit corner transport upwind method of @xcite coupled with the third - order in space piecewise parabolic method of @xcite . we use the hllc riemann solver to calculate the numerical fluxes @xcite . a detailed description of the base athena algorithm and the results of various test problems are given in @xcite , @xcite , and @xcite . the simulations employ a local shearing box approximation . the shearing box models a co - rotating disk patch whose size is small compared to the radial distance from the central object , @xmath18 . this allows the construction of a local cartesian frame @xmath19 that is defined in terms of the disk s cylindrical co - ordinates @xmath20 via @xmath21 , @xmath22 , and @xmath23 . the local patch co - rotates with an angular velocity @xmath24 corresponding to the orbital frequency at @xmath18 , the center of the box ; see @xcite . there are two sets of equations to solve . comprising the first set are the continuity and momentum equation for the gas dynamics :    @xmath25    @xmath26    where @xmath27 is the mass density , @xmath28 is the momentum density , @xmath29 is the gas pressure , @xmath30 is the identity matrix , @xmath31 is the ( dimensional ) stopping time of the particles , and @xmath32 is the shear parameter , defined as @xmath33ln@xmath34ln@xmath35 . we use @xmath36 , appropriate for a keplerian disk . for simplicity and numerical convenience , we assume an isothermal equation of state @xmath37 , where @xmath38 is the isothermal sound speed . from left to right , the source terms in equation  ( [ momentum_eqn ] ) correspond to radial tidal forces ( gravity and centrifugal ) , vertical gravity , the coriolis force , and the feedback from the particle momentum onto the gas . the feedback term consists of the local particle mass density @xmath39 , the difference between the particle velocity @xmath40 and gas velocity , and the stopping time @xmath31 of particles due to gas drag . as we describe below , this feedback term is calculated at the location of every particle and then distributed to the gas grid points . the second set of equations describes the particle evolution . the equation of motion for particle @xmath41 is given by    @xmath42    where the prime denotes a frame in which the background shear velocity has been subtracted . this is part of the orbital advection scheme @xcite , which has been implemented for the gas dynamics as well . the @xmath43 term accounts for the inward radial drift of particles resulting from a gas headwind , where @xmath44 is the fraction of the keplerian velocity by which the orbital velocity of particles is reduced ( see section  [ setup ] ) . in real disks , this headwind results from a radial pressure gradient that causes the gas to orbit at sub - keplerian speeds while the particles continue to orbit at keplerian velocities . however , such a radial pressure gradient is inconsistent with the radial ( shearing ) periodic boundary conditions in the shearing box model . following @xcite , we circumvent this issue by imposing an inward force on the particles , resulting in the @xmath43 term as described above . as a result , both the particles and gas ( azimuthal ) velocities are shifted to slightly higher values ( by @xmath43 ) than what would be present in a real disk , but the essential physics of differential motion between the gas and particles is accurately captured . equation  ( [ particle_motion ] ) is solved using the algorithms described in @xcite ; in particular , we use the semi - implicit integration method combined with a triangular shaped cloud ( tsc ) scheme to map the particle momentum feedback to the grid cell centers and inversely to interpolate the gas velocity to the particle locations ( @xmath45 ) . the force due to the particle self - gravity is denoted by @xmath46 , which is found by first solving poisson s equation for particle self - gravity ,    @xmath47    where @xmath48 is the gravitational potential of the particle self - gravity . the force is then calculated via ,    @xmath49    in solving equation  ( [ poisson ] ) , we follow the methodology outlined in section 2.3 and the appendix of @xcite , which consists of a discrete 3d fft adapted to handle the shearing - periodic boundaries in @xmath50 and the vacuum boundaries in @xmath51 . solving the poisson equation with fft requires periodicity in all three dimensions . in the azimuthal dimension , this is trivially satisfied . for the radial boundaries , the particle mass density ( which is distributed to the gas grid points using the same interpolation method as used to calculate the momentum exchange terms ; tsc ) is mapped to the nearest time in which the shearing - periodic boundaries are purely periodic . from @xcite , the times at which the radial boundaries are purely periodic are @xmath52 with @xmath53 . for each value of @xmath50 , the particle density is reconstructed along @xmath54 via a conservative remap ; the density is calculated by differencing numerical  fluxes \" along @xmath54 . these fluxes are calculated via third order reconstruction coupled with the extremum preserving algorithm of @xcite . note that this reconstruction is the same method employed to remap the fluid quantities in the radial ghost zones as part of the shearing - periodic boundary conditions @xcite . in the vertical direction , the solution to equation  ( [ poisson ] ) is found using the green s function of the poisson equation for a horizontal sheet of sinusoidal source mass , as described in detail in the appendix of @xcite . the authors of that work developed this method to calculate the potential of self - gravitating gas , but we have trivially extended this same algorithm to use the particle mass density instead of the gas density .    with these methods in hand , the potential is calculated as follows . the particle mass density is reconstructed along @xmath54 via the same third - order conservative remap as is used for the boundary conditions , multiplied by appropriate functions of @xmath51 , as described above ( see equation ( a11 ) of * ? ? ? * ) , and then fourier transformed via a 3d fft . the density in fourier space is then multiplied by the appropriate coefficients and transformed back to real space via another 3d fft ( see equation ( a8 ) of * ? ? ? in calculating the 3d fft s , a domain of size @xmath55 is used ; twice the vertical domain size is required for the use of green s function in solving the potential with vacuum boundaries . finally , the gravitational potential is mapped back to the original time using the third - order conservative remap that was used on the particle mass density . the resulting @xmath48 is a cell - centered quantity , and we calculate the forces at the cell center using a central finite difference method over three grid cells in every direction . thus , the force ( equation  [ grav_force ] ) in the @xmath50-direction in cell @xmath56 is calculated by    @xmath57    and similarly for the @xmath54 and @xmath51 directions . the forces then have to be interpolated back to the location of the particles , and we again use the tsc method . we add the self - gravity force to the particles simultaneously with the drag force . the boundary conditions are the shearing - periodic boundaries in the radial direction , purely periodic in the azimuthal direction , and a modified outflow condition in the vertical direction in which the gas density is extrapolated via an exponential function into the grid zones ( * ? ? ? * li et al . 2016 in prep ) . this latter boundary condition is not standard in shearing box setups for the streaming instability as the small domain size makes it difficult to prevent substantial outflow in the vertical direction . however , in a forthcoming publication by the authors ( li et al . 2016 in prep ) , we have experimented with the vertical boundary conditions and find that coupled with a routine to renormalize the total mass in the domain to make it constant in time , the outflow boundaries work reasonably well . the boundary conditions for the gravitational potential are essentially the same as the hydrodynamic variables ; shearing - periodic in @xmath50 and purely periodic in @xmath54 . the vertical boundary conditions are open , and the potential is calculated in the ghost zones via a third order extrapolation .      in this section , we carry out two tests of our numerical algorithm for particle self - gravity . the first test is the collapse of a uniform density sphere of particles . the second test consists of the self - gravitating , shearing wave of particles described in the supplementary material of @xcite . the collapse of a uniform density sphere under its own gravity has a simple analytic solution with which to compare the numerical solution . the equation of motion for a test particle at radius @xmath58 starting at the outer edge of the sphere is    @xmath59    where @xmath60 is the total mass within the sphere and remains constant in time . parameterizing the time dependence of @xmath58 via @xmath61 , we assume that @xmath62 , where @xmath63 is the initial radius of the uniform density sphere , and find that    @xmath64    the analytical solutions to the radius and mass density are given by    @xmath65    @xmath66    where @xmath67 is given by equation  ( [ alphat ] ) . to test our self - gravity solver against this analytic solution , we initialize a sphere of particles with radius @xmath68 on a cubic domain of @xmath69 resolved by @xmath70 zones . every zone within the radius of the sphere has one particle per grid cell initially . we turn off gas drag on the particles in order to only test the particle self - gravity module . we use tsc interpolation , and the semi - implicit particle integrator . the boundary conditions are open in all three dimensions , and consequently we use the green s function approach of @xcite to solving for the potential with vacuum boundaries ; here applied to all three dimensions instead of only the vertical as described above . we arbitrarily set the value of g to @xmath71 . the solution to this test problem is shown in fig . [ collapse ] , which depicts the evolution of @xmath72 and @xmath73 versus time in units of the free fall time @xmath74 where @xmath75 is the initial particle mass density . as the figure shows , the numerical solution matches the analytic solution quite well . the differences between the two curves that show up at late times is a result of the fft solver becoming less accurate as the particles are concentrated into fewer and fewer grid cells . at such particle densities , the discretization error of the fft solution starts to dominate , as we discuss more below . even with these errors , the numerical solution does not deviate too much from the analytic solution . this limitation should be kept in mind when considering the formation of planetesimals . in fact , the natural softening length of our fft solver is @xmath76 where @xmath77 is the length of a grid cell .. ]    to further test our gravity module , we have also implemented a direct summation method for calculating the mutual gravitational forces between particles . this method is exact , but scales as @xmath78 , where @xmath79 is the number of particles . for large numbers of particles the direct summation method becomes prohibitively expensive . however , for small numbers of particles we can use this method to compare the forces calculated by the fft method with the forces from the direct summation , which will be exact to within machine precision . the comparison also tests the accuracy of our interpolation scheme since the direct sum method does nt require any interpolation of the gravitational forces to the particle locations . we calculate the error in the force in the @xmath41-th direction as    @xmath80    where @xmath81 is the force due to self - gravity on particle @xmath82 calculated via the fft method and @xmath83 is the same but calculated with the direct summation method . we run the particle sphere collapse problem at a resolution of @xmath84 ( and again , one particle per grid cell within the sphere initially ) and find that the errors are typically very small early on ( on the order of @xmath85 or less ) . as time progresses , the errors grow ; as the particles get more concentrated within a smaller number of grid cells , the truncation level error from the particle self - gravity solver will become more and more dominant . at @xmath86 , the average errors are approximately @xmath87% or less , and near @xmath88 , the average errors are on order of a few percent . while the spherical collapse problem tests the core of our poisson solver , we require a problem to test the implementation of this solver in the shearing box setup . to this end , we employ the linearized self - gravitating , shearing particle wave with gas drag described in detail in section 1.3.1 of the supplementary material of @xcite . following that work , we linearize the continuity equation , equation of motion , and poisson s equation for a particle  fluid \" of density @xmath89 , velocity @xmath90 , and self - gravity potential @xmath91 where prime represents the linear perturbation on the background . the perturbation is assumed to be of the form @xmath92 $ ] . note that we assume uniformity along the vertical direction . the evolution of the density and velocity perturbations are then governed by the following equations ,    @xmath93,\\ ] ]    @xmath94    @xmath95    where the radial wavenumber @xmath96 is time - dependent ,    @xmath97    we set @xmath98 , @xmath99 , @xmath100 , @xmath101 , and @xmath102 . we solve equations  ( [ perturbed_continuity])-([perturbed_vy ] ) using a simple finite difference algorithm to obtain our linear solution to the self - gravitating , shearing wave problem in the linear limit . for the numerical test of our algorithm , we initialize a grid of size @xmath103 at resolution @xmath104 and with one particle per cell initially ; the small size / resolution in the vertical direction makes the problem effectively two - dimensional while still testing the full 3d fft algorithm . in this setup , the boundary conditions are shearing - periodic in @xmath50 and purely periodic in both @xmath54 and @xmath51 . note that we turn off particle feedback to the gas for this test problem . the time evolution of the amplitude of the perturbations are shown in fig . [ shear_test ] . the numerical solution agrees very well with the linear solution up to amplitudes of @xmath105 . at this point , the numerical solution approaches the non - linear regime , and agreement between the linear and numerical solutions is not expected . this test problem , which includes several essential ingredients relevant to the streaming instability calculations in this paper , ( i.e. , shear , self - gravity , and drag ) , demonstrates the validity of our self - gravity implementation in the shearing box setup .    ) in the self - gravitating , shearing wave test . the red lines show the numerical solution , whereas the black lines show the linear solution . the solid lines are the density perturbation , @xmath106 , the dashed lines are the @xmath50 velocity perturbations , @xmath107 , and the dot - dashed lines are the @xmath54 velocity perturbations , @xmath108 . there is excellent agreement between the numerical and linear solutions up to amplitudes of @xmath105 , where the numerical solution begins to go non - linear . , scaledwidth=50.0% ]      all of our streaming instability simulations use a shearing box domain of size @xmath109 = @xmath110 . here , @xmath111 is the vertical scale height of the gas , which is initialized with a hydrostatic ( gaussian ) vertical profile ,    @xmath112    where @xmath113 is the mid - plane gas density . we choose code units so that the standard gas parameters are unity ; @xmath114 . given the limited vertical extent of our domain , the gas density does not vary significantly . the particles are distributed uniformly in @xmath50 and @xmath54 and with a gaussian profile in @xmath51 . the scale height of this profile is @xmath115 . while we add random noise to the particle locations to seed the streaming instability , it is worth mentioning that the particles are not initially in an equilibrium state . there is radial motion induced by the radial drift term @xmath43 as described above , and the lack of a pressure gradient to counteract vertical gravity means that the particles will settle towards the disk mid - plane . four dimensionless quantities characterize the evolution of the streaming instability and the ability of dense clumps to gravitationally collapse . the streaming instability depends upon the dimensionless stopping time , @xmath116 which characterizes the aerodynamic interaction between a single particle species and the gas , the metallicity , @xmath117 which is the ratio of the particle mass surface density @xmath118 to the gas surface density @xmath119 , and a radial pressure gradient parameter that accounts for the sub - keplerian gas in real disks @xmath120 this radial pressure gradient produces a headwind on the particles , which has velocity a fraction @xmath44 of the keplerian velocity . for all of our runs , @xmath6 , metallicity is moderately super - solar , @xmath121 , and @xmath122 .    with the inclusion of self - gravity , an additional parameter is needed to describe the relative importance of self - gravity and tidal shear . we define a parameter @xmath123 , @xmath124 which describes the strength of self - gravity in the simulation . physically , varying @xmath123 is equivalent to changing the gas density ( and thus through assuming the same @xmath125 , the particle mass density ) or the strength of tidal stretching ( i.e. , changing @xmath24 ) or both . thus , in a real disk , @xmath123 will vary with radius , and in a minimum mass solar nebula model ( mmsn ; * ? ? ? * ) , this parameter increases very gradually with radius .    in what follows , we convert code units to physical units using the mass unit @xmath126 and assuming a radius of 3 au in a mmsn . for @xmath127 , this equates to @xmath128 . this physical unit conversion depends on @xmath123 , as we discuss further below . our fiducial simulation is a relatively low resolution run with @xmath129 = @xmath13 gas zones and 2,400,000 particles . for this simulation , we turn on self - gravity at a time @xmath130 and set @xmath127 . we then explore parameter space by varying one parameter in each simulation subset ( demarcated in table  [ tbl : sims ] by separate boxes ) . in the first subset , we vary the numerical resolution and the number of particles . we explore a lower resolution @xmath12 with 300,000 particles , and two higher resolutions : @xmath14 with 19,200,000 particles and @xmath15 with 153,600,000 particles . in the next subset , we vary the value of @xmath123 from 0.02 to 0.1 ; this was chosen to match the test carried out by @xcite in which the strength of gravity was varied .    finally , we determine the effect of the state at which self - gravity is initiated by examining two diagnostics in a simulation identical to the fiducial one , but with no self - gravity . the first is the maximum value of the volume - averaged particle mass density , @xmath131 , and the second is a weighted version of the volume - averaged particle mass density , defined as @xmath132 . in general , these two quantities behave similarly , but while the maximum density has been used more frequently in the literature to track the degree of clumping via the streaming instability , it can be largely affected by a small number of grid cells ( or even one cell ) , and the latter quantity is more representative of the degree of clumping over the entire domain . using both of these diagnostics in concert , we chose restart times of @xmath133 ( the  low clumping \" case ) , @xmath130 ( medium clumping ; this is the same as the fiducial simulation ) , and @xmath134 ( high clumping ) . we also run one case with self - gravity turned on from the beginning state @xmath135 . all of these runs are labelled by the numerical resolution employed , the strength of self - gravity , and any other modifying information . for example , run si128-g0.05-low_clump has 128 zones per dimension , @xmath127 , and is initiated from a  low clumping \" state , as described above . all simulations are shown in table  [ tbl : sims ] with the parameters outlined and any additional , relevant comments . there are several diagnostics employed in section  [ results ] that we now describe . first is the maximum particle mass density , as described above , as a proxy for the degree of clumping during the streaming instability . another often employed quantity is the particle mass surface density , which is simply the integral of @xmath131 over the vertical extent of the domain . most of our diagnostics require that we locate gravitationally bound mass clumps ( after self - gravity has been included ) and calculate their mass . following the basic arguments in @xcite , we calculate @xmath118 at a given time and use a peak - finding algorithm to locate local maxima in the surface density above a certain threshold . the mass of any given clump is determined by calculating a circular region surrounding the clump and iteratively increasing the radius of this region until the mass enclosed within it equals the mass of a clump that is bound by self - gravity compared to tidal effects . mathematically , we seek a radius @xmath35 such that the tidal term , @xmath136 , and the gravitational acceleration of a test particle at the edge of the clump s hill sphere , @xmath137 are in balance ;    @xmath138    when the mass enclosed within our test circle equals @xmath139 , we set @xmath35 as the hill radius and @xmath139 as the clump mass . there are two limitations to our algorithm . first , it has difficulty determining the masses of clumps when two or more clumps are very close together in the @xmath140 plane . this is alleviated somewhat by setting a minimum distance , equivalent to the hill radius of a 0.1 @xmath141 mass ( which , as we will see , is consistent with masses at the higher end of the resulting mass distributions ) , below which the algorithm counts two clumps as being one . furthermore , we subtract contributions of neighboring clumps that are beyond this minimum distance but still within each clump s hill radius . this limitation with overlapping clumps is particularly troublesome at early times when gravitationally bound clumps have yet to fully form , yet there are still peaks in @xmath118 . the error associated with overlapping clumps commonly manifests itself as very sharp peaks or troughs in the time evolution of the clump masses . while this limitation causes issues on short timescales when clumps temporarily interact , it does not affect the clump mass on long timescales . as a first order approach to remove this effect , we apply a simple boxcar smoothing technique to the time evolution of clump masses in all that follows . the second limitation arises from applying a two - dimensional approach to a fully three - dimensional problem . however , even though clumps exist in three dimensions , the particle layer is vertically thin enough to make the two - dimensional clump finding approach a good approximation . indeed , the algorithm appears to do a sufficient job at finding clumps that remain gravitationally bound as the simulation progresses and does not find too many false positives . furthermore , as shown in section  [ results ] , the diagnostics that employ this algorithm return results roughly consistent with @xcite , lending support to the idea that our analysis works reasonably well .    from this clump finding algorithm , we calculate both the time history of the mass of the formed clumps and the mass distribution function for these clumps . many of the simulations form only small numbers of clumps , so we seek a simple functional form to fit to the mass distribution . consistent with prior work , a power - law differential mass distribution ,    @xmath142    works well . here , @xmath143 is a constant that for the purposes of this paper is arbitrary . we also consider the cumulative mass distribution ,    @xmath144    where @xmath145 is another arbitrary constant . we can easily translate equation  ( [ mass_dist ] ) to a size distribution to find @xmath146 where @xmath147 .    under the assumption that the data is drawn from a power - law distribution , the power law index @xmath148 of the differential distribution can be determined directly from the set of measured masses @xmath149 using a maximum likelihood estimator ( mle ; * ? ? ? * ) . from equation  ( 3.1 ) in @xcite , we estimate the value of the power law index by    @xmath150^{-1},\\ ] ]    where @xmath151 is the minimum value of the planetesimal mass in our data , and @xmath82 is the total number of planetesimals . the error is given by their equation ( 3.2 ) ,    @xmath152    using the mle for @xmath148 avoids any binning step , which can introduce bias into the estimate . to visually represent the differential distribution , however , we make a local estimate of @xmath153 by taking @xmath154 to be half the distance in the mass co - ordinate between a given planetesimal and its nearest neighbors . a least squares linear fit in log - log space to @xmath155 vs @xmath139 gives an alternate measure of @xmath148 , that is very roughly consistent but generally slightly smaller . irrespective of the statistical methods used , two cautions are in order . first , the underlying distribution of planetesimal masses formed in the simulations can not in reality be a simple power - law , because there is zero probability of forming a body with a mass greater than the total mass of solids in the domain . if the actual distribution is a truncated power - law , then our naive fit will over - estimate the value of @xmath148 . second , our lower resolution runs form rather small number of planetesimals , and any method for estimating @xmath148 in this situation is noisy , possibly biased , and liable to return a non - gaussian distribution of slope estimates . simple experiments suggest that only the higher resolution runs , for which there are on order 100 planetesimals , can be expected to return robust estimates of the distribution .","summary":"we study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over - densities generated via the streaming instability . to carry out these studies , we implement and test a particle - mesh self - gravity module for the athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self - gravitating solid particles . upon employment of our algorithm to planetesimal formation simulations we find no significant trends with resolution from a convergence study of up to grid zones and particles .","abstract":"we study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over - densities generated via the streaming instability . to carry out these studies , we implement and test a particle - mesh self - gravity module for the athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self - gravitating solid particles . upon employment of our algorithm to planetesimal formation simulations , we find that ( when a direct comparison is possible ) the athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques . in particular , the gravitational collapse of streaming - initiated clumps leads to an initial planetesimal mass function that is well - represented by a power - law , , with , which equates to a differential size distribution , with . we find no significant trends with resolution from a convergence study of up to grid zones and particles . likewise , the power - law slope appears indifferent to changes in the relative strength of self - gravity and tidal shear , and to the time when ( for reasons of numerical economy ) self - gravity is turned on , though the strength of these claims is limited by small number statistics . for a typically assumed radial distribution of minimum mass solar nebula solids ( assumed here to have dimensionless stopping time ) , our results support the hypothesis that bodies on the scale of large asteroids or kuiper belt objects could have formed as the high - mass tail of a primordial planetesimal population"}
{"article_id":"1312.3987","section_id":"i","document":"the quantum mechanical geometric phase was discovered by berry in 198384@xcite . the context was unitary evolution governed by the schrdinger equation in the adiabatic approximation , i.e. , with a hermitian hamiltonian possessing a ` gentle ' time - dependence . assuming that as an operator the hamiltonian is cyclic , i.e. , it returns to its original form after a certain interval of time ( during which there are no level crossings ) , the approximate solutions to the schrdinger equation are also cyclic . the geometric phase is then seen explicitly in these solutions at the end of the cycle .    immediately after berry s discovery , it was pointed out by barry simon@xcite that the geometric phase expresses the non - integrability , or anholonomy , of a natural ` rule of parallel transport ' ( a connection ) in a principal fibre bundle , with structure group @xmath0 , which occurs in the framework of quantum mechanics . this was therefore a characterisation of this phase in the language of differential geometry . the ensuing years saw two streams of work relating to the geometric phase . one consisted of extensions of berry s original work , in the sense of relaxing the conditions under which the phase is definable . the other consisted of interesting earlier results which could be reinterpreted as instances of this phase , and so as precursors to it . we recall three significant efforts of the first kind . aharonov and anandan@xcite showed that the adiabatic condition is not necessary  given a cyclic solution to the schrdinger equation involving any ( time - dependent ) hamiltonian , one can reconstruct a corresponding geometric phase . this was followed by the work of samuel and bhandari@xcite , in which the cyclic condition on a solution was also dispensed with . given a solution of the schrdinger equation involving any ( time - dependent ) hamiltonian , over any stretch of time , one can in a simple way extend it to a closed or cyclic solution , then use the aharonov - anandan method to identify a geometric phase . both these extensions of berry s original framework used quantum mechanical notions , specifically the schrdinger equation . the third step in the direction of increasing generality was taken by mukunda and simon@xcite : the geometric phase is entirely kinematical in content , not requiring a hamiltonian operator and associated schrdinger equation . it is determined once one is given a ( sufficiently smooth ) curve of unit vectors in any complex hilbert space , without reference to any specifically quantum mechanical notions . ( the relevant expressions and definitions are recalled below ) .    turning to the efforts of the second kind , within quantum mechanics we may cite the bohm - aharonov effect ( already dealt with by berry in his original work ) , and the clarification of the connection between bargmann invariants and geometric phases@xcite . beyond these , it is interesting that many instances of the geometric phase have been identified within classical ( wave ) optics  the gouy phase from 1890@xcite ; the work by rytov , and vladimirskii@xcite in 1938 and 1941 on the behavior of light polarisation in the short wavelength limit of wave optics ; and pancharatnam s studies in 1956@xcite on light polarisation and an associated phase . these classical optics examples will be reviewed briefly in the next section . it will be seen that even in these situations the basic idea of a complex linear vector space carrying a hermitian inner product , usually regarded as characteristic of quantum mechanics , is essential to be able to identify ` classical geometric phases ' . in this way , the deep link between bargmann invariants and geometric phases , and the connection to berry s original discovery , are always kept in evidence .    with this background , we now describe briefly the kinematic approach to the geometric phase . let @xmath1 be a complex hilbert space of any dimension , with vectors @xmath2 and inner product @xmath3@xcite . in quantum mechanics @xmath4 is related to a probability ; in classical wave optics @xmath5 generally stands for light intensity which can , but need not be , normalised . we next denote by @xmath6 the unit sphere in @xmath1 : @xmath7 the group @xmath0 of complex phase factors acts on @xmath6 ( also on @xmath1 ) in a natural way : @xmath8 the quotient @xmath9 , i.e. , collections or equivalence classes of vectors @xmath10 differing only by phases , forms the ` ray space ' @xmath11 : @xmath12 whereas @xmath6 is a subset of @xmath1 , _ the ray space @xmath13 is not _ : the @xmath14 relationship is that there is a projection map @xmath15 from the former to the latter : @xmath16 referring to an earlier comment , @xmath6 is a @xmath0 principal fibre bundle over the base @xmath11 . in the quantum mechanics context , points in @xmath11 correspond one - to - one to physical pure states .    in this framework , given any continuous piecewise once differentiable parametrised curve @xmath17 in @xmath6 , @xmath18 with image @xmath19 in @xmath11 , @xmath20 \\nonumber\\\\ & = \\{\\rho(s ) = \\rho(\\psi(s ) ) = \\psi(s)\\psi(s)^\\dag\\,|\\ , s_1\\le s \\le s_2\\}\\subset\\mathcal{r}\\,,\\end{aligned}\\ ] ] the geometric phase @xmath21 $ ] is defined : @xmath22 & = \\varphi_{\\rm tot}[\\mathcal{c } ]         -\\varphi_{\\rm dyn}[\\mathcal{c}]\\,,\\nonumber\\\\ \\varphi_{\\rm tot}[\\mathcal{c } ] & = \\arg(\\psi(s_1),\\psi(s_2)),\\nonumber\\\\ \\varphi_{\\rm dyn}[\\mathcal{c } ] & = \\text{im } \\int_{s_1}^{s_2 } ds \\left(\\psi(s ) , \\frac{d\\psi(s ) } { ds}\\right)\\,.\\end{aligned}\\ ] ] as indicated , @xmath21 $ ] is a functional of @xmath23 , while @xmath24 and @xmath25 are both functionals of @xmath26 . an important consequence of this definition is a result involving the so - called bargmann invariants@xcite . the simplest such invariant involves three pairwise nonorthogonal vectors @xmath27 and is the expression @xmath28 which is in general complex . the fact that @xmath29 = @xmath30 for all real @xmath31 shows that @xmath32 lives in @xmath13 rather than in @xmath33 . indeed bargmann , during the course of his famous proof of wigner s theorem , introduced @xmath32 simply to point out this gauge - invariance property and to indicate that it could be used to distinguish between unitaries and antiunitaries : while @xmath32 is invariant under unitaries , its argument changes signature under antiunitaries . it is in @xcite that this object introduced by bargmann almost in passing was elevated to become the basis of a complete kinematic theory of geometric phase . it is worth emphasizing that the framework described above , based on the triplet of spaces @xmath44 , supports the geometric phase concept in a simple and direct way . though suggested by the formal ( complex linear space ) structure of quantum mechanics , it can be used in other situations as well , such as classical wave optics . we adopt this viewpoint in trying to define geometric phases in various physical , particularly classical optical , situations . before we outline the organization of the material of this paper , it may be useful to add an extended remark by way of pointing to the precise context of this work . there has been considerable interest in recent times to understand the interplay between the spatial degree of freedom ( coherence ) and polarisation degree of _ electromagnetic _ beams [ see , for instance , @xcite and references therein ] . it is equally important to understand the behaviour of this interplay as the maxwell beam passes through an optical system . indeed , it turns out that the _ defining _ properties of the age old mueller matrix can not be correctly enumerated without consideration of this interplay or entanglement@xcite . a lens of focal length @xmath45 relates the output field amplitude @xmath46 ( just after the lens plane ) to the input @xmath47 ( just before the lens plane ) , @xmath48 being cartesian variables in the transverse plane , through @xmath49 but when it comes to vector waves , it is clear that the same transformation applied to every ( cartesian ) component of the electric field vector @xmath50 will not map solutions of maxwell equations at the input plane to solutions at the output , for such a democratic action on the electric field components _ does not _ respect the transversality condition @xmath51 . since this condition is a _ constraint _ connecting the spatial degrees of freedom to the polarization degree , it would be respected only if the spatial modulation @xmath52 is accompanied by ` appropriate ' _ local rotations _ of the electric field components ( local polarization)@xcite . let us arrange the components of the electric and magnetic field amplitude vectors @xmath50 , @xmath53 in a transverse plane @xmath54 = constant into a six - component electromagnetic vector @xmath55 the approach of@xcite rooted at the very poincar symmetry of the maxwell system of equations led to this fundamental result : if @xmath56 is the amplitude transmittance function of an optical system in scalar fourier optics [ a lens , for instance , has @xmath57 , then the action @xmath58 where @xmath59 are a pair of @xmath60 _ numerical _ matrices arising from the structure of the poincar group@xcite , _ does take _ solutions @xmath61 of maxwell s equations to solutions @xmath62 . that is , the matrices @xmath59 effect on the components of @xmath63 the correct local rotations alluded to above@xcite . this result readily leads to fourier optics for maxwell beams@xcite and to electromagnetic gaussian beams@xcite , resulting in a straight forward description of not only the longitudinal component but also the cross - polarisation component@xcite . it is in respect of this result that the late henri bacry anticipated : `` it is highly probable that a rigorously gauge theory will be developed in a near future '' , the local rotations referred to above constituting `` an @xmath64 gauge group''@xcite . the work presented here is only the first step of an ambitious programme constituting our attempt towards a possible realization of this anticipation . while the earlier formulation of fourier optics for maxwell beams@xcite concentrated on paraxial propagation about a _ fixed direction _ , the present work aims at laying a global and structurally robust skeleton in the _ space of directions _ , handling satisfactorily the well known topological obstructions . in the sequel , we plan to adapt suitably the methods of @xcite in local patches of the space of directions , and then ` stitch ' together the patches in a smooth manner to arrive at the general case . the contents of this paper are organised as follows . section  ii gives brief accounts of three applications of the geometric phase concept to classical optical situations : the gouy phase in scalar paraxial wave optics ; the pancharatnam study of phases in pure polarization optics with fixed propagation direction ; and the behaviour of polarisation in the eikonal or ray limit of maxwell s equations in a transparent medium with given refractive index function . the pancharatnam case uses the poincar sphere @xmath65 of polarisation states , for a fixed direction of propagation , while the ray case uses the sphere of propagation directions @xmath66 . in all these cases , the use of the basic quantum mechanical framework is highlighted . section  iii builds on the last example of section  ii in two ways  the generalisation from the unphysical case of a single ray to a physical beam of finite cross - sectional area made up of a narrow bundle of nearly parallel rays ; and the inclusion of polarization gadgets in the path of the beam . once again the quantum mechanical framework proves adequate , and now both spheres @xmath65 , @xmath66 come into the picture . section  iv takes up certain global features of the sphere of directions @xmath66 , and builds on a recent suggestion@xcite that passage to the complex extension of the tangent planes to @xmath66 removes an obstruction which exists in the real domain . ( the work of@xcite was motivated in part by earlier works of@xcite . ) using elementary group theoretical arguments , based on the groups @xmath64 and @xmath67 , a particularly simple global basis of complex orthonormal vector fields tangent to @xmath66 is constructed . section  v uses the constructions of section  iv to study again the beams of section  iii and their geometric phases : in appropriate situations , the complete geometric phase separates into a contribution from @xmath65 and another from @xmath66 . the final section  vi contains some concluding remarks , while the appendix compares the present framework for handling geometric phases with that proposed in @xcite .","summary":"important physical situations taken from scalar wave optics , pure polarisation optics , and the behaviour of polarisation in the eikonal or ray limit of maxwell s equations in a transparent medium are considered . the case of a beam of light whose propagation direction and polarisation state are both subject to change is dealt with , attention being paid to the validity of maxwell s equations at all stages .","abstract":"we present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics . important physical situations taken from scalar wave optics , pure polarisation optics , and the behaviour of polarisation in the eikonal or ray limit of maxwell s equations in a transparent medium are considered . the case of a beam of light whose propagation direction and polarisation state are both subject to change is dealt with , attention being paid to the validity of maxwell s equations at all stages . global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas , and the effects on geometric phases are elucidated . +  _ ocis codes _ : ( 030.1640 ) coherence ; ( 350.5500 ) propagation ; ( 260.5430 ) polarization"}
{"article_id":"1312.3987","section_id":"c","document":"we hope to have shown that in all geometric phase considerations in the domain of classical optics , the mathematical framework of quantum mechanics is adequate and flexible enough to provide a basis for the entire analysis . this is so in scalar wave , pure polarisation , as well as beam propagation problems . we have attempted to provide a clear physical picture of the situations being considered , fully tracing the phenomena ultimately to maxwell s equations in every case . the relevance of global topological aspects when discussing propagation direction and polarisation state simultaneously was pointed out in @xcite . in our treatment we have addressed these using elementary group theoretical arguments relevant to the situation  leading , in our view , to particularly simple and elegant results . the approach of this work now needs to be extended to other situations where , in place of a narrow beam endowed with polarisation properties , an extended polarised wave field in space is contemplated . this and other similar extensions will be taken up elsewhere .","summary":"we present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics .","abstract":"we present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics . important physical situations taken from scalar wave optics , pure polarisation optics , and the behaviour of polarisation in the eikonal or ray limit of maxwell s equations in a transparent medium are considered . the case of a beam of light whose propagation direction and polarisation state are both subject to change is dealt with , attention being paid to the validity of maxwell s equations at all stages . global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas , and the effects on geometric phases are elucidated . +  _ ocis codes _ : ( 030.1640 ) coherence ; ( 350.5500 ) propagation ; ( 260.5430 ) polarization"}
{"article_id":"hep-th0209161","section_id":"i","document":"the derived category approach to b - type d - branes @xcite appears to be extremely powerful . it allows one to go beyond the picture of d - branes as vector bundles over submanifolds so that @xmath0-corrections can be correctly understood . for example , the fact that b - type d - branes must undergo monodromy as one moves about the moduli space of complexified khler forms can be expressed in the derived category language @xcite . the main purpose of this paper is to try to classify which d - branes can become massless at a given point in the moduli space . again the language of derived categories will be invaluable .    in order for an object in the bounded derived category of coherent sheaves to represent a d - brane it must be `` @xmath1-stable '' . criteria for @xmath1-stability have been discussed in @xcite although it is not clear that we yet have a mathematically rigorous algorithm for determining stability . despite this , in simple examples such as in the above references and @xcite one can compute stability with a fair degree of confidence . in particular if you have reason to believe that a certain set of a d - branes are stable at a given point in the moduli space then one can move along a path in moduli space and see how the spectrum of stable states changes . there is considerable evidence @xcite that such changes in @xmath1-stability depend only on the homotopy class of the path in the moduli space of conformal field theories . the fact that changes in @xmath1-stability _ do _ depend on the homotopy class of such paths was used in @xcite to `` derive '' kontsevich s picture of monodromy at least in the case of the quintic  threefold .    the moduli space of conformal field theories may be compactified by including the `` discriminant locus '' consisting of badly - behaved worldsheet theories . typically one expects such theories to be bad because some d - brane has become massless @xcite . indeed , the monodromy seen in @xcite around parts of this discriminant locus was intimately associated to massless d - branes . it is this link between massless d - branes and monodromy that we wish to study more deeply in this paper . in simple cases as one approaches a point in the discriminant locus , a single d - brane becomes massless . of more interest to us is the case where an infinite number become massless .    in @xcite one of the authors studied components of the discriminant locus corresponding to what was called `` ez - transformations '' . namely if one has a  threefold @xmath2 with some complex subspace @xmath3 , there may be a point in khler moduli space where @xmath3 collapses to a complex subspace @xmath4 of lower dimension than @xmath3 . we will see that it is then _ the derived category of @xmath4 _ that describes the massless d - branes associated to this transformation . a particular autoequivalence was naturally associated to a particular ez - transformation and it was conjectured in @xcite that such an autoequivalence resulted from the associated monodromy . we will call this conjecture the `` ez - monodromy conjecture '' . one purpose of this paper is to justify this conjecture . because of the nature of our understanding of d - branes and string theory it will not be possible to rigorously _ prove _ any hard theorems about d - branes . instead we will have to play with a number of conjectures whose interdependence leads to considerable evidence of the validity of the overall story . in particular , on the one hand we have the ez - monodromy conjecture and , on the other hand , we have our conjecture concerning which d - branes become massless . these two conjectures are interlinked by @xmath1-stability as we discuss in section [ s : mon ] . in particular , in section [ ss : single ] we discuss an older conjecture concerning single massless d - branes . in section [ ss : gen ] we then review a framework for the more general case which is linked to the simpler case in section [ ss : new ] for a particular example . the physical interpretation of the general case is then given in section [ ss : int ] . the link discussed in section [ ss : new ] between the simple case of a single d - brane becoming massless and an infinite number becoming massless depends upon a mathematical result which is derived in section [ s : comp ] . this section is more technical than the other sections and may be omitted by the reader if need be . that said , it shows how the sophisticated methods of derived categories are directly relevant to the physics of d - branes .    in section [ s : app ] we discuss a natural hierarchy of cases . the familiar `` conifold''-like situation arises where @xmath4 is a point and only one soliton becomes massless . if @xmath4 has dimension one then the derived category of @xmath4 has more structure . this case corresponds to seiberg  witten theory of some nonabelian gauge group . we study an explicit example of this elsewhere @xcite . the case where @xmath4 has complex dimension two is more complicated as the derived category now has a rich structure . we show that it appears to be similar to the spectrum of massless d - branes one gets from a decompactification . we also see that it demonstrates how 2-branes wrapped around a 2-torus can become massless . at first sight this appears to contradict t - duality but we will see that this is not actually the case .    finally , for completeness , in section [ ss : exof ] we discuss the case of an exoflop which is awkward to fit into our general classification but still yields a simple result .","summary":"we analyze the link between the occurrence of massless b - type d - branes for specific values of moduli and monodromy around such points in the moduli space . this allows us to propose a classification of all massless b - type d - branes at any point in the moduli space of s . our analysis is based on using monodromies around points in moduli space where a single d - brane becomes massless to generate monodromies around points where an infinite number become massless . we discuss the various possibilities within the classification .    0","abstract":"we analyze the link between the occurrence of massless b - type d - branes for specific values of moduli and monodromy around such points in the moduli space . this allows us to propose a classification of all massless b - type d - branes at any point in the moduli space of s . this classification then justifies a previous conjecture due to horja for the general form of monodromy . our analysis is based on using monodromies around points in moduli space where a single d - brane becomes massless to generate monodromies around points where an infinite number become massless . we discuss the various possibilities within the classification .    0"}
{"article_id":"math0607480","section_id":"i","document":"for a fibration of compact manifolds @xmath0 where the fibre is a compact manifold with boundary , the cobordism of the index can be interpreted as the vanishing of the ( suspended ) family index for the boundary @xmath1 on the image of the restriction map @xmath2 this was realized analytically in @xcite in terms of cusp pseudodifferential operators , namely that any elliptic family of cusp pseudodifferential operators can be perturbed by a family of order @xmath3 to be invertible ; this is described as the universal case in @xcite . for the odd version of and in the special case of dirac operators , dai and freed in @xcite , showed that the @xmath4 ( i.e. exponentiated @xmath5 ) invariant of a self - adjoint dirac operator on an odd dimensional compact oriented manifold with boundary , with augmented atiyah - patodi - singer boundary condition , defines an element of the inverse determinant line for the boundary dirac operator . here we give a full pseudodifferential version of this , showing that the @xmath4 invariant for a suspended ( hence ` odd ' ) family of elliptic cusp pseudodifferential operators , @xmath6 trivializes the determinant bundle for the indicial family @xmath7 @xmath8 which in this case is a doubly - suspended family of elliptic pseudodifferential operators ; the relation to the dirac case is discussed in detail . this paper depends substantially on @xcite where the determinant on @xmath9 times suspended smoothing families is discussed . this determinant in the doubly suspended case is used to define the determinant bundle for any doubly - suspended elliptic family of pseudodifferential operators on a fibration ( without boundary ) . as in the unsuspended case ( see bismut and freed @xcite ) , the first chern class of the determinant bundle is the 2-form part of the chern character of the index bundle . the realization of the eta invariant for singly suspended invertible families in @xcite is extended here to the case of invertible families of suspended cusp operators . in the dirac case this is shown to reduce to the eta invariant of atiyah , patodi and singer for a self - adjoint dirac operator with augmented aps boundary condition .    in the main body of the paper the consideration of a self - adjoint dirac operator , @xmath10 is replaced by that of the suspended family , generalizing @xmath11 where @xmath12 is the suspension variable . this effectively replaces the self - adjoint fredholm operators , as a classifying space for odd k - theory , by the loop group of the small unitary group ( see @xcite , p.81 ) . one advantage of using suspended operators in this way is that the regularization techniques of @xcite can be applied to define the eta invariant as an extension of the index . in order to discuss self - adjoint ( cusp ) pseudodifferential operators using this suspension approach , it is necessary to consider somewhat less regular ( product - type ) families , generalizing @xmath13 so we show how to extend the analysis to this larger setting .    as in @xcite , we introduce the various determinant bundles in a direct global form , as associated bundles to principal bundles ( of invertible perturbations ) instead of using the original spectral definition of quillen @xcite . in this way , the fact that the @xmath4 invariant gives a trivialization of the determinant bundle follows rather directly from the log - multiplicative property @xmath14 of the eta invariant . the paper is organized as follows . in section  [ cs.0 ] , we review the main properties of cusp operators . in section  [ ld.0 ] , we consider a conceptually simpler situation which can be thought as an ` even ' counterpart of our result . in section  [ detb ] , we present the determinant bundle as an associated bundle to a principal bundle ; this definition is extended to family of @xmath9-suspended elliptic operators in section  [ 2n - sus ] . this allows us in section  [ totdlb ] to rederive a well - known consequence of the cobordism invariance of the index at the level of determinant bundles using the contractibility result of @xcite . in section  [ tsc.0 ] , we introduce the notion of cusp suspended @xmath15-algebra , which is used in section  [ lifting ] to lift the determinant from the boundary . this lifted determinant is defined using the eta invariant for invertible suspended cusp operators introduced in section  [ eta - inv ] . in section  [ tdb.0 ] , we prove the trivialization result and in section  [ diracfami ] we relate it to the result of dai and freed @xcite for dirac operators . finally , in section  [ asg.0 ] , these results are extended to include the case of a self - adjoint family of elliptic cusp pseudodifferential operators . this involves the use of product - type suspended operators , which are discussed in the appendix .","summary":"cobordism invariance shows that the index , in k - theory , of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration . for dirac operators with spectral boundary condition , dai and freed gave an explicit version of this at the level of the determinant bundle .","abstract":"cobordism invariance shows that the index , in k - theory , of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration . for dirac operators with spectral boundary condition , dai and freed gave an explicit version of this at the level of the determinant bundle . their result , that the eta invariant of the interior family trivializes the determinant bundle of the boundary family , is extended here to the wider context of pseudodifferential families of cusp type ."}
{"article_id":"cond-mat9608081","section_id":"i","document":"the experimental study of tunneling through zero - dimensional states in quantum dots with high charging energies has received recently considerable interest @xcite . theoretical studies cover the classical regime ( high temperatures ) @xcite as well as the quantum - mechanical regime ( low temperatures ) @xcite . in the latter case , coulomb blockade and resonant - tunneling phenomena together with nonequilibrium generalizations of the kondo effect are expected to occur . this leads to zero - bias anomalies in the differential conductance , which recently have been observed by ralph & buhrman @xcite . in this article , we present a new real - time diagrammatic approach to describe resonant tunneling at low temperatures and compare our results to the latter experiment . the experiments for coulomb blockade phenomena in zero - dimensional systems are usually performed in double - barrier resonant - tunneling structures @xcite , split - gate quantum - dot devices @xcite , quantum point - contacts with single - charge trap states @xcite and quite recently also in ultrasmall metallic tunnel junctions @xcite with al particles of diameter below @xmath1 . in the latter experiment , the level spacing is of order @xmath2 which is comparable to the coulomb charging energy in usual quantum dots . therefore , the quantum dot is described by the nonequilibrium anderson model where the energy level @xmath3 ( with spin label @xmath4 ) is coupled via tunneling barriers to two electron reservoirs with different electrochemical potentials @xmath5 and @xmath6 . the charging energy is described by a strong on - site coulomb repulsion @xmath7 which suppresses double occupancy of the dot level . in equilibrium , it is well known from the theory of strongly correlated fermions @xcite that the spectral density of the dot can exhibit a kondo resonance at the fermi level . it occurs for a low lying level @xmath8 and weak zeeman splitting @xmath9 , where @xmath10 is the level width in the noninteracting case , and provided that temperature is lower than the kondo temperature @xcite @xmath11}$ ] . since the weight of the equilibrium spectral density at the fermi level is proportional to the linear conductance , an enhancement of the latter due to kondo - assisted tunneling was predicted @xcite . typical values for quantum dots are @xmath12 and @xmath13 which , for @xmath14 , yield a kondo temperature of the order @xmath15 . due to heating effects such temperatures are still hard to realize in realistic dots . a more pronounced feature was found for the nonlinear conductance which shows a zero - bias maximum even for temperatures above the kondo temperature @xcite . at zero magnetic field the spectral density of each spin channel exhibits a kondo resonance at each of the chemical potentials . an applied magnetic field causes the kondo peaks to shift from the chemical potential by the zeeman energy , in opposite directions for the different spin channels . as a consequence , kondo - assisted tunneling can only occur if the bias voltage exceeds the zeeman energy . therefore , the zero - bias anomaly is split by an applied magnetic field @xcite . these features have been observed experimentally by ralph & buhrman @xcite . they measured the differential conductance through single - charge traps in a metallic quantum point - contact . although this system does not allow a controlled variation of the level position , the appearance of a zero - bias maximum with a peak height varying logarithmically with temperature clearly demonstrates the mechanism of kondo - assisted tunneling . however , the detailed comparison of the line shape in the experiment and the existing theory showed significant deviations .    in this paper , we will describe a new approach to calculate nonequilibrium properties of strongly correlated mesoscopic systems coupled to fermionic or bosonic baths via particle and energy exchange . it consists in a real - time diagrammatic approach closely related to path - integral methods formulated in connection with dissipation @xcite or tunneling in metallic junctions @xcite . one of the difficulties of the present problem lies in the fact that we have to account for the coulomb interaction in a nonperturbative way . therefore , the standard many - body diagrammatic approaches are not sufficient ( since wick s theorem can not be applied naively ) . we circumvent the problem by keeping track explicitly of the time evolution of the density matrix of the dot and tracing out only the bath degrees of freedom , which are assumed to be in equilibrium . the final diagrammatic language is set up by an expansion in the coupling to the fermionic reservoirs whereas the strong correlations on the local system are exactly taken into account . the basic step is the calculation of transition and current rates between different states of the dot . we present an exact expression for these rates as the sum over all irreducible diagrams . the transition rate is used to set up a formally exact master equation from which the time - dependent probability distribution for the dot can be calculated . the current rate is generally not identical to the transition rate since it contains also the number of particles transferred to the reservoir where the current is calculated . this number can take arbitrary values if one considers all higher order processes . the occupation probabilities multiplied with the current rates are used to calculate the current flowing through the system . in earlier publications , we have presented this technique in connection with tunneling through a metallic island with a continuum of states @xcite and demonstrated the equivalence to path - integral methods @xcite . there we used an approximation for the rate to sum up `` inelastic resonant tunneling '' processes to arbitrary order where different electrons tunnel coherently back and forth between the island and the reservoirs . here , we apply an equivalent approximation to describe resonant tunneling between metallic leads through an ultrasmall quantum dot with a single level . an important advantage of our approach is that we can solve the noninteracting limit exactly and can control systematically if this limit is contained within a given approximation for the correlated case . the theory is current conserving and can be used for the calculation of correlation functions or green s functions as well .    for the case where the dot level is @xmath16-fold degenerate we recover for @xmath17 and a low lying dot level a kondo peak in the spectral function . an applied transport voltage leads to a splitting of the kondo peak ( at @xmath18 where @xmath19 denotes the lead ) , which results in a zero - bias anomaly in the differential conductance , such that the conductance has a maximum at @xmath20 . on the other hand , if the dot level lies above the fermi levels of the leads @xmath18 we predict @xcite a zero - bias anomaly in the conductance which has a minimum at @xmath20 .    several extensions will be considered . we study the case where the ( spin- ) degeneracy of the dot level is lifted , e.g. , by an applied magnetic field . in this case the kondo peaks of both spin channels move apart from each other by the level spacing @xmath21 , and kondo - assisted tunneling sets in only at transport voltages @xmath22 exceeding this splitting . the calculated conductance agrees well with the experimental results of ref .  . we , furthermore , account for inelastic interactions with bosonic modes coupled to the dot . they describe applied time - dependent fields , interaction with phonons , or the fluctuations in the electrodynamic environment . the investigation of this field has started only recently in connection with transport through interacting quantum dots . the classical regime ( @xmath23 ) has been analyzed for time - dependent fields @xcite and bosonic environments @xcite . photon- and boson - assisted tunneling leads here to resonant side peaks in the coulomb oscillations which can be used to analyze the complete excitation spectrum of the dot . the results agree well with experiments @xcite . in the kondo regime it has been found @xcite that time - dependent perturbations split the kondo resonances which leads to satellite anomalies in the differential conductance and offers the possibility to realize pump effects which are purely based on the presence of kondo resonances . the linear ac - conductance has been analyzed in ref .  . in this paper , we will investigate the influence of an external bosonic field on transport phenomena through ultrasmall quantum dots at low temperatures and small boson frequencies ( compared to @xmath24 ) . the emission and absorption of bosons causes additional kondo singularities , for a one - mode field at @xmath25 , where @xmath26 . again , these resonances lead to corresponding anomalies in the differential conductance , which are inverted if the level position of the dot is moved through the fermi energy .","summary":"this leads to zero - bias anomalies in the differential conductance , which agree well with recent experimental results for the electron transport through single - charge traps . furthermore , we predict that the sign of the zero - bias anomaly depends on the level position relative to the fermi level of the leads .   ","abstract":"we study resonant tunneling through a single - level quantum dot in the presence of strong coulomb repulsion beyond the perturbative regime . the level is either spin - degenerate or can be split by a magnetic field . we , furthermore , discuss the influence of a bosonic environment . using a real - time diagrammatic formulation we calculate transition rates , the spectral density and the nonlinear characteristic . the spectral density shows a multiplet of kondo peaks split by the transport voltage and the boson frequencies , and shifted by the magnetic field . this leads to zero - bias anomalies in the differential conductance , which agree well with recent experimental results for the electron transport through single - charge traps . furthermore , we predict that the sign of the zero - bias anomaly depends on the level position relative to the fermi level of the leads .   "}
{"article_id":"cond-mat9608081","section_id":"r","document":"what we have done so far is to derive a diagrammatic language which allows a systematic description of transport processes . we have , furthermore , shown how the physical quantities of interest , the stationary probability distribution and the current , can be obtained if we know the value of special diagrams . in this section , now , we will explicitly calculate the value of the corresponding diagrams . we consider here the case of strong coulomb repulsion @xmath7 , i.e. , we restrict ourselves to the states with @xmath62 . diagrams in which a higher occupancy occurs do not contribute since they have resolvents of the order @xmath213 .    in the following , the index @xmath4 labels the singly occupied state with spin @xmath214 . the label @xmath127 additionally allows an empty dot , @xmath215 .    in general , we can not sum up _ all _ possible diagrams therefore , we have to find a systematic criterion which diagrams should be retained and summed .    the simplest approximation is to neglect all diagrams where two or more tunneling lines overlap in time ( see the leftmost diagram parts in fig .  [ fig1 ] ) . this means we include those processes which are also described by the master equation with rates obtained in lowest order perturbation theory ( sequential tunneling ) , which is a good description at high temperature , @xmath216 .    in situations when sequential tunneling is suppressed by coulomb blockade , the lowest order contribution to the current arises due to cotunneling . the rates for a process in which an electron enters the dot from the left lead and leaves to right one is described by diagrams with two overlapping lines ( see the diagram part in the middle of fig . [ fig1 ] ) .    at lower temperature the perturbative approach is not sufficient . higher - order processes become important . in generalization to cotunneling we have to take into account irreducible diagrams with an arbitrary number of correlated tunneling processes , i.e. , we include resonant tunneling . similar to the case of metallic islands @xcite we proceed in a conserving approximation , taking into account non - diagonal matrix elements of the total density matrix up to the difference of one electron - hole pair excitation in the leads . the graphical representation of this constriction is that only diagrams in which any vertical line will cut at most two tunneling lines are taken into account . we give two arguments why this class of diagrams is the most important one . firstly , since we treat the leads as large equilibrium reservoirs there should be a tendency of the system to stay close to diagonal states . secondly , our approximation contains the exact solution for the noninteracting limit @xmath217 : if there is no electron - electron interaction in the dot , electrons with different spin do not influence each other , so that this limit is described within our model by choosing @xmath218 . in this case , the selected diagrams are the only contributing ones . the sum of all other , more complicated , diagrams is zero . furthermore , we include only boson lines between vertices which are already connected by tunneling lines , i.e. , @xmath219 where the pairs @xmath220 are already coupled by tunneling lines running from @xmath221 to @xmath142 . this amounts to a dressing of the tunneling lines @xmath222 . this approximation , while neglecting many diagrams , describes well the spectral density of the dot at resonance points . the reason is that position and value of the peaks of the spectral density are determined by a self - energy @xmath4 ( see eq . ( [ sigma2 ] ) ) which is calculated here in lowest order perturbation theory in @xmath24 including the bosons . higher orders are small for high tunnel barriers . first , we relate the rate @xmath181 to an irreducible diagram labeled by @xmath223 ( see fig . [ fig.phi ] ) . it has an open tunneling line associated with tunneling of an electron with spin @xmath4 in the junction @xmath19 carrying the energy @xmath71 . the line is directed from the right to the left and its value together with the corresponding resolvent is included in @xmath224 . the self - energy is then constructed by attaching the open tunneling line of these diagrams to the upper and lower propagator ( see fig .  [ sigmaphi ] ) with the result @xmath225 where the current rates @xmath226 correspond to the first and second term , respectively . again we have made use of the fact that a diagram becomes the conjugate complex if we change the vertical position of all vertices and the direction of all tunneling and boson lines . as pointed out in appendix  [ append proof ] , any approximation for @xmath224 will lead to a current conserving theory . we construct the diagram @xmath224 by iteration ( see figs . [ phidot1 ] and [ phidot2 ] ) . to do so , we need the diagram @xmath227 which is the propagator @xmath227 while a tunneling line with energy @xmath71 is running in parallel from the right to the left . this diagram can also be expressed as an iteration in the style of a dyson equation ( see fig .  [ fig.dyson2 ] ) @xmath228    in analogy to @xmath166 , the self - energy @xmath229 denotes the sum of all irreducible diagrams with a tunneling line going backward in time . here , the free propagator in energy space is given by @xmath230 hence , we can solve eq . ( [ pi - dyson ] ) and find in matrix notation the general relation @xmath231^{-1 } - \\sigma(e)]^{-1 } \\ , .\\ ] ]    because of the restriction to two charge states , only the matrix elements @xmath232 of @xmath233 and @xmath234 of @xmath229 are involved , and we deduce from eq . ( [ pi ] ) @xmath235 since at most two tunneling lines are allowed at once , the irreducible self - energy @xmath236 consists of only one tunneling line . we calculate all contributions , which are depicted in fig . [ somegadot ] , and get @xmath237 in the spin degenerate case , this is exactly the relation ( [ sigma ] ) which we found from intuitive arguments .    according to our rules , figs . [ phidot1 ] and [ phidot2 ] lead to the self - consistent equation for the diagram @xmath238 @xmath239\\end{aligned}\\ ] ] and @xmath240\\,\\,\\end{aligned}\\ ] ]    the stationary probabilities and the current are derived from eqs . ( [ stationary master ] ) and ( [ stationary current ] ) . to calculate the rates we specify eq . ( [ partial rates ] ) and obtain @xmath241 whereas all other rates are zero . the correlation functions can be calculated from the diagrams shown in figs . [ cdotgr ] and [ cdotkl ] . we have to consider only the latest ( i.e. rightmost ) correlated part of the diagram . the processes before end up with probability @xmath242 in a diagonal state @xmath127 . we have used the same criterion as for the calculation of the density matrix with one exception . if a vertical line lies between the external vertices we allow a cut through at most one tunneling line . here we have used the fact that such a vertical line will in addition always cut the virtual line connecting the external vertices . the sum of all these diagrams gives ( where we can combine always two diagrams to the imaginary part of one of them ) @xmath243 with @xmath244\\right\\ }      \\\\ \\label{correlation function2 }      \\bar{g}_\\sigma^<(e)&=&-2i\\,\\mbox{im}\\left\\{\\pi^\\sigma ( e ) \\left [      p_{\\sigma}^{st } +      \\sum_\\alpha \\int \\ , de'{p_0^{st}{\\phi^*}^{0,\\sigma}_{0,0 }      ( \\alpha,\\sigma , e ' )      + \\sum_{\\sigma'}p_{\\sigma'}^{st}{\\phi^*}^{\\sigma',\\sigma}_{\\sigma',0 }      ( \\alpha,\\sigma , e ' )      \\over e - e'+i0^+ } \\right ] \\right\\}\\ , .\\end{aligned}\\ ] ]    in the following , we discuss for transparency the effect of the coupling to bosons and the presence of a magnetic field separately . for zero magnetic field , i.e. @xmath245 for all @xmath4 , we can perform the resummation of the corresponding diagrams for the rates and the green s functions analytically ( details are given in appendix  [ append boson ] ) and find @xmath246\\,|\\pi ( e)|^2\\,\\ ] ] with @xmath247 . we can write this equation in a more intuitive way by inserting the definition ( [ gamma ] ) for @xmath248 @xmath249 where @xmath250 can be interpreted as a transmission probability for an electron to start from reservoir @xmath19 with energy @xmath71 and end in reservoir @xmath251 with energy @xmath252 . from the detailed balance condition ( [ detailed balance ] ) we get @xmath253 this guarantees that the current is zero if all chemical potentials of the reservoirs are identical .    however , the interpretation of @xmath254 as a one - particle transmission probability in analogy to a generalization of the landauer - bttiker formula to inelastic interactions @xcite is not correct . we see that the transmission probability still depends on the fermi distribution functions via the self - energy @xmath255 in the denominator of the propagator @xmath227 . this reflects the many - particle aspect of the electron - electron and electron - boson interaction in our model . comparing our result for @xmath254 with other approaches in the case @xmath218 @xcite , we see that the energy dependence of @xmath229 has been neglected in all previous treatments . we find that even in the @xmath218 case , the energy dependence of @xmath229 can not been neglected if the temperature @xmath96 and the typical frequency @xmath256 of the bosons are smaller than @xmath24 .    without bosons , the current formula is exact up to order @xmath257 , i.e. , sequential and electron cotunneling are fully taken into account . with bosons , cotunneling is not described correctly since we have treated the bosons only by a dressing of the tunneling lines . this means that our approximation is not valid in regions where the current is very small . however , at resonance we believe our treatment to be correct since there we expect that sequential tunneling will be just modified by a renormalization and broadening of the local state of the dot which is described by the self - energy @xmath255 which is calculated in lowest order in @xmath24 here . higher orders will be small for high tunneling barriers . finally , we calculate the green s functions and find @xmath258 in equilibrium , i.e. @xmath259 for all @xmath19 , we obtain the correct sum rule @xmath260 . furthermore , for the @xmath218 case , particle - hole symmetry is satisfied . the spectral density has the form @xmath261 |\\pi(e')|^2\\ , . \\label{spec}\\ ] ] the effect of the resonant - tunneling processes is described by the resolvent @xmath233 containing the self - energy @xmath229 , eq . ( [ sigma2 ] ) . the real and imaginary part of the self - energy express energy renormalization and broadening and determine , therefore , the position and the width of the maxima in the spectral density .    to proceed we consider from now on a one - mode environment ( einstein model ) with boson frequency @xmath262 . experimentally realizations of this model are optical phonons @xcite or by fluctuations of an external @xmath263-circuit with frequency @xcite @xmath264 . the results for a general environment can be anticipated approximately from the one - mode case by a superposition . furthermore , we choose the special case of two reservoirs @xmath265 and constant level broadening @xmath266 .    defining @xmath267 we obtain @xmath268 , where @xmath269 is the probability for the emission of @xmath270 bosons with frequency @xmath256 . here , @xmath271 is the bose function and @xmath272 the modified bessel function . using eq . ( [ sigma2 ] ) we obtain @xcite @xmath273 } \\label{resigma}\\ ] ] @xmath274 \\ , .\\ ] ] here @xmath275 denotes the digamma function , and we have chosen in the energy integrals a lorentzian cut - off at @xmath276 .    the real part of @xmath229 renormalizes the level position to higher energies . furthermore , it depends logarithmically on energy , temperature , voltage and frequency . these logarithmic terms are typical for the occurrence of kondo peaks . hence , we anticipate logarithmic singularities either for @xmath17 or for @xmath277 . this includes not only the degenerate case but also the case of a single dot level without spin ( @xmath218 ) since the probabilities for absorption and emission of bosons are different . it is important to remark here , that for systems coupled to classical time - dependent fields@xcite the situation is different since then both probabilities are equal . at low enough temperatures we obtain logarithmic peaks in @xmath229 at @xmath278 ( @xmath279 for @xmath218 ) . they lead to maxima of the resolvent @xmath233 at @xmath278 ( @xmath280 for @xmath218 , @xmath281 for @xmath282 ) for @xmath283 and at @xmath278 ( @xmath284 ) for @xmath285 . the spectral density ( [ spec ] ) shows resonances at the same points but , due to the additional @xmath286 functions in the integrand , they are shifted by multiples of @xmath256 . this boson - assisted tunneling is completely independent from the influence of the bosons on the self - energy @xmath229 .    the spectral density at different voltages for a low lying level @xmath287 is depicted in fig .  [ fig2 ] . without an applied bias voltage , we obtain ( for @xmath288 ) the usual kondo peak near the fermi level ( which we choose as zero energy ) . the emission of bosons leads to additional resonances at multiples of @xmath256 . for @xmath218 and @xmath283 , resonances occur for negative energies and in the case @xmath285 we find resonances at positive energies . in these cases , the effects are less pronounced and are only visible for very low temperatures . at finite bias voltages all peaks split and decrease in magnitude . the resonances in the spectral density can be probed by the nonlinear differential conductance as function of the bias voltage @xmath289 , as shown in fig . [ fig3 ] for the case @xmath287 . the splitting of the kondo peak leads to an overall decrease of the spectral density in the energy range @xmath290 ( see inset of fig .  [ fig3 ] ) . for this reason , the conductance shows the well - known @xcite maximum at zero bias . the emission of bosons produces a set of symmetric satellite maxima . they can be traced back to the fact that pairs of kondo peaks can merge if the bias voltage is a multiple of the boson frequency ( see fig . [ fig2 ] ) . this gives rise to pronounced kondo peaks at @xmath291 and thus to an increase of the spectral density with bias voltage near these points . [ fig4 ] shows the differential conductance for @xmath292 with and without bosons . a striking result is that the whole structure is inverted compared to the case @xmath283 , and we find a zero - bias anomaly although the kondo peak at zero energy is absent . the coupling to bosons yields satellite steps at @xmath293 . the contributions of sequential and cotunneling lead , compared to resonant tunneling , only to a weak bias voltage dependence of the differential conductance . this shows clearly that the influence of the logarithmic terms in @xmath229 are still important . the logarithmic peaks in @xmath294 decrease with increasing bias voltage and approach the value of @xmath295 if @xmath296 is large enough . thus the value of @xmath297 decreases which in turn leads to an overall increase of the resolvent @xmath233 and the spectral density @xmath298 near zero energy ( see the inset of fig . [ fig4 ] ) . zero - bias minima are known from kondo scattering from magnetic impurities . @xcite they have been observed in recent experiments @xcite and have been interpreted as 2-channel kondo scattering from atomic tunneling systems @xcite or by tunneling into a disordered metal . @xcite here we have shown that zero - bias minima can also arise due to resonant tunneling via local impurities if the level position is high enough such that we are in the mixed valence regime . finally , we have investigated the differential conductance at fixed bias voltage as function of the position of the dot level , which experimentally can be varied by a gate voltage coupled capacitively to the dot ( see fig .  [ fig5 ] ) . the result shows a ( classical ) pair of peaks at @xmath299 together with satellites ( due to emission and absorption of bosons ) and peaks for @xmath300 ( only due to absorption ) . the energy dependence of @xmath301 gives rise to an asymmetry of the peak heights . the peak at @xmath302 is higher than the one at @xmath303 since @xmath304 is smaller for higher energies ( except for @xmath218 when particle - hole symmetry holds ) . this significant effect is due to the broadening of the spectral density by quantum fluctuations .      in this section we discuss the effect of an applied magnetic field and do not take into account the coupling to bosons . again we consider the case of two reservoirs and constant level broadenings . since the energy levels @xmath305 are now spin dependent , we can no longer solve the self - consistent equations analytically but have to solve them numerically . we find kondo resonances in the spectral density @xmath306 at energies @xmath307 with @xmath308 . this is due to the fact , that the correlation functions @xmath309 and @xmath310 are mainly determined by the resolvent @xmath311 ( see eqs . ( [ correlation function1 ] ) and ( [ correlation function2 ] ) ) which contains via the self - energy @xmath236 logarithmic singularities at the corresponding energies , @xmath312 }      \\\\ \\mbox{im}\\ , \\sigma^\\sigma(e)&=&-\\pi \\left [ \\bar{\\gamma}^-(e )      + \\sum_{\\sigma ' } \\bar{\\gamma}^+(e+\\epsilon_{\\sigma'}-\\epsilon_\\sigma )      \\right ] \\ , .\\end{aligned}\\ ] ]    from eq . ( [ strom ] ) we see that only energies within the window defined by the difference of the fermi functions contribute to the current . for this reason , there is no kondo - assisted tunneling at low transport voltage but sets on if transport voltage and level splitting are equal . therefore , for low lying levels the conductance peak at zero bias found in the previous section now splits up into two peaks separated by the twice the level splitting @xcite ( see fig .  [ fig.experiment ] ) . ralph and buhrman recently measured kondo - assisted tunneling via a single charge trap of a point contact tunnel barrier.@xcite we follow the model proposed by the authors interpretating the experiment as a realization of the anderson model with strong coulomb repulsion such that double occupancy does not occur . however we think that the interaction energy @xmath7 and not the conduction band width is the relevant cut - off in this situation . a comparison of the experiment and our theory is given in fig . [ fig.experiment ] , fig . [ fig.expgross ] and fig . [ fig.exptemp ] . we find a good agreement for the peaks induced by kondo - assisted tunneling processes if we set the cut - off @xmath313 . the authors suspect the single - charge trap to be a dangling bond , for which they expect @xmath314 . our result agrees in the order of magnitude , it gives a hint however , that the state may have a larger extension than an ordinary dangling bond or that there is screening due to the copper electrodes or both . the peaks for larger magnetic fields show , however , a stronger broadening than predicted from our calculation . nevertheless , our theory reproduces the experimental curves much better than the fits given in ref . using perturbation theory since we have taken into account nonperturbative effects which are obviously important here .    the model proposed by the authors of ref . explains the broad peaks at large voltages by the matching of the energies of the empty and the singly occupied dot . our calculations for this case , however , lead to a broader and lower peak for positive voltages in comparison with experiment ( see fig .  [ fig.expgross ] ) . we think , therefore , that due to the capacitance asymmetry the system becomes doubly occupied before the empty state is energetically favorable . the capacitance asymmetry @xmath51 makes then the corresponding resonance peak sharper . an energy dependent transparency of the barriers could then explain the different heights . a generalization of our theory to situations , where multiple occupancy of the dot is important , is currently under way and will be presented elsewhere . finally , we consider the case when the energy level is above the fermi energies of the leads . the zero - bias minimum found in the previous section splits for finite magnetic field into two minima separated by twice the level splitting ( see fig .  [ fig.minimum ] ) .","summary":"we study resonant tunneling through a single - level quantum dot in the presence of strong coulomb repulsion beyond the perturbative regime . the spectral density shows a multiplet of kondo peaks split by the transport voltage and the boson frequencies , and shifted by the magnetic field .","abstract":"we study resonant tunneling through a single - level quantum dot in the presence of strong coulomb repulsion beyond the perturbative regime . the level is either spin - degenerate or can be split by a magnetic field . we , furthermore , discuss the influence of a bosonic environment . using a real - time diagrammatic formulation we calculate transition rates , the spectral density and the nonlinear characteristic . the spectral density shows a multiplet of kondo peaks split by the transport voltage and the boson frequencies , and shifted by the magnetic field . this leads to zero - bias anomalies in the differential conductance , which agree well with recent experimental results for the electron transport through single - charge traps . furthermore , we predict that the sign of the zero - bias anomaly depends on the level position relative to the fermi level of the leads .   "}
{"article_id":"cond-mat9608081","section_id":"c","document":"in conclusion , we have studied low - temperature transport in the nonequilibrium anderson model with bosonic interactions . the latter yield new kondo resonances in the spectral density which can be probed by the measurement of the nonlinear differential conductance . both the gate and bias voltage dependence are important . quantum fluctuations due to resonant tunneling yield zero - bias anomalies as function of the bias voltage , _ which can be changed from maxima to minima by varying the gate voltage_. we , furthermore , discussed the splitting of the zero - bias anomaly by an external magnetic field and found good agreement with recent experiments . we have presented a real - time approach which is based on a nonperturbative calculation of transition rates between different states of a local strongly correlated system coupled to fermionic or bosonic baths . we present systematic rules of how to set up well defined perturbation expansions for the rates in terms of the tunneling matrix elements between dot and leads . the formally exact rates are used to calculate occupation probabilities and the current from master equations and current formulas which are intuitively obvious . the method has a wide applicability , ranging from the study of arbitrary dot level structures up to the investigation of macroscopic quantum coherence phenomena . the latter can arise from the time evolution of non - stationary initial states or by the application of explicitly time - dependent fields . the usage of real - time methods to understand low - temperature behavior of strongly correlated fermions either in equilibrium or non - equilibrium situations is a rather new field and has not yet been applied extensively . compared with the conventional methods in imaginary time @xcite they offer the possibility to set up new approximation schemes . in this paper we have performed a nonperturbative resummation of higher order coherent tunneling processes to calculate transition and current rates analytically for temperatures smaller than the intrinsic broadening @xmath24 . although the criterium for considering certain diagrams is yet not motivated by the usage of a `` small '' parameter , the diagrams are selected in a systematic way . we have chosen all diagrams which keep the total density matrix as close as possible to the diagonal state up to one electron - hole pair excitation in the reservoirs . this reminds of techniques applied within variational wave function ansatzes @xcite but here formulated on the basis of density matrices for nonequilibrium systems at finite temperatures . furthermore , there are many possibilities to improve our approximation by considering more diagrams by analytical or numerical methods . simple limiting cases as e.g. the noninteracting case are already exactly incorporated within our approximation . since the strongly interacting case gives also at least qualitatively good results , our method may be a good candidate to cover the whole range from weak to strong interaction within the same approximation scheme . we like to thank d. averin , j. von delft and m. hettler for useful discussions . the support by the deutsche forschungsgemeinschaft , through sfb 195 , by the swiss national science foundation ( h.s . ) , and by the a.v.humboldt award of the academy of finland ( g.s . ) is gratefully acknowledged .","summary":"the level is either spin - degenerate or can be split by a magnetic field . we calculate transition rates , the spectral density and the nonlinear characteristic .","abstract":"we study resonant tunneling through a single - level quantum dot in the presence of strong coulomb repulsion beyond the perturbative regime . the level is either spin - degenerate or can be split by a magnetic field . we , furthermore , discuss the influence of a bosonic environment . using a real - time diagrammatic formulation we calculate transition rates , the spectral density and the nonlinear characteristic . the spectral density shows a multiplet of kondo peaks split by the transport voltage and the boson frequencies , and shifted by the magnetic field . this leads to zero - bias anomalies in the differential conductance , which agree well with recent experimental results for the electron transport through single - charge traps . furthermore , we predict that the sign of the zero - bias anomaly depends on the level position relative to the fermi level of the leads .   "}
{"article_id":"1504.02067","section_id":"i","document":"the ads / cft correspondence @xcite has become a prevalent new theoretical tool for understanding strongly  coupled , non  gravitational physics . its influence has extended beyond the realm of strict high energy physics , like understanding the quark  gluon plasma @xcite , into condensed matter systems . of interest are strongly  coupled charged fermionic systems , where it is hoped the low  energy physics can be studied via the correspondence ( see refs . @xcite ) . in particular , progress has been made in understanding fermi liquids ( fl ) , non  fermi liquids ( nfl ) and fractionalized fermi liquids ( fl * ) , phases of compressible metallic states of quantum matter @xcite . these different phases with finite charge density can be characterized in terms of their violation / agreement with the luttinger relation , which relates the total charge density @xmath1 to the volumes enclosed by the fermi surfaces at zero temperature . compressible states of matter with finite charge density dual to charged black holes @xcite violate the luttinger relation . however , holographic duals to metallic states , such as the electron star solutions of refs . @xcite , do satisfy the luttinger relation @xcite . the essential idea @xcite is that when the field theory charge density @xmath1 is dual to gauge - invariant fermions   mesinos \"  in the gravity bulk , their fermi surfaces do satisfy the luttinger relation and are said to have _ visible _ fermi surfaces . when the charge density is instead sourced by a charged horizon , then the fermi surfaces are said to be _ hidden _ , leading to a violation of the luttinger relation and thus describe  fractionalized \" charged degrees of freedom . in the case when there are both gauge  invariant fermions and a charged horizon in the bulk , like the solutions in ref . @xcite , then the phase is considered to be  partially fractionalized . \"    among the interesting questions posed about nfl and fl * phases is the issue of how to characterize the presence of fermi surfaces when the conventional methods from field theory are not easily applicable . it was shown in ref . @xcite that such phases in the field theory have a logarithmic violation of the area law for the entanglement entropy , and this sets a strict criterion for gravitational models to be considered dual to such phases . the prescription of ryu and takayanagi @xcite for the calculation of the holographic entanglement entropy allows us to directly address this question . results of holographic computations suggest that the mesonic phases are dual to fls , whereas the fractionalized phases are dual to nfls and partially fractionalized to fl*s @xcite . in particular , it was found in refs . @xcite that the hidden , gauge  charged fermi surfaces in the bulk do lead to a logarithmic violation of the area law when the metric is of hyperscaling  violating form with particular values of the dynamical critical exponent and the hyperscaling violating exponent . in the case of the electron star , the logarithmic violation depends only on the charge sourced by the horizon and not that coming from the star itself @xcite . here we extend existing work in the literature by computing the entanglement entropy of solutions to a @xmath2dimensional einstein  dilaton ( emd ) theory in the bulk that are not of hyperscaling  violating type and additionally have an external , constant background magnetic field turned on , including the magnetic electron star solutions found in ref . @xcite . magnetic fields are also important probes of the physics of transport ( especially for @xmath0dimensional systems , to which our gravity solutions are dual ) , and our work is intended to be part of a program of trying to understand , using such external fields , possible new ways to classify characteristic behaviours in the phases we capture . in this paper we will focus on studies of the behaviour of the entanglement entropy in the presence of the magnetic field . since , as stated above ( see also further discussion below ) our geometries are not of hyperscaling  violating type , we do not expect the characteristic logarithmic violations of the area law , and so we seek to explore and exhibit the entanglement entropy s behavior in the various regimes to which we have access . our work studies gravitational backgrounds not previously studied in the literature ; in the notation of ref . @xcite , their @xmath3 and @xmath4 , which determine the dilaton s potential and coupling to the maxwell sector , in our cases are equal : @xmath5 . in terms of the dynamical critical exponent @xmath6 , this corresponds to @xmath7 and a hyperscaling violating exponent @xmath8 . these values are incompatible with the form of the hyperscaling  violating metric , and in particular do not satisfy the requirements of ref .  @xcite that @xmath9 and @xmath10 .    in ref . @xcite , the authors consider an emd theory using a potential for the dilaton of the form @xmath11 and coupling to the maxwell sector @xmath12 . they study the entanglement entropy of purely electric , purely magnetic ( argued for via electromagnetic duality ) , and dyonic solutions of this system , adding the magnetic field as a small perturbation , @xmath13 , in their dyonic system . ( here , @xmath14 is the chemical potential . ) in their notation , our solutions correspond to the choice @xmath15 , which is a case they do not consider in their work and find that it exhibits non  fermi liquid behavior . ] . in particular , they start with a hyperscaling  violating metric for the purely electric solution parameterized by their @xmath16 , but in the case @xmath15 , the dynamical exponent and the hyperscaling violating exponent both diverge , positively and negatively , respectively . thus , our emd solutions lie along a line in their phase diagram for which they do not explore the entanglement entropy . in addition , our dyonic solutions have @xmath17 . we present our work as follows . in section [ eereview ] we begin with a review of the holographic entanglement entropy , but present the detailed derivations of the formulae we display in the appendix . in section [ gravitybackgrounds ] we present our gravity backgrounds , although for more information on their derivation and the magnetic electron star solutions we refer to ref . @xcite . section [ ped ] shows the results for the strip and disk ( see section [ eereview ] for a definition of these ) entanglement entropy for the purely electric dilaton black holes , and section [ pmd ] for the purely magnetic dilaton black holes . section [ emdual ] studies the behavior of the strip entanglement entropy under electromagnetic duality for the purely electric and purely magnetic dilaton black holes . in particular , it is shown how the entanglement entropy is invariant as long as one is careful to take into consideration the relative positions of the physical horizons . the entanglement entropy for the strip and disk for the dilaton  dyon black hole is presented in section [ dd ] , and then in section [ mes ] we consider the mesonic phase of the magnetic electron star solutions of ref . we end in section [ conclusion ] with our conclusions and a discussion of future work .","summary":"we study the behavior of the entanglement entropy indimensional strongly coupled theories via the ads / cft correspondence . restricting to black hole and electron star solutions at zero temperature in the presence of a background magnetic field , we compute their holographic entanglement entropy using the ryu - takayanagi prescription for both strip and disk geometries . in the case of the electric or magnetic zero temperature black holes , _ department of physics and astronomy _    _ university of southern california _    _ los angeles , ca 90089 - 0484 , u.s.a . _    albash , johnson1 , smacdona , [ at ] usc.edu","abstract":"we study the behavior of the entanglement entropy indimensional strongly coupled theories via the ads / cft correspondence . we consider theories at a finite charge density with a magnetic field , with their holographic dual being einstein - maxwell - dilaton theory in four dimensional anti  de sitter gravity . restricting to black hole and electron star solutions at zero temperature in the presence of a background magnetic field , we compute their holographic entanglement entropy using the ryu - takayanagi prescription for both strip and disk geometries . in the case of the electric or magnetic zero temperature black holes , we are able to confirm that the entanglement entropy is invariant under electric - magnetic duality . in the case of the electron star with a finite magnetic field , for the strip geometry , we find a discontinuity in the first derivative of the entanglement entropy as the strip width is increased .    _ department of physics and astronomy _    _ university of southern california _    _ los angeles , ca 90089 - 0484 , u.s.a . _    albash , johnson1 , smacdona , [ at ] usc.edu"}
{"article_id":"1504.02067","section_id":"c","document":"we have computed the finite part of the holographic entanglement entropy for the strip and disk geometry for purely electric , purely magnetic , and dyonic dilatonic black holes , as well as the strip entanglement entropy for the magnetic electron star solutions of ref . we observed how the entanglement entropy for the ped solution backgrounds at large @xmath44 approach the in  falling solution , which contributes a non  zero value to the entanglement entropy . we also found that different uv regulators , due to having different coordinate systems , can introduce a shift in the entanglement entropy . similar results are obtained for the pmd backgrounds , and we are able to show that the entanglement entropy is invariant under electromagnetic duality , as long as one shifts the relative location of the physical horizons between the ped and pmd solutions .    for the dilaton  dyon black hole , we found that the entanglement entropy for the disk , at large @xmath44 , grows linearly with @xmath44 , with a coefficient approximately equal to the ground state degeneracy of our solutions . this suggests a volume law rather than an area law for these backgrounds . lastly , for the mesonic phase of the magnetic electron star solution , we found that the entanglement entropy smoothly passes into the star , but that at a certain value of @xmath44 , it is actually the in  falling solution that has lower entropy than the hanging surface . this suggests that at a value of @xmath6 , with @xmath227 , the minimal surface breaks to the in  falling one . this strongly suggests the presence of a `` phase transition , '' however , pending further investigation we can not say for certain ; regardless , our results indicate at least some non  trivial behavior in the far ir for the entanglement entropy . in all cases , we find a dependence of the large @xmath44 behavior of the entanglement entropy on the various dimensionless ratios in the theory . there are several directions for future work . we mentioned in section [ mes ] that one could study the disk entanglement entropy for the mesonic case , as well as the entanglement entropy of the partially fractionalized phases of the magnetic electron stars . for the case of zero magnetic field but with a charged star and electrically charged horizon  a partially fractionalized phase  the entanglement entropy s dependence on the charge was studied in refs . @xcite and there it was found that there was a logarithmic violation to the area law due to the charged horizon but not the star . it would be interesting to see if the presence of the magnetic field in such phases changes this behavior . since we have only studied the mesonic phase in this paper , we do not expect the logarithmic violation , at least in the electric sector . perhaps , however , even in the mesonic phase the presence of the horizon for the magnetic sector will modify the area law behavior of the entanglement entropy in an interesting way . additionally , one could construct and study finite temperature versions of our solutions . these points are left for future work .","summary":"we are able to confirm that the entanglement entropy is invariant under electric - magnetic duality . in the case of the electron star with a finite magnetic field , for the strip geometry","abstract":"we study the behavior of the entanglement entropy indimensional strongly coupled theories via the ads / cft correspondence . we consider theories at a finite charge density with a magnetic field , with their holographic dual being einstein - maxwell - dilaton theory in four dimensional anti  de sitter gravity . restricting to black hole and electron star solutions at zero temperature in the presence of a background magnetic field , we compute their holographic entanglement entropy using the ryu - takayanagi prescription for both strip and disk geometries . in the case of the electric or magnetic zero temperature black holes , we are able to confirm that the entanglement entropy is invariant under electric - magnetic duality . in the case of the electron star with a finite magnetic field , for the strip geometry , we find a discontinuity in the first derivative of the entanglement entropy as the strip width is increased .    _ department of physics and astronomy _    _ university of southern california _    _ los angeles , ca 90089 - 0484 , u.s.a . _    albash , johnson1 , smacdona , [ at ] usc.edu"}
{"article_id":"cond-mat0502403","section_id":"i","document":"the ising model with arbitrary interactions is perhaps the most successful one in statistical physics . despite its ( relative ) simplicity , it has been used to model such a variety of complex systems exhibiting cooperative phenomena that it can be regarded with fairness as a paradigm of a model system . besides its multiple applications in theoretical physics ( in fact , onsager s solution of the two - dimensional model was the cornerstone of the modern theory of critical phenomena ) one of its most conspicuous application in condensed matter ( and its original motivation ) is related to the description of anisotropic magnetic materials . while mostly applied in the past decades to bulk magnetic materials , the advances in film growth techniques , such as atomic or molecular epitaxy , has raised a renewed interest in the behavior of the two - dimensional version of the model . in particular , the study of thin magnetic films and quasi two  dimensional magnetic materials ( like the rare earth layers that occur in perovskite structures of re@xmath0@xmath1@xmath2 , re being a rare earth of the lanthanide series @xcite ) has experimented an increasing interest during the last years . part of this interest is obviously motivated by the great amount of applications they find nowadays in many different technological fields , such as data storage , catalysis and electronic uses are only a few examples , among many others . nevertheless , they have also caught the attention of both theoretical and experimental physicists due to the rich insight they provide into the fundamental role that microscopic interactions play in determining the macroscopic properties of a material . one of the most interesting applications of the two - dimensional ising model is related to the theoretical description of ultra - thin magnetic films , like metal films on metal substrates ( e.g. fe on cu @xcite , co on au @xcite , see also @xcite for a recent review on the topic ) . if the magnetic film is thin enough ( less than approximately five monolayers ) the atomic magnetic moments tend to align out of the plane defined by the proper film . this occurs because the surface anisotropy overcomes the anisotropy of the dipolar interactions , which favor in  plane ordering . under these circumstances , one can then model the local magnetic momenta of the material by using ising variables . any realistic theoretical description of a magnetic thin film must include , besides the usual short  range exchange interactions , also the long  range antiferromagnetic dipolar interactions . it is worth mentioning that dipolar interactions have been usually neglected , specially in thermodynamical studies , due to the small magnitude of dipolar interactions relative to the magnitude of the exchange interactions . nevertheless , it is a well established fact that dipolar interactions can give place to very rich phenomenological scenarios , concerning both thermodynamical and nonequilibrium properties . in particular , when both interactions are present , the system is inherently frustrated , and many of the interesting static and dynamical properties of systems with dipolar interactions result , precisely , from this property .    in this paper we will review the recent advances in the study of equilibrium ( _ i.e. , thermodynamical _ ) and out of equilibrium properties of the ising model with competition between short  range ferromagnetic exchange interactions and long  range antiferromagnetic dipolar interactions defined on a square lattice and ruled by the following dimensionless hamiltonian : @xmath3 where @xmath4 and @xmath5 stands for the quotient between the exchange @xmath6 and the dipolar @xmath7 interactions parameters , i.e. , @xmath8 . the first sum runs over all pairs of nearest neighbor spins and the second one over all distinct pairs of spins of the lattice . @xmath9 is the distance , measured in crystal units , between sites @xmath10 and @xmath11 . the energy is measured in units of @xmath7 , which is assumed to be always positive ( antiferromagnetic ) ; hence @xmath12 means ferromagnetic exchange couplings .","summary":"the two - dimensional ising model with competing short range ferromagnetic interactions and long range antiferromagnetic interactions is perhaps the most simple one containing the minimal microscopic ingredients necessary for an appropriate description of the macroscopic properties of ultrathin films and quasi  two  dimensional magnetic materials . despite such relative simplicity we review recent advances in the understanding of both equilibrium and non - equilibrium properties of the model .","abstract":"the two - dimensional ising model with competing short range ferromagnetic interactions and long range antiferromagnetic interactions is perhaps the most simple one containing the minimal microscopic ingredients necessary for an appropriate description of the macroscopic properties of ultrathin films and quasi  two  dimensional magnetic materials . despite such relative simplicity , the frustration introduced by the competition between interactions generates complex behaviors that have eluded , up to now , a complete understanding of its general properties . in this work we review recent advances in the understanding of both equilibrium and non - equilibrium properties of the model . this includes a detailed description of several known properties of the thermodynamical phase diagram , as well as the existence of several types of metastable states and their influence in the low temperature dynamics ."}
{"article_id":"hep-th0612156","section_id":"i","document":"in classical mechanics one can define entropy by specifying macro states , @xmath1 , as boltzmann s constant times the logarithm of the phase space volume of the space of micro states corresponding to such a macro state : @xmath2 here @xmath3 phase space , ( ps for short ) , is the set of all the micro states @xmath4 that agree with the macro state @xmath1 ; @xmath5    we suppose that we can distinguish various `` macro states '' in the sense that collections ( subset , roughly speaking ) of states of the system at the fundamental level correspond to what we collect under one state in macroscopic thermodynamics . if we can assign these macro states entropies , we can define them as logarithms of the number of states in the macro state , according to usual definition @xcite@xcite@xcite . this `` number of states '' in the macro state may be able to be defined in quantum mechanics , but in a classical description we either have to replace the number of states by a volume of the corresponding phase space or we have to discretize the phase space . when the system is described macroscopically and behaves adiabatically , we shall seek to define a kind of currents very generally as below . the point @xmath4 is phase - space point = micro state . usually one specifies a reversible development of the macro state by taking it to be very slow . this means that one can invert the rate of development of the macro state in time . if there is no such fact , it may cause significant influence on the micro physics and micro development to the second order in the development rate of the macro state @xmath6 . combining this approximation with the second order effect of @xmath7 in the second law of thermodynamics @xmath8 , requires @xmath9 which is nothing but conservation of @xmath10 , if we use a simple formal taylor expansion @xmath11 here we neglect all but first term in the slow limit . part of the motivation of the present article is the hope to make more general definition of reversibility criteria .    a direction in which such generalization has already been done in many articles and textbooks . we also go and seek to construct entropy distribution in space and entropy current , so to speak answer where the entropy is . we would contemplate to specify in which field variables would sit the entropy in a latticized field theory . in such a latticized field theory one has collections of variables and equations of motion . one could hope to obtain a general description as to how the entropy flows under certain restrictions of macro state .    in the long run one might seek to study entropy flow in a euclidean field theory ( latticized or not ) . in studying this it is most elegant and easy to work in the case of reversible processes because the entropy gets conserved . in such processes @xmath12 holds so that the second law of thermodynamics is fulfilled in a trivial manner and furthermore time reversal invariance too . therefore this second law is not very relevant if we restrict ourself to reversible processes as is actually the case in the present article . this touches on a motivation of ours for present work : we study entropy flow without necessarily assuming second law at the outset . this paper is the first attempt in a series of papers on this entropy flow subject . we then expect that the entropy will be conserved . in fact in cases where we have latticized field theories we would expect that we could find a conserved current @xmath13 of entropy @xmath14    it is the main purpose in the present article to discuss and construct such an entropy current under an abstract and general set up . however we investigate in detail only in a couple of examples the most important of which is a certain triangular lattice in two space time dimensions . we shall meet in this article a few surprising results in connection with defining such entropy currents for the latticized field theory models : it turns out that in two dimensional space time we actually have to define different entropy currents @xmath15 , @xmath16 and @xmath17 rather than just one as one might have a priori expected . when one talks about entropy it is normal to think about the second law of thermodynamics tells that entropy @xcite will always increase or stay constant , but never fall down . if we , however , as in this article , restrict ourselves to the adiabatic process the entropy gets constant and the second law is not so relevant anymore . in fact it is realized trivially . we would rather like in the present work to think of it under the condition that we have imposed an abstractly defined adiabaticity @xcite condition . once this is assumed to be valid for our model we will be able to find the conserved entropy current without having to make any use of the second law of thermodynamics . we therefore would like to think of our calculations as performed in a world without having any second law of thermodynamics at all . in other words we should rather think of the present article as a work relevant for working prior to the second law of thermodynamics . thus we should be able to make use of our considerations in an attempt to derive the second law from physics assumed at a more fundamental level . we must though admit that in the present article we assume adiabaticity : it is defined though in a so abstract manner that we do not need second law for that either . thus our considerations could be especially relevant for models with compact space time for which non - trivial relevance of second law of thermodynamics may not be possible . since we only consider trivial realization of the second law of thermodynamics , @xmath18 , the time orientation associated with this second law becomes quite relevant . thus we also do not really use the metric tensor for space time and through most of the present article it is not specified whether we use minkowskian or euclidean metric . however the lattice which we use in the example is a two dimensional triangular one and it has a @xmath19 degree rotation symmetry . this symmetry suggests a euclidean metric since it is a subgroup of the euclidean rotation . the lack of specification of a time axis orientation immediately calls attention to the fact that it needs a convention of sign in order to define an entropy density @xmath20 which is part of an entropy current @xmath13 . the present paper is organized as follows : all through the article we shall make use of the concept of macro states or rather macro restriction in the sense of a subset of all the micro states . there are fundamental field configurations , corresponding to a class of such states conceived as not distinguished in the macroscopic description .    in section 2 we introduce our two dimensional classical lattice field theory . in section 3 we describe the restriction on the field @xmath21 . in section 4 argue a reversability ( or adiabaticity ) requirement as a local principle of no loss of micro solutions by local interplay . in section 5 we give a one dimensional example that illustrates our formalism . in section 6 we then go to our main example , the two dimensional latticized theory . in section 7 we then define entropy currents @xmath22 , @xmath23 and @xmath24 associated with each  class of half curves on the lattice \" . in section 8 we connect these quantities with our entropy flow currents by some equations . in section 9 we emphasize that we obtained three entropy currents . in section 10 we point out two alternative way of constructing our three entropy currents . in section 11 we then actually construct one of them , @xmath22 using conservation law in our formalism . in section 12 the continuum limit is considered for this current @xmath22 . in section 13 the formalism is described analogously for the rest two currents @xmath23 and @xmath24 . in section 14 a relation between the three entropy currents is presented . in section 15 we seek to understand three entropy currents by relating them to numbers of solution . section 16 is devoted to present conclusion and outlook .","summary":"it is shown that we can define various entropy currents , not only one .","abstract":"we consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory . we define macro state restrictions for such a system analogous to thermodynamical states of a system in statistical mechanics . for the case in which we have assumed adiabaticity in a generalized way which is equivalent to reversible processes . it is shown that we can define various entropy currents , not only one . it is indeed surprising that , for a two dimensional example of lattice field theory , we get three different entropy currents , all conserved under the adiabaticity condition .     yitp-06 - 31 + oiqp-05 - 16 + hep - th/0612156     entropy currents for reversible processes in + a system of differential equations . +  the case of latticized classical field theory  +    holger b. nielsen + _ niels bohr institute , + university of copenhagen + 17 blegdamsvej , copenhagen , , denmark _   + and + masao ninomiya _ + yukawa institute for theoretical physics , + kyoto university + kyoto 606 - 8502 , japan _"}
{"article_id":"hep-th0612156","section_id":"c","document":"we have considered a `` classical '' lattice field theory on a two dimensional regular triangular lattice of a very general type . that is to say we did never write what the supposedly complicated equations would be . rather we just in a extremely abstract manner assumed that we looked for a big class of solutions obeying all over the lattice some macro constraints which were meant to be the features to what a macroscopic observer would notice . we assumed also in a general way that the macro scenario imposed corresponding to an adiabatic development formulated by the assumptions we called reversibility in either way . our assumption of reversibility or adiabaticity  either way \" was the assumption ( [ 4.2 ] ) in section 4 . it means that entropy would be constant . thus it becomes a setting for studying conserved entropy currents . it should be understood that such entropy flows are given in a macroscopic picture which means a system of macro restrictions , consistent with our reversibility . now our main study was for such macroscopic pictures or macro scenarios with our ( slightly generalized ) adiabaticity assumption to find and define conserved entropy currents because of the adiabaticity . the surprise is , however , that instead of finding only one - as one would presumably have expected - we found conserved entropy currents , @xmath15 , @xmath16 , and @xmath17 as we denoted them in the continuum limit ( lattice constant @xmath284 ) . we can say that we found in our rather general latticized field theory different kinds of entropy ! it turned out that with our special simplification of the lattice model having only restrictions by the field values that are related inside a certain system of triangles the three different currents of entropy could be described - in the continuum limit - in terms of two scalar fields @xmath152 and @xmath153 describing the prescribed macro scenario . from the conservation laws of these three entropies we got a certain homogeneous third order differential equation @xmath285 where the third order tensor @xmath286 is related to the lattice orientation . what we did by means of the lattice non rotational invariance was to let the lattice select some direction in which to say that the entropy flows . we have these different crude directions @xmath1 , @xmath37 , and @xmath158 `` half - curves '' . in minkowskian relativistic theories one must use the distinction between forward in time going and backward going ( half ) curves . to keep the precise analogy we should though rather think of right going and left going half - curves . but we managed under some more general condition to obtain even several entropy current definitions . we do probably best by admitting that we do not fully yet understand what is going on with these the somewhat mysterious entropies . it is rather obvious that as it comes out these entropies are seemingly lattice artifacts in as far as the bunches of `` half '' curves extending from some point @xmath150 which we used for the definition of the three entropies were clearly defined by means of our lattice only . so from the very definition we had our three entropies attached to the lattice . it is our next important subjects of works to study further detailed investigations of the properties of three entropy currents in two dimensional example and to generalize our method of constructing entropy currents into any dimensions . furthermore most importantly we will have to clarify the question whether all the three entropy currents are relevant ones in actual physical situation . the authors acknowledge the niels bohr institute ( univ . copenhagen ) and yukawa institute for theoretical physics ( kyoto univ . ) for their hospitality extended to one of them each . the work is supported by grand - in - aids for scientific research on priority areas , number of area 763  dynamics of strings and fields \" , from the ministry of education of culture , sports , science and technology , japan . 99 s.  carnot ,  rflexions sur la puissance motrice du feu et sur les machines propres  dvlopper cette puissance \" , bachelier , paris 1824 ; see  the second law of thermodynamics \" , translated and edited by w.  f.  magie , harper and brothers , new york 1899 , pp 3 - 61 . r.  clausius , ann . 79 ( 1859 ) 368 - 397 , 500 - 524 , _ ibid _ 93 ( 1854 ) 418 - 506 ; _ ibid _ 125 ( 1865 ) 353 - 400 ; see  the mechanical theory of heat \" , translated by w.r.brown , macmillan and co. london , 1897 ; see also w.  f  .magie @xcite pp 65 - 108 . l. boltzmann , ann . physik , * 60 * , 392 , ( 1897 ) , as translated in s.  g.  brush ,  kinetic theory \" , ( pergamon press , new york , 1965 ) ; j.  b.  hartle ,  quantum pasts and the utility of history \" , gr - qc/9712001 , talk given at nobel symposium on modern studies of basic quantum concepts and phenomena , gimo , sweden , 13 - 17 jun 1997 . i. prigogine ,  thermodynamics of irreversible processes \" , interscience , a division of wiley and sons , ny , london 1961 : see also j. kirkwood , j. chem . * 14 * , p.180 ( 1946 ) ; m. born and h. s. green , proc . roy . soc . * a190 * , p.455 ( 1947 ) ; g. klein and i. prigogine , physics * 13 * , p.74 - 89 ( 1957 ) . h. b. nielsen and m. ninomiya ,  compactified time and likely entropy  world inside of time machine  \" in proc . of the 8th workshop  what comes beyond standard model \" , bled , july 19 - 29 , 2005 , slovenia , eds . n. mankoc borstink and h. b. nielsen et al , hep - ph/0512061 ;  unification of cosmology and second law of thermodynamics \" , hep - th/0509205 ;  intrinsic periodicity of time and non - maximal entropy of universe \" , to appear in ijmpa , hep - th/0601021 ;  law behind second law of thermodynamics  unification with cosmology  \" , jhep , 03 , 057 - 072(2006 ) , hep - th/0602020 .","summary":"+    holger b. nielsen + _ niels bohr institute , + university of copenhagen + 17 blegdamsvej , copenhagen , , denmark _   + and + masao ninomiya _ + yukawa institute for theoretical physics , + kyoto university + kyoto 606 - 8502 , japan _","abstract":"we consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory . we define macro state restrictions for such a system analogous to thermodynamical states of a system in statistical mechanics . for the case in which we have assumed adiabaticity in a generalized way which is equivalent to reversible processes . it is shown that we can define various entropy currents , not only one . it is indeed surprising that , for a two dimensional example of lattice field theory , we get three different entropy currents , all conserved under the adiabaticity condition .     yitp-06 - 31 + oiqp-05 - 16 + hep - th/0612156     entropy currents for reversible processes in + a system of differential equations . +  the case of latticized classical field theory  +    holger b. nielsen + _ niels bohr institute , + university of copenhagen + 17 blegdamsvej , copenhagen , , denmark _   + and + masao ninomiya _ + yukawa institute for theoretical physics , + kyoto university + kyoto 606 - 8502 , japan _"}
{"article_id":"1702.03065","section_id":"i","document":"software - defined networking ( sdn ) holds great promises to improve network performance and management . the key idea of sdn is to decouple the control plane from the data plane @xcite . data plane can focus on performing basic functionalities such as packet forwarding at high speed , while the logically centralized control plane manages the network . usually , switches at data plane send requests to control plane for processing some flow events , e.g. flow - install events . the control plane is a potential bottleneck of sdn in terms of scalability and reliability . as the data plane expands , control plane may not be able to process the increasing number of requests if implemented with a single controller , resulting unacceptable latency to flow setup . reliability is also an issue since a single controller is a single point of failure , resulting in disastrous break - down of the control plane and the network . existing proposals to address such problems fall broadly into two categories . one is to implement the control plane as a distributed system with multiple controllers @xcite @xcite . each switch then associate with certain controllers for fault - tolerance and load balancing @xcite @xcite@xcite@xcite . the other is to devolve partial loads of request processing from controllers to switches @xcite @xcite @xcite , reducing the work load of controllers .    for switch - controller association , the first category of solution , initial design choice is to make a static switch - controller association @xcite @xcite . however , such static association may result in overloading of controllers and increasing flow setup latency due to its inflexibility to handle traffic variations . an elastic distributed controller architecture is proposed in @xcite , with an efficient protocol to migrate switches across controllers . however , it remains open to determine the switch - controller association . then @xcite took a step further by formulating the switch - controller association problem as a deterministic optimization problem , i.e. , an integer linear problem with prohibitively high computational complexity . a local search algorithm was proposed to find suboptimal associations within a given time limit ( e.g. , 30 seconds ) . in @xcite , the controller is assumed to be modeled as m / m/1 queue ( poisson arrival and exponential service ) . under such assumption , the switch - controller association problem with steady - state objective function was formulated as a many - to - one stable matching problem with transfers . then a novel two - phase algorithm was proposed to connect stable matching with utility - based game theoretic solutions , i.e. , coalition formation game with nash stable solutions .    for control devolution , the second category of solution , an obvious design choice is static devolution for certain functions and flows @xcite @xcite @xcite ; i.e. , switches locally process requests that do not require network - wide state , such as link - layer discovery service . static devolution mitigates the loads on control plane in some ways , but it could be inflexible in face of traffic variations . as an alternative , dynamic devolution allows switches to decide processing those requests locally or uploading them to control plane , depending on their amounts of loads at the moment . however , the design of dynamic devolution with respect to traffic variations remains open . then several interesting questions are raised and answers to such questions will definitely shape our design for sdn networks :    * instead of deterministic switch - controller association with infrequent re - association @xcite @xcite , can we directly perform dynamic switch - controller association with respect to the traffic variation ? what is the benefit that we can obtain from a fine - grained control at the request level ? * how to perform dynamic devolution ? * how to make a trade - off between dynamic switch - controller association and dynamic control devolution ?    in this paper , we consider a general sdn network with traffic variations , resulting variations of requests to handle with flow events . we assume each request can be either processed at switch ( incurs computation costs ) or be uploaded to certain controllers ( incurs communication costs ) . we aim at reducing the computational cost by control devolution at data plane , the communication cost by switch - controller association between data plane and control plane , and the response time experienced by switches , which is mainly caused by queueing delay on controllers . under such settings , we provide a new perspective and a novel scheme to answer those questions . our key results and contributions are summarized as follows :    * _ problem formulation _ : according to the best of our knowledge , this paper is the first to study the joint optimization problem of dynamic switch - controller association and dynamic control devolution . * _ finer granularity control _ : according to the best of our knowledge , this paper is the first to perform the control decisions at the granularity of request - level . note that request - level information such as time - varying queue backlog sizes and number of request arrivals presents the actual time - varying state of data plane . hence it d help for more accurate decision making of dynamic association and dynamic devolution when compared to coarse - grained control . * _ online algorithm design_ we formulate a stochastic network optimization problem , aiming at minimizing the long - term average sum of communication cost and computational cost , while keeping time - average queue backlogs of both switches and controllers small . by employing lyapunov drift technique @xcite and exploiting sub - problem s structure , we develop an efficient greedy algorithm to achieve optimality asymptotically . our algorithm is online , which means it does not need the statistics of traffic workloads and does not need the prior assumption of traffic distribution . * _ algorithm analysis _ : we show that our algorithm yields a tunable trade - off between @xmath1 deviation from minimum long - term average sum of communication cost and computational cost and @xmath2 bound for average queue backlogs . we also find that the positive parameter @xmath0 determines the switches willingness of uploading requests to controllers , i.e. , performing switch - controller association . * _ simulation _ : we conduct large - scale trace - driven simulations to evaluate the performance of our algorithm within two widely adopted data center networking topologies , i.e. , canonical 3-tiered topology and fat - tree topology . simulation results verify the effectiveness and the trade - off of our algorithm . in addition , in the extreme case that without control devolution , we compare our dynamic association scheme with other association schemes including static , random , and jsq ( join - the - shortest - queue ) . simulation results verify the advantages of our scheme . we organize the rest of paper as follows . we present the basic idea and formulation in section ii . then we show our algorithm design and corresponding performance analysis in section iii . in section iv , we present simulation results . we conclude this paper in section v.","summary":"in software - defined networking ( sdn ) , as data plane scale expands , scalability and reliability of the control plane have become major concerns . to mitigate such concerns , two kinds of solutions have been proposed separately . one is multi - controller architecture , i.e. , a logically centralized control plane with physically distributed controllers . most of existing solutions adopt either static switch - controller association or static devolution , which may not adapt well to the traffic variation , leading to high communication costs between switches and controller , and high computation costs of switches . in this paper , we propose a novel scheme to jointly consider both solutions , i.e. , we dynamically associate switches with controllers and dynamically devolve control of flows to switches . our scheme is an efficient online algorithm that does not need the statistics of traffic flows . by adjusting some parameter , we can make a trade - off between costs and queue backlogs . theoretical analysis and extensive simulations show that our scheme yields much lower costs and latency compared to static schemes , and balanced loads among controllers .","abstract":"in software - defined networking ( sdn ) , as data plane scale expands , scalability and reliability of the control plane have become major concerns . to mitigate such concerns , two kinds of solutions have been proposed separately . one is multi - controller architecture , i.e. , a logically centralized control plane with physically distributed controllers . the other is control devolution , i.e. , delegating control of some flows back to switches . most of existing solutions adopt either static switch - controller association or static devolution , which may not adapt well to the traffic variation , leading to high communication costs between switches and controller , and high computation costs of switches . in this paper , we propose a novel scheme to jointly consider both solutions , i.e. , we dynamically associate switches with controllers and dynamically devolve control of flows to switches . our scheme is an efficient online algorithm that does not need the statistics of traffic flows . by adjusting some parameter , we can make a trade - off between costs and queue backlogs . theoretical analysis and extensive simulations show that our scheme yields much lower costs and latency compared to static schemes , and balanced loads among controllers ."}
{"article_id":"1509.03890","section_id":"i","document":"for an isolated quantum many - body system totally decoupled from the environment , the system can act as its own heat bath . one way to distinguish systems which reach the thermalized state from those which do nt is by studying the entanglement entropy of a subsystem . if a subsystem is in thermal equilibrium , the entanglement and thermal entropies must be the same and thus must satisfy a volume law , i.e. , the entropy should scale like @xmath0 in @xmath1 dimensions . this is different from the typical scaling behavior of the entanglement entropy of ground states , which under some constraints , satisfy an area law scaling.@xcite    evidence has recently accumulated for a certain class of interacting systems with quenched disorder which fail to thermalize . these systems go under the name many - body localization@xcite ( mbl ) and are the interacting analogue of anderson insulators.@xcite this failure to thermalize has been attributed to an extensive number of locally conserved charges.@xcite for a review of mbl phases , see the recent review of ref . . in an anderson insulator , all single - particle eigenstates are exponentially localized in real space , quantum diffusion is impossible at zero temperature and the system is an insulator on macroscopic scales.@xcite in such a state thermalization is not possible ( without an external heat bath ) . it has been suggested that many - body localization results from a similar localization of states in hilbert space.@xcite    the phenomenon of mbl is principally ( and theoretically ) observed in states deep in the excited state spectrum of a macroscopic system , and hence have an extensive _ excitation energy _ which , following standard ( but somewhat inexact ) terminology , we will call ` finite energy density ' states . as a function of some tuning parameter ( typically disorder ) , there can be a phase transition from an ergodic ( thermalized ) phase to an mbl phase . in contrast to its non - interacting counterpart ( the anderson insulator ) , an mbl phase transition can occur at finite temperature.@xcite we should note that phonons may interfere with the observation of an mbl phase in solids , but mbl may be physically realized in optical lattice systems , see e.g. ref . . in this paper we consider the problem of the mbl phase transition by constructing an ensemble of simple ` model ' many - body wave functions with a simple structure parameterized by a ` disorder ' strength , and study the phase transition as a function of this parameter . we will show that , in spite of their simple structure , these model wave function can represent both thermal states and mbl states . the wave functions that we consider have a structure similar to the rokhsar - kivelson ( rk ) states@xcite and their generalizations.@xcite more specifically , we consider states that are linear superpositions of quantum states labeled by the classical configurations of a system of @xmath2 ising spins , and have the form |_rem = _ \\ { } w [ ] | , [ eq : rk ] here the quantum mechanical amplitude @xmath3 $ ] for a configuration @xmath4 of the ising spins is given by the gibbs weight of a classical spin glass model known as the random energy model , i.e. @xmath5 \\propto e^{-\\beta e[\\mathcal{c } ] } \\label{eq : rem - weights}\\ ] ] where the ` energy ' @xmath6 $ ] assigned to the configuration @xmath4 is taken to be a random number drawn from a gaussian distribution . by construction , the amplitudes of these states @xmath3 $ ] are positive real numbers . the associated classical spin glass model in infinite space dimension ( since each spin is coupled to all the other @xmath7 spins ) is known to have a classical thermodynamic phase transition to a spin glass state.@xcite the parameter @xmath8 , which in the classical spin glass model is the inverse temperature , but in this work will be used as a parameter of the wave function . notice that we have not defined a quantum hamiltonian for which the wave function of eq . is an eigenstate and , hence , we have not actually defined an energy for the quantum system . thus , the ` energy ' of the random energy model should not be confused with the energy of the quantum state . the quantum state @xmath9 has the manifestly positive weights shown in eq .. such a state can be a natural candidate for a ground state of a hamiltonian but not for a typical excited state whose amplitudes are generally non - positive . to mimic a ` typical ' state deep in the spectrum of a quantum system , we generalize this construction so that , for a given configuration @xmath10 , the amplitudes for these new states are just a _ random sign _ multiplied by the amplitude @xmath11 discussed above ( a similar approach has been used in ref . and ref .. ) we will denote the new wave functions by @xmath12\\rangle$ ] . here we will also consider the wave function without random signs denoted by @xmath13\\rangle$ ] and compare the physical properties of both types of wave functions . an advantageous aspect of our approach is that we have more analytical control over this system then is typical in interacting disorder systems . in addition we are able to perform numerical calculations with a system size ( @xmath14 ) which can only be achieved in other numerical mbl studies with the use of matrix - product states @xcite . these wave functions are also conceptually simple , making them an ideal setting to further our understanding of mbl . laumann , pal and scardicchio studied numerically the mbl state in the _ quantum _ random energy model and found that the mbl quantum phase transition is distinct from the quantum phase transition to the spin - glass phase.@xcite here we will find that in the rk wave functions @xmath15 , although they are not actual eigenstates of the quantum rem model , the mbl and spin - glass transitions are also separate .    in this work we will be focused on three particular aspects of the problem- the transition to the mbl phase , the scaling of the entanglement entropy with subsystem size and the transition from being geometrically delocalized to localized in the hilbert space . to identify the ergodic and mbl phases , we use the rnyi entanglement entropies @xmath16 ( where @xmath17 is the rnyi index ) @xmath18 of a subsystem @xmath19 whose size @xmath20 is smaller than half of the entire system . in the limit @xmath21 , @xmath16 converges to the von neumann entropy . in an ergodic system , there is a regime where the rnyi entropy obeys a volume law which changes linearly as a function of @xmath22 . bauer and nayak have argued that , for most states in an mbl phase , their entanglement entropy scales at most as an area law of the subsystem size.@xcite we will show below that , in our mbl phase , the rnyi entropy is sub - extensive as a function of subsystem size and is bounded by a finite constant deep inside the mbl phase ( fig . [ fig : schematic ] ) . we take particular note of volume laws at an energy density that corresponds to infinite temperature ( itv ) which scales as @xmath23 . the scaling behavior of the entanglement entropy may depend on the subsystem size often showing a crossover from itv to sub - extensive as the subsystem gets larger . an important subtlety of our model comes from the lack of correlation length in the rem ( inherent in a system at infinite dimension ) . this makes the relevant parameter to consider in looking for such a crossover not the absolute size @xmath22 but the ratio @xmath24 and our results will be quoted as a function of this parameter . while entanglement entropy can be used to distinguishing mbl from ergodic phases , geometric localization is a measure of compactness of the wave function in hilbert space . in an anderson insulator , the localization is of the single - particle wave function in real space and can be characterized by the inverse participation ratio defined as @xmath25 where @xmath26 is the probability distribution of single - particle state in real space.@xcite generically , @xmath27 takes the scaling form @xmath28 where the exponent @xmath29 . for the extensive ( delocalized ) state , @xmath30 , while for the localized state @xmath31 . for the critical single - particle wave function at the mobility edge , @xmath32 has a non - trivial dependence on @xmath17 , and it indicates that the critical wave function has a multifractal nature . @xcite for non - interacting systems , this multifractal behavior@xcite is also manifest in the rnyi entropy for the single - particle critical wave function.@xcite    here we will present evidence that multifractal behavior also appears in the entanglement near the phase transition into the mbl phase by looking at the scaling behavior of the rnyi entropies . loosely speaking the many - body generalization of this multifractality measures the degree of localization of states in the multi - dimensional hilbert space ( in a real - space basis ) and not just those of a single particle orbital . multifractal behavior of weight of a state in a hilbert space has been studied recently by several authors.@xcite in these studies multifractality is used to characterize the geometry of a state in hilbert space , i.e. its degree of localization in the hilbert space . in those works , the shannon - rnyi entropies used to quantify the multifractal behavior of the many - body states is a measure of the statistical properties of the wave functions as probability distributions and are unrelated to the concept of quantum entanglement . multifractality has also been discussed in connection with the fidelity of the ground state wave functions in systems at the infinite - disorder fixed point.@xcite so far as we know , multifractal behavior of quantum entanglement in wave functions close to the mbl transition has not been discussed previously in the literature . this is one of the main questions that we address in our work .      in this paper , we consider the mbl transition , the value of @xmath33 and the geometric localization of the wave function @xmath34\\rangle$ ] . we show that the wave - function geometrically localizes in hilbert space at @xmath35 . we also find three regimes of entanglement scaling for @xmath36 : a thermalized regime ( at infinite temperature ) where the entanglement entropies for a partition show volume law scaling as a function of the subsystem size @xmath22 ; a regime bounded by constant entanglement entropy ; and a regime which is sub - extensive but not constant . the transition from sub - extensive to constant happens at , or before , the geometric localization transition . notice that the presence of extensive scaling for any @xmath37 implies that the finite size scaling of @xmath38 as a function of @xmath2 at a fixed @xmath22 is also extensive . because @xmath39 is hard to compute exactly , we analytically calculate lower and upper bounds for it . in addition , we identify the mbl transition ( with respect to the second renyi entropy ) via a numerical scaling collapse with @xmath40 and @xmath41 @xcite ( see section [ sec : finite_size - scaling ] ) . we find that the the mbl transition is different from the geometric localization transition and therefore the wave - function is still geometrically delocalized in hilbert space at the mbl transition @xcite . while the entanglement entropy @xmath42 scales sub - extensively with @xmath22 at the mbl transition , the transition to sub - extensive scaling does nt correspond to the mbl transition . in addition , the numerical evidence suggests that the mbl transition ( for @xmath43 , at @xmath44 ) happens at a @xmath8 where @xmath45 as a function of @xmath2 still scales extensively . while these statements hold for @xmath43 , we also consider @xmath16 , finding that the mbl transition as well as the analytic bounds for sub - itv scaling happen for different @xmath17 at different @xmath8 . the former of these appears to scale linearly in @xmath46 . in addition , the scaling exponents identified from scaling collapse are different for different @xmath17 . this is an indication of multifractal behavior . we further study the entanglement spectrum in this regime and observe an entanglement gap between the lower continuous band and the other higher eigenvalues and show that this feature explains transitions which differ for different @xmath17 . in fig.[fig : schematic ] a and b , we give a succinct and broad summary of the phase diagram ( including the phase diagram of the classical rem for comparison ) . we also explain the importance of the random sign structure . this effect we compare the behavior of the second rnyi entropies @xmath47 for @xmath15 with @xmath9 without random sign . the difference , @xmath48 , is found to decrease monotonically as a function of disorder strength . in the low disorder regimes , @xmath47 for @xmath9 is a constant and thus their difference @xmath48 takes the maximal value . at the values of @xmath49 , the difference disappears before entering into the mbl phase .    . the spin glass phase transition occurs at @xmath50 . the shaded region between @xmath51 and @xmath52 has non - gaussian fluctuation . ( b ) schematic phase diagram for the rem wave function in terms of the entanglement entropy showing different scaling behaviors in four different regimes as a function of @xmath8 . in the regime ( i ) @xmath53 is equal to @xmath54 for all @xmath22 . in the intermediate regime ( ii ) , @xmath55 is sub - extensive but does not saturate to a constant . regime ( iii ) is the mbl phase . in this regime , the wavefunction is not localized in the hilbert space . ( iv ) is also the mbl phase with the wavefunction localized in hilbert space . ] the rest of the paper is organized as follows . in section [ sec : rk ] , we explain the construction of a rokhsar - kivelson - type wave function which assigns to the amplitude of a quantum many - body state the gibbs weight of a classical spin glass model ( the random energy model ) and introduce a random sign structure into it to access represent typical excited states with a _ finite excitation energy density_. in section [ sec : rem ] we briefly review the classical random energy model ( rem ) and interpret the classical spin glass phase transition in it . in the section [ sec : random_sign ] we construct a rem wave function with a random sign structure to mimic a highly excited state for a hamiltonian with disorder . we will analytically compute the rnyi entropy to show that there is a thermalized regime and a many - body localized phase . in section [ sec : numerical - results ] we calculate the rnyi entropy numerically and find the location of mbl phase transition by finite size scaling . in the section [ sec : random - sign - structure ] we study the rnyi entropy for the rem wave function without random sign and demonstrate the importance of the sign structure . in the section [ sec : conclusions ] we summarize our results and conclude that there is a mbl phase transition in the rem wave function with random sign structure .","summary":"we construct a family of many - body wave functions to study the many - body localization phase transition . the wave functions have a rokhsar - kivelson form , in which the weight for the configurations are chosen from the gibbs weights of a classical spin glass model , known as the random energy model , multiplied by a random sign structure to represent a highly excited state . these wave functions show a phase transition into an mbl phase . in addition , we see three regimes of entanglement scaling with subsystem size : scaling with entanglement corresponding to an infinite temperature thermal phase , constant scaling , and a sub - extensive scaling between these limits . near the phase transition point , the fluctuations of the rnyi entropies are non - gaussian .","abstract":"we construct a family of many - body wave functions to study the many - body localization phase transition . the wave functions have a rokhsar - kivelson form , in which the weight for the configurations are chosen from the gibbs weights of a classical spin glass model , known as the random energy model , multiplied by a random sign structure to represent a highly excited state . these wave functions show a phase transition into an mbl phase . in addition , we see three regimes of entanglement scaling with subsystem size : scaling with entanglement corresponding to an infinite temperature thermal phase , constant scaling , and a sub - extensive scaling between these limits . near the phase transition point , the fluctuations of the rnyi entropies are non - gaussian . we find that rnyi entropies with different rnyi index transition into the mbl phase at different points and have different scaling behavior , suggesting a multifractal behavior ."}
{"article_id":"1509.03890","section_id":"c","document":"we have studied the many - body localization phase transition in a class of many - body wave functions . we focused our analysis in a class of wave functions , @xmath9 , whose amplitudes are the boltzmann weights of a classical spin glass model in infinite dimension , the random energy model . in order to mimic the structure of wave functions of highly excited states with a finite excitation energy density we considered another class of states , @xmath281 , whose amplitudes are obtained by multiplying the amplitudes of @xmath9 by a random sign for each configuration . we studied the mbl problem in the @xmath281 wave function , for different regime of the parameter @xmath8 , by using both analytical and numerical approaches . we showed that there is a direct phase transition into the mbl phase . here we assume that the mbl phase is characterized that the entanglement entropies , as a function of the size of the observed region @xmath22 , scale to a constant value , a feature that we observed explicitly for large enough values of @xmath8 . the location of the phase transition point is identified by scaling collapse of rnyi entropy and its standard deviation . in the thermalized regime , there is a regime where the rnyi entropies with different rnyi index all equal to the thermal entropy @xmath200 at @xmath151 . when @xmath282 , the system enters into the mbl phase where the entanglement entropy is sub - extensive . the mbl phase transition point @xmath205 is smaller than @xmath152 and this suggests that the mbl phase transition and the classical spin glass phase transition are different . upon entering the mbl phase , the random sign structure is not important any more and @xmath283 between @xmath15 and @xmath9 is zero . for @xmath95 , the wave function is deep inside the mbl phase and only @xmath96 number of the configurations in the rem wave function contributes significantly to the statistical average . the rnyi entropy in this regime will reduce to a finite constant . we find that close to the phase transition point @xmath205 , the fluctuation of rnyi entropy is strong in the finite size system . in this regime , rnyi entropies with different rnyi index show different scaling behavior and are similar to the multifractal behavior observed at the anderson localization phase transition point . moreover , @xmath53 has a phase transition at different @xmath205 . finally we note that we have refrained ourselves from performing the same extensive studies for the wave function without random signs , @xmath9 . while we have evidence that this wave function too has a thermalized regime , since it has only strictly positive amplitudes we do not expect it to provide an useful description of the mbl problem . nevertheless it may be useful to investigate its properties in a separate publication . _ note added in the proof _ : after this work was accepted for publication we became aware of the recent independent work of yang , chamon , hamma and mucciolo@xcite who have also discussed the spectrum of the reduced density matrix in several models , including the wave functions discussed in this work . we thank dmitry abanin , david huse , and shivaji sondhi for useful conversations and comments . ef thanks the kitp ( and the simons foundation ) and its entangled15 program for support and hospitality . this work was supported in part by the national science foundation grants dmr-1064319 and dmr-1408713 ( xc , gyc , ef ) at the university of illinois , phy11 - 25915 at kitp ( ef ) , doe , scidac fg02 - 12er46875 ( bkc and xy ) , and the brain korea 21 plus project of korea government ( gyc ) . this research is part of the blue waters sustained - petascale computing project , which is supported by the national science foundation ( award numbers oci-0725070 and aci-1238993 ) and the state of illinois . blue waters is a joint effort of the university of illinois at urbana - champaign and its national center for supercomputing applications .","summary":"we find that rnyi entropies with different rnyi index transition into the mbl phase at different points and have different scaling behavior , suggesting a multifractal behavior .","abstract":"we construct a family of many - body wave functions to study the many - body localization phase transition . the wave functions have a rokhsar - kivelson form , in which the weight for the configurations are chosen from the gibbs weights of a classical spin glass model , known as the random energy model , multiplied by a random sign structure to represent a highly excited state . these wave functions show a phase transition into an mbl phase . in addition , we see three regimes of entanglement scaling with subsystem size : scaling with entanglement corresponding to an infinite temperature thermal phase , constant scaling , and a sub - extensive scaling between these limits . near the phase transition point , the fluctuations of the rnyi entropies are non - gaussian . we find that rnyi entropies with different rnyi index transition into the mbl phase at different points and have different scaling behavior , suggesting a multifractal behavior ."}
{"article_id":"astro-ph0101067","section_id":"i","document":"galaxies and clusters of galaxies formed when gravitational instability amplified density fluctuations in the expanding cosmological background universe . regions denser than average eventually stopped expanding and recollapsed to form virialized objects . the question of what equilibrium structure results when a density perturbation collapses out of the expanding background universe and virializes is central to the theory of galaxy formation . the nonlinear outcome of the growth of gaussian - random - noise cosmological density fluctuations due to gravitational instability in a hierarchical clustering model like cdm is not amenable to direct analytical solution , however . instead , numerical simulations are required . as a guide to understanding these simulations , as a check on their accuracy , and as a means of extrapolating from simulation results of limited dynamic range , analytical approximations are nevertheless an essential tool . one such tool of great utility has been the solution of the spherical top - hat perturbation problem ( e.g. peebles 1980 , padmanabhan 1993 ) . as used in the press - schechter ( `` ps '' ) approximation ( press & schechter 1974 ) and its various refinements , the top - hat model serves to predict well the number density of virialized haloes of different mass which form at different epochs in n - body simulations . an analytical model for the internal structure ( e.g. mass profile , temperature , velocity dispersion , radius ) of these virialized haloes would be a further tool of great value for the semi - analytical modelling of galaxy and cluster formation , therefore . shapiro , iliev & raga ( 1998 ; paper i ) derived such a model for an eds universe . here we shall generalize the analysis of paper i to the case of a low - density universe ( @xmath1 ) which is either matter - dominated or flat with a cosmological constant ( i.e. @xmath2 ) . we shall also describe how the tis model can be generalized to other cosmologies with a nonclumping background component , such as quintessence . it is generally assumed that the collapse to infinite density predicted by the exact , nonlinear solution of the spherical top - hat perturbation problem is interrupted by a violent relaxation to virial equilibrium at a finite density , as a result of the growth of initially small - amplitude inhomogeneities in the density distribution . earlier work adopted the crude approximation that the postcollapse object which emerges from this violent relaxation is either a uniform sphere or a singular isothermal sphere , with the same total mass and energy as the collapsing top - hat and with a radius and velocity dispersion ( or , equivalently , gas temperature ) fixed in accordance with the virial theorem . our first motivation , therefore , was simply to improve upon this earlier treatment by finding a more realistic outcome for the top - hat problem . as a starting point , we adopted the assumption that the final equilibrium is spherical , isotropic , and isothermal , a reasonable first approximation to the n - body and gasdynamic simulation results of the cdm model . the postcollapse analytical solution we derived in paper i from this assumption quantitatively reproduces many of the average properties of the haloes found in those simulations to good accuracy , so we are encouraged to believe that our approximation is well justified for haloes which form from realistic initial conditions . our model is in disagreement , however , with one detail of the n - body simulation results that , in their very centers , simulated haloes have cuspy profiles ( e.g. navarro , frenk & white 1997 ; `` nfw '' ) . by contrast , our model predicts a density profile with a small , uniform - density core , in good agreement with the observed rotation curves of dark matter  dominated galaxies ( iliev and shapiro 2001 ) and with cluster mass profiles inferred from gravitational lensing ( iliev and shapiro 2000 , shapiro and iliev 2000 ) . this apparent discrepancy between the cuspy profiles of the n - body results and the observed dark matter  dominated haloes ( e.g. moore et al . 1999 ) has led recently to a vigorous reexamination of the cold , collisionless nature of cdm , itself , and the suggestion that a variation of the microphysical properties of the dark matter might make it more `` collisional '' , enabling it to relax dynamically inside these haloes so as to eliminate the central cusp ( e.g. spergel & steinhardt 2000 ; burkert 2000 ; dav et al . 2000 , firmani et al . 2000 and references therein ) . while the details of this suggestion are still uncertain , our model can also be applied in that case , to the extent that we are able to ignore the details of the relaxation process inside the halo and approximate the final equilibrium as isothermal . as described in paper i , our model is as follows : an initial top - hat density perturbation collapses and virializes , which leads to a truncated nonsingular isothermal sphere in hydrostatic equilibrium ( tis ) , a solution of the isothermal lane - emden equation . although the mass and total energy of the top - hat are conserved thru collapse and virialization , and the postcollapse temperature is set by the virial theorem ( including the effect of a finite boundary pressure ) , the solution is not uniquely determined by these requirements alone . in order to find a unique solution , some additional information is required . we adopted the anzatz that the solution selected by nature is the `` minimum - energy solution '' such that the boundary pressure is that for which the conserved top - hat energy is the minimum possible for an isothermal sphere of fixed mass within a finite truncation radius . this assumption fixes the ratio of the radius of the postcollapse sphere to the radius of the top - hat perturbation which created it , as measured at the latter s epoch of maximum expansion , uniquely . for comparison , we appealed to the details of the exact , self - similar , spherical , cosmological infall solution of bertschinger ( 1985 ) . in this solution , an initial overdensity causes a continuous sequence of spherical shells of cold matter , both pressure - free dark matter and baryonic fluid , centered on the overdensity , to slow their expansion , turn around and recollapse . the baryonic infall is halted by a strong accretion shock , while density caustics form in the collisionless dark matter , instead , due to shell - crossing . the postcollapse , virialized object we wish to model is then identified with the spherical region of shell - crossing dark matter and shock - bounded baryonic fluid in this infall solution ( for ratio of specific heats @xmath3 ) for which the mass is the same as that of our top - hat and the trajectory of its outermost spherical mass shell was identical to that of the outer boundary of our collapsing top - hat at all times until it encountered the shock . according to the detailed similarity solution for this infall problem , this spherical region of post - shock gas and shell - crossing dark matter , it turns out , is very close to hydrostatic and isothermal and has virtually the same radius as that of the minimum - energy solution for the matching tis . this offers some support for our `` minimum - energy '' anzatz and explains the dynamical origin of the boundary pressure as that which results from thermalizing the kinetic energy of infall .    with this `` minimum - energy '' anzatz , we found that top - hat perturbation collapse leads to a unique , nonsingular tis , which yields a universal , self - similar density profile for the postcollapse equilibrium of virialized cosmological haloes . our solution has a unique length scale and amplitude set by the top - hat mass and collapse epoch , with a density at every point which is proportional to the background density at that epoch . the density profiles for gas and dark matter are assumed to be the same ( no bias ) . the final virialized halo has a small but flat - density core . for the eds case , this core radius @xmath4 is about 1/30 of the total size @xmath5 of the halo ( i.e. the truncation radius ) . [ we note that this core radius @xmath6 , where @xmath7 is the `` king radius '' defined by binney & tremaine ( 1987 , equ . [ 4 - 124b ] ) ] . the central density @xmath8 is about 500 times the density @xmath9 at the surface and 18,000 times the background density at the collapse epoch . at intermediate radii , @xmath10 drops faster than @xmath11 , as fast as @xmath12 . the one - dimensional velocity dispersion @xmath13 of the dark matter and the gas temperature @xmath14 are given simply by @xmath15 , where @xmath16 is the mean gas mass per gas particle . this temperature is significantly different from that predicted by the standard uniform sphere ( sus ) and singular isothermal sphere ( sis ) approximations adopted previously in the literature , with @xmath17 .    the derived mass profile of our tis solution as a function of its virial temperature ( or velocity dispersion ) and its formation epoch reproduces to remarkably high accuracy ( i.e. of order 1% ) the cluster mass - radius - temperature relationships and average mass profile for cdm haloes which evrard , metzler , and navarro ( 1996 ) derived empirically by fitting a large set of detailed numerical gas dynamical and n - body simulation results of cluster formation in the cdm model . the tis and nfw halo mass profiles are also in very close agreement ( fractional deviation of less than @xmath18 ) at all radii outside of a few tis core radii ( i.e. about one king radius ) for nfw concentration parameters @xmath19 . in short , our tis model is in good agreement with the average properties of simulated cdm haloes although it differs from these numerical results at very small radii . the purpose of this paper is to generalize the results of paper i to the case of a low - density universe , either open and matter - dominated ( @xmath1 , @xmath20 ) , or flat with cosmological constant ( @xmath2 ) . in the former case , the internal structure of the tis haloes will be the same as for the eds results of paper i , when radius and density are expressed in dimensionless terms in units of the core radius and central density . however , these latter dimensional quantities will be functions of the total mass and the formation epoch of the halo , functions which differ from the eds results and depend upon the value of @xmath21 . these differences between the eds solution for the tis model in paper i and that presented here for the open , matter - dominated universe ( @xmath1 ) can be understood as a reflection of the different solutions for the spherical top - hat problem in the two cases . for the case with a cosmological constant , however , the differences with respect to the eds solution are much more extensive . in this case , not only is it necessary to consider the differences which result from the different solution for the spherical top - hat problem , but it is also necessary to take proper account of nonzero @xmath22 in the virial theorem , the conservation of energy , and the isothermal lane - emden equation , as well . in  [ top_low_dens ] , we shall summarize the spherical top - hat perturbation problem generalized to these low - density friedmann universe cases . we will also briefly describe how the conservation of energy and the virial theorem are generalized in the presence of some uniform background component x of energy density , such as the cosmological constant or quintessence , and how these are combined with the top - hat solution to derive the properties of the postcollapse virialized object when the latter is assumed to be a uniform sphere [ i.e. the `` standard uniform sphere approximation '' in the presence of the x - component ] . we will then specialize these general results to the case in which the uniform component x is the cosmological constant . in  [ isoth_x ] , we will generalize the lane - emden equation for an isothermal sphere in hydrostatic equilibrium to take account of the presence of the x - component and specialize our discussion of its solutions to the cosmological constant case . [ virial_low ] , we shall apply the virial theorem to these generalized isothermal lane - emden spheres , taking care to account properly for the important effect of finite boundary pressure . in  [ min_en ] , we will derive the minimum - energy tis solutions for these low - density universe cases , including convenient analytical fitting formulae for practical application , in which all properties of the virialized post - collapse object are given as explicit functions of the mass and collapse redshift of the object for a given background cosmology . our results and conclusions are summarized in  [ summary ] , where we compare the tis solutions for low - density universes derived here with the sus and sis approximations for those cases , as well as with the tis solution of paper i for the eds case . finally , in view of the suggestive physical correspondence between our tis solution in the eds case and the shock- and caustic - bounded sphere in the self - similar , spherical infall solution of bertschinger ( 1985 ) , we have added an appendix  [ appendix1 ] in which we show how the latter solution ( for an eds universe ) can also be applied at early times in the generalized low - density universe cases described here , by a simple rescaling of parameters .","summary":"an analytical model is presented for the postcollapse equilibrium structure of virialized objects which condense out of a low - density cosmological background universe , either matter - dominated or flat with a cosmological constant . the model is based upon the assumption that cosmological haloes form from the collapse and virialization of `` top - hat '' density perturbations and are spherical , isotropic , and isothermal . this leads to the prediction of a unique , nonsingular , truncated isothermal sphere ( tis ) , a particular solution of the lane - emden equation ( suitably modified when ) . the size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe . this tis model is in good agreement with observations of the internal structure of dark matter  dominated haloes on scales ranging from dwarf galaxies to x - ray clusters . it also reproduces many of the average properties of haloes in simulations of the cold dark matter ( cdm ) model to good accuracy , suggesting that it is a useful analytical approximation for haloes which form from realistic initial conditions . [ firstpage ]    cosmology : theory  dark matter  galaxies : clusters : general  galaxies : formation  galaxies : haloes  galaxies : kinematics and dynamics","abstract":"an analytical model is presented for the postcollapse equilibrium structure of virialized objects which condense out of a low - density cosmological background universe , either matter - dominated or flat with a cosmological constant . this generalizes the model we derived previously for an einstein - de  sitter ( eds ) universe . the model is based upon the assumption that cosmological haloes form from the collapse and virialization of `` top - hat '' density perturbations and are spherical , isotropic , and isothermal . this leads to the prediction of a unique , nonsingular , truncated isothermal sphere ( tis ) , a particular solution of the lane - emden equation ( suitably modified when ) . the size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe . the central density is roughly proportional to the critical density of the universe at the epoch of collapse . this tis model is in good agreement with observations of the internal structure of dark matter  dominated haloes on scales ranging from dwarf galaxies to x - ray clusters . it also reproduces many of the average properties of haloes in simulations of the cold dark matter ( cdm ) model to good accuracy , suggesting that it is a useful analytical approximation for haloes which form from realistic initial conditions . our tis model matches the density profiles of haloes in cdm n - body simulations outside the innermost region , while avoiding the steep central cusp of the latter which is in apparent conflict with observations . the tis model may also be relevant to nonstandard cdm models , like self - interacting dark matter , recently proposed to resolve this conflict .    [ firstpage ]    cosmology : theory  dark matter  galaxies : clusters : general  galaxies : formation  galaxies : haloes  galaxies : kinematics and dynamics"}
{"article_id":"1308.3644","section_id":"i","document":"surveys for planetary transits monitor tens or hundreds of thousands of stars at high precision , with rapid time sampling , and over long periods . the resulting datasets can be used not only to discover and characterise transiting exoplanets , but also to study a wide range of phenomena of stellar origin , such as pulsations , rotation , and binarity . however , transit survey data are typically affected by a wide range of artefacts , many of which affect all the target stars simultaneously , although to varying degrees .    the kepler space mission , launched on march 6 , 2009 @xcite , exemplifies this opportunity and the associated challenges . the unprecedented precision and baseline of the @xmath0150000 kepler light curves , most of which are now in the public domain , opens up the possibility of studying the micro - variability of stars other than the sun for the first time , probing amplitudes ranging from a few parts per thousand to a few parts per million , and timescales of weeks to years . however , there are also artefacts in the raw data , particularly long term trends , which are prominent in the light curves of all but the highest variability stars . this is visible in figure  [ fig : eg_curves ] , which shows a set of example light curves from the first month of kepler observations , known as quarter 1 ( hereafter q1 ; see section  [ sec : results_q1 ] for more details ) . these common - mode instrumental effects are usually known as _ systematics_. when the cause of the systematics is understood well enough , it is possible to formulate explicit models for their removal . in many other situations , however , we have little knowledge regarding the nature or number of systematic trends in the data . in this paper we present the development of a new methodology , which we refer to as _ astrophysically robust correction _ ( arc ) , which addresses the issue of discovering and removing underlying systematics in astronomical data . we apply the method to data from the first quarter ( q1 ) of kepler data , and show that it efficiently removes the systematic artefacts in that dataset . @xcite used the resulting cleaned data to perform a preliminary statistical study of the variability of the kepler target stars on month timescales . the problem of trend identification and removal in ensembles of stellar light curves was first addressed in the context of ground - based transit surveys , such as ogle @xcite , hatnet @xcite , or superwasp @xcite . the sources of systematics in these surveys are atmospheric ( e.g.  differential airmass variations across the field - of - view , seeing and atmospheric transparency variations ) as well as instrumental ( e.g.  pointing jitter combined with inter- and intra - pixel sensitivity variations ) . the two methods , which are most widely used to identify and remove systematics in ground - based transit surveys are known as sysrem @xcite and tfa ( trend filtering algorithm , @xcite ) . sysrem attempts to explain each light curve as a linear superposition of all the other light curves , and adjusts the coefficients of this linear basis model so as to minimise the total squared variance of all the light curves . the resulting algorithm is very similar to principal component analysis ( pca , see e.g.@xcite ) , although it allows for individual weighting of each observation of each star . because of this , the trends are not strictly orthogonal , and must be identified and removed iteratively . the number of times this is done must then represent a trade - off between removing systematics and preserving real variability . tfa proceeds in a similar fashion , but the trends are identified in a limited subset of the light curves , which is selected by the user , so as to contain a representative sample of the systematics , but minimal intrinsic variability .    the images from which the photometry is extracted , or ancillary sensors , can also be used to measure meteorological and instrumental parameters , which are thought to affect the photometry , for example seeing , airmass , detector temperature , etc  from these , one may construct a linear basis with which to model the systematics , a procedure known as external parameter decorrelation , ( epd , @xcite ) . epd is usually applied as a preliminary step prior to running a search for additional trends using ( e.g. ) sysrem or tfa . although the epd method as described in @xcite is designed for large ensembles of light curves , the same principle , namely fitting a given light curve with a linear combination of external parameters , can also be applied in situations where a single star is being monitored , for example high - precision observations of planetary transits or eclipses . all three of the methods outlined above make a number of important assumptions :    * that the relationship between the trends and the light curves is linear ; * that the data used to identify the trends ( light curves or external parameter data ) is sufficient to describe them completely ; * that the majority of the stars are not significantly variable , so that systematics dominate the global sum of the squared residuals which is used as a figure of merit . the third assumption becomes problematic in the case of space - based transit surveys such as kepler and corot @xcite , which routinely reach sub - millimagnitude precision . as these missions are revealing , many , if not most , stars are intrinsically variable at that level . intrinsic variability can become an important , if not dominant , contribution to the global figure of merit one is trying to optimize , exacerbating the problem of preserving this variability whilst removing the systematics . as a result , in pca - like approaches , the first few principal components can easily be dominated by a small number of highly variable stars , which happen to account for a large fraction of the overall variance of the data . this problem is exacerbated by the fact that these methods are couched in the framework of maximum likelihood , and therefore are not robust against overfitting . @xcite partially address this problem , by identifying and removing from the training set any light curves , whose basis coefficients are deemed anomalous . in this paper we go further , introducing a criterion which explicitly expresses our desiderata that the trends should be constituted of many small contributions from many light curves , and using a fully bayesian model to avoid over - fitting ( see section  [ sec : arcintro ] ) . the pipeline used to process kepler data before releasing it to the public incorporates a ` pre - search data conditioning ' ( pdc ) stage . the pdc is designed to remove instrumental systematics so as to optimize the efficiency of the transit detection process . early implementations of the pdc @xcite followed a procedure similar to epd , but attempted to identify and remove signals of stellar origin in the frequency domain before applying the correction . this preserved astrophysical variability in some , but not all cases . additionally , in some cases the pdc was found to introduce high - frequency noise into the light curves . this effect has been noted in a previous publication @xcite in which the noise properties of short ( 1-min ) and long ( 30-min ) cadence data were compared for the same targets . it is due to the fact that the estimate of each systematic trend is necessarily noisy . these issues made the pdc - processed light curves unsuitable for variability studies , and motivated the development of the alternative method , which is the subject of this paper . in the mean time , kepler pipeline has also evolved . in more recent implementations of the pdc , known as pdc - map ( maximum a - posteriori , @xcite ) , a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set , as well as a set of priors over the coefficients of each basis vector , which is then used in the correction of all the light curves . this leads to a significant improvement in robustness , but we shall defer a detailed comparison to section  [ sec : results_q1 ] . our starting point in the development of a robust detection and correction methodology for the kepler data was not fundamentally different to those of previously published methods : like virtually all of them , we use a linear basis model and identify the trends from the light curves themselves , as is done in sysrem and tfa . however , our approach differs in the following important ways :    * we perform the linear basis regression using the _ variational bayes _ ( vb ) method of approximate bayesian inference to ensure that the procedure is robust to uncertainties in the data , while maintaining computational tractability and scalability to large datasets ; * we apply _ automatic relevance determination(ard ) _ priors to the coefficients of the basis vectors . these priors have zero mean and their individual widths are adjusted iteratively to maximise the model evidence . this ensures that trends are identified and removed only if there is significant evidence for them in the data ; * we formulate an explicit criterion , based on a measure of the _ entropy _ of each trend , to reflect our belief that the trends are systematic i.e.  that they are present , at some level , in the majority of light curves , and that the contribution of any single light curve to any given trend should be small ; * we incorporate a de - noising step after the identification of each trend , which uses the _ empirical mode decomposition _ ( emd ) algorithm , chosen to avoid any intrinsic bias towards trends on particular timescales . the entropy criterion is similar in spirit to the modified pca method of @xcite , but it actively selects trends which satisfy our desiderata , rather than merely rejecting problematic light curves . this paper is structured as follows . section [ sec : method ] gives an overview of the arc , focussing on aspects which are new and/or with which our intended readership may be unfamiliar , namely our trend selection and stopping criteria and the emd algorithm . section  [ sec : results ] shows some illustrative results , starting with a walk - through on a synthetic example dataset , and then moving on to the kepler q1 data . in section  [ sec : disc ] , we compare the performance of the pdc - map and the arc . finally , section  [ sec : conclusions ] summarises the advantages and limitations of the arc and discusses open questions on which future work will focus . detailed descriptions of the bayesian linear basis regression model and of the vb inference method are given for reference in appendices  [ sec : vblbm ] and [ sec : vb ] .","summary":"space - based transit search missions such as kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage . however , before this scientific goldmine can be exploited fully , the data must be cleaned of instrumental artefacts . we compare the results , which are publicly available , to the output of the kepler pipeline s pre - search data conditioning , and show that the two generally give similar results , but the light curves corrected using our approach have lower scatter , on average , on both long and short timescales . [ firstpage ]    kepler space telescope , systematics correction , variational bayesian inference .","abstract":"space - based transit search missions such as kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage . however , before this scientific goldmine can be exploited fully , the data must be cleaned of instrumental artefacts . we present a new method to correct common - mode systematics in large ensembles of very high precision light curves . it is based on a bayesian linear basis model and uses shrinkage priors for robustness , variational inference for speed , and a de - noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves . after demonstrating the performance of our method on a synthetic dataset , we apply it to the first month of kepler data . we compare the results , which are publicly available , to the output of the kepler pipeline s pre - search data conditioning , and show that the two generally give similar results , but the light curves corrected using our approach have lower scatter , on average , on both long and short timescales . we finish by discussing some limitations of our method and outlining some avenues for further development . the trend - corrected data produced by our approach are publicly available .    [ firstpage ]    kepler space telescope , systematics correction , variational bayesian inference ."}
{"article_id":"1308.3644","section_id":"r","document":"in this section we apply the arc method outlined above to two example datasets : first , a synthetic example for explanatory purposes , and the kepler q1 data , where we compare our results to the output of the existing pdc - map pipeline . in this subsection we present a simple synthetic example , to act as a ` walk - through ' guide to the methodology and as a proof of concept . we start with a set of 200 synthetic ` light curves ' formed from random phase , frequency and amplitude sine curves , plus additive gaussian noise . to these we add random amounts of two ` systematic trends ' : an exponential decay with long time constant , and a quadratic term . this constitutes our input dataset , examples of which may be seen in the top panel of figure [ fig : synth_eg ] . note that , without loss of generality , we normalise the curves such that each have unit variance and zero mean . % of the variance . bottom panel : the two basis trends discovered by the algorithm ( solid lines ) and the corresponding trends injected into the data ( dashed lines ) ; we note that the solid and dashed lines are almost undistinguishable as the recovered trends are very close to the originals . ] the steps of the method are illustrated in figure [ fig : synth_eg ] . the trends were identified in a representative subset of 50 ` light curves ' chosen at random , and the basis @xmath35 was constructed from the ten highest - entropy trends at each iteration . two systematic trends were identified before the stopping criterion was reached using @xmath62 . the resulting correction is illustrated on an example ` light curve ' ( not one of the subset in which the trends were identified ) in figure  [ fig : synth_eg_res ] .        in this synthetic example we may compare the original data , prior to addition of systematic trend artefacts , with the recovered detrended traces , as we have the luxury of knowing the ` ground truth ' . the resultant linear correlations between the true ` light curves ' and those recovered by the algorithm lie between 0.94 and 0.999 , with a median value of 0.98 , indicating a very high reconstruction accuracy ( we note that the median correlation between the original curves and the trend - corrupted versions is only 0.11 ) . we now apply the arc to the first month of kepler data , known as q1 . the arc - corrected q1 data were already used by @xcite to study the statistics of stellar variability , but here we present a detailed description of the results and a comparison with the more recently released pdc - map data . the pdc - map data we use in this paper were made public on 25 april 2012 as part of data release 14 , although the only significant difference between this and the earlier release of q1 used by @xcite is the replacement of the original pdc results with the output of the newer pdc - map pipeline . the data to which the arc was applied are essentially the same . the q1 data consist of 1639 observations of 156097 stars taken over 33.5 days in may  june 2009 . the data we consider has been pre - processed only to convert it from pixel - level data to light curves , as described in @xcite . the incident light is collected by 24 square modules , arranged to cover the focal plane of the telescope @xcite . each module consists of two rectangular charge - coupled device ( ccd ) detectors , each of which has two readout channels , resulting in a total of 84 channels and 94.6 million pixels . we first identified a single set of basis trends for all the light curves using a randomly selected subset of 200 light curves and using a threshold @xmath56 . these are shown in figure [ fig : global_basis ] . the first two have low - complexity , and are roughly linear and quadratic in nature , respectively . the third shows more complex dynamics , but is nonetheless present in a very large number of q1 light curves . it is caused by the on / off switching of the reaction wheel heaters @xcite . we note that , although the first two trends resemble low - order polynomials , they are _ not _ simply linear and quadratic components . furthermore , if we were to remove such low - order polynomials from each light curve individually , we would be failing to take into account the fact that the systematic trends are _ global _ rather than specific to each light curve . we then repeated the trend identification step , first on a module - by - module basis , then separately for each output channel . the basis trends identified in the latter case are shown in figure  [ fig:4x4trends ] . we compared the results from all three approaches , and ultimately settled on the output channel specific basis . the motivation for this is two fold . first , it is reasonable to expect that the systematics affecting the data collected on different detectors and read by different sets of electronics might differ , and visual examination of the corrected light curves appeared to bear this out , although the differences were very small . each of the q1 light curves was then corrected using the set of basis trends identified for the corresponding output channel . the full set of basis trends and corrected light curves is available online at www.physics.ox.ac.uk / users / aigrain / keplersys/.","summary":", we apply it to the first month of kepler data .","abstract":"space - based transit search missions such as kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage . however , before this scientific goldmine can be exploited fully , the data must be cleaned of instrumental artefacts . we present a new method to correct common - mode systematics in large ensembles of very high precision light curves . it is based on a bayesian linear basis model and uses shrinkage priors for robustness , variational inference for speed , and a de - noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves . after demonstrating the performance of our method on a synthetic dataset , we apply it to the first month of kepler data . we compare the results , which are publicly available , to the output of the kepler pipeline s pre - search data conditioning , and show that the two generally give similar results , but the light curves corrected using our approach have lower scatter , on average , on both long and short timescales . we finish by discussing some limitations of our method and outlining some avenues for further development . the trend - corrected data produced by our approach are publicly available .    [ firstpage ]    kepler space telescope , systematics correction , variational bayesian inference ."}
{"article_id":"1308.3644","section_id":"c","document":"we have presented a novel method to correct systematic trends present in large ensembles of light curves , while preserving ` true ' astrophyiscal variability , which we call the arc method . the arc is specifically designed for continuous , high - precision observations , where most stars display significant variability . it follows established practice in using linear basis models , but incorporates a number of new features , which are intended to ensure its robustness ( bayesian framework , use of shrinkage priors ) , and its computational efficiency ( approximate inference using variational bayes ) . a de - noising step is used to prevent the introduction of spurious random noise into the light curves . we demonstrated the performance of the method on a simple synthetic dataset , and on the data from the first month of kepler operations . the results were satisfactory in both cases . in the synthetic example , the systematic trends were correctly identified . the original light curves included the building blocks of realistic stellar signals , namely harmonic functions with random , variable phases and amplitudes , and were recovered robustly , with no evidence of systematic changes in amplitude or frequency . for the kepler data , the arc results are similar to those of the pdc - map component of the kepler pipeline for most targets , but with some important differences . in particular , we find that the pdc - map still tends to introduce high - frequency noise into the light curves ( just as noted by @xcite for the original pdc ) . importantly , this effect remains noticeable on the timescales typical of planetary transits . to address this problem , the kepler team recently developed a new incarnation of the pdc , known as multi - scale map , or msmap for short @xcite , which uses a band - splitting approach to separate systematics on different timescales . this does reduce the injection of high - frequency noise into the light curves compared to the pdc - map . however , in msmap the treatment of long - term systematics ( on timescales @xmath74 days ) has reverted to the maximum likelihood approach of the original pdc pipeline . consequently there is no protection against overfitting , and msmap suppresses all variations on timescales longer than @xmath75 days  whether astrophysical or instrumental ( see fig .  1 in * ? ? ? therefore , although we have not had the opportunity to make a detailed comparison between the new msmap data and the arc , we expect the letter to be preferrable for variability studies . we did , however , identify certain types of systematics which are not well - corrected by either the pdc - map or arc . further work needs to be done on these : one area in particular which could be improved is the de - noising step , as the emd method used for that step in the present paper is not suitable for sharp systematic effects . another possibility , which we intend to investigate , is to treat the systematics as multiplicative , rather than additive , by working in log flux units . this which would account for gradual amplitude changes , which could occur due to the combined effect of pixel drift and aperture contamination ( if one of the stars in the aperture is more variable than the other ) . the impact of the residual systematic effects should be relatively limited , because they are confined to well - defined frequency ranges . overall , we therefore conclude that the arc - corrected light curves could become a very useful resource for both stellar astrophysics and exoplanet searches , and we have made the q1 data publicly available ( the code is also available on request ) . however , the full potential of the kepler data lies in its very long baseline . this paper focused on the first month of data only , whereas more than three years are now in the public domain . a number of additional difficulties arise when trying to process the additional quarters , and to stitch together multiple quarters . many of the quarters contain discontinuities , most of which are associated with monthly interruptions in the observations to transfer data back to earth . many of the discontinuities are followed by quasi - systematic trends which are present in most light curves , but with slightly different shapes . as the satellite rotates by @xmath76 about its viewing axis between each quarter , each star falls on a different detector , and this causes changes in both the median flux level and the nature and amplitude of the systematic trends . the arc is not designed to address these problems . we are in the process of developing a complementary set of ` fault - correction ' tools , to be applied on a light - curve by - light - curve basis before running the arc on each channel . the same methodology can then be used to stitch together data from different quarters . these developments will be covered in a forthcoming paper .    as a final cautionary note , we wish to stress that the arc is intended to provide a fast , automated and robust treatment of a large ensemble of light curves . it is not intended to replace the detailed examination of the pixel - level data @xcite , which remains the method of choice for the correction of systematic trends and artefacts in small numbers of light curves .","summary":"we present a new method to correct common - mode systematics in large ensembles of very high precision light curves . it is based on a bayesian linear basis model and uses shrinkage priors for robustness , variational inference for speed , and a de - noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves . after demonstrating the performance of our method on a synthetic dataset the trend - corrected data produced by our approach are publicly available .   ","abstract":"space - based transit search missions such as kepler are collecting large numbers of stellar light curves of unprecedented photometric precision and time coverage . however , before this scientific goldmine can be exploited fully , the data must be cleaned of instrumental artefacts . we present a new method to correct common - mode systematics in large ensembles of very high precision light curves . it is based on a bayesian linear basis model and uses shrinkage priors for robustness , variational inference for speed , and a de - noising step based on empirical mode decomposition to prevent the introduction of spurious noise into the corrected light curves . after demonstrating the performance of our method on a synthetic dataset , we apply it to the first month of kepler data . we compare the results , which are publicly available , to the output of the kepler pipeline s pre - search data conditioning , and show that the two generally give similar results , but the light curves corrected using our approach have lower scatter , on average , on both long and short timescales . we finish by discussing some limitations of our method and outlining some avenues for further development . the trend - corrected data produced by our approach are publicly available .    [ firstpage ]    kepler space telescope , systematics correction , variational bayesian inference ."}
{"article_id":"1502.00034","section_id":"i","document":"after the initial run of the lhc , the constraints on new physics are rather severe @xcite . although models can still be made to realize weak - scale mass spectra , sfermion masses of generic models like the constrained minimal supersymmetric standard model ( cmssm ) @xcite are now required to be larger than about a tev . as a result , the naturalness of supersymmetry ( susy ) has been called into question . however , it was perhaps naive to expect nature to fall into our strict definition of naturalness with less than @xmath5 fine - tuning . supersymmetry , with sfermion masses larger than a tev , still solves the larger hierarchy problem associated with grand unification and/or the plank scale . furthermore , if the sfermion masses are set by the gravitino mass , @xmath6 , and are larger than about 10 tev , the gravitino lifetime is short enough that it decays before bbn @xcite . moreover , as the mass scale of the sfermions is pushed beyond the weak scale , the constraints on susy models from flavor and cp violation in the sfermion sector are greatly relaxed @xcite . these advantages , plus the fact that sfermion masses this large are consistent with a larger higgs mass like the @xmath7  gev higgs boson seen at the lhc @xcite suggest we relax our strict definition of naturalness . large sfermion masses like those found in split supersymmetry @xcite are realized in models such as pure gravity mediation ( pgm ) @xcite , which can be parametrized by a single parameter @xcite @xmath6 . this minimal model of pure gravity mediation is similar in many ways to minimal supergravity ( msugra ) . universal masses equal to @xmath6 are imposed at the grand unified theory ( gut ) scale based on the assumption that the khler manifold is flat for all matter fields . unlike the cmssm , gauginos do not get a tree - level mass . this is because the supersymmetry breaking field is not a singlet and so is excluded from coupling to the gauge kinetic function to leading order . thus , the leading order contribution to the mass of the gauginos comes from anomaly mediation @xcite and is loop suppressed relative to the sfermion masses . the @xmath8-term , which contributes to electroweak symmetry breaking , is identical to that in msugra , @xmath9 . however , since the @xmath10-terms of pgm are effectively zero , @xmath11 and @xmath8 is fixed for a given value of @xmath6 . this makes radiative electroweak symmetry breaking ( ewsb ) difficult . however , by adding a giudice - masiero term @xcite , @xmath8 is no longer fixed by @xmath6 alone , but also depends on the coupling of the giudice - masiero term . this additional freedom in @xmath8 makes radiative ewsb possible , but only for small values of @xmath12 . once the higgs mass constraint is taken into consideration , these models have a single free parameter which is some combination of @xmath6 and @xmath12 @xcite . however , because @xmath12 is restricted to be less than about 3 , @xmath6 tends to be rather large . the constraints on @xmath12 can be removed , if the higgs soft masses at the gut scale are taken to be non - universal @xcite . in this case , @xmath6 can be taken to be smaller for larger values of @xmath12 . another important motivation for susy is grand unification @xcite . in the standard model ( sm ) , the gauge couplings approach each other as they are run up to the high scale @xcite . however , the quality of the coupling unification is less than convincing . if the sm is supersymmetrized , on the other hand , the unification of the gauge couplings becomes quite good @xcite . furthermore , grand unification in the sm would generate enormous quadratic divergences for the higgs boson . however , these quadratic divergences are significantly reduced for supersymmetric grand unified theories , even if the sfermions are larger than a tev . clearly , grand unification is another motivation for pgm . the signatures of these simple pgm - type models are limited . one possible signature at the lhc for small @xmath6 is the wino @xcite . for larger @xmath6 , on the other hand , the wino can not be seen at the lhc but could be a viable thermal relic dark matter candidate @xcite . if this is indeed the case , it could be seen by indirect detection experiments in the near future @xcite . however , this scenario is already under tension from existing indirect detection experiments @xcite . the direct detection of wino dark matter is challenging as its scattering cross section with a nucleon is as small as @xmath13 @xcite . a higgsino signature at the lhc is another possible observable which arises from tuning @xmath14 to be small @xcite . however , this is also difficult to see . this scenario could also have higgsino - like dark matter which could possibly be seen in future indirect detection experiments @xcite . the scattering cross section of the higgsino with a nucleon is dependent on the size of the wino component of the lsp , and may be probed in future experiments @xcite .    in this work , we will examine another possible signature of these models . since the colored triplet higgs gives threshold corrections to the gauge couplings when integrated out , the quality of the coupling unification determines the mass of the colored triplet higgs @xcite and so affects the lifetime of the proton . when the colored higgs is integrated out , it also generates a dimension - five operator proportional to down - type yukawa couplings which lead to proton decay @xcite . since this dimension - five operator is proportional to the down - type yukawa couplings , it will be enhanced for large @xmath12 . proton decay from this dimension - five operator arises from a loop diagram with a higgsino mass insertion @xcite . proton decay of this type can then be suppressed for small @xmath14 . when unification is not ideal and @xmath12 is large , a larger higgsino mass can increase the rate of proton decay from this dimension 5 operator . parameters of this size are viable in pgm models . since proton decay of this type is also suppressed by @xmath6 , the more interesting parameter space will be for smaller @xmath6 and larger @xmath12 . therefore , we will need to consider non - universal higgs soft masses . we will find that if @xmath6 is small and @xmath12 is larger , which is also consistent with the higgs mass measurement , the proton lifetime may be in reach of future experiments . however , for much of the parameter space the lifetime tends to be well beyond the reach of future experiments . we will also look at the quality of the gauge coupling unification determined by the deviation of the colored triplet higgs mass , @xmath15 , from the gut - scale as well as the deviation of @xmath16 , where @xmath17 represents the gut scale su(5 ) gauge bosons that become massive and @xmath18 is the @xmath19 which breaks su(5 ) at the gut scale .","summary":"pure gravity mediation offers a simple framework for studying su(5 ) grand unified theories with a split supersymmetry like spectra . we find that for much of the parameter space gauge coupling unification is quite good leading to rather long lifetimes for the proton . ftpi - minn-15/02 + umn","abstract":"we discuss the proton lifetime in pure gravity mediation models with non - universal higgs soft masses . pure gravity mediation offers a simple framework for studying su(5 ) grand unified theories with a split supersymmetry like spectra . we find that for much of the parameter space gauge coupling unification is quite good leading to rather long lifetimes for the proton . however , for  tev and , for which gauge coupling unification is also good , the proton lifetime is short enough that it could be in reach of future experiments .    ftpi - minn-15/02 + umn  th3417/15 + ipmu15 - 0011    1.35 cm    1.2 cm    jason l. evans , natsumi nagata , and keith a. olive    0.4 cm    _william i. fine theoretical physics institute , school of physics and astronomy , + university of minnesota , minneapolis , mn 55455 , usa _ + [ 3pt ]    _kavli ipmu ( wpi ) , todias , university of tokyo , kashiwa 277 - 8583 , japan _    1.5 cm"}
{"article_id":"1502.00034","section_id":"r","document":"we are now in a position to discuss the proton lifetime and mass scales associated with gauge coupling unification in a variety of models which have varying degrees of non - universality in the higgs sector . we begin by displaying in fig . [ m1eqm2p ] the @xmath123 vs. @xmath119 plane for fixed gravitino mass . this is a one - parameter extension of the minimal ( two - parameter ) pgm model and resembles nuhm1 models @xcite . in the left panel we have fixed @xmath124 tev . for this value of the gravitino mass , the higgs mass lies between 124 and 128 gev for @xmath119 roughly between 49 as shown by the red dot - dashed curves . the thin blue lines show the values of the lsp ( wino ) mass and are solid for @xmath125 and dashed for @xmath126 . the anomaly mediated contribution to @xmath127 for @xmath124 tev is 170 gev . at low @xmath119 , threshold corrections from the heavy higgs bosons and the higgsinos increase the mass for @xmath126 and decrease the mass for @xmath125 . at large @xmath119 , the wino mass , for both positive and negative @xmath14 , tends to its anomaly mediated value . the curves end at high and low values of the higgs soft masses due to the absence of radiative electroweak symmetry breaking . for large and negative values of @xmath128 ( the sign on the axis refers to the sign of the mass squared ) , the higgs pseudoscalar mass squared is negative , and for large positive @xmath128 , the electroweak conditions yield @xmath129 . the thicker black curves in fig .  [ m1eqm2p ] show the values of the proton lifetime . as discussed earlier , as there is some uncertainty as to how we match the yukawa couplings at the gut scale , we have results based on quark yukawa couplings ( shown by the solid curves ) and results based on lepton yukawa couplings ( shown by the dashed curves ) . as one can see from the figure , the calculated proton lifetime is sensitive to @xmath119 yet relatively insensitive to the value of @xmath130 for fixed gravitino mass . in general , the proton lifetime is lower at high @xmath119 due to the increase in the down - like yukawa couplings when @xmath119 is increased , whereas the higgs mass increases with @xmath119 . for these relatively low values of the gravitino mass used in the left panel , the proton lifetimes based on quark yukawas drop below @xmath131 years only when @xmath132 where @xmath133 gev . the lifetime increases rapidly at lower @xmath119 and exceeds @xmath134 years when @xmath135 where @xmath136 gev . however , the wino mass requires @xmath137 and @xmath138 . recall that these lifetimes are computed from eq . ( [ tp5 ] ) and when the lifetime exceeds 3 @xmath139 years , the dominant contribution to the decay rate comes from the dimension - six operator given in eq . ( [ tp6 ] ) . proton lifetimes based on lepton yukawas are significantly smaller ( by a factor of roughly 20 ) , so that @xmath140 years when @xmath141 and is still smaller than @xmath142 years when @xmath143 .    in the right panel of fig . [ m1eqm2p ] , we have taken @xmath144 tev and as expected the higgs mass for a given value of @xmath119 is higher . the range 124  128 gev now requires @xmath145  6 . the uncorrected wino mass is now about 290 gev and in the figure we see lower ( higher ) wino masses when @xmath146 . the proton lifetimes are now significantly higher . at @xmath147 , the quark based value of @xmath148 determined by the dimension five operator is now @xmath149 years and increases as @xmath119 is lower . the lepton based lifetimes remain a factor of about 20 lower and may still be as low as @xmath131 years at @xmath147 .    to see more clearly the dependence of the proton lifetime on the pgm parameters , we show in the left panel of fig . [ tpm32 tb ] the behavior of the proton lifetime as a function of @xmath119 for fixed @xmath124 and 200 tev with @xmath150 . the lifetime falls off monotonically with @xmath119 . the ratio between the quark and lepton evaluation of @xmath148 is seen to be nearly constant as @xmath119 is varied with a ratio of about 20 . we also see the substantial increase in @xmath148 when @xmath6 is increased to 200 tev . the experimental limit on the proton lifetime , @xmath97  years @xcite , is shown by the horizontal line . in the right panel , we show this increase in @xmath148 with @xmath6 for fixed values of @xmath151 and 5 . in both panels , we also show the higgs mass as a function of @xmath119 and @xmath6 with its value displayed on the right edge of each panel . restricting the higgs mass to the range 124128 gev allows one to focus on the relevant ranges of either @xmath152 or @xmath6 and hence on the predicted proton lifetime . in contrast to the proton lifetime , the relevant gut mass scales , @xmath15 and @xmath78 , are relatively insensitive to the pgm parameter choices as seen in fig . [ mm32 tb ] . as one can see in the left panel , there is very little dependence on @xmath119 . the mass parameter @xmath153 is always close to @xmath154  gev independent of @xmath6 ( as also seen in the right panel ) . while the color - triplet mass is insensitive to @xmath152 , it does have a mild dependence on the gravitino mass and ranges from a few @xmath155  few @xmath156  gev . notice that in the weak - scale susy scenario the mass of the color - triplet higgs multiplet is predicted to be around @xmath157  gev @xcite . a heavier color triplet mass makes the proton lifetime long enough to evade the current experimental bound . furthermore , in some of the parameter space of pgm , the gut - scale parameters @xmath15 and @xmath78 are both of @xmath158 . in these cases , the threshold corrections at the gut scale become very small , which implies the unification of the gauge couplings is quite good . in fact , for @xmath159 tev and @xmath160 , we get good gauge coupling unification and a proton lifetime which could be in reach of future experiments .    in fig . [ muma ] , we offer two additional planes which show the dependence of the proton lifetime on other pgm parameters . in the left panel , we plot the lifetime contours in the @xmath123 , @xmath6 plane . this is again a nuhm1-like model and we have fixed @xmath161 . as in fig . [ m1eqm2p ] , the red - dashed curves show the higgs mass contours which vary from about 124128 gev for the plane shown . as before , the curves extend across a limited range in @xmath123 where the ewsb conditions can be satisfied . at large positive @xmath162 , @xmath163 goes to 0 ( where the curve is cutoff ) . at very small @xmath14 , the higgs masses increases rapidly causing the sudden downturn in the mass contours . as expected , we see the wino mass varies considerably as @xmath6 is varied . for the range in @xmath6 shown , the proton lifetime varies from as low as @xmath164 years using the lepton yukawas and low @xmath6 to as high as @xmath165 years using quark yukawas and @xmath166 tev .    in the right panel of fig . [ muma ] , we show a two - parameter extension of the two - parameter pgm similar to the nuhm2 @xcite . results are displayed in the @xmath167 plane for fixed @xmath168 and @xmath124 tev . in this case , the ewsb conditions , are used to solve for the two higgs soft masses which now differ . as the higgs mass is largely independent of @xmath122 , the higgs mass contours are nearly vertical . at the center of the plot , as @xmath169 gets to be very small , @xmath170 gets large and exceeds 130 gev . at large @xmath169 , @xmath170 is always larger than 125 gev in the ranges shown . the threshold corrections to the wino mass are sensitive to @xmath14 and @xmath122 and that accounts for the variation of @xmath127 as these parameters are varied . the proton lifetime varies between @xmath171 and @xmath149 years but shows significantly more variability . this is due to the competing effects of changing @xmath14 . the proton lifetime depends both on the color - triplet higgs mass and on @xmath14 itself . through the loop function @xmath96 in eq .  . when @xmath172 , @xmath173 , while if @xmath174 , @xmath175 , as can be seen from eq .  . ] as @xmath14 is lowered , the color - triplet higgs mass decreases which tends to decrease the proton lifetime . but as @xmath169 is further decreased , the proton lifetime dependence on @xmath14 overcomes its dependence on @xmath15 and the lifetime increases very rapidly at small @xmath169 seen by the sharp downturn in the contours near @xmath176 . these effects can be better understood by examining figs . [ tpmu ] and [ mmu ] which show the behavior of the proton lifetime and gut - scale masses , including the heavy higgs mass , as a function of @xmath14 for fixed @xmath119 and @xmath6 . here we see the first gradual and then rapid decrease in the color - triplet mass as @xmath169 is lowered from large values toward @xmath176 . there is no substantial difference in this behavior between the two values of @xmath119 shown . once again , we see that @xmath78 depends very little on our parameter choices and is always near @xmath154  gev .    finally , in fig . [ mmu ] , we see the sharp increase in the proton lifetime as @xmath169 gets small . much greater than the wino mass . ] here we see also that the higgs mass rises sharply as @xmath14 tends to zero . it is important to recall that the lifetime plotted corresponds only to that given by the dimension - five operator given in eq .   and would not exceed @xmath177 years when the dimension - six operator is included . the latter is fairly insensitive to parameter choices .","summary":"we discuss the proton lifetime in pure gravity mediation models with non - universal higgs soft masses . however , for  tev and , for which gauge coupling unification is also good , the proton lifetime is short enough that it could be in reach of future experiments .   ","abstract":"we discuss the proton lifetime in pure gravity mediation models with non - universal higgs soft masses . pure gravity mediation offers a simple framework for studying su(5 ) grand unified theories with a split supersymmetry like spectra . we find that for much of the parameter space gauge coupling unification is quite good leading to rather long lifetimes for the proton . however , for  tev and , for which gauge coupling unification is also good , the proton lifetime is short enough that it could be in reach of future experiments .    ftpi - minn-15/02 + umn  th3417/15 + ipmu15 - 0011    1.35 cm    1.2 cm    jason l. evans , natsumi nagata , and keith a. olive    0.4 cm    _william i. fine theoretical physics institute , school of physics and astronomy , + university of minnesota , minneapolis , mn 55455 , usa _ + [ 3pt ]    _kavli ipmu ( wpi ) , todias , university of tokyo , kashiwa 277 - 8583 , japan _    1.5 cm"}
{"article_id":"math0702239","section_id":"i","document":"by the farkas - minkowski - weyl theorem a convex polyhedron in @xmath0 has two representations . it can either be described by a finite set of linear inequalities ( facets ) or by a finite set of generators ( vertices and rays ) . precise definitions are given in section [ sec : basic_notations ] . one of the most fundamental problems in the theory of polyhedra and its applications , such as combinatorial optimization or computational geometry , is the conversion between two different descriptions . many algorithms for this representation conversion have been proposed ( see for example @xcite , @xcite , @xcite , @xcite ) . for certain classes of polyhedra efficient methods are known , but there is no approach known which efficiently solves the problem in general . programs like cdd @xcite , lrs @xcite , pd @xcite , porta @xcite ( or polymake @xcite either relying on some of the others or using its own method closely related to ` cdd ` ) allow conversion of the representation of a polyhedron . since the programs are implementations of quite different methods , their efficiency may vary tremendously on a given example . many interesting polyhedra both pose difficulties for the standard representation conversion approaches and have many symmetries that could potentially be exploited . in many applications it is sufficient ( or at least necessary ) to obtain a list of inequalities or generators up to symmetries . in the present paper we give a brief survey of approaches that can be used for the representation conversion problem up to symmetries . we do not discuss their asymptotic complexity ( which , in the worst case , is not encouraging ) , but rather refer to previous papers where the methods have proven themselves on difficult instances that could not otherwise be solved . for the new approach discussed in section [ sec : sym - pivoting ] we provide some experimental data ourselves . the paper is organized as follows . in section [ sec : basic_notations ] we give some basic notations and facts from the theory of convex polyhedra . in section [ sec : symmetries ] we consider different notions of symmetries and describe how they can practically be obtained using a graph automorphism computation . in section [ sec : orbits ] we describe the group theoretical notions used in the representation conversion methods discussed in the remainder of the paper . in section [ sec : subpolytope ] we consider decomposition methods which reduce the given problem to a number of smaller problems . these approaches have been used quite successfully by different authors . in section [ sec : cascade ] we describe the incremental _ cascade algorithm _ and in section [ sec : sym - pivoting ] we show how symmetry can be exploited in a simplex pivot based algorithm .","summary":"we give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries . we in particular discuss decomposition methods , which reduce the problem to a number of lower dimensional subproblems . these methods have been successfully used by different authors in special contexts . moreover","abstract":"we give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries . we in particular discuss decomposition methods , which reduce the problem to a number of lower dimensional subproblems . these methods have been successfully used by different authors in special contexts . moreover , we sketch an incremental method , which is a generalization of fourier  motzkin elimination , and we give some ideas how symmetry can be exploited using pivots ."}
{"article_id":"math0702239","section_id":"m","document":"we briefly sketch here the _ cascade algorithm _ by jaquet @xcite , which is a symmetry exploiting version of _ fourier  motzkin elimination_. for this observe first that a @xmath71-dimensional polyhedral cone @xmath10 generated by @xmath82 can be obtained as the projection of an @xmath72-dimensional polyhedral cone with @xmath72 linear independent generators @xmath224 . without loss of generality , we may assume that @xmath225 is a basis of @xmath0 . we set @xmath226 for @xmath227 and @xmath228 for @xmath229 . let @xmath230 be the orthogonal projection of @xmath231 onto @xmath232 . then for the cone @xmath233 we have @xmath234 . the cone @xmath87 is simplicial , since the family @xmath235 is a basis of @xmath231 . take the @xmath72-dimensional polyhedral cone @xmath87 and the projection @xmath236 of @xmath231 on a @xmath237-dimensional hyperplane . the facets of the projection @xmath238 are either projections of facets of @xmath87 or projections of intersections of facets of @xmath87 . in the fourier  motzkin elimination we first compute the facets of @xmath87 and then successively obtain the facets of @xmath239 from one of these two cases . note , since @xmath87 is a simplex , the facets of @xmath87 are simply given by the @xmath237-subsets of extreme rays of @xmath87 .    in the cascade algorithm we also consider symmetries in each step : if @xmath75 is a group of symmetries of the polyhedral cone @xmath10 , then the induced symmetry group on @xmath240 is the stabilizer of the set of vertices @xmath241 under @xmath75 , which we denote by @xmath242 . so , in order to compute the orbits of facets of @xmath240 under @xmath242 we need to compute the orbits of facets and ridges of @xmath243 , first under @xmath244 and then under @xmath245 using the double coset method . it is well known that the fourier  motzkin method depends in a critical way on the ordering of generators @xmath193 of @xmath10 ( see @xcite and @xcite ) . the cascade algorithm introduces another such dependency as the size of the set - stabilizers vary enormously according to the chosen ordering . among the many possible orders of the generators , it is not clear which ordering is best .    in practice fourier  motzkin elimination suffers from generating many redundant inequalities . this problem can be eliminated by using the related _ double description method _  @xcite . for a description of how to use the double description method to perform the fourier  motzkin projection steps without introducing redundant inequalities , see  @xcite , section  4.1 .","summary":", we sketch an incremental method , which is a generalization of fourier  motzkin elimination , and we give some ideas how symmetry can be exploited using pivots .","abstract":"we give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries . we in particular discuss decomposition methods , which reduce the problem to a number of lower dimensional subproblems . these methods have been successfully used by different authors in special contexts . moreover , we sketch an incremental method , which is a generalization of fourier  motzkin elimination , and we give some ideas how symmetry can be exploited using pivots ."}
{"article_id":"cond-mat0508750","section_id":"i","document":"the density matrix is a very useful tool in the numerical study of interacting systems . besides being used in the density - matrix renormalization group ( dmrg)@xcite and its higher - dimensional generalizations,@xcite the density matrix is also used as a diagnostic tool in the contractor renormalization ( core ) method for numerical renormalization group in two dimensions,@xcite and forms the basis of a method to identify the order parameter related to a quasi - degeneracy of ground states.@xcite    in previous work,@xcite we extended the results of chung and peschel@xcite to write the density matrix ( dm ) of a cluster of @xmath3 sites cut out from a system of noninteracting spinless fermions in @xmath4 dimensions as the exponential of a quadratic operator , called the pseudo - hamiltonian , as it resembles the hamiltonian of a noninteracting system . that result was then applied in numerical studies of noninteracting spinless fermions in one dimension , to better understand how the distribution of cluster dm eigenvalues scale with @xmath3 , and to explore the possibility of designing truncation schemes based on the pseudo - hamiltonian.@xcite we believe truncation schemes such as that described in ref . will be helpful to the choice of basis states in renormalization groups such as core . thus , some questions motivating the present paper were : ( i ) does the density matrix of an interacting fermi - liquid system resembles that of a noninteracting one ? ( ii ) can we apply our exact result in ref .   to two dimensions as well as for one dimension ? ( iii ) is it numerically practical to compute this sort of density matrix in a fermion system . to answer these questions , we investigated a spinless analog of the extended hubbard model , given by the hamiltonian @xmath5 in the limit of @xmath6 , so that fermions are not allowed to be nearest neighbors of each other . this model is chosen for two reasons : ( i ) for a given number of particles , the @xmath6 hilbert space is significantly smaller than the @xmath7 hilbert space , and we can work numerically with larger system sizes ; and ( ii ) the model , in spite of its simplicity , has a rich zero - temperature phase diagram,@xcite where we find practically free fermions in the limit @xmath8 , and an inert solid at half - filling @xmath9 . as the filling fraction approaches quarter - filling from below , @xmath10 , the system becomes congested , highly correlated , but is nonetheless a fermi liquid , perhaps with additional orders that are not clear in small systems . slightly above quarter - filling , the dense fluid and inert solid coexists , while slightly below half - filling , the system is expected to support stable arrays of stripes .    to probe this rich variety of structures in the ground state at different filling fraction @xmath2 , we describe in section  [ sect : formulation ] how the reduced dm of a small cluster , with the appropriate symmetry properties , can be calculated from a finite non - square system subject to twist boundary conditions . then in section  [ sect : ni ] , we investigate in great details the cluster dm spectra of the noninteracting system , particularly on how to handle finite size effects in the numerics , for comparison with the cluster dm spectra of a strongly - interacting system , presented in section  [ sect : strong ] . finally , in section  [ sect : summary ] , we summarized our findings , and discuss the prospects of designing an operator - based dm truncation scheme for interacting systems , at some , if not at all , filling fractions .","summary":"the reduced density matrix of an interacting system can be used as the basis for a truncation scheme , or in an unbiased method to discover the strongest kind of correlation in the ground state . in this paper , we investigate the structure of the many - body fermion density matrix of a small cluster in a square lattice .","abstract":"the reduced density matrix of an interacting system can be used as the basis for a truncation scheme , or in an unbiased method to discover the strongest kind of correlation in the ground state . in this paper , we investigate the structure of the many - body fermion density matrix of a small cluster in a square lattice . the cluster density matrix is evaluated numerically over a set of finite systems , subject to non - square periodic boundary conditions given by the lattice vectors and . we then approximate the infinite - system cluster density - matrix spectrum , by averaging the finite - system cluster density matrix ( i ) over degeneracies in the ground state , and orientations of the system relative to the cluster , to ensure it has the proper point - group symmetry ; and ( ii ) over various twist boundary conditions to reduce finite size effects . we then compare the eigenvalue structure of the averaged cluster density matrix for noninteracting and strongly - interacting spinless fermions , as a function of the filling fraction , and discuss whether it can be approximated as being built up from a truncated set of single - particle operators ."}
{"article_id":"1603.09216","section_id":"i","document":"thermodynamics was the great product of nineteenth century physics ; it is epitomised by the concept that there is an upper bound on the efficiency of any thermodynamic machine , known as the carnot limit . this concept survived the quantum revolution with little more than a scratch ; at present few physicists believe that a quantum machine can produce a significant amount of work at an efficiency exceeding the carnot limit . however , carnot s limit is only achievable for vanishing power output . it was recently observed that quantum mechanics imposes a _ stricter _ upper bound on the efficiency at finite power output@xcite . this upper bound coincides with that of carnot at vanishing power output , but decays monotonically as one increases the desired power output . this upper bound was found for two - terminal thermoelectric machines .    in recent years , there has been a lot of theoretical @xcite and experimental @xcite interest in three - terminal thermoelectrics , see fig .  [ fig : three - term ] . in particular , it is suggested that chiral three - terminal thermoelectrics@xcite could have properties of great interest for efficient power generation . all these three - terminal systems are quantum versions of traditional thermocouples @xcite , since they have one terminal in contact with a thermal reservoir and two terminals in contact with electronic reservoirs . see fig . [ fig : three - term ] . they turn heat flow from the thermal reservoir into electrical power in the electronic reservoirs , or vice versa . we refer to such three - terminal systems as _ quantum thermocouples _ , since they are too small to be treated with the usual boltzmann transport theory . there are two quantum lengthscales which enter into consideration ; the electron s wavelength and its decoherence length . in this work we will be interested in devices in which the whole thermocouple is much smaller than the decoherence length @xcite . such thermocouples would typically be larger than the electron wavelength , although they need not be . the crucial point is that electrons flow elastically ( without changing energy or thermalizing ) through the central region in fig . [ fig : three - term]a . this can also be a simple phenomenological model of the system in fig . [ fig : three - term]c , see section  [ sect : voltage - probe ] . in these systems , quantum interference effects can have a crucial effect on the physics . such phase - coherent transport effects are not captured by the usual boltzmann transport theory , but they can be modelled using christen and bttiker s nonlinear scattering theory @xcite , in the cases where it is acceptable to treat electron - electron interactions at the mean - field level . such three - terminal systems are about the simplest self - contained quantum machines . there is a heat current into the system from reservoir m , @xmath0 , but no electrical current from reservoir m , @xmath3 see fig . [ fig : phenomenological ] . if reservoir l and r are at the same temperature @xmath4 , and reservoir m is hotter at @xmath5 , we can use the heat flow @xmath0 to drive an electrical current from l to r. if this electrical current flows against a potential difference , then the system turns heat into electrical power , and so is acting as a thermodynamic _ heat - engine_. alternatively , we can make the system act as a _ refrigerator _ , by applying a bias which drives a current from l to r , and `` sucks '' heat out of a reservoir m ( peltier cooling ) taking it to a lower temperature than reservoirs l and r , @xmath6 .    in this work , we consider arbitrary phase - coherent three - terminal quantum systems that fall in to the category described by christen and buttiker s nonlinear scattering theory @xcite . we find upper bounds on such a system s efficiency as a heat - engine or a refrigerator at finite power output . we will show that these bounds coincide with those of two - terminal quantum systems considered in ref . [ ] , irrespective of whether the three - terminal system s time - reversal symmetry is broken ( by an external magnetic field ) or not . thus our bound applies equally to normal and _ chiral _ thermoelectrics@xcite . when the system acts as a heat - engine ( or energy - harvester@xcite ) , the input is the heat current out of the thermal reservoir ( reservoir m ) , @xmath0 , and the output is the electrical power generated by the system , @xmath7 . this power flows into a load attached between reservoirs l and r ; this load could be a motor turning electrical work into mechanical work , or some sort of work storage device . the heat - engine ( eng ) efficiency is defined as @xmath8 this never exceeds carnot s limit , @xmath9 where we recall that @xmath5 . carnot s limit is the upper bound on efficiency , but it is only achievable at zero power output .    for the refrigerator the situation is reversed , the load is replaced by a power supply , and the system absorbs power , @xmath10 , from that supply . the cooling power output is the heat current out of the colder reservoir ( reservoir m ) , @xmath0 . thus the refrigerator ( fri ) efficiency or _ coefficient of performance _ ( cop ) is , @xmath11 this never exceeds carnot s limit , @xmath12 where we have @xmath6 ( which is the opposite of heat - engine ) . carnot s limit is the upper bound on efficiency , but it is only achievable at zero cooling power . bekenstein @xcite and pendry @xcite independently noted that there is an upper bound on the heat that can flow through a single transverse mode . as a result , the heat that any wave ( electron , photon , etc ) can carry away from reservoir @xmath13 at temperature @xmath14 through a cross - section carrying @xmath15 transverse modes is @xmath16 where the number of transverse modes is of order the cross - section in units of the wavelength of the particles carrying the heat . this bekenstein - pendry bound was observed experimentally in point - contacts@xcite , and recently verified to high accuracy in quantum hall edge - states @xcite . [ ] pointed out that this upper bound on heat flow , must place a similar upper bound on the power generated by a heat - engine ( since the efficiency is always finite ) . those works used the nonlinear version of landauer scattering theory @xcite to find this upper bound on the power generated , which they called the quantum bound ( qb ) , since its originates from the wavelike nature of electrons in quantum mechanics . it takes the form @xmath17 where @xmath18 . [ ] then calculated the upper bound on an heat engines efficiency for given power generation @xmath7 and showed that it is a monotonically decaying function of @xmath19 . there is no closed form algebraic expression for this upper bound at arbitrary @xmath19 , it is given by the solution of a transcendental equation . however , for @xmath20 one has @xmath21 with the next term in the expansion being of order @xmath22 . in the limit of maximum power generation , @xmath23 , the upper bound onefficiency is @xmath24 refs . [ ] calculated similar expressions for the upper bound on refrigerator efficiency as a function of cooling power . in this case , the upper bound is found to be half the bekenstein - pendry bound on heat - flow . again , the maximum efficiency equals that of carnot for cooling powers much less than the bekenstein - pendry bound , and decays monotonically as one increases the desired cooling power towards its upper limit .    in the naive classical limit of vanishing wavelength compared to system size , one has @xmath25 and so the quantum bound @xmath26 and @xmath27 become irrelevant ( they go to infinity ) . so in this limit , it appears that one can achieve carnot efficiency for any power output . however quantum mechanics says that this is not the case , that for any power output that is a significant fraction of @xmath26 or @xmath27 , the upper bound on efficiency is lower than carnot efficiency . this efficiency bound was derived for two - terminal quantum systems , here we will show that exactly the same bounds apply to three - terminal quantum systems . a sketch of a system for which the voltage - probe model discussed in section  [ sect : voltage - probe ] is correct . the role of reservoir m is played by the island which is large enough that any electron entering it thermalizes at temperature @xmath28 before escaping back into the dot . the electro - neutrality of the island ensures that @xmath1 in the steady - state . however , the fact the island exchanges heat ( in the form of photons or phonons ) with a thermal reservoir , means that it can still deliver heat to the three - terminal system . the island is in a steady - state at temperature @xmath28 , for which the heat flow out of the island due to electrons , @xmath0 , equals the heat flow into the island due to photons ( or phonons ) . ]      here we discuss two examples of systems for which the bounds we derive here apply . the first example is the _ chiral thermoelectric _ sketched in fig . [ fig : three - term]b , as discussed in refs . [ ] . this is a three - teminal system exposed to such a strong external magnetic field that the electron flow only occurs via edge - states ( all bulk states are localized by the magnetic field ) . these edge - state are chiral , which means they circulate in a preferred direction in the scattering region ( anticlockwise in fig . [ fig : three - term]b ) , this is an intriguing situation for a heat - engine in which one wants to generate electrical power by driving a flow of electrons from reservoir l ( at lower chemical potential ) to reservoir r ( at higher chemical potential ) . the b - field alone generates an electron flow directly from l to r _ without _ a corresponding direct electron flow from r to l. thus it would seem plausible that one could take advantage of this , with a suitable choice of reservoir m and of the central scattering region to achieve higher efficiencies than in a two - terminal device ( where every flow from l to r has a corresponding flow from r to l ) . unfortunately , our general solution for a three - terminal system will show that the upper bound on efficiency at given power output is independent of the external magnetic field , so it is the same for chiral or non - chiral systems . the second example is the quantum thermocouple sketched in fig . [ fig : three - term]c . here , the third terminal ( reservoir m ) supplies heat in the form of photons ( or phonons ) . such systems have been considered using microscopic models of the photon flow @xcite , however here we instead use a phenomenological argument to replace the reservoir of photons sketched in fig . [ fig : three - term]c by the reservoir of electrons sketched in fig . [ fig : three - term]a . this is the `` voltage probe '' model @xcite , in which inelastic scattering ( such as electrons scattering from photons ) is modelled by a reservoir of electrons whose chemical potential is chosen such that that on average every electron that escapes the system into that reservoir is replaced by one coming into the system from that reservoir , so @xmath1 . [ fig : phenomenological ] shows a system for which this voltage probe model is correct . the island is large enough that any electron entering it thermalizes at temperature @xmath28 before escaping back into the dot . since the island is in a steady - state at temperature @xmath28 , the heat flow out of the island due to electrons must equal the heat flow into the island due to photons . however , one can also argue phenomenologically that the same model is a simplified description of the system sketched in fig . [ fig : three - term]c . this phenomenological model treats the exchange of a photon between the dot and reservoir m , as the replacement of an electron in the dot which has the dot s energy distribution , with an electron which has reservoir m s energy distribution . of course , this is not the most realistic model of electron - photon interactions . in particular , it assumes that each electron entering from reservoir l or r either escapes into one of those two reservoirs without any inelastic scattering from the photon - field , or it escapes after undergoing so many scatterings from the photon - field that it has _ completely _ thermalized with the photon - field . as such , this model does not capture the physics of electrons that undergo one or two inelastic scatterings from the photon - field before escaping into reservoir l or r. at this simplistic level of modelling , nothing would change if it were phonons rather than photons coming from reservoir m. while this voltage probe model has been successfully used to understand the basics of many inelastic effects in nanostructures , it should not be considered a replacement for a proper microscopic theory ( see e.g.  refs . [ ] for a discussion of how the voltage probe model fails to capture aspects of inelastic scattering in ultra - clean nanostructures ) . one should be cautious about applying results for a system of the type in fig . [ fig : three - term]a to a system of the type in fig . [ fig : three - term]c , but it is none the less a reasonable first step to understanding its physics .","summary":"such a system is a quantum phase - coherent version of a thermocouple , and the theory applies to systems in which interactions can be treated at a mean - field level . we show that the upper bound on efficiency at given power output is of quantum origin and is stricter than carnot s bound . -25 mm   ( a ) the three - terminal machine ( heat - engine or refrigerator ) that we consider , the exchange of electrons with reservoir m carries a heat current , , but not an electrical current , . ( b ) a chiral thermoelectric device reproduced from ref .  [ ] . ( c ) a system in which photons deliver the heat , this can be phenomenologically modelled by ( a ) , see section  [ sect : voltage - probe ] . , title=\"fig : \" ]   ","abstract":"we consider the nonlinear scattering theory for three - terminal thermoelectric devices , used for power generation or refrigeration . such a system is a quantum phase - coherent version of a thermocouple , and the theory applies to systems in which interactions can be treated at a mean - field level . we consider an arbitrary three - terminal system in any external magnetic field , including systems with broken time - reversal symmetry , such as chiral thermoelectrics , as well as systems in which the magnetic field plays no role . we show that the upper bound on efficiency at given power output is of quantum origin and is stricter than carnot s bound . the bound is exactly the same as previously found for two - terminal devices , and can be achieved by three - terminal systems with or without broken time - reversal symmetry . thus the bound appears to be universal for two - terminal and three - terminal ( chiral and non - chiral ) thermoelectrics .    -25 mm   ( a ) the three - terminal machine ( heat - engine or refrigerator ) that we consider , the exchange of electrons with reservoir m carries a heat current , , but not an electrical current , . ( b ) a chiral thermoelectric device reproduced from ref .  [ ] . ( c ) a system in which photons deliver the heat , this can be phenomenologically modelled by ( a ) , see section  [ sect : voltage - probe ] . , title=\"fig : \" ]   "}
{"article_id":"1603.09216","section_id":"c","document":"we have used scattering theory to find the upper bound on the efficiency of a three - terminal thermoelectric quantum machine at given power output . we find that this bound can be achieved at any external magnetic fields , so the bound is the same for chiral thermoelectrics as for those with no external field . this bound is the same as already found for two - terminal thermoelectric systems in refs . the upper bound on efficiency equals the carnot efficiency when the power output is vanishingly small , but it decays monotonically for increasing power output , as shown in fig .  2 of ref .  [ ] .    it would be worth seeing if one can derive the similar bound for the system in fig . [ fig : three - term]c with a microscopic model of the photon ( or phonon ) exchange , rather than the phenomenological model used here . most real quantum systems also loose heat to the environment ( through photon or phonon exchange ) , this can be modelled as a fourth terminal which exchanges heat but not charge with the system . a similar four - terminal geometry was discussed in ref . [ ] , which showed that such system operates in a non - thermal state and so exhibits non - local laws of thermodynamics . intriguingly , such a system can have a higher efficiency under given conditions than an equivalent classical machine operating in a thermal state , even if that classical machine is carnot efficient . it would be interesting to see how this bound behaves in such a situation , although we doubt that the pedestrian ( brute - force ) optimization used in this work will be extendable to more than three - terminals .","summary":"we consider the nonlinear scattering theory for three - terminal thermoelectric devices , used for power generation or refrigeration .","abstract":"we consider the nonlinear scattering theory for three - terminal thermoelectric devices , used for power generation or refrigeration . such a system is a quantum phase - coherent version of a thermocouple , and the theory applies to systems in which interactions can be treated at a mean - field level . we consider an arbitrary three - terminal system in any external magnetic field , including systems with broken time - reversal symmetry , such as chiral thermoelectrics , as well as systems in which the magnetic field plays no role . we show that the upper bound on efficiency at given power output is of quantum origin and is stricter than carnot s bound . the bound is exactly the same as previously found for two - terminal devices , and can be achieved by three - terminal systems with or without broken time - reversal symmetry . thus the bound appears to be universal for two - terminal and three - terminal ( chiral and non - chiral ) thermoelectrics .    -25 mm   ( a ) the three - terminal machine ( heat - engine or refrigerator ) that we consider , the exchange of electrons with reservoir m carries a heat current , , but not an electrical current , . ( b ) a chiral thermoelectric device reproduced from ref .  [ ] . ( c ) a system in which photons deliver the heat , this can be phenomenologically modelled by ( a ) , see section  [ sect : voltage - probe ] . , title=\"fig : \" ]   "}
{"article_id":"1204.0333","section_id":"i","document":"multiple - spin exchange interactions have attracted much interest for a long time . these interactions appears either as many - body direct exchange processes@xcite or as higher - order corrections in the strong - coupling expansion of the half - filled hubbard model . @xcite in most cases ( especially in mott insulators ) , the four - spin ring ( or cyclic ) exchange is rather small compared with the usual heisenberg term . however , it may play a significant role in @xmath0he , where hardcore repulsion makes many - body exchanges more likely than the standard two - body one , and mott insulators close to the metal - insulator transitions . in fact , such interactions are expected to be crucial for explaining unusual magnetic behavior in @xmath0he absorbed on graphite@xcite , wigner crystals @xcite and some mott insulators on triangular lattices.@xcite the relevance of the four - spin cyclic exchange has also been reported@xcite in fully describing the inelastic neutron - scattering experiments for such cuprates as la@xmath1cuo@xmath2 , la@xmath3ca@xmath4cu@xmath5o@xmath6 , la@xmath2ca@xmath7cu@xmath5o@xmath6 , cacu@xmath1o@xmath8 , and srcu@xmath1o@xmath8 . a second motivation to investigate multiple - spin exchange interactions stems from the exotic physics that emerges from their competition with the heisenberg spin exchange . for instance , certain sorts of spin nematic phases are known to be stabilized in some two - dimensional heisenberg magnets with ring - exchange interaction . @xcite also multiple - spin exchanges can lead to new emerging quantum critical behaviors like the deconfined quantum criticality @xcite or the spin bose - metal . @xcite on top of these novel phases , even more exotic topological phases have been predicted to be realized with such interactions . @xcite    a paradigmatic and minimal model that realizes these two aspects of the multiple - spin exchange interactions would be the two - leg spin ladder with a ring - exchange : @xmath9 where @xmath10 ( @xmath11 ) denotes the spin-1/2 operator on the chain-@xmath12 and the rung @xmath13 of the spin ladder . the parameters @xmath14 and @xmath15 respectively are the intrachain- and the interchain exchange coupling ( fig . [ fig:2leg_ladder ] ( a ) ) . the ring exchange @xmath16 is defined on each plaquette ( two - rung cluster : fig . [ fig:2leg_ladder ] ( b ) ) and cyclically permutes the states of the four spins on the plaquette . this model is considered as relevant to describe the physical properties of ladder compounds e.g. la@xmath2ca@xmath7cu@xmath5o@xmath6 ( refs .  ) and cacu@xmath1o@xmath8 ( ref .  ) . the model ( [ eqn : ladder ] ) is interesting in its own right and has been studied extensively over the years and its phase diagram@xcite , ground - state- and dynamical properties@xcite , quantum phase transitions@xcite , and entanglement properties@xcite have been explored by both analytical and numerical approaches . is defined . [ fig:2leg_ladder ] ]    the zero - temperature phase diagram is rich and six different phases have been identified @xcite : the ferromagnetic phase , the rung - singlet ( rs ) phase , the staggered dimerized phase , the scalar chirality phase , the dominant vector chirality ( vc ) phase , and the dominant collinear spin phase . all phases are gapful except the ferromagnetic phase . the four - spin cyclic exchange manifests itself by stabilizing the scalar chirality phase , which spontaneously breaks the time - reversal symmetry , and the vc phase . the latter phase has a unique singlet ground state with a finite gap . in sharp contrast to the usual rs phase of the two - leg spin ladder , the lowest triplet excitation of the vc phase is not the standard triplon created by the spin operators @xmath10 but is built from the vector chirality @xmath17 as we will show below consequently , the dominant ground - state correlations of this phase occur not in the spin - spin channel but rather in the vector - chirality channel.@xcite the relationship between the rs and vc phases can be simply understood by means of a spin - chirality duality transformation . @xcite under the transformation @xmath18 the nel staggered magnetization @xmath19 is interchanged with the vc order parameter @xmath20 and vice - versa . @xcite model ( [ eqn : ladder ] ) is invariant , i.e. self - dual , under the duality transformation ( [ spinchirality ] ) when @xmath21 . physics in the vicinity of this point is dictated by the competition between the rs and the vc orders .    in this paper , we investigate the competition between these orders by means of a semiclassical approach which treats the nel antiferromagnetic ( naf ) and the vc order parameters on an equal footing . to this end , the model ( [ eqn : ladder ] ) is first expressed in terms of spin-1 hardcore boson operators that create triplet states out of the vacuum . @xcite in this basis , the spin - chirality transformation ( [ spinchirality ] ) has a simple interpretation as the u(1 ) gauge transformation of the bosons.@xcite the next step of the approach is to perform a simple mean - field approximation of the phases of the bosonic model . we then incorporate quantum fluctuations by constructing semiclassical low - energy hamiltonians which describe the competition of the rs and the vc orders as well as the usual rotational fluctuations . it is important to observe that our approach is not restricted to one dimension but applies to e.g. higher - dimensional systems consisting of two - spin clusters as well . in this respect , the approach is directly relevant to two - dimensional half - filled bilayer spin-1/2 fermions with ring - exchange interaction.@xcite finally , we investigate the interesting mutual induction phenomenon between spin and chirality degrees of freedom within our semiclassical approach which signals , for instance , the emergence of a vc phase by the application of a magnetic field . this last result has been first predicted in one dimension by means of the bosonization approach.@xcite    the rest of the paper is organized as follows . in sec . [ sec : effective - spin1-model ] , the mapping of model ( [ eqn : ladder ] ) onto that of spin-1 hardcore bosons and the path - integral representation of the resulting model , on which our semiclassical approach is based , are presented . then , we draw the semiclassical phase diagram in sec . [ sec : mean - field - pd ] by minimizing the classical energy , which is equivalent to mean - field approximation . the low - energy effective actions for the main phases are then derived in sec . [ sec : effective - action ] . as an application of our method , we investigate the mutual induction phenomenon between spin and chirality in sec . [ sec : effect - magnetic - field ] . finally , our concluding remarks are presented in sec . [ sec : concluding - remark ] . the paper is supplied with one appendix which provides some technical information on the semiclassical approach .","summary":"the latter is defined in terms of spin-1 hardcore bosons which treat the nel and vector chirality order parameters on an equal footing . , we reveal the mutual induction phenomenon between spin and chirality with , for instance , the emergence of a vector - chirality phase from the application of a magnetic field in bilayer systems coupled by four - spin exchange interactions .","abstract":"we investigate the competition between different orders in the two - leg spin ladder with a ring - exchange interaction by means of a bosonic approach . the latter is defined in terms of spin-1 hardcore bosons which treat the nel and vector chirality order parameters on an equal footing . a semiclassical approach of the resulting model describes the phases of the two - leg spin ladder with a ring - exchange . in particular , we derive the low - energy effective actions which govern the physical properties of the rung - singlet and dominant vector chirality phases . as a by - product of our approach , we reveal the mutual induction phenomenon between spin and chirality with , for instance , the emergence of a vector - chirality phase from the application of a magnetic field in bilayer systems coupled by four - spin exchange interactions ."}
{"article_id":"cond-mat0308601","section_id":"i","document":"if a liquid is cooled and crystallization is avoided , one obtains a supercooled liquid . upon further cooling the system falls out of equilibrium and results in a glass . during the transition from liquid to supercooled liquid to glass the thermodynamic properties change and even more drastic changes occur in the dynamics @xcite . the viscosity increases by many orders of magnitude upon cooling and the mean square displacement ( msd ) as a function of time develops a plateau at intermediate times . the lower the temperature the longer the waiting time within the plateau until a second rise in the mean square displacement occurs @xcite . one common explanation for the plateau is that while at high temperatures one has ( at late enough times ) normal diffusion , at lower temperatures particles are caged in , i.e. trapped by their neighbors , and spend longer time within this cage with decreasing temperatures . the second increase in the msd indicates that after long enough waiting time the particles manage to escape their cage . this escape out of the cage ( `` jump '' ) is the focus of this paper .    to set the work of this paper in context , we review briefly previous studies on the dynamics of supercooled liquids and glasses . we restrict ourselves mostly to simple glass formers , excluding major work about strong glass formers , ionic systems , polymers and crystals . central quantities in both * experiments and computer simulations * are the viscosity , diffusion constant and msd . the msd , which is an average over single particle @xmath0 displacements , @xmath1 and variations thereof @xcite @xmath2 show jumps when viewed with fine enough time resolution , and when studied at low enough temperatures and for single configurations @xcite . detailed studies of these jumps indicate collective motion @xcite . one learns about the interplay between regular diffusion and hopping motion via four - point correlation functions @xcite and the van hove correlation function @xmath3 @xcite where @xmath4 is the self part and @xmath5 is the distinct part . the hopping shows up in an additional peak in @xmath4 and an increase in the amplitude at @xmath6 of @xmath5 . recently attention has been drawn to the non - gaussian tail of @xmath7 @xcite and the non - gaussian parameter @xmath8 @xcite which is the second coefficient of the cumulant series of @xmath9 , the fourier transform of @xmath4 . they are signatures of non - exponential behavior , which might be either due to homogeneous complex dynamics and/or due to spatially heterogeneous dynamics @xcite . this has been studied both with experiments @xcite and in simulations of two - dimensional @xcite and three - dimensional systems @xcite . studies of the most mobile particles reveal that they move increasingly more collectively with decreasing temperature . one distinct feature of this collective dynamics is that some particles are moving along a string @xcite . similar motion has been found via the study of normal modes which are commonly used to study the dynamics at low temperatures @xcite . the dynamics of glasses out of equilibrium , i.e. systems which have been quenched from high to low temperature , displays additional complexity , since the system might `` age '' @xcite . this means that the dynamics depends on the waiting time between the quench and the measurement @xcite which results in the violation of the fluctuation dissipation theorem @xcite . another fruitful approach to gain insight into the dynamics of supercooled liquids and glasses has been to investigate the energy landscape of the inherent structure , that means of the instantaneous configurations which have been quenched to their local potential energy minimum @xcite . at the same temperature when the system starts slowing down drastically , the potential energy of the inherent structure undergoes a qualitative change @xcite . the long time behavior of this potential energy shows jumps between metabasins , where the latter are groups of strongly correlated local minima @xcite . the mean average waiting time @xmath10 between these jumps turns out to be dominated by the long times . @xmath10 together with the diffusion constant allow an estimate of the cage size @xcite . direct studies of the cage have been done via three - time correlations @xcite , velocity - velocity correlations @xcite , via the cage correlation function @xcite , and a passage time before a particle escapes @xcite . the results of these studies tell us about cage properties such as the cage size and waiting time within a cage ( or jump rate ) . hand in hand with the experiments and simulations are the * theoretical models * for supercooled liquids and glasses . one of the very successful theories is the mode coupling theory of the glass transition ( mct ) @xcite , which describes the dynamics of supercooled liquids via non - linear dynamics of coupled density modes and makes predictions for quantities such as @xmath11 , @xmath12 , and the susceptibility @xmath13 . the extended version of mct includes hopping processes via the coupling to current fluctuations @xcite . the comparison of experiment and this theory for @xmath14 @xcite and @xmath8 @xcite shows very good agreement . the mct is a theory for the glass transition for temperatures above the glass transition . below the glass transition there exists no equivalent of a microscopic theory such as mct . some phenomenological theories which are more general models for solids build in hopping either indirectly as in the free volume model @xcite or directly in hopping models @xcite . direct hopping models are based on the assumption that hopping is the main process which explains the dynamics . the starting point in these models is usually a random walk and the anomalous diffusion is incorporated via a distribution of waiting times ( or jump rates ) . the jumping entities are either defects @xcite , uncharged carriers @xcite or ( in the case of predictions for ac and dc conductivity ) charged carriers @xcite . the goal of this paper is to obtain via single particle trajectories direct information about jump processes such as jump sizes and waiting times between jumps . specific examples of the dynamics of single particle jumps , in the form of a plot of one component of @xmath15 @xcite or in the form of a two- or three - dimensional picture of the particle trajectory @xcite , are very helpful to get an idea of some qualitative features of jumps , such as the detailed geometry of jump processes @xcite . in this paper , however , we go beyond single examples by defining a systematic search algorithm for jump processes . for the case of single particle trajectories a similar approach has been used in the work @xcite , where the jump criterion is a minimum hopping distance , which is the same for all particles . in contrast , we use a relative criterion , where for each particle its size of fluctuations is compared to its jump size . we choose this relative criterion to be able to identify jumps of particles of different sizes and neighborhood . that means the criterion is adjusted to the cage size of each individual particle . as criterion for the occurrence of a jump we use the positions of particles instead of their energy . while both approaches are fruitful , we believe that many theoretical models and interpretations of simulations and experiments are based on an intuitive picture of the particle motion in real space . similarly our goal is to mimic a careful observer of each particles motion in our system . we therefore use single particle trajectories , instead of a quantity which is an average over all particles ( as in the work @xcite ) . for the case of single particle trajectories the distinction between vibrational and hopping motion turns out to be clearer by taking time averages than by using trajectories of the inherent structure .    in the following we define our model , and give details about the simulation ( sec . [ sec : model ] ) . our precise definition of a jump is given in sec . [ sec : jumpdef ] . we find two types of jumps ( irreversible and reversible ) . the latter are distinguished for the rest of the paper ( in distinction from @xcite . ) in sec . [ sec : nojumps ] we count as a function of temperature the number of jumping particles , and in sec . [ sec : nostates ] the number of visited different cages . in sec . [ sec : times ] we investigate the times during a jump and between successive jumps . the jump size both in position and in potential energy are presented in secs . [ sec : jumplengths ] and [ sec : energy ] . in sec . [ sec : conclusions ] we conclude with a summary of our results , a comparison with the results of previous work and with our resulting picture of jump processes . we finish with open questions suggesting future work .","summary":"using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position . the ratio of irreversible to reversible jumps is also increasing with increasing temperature , which we interpret as a consequence of the increased likelihood of changes in the cages , i.e. a blocking of the `` entrance '' back into the previous cage . in accordance with this interpretation ,","abstract":"we study a binary lennard - jones system below the glass transition with molecular dynamics simulations . to investigate the dynamics we focus on events ( `` jumps '' ) where a particle escapes the cage formed by its neighbors . using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position . we find two kinds of jumps : `` reversible jumps , '' where a particle jumps back and forth between two or more average positions , and `` irreversible jumps , '' where a particle does not return to any of its former average positions , i.e. successfully escapes its cage . for all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur . with increasing temperature relaxation is enhanced by an increasing number of jumps , and growing jump lengths in position and potential energy . however , the waiting time between two successive jumps is independent of temperature . this temperature independence might be due to aging , which is present in our system . the times of jump duration are at all temperatures significantly shorter than the waiting times . the ratio of irreversible to reversible jumps is also increasing with increasing temperature , which we interpret as a consequence of the increased likelihood of changes in the cages , i.e. a blocking of the `` entrance '' back into the previous cage . in accordance with this interpretation , the fluctuations both in position and energy are increasing with increasing temperature . a comparison of the fluctuations of jumping particles and non - jumping particles indicates that jumping particles are more mobile even when not jumping . the jumps in energy normalized by their fluctuations are decreasing with increasing temperature , which is consistent with relaxation being increasingly driven by thermal fluctuations . in accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position ."}
{"article_id":"cond-mat0308601","section_id":"c","document":"we study the dynamics of a binary lennard - jones system below the glass transition . our focus is on jump - processes , which we identify via single particle trajectories . two kind of jumps are found : `` reversible jumps , '' where a particle jumps back and forth between one or more average positions , and `` irreversible jumps , '' where a particle does not return to any of its former average positions , i.e. successfully escapes its cage of neighbors . both irreversible and reversible jumps of a and b particles occur at all temperatures . with increasing temperature more particles jump , more average positions are visited , the jump size both in position and in the absolute value of the potential energies @xmath157 and @xmath158 ( total and single - particle , not minimized and minimized ) increase , and the fluctuations in position @xmath159 and potential energy @xmath160 increase . the fluctuations are larger for jumping particles than for non - jumping particles even if fluctuations during the jump are not part of the average , which indicates that jumping particles are not only during jump times more mobile than non - jumping particles . the ratio @xmath161 of irreversible jumps decreases with increasing temperature . this confirms a commonly used assumption that with increasing temperature the irreversible jumps become more driven by fluctuations .    with increasing temperature also irreversible jumps become proportionally more frequent than reversible jumps . we interpret this such that irreversible and reversible jumps are similar in that sense that a particle tries to escape its cage . in the case of reversible jumps the particle finds its way back into the cage whereas in the case of an irreversible jump the path back into the cage becomes blocked due to rearrangements of the cage . at larger temperature these rearrangements of the cage become more likely ( since for example the fluctuations increase ) and therefore irreversible jumps occur more often . irreversible and reversible jumps show in most quantities qualitatively the same behavior , such as their temperature dependence of jump size in position and energy , and differ only in size . an exception to this similarity is the distribution of jump sizes , which suggests that there might be an additional jump process in the case of reversible jumps indicated by an additional peak at small jump sizes . the most surprising result of our work is that the times between successive jumps are independent of temperature . this is most likely due to aging , which could mean on the time scale of our simulation that @xmath66 reflects the time scale of @xmath40 from which we quenched the system , and that @xmath66 might show temperature dependence at later times . the latter would be consistent with the work of doliwa _ et al . _ @xcite who find in their simulations of very long times that the distribution of waiting times ( however , identified via the collective quantity of the minimized potential energy ) initially is temperature independent and of different power law than at later times when temperature dependence occurs . we do find aging in that sense that the times before the first jump are shorter than the times after the last jump of a particle ( an effect which becomes less for temperatures near @xmath162 ) . future work ( which is in progress ) will tell us if in our system @xmath66 becomes temperature dependent after longer times . however , the dynamics does depend on temperature for all other here investigated quantities such as the number of jumps and the fraction of reversible jumps . another question which we would like to raise for future work is how much single particle jumps can tell us about relaxations of a glass which might include collective motion . it seems plausible that single particle jumps are strongly correlated with collective jumps and in that sense give us very similar information to studies of collective quantities . we find that many of the single particle jumps in our system are spatially and temporally correlated , i.e. are showing collective motion . systematic studies for confirmation remain to be done in the future . we also find the signature of many - 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[ sec : model ] , we start with the periodically ( every 2000 md steps of step size @xmath164 ) stored configurations @xmath130 where @xmath149 . for the single particle fluctuations we use the time averages @xmath165 , their squares @xmath166 , and @xmath167 at times @xmath168 . we first make a preliminary estimate of the fluctuations @xmath169 and then obtain the final estimate for the fluctuations @xmath44 by redoing the average over @xmath170 but by averaging only over all @xmath171 for which @xmath172 to roughly exclude jumps from the average . we define @xmath15 to be a spike if @xmath173 where @xmath99 is defined as in sec . [ sec : jumplengths ] . similar to case 1 we say that the spike @xmath15 returns to the previous average position if @xmath174 . c.  oligschleger and h.  r.  schober , solid  state  commun . * 93 * , 1031 ( 1995 ) . c.  f.  vardeman ii and j.  d. gezelter , j.  phys . a * 105 * , 2568 ( 2001 ) . e.  r. weeks and h.  l. swinney , phys.rev . e * 57 * , 4915 ( 1998 ) . m.  a. fogleman , m.  j. fawcett and t.  h. solomon , phys . e * 63 * , 020101(r ) . to determine the starting time @xmath64 and ending time @xmath65 of a jump we use an approach similar to our definition for the occurrence of a jump ( eq . ( [ eq : jumpoccur ] ) ) . we compare the differences in averaged positions @xmath175 and the fluctuations @xmath44 ( see @xcite ) . if a jump has been detected at time @xmath176 ( because @xmath177 ) then the starting time @xmath64 is the largest time @xmath96 for which @xmath178 within the boundaries of @xmath179 , where in the case of a first jump @xmath180 corresponds to the beginning of the production run and in the case of the existence of a previous jump with @xmath181 then @xmath182 . similarly after a jump has started it is detected to be finished at the earliest time @xmath183 for which @xmath184 . the finishing time of the jump @xmath65 is then the maximum of @xmath176 and @xmath185 where we subtract @xmath186 ( @xmath187 ) because @xmath188 ( see eq . ( [ eq : deltaoverlri ] ) and @xcite ) . if the condition for @xmath183 never occurs , then @xmath65 is equal to the length of the simulation run . to determine @xmath66 in case 2 of fig . [ fig : jumptype ] , we use for the first spike the time between the previous @xmath64 and the time of the spike and for successive spikes their time differences . f.  h.  stillinger and t.  a.  weber , j.  chem . phys . * 80 * , 4434 ( 1984 ) ; t.  a.  weber and f.  h.  stillinger , phys . b * 32 * , 5402 ( 1985 ) . in fig . [ fig : sigei_sigeinojump]a and fig . [ fig : sigei_sigeinojump]b we use the time average windows @xmath55 . in fig . [ fig : sigei_sigeinojump]a we then average over jumps of a certain kind . in the case of a particle with multiple jumps this means that the times after the first jump and before the last jump are counted twice . in fig . [ fig : sigei_sigeinojump]b however we compare the behavior of _ particles _ ( instead of jump events ) and therefore count these time windows only once .","summary":"we study a binary lennard - jones system below the glass transition with molecular dynamics simulations . to investigate the dynamics we focus on events ( `` jumps '' ) where a particle escapes the cage formed by its neighbors . we find two kinds of jumps : `` reversible jumps , '' where a particle jumps back and forth between two or more average positions , and `` irreversible jumps , '' where a particle does not return to any of its former average positions , i.e. successfully escapes its cage . the fluctuations both in position and energy are increasing with increasing temperature . a comparison of the fluctuations of jumping particles and non - jumping particles indicates that jumping particles are more mobile even when not jumping .","abstract":"we study a binary lennard - jones system below the glass transition with molecular dynamics simulations . to investigate the dynamics we focus on events ( `` jumps '' ) where a particle escapes the cage formed by its neighbors . using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position . we find two kinds of jumps : `` reversible jumps , '' where a particle jumps back and forth between two or more average positions , and `` irreversible jumps , '' where a particle does not return to any of its former average positions , i.e. successfully escapes its cage . for all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur . with increasing temperature relaxation is enhanced by an increasing number of jumps , and growing jump lengths in position and potential energy . however , the waiting time between two successive jumps is independent of temperature . this temperature independence might be due to aging , which is present in our system . the times of jump duration are at all temperatures significantly shorter than the waiting times . the ratio of irreversible to reversible jumps is also increasing with increasing temperature , which we interpret as a consequence of the increased likelihood of changes in the cages , i.e. a blocking of the `` entrance '' back into the previous cage . in accordance with this interpretation , the fluctuations both in position and energy are increasing with increasing temperature . a comparison of the fluctuations of jumping particles and non - jumping particles indicates that jumping particles are more mobile even when not jumping . the jumps in energy normalized by their fluctuations are decreasing with increasing temperature , which is consistent with relaxation being increasingly driven by thermal fluctuations . in accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position ."}
{"article_id":"1510.00834","section_id":"i","document":"quite a number of observations of type i and ii superluminous supernovae ( slsne , slsne - i , and slsne - ii ) have appeared during the last few years @xcite . the definitions of slsn - i , slsn - ii , and other relevant material are reviewed in  @xcite . there are signs that these objects have been observed even at high redshifts , @xmath5 @xcite . the mechanism of the explosion for such bright and long lasting events is still not fully understood . one can consider either an unusually energetic explosion through which a huge amount of @xmath6niis produced @xcite , or an additional energy source , like a millisecond magnetar , that somehow transforms its rotation energy into the energy of the sn ejecta @xcite , or an interaction of the ejecta with an extended and dense circumstellar ( cs ) envelope , which we focus on in this paper . @xcite have shown that the width of the sn light curve depends on the mass through which the shock wave breaks out . if an exploding star possesses just a standard hydrostatic envelope , like an atmosphere of a supergiant star , the broadening of its light curve can not be extremely large . however , sometimes the star , especially the massive one , can be surrounded by rather dense and extended envelope originated from slow wind , preexplosions , or stellar mergers . in section  [ sec : summary ] we will discuss several possible ways to form such an envelope in a little more detail . the idea of producing large radiative flux during the interaction of the gas ejected in two subsequent explosions was suggested by @xcite for the explanation of sne  iin . @xcite successfully applied this model to the explanation of spectral and light curve features of type iin sn  1994w . a physical mechanism for those multiple explosions ( pulsational pair instability ) was proposed by @xcite . @xcite used this model to explain type ii superluminous sn  2006gy as a moderately energetic explosion ( @xmath7  ergs ) without any radioactive material . sn light curves for the interacting model have been constructed analytically in a number of papers . @xcite compared the light curves for optically thin vs. optically thick cases . @xcite found a good agreement of analytical interacting models with the light curves of slsne  iin . @xcite present several semi - analytical models of the slsn light curves for three feasible power inputs mentioned above and their combinations . they found that the ejecta - csm interaction model provided a better fit to the light curves of most of the observed hydrogen - rich events ( slsne - ii ) they investigated , and they suggested that the same mechanism can be applied to hydrogen - poor events ( slsne - i ) . numerically , the interaction model for slsne is the most difficult for calculation among all the possibilities under consideration . the cause of difficulties is the complicated hydrodynamical structure of the model . most of the gas is gathered into a thin and dense layer behind the radiation dominated shock wave , which can lead to thermal and hydrodynamical instabilities . there are only a very few numerical codes in the world that are able to cope with this problem . a few papers have been published in which slsne - ii were modeled @xcite . the shock interaction with csm is generally considered the most probable explanation for the high luminosity of slsne - ii . in this paper , we will focus on another type of slsne : hydrogen - poor slsne - i . the work was started in @xcite , where we followed @xcite who calculated light curves for the explosion caused by a carbon - oxygen ( co ) white dwarf merger . after the explosion , the model is hydrodynamically similar to the interacting slsn model : the explosion also happens inside a dense ( but probably a bit less extended ) envelope . in @xcite , we show that in principle superluminous sn  2010gx can also be explained by the interaction model with moderate values for the explosion parameters . after that work , we have improved our radiation hydrodynamics numerical code stella @xcite in order to make it more appropriate to solve the slsn problem . in the current paper , we demonstrate a few more carbon - oxygen and helium interacting models for sn  2010gx and ptf09cnd , which are among supernovae with the narrowest and broadest light curves , respectively , known for slsne - i . both models require moderate explosion energy and a reasonable radius of the extended envelope , though the mass of carbon in the envelope must be quite large to reproduce the broad light curve . we briefly discuss some possibilities to create such a system through stellar evolution in the last section of the paper . if these systems really exist this would allow us to claim that the bulk of slsne might have a similar origin and that most of their radiation might be produced during an interaction of sn ejecta with extended envelopes or detached shells . the differences between slsne - i can be explained by different cs envelope structures . this does not relate to some very exotic objects , like asassn15lh @xcite , which stands apart from the bulk of slsne - i due to its extremely high luminosity , and origin of which is still questionable . the structure of the paper is as follows . in section  [ sec : presn ] we describe the models we use . section  [ sec : simul ] explains how we have carried out simulations of sn light curves . in sections  [ sec : hydroprofiles ] and [ sec : lcsp ] we present the results of our calculations and compare them to the observed broad band light curves of sn  2010gx and ptf09cnd . in section  [ sec : summary ] we compare the advantages and limitations of the interaction mechanism to other mechanisms , such as magnetar - powered sne and pair instability sne , and some feasible ways these dense circumstellar envelopes might form .","summary":"a number of type i ( hydrogenless ) superluminous supernova ( slsn ) events have been discovered recently . we briefly discuss possible ways to form such unusual envelopes .","abstract":"a number of type i ( hydrogenless ) superluminous supernova ( slsn ) events have been discovered recently . however , their nature remains debatable . one of the most promising ideas is the shock - interaction mechanism , but only simplified semi - analytical models have been applied so far . we simulate light curves for several type  i slsn ( slsn - i ) models enshrouded by dense , non - hydrogen circumstellar ( cs ) envelopes , using a multi - group radiation hydrodynamics code that predicts not only bolometric , but also multicolor light curves . we demonstrate that the bulk of slsne - i including those with relatively narrow light curves like sn  2010gx or broad ones like ptf09cnd can be explained by the interaction of the sn ejecta with the cs envelope , though the range of parameters for these models is rather wide . moderate explosion energy (  ergs ) is sufficient to explain both narrow and broad slsn  i light curves , but ejected mass and envelope mass differ for those two cases . only 5 to 10  of non - hydrogen material is needed to reproduce the light curve of sn  2010gx , while the best model for ptf09cnd is very massive : it contains almost in the cs envelope and only in the ejecta . the cs envelope for each case extends from 10  to  (  cm ) , which is about an order of magnitude larger than typical photospheric radii of standard sne near the maximum light . we briefly discuss possible ways to form such unusual envelopes ."}
{"article_id":"1510.00834","section_id":"m","document":"we calculate the synthetic light curves using our multi - group radiation hydrodynamic code stella in its standard setup @xcite . the code simulates spherically symmetric hydrodynamic flows coupled with multi - group radiative transfer . standard runs use 300 radial lagrangean mesh zones . when compared to 500 mesh zones , the results do not change significantly . the opacity routine takes into account electron scattering , free - free , and bound - free processes . contribution of spectral lines ( i.e. bound - bound processes ) is treated in approximation of `` expansion '' opacity . various approaches to the expansion opacity are described in detail by @xcite . we use the method suggested by @xcite , see also @xcite . all runs employed 100 frequency groups in the transport solver and a relatively short spectral line list ( @xmath25  lines ) in the opacity routine . stella in its standard version calculates variable eddington factors in a static approximation once per every 50 hydrodynamic steps . we checked some runs with the results of the rada code , which computes full time - dependent radiative transfer for intensity and uses more reliable eddington factors @xcite . the comparison with stella runs shows that the difference is not large ( see the discussion below ) . the explosions have been simulated as a `` thermal bomb '' with variable energy @xmath26 ( see table  [ table : models ] ) . the burst duration is 10  seconds in the innermost layers of ejecta with @xmath27 .","summary":"we simulate light curves for several type  i slsn ( slsn - i ) models enshrouded by dense , non - hydrogen circumstellar ( cs ) envelopes , using a multi - group radiation hydrodynamics code that predicts not only bolometric , but also multicolor light curves .","abstract":"a number of type i ( hydrogenless ) superluminous supernova ( slsn ) events have been discovered recently . however , their nature remains debatable . one of the most promising ideas is the shock - interaction mechanism , but only simplified semi - analytical models have been applied so far . we simulate light curves for several type  i slsn ( slsn - i ) models enshrouded by dense , non - hydrogen circumstellar ( cs ) envelopes , using a multi - group radiation hydrodynamics code that predicts not only bolometric , but also multicolor light curves . we demonstrate that the bulk of slsne - i including those with relatively narrow light curves like sn  2010gx or broad ones like ptf09cnd can be explained by the interaction of the sn ejecta with the cs envelope , though the range of parameters for these models is rather wide . moderate explosion energy (  ergs ) is sufficient to explain both narrow and broad slsn  i light curves , but ejected mass and envelope mass differ for those two cases . only 5 to 10  of non - hydrogen material is needed to reproduce the light curve of sn  2010gx , while the best model for ptf09cnd is very massive : it contains almost in the cs envelope and only in the ejecta . the cs envelope for each case extends from 10  to  (  cm ) , which is about an order of magnitude larger than typical photospheric radii of standard sne near the maximum light . we briefly discuss possible ways to form such unusual envelopes ."}
{"article_id":"1510.00834","section_id":"i","document":"the aim of the current work is to test the role of shock interaction in producing light in the non - hydrogen cs envelopes around slsne - i and to see if the bulk of slsne - i can originate from this kind of system . our calculations indicate that if this envelope structure forms in nature , then it can indeed give rise to extremely bright and long - lived supernova light curves . there have been no detailed numerical simulations of the broad band light curves of slsne - i except for @xcite and @xcite . in the current paper , we succeeded in reproducing the narrow light curves of slsne - i as well as the broad ones . we got the correct duration of the light curves and correct fluxes in different bands . we also get very good agreement in reproducing continuum spectral - energy distributions for both cases . we show that the details of the light curves over the fading stage depend on the structure of the cs envelope . both sn  2010gx and ptf09cnd can be explained with moderate explosion energies @xmath0  ergs for an envelope extending up to @xmath54 cm with an almost flat density profile . energetics is one of the main advantages of the interacting mechanism of slsne compared to pair - instability or magnetar - powered slsne : the shock wave is very effective in producing thermal energy , so models with csm require explosion energies only a little higher than that of `` normal '' sne , while in all other mechanisms the energetics must be at least an order of magnitude higher than normal .    the mass of the surrounding envelope must be high enough for the effective transformation of kinetic energy of the ejecta into observed light . the main difference between models with narrow and broad light curves is their masses . models for sn  2010gx require 5 to 10  of carbon and oxygen in the envelope , which is right in line with the ejected masses expected for pre - explosion from the pulsational pair instability mechanism , though the possibility of loosing all hydrogen and even helium long before the explosion is controversial . a much more massive c+o envelope with @xmath55 55 is needed to reproduce the broad band light curves of ptf09cnd . there are predictions , however , for stars in the last stages of stellar evolution with the requisite large helium and carbon - oxygen core masses @xcite . models with an extended envelope contiguous to the ejecta fit sn  2010gx and ptf09cnd better , but a detached shell or another feature in the envelope s density distribution might also be a good possibility to reproduce features on the light curve for some other slsne . models with detached shells can change the light curve shape during the fading stage . we encounter two kinds of problems in simulating slsne with the shock interaction mechanism , physical and numerical , which limit either the applicability of the model to the observed slsne or the applicability of the numerical code to the problem . _ mass of hydrogen - poor envelope . _ one of the obvious physical limitations of the interaction models is provided by the duration of the light curve tail . broad light curves require non - hydrogen envelopes of very large masses in the shock interacting model to explain slsne . for example , the model b0 for ptf09cnd contains almost 50  of c and o in the extended envelope . if slsne - i with longer light curve tails are discovered , the interaction scenario would require even higher envelope masses , which may not be very realistic . the solution of the problem may require including an appreciable amount of radioactive material to the shock interaction model . pure pair instability sn models are too diffusive and have a rise time to maximum that is too long @xcite , though the amount of @xmath6ni  they contain can easily explain the slsne - i tails . the shock interaction models can help to solve the problem of rising time @xcite . thus , the combined models of shock plus radioactivity may provide the best solution for the problem . then the shock will be responsible for the maximum of the light curve , while the radioactivity will determine the behavior of the tail . this may be most relevant to slsne with long tails of constant decline . _ high velocities . _ the combined model ( radioactivity plus interaction ) can also help to explain the high velocities observed in slsne - i . another type of shock interaction supernovae , sne  iin , clearly demonstrates narrow emission lines produced in the shells . not so in slsne - i : narrow circumstellar lines are not seen @xcite . there is no easily excited hydrogen in this type of sne , and the most abundant elements ( probably , carbon and oxygen ) should present as c  ii and o  ii ions in the envelope . these ions do not have many strong lines in visible light . it is not easy to identify c and o lines in the photospheric stage in sne  i @xcite , and for slsne they should be excited even in the absence of the radioactive material . thus , one has to look for weak lines in noisy spectra . this problem certainly deserves further investigation to account for different conditions of ionization / excitation of shells under the shock radiation . shock interaction models with fast expansion of the envelope produce rather narrow light curves . for the slsne - i with the broadest light curves we again encounter the problem that , under the assumption of an expanding cs envelope , extremely high envelope masses are required to fit the light curves . computation of the shock - interacting models on a fine grid is often time consuming . in some cases , semianalytic models ( e.g. , * ? ? ? * ; * ? ? ? * ) can help , but accurate calibration against more sophisticated numerical calculations may be needed . currently , we see discrepancies in some parameters of our models with the models from @xcite for the same slsne . the fits to slsn fluxes in individual filters are not yet perfect in our simulations . this is natural : we have taken quite arbitrary and primitive chemical compositions , density distributions , etc . however , there is no principal problem for us to reproduce typical brightness and duration of the light curves within pure interacting models . one can try to build a better fit to the observations by varying the initial conditions in the model , especially , the density distribution in the envelope and its chemical composition . however , it seems that it is too early to optimize the models along these lines . this optimization will probably not give us a true insight and a better understanding of the problem . _ expansion opacities . _ before optimizing the models , we have to improve the physics in our simulations . one of the main difficulties is the treatment of line opacity . sophisticated monte - carlo codes ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) or direct integrations @xcite for radiative transfer in spectral lines are not applicable for flows with complicated non - monotonic velocity profiles .    in our simulations , we use the approximation of expansion opacity @xcite . some modifications are needed for corrections of the expansion effect not only in the flux equation , but also in the energy equation as discussed by @xcite . moreover , there is another complication with the anisotropic velocity gradient .    _ velocity gradient in expansion opacity calculations . _ in the standard stella setup , the expansion opacity in lines is treated as for type  ia supernovae , where expansion is homologous and velocity gradient is isotropic , @xmath56 , with @xmath57  time elapsed after the explosion . in the interacting models of slsne , the source of light is a long - living shock wave . in this case , the velocity gradient is not isotropic and changes along the radius . moreover , it is negative on the shock front , with @xmath58 during several months , while the shock passes through the envelope . the influence of the expansion on the opacity in this region must be stronger than in the isotropic case . the current version of stella does not take into account this anisotropy in the expansion opacity calculation , and this is a source of uncertainty in resulting light curves . to estimate the uncertainty of line opacity calculations , we have run several tests when the expansion opacity is calculated with the fixed value @xmath59 , which crudely takes into account the fact that the light originates from the shock wave with the enhanced value of the velocity gradient @xcite . the observed flux becomes higher in many bands , and the shape of light curves changes noticeably as compared with the standard stella calculations , which shows the uncertainty range of our results . _ dimensionality . _ the main complication to the whole picture is possible fragmentation of the dense shell . the attempts on multi - d treatment of sn ejecta evolution are rather old @xcite , more recent results and references may be found in @xcite . see also @xcite for the case of sn  2006gy , but without real treatment of radiative transfer . there are several 3d mc transport codes @xcite , but they are not actually coupled to hydrodynamics and there are many difficulties in doing this @xcite . _ full nlte treatment is needed to predict spectra , but very little is done on this even for sn  iin . for example , @xcite are successful in reproducing the spectra of sn  1994w in a set of atmospheric models , though their method is applicable only to monotonic velocity structures , not to shocked shells . moreover , one should be cautioned about the relation of the `` photospheric '' radius found by @xcite , which shrinks , and the radius of the shocked shell in sne  iin , which grows . this has already been explained by @xcite .        in our numerical modeling , we take into account a lot of physical processes and examine their effects on the light curves . to demonstrate that this would be a challenging task in the analytical approach , we calculated the light curves for sn  2010gx by adopting the same model parameters as in the analytical model by @xcite for sn  2010gx in the interaction scenario : @xmath60 , @xmath61  cm , @xmath62 , @xmath63 , @xmath64  ergs , @xmath65  cm . @xcite provided the results for two models of the interaction scenario with a different density distribution in the cs envelope . we chose the model with @xmath66 because it is more similar to the density distribution in our models . the results of our numerical run of the model with the parameters listed above are shown by the dashed lines ( chat13 ) in figure  [ pic : analyt ] . for comparison , the light curves for our model n0 , which are in good agreement with broad - band fluxes from sn  2010gx , are shown by the solid curves ( sor16 ) . our numerical light curves chat13 are noticeably different from the analytic model by @xcite . the light curves chat13 are less luminous and much shorter than the analytical formula predicts ( figure  4 of @xcite ) . most probably , the difference in brightness is explained by an order of magnitude smaller radius of the sc envelope in chat13 model , while the difference in the duration is due to a smaller diffusion time as a consequence of a smaller cs envelope mass . such a difference in light curves is very similar to that found in the comparison between the analytic and numerical models for type ii slsn 2006gy ( figure  14 of @xcite ) . further details will be presented in the forthcoming paper . our best models for sn  2010gx and ptf09cnd require circumstellar envelopes of 5 to 50  , which consist of 7090% carbon and 3010% oxygen and must be formed before the explosion . stellar evolution theory tells us that it is difficult to create a star with almost all helium lost well before the sn explosion and such a huge amount of almost pure carbon and oxygen lost a few months before the explosion . our modeling excludes the possibility of a purely helium cs envelope because it demonstrates wrong colors near the maximum . in order to make a more evolutionary plausible model , we implemented one chemically non - uniform model for ptf09cnd : the cs envelope of model b6 consists of 25  helium , 22  carbon , and 3  oxygen , while the ejecta is mostly co. this model confirmed our prediction that unless helium is overwhelmingly abundant , the calculated light curve is changed only slightly . a larger amount of helium may reduce the envelope mass needed to reproduce the slow rise time of the slsn , because the rise time is longer for a pure helium envelope of the same mass . on the other hand , the pure helium envelope makes the sn model bluer than the observed sn near maximum , as seen in model b3 for ptf09cnd ( figure  [ pic:09cnd_composition ] ) . thus , more detailed work related to the dependence of the light curve shape on the chemical composition is still necessary .    until recently , there was no sign of helium in slsn - i spectra , but the observations of @xcite changed the situation . not only helium , but even hydrogen is observed in the late ( about a year after the explosion ) specta of iptf13ehe and some other slsne - i , which means that the cs envelope in the interacting scenario must be non - homogeneous , and its outermost layers contain he and h. such systems are easier to understand from the point of view of stellar evolution . this clearly demonstrates that chemically uniform models from our current work are a bit idealized . in the future we plan to investigate more complicated kinds of models with stratified co  he  h layers as well as models with different mixtures of co@xmath24he . both of them look more natural than the current models , which are still very good as a first approach to numerical modeling of slsne - i in the interaction scenario . our first approach to the mixed co@xmath24he models shows that the light curve is not much affected unless the amount of helium would become sufficiently large , because the rising time must be determined by a more opaque element . only colors are changed a little . here we agree with the conclusion of @xcite that the total helium mass of stripped envelope sne is difficult to be measured from simple light curve modeling . future research must answer two main question regarding the mixed models : put more definite upper limit to the mass fraction of helium in the cs envelopes and estimate how much cs envelope mass can be reduced for the most abundant he models . the stratified models can possibly provide us with some interesting features on the light curve when the photospheric radius would stumble upon the borders between different element layers . spectroscopically , models with and without helium can also look very similar . for example , @xcite argue that he features can easily be hidden in the spectra . they described a model for type ic supernova with 30% surface helium mass fraction , and found that he i lines were always absent in the visible light . there is no source of the excitation of helium if radioactive material is not mixed toward the surface . only a weak 10 830    line is present . in our models , we normally have a rather low color temperature ( see figure  [ fig : animspn0b0 ] ) . for early times , it may reach @xmath67  k , so some thermal excitation of he may be expected as in b - stars , but the presence of large amounts of c may hide it , like in @xcite . this question deserves further investigation , which is outside the scope of the current paper . direct evidence of the existence of hydrogen- and helium - poor envelopes around an exploding star has been seen , for example , by  @xcite . they present the observations of type ic sn2010 mb lacking spectroscopic signatures of h and he ( which should be the case for the models that we build in the current work ) . sn2010 mb has a slowly declining light curve ( @xmath68days ) that can not be powered by @xmath69ni/@xmath69co radioactivity . the signatures of interaction with hydrogen - free csm include a blue quasi - continuum as well as narrow oxygen emission lines that require high densities ( @xmath70@xmath71 ) . this is again similar to our models of the dense cs envelope . the difference is in the mass involved in the interaction : they estimate that the total amount of interacting gas is about 3  , while we need 50  for our most massive model . the estimations of the parameters of the h- and he - poor envelope around sn  2010 mb by  @xcite are in agreement with the masses and compositions of some models of pulsational pair - instability sne @xcite .      the main question , which remains unclear , is the origin of the extended and dense cs envelope , either carbon - oxygen , helium , or a mixture of both . what is the time scale of the formation of the envelope ? how far can the envelope extend ? what is the density profile and the temperature of matter before the core explosion ? these questions deserve further investigation . the theory of stellar evolution suggests several possible scenarios , which can result in such a system with a cs envelope . one of them is an explosion through the pulsational pair - instability mechanism as a means to form a detached cs shell . for instance , in the models of @xcite ejected masses and energies of preexplosions for the stars with helium core masses of about 50  are similar to those needed to form the cs envelope with the parameters we use in our calculations . evolutionary calculations of helium cores of the most massive stars in @xcite also lead to the loss of several tens of solar masses of the gas before the final explosion . a major part of the lost material is helium and oxygen in their calculation . the fact that slsne - i are typically observed in low - metallicity , star - forming galaxies favors the explosion of stars with very high initial masses , which are able to retain a large part of their mass during the evolution and loose a large amount of mass just before the explosion . evolutionary calculations of very massive stars ( a few hundreds of solar masses ) of different metallicities show that most of the hydrogen burns into helium during the main sequence evolution of such stars , before the stage of an intensive mass loss @xcite . this happens due to convective cores of such stars that extend up to outer layers of stars . in the very later phase of evolution , helium shell burning produces a substantial amount of carbon ( more than oxygen ) in the helium shell . in addition , the rotation of a star forms a meridional circulation , which also helps most of the hydrogen burn into helium ( and , possibly , some part of helium into c@xmath24o ) even at the surface . the combination of the formation of such a hydrogen - poor star with a powerful blowout from it as a wind in the latest stages of evolution , or with the ejection due to the pulsational pair - instability , can lead to the formation of a system required in this paper as an initial model for slsn - i . the pulsational pair - instability mechanism is more preferable because the explosive processes can more easily produce very high velocities of the cs envelope , of the order of 10,000  km / s , observed in the slsn - i spectra . these velocities are too high to have originated from a wind .    one can also speculate about the merger ( or even multiple mergers ) of a co core from an evolved wr star with another hydrogen - deficient star , like a neutron star , a white dwarf , or another wr star @xcite . a rich variety of probable binary pre - slsn evolution is considered in @xcite . these events are very probable in close binary systems and in the central regions of young stellar clusters ( like the ejection of the common envelope in pre - sn  ia binaries considered by @xcite ) . the merging can lead to a moderate explosion with energy of a few percent of @xmath23  ergs which forms a relatively large cloud of matter around the combined core . the size of this envelope can be enough to provide a long - living shock wave when the central core collapses within a few years after the merger . such an extended envelope would produce a very bright supernova , though the envelope expansion velocity would doubtfully be high enough . more detailed numerical calculations of merging systems are needed .    analyzing all the possibilities above , we can not choose one of them with certainty . however , with the current state of knowledge , the most plausible progenitor of slsne - i is a very massive star ( maybe with fast rotation ) , in which all of the hydrogen and a large part of the helium is burned out or expelled ( or lost ) during presupernova evolution and which is still massive enough to pass through the pulsational pair - instability stage . this scenario can explain both chemical composition and high envelope velocities in the interaction model for slsn . we conclude that , provided the formation of rather dense and extended circumstellar envelopes by any pre - sn scenario , extremely powerful events , like sn  2010gx and ptf09cnd , can be explained with moderate explosion energies without invoking any radioactive material . in principle , this mechanism can be the same for all slsne - i observed so far . sb is thankful to victor utrobin and to takashi moriya for discussions on bright sn  i spectra , light curves , and on numerical modeling of radiation dominated shocks with our code stella . kn and at would like to thank raphael hirschi for a discussion on the evolution of very massive stars and the formation of dense csm during his stay at kavli ipmu as an affiliate member . the work in russia ( calculation of the slsn light curves ) was supported by a grant of russian science foundation 14 - 12 - 00203 . the work in japan has been supported by the world premier international research center initiative ( wpi ) , mext , japan , and by the grants - in - aid for scientific research of the jsps ( 26400222 and 16h02168 ) . , k. , tominaga , n. , tanaka , m. , maeda , k. , & umeda , h. 2007 , in american institute of physics conference series , vol . 937 , supernova 1987a : 20 years after : supernovae and gamma - ray bursters , ed . s.  immler , k.  weiler , & r.  mccray , 412426                                , m. , maeda , k. , mazzali , p.  a. , & nomoto , k. 2008 , in american institute of physics conference series , vol . 1016 , origin of matter and evolution of galaxies , ed . t.  suda , t.  nozawa , a.  ohnishi , k.  kato , m.  y.  fujimoto , t.  kajino , & s.  kubono , 249254","summary":"one of the most promising ideas is the shock - interaction mechanism , but only simplified semi - analytical models have been applied so far .","abstract":"a number of type i ( hydrogenless ) superluminous supernova ( slsn ) events have been discovered recently . however , their nature remains debatable . one of the most promising ideas is the shock - interaction mechanism , but only simplified semi - analytical models have been applied so far . we simulate light curves for several type  i slsn ( slsn - i ) models enshrouded by dense , non - hydrogen circumstellar ( cs ) envelopes , using a multi - group radiation hydrodynamics code that predicts not only bolometric , but also multicolor light curves . we demonstrate that the bulk of slsne - i including those with relatively narrow light curves like sn  2010gx or broad ones like ptf09cnd can be explained by the interaction of the sn ejecta with the cs envelope , though the range of parameters for these models is rather wide . moderate explosion energy (  ergs ) is sufficient to explain both narrow and broad slsn  i light curves , but ejected mass and envelope mass differ for those two cases . only 5 to 10  of non - hydrogen material is needed to reproduce the light curve of sn  2010gx , while the best model for ptf09cnd is very massive : it contains almost in the cs envelope and only in the ejecta . the cs envelope for each case extends from 10  to  (  cm ) , which is about an order of magnitude larger than typical photospheric radii of standard sne near the maximum light . we briefly discuss possible ways to form such unusual envelopes ."}
{"article_id":"1207.1580","section_id":"i","document":"many systems of polynomial equations which are of practical interest can be represented by a graph . an important example occurs in computer aided design ( cad ) when the location of the geometric elements in a drawing such as points and lines ( corresponding to vertices in the graph ) are determined by relationships between them such as tangency , coincidence and the relative separations or angles between them ( corresponding to edges in the graph ) . the ability to solve such systems of equations rapidly allows a design engineer to modify input parameters such as the values for the separations or angles ( collectively called `` dimensions '' in a dimensioned drawing ) and to realise a computer model for many variants of a basic design @xcite . most modern cad systems incorporate the ability to solve these so - called dimensional constraint equations , see for example @xcite . a simple example of dimensional constraint equations is provided by points in a plane with certain specified relative distances . both the equations and a particular solution can be represented by a framework @xmath0 where @xmath1 is a graph and @xmath2 is a vector comprising of all the coordinates of the points . the graph @xmath1 has a vertex for each point and an edge for each specified distance . since the coordinates of the points are specified in @xmath0 it is a simple matter to determine the relative distance corresponding to any edge of @xmath1 . the framework @xmath0 therefore represents both a system of polynomial equations and a particular solution to these equations . we will call these equations the framework equations - they correspond to the dimensional constraint equations referred to above . in general the framework vector @xmath2 will be just one of the many possible solutions to the framework equations . ( estimates on the number of solutions have been obtained by several authors , see for example @xcite . ) efficient algorithms for solving the framework equations are extremely useful . a particularly desirable case is when there are only a finite number of solutions , and these solutions can be expressed as a sequence of square , or higher power , roots of combinations of the squared edge distances . such frameworks are said to be quadratically solvable ( or ruler - and - compass - constructible @xcite ) and radically solvable , respectively . we will consider the problem of determining which generic frameworks are quadratically or radically solvable . the condition that the framework equations should have only finitely many solutions is equivalent to the statement that the framework is rigid . this property has been extensively studied and we refer the reader to @xcite for an excellent survey of the area . previous work on quadratic / radical solvability @xcite considered generic frameworks which are minimally rigid i.e. cease to be rigid when any edge is removed . a conjectured characterisation of quadratically / radically solvable minimally rigid generic frameworks was given in @xcite and this conjecture was verified for the special case when the underlying graph is 3-connected and planar in @xcite . we will extend the study of quadratic and radical solvability to include generic frameworks which are rigid but not necessarily minimally rigid . we first show in lemma [ radgen ] that the quadratic or radical solvability of a generic framework depends only on the underlying graph . this means that if a graph is quadratically or radically solvable then there will be a quadratic or radical solution to the corresponding system of framework equations for any sufficiently general but consistent set of input distances . we next consider globally rigid graphs i.e. graphs for which every generic realisation is a unique solution to the corresponding framework equations . we show in theorem [ globallyrigid ] that all such graphs are quadratically solvable . we develop a reduction scheme in section [ 3con ] which shows how the radical or quadratic solvability of a rigid graph is related to the corresponding property for a derived graph which may be chosen to be minimally rigid . we use this and the main result of @xcite to show in theorem [ planar ] that a rigid 3-connected planar graph is radically solvable if and only if it is globally rigid . this leads us to consider rigid graphs which are not 3-connected i.e. graphs @xmath3 which can be separated into two subgraphs @xmath4 with @xmath5 . we show in theorem [ 2sep ] that the radical or quadratic solvability of @xmath1 is determined by the corresponding property of @xmath6 and @xmath7 when @xmath8 and @xmath9 are both rigid , and of @xmath6 and @xmath9 when @xmath8 is not rigid and @xmath9 is minimally rigid . we use this analysis to give a constructive definition for a family of quadratically solvable graphs @xmath10 . we conjecture that every radically solvable graph belongs to @xmath10 and prove in theorem [ planar2con ] that this holds for planar graphs .","summary":"we show that the radical solvability of a generic framework depends only on its underlying graph and characterise which planar graphs give rise to radically solvable generic frameworks . we conjecture that our characterisation extends to all graphs .   ","abstract":"a 2-dimensional framework is a straight line realisation of a graph in the euclidean plane . it is radically solvable if the set of vertex coordinates is contained in a radical extension of the field of rationals extended by the squared edge lengths . we show that the radical solvability of a generic framework depends only on its underlying graph and characterise which planar graphs give rise to radically solvable generic frameworks . we conjecture that our characterisation extends to all graphs .    2010 _ mathematics subject classification _ : 05c10 , 12f10 , 52c25 , 68r10 ."}
{"article_id":"0906.3685","section_id":"i","document":"over the past half a century , since the development of the first solar dynamo model by parker ( 1955 ) , significant investigations have been performed to find the saturation mechanism that would limit the growth of a dynamo . such mechanisms are likely to include feedback processes , such as the back - reaction of magnetic fields on the flow fields , including mean flows ( differential rotation and meridional circulation ) , as well as turbulent flows .    the feedback process that has been most extensively studied in the mean - field electrodynamics is the back - reaction of magnetic fields on the helical part of the turbulent flow . this process , often known as @xmath0-quenching , was first believed to be mainly due to the back - reaction of the magnetic field on the convection , causing the suppression of kinetic helicity , and hence quenching the inducing effects of the turbulent electromotive force @xcite . currently it is believed that the saturation process in the non - kinematic regime occurs due to the reduction of the kinetic @xmath0-effect caused by a magnetic contribution of opposite sign , coming from the equation of the @xmath0 . this contribution appears asa product of the magnetic helicity conservation constraint . there exists a large literature on @xmath0-quenching and , instead of detailed review , we refer to the following papers on this topic : @xcite .    however , the back - reaction due to induced magnetic field on the mirror - symmetric non - helical part of the turbulent flow is a relatively less explored subject . such back reaction has the effect of reducing the eddy diffusivity . this back - reaction process has been named the @xmath1-quenching , first derived by @xcite using mean - field electrodynamics . later , the role of @xmath1-quenching in a dynamo has been investigated by several authors @xcite , primarily in the context of @xmath4-type stellar dynamo models . @xcite incorporated @xmath1-quenching in one - dimensional @xmath4 type and two - dimensional @xmath5 type stellar dynamo models . for supercritical dynamo regimes , @xcite found that in one - dimensional dynamo models with @xmath1-quenching , the field strength increased a bit , but not much , whereas the cycle period decreased significantly . by contrast , for their two - dimensional stellar dynamo models , @xcite found a significant field amplification , almost two times more magnetic field was produced with @xmath1-quenching , but the cycle period did not change much from that without @xmath1-quenching . while field amplification due to @xmath1-quenching is intuitively expected , the change in dynamo cycle period , @xmath6 , will depend on how @xmath6 is determined in different classes of dynamo models . for example , in the convection zone @xmath4 dynamo models , the cycle frequency ( @xmath7 ) follows @xmath8 ; hence an expected increase in cycle period with @xmath1-quenching .    by employing an @xmath4 type interface dynamo model , @xcite found that for weak magnetic fields , the diffusivity is not much quenched , and the dynamo solutions are not influenced by the presence of @xmath1-quenching . in the case of strong magnetic fields , @xcite showed that the diffusivity near the base of the convection zone can be so heavily quenched that the fields can be trapped there without making their buoyant escape towards the solar surface .    in a more recent calculation @xcite showed , by solving the induction equation for the toroidal magnetic field component including the back - reactions of magnetic fields on the turbulent diffusivity as well as on the shear , that there exists a competition between a field amplification by @xmath1-quenching and a field reduction due to the fact that the the lorentz force feedback on the shear moves the latitudinal shear layer away from the mid - latitudes . however , @xcite argued that a significant field amplification might be possible if the latitudinal shear is replenished in a much shorter time - scale compared to the solar cycle . there is an effect common to all the above studies which either solved an @xmath4 convection zone dynamo @xcite , an interface dynamo @xcite , or an induction equation for the toroidal magnetic field component @xcite  there is field amplification due to @xmath1-quenching . but the influence of @xmath1-quenching on solar cycle features , namely the butterfly diagram and the evolutionary pattern of magnetic fields in the convection zone and tachocline , has not yet been explored . our aim here is to simulate a babcock - leighton flux - transport dynamo including the back - reactions of magnetic fields on both the helical and non - helical parts of the turbulent flow , i.e. by including both the @xmath0-quenching and @xmath1-quenching . we specifically seek the answers to the following questions : ( i ) what is a characteristic value of field amplification due to @xmath1-quenching in a babcock - leighton flux - transport dynamo model ? ( ii ) how is the butterfly diagram changed or modified due to @xmath1-quenching ? ( iii ) where in the solution domain that extends from pole - to - equator in latitude and from the tachocline to the solar surface in radial extent does @xmath1-quenching have the most effect ? ( iv ) is the conveyor - belt mechanism preserved , or does it break down if @xmath1 is more and more quenched ? ( v ) to what extent can the @xmath1-quenching affect the dynamo cycle period which is primarily determined by the meridional circulation in this class of models ? ( vi ) since the @xmath0-quenching saturates the growth of the dynamo field and the @xmath1-quenching works in amplifying the field , how does the dynamo behave in presence of the competition between these two quenching mechanisms ? ( vii ) can the @xmath1-quenching take a diffusion - dominated dynamo into the advection - dominated regime ?    in the next section we present the formulation of the model , including the prescriptions of the dynamo ingredients , such as the velocity fields ( differential rotation and meridional circulation ) , diffusivity profile with @xmath1-quenching formula , and the @xmath0-effect profile . we present the solution method , boundary conditions and initial conditions in section 3 and the detailed description of our results in section 4 . we conclude in section 5 .","summary":"in the non - linear phase of a dynamo process , the back - reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification ( the-quenching effect ) and the turbulent magnetic diffusivity ( the-quenching effect ) . while the former has been widely explored , the effects of-quenching in the magnetic field evolution have rarely been considered . in this work our results indicate that , although for-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear , the magnetic field response to-quenching is non - linear and spatially non - uniform .","abstract":"in the non - linear phase of a dynamo process , the back - reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification ( the-quenching effect ) and the turbulent magnetic diffusivity ( the-quenching effect ) . while the former has been widely explored , the effects of-quenching in the magnetic field evolution have rarely been considered . in this work we investigate the role of the suppression of diffusivity in a flux - transport solar dynamo model that also includes a non - linear quenching term . our results indicate that , although for-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear , the magnetic field response to-quenching is non - linear and spatially non - uniform . we have found that the magnetic field can be locally amplified in this case , forming long - lived structures whose maximum amplitude can be up to times larger at the tachocline and up to times larger at the center of the convection zone than in models without quenching . however , this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram . since the dynamo cycle period increases when the efficiency of the quenching increases , we have also explored whether the-quenching can cause a diffusion - dominated model to drift into an advection - dominated regime . we have found that models undergoing a large suppression in produce a strong segregation of magnetic fields that may lead to unsteady dynamo - oscillations . on the other hand , an initially diffusion - dominated model undergoing a small suppression in remains in the diffusion - dominated regime ."}
{"article_id":"0906.3685","section_id":"i","document":"we have explored here the effects of diffusivity quenching on babcock - leighton flux - transport solar dynamo models . we used as initial condition a converged solution of a dynamo model that reproduces most of the main features of an observed solar butterfly diagram . the @xmath1-quenching was then included in the model through an algebraic function that is similar to the usual @xmath0-quenching formula . after some years of evolution , the system reaches a new steady state configuration in which the poloidal and toroidal components of the magnetic field , @xmath21 and @xmath22 , respectively , as well as the magnetic diffusivity , @xmath1 , exhibit a cyclic behavior .    with the new @xmath1 profile ( equation 5 ) , the decrease in the diffusivity can be as large as three orders of magnitude , but it is not homogeneous over the whole domain since it presents a pattern with peaks and valleys that anti - correlate with the spatial distribution of the amplitude of the toroidal fields - the smaller the @xmath50 ( the value of the magnetic field at which the diffusivity begins to be quenched ; eq . 5 ) the narrower the final @xmath1 profile ( figs . [ fig8 ] and [ fig9 ] ) . this spatial fluctuation in the magnetic diffusion results in the formation of small and long - lived regions of concentrated magnetic field that appear predominantly at the equatorial part of the overshoot tachocline as well as in the middle of the convection zone . the role of the meridional flow is very important in this result , since the toroidal fields have time enough to increase and be dragged along with the poloidal field lines before being dissipated . note that if these strong flux tubes produced at the middle convection zone emerge to the surface they may not agree with the joy s law . we have found that , contrary to the effects of @xmath0-quenching , which shows an almost linear coupling between the saturation field , @xmath84 and the final value of @xmath0 ( see fig . [ fig4 ] ) , the dependence between the diffusivity saturation field , @xmath50 , and the final value of @xmath1 is predominantly non - linear , especially at the base of the convection zone where both the radial and the latitudinal shear are competing with the advective transport and with diffusive spreading . it was found that at the tachocline ( @xmath59@xmath16@xmath31 ) the magnetic field can be amplified by a factor up to @xmath2 at the highest latitudes , while for the equatorial regions the magnetic field decreases by approximately the same factor . on the other hand , at the center of the convection zone ( @xmath59@xmath16@xmath107 ) , the magnetic field for both low and mid - latitudes have the same increase , by a factor as large as @xmath127 with respect to the no - quenching case . the consequence of these effects on the butterfly diagram is the increase ( decrease ) of the toroidal fields at the high ( low ) latitudes and the increase of the cycle period for an enhanced @xmath1-quenching . this new distribution of magnetic fields with latitude not only shows a gradual departure from observations , but also could cause other problems in the dynamo models , such as the loss of coupling between hemispheres when solved in a full spherical shell , resulting in a quadrupole parity solution . since the period of the cycle diminishes when the efficiency of the quenching increases , we have also explored if the @xmath1-quenching can make a diffusion dominated dynamo , which is characterized by a small cycle - period , to evolve to an advection dominated dynamo . we have found that a diffusion - dominated dynamo with a meridional flow remains in the diffusion regime even when the diffusivity is locally suppressed due to the strong magnetic fields . the results summarized above indicate that in the scenario of a pure babcock - leighton dynamo , with a meridional flow operating as a conveyor - belt and strong magnetic flux tubes emerging from the base of the convection zone , the turbulent diffusivity is probably weakly suppressed , i.e. , it is quenched only for high values of the magnetic field . this implies that its role in the amplification of the magnetic field to values above the equipartition field should not be significant enough . notice , however , that other effects , like turbulent pumping , which have been demonstrated to be important in the dynamo operation @xcite , have not been considered here . the contribution of turbulent pumping might , for instance , result in a different transport of the magnetic fields , changing the parts of the parameter space where the @xmath1-quenching would become dominant . this will be explored in forthcoming work . finally , it is also important to remark that the quenching effects of the diffusivity still need to be explored in other classes of dynamo models , for example , the ones operating with a surface shear layer . these will also be considered in future work . we thank e. j. zita , matthias rempel and peter gilman for helpful discussion on this work . we extend our thanks to an anonymous referee for a very thorough review and for many constructive comments and criticism on an earlier version of this paper  incorporating them in the revised manuscript has significantly improved the paper . g. g and e.m.g.d.p acknowledge partial support from grants of the brazilian science foundations fapesp and cnpq . this work is partially supported by nasa grant nnx08aq34 g . national center for atmospheric research is sponsored by the national science foundation . bhattacharjee , a. & yuan , y. 1995 , , 449 , 739 blackman , e. g. & field , g. b. 2001 , phys . of plasmas , 8 , 2407 bonnano , a. , elstner , d. , rdiger , g. , & belvedere , g. 2002 , , 390 , 673 bonnano , a. , elstner , d. & belvedere , g. 2006 , astron . nachr , 327 , 680 brandenburg , a. 2001 , , 550 , 824 brandenburg , a. 2005 , , 625 , 539 brandenburg , a. & donner , k. j. 1997 , mnras , 288 , l29 brandenburg , a. & subramanian , k. 2005 , physics reports , 417 , 1 cattaneo , f. & hughes , d. w. 1996 , phys . , 54 , 4532 cattaneo , f. & vainshtein , s. i. 1991 , , 376 , l21 cattaneo , f. 1994 , , 434 , 200 charbonneau , p. 2007 , adv . in space res . , 39,1661 dsilva , s. z. & howard , r. f. 1993 , solp , 148 , 1 dikpati , m. & choudhuri , a. r. 1994 , , 291 , 975 dikpati , m. & charbonneau , p. 1999 , , 518 , 508 dikpati , m. , corbard , t. thompson , m. j. & gilman , p. a. 2002 , , 575 , l41 dikpati , m. , de toma , g. , gilman , p. , arge , c. , white , o. 2004 , , 601 , 1136 dikpati , m. , rempel , m. , gilman , p. a. & macgregor , k. b. 2005 , , 437 , 699 dikpati , m. , de toma , g. & gilman , p. a. 2006 , geophys . lett . , 33 , l05102 dorch , s. b. f. & norlund , a. 2001 , , 365 , 562 fan , y. , fisher , g. h. & mcclymont , a. n. 1994 , , 436 , 907 field , g. b. , blackman , e. g. & chou , h. 1999 , , 513 , 638 field , g. b & . blackman , e. g. 2002 , , 572 , 685 gilman , p. a. & rempel , m. 2005 , , 630 , 615 gruzinov , a. & diamond , p. h. 1994 , phys . lett . , 72 , 1651 guerrero g. & mnoz , a. 2004 , mnras , guerrero g. , de gouveia dal pino , e. m. 2007a , , 464 , 341 guerrero g. , de gouveia dal pino , e. m. 2007b , astron . nachr , 328,1122 guerrero g. , de gouveia dal pino , e. m. 2008 , , 485 , 267 jouve , l. & brun , a. s. 2007 , , 474 , 239 kpyl , p. j. , korpi , m. j. , ossendrijver , m. & stix , m. 2006 , , 455 , 401 kpyl , p. j. , korpi , m. j. , & tuominen , i. 2006 , astron . nachr . , 327 , 884 kpyl , p. j. , korpi , m. j. , & brandenburg , a. 2009 , astron . astrophys . , submitted kitchatinov , l.l . & rdiger , g. 1992 , , 260 , 494 kitchatinov , l.l . , pipin , v.v . & rdiger , g. 1994 , astron . nachr . , 315 , 157 kraichnan , r. h. 1979 , phys . rev . , 113 , 1181 kker , m. , rdiger , g. & schultz , m. 2001 , , 374 , 301 nandy , d. & choudhuri , r. a. 2001 , , 551 , 576 ossendrijver , m. , stix , m , brandenburg , a. & rdiger , g. 2002 , , 394 , 735 parker , e. n. , , 122 , 293 remple , m. , , 647 , 662 roberts , p. h. & soward , a. m. 1975 , astron . nachr . , 296 , 49 rogachevskii , i. & kleeorin , n. 2001 , phys . rev . e. , 64 , 056307 rdiger , g. & kitchatinov , l. l. 2000 , astron . nachr . , 321 , 75 rdiger , g. , kitchatinov , l. l. , kker , m. & schultz , m. 1994 , geophys . astrophys . fluid dyn . , 78 , 247 stix , m. , , 20 , 9 sur , s. , brandenburg , a. & subramanian , k. 2008 , mnras , 385 , l15 tobias , s. m. , , 467 , 870 thompson , m. j. , christensen - dalsgaard , j. , miesch , m. s. & toomre , j. 2003 , , 41 , 599 wang , y. m. , nash , a. g. & sheeley jr , n. r. 1989 , science , 245 , 712 wang , y. m. & sheeley jr , n. r. 1991 , , 375 , 761 yousef , t. a. , brandenburg , a. & rdiger , g. 2003 , , 411 , 321 ziegler , u. & rdiger , g. 2003 , , 401 , 433","summary":"we have found that the magnetic field can be locally amplified in this case , forming long - lived structures whose maximum amplitude can be up to times larger at the tachocline and up to times larger at the center of the convection zone than in models without quenching . however , this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram . since the dynamo cycle period increases when the efficiency of the quenching increases , we have also explored whether the-quenching can cause a diffusion - dominated model to drift into an advection - dominated regime . we have found that models undergoing a large suppression in produce a strong segregation of magnetic fields that may lead to unsteady dynamo - oscillations . on the other hand , an initially diffusion - dominated model undergoing a small suppression in remains in the diffusion - dominated regime .","abstract":"in the non - linear phase of a dynamo process , the back - reaction of the magnetic field upon the turbulent motion results in a decrease of the turbulence level and therefore in a suppression of both the magnetic field amplification ( the-quenching effect ) and the turbulent magnetic diffusivity ( the-quenching effect ) . while the former has been widely explored , the effects of-quenching in the magnetic field evolution have rarely been considered . in this work we investigate the role of the suppression of diffusivity in a flux - transport solar dynamo model that also includes a non - linear quenching term . our results indicate that , although for-quenching the dependence of the magnetic field amplification with the quenching factor is nearly linear , the magnetic field response to-quenching is non - linear and spatially non - uniform . we have found that the magnetic field can be locally amplified in this case , forming long - lived structures whose maximum amplitude can be up to times larger at the tachocline and up to times larger at the center of the convection zone than in models without quenching . however , this amplification leads to unobservable effects and to a worse distribution of the magnetic field in the butterfly diagram . since the dynamo cycle period increases when the efficiency of the quenching increases , we have also explored whether the-quenching can cause a diffusion - dominated model to drift into an advection - dominated regime . we have found that models undergoing a large suppression in produce a strong segregation of magnetic fields that may lead to unsteady dynamo - oscillations . on the other hand , an initially diffusion - dominated model undergoing a small suppression in remains in the diffusion - dominated regime ."}
{"article_id":"1211.0300","section_id":"i","document":"the notion of poissonian ensembles of markov loops ( loop soups ) was introduced by lawler and werner in @xcite in the context of two dimensional brownian motion ( it already appeared informally in @xcite ) : the loops of a brownian loop soup on a domain @xmath3 are the points of a poisson point process with intensity @xmath4 where @xmath5 is a positive real and @xmath6 is the brownian loop measure on @xmath7 . loop clusters induced by a brownian loop soup were used to give a construction of the conformal loop ensembles ( cle ) in @xcite and @xcite . they are defined as follows : _ two loops @xmath8 and @xmath9 are said to be in the same cluster if one can find a finite chain of loops @xmath10 such that @xmath11 , @xmath12 and for all @xmath13 , @xmath14_. poissonian ensembles of markov loops can also be defined on graphs . they were studied in details in @xcite and @xcite . in particular poissonian ensembles of loops on the integer lattice @xmath15 induced by simple ( nearest neighbor ) random walks give a discrete version of brownian loop soup ( see @xcite ) . the aim of this paper is to study loop clusters induced by markov loop ensembles on graphs . the facts presented here , which are built on the results presented in @xcite , are more elementary than in the brownian loop soup theory , but they point out that poissonian ensembles of markov loops and related partitions are of more general interest . the examples we develop show relations with several theories : coalescence , percolation and random graphs .    in section 1 , we recall the different objects needed to define the markovian loop clusters on a graph and the coalescent process induced by the partition of vertices they define . in section 2 , we state general properties of the clusters and establish some formulae useful to study the semigroup of the coalescent process . in the last three sections we address several aspects of the loop clusters induced by a simple random walk killed at a constant rate @xmath16 on different graphs :    * on @xmath17 , the loop cluster model reduces to a renewal process . we establish a convergence result by rescaling space by @xmath18 , killing rate by @xmath19 and let @xmath19 converge to @xmath20 . * the loop cluster model can be seen as a percolation model with two parameters @xmath5 and @xmath16 . bernoulli percolation appears as a limit if @xmath5 and @xmath16 tend to @xmath21 so that @xmath22 converges to a positive real . we show that a non - trivial percolation threshold occurs for the loop cluster model on the lattice @xmath23 with @xmath2 . * as a last example , we consider the complete graph . we give a simple construction of the coalescent process on the complete graph and we deduce a construction of a coalescent process on the interval @xmath24 $ ] . letting the size of the graph increase to @xmath21 , we determine the asymptotic distribution of the coalescence time : it appears to be essentially the same as in the erds - rnyi random graph model ( see @xcite ) though the lack of independence makes the proof significantly more difficult .","summary":"we study the loop clusters induced by poissonian ensembles of markov loops on a finite or countable graph ( markov loops can be viewed as excursions of markov chains with a random starting point , up to re - rooting ) . poissonian ensembles are seen as a poisson point process of loops indexed by ` time ' . the evolution in time of the loop clusters defines a coalescent process on the vertices of the graph . after a description of some general properties of the coalescent process , we address several aspects of the loop clusters defined by a simple random walk killed at a constant rate on three different graphs : the integer number line , the integer lattice with and the complete graph . these examples show the relations between poissonian ensembles of markov loops and other models : renewal process , percolation and random graphs .","abstract":"we study the loop clusters induced by poissonian ensembles of markov loops on a finite or countable graph ( markov loops can be viewed as excursions of markov chains with a random starting point , up to re - rooting ) . poissonian ensembles are seen as a poisson point process of loops indexed by ` time ' . the evolution in time of the loop clusters defines a coalescent process on the vertices of the graph . after a description of some general properties of the coalescent process , we address several aspects of the loop clusters defined by a simple random walk killed at a constant rate on three different graphs : the integer number line , the integer lattice with and the complete graph . these examples show the relations between poissonian ensembles of markov loops and other models : renewal process , percolation and random graphs ."}
{"article_id":"0712.0763","section_id":"i","document":"it has been known since the early eighties that light can transfer its angular momentum to liquid crystals with high efficiency , causing the rotation of the average molecular orientation , as specified by the molecular director @xcite .    in the early 90 s it was discovered that adding small amounts of certain dyes to the liquid crystals , the light - induced torque on the molecular director could be greatly enhanced @xcite . this effect , initially rather puzzling , was later explained by a model relying on the reversible changes of intermolecular forces occurring between photoexcited dye molecules and liquid crystal host @xcite . this model was subsequently extended and refined @xcite and confirmed with several independent experiments @xcite .    the understanding achieved with this model has also provided an answer to a fundamental question related to the observed torque enhancement : where does the additional angular momentum come from ? clearly , the angular momentum that is transported by the optical wave impinging on the material can not be affected by the presence of dye . it is true that absorption of light due to the dye does lead to some additional transfer of angular momentum from light to matter and therefore to a variation of the light - induced torque . however , this effect can not account for the magnitude of the observed torque enhancement @xcite and for its peculiar dye - structure dependence @xcite . the clearest solution to this puzzle was put forward in refs . @xcite and @xcite and is as follows . the angular momentum transfer from light is indeed approximately unchanged . light absorption however triggers a transfer of angular momentum between different _ internal degrees of freedom _ of the liquid crystal , namely from the center - of - mass molecular degrees of freedom , corresponding macroscopically to fluid flow , to the molecular - orientation degrees of freedom , corresponding to the molecular director . being an internal transfer , the _ total _ angular momentum given to the material as a whole is not affected by the presence of dye . another consequence of this internal transfer is that , by the force action - reaction principle , in dye - doped liquid crystals there should be another ( opposite ) torque acting on the fluid in the form of a photoinduced stress - tensor @xcite . however plausible they may be , both these predictions have never been tested directly in an experiment . here we address these questions by studying the rotational behavior of pure and dye - doped liquid crystal droplets of micrometric size , optically trapped in water , under the effect of circularly and elliptically polarized infrared and visible laser light . in particular , we measured the rotation speed of dye - doped droplets illuminated with visible light , having a wavelength in the dye absorption domain , and compared it with that of undoped droplets and with the case in which the illumination is by infrared light , not absorbed by the dye . should we observe some significant dye - induced enhancement ( or other anomalies ) of the droplet rotation speed , this would imply that the current understanding of the photoinduced torque as entirely due to an internal exchange of angular momentum is not correct , or at least not complete . but what do we exactly mean by droplet rotation ? from a theoretical point of view , a liquid crystal droplet actually has two independent rotational degrees of freedom : the average molecular director , corresponding to the average orientation of the liquid crystal molecules in the droplet , and the internal rotational flow , corresponding to a fluid - like motion of the molecule centers of mass ( this is already a strong simplification : a liquid crystal droplet has actually an infinite number of rotational degrees of freedom associated with changing inhomogeneous configurations of director and flow ) . these two rotational degrees of freedom of the droplet are always strongly interacting with each other , via viscosity , elastic forces , and possibly also photoinduced effects . this interaction may be strong enough to lock the two degrees of freedom together into a single one , so that the droplet effectively behaves as a rigid body . this is what we actually observed in our experiments . nonetheless , by properly choosing the experimental parameters , it should be possible to reach a regime in which the two rotational degrees of freedom become effectively unlocked . we would expect that in this `` unlocked '' regime , photoinduced dye effects become important , even if the angular momentum exchange is entirely internal . we investigated theoretically this case and predicted the occurrence of highly non - trivial photoinduced rotational effects , which we then tried to observe experimentally . this article is organized as follows . the general continuum theory of the light - induced dynamics of dye - doped liquid crystals is reviewed in sec . ii . in sec . iii , we then apply this theory to the case of a spherical droplet immersed in water . with the help of several strongly - simplifying approximations , analytical solutions are found , predicting what should be the light - induced rotational behavior of the droplets as a function of light power and polarization and of droplet size . our experiments are then described and discussed in sec . our results are finally summarized in sec .","summary":"we investigate both theoretically and experimentally the rotational dynamics of micrometric droplets of dye - doped and pure liquid crystal induced by circularly and elliptically polarized laser light . the droplets are dispersed in water and trapped in the focus of the laser beam . we searched for such enhancement by measuring and comparing the rotation speed of dye - doped droplets induced by a laser beam having a wavelength either inside or outside the dye absorption band , and also comparing it with the rotation of pure liquid crystal droplets . finally , peculiar photoinduced dynamical effects are predicted to occur in droplets in which the molecular director is not rigidly locked to the flow , but so far they could not be observed .","abstract":"we investigate both theoretically and experimentally the rotational dynamics of micrometric droplets of dye - doped and pure liquid crystal induced by circularly and elliptically polarized laser light . the droplets are dispersed in water and trapped in the focus of the laser beam . since the optical torque acting on the molecular director is known to be strongly enhanced in light - absorbing dye - doped materials , the question arises whether a similar enhancement takes place also for the overall optical torque acting on the whole droplets . we searched for such enhancement by measuring and comparing the rotation speed of dye - doped droplets induced by a laser beam having a wavelength either inside or outside the dye absorption band , and also comparing it with the rotation of pure liquid crystal droplets . no enhancement was found , confirming that photoinduced dye effects are only associated with an internal exchange of angular momentum between orientational and translational degrees of freedom of matter . our result provides also the first direct experimental proof of the existence of a photoinduced stress tensor in the illuminated dye - doped liquid crystal . finally , peculiar photoinduced dynamical effects are predicted to occur in droplets in which the molecular director is not rigidly locked to the flow , but so far they could not be observed ."}
{"article_id":"0712.0763","section_id":"c","document":"in summary , we have studied for the first time the dynamical behavior of droplets of dye - doped nematic liquid crystal trapped in water by a strongly focussed laser beam and set in rotation by the optical torques generated by the same beam . we searched for evidences of a dye - induced enhancement of the droplet rotation speed associated with photoinduced effects , but no enhancement was found . this null result is in accordance with the leading first - order theory of these photoinduced effects @xcite and directly proves that the dye - enhanced optical torque is not associated with an exchange of angular momentum with light or other external degrees of freedom , but that it must instead be associated with a fully internal exchange of angular momentum between the molecular orientation and fluid flow degrees of freedom . the latter exchange is correctly described only by assuming the existence of a dye - induced stress tensor acting on the fluid flow in the illuminated region , as first proposed in ref . this photoinduced stress tensor embodies the internal `` reaction '' to the photoinduced torque acting on the molecular director . our null result is therefore also a direct proof of the actual existence of this stress tensor . the interplay between fluid flow and director dynamics within the droplet is also predicted by our models to give rise to very peculiar effects , such as a continuous droplet fluid rotation induced by two linearly polarized optical waves having different polarization planes . however , the occurrence of these phenomena requires to unlock the constraint existing between the droplet fluid and the molecular director . this constraint is partly due to viscous forces , but it may also be due to elastic interactions combined with anchoring forces . experimentally , we could not reach a situation in which this constraint was effectively broken , so we could not demonstrate the predicted effect . we thank r. eidenschink of nematel for providing hk271 . this work was supported by the fondo per gli investimenti della ricerca di base ( firb ) of the italian ministero dellistuzione , delluniversit e della ricerca . i. j. acknowledges the support from the hungarian research grants otka t-037275 and nkfp-128/6 .","summary":"no enhancement was found , confirming that photoinduced dye effects are only associated with an internal exchange of angular momentum between orientational and translational degrees of freedom of matter . our result provides also the first direct experimental proof of the existence of a photoinduced stress tensor in the illuminated dye - doped liquid crystal .","abstract":"we investigate both theoretically and experimentally the rotational dynamics of micrometric droplets of dye - doped and pure liquid crystal induced by circularly and elliptically polarized laser light . the droplets are dispersed in water and trapped in the focus of the laser beam . since the optical torque acting on the molecular director is known to be strongly enhanced in light - absorbing dye - doped materials , the question arises whether a similar enhancement takes place also for the overall optical torque acting on the whole droplets . we searched for such enhancement by measuring and comparing the rotation speed of dye - doped droplets induced by a laser beam having a wavelength either inside or outside the dye absorption band , and also comparing it with the rotation of pure liquid crystal droplets . no enhancement was found , confirming that photoinduced dye effects are only associated with an internal exchange of angular momentum between orientational and translational degrees of freedom of matter . our result provides also the first direct experimental proof of the existence of a photoinduced stress tensor in the illuminated dye - doped liquid crystal . finally , peculiar photoinduced dynamical effects are predicted to occur in droplets in which the molecular director is not rigidly locked to the flow , but so far they could not be observed ."}
{"article_id":"1404.5960","section_id":"i","document":"the large majority of the point sources detected by the compton gamma - ray observatory in the 1990s ( e.g. , * ? ? ? * ) are still lacking an association with a low - energy candidate counterpart , and given their sky distribution , a significant fraction of these unresolved objects are expected to have extragalactic origin ( e.g. , * ? ? ? * ; * ? ? ? * ) . unveiling the origin of the unidentified @xmath0-ray sources ( ugss ) is also one of the key scientific objectives of the recent _ fermi _  mission that still lists about 1/3 of the @xmath0-ray sources as unassociated in the second _ fermi_-lat catalog ( 2fgl ; * ? ? ? * ) .    a large fraction of ugss is expected to be blazars , the largest known population of @xmath0-ray active galaxies , not yet associated and/or recognized due to the lack of multifrequency observations @xcite . therefore a better understanding of the nature of the ugss is crucial to estimate accurately the blazar contribution to the extragalactic gamma - ray background ( e.g. , * ? ? ? * ; * ? ? ? * ) , and it is essential to constrain exotic high - energy physics phenomena ( e.g. , * ? ? ? many attempts have been adopted to decrease ugss number and to understand their composition . pointed _ swift _ observations + ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) to search for x - ray counterparts of ugss as well as radio follow up observations were already performed or are still in progress ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? in addition , statistical approaches based on different techniques have been also developed and successfully used ( e.g. * ? ? ? * ; * ? ? ? * ) . we recently addressed the problem of searching @xmath0-ray blazar candidates as counterparts of the ugss adopting two new approaches : the first is based on the wide - field infrared survey explorer ( _ wise _ ) all - sky observations @xcite aiming at recognizing @xmath0-ray blazar candidates using their peculiar ir colors @xcite while the second employs the low - frequency radio observations @xcite . in particular , this second method was indeed based on the combination of the radio observations westerbork northern sky survey ( wenss ; * ? ? ? * ) at 325 mhz with those of the nrao very large array sky survey ( nvss ; * ? ? ? * ) and of the very large array faint images of the radio sky at twenty - centimeters ( first ; * ? ? ? * ; * ? ? ? * ) at about 1.4 ghz . it is worth noting that all the _ fermi _  extragalactic sources associated in the 2fgl catalog have a clear radio counterpart @xcite , this is the basis of the radio-@xmath0-ray connection , that has been found in the case of blazars ( e.g. , * ? ? ? ? * ; * ? ? ? thus , motivated by this observational evidence we propose a different approach to search for the blazar - like counterparts of the ugss . we combine the radio and the ir information available for the sources lying within the positional uncertainty regions of the _ fermi _  ugss to select @xmath0-ray blazar candidates .    with respect to our previous ir based search for blazar - like counterparts + ( e.g. , * ? * ; * ? ? ? * ) our new analysis relaxes the constraint on the 22@xmath1 m detection of the _ wise_-selected candidates , and does not take into account their [ 12]-[22 ] @xmath1 m color , replacing these features with the presence of a radio counterpart . the number of @xmath0-ray blazars undetected at 22@xmath1 m is only a small fraction ( @xmath28%of the total number of @xmath0-ray blazars * ? ? ? * ) , but includes several high redshift sources that lying at larger distance than the whole population .    to perform our analysis , we search all the radio sources detected in the + nvss @xcite and in the sydney university molonglo sky survey ( sumss ; * ? ? ? * ) surveys that lie within the positional uncertainty region , at 95% level of confidence , of the ugss listed in the 2fgl . then we associate them with their _ wise _ counterparts to compare their ir colors with those of the known @xmath0-ray blazars in the [ 3.4]-[4.6]-[12 ] @xmath1 m plot using the kernel density estimation ( kde ) technique ( e.g. , * ? ? ? * ; * ? ? ? we also verified if the radio sources found in the recent deep radio observations performed by australia telescope compact array ( atca ) and presented by petrov et al . ( 2013 ) have an ir counterpart with _ wise _ colors consistent with those of the @xmath0-ray blazar population . our analysis of the ir colors is restricted only to the [ 3.4]-[4.6]-[12 ] @xmath1 m color - color plot . the paper is organized as follows : section  [ sec : sample ] is devoted to the definitions of the samples used while in section  [ sec : kde ] we describe the kde technique used to perform our investigation ; we then applied our selection in section  [ sec : ugs ] to identify those radio sources that could be considered blazar - like counterpart of the ugss listed in the 2fgl catalog . we also verified the presence of optical and x - ray counterparts for the selected @xmath0-ray blazar candidates and we compare our results with different approaches previously developed . finally , section  [ sec : summary ] is dedicated to our conclusions .    for our numerical results , we use cgs units unless stated otherwise . spectral indices , @xmath3 , are defined by flux density , s@xmath4 and _ wise _  magnitudes at the [ 3.4 ] , [ 4.6 ] , [ 12 ] , [ 22 ] @xmath1 m ( i.e. , the nominal _ wise _  bands ) are in the vega system respectively . all the magnitudes and the ir colors reported in the paper have been corrected for the galactic extinction according to the formulae reported in draine ( 2003 ) as also performed in our previous analysis ( e.g. , * ? ? ? * ; * ? ? ? the most frequent acronyms used in the paper are listed in table  [ tab : acronym ] . multifrequency catalog of blazars & roma - bzcat   + second _ fermi _  large area telescope catalog & 2fgl + bl lac object & bzb + flat spectrum radio quasar & bzq + blazar of uncertain type & bzu + unidentified gamma - ray source & ugs + training blazar sample & tb + northern ugs sample & nu + southern ugs sample & su + southern deep atca sample & sda + kernel density estimation & kde +     + [ tab : acronym ]","summary":"nearly one - third of the-ray sources detected by _ fermi _  all the-ray extragalactic sources associated in the second _ fermi_-lat catalog have a radio counterpart . first we search for their infrared counterparts in the all - sky survey performed by the wide - field infrared survey explorer ( _ wise _ ) and then we analyze their ir colors in comparison with those of the known-ray blazars . we find fifty - five ugs s likely correspond to radio sources with blazar - like ir signatures .","abstract":"nearly one - third of the-ray sources detected by _ fermi _  are still unidentified , despite significant recent progress in this effort . on the other hand , all the-ray extragalactic sources associated in the second _ fermi_-lat catalog have a radio counterpart . motivated by this observational evidence we investigate all the radio sources of the major radio surveys that lie within the positional uncertainty region of the unidentified-ray sources ( ugss ) at 95% level of confidence . first we search for their infrared counterparts in the all - sky survey performed by the wide - field infrared survey explorer ( _ wise _ ) and then we analyze their ir colors in comparison with those of the known-ray blazars . we propose a new approach , based on a 2-dimensional kernel density estimation ( kde ) technique in the single [ 3.4]-[4.6]-[12 ] m _ wise _  color - color plot , replacing the constraint imposed in our previous investigations on the detection at 22 m of each potential ir counterpart of the ugss with associated radio emission . the main goal of this analysis is to find distant-ray blazar candidates that , being too faint at 22 m , are not detected by _ wise _  and thus are not selected by our purely ir based methods . we find fifty - five ugs s likely correspond to radio sources with blazar - like ir signatures . additional eleven ugss having , blazar - like ir colors , have been found within the sample of sources found with deep recent atca observations ."}
{"article_id":"1404.5960","section_id":"i","document":"in this paper we presented an non - parametric method to search for @xmath0-ray blazar candiates within two samples of ugss . first we identify all the radio sources in the two major surveys ( i.e. , nvss and sumss * ? ? ? * ; * ? ? ? * respectively ) that lie within the positional uncertainty region at 95% level of confidence , then we investigate the ir colors of their _ wise _ counterparts to recognize those with similar spectral properties in the simple [ 3.4]-[4.6]-[12 ] color - color plot . with respect to our previous _ wise _ selection of @xmath0-ray blazar candidates ( e.g. , * ? ? ? * ; * ? ? ? * ) the criteria adopted in the present analysis are less conservative , since the detection of the _ wise _ counterpart at 22@xmath1 m is not required . a small fraction ( @xmath28% ) of the _ fermi _  blazar are in fact not detected at 22@xmath1 m . thus , to compare the ir colors of the _ fermi _  blazars with those of the radio sources selected , we adopted a kde technique as already presented in massaro et al . ( 2011a ) , massaro et al . ( 2012a ) and more recently in paggi et al . ( 2013 ) . our new approach , being less restrictive than those adopted in our previous associations , permits to search for faint @xmath0-ray blazar candidates that were not previously selected because too faint at 22@xmath1 m . by relaxing the requirement on the detection at 22@xmath1 m and thus on the [ 12]-[22 ] color , this method would select candidate blazars at the cost of a larger contamination , mitigated by the requirement on the presence of a radio counterpart . we found 41 and 14 radio sources with ir similar to those of the _ fermi _  blazars within the nu and the su samples , respectively . in addition , we investigated the sample of radio sources discovered with recent deep atca observations performed to search for radio counterparts of the ugs in the southern hemisphere . among 416 radio objects listed in petrov et al . ( 2013 ) only 11 sources have an ir counterpart consistent with the @xmath0-ray blazars . the total number of @xmath0-ray blazar candidates is 66 all listed in table  [ tab : table1 ] and table  [ tab : table2 ] . without no multiple candidates within the positional uncertainty regions of the ugss analyzed . we estimate a probability of spurious association for the @xmath0-ray blazar candidates selected according to our method of the order of 4% and 3% for the nu and su samples , respectively . it is worth noting that the large majority of our candidates show ir colors more consistent with the region occupied by the bzbs in the [ 3.4]-[4.6]-[12 ] @xmath1 m color - color diagram rather than that of bzqs . thus they could be potential faint and so distant bzbs that were not previously selected with different methods because lacking of the ir flux at 22@xmath1 m . more detailed investigations based on ground - based , optical and near ir , spectroscopic follow up observations will be planned for the selected @xmath0-ray blazar candidates to confirm their nature and to obtain their redshifts .     name & mag & mag & mag & mag & mag & arcsec + j003119.70 + 072453.6 & 19.03 & 18.17 & 19.84 & 18.63 & 18.67 & 0.14 + j003908.14 + 433014.6 & 19.9 & 19.61 & 21.42 & 20.77 & & 0.14 + j010345.73 + 132345.4 & 17.98 & 17.73 & 18.69 & 17.38 & 17.24 & 0.07 + j011619.59 - 615343.5 & & 17.72 & 18.22 & 17.78 & 17.91 & 0.27 + j013306.35 - 441421.3 & & 18.38 & 19.7 & 18.12 & 18.76 & 0.26 + j014347.39 - 584551.3 & & 16.7 & 18.48 & 16.64 & 17.04 & 0.04 + j015248.80 + 855703.6 & 20.57 & 18.84 & 19.63 & 18.71 & 17.82 & 0.38 + j020020.94 - 410935.6 & & 19.84 & 21.1 & 18.79 & 18.75 & 0.6 + j022744.35 + 224834.3 & & & 20.82 & 20.22 & 19.28 & 0.35 + j031240.54 + 201142.8 & & 19.34 & 21.22 & 19.42 & 19.07 & 2.63 + j031614.31 - 643731.4 & & 16.59 & 18.19 & 16.57 & 16.82 & 0.22 + j033153.90 + 630814.1 & & & 20.66 & 19.92 & 18.35 & 0.35 + j034022.89 - 242407.2 & & 19.56 & 20.07 & & & 0.21 + j035309.54 + 565430.8 & 20.09 & 19.24 & 20.43 & 18.76 & 18.53 & 0.55 + j040946.57 - 040003.4 & 19.45 & 19.18 & 17.53 & 16.98 & 16.86 & 0.07 + j041605.81 - 435514.6 & & 18.49 & 18.7 & 18.17 & 18.0 & 0.18 + j042025.09 - 374445.0 & & 20.44 & 20.73 & 19.71 & 18.17 & 0.38 + j052313.07 - 253154.4 & & 19.2 & 20.83 & 20.07 & 18.95 & 0.17 + j055618.74 - 435146.1 & & 19.23 & 18.88 & 19.08 & 18.08 & 0.31 + j060102.86 + 383829.2 & & 19.11 & & 19.84 & 18.48 & 0.04 + j064435.72 + 603851.2 & 20.01 & 19.58 & 20.7 & 18.75 & 18.37 & 0.3 + j065845.02 + 063711.5 & 20.25 & & & 19.12 & 18.3 & 0.39 + j072354.83 + 285929.9 & 19.78 & 19.05 & 19.97 & 18.72 & & 0.19 + j074627.03 - 022549.3 & 19.03 & & 18.59 & 18.43 & 16.53 & 0.31 + j092849.83 - 352948.9 & & 18.56 & 19.64 & 18.07 & 18.23 & 0.23 + j093754.72 - 143350.3 & 18.82 & 17.92 & 18.64 & 17.73 & 17.56 & 0.1 + j101544.44 + 555100.7 & 19.69 & 19.42 & 20.61 & 19.35 & & 0.37 + j103015.35 - 840308.7 & & 19.36 & 19.26 & 18.84 & 18.03 & 0.15 + j111511.74 - 070239.9 & & 19.86 & 20.68 & 19.05 & 18.66 & 0.14 + j112325.38 - 252857.0 & 16.9 & 15.76 & 15.87 & 15.56 & 15.51 & 0.19 + j112903.25 + 375657.4 & 19.9 & 19.23 & 19.35 & 19.48 & 18.58 & 0.65 + j122358.17 + 795327.8 & & 17.6 & 20.18 & 18.46 & 17.63 & 1.04 + j125422.47 - 220413.6 & & 19.88 & 18.67 & 19.11 & 18.22 & 0.41 + j125949.80 - 374858.1 & & 17.44 & 18.07 & 16.78 & 17.35 & 0.17 + j131552.98 - 073301.9 & 19.78 & 18.68 & 18.75 & 17.75 & 17.56 & 0.16 + j132840.61 - 472749.2 & & 17.75 & 18.23 & 16.8 & & 0.98 + j133916.44 - 234829.4 & 20.3 & 19.3 & 20.43 & 19.79 & 18.5 & 0.31 + j134042.02 - 041006.8 & 18.21 & 17.21 & 17.59 & 16.46 & 17.08 & 0.19 + j134543.05 - 335643.3 & & 17.98 & 19.58 & 18.65 & 18.12 & 0.38 + j134706.89 - 295842.3 & 17.85 & 17.09 & 18.8 & 17.14 & 17.09 & 0.41 + j151303.66 - 253925.9 & 19.92 & 18.96 & 19.77 & 20.35 & & 0.5 + j151649.26 + 365022.9 & 20.9 & & 21.49 & 20.07 & 19.16 & 1.58 + j154824.39 + 145702.8 & 20.51 & 18.29 & 19.86 & 17.74 & 17.45 & 0.41 + j164619.95 + 435631.0 & 20.43 & 19.73 & 20.42 & 19.67 & & 0.34 + j170409.59 + 123421.7 & 19.86 & 18.04 & 18.62 & 17.63 & 17.46 & 0.47 + j170433.84 - 052840.6 & 19.62 & 18.97 & 18.42 & 17.28 & 17.98 & 0.45 + j200506.02 + 700439.3 & 20.73 & 19.25 & 19.24 & 18.65 & & 0.45 + j202155.45 + 062913.7 & 17.27 & 16.13 & 17.01 & 16.67 & 16.03 & 0.43 + j203451.08 - 420038.2 & & 18.97 & 19.34 & 18.87 & 18.27 & 0.44 + j204201.92 - 731913.5 & & 17.46 & 17.9 & 18.36 & 18.04 & 0.29 + j211522.00 + 121802.8 & 18.15 & 18.15 & 17.68 & 17.31 & 17.58 & 0.16 + j213253.05 + 261143.8 & 20.04 & 19.29 & 19.14 & 19.62 & 18.44 & 0.07 + j213430.18 - 213032.6 & 19.77 & 18.65 & 18.96 & 16.8 & 17.7 & 0.09 + j213349.21 + 664704.3 & & & & 19.37 & 18.8 & 0.45 + j221330.33 - 475425.0 & & 18.12 & 18.6 & 18.34 & 18.33 & 0.05 + j222830.19 - 163642.8 & 18.57 & 19.34 & 19.95 & 19.04 & 17.91 & 0.29 + j224604.98 + 154435.3 & 19.14 & 18.27 & 19.57 & 18.53 & 17.65 & 0.13 + j225128.69 - 492910.6 & & 18.8 & 19.21 & 18.45 & 18.03 & 0.42 + j234302.29 - 475749.9 & & 19.84 & 18.92 & 21.3 & 18.32 & 0.29 + j235836.83 - 180717.3 & 19.14 & 18.45 & 18.28 & 17.22 & 17.53 & 0.3 +      the work is supported by the nasa grants nnx12ao97 g . r. dabrusco gratefully acknowledges the financial support of the us virtual astronomical observatory , which is sponsored by the national science foundation and the national aeronautics and space administration . the work by g. tosti is supported by the asi / inaf contract i/005/12/0 . howard a. smith acknowledges partial support from nasa - jplrsa contract 717437 . topcat[multiblock footnote omitted ] @xcite for the preparation and manipulation of the tabular data and the images . the wenss project was a collaboration between the netherlands foundation for research in astronomy and the leiden observatory . we acknowledge the wenss team consisted of ger de bruyn , yuan tang , roeland rengelink , george miley , huub rottgering , malcolm bremer , martin bremer , wim brouw , ernst raimond and david fullagar for the extensive work aimed at producing the wenss catalog . part of this work is based on archival data , software or on - line services provided by the asi science data center . this research has made use of data obtained from the high energy astrophysics science archive research center ( heasarc ) provided by nasa s goddard space flight center ; the simbad database operated at cds , strasbourg , france ; the nasa / ipac extragalactic database ( ned ) operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . part of this work is based on the nvss ( nrao vla sky survey ) ; the national radio astronomy observatory is operated by associated universities , inc . , under contract with the national science foundation . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . abdo , a. a. et al . 2010a apjs 188 405 abdo , a. a. et al . 2010b apj , 720 , 435 ackermann , m. et al . 2011b apj , 743 , 171 ackermann , m. et al . 2011a apj , 741 , 30 ackermann , m. et al . 2012 apj , 753 , 83 adelman - mccarthy , j. , agueros , m.a . , allam , s.s . , et al . 2008 , apjs , 175 , 297 becker , r. h. , white , r. l. , helfand , d. j.1995 apj , 450 , 559 condon , j. j. , cotton , w. d. , greisen , e. w. , yin , q. f. , perley , r. a. , taylor , g. b. , & broderick , j. j. 1998 , aj , 115 , 1693 cutri et al . 2012 wise.rept , 1c dabrusco , r. , longo , g. , walton , n. a. 2009 mnras , 396 , 223 dabrusco , r. , massaro , f. , ajello , m. , grindlay , j. e. , smith , howard a. & tosti , g. 2012 apj , 748 , 68 dabrusco , r. , massaro , f. , paggi , a. , masetti , n. , giroletti , m. , tosti , g. , smith , howard , a. 2013 apjs , 206 , 12 draine b. t. 2003 ara&a , 41 , 241 ghirlanda , g. , ghisellini , g. , tavecchio , f. , foschini , l. 2010 mnras , 407 , 791 hartman , r.c . et al . , 1999 apjs , 123 , 79 kovalev , y. y. 2009 apj , 707l , 56 kovalev , y. y. et al . 2009 apj , 696l , 17 jones , h. d. et al . 2004 mnras , 355 , 747 jones , h. d. et al . 2009 mnras , 399 , 683 laurino , o. & dabrusco 2011 mnras in press mahony , e. k. , sadler , e. m. , murphy , t. , ekers , r. d. , edwards , p. g. , massardi , m. 2010 apj , 718 , 587 massaro , e. , giommi , p. , leto , c. , marchegiani , p. , maselli , a. , perri , m. , piranomonte , s. , sclavi , s. 2009 a&a , 495 , 691 massaro , e. , giommi , p. , leto , c. , marchegiani , p. , maselli , a. , perri , m. , piranomonte , s. , sclavi , s. 2010 http://arxiv.org/abs/1006.0922 massaro , f. , dabrusco , r. , ajello , m. , grindlay , j. e. & smith , h. a. 2011a apj , 740l , 48 massaro , e. , giommi , p. , leto , c. , marchegiani , p. , maselli , a. , perri , m. , piranomonte , s. , 2011b  multifrequency catalogue of blazars ( 3rd edition ) \" , aracne editrice , rome , italy massaro , f. , dabrusco , r. , tosti , g. , ajello , m. , gasparrini , d. , grindlay , j. e. & smith , howard a. 2012a apj , 750 , 138 massaro , f. , dabrusco , r. , tosti , g. , ajello , m. , paggi , a. , gasparrini , d. 2012b apj , 752 , 61 massaro , e. , nesci , r. , piranomonte , s. 2012 mnras , 422 , 2322 massaro , f. et al . 2013a apjs , 206 , 13 massaro , f. et al . 2013b apjs , 207 , 4 mauch , t. , murphy , t. , buttery , h. j. , curran , j. , hunstead , r. w. , piestrzynski , b. , robertson , j. g. , sadler , e. m. 2003 mnras , 342 , 1117 mirabal , n. 2009 [ arxiv.org/abs/0908.1389v2 ] mirabal , n. 2009 apj , 701 , 129 mirabal , n , d. & pardo , s. 2010 a&a submitted , [ arxiv.org/abs/1007.2644v2 ] monet , d. g. et al . 2003 aj , 125 , 984 mukherjee , r. et al . , 1997 apj , 490 , 116 nolan et al . 2012 apjs , 199 , 31 petrov , l. , mahony , e. k. , edwards , p. g. , sadler , e. m. , schinzel , f. k. , mcconnell , d. 2013 mnras , 432 , 1294 paggi , a. , massaro , f. , dabrusco , r. et al . 2013 apjs submitted paris , i. et al . 2012 a&a , 548a , 66 rengelink , r. et al . 1997 , a&a suppl . 124 , 259 richards , g. t. et al . , 2004 apjs , 155 , 257 skrutskie , m. f. et al . 2006 , aj , 131 , 1163 takeuchi y. et al . , 2013 , apjs submitted taylor m.  b. , 2005 , aspc , 347 , 29 thompson , d. j. 2008 rpph , 71 , 11 , 116901 ungruhe , r. , seitter , w. c. , duerbeck , h. w. 2003 jad , 9 , 1 voges , w. et al . 1999 a&a , 349 , 389 white , r. l. , becker , r. h. helfand , d. j. , gregg , m. d. et al . 1997 apj , 475 , 479 wright , e. l. , et al . 2010 aj , 140 , 1868 zechlin , h .- s . , fernandes , m. v. , elsasser , d. , horns , d. 2012 a&a , 538a , 93","summary":"the main goal of this analysis is to find distant-ray blazar candidates that , being too faint at 22 m , are not detected by _ wise _  and thus are not selected by our purely ir based methods . additional eleven ugss having , blazar - like ir colors , have been found within the sample of sources found with deep recent atca observations .","abstract":"nearly one - third of the-ray sources detected by _ fermi _  are still unidentified , despite significant recent progress in this effort . on the other hand , all the-ray extragalactic sources associated in the second _ fermi_-lat catalog have a radio counterpart . motivated by this observational evidence we investigate all the radio sources of the major radio surveys that lie within the positional uncertainty region of the unidentified-ray sources ( ugss ) at 95% level of confidence . first we search for their infrared counterparts in the all - sky survey performed by the wide - field infrared survey explorer ( _ wise _ ) and then we analyze their ir colors in comparison with those of the known-ray blazars . we propose a new approach , based on a 2-dimensional kernel density estimation ( kde ) technique in the single [ 3.4]-[4.6]-[12 ] m _ wise _  color - color plot , replacing the constraint imposed in our previous investigations on the detection at 22 m of each potential ir counterpart of the ugss with associated radio emission . the main goal of this analysis is to find distant-ray blazar candidates that , being too faint at 22 m , are not detected by _ wise _  and thus are not selected by our purely ir based methods . we find fifty - five ugs s likely correspond to radio sources with blazar - like ir signatures . additional eleven ugss having , blazar - like ir colors , have been found within the sample of sources found with deep recent atca observations ."}
{"article_id":"1208.3899","section_id":"i","document":"the large magellanic cloud ( lmc ) has long been recognized as a fundamental benchmark for a wide variety of astrophysical studies . as the closest bulge - less dwarf disk galaxy @xcite , it has turned out to be the ideal local analog for the detailed study of these most common and primeval galaxies . ages and abundances of lmc field star populations are prime indicators of the galaxy s chemical evolution and star formation history ( sfh ) . this becomes even more relevant since its formation and chemical evolution can not be fully traced from its star cluster populations , due to the well - known extended age gap . the lmc age - metallicity relationship ( amr ) has been the subject of a number of studies ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * among others ) . among them , two perhaps best summarize our current knowledge in this field . first , ( * ? ? ? * hereafter cgah ; see also references therein ) have examined the amr for field star populations , based on calcium triplet spectroscopy of individual red giants and bvri photometry in ten 34@xmath5@xmath633@xmath5 lmc fields . they found that : i ) the amrs for their fields are statistically indistinguishable ; ii ) the disk amr is similar to that of the lmc star clusters and is well reproduced by closed - box models or models with a small degree of outflow ; iii ) the lack of clusters with ages between 3 and 10 gyr is not observed in the field population ; iv ) the age of the youngest population observed in each field increases with galactocentric distance ; v ) the rapid chemical enrichment observed in the last few gyrs is only observed in fields with r@xmath77kpc ; vi ) the metallicity gradient observed in the outer disk can be explained by an increase in the age of the youngest stars and a concomitant decrease in their metallicity ; and vii ) they find much better evidence for an outside - in than inside - out formation scenario , in contradiction to generic @xmath8 models . secondly , ( * ? ? ? * hereafter hz09 ; see also references therein ) ) presented the first - ever global , spatially - resolved reconstruction of the sfh , based on the application of their starfish analysis software to the multiband photometry of twenty million stars from the magellanic clouds photometric survey . they found that there existed a long relatively quiescent epoch ( from @xmath1 12 to 5 gyr ago ) during which the star formation was suppressed throughout the lmc ; the metallicity also remained stagnant during this period . they concluded that the field and cluster star formation modes have been tightly coupled throughout the lmc s history . although these studies represent the state - of - the - art of our knowledge of the lmc amr , they leave unanswered a number of outstanding questions : what caused the general lull in sf between @xmath1 5 and 12 gyr ago ? are the cluster and field amrs really tightly coupled ? can the lmc amr best be described by a closed - box , bursting or other chemical evolution model ? what , if any , are the radial dependences ? in addition , hz09 did not go deep enough to derive the full sfh from information on the main sequence ( ms ) . they reached a limiting magnitude between @xmath9 = 20 and 21 mag , depending on the local degree of crowding in the images , corresponding to stars younger than 3 gyr old on the ms if the theoretical isochrones of @xcite and a lmc distance modulus of 18.5 mag are used . thus , the advantages of covering an enormous extension of the lmc is partially offset by the loss in depth of the limiting magnitude . on the other hand , the ten fields of cgah cover a rather small fraction of the whole lmc . therefore , it is desirable to obtain an overall deeper amr for the lmc which also covers a larger area . previous amrs have been founded on theoretical isochrones , numerical models , or synthetic color - magnitude diagrams ( cmds ) , so that an amr built from actual measured ages and metallicities is very valuable . a comprehensive comparison between the field and cluster amrs obtained using the same procedure is also lacking . all these aims demand the availability of a huge volume of high quality data as well as a powerful technique to provide both accurate ages and metallicities .    in this paper we address these issues for the first time . we make use of an unprecedented database of some 5.5 million stars measured with the washington @xmath0 photometric system , which are spread over a large part of the lmc main body . from this database , we produce the lmc field amr from the birth of the galaxy until @xmath1 1 gyr ago , using the @xmath10@xmath11 index and the standard giant branch isoabundance curves to estimate ages and metallicities , respectively , of the most representative field populations . these provide approximately independent measurements of these two quantities , minimizing the age - metallicity degeneracy problem . in addition , this is the first overall lmc field star amr obtained from washington data ; thus complementing those derived from other data sets such as hz09 or the amr obtained from washington data for lmc clusters @xcite . finally , we homogeneously compared the derived field star amr to that for the lmc cluster population with ages and metallicities put on the same scales using these two washington datasets . this kind of comparison has not been accomplished before . the paper is organized as follows : section 2 briefly describes the data handling and analysis from which @xcite estimated the field star ages and metallicities . section 3 deals with the aforementioned issue of a comprehensive amr of the lmc field star population . in section 4 we discuss our results and compare them with previous studies , while section 5 summarizes our major findings .","summary":"we produce a comprehensive field star age - metallicity relationship ( amr ) from the earliest epoch until 1 gyr ago .","abstract":"we analyze age and metallicity estimates for an unprecedented database of some 5.5 million stars distributed throughout the large magellanic cloud ( lmc ) main body , obtained from ccd washington photometry , reported on in piatti et al . 2012 . we produce a comprehensive field star age - metallicity relationship ( amr ) from the earliest epoch until 1 gyr ago . this amr reveals that the lmc has not evolved chemically as either a closed - box or bursting system , exclusively , but as a combination of both scenarios that have varied in relative strength over the lifetime of the galaxy , although the bursting model falls closer to the data in general . furthermore , while old and metal - poor field stars have been preferentially formed in the outer disk , younger and more metal - rich stars have mostly been formed in the inner disk , confirming an outside - in formation . we provide evidence for the formation of stars between 5 and 12 gyr , during the cluster age gap , although chemical enrichment during this period was minimal . we find no significant metallicity gradient in the lmc . we also find that the range in the metallicity of an lmc field has varied during the lifetime of the lmc . in particular , we find only a small range of the metal abundance in the outer disk fields , whereas an average range of[fe / h ] = + 0.3 0.1 dex appears in the inner disk fields . finally , the cluster and field amrs show a satisfactory match only for the last 3 gyr , while for the oldest ages ( 11 gyr ) the cluster amr is a remarkable lower envelope to the field amr . such a difference may be due to the very rapid early chemical evolution and lack of observed field stars in this regime , whereas the globular clusters are easily studied . this large difference is not easy to explain as coming from stripped ancient small magellanic cloud ( smc ) clusters , although the field smc amr is on average 0.4 dex more metal - poor at all ages than that of the lmc but otherwise very similar ."}
{"article_id":"1208.3899","section_id":"c","document":"in fig . 5 , we have overplotted with solid lines different field star amrs along with our presently derived composite amr , namely : hz09 ( yellow ) , @xcite ( black ) , ( * ? ? ? * hereafter pt98 ) ( blue ) , and @xcite ( red ) . the red line amr is based on a closed - box model , while the blue curve is a bursting model . we also included with red and blue filled circles the amrs derived by @xcite for the lmc bar and disk , respectively . at first glance , we find that the bursting sfh modeled by pt98 appears to be the one which best resembles the amr derived by @xcite , instead of closed - box models as carrera et al . suggested . however , such a resemblance is only apparent since pt98 constructed their model using nearly no star formation from @xmath1 12 up to 3 gyr ago ( see their fig . this clearly contradicts not only carrera et al.s result but also ours , which show that there were many stars formed in the lmc in that period ( see fig . 4 ) . indeed , we actually see no significant chemical evolution from about 12 - 6 gyr , even though stars were formed . in turn , the closed - box models appear to be qualitatively closer to hz09 s reconstructed amr .    since hz09 s amr is based on a relatively bright limiting magnitude database and cgah s amrs rely on ages and metallicities for stars distributed in ten fields ( each only slightly smaller than ours ) , we believe that the present composite amr has several important advantages over these previous ones , and possibly reconciles previous conclusions about the major enrichment processes that have dominated the chemical evolution of the lmc from its birth until @xmath1 1 gyr ago . note that a large number of fields distributed through the galaxy are analysed here and their representative oldest ms tos are well measured in all fields . the composite amr we derive results in a complex function having hz09 s amr ( or alternatively the closed - box model ) and cgah s amrs ( or alternatively the bursting model ) as lower and approximately upper envelopes in metallicity , respectively , although the bursting model is a much better fit . therefore , we find evidence that the lmc has not chemically evolved as a closed - box or bursting system , exclusively , but as a combination of both scenarios that likely have varied in importance during the lifetime of the galaxy , but with the bursting model dominating . the closed - box model presumably reproduces the metallicity trend that the lmc would have had if bursting formation episodes had not taken place . however , since the lmc would appear to have experienced such an enhanced formation event(s ) , important chemical enrichment has occurred from non well - mixed gas spread through the lmc . cgah also found that the amrs for their ten fields are statistically indistinguishable . we note , however , that six of their fields are aligned somewhat perpendicular to the lmc bar , reaching quite low density outer regions , and therefore , that their coverage represents a relatively small percentage of the whole field population . we show in fig . 1 that , when more field stars distributed through the lmc are analyzed with age and metallicity uncertainties robustly considered , distinct individual amrs do arise . indeed , figs . 2 and 3 illustrate how different amrs are for inner and outer fields . when inspecting in detail our composite field lmc amr , the relatively quiescent epoch ( @xmath22 @xmath1 5 to 12 gyr ) claimed by hz09 and also frequently considered as a feature engraved in the cluster formation processes , i.e. the cluster age - gap ( * ? ? ? ? * ; * ? ? ? * among others ) is not observed . on the contrary , there exists a noticeable number of fields with representative ages spanning the age gap ( from @xmath1 12 gyr to 3 gyr ) , which further strengthens the difference between cluster and field star formation during this epoch . of course , we do not quantitatively compare the level of sf in different epochs , we simply measure the properties of the dominant population . however , during this extended period , although some star formation occurred , it was not accompanied by any significant chemical evolution until starting @xmath16 gyr ago . again curiously , there were several gyr of star formation and chemical evolution before the cluster age gap ended . in addition , although the ages estimated by cgah of field stars spanning the cluster age gap could have uncertainties necessarily large for individual stars , and consequently their sfh would still indicate a relatively quiescent epoch between 5 and 10 gyr as hz09 pointed out , we provide here evidence of the existence of stars formed between 5 and 12 gyr that represent the most numerous populations in their respective regions . note that our metallicities are generally about 0.1 - 0.2 dex lower than cgah for younger ages but higher for the oldest stars , indicating a smaller total chemical enrichment over the lifetime of the galaxy compared to that found by cgah . our agreement with @xcite is somewhat better . we also find that the amount of chemical evolution ( as measured by the increase in the metallicity ) of the lmc fields has varied during the lifetime of the lmc . particularly , we find only a small range of the metal abundance within the considered uncertainties for the outer disk fields , whereas an average increase of @xmath2[fe / h ] = 0.3 @xmath3 0.1 dex appears in the inner disk fields , and this increase occurred over a relatively shorter time period . hence , a bursting star formation scenario turns out to be a plausible explanation if the enhanced star formation is accompanied by a vigorous nucleosynthesis process that takes place during the burst .    finally , we present a homogeneous comparison between the composite field amr with that for 81 lmc clusters with ages ( @xmath35 1 gyr ) and metallicities derived on the same scales as here . we use the ages and metallicities compiled by @xcite for 45 clusters observed in the washington system , to which we add 36 clusters with ages estimated by @xcite from similar data . we estimate here their metallicities following the same procedure used for the studied fields ( see section 2 ) . the resulting cluster amr is depicted in fig . 6 with dark - gray filled boxes superimposed onto the composite field lmc ( open boxes with error bars ) . as can be seen , the cluster amr satisfactorily matches the field amr only for the last 3 gyr , while it is a remarkable lower envelope of the field amr for older ages ( @xmath22 @xmath4 11 gyr ) . the most likely explanation is a very rapid early chemical enrichment traced by the very visible globular clusters , but their coeval , low metallicity field counterparts are so rare that they are missed in our data . the origin of the 15 oldest lmc clusters still remains unexplained and constitutes one of the most intriguing enigmas in our understanding of the lmc formation and evolution . different studies show that they have very similar properties to the globular clusters in the milky way ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * among others ) , except for their orbits , which are within the lmc disk instead of in an isothermal halo @xcite . on the other hand , fig . 4 show that there exist field star populations older than 10 gyr and about as old as the old globulars . these results go along with the curious conundrum of the absence of clusters during the infamous age gap @xcite . since hz09 found that there was a relatively quiescent epoch in the field star formation from approximately 12 to 5 gyr ago ( similar to that observed for star clusters ) , they also concluded that field and cluster star formation modes are tightly coupled . notice that the ages and metallicities used by hz09 for the 85 clusters are not themselves on a homogeneous scale nor on the same field age / metallicity scales .    in order to look for clues for the very low metallicities of the oldest lmc clusters , we reconstructed the cluster and field amrs of the smc , also from washington photometry obtained by us . as for the field amr we used the ages and metallicities derived by ( * ? ? ? * his table 4 ) ) and applied to them the same binning and error analyses as for the composite lmc field amr ( fig . 4 ) . note that these ages and metallicities are all set on the present age / metallicity scales . we also compiled 59 smc clusters ( @xmath22 @xmath36 1 gyr ) from @xcite , and @xcite with ages and metallicities tied to the same scales . 6 shows the resulting smc amrs depicted with open triangles for its field stars and with filled triangles for its star cluster population . as can be seen , cluster and field stars apparently share similar chemical enrichment histories in the smc , although the population of old clusters drastically decreases beyond @xmath1 7 gyr and there is only 1 older than 10 gyr . @xcite showed , based on the statistics of catalogued and studied clusters , that a total of only seven relatively old / old clusters remain to be studied , and an even smaller number is obtained if the cluster spatial distribution is considered . from this result , we conclude that the smc cluster amr is relatively well - known , particularly towards its older and more metal - poor end . therefore , it does not seem easy to connect the origin of the oldest lmc cluster population to stripping events of ancient smc star clusters . moreover , the composite smc field amr is on average @xmath1 0.4 dex more metal - poor at all ages than that of the counterpart in the lmc , with little variation , indicating that the global chemical evolution in these two galaxies was quite similar in nature but with an offset to lower metallicity in the smc . in particular , there was a very early and rapid period of enrichment , followed by a long quiescent epoch with some star formation in both clouds but cluster formation only in the smc and little to no metallicity increase and finally a recent period of substantial enrichment starting about 6gyr ago . this is in very good agreement with the smc amr found by @xcite . the relative deficiency in heavy elements of the smc could explain the metallicity of a few old lmc clusters , if they were captured from the smc @xcite , but this is an unlikely argument to explain the majority of them . in fact , it is curious in this context that the the oldest smc cluster is at the young and metal - rich extreme of the lmc globular cluster distributions .","summary":"this amr reveals that the lmc has not evolved chemically as either a closed - box or bursting system , exclusively , but as a combination of both scenarios that have varied in relative strength over the lifetime of the galaxy , although the bursting model falls closer to the data in general . in particular , we find only a small range of the metal abundance in the outer disk fields , whereas an average range of[fe / h ] = + 0.3 0.1 dex appears in the inner disk fields . finally , the cluster and field amrs show a satisfactory match only for the last 3 gyr , while for the oldest ages ( 11 gyr ) the cluster amr is a remarkable lower envelope to the field amr . such a difference may be due to the very rapid early chemical evolution and lack of observed field stars in this regime , whereas the globular clusters are easily studied .","abstract":"we analyze age and metallicity estimates for an unprecedented database of some 5.5 million stars distributed throughout the large magellanic cloud ( lmc ) main body , obtained from ccd washington photometry , reported on in piatti et al . 2012 . we produce a comprehensive field star age - metallicity relationship ( amr ) from the earliest epoch until 1 gyr ago . this amr reveals that the lmc has not evolved chemically as either a closed - box or bursting system , exclusively , but as a combination of both scenarios that have varied in relative strength over the lifetime of the galaxy , although the bursting model falls closer to the data in general . furthermore , while old and metal - poor field stars have been preferentially formed in the outer disk , younger and more metal - rich stars have mostly been formed in the inner disk , confirming an outside - in formation . we provide evidence for the formation of stars between 5 and 12 gyr , during the cluster age gap , although chemical enrichment during this period was minimal . we find no significant metallicity gradient in the lmc . we also find that the range in the metallicity of an lmc field has varied during the lifetime of the lmc . in particular , we find only a small range of the metal abundance in the outer disk fields , whereas an average range of[fe / h ] = + 0.3 0.1 dex appears in the inner disk fields . finally , the cluster and field amrs show a satisfactory match only for the last 3 gyr , while for the oldest ages ( 11 gyr ) the cluster amr is a remarkable lower envelope to the field amr . such a difference may be due to the very rapid early chemical evolution and lack of observed field stars in this regime , whereas the globular clusters are easily studied . this large difference is not easy to explain as coming from stripped ancient small magellanic cloud ( smc ) clusters , although the field smc amr is on average 0.4 dex more metal - poor at all ages than that of the lmc but otherwise very similar ."}
{"article_id":"1208.3899","section_id":"i","document":"in this study we present , for the first time , the amr of the lmc field star population from ages and metallicities derived using ccd washington @xmath0 photometry of some 5.5 million stars in twenty - one 36@xmath5@xmath636@xmath5 fields distributed throughout the lmc main body presented in @xcite . the analysis of the photometric data -subdivided in 336 smaller 9@xmath5@xmath69@xmath5 subfields - leads to the following main conclusions :    \\i ) from ages and metallicities of the representative star population in each subfield estimated by using the @xmath10@xmath11 index and the sgb technique , respectively , we produced individual field amrs with a robust treatment of their age and metallicity uncertainties . these individual amrs show some noticeable differences from field to field in several aspects : starting and ending ages , metallicity range , shape , etc . this is contrary to cgah , who found very similar amrs in their sample . the composite amr for the lmc fields reveals that , while old and metal - poor field stars have been preferentially formed in the outer disk , younger and more metal - rich stars have mostly been formed in the inner disk . this result confirms an outside - in evolution of the galaxy , as found by @xcite . in addition , we provide evidence of the existence of stars formed between 6 and 12 gyr that represent the most numerous populations in their respective regions , although little or no chemical evolution occured during this extended period . \\ii ) the resulting distribution of the ages and the metallicities as a function of the deprojected distance reveals that there is no significant metallicity gradient in the lmc ( ( -0.01 @xmath3 0.01 ) dex kpc@xmath34 ) . the relatively more metal - poor stars found in the outermost regions is mainly a consequence of the fact that such regions are dominated by old stars which are relatively metal - poor , whereas intermediate - age stars which are more metal - rich prevail in the innermost regions . we also find that the range in the metallicity of the lmc fields has varied during the lifetime of the lmc . in particular , we find only a small range of the metal abundance for the outer disk fields , whereas an average range of @xmath2[fe / h ] = + 0.3 @xmath3 0.1 dex is found in the inner disk fields . \\iii ) from the comparison of our composite amr with theoretical ones , we conclude that the lmc has not chemically evolved as a closed - box or bursting system , exclusively , but as a combination of both scenarios that have had different prominence during the lifetime of the galaxy , with the bursting model generally more dominant . enhanced formation episodes could have possibly taken place as a result of its interactions with the milky way and/or smc . iv ) we finally accomplish a homogeneous comparison between the composite field amr with that for lmc clusters with ages and metallicities on the same scales . we find a satisfactory match only for the last 3 gyr , while for older ages ( @xmath4 11 gyr ) the cluster amr results in a remarkable lower envelope of the field amr . the most likely explanation is a very rapid early chemical enrichment traced by the very visible globular clusters , but their coeval , low metallicity field counterparts are so rare that they are missed in our data . we find that such a large difference between the metallicities of lmc field stars and clusters is not easy to explain as coming from stripped ancient smc clusters , although the field smc amr is on average @xmath1 0.4 dex more metal - poor at all ages than that of the lmc . the two galaxies otherwise show a very similar chemical evolution . we greatly appreciate the comments and suggestions raised by the reviewer which helped us to improve the manuscript . this work was partially supported by the argentinian institutions conicet and agencia nacional de promocin cientfica y tecnolgica ( anpcyt ) . d.g . gratefully acknowledges support from the chilean basal centro de excelencia en astrofsica y tecnologas afines ( cata ) grant pfb-06/2007 .                                                                                                                                  1 & 9.0 & 9.0 & 11.7 & 9.0 & 9.0 & 11.1 & 11.1 & 11.7 & 9.0 & 11.1 & 11.1 & 11.7 & 8.6 & 11.1 & 11.1 & 11.7 + & 2.8 & 2.8 & 3.5 & 2.8 & 2.8 & 3.3 & 3.3 & 3.5 & 2.8 & 3.3 & 3.3 & 3.5 & 2.7 & 3.3 & 3.3 & 3.5 + 2 & 9.5 & 9.5 & 10.5 & 11.1 & 8.1 & 10.5 & 10.5 & 8.6 & 10.0 & 8.1 & 10.5 & 11.1 & 10.5 & 10.5 & 8.1 & 8.1 + & 2.9 & 2.9 & 3.2 & 3.3 & 2.6 & 3.2 & 3.2 & 2.7 & 3.1 & 2.6 & 3.2 & 3.3 & 3.2 & 3.2 & 2.6 & 2.6 + 3 & 8.6 & 11.1 & 8.6 & 11.7 & 9.0 & 11.1 & 11.1 & 9.0 & 11.7 & 11.1 & 8.6 & 11.7 & 8.6 & 9.0 & 11.7 & 9.0 + & 2.7 & 3.3 & 2.7 & 3.5 & 2.8 & 3.3 & 3.3 & 2.8 & 3.5 & 3.3 & 2.7 & 3.5 & 2.7 & 2.8 & 3.5 & 2.8 + 4 & 11.1 & 9.5 & 9.5 & 9.5 & 9.5 & 7.7 & 10.0 & 10.5 & 9.5 & 10.0 & 10.0 & 10.5 & 12.9 & 8.1 & 8.1 & 8.6 + & 3.3 & 2.9 & 2.9 & 2.9 & 2.9 & 2.5 & 3.1 & 3.2 & 2.9 & 3.1 & 3.1 & 3.2 & 3.8 & 2.6 & 2.6 & 2.7 + 5 & 9.5 & 11.7 & 11.7 & 11.7 & 11.7 & 11.7 & 9.0 & 11.7 & 11.7 & 11.7 & 9.0 & 6.5 & 11.7 & 12.3 & 7.3 & 9.5 + & 2.9 & 3.5 & 3.5 & 3.5 & 3.5 & 3.5 & 2.8 & 3.5 & 3.5 & 3.5 & 2.8 & 2.1 & 3.5 & 3.6 & 2.3 & 2.9 + 6 & 9.0 & 9.0 & 9.0 & 9.5 & 11.7 & 9.0 & 11.1 & 9.0 & 9.0 & 9.0 & 11.7 & 9.0 & 9.0 & 11.7 & 9.0 & 9.5 + & 2.8 & 2.8 & 2.8 & 2.9 & 3.5 & 2.8 & 3.3 & 2.8 & 2.8 & 2.8 & 3.5 & 2.8 & 2.8 & 3.5 & 2.8 & 2.9 + 7 & 11.1 & 10.0 & 4.7 & 10.5 & 10.5 & 10.5 & 8.1 & 8.1 & 10.5 & 10.5 & 13.5 & 10.5 & 12.9 & 8.1 & 8.1 & 11.1 + & 3.3 & 3.1 & 1.5 & 3.2 & 3.2 & 3.2 & 2.6 & 2.6 & 3.2 & 3.2 & 3.9 & 3.2 & 3.8 & 2.6 & 2.6 & 3.3 + 8 & 8.6 & 11.1 & 8.6 & 8.6 & 9.0 & 11.1 & 8.6 & 9.0 & 9.0 & 8.6 & 8.6 & 8.6 & 7.3 & 6.9 & 9.0 & 9.0 + & 2.7 & 3.3 & 2.7 & 2.7 & 2.8 & 3.3 & 2.7 & 2.8 & 2.8 & 2.7 & 2.7 & 2.7 & 2.3 & 2.2 & 2.8 & 2.8 + 9 & 6.5 & 6.5 & 4.9 & 5.2 & 8.6 & 4.9 & 3.7 & 4.9 & 6.5 & 8.6 & 6.5 & 4.9 & 9.0 & 6.9 & 5.2 & 6.5 + & 2.1 & 2.1 & 1.6 & 1.7 & 2.7 & 1.6 & 1.2 & 1.6 & 2.1 & 2.7 & 2.1 & 1.6 & 2.8 & 2.2 & 1.7 & 2.1 + 10 & 2.7 & 2.1 & 3.5 & 2.7 & 3.5 & 2.1 & 2.1 & 2.1 & 2.1 & 2.1 & 2.7 & 2.1 & 2.7 & 2.7 & 1.7 & 2.1 + & 0.8 & 0.5 & 1.1 & 0.8 & 1.1 & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 & 0.8 & 0.5 & 0.8 & 0.8 & 0.3 & 0.5 + 11 & 2.7 & 4.7 & 3.5 & 4.7 & 3.5 & 2.8 & 4.9 & 4.9 & 4.7 & 6.5 & 3.7 & 4.9 & 3.7 & 4.9 & 3.7 & 5.2 + & 0.8 & 1.5 & 1.1 & 1.5 & 1.1 & 0.8 & 1.6 & 1.6 & 1.5 & 2.1 & 1.2 & 1.6 & 1.2 & 1.6 & 1.2 & 1.7 + 12 & 2.8 & 3.7 & 3.5 & 2.7 & 4.9 & 4.9 & 3.7 & 4.7 & 3.7 & 3.7 & 4.9 & 2.8 & 3.7 & 3.9 & 3.9 & 5.2 + & 0.8 & 1.2 & 1.1 & 0.8 & 1.6 & 1.6 & 1.2 & 1.5 & 1.2 & 1.2 & 1.6 & 0.8 & 1.2 & 1.3 & 1.3 & 1.7 + 13 & 3.0 & 2.8 & 2.8 & 2.8 & 3.0 & 3.9 & 3.7 & 3.7 & 3.9 & 5.2 & 3.7 & 3.7 & 2.3 & 3.9 & 3.0 & 3.7 + & 0.9 & 0.8 & 0.8 & 0.8 & 0.9 & 1.3 & 1.2 & 1.2 & 1.3 & 1.7 & 1.2 & 1.2 & 0.6 & 1.3 & 0.9 & 1.2 + 14 & 2.0 & 1.6 & 1.6 & 2.0 & 1.5 & 1.4 & 2.0 & 2.3 & 1.6 & 1.5 & 2.4 & 4.2 & 3.7 & 3.2 & 3.7 & 3.7 + & 0.4 & 0.3 & 0.3 & 0.4 & 0.2 & 0.2 & 0.4 & 0.6 & 0.3 & 0.2 & 0.7 & 1.4 & 1.2 & 1.0 & 1.2 & 1.2 + 15 & 3.9 & 4.9 & 3.7 & 3.7 & 4.9 & 3.9 & 3.9 & 3.9 & 3.7 & 3.9 & 3.9 & 3.2 & 3.7 & 3.2 & 3.0 & 2.4 + & 1.3 & 1.6 & 1.2 & 1.2 & 1.6 & 1.3 & 1.3 & 1.3 & 1.2 & 1.3 & 1.3 & 1.0 & 1.2 & 1.0 & 0.9 & 0.7 + 16 & 5.5 & 4.7 & 4.7 & 4.9 & 6.5 & 4.7 & 6.2 & 6.2 & 4.7 & 6.2 & 6.2 & 3.5 & 5.2 & 6.5 & 4.9 & 3.7 + & 1.8 & 1.5 & 1.5 & 1.6 & 2.1 & 2.1 & 2.0 & 2.0 & 1.5 & 2.0 & 2.0 & 1.1 & 1.7 & 2.1 & 1.6 & 1.2 + 17 & 6.9 & 6.9 & 11.7 & 11.7 & 12.3 & 9.5 & 9.5 & 6.5 & 10.0 & 11.7 & 11.7 & 9.0 & 10.0 & 9.5 & 9.5 & 9.0 + & 2.2 & 2.2 & 3.5 & 3.5 & 3.6 & 2.9 & 2.9 & 2.1 & 3.1 & 3.5 & 3.5 & 2.8 & 3.1 & 2.9 & 2.9 & 2.8 + 18 & 4.4 & 6.2 & 8.1 & 8.1 & 4.4 & 8.1 & 8.6 & 10.0 & 4.4 & 4.7 & 5.8 & 10.0 & 3.5 & 6.2 & 5.8 & 4.4 + & 1.4 & 2.0 & 2.6 & 2.6 & 1.4 & 2.6 & 2.7 & 3.1 & 1.4 & 1.5 & 1.9 & 3.1 & 1.1 & 2.0 & 1.9 & 1.4 + 19 & 9.5 & 11.7 & 6.9 & 11.7 & 9.0 & 11.7 & 9.0 & 9.0 & 9.0 & 9.0 & 9.0 & 9.0 & 9.0 & 6.9 & 12.3 & 9.5 + & 2.9 & 3.5 & 2.2 & 3.5 & 2.8 & 3.5 & 2.8 & 2.8 & 2.8 & 2.8 & 2.8 & 2.8 & 2.8 & 2.2 & 3.6 & 2.9 + 20 & 10.0 & 12.9 & 10.0 & 10.0 & 10.0 & 10.0 & 12.9 & 10.0 & 10.0 & 12.9 & 7.7 & 12.9 & 10.0 & 10.0 & 7.7 & 8.1 + & 3.1 & 3.8 & 3.1 & 3.1 & 3.1 & 3.1 & 3.8 & 3.1 & 3.1 & 3.8 & 2.5 & 3.8 & 3.1 & 3.1 & 2.5 & 2.6 + 21 & 8.6 & 12.3 & 9.5 & 9.5 & 12.3 & 12.3 & 12.3 & 12.3 & 9.5 & 12.3 & 9.5 & 12.3 & 9.5 & 9.5 & 12.3 & 10.0 + & 2.7 & 3.6 & 2.9 & 2.9 & 3.6 & 3.6 & 3.6 & 3.6 & 2.9 & 3.6 & 2.9 & 3.6 & 2.9 & 2.9 & 3.6 & 3.1 +      1 & -0.96 & -0.86 & -0.90 & -0.76 & -0.91 & -1.00 & -0.95 & -1.00 & -0.96 & -0.95 & -0.95 & -0.95 & -0.85 & -0.95 & -0.95 & -0.90 + & 0.31 & 0.31 & 0.20 & 0.31 & 0.31 & 0.20 & 0.20 & 0.20 & 0.31 & 0.20 & 0.20 & 0.20 & 0.28 & 0.20 & 0.20 & 0.20 + 2 & -0.88 & -0.88 & -0.90 & -0.90 & -0.74 & -0.90 & -0.90 & -0.85 & -0.80 & -0.84 & -0.90 & -0.85 &  & -0.90 & -0.84 & -0.89 + & 0.35 & 0.35 & 0.20 & 0.20 & 0.26 & 0.20 & 0.20 & 0.28 & 0.20 & 0.26 & 0.20 & 0.20 & 0.20 & 0.20 & 0.26 & 0.26 + 3 & -0.85 & -0.95 & -0.90 & -0.90 & -0.91 & -0.95 & -0.95 & -0.86 & -0.95 & -0.95 & -0.90 & -0.90 & -0.85 & -0.86 & -0.90 & -0.86 + & 0.28 & 0.20 & 0.28 & 0.20 & 0.31 & 0.20 & 0.20 & 0.31 & 0.20 & 0.20 & 0.28 & 0.20 & 0.28 & 0.31 & 0.20 & 0.31 + 4 & -0.90 & -0.88 & -0.88 & -0.93 & -0.83 & -0.93 & -1.00 & -1.00 & -0.88 & -1.00 & -0.95 & -0.95 & -0.90 & -0.94 & -0.89 & -0.90 + & 0.20 & 0.35 & 0.35 & 0.35 & 0.35 & 0.25 & 0.20 & 0.20 & 0.35 & 0.20 & 0.20 & 0.20 & 0.20 & 0.26 & 0.26 & 0.28 + 5 & -0.78 & -0.90 & -0.90 & -0.90 & -0.90 & -0.90 & -0.86 & -0.90 & -0.90 & -0.90 & -0.86 & -0.86 & -0.85 & -0.85 & -0.77 & -0.88 + & 0.35 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.31 & 0.20 & 0.20 & 0.20 & 0.31 & 0.25 & 0.20 & 0.20 & 0.24 & 0.35 + 6 & -0.86 & -0.91 & -0.86 & -0.93 & -0.85 & -0.96 & -0.95 & -0.91 & -0.91 & -0.96 & -1.00 & -0.91 & -0.86 & -1.00 & -0.91 & -1.08 + & 0.31 & 0.31 & 0.31 & 0.35 & 0.20 & 0.31 & 0.20 & 0.31 & 0.31 & 0.31 & 0.20 & 0.31 & 0.31 & 0.20 & 0.31 & 0.35 + 7 & -0.85 & -0.95 & -0.78 & -0.95 & -0.90 & -0.95 & -0.89 & -0.89 & -0.90 & -0.95 & -0.90 & -1.00 & -0.80 & -0.89 & -0.89 & -1.00 + & 0.20 & 0.20 & 0.31 & 0.20 & 0.20 & 0.20 & 0.26 & 0.26 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.26 & 0.26 & 0.20 + 8 & -0.90 & -1.00 & -0.95 & -1.00 & -0.96 & -1.10 & -1.05 & -1.06 & -1.01 & -1.10 & -1.05 & -1.05 & -1.02 & -1.06 & -1.11 & -1.26 + & 0.28 & 0.20 & 0.28 & 0.28 & 0.31 & 0.20 & 0.28 & 0.31 & 0.31 & 0.28 & 0.28 & 0.28 & 0.24 & 0.24 & 0.31 & 0.31 + 9 & -0.81 & -0.81 & -0.80 & -0.86 & -0.85 & -0.85 & -0.70 & -0.80 & -0.81 & -0.95 & -0.86 & -0.80 & -0.81 & -0.81 & -0.76 & -0.91 + & 0.25 & 0.25 & 0.30 & 0.29 & 0.28 & 0.30 & 0.33 & 0.30 & 0.25 & 0.28 & 0.25 & 0.30 & 0.31 & 0.24 & 0.29 & 0.25 + 10 & -0.61 & -0.66 & -0.88 & -0.71 & -0.83 & -0.61 & -0.61 & -0.66 & -0.66 & -0.61 & -0.71 & -0.61 & -0.56 & -0.66 & -0.48 & -0.56 + & 0.33 & 0.31 & 0.34 & 0.33 & 0.34 & 0.34 & 0.31 & 0.31 & 0.31 & 0.31 & 0.33 & 0.31 & 0.33 & 0.33 & 0.28 & 0.31 + 11 & -0.56 & -0.78 & -0.68 & -0.78 & -0.68 & -0.58 & -0.85 & -0.85 & -0.83 & -0.91 & -0.70 & -0.80 & -0.65 & -0.80 & -0.70 & -0.81 + & 0.33 & 0.31 & 0.34 & 0.31 & 0.34 & 0.34 & 0.30 & 0.30 & 0.31 & 0.25 & 0.33 & 0.30 & 0.33 & 0.30 & 0.33 & 0.29 + 12 & -0.53 & -0.70 & -0.68 & -0.51 & -0.80 & -0.85 & -0.75 & -0.78 & -0.70 & -0.70 & -0.80 & -0.53 & -0.60 & -0.72 & -0.72 & -0.86 + & 0.34 & 0.33 & 0.34 & 0.33 & 0.30 & 0.30 & 0.33 & 0.31 & 0.33 & 0.33 & 0.30 & 0.34 & 0.33 & 0.33 & 0.33 & 0.29 + 13 & -0.61 & -0.58 & -0.58 & -0.48 & -0.66 & -0.77 & -0.75 & -0.70 & -0.77 & -0.91 & -0.75 & -0.70 & -0.50 & -0.72 & -0.66 & -0.70 + & 0.34 & 0.34 & 0.34 & 0.34 & 0.34 & 0.33 & 0.33 & 0.33 & 0.33 & 0.29 & 0.33 & 0.33 & 0.32 & 0.33 & 0.34 & 0.33 + 14 & -0.52 & -0.40 & -0.45 & -0.52 & -0.36 & -0.40 & -0.42 & -0.45 & -0.35 & -0.31 & -0.52 & -0.69 & -0.65 & -0.58 & -0.65 & -0.65 + & 0.30 & 0.27 & 0.27 & 0.30 & 0.26 & 0.25 & 0.30 & 0.32 & 0.27 & 0.26 & 0.33 & 0.32 & 0.33 & 0.34 & 0.33 & 0.33 + 15 & -0.67 & -0.80 & -0.70 & -0.65 & -0.80 & -0.77 & -0.77 & -0.77 & -0.70 & -0.77 & -0.77 & -0.73 & -0.65 & -0.68 & -0.71 & -0.67 + & 0.33 & 0.30 & 0.33 & 0.33 & 0.30 & 0.33 & 0.33 & 0.33 & 0.33 & 0.33 & 0.33 & 0.34 & 0.33 & 0.34 & 0.34 & 0.33 + 16 & -0.67 & -0.73 & -0.68 & -0.75 & -0.81 & -0.73 & -0.80 & -0.80 & -0.73 & -0.75 & -0.80 & -0.63 & -0.66 & -0.76 & -0.75 & -0.60 + & 0.28 & 0.31 & 0.31 & 0.30 & 0.25 & 0.31 & 0.26 & 0.26 & 0.31 & 0.26 & 0.26 & 0.34 & 0.29 & 0.25 & 0.30 & 0.33 + 17 & -0.91 & -0.91 & -1.15 & -1.05 & -1.20 & -1.18 & -1.13 & -0.96 & -1.25 & -1.15 & -1.15 & -1.06 & -1.15 & -1.13 & -1.13 & -1.11 + & 0.24 & 0.24 & 0.20 & 0.20 & 0.20 & 0.35 & 0.35 & 0.25 & 0.20 & 0.20 & 0.20 & 0.31 & 0.20 & 0.35 & 0.35 & 0.31 + 18 & -0.71 & -0.70 & -0.74 & -0.74 & -0.61 & -0.74 & -0.75 & -0.80 & -0.71 & -0.63 & -0.69 & -0.80 & -0.63 & -0.70 & -0.69 & -0.61 + & 0.31 & 0.26 & 0.26 & 0.26 & 0.31 & 0.26 & 0.28 & 0.20 & 0.31 & 0.31 & 0.27 & 0.20 & 0.34 & 0.26 & 0.27 & 0.31 + 19 & -1.13 & -1.10 & -0.96 & -0.95 & -1.01 & -1.15 & -1.11 & -1.11 & -1.06 & -1.11 & -1.11 & -1.11 & -0.96 & -1.06 & -1.15 & -1.28 + & 0.35 & 0.20 & 0.24 & 0.20 & 0.31 & 0.20 & 0.31 & 0.31 & 0.31 & 0.31 & 0.31 & 0.31 & 0.31 & 0.24 & 0.20 & 0.35 + 20 & -1.15 & -1.30 & -1.30 & -1.10 & -1.25 & -1.30 & -1.25 & -1.20 & -1.20 & -1.20 & -1.13 & -1.15 & -1.10 & -1.20 & -1.13 & -1.24 + & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.20 & 0.25 & 0.20 & 0.20 & 0.20 & 0.25 & 0.26 + 21 & -0.85 & -0.95 & -0.93 & -0.98 & -0.95 & -1.00 & -1.00 & -1.00 & -0.93 & -1.05 & -1.03 & -1.00 & -0.88 & -1.03 & -1.10 & -1.15 + & 0.28 & 0.20 & 0.35 & 0.35 & 0.20 & 0.20 & 0.20 & 0.20 & 0.35 & 0.20 & 0.35 & 0.20 & 0.35 & 0.35 & 0.20 & 0.20 +","summary":"we analyze age and metallicity estimates for an unprecedented database of some 5.5 million stars distributed throughout the large magellanic cloud ( lmc ) main body , obtained from ccd washington photometry , reported on in piatti et al . furthermore , while old and metal - poor field stars have been preferentially formed in the outer disk , younger and more metal - rich stars have mostly been formed in the inner disk , confirming an outside - in formation . we provide evidence for the formation of stars between 5 and 12 gyr , during the cluster age gap , although chemical enrichment during this period was minimal . we also find that the range in the metallicity of an lmc field has varied during the lifetime of the lmc . this large difference is not easy to explain as coming from stripped ancient small magellanic cloud ( smc ) clusters , although the field smc amr is on average 0.4 dex more metal - poor at all ages than that of the lmc but otherwise very similar .","abstract":"we analyze age and metallicity estimates for an unprecedented database of some 5.5 million stars distributed throughout the large magellanic cloud ( lmc ) main body , obtained from ccd washington photometry , reported on in piatti et al . 2012 . we produce a comprehensive field star age - metallicity relationship ( amr ) from the earliest epoch until 1 gyr ago . this amr reveals that the lmc has not evolved chemically as either a closed - box or bursting system , exclusively , but as a combination of both scenarios that have varied in relative strength over the lifetime of the galaxy , although the bursting model falls closer to the data in general . furthermore , while old and metal - poor field stars have been preferentially formed in the outer disk , younger and more metal - rich stars have mostly been formed in the inner disk , confirming an outside - in formation . we provide evidence for the formation of stars between 5 and 12 gyr , during the cluster age gap , although chemical enrichment during this period was minimal . we find no significant metallicity gradient in the lmc . we also find that the range in the metallicity of an lmc field has varied during the lifetime of the lmc . in particular , we find only a small range of the metal abundance in the outer disk fields , whereas an average range of[fe / h ] = + 0.3 0.1 dex appears in the inner disk fields . finally , the cluster and field amrs show a satisfactory match only for the last 3 gyr , while for the oldest ages ( 11 gyr ) the cluster amr is a remarkable lower envelope to the field amr . such a difference may be due to the very rapid early chemical evolution and lack of observed field stars in this regime , whereas the globular clusters are easily studied . this large difference is not easy to explain as coming from stripped ancient small magellanic cloud ( smc ) clusters , although the field smc amr is on average 0.4 dex more metal - poor at all ages than that of the lmc but otherwise very similar ."}
{"article_id":"1601.05549","section_id":"i","document":"the existence of fluctuations of the electromagnetic field of both quantum and thermal origin gives rise to a force acting on neutral atoms in proximity to polarizable macroscopic bodies . this force , which is the generalization of the van der waals interaction , was theoretically investigated by casimir and polder @xcite , and can be considered as the atomic counterpart of the casimir force acting between macroscopic bodies @xcite . because of its simple geometry , particular attention has been devoted to the interaction between an atom and a planar slab . for this configuration , the theoretical predictions have been confirmed by several experiments , based on different setups , including deflection of atomic beams close to surfaces @xcite , classical and quantum reflection of cold atoms @xcite and bose - einstein condensates ( becs ) @xcite , and dipole oscillations of becs above dielectric substrates @xcite .    deviations from the ideal case initially considered by casimir and polder , namely equilibrium systems at zero temperature and perfectly conducting plates , have been studied in the literature . for instance , it was shown that the qualitative and quantitative features of casimir - polder forces can be tailored by acting on the optical properties of the surface @xcite . in this context , an important role is played by surface resonances ( such as surface plasmons in metals ) , i.e. collective coupled light - charge excitations propagating along the surface and exponentially decaying in the orthogonal direction . these are known to give a relevant contribution in several fluctuation - induced phenomena , such as casimir - related effects @xcite and radiative heat transfer @xcite . moreover , the geometry of the slab can also play an important role , as it was recently shown by studying the interaction between an atom and a corrugated surface @xcite . recently , it has been shown that placing the atom in an environment out of thermal equilibrium can modify the behavior of the force , giving rise to repulsive interactions and anomalous power - law dependencies @xcite . out - of - equilibrium configurations can be realized with different setups , including configurations where different temperatures are simultaneously present in the system ( e.g. a different temperature of the slab and the environment  @xcite ) and also scenarios where one or more external lasers are acting on a system initially in thermal equilibrium . in this last case the populations of one or more field s modes are modified , thus affecting the atom - field interaction . in experiments lasers have already been used to actively tailor the potential felt by the atoms in order to produce atomic traps  @xcite or to study the reflection of atomic beams @xcite , and these methods were also employed to investigate the casimir - polder interaction in a variety of atom - surface distance regimes . our work is motivated by the opportunities offered by nonequilibrium configurations when coupled to material s optical properties and by the wide theoretical and experimental efforts in tailoring casimir - polder forces . we start by studying how the atom - surface interaction energy is modified when the population of the surface - plasmon modes deviates with respect to its value at thermal equilibrium . to this aim , we first theoretically assume a thermal imbalance between the surface - plasmon population and all the other modes , showing that this can modify the shape of the atomic potential giving rise , for instance , to a potential barrier . inspired by these results , we move to a scenario where one or two lasers undergo total internal reflection behind the surface , thus unbalancing the surface - plasmon population . by using a density - matrix description of the electromagnetic field , we show that the force produced by the laser(s ) can be safely treated as an additive contribution with respect to the ordinary thermal - equilibrium casimir - polder force . our paper is structured as follows . in sec . [ secatomsurface ] we present the general formalism and the main ingredients of our calculation , stressing the role of the different contributions to the atom - surface interaction . in sec . [ secthermal ] we discuss how a thermally unbalanced population of surface plasmons affects the casimir - polder interaction . sec . [ seclaser ] is devoted to laser - modified interactions and provides analytic expressions of the one- and two - laser forces in terms of experimentally relevant parameters . these expressions are used in sec . [ secnumerics ] , where we numerically explore how the atomic potential can be widely tailored in the presence of one or two external lasers . we show that both atomic barriers and traps can be produced . we finally give in sec . [ secconclusions ] some final remarks .","summary":"we investigate how the combination of nonequilibrium effects and material properties impacts on the casimir - polder interaction between an atom and a surface . by addressing systems with temperature inhomogeneities and laser interactions , we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear . our treatment provides a self - consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom - surface interactions .","abstract":"we investigate how the combination of nonequilibrium effects and material properties impacts on the casimir - polder interaction between an atom and a surface . by addressing systems with temperature inhomogeneities and laser interactions , we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear . our treatment provides a self - consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom - surface interactions ."}
{"article_id":"0801.0199","section_id":"i","document":"bill lawvere s 1973 milestone paper `` metric spaces , generalized logic , and closed categories '' helped us to detect categorical structures in previously unexpected surroundings . his revolutionary idea was not only to regard individual metric spaces as categories ( enriched over the monidal - closed category given by the non - negative extended real half - line , with arrows provided by @xmath3 and tensor by @xmath4 ) , but also to expose the purely categorical nature of the key concept of the theory , cauchy completeness . the first step to this end was to disregard metric conditions that actually obscure the categorical intuition . in fact , once one has dropped the symmetry requirement it seems much more natural to regard the metric @xmath5 of a space @xmath6 as the categorical hom and , given a cauchy sequence @xmath7 in @xmath6 , to associate with it the pair of functions @xmath8 lawvere s great insight was to expose these functions as pairs of adjoint ( bi)modules whose representabilty as @xmath9 is facilitated precisely by a limit @xmath10 for @xmath7 . hence , a new notion of completeness for categories enriched over any symmetric monoidal - closed category @xmath0 was born . also in the enriched category context it is often referred to as cauchy completeness . but since lawvere s brilliant notion entails no sequences at all , just the representability requirement for bimodules , this name seems to be far - fetched and , contrary to popular belief , was in fact not proposed in his paper . hence , here we use _ l - completeness _ instead .    in the first part of this paper we give a quick introduction to @xmath0-category theory ( see @xcite ) in the special case of a commutative unital quantale @xmath0 , focussing on the themes of l - completion and _ l - separation_. we are not aware of an explicit prior occurrence of the latter notion , and both themes are treated with the help of a new closure operator that arises most naturally in the 2-category @xmath11 , as follows . call a @xmath0-functor @xmath12 _ l - dense _ if @xmath13 implies @xmath14 for all @xmath0-functors @xmath15 ; the _ l - closure _ of a subobject @xmath16 of @xmath6 is then the largest subobject @xmath17 of @xmath6 for which @xmath18 is l - dense . for l - separated @xmath0-categories , l - dense simply means epimorphism . the l - separated reflection of a @xmath0-category @xmath6 is its image under the yoneda functor @xmath19 , and its l - completion is the l - closure of that image in @xmath20 . the main part of the paper is devoted to a substantial generalization of the first part which , however , without the reader s recalling of the more familiar @xmath0-category context , may be hard to motivate , especially in view of the considerable additional `` technical '' difficulties . the quantale @xmath0 gets augmented by a _ topological theory _ @xmath21 which now entails also a set - monad @xmath2 and a @xmath2-algebra structure @xmath22 on @xmath0 , with suitable compatibility conditions ( see @xcite ) . while a @xmath0-category @xmath6 comes with a @xmath0-relation @xmath23 ( given by a function @xmath24 ) , @xmath1-categories come with a @xmath0-relation @xmath25 making @xmath6 a lax @xmath2-algebra . for @xmath2 the ultrafilter monad and @xmath26 , @xmath27 provides barr s @xcite relational description of the category of topological spaces ( which , in turn , was based on manes @xcite description of compact hausdorff spaces ) ; for the same monad but with @xmath0 the lawvere half - line , one obains lowen s approach spaces @xcite , as shown by clementino and hofmann @xcite . the @xmath0-to-@xmath1 generalization must necessarily entail the provision of a yoneda functor for a @xmath1-category @xmath6 . but what is @xmath28 supposed to be in this highly asymmetric context ? fortunately , this problem was solved in @xcite : the underlying set of @xmath29 is @xmath30 , provided with a suitable @xmath1-structure . this structure needs to be considered in addition to the free @xmath2-algebra structure on @xmath30 , leading to the surprising fact that the @xmath1-equivalent of the yoneda functor of the the familiar @xmath0-context has now two equally important facets . once one has fully understood this `` technical '' part of the general theory , it is in fact rather straightforward to extend the @xmath0-categorical results on l - completion and l - separation to @xmath1-categories , again with the help of the l - closure . we could therefore often keep the proofs in the @xmath1-context quite short , especially when no new ideas beyond the initial `` yoneda investment '' are needed . completeness of @xmath0-categories and the induced topology was also investigated by flagg @xcite ( who called them @xmath0-continuity spaces ) . an alternative approach to the categories of interest in this paper was presented by burroni @xcite .","summary":"for a quantale , first a closure - theoretic approach to completeness and separation in-categories is presented . this approach is then generalized to-categories , where is a topological theory that entails a set monad and a compatible-algebra structure on .","abstract":"for a quantale , first a closure - theoretic approach to completeness and separation in-categories is presented . this approach is then generalized to-categories , where is a topological theory that entails a set monad and a compatible-algebra structure on ."}
{"article_id":"1405.7173","section_id":"i","document":"the literature devoted to change - point models is vast , particularly in the areas of economics , genome research , quality control , and signal processing . when there are notable changes in a sequence of data , we can typically break the sequence into several data segments , so that the observations within each segment are relatively homogeneous . in the conventional change - point problems , the posited models for different data segments are often of the same structure but with different parameter values . however , the underlying distributions are typically unknown , and thus parametric methods potentially suffer from model misspecification . the least - squares fitting is the standard choice for the mcp , while its performance often deteriorates when the error follows a heavy - tailed distribution or when the data contain outliers .    without imposing any parametric modeling assumption , we consider the multiple change - point problem ( mcp ) based on independent data @xmath0 , such that @xmath1 where @xmath2 is the true number of change - points , @xmath3 s are the locations of these change - points with the convention of @xmath4 and @xmath5 , and @xmath6 is the cumulative distribution function ( c.d.f . ) of segment @xmath7 satisfying @xmath8 . the number of change - points @xmath2 is allowed to grow with the sample size @xmath9 . although extensive research has been conducted to estimate the number of change - points @xmath2 and the locations of these change - points @xmath3 s , most of the work assumes that @xmath6 s belong to some - known parametric functional families or that they differ only in their locations ( or scales ) . for a comprehensive coverage on single change - point problems @xmath10 , see @xcite . the standard approach to the mcp is based on least - squares or likelihood methods via a dynamic programming ( dp ) algorithm in conjunction with a selection procedure such as the bayesian information criterion ( bic ) for determining the number of change - points [ @xcite ; @xcite ; @xcite ; @xcite ( @xcite ) ; @xcite ; @xcite ; @xcite ] . by reframing the mcp in a variable selection context , @xcite proposed a penalized least - squares criterion with a lasso - type penalty [ @xcite ] . @xcite developed a graph - based approach to detecting change - points , which is applicable in high - dimensional data and non - euclidean data . other recent development in this area includes @xcite , @xcite and @xcite . our goal is to develop an efficient nonparametric procedure for the mcp in ( [ om1 ] ) without imposing any parametric structure on the @xmath6 s ; virtually any salient difference between two successive c.d.f.s ( say , @xmath6 and @xmath11 ) would ensure detection of the change - point asymptotically . in the nonparametric context , most of the existing work focuses on the single change - point problem by using some seminorm on the difference between pre- and post - empirical distributions at the change - point [ @xcite ; @xcite ; @xcite ] . @xcite studied a semiparametric change - point model based on the empirical likelihood , and applied the method to detect the change from a distribution to a weighted one . @xcite proposed another empirical likelihood approach without assuming any relationship between the two distributions . however , extending these methods to the mcp is not straightforward . @xcite proposed to use the weighted empirical measure to detect two different nonparametric distributions over a window of observations and then run the window through the full data sequence to detect the number of change - points . although the approach of @xcite is simple and easy to implement , our simulation studies show that even with elaborately chosen tuning parameters the estimates of the locations @xmath3 s as well as the number of change - points are not satisfactory . this may be partly due to the `` local '' nature of the running window , and thus the information in the data is not fully and efficiently utilized . @xcite proposed a new estimation method , ecp , under multivariate settings , which is based on hierarchical clustering by recursively using a single change - point estimation procedure .    observing the connection between multiple change - points and goodness - of - fit tests , we propose a nonparametric maximum likelihood approach to the mcp . our proposed nonparametric multiple change - point detection ( nmcd ) procedure can be regarded as a nonparametric counterpart of the classical least - squares mcp method [ @xcite ] . under some mild conditions , we demonstrate that the nmcd can achieve the optimal rate , @xmath12 , for the estimation of the change - points without any distributional assumptions . due to the use of empirical functions , technical arguments for controlling the supremum of the nonparametric likelihood function are nontrivial and are interesting in their own rights . as a matter of fact , some techniques regarding the empirical process have been nicely integrated with the mcp methodologies . in addition , our theoretical results are applicable to the situation with a diverging number of change - points , that is , when the number of change - points , @xmath2 , grows as @xmath9 goes to infinity . this substantially enlarges the scope of applicability of the proposed method , from a traditional fixed dimensionality to a more challenging high - dimensional setting .    in the proposed nmcd procedure , the number of change - points , @xmath2 , is determined by the bic . given @xmath2 , the dp algorithm utilizes the intrinsic order structure of the likelihood to recursively compute the maximizer of the objective function with a complexity of @xmath13 . to exclude most of the irrelevant points , we also suggest an initial screening procedure so that the nmcd is implemented in a much lower - dimensional space . compared with existing parametric and nonparametric approaches , the proposed nmcd has satisfactory performance of identifying multiple change - points in terms of estimation accuracy and computation time . it offers robust and effective detection capability regardless of whether the @xmath6 s differ in the location , scale , or shape . the remainder of the paper is organized as follows . in section  [ sec2 ] , we first describe how to recast the mcp in ( [ om1 ] ) into a maximization problem and then introduce our nonparametric likelihood method followed by its asymptotic properties . the algorithm and practical implementation are presented in section  [ sec3 ] . the numerical performance and comparisons with other existing methods are presented in section  [ sec4 ] . section  [ sec5 ] contains a real data example to illustrate the application of our nmcd method . several remarks draw the paper to its conclusion in section  [ sec6 ] . technical proofs are provided in the , and the proof of a corollary and additional simulation results are given in the supplementary material [ @xcite ] .","summary":"in multiple change - point problems , different data segments often follow different distributions , for which the changes may occur in the mean , scale or the entire distribution from one segment to another . without the need to know the number of change - points in advance , we propose a nonparametric maximum likelihood approach to detecting multiple change - points . our method does not impose any parametric assumption on the underlying distributions of the data sequence , which is thus suitable for detection of any changes in the distributions . the number of change - points is determined by the bayesian information criterion and the locations of the change - points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function . under some mild conditions , we also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method . simulation studies show that the proposed method has satisfactory performance of identifying multiple change - points in terms of estimation accuracy and computation time .    ,    ,     +","abstract":"in multiple change - point problems , different data segments often follow different distributions , for which the changes may occur in the mean , scale or the entire distribution from one segment to another . without the need to know the number of change - points in advance , we propose a nonparametric maximum likelihood approach to detecting multiple change - points . our method does not impose any parametric assumption on the underlying distributions of the data sequence , which is thus suitable for detection of any changes in the distributions . the number of change - points is determined by the bayesian information criterion and the locations of the change - points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function . under some mild conditions , we show that the new method provides consistent estimation with an optimal rate . we also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method . simulation studies show that the proposed method has satisfactory performance of identifying multiple change - points in terms of estimation accuracy and computation time .    ,    ,     +"}
{"article_id":"0909.5651","section_id":"i","document":"damped lyman alpha ( dla ) absorbers are the primary reservoir of cool , neutral gas in the universe and the ability to detect them easily over a wide range of redshifts make them an important tracer of the evolution of gas in galaxies or protogalaxies over cosmic time . dla systems are identified at redshifts 0@xmath2z@xmath26 in the spectra of qsos @xcite . identified from the strong n=1 to n=2 absorption line of hi , the detection of these absorption - selected objects depends primarily on the brightness of the background qso rather than on emission from stars or gas . it is noteworthy that the column density of @xmath3 atoms  @xmath4 , that defines a dla @xcite , is similar to the threshold column density required for the onset of star formation in the local universe @xcite . dlas , then , should be associated with present - day visible galaxies @xcite . however , difficulty still remains in connecting observations of high - redshift dlas with those of low - redshift dlas , as well as connecting galaxy - evolution simulations with dla observations . simulations at low redshift by @xcite and @xcite indicate that the dla incidence is dominated by more compact , faint galaxies with a narrow impact parameter distribution ( @xmath23 kpc ) , rather than by large disk galaxies . observationally , low redshift dla systems have been shown to consist of galaxies spanning a wide range of luminosities , surface brightnesses , impact parameters , and morphologies @xcite . at higher redshifts , the associated host galaxy to the dla has proven difficult to identify due to the high brightness contrast between the quasar and the absorbing galaxy . another issue in the identification of the host galaxy at high redshift is the fact that one can no longer detect faint galaxies that may be intercepting your sightline . this may cause a misidentification of the host galaxy , especially in high density regions like groups . this may contribute to the larger impact parameters being measured for high redshift systems . @xcite identified candidate hosts to high - redshift ( 2@xmath2z@xmath24 ) dlas through ifu observations of the ly@xmath5-emission line . while they have a small sample size , they find an average impact parameter of 16 kpc , and suggest the distribution of hi clouds for dlas extends far beyond the optical sizes of dwarfs . simulations by @xcite resulted in larger impact parameters ( 10 - 15 kpc ) for 2@xmath2z@xmath24 . selecting systems by identifying damped lyman-@xmath5 absorption provides only a pencil - beam examination of the gas content of dla host galaxies , missing the full gas content that can be probed . an alternative then , to searching for gas through lyman - alpha absorption , is to use the 21  cm emission line , which probes the global gas content in galaxies , to search for systems that are likely to show damped lyman-@xmath5 profiles if there were a background source . the hi hyperfine structure line at 21  cm is very weak , and its detection is currently limited to low redshifts . hi 21  cm observations probe the cold , neutral hydrogen gas in a galaxy and come in two forms , 21  cm absorption and 21  cm emission . 21  cm absorption , like other absorption - line probes , provides a pencil - beam look at the hi content of a galaxy . it requires a background radio - loud point source and allows for a direct determination of @xmath6 . 21  cm line emission is a probe of the gas contained within the beam of the telescope , smoothed according to the spatial resolution of the telescope . the resulting hi emission spectrum reveals the global hi content of the galaxy and allows for determination of the hi mass while maps show the distribution and cross - sections of hi gas around a galaxy . estimates of the gas column density within the beam can be obtained by the ratio of the hi flux to the area covered . a probe of emission might reveal an average hi column above @xmath7 , however this is over a much larger area than that probed by absorption , therefore there is no guarantee that a qso probe will reveal a dla at every position within the emission beam . emission - line probes above @xmath7 only say that somewhere they generally exceed the dla limit . @xcite showed that hi - emission selected galaxies generally show more cross - section at higher column densities than they do at lower column densities and most exhibit column densities that are above the dla limit . the hi - emission - selected galaxies are consistent with the hypothesis that the local galaxy population can explain the properties of the local dlas . @xcite , and @xcite studied the expected properties of the z=0 dla population using blind 21  cm emission surveys , and found that , while a large fraction of hi - selected galaxies are dwarf or low surface brightness galaxies , there is no need for an optically invisible population of galaxies to explain the hi population or to contribute significantly to the dla cross section . there are presently only a small number of ( sub ) dlas or dla candidates known at low - redshift and an even smaller number that have hi measured in emission . it should be noted that a dla ( and sub - dla ) system is classically defined as a system with an observed @xmath3  atoms  @xmath4 ( @xmath8  @xmath4 @xmath2 @xmath6 @xmath2 @xmath7  @xmath4 ) measured via the ly-@xmath5 absorption line . the term `` candidate dla '' is used to describe all galaxies that have @xmath3 atoms  @xmath4 measured through other means , or those with no @xmath6 measurement but meet the criteria of various metal - dla relationships ( e.g. mg  ii , ca  ii , na  i ) . @xcite compared the properties of 20 low - redshift ( z@xmath21 ) dla / sub - dla galaxies with a sample of local , optically selected galaxies studied in hi 21  cm . only 2 of the 20 dlas , sbs  1543 + 593 and ngc  4203 , have measured hi 21  cm emission . one other dla , the absorber towards the qso oi  363 , and two sub - dlas , the absorbers towards the qsos pks  0439 - 433 and pg  1216 + 069 , have been searched for 21  cm emission . we use the hi observations of these objects , along with the ones reported here , to further investigate the properties of dlas at z=0 and expand on the number of dlas or candidates known at low - z with hi 21  cm emission measurements . table 1 lists the hi and optical properties of the known / candidate dlas . a summary of the hi 21  cm observations of these five known / candidate dlas is as follows . the z=0.009 dwarf galaxy sbs  1543 + 593 has an hi column density of log @xmath6=20.41 @xcite as measured by the lyman  @xmath5 line , while @xcite find a column density of log @xmath9 from the 21  cm emission mapped at the position of the qso . the z=0.004 s0 galaxy ngc  4203 was first mapped at 21  cm before the presence of the background qso ton  1480 was revealed by x - ray observations . the hi absorption in the x - ray spectrum of ton  1480 suggests a sufficiently high column density ( log @xmath10 ) to make this system a candidate dla . another known dla , the z=0.0912 absorber towards b  0738 + 313 ( oi  363 ) , has been searched for 21  cm emission but was undetected @xcite . two sub - dla s have also been searched for 21  cm emission . the z=0.101 absorber towards pks  0439 - 433 was thought to be a candidate dla system based on its x - ray spectrum but measurement of the lyman  @xmath5 line @xcite revealed a column density ( log @xmath11 ) just below the limit for dlas and it was undetected in 21  cm emission @xcite . @xcite report a weak 21  cm emission detection along the line of sight towards the qso pg  1216 + 069 , which is consistent with the velocity of the z=0.0063 sub - dla absorber .    in this paper we present the 21  cm emission detection of mrk  1456 with the green bank telescope ( gbt ) and of sdss  j211701.26 - 002633.7 with the arecibo telescope . section 2 describes the sample selection , observations , data reductions and analysis . in section 3 , we discuss the hi properties of our sample and compare them to hi - detected dlas and hi - selected galaxies . we adopt a cosmology of @xmath12=71  km  @xmath13 , @xmath14=0.27 , @xmath15=0.73 throughout this paper .","summary":"in an effort to study damped lyman alpha galaxies at low redshift , we have been using the sloan digital sky survey to identify galaxies projected onto qso sightlines and to characterize their optical properties . for low redshift galaxies we also report on the 21  cm line emission of mrk  1457 , a seyfert galaxy observed within the beam of the green bank telescope .","abstract":"in an effort to study damped lyman alpha galaxies at low redshift , we have been using the sloan digital sky survey to identify galaxies projected onto qso sightlines and to characterize their optical properties . for low redshift galaxies , the hi  21 cm emission line can be used as an alternate tool for identifying possible dla galaxies , since hi emitting galaxies typically exhibit hi columns that are larger than the classical dla limit . here we report on follow - up hi 21  cm emission line observations of two dla candidates that are both low - redshift spiral galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 . the observations were made using the green bank and arecibo telescopes , respectively . analysis of their hi properties reveal the galaxies to be about one and two galaxies , respectively , and to have average hi mass , gas - richness , and gas mass fraction for their morphological types . we consider mrk  1456 and sdss  j211701.26 - 002633.7 to be candidate dla systems based upon the strength of the caii absorption lines they cause in their qso s spectra , and impact parameters to the qso that are smaller than the stellar disk . compared to the small numbers of other hi - detected dla and candidate dla galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 have high hi masses . mrk  1456 and sdss  j211701.26 - 002633.7 have also been found to lie in galaxy groups that are high in hi gas mass compared to the group containing sbs  1543 + 593 , the only dla galaxy previously known to be situated in a galaxy group . when compared with the expected properties of low - z dlas from an hi - detected sample of galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 fall within the ranges for impact parameter and ; and the hi mass distribution for the hi - detected dlas agrees with that of the expected hi mass distribution for low - z dlas . our observations support galaxy - evolution models in which high mass galaxies make up an increasing contribution to the dla cross - section at lower redshifts . we also report on the 21  cm line emission of mrk  1457 , a seyfert galaxy observed within the beam of the green bank telescope ."}
{"article_id":"0909.5651","section_id":"c","document":"we find that both mrk  1456 and sdss  21 - 00 have typical hi properties , ie . hi mass , gas richness , gas mass fraction , for galaxies with their given morphological types @xcite . mrk  1457 , when compared to other seyferts , lies at the high end of the normal range of hi masses ( [ 0.2 - 9.0]x10@xmath48 ) and appears to have an unusually large gas - mass fraction relative to the average @xmath49 of 0.009@xmath250.002 for seyferts @xcite .    using the value of @xmath50 from @xcite , mrk  1456 and mrk  1457 are slightly sub-@xmath0 galaxies , while sdss  21 - 00 is twice an @xmath0 galaxy . mrk  1456 and sdss  21 - 00 are representative of average sb - sc spiral galaxies with a fair amount of hi gas remaining , while having typcial sfr rates of most spirals , indicative of an on - going sfr process and conversion of their neutral gas reservoir into stars .      in the following , we discuss hi observations of known / candidate dlas and sub - dlas , namely , sbs  1543 + 593 , ngc  4203 , and the absorbers towards oi  363 , pks  0439 - 433 , and pg  1216 + 069 . the data are collected in table 1 . all values listed have been recalculated using the cosmology adopted in this paper , and all magnitudes listed are johnson - morgan - cousins b - band magnitudes converted to the ab zeropoint system , except the magnitude of the oi  363 absorber which is a k - band magnitude . presently , only one bonafide dla has been successfully detected in hi 21  cm emission @xcite . sbs  1543 + 593 , a z=0.009 dwarf spiral @xcite is a quasar absorption line galaxy , first found through study of its emission lines @xcite . sbs  1543 + 593 is a low surface brightness system that has been extensively studied in emission and absorption @xcite . it has hi properties consistent with other dwarf spirals @xcite including a low hi mass , a large @xmath47 , and a small gas mass fraction . ngc  4203 was mapped in 21  cm @xcite and exhibits a typical hi mass and @xmath49 for the average s0 , but an atypically large gas richness @xcite . the absorbers toward the qsos oi  363 and pks  0439 - 433 were undetected in 21  cm emission @xcite but have 3@xmath51 upper limits to the hi mass . for the oi  363 absorber , it was not optically detected with the exception of two regions of patchy structure neat the qso oi  363 , referred to as the `` jet '' and the `` arm '' @xcite . although no optical counterpart has been found in conjunction with the z=0.0063 absorber towards pg  1216 + 069 , a weak 21  cm emission signal was found at 3@xmath51 significance within 30  ( 3.8 kpc ) of the qso @xcite . figure  3 provides a comparison of several of the galaxy properties listed in tables 1 and 2 . for the morphological type , we assign a value to each type ranging from 0-e to 6-irr , with intermediates taking half - integer values , ie . 2.5-sab . for the z=0.101 galaxy associated with pks  0439 - 433 , @xcite report two upper limits to the hi mass , listed in table 1 and in figure  3 , we plot the larger value for the upper limit to the hi mass and @xmath47 . the absorbers associated with oi  363 and pg  1216 + 069 are not included as no host galaxy has , as of yet , been clearly identified with the absorbing system . five objects do not carry statistical weight , but are used to just highlight some broad trends and consistencies . the morphologies of the dlas / candidates in fig . 3 consist of one dwarf , one s0 galaxy , and three giant late - type spirals . this diversity in galaxy types naturally accounts for some spread in the derived hi and optical properties shown in fig .  3 . with regards to their optical properties , sdss  21 - 00 and mrk  1456 fall right in the middle of the distribution of @xmath52 , and @xmath53 values in the given sample . they do , however , exhibit one noteworthy property : they have the highest hi masses of the sample . our observations of mrk  1456 and sdss  21 - 00 have added two candidate dla galaxies with morphologies and luminosities of giant late - type spirals . thus they are most directly comparable to the galaxy toward pks  0439 - 433 , also a late - type giant spiral . the pks galaxy is an sab class sub - dla with an hi column just below the dla limit , and an impact parameter that is just outside its stellar disk . given that hi column densities are higher at lower radii and in later morphological subtypes , we expect that future observations on the qso sightlines of mrk  1456 and sdss  21 - 00 might reveal hi column densities larger than the dla limit , as both are later subtypes than the pks galaxy and both have sightlines to their qsos that lie inside their stellar disks . the properties of mrk  1456 and sdss  21 - 00 agree within the distributions of expected optical properties of z=0 dlas . @xcite found that sbs 1543 + 593 is in a small galaxy group with three other companions , a disk galaxy and two dwarfs , all of which are of low luminosity . all three companions are gas rich systems , with low hi mass ( @xmath54 ) , and average gas content for disk and late - type dwarf galaxies ( see * ? ? ? * table 2 ) . this group , and other small groups like it , are likely to be fairly common and important in the contribution to the dla population . furthermore , if young , gas - rich galaxy groups are more prevalent at higher redshifts , then these systems might be important to the dla cross - section . from a search using the nasa / ipac extragalactic database ( ned ) , none of the other dlas that have been observed in 21  cm have associated groups , but faint dwarfs could have been missed . @xcite completed a sample of galaxy groups in the dr3 of the sloan digital sky survey ( sdss ) . mrk  1456 is in one such group , with four other members . mrk  1457 is one such member . all other galaxies in the group are contained within the beam of the gbt , centered on mrk  1456 , but mrk  1457 was the only other member to be detected in hi 21  cm emission . @xcite also show that sdss  21 - 00 is in a group , consisting of seven other members . table 4 lists a few global properties of the group , ie . the group coordinates , group systematic velocity , group velocity width , virial mass and radius of the group , as calculated by @xcite and table 5 lists each group s members and their properties . as both galaxies are situated in groups , the question of misidentification of the dla host galaxy becomes an issue . traditionally , identifying dla hosts has proven difficult since either no obvious galaxy is visible or identifying the correct host in a group is difficult as the galaxy giving rise to the line may not be the brightest or closest galaxy to the qso . this is not an issue with mrk  1456 or sdss  21 - 00 . for both systems , the qso lies within the stellar disk of the galaxy , and in both groups , the closest companion outside the named galaxy here lies more than 120 kpc from the qso .    without hi observations of the galaxies in these groups , it is hard to determine the richness of the group and the environment these galaxies live in . we use u - r color and morphological type as a rough indicator of the gas content of the other galaxies in these groups . the reliability , however , of using optical properties as a predictor of gas content is uncertain as hi - selected galaxies differ more in their optical properties than optically - selected ones , the exception being the most blue galaxies , as they have retained most of their primordial gas . figure 5 shows how galaxies of different morphologies segregate in color and concentration . we plot the galaxies from @xcite overlaid with the mrk  1456 group ( black circles ) and the sdss  21 - 00 group ( black diamonds ) . the galaxies in the mrk  1456 group , with the exception of mrk  1456 , fall in the region of the diagram occupied by early types . the galaxies in the sdss  21 - 00 galaxy group , on the other hand , are predominantly sb - sc morphological types with only two e / s0 galaxies . @xcite showed that there is a relationship between u - r color and gas richness . galaxies with u - r @xmath2 1.5 are gas - rich , 1.5 @xmath2 u - r @xmath2 2.5 are intermediate in gas richness , and those with u - r @xmath17 2.5 are generally gas - poor . the u - r colors of the galaxies in the two galaxy groups are listed in table 5 . these results indicate that both the mrk  1456 and sdss  21 - 00 galaxy groups are intermediate in their gas - richness . the total hi mass of all 4 galaxies detected in the sbs  1543 + 593 galaxy group adds up to @xmath23@xmath55 . with two of four galaxies detected in the mrk  1456 group , its hi content is already much larger , @xmath2312@xmath55 . the single galaxy detected in the sdss  21 - 00 galaxy group has an hi mass of @xmath5614@xmath55 , much larger than the entire sbs  1543 + 593 galaxy group . @xcite used sdss to identify optical counterparts of hi - selected galaxies from hipass and found that hi - selection yields a high fraction of late - type galaxies . for hi - selected spirals , @xcite give the following median properties : @xmath47 = 0.5 , @xmath57 = @xmath0 , and @xmath58 = 0.6 @xmath29 . our ca  ii absorbing galaxies appear to have properties that are comparable to those of hi - selected galaxies . @xcite and @xcite also looked at hi - selected galaxies , and focused more specifically on the question of how these contribute to the dla cross - section . @xcite find a tight correlation between the expected dla cross - section and the hi mass . their equation 3 predicts the following dla cross - sections for mrk  1456 and sdss  21 - 00 : 853.7 @xmath59 and 2058.4 @xmath59 . using these sizes to estimate the average column density for the galaxies , we find for mrk  1456 , @xmath60 , and for sdss  21 - 00 , @xmath61 . rosenberg @xmath62 salzer ( in prep . ) looked at the predicted optical properties for z=0 dlas from an hi - selected sample and find that the most common morphological type is spiral ( 45@xmath24 ) and that 50@xmath24 of the dlas should have an @xmath47 @xmath17 0.77 ( 2 of the 6 galaxies from the rosenberg @xmath62 salzer ( in prep . ) sample are from this sample ) . @xcite also find that gas - rich , late - type spirals contribute most to the dla cross - section . figure 4 shows the hi mass contribution to dn / dz , the number of expected systems per unit redshift , for z@xmath230 , for a sample of hi - selected galaxies with an hi column larger than the dla limit from the arecibo dual - beam survey ( adbs , see @xcite for details ) . the figure shows that 50@xmath24 of the cross - sectional area is from galaxies with hi masses between 2.9@xmath63 and 3.5@xmath64 . the red - hatched histogram overlayed on top is the hi mass distribution of the objects listed in tables 1 and 2 , with the exception of the oi  363 absorber . the right hand axis lists the values for this histogram , n , the number of galaxies . one might expect the hi mass distribution of dlas in general to follow the same hi mass distribution of hi - selected galaxies expected to be dlas . it should be noted that the two galaxy / qso pairs we add here were not selected using the traditional selection method for quasar absorption line systems , ie . through uv absorption lines . thus , they introduce some bias in the hi mass distribution as they are giant spirals optically - selected from sdss with quasars projected within their stellar disks . however , even with this caveat and low statistics , it appears the hi mass distribution of the ( candidate ) dlas mimics the distribution of hi - selected galaxies expected to be dlas . @xcite looked at an optically - selected sample of the local galaxy population ( z@xmath230 ) , mapped in 21  cm emission , in order to connect them to the low - redshift ( z@xmath21 ) dla population and calculated expected probability distribution functions of different properties for the low - redshift dlas . they find that , for expected dla systems , most will be late - type , with a median impact parameter of 8.0 kpc@xmath65 , median log @xmath57 of 9.3@xmath66 , and median @xmath1=-17.98@xmath67 . mrk  1456 and sdss  21 - 00 are indeed late - types within the range for the expected impact parameter and have values for hi mass and absolute magnitude that lie close to the expected values , on the high end .","summary":", the hi  21 cm emission line can be used as an alternate tool for identifying possible dla galaxies , since hi emitting galaxies typically exhibit hi columns that are larger than the classical dla limit . here analysis of their hi properties reveal the galaxies to be about one and two galaxies , respectively , and to have average hi mass , gas - richness , and gas mass fraction for their morphological types .","abstract":"in an effort to study damped lyman alpha galaxies at low redshift , we have been using the sloan digital sky survey to identify galaxies projected onto qso sightlines and to characterize their optical properties . for low redshift galaxies , the hi  21 cm emission line can be used as an alternate tool for identifying possible dla galaxies , since hi emitting galaxies typically exhibit hi columns that are larger than the classical dla limit . here we report on follow - up hi 21  cm emission line observations of two dla candidates that are both low - redshift spiral galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 . the observations were made using the green bank and arecibo telescopes , respectively . analysis of their hi properties reveal the galaxies to be about one and two galaxies , respectively , and to have average hi mass , gas - richness , and gas mass fraction for their morphological types . we consider mrk  1456 and sdss  j211701.26 - 002633.7 to be candidate dla systems based upon the strength of the caii absorption lines they cause in their qso s spectra , and impact parameters to the qso that are smaller than the stellar disk . compared to the small numbers of other hi - detected dla and candidate dla galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 have high hi masses . mrk  1456 and sdss  j211701.26 - 002633.7 have also been found to lie in galaxy groups that are high in hi gas mass compared to the group containing sbs  1543 + 593 , the only dla galaxy previously known to be situated in a galaxy group . when compared with the expected properties of low - z dlas from an hi - detected sample of galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 fall within the ranges for impact parameter and ; and the hi mass distribution for the hi - detected dlas agrees with that of the expected hi mass distribution for low - z dlas . our observations support galaxy - evolution models in which high mass galaxies make up an increasing contribution to the dla cross - section at lower redshifts . we also report on the 21  cm line emission of mrk  1457 , a seyfert galaxy observed within the beam of the green bank telescope ."}
{"article_id":"0909.5651","section_id":"c","document":"we report on the hi 21  cm emission observations of two galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 . both are average disk galaxies and candidate dlas , based on the strengths of their ca  ii  k ew s and their low impact parameters to the qso . in terms of their hi properties , both galaxies have typical hi properties for their morphological types with @xmath57 @xmath23 @xmath0 , average gas richness , and gas mass fractions that are representative of disk galaxies .    these data add to the total number of strong candidate dlas with hi observations , in the local universe . compared with other hi - detected dlas , mrk  1456 and sdss  21 - 00 are similar in most respects , with comparatively higher hi masses . when compared to the expected properties of z=0 dlas from hi - detected galaxies , we find that mrk  1456 and sdss  21 - 00 fall within range of the expected hi mass distribution , median impact parameter , and absolute magnitudes for local dlas . we also find that both mrk  1456 and sdss  21 - 00 reside in groups , adding two dlas in gas - rich groups to the known population . this may indicate a common phenomenon with regards to the environment of dlas .    in spite of many years of observational effort , associated galaxies have only been identified in a very small fraction of known dla systems . therefore , the nature of the evolving dla galaxy population has continued to be under investigation , both observationally and theoretically . historically , two very different scenarios were developed to explain what kind of galaxies produce dlas . in the explanation put forth by @xcite , dlas are associated with massive spiral galaxies . in the model proposed by @xcite , dlas instead arise in low - mass dwarf galaxies . the numerical and semi - analytical galaxy formation simulations presented over the last decade have modified our view of dlas . current models suggest that the median properties of dla galaxies and their range evolve as a function of cosmic time . in this scenario , dwarfs make up most of the dla cross - section at high redshifts , with massive disk galaxies contributing more as the universe evolves . @xcite find that higher mass systems make an increasing contribution to the dla population as redshift decreases . specifically , @xcite predict a median dla hydrogen mass of @xmath57 = 2@xmath68 @xmath69 at z=0 ; in good agreement with the results for hi - selected galaxies @xcite , and what we find here ( cf . fig .  4 ) . thus , although mrk 1456 and sdss  21 - 00 are case studies of bright qsos seen through the disks of nearby spiral galaxies , we do not conclude that they support the original @xcite picture . rather , we interpret our results to be compatible with the current theoretical models , as galaxies contributing to the fraction of disk galaxies that make up the dla cross - section at low redshift . we conclude that our result further strengthens the picture that the local galaxy population , in its variety of gas rich galaxy types that randomly intercept qso sightlines , can explain the properties of the low - redshift dlas . we are grateful to toney minter , karen oneil , and jay lockman at the gbt for their help in the observations and reduction of the data . the national radio astronomy observatory is a facility of the national science foundation operated under cooperative agreement by associated universities , inc . + we thank chris salter and tapasi ghosh for handling the arecibo observations . the arecibo observatory is part of the national astronomy and ionosphere center , which is operated by cornell university under a cooperative agreement with the national science foundation . + we wish to thank andrew west for making details of his ph.d thesis available to us . + we also made use of data obtained at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the national science foundation ( united states ) , the science and technology facilities council ( united kingdom ) , the national research council ( canada ) , conicyt ( chile ) , the australian research council ( australia ) , ministrio da cincia e tecnologia ( brazil ) and secyt ( argentina ) . + funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - 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verlag , 1974 . wild , v. , & hewett , p.  c.  2005 , , 361 , l30 wild , v. , hewett , p.  c. , & pettini , m.  2006 , , 367 , 211 west , a.  a.  2005 , ph.d .  thesis west , a. a. , garcia - appadoo , d. a. , dalcanton , j. j. , disney , m. j. , rockosi , c. m. , ivezi ,  , bentz , m. c. , & brinkmann , j.  2008 , , submitted wolfe , a.  m. , turnshek , d.  a. , smith , h.  e. , & cohen , r.  d.  1986 , , 61 , 249 wolfe , a.  m. , gawiser , e. , & prochaska , j.  x.  2005 , , 43 , 861 zwaan , m.  a. , van der hulst , j.  m. , briggs , f.  h. , verheijen , m.  a.  w. , & ryan - weber , e.  v.   2005 , , 364 , 1467          , @xmath58 , @xmath47 , and ratio of impact parameter to optical radius of the hi dla sample . the morphological type is represented with numbers from 0 - 6 for types e - irr , respectively . @xmath57 is in units of @xmath0 and @xmath58 is in units of @xmath29 . the absorbers associated with oi  363 and pg  1216 + 069 are omitted from the diagram . ] ccccccc property & sbs  1543 + 593 & ngc  4203 & galaxy & `` jet''@xmath70 & `` arm '' &  + type@xmath71 & sdm & so & sab & lsb & lsb &  + z & 0.009@xmath250.001 & 0.0036@xmath250.00001 & 0.101@xmath250.001 & 0.09118@xmath250.00001 & 0.09118@xmath250.00001 & 0.00632@xmath250.00002 + @xmath72[mpc ] & 38.3@xmath254.3 & 15.25@xmath250.4 & 460.0@xmath254.6 & 412.46@xmath250.04 & 412.46@xmath250.04 & 26.84@xmath250.08 + qso & hs  1543 + 5921 & ton  1408 & pks  0439 - 433 & oi  363 & oi  363 & pg  1216 + 069 + @xmath16 & 0.807@xmath250.002 & 0.6156@xmath250.0002 & 0.593@xmath250.003 & 0.631@xmath250.002 & 0.631@xmath250.002 & 0.3313@xmath250.0003 + b [  ] & 2.4 & 126 & 3.9 & @xmath22 & @xmath22 & @xmath230 + b[kpc ] & 0.4 & 9.2 & 7.2 & @xmath23.4 & @xmath23.4 & @xmath23.9 + r[]@xmath73 & 4.8 & 105 & 3.7 & 4 & 4 &  + r[kpc]@xmath73 & 0.9 & 7.7 & 6.8 & 6.7 & 6.7 &  + axis ratio b / a & 0.777 & 0.880 & 0.556 &  &  &  + @xmath74[@xmath27 ] & 40 & 29 & 58 &  &  &  + @xmath76 & -16.1@xmath250.2 & -19.65@xmath250.01 & -20.96@xmath250.08 & -14.72@xmath77 & -15.12@xmath77 &  + @xmath78 $ ] & 0.04@xmath250.01 & 0.96@xmath250.02 & 3.2@xmath250.2 & 0.01 & 0.02 &  + @xmath29 & 0.01 & 0.32 & 1.06@xmath250.07 & 0.0001 & 0.0002 &  + @xmath79^g$ ] & 0.006 & 0.16 &  &  &  &  + @xmath80 $ ] & 75 & 243 &  &  &  &  + @xmath81 $ ] & 1.3@xmath250.1 & 1.3 & @xmath2(2.15 - 3.02 ) & @xmath23 & @xmath23 & ( 0.006 - 0.017 ) + @xmath0 & 0.21 & 0.21 & @xmath20.34 - 0.48 & @xmath20.48 & @xmath20.48 & ( 0.001 - 0.002 ) + @xmath82 $ ] & 0.07 & 1.2 &  &  &  &  + @xmath83 & 3.6@xmath250.9 & 0.14@xmath250.01 & @xmath2(0.06 - 0.09 ) & @xmath230 & @xmath220 &  + @xmath84 & 0.19 & 0.01 &  &  &  &  + @xmath85^h$ ] & 20.42@xmath250.04 & 20.34 & 19.85@xmath250.10 & 21.18@xmath250.06 & 21.18@xmath250.06 & 19.32@xmath250.03 + refs@xmath86 & 1,2,3,4 & 5,6 & 7,8,9,10 & 11,12,13 & 11,12,13 & 14,15,16 +    ccc property & mrk  1456 & sdss  21 - 00 + type & sc & sb + z & 0.04757@xmath250.00008 & 0.05792@xmath250.00009 + @xmath72[mpc ] & 208.5@xmath250.3 & 255.8@xmath250.4 + qso & sdss  j114719.89 + 522923.1 & sdss j211701.31 - 0026.38.8 + @xmath16 & 1.99 & 1.14 + b [  ] & 5.3 & 5.1 + b[kpc ] & 4.9 & 5.7 + r [  ] & 7.7 & 6.7 + r[kpc ] & 7.1 & 7.5 + axis ratio b / a & 0.724 & 0.638 + i[@xmath27 ] & 45 & 52 + @xmath87 & -20.58@xmath250.01 & -20.14@xmath250.01 + @xmath88 & -19.14@xmath250.02 & -18.55@xmath250.04 + @xmath89 $ ] & 3.1@xmath250.2 & 5.6@xmath251.2 + @xmath90 & -20.40@xmath250.09@xmath70 & -20.07@xmath250.09 + @xmath78^b$ ] & 1.92@xmath250.16 & 1.41@xmath250.12 + @xmath29 & 0.63@xmath250.05 & 0.46@xmath250.04 + rew(caii ) & 1.24@xmath250.15 & 1.1@xmath250.2 + h@xmath5 [ @xmath91ergs @xmath92 @xmath37 ] & 65.65@xmath250.3 & 20.3@xmath250.2 + @xmath94 [ @xmath95ergs @xmath37]@xmath73 & 8.64@xmath251.69 & 13.8@xmath250.2 + @xmath96 [ @xmath97 @xmath92]@xmath99 & 1.8 & 3.0 + h@xmath30 [ @xmath91ergs @xmath92 @xmath37 ] & 15.15@xmath250.2 & 2.8@xmath250.2 + @xmath100\\lambda$]6550 [ @xmath91ergs @xmath92 @xmath37 ] & 6.8@xmath250.2 & 2.09@xmath250.14 + @xmath100\\lambda$]6585 [ @xmath91ergs @xmath92 @xmath37 ] & 19.40@xmath250.3 & 5.29@xmath250.15 + @xmath101\\lambda$]3727 [ @xmath91ergs @xmath92 @xmath37 ] & 35.25@xmath250.2 & 9.3@xmath250.8 + @xmath102\\lambda$]5008 [ @xmath91ergs @xmath92 @xmath37 ] & 9.33@xmath250.1 & 2.1@xmath250.2 + 12+log(o / h)[o3n2]@xmath103 & 8.6@xmath250.1@xmath250.14 & 8.58@xmath250.02@xmath250.14 + 12+log(o / h)[n2]@xmath103 & 8.5@xmath250.2@xmath250.18 & 8.56@xmath250.01@xmath250.18 + 12+log(o / h)[r23]@xmath103 & 8.7@xmath250.2@xmath250.10 & 8.10@xmath250.11@xmath250.10 +    ccccccccccc galaxy & sdv & @xmath104 & @xmath105 & @xmath106 & @xmath57 & @xmath0 & @xmath107 & @xmath83 & @xmath108 & @xmath84 + & [ @xmath109 & [ @xmath110&[@xmath110 & [ @xmath110 & [ @xmath69 ] & & [ @xmath112 & & & + mrk  1456 & 1.0808@xmath250.0016 & 271.3 & 322.53 & 14262.1 & 5.64@xmath250.002 & 0.89 & 0.9@xmath250.4 & 0.30@xmath250.02 & 4.8@xmath250.6 & 0.062@xmath250.006 + sdss  21 - 00 &  & 255.6 & 281.8 & 17357.7 & 13.6@xmath250.3 & 2.03 & 0.69@xmath250.15 & 1.2@xmath250.1 & 6.1@xmath250.9 & 0.20@xmath250.03 + mrk  1457 & 1.0953@xmath250.0012 & 294.1 & 344.94 & 14631.1 & 5.97@xmath250.02 & 0.94 & 2.1@xmath250.7 & 0.14@xmath250.01 & 5.0@xmath250.4 & 0.029@xmath250.002 +    ccccccccc group & com & com @xmath113 & w & @xmath114 & no . of members & @xmath115 & & + & [ hh : mm : ss , dd : mm : ss ] & [ km @xmath37 ] & [ km @xmath37 ] & [ @xmath116 & & [ mpc ] & & + mrk 1456 & 11:47:23.76 , + 52:27:32.40 & 14390.04 & 172.275 & 0.7352 & 4 & 0.3551 & + sdss j211701.26 - 002633.7 & 21:17:18.96 , -00:21:14.40 & 17339.520 & 70.697 & 0.3911 & 7 & 1.1219 & +    ccccccccc + members & ra & dec & @xmath106 & z & b & @xmath117 & type & u - r + & [ hh : mm : ss ] & [ dd : mm : ss ] & [ km @xmath37 ] & & [  ] & [  ] & & + mrk 1456 & 11:47:20.20 & + 52:29:18.60 & 14261@xmath2524 & 0.04757@xmath250.00008 &  & 1.9 & sc & 1.47 + mrk 1457 & 11:47:21.61 & + 52:26:58.31 & 14562@xmath2528 & 0.04857@xmath250.00009 & 2.3 & 0.7 & sy2 & 1.94 + mrk 1458 & 11:47:41.67 & + 52:26:55.88 & 14431@xmath2527 & 0.04814@xmath250.00009 & 4.0 & 2.8 & sa & 2.29 + sdss j114711.09 + 522653.4 & 11:47:11.10 & + 52:26:53.40 & 14308@xmath2546 & 0.0477@xmath250.0002 & 2.8 & 2.0 & e / s0 & 2.57 +   + members & ra & dec & @xmath106 & z & b & @xmath117 + & [ hh : mm::ss ] & [ dd : mm : ss ] & [ km @xmath37 ] & & [  ] & [  ] + sdss j211701.26 - 002633.7 & 21:17:01.27 & -00:26:33.80 & 17363@xmath2527 & 0.05792@xmath250.00009 &  & 6.9 & sbc & 1.69 + sdss j211716.84 - 002715.6 & 21:17:16.85 & -00:27:15.60 & 17423@xmath2528 & 0.05812@xmath250.00009 & 4.0 & 6.0 & sbc & 1.83 + sdss j211715.44 - 002435.5 & 21:17:15.44 & -00:24:35.50 & 17310@xmath2540 & 0.0577@xmath250.0001 & 4.1 & 3.5 & e / s0 & 2.60 + sdss j211709.94 - 003028.3 & 21:17:09.94 & -00:30:28.30 & 17365@xmath2517 & 0.05792@xmath250.00006 & 4.5 & 9.5 & sc & 1.41 + sdss j211723.72 - 001845.9 & 21:17:23.72 & -00:18:45.90 & 17391@xmath2516 & 0.05801@xmath250.00005 & 9.6 & 2.7 & sbc & 1.97 + sdss j211731.47 - 001246.9 & 21:17:31.47 & -00:12:46.90 & 17308@xmath2546 & 0.0577@xmath250.0002 & 15.7 & 9.0 & s0 & 2.70 + sdss j211733.50 - 000805.0 & 21:17:33.50 & -00:08:05.00 & 17217@xmath2519 & 0.05743@xmath250.00007 & 20.2 & 13.7 & sc & 2.09 +","summary":"we report on follow - up hi 21  cm emission line observations of two dla candidates that are both low - redshift spiral galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 . we consider mrk  1456 and sdss  j211701.26 - 002633.7 to be candidate dla systems based upon the strength of the caii absorption lines they cause in their qso s spectra , and impact parameters to the qso that are smaller than the stellar disk . compared to the small numbers of other hi - detected dla and candidate dla galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 have high hi masses . mrk  1456 and sdss  j211701.26 - 002633.7 have also been found to lie in galaxy groups that are high in hi gas mass compared to the group containing sbs  1543 + 593 , the only dla galaxy previously known to be situated in a galaxy group . when compared with the expected properties of low - z dlas from an hi - detected sample of galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 fall within the ranges for impact parameter and ; and the hi mass distribution for the hi - detected dlas agrees with that of the expected hi mass distribution for low - z dlas . our observations support galaxy - evolution models in which high mass galaxies make up an increasing contribution to the dla cross - section at lower redshifts .","abstract":"in an effort to study damped lyman alpha galaxies at low redshift , we have been using the sloan digital sky survey to identify galaxies projected onto qso sightlines and to characterize their optical properties . for low redshift galaxies , the hi  21 cm emission line can be used as an alternate tool for identifying possible dla galaxies , since hi emitting galaxies typically exhibit hi columns that are larger than the classical dla limit . here we report on follow - up hi 21  cm emission line observations of two dla candidates that are both low - redshift spiral galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 . the observations were made using the green bank and arecibo telescopes , respectively . analysis of their hi properties reveal the galaxies to be about one and two galaxies , respectively , and to have average hi mass , gas - richness , and gas mass fraction for their morphological types . we consider mrk  1456 and sdss  j211701.26 - 002633.7 to be candidate dla systems based upon the strength of the caii absorption lines they cause in their qso s spectra , and impact parameters to the qso that are smaller than the stellar disk . compared to the small numbers of other hi - detected dla and candidate dla galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 have high hi masses . mrk  1456 and sdss  j211701.26 - 002633.7 have also been found to lie in galaxy groups that are high in hi gas mass compared to the group containing sbs  1543 + 593 , the only dla galaxy previously known to be situated in a galaxy group . when compared with the expected properties of low - z dlas from an hi - detected sample of galaxies , mrk  1456 and sdss  j211701.26 - 002633.7 fall within the ranges for impact parameter and ; and the hi mass distribution for the hi - detected dlas agrees with that of the expected hi mass distribution for low - z dlas . our observations support galaxy - evolution models in which high mass galaxies make up an increasing contribution to the dla cross - section at lower redshifts . we also report on the 21  cm line emission of mrk  1457 , a seyfert galaxy observed within the beam of the green bank telescope ."}
{"article_id":"1305.4888","section_id":"i","document":"we consider the wave guide @xmath2 , where @xmath3 is a @xmath7 bounded connected domain of @xmath4 . we set @xmath8 and @xmath9 . consider the following initial - boundary value problem ( ibvp in short ) for the wave equation @xmath10 recall that @xmath11 . since @xmath12 is not bounded , for all @xmath13 we give the following definition of the the space @xmath14 : @xmath15 then , we introduce the usual space @xmath16 where @xmath17 or @xmath18 . set the space @xmath19 with @xmath20 defined by @xmath21 here , we denote by @xmath22 a tangential derivative with respect to @xmath23 . we denote by @xmath24 the unit outward normal vector to @xmath25 . notice that for @xmath26 the unit outward normal vector to @xmath27 , we have @xmath28 . we prove ( see theorem [ t2 ] in the appendix ) that for @xmath29 and @xmath30 the ibvp ( [ eq1 ] ) has a unique solution @xmath31;h^1(\\omega))\\cap\\mathcal c^1([0,t];l^2(\\omega))\\ ] ] such that @xmath32 . in addition , for any positive constant @xmath33 , there exists a positive constant @xmath34 depending only of @xmath35 , @xmath36 and @xmath33 , such that for all @xmath29 with @xmath37 , the following estimate holds @xmath38;h^1(\\omega))}+{\\left\\vertu\\right\\vert}_{\\mathcal c^1([0,t];l^2(\\omega))}+{\\left\\vert\\partial_\\nu u_q\\right\\vert}_{l^2(\\sigma)}{\\leqslant}c{\\left\\vertf\\right\\vert}_{l}.\\ ] ] in particular the following operator , usually called the dirichlet to neumann ( dn map in short ) , @xmath39 is bounded . in the present paper , we consider the inverse problem which consists in determining the electric potential @xmath0 from the dn map @xmath40 . we establish a stability estimate for this inverse problem . for @xmath41 and @xmath42 , we set @xmath43_\\alpha=\\sup\\left\\{\\frac{{\\left\\verth(x)-h(y)\\right\\vert}}{{\\left\\vertx - y\\right\\vert}^\\alpha}:\\ x , y\\in\\overline{\\omega},\\ x\\neq y\\right\\}\\ ] ] and we consider the space @xmath44_\\alpha<\\infty\\}\\ ] ] with the norm @xmath45_\\alpha.\\ ] ] our first main result can be stated as follows . [ t1 ] let @xmath46 , @xmath41 and let @xmath47 be the ball centered at @xmath48 and of radius @xmath33 of @xmath49 . then , for @xmath50 and @xmath51 , we have @xmath52 with @xmath34 depending of @xmath33 , @xmath36 and @xmath35 . here @xmath53 is the norm of @xmath54 with respect to @xmath55 . let us remark that in this result we consider the full dn map . this means that we determine the coefficient @xmath0 from measurements on the whole lateral boundary @xmath56 which is an unbounded set . this is due to the fact that we consider a large class of coefficients @xmath0 without any restriction on their behavior outside a compact set ( we only assume that the coefficients are uniformly bounded and hlderian ) . in order to extend this result to the determination of @xmath0 from measurements in a bounded subset of @xmath56 , we need more informations about @xmath0 . namely , we need that the gap between two coefficients @xmath57 reach its maximum in a fixed bounded subset of @xmath5 . more precisely , let @xmath58 and consider the spaces @xmath59 which consists of functions @xmath30 satisfying @xmath60 let us introduce the partial dn map defined by @xmath61 our second result is the following . [ tt1 ] let @xmath46 , @xmath41 and let @xmath47 be the ball centered at @xmath48 and of radius @xmath33 of @xmath49 . let @xmath50 , @xmath51 and assume that there exists @xmath62 such that @xmath63 then , for all @xmath64 we have @xmath65 with @xmath34 depending of @xmath33 , @xmath36 , @xmath35 and @xmath66 . here @xmath67 is the norm of @xmath68 with respect to @xmath69 . clearly condition ( [ tt1a ] ) will be fulfilled if we assume that @xmath57 are compactly supported . let us remark that this condition can also be fulfilled in more general cases . for example , consider the condition @xmath70 let @xmath71 be a non negative continuous even function which is decreasing in @xmath72 . then , condition ( [ tt1a ] ) will be fulfilled if we assume that @xmath57 are lying in the set @xmath73    in recent years the problem of recovering time - independent coefficients for hyperbolic equations in a bounded domain from boundary measurements has attracted many attention . in @xcite , the authors proved that the dn map determines uniquely the time - independent electric potential in a wave equation and @xcite has extended this result to the case of time - dependent potential . isakov @xcite considered the determination of a coefficient of order zero and a damping coefficient . note that all these results are concerned with measurements on the whole boundary . the uniqueness by local dn map has been considered by @xcite and @xcite . the stability estimate in the case where the dn map is considered on the whole lateral boundary were treated by stefanov and uhlmann @xcite . the uniqueness and hlder stability estimate in a subdomain were established by isakov and sun @xcite and , assuming that the coefficients are known in a neighborhood of the boundary , bellassoued , choulli and yamamoto @xcite proved a log - type stability estimate in the case where the neumann data are observed in an arbitrary subdomain of the boundary . in @xcite , @xcite and @xcite the authors established results with a finite number of data of dn map . let us also mention that the method using carleman inequalities was first considered by bukhgeim and klibanov @xcite . for the application of carleman estimate to the problem of recovering time - independent coefficients for hyperbolic equations we refer to @xcite , @xcite and @xcite . let us observe that all these results are concerned with wave equations in a bounded domain . several authors considered the problem of recovering time - independent coefficients in an unbounded domain from boundary measurements . most of them considered the half space or the infinite slab . in @xcite , rakesh considered the problem of recovering the electric potential for the wave equation in the half space from neumann to dirichlet map . applying a unique continuation result for the timelike cauchy problem for the constant speed wave equation and the result of x - ray transform obtained by hamaker , smith , solmon , wagner in @xcite , he proved a uniqueness result provided that the electric potentials are constant outside a compact set . in @xcite , nakamura extended this work to more general coefficients . in @xcite , eskin proved uniqueness modulo gauge invariance of magnetic and electric time - dependent potential with respect to the dn map for the schrdinger equation in a simply - connected bounded or unbounded domain . in @xcite and @xcite , the authors considered the inverse problem of identifying an embedded object in an infinite slab . in @xcite , the authors considered the problem of determining coefficients for a stationary schrdinger equation in an infinite slab . assuming that the coefficients are compactly supported , they proved uniqueness with respect to dirichlet and neumann data of the solution on parts of the boundary . this work was extended to the case of a magnetic stationary schrdinger equation by @xcite . in @xcite , the authors considered the problem of determining the twisting for an elliptic equation in an infinite twisted wave guide . assuming that the first derivative of the twisting is sufficiently close to some _ a priori _ fixed constant , they established a stability estimate of the twisting with respect to the dn map . to our best knowledge , with the one of @xcite , this paper is the first where one establishes a stability estimate for the inverse problem of recovering a coefficient in an infinite domain with dn map without any assumption on the coefficient outside a compact set . the main ingredient in the proof of the stability estimates ( [ t1a ] ) and ( [ tt1b ] ) are geometric optic solutions . the novelty in our approach comes from the fact that we take into account the cylindrical form of the infinite wave guide and we use suitable geometric optic solutions for this geometry . this paper is organized as follows . in section 1 we introduce the geometric optic solutions for our problem and , in a similar way to @xcite ( see also section 2.2.3 of @xcite ) , we prove existence of such solutions . using these geometric optic solutions , in section 2 we prove theorem [ t1 ] and in section 3 we prove theorem [ tt1 ] . in the appendix , we treat the direct problem . we prove existence of solutions and we define the dn map . let us remark that in the case of a bounded domain @xmath35 , applying some results of @xcite , @xcite have treated the direct problem . since in this paper we consider an unbounded domain @xmath35 , it was necessary to treat this problem .","summary":"we consider the stability in the inverse problem consisting in the determination of an electric potential , appearing in a dirichlet initial - boundary value problem for the wave equation in an unbounded wave guide with a bounded smooth domain of , from boundary observations . the observation is given by the dirichlet to neumann map associated to a wave equation . we prove a hlder stability estimate in the determination of from the dirichlet to neumann map . moreover , provided that the gap between two electric potentials rich its maximum in a fixed bounded subset of , we extend this result to the same inverse problem with measurements on a bounded subset of the lateral boundary .","abstract":"we consider the stability in the inverse problem consisting in the determination of an electric potential , appearing in a dirichlet initial - boundary value problem for the wave equation in an unbounded wave guide with a bounded smooth domain of , from boundary observations . the observation is given by the dirichlet to neumann map associated to a wave equation . we prove a hlder stability estimate in the determination of from the dirichlet to neumann map . moreover , provided that the gap between two electric potentials rich its maximum in a fixed bounded subset of , we extend this result to the same inverse problem with measurements on a bounded subset of the lateral boundary ."}
{"article_id":"0801.4641","section_id":"i","document":"the interaction between itinerant carrier spins and localized magnetic moments leads to carrier  mediated ferromagnetic order in a wide variety of systems , ranging from ferromagnetic semiconductors such as euo , eus , chrome spinels , or pyrochlore @xcite to manganese oxides ( manganites ) @xcite and iii - mn - v ferromagnetic semiconductors @xcite . such materials offer potential for novel spintronics applications @xcite . their magnetic and transport properties are intimately related and can be controlled by varying e.g. the carrier density , spin , and distribution .    the non  equilibrium and dynamical properties of ferromagnetic semiconductors and magnetically  ordered systems are currently under investigation . for thz spintronic and magnetic devices , ultrafast information storage , recovery , and processing is required , e.g. the development of devices with sub - picosecond readout times of the magnetic states . this goal requires femtosecond spin manipulation and control . the physical processes that govern the magnetization dynamics during timescales shorter than the characteristic response times of the magnetic system are still under debate . during such timescales , the validity of conventional thermodynamic concepts for describing a magnetic system become questionable . ultrafast pump - probe magneto - optical spectroscopy can shed light into this fundamental problem . in these experiments , an ultra  short pump optical pulse excites optical polarizations , non  thermal populations , and carrier spins , which then trigger a magnetization dynamics measured as function of time ( faraday or kerr rotation ) @xcite .    to interpret such experiments , it is useful to distinguish between different stages of time evolution of the photoexcited system . during the initial sub - picosecond regime , shorter than the dephasing times or optical pulse duration , the dynamics of the collective magnetization is triggered by optical polarizations and photoexcited carrier spins . the response of the magnetic system is controlled by the nonlinear optical excitation and conventional thermodynamic concepts do not apply . in this initial regime , magnetic anisotropy can play a role by affecting the photoexcited carrier spin . after the pulse is gone , the light  induced quantum mechanical coherences decay and the photoexcited carriers relax by interacting with the hole fermi sea . the carrier temperature is thus elevated above the lattice temperature within hundreds of femtoseconds . the hole population is eventually described by a hot fermi  dirac distribution , which transfers its excess energy to the lattice within a few picoseconds . at the same time , the magnetic axes of the system change , due to e.g. the transient temperature elevation . such quasi  thermal changes in the magnetic anisotropy are due to the fermi sea carriers and should be contrasted to the magnetic anisotropy contribution of the non  thermal photoexcited carriers in the initial temporal regime . after the equilibration of the carrier and lattice systems , their common temperature relaxes via a slow ( nanosecond ) thermal diffusion process , which returns the magnetic system to its equilibrium configuration . in this paper we discuss a mechanism for coherent non  thermal magnetization manipulation and neglect all thermal effects due to elevated carrier and spin temperatures . most of the ultrafast magneto  optical experiments performed so far in magnetic metals , insulators , and semiconductors observed magnetization dynamics that could be interpreted in terms of light  induced time  dependent thermal effects . following the observation of ref . , many works focussed on ultrafast light  induced demagnetization , which involves the time  dependent collective magnetization _ amplitude_. the physical mechanisms that lead to quenching of the magnetization within a picosecond or less in materials ranging from transition metals to iii(mn)v semiconductors are still under debate , but are mostly believed to be triggered by transient changes in the carrier and spin effective temperatures . @xcite however , transient magnetic effects have also been observed in the initial non  thermal temporal regime , where the concept of carrier temperature is not meaningful . @xcite light  induced changes in the magnetization _ orientation _ have also been observed in both metals and semiconductors and mostly attributed to transient changes in the magnetic easy axes due to temperature elevation . @xcite such thermal quasi  equilibrium effects induce a magnetization precession with a period @xmath0100ps .    in most of the above experiments , the observed magnetization changes result from the transient temperature rise following optical absorption and carrier relaxation . however , there is a limit in the magnetization speed that can arise from incoherent processes largely based on the heating of the magnetic system . far more desirable is magnetization control based on _ coherent _ and non  thermal physical processes . the femtosecond coherent temporal regime offers the most flexibility for fast magnetization control limited only by the optical pulse duration . coherent manipulation of the magnetization was demontrated experimentally in magnetic dielectrics and insulators @xcite , while the interplay of coherent excitation and spin  orbit interaction in magnetic insulators was addressed theoretically in refs . . compared to other magnetically  ordered materials , iii - mn - v ferromagnetic semiconductors offer certain advantages and new possibilities for ultafast magnetization control and dynamics . these advantages stem from the carrier  induced nature of the magnetic order and the clear distinction between localized ( mn ) and itinerant ( valence band hole ) spins . static measurements have shown that iii - mn - v heterostructures are highly sensitive to external stimuli such as electrical gate , currents , or light . @xcite a light  induced out - of - plane magnetization rotation towards the direction of propagation of a circularly polarized optical field perpendicular to the ground state magnetization was reported in refs . for ga(mn)as epilayers . later ultrafast experiments interpreted their findings in terms of photoexcited carrier spin @xcite and thermal @xcite effects ( for a review see ref . ) . recently , wang _ _ @xcite reported an enhancement of the magnetization amplitude and the ferromagnetic order in gamnas induced by the photoexcited hole population . this enhancement occurs on a @xmath0100ps time scale , following the initial subpicosecond demagnetization @xcite and thermalization . more recently , wang _ _ @xcite reported the first observation of two temporal regimes of magnetization dynamics in iii - mn - v semiconductors . the first regime lasts for a few hundreds of fs and is governed by a _ quasi  instantaneous _ tilt of the collective magnetization in response to optical excitation at high energies ( @xmath0 3.1ev ) . in this femtosecond regime , a photoinduced four  state ferromagnetic hysterisis was measured , which implies femtosecond detection of magnetic memory states . this initial magnetization dynamics is clearly distinguished from the subsequent thermal regime , which is governed by magnetization precession on the 100ps timescale around the magnetic easy axes . the observations of ref . point out the need for a microscopic theory of collective spin dynamics in the initial coherent regime of iii(mn)v semiconductors , which treats the nonlinear response of the magnetization to the ultrafast optical excitation . the theoretical prediction of a light  induced magnetic interaction resulting in a kondo resonance in the nonlinear optical response and the pump  probe spectra of doped semiconductors was reported in ref .. this light  induced many  body effect is generated by a second order raman  like process and should be most pronounced in the case of below  resonance photoexcitation in the transparency regime , where heating effects are suppressed . ref . suggested the possibility of inducing ferromagnetic order by exciting undoped paramagnetic ii - mn - vi semiconductors well below the optical absorption threshold . a brief description of a microscopic mechanism for coherent ultrafast magnetization dynamics in iii - mn - v ferromagnetic semiconductors was presented in ref . , while ref . addressed the subsequent incoherent regime and attributed the ultrafast demagnetization to the scattering of the mn spins with spin  flip excitations of the hot hole fermi sea .    in this paper we develop in detail a theory that describes the ultrafast nonlinear response of the collective spins in ferromagnetic semiconductors . we present calculations for the most basic hamiltonian that applies to a wide range of ferromagnetic semiconductor systems . the magnetic exchange interaction and the coupling to the optical field are treated within the mean field approximation , which has been shown to describe well the ground state and thermodynamic properties of iii - mn - v semiconductors @xcite as well as the ultarafast nonlinear optical response of semiconductors for strong photoexcitation . @xcite in section [ setup ] we set up the problem at hand , while in section [ sec : eom ] we derive the mean field equations of motion in the coherent limit in the case of several coupled valence bands . the dephasing effects due to the mixing of the hole spin states are described in section [ sec : relax ] with the lindblad semigroup method . @xcite this method allows us to treat consistently both hole spin relaxation / dephasing and interband polarization dephasing resulting from hole spin  flip interactions . in section [ sec : single ] we extract a simple one  band model from the full theory and use it in section [ sec : numer ] to calculate the light  induced mn spin trajectories and discuss the role of hole spin and interband polarization dephasing , magnetic anisotropy , and photoexcitation intensity and duration . our numerical results predict an ultrafast tilt of the mn spin away from its initial ( equilibrium ) value , which develops on a timescale comparable to the optical pulse duration . the magnitude of this tilt is controlled by the optical pulse intensity and duration . the direction of the tilt and overall shape of the mn spin trajectory depend sensitively on the hole spin dephasing and on the interband polarizations . in section [ sec : inter ] we interpret the above numerical results by deriving from the full theory an effective landau  gilbert  like @xcite equation of motion for the mn spin using the adiabatic following approximation . we show that the effective magnetic anisotropy fields that govern the precession and relaxation within the above landau  gilbert picture acquire a time  dependent correction determined by the optical pulse amplitude , the photoexcited interband polarizations , and the mixing of the hole spin states . this correction results in magnetization dynamics on a timescale comparable to the optical pulse duration and may be interpeted in terms of light  induced precession and relaxation . after the pulse is gone , the mn spin trajectory is controlled by the magnetic anisotropies due to the fermi sea ( thermal ) carriers . if the initial magnetization response to the optical excitation results in a sufficiently small tilt , the mn spin precesses around its initial configuration , with a period determined by the zero  momentum magnon energy , as described by linearizing the equations of motion . on the other hand , for sufficiently high photoexcitation intensity , the initial light  induced magnetization tilt brings the magnetic system sufficiently far from the magnetic energy minimum so that nonlinear magnetic effects become important . in this case , the mn spin evolution differs from a simple precession . our theory predicts two distinct temporal regimes of magnetization evolution , the first of which is governed by the optical excitation while the second is governed by the magnetic anisotropies due to the thermal carriers . we discuss the signatures of the above transient and nonlinear magnetic effects in ultrafast magneto  optical pump  probe spectroscopy and end with our conclusions in section [ sec : concl ] . the details of our calculations are presented in the five appendices .","summary":"this femtosecond dynamics in the coherent temporal regime is governed by the interband nonlinear optical polarizations and is followed by a second temporal regime governed by the magnetic anisotropy of the fermi sea .","abstract":"we develop a theory of collective spin dynamics triggered by ultrafast optical excitation of ferromagnetic semiconductors . using the density matrix equations of motion in the mean field approximation and including magnetic anisotropy and hole spin dephasing effects , we predict the development of a light  induced magnetization tilt during ultra  short time intervals comparable to the pulse duration . this femtosecond dynamics in the coherent temporal regime is governed by the interband nonlinear optical polarizations and is followed by a second temporal regime governed by the magnetic anisotropy of the fermi sea . we interpret our numerical results by deriving a landau  gilbert  like equation for the collective spin , which demonstrates an ultrafast correction to the magnetic anisotropy effective field due to second order coherent nonlinear optical processes . using the lindblad semigroup method , we also derive a contribution to the interband polarization dephasing determined by the mn spin and the hole spin dephasing . our predicted magnetization tilt and subsequent nonlinear dynamics due to the magnetic anisotropy can be controlled by varying the optical pulse intensity , duration , and helicity and can be observed with pump  probe magneto  optical spectroscopy ."}
{"article_id":"0801.4641","section_id":"r","document":"within the mean field approximation , light  induced mn spin dynamics is triggered initially by the photoexcitation of a hole spin component perpendicular to the ground state mn spin . in the simple one  band approximation , the magnitude of such a spin component is determined by the ratio @xmath130 between the rabi energies that describe the coupling of the right and left  circularly polarized components of the optical field . this ratio is determined by the selection rules and the nature of the bands that contribute to the magnetization dynamics . within our simplified one  band model , @xmath130 also reflects the magnetic anisotropy of the system due to the bandstructure . in the absence of a complete theoretical understanding of such bandstructure effects , especially for the high energy ( @xmath03.1ev ) transitions observed experimentally to trigger ultrafast magnetization dynamics in ga(mn)as,@xcite we consider here the extreme case of @xmath131 , which corresponds to right  circularly polarized light . for all the calculations presented in this paper , we consider a magnetic exchange energy @xmath132=125 mev comparable to the fermi energy @xmath133=100 mev , fraction of initial holes 0.33 of the mn impurities , a hole mass @xmath134 , and a carrier thermalization time @xmath135=165fs . our results are not very sensitive to the above parameters , with the exception of the exchange interaction @xmath18 that changes the magnitude of the effect . to make the connection between the calculated quantities and the experiment , we note that ultrafast magneto  optical pump  probe spectroscopy can be used to deduce the time evolution of the z  component of the magnetization , @xmath136 . @xcite    we start with our results in the absence of magnetic anisotropy . fig.[fig1 ] shows the light  induced time evolution of the mn spin and its dependence on the hole spin and polarization dephasing , the rabi energy , and the optical pulse duration . by comparing three different dephasing regimes in fig.[fig1 ] , one can see that the shape of the mn spin trajectory depends sensitively on the hole spin and polarization dephasing . regime 1 corresponds to very short dephasing times , @xmath137=21fs and @xmath83=10.5fs , which are typical in iii(mn)v semiconductors . @xcite regime 2 corresponds to @xmath83=330fs with very short hole spin dephasing @xmath137=21fs . finally , regime 3 neglects the spin dephasing altogether , @xmath138 , @xmath83=330fs , which assumes that the hole spin is a good quantum number . as can be seen in fig.[fig1 ] , the dephasing changes qualitatively the shape of the mn spin trajectory , from the precession within the x  y plane expected in the absence of magnetic anisotropy to a complex magnetization tilt out of the x  y plane , in the direction of pulse propagation . the magnitude of this out  of  plane tilt and the mn spin z  component are enhanced by increasing @xmath87 or the pulse duration @xmath22 and by the short @xmath83 . furthermore , the mn spin component within the x  y plane rotates in a _ clockwise _ direction , opposite to the _ counter  clockwise _ direction expected for an effective magnetic field along the + z axis of pulse propagation . for right  circular  polarization , the latter is the expected direction of the photoexcited hole spin in the absence of magnetic exchange interaction or spin dephasing . however , our numerical results show that the photoexcited hole spin z  component is in fact _ negative _ , due to the magnetic exchange interaction and the mixing of the hole spin states . the dependence of the trajectories in fig.[fig1 ] on the pulse duration shows that the light  induced mn spin dynamics terminates soon after the end the photoexcitation , as expected in the absence of magnetic anisotropy . furthermore , the magnitude of the mn spin tilt increases with photoexcitation intensity . the spin dynamics of fig.[fig1 ] describes the fundamental response of the spin system to the optical excitation within the mean field approximation . the mn spin response is seen more clearly in fig.[fig2 ] , which shows the development with time of the y- and z  components of @xmath36 . both of these components vanish in the ground state . they develop on a timescale determined by the pulse duration and have comparable magnitudes for sufficiently large @xmath87 . the importance of the hole spin dephasing can be seen by comparing fig.[fig2 ] , obtained for very short spin and polarization dephasing times , with fig.[fig3 ] , obtained for @xmath138 . the most striking difference is the very small magnitude of the out - of  plane component @xmath139 when the hole spin is conserved ( @xmath138 ) . the hole spin follows the overall mn spin and remains more or less antiparallel to @xmath85 at all times , with the exception of a small component perpendicular to @xmath36 that triggers the spin dynamics . we now turn to the effects of the magnetic anisotropy on the spin dynamics . as discussed above , the magnetic anisotropy of the thermal carriers leads to preferred mn spin directions that minimize the total fermi sea energy @xmath39 , eq.([tot - en ] ) . its effects on the mn spin dynamics can be treated phenomenologically by adding the magnetic field @xmath140 to eq.([mn - spin ] ) . @xcite such an anisotropy field causes a nonlinear rotation and relaxation of the mn spin until it aligns with the easy axis direction that minimizes @xmath141 , so that @xmath142 . we would like to distinguish between the above effect , due to the thermal carriers , and the anisotropy effects on the photoexcitation . the latter can be treated microscopically as discussed in section iii and determine the photoexcited hole spin ( see e.g. eq.([hole - spin ] ) ) .    in ga(mn)as , @xmath143 , and @xmath144 . @xcite in this parameter regime , there are two degenerate ground states , which correspond to mn spin pointing at angles @xmath58 from the x  axis such that @xmath59 . the system can be prepared so that , prior to the photoexcitation , the mn spin points along either one of the above two easy axes . in the absence of magnetic anisotropy , both these initial conditions would result in the same mn spin trajectory . figs.[fig4](a ) and [ fig4](b ) compare the three mn spin components as function of time , starting with mn spin pointing along the two different ground state configurations . to make this comparison more meaningful , in both cases we chose the x  axis of the coordinate system to coincide with the initial magnetization direction . fig.[fig4 ] clearly shows that , as the rabi energy increases , the two initial conditions lead to different time evolution , which implies that the two magnetic ground states can be distinguished . as can be seen by comparing fig.[fig4 ] with fig.[fig5 ] , the mn spin dynamics depends on the hole spin dephasing , especially as the photoexcitation intensity increases .    the dependence of the mn spin dynamics on the initial magnetic state becomes more clear in figs.[fig6 ] and [ fig7 ] , which plot the mn spin trajectories for the two initial conditions in the same coordinate system , whose x  axis coincides with the initial magnetizations . two different temporal regimes can be clearly distinguished . the first regime lasts for a time interval comparable to the pulse duration . here the dynamics is governed by the optical pulse intensity , duration , and helicity , as well as by the ratio @xmath145 and the mixing of the hole spin states that depend on the magnetic anisotropy . on the other hand , the magnetic anisotropy field eq.([h ] ) , due to the thermal carriers , plays a very minor role in this initial temporal regime for sufficiently large rabi energies that exceed the anisotropy constants . the trajectories for the different initial conditions coincide in this sub  picosecond regime , which gives an ultrafast magnetization tilt determined by the response to the hole spin photoexcited by the coherent spin raman processes described by eqs.([hole - spin ] ) and ( [ h ] ) . as can be seen by comparing figs.[fig6 ] and [ fig7 ] , the shape of the mn spin trajectories is strongly influenced by the spin and polarization dephasing . figs.[fig6 ] and [ fig7 ] show a rather abrupt change in the mn spin trajectory at times @xmath146 . at later times , the temporal evolution is determined by the magnetic anisotropy field eq.([h ] ) . the shape of the trajectory during many picoseconds depends critically on the magnetization tilt that develops during the femtosecond initial stage . if this tilt is sufficiently small , the mn spin dynamics is described by linearized equations of motion , expanded around the equilibrium spin values that minimize the fermi sea magnetic energy @xmath39 . this harmonic oscillation corresponds to zero  momentum magnon excitations , whose frequency is the same for the two easy axes . since the magnitude of the magnetization tilt can be controlled by the optical pulse intensity and duration , we conclude that for sufficiently short pulses and sufficiently small rabi energies , @xmath147 , the mn spin trajectories are very similar for both initial conditions . they correspond to magnetization precession around the easy axis ( magnons ) . however , with increasing photoexcitation intensity and duration , the deviation from the easy axis due to the sub  picosecond magnetization tilt increases , and eventually the mn spin dynamics can not be described by expanding @xmath39 around its minimum . such nonlinearities result in a complex trajectory , determined by the full nonlinear equations eqs.([mn - spin ] ) and ( [ h ] ) , which can differ substantially from a simple magnon precession . as demsonstrated by figs.[fig6 ] and [ fig7 ] , in this nonlinear dynamics regime , the mn spin trajectories depend on the initial condition . one can then distinguish between the different magnetic states , which can provide the basis for an ultrafast magnetic memory read  out scheme with speed limited only by the optical pulse duration . such a scheme would be based on controlling the ultrafast response of the spin system via the optical pulse intensity , duration , and helicity . furthermore , the strong dependence of the trajectory shape on the spin dephasing implies that the valence bandstructure and mixing of the hole spin states by the spin orbit interaction plays an important role . in the next section we interpret our numerical results by deriving from the full theory an effective landau  gilbert  like equation for the mn spin after expanding around the adiabatic limit .","summary":"we interpret our numerical results by deriving a landau  gilbert  like equation for the collective spin , which demonstrates an ultrafast correction to the magnetic anisotropy effective field due to second order coherent nonlinear optical processes . our predicted magnetization tilt and subsequent nonlinear dynamics due to the magnetic anisotropy can be controlled by varying the optical pulse intensity , duration , and helicity and can be observed with pump  probe magneto  optical spectroscopy .","abstract":"we develop a theory of collective spin dynamics triggered by ultrafast optical excitation of ferromagnetic semiconductors . using the density matrix equations of motion in the mean field approximation and including magnetic anisotropy and hole spin dephasing effects , we predict the development of a light  induced magnetization tilt during ultra  short time intervals comparable to the pulse duration . this femtosecond dynamics in the coherent temporal regime is governed by the interband nonlinear optical polarizations and is followed by a second temporal regime governed by the magnetic anisotropy of the fermi sea . we interpret our numerical results by deriving a landau  gilbert  like equation for the collective spin , which demonstrates an ultrafast correction to the magnetic anisotropy effective field due to second order coherent nonlinear optical processes . using the lindblad semigroup method , we also derive a contribution to the interband polarization dephasing determined by the mn spin and the hole spin dephasing . our predicted magnetization tilt and subsequent nonlinear dynamics due to the magnetic anisotropy can be controlled by varying the optical pulse intensity , duration , and helicity and can be observed with pump  probe magneto  optical spectroscopy ."}
{"article_id":"0801.4641","section_id":"c","document":"in conclusion , we presented a theory of nonlinear spin dynamics in ferromagnetic semiconductors and demonstrated the main effects common in all such systems by considering a single spin  degenerate electron and hole band . our main result of relevance to experiments is the existence of two different temporal regimes of magnetization dynamics . the initial regime lasts for time scales comparable to the optical pulse duration . it is governed by magnetization precession and relaxation around an effective magnetic field pulse generated by the optical excitation via second  order coherent nonlinear processes . the second temporal regime is governed by the magnetic anisotropy due to the thermal carriers . we showed that the shape of the magnetization trajectory depends sensitively on the hole spin dephasing , the magnetic easy axes , the transition matrix elements , and the optical pulse intensity , duration , and helicity . the latter determine the magnitude and direction of the ultrafast magnetization tilt from the magnetic easy axis in response to the photoexcitation of hole spin , which in turn determines the importance of nonlinear magnetic effects during many picoseconds . to interpret our numerical results , we derived an effective landau  gilbert  like equation of motion . this equation shows that an effective magnetic field pulse , generated by the interband optical polarizations via a raman  like process , triggers precession and relaxation during femtosecond time scales . this magnetic field pulse may be thought of as an ultrafast correction to the anisotropy field . the picture of ultrafast magnetization dynamics conveyed by our results and , in particular , the existence of two temporal regimes is consistent with the recent experimental observation of a light  induced modification of the magnetic anisotropy field in ga(mn)as during femtosecond timesales , induced by nonthermal high energy carriers . @xcite a more detailed comparison between theory and experiment must be performed in the future . our calculations point out the need for further experiments in order to explore the control of the magnetization trajectory by changing the optical excitation intensity , duration , central frequency , and helicity . for a complete understanding of the magnetization dynamics in ferromagnetic semiconductors , the role of fluctuations and carrier  spin correlations , @xcite the bandstructure , and disorder must also be considered .        in this appendix we derive the relaxation and dephasing contributions to the hole spin equations of motion . the hole spin is expressed in the basis of hole spin eigenstates as @xmath167 , \\label{def - hole - spin - z}\\\\ { \\bf s}_{{\\bf k}m + } ^h =    { \\bf s}_{{\\bf k } m x}^h + i    { \\bf s } _ { { \\bf k } m y}^h =   \\langle \\hat{h}_{-{\\bf k}m \\uparrow}^\\dag \\hat{h}_{-{\\bf k } m \\downarrow } \\rangle . \\label{def - hole - spin - perp}\\end{aligned}\\ ] ] from eqs.([lind ] ) and ( [ lind - op ] ) we obtain for the corresponding hole density matrices after using straightforward algebra and the property @xmath168 : @xmath169 by choosing the z  axis parallel to the mn spin and noting the expression eq.([def - hole - spin - perp ] ) , we obtain eq.([spineom - perp ] ) that describes the dephasing of the hole spin component @xmath170 perpendicular to the mn spin . similarly we obtain from eqs.([lind ] ) and ( [ lind - op ] ) @xmath171 which conserve the total hole population @xmath172 using the factorization @xmath173 and the relation ( obtained from eqs.([def - hole - spin - z ] ) and ( [ n ] ) ) @xmath174 where @xmath175 , we obtain eq.([spineom - par ] ) for the hole spin relaxation .      in this appendix we derive the polarization dephasing @xmath176 by using eqs.([lind ] ) and ( [ lind - op ] ) . after straightforward algebra and using the properties @xmath177 , @xmath178 , we obtain after noting that the terms in the summation of eq.([lind ] ) vanish unless @xmath179 : @xmath180 we now note the relation between the hole operators with spin along the z  axis of pulse propagation or along the mn spin direction : @xmath181 where @xmath182 and @xmath183 are the polar coordinates that define the direction of the mn spin @xmath85 and the operators @xmath184 and @xmath185 create hole states with spin along the z  axis . using eqs . ( [ spin - up ] ) and ( [ spin - down ] ) , the property @xmath178 , and the relations @xmath186 we obtain from eq.([step1 ] ) after straightforward algebra @xmath187   \\nonumber \\\\ & & - \\gamma_\\perp \\left [ \\frac { 1 + { \\bf s}_z / s}{2 }   \\langle   \\hat{h}_{-{\\bf k } m \\uparrow }   \\hat{e}_{{\\bf k } n \\downarrow } \\hat{h}_{-{\\bf k } m \\downarrow } \\hat{h}^\\dag_{-{\\bf k } m \\downarrow } \\rangle   \\right . \\nonumber \\\\ & & \\left . - \\frac{{\\bf s}_{-}}{2s } \\langle   \\hat{h}_{-{\\bf k } m \\uparrow }   \\hat{e}_{{\\bf k } n \\downarrow }   \\hat{h}_{-{\\bf k } m \\downarrow }   \\hat{h}^\\dag_{-{\\bf k } m \\uparrow } \\rangle    \\right]\\end{aligned}\\ ] ] and @xmath188 \\nonumber \\\\ & & - \\gamma_{\\perp } \\left [ \\frac { 1 - { \\bf s}_z / s}{2 } \\langle   \\hat{h}_{-{\\bf k } m \\downarrow }   \\hat{e}_{{\\bf k } n \\downarrow } \\hat{h}_{-{\\bf k } m \\uparrow } \\hat{h}^\\dag_{-{\\bf k } m \\uparrow }   \\rangle \\right . \\nonumber \\\\ & & - \\frac{{\\bf s}_{+}}{2s }   \\langle   \\left . \\hat{h}_{-{\\bf k } m \\downarrow }   \\hat{e}_{{\\bf k } n \\downarrow } \\hat{h}_{-{\\bf k } m \\uparrow } \\hat{h}^\\dag_{-{\\bf k } m \\downarrow } \\rangle   \\right ] . \\end{aligned}\\ ] ] we now factorize the higher density matrices in the above equations as follows : @xmath189 we thus obtain that @xmath190 \\nonumber \\\\ & & \\left . + \\frac{{\\bf s}_{-}}{2s } \\left [ { \\bf s}^h_{{\\bf k } m + }   p_{{\\bf k } m n \\uparrow }   +   p_{{\\bf k } m n \\downarrow } ( 1 - n^h_{{\\bf k } m \\uparrow } ) \\right ]   \\right\\}.\\end{aligned}\\ ] ] and @xmath191 \\nonumber \\\\ & & \\left . + \\frac{{\\bf s}_{+}}{2s } \\left [ { \\bf s}^h_{{\\bf k } m - }   p_{{\\bf k } m n \\downarrow }   +   p_{{\\bf k } m n \\uparrow } ( 1 - n^h_{{\\bf k } m \\downarrow } ) \\right ]   \\right\\},\\end{aligned}\\ ] ] where @xmath192 are the spin  polarized hole populations . after expressing the latter by using eq.([n - n ] ) we obtain after some algebra the polarization dephasing contributions eqs . ( [ pol - deph - up ] ) and ( [ pol - deph - down ] ) .      in this appendix we derive an effectve equation of motion for the mn spin by expanding around the adiabatic limit . first we use the hole spin decomposition eq.([decomp ] ) into a component parallel @xmath193 ( @xmath194 ) and a component perpendicular to @xmath193 ( @xmath195 ) . the unadiabatic contribution @xmath195 is responsible for triggering the mn spin precession . after substituting eq.([decomp ] ) into eq.([hole - spin ] ) and noting that the mn spin magnitude @xmath28 remains constant in time we obtain @xmath196 - \\gamma_{\\perp }    { \\bf s}^{h}_{{\\bf k } \\perp}.\\end{aligned}\\ ] ] by projecting out the components parallel and perpendicular to @xmath93 and using the relations @xmath197 and @xmath198 we obtain that @xmath199 and @xmath200 we now focus on the perpendicular component @xmath201 . we note from eq.([mn - spin ] ) that the motion of @xmath85 is characterized by a precession frequency @xmath202 determined by the field @xmath65 and the mean hole spin @xmath203 : @xmath204 where @xmath205 is the mean hole spin . in iii - mn - v semiconductors , this precession is much slower than the motion of the hole spin @xmath206 , which is characterized by the precession energy @xmath132 and the relaxation rate @xmath87 . when considering the slower mn spin dynamics , we can then substitute @xmath207 by its steady state value in the frame of reference that rotates with the mn spin and @xmath193 . the rate of change of any vector @xmath107 as seen by an observer in the rotating frame , @xmath208 , is related to the corresponding rate of change in the inertial frame , @xmath209 , by @xmath210 we thus obtain in the case of the hole spin @xmath211 projecting in the direction perpendicular to the mn spin using eq.([perp ] ) we obtain that @xmath212 where we used the vector property @xmath213 the rotating frame approximation corresponds to neglecting @xmath214 . to obtain an effective equation of motion for the mn spin , we use eq.([mn - spin ] ) for @xmath215 to eliminate the hole spin @xmath206 , defined by eqs ( [ sum - s ] ) and ( [ perp ] ) , from eq.([s - perp - eom ] ) : @xmath216 by summing eq.([s - perp - eom ] ) over all momenta we thus obtain within the rotating frame approximation after using the definition eq.([h - eff ] ) that @xmath217 the above nonlinear equation of motion is governed by the magnetic field @xmath65 , the effective magnetic field @xmath149 determined by the interband e  h polarizations , and the hole spin relaxation ( @xmath218 ) and dephasing ( @xmath87 ) rates . eq.([eff - eom-1 ] ) can be transformed into an effective time  dependent landau  gilbert  like equation of motion by taking the cross product of both sides with @xmath93 and using the vector property eq.([cross ] ) and the property @xmath219 : @xmath220 substituting the above expression into eq.([eff - eom-1 ] ) we obtain eq.([eom - eff ] ) . in this appendix we derive the relaxation of the hole spin component @xmath221 parallel to the mn spin @xmath85 , determined by eq.([s - parall - eom ] ) . we eliminate @xmath206 from eq.([s - parall - eom ] ) by using the property @xmath222 , obtained after using the properties @xmath223 , @xmath224 , and some algebra . we also eliminate @xmath225 from eq.([s - parall - eom ] ) by projecting both sides of eq.([eom - eff ] ) with @xmath65 and using the vector property @xmath226 and the relations @xmath227 and @xmath228 . by summing both sides of eq.([s - parall - eom ] ) over all momenta we finally obtain the equation of motion @xmath229      in this appendix we derive the equation of motion that determines the time evolution of the effective magentic field pulse @xmath230 that governs the intial femtosecond magnetization re  orientation and relaxation . using the equations of motion of the interband polarizations , eqs.([pup1 ] ) , ( [ pdown1 ] ) , ( [ pup2 ] ) , and ( [ pdown2 ] ) , we obtain the equation of motion @xmath231 where @xmath232 and @xmath121 were defined by eqs.([omega ] ) and ( [ delta ] ) , @xmath233 satisfies the equation of motion @xmath234 where @xmath235 \\nonumber \\\\   - \\left ( |\\mu_{+}|^2 - |\\mu_{-}|^2 \\right )   \\left(s_{{\\bf k}z}^h - s_{{\\bf k}z}^e \\right),\\end{aligned}\\ ] ] and @xmath236 \\nonumber \\\\ & & + \\left ( |\\mu_{+}|^2 +   |\\mu_{-}|^2 \\right ) \\left ( s_{{\\bf k}z}^h   - { \\bf s}_{{\\bf k}z}^e \\right ) . \\label{cals}\\end{aligned}\\ ] ] we note from the above equations that , in the absence of spin polarization in the ground state , @xmath237 , @xmath158 points along the z  direction of optical field propagation . on the other hand , in the presence of spin  polarized holes in the ground state as in ferromagnetic semiconductors , @xmath149 develops additional components determined by @xmath109 , the mn spin and exchange interaction @xmath238 , and by the magnetic anisotropy . l. d. landau , e. m. lifshitz , and l. p. pitaevski , _ statistical physics , part 2 _ , 3rd ed . ( pergamon press , oxford , 1980 ) ; l. landau and e. lifshitz , phys . union * 8 * , 153 ( 1935 ) ; t. l. gilbert , phys . rev . * 100 * , 1243 ( 1955 ) .                        m. d. kapetanakis and i. e. perakis , phys . rev . b * 75 * , 140401(r ) ( 2007 ) ; m. d. kapetanakis , a. manousaki , and i. e. perakis , phys . b , * 73 * , 174424 , ( 2006 ) ; m. d. kapetanakis and i. e. perakis , unpublished .","summary":"we develop a theory of collective spin dynamics triggered by ultrafast optical excitation of ferromagnetic semiconductors . using the density matrix equations of motion in the mean field approximation and including magnetic anisotropy and hole spin dephasing effects , we predict the development of a light  induced magnetization tilt during ultra  short time intervals comparable to the pulse duration .","abstract":"we develop a theory of collective spin dynamics triggered by ultrafast optical excitation of ferromagnetic semiconductors . using the density matrix equations of motion in the mean field approximation and including magnetic anisotropy and hole spin dephasing effects , we predict the development of a light  induced magnetization tilt during ultra  short time intervals comparable to the pulse duration . this femtosecond dynamics in the coherent temporal regime is governed by the interband nonlinear optical polarizations and is followed by a second temporal regime governed by the magnetic anisotropy of the fermi sea . we interpret our numerical results by deriving a landau  gilbert  like equation for the collective spin , which demonstrates an ultrafast correction to the magnetic anisotropy effective field due to second order coherent nonlinear optical processes . using the lindblad semigroup method , we also derive a contribution to the interband polarization dephasing determined by the mn spin and the hole spin dephasing . our predicted magnetization tilt and subsequent nonlinear dynamics due to the magnetic anisotropy can be controlled by varying the optical pulse intensity , duration , and helicity and can be observed with pump  probe magneto  optical spectroscopy ."}
{"article_id":"1207.2047","section_id":"i","document":"metastability is a broad term describing the existence of a very sensitive equilibrium , possessing a weak form of stability / instability . usually , such behavior is related to the presence of a small first eigenvalue for the linearized operator at the given equilibrium state , revealed at dynamical level by the appearance of slowly moving structures . such circumstance comes into view in the analysis of different classes of evolutive pdes , and it has been object of a wide amount of studies , covering many different areas . among others , we emphasize the explorations on the allen  cahn equation , started in @xcite , and the investigations on the cahn  hilliard equation , with the fundamental contributions @xcite . the analysis has been continued by many other scholars by means of a broad spectrum of techniques , and extended to a number of different models such as the gierer  meinhardt and gray  scott systems ( see @xcite ) , keller  segel chemotaxis system ( see @xcite ) , general gradient flows ( see @xcite ) and many others . the number of references is so vast that it would be impossible to mention all the contributions given in the area . a pionereeing article in the analysis of slow dynamics for parabolic equations has been authored by g.  kreiss and h .- o . kreiss @xcite and concerns with the scalar viscous conservation law @xmath6 with the space variable @xmath7 belonging to a one - dimensional interval @xmath8 , @xmath9 . the primary prototype for the flux function @xmath10 is given by the classical quadratic formula @xmath11 , so that partial differential equation in becomes the so - called _ ( viscous ) burgers equation_. the parameter @xmath12 is small . problem is complemented with dirichlet boundary conditions @xmath13 for given data @xmath14 to be discussed in details . burgers equation is considered as a ( simplified ) archetype of more complicate systems of partial differential equations arising in different fields of applied mathematics . inspired by the equations of fluid - dynamics , the parameter @xmath15 is interpreted as a _ viscosity coefficient _ and the main problem is to identify and quantify its rle in the emergence and/or disappearance of structures . formally , in the limit @xmath16 , the initial value problem reduces to a first - order quasi - linear equation of hyperbolic type @xmath17 whose standard setting is given by the _ entropy formulation_. hence solutions may have discontinuities , which propagate with speed @xmath18 such that @xmath19\\!]}={[\\![}f(u){]\\!]}\\qquad\\qquad   \\textrm{({\\sf rankine -- hugoniot relation})}\\ ] ] and satisfy appropriate entropy conditions ( here @xmath20\\!]}$ ] denotes the jump ) . in addition , the treatment of the boundary conditions is more delicate than the parabolic case , because of the eventual appearance of boundary layers , @xcite . concerning the flux function @xmath10 , let us assume that , for some @xmath21 , @xmath22 where @xmath23 are the boundary data prescribed in . the last two assumptions guarantee that a jump with left value @xmath24 and right value @xmath25 satisfy the entropy condition and has speed of propagation equal to zero , as dictated by the rankine  hugoniot relation . therefore , the one - parameter family of functions @xmath26 defined by @xmath27 ( where @xmath28 denotes the characteristic function of the set @xmath29 ) is composed by stationary solutions of the equation in satisfying the boundary conditions . the dynamics determined by boundary - initial value problem - is simple : for any datum @xmath30 with bounded variation , the solution converges _ in finite time _ to an element of @xmath26 ( see section [ sect : appl ] ) . hence , at the level @xmath31 , there are infinitely many stationary solutions , generating a `` finite - time '' attracting manifold for the dynamics . .15 cm    for @xmath12 , the situation is different . apart from the well - known smoothing effect , the presence of the laplace operator in has the effect of a drastic reduction of the number of stationary solutions satisfying : from infinitely many to a single stationary state ( see section [ sect : appl ] ) . such solution , denoted here by @xmath32 , converges in the limit @xmath16 to a specific element @xmath33 of the family @xmath26 . the dynamical properties of  for initial data close to the equilibrium configuration @xmath34 can be analyzed linearizing at the state @xmath34 @xmath35 in @xcite it shown that , in the case of burgers flux @xmath11 , the eigenvalues of @xmath36 with homogeneous dirichlet boundary conditions , are real and negative . moreover , as a consequence of the requiremente @xmath37 , there holds as @xmath38 @xmath39 for some @xmath21 independent on @xmath15 . negativity of the eigenvalues implies that the steady state @xmath34 is asymptotically stable with exponential rate ; the precise description of the eigenvalue distribution shows that the large time behavior is described by term of the order @xmath40 and thus the convergence is very slow when @xmath15 is small to quantify the reduction order of the mapping @xmath41 , note that @xmath42 has order @xmath43 for @xmath44 and order @xmath45 for @xmath46 . such is the picture relative to the behavior determined by an initial data close to the equilibrium solution @xmath34 . the next question concerns with the dynamics generated by initial data presenting a sharp transition from @xmath47 to @xmath48 localized far from the position of the steady state @xmath34 . [ fig1 ]    , @xmath49 and @xmath50.,width=340 ]    figure [ fig1 ] represents a numerical simulation of the solution to the initial value problem with boundary conditions , relative to the initial condition @xmath50 . starting with a decreasing initial datum , a shock layer is formed in a short time scale , so that the solution is approximately given by a translation of the ( unique ) stationary solution of the problem . once such a layer is formed , on a longer time scale , it moves towards the location corresponding to the equilibrium solution . this article deals with the dynamics after the shock layer formation for @xmath15 small . in order to provide a detailed description of such regime , with special attention to the relation between the unviscous and the low - viscosity behavior , it is rational : +  to build up a one - parameter family of functions @xmath51 such that @xmath52 as @xmath38 , in an appropriate sense ; +  to describe the dynamics of the solution to the initial - boundary value problem  in a tubular neighborhood of the family @xmath51 . a specific element @xmath53 of the manifold @xmath54 corresponds to the steady state @xmath34 of  and the dynamics will asymptotically lead to such configuration . .15 cm    before describing in details the contribution of the paper , let us recast the state of the art on the topic . among others , the problem of slow dynamics for the burgers equation has been examined in @xcite and in @xcite , where different approaches have been considered . the former is based either on _ projection method _ or on _ wkb expansions _ ; the latter stands on an adapted version of the _ method of matched asymptotics expansion_. the common aim is to determine an expression and/or an equation for the parameter @xmath55 , considered as a function of time , describing the movement of the transition from a generic point of the interval @xmath56 toward the equilibrium location @xmath57 . in both the contributions , the analysis is conducted at a formal level and validated numerically by means of comparision with significant computations . a rigorous analysis has been performed in @xcite ( and generalized to the case of nonconvex flux in @xcite ) , where one - parameter family of reference functions is chosen as a family of traveling wave solutions to the viscous equation satisfying the boundary conditions and with non - zero ( but small ) velocity . the approach is based on the use of such traveling waves to obtain upper and lower estimates by the maximum principle , from which rigorous asymptotic formulae for the slow velocity are obtained . slow motion for the viscous burgers equation in unbounded domains has been also considered in literature . in @xcite , it is analyzed the case of the half - line @xmath58 for the space variable @xmath7 , with constant initial and boundary data chosen so that speed of the shock generated at @xmath59 is stationary for the corresponding hyperbolic equation . the presence of the viscosity generates a motion of the transition layer , which is precisely identified by means of the lambert s @xmath60 function . later , the ( slow ) motion of a shock wave , with zero hyperbolic speed , for the burgers equation in the quarter plane has been considered in @xcite , where it is shown that the location of the wave front is of order @xmath61 ; the same result has been generalized in @xcite in the case of general fluxes ( for other contributions to the same problem , we refer also to @xcite ) . the case of the whole real line has been examined in @xcite with emphasis on the generation of @xmath62wave like structures and their evolution towards nonlinear diffusion waves . the analysis is based on the use of self - similar variables , suggested by the invariance of the burgers equation under the group of transformations @xmath63 ( for subsequent contributions in the same direction , see @xcite ) . more recently , it has been shown in @xcite that the slow motion is determined by the presence of a one - dimensional center manifold of steady states for the equation in the self - similar variables ( corresponding to the diffusion waves ) and a relative family of one - dimensional global attractive invariant manifold . in a short - time scale , the solution approaches one of the attractive manifolds and remains close to it in a long - time scale . at the present day , results relative to metastability in the case of systems appear to be rare . slow dynamics analysis for systems of conservation laws have been considered in @xcite , basic model examples being the navier - stokes equations of compressible viscous heat conductive fluid and the keyfitz - kranzer system , arising in elasticity . the approach is based on asymptotic expansions and consists in deriving appropriate limiting equations for the leading order terms , in the case of periodic data . in @xcite , the problem of proving convergence to a stationary solution for a system of conservation laws with viscosity is addressed , with an approach based on a detailed analysis of the linearized operator at the steady state . a recent contribution is the reference @xcite , where the authors consider the saint - venant equations for shallow water and , precisely , the phenomenon of formation of roll - waves . the approach merges together analytical techniques and numerical results to present some intriguing properties relative to the dynamics of solitary wave pulses . .15 cm    summing up , apart for the formal expansions methods , the rigorous approaches used in the literature are largely based on typical scalar equations features . the first of these properties is the direct link between the scalar burgers equation and the heat equation given by the hopf  cole transformation : @xmath64 , and the consequent invariance of the burgers equation under the group of scaling transformations @xmath63 . on the one hand , the presence of such a connection is an evident advantage , since it permits to determine optimal descriptions for the behavior under study ( see @xcite ) ; on the other hand , to use such exceptional property makes the approach very stiff and difficult to apply to more general cases . a different `` scalar hallmark '' is the base of the approach considered in @xcite , where the authors make wide use of maximum principle and comparison arguments , taking benefit from the fact that the equation is second - order parabolic .    in order to extend the results to more general settings and specifically for systems of pdes , it is useful to determine strategies and techniques that are more flexible , paying , if necessary , the price of a less accurate description of the dynamics . a contribution in this direction has been given in @xcite , where the location of the shock transition for a scalar conservation law in the quarter plane has been proved by means of weighted energy estimates , extending the result proved in @xcite , that used an explicit formula determined by means of the hopf  cole transformation for the green function of the linearization at the shock profile of the burgers equation . .15 cm    the present article intends to contribute to the definition of a versatile language for metastability , suitable for general class of partial differential equations of evolutive type . with this direction in mind , we follow an approach that it is strictly related with the _ projection method _ considered in @xcite and we go behind the philosophy tracked in the analysis of stability of viscous shock waves by k.zumbrun and co - authors ( see @xcite ) . precisely , we separate three distinct phases :    to choose a family of functions @xmath65 , considered as approximate solutions , and to measure how far they are from being exact solutions ; + to investigate spectral properties of the linearized operators at such states ; + to show that appropriate assumptions on the approximate solutions ( step * i * ) and on the spectrum of the linearized operators ( step * ii * ) imply the appearance of a metastable behavior . .15 cm    with respect to the framework of shock waves stability analysis , there are two main differences . first of all , we concentrate on the case of bounded domains and , therefore , the spectrum of the linearized operators is discrete . additionally , since the reference states @xmath66 are approximate solutions , the perturbations of such states satisfy at first order a _ non - homogeneous _ linear equation , with forcing term negligible as @xmath16 . the defect of working in a neighborhood of a manifold that is not invariant has the counterpart of a wider flexibility in its construction that leads , in particular , to ( more or less ) explicit representations . thus , it should be possible in principle to obtain numerical evidence of special spectral properties even in cases where analytical results appear to be not achievable . the article is organized as follows . to start with , in section [ sect : abs ] , we consider a general framework containing scalar viscous conservation laws as a very specific case . given a family of approximate solutions @xmath67 , our approach consists in representing the solution to the initial - bondary value problem as the sum of an element @xmath68 moving along the family @xmath67 plus a perturbation term @xmath5 . the equation for the unknown @xmath2 is chosen in such a way that the slower decaying terms in the perturbation @xmath5 are canceled out . in order to state a general result , we consider an approximation of the complete nonlinear equations for the couple @xmath69 , obtained by disregarding quadratic terms in @xmath5 and keeping the nonlinear dependence on @xmath55 , in order to keep track of the nonlinear evolution along the manifold @xmath67 . such reduced system for @xmath70 is called quasi - linearized system and it is the concern of theorem [ thm : metal ] , the main contribution of the paper . under appropriate assumptions on the manifold @xmath66 , the linearized operators at such states , and the coupling between the two objects , such result gives an explicit representation for the solution to the evolutive problem together with an estimate on the remainder , vanishing in the limit @xmath38 . this gives a sound justification to the reduced equation for the unknown @xmath2 obtainable by neglecting also the linear term in @xmath5 . dealing with the complete system for the couple @xmath70 brings into the analysis also the specific form of the quadratic terms . as a consequence , in case of parabolic systems of reaction - diffusion type , we expect that a results analogous to theorem [ thm : metal ] could be proved , under the assumption of an _ a priori _ @xmath71 bound on the solution . differently , when a nonlinear first order space derivative term is present ( as is the case for viscous conservation laws ) , the quadratic term involve a dependence on the space derivative of the solution and a rigorous result needs an additional bound , which we are not presently able to achieve . in section [ sect : appl ] we consider the application of the general framework to the case of viscous scalar conservation laws . firstly , we present the dynamics of the hyperbolic equation obtained in the vanishing viscosity limit , proving a result on finite - time convergence to the one - parameter manifold of steady states ( theorem [ thm : stabhyp ] ) . then , we pass to consider the parabolic equation in under assumption and we build up a specific family @xmath67 by matching continuously stationary solutions at a given point @xmath55 . to apply the general result of section [ sect : abs ] , we need to measure how far are states @xmath66 from being stationary solutions , and this amounts in estimating the jump of the space derivative at the matching point . such task is completed , showing that the residual has order @xmath72 , hence it is exponentially small in the limit @xmath16 . as a by - product , we deduce a formal equation for the motion of the shock layer , which generalizes the one known for the case of the burgers flux @xmath73 .    in section [ sect : spec ] , we analyze spectral properties of the diffusion - transport linear operator , arising from the linearization at the state @xmath74 . we show that , under appropriate assumption on the limiting behavior of @xmath66 as @xmath16 , the spectrum can be decomposed into two parts : the first eigenvalue of order @xmath75 ; all of the remaining eigenvalues are less than @xmath76 ( where @xmath77 denotes a generic positive constant independent on @xmath15 ) . additionally , precise asymptotics for the first eigenvalue are achieved by considering the linear operator with piecewise constant coefficient , obtained by taking the limit of functions @xmath74 as @xmath16 . this analysis is needed to give evidence of the validity of the coupling assumption required in theorem [ thm : metal ] .","summary":"the aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type . a general framework suited for parabolic equations in one dimensional bounded domains is proposed , based on choosing a family of approximate steady states and on the spectral properties of the linearized operators at such states . the slow motion for solutions belonging to a cylindrical neighborhood of the family is analyzed by means of a system of an ode for the parameter , coupled with a pde describing the evolution of the perturbation .    we state and prove a general result concerning the reduced system for the couple , called quasi - linearized system , obtained by disregarding the nonlinear term in , and we show how such approach suits to the prototypical example of scalar viscous conservation laws with dirichlet boundary condition in a bounded one - dimensional interval with convex flux .    corrado mascia , marta strani    0.3 cm * key words * metastability ; slow motion ; spectral analysis ; viscous conservation laws .    0.3 cm * ams subject classification * 35b25 ( 35p15 , 35k20 )","abstract":"the aim article is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type . a general framework suited for parabolic equations in one dimensional bounded domains is proposed , based on choosing a family of approximate steady states and on the spectral properties of the linearized operators at such states . the slow motion for solutions belonging to a cylindrical neighborhood of the family is analyzed by means of a system of an ode for the parameter , coupled with a pde describing the evolution of the perturbation .    we state and prove a general result concerning the reduced system for the couple , called quasi - linearized system , obtained by disregarding the nonlinear term in , and we show how such approach suits to the prototypical example of scalar viscous conservation laws with dirichlet boundary condition in a bounded one - dimensional interval with convex flux .    corrado mascia , marta strani    0.3 cm * key words * metastability ; slow motion ; spectral analysis ; viscous conservation laws .    0.3 cm * ams subject classification * 35b25 ( 35p15 , 35k20 )"}
{"article_id":"0912.3245","section_id":"i","document":"quantum computation makes it possible to achieve polynomial complexity for many classical problems that are believed to be hard @xcite . to preserve coherence , quantum operations need to be protected by quantum error correcting codes ( qeccs ) @xcite . with error probabilities in elementary gates below a certain threshold , one can use multiple layers of encoding ( concatenation ) to reduce errors at each level and ultimately make arbitrarily - long quantum computation possible @xcite . the actual value of the threshold error probability strongly depends on the assumptions of the error model and on the chosen architecture , and presently varies from @xmath3 for a chain of qubits with nearest - neighbor couplings @xcite and @xmath4 for qubits with nearest - neighbor couplings in two dimensions @xcite , to @xmath5 with postselection @xcite , or even above @xmath6 if additional constraints on errors are imposed @xcite . the quoted estimates have been made using stabilizer codes , an important class of codes which originate from additive quaternary codes , and have a particularly simple structure based on abelian groups @xcite . recently , a more general class of codeword stabilized ( cws ) quantum codes was introduced in refs . this class includes stabilizer codes , but is more directly related to non - linear classical codes . this direct relation to classical codes is , arguably , the most important advantage of the cws framework . specifically , the classical code associated with a given cws quantum code has to correct certain error patterns induced by a graph associated with the code . the graph also determines the graph state @xcite serving as a starting point for an encoding algorithm exploiting the structure of the classical code @xcite . with the help of powerful techniques from the theory of classical codes , already several new families of non - additive codes have been discovered , including codes with parameters proven to be superior to any stabilizer code @xcite . both classical additive codes and additive quantum codes can be corrected by first finding the syndrome of a corrupted vector or quantum state , respectively , and then looking up the corresponding error ( coset leader ) in a precomputed table @xcite . this is not the case for non - linear codes . in fact , even the notions of a syndrome and a coset become invalid for general non - linear codes . furthermore , since quantum error correction must preserve the original quantum state in all intermediate measurements , it is more restrictive than many classical algorithms . therefore , the design of a useful cws code must be complemented by an efficient quantum error correction algorithm . the goal of this work is to address this important unresolved problem for binary cws codes . first , we design a procedure to _ detect _ an error in a narrower class , the _ union stabilizer _ ( ust ) codes , which possess some partial group structure @xcite . then , for a general cws code and a set of graph - induced maps of correctable errors forming a group , we construct an auxiliary ust code which is the union of the images of the original cws code shifted by all the elements of the group . finally , we construct abelian groups associated with correctable errors located on certain _ index sets _ of qubits . the actual error is found by first applying error - detection to locate the index set with the relevant auxiliary ust code , then using a collection of smaller ust codes to pinpoint the error in the group . since we process large groups of errors simultaneously , we make a significant reduction of the number of measurements compared with the brute force error correction for non - linear ( quantum or classical ) codes . more precisely , we consider an arbitrary distance-@xmath7 cws code @xmath8 that uses @xmath0 qubits to encode a hilbert space of dimension @xmath9 and can correct all @xmath1-qubit errors , where @xmath10 . in sec . [ sec : background ] we give a brief overview of the notations and relevant facts from the theory of quantum error correction . then in sec . [ sec : generic ] , we construct a reference recovery algorithm that deals with errors individually . this algorithm requires up to @xmath11 measurements , where @xmath12 is the total number of errors of size up to @xmath1 ( this bound is tight for non - degenerate codes ) . each of these measurements requires up to @xmath13 two - qubit gates . in order to eventually reduce the overall complexity , we consider the special case of ust codes in sec . [ sec : ust - measurement ] . here we design an error - detecting measurement for a ust code with a translation set of size @xmath9 that requires @xmath14 two - qubit gates to identify a single error . our error grouping technique presented in sec . [ sec : clusters ] utilizes such a measurement to check for several errors at once . for additive cws codes the technique reduces to stabilizer - based recovery [ sec . [ sec : additive ] ] . in the case of generic cws codes [ sec : generic - cws ] ] , we can simultaneously check for all errors located on size-@xmath1 qubit clusters ; graph - induced maps of these errors form groups of size up to @xmath15 . searching for errors in blocks of this size requires up to @xmath16 measurements to locate the cluster , plus up to @xmath17 additional measurements to locate the error inside the group . in sec . [ sec : conclusions ] we discuss the obtained results and outline the directions of further study . finally , in appendix  [ app : orthogonality ] we consider some details of the structure of corrupted spaces for the codes discussed in this work . note that some of the reported results have been previously announced in ref .","summary":"in this paper , we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement . while it still leaves exponentially many measurements for a generic cws code , the technique is equivalent to syndrome - based recovery for the special case of additive cws codes .    by -0.05 in","abstract":"codeword stabilized ( cws ) codes are , in general , non - additive quantum codes that can correct errors by an exhaustive search of different error patterns , similar to the way that we decode classical non - linear codes . for an-qubit quantum code correcting errors on up to qubits , this brute - force approach consecutively tests different errors of weight or less , and employs a separate-qubit measurement in each test . in this paper , we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement . this structured error recovery technique exponentially reduces the number of measurements by about times . while it still leaves exponentially many measurements for a generic cws code , the technique is equivalent to syndrome - based recovery for the special case of additive cws codes .    by -0.05 in"}
{"article_id":"math9910054","section_id":"i","document":"let @xmath3 be a polynomial map . the polynomial describes a family of complex affine hypersurfaces @xmath4 , @xmath5 . the family is locally trivial , so the hypersurfaces have constant topology , except at finitely many _ irregular _ fibers @xmath4 whose topology may differ from the generic or _ regular _ fiber of @xmath6 . we would like to give a full description of the topology of this family in terms of easily computable data . this paper describes some progress . we will restrict mostly to the case that @xmath6 has only isolated singularities . we show that the data then needed are local monodromy maps obtained by transporting a fixed generic fiber @xmath7 around the irregular fibers , and the `` milnor fibers '' of the singular points and singularities at infinity of @xmath6 : these are certain submanifolds of @xmath7 that describe the loss of topology at irregular fibers . it is convenient to subdivide this necessary data as follows . for each irregular fiber we need    * the milnor fibers associated with it ; * the local monodromy for the irregular fiber restricted to each milnor fiber ; * the embeddings of the milnor fibers into a fixed `` reference '' regular fiber @xmath7 . the first two items are local ingredients , while the third is global . we are able to give complete computation of the local ingredients for @xmath2 ( see theorem [ th : dim2 ] ) . the remaining problem for @xmath2 is therefore the third item , although we obtain enough constraints that the complete topology can be sometimes be deduced . we use the brianon polynomial as an illustrative example . in this case our general results quickly yield the previous homological monodromy computations of artal - bartolo , cassou - nogues , and dimca @xcite and dimca and nemethi @xcite . since our computations are geometric , we obtain sharper information ( action on the intersection form , etc . ) . in fact , our computations strongly suggest a candidate description for the complete topology . however , this description remains conjectural , so the example illustrates both the strengths and current limitations of our approach . as in the paper @xcite , we also give a detailed description on the level of homology . that paper shows that , if @xmath6 is _ good _ , that is , it has only isolated singularities and no singularities at infinity , then for @xmath8 the homological data describes the complete topology . our results prepare the ground for an extension of this result to the case that there are singularities at infinity ( at least if the singularities at infinity are also isolated ) , by extending the topological model of @xcite to allow singularities at infinity . before we describe our results in more detail , we say a bit more about the basic set - up . a fiber can be irregular in two ways :    * it may have singularities ; * it may be `` irregular at infinity '' : failure of local triviality near the given fiber occurs outside arbitrarily large compact sets .    of course a fiber can be both singular and irregular at infinity ; this will , for instance , always be the case if the fiber has non - isolated singularities . there have been many papers dealing with algebraic conditions that imply regularity at infinity ( m - tameness of @xcite which asks that the given fiber and all nearby fibers be transverse to sufficiently large spheres ; @xmath9-regularity of @xcite and @xcite which generalizes this to allow non - round spheres ; the stronger t - regularity of @xcite , equivalent to the `` malgrange condition '' of @xcite ) . for @xmath2 these conditions are all equivalent to regularity at infinity ( see @xcite , @xcite ) , but in higher dimensions they are not mutually equivalent . for our purposes the weakest concept of irregularity at infinity , namely the topological one given above , suffices . in @xcite we described results that hold under no conditions on singularities . as already mentioned , we will here be particularly interested in fibers which have only isolated singularities , but no restriction on singularities at infinity . there have been several recent studies of polynomial maps for which the singularities at infinity are also restricted to be isolated in an appropriate sense ( e.g. , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . however most of our results are new even for this case . in particular , the second part of this paper deals only with the case of dimension @xmath2 , in which case singularities at infinity are always isolated .    at an irregular fiber there is a loss of topology compared with the regular fiber . for an isolated singularity the change in topology is captured by the milnor fiber @xcite of the singularity . if @xmath6 is `` good '' ( no singularities at infinity ) then these milnor fibers account for all the topology of the regular fiber in a way that is made precise by neumann and rudolph @xcite .    for a singularity at infinity there is a `` milnor fiber at infinity , '' first described by suzuki @xcite for @xmath2 . one point of this paper is to extend the theory of @xcite to encompass the milnor fibers at infinity also , and to show that the new ingredients  the topology of the singularities at infinity of an irregular fiber , as encoded by the milnor fibers at infinity and the monodromy maps on these milnor fibers  are recoverable for @xmath2 in full from the link at infinity of the irregular fiber .","summary":"this is motivated out of the `` unfolding of links '' described earlier by the first author and lee rudolph . the topological model gives a useful encoding of the local and global monodromy for the map . the new ingredients  the topology of the singularities at infinity of an irregular fiber , as encoded by the milnor fibers at infinity and the monodromy maps on these milnor fibers  are recoverable for in full from the link at infinity of the irregular fiber .","abstract":"we give a topological model for a polynomial map from to in the neighborhood of a fiber with isolated singularities . this is motivated out of the `` unfolding of links '' described earlier by the first author and lee rudolph . the topological model gives a useful encoding of the local and global monodromy for the map . the new ingredients  the topology of the singularities at infinity of an irregular fiber , as encoded by the milnor fibers at infinity and the monodromy maps on these milnor fibers  are recoverable for in full from the link at infinity of the irregular fiber . they can thus be computed completely in terms of splice diagrams ."}
{"article_id":"astro-ph0204077","section_id":"i","document":"a thorough understanding of the orbital structure in a barred galaxy potential can provide useful insight to the stellar dynamics of barred galaxies and therefore to the dynamical evolution of these objects , as reviewed e.g. by athanassoula ( 1984 ) , contopoulos & grosbl ( 1989 ) , sellwood & wilkinson ( 1993 ) and pfenniger ( 1996 ) . stable periodic orbits trap around them regular orbits and thus constitute the backbone of galaxy structure ( athanassoula , bienayme , martinet et al . thus the appearance of a given morphological feature can often be associated with the properties of one of the main families of periodic orbits . in the 90s , starting with athanassoula ( 1992a ; 1992b ) , many papers have pointed out that the gaseous response to steady barred potentials is , to a large degree , determined by the morphology of the periodic orbits in the corresponding stellar case . thus , orbital and gaseous dynamics are linked . this has provided added incentive for studies of the morphology and the stability of periodic orbits in hamiltonian systems representing disc galaxies . orbital theory has often provided useful information on the structure of galactic bars . thus it is now understood that a bar is basically due to regular orbits trapped around the so called ` x1 ' periodic orbits , which are elongated along the bar major axis @xcite . such orbits do not extend beyond the corotation resonance , and in many cases no suitable elongated orbits can be found beyond the 4:1 resonance . this led orbital theory to predict that bars should end at or before corotation @xcite . orbital theory was also able to predict - at the right distance from the center - the loops of the near - infrared isophotes ( see the case of ngc 4314 in patsis , athanassoula & quillen 1997 ) . yet not all important morphological features have been so far explained with the help of periodic orbits . thus orbital theory has difficulties to explain the boxy isophotes surrounding the bars of , mainly , early - type barred galaxies ( athanassoula 1996 , patsis et al . another point still under discussion is the morphology of the peanut - shaped bulges observed in edge - on disc galaxies . they are considered by many authors as revealing the presence of a bar , and to be associated with the 2:1 vertical resonance . it is not clear , however , which families can make this vertical structure . could a bar without a vertical 2:1 resonance be boxy or peanut - shaped when viewed edge - on ? could we have stellar rings out of the equatorial plane at the ilr region ? furthermore , the detailed dynamics of the corotation region and the differences in the vertical structure between fast and slow bars remain open issues .    in this series of papers we use orbital theory to address the above questions . this is a first step towards understanding both the orbital behavior in @xmath3-body models and the responses of gaseous discs to potentials derived from near - infrared observations . the differences between our model and the well studied corresponding 2d case of the ferrers bar @xcite reflect the changes due to the inclusion of the third dimension . in separate papers we address the question of the morphology of the peanut shaped - bulges ( patsis , skokos & athanassoula , 2002a - paper iii ) and of the boxy isophotes of bars seen face - on ( patsis , skokos & athanassoula , 2002b - paper iv ) . our first goal is to make a thorough study of the orbital structure in 3d barred potentials , to classify the important families , and to follow their morphological evolution as a function of the jacobi integral . we start with a fiducial case . many of the families we find in this model have been previously mentioned ( e.g heisler , merritt & schwarzschild 1982 ; pfenniger 1984 , 1985b ; martinet & de zeeuw 1988 ; hasan , pfenniger & norman 1993 ) . however , other , equally important families , have not yet been studied . studying the orbital stability in a hamiltonian system approximating the dynamics of a barred galaxy we get the periodic orbits that could be used as building blocks for a density model . the general rule is to look for stable periodic orbits , since they trap around them the regular orbits . _ not all _ of them , however , are equally important . the isodensities of the model we use show us the topological limits within which we should look for the significant orbits . stable representatives of families of periodic orbits which do not support the imposed morphology , i.e. that of a bar embedded in an axisymmetric disc with a central bulge , should be considered as less important . as an example , in 2d models , let us mention the case of the retrograde family x4 , which is stable over a very large interval of energies ( athanassoula et al . 1983 ) . this family , however , should get a minimum weight when one tries to construct a self consistent model using a schwarzschild ( 1979 ) or a contopoulos & grosbl ( 1988 ) method . in a model of a 3d disc galaxy , besides the counter - rotating x4 family on the equatorial plane , one has to filter out also stable orbits with large @xmath4 , i.e. orbits with large mean vertical deviations , since these orbits do not contribute much to the density of the barred galaxy .    this paper is organized as follows : in section 2 we review briefly the parts of orbital theory that are necessary for understanding this paper . in particular we explain the use of characteristic and stability diagrams in following the dynamical evolution of a family of periodic orbits . we describe also the various types of instabilities encountered in 3d hamiltonian systems and we introduce the nomenclature of the main families . the latter is necessary since a number of the families presented here have not been previously discussed and thus need to be incorporated in a unique nomenclature scheme . in section 3 we introduce our 3d model and the orbital structure in a 2d counterpart . in section 4 we present the main families x1 , x2 and x3 and their bifurcations . in section 5 we describe the orbits around l@xmath5 ( or l@xmath6 ) and around l@xmath7 ( or l@xmath8 ) , as well as families outside corotation . we conclude in section 6 .","summary":"in this series of papers we investigate the orbital structure of 3d models representing barred galaxies . in the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three - dimensional bars . we show that , in a 3d bar , the backbone of the orbital structure is not just the x1 family , as in 2d models , but a tree of 2d and 3d families bifurcating from x1 . besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance . the families of this group bifurcate from x1 and influence the dynamics of the system only locally .","abstract":"in this series of papers we investigate the orbital structure of 3d models representing barred galaxies . in the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three - dimensional bars . we show that , in a 3d bar , the backbone of the orbital structure is not just the x1 family , as in 2d models , but a tree of 2d and 3d families bifurcating from x1 . besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance . the families of this group bifurcate from x1 and influence the dynamics of the system only locally . we also find that 3d orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family . they can support 3d bar - like structures along the minor axis of the main bar . banana - like orbits around the stable lagrangian points build a forest of 2d and 3d families as well . the importance of the 3d x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in or in .     wasyfont    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    galaxies : evolution  kinematics and dynamics  structure"}
{"article_id":"astro-ph0204077","section_id":"i","document":"in this section we will briefly review some parts of orbital theory which are necessary for the understanding of this paper . a clear , easily readable introduction to the subject has been given by sellwood & wilkinson ( 1993 ) . we also refer the reader to the pioneering works of pfenniger ( 1984 , 1985b ) and contopoulos & magnenat ( 1985 ) . we study the stability of simple - periodic orbits in a barred potential in cartesian coordinates . the 3d bar is rotating around its short @xmath0 axis . the @xmath9 axis is the intermediate and the @xmath10 axis the long one . the system is rotating with an angular speed @xmath11 and the hamiltonian governing the motion of a test - particle can be written in the form :    @xmath12    where @xmath13 and @xmath14 are the canonically conjugate momenta . we will hereafter denote the numerical value of the hamiltonian by @xmath15 and refer to it as the jacobi constant or , more loosely , as the ` energy ' . the corresponding equations of motion are : @xmath16    the space of section in the case of a 3d system is 4d . the equations of motion are solved for a given value of the hamiltonian , starting with initial conditions @xmath17 in the plane @xmath10=0 , for @xmath18 . the next intersection with the @xmath10=0 plane with @xmath18 is found and the exact initial conditions for the periodic orbit are calculated using a newton iterative method . a periodic orbit is found when the initial and final coordinates coincide with an accuracy at least 10@xmath19 . the integration scheme used was a fourth order runge - kutta scheme . the estimation of the linear stability of a periodic orbit is based on the theory of variational equations . we first consider small deviations from its initial conditions , and then integrate the orbit again to the next upward intersection . in this way a transformation @xmath20 is established , which relates the initial with the final point . the relation of the final deviations of this neighboring orbit from the periodic one , with the initially introduced deviations can be written in vector form as : @xmath21 . here @xmath22 is the final deviation , @xmath23 is the initial deviation and @xmath24 is a @xmath25 matrix , called the monodromy matrix . it can be shown that the characteristic equation is written in the form @xmath26 . its solutions @xmath27 obey the relations @xmath28 and @xmath29 and for each pair we can write : @xmath30,\\ ] ] where @xmath31 and @xmath32 . the quantities @xmath33 and @xmath34 are called the stability indices . if @xmath35 , @xmath36 and @xmath37 , the 4 eigenvalues are on the unit circle and the periodic orbit is called ` stable ' . if @xmath35 , and @xmath38 , @xmath37 , or @xmath39 , @xmath36 , two eigenvalues are on the real axis and two on the unit circle , and the periodic orbit is called ` simple unstable ' . if @xmath35 , @xmath38 , and @xmath39 , all four eigenvalues are on the real axis , and the periodic orbit is called ` double unstable ' . finally , @xmath40 means that all four eigenvalues are complex numbers but _ off _ the unit circle . the orbit is characterized then as ` complex unstable ' ( contopoulos & magnenat 1985 , heggie 1985 , pfenniger 1985a , b ) . we use the symbols @xmath41 to refer to @xmath42 , @xmath43 , @xmath44 and @xmath45 periodic orbits respectively . for a general discussion of the kinds of instability encountered in hamiltonian systems of n degrees of freedom the reader may refer to skokos ( 2001 ) . the method described above has been initially presented by broucke ( 1969 ) and hadjidemetriou ( 1975 ) , and has been used in studies of the stability of periodic orbits in systems of three degrees of freedom . the reader is referred to pfenniger ( 1984 ) and contopoulos & magnenat ( 1985 ) for an extended description . a diagram that describes the stability of a family of periodic orbits in a given potential when one of the parameters of the system varies ( e.g. the numerical value of the hamiltonian @xmath15 ) , while all other parameters remain constant , is called a ` stability diagram ' ( contopoulos & barbanis 1985 , contopoulos & magnenat 1985 ) . with the help of such a diagram one is able to follow the evolution of the stability indices @xmath33 and @xmath34 , and the transitions from stability to instability or from one to another kind of instability . we will loosely refer to the @xmath46 and @xmath47 lines on a stability diagram as the @xmath46 and @xmath47 axes . the su transitions , when one of the stability indices has an intersection with the @xmath47 axis , or tangencies of the stability curves with the @xmath47 axis , are of special importance for the dynamics of a system . in this case a new stable family is generated by bifurcation of the initial one and has the same multiplicity as the parent family . that means that the periodic orbits of the bifurcating family have , before closing , as many intersections with the plane @xmath10=0 , for @xmath18 , as the orbits of the parent family . the new family may play an important role in the dynamics of the system . s u transitions after an intersection of a stability curve with the @xmath46 axis , or tangencies of a stability curve with the @xmath46 axis , also generate a stable family but are accompanied by period doubling . this means that the number of intersections with the plane @xmath10=0 ( always with @xmath18 ) , needed for the periodic orbits to close , is double the corresponding number of the parent family . since the most important families we examine here are simple - periodic , i.e. of multiplicity 1 , intersections or tangencies of their stability indices with the @xmath46 axis introduce in the system families of orbits with multiplicity 2 . ud and dtransitions do not bring new stable families in the system and thus in principle are only of theoretical interest . as we will see , however , the evolution of a family which is found to be initially unstable may be very important for the dynamics of our model . the family could simply become stable in another energy interval , or it may play a major role in a collision of bifurcations , an inverse bifurcation or other dynamical phenomena @xcite . finally in the case swe have in general no bifurcating families of periodic orbits . another very useful diagram is the ` characteristic ' diagram @xcite . it gives the @xmath9 coordinate of the initial conditions of the periodic orbits of a family as a function of their jacobi constant @xmath15 . in the case of orbits lying on the equatorial plane and starting perpendicular to the @xmath9 axis , we need only one initial condition , @xmath9 , in order to specify a periodic orbit on the characteristic diagram . thus , for such orbits this diagram gives the complete information about the interrelations of the initial conditions in a tree of families of periodic orbits and their bifurcations . however , even for orbits completely on the equatorial plane , but not starting perpendicular to the @xmath9 axis we need to give initial conditions as position  velocity pairs @xmath48 and the characteristic diagram is three - dimensional @xmath49 . in the general case of orbits in a 3d system , one has a set of four initial conditions and the characteristic diagram is five - dimensional . the representation of such a diagram is difficult , but when necessary we will give just the @xmath50 projection . @xmath50 diagrams that can be compared with the corresponding 2d models will always be given . in all characteristic diagrams the region to which the orbits are confined is bounded by a curve known as the zero velocity curve ( zvc ) , since the velocity on it becomes zero . our orbital study is more extended than previous ones and thus brings in new families of orbits which have not been studied so far . we were thus brought to introduce a new nomenclature system , extension of the contopoulos & grosbl ( 1989 ) system , which covers all the new types of orbits .    for the main 2d families of simple periodic orbits the nomenclature in the present paper follows the standard notation of contopoulos & grosbl ( 1989 ) . we thus have the x1 family , where orbits are elongated along the bar and which is the main family in the case of barred potentials , families x2 and x3 , whose orbits are elongated perpendicular to the bar , and the retrograde family x4 . 2d families bifurcated from x1 at the 3:1 resonance region on the equatorial plane are denoted by t1 , t2 , ... , for consistency with the names used in patsis et al . 2d families bifurcated at the 4:1 resonance region on the equatorial plane are called q1 , q2 , q3 , .... planar orbits related with the 1:1 radial resonance will be called o1 , o2 .... they are encountered only in some models . the fiducial case presented in the present paper is not one of them . further planar families appear beyond the x1 family , at the gaps of the even resonances 4:1 , 6:1 , 8:1 etc . they are given the names ` f ' , ` s ' , ` e ' ... respectively . these families , not directly related to the morphological problems we address in this series , will be discussed elsewhere . we name the 3d families bifurcated from the basic family x1 at the vertical resonances as x1v@xmath51 , where @xmath51 denotes the order of their appearance in our fiducial model a ( see below section 4 ) . this is a convenient model to be used for our nomenclature , since there are families of 3d orbits associated with _ all _ basic vertical resonances . so x1v1 is the one bifurcated at the first su transition , which happens at the vertical 2:1 resonance region , x1v2 is the one bifurcated at the us transition ( second stability transition of the model also at the vertical 2:1 resonance region ) , x1v3 is the one bifurcated at the su transition at the vertical 3:1 resonance and so on . further bifurcations of these x1v@xmath51 families are indicated with an ` .@xmath51 ' ( for the @xmath51-th bifurcation ) attached to the name of the parent family ; i.e. the first bifurcation of x1v1 will be x1v1.1 , the second x1v1.2 , etc . further bifurcations of these families will be indicated by further ` .@xmath51 ' attached to the name of the parent family . thus x1v1.1.1 is the first bifurcation of x1v1.1 . the naming system is thus extendable at will . in general at each vertical resonance we have two bifurcating families introduced in the system . the number of oscillations along the rotation axis @xmath0 corresponds to the vertical resonance at which the family is born . e.g. families x1v1 and x1v2 , which are bifurcated at the vertical 2:1 resonance region , have orbits with two oscillations along the @xmath0 axis . this determines only partially their morphology , since the bifurcating family can be introduced either in the @xmath0 or the @xmath1 coordinate of the initial conditions . if we know the number of oscillations of a family along each axis and also whether it is a bifurcation in @xmath0 or @xmath1 , then we know its morphology . families with similar morphology are similar in their corresponding @xmath52 , @xmath53 and @xmath54 projections . in the fiducial case , where each vertical resonance is associated with two bifurcating families , the families x1v(2*n*-3 ) and x1v(2*n*-2 ) are born at the * n*:1 resonance . we note , however , that the first vertical bifurcation is not in every model the x1v1 family , as in the fiducial case . in other models ( skokos , patsis & athanassoula , 2002 - paper ii ) it can happen that the first 3d bifurcation of x1 is not related with the 2:1 vertical resonance , but with a different one . in such a model the first vertical bifurcation of x1 will have the same name as the family of the fiducial model which has similar morphology . equivalently , it will have the same name as the family of the fiducial model which is introduced in the same n:1 resonance and in the same ( @xmath0 or @xmath1 ) coordinate . this way we make sure that families with similar morphologies share the same name in the various models . in addition , if for some reason we have more than one vertical bifurcation of x1 associated with a vertical resonance , we introduce appropriate primes in our nomenclature . e.g. in a model with two vertical 4:1 resonances we will have the pairs of bifurcating families x1v5 , x1v6 and x1v5@xmath55 , x1v6@xmath55 . by keeping the basic name of the family similar for all families associated with the same vertical resonance , we underline again the dependence of the name on the encountered morphology . nevertheless , the basic names are given in the fiducial model , which thus becomes a reference case for all our work . we use the same nomenclature not only for the bifurcations of the basic family x1 , but in general for the vertical bifurcations of every 2d family . their name consists of the name of the parent family , followed by ` v@xmath51 ' , where @xmath51 indicates its @xmath51-th vertical bifurcation . also the names of the bifurcations of the bifurcating families are characterized by the addition of ` .1 ' , ` .2'@xmath56 etc . at the end of the name of the 3d family , as described above for the corresponding families associated with x1 . we will use the same system in order to name also radially bifurcating families . in general a radial bifurcation will be named as ` wr@xmath51 ' , where ` w ' the name of the parent family . e.g. the @xmath51-th radial bifurcation of family f will be ` fr@xmath51 ' ( fr1 , fr2 ... etc . ) . let us now turn to orbits related with the axis of rotation . the family on the axis of rotation is called ` z - axis ' family @xcite . its two first bifurcations are introduced at the first su transition and the first us transition respectively and they are the ` sao ' and ` uao ' orbits of heisler , merritt & schwarzschild ( 1982 ) . this nomenclature , however , does not lend itself to extension which can include what poincar ( 1899 ) called the ` deuxime genre ' families ( cf . polymilis , servizi & skokos , 1997 ) which can play an important role in some ferrers bars ( paper ii ) , so we will not adopt it here for other families related with the z - axis orbits . _ in practice _ ` deuxime genre ' orbits are found on the stability diagrams as bifurcations of the parent family when this family is considered as being of higher multiplicity , i.e. if its orbits are repeated many times . thus , the z - axis family , when its orbits are repeated twice , is called z2 . bifurcations of the z2 family are called z2.1 , z2.2 etc . the same rule applies for the bifurcations of z3 , i.e. for the bifurcations of z - axis if this is described three times . we then have z3.1 , z3.2 and so on . these bifurcating families always come in pairs . a further index ( s or u ) is attached to their names and is related with their stability .    around the lagrangian points @xmath57 we have the long period banana - like orbits , which form a tree of families , and the short period orbits . for the latter we keep the contopoulos & grosbl ( 1989 ) notation ( spo ) . for the banana - like orbits we use the notation ban1 , ban2, ... ban@xmath51 in the 2d cases . their 2d bifurcations are the families ban@xmath51.1 , ban@xmath51.2 , ... etc . and their 3d bifurcations the families ban@xmath51v1 , ban@xmath51v2 , ... etc . 3d banana - like orbits not related with a 2d one are named banv@xmath51 . a 2d family found around the unstable lagrangian points @xmath58 is called @xmath59 .    throughout the papers we give also the names used by other authors for families that have been previously studied . however , since our study is more extended , there are several families mentioned for the first time .","summary":" wasyfont    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    galaxies : evolution  kinematics and dynamics  structure","abstract":"in this series of papers we investigate the orbital structure of 3d models representing barred galaxies . in the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three - dimensional bars . we show that , in a 3d bar , the backbone of the orbital structure is not just the x1 family , as in 2d models , but a tree of 2d and 3d families bifurcating from x1 . besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance . the families of this group bifurcate from x1 and influence the dynamics of the system only locally . we also find that 3d orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family . they can support 3d bar - like structures along the minor axis of the main bar . banana - like orbits around the stable lagrangian points build a forest of 2d and 3d families as well . the importance of the 3d x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in or in .     wasyfont    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    galaxies : evolution  kinematics and dynamics  structure"}
{"article_id":"astro-ph0204077","section_id":"c","document":"in this paper we have made an extensive study of both the 2d and 3d periodic orbits in a fiducial model representative of a barred galaxy . we report on the stability and morphology of the main families . our main conclusions are :    1 . so far the x1 orbits were considered the backbone of bars . this , however , can only be the case for 2d bars , since the x1 can only populate the @xmath0=0 plane . for 3d bars the backbone is the x1 , together with the tree of its 3d bifurcating families . trapping around these families will determine the thickness and the vertical shape of galaxies in and around the bar region . major building blocks for the 3d bars can be supplied also by families initially introduced as unstable . thus the family x1v4 , introduced in the system after a us transition , is a basic family , giving stable representatives for large energy intervals in the system . 2 .   the @xmath52 projections of the 3d families of the x1-tree retain in general a morphological similarity with their parent family at the same energy . this has important implications for the morphology of a galaxy since it introduces building blocks which have similar morphology as the x1 orbits , but have a considerable vertical extensions . especially at the regions close to the bifurcating points the @xmath52 morphology of a x1v@xmath51 family is not only geometrically similar , but actually very close to the morphology of the corresponding x1 orbit . 3 .   the way the 3d families of the x1-tree are introduced in the system at an instability strip determines the importance of the bifurcations in @xmath0 or @xmath1 . particularly in the present model , all 3d families of the x1-tree at the increasing part of the characteristic which are bifurcated in @xmath0 are introduced in the system as stable . on the other hand the stable family associated with the 5:1 vertical resonance ( x1v7 ) , bifurcated at the decreasing part of the x1 characteristic , beyond its local maximum , is bifurcated in @xmath1 . whether the stable family of the last sus transition is the bifurcation in @xmath0 or @xmath1 determines in a large degree the model s morphology at its outer parts . the radial 3:1 resonance region provides in the system several 2d and 3d stable families . their role , however , is locally confined , as in 2d models . 3d orbits elongated along the minor axis of the bar can be given by bifurcations of the planar x2 family . we have found several families of 3d banana - like orbits around l@xmath133 . their extent is always restricted by a s transition . stable families found beyond corotation circulate material between the outer parts of the system and regions as far inwards as 1  kpc . this contributes to the mixing of the elements in a disc galaxy . the families of periodic orbits we described up to now are indeed the basic families of a 3d ferrers bar . as we explore the parameter space , however , their properties change , while new important families may appear and play a crucial role . a notable example is z3.1s , a family related to the z - axis orbits along the rotational axis , which will be described in paper ii . however , these are rather particular cases and are not encountered in every model . athanassoula e. , 1984 phys . 114 , 319    athanassoula e. , 1992a , mnras 259 , 328    athanassoula e. , 1992b , mnras 259 , 354    athanassoula e. , 1996 , in ` spiral galaxies in the near - ir ' , d. minniti & h .- w . rix ( eds . ) , p. 147 , springer    athanassoula e. , bienayme o. , martinet l. , pfenniger d. , 1983 , a&a 127 , 349    binney j. , tremaine s. , 1987 , ` galactic dynamics ' , princeton university press , princeton , n.j . broucke r. , 1969 , nasa techn . 32 , 1360    combes f. , debbasch f. , friedli d. , pfenniger d. , 1990 , a&a 233 , 95    contopoulos g. , 1980 , a&a 81 , 198    contopoulos g. , 1985 , in ` chaos in astrophysics ' , j.r . buchler et al ( eds . ) , p. 259 , reidel    contopoulos g. , 1986 , celest . 38 , 1    contopoulos g. , barbanis b. , 1985 , a&a 153 , 44    contopoulos g. , grosbl p. , 1988 , a&a 197,83    contopoulos g. , grosbl p. , 1989 , a&ar , 1,261    contopoulos g. , magnenat p. , 1985 37 , 387    contopoulos g. , mertzanides c. , 1977 , a&a 61 , 477    hadjidemetriou j. , 1975 , celest 12 , 255    hasan h. , pfenniger d. , norman c. , 1993 , apj 409 , 91    heggie d.c . , 1985 , celest . 35 , 357    heisler j. , merritt d. , schwarzschild m. , 1982 , apj 258 , 490    kormendy j. , 1982 , in ` morphology and dynamics of galaxies ' , l. martinet and m. mayor eds . , 12th advanced course , saas - fee , p. 113 , geneva obs . , sauverny    martinet l. , pfenniger d. , 1987 , a&a 173 , 81 martinet l. , de zeeuw t. , 1988 , a&a 206 , 269    miller r.h . , smith b.f . , 1979 , apj 1979 , 227 , 785    miyamoto m. , nagai r. , 1975 , pasj 27 , 533    olle m. , pfenniger d. , 1998 a&a 334 , 829    patsis p.a . , athanassoula e. , quillen a.c . , 1997 , apj 483 , 731    patsis p.a . , grosbl p. , 1996 , a&a 315 , 371    patsis p.a . , skokos ch . , athanassoula e. , 2002 ( _ paper iii - in preparation _ )    patsis p.a . , skokos ch . , athanassoula e. , 2002 ( _ paper iv - in preparation _ )    pfenniger d. , 1984 , a&a 134 , 373    pfenniger d. , 1985a , a&a 150 , 97    pfenniger d. , 1985b , a&a 150 , 112    pfenniger d. , 1987 , a&a 180 , 79    pfenniger d. , 1990 , a&a 230 , 55    pfenniger d. , 1996 , in ` barred galaxies ' , ed . r. buta , d. a. crocker and b. g. elmegreen , asp conf . 91 , p.273    poincar h , 1899 , ` les methodes nouvelles de la mechanique celeste ' , vol iii , gauthier - villars , paris    polymilis c. , servizi g. , skokos ch . , 1997 , 66 , 365    sellwood j. , wilkinson a. , 1993 , rep . 56 , 173    schwarzschild m. , 1979 , apj 232,236    skokos ch . , 2001 , physica d 159 , 155    skokos ch . , patsis p.a . , athanassoula e. , 2002 mnras - this issue","summary":"we also find that 3d orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family . the importance of the 3d x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in or in .   ","abstract":"in this series of papers we investigate the orbital structure of 3d models representing barred galaxies . in the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three - dimensional bars . we show that , in a 3d bar , the backbone of the orbital structure is not just the x1 family , as in 2d models , but a tree of 2d and 3d families bifurcating from x1 . besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance . the families of this group bifurcate from x1 and influence the dynamics of the system only locally . we also find that 3d orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family . they can support 3d bar - like structures along the minor axis of the main bar . banana - like orbits around the stable lagrangian points build a forest of 2d and 3d families as well . the importance of the 3d x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in or in .     wasyfont    = = = = = = = =    # 1 # 1 # 1 # 1 @mathgroup@group @mathgroup@normal@groupeurmn @mathgroup@bold@groupeurbn @mathgroup@group @mathgroup@normal@groupmsamn @mathgroup@bold@groupmsamn = `` 019 = ' ' 016 = `` 040 = ' ' 336 = \" 33e = = = = = = = =    # 1 # 1 # 1 # 1 = = = = = = = =    [ firstpage ]    galaxies : evolution  kinematics and dynamics  structure"}
{"article_id":"0908.0353","section_id":"i","document":"third - generation gravitational wave detectors are envisaged to be observatories providing a continuous stream of astrophysical meaningful data . in order to achieve this goal these detectors need to be designed and planned to be robust machines with a sensitivity ten times better than the advanced detectors currently under construction . in this article we have discussed how these goals affect the design of the core instrument , in other words the optical layout of the laser interferometer(s ) of the detector . from the nature of the gravitational radiation follows that long - baseline , l - shaped interferometers represent the ideal instruments . in order to maximise the data quality of a single detector or of a detector integrated in a network , we found that the use of co - located interferometers are essential . a triangular geometry of three co - located interferometers is currently under investigation within the einstein telescope design study . further constraints of the interferometer topology and configuration are not obvious from general principles but are expected to follow from the technical detailed of optical schemes for reducing the quantum noise and the thermal noise in the detectors . we have reviewed the preliminary design work on the einstein telescope and showed that the envisaged sensitivity can possibly be reached by an moderately optimistic scaling of current technologies . in particular , we have reviewed the noise contributions in a potential et detector and have shown that a design featuring several small - band interferometers might be superior over a single broadband design . in addition , several new , advanced techniques can be used to provide a margin for further sensitivity improvements . we have presented several such techniques , concentrating mainly on those whose technical readiness is sufficient for a potential integration in future large scale projects over the next decade . several research programs within the world - wide gravitational wave collaborations are dedicated to the experimental realisation and testing of advanced techniques for third - generation detectors . we thus expect that we will be able to significantly beat the sensitivity of the advanced detectors which are currently under construction . this is an exciting outlook for the time when said advanced detectors have made the first detections of gravitational waves and increasing the signal to noise ratio would enable us to tap the full potential of the new field of gravitational wave astronomy .","summary":"the third generation of gravitational wave observatories , aiming to provide 100 times better sensitivity than currently operating interferometers , is expected to establish the evolving field of gravitational wave astronomy . a key element for achieving the ambitious sensitivity goal","abstract":"the third generation of gravitational wave observatories , aiming to provide 100 times better sensitivity than currently operating interferometers , is expected to establish the evolving field of gravitational wave astronomy . a key element for achieving the ambitious sensitivity goal is the exploration of new interferometer geometries , topologies and configurations . in this article we review the current status of the ongoing design work for third - generation gravitational wave observatories . the main focus is set on the evaluation of the detector geometry and detector topology . in addition we discuss some promising detector configurations and potential noise reduction schemes ."}
{"article_id":"1405.5349","section_id":"i","document":"a frequently used method for edge - preserving image denoising is the variational approach which minimizes the rudin - osher - fatemi ( rof ) functional  @xcite . in a discrete ( penalized ) form the rof functional can be written as @xmath2 where @xmath3 is the given corrupted image and @xmath4 denotes the discrete gradient operator which contains usually first order forward differences in vertical and horizontal directions . the regularizing term @xmath5 can be considered as discrete version of the total variation ( tv ) functional . since the gradient does not penalize constant areas the minimizer of the rof functional tends to have such regions , an effect known as staircasing . an approach to avoid this effect consists in the employment of higher order differences / derivatives . since the pioneering work  @xcite which couples the tv term with higher order terms by infimal convolution various techniques with higher order differences / derivatives were proposed in the literature , among them  @xcite .    in various applications in image processing and computer vision the functions of interest take values on the circle @xmath0 or another manifold . processing manifold - valued data has gained a lot of interest in recent years . examples are wavelet - type multiscale transforms for manifold data   @xcite and manifold - valued partial differential equations   @xcite . finally we like to mention statistical issues on riemannian manifolds  @xcite and in particular the statistics of circular data  @xcite . the tv notation for functions with values on a manifold has been studied in  @xcite using the theory of cartesian currents . these papers were an extension of the previous work  @xcite were the authors focus on @xmath0-valued functions and show in particular the existence of minimizers of certain energies in the space of functions with bounded total cyclic variation . the first work which applies a cyclic tv approach among other models for imaging tasks was recently published by cremers and strekalovskiy in  @xcite . the authors unwrapped the function values to the real axis and proposed an algorithmic solution to account for the periodicity . an algorithm which solves tv regularized minimization problems on riemannian manifolds was proposed by lellmann et al . in they reformulate the problem as a multilabel optimization problem with an infinite number of labels and approximate the resulting hard optimization problem using convex relaxation techniques . the algorithm was applied for chromaticity - brightness denoising , denoising of rotation data and processing of normal fields for visualization . another approach to tv minimization for manifold - valued data via cyclic and parallel proximal point algorithms was proposed by one of the authors and his colleagues in  @xcite . it does not require any labeling or relaxation techniques . the authors apply their algorithm in particular for diffusion tensor imaging and interferometric sar imaging . for cartan - hadamard manifolds convergence of the algorithm was shown based on a recent result of bak  @xcite . unfortunately , one of the simplest manifolds that is not of cartan - hadamard type is the circle  @xmath0 .    in this paper we deal with the incorporation of higher order differences into the energy functionals to improve denoising results for @xmath0-valued data . note that the ( second - order ) total generalized variation was generalized for tensor fields in  @xcite . however , to the best of our knowledge this is the first paper which defines second order differences of cyclic data and uses them in regularization terms of energy functionals for image restoration . we focus on a discrete setting . first we provide a meaningful definition of higher order differences for cyclic data which we call _ absolute cyclic differences_. in particular our absolute cyclic first order differences resemble the geodesic distance ( arc length distance ) on the circle . as the geodesics the absolute cyclic second order differences take only values in @xmath1 $ ] . this is not necessary the case for differences of order larger than two . following the idea in  @xcite we suggest a cyclic proximal point algorithm to minimize the resulting functionals . this algorithm requires the evaluation of certain proximal mappings . we provide analytical expression for these mappings . further , we suggest an appropriate choice of the cycles such that the whole algorithm becomes very efficient . we apply our algorithm to artificial data as well as to real - world interferometric sar data . the paper is organized as follows : in section  [ sec : diff ] we propose a definition of differences on @xmath0 . then , in section  [ sec : prox ] , we provide analytical expressions for the proximal mappings required in our cyclic proximal point algorithm . the approach is based on unwrapping the circle to  @xmath6 and considering the corresponding proximal mappings on the euclidean space . the cyclic proximal point algorithm is presented in section  [ sec : cpp ] . in particular we describe a vectorization strategy which makes the matlab implementation efficient and provides parallelizability , and prove its convergence under certain assumptions . section  [ sec : numerics ] demonstrates the advantageous performance of our algorithm by numerical examples . finally , conclusions and directions of future work are given in section  [ sec : conclusions ] .","summary":"in many image and signal processing applications , as interferometric synthetic aperture radar ( sar ) or color image restoration in hsv or lch spaces the data has its range on the one - dimensional sphere . this effect can be avoided by involving higher order derivatives into the functional .    this is the first paper which uses higher order differences of cyclic data in regularization terms of energy functionals for image restoration . we introduce absolute higher order differences for-valued data in a sound way which is independent of the chosen representation system on the circle . our absolute cyclic first order difference is just the geodesic distance between points . similar to the geodesic distances the absolute cyclic second order differences have only values in $ ] . we update the cyclic variational tv approach by our new cyclic second order differences . to minimize the corresponding functional we apply a cyclic proximal point method which was recently successfully proposed for hadamard manifolds . choosing appropriate cycles various numerical examples with artificial as well as real - world data demonstrate the advantageous performance of our algorithm .","abstract":"in many image and signal processing applications , as interferometric synthetic aperture radar ( sar ) or color image restoration in hsv or lch spaces the data has its range on the one - dimensional sphere . although the minimization of total variation ( tv ) regularized functionals is among the most popular methods for edge - preserving image restoration such methods were only very recently applied to cyclic structures . however , as for euclidean data , tv regularized variational methods suffer from the so called staircasing effect . this effect can be avoided by involving higher order derivatives into the functional .    this is the first paper which uses higher order differences of cyclic data in regularization terms of energy functionals for image restoration . we introduce absolute higher order differences for-valued data in a sound way which is independent of the chosen representation system on the circle . our absolute cyclic first order difference is just the geodesic distance between points . similar to the geodesic distances the absolute cyclic second order differences have only values in $ ] . we update the cyclic variational tv approach by our new cyclic second order differences . to minimize the corresponding functional we apply a cyclic proximal point method which was recently successfully proposed for hadamard manifolds . choosing appropriate cycles this algorithm can be implemented in an efficient way . the main steps require the evaluation of proximal mappings of our cyclic differences for which we provide analytical expressions . under certain conditions we prove the convergence of our algorithm . various numerical examples with artificial as well as real - world data demonstrate the advantageous performance of our algorithm ."}
{"article_id":"1405.5349","section_id":"m","document":"the proximal point algorithm ( ppa ) on the euclidean space goes back to  @xcite . recently this algorithm was extended to riemannian manifolds of non - positive sectional curvature  @xcite and also to hadamard spaces  @xcite . a cyclic version of the proximal point algorithm ( cppa ) on the euclidean space was given in  @xcite , see also the survey  @xcite . a cppa for hadamard spaces can be found in  @xcite . in the cppa the original function @xmath316 is split into a sum @xmath317 and , iteratively , the proximal mappings of the functions @xmath318 are applied in a cyclic way . the great advantage of this method is that often the proximal mappings of the summands @xmath318 are much easier to compute or can even be given in a closed form . in the following we develop a cppa for functionals of @xmath0-valued signals and images containing absolute cyclic first and second order differences . first we have a look at the one - dimensional case , i.e. , at signals . for given @xmath0-valued signals represented by @xmath319 , @xmath320 , and regularization parameters @xmath321 , @xmath322 , we are interested in @xmath323 where @xmath324 to apply a cppa we set @xmath325 , split @xmath326 into an even and an odd part @xmath327 and @xmath328 into three sums @xmath329 then the objective function decomposes as @xmath330 we compute in the @xmath331-th cycle of the cppa the signal @xmath332 the different proximal values can be obtained as follows :    1 .   by proposition  [ theo : prox_quad ] with @xmath333 playing the role of @xmath334 we get @xmath335 2 .   for @xmath336 , we obtain the vectors @xmath337 by applying theorem  [ lem : proxy_b1 ] with @xmath246 independently for the pairs @xmath338 , @xmath339 . 3 .   for @xmath340 , we compute @xmath341 by applying theorem  [ lem : proxy_b1 ] with @xmath342 independently for the vectors @xmath343 , @xmath344 . the parameter sequence @xmath345 of the algorithm should fulfill @xmath346 this property is also essential for proving the convergence of the cppa for real - valued data and data on a hadamard manifold , see  @xcite . in our numerical experiments we choose @xmath347 with some initial parameter @xmath348 which clearly fulfill  . the whole procedure is summarized in algorithm  [ alg : cppa ] . * input * @xmath349 fulfilling   and @xmath350 , @xmath351 or @xmath352 , @xmath353 , @xmath354 data @xmath355 or @xmath356 + initialize @xmath357 , @xmath306 initialize the cycle length as @xmath358 ( 1d ) or @xmath359 ( 2d ) @xmath360 @xmath361 a convergence criterion are reached @xmath362      next we consider two - dimensional data , i.e. , images of the form  @xmath363 , @xmath364 . our functional includes _ _ h__orizontal and _ _ v__ertical cyclic first and second order differences @xmath365 and @xmath110 and _ _ d__iagonal ( mixed ) differences @xmath120 . for non - negative regularization parameters @xmath366 , @xmath367 and @xmath354 not all equal to zero we are looking for @xmath368 where @xmath369 here the objective function splits as @xmath370 with the following summands : again we set @xmath371 and compute the proximal value of @xmath372 by proposition  [ theo : prox_quad ] . each of the sums in @xmath373 and  @xmath374 can be split analogously as in the one - dimensional case , where we have to consider row and column vectors now . this results in @xmath375 functions @xmath376 whose proximal values can be computed by theorem  [ lem : proxy_b1 ] . finally , we split @xmath377 . into the four sums @xmath378 and denote the inner sums by @xmath379 . clearly , the proximal values of the functions @xmath380 , @xmath381 can be computed separately for the vectors @xmath382 by theorem  [ lem : proxy_b1 ] with @xmath383 . in summary , the computation can be done by algorithm  [ alg : cppa ] . note that the presented approach immediately generalizes to arbitrary dimensions . since @xmath0 is not a hadamard space , the convergence analysis of the cppa in  @xcite can not be applied . we show the convergence of the cppa for the 2d @xmath0-valued function   under certain conditions . the 1d setting in   can then be considered as a special case . in the following , let @xmath384 . our first condition is that the data @xmath385 is dense enough , this means that the distance between neighboring pixels @xmath386 is sufficiently small . similar conditions also appear in the convergence analysis of nonlinear subdivision schemes for manifold - valued data in  @xcite . in the context of nonlinear subdivision schemes , even more severe restrictions such as ` almost equally spaced data ' are frequently required  @xcite . this imposes additional conditions on the second order differences to make the data almost lie on a ` line ' . our analysis requires only bounds on the first , but not on the second order differences . our next requirement is that the regularization parameters  @xmath387 in   are sufficiently small . for large parameters any solution tends to become almost constant . in this case , if the data is for example equidistantly distributed on the circle , e.g. , @xmath388 in 1d , any  @xmath389 shift is again a solution . in this situation the model loses its interpretation which is an inherent problem due to the cyclic structure of the data .    finally , the parameter sequence @xmath345 of the cppa has to fulfill   with a small @xmath390 norm . the later can be achieved by rescaling . our convergence analysis is based on a convergence result in  @xcite and an unwrapping procedure . we start by reformulating the convergence result for the cppa of real - valued data , which is a special case of  @xcite and can also be derived from  @xcite . [ thm : bacak ] let @xmath391 , where @xmath392 , @xmath393 , are proper , closed , convex functionals on @xmath394 . let @xmath183 have a global minimizer . assume that there exists @xmath395 such that the iterates @xmath396 of the cppa ( see algorithm  [ alg : cppa ] ) satisfy @xmath397 for all @xmath398 . then the sequence @xmath399 converges to a minimizer of @xmath183 . moreover the iterates fulfill @xmath400          + 2 \\lambda_k^2 l^2 c(c+1 ) \\quad \\mbox{for all } \\ ; x \\in \\mathbb r^{n \\times m}.\\label{noch_1 }          \\end{aligned}\\ ] ]    the next lemma states a discrete analogue of a well - known result on unwrapping or lifting from algebraic topology . we supply a short proof since we did not found it in the literature . [ lem : discretecovering ] let @xmath401 with @xmath402 . for @xmath9 not antipodal to @xmath403 fix an  @xmath404 such that  @xmath405 . then there exists a unique @xmath406 such that for all  @xmath407 the following relations are fulfilled :    1 . @xmath408 2 . @xmath409 . we call @xmath410 the lifted or unwrapped image of @xmath411 ( w.r.t .  a fixed @xmath412 ) . for  @xmath413 , @xmath414 , it holds by assumption on @xmath415 that  @xmath416 . hence we have @xmath417 , where with an abuse of notation @xmath413 stands for an arbitrary representative in @xmath418 of @xmath413 . then obviously @xmath419 , @xmath420 are the unique values satisfying i ) and ii ) .    for @xmath421 consider @xmath422 by assumption on @xmath415 we see that @xmath423 so that @xmath424 . thus @xmath425 is the unique value with properties i ) and ii ) . proceeding this scheme successively , we obtain the whole unique image @xmath426 fulfilling i ) and ii ) .    for @xmath427 we define @xmath428 where @xmath429 to measure how ` near ' the images @xmath191 and @xmath411 are to each other . [ lem : convlem2 ] let @xmath430 with  @xmath431 and @xmath9 be not antipodal to @xmath432 . fix @xmath433 with @xmath434 and let @xmath435 be the corresponding lifting of @xmath191 . let @xmath436 $ ] .    1 .   then every @xmath437 has a unique lifting  @xmath410 w.r.t . to the base point @xmath12 with @xmath438 . 2 .   for @xmath439 defined by  , let @xmath440 denote its analog for real - valued data , i.e. , @xmath441 where the cyclic distances in @xmath442 and in the  @xmath443 terms are replaced by absolute differences in @xmath444 and @xmath445 . then it holds @xmath446    by definition of @xmath447 and assumption on @xmath191 we have for any  @xmath437 that @xmath448 and hence @xmath449 . further it holds  @xmath450 . consequently , every @xmath437 has a unique lifting  @xmath410 by lemma  [ lem : discretecovering ] w.r.t .  to the base point @xmath12 fulfilling @xmath438 .    to see   we show the equality for the involved summands in  @xmath316 and  @xmath440 separately . first we consider @xmath373 . by properties of the lifting in lemma  [ lem : discretecovering ] we have @xmath451 and @xmath452 . by the definition of @xmath373 and  @xmath453 , this implies  @xmath454 . next we consider @xmath455 . the corresponding second order differences are given by the expressions  @xmath456 and  @xmath457 , respectively . we exemplarily consider the first term . since @xmath458 the distance between any two members of the triple is smaller than @xmath459 . due to the properties of the lifting  @xmath426 this implies @xmath460 . then we conclude by proposition  [ diff_sec ] that @xmath461 . similarly it follows that @xmath462 .    concerning the data term @xmath463 we consider @xmath464 and @xmath465 . by definition of @xmath447 we have @xmath466 and by construction of @xmath435 and @xmath426 that @xmath467 , @xmath468 and @xmath469 . furthermore it holds @xmath470 . if @xmath471 , then there exists @xmath472 such that @xmath473 which is a contradiction . thus @xmath474 . similarly we conclude @xmath475 . in summary we obtain @xmath476 for all @xmath477 which implies  @xmath478 . this finishes the proof . [ rem : conv ] the set @xmath447 is a convex subset of @xmath479 which means that for @xmath480 and @xmath481 $ ] we have @xmath482_t \\in { \\mathcal s}(f,\\delta)$ ] . here @xmath482_t$ ] denotes the point reached after time t on the unit speed geodesic starting at @xmath411 in direction of  @xmath483 . recall that a function @xmath484 is convex on @xmath447 if for all  @xmath480 and all @xmath485 $ ] the relation @xmath486_t ) \\le t\\varphi(x ) + ( 1-t ) \\varphi(y)$ ] holds true . let @xmath430 with  @xmath431 and  @xmath436 $ ] . then we conclude by lemma  [ lem : convlem2 ] , since @xmath440 is convex , that @xmath439 is convex on @xmath487 . [ lem : convlem1 ] let @xmath488 and @xmath489 . let @xmath490 such that @xmath491 then any minimizer  @xmath492 of @xmath316 in   fulfills @xmath493    any minimizer @xmath494 of   satisfies @xmath495 as a consequence we obtain @xmath496    [ rem : tildej ] lemma  [ lem : convlem1 ] holds also true for real - valued data and @xmath440 in  . now we combine lemma  [ lem : convlem1 ] and  [ lem : convlem2 ] to locate the minimizers of @xmath316 and @xmath440 . [ lem : convlem3 ] let @xmath497 with  @xmath498 and  @xmath499 be given . choose the parameters @xmath500 of @xmath316 in   such that   with @xmath501 holds true . then any minimizer @xmath492 of  @xmath316 lies in @xmath487 . furthermore , if @xmath502 is the unique lifting of @xmath191 w.r.t . a base point  @xmath12 and fixed @xmath503 with @xmath504 , then each minimizer  @xmath505 of  @xmath506 defines a minimizer @xmath507 of  @xmath316 . conversely , the uniquely defined lifting @xmath508 of a minimizer  @xmath492 of @xmath316 is a minimizer of @xmath506 .    by lemma  [ lem : convlem1 ] we obtain  @xmath509 so that @xmath510 .    in order to show the second statement note that the mapping  @xmath511 is a bijection from @xmath487 to the set @xmath512 defined by @xmath513.\\ ] ] if @xmath505 minimizes @xmath506 , then it lies in @xmath514 which follows by remark  [ rem : tildej ] . by   and the minimizing property of @xmath505 we obtain for any @xmath437 that @xmath515 as a consequence , @xmath516 is a minimizer of @xmath316 on @xmath447 . by lemma  [ lem : convlem1 ] all the minimizers of @xmath316 are contained in @xmath447 so that @xmath516 is a minimizer of @xmath316 on @xmath479 . we proceed with the last statement . let @xmath492 be a minimizer of @xmath316 with lifting @xmath508 . then we get for any  @xmath517 that @xmath518 this shows that @xmath508 is a minimizer of @xmath506 on @xmath514 . since by remark  [ rem : tildej ] all minimizers of @xmath506 lie in  @xmath514 , the last assertion follows . next we locate the iterates of the cppa for real - valued data on a ball whose radius can be controlled . [ lem : convlem4 ] for @xmath519 and @xmath520 with property  , let @xmath521 be the sequence produced by algorithm  [ alg : cppa ] for @xmath506 . assume that @xmath522 . let @xmath523 be the minimizer of @xmath506 . then , for @xmath524 and @xmath525 , it holds @xmath526 where @xmath359 denotes the number of inner iterations and @xmath527 . the assumption on the distances @xmath528 , @xmath407 , to be smaller than @xmath529 is automatically fulfilled for any unwrapping of @xmath0-valued data .    by theorem  [ thm : bacak ] we know that @xmath530          + 2 \\lambda_k^2 l^2 c(c+1).\\ ] ] as a constant @xmath531 we can choose the maximum of the lipschitz constants of the involved summands . for @xmath453 , @xmath532 and  @xmath533 the lipschitz constants are  @xmath534 , @xmath535 , and @xmath535 , respectively . for the quadratic data term we have @xmath536 therefore , we can set @xmath537 . plugging in the minimizer  @xmath538 into   and using @xmath357 yields @xmath539 by theorem  [ thm : bacak ] it holds @xmath540 using the triangle inequality we obtain @xmath541 which implies the assertion by   and  . now we compare the proximal mappings acting on data with values in  @xmath542 and @xmath543    [ lem : convlem5 ] for @xmath544 with  @xmath498 , let @xmath316 be defined by   with the splitting  . let @xmath502 be the unique lifting of @xmath191 w.r.t . a base point  @xmath12 not antipodal to @xmath432 and fixed @xmath503 with @xmath504 . further , denote by @xmath440 the functional   corresponding to @xmath316 . then , for any @xmath545 , @xmath546 $ ] and its lifting  @xmath426 w.r.t . @xmath12 , we have @xmath547 i.e. , the canonical projection @xmath548 commutes with the proximal mappings . the function @xmath549 is based on the distance to the data @xmath191 . since @xmath545 , we have @xmath550 for all @xmath407 . the components of the proximal mapping @xmath551 are given by proposition  [ theo : prox_quad ] from which we conclude   for @xmath552    the proximal mappings of @xmath318 , @xmath553 , are given via proximal mappings of the first and second order cyclic differences . we consider the first order difference @xmath554 . by the triangle inequality , we have  @xmath555 as well as  @xmath556 . by the explicit form of the proximal mapping in theorem  [ lem : proxy_b1 ] we obtain   for  @xmath318 , @xmath557 . next we consider the horizontal and vertical second order differences  @xmath456 and  @xmath457 . we have that  @xmath558 , @xmath559 as well as  @xmath560 . hence all contributing values of  @xmath411 lie on a quarter of the circle . applying the proximal mapping in theorem  [ lem : proxy_b1 ] the resulting data lie on one half of the circle . an analogous statement holds true for the horizontal part . hence the proximal mappings of the ordinary second differences agree with the cyclic version ( under identification via @xmath548 ) . this implies   for @xmath318 , @xmath561 . finally , we consider the mixed second order differences  @xmath562 . as above , we have for neighboring data items that the distance is smaller than  @xmath563 . for all four contributing values of @xmath411 we have that the pairwise distance is smaller by @xmath459 . thus again they lie on a quarter of the circle . hence , the proximal mapping for the ordinary mixed second differences agree with the cyclic version ( under identification via @xmath548 ) . this implies   for @xmath318 , @xmath381 . we note that lemma  [ lem : convlem5 ] does not guarantee that  @xmath564 remains in @xmath565 . therefore it does not allow for an iterated application . in the following main theorem we combine the preceding lemmas to establish this property . [ thm : convergence ] let @xmath544 with @xmath566 . let @xmath520 fulfill property   and @xmath567 for some @xmath490 , where @xmath568 and @xmath527 . further , assume that the parameters  @xmath500 of the functional @xmath316 in   and @xmath501 satisfy  . then the sequence @xmath399 generated by the cppa in algorithm  [ alg : cppa ] converges to a global minimizer of @xmath316 . let @xmath502 be the lifting of of @xmath191 with respect to a base point @xmath12 not antipodal to @xmath432 and fixed @xmath433 with @xmath504 . further , let @xmath440 denote the real analog of @xmath316 . by lemma  [ lem : convlem2 ] we have @xmath569 and @xmath570 for @xmath571 such that is also fulfilled for the real - valued setting . then we can apply remark  [ lem : convlem1 ] and conclude that the minimizer  @xmath505 of  @xmath506 fulfills @xmath572 . by we obtain @xmath573 by lemma  [ lem : convlem4 ] the iterates @xmath574 of the real - valued cppa fulfill @xmath575 hence  @xmath576 which means that all iterates @xmath574 stay within @xmath577 . next , we consider the sequence @xmath578 of the cppa for the @xmath0-valued data @xmath191 . we use induction to verify @xmath579 . by definition we have @xmath580 . assume that @xmath581 . by bijectivity of the lifting , cf . lemma  [ lem : convlem2 ] , and since @xmath582 , we conclude @xmath583 . by lemma  [ lem : convlem5 ] we obtain @xmath584 by the same argument as above we have again @xmath585 . finally , we know by theorem  [ thm : bacak ] that @xmath586 and by lemma  [ lem : convlem3 ] that @xmath587 is a global minimizer of @xmath316 . this completes the proof .","summary":"this algorithm can be implemented in an efficient way . the main steps require the evaluation of proximal mappings of our cyclic differences for which we provide analytical expressions . under certain conditions we prove the convergence of our algorithm .","abstract":"in many image and signal processing applications , as interferometric synthetic aperture radar ( sar ) or color image restoration in hsv or lch spaces the data has its range on the one - dimensional sphere . although the minimization of total variation ( tv ) regularized functionals is among the most popular methods for edge - preserving image restoration such methods were only very recently applied to cyclic structures . however , as for euclidean data , tv regularized variational methods suffer from the so called staircasing effect . this effect can be avoided by involving higher order derivatives into the functional .    this is the first paper which uses higher order differences of cyclic data in regularization terms of energy functionals for image restoration . we introduce absolute higher order differences for-valued data in a sound way which is independent of the chosen representation system on the circle . our absolute cyclic first order difference is just the geodesic distance between points . similar to the geodesic distances the absolute cyclic second order differences have only values in $ ] . we update the cyclic variational tv approach by our new cyclic second order differences . to minimize the corresponding functional we apply a cyclic proximal point method which was recently successfully proposed for hadamard manifolds . choosing appropriate cycles this algorithm can be implemented in an efficient way . the main steps require the evaluation of proximal mappings of our cyclic differences for which we provide analytical expressions . under certain conditions we prove the convergence of our algorithm . various numerical examples with artificial as well as real - world data demonstrate the advantageous performance of our algorithm ."}
{"article_id":"cond-mat0509695","section_id":"i","document":"optical spectroscopy is a powerful tool to study the energy spectrum of electronic states in low - dimensional heterostructures . it was successfully used for investigation of two - dimensional electron gases ( 2deg ) ( for review see e.g. ref .  ) , providing additional information not available from transport measurements alone . however , in optical experiments the presence of photoexcited holes perturbs the energy spectrum of the 2deg via electron - hole coulomb interactions , an effect which should be taken into account for proper interpretation of optical spectra . this is already the case for iii - v semiconductor heterostructures based on gaas , where the coulomb interaction is relatively weak ( e.g. the exciton binding energy in bulk gaas is 4.2  mev ) . however , coulomb interactions are of major importance for ii - vi semiconductors ( e.g. the exciton binding energy in bulk znse is 20  mev ) . modification of the optical spectra of modulation - doped quantum wells ( qw ) containing a 2deg has been the subject of extensive theoretical @xcite and experimental studies @xcite .    in undoped qws , the ground state of an optically excited single electron - hole pair is an exciton ( @xmath2 ) , which is formed by the coulomb interaction between the electron and the hole . for qws with a very dilute two - dimensional electron gas ( 2deg ) where the electron concentration @xmath3 ( here @xmath4 is the radius of the quasi - two - dimensional exciton ) , a negatively charged exciton complex is the energetically lowest excitation @xcite . the negatively charged exciton is composed of two electrons and a hole , and is commonly called a trion ( @xmath5 ) , and is analogous to the negatively charged @xmath6 state of the hydrogen atom . in semiconductor qws trions have binding energies of a few mev and are observed in optical spectra below the exciton resonance . in the limit of zero electron concentration , the energy separation between trion and exciton optical transitions corresponds to the binding energy of `` isolated '' trions @xmath7 ( i.e. the trion state which is not perturbed by interaction with the 2deg ) . it varies usually from 5 to 20% of the exciton binding energy @xmath8 depending on the qw thickness and the height of the barriers ( see e.g. ref .   and references therein ) .    for a high density 2deg with @xmath9 , screening and phase space filling effects destroy the strong coulomb attraction between an individual electron and hole , i.e. the exciton is suppressed @xcite . as a result , instead of a narrow excitonic emission , a broad emission band with a linewidth determined by the 2deg fermi energy @xmath10 is characteristic of this regime . also , a fermi - edge singularity ( @xmath11 ) appears in optical spectra owing to the coulomb interaction of a photocreated hole with the electrons at the fermi - surface @xcite . optical spectra are usually interpreted in terms of band to band transitions , dressed with many - body interactions of the excited or annihilated electron - hole pair with electrons of the fermi sea @xcite . the energies of the emission and absorption thresholds are shifted following to a band - gap renormalization . extended numerical calculations are needed to model optical spectra of a qw with a dense 2deg . on the basis of such calculations hawrylak _ et al . _ predicted the presence of two thresholds ( two peaks ) in the absorption spectrum corresponding to the bound states of the photoexcited hole interacting with a 2deg . the first threshold occurs at an energy @xmath12 and is a doubly occupied trion complex . the second threshold with an energy @xmath13 corresponds to an exciton created in the 2deg @xcite . this approach allows to explain the main features in the optical spectra of modulation doped gaas qws @xcite . evolution of the optical spectra with increasing electron density from the low - density to the high - density limit is an important issue which has been examined experimentally in recent years for gaas [ 33 ] , cdte @xcite and znse @xcite based qws . general trends have been established and attempts to formulate a phenomenological description have been undertaken . it has been shown that for all studied material systems the filling factor @xmath14 separates landau - level - like behavior from an excitonic - like behavior in external magnetic fields . in high magnetic fields for @xmath15 the broad emission band transforms into a narrow line that shifts diamagnetically , reminiscent of the trion line in low - doped samples . further field increase to @xmath16 revives one more line in optical spectra , which is excitonic like . in these fields , optical spectra of moderately - doped and very weakly - doped qws look identical . despite the considerable progress in experiment the situation is still far from completely understood , in major part due to the absence of a proper model description of the intermediate concentration regime . in this regime with @xmath17 the fermi energy of the 2deg falls in the range between the trion and exciton binding energies @xmath18 , and the effect of the coulomb interaction on the optical spectra can be discussed in terms of comparing these three characteristic energies . znse - based qws exhibit very strong coulomb electron - hole interactions ( the exciton binding energy is twice as large as compared to cdte qws and four times larger than in gaas qws ) . the coulomb energy amounts to 30 - 40  mev . in earlier studies of n - type doped ( zn , cd)se / znse qws the well layers were made of ternary alloy ( zn , cd)se @xcite . this results in a considerable broadening of optical lines by alloy fluctuations which obscures fine details in the spectroscopic analysis .    in this paper we present a comprehensive optical study of n - type modulation - doped znse/(zn , be , mg)se qws , with an aim to investigate the modification of optical spectra in structures with strong coulomb interactions , and at the intermediate electron densities satisfying the condition @xmath19 . photoluminescence ( pl ) , pl excitation ( ple ) and reflectivity spectra have been measured in high magnetic fields up to 48  t. the paper is organized as follows : in section  [ sec2 ] details of the sample structure and the experimental techniques are described . in section  [ sec3 ] optical spectra at a zero magnetic field are discussed . the modification of optical spectra in high magnetic fields is presented in section  [ sec4 ] .","summary":"the optical properties of two - dimensional electron gases in znse/(zn , be)se and znse/(zn , be , mg)se modulation - doped quantum wells with electron densities up to  were studied by photoluminescence , photoluminescence excitation and reflectivity in a temperature range between 1.6 and 70  k and in external magnetic fields up to 48  t. in these structures , the fermi energy of the two - dimensional electron gas falls in the range between the trion binding energy and the exciton binding energy . optical spectra in this regime are shown to be strongly influenced by the coulomb interaction between electrons and photoexcited holes . in high magnetic fields , when the filling factor of the two - dimensional electron gas becomes smaller than two , a change from landau - level - like spectra to exciton - like spectra occurs . we attempt to provide a phenomenological description of the evolution of optical spectra for quantum wells with strong coulomb interactions .","abstract":"the optical properties of two - dimensional electron gases in znse/(zn , be)se and znse/(zn , be , mg)se modulation - doped quantum wells with electron densities up to  were studied by photoluminescence , photoluminescence excitation and reflectivity in a temperature range between 1.6 and 70  k and in external magnetic fields up to 48  t. in these structures , the fermi energy of the two - dimensional electron gas falls in the range between the trion binding energy and the exciton binding energy . optical spectra in this regime are shown to be strongly influenced by the coulomb interaction between electrons and photoexcited holes . in high magnetic fields , when the filling factor of the two - dimensional electron gas becomes smaller than two , a change from landau - level - like spectra to exciton - like spectra occurs . we attempt to provide a phenomenological description of the evolution of optical spectra for quantum wells with strong coulomb interactions ."}
{"article_id":"1308.4344","section_id":"i","document":"white - dwarf  main - sequence ( wdms ) binaries consist of a ( blue ) white dwarf primary and a ( red ) low - mass main - sequence ( ms ) companion formed from ms binaries where the primary has a mass @xmath1 . most of the wdms binaries ( @xmath2 ) are wide binaries @xcite , of which the initial ms binary separation is large enough that the two components will never interact and evolve like single stars @xcite . consequently , the orbital period of these systems will increase because of the mass loss of the primary ( the white dwarf precursor ) . the remaining @xmath3 of the wdms binaries are close binaries . when the more massive star of a close binary leaves the ms and evolves into the giant branch or asymptotic giant branch phase , there is a dynamically unstable mass transfer to the ms companion and then the system goes through a common - envelope phase @xcite during which it may continue evolving to an even shorter orbital period through angular momentum loss mechanisms ( magnetic braking and gravitational radiation ) or undergo a second common envelope . binary population synthesis models @xcite indicate the bimodal nature of the orbital period distribution of the entire population of wdms binaries .    during the common - envelope phase of close binaries , the binary separation undergoes a rapid decrease and consequently orbital energy and angular momentum are extracted from the orbit , leading to the ejection of the envelope and exposing a post - common - envelope binary ( pceb ) . these pcebs are important objects that may be progenitor candidates of cataclysmic variables @xcite and perhaps type ia supernovae @xcite . they can also improve the theory of close binary evolution @xcite , especially the understanding of the physics of common - envelope evolution @xcite . among the variety of pcebs ( such as sdob+ms binaries , wdms binaries , and double degenerates ) , wdms binaries are intrinsically the most common ones and the stellar components ( white dwarfs and m dwarfs ) of wdms binaries are relatively simple . there are more and more wdms binaries being found from the sloan digital sky survey ( sdss ; * ? ? ? * ) , making them the most ideal population to help us understand common - envelope evolution . in addition , wdms binaries , especially eclipsing wdms binaries , also provide an interesting test of stellar evolution for both the white dwarf primary and the secondary low - mass ms in the binary environment @xcite .    until now , a large number of wdms binaries @xcite have been efficiently identified from the sdss . @xcite first attempted to study the wdms pairs using sdss data from the early data release @xcite and data release one @xcite . they identified 109 wdms pairs with @xmath4 20th magnitude . @xcite presented 747 spectroscopically identified wdms binary systems from the sdss fourth data release @xcite , and a further 1253 wdms binary systems @xcite from the sdss data release five @xcite . @xcite identified 857 wdms binaries from the sdss data release six @xcite through a photometric selection method . @xcite identified 523 wdms binaries from the sdss data release seven ( dr7 ; * ? ? ? * ) based on their optical and near - infrared color - selection criteria . @xcite provided a final catalog of 2248 wdms binaries identified from the sdss dr7 , among which approximately 200 strong pceb candidates have been found @xcite , and they further developed a publicly available interactive online database for these spectroscopic sdss wdms binaries .    with these cumulative rich sdss wdms binary samples and the identified pcebs , some important work has been done to test binary population models as well as study the stellar structures , magnetic activity , common - envelope evolution , and other properties . for example , @xcite pointed out that 21%24% of sdss wdms binaries have undergone common - envelope evolution , which is in good agreement with the predictions of binary population models @xcite . @xcite found that the majority of low - mass ( @xmath5 0.5 @xmath6 ) white dwarfs are formed in close binaries by investigating the white dwarf mass distributions of pcebs . @xcite studied the apparent period variations of eclipsing pcebs and provided two possible interpretations : second - generation planet formation or variations in the shape of a magnetically active secondary star . @xcite investigated the magnetic - activity  rotation  age relations for m stars in close wdms binaries and wide wdms binaries using what is so far the largest and most homogeneous sample of sdss wdms binaries @xcite . they found that m dwarfs in wide wdms binaries are younger and more active than field m dwarfs and the activity of m dwarfs in close binaries is independent of the spectral type . as discussed above , several previous studies had developed color selection criteria based on the model colors of binary systems in order to select wdms binaries from the sdss @xcite . for example , @xcite developed an initial set of photometric selection criteria ( @xmath7 , @xmath8 , @xmath9 , @xmath10 to a limiting magnitude of @xmath4 20 ) to identify binary systems using sdss photometry and yielded reliable results . here we present a sample of wdms binaries also selected with a series of photometric criteria from the spectra of large sky area multi - object fiber spectroscopic telescope ( lamost , also called the guo shou jing telescope , gsjt ; * ? ? ? * ; * ? ? ? * ) pilot survey @xcite . we discuss the sample selection and provide stellar parameters of the individual components of some binary systems ( e.g. , effective temperature , surface gravity , radius , mass and cooling age for the white dwarf ; effective temperature , surface gravity , metallicity , spectral type , radius , and mass of the m dwarf ) . the structure of this paper is as follows . in section 2 , we describe our sample selection criteria . in section 3 , we present the method of the spectral decomposition of some our wdms binaries and derive the parameters for the two constituents of the binaries . section 4 contains the analysis of the spectroscopic parameters of the binaries and the possible pceb candidates in our sample . finally , a brief conclusion is provided in section 5 .","summary":"we present a set of white - dwarf  main - sequence ( wdms ) binaries identified spectroscopically from the large sky area multi - object fiber spectroscopic telescope ( lamost , also called the guo shou jing telescope ) pilot survey . we derive the stellar atmospheric parameters , masses , and radii for the two components of 10 of our binaries . we also provide cooling ages for the white dwarf primaries as well as the spectral types for the companion stars of these 10 wdms binaries .","abstract":"we present a set of white - dwarf  main - sequence ( wdms ) binaries identified spectroscopically from the large sky area multi - object fiber spectroscopic telescope ( lamost , also called the guo shou jing telescope ) pilot survey . we develop a color selection criteria based on what is so far the largest and most complete sloan digital sky survey ( sdss ) dr7 wdms binary catalog and identify 28 wdms binaries within the lamost pilot survey . the primaries in our binary sample are mostly da white dwarfs except for one db white dwarf . we derive the stellar atmospheric parameters , masses , and radii for the two components of 10 of our binaries . we also provide cooling ages for the white dwarf primaries as well as the spectral types for the companion stars of these 10 wdms binaries . these binaries tend to contain hot white dwarfs and early - type companions . through cross - identification , we note that nine binaries in our sample have been published in the sdss dr7 wdms binary catalog . nineteen spectroscopic wdms binaries identified by the lamost pilot survey are new . using the 3 radial velocity variation as a criterion , we find two post - common - envelope binary candidates from our wdms binary sample ."}
{"article_id":"1308.4344","section_id":"r","document":"our wdms binary sample is not complete and we only provide stellar parameters for 10 binaries , so the statistical distribution analysis of parameters is not given . the white dwarf effective temperatures are between 21,000 k and 48,000 k and have a mean value 29,900 k. this may suggest that this wdms binary sample tends to have hot white dwarfs . the mean value of white dwarf surface gravities is around 8.0 , which is consistent with the peak value of surface gravity distribution of @xcite . @xcite give an m dwarf catalog from the lamost pilot survey , for which the spectral type has a peak around m1 @xmath18 m2 . the spectral types of the secondary stars of our wdms binaries also cluster together around m1.5 . all of these imply that our sample favours binaries with hot white dwarfs and early - type companion stars . the white dwarf masses of the 10 binaries for which we provided stellar parameters tend to be higher than the typical peak of wd mass @xmath18 0.6 @xmath84 @xcite . that may be because of the selection effect and the small sample size . our binary sample is still not large enough for parameter distribution analysis and is waiting to be enlarged by the ongoing lamost formal survey .      for the binary spectra that exhibit the resolved spectral h@xmath85 @xmath86 6564.61 emission line and nai doublet @xmath87 8183.27 , and 8194.81 lines , we try to derive radial velocities by fitting the h@xmath85 emission line with a gaussian line profile plus a second order polynomial as well as fitting the nai doublet with a double gaussian profile of fixed separation and a second order polynomial @xcite . the total error of the radial velocities is computed by quadratically adding the uncertainty of the lamost wavelength calibration ( 10 km s@xmath88 ; see * ? ? ? * ) and the error in the position of the h@xmath85/nai lines determined from the gaussian fits . the lamost spectra are generally combined from three exposures ( which we call ` subspectra ' following @xcite ) , with each exposure lasting for either 30 minutes or 15 minutes ( see section 2 ) . we then measure radial velocities for these lamost subspectra and the combined spectra . last , we derive radial velocities for 17 binaries ( see table 3 ) , of which j085900.86 + 493519.8 and j101616.82 + 310506.5 have been observed two and four times , respectively , by lamost . figure [ fig : rv ] shows the fitting results of the h@xmath85 @xmath86 6564.61 emission line and the nai doublet @xmath87 8183.27 , and 8194.81 lines of two lamost spectra .      from table 3 , 10 binaries have been measured with multiple radial velocities ( including the radial velocities measured from lamost subspectra and provided by the sdss wdms binary catalog @xcite ) . following @xcite and @xcite , we consider those systems showing radial velocity variations with 3@xmath0 significance to be strong pceb candidates . we used a @xmath60 test with respect to the mean radial velocity for the detection of radial velocity variations . if the probability @xmath89 that the @xmath60 test returns is below 0.0027 ( meaning the probability @xmath90 of a system showing large radial velocity variation is above 0.9973 where @xmath91 ) , we can say that we detect 3@xmath0 radial velocity variation and the corresponding wdms binary can be considered a strong pceb candidate . here we find two pceb candidates , lamost j105421.88@xmath44512254.1 and lamost j122037.01@xmath44492334.0 , using the nai doublet radial velocities . lamost j105421.88@xmath44512254.1 shows 3@xmath0 radial velocity variation using either nai doublet or h@xmath85 emission , while for lamost j122037.01@xmath44492334.0 , we detect 3@xmath0 radial velocity variation using the nai doublet . by cross - referencing 195 pceb candidates provided by @xcite , we find that lamost j105421.88@xmath44512254.1 has already been identified as a pceb candidate . limited by the sample size , we only find one new pceb candidate : lamost j122037.01@xmath44492334.0 . we estimate the upper limits to orbital periods for these two pceb candidates in the same way as described in @xcite . because we do not provide stellar parameters for these two binaries , the white dwarf masses and the secondary star masses are taken from @xcite . the radial velocity amplitudes of the secondary stars are obtained by using the nai doublet radial velocities ( table 3 ) . table 4 presents the probability @xmath90 of measuring large radial velocity variations for these two binaries and the calculated upper limits to their orbital periods . both pceb candidates need intense follow - up spectroscopic observations in order to obtain orbital periods .","summary":"these binaries tend to contain hot white dwarfs and early - type companions . through cross - identification","abstract":"we present a set of white - dwarf  main - sequence ( wdms ) binaries identified spectroscopically from the large sky area multi - object fiber spectroscopic telescope ( lamost , also called the guo shou jing telescope ) pilot survey . we develop a color selection criteria based on what is so far the largest and most complete sloan digital sky survey ( sdss ) dr7 wdms binary catalog and identify 28 wdms binaries within the lamost pilot survey . the primaries in our binary sample are mostly da white dwarfs except for one db white dwarf . we derive the stellar atmospheric parameters , masses , and radii for the two components of 10 of our binaries . we also provide cooling ages for the white dwarf primaries as well as the spectral types for the companion stars of these 10 wdms binaries . these binaries tend to contain hot white dwarfs and early - type companions . through cross - identification , we note that nine binaries in our sample have been published in the sdss dr7 wdms binary catalog . nineteen spectroscopic wdms binaries identified by the lamost pilot survey are new . using the 3 radial velocity variation as a criterion , we find two post - common - envelope binary candidates from our wdms binary sample ."}
{"article_id":"1308.4344","section_id":"c","document":"we have presented a catalog of 28 wdms binaries from the spectroscopic lamost pilot survey in this paper . using the colors of the 2248 binaries from the sdss wdms binary catalog , we develop our own color selection criteria for the selection of wdms binaries from the lamost pilot survey based on the lamost magnitudes obtained by convolving the lamost spectra with the sdss @xmath19 filter response curve . this method is efficient for searching for binaries in the spectroscopic survey without having our own optical or infrared photometric data equipment like the lamost survey . using the color selection criteria , we identify 28 wdms binaries from the lamost pilot survey . nine of these binaries have been published in previous works and 19 of these wdms binaries are new . for 10 of our binaries , we have used a @xmath60 minimization technique to decompose the binary spectra and determine the effective temperatures , surface gravities of the white dwarfs , as well as the effective temperatures , surface gravities , and metallicities for the m - type companions . the cooling ages , masses and radii of white dwarfs are provided by interpolating the white dwarf cooling sequences for the derived effective temperatures and surface gravities . we also derive the spectral types , masses , and radii of the m stars by using empirical spectral type  effective temperature , spectral type  mass , and spectral type  radius relations . in addition , the radial velocities are measured for most of our sample . we also discuss the possible pceb candidates among the binary systems with multiple spectra in our sample , finally giving two possible pceb candidates , one of which has already been identified as a pceb candidate by the sdss . the wdms binary catalog is the first provided by the lamost survey , and demonstrates the capability of lamost to search for wdms binaries . with the ongoing formal lamost survey , we hope to find many more wdms binaries and present a more complete catalog of wdms binaries , which will increase the number of known wdms binary systems . enlarging the wdms binary sample will lead to a deeper understanding of close compact binary star evolution and other follow - up studies . we thank the anonymous referee for very useful comments and suggestions that greatly improved this paper . we thank alberto rebassa - mansergas for the discussion about the detection of pcebs . we also thank detlev koester for kindly providing the white dwarf atmospheric models and bengt edvardsson for useful discussion of the marcs models . we acknowledge the web site http://www.astro.umontreal.ca/~bergeron/coolingmodels for providing the white dwarf cooling sequences . we thank george comte for the discussion of m dwarf models and xiaoyan chen , yue wu , and fang zuo for discussion . this study is supported by the national natural science foundation of china under grant nos . 10973021 , 11078019 , 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j025306.36@xmath44001329.6 & 43.2765 & 0.22491 & 55859 & f5907 & sp14 & 137 & 0.509917 & 0.248582 & 19.359 & 18.916 & 19.308 & 19.818 & 20.025 & 14.173 & 13.546 & 13.272 & 19.601 & 19.429 & e , r + j052529.17@xmath44283705.4 & 81.37156 & 28.61819 & 55859 & f5909 & sp04 & 114 & 0.360057 & 0.324585 & ... & ... & ... & ... & ... & 15.354 & 14.596 & 14.368 & ... & ... & + j052531.26@xmath44283807.6 & 81.38025 & 28.63545 & 55951 & gac@xmath16080n28@xmath16m1 & sp04 & 114 & 0.280857 & 0.361304 & ... & ... & ... & ... & ... & 13.401 & 12.77 & 12.553 & ... & ... & + j052531.33@xmath44284549.4 & 81.38058 & 28.76375 & 55859 & f5909 & sp04 & 120 & 0.387878 & 0.332709 & ... & ... & ... & ... & ... & 15.583 & 15.027 & 14.71 & ... & ... & + j073128.30@xmath44264353.8 & 112.86793 & 26.73163 & 55921 & gac@xmath16113n28@xmath16m1 & sp01 & 044 & 0.510806 & 0.327412 & 18.46 & 17.772 & 17.248 & 16.204 & 15.498 & 14.049 & 13.459 & 13.283 & 19.6 & 18.689 & + j081934.63@xmath44024802.7 & 124.8943 & 2.80077 & 55921 & f5592103 & sp08 & 044 & 0.631215 & 0.293536 & 17.721 & 17.255 & 16.561 & 15.686 & 15.074 & 13.708 & 13.076 & 12.897 & ... & ... & + j081959.21@xmath44060424.2 & 124.996713 & 6.073391 & 55892 & f9205 & sp06 & 053 & 0.444555 & 0.446157 & 19.665 & 19.433 & 19.456 & 18.811 & 18.154 & 16.58 & 16.357 & 15.847 & 19.188 & 19.421 & r + j084006.40@xmath44143025.9 & 130.02669 & 14.50722 & 55977 & f5597707 & sp01 & 145 & 0.304351 & 0.269564 & 18.048 & 18.109 & 17.996 & 17.318 & 16.819 & 15.447 & 14.934 & 14.594 & ... & ... & + j085900.86@xmath44493519.8 & 134.75359 & 49.58885 & 56021 & vb3@xmath16136n49@xmath16v1 & sp03 & 087 & @xmath450.034498 & 0.182911 & 16.466 & 15.049 & 13.9 & 13.297 & 12.539 & 11.251 & 10.577 & 10.364 & 16.736 & 16.678 & + j101616.82@xmath44310506.5 & 154.07012 & 31.08516 & 55907 & b90705 & sp03 & 065 & 0.634328 & 0.283063 & 17.38 & 16.751 & 16.167 & 15.317 & 14.787 & 13.47 & 12.885 & 12.698 & 17.296 & 17.241 & + j103514.80@xmath44390717.7 & 158.8117 & 39.1216 & 55930 & f5593001 & sp04 & 124 & 0.425026 & 0.208033 & 18.423 & 18.178 & 17.919 & 17.301 & 16.859 & 15.565 & 15.034 & 14.849 & 17.768 & 18.07 & s , r + j105405.25@xmath44283916.7 & 163.52188 & 28.65466 & 55931 & b5593104 & sp16 & 214 & 0.519861 & 0.284815 & 17.824 & 17.146 & 16.645 & 15.477 & 14.657 & 13.202 & 12.569 & 12.339 & 18.024 & 17.794 & r + j105421.88@xmath44512254.1 & 163.59118 & 51.38171 & 55915 & f5591506 & sp11 & 205 & 0.526326 & 0.275433 & 17.258 & 16.778 & 16.134 & 15.271 & 14.729 & 13.455 & 12.813 & 12.575 & 16.46 & 16.817 & s , r + j111035.16@xmath44280733.2 & 167.64653 & 28.1259 & 55931 & b5593104 & sp13 & 180 & 0.687018 & 0.232178 & 17.786 & 17.161 & 16.427 & 15.554 & 15.024 & 13.729 & 13.099 & 12.911 & 17.371 & 17.506 & + j112512.36@xmath44290545.4 & 171.30153 & 29.09597 & 56018 & b5601803 & sp02 & 195 & 0.228522 & 0.345777 & 18.817 & 18.215 & 17.521 & 16.481 & 15.856 & 14.531 & 13.907 & 13.635 & 18.474 & 18.611 & r + j114732.25@xmath44593921.9 & 176.8844 & 59.65611 & 55931 & f5593101 & sp11 & 001 & 0.424084 & 0.243105 & 17.127 & 16.796 & 16.474 & 15.514 & 14.882 & 13.485 & 12.832 & 12.635 & 16.682 & 16.783 & + j120024.56@xmath44292310.3 & 180.10235 & 29.3862 & 55961 & b5596106 & sp02 & 085 & 0.432907 & 0.216112 & 20.275 & 17.715 & 16.386 & 15.665 & 15.216 & 14.068 & 13.44 & 13.273 & ... & ... & + j122037.01@xmath44492334.0 & 185.1542208 & 49.3927944 & 55923 & f5592306 & sp03 & 077 & 0.63171 & 0.255231 & 18.719 & 18.14 & 17.417 & 16.809 & 16.405 & 15.172 & 14.505 & 14.396 & ... & ... & s , r + j125555.30@xmath44560033.0 & 193.98043 & 56.00917 & 55952 & f5595206 & sp04 & 123 & 0.623711 & 0.288381 & 22.695 & 20.013 & 18.701 & 17.558 & 16.898 & 15.682 & 15.063 & 15.027 & ... & ... & + j131208.11@xmath44002058.0 & 198.0338083 & 0.3494583 & 55932 & f5593201 & sp16 & 071 & 0.0403807 & 0.232714 & 18.79 & 18.472 & 18.35 & 17.564 & 16.927 & 15.625 & 15.029 & 14.787 & 18.247 & 18.53 & r , c + j132417.76@xmath44280755.8 & 201.07402 & 28.13217 & 55975 & b5597505 & sp01 & 195 & 0.477785 & 0.203373 & 17.477 & 16.903 & 16.524 & 15.593 & 14.979 & 13.57 & 12.941 & 12.658 & 17.325 & 17.378 & + j135635.32@xmath44084841.7 & 209.1472 & 8.81159 & 56062 & vb3@xmath16210n09@xmath16v2 & sp10 & 161 & 0.544101 & 0.38414 & 17.524 & 16.798 & 16.057 & 15.021 & 14.403 & 13.042 & 12.416 & 12.169 & 17.387 & 17.417 & + j150626.53@xmath44275925.2 & 226.61058 & 27.99036 & 56063 & b5606303 & sp09 & 122 & @xmath450.260791 & 0.260247 & 18.258 & 18.177 & 18.053 & 17.5 & 17.043 & 15.852 & 15.253 & 14.698 & 17.347 & 17.602 & r + j162617.40@xmath44384029.9 & 246.57251 & 38.67499 & 55999 & b5599908 & sp15 & 040 & 0.253555 & 0.159056 & 17.361 & 16.938 & 16.697 & 15.7 & 15.111 & 12.513 & 11.947 & 11.663 & ... & ... & + j221102.56@xmath45002433.5 & 332.76069 & @xmath450.40933 & 55859 & f5902 & sp08 & 169 & 0.477924 & 0.309289 & 18.634 & 18.307 & 17.941 & 16.993 & 16.415 & 15.154 & 14.501 & 14.352 & 18.213 & 18.466 & + j224609.42@xmath44312912.2 & 341.53925 & 31.48674 & 55863 & b6302 & sp09 & 187 & 0.235289 & 0.387328 & 16.952 & 15.671 & 15.19 & 15.018 & 14.936 & 14.11 & 13.728 & 13.584 & ... & 20.489 & + j232004.01@xmath44270623.7 & 350.01673 & 27.10659 & 55878 & b87802@xmath161 & sp15 & 083 & @xmath450.305056 & 0.0273775 & 15.852 & 16.072 & 16.378 & 16.168 & 15.811 & 14.609 & 14.074 & 13.783 & 14.747 & 15.203 &    lccccccccccc j014141.83@xmath44311852.9 & 21000 & 8.25 & 3700 & 4.0 & 0.00 & 0.78 & 101.6 & 0.011 & 1.0 & 0.464 & 0.480 + j081934.63@xmath44024802.7 & 32000 & 7.00 & 3600 & 3.5 & @xmath450.25 & 0.33 & 5.0 & 0.030 & 1.5 & 0.450 & 0.465 + j084006.40@xmath44143025.9 & 38000 & 8.50 & 3500 & 4.0 & @xmath450.50 & 0.96 & 16.4 & 0.009 & 2.0 & 0.431 & 0.445 + j085900.86@xmath44493519.8 & 32000 & 8.50 & 3500 & 3.5 & @xmath450.75 & 0.95 & 36.4 & 0.009 & 2.0 & 0.431 & 0.445 + j101616.82@xmath44310506.5 & 25000 & 8.25 & 3600 & 4.5 & @xmath450.25 & 0.78 & 50.1 & 0.011 & 1.5 & 0.450 & 0.465 + j111035.16@xmath44280733.2 & 24000 & 7.75 & 3700 & 4.0 & @xmath450.25 & 0.51 & 18.9 & 0.016 & 1.0 & 0.464 & 0.480 + j114732.25@xmath44593921.9 & 22000 & 8.25 & 3700 & 5.5 & 0.50 & 0.78 & 84.5 & 0.011 & 1.0 & 0.464 & 0.480 + j120024.56@xmath44292310.3 & 48000 & 7.75 & 3700 & 4.5 & @xmath450.25 & 0.58 & 2.3 & 0.017 & 1.0 & 0.464 & 0.480 + j221102.56@xmath45002433.5 & 23000 & 8.50 & 3600 & 5.0 & 0.25 & 0.94 & 126.2 & 0.009 & 1.5 & 0.450 & 0.465 + j232004.01@xmath44270623.7 & 34000 & 7.50 & 3300 & 4.0 & 0.00 & 0.45 & 5.0 & 0.020 & 3.5 & 0.350 & 0.359    lrccccc j014141.83@xmath44311852.9 & 2455918.0249 & ... & ... & 13.5 & 13.1 & a + j052531.26@xmath44283807.6 & 2455951.0953 & 60.7 & 12.6 & 18.6 & 13.7 & a + j073128.30@xmath44264353.8 & 2455921.2338 & ... & ... & @xmath45102.4 & 15.0 & a + j081934.63@xmath44024802.7 & 2455921.3048 & 42.9 & 12.7 & 23.7 & 11.7 & a + & 2455921.2920 & 49.1 & 11.9 & 23.3 & 11.1 & b + & 2455921.3176 & 42.0 & 12.9 & 21.9 & 12.0 & b + j084006.40@xmath44143025.9 & 2455977.1160 & 48.7 & 14.1 & 64.9 & 14.5 & a + j085900.86@xmath44493519.8 & 2456021.0491 & ... & ... & @xmath454.8 & 11.7 & a + & 2456021.0432 & ... & ... & @xmath455.7 & 10.4 & b + & 2456021.0551 & ... & ... & @xmath450.9 & 10.4 & b + & 2456021.0801 & @xmath4533.9 & 16.5 & 4.02 & 10.6 & a + & 2456021.0742 & ... & ... & 1.9 & 10.4 & b + & 2456021.0859 & ... & ... & 3.8 & 10.5 & b + j101616.82@xmath44310506.5 & 2455907.3713 & @xmath4516.6 & 12.7 & @xmath453.8 & 16.3 & a + & 2455907.3624 & @xmath4511.2 & 11.3 & @xmath450.3 & 11.0 & b + & 2455907.3802 & @xmath4511.6 & 12.7 & @xmath452.4 & 11.0 & b + & 2455959.2835 & @xmath4517.1 & 12.7 & 2.0 & 11.1 & a + & 2455959.2681 & @xmath4514.0 & 12.2 & 9.1 & 10.6 & b + & 2455959.2835 & @xmath456.3 & 14.0 & @xmath458.7 & 12.0 & b + & 2455960.3033 & @xmath4519.8 & 11.6 & @xmath457.4 & 11.5 & a + & 2455960.2868 & @xmath4510.9 & 10.6 & @xmath451.2 & 10.4 & b + & 2455960.3036 & ... & ... & @xmath4521.3 & 11.6 & b + & 2455960.3198 & ... & ... & 3.0 & 11.4 & b + & 2455978.1927 & @xmath4513.3 & 13.7 & @xmath4520.6 & 13.8 & a + & 2455978.1676 & ... & ... & @xmath4511.5 & 11.7 & b + & 2455978.1846 & @xmath4528.4 & 14.8 & 4.2 & 12.0 & b + & 2455978.2177 & @xmath458.5 & 13.1 & @xmath4510.1 & 12.5 & b + j105405.25@xmath44283916.7 & 2455931.3041 & 10.3 & 12.1 & ... & ... & a + & 2455931.2880 & 3.3 & 12.9 & 10.6 & 11.3 & b + & 2455931.3031 & 25.9 & 11.9 & 11.5 & 11.0 & b + & 2455931.3203 & 15.7 & 11.6 & 4.4 & 11.4 & b + & 2453826.8103 & 30.0 & 15.0 & 32.4 & 10.4 & c + & 2453826.7958 & 35.2 & 15.2 & ... & ... & c + & 2453826.8086 & 35.2 & 15.1 & ... & ... & c + & 2453826.8231 & 33.3 & 15.2 & ... & ... & c + & 2454887.2906 & 33.7 & 14.8 & 25.1 & 10.1 & c + j105421.88@xmath44512254.1 & 2455915.3897 & 33.0 & 15.4 & 23.0 & 12.9 & a + & 2455915.4032 & 6.8 & 12.0 & 26.9 & 14.2 & b + & 2452669.8635 & 31.9 & 14.5 & 31.5 & 10.8 & c + & 2452669.8635 & 34.8 & 10.5 & ... & ... & c + & 2453759.6249 & @xmath4560.8 & 4.2 & ... & ... & c + & 2453759.7157 & @xmath4542.9 & 4.3 & ... & ... & c + & 2452345.3158 & @xmath4554.6 & 14.7 & @xmath4567.6 & 10.7 & c + j111035.16@xmath44280733.2 & 2455931.3041 & ... & ... & @xmath4513.1 & 14.9 & a + j112512.36@xmath44290545.4 & 2456018.1430 & @xmath45117.2 & 18.3 & ... & ... & a + & 2453794.9024 & @xmath4552.0 & 15.3 & @xmath4541.1 & 10.8 & c + & 2453794.8889 & @xmath4564.8 & 17.4 & ... & ... & c + & 2453794.9047 & @xmath4550.6 & 15.6 & ... & ... & c + & 2453794.9182 & @xmath4546.9 & 16.7 & ... & ... & c + j114732.25@xmath44593921.9 & 2455931.3750 & ... & ... & @xmath45121.0 & 10.9 & a + & 2455931.3485 & ... & ... & @xmath45115.9 & 16.6 & b + & 2455931.3739 & ... & ... & @xmath45122.9 & 11.9 & b + & 2455931.4016 & ... & ... & @xmath45140.6 & 11.5 & b + j122037.01@xmath44492334.0 & 2455923.4110 & ... & ... & @xmath4591.4 & 11.2 & a + & 2452413.6647 & @xmath4525.3 & 15.5 & @xmath4523.8 & 11.2 & c + & 2452413.6465 & @xmath4511.4 & 19.1 & ... & ... & c + & 2452413.6625 & @xmath4533.3 & 17.0 & ... & ... & c + & 2452413.6810 & @xmath4537.7 & 17.2 & ... & ... & c + j135635.32@xmath44084841.7 & 2456062.1763 & ... & ... & 23.3 & 15.1 & a + j162617.40@xmath44384029.9 & 2455999.3847 & @xmath4525.5 & 11.5 & @xmath4516.4 & 10.9 & a + & 2455999.3693 & @xmath4522.0 & 13.4 & @xmath4518.7 & 10.9 & b + & 2455999.3850 & @xmath4527.0 & 11.9 & @xmath4518.5 & 11.5 & b + & 2455999.4001 & @xmath4532.4 & 11.7 & @xmath4513.2 & 13.7 & b + j224609.42@xmath44312912.2 & 2455863.0592 & @xmath4518.0 & 10.7 & @xmath453.6 & 10.7 & a + & 2455863.0417 & @xmath4518.3 & 10.8 & @xmath4512.6 & 10.9 & b + & 2455863.0582 & @xmath4519.4 & 10.8 & @xmath454.0 & 11.6 & b + & 2455863.0767 & @xmath458.3 & 11.1 & @xmath457.8 & 26.2 & b + j232004.01@xmath44270623.7 & 2455878.0210 & @xmath4587.9 & 13.7 & ... & ... & a +","summary":"nineteen spectroscopic wdms binaries identified by the lamost pilot survey are new . using the 3 radial velocity variation as a criterion , we find two post - common - envelope binary candidates from our wdms binary sample .","abstract":"we present a set of white - dwarf  main - sequence ( wdms ) binaries identified spectroscopically from the large sky area multi - object fiber spectroscopic telescope ( lamost , also called the guo shou jing telescope ) pilot survey . we develop a color selection criteria based on what is so far the largest and most complete sloan digital sky survey ( sdss ) dr7 wdms binary catalog and identify 28 wdms binaries within the lamost pilot survey . the primaries in our binary sample are mostly da white dwarfs except for one db white dwarf . we derive the stellar atmospheric parameters , masses , and radii for the two components of 10 of our binaries . we also provide cooling ages for the white dwarf primaries as well as the spectral types for the companion stars of these 10 wdms binaries . these binaries tend to contain hot white dwarfs and early - type companions . through cross - identification , we note that nine binaries in our sample have been published in the sdss dr7 wdms binary catalog . nineteen spectroscopic wdms binaries identified by the lamost pilot survey are new . using the 3 radial velocity variation as a criterion , we find two post - common - envelope binary candidates from our wdms binary sample ."}
{"article_id":"1502.00920","section_id":"i","document":"rare b decays constitute one of the cornerstones in the search for physics beyond the standard model ( sm ) . among them , the semileptonic mode @xmath7 represents a particularly interesting channel as the measurement of the 4-body angular distribution provides a plethora of information which can be used to probe and discriminate different scenarios of new physics ( np ) . in 2013 , lhcb presented results of the measurement of an optimized set @xmath8 of angular observables @xcite based on 1fb@xmath9 data . these observables are constructed in such a way that , to leading order in the strong coupling constant @xmath10 and in the large - recoil expansion , non - perturbative form factors cancel in the region of low squared invariant mass @xmath11 of the dilepton pair , a unique and powerful feature in the hadronic environment . experimental data showed several interesting tensions with respect to sm expectations @xcite : most striking is the @xmath12 anomaly tension between the experimental result and the 68.3% confidence level of the theoretical prediction , while we have quoted the tension between the experimental result and the theoretical central value . note also that using the updated predictions @xcite for all observables , including parametric and form factor errors , factorizable power corrections together with an estimate of non - factorizable ones and charm - loop effects , the tensions with data , albeit slightly reduced , are still clearly present . ] encountered in the observable @xmath5  @xcite in the bin @xmath13$]gev@xmath14 . the observable @xmath3  @xcite further displayed a @xmath15 deviation in the @xmath11-bin @xmath16$]gev@xmath14 . the position of its zero ( @xmath17 gev@xmath14 ) , which is identical to the zero of the forward - backward asymmetry @xmath18 , is in agreement with the sm prediction @xmath19 gev@xmath14 but allows for higher values . it is remarkable that all these deviations point to the same negative np contribution @xmath20 to the wilson coefficient of the semileptonic operator @xmath21 , possibly accompanied by a np contribution @xmath22 to the wilson coefficient of the magnetic operator @xmath23 . new physics contributions to the wilson coefficient @xmath24 , and , in particular , to the coefficients @xmath25 of the chirality - flipped operators are consistent with zero already at @xmath26 . the full pattern , first pointed out in ref . @xcite and obtained using all available experimental bins in @xmath27 together with data on @xmath28 , @xmath29 , @xmath30 and @xmath31 , is given by the @xmath26 ranges @xmath32 , \\quad\\quad\\quad\\;\\ , c_7^{\\rm np}\\in[-0.05,-0.01 ] , \\quad\\quad\\quad   c_{10}^{\\rm np}\\in[-0.4,1.0 ] , \\nonumber\\\\   c_9^{\\prime \\rm np}&\\in&[-0.2,0.8 ] , \\quad\\quad\\quad\\quad c_7^{\\prime \\rm np}\\in[-0.04,0.02],\\quad\\quad\\quad\\;\\ ; c_{10}^{\\prime \\rm np}\\in[-0.4,0.4 ] , \\end{aligned}\\ ] ] where the mild preference for a positive @xmath33 is mainly driven by @xmath31 data .    the large negative np contribution to @xmath34 was independently confirmed later on by other groups , using different observables @xmath35  @xcite ( relying on the single large - recoil bin [ 1,6]gev@xmath14 and low recoil data ) , different statistical approaches @xcite or form factor input from lattice @xcite . although it had been shown in refs . @xcite that a large @xmath36 was preferred in order to explain the @xmath5 anomaly , the possibility of a substantial positive @xmath37 enforcing @xmath38 was discussed in refs . @xcite , driven mainly by the 1 fb@xmath9 data @xcite on the charged @xmath39 decay @xmath40 in the region of low hadronic recoil . the situation has become more coherent recently as the latest 3 fb@xmath9 data on @xmath40 and @xmath41 provided by lhcb @xcite is also in good agreement with the solution @xmath42 @xcite , both in the region of large as well as low hadronic recoil @xcite . the three modes thus seem to point to a consistent overall picture of np in agreement with the pattern given by eq . ( [ pat ] ) . moreover , under the assumption that np affects only muons but not electrons , also the @xmath43 deviation measured by lhcb  @xcite in the observable @xmath44 can be explained within the same scenario  @xcite . in order to be able to draw solid conclusions and to see how this pattern evolves , it will be crucial to know the 3fb@xmath9 data on the observables @xmath45 in @xmath46 .    in parallel , the question has been raised if the observed discrepancies between data and sm predictions could be attributed to non - perturbative qcd effects  @xcite , even though hadronic form factors enter optimized observables @xmath2 only at order @xmath10 or through corrections breaking the large - recoil symmetries ( _ factorisable power corrections _ ) . there exist two different approaches to account for factorisable power corrections : they can either be calculated ( under certain modelling assumptions ) within a non - perturbative framework like light - cone sum - rules ( lcsr )  @xcite , or they can be estimated exclusively on the basis of dimensional arguments and fundamental model - independent relations  @xcite . while the first method with full correlations among the form factors is suitable in order to extract the maximal information from a particular non - perturbative calculation , the second option in which correlations are included via large - recoil symmetry relations reduces the dependence on non - perturbative input to a minimum . the two approaches are thus complementary and , because the large - recoil symmetries are expected to be the dominant source of correlations , they should give similar results . indeed , the resulting uncertainties obtained with the first method in ref .  @xcite and with the second method in ref . @xcite are of the same order of magnitude ( see also ref . both these analyses find hadronic uncertainties from form factors to be under control power correction is not unique but ( as in any fixed - order calculation ) introduces a scheme dependence of observables at neglected higher orders in @xmath47 . as the observables are effectively calculated at leading order ( @xmath48 effects are not calculated but only estimated ) , they exhibit a scheme dependence at @xmath48 implying a @xmath49 scheme dependence of power corrections . in order to ensure predictivity of the method , it is hence crucial to exploit the freedom of choosing a scheme to minimize the impact of the unknown power corrections on the relevant observables ( in the same way as in a fixed - order calculation in quantum field theory the renormalization scheme is chosen such that neglected higher orders do not spoil the perturbative expansion ) . it was demonstrated in ref . @xcite that the sensitivity to factorizable power corrections of the key observables like @xmath5 is significantly reduced if a different scheme is chosen than the one employed in refs .  @xcite . ] .    as a different explanation of the anomaly , the possibility of a large non - perturbative charm - loop contribution has been proposed @xcite , requiring a huge correction with respect to theory predictions within the factorization approximation . the discussion in ref . @xcite relies on two model - dependent assumptions : first that the resonance structure obtained from a fit to high-@xmath11 data on the scalar mode @xmath50 can directly be transferred to the vector mode @xmath51 , and second that it can be extrapolated to low values of @xmath11 . the only existing calculation @xcite seems to be in contradiction with the low-@xmath11 scenarios of @xmath27 obtained with this ansatz in ref .  @xcite as it finds a much smaller size for the charm loop and , moreover , the opposite sign for its contribution in @xmath50 as compared to @xmath52 ( contrary to the assumption in ref . @xcite ) . furthermore , if the 2.6@xmath53 deviation in the observable @xmath54 persists , it poses a serious problem for the charm - loop or any other low - energy qcd explanation which can not generate effects violating lepton - flavor universality . also the observable @xmath3 in @xmath52 can be instrumental in testing the charm - loop hypothesis proposed in ref . @xcite ( see also @xcite ) . while the polluting effects from non - perturbative qcd have been studied in detail in the literature , less attention has been paid to the so - called s - wave pollution , generated by the background decay @xmath55 where @xmath1 is a broad scalar resonance . in ref . @xcite a detailed and complete calculation of the s - wave background was performed and it was concluded that any observable will unavoidably suffer from its pollution . while this conclusion is correct in the case of uniangular distributions , it does not apply to full or folded distributions where the p- and the s - wave parts can be separated according to their different angular dependence . as shown in ref . @xcite , s - wave pollution can be avoided for the @xmath2 observables if folded distributions are used instead of uniangular ones . a discussion of the experimental implications of the s - wave contribution was presented in ref . @xcite ( see also ref . @xcite ) . experimental analyses of @xmath27 rely on theoretical information regarding the s - wave background . to this end , a set of model - independent bounds on the coefficients of the s - wave part of the angular distribution was presented in ref . @xcite , derived from application of the cauchy - schwarz inequality . on the other hand , it was shown in refs . @xcite that the coefficients of the p - wave part are not independent parameters but that they are correlated through the spin - symmetry of the angular distribution . in this work we transfer this idea to the s - wave sector . we derive two relations which effectively reduce the number of free coefficients of the s - wave distribution from six to four . it is expected that the inclusion of these relations into the data analysis can help to further improve the background estimation . we illustrate the effect of the correlations for the ratio of the s - wave observables @xmath56 and @xmath57 and study implications at the position @xmath58 of the maximum of the observable @xmath3 . moreover , we point out a relation between @xmath4 and @xmath5 at @xmath58 and suggest to use the maximum of @xmath3 as a golden observable to probe right - handed currents ( for an explicit model generating right - handed currents see e.g. ref . @xcite ) . the outline of this paper is the following : in sec . [ sec : spinsym ] we discuss the spin - symmetry of the differential @xmath27 decay rate and determine the number of independent observables in the p- and in the s - wave sector . in sec . [ sec : symrel ] we derive the resulting symmetry relations . their phenomenological consequences are discussed in sec . [ sec : pheno ] . first , we study the discriminating power of the maximum of @xmath3 as a test for right - handed currents , then we determine a relation between @xmath4 and @xmath5 at the position of the maximum of @xmath3 , and finally we investigate constraints on the s - wave observables @xmath59 and derive simple relations among them at the position of the maximum and the zero of @xmath3 . sec . [ sec : conclu ] contains our conclusions . in appendix a we present an explicit example of how to use the freedom introduced by the symmetries to fix a possible convention for the amplitudes , while appendix  b contains details of the derivation of the bound on @xmath60 .","summary":"while we recover in the p - wave sector the known relation between the angular observables , we find in the s - wave sector two new relations connecting the coefficients of the s - wave angular distribution and reducing the number of independent s - wave observables from six to four . moreover , we show that in absence of right - handed currents the angular observables and fulfill the relation at the position where reaches its maximum .","abstract":"after summarizing the current theoretical status of the four - body decay , we apply the formalism of spin - symmetries to the full angular distribution , including the s - wave part involving a broad scalar resonance . while we recover in the p - wave sector the known relation between the angular observables , we find in the s - wave sector two new relations connecting the coefficients of the s - wave angular distribution and reducing the number of independent s - wave observables from six to four . included in the experimental data analysis , these relations can help to reduce the background from s - wave pollution . we further point out the discriminative power of the maximum of the angular observable as a charm - loop insensitive probe of right - handed currents . moreover , we show that in absence of right - handed currents the angular observables and fulfill the relation at the position where reaches its maximum ."}
{"article_id":"1502.00920","section_id":"c","document":"in this article we have exploited the spin symmetry of the angular distribution of the decay @xmath27 , both in the p - wave as well as in the s - wave sector . we have shown that the symmetry reduces the number of independent s - wave observables from six to four , implying two non - trivial relations among the observables @xmath151 , @xmath60 , @xmath56 , @xmath57 , @xmath149 and @xmath150 which we derived explicitly . the relations allowed us to obtain individual bounds on the @xmath59 which agree with the ones determined in ref . @xcite via the cauchy - schwartz inequality . however , the constraining power of the symmetry relations goes beyond these individual bounds as they correlate the s - wave observables among each other . the implementation of these correlations into the experimental data analysis is expected to reduce the background from s - wave pollution . as an example , we have shown how for @xmath241 the correlations fix @xmath56 from a measurement of @xmath57 and @xmath151 ( or @xmath57 from a measurement of @xmath56 and @xmath151 ) in the whole range of the of the squared dilepton invariant mass @xmath11 . we further showed that @xmath250 and @xmath251 are completely fixed at a point @xmath58 where @xmath173 coincides with the position of the maximum of the p - wave observable @xmath3 in the absence of new right - handed currents . we also pointed out the strong potential of the maximum of @xmath3 for probing np beyong the sm , in particular the presence of new right - handed currents , in a region far away from charm resonances . we have shown that a shift of the position of the maximum of @xmath3 compared to its sm expectation , with the height of the maximum @xmath185 kept at the sm value @xmath172 , would be a signal of a np contribution to the sm - like wilson coefficients @xmath252 , @xmath34 , @xmath24 . a maximum value @xmath253 , on the other hand , would detect the presence of new right - handed currents and thus complement information from the ( currently not very precisely measured ) observable @xmath152 . we have further proven and illustrated that for @xmath177 the angular observables @xmath4 and @xmath5 fulfill @xmath254 at the position of the maximum of @xmath3 , so that any deviation from this relation would equally signal the presence of new right - handed currents . we would like to thank k.  a.  petridis and n.  serra for many useful discussions . l.h . has been supported by fpa2011 - 25948 and the grant 2014 sgr 1450 , and in part by the centro de excelencia severo ochoa sev-2012 - 0234 . j.m . acknowledges financial support from the explora project fpa2014 - 61478-exp .","summary":"included in the experimental data analysis , these relations can help to reduce the background from s - wave pollution . we further point out the discriminative power of the maximum of the angular observable as a charm - loop insensitive probe of right - handed currents .","abstract":"after summarizing the current theoretical status of the four - body decay , we apply the formalism of spin - symmetries to the full angular distribution , including the s - wave part involving a broad scalar resonance . while we recover in the p - wave sector the known relation between the angular observables , we find in the s - wave sector two new relations connecting the coefficients of the s - wave angular distribution and reducing the number of independent s - wave observables from six to four . included in the experimental data analysis , these relations can help to reduce the background from s - wave pollution . we further point out the discriminative power of the maximum of the angular observable as a charm - loop insensitive probe of right - handed currents . moreover , we show that in absence of right - handed currents the angular observables and fulfill the relation at the position where reaches its maximum ."}
{"article_id":"hep-ph0207042","section_id":"i","document":"the identification of the higgs boson(s ) is one of the main goals of the large hadron collider ( lhc ) being constructed at cern . according to current theoretical prejudice it is likely that a higgs boson will exist in the mass range @xmath8  gev . in the standard model description of electroweak data , the virtual effects favour a higgs with mass at , or just above , the lep bound of 114  gev . moreover , in the minimal supersymmetric model a scalar standard - model - like higgs boson with mass below 135  gev should exist . however , the experimental detection of such a ` light ' higgs boson at the lhc will be challenging . there is no obvious perfect detection process . rather there is a range of complementary possibilities , as illustrated in table  1 . the table shows the number of identified higgs events and the number of background events , for a standard model higgs boson of mass @xmath9  gev for the integrated luminosity of 30  fb@xmath10 planned for the first two or three years of lhc running , for each of the various proposed detection channels . a glance at the table shows that , _ either _ large signals are accompanied by a huge background , _ or _ the processes have comparable signal and background rates for which the number of higgs events is rather small .    [ cols=\"<,^,^,^,^ \" , ]     the number of signal and background events for various methods of higgs detection at the lhc . the significance of the signal is also given . the mass of the higgs boson is taken to be 120  gev and the integrated luminosity is taken to be 30 fb@xmath10 . the notation @xmath11 is to indicate that the gluons originate within overall colour - singlet ( hard pomeron ) @xmath12-channel exchanges ; see , for example , fig .  1 . the entries for the various processes are taken , or scaled from the results for 100 fb@xmath10 luminosity , from references ( a ) @xcite , ( b ) @xcite , ( d ) @xcite , ( e ) @xcite , ( g , h ) @xcite and ( i ) @xcite , where the @xmath13 factors have been omitted . processes ( c ) and ( f ) are discussed in detail in sections  2 and 3 , respectively , of this paper . a detailed study of the nlo contributions to the irreducible background to the @xmath14 signal shows the @xmath13 factor is 0.65  that of the signal @xcite . taking these @xmath13 factors into account the authors find that the significance of the @xmath14 signal may increase to @xmath15 .    besides containing the conventional processes for the detection of a light higgs boson , the table also lists processes ( c , d , f ) with a rapidity gap on either side of the boson , which provide a clean environment for its production . these processes are often overlooked , but they have special advantages . here we shall study two of these processes in detail . first , in section  2 , we discuss the exclusive process @xmath16 , where the + sign indicates the presence of a rapidity gap . we show that it is possible to tag the outgoing protons such that the higgs may be identified , and its mass measured to an accuracy of about 1  gev , using the ` missing mass ' method . that is using tagged protons we have @xmath17 with @xmath18 . importantly , the process allows an independent measurement of the higgs mass via the @xmath0 decay , @xmath19 , although now the resolution is much poorer with @xmath20 . the existence of matching peaks , centred about @xmath21 , is a unique feature of the exclusive diffractive higgs signal spectrum , see process  ( a ) of table  1 . ] . besides its obvious value in identifying the higgs and in sharpening the determination of its mass , we will see that the mass equality also plays a key role in reducing background contributions . another advantage of the @xmath22 signal is that , at leading order , the @xmath23 background process is suppressed by a @xmath24 selection rule , see section  2.3 @xcite . of course , we have to pay a price for the survival of the rapidity gaps , so the event rate is low . nevertheless the process has the advantage that the signal exceeds the background . the absolute value of the @xmath25 cross section has been calculated in refs . the derivation is outlined in section  2.1 . moreover the predicted value can be checked experimentally by measuring the rate of the double - diffractive production of dijets ( of comparable mass ) . the uncertainties of the calculation of the @xmath26 cross section are discussed in section  2.2 . equally important to the calculation of the exclusive double - diffractive @xmath27 signal , is the estimation of the @xmath1 background . the background processes are found to be suppressed by their spin and colour structure , and are interesting in their own right . the various sources of the background are discussed in sections  2.3 and 2.4 . first , in section  2.3 , we summarize the sources , together with their sizes relative to the higgs signal , and then , in section  2.4 , we give the detailed justification of the results . section  2.5 is devoted to a study of production by soft pomeron - pomeron collisions . we find that it gives a negligible contribution both to the exclusive @xmath0 signal and to the background . in section  2.6 , we turn to a discussion of the experimental issues connected with the exclusive diffractive signal . we study the experimental efficiencies , the choice of cuts , the accurate determination of the ` missing mass ' via the measurement of the forward protons and , finally , the problems connected with the ` pile - up ' of multiple interactions in each beam crossing . the second process that we study is the central production of a higgs boson via @xmath28 fusion @xmath29 see section  3 . we may suppress the background to this process by exploiting the fact that the cross section is rather flat as a function of the transverse momentum , @xmath30 , of the higgs boson , on account of the large @xmath31 boson mass . moreover , since this process is mediated by @xmath12 channel @xmath31 exchange , which is a point - like colourless object , there is no corresponding bremsstrahlung in the central region @xcite and hence no sudakov suppression of the rapidity gaps .","summary":"petersburg , 188300 , russia + department of physical sciences , university of helsinki , and helsinki institute of physics , finland +","abstract":"we summarize the possible processes which may be used to search for a higgs boson , of mass in the range 114130  gev , at the lhc . we discuss , in detail , two processes with rapidity gaps : exclusive higgs production with tagged outgoing protons and production by weak boson fusion , in each case taking as the signal . we make an extensive study of all possible backgrounds , and discuss the relevant experimental issues . we emphasize the special features of these signals , and of their background processes , and show that they could play an important role in identifying a light higgs boson at the lhc .    plus 2 mm minus 2 mm 23.0 cm 17.0 cm -1.0 in -42pt    ippp/02/29 + dcpt/02/58 + 12 august 2002 +    * ways to detect a light higgs boson at the lhc *    a. de roeck , v.a . khoze , a.d . martin , r. orava and m.g . ryskin + cern , geneva + institute for particle physics phenomenology , university of durham , dh1 3le , uk + petersburg nuclear physics institute , gatchina , st .  petersburg , 188300 , russia + department of physical sciences , university of helsinki , and helsinki institute of physics , finland +"}
{"article_id":"hep-ph0207042","section_id":"c","document":"as emphasized in the introduction there is no single obvious best discovery channel for a light higgs boson at the lhc . rather the search should employ all possibilities . the comparability of channels has some advantages in the measurement of higgs couplings . the double - diffractive higgs production processes ( entries ( c ) and ( d ) of table  1 ) are mediated by the subprocess @xmath225 , and are thus proportional to the @xmath226@xmath227 coupling ( squared ) . the same is true for production processes ( a ) and ( b ) . for process ( a ) the @xmath14 decay is mainly controlled by the @xmath226@xmath28 coupling , while processes ( b ) and ( c ) are proportional to the @xmath226@xmath1 coupling ( squared ) . from table  1 we note the relatively large significance of the wbf processes , ( e ) and ( f ) , in which the higgs signal is separated from forward and backward high @xmath211 jets by rapidity gaps . these wbf processes are , of course , driven by the @xmath226@xmath28 coupling . if the @xmath228 decay process is observed , then we can study the higgs - lepton coupling . the estimates presented in table  1 for this @xmath229 process are taken from ref . the values agree reasonably well with the results results in table  1 of @xcite included a 10% efficiency to identify the two @xmath230 leptons . ] shown in table  1 of ref . thus by measuring combinations of the above processes it is possible to determine the higgs coupling to @xmath33 and @xmath12 quarks , @xmath31 bosons and the @xmath230 lepton . this paper has concentrated on the production of a light higgs boson accompanied by rapidity gaps . in section  2 we discussed exclusive double - diffractive ( cp - even ) higgs production @xmath231 and in section  3 , weak boson fusion via the subprocess @xmath232 in both cases we estimated the cross section for the @xmath22 signal and for the qcd @xmath1 background , at the lhc . the results obtained are summarised in entries ( c ) and ( f ) of table  1 .    provided that appropriate proton taggers are installed ( see section  2.6 ) , process ( [ eq : pp ] ) has the special advantage that the higgs can be identified by a sharp peak in the protons ` missing mass ' spectrum and , simultaneously , as a peak in the @xmath1 mass spectrum . the required equality @xmath131 , allowing for resolution , is of great value , not only to establish the signal , but also to suppress the @xmath233 background . in addition , the existence of a @xmath24 selection rule automatically greatly suppresses the leading order ( lo ) qcd @xmath1 background . we estimated the lo , nlo and nnlo contributions to the @xmath233 background . it turned out that , for production from a colour - singlet two - gluon system , the special colour and helicity structure of the subprocess is such that even the higher order ( nlo , ... ) contributions to the background are suppressed . in summary , we find factor ) as the signal . ] @xmath234 for the exclusive double - diffractive production of a light higgs boson , decaying via @xmath1 , at the lhc . the favourable signal - to - background ratio is offset by a low event rate , caused by the necessity to preserve the rapidity gaps so as to ensure an exclusive signal . nevertheless , entry  ( c ) of table  1 shows that the signal has comparable significance signal and background are included , the significance of this signal is increased to about @xmath15 for 30  fb@xmath10 lhc luminosity and higgs mass @xmath235  @xcite . ] to the standard @xmath14 and @xmath236 search modes ( entries  ( a ) and ( b ) ) . the cross section for the production of a 120  gev higgs boson at the lhc , via the exclusive @xmath25 process , was calculated to be 3  fb ( see section  2.1 ) , but after including the @xmath0 branching fraction , and the acceptance and efficiency cuts , we arrive at only 12% of the signal . the breakdown of the depletion of the signal is summarized at the end of section  2.6 . thus for an integrated luminosity of 30  fb@xmath10 ( 300  fb@xmath10 ) we would register 11 ( 110 ) events . noting the @xmath85 ratio of ( [ eq : stob4 ] ) , we see that these signals have a significance of about @xmath237 and @xmath238 respectively . we estimate a factor of two uncertainty in the cross section for this exclusive higgs signal ( see section  2.2 ) , but a much better reliability for the signal - to - background prediction , ( [ eq : stob4 ] ) , since the main theoretical uncertainties cancel in the ratio ( see section  2.3 ) .    the weak boson fusion signal , ( [ eq : qqconclusion ] ) , does not need the installation of proton taggers , and has a favourable significance ; see section  3 and table  1 . as discussed in section  3.2 , the main problem is to identify these rapidity gap events from the additional pile - up events , that is from overlap interactions in the same bunch crossing . there is good reason to believe that , at the medium luminosity of @xmath222 of the lhc , the problem can be overcome , and that we can go a considerable way to achieving the numbers quoted in entry  ( f ) of table  1 .    in conclusion , we have shown how the rapidity gap processes , ( [ eq : pp ] ) and ( [ eq : qqconclusion ] ) , may play a key role in identifying and studying a light higgs boson at the lhc .","summary":"we discuss , in detail , two processes with rapidity gaps : exclusive higgs production with tagged outgoing protons and production by weak boson fusion , in each case taking as the signal . we emphasize the special features of these signals , and of their background processes , and show that they could play an important role in identifying a light higgs boson at the lhc .    plus 2 mm minus 2 mm 23.0 cm 17.0 cm -1.0 in -42pt    ippp/02/29 + dcpt/02/58 + 12 august 2002 +    * ways to detect a light higgs boson at the lhc *    a. de roeck , v.a .","abstract":"we summarize the possible processes which may be used to search for a higgs boson , of mass in the range 114130  gev , at the lhc . we discuss , in detail , two processes with rapidity gaps : exclusive higgs production with tagged outgoing protons and production by weak boson fusion , in each case taking as the signal . we make an extensive study of all possible backgrounds , and discuss the relevant experimental issues . we emphasize the special features of these signals , and of their background processes , and show that they could play an important role in identifying a light higgs boson at the lhc .    plus 2 mm minus 2 mm 23.0 cm 17.0 cm -1.0 in -42pt    ippp/02/29 + dcpt/02/58 + 12 august 2002 +    * ways to detect a light higgs boson at the lhc *    a. de roeck , v.a . khoze , a.d . martin , r. orava and m.g . ryskin + cern , geneva + institute for particle physics phenomenology , university of durham , dh1 3le , uk + petersburg nuclear physics institute , gatchina , st .  petersburg , 188300 , russia + department of physical sciences , university of helsinki , and helsinki institute of physics , finland +"}
{"article_id":"1003.1637","section_id":"i","document":"the interaction of matter with the electromagnetic field has played a dominant role in the development of our understanding of nature . in classical newtonian continuum mechanics one is concerned with dynamic processes involving the interaction of ( bounded ) classical continua with external forces and torques in space ( see e.g. @xcite ) . in relativistic continuum mechanics the theory is generalized to incorporate the concept of the spacetime manifold and formulated in terms of tensors on this manifold ( see e.g. @xcite ) . in both formulations the histories of configuration variables must be compatible with balance laws associated with possible translational and rotational symmetries of a metric structure and an associated balance law of ` energy ' . if electromagnetic fields are involved these laws are supplemented with the macroscopic maxwell equations in media . as a result of cohesive forces originating at the molecular level the interaction of a material with these ( and gravitational influences ) results in locally induced strains . these strains determine material stresses that are encoded into various ` stress - tensors ' . these in turn describe the local distribution of force and torque densities in the medium . the mathematical structure of such tensors characterizes the response of different materials to external influences . _ constitutive relations _ are relations that are used together with field equations , equations of motion and boundary conditions to fix the dynamic evolution of the independent dynamical variables . if the configuration of the system ( open or closed ) involves thermodynamic variables the classical laws of thermodynamics can be used to constrain these relations for real media . in the newtonian formulation one uses the maxwell and cauchy stress tensors @xcite , together with certain equations of state . in the relativistic formulation a primary role is played by the total stress - energy - momentum tensor for the system . the determination of these tensors , together with appropriate constitutive relations for different types of polarizable uncharged media often requires input from experiment . the electromagnetic constitutive properties and the appropriate electromagnetic stress - energy - momentum for light in moving media has been a subject of debate ( and possible confusion ) for over a century . difficulties arise in properly accounting for the local nature of the wave - matter interaction in terms of experimentally measurable effects . even for static electromagnetic fields there are ( often non - linear ) subtle interactions that induce changes in shape or volume in deformable media dependent on its thermodynamic state . there is a considerable body of opinion suggesting that in some sense the choice between different stress - energy - momentum tensors describing interactions of a material medium with an electromagnetic field is a matter of convenience and that different choices simply provide alternative descriptions of the same overall interaction @xcite . since there is no preferred tensor partition of the _ total _ stress - energy - momentum tensor into sub - tensors describing the behaviour of interacting _ sub - systems _ there can be no unique definition of a stress - energy - momentum tensor describing an interacting subsystem . thus for electromagnetic fields interacting with an electrically neutral bounded continuum it is always possible to _ redefine _ integrated electromagnetic forces and torques on the medium associated with sub - tensors according to taste , particularly if the medium is composed of piecewise inhomogeneous material subsystems or the fields are time dependent . however in order to model the _ total _ interacting system the choice of a total stress - energy - momentum tensor is necessary . if one has decided how to model a neutral but polarizable medium in the _ absence _ of externally applied electromagnetic fields then different choices of a stress - energy - momentum tensor for electromagnetic fields in the medium to describe the additional interactions with such fields will inevitable lead in general to different predictions for the interacting system . although the laws of classical electromagnetism in the vacuum are firmly established in a relativistic context there is no general agreement on how best to accommodate the dynamics of deformable media as a self consistent theory on spacetime , ( see e.g. @xcite ) . this makes any rigorous formulation of relativistic continuum mechanics of inhomogeneous dispersive polarizable media interacting with electromagnetic and gravitational fields difficult even if one contemplates using it for systems in non - relativistic motion in some frame of reference .    despite these shortcomings there has recently been a resurgence of interest in the so - called abraham - minkowski controversy and its relevance to the use of either the abraham or the minkowski form of stress - energy - momentum tensor in interpreting experiments involving electromagnetic fields in media @xcite . part of this difficulty is no doubt due to the complex nature of material responses to forces in general . from our perspective such experiments are seeking constitutive relations involving _ particular _ material systems and the macroscopic maxwell fields in media . as such it should come as no surprise that different systems might yield different responses particularly if the competing effects of electro- or magneto - striction mentioned above are contributing differently in different experiments . a number of historic experiments have sought to detect the discriminating _ abraham force _ this is strictly discriminatory only for homogeneous non - dispersive _ stationary _ media , so calls into question those experiments that involve media in motion . indeed the fundamental difference between the forces or torques induced by the divergence of the abraham and minkowski electromagnetic stress - energy - momentum tensors is that the former , unlike the latter , can depend _ explicitly _ on the acceleration of the medium . from this observation it is our contention that , for any specified electromagnetic constitutive relation , there remain experimental avenues offering new means to discriminate between alternative proposals for the form of the electromagnetic stress - energy - momentum tensor in media , despite the attendant inherent material constitutive complexities . in particular we argue that , in principle , the observed dependence of a time - averaged electromagnetic wave - induced torque on the angular speed of a _ materially isotropic but inhomogeneous _ uniformly rotating electrically neutral medium could be used to discriminate between the electromagnetic wave interactions described by the abraham tensor from those described by the symmetrized version of the tensor introduced by minkowski , and possibly those proposed by others . it is therefore of interest to calculate how such a torque depends on geometric properties of a cylindrical insulator , its speed of rotation and its _ electromagnetic constitutive properties_. since the medium will be assumed electrically polarizable and magnetizable ( but non - conducting ) one is immediately confronted with a number of subtleties associated with the form of this tensor and the _ material constitutive properties _ of the medium . these issues have a bearing on how one formulates the classical electromagnetic force on a macroscopic body particularly one that is accelerating . since this has led to a number of related questions in the recent literature @xcite , this article attempts to make explicit our perspective . after reviewing approaches in the newtonian framework the use of a fully covariant special relativistic framework is advocated . the essentials of this formulation are described below which should be read in conjunction with the expository material on electromagnetic theory in the language of differential forms contained in the appendix . in the following paper , applications to rotating media are discussed in this context .","summary":"the relevance of tensors , associated with the electromagnetic fields that appear in maxwell s equations for polarizable media , to the forces and torques that they induce has been a matter of some debate since minkowski , einstein & laub and abraham considered these issues over a century ago . the notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium . the fact that , unlike the tensor proposed by minkowski , the divergence of the abraham tensor depends _ explicitly _ on the local acceleration field of the medium as well as the electromagnetic field , sets it apart from many other terms in the total stress - energy - momentum tensor for a medium .    in this paper","abstract":"this is paper i of a series of two papers , offering a self - contained analysis of the role of electromagnetic stress - energy - momentum tensors in the classical description of continuous polarizable perfectly insulating media . while acknowledging the primary role played by the _ total _ stress - energy - momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor , when defined with respect to a particular splitting . the relevance of tensors , associated with the electromagnetic fields that appear in maxwell s equations for polarizable media , to the forces and torques that they induce has been a matter of some debate since minkowski , einstein & laub and abraham considered these issues over a century ago . the notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium . consistency with the laws of newtonian continuum mechanics demands that the _ total _ force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the _ total _ stress - energy - momentum tensor . the fact that , unlike the tensor proposed by minkowski , the divergence of the abraham tensor depends _ explicitly _ on the local acceleration field of the medium as well as the electromagnetic field , sets it apart from many other terms in the total stress - energy - momentum tensor for a medium .    in this paper we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular killing symmetries . it is shown how the drive - forms associated with translational killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature ."}
{"article_id":"1003.1637","section_id":"c","document":"the general theory of drive - forms has been developed starting from the vanishing divergence of a total stress - energy - momentum in an arbitrary spacetime using the language of exterior systems . it has been shown that a decomposition of a drive 3-form , relative to a unit timelike vector field , on a spacetime with sufficient killing vectors yields forms that can be associated with force and torque densities in continuous media . for material subject to the electromagnetic constitutive relations proposed by minkowski it has also been shown how the computation of the electromagnetic force density on a non - accelerating polarizable perfectly insulating medium in an electromagnetic field can be effectively carried out in terms of a particular split of the total stress - energy - momentum into parts describing its inertial and electromagnetic properties . in paper ii this theory is applied to homogeneous and inhomogeneous dielectric media where it is argued that a means of discriminating between a split into the electromagnetic stress - energy - momentum tensors proposed by abraham and minkowski ( and possibly others ) can be explored experimentally using rotating media .","summary":"consistency with the laws of newtonian continuum mechanics demands that the _ total _ force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the _ total _ stress - energy - momentum tensor . we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular killing symmetries . it is shown how the drive - forms associated with translational killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature .","abstract":"this is paper i of a series of two papers , offering a self - contained analysis of the role of electromagnetic stress - energy - momentum tensors in the classical description of continuous polarizable perfectly insulating media . while acknowledging the primary role played by the _ total _ stress - energy - momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor , when defined with respect to a particular splitting . the relevance of tensors , associated with the electromagnetic fields that appear in maxwell s equations for polarizable media , to the forces and torques that they induce has been a matter of some debate since minkowski , einstein & laub and abraham considered these issues over a century ago . the notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium . consistency with the laws of newtonian continuum mechanics demands that the _ total _ force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the _ total _ stress - energy - momentum tensor . the fact that , unlike the tensor proposed by minkowski , the divergence of the abraham tensor depends _ explicitly _ on the local acceleration field of the medium as well as the electromagnetic field , sets it apart from many other terms in the total stress - energy - momentum tensor for a medium .    in this paper we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular killing symmetries . it is shown how the drive - forms associated with translational killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature ."}
{"article_id":"1005.1086","section_id":"i","document":"cluster algebras are encountered in many algebraic and geometric contexts , with combinatorics providing a unifying framework . this short paper reviews the origins of cluster algebras , their deep connections with total positivity phenomena , and some of their recent manifestations in teichmller theory . the introduction of cluster algebras , made in joint work with a.  zelevinsky  @xcite , was rooted in the desire to understand , in a concrete and combinatorial way , g.  lusztig s theory of total positivity and canonical bases in quantum groups ( see , e.g. , @xcite ) . although this goal remains largely elusive ( cf . @xcite ) , the concept proved valuable due to its surprising ubiquity , and to the connections it helped uncover between diverse and seemingly unrelated areas of mathematics .    this paper gives a popular and quick introduction to the subjects in the title , aimed at an uninitiated reader , and roughly following the historical order of modern developments in the two related fields . cumbersome technicalities involved in the usual definition of cluster algebras are largely omitted , giving way to prototypical examples from which the reader is invited to generalize , to discussions of underlying motivations , and to hints concerning further applications and extensions of the basic theory . many important aspects are left out due to space limitations . the style is rather informal , owing to the desire to see the forest through the trees , and to make the paper accessible to a general mathematical audience . there are no numbered formulas or theorems : results are stated as part of the general narrative . some attributions are missing ; they can be found in the sources quoted . the goal is to give the reader an intuitive feel for what cluster algebras are , and motivate her / him to read the more formal expositions elsewhere . several survey / introductory papers dedicated to the subjects in the title , approached from various perspectives , have already appeared in the literature ; see  in particular @xcite . an excellent introduction to applications of cluster algebras in representation theory is given in b.  leclerc s contribution  @xcite to these proceedings . besides consulting these sources and references therein , the reader is invited to visit the _ cluster algebras portal _ @xcite , which provides numerous links to publications , conferences , seminars , thematic programs , software packages , etc . our presentation is loosely based on the papers @xcite , joint with a.  berenstein , m.  shapiro , d.  thurston , and a.  zelevinsky . section  [ sec : tp ] introduces total positivity and the idea of a positive / nonnegative part of an algebraic variety . section  [ sec : cluster ] presents the basic notions of cluster algebra theory , emphasizing its  roots in total positivity . section  [ sec : teich ] discusses the occurence of cluster algebras in combinatorial topology of triangulated surfaces , and connections with teichmller spaces . the format of this brief survey does not allow us to discuss several important directions of current research on cluster algebras and related fields . in particular , not covered here are the theory of _ cluster categories _ and the various facets of _ categorification _ @xcite ; the connections between cluster algebras and _ poisson geometry _ @xcite ; closely related work on cluster varieties arising in _ higher teichmller theory _ @xcite ; the polyhedral combinatorics of _ cluster fans _ and _ cambrian lattices _ @xcite ; applications to _ discrete integrable systems _ @xcite ; the machinery of _ quivers with potentials _ @xcite ; connections with _ donaldson - thomas invariants _ @xcite ; and other exciting topics . * acknowledgments . * the discovery of cluster algebras , the main work leading  to it , and the development of fundamentals of the general theory were all done jointly with my longtime collaborator andrei zelevinsky . i  am indebted to him , and to my co - authors arkady berenstein , michael shapiro , and dylan thurston for their invaluable contributions to our joint work discussed below . catharina stroppel persuaded me to give a talk in bonn whose design this presentation follows . bernhard keller , george lusztig , and kelli talaska made valuable editorial suggestions .","summary":"this is a brief and informal introduction to cluster algebras . it roughly follows the historical path of their discovery , made jointly with a.  zelevinsky . primary 13f60 , secondary 05e10 , 05e15 , 14m15 , 15a23 , 15b48 , 20f55 , 22e46 .   ","abstract":"this is a brief and informal introduction to cluster algebras . it roughly follows the historical path of their discovery , made jointly with a.  zelevinsky . total positivity serves as the main motivation .    primary 13f60 , secondary 05e10 , 05e15 , 14m15 , 15a23 , 15b48 , 20f55 , 22e46 .    total positivity , cluster algebra , chamber minors , quiver mutation ."}
{"article_id":"1103.6031","section_id":"i","document":"cold dark matter density perturbations drive all of cosmological structure formation ( e.g. * ? ? ? * ; * ? ? ? * ) in the current paradigm . their non - linear growth is followed with numerical simulations over an enormous range of scales . from scales of hundreds of megaparsecs ( e.g. * ? ? ? * ; * ? ? ? * ) studying cosmological large - scale structure ; to several hundred kilo parsecs modeling the formation and evolution of galaxies including aspects of the interstellar medium , molecular cloud - formation and black - hole accretion processes ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ; and even the formation of the first proto - stars formed at scales of a few solar radii ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) are studied in cosmic context . the fluctuations in the standard model would extend from solar system size to giga parsec scales . no single calculation would be able to capture all these scales . one may therefore strive to carry out simulations in as large volumes as possible to study a range of representative environments for the formation of particular cosmological objects . at the same time , however , high resolution is necessary to sample the underlying gravitational potential wells . a popular way to achieve large simulation boxes with as high as possible resolution for individual objects is the so - called `` zoom - in '' technique ( following versions of e.g. * ? ? ? * ; * ? ? ? in this technique , a small region encapsulating the formation history of the object of interest is studied with much higher resolution inside of a lower resolution representation of its larger - scale cosmic environment interacting with the object through long - range gravitational forces . the aim is to represent both the variance of the fluctuations on scales of the object ( sample variance ) due to the use of a large volume which provides a fair sample of cosmic environments ( cf . * ; * ? ? ? * ) , as well as the smaller scale fluctuations affecting the structure of the object directly .    typically , two approaches have been followed for initial conditions of `` zoom - in simulations '' . either , initial conditions are generated on a uniform grid at the full resolution ( which can amount to a huge need for computational resources for deeply nested grids , see e.g. * ? ? ? * ; * ? ? ? * ) and subsequently degraded by either averaging over regions of @xmath1 particles , where @xmath2 is the de - refinement factor outside the high resolution region , or by fourier resampling . there are several disadvantages with this approach : first , the computational requirements are immense compared to the solution sought ; and second , the simple averaged velocity fields are neither continuous nor differentiable across coarse - fine boundaries , leading to spurious shocks in baryonic simulations . alternatively , e.g. the grafic-2 code @xcite is used which employs discrete fourier transforms to add small scales perturbations to coarser perturbations . the grafic-2 approach however requires the use of an anti - aliasing filter which damps out small - scale power and shows oscillatory errors at the few per - cent level that result from the combination of discrete fourier transforms of different resolution . furthermore , it does not incorporate the sampling of the real - space transfer function advocated by @xcite and @xcite . this latter aspect is a feature of all codes that generate initial conditions by an inverse fourier transform of a sampled power spectrum on a three - dimensional lattice and thus also plagues most applications of the previous approach . @xcite has shown conclusively that this conventional method can lead to a significant error in the real - space statistical properties , in particular for small cosmological box sizes . this paper extends on previous work by proposing a new algorithm to generate multi - scale nested initial conditions ( as * ? ? ? * ) , but using a real - space convolution kernel to represent the fourier space transfer function of density perturbations ( cf . * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) in a multi - scale convolution algorithm combined with an adaptive multi - grid algorithm to determine initial velocities , particle positions and densities compatible with lagrangian cosmological perturbation theory up to second order . more specifically , the approach uses mass conservation constraints to determine the convolution kernel from an accurate real space representation of the transfer function kernel on a hierarchy of levels , which are used in fft convolutions to obtain the density field from a hierarchical white noise field , and a two - way interface multigrid poisson solver that achieves smooth gradients across coarse - fine boundaries . the resulting errors are confined to the boundaries and at the level of a few @xmath0 in units of the standard deviation of the respective fields for the interior of the refined region . we furthermore show that using a hybrid poisson solver ( using multi - grid for the hierarchy of grids and fft for the finest grid ) , our method produces particle distributions that closely match the input power spectrum also on the smallest scales and make our approach attractive also for uni - grid simulations . all the methods discussed in this paper are implemented in the initial conditions code music ( multi - scale initial conditions ) . the code also includes an implementation of a linearized boltzmann solver based on linger @xcite that allows the calculation of cosmological density and velocity perturbations for dark matter and baryons . the paper is organised as follows . in section [ sec : densities ] , we discuss a multi - scale convolution method that produces a nested density field that is consistent with both the input correlation function and the input power spectrum , and which is then used as the source field for lagrangian perturbation theory . computing displacement and velocity fields in lagrangian perturbation theory ( lpt ) requires a numerical solution to poisson s equation . in section [ sec : dispvel ] , after briefly summarizing lpt , we describe the adaptive multi - grid algorithm that we use to obtain displacement and velocity fields . we also introduce a hybrid fourier - space / multi - grid based poisson solver which has better fourier - space properties on small scales compared to the pure multi - grid algorithm . in section [ sec : error_analysis ] , we discuss the performance of our method compared to initial conditions generated purely in fourier - space both in unigrid and nested grid set - ups . we generalize our approach to initial conditions for two - component dark - matter and baryon simulations in section [ sec : baryon_ics ] and propose the usage of the local lagrangian approximation to generate inital baryon density fields for grid codes before we summarize and conclude our results in section [ sec : summary ] .","summary":"finally , we generalize our approach for two - component baryon and dark - matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory . for initial baryon density fields , it is suggested to use the local lagrangian approximation in order to generate a density field for mesh based codes that is consistent with lagrangian perturbation theory instead of the current practice of using the eulerian linearly scaled densities .    = 1    [ firstpage ]    cosmology : theory , large - scale structure of universe  galaxies : formation  methods : numerical","abstract":"we discuss a new algorithm to generate multi - scale initial conditions with multiple levels of refinements for cosmological `` zoom - in '' simulations . the method uses an adaptive convolution of gaussian white noise with a real space transfer function kernel together with an adaptive multi - grid poisson solver to generate displacements and velocities following first ( 1lpt ) or second order lagrangian perturbation theory ( 2lpt ) . the new algorithm achieves rms relative errors of order for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches . in addition , errors are localized at coarse - fine boundaries and do not suffer from fourier - space induced interference ringing . an optional hybrid multi - grid and fast fourier transform ( fft ) based scheme is introduced which has identical fourier space behaviour as traditional approaches . using a suite of re - simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions , density profiles , key halo properties and subhalo abundances with per cent level accuracy . finally , we generalize our approach for two - component baryon and dark - matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory . for initial baryon density fields , it is suggested to use the local lagrangian approximation in order to generate a density field for mesh based codes that is consistent with lagrangian perturbation theory instead of the current practice of using the eulerian linearly scaled densities .    = 1    [ firstpage ]    cosmology : theory , large - scale structure of universe  galaxies : formation  methods : numerical"}
{"article_id":"1103.6031","section_id":"i","document":"we have presented and implemented a method to generate real - space sampled initial conditions for nested grids , extending prior work by @xcite , @xcite and @xcite . these initial conditions are suitable for `` zoom - in '' cosmological simulations of structure formation with several levels of refinement that allow the study of single cosmological objects , such as e.g. groups and clusters of galaxies , single galaxies , or first stars , in a cosmological context at very high resolution while maintaining a small computer memory footprint . apart from the general advantage of real - space sampled initial conditions discussed by @xcite and @xcite , namely a correct reproduction of real - space statistical properties , such as the two - point correlation function and mass variance in spheres , we demonstrate that our multi - scale convolution approach for nested grids has very favourable error properties : ( 1 ) no interference of different modes between different refinement levels , and ( 2 ) errors confined to coarse - fine boundaries . we find rms errors of velocity / displacement fields in the refined region at the order of @xmath0 in units of the standard deviation of the respective fields which is an improvement of about two orders of magnitude over previous approaches .    in order to determine particle displacement and velocity fields , at first and second order lagrangian perturbation theory , we followed two approaches . first , a pure multi - grid poisson solver is used . we show that the finite volume discretization it assumes leads to a suppression of perturbations at the smallest scales that can however be corrected by a deconvolution . second , a hybrid poisson solver is developed , which uses an adaptive multi - grid algorithm for inter - level gravity and an fft - based poisson solver for the finest grid . this hybrid approach leads to no suppression of small scale perturbations . analyzing statistical properties of unigrid simulations for which initial conditions have been generated with the two different approaches , we find however that non - linear objects are not sensitive to the lack of power at these very small scales and differences are only seen in the mildly non - linear regime and at the lowest halo masses . we conclude that our real - space based approach is well suited also for initial conditions for unigrid simulations .    in order to verify the accuracy of nested initial conditions generated with our method , we investigated the properties of a galaxy cluster both in a unigrid simulation and a `` zoom - in '' simulation with one and two levels of refinement . we find that the gross properties of the cluster , such as virial mass , radius , spin , shape and velocity dispersion , are recovered at per cent level or better in the re - simulations . density profiles show no bias with scatter at the level of a few per cent , mainly attributable to slight changes in the positions of sub - structures in the re - simulations . we also find that the sub - halo mass function is recovered with an accuracy of a few per cent in all re - simulations , and observe that the hybrid poisson solver performs slightly better than the pure multi - grid approach . we thus conclude that our algorithm does not introduce bias or unreasonable scatter in observables that will be deduced from such a re - simulation and will thus provide a reliable tool to study the internal structure of cosmological observables at high resolution in large cosmological volumes . finally , we study the inclusion of a baryonic component in our approach by generalising the use of real space transfer functions also for distinct baryon and cdm density and velocity perturbations . we demonstrate that our approach reproduces the evolution expected from linear perturbation theory correctly . furthermore , we propose to set the initial baryon density field based on a local lagrangian approximation which is consistent with lagrangian perturbation theory of first or second order and which greatly reduces the dependence of the baryon density field on the starting redshift of the simulation , thus reducing transient behaviour .","summary":"the method uses an adaptive convolution of gaussian white noise with a real space transfer function kernel together with an adaptive multi - grid poisson solver to generate displacements and velocities following first ( 1lpt ) or second order lagrangian perturbation theory ( 2lpt ) . the new algorithm achieves rms relative errors of order for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches . fast fourier transform ( fft ) based scheme is introduced which has identical fourier space behaviour as traditional approaches . using a suite of re - simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions , density profiles , key halo properties and subhalo abundances with per cent level accuracy .","abstract":"we discuss a new algorithm to generate multi - scale initial conditions with multiple levels of refinements for cosmological `` zoom - in '' simulations . the method uses an adaptive convolution of gaussian white noise with a real space transfer function kernel together with an adaptive multi - grid poisson solver to generate displacements and velocities following first ( 1lpt ) or second order lagrangian perturbation theory ( 2lpt ) . the new algorithm achieves rms relative errors of order for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches . in addition , errors are localized at coarse - fine boundaries and do not suffer from fourier - space induced interference ringing . an optional hybrid multi - grid and fast fourier transform ( fft ) based scheme is introduced which has identical fourier space behaviour as traditional approaches . using a suite of re - simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions , density profiles , key halo properties and subhalo abundances with per cent level accuracy . finally , we generalize our approach for two - component baryon and dark - matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory . for initial baryon density fields , it is suggested to use the local lagrangian approximation in order to generate a density field for mesh based codes that is consistent with lagrangian perturbation theory instead of the current practice of using the eulerian linearly scaled densities .    = 1    [ firstpage ]    cosmology : theory , large - scale structure of universe  galaxies : formation  methods : numerical"}
{"article_id":"astro-ph9810407","section_id":"i","document":"the type ii linear supernova ( sn ii - l ) sn 1980k in ngc 6946 reached a peak brightness of v = 11.4 in november 1980 ( see barbon , ciatti , & rosino 1982 ; @xcite and references therein ) . despite a steadily declining flux through 1982 ( @xcite ) , faint h@xmath1 emission from sn 1980k was detected in 1987 through narrow passband imaging ( @xcite , hereafter fb90 ) . low - disperson optical spectra obtained in 1988 and 1989 showed broad , 6000 km s@xmath0 h@xmath1 and [ o  i ] 6300,6364   emission , along with weaker line emission from [ ca  ii ] 7291,7324    and/or [ o  ii ] 7319,7330  , [ o  iii ] 4959,5007  , and [ fe  ii ] 7155   ( fb90 ; @xcite ; leibundgut et al . monitoring of its optical flux from 1988 through 1992 indicated a nearly constant luminosity ( leibundgut , kirshner , & porter 1993 ; fesen , & matonick 1994 , hereafter fm94 ) . following the optical recovery of sn  1980k , a handful of other sne ii - l have been optically detected 7  25 yr after maximum light . these include sn  1986e in ngc  4302 ( @xcite ) , sn  1979c in m100 ( @xcite ) , and sn  1970 g in m101 ( @xcite ) . the late - time optical spectra of all these sne show broad h@xmath1 and forbidden oxygen emission lines , and these characteristics have been exploited in searching for fainter , late - time sne ii - l ( e.g. , sn 1985l in ngc  5033 ; fesen 1998 ) .    of the few sne ii - l recovered at late times , sn  1979c in m100 ( ngc 4321 ) is particularly noteworthy . this sn was exceptionally bright at outburst for a type ii event , with a peak @xmath10 of 20 mag ( @xcite ; @xcite ) , and became bright in the radio as well , eventually reaching a 6 cm luminosity more than 200 times that of cas a ( weiler et al . 1989 ) . it also exhibits among the highest , late - time h@xmath1 luminosity ( @xmath11 @xmath12 10@xmath13 erg s@xmath0 ) and shows radio emission variability which may be due to a periodic modulation of the progenitor s pre - sn mass loss ( @xcite ) . late - time optical sn ii emission lines are thought to arise from interactions with surrounding circumstellar mass loss material ( csm ) . these interactions lead to the formation of a reverse shock moving back into the expanding ejecta which then subsequently ionizes , either by far - uv or x - ray emission , a broad inner ejecta region from which the optical lines are produced ( chevalier & fransson 1994 , hereafter cf94 ) . this model is also consistent with the presence of accompanying nonthermal radio emission in all optically recovered sne ii - l , with radio light curves like those predicted from the `` mini - shell '' model involving shock generated synchrotron emission from the forward shock ( chevalier 1982 ; weiler et al . 1993 ) . late - time sn ii emission lines are important for the information they can provide on sne ejecta abundances , late - time shock emission processes , and the mass - loss history and evolutionary status of sn progenitors ( leibundgut et al . 1991 ; @xcite , montes et al . 1998 ) . unfortunately , optical emission lines from old sne ii - l are quite faint ( @xmath14 10@xmath15 erg @xmath5 s@xmath0 @xmath0 ) , making accurate measurements difficult even using 4-m class telescopes . consequently , much is still uncertain about their spectra , even for sn  1980k , the best and longest studied object . for example , virtually nothing is known about sn ii - l spectra below 5000  , and uncertainties remain as to whether [ ca  ii ] or [ o  ii ] is chiefly responsible for the strong emission commonly seen near 7300  . sn  1980k s current optical properties are of special interest due to a recently reported sharp decline in nonthermal radio flux in the interval 19941997 ( montes et al . 1998 ) .    here we present a 1995 keck spectrum of sn 1980k which shows the region below 5000   for the first time , and a november 1997 mdm spectrum useful for investigating its recent h@xmath1 flux . we then compare these sn  1980k data to a 1993 mmt spectrum of sn  1979c at a similar age to the keck sn  1980k spectrum . we also present a 1997 _ hst _ uv spectrum of sn  1979c which reveals several strong uv and near - uv lines which help clarify the nature of the observed emission . finally , we outline some general observed properties of late - time sne ii - l and compare them with young galactic supernova remnants ( snrs ) .","summary":"we review the overall observed range of late - time sne ii - l properties and briefly discuss their properties relative to young , ejecta dominated galactic snrs .","abstract":"a low - dispersion keck i spectrum of sn  1980k taken in august 1995 ( t = 14.8 yr after explosion ) and a november 1997 mdm spectrum ( t = 17.0 yr ) show broad 5500 km s emission lines of h , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  . weaker but similarly broad lines detected include [ fe  ii ] 7155  , [ s  ii ] 4068,4072  , and a blend of [ fe  ii ] lines at 50505400  . the presence of strong [ s  ii ] 4068,4072   emission but a lack of [ s  ii ] 6716,6731   emission suggests electron densities of 10 . from the 1997 spectra , we estimate an h flux of erg s indicating a 25% decline from 19871992 levels during the period 1994 to 1997 , possibly related to a reported decrease in its nonthermal radio emission .    a may 1993 mmt spectrum of sn  1979c ( t = 14.0 yr ) shows a somewhat different spectrum from that of sn  1980k . broad , 6000 km s emission lines are also seen but with weaker h , stronger [ o  iii ] 4959,5007  , more highly clumped [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph , near - uv spectrum ( 2200  4500  ) shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weak [ ne  iii ] 3969  , [ s  ii ] 4068,4072   and [ o  iii ] 4363   emissions . the uv emission lines show a double - peak profile with the blueward peak substantially stronger than the red , suggesting dust extinction within the expanding ejecta ( e[b  v ] = mag ) . the lack of detectable [ o  ii ] 3726,3729   emission together with [ o  iii ] ( 4959 + 5007)/4363 4 imply electron densities 10 .    these new sne ii - l spectra show general agreement with the lines expected in a circumstellar interaction model , but the specific models that are available show several differences with the observations . high electron densities ( 10 ) result in stronger collisional de - excitation than assumed in the models , thereby explaining the absence of several moderate to strong predicted lines such as [ o  ii ] 3726,3729  , [ n  ii ] 6548,6583  , and [ s  ii ] 6716,6731  . interaction models are needed that are specifically suited to these supernovae . we review the overall observed range of late - time sne ii - l properties and briefly discuss their properties relative to young , ejecta dominated galactic snrs ."}
{"article_id":"astro-ph9810407","section_id":"r","document":"the keck and mdm spectra of sn  1980k are shown in figures 1 and 2 respectively . though the keck spectrum has significantly higher s / n , both show broad h@xmath1 and [ o  i ] 6300,6364   lines plus emission near 7100   and 7300  . these features have been seen in earlier sn  1980k spectra with roughly the same relative strengths and widths as seen here . however , the line profiles are better defined in the keck data and the spectrum reveals other fainter emission lines not previously seen . * h@xmath1 : * sn 1980k s late - time optical flux was first detected in 1987 via its strong h@xmath1 emission and it remains among the strongest optical lines observed a decade later . the 1995 keck spectrum shows the h@xmath1 line profile with an expansion velocity of 5700 to + 5500 km s@xmath0 with a strong asymmetry toward the blue , in good agreement with earlier 1992 and 1994 measurements ( fm94 ; fesen , hurford , & matonick 1995 , hereafter fhm94 ) . a comparison of sn  1980k s h@xmath1 line profile and strength changes over the last ten years is shown in figure 3 using the lick june 1988 spectrum ( fb90 ) and our november 1997 mdm data . besides illustrating a drop in h@xmath1 flux over this time period ( see section 4 below ) , one also sees a substantial decrease in the line width , most noticeable toward the blue edge . in 1988 , the fwhm of h@xmath1 was around 220  , compared to 190   in 1997 . this decrease is consistent with earlier measurements ( fm94 ) and is predicted by sn  csm interaction models ( cf94 ) . however , the asymmetric profile of h@xmath1 appears not to have changed much during the last ten years , with a sharp blue emission edge and an emission peak near 6500   visible in both the 1988 and 1997 line profiles . a faint , unresolved line is seen on top of the broader h@xmath1 emission around zero radial velocity . a narrow h@xmath1 emission feature was evident in the 1988 lick spectrum , but much less so in subsequent data ( fm94 ; fhm95 ) . well detected again here , this narrow h@xmath1 emission may be due to a small h  ii region near the sn site or ionized wind material associated with the progenitor ( fb90 ; fhm95 ) .    from the 1997 mdm spectrum , we estimate a broad emission h@xmath1 flux of @xmath4 erg @xmath5 s@xmath0 . this is close to the 1.4 @xmath24 10@xmath25 erg @xmath5 s@xmath0 value reported by fhm95 for a 1994 spectrum and supports the conclusion of a @xmath7 25% fading from flux levels observed in the late 1980s and early 1990s . * h@xmath26 : * there is broad emission near 4850  , some of which may be due to h@xmath26 4861  . its line strength , however , is difficult to disentangle from other possible emission lines between 4800 and 5000   ( see below ) . nonetheless , the observed h@xmath1/h@xmath26 line ratio must be @xmath27 6 , suggesting , after correcting for a foreground reddening of e(b  v ) = 0.40 mag ( @xcite ) , an intrinsic value @xmath27 4 . * h@xmath28 : * weak emission near 4350   may be attributable in part to h@xmath28 emission , blended with [ o  iii ] 4363  .    * [ o  i ] : * the broad [ o  i ] 6300,6364   emission is asymmetric towards the blue with a steep blue edge and a more gradual decline toward the red . the line s full velocity range is 6000 km s@xmath0 if attributed to 6300   on the blue side , and @xmath27 + 1700 km s@xmath0 if attributed to 6363   on the red . the blueward velocity is larger than the 4800 km s@xmath0 estimated by fm94 , probably due in part to weaker emission detected due to the higher s / n in the keck spectrum . in addition , a prominent emission peak at 6280    suggests strong clumping of the o - emitting material in the sn s facing expanding hemisphere .    * [ o ii ] : * one of the strongest emission features in the spectrum , rivaling h@xmath1 and [ o  i ] , lies near 7300  , and extends from 7180 to 7420  . it has been alternatively identified as [ ca ii ] 7291,7324   ( @xcite ; fhm95 ) , [ o  ii ] 7319,7330 (in sn1979c ; fm93 ) , or a combination of the two ( fb90 ; fm94 ) . cf94 suggest it is likely to be solely [ ca ii ] since these [ o  ii ] lines are weak in a variety of sn  csm models and in a variety of photoionized objects . however , these models also predict appreciable ca  ii infrared triplet emission ( 8498 , 8542 , 8662  ) which is absent in sn  1980k s near - ir spectrum ( fm94 ; fhm95 ) . figure 4a shows sn  1980k s [ o  i ] 6300,6364   line profile in terms of expansion velocity relative to 6300   compared to the 7300   feature if identified as the [ o  ii ] line blend at 7325   ( top panel ) , or [ ca  ii ] using the stronger 7291   [ ca  ii ] line ( bottom panel ) . the [ o  ii ] blend interpretation is seen to provide a better match to [ o  i ] s line width and its emission substructure than a [ ca  ii ] interpretation . for instance , the 6280   emission peak in the [ o  i ] line profile matches well with the 7300   feature s emission feature at 7300   if interpretated as an [ o  ii ] blend . in addition , the velocity of the 7300   feature s fwhm blueward edge agrees within measurement uncertainties to those of [ o  i ] and h@xmath1 using the 7319   [ o  ii ] line : namely , 4750 , 4500 , and 4600 km s@xmath0 for [ o  i ] , h@xmath1 , and 7300 respectively , compared to 3450 km s@xmath0 using [ ca  ii ] 7291  .    a possible complication is an atmospheric absorption band at 7190   which might have affected the 7300   feature s blue emission . this telluric absorption band is not especially strong , however , and though it could help to explain the poor [ ca  ii ] profile match to that of [ o  i ] at large negative velocities ( see fig . 4 ) , there still would remain the discrepancy along the line s red end . we therefore conclude that [ o  ii ] 7319,7330   emission is the dominant cause for the 7300   emission feature .    * [ o iii ] : * previous sn 1980k spectra detected broad emission near 5000 with an emission peak near 4955  . the broad emission was initially identified as [ o  iii ] 4959,5007   emission ( fb90 ; @xcite ; fm94 ) although @xcite suggested it might be a blend of permitted fe  ii lines . as seen in figure 1 , broad emission extends from 4750 to 5020 and from 5100 to 5400  , with little emission between 5020 and 5100  . absence of strong emission just redward of 5007   is hard to reconcile with a broad , 5000 km s@xmath0 [ o  iii ] line profile like seen for [ o  i ] , [ o  ii ] , and h@xmath1 unless the [ o  iii ] emission is weak and has a strong blue asymmetry . in fact , the sharp cutoff of emission at 5020   places an expansion limit on strong [ o  iii ] 5007   emission of @xmath29 km s@xmath0 . nonetheless , [ o  iii ] appears a much more likely identification than either permitted or forbidden fe  ii and fe  iii lines ( cf . fhm95 ) , especially in view of the clear [ o  iii ] emission in other sne ii - l ( e.g. , sn 1979c ; see section 3.2 ) . the far blue side of the feature is probably due to h@xmath26 4861  . finally , weak emission near 4350   may be a blend of [ o  iii ] 4363   and h@xmath28 . the keck spectrum also shows two narrow lines at 4957 and 5005  . these are probably related to the narrow h@xmath1 emission observed . however , in many earlier spectra , only one emission spike , around 4950  4960  , could be clearly seen ( fb90 ; @xcite ; fm94 ) and was interpreted as possible evidence of emission substructure in the 4959,5007 [ o iii ] blend . an alternative explanation is that the narrow 4959   line emission happens to coincide with a @xmath30 km s@xmath0 emission feature in the broad [ o  iii ] line , like that seen in the [ o  i ] and [ o  ii ] line profiles .    * [ fe ii ] : * emission near 7100   which merges into the red wing of the 7300   line is likely [ fe  ii ] 7155   ( fb90 ; fm94 ) . adopting a line center of 7100   gives an emission centroid velocity of 2300 km s@xmath0 . emission extends toward the blue as far as @xmath7 7010   suggesting a maximum velocity of 6000 km s@xmath0 . due to the blend with the [ o  ii ] 7300   feature , little can be determined regarding its maximum recession velocity . however , the line extends at least to 7175   ( + 800 km s@xmath0 ) .    broad weak emission from 5020 to 5400   can be understood in terms of blends of several [ fe  ii ] lines  specifically the 5112 ( 19f ) , 5158 ( 18f ) , 5159 ( 19f ) , 5262 ( 19f ) , 5269 ( 18f ) , 5273 ( 18f ) , and 5334 ( 19f )   lines . these represent all of the stronger [ fe  ii ] lines from the multiplets 18f and 19f typically seen in shocked supernova remnant emissions ( cf . fesen & hurford 1996 ) . adopting a line center shift of 2300 km s@xmath0 and a velocity width of 6000 to + 3500 km s@xmath0 like that seen for the [ fe  ii ] 7155   line , a blend of [ fe  ii ] lines can explain the 50205400   emission : specifically , its width , peak intensity near the strong 5158 and 5159 [ fe  ii ] lines , and the lack of emission longward of 5400   and shortward of 5050  . * [ s ii ] : * the weak emission feature near the blue end of the keck spectrum appears to be [ s  ii ] 4069,4076  . adopting this identification , sulfur has a velocity range of @xmath31 to + 4000 km s@xmath0 , comparable to the broad h and o lines . as with other lines , the [ s  ii ] profile also shows a strong blue asymmetry , with a line center shifted to the blue at least 2000 km s@xmath0 . finally , we note there is no obvious emission from the nebular [ s  ii ] 6716,6731 lines in either the keck or mdm spectra , and previous sn  1980k studies have failed to detect any [ s  iii ] 9069,9531   emission ( fhm95 ) .        a 1993 mmt spectrum of sn  1979c taken 14 yr after maximum light , or roughly the same age as sn  1980k when the 1995 keck spectrum was obtained , is shown in figure 5 . the spectrum is similar to those presented by fm93 but with much improved s / n especially in the blue . * h@xmath1 : * broad h@xmath1 emission is detected with an expansion velocity of @xmath32 km s@xmath0 . a strong , narrow h@xmath1 component is also seen at + 120 velocity in m100 s rest frame ( v = + 1570 km s@xmath0 ) . the broad h@xmath1 emission has a flux of @xmath33 erg @xmath5 s@xmath0 , or slightly larger than the @xmath34 erg @xmath5 s@xmath0 reported by fm93 . s peak flux is somewhat weaker than [ o  i ] 6300   and the profile shows a strong blue asymmetry . narrow [ s  ii ] 6716,6731   emission is seen along its red edge , presumably associated with the narrow h@xmath1 emission .    * [ o i ] : * sn  1979c s late - time [ o i ] 6300,6364   emission profile is double - peaked much like that reported by fm93 but with different peak velocities . from the mmt spectrum , we measure peaks at 6230 and 6320    ( @xmath35 and @xmath36 km s@xmath0 if attributed to just the 6300   line ) , whereas fm93 found peaks at 6214 and 6329    ( @xmath37 and @xmath38 km s@xmath0 ) . however , [ o  i ] s full expansion velocity in the mmt spectrum is @xmath39 to @xmath40 km s@xmath0 and in good agreement with fm93 . a june 1998 2.4 m mdm [ o  i ] image of sn  1979c taken using the same filter used by fm93 indicates a 10% increase in [ o  i ] luminosity between 1991.5 and 1998.5 .    * [ o ii ] : * fm93 identified the emission near 7300   as [ o  ii ] 7319,7330   based upon the excellent match of the feature s double - peaked velocity profile with the [ o  i ] emission peaks . two strong emission peaks can also be seen in the mmt spectrum at 7240   and 7347  . these correspond to @xmath41 and @xmath42 km s@xmath0 in m100 s rest frame , in agreement with the above measured [ o  i ] peak velocities . this is graphically shown in figure 4b and helps validate the [ o  ii ] identification made for the sn  1980k spectrum . we note that the [ o  ii ] 7319,7330   emission appears stronger in 1993 relative to [ o  i ] when compared to 1991/1992 data ( fm93 ) , making it now the strongest feature in sn  1979c s optical spectrum .    * [ o iii ] : * the mmt spectrum of sn  1979c also shows broad , strong [ o  iii ] emission centered at 4965   and spanning 4880 to 5060  , which translate to @xmath39 to + 1600 km s@xmath0 . no emission peaks like those seen for [ o  i ] and [ o  ii ] are evident from these data . we measure an observed [ o  iii ] flux of @xmath43 erg @xmath5 s@xmath0 .    broad emission at 5750  : weak but very broad emission is also seen near 5750   and extending from 5550 to 6000  . though faint , this emission is consistent with an earlier report of broad emission at 57005900   by fm93 . possible identifications include blends of [ n  ii ] 5755  , na  i 5890,5896  , and he  i 5876  . figure 6 shows the combined 1997 fos spectra ( g270h and g400h ) of sn  1979c covering the wavelength region 2200 to 4750  . the continuum levels at the g270h / g400h 3250   crossover point agreed quite well and no zero - point correction was applied . three prominent emission lines were detected below 3000  : c  ii ] 2324,2325  , [ o  ii ] 2470,2470  , and mg  ii 2796,2803  . these lines show clumpy and strongly asymmetric profiles with the blueward peaks about twice as bright as those along the redward side , suggestive of internal dust extinction of the receding emission regions . sharp blue emission peaks in these lines match well those seen in the optical lines from the mmt spectrum ; specifically , the c  ii ] , [ o  ii ] and mg  ii emission peaks at 2297  , 2440  , and 2767   correspond to the @xmath44 km s@xmath0 peaks in the [ o  i ] 6300   and [ o  ii ] 7325    optical lines . the mg  ii 2800   line appears broader than the two other uv lines , and this might indicate the presence of weak mg  i 2852 along its red wing . it is also possible that weak si  ii ] 2335   emission might also be blended with the c  ii ] 2324,2325   feature . the [ o  ii ] 2470   lines arise from the same upper level ( @xmath45 @xmath46 ) as the near - ir [ o  ii ] 7319,7330   lines . the relative strength of the 2470/7325 ratio is determined by radiative transition probabilities ( 0.78 ; mendoza 1983 ) and thus can be used to derive an estimate of the foreground extinction . assuming no contribution from [ ca  ii ] 7291,7330  , the observed 2470/7325 ratio of @xmath47 suggests that e(b  v ) = @xmath48 mag . however , this includes dust extinction within the sn s ejecta as indicated by the weaker red emission peaks in these uv lines compared to the near infrared lines . therefore , measuring only the blue emission peaks in the [ o  ii ] 2470 and 7325   lines , we find a 2470/7325 ratio of @xmath49 which implies e(b  v ) = @xmath50 assuming r = a@xmath51/e(b  v ) = 3.1 . this should be a reasonable estimate of the foreground extinction ( both galactic and in m100 ) for sn  1979c . however , it is larger than the previous total reddening value of @xmath52 estimated toward sn  1979c ( @xcite ) and may indicate that some weak [ ca  ii ] 7291,7330   emission contributes to the 7300   feature s strength . this would make the 2470/7325 ratio appear smaller and hence the reddening larger . alternatively , there might have been changes in [ o  ii ] line strengths during the four year interval between when the optical ( 1993 ) and uv ( 1997 ) data were taken . one can also estimate the internal dust extinction in the young , developing remnant by comparing the red emission spikes in the [ o  ii ] 2470 and 7325 lines . the observed 2470/7325 ratio of 0.15 suggests e(b  v ) = @xmath53 implying an internal reddening of e(b  v ) = @xmath6 in addition to the foreground e(b  v ) of @xmath54 . although the evidence for internal extinction is strong due to the consistently weaker red emission spikes in the uv line profiles , our measurement is not very accurate from this single measurement . although the red emission peak is comparable or slightly stronger than the blue in the optical lines of [ o  i ] 6300,6364 and [ o  ii ] 7319,7330 , much greater variation in blue / red peak strengths is seen for the uv lines in the _ hst _ data . for example , the red emission peak in the [ o  ii ] 2470   line is about 45% as strong as the blue emission peak , around 65% in the c  ii ] 2324   line , and less than 35% for the mg  ii 2800   line . emission features detected between 3000 and 4600   in the short g400h exposure are considerably weaker and consequently have less certain identifications but appear to be [ ne iii ] 3869  , [ s  ii ] 4068,4076  , and [ o  iii ] 4363  . the strength of the temperature sensitive [ o  iii ] 4363 line is surprisingly large relative to the [ o  iii ] 4959,5007 lines and suggests electron densities @xmath55 10@xmath56 @xmath3 . the only other viable line identification for the 4335   emission is h@xmath28 . this seems unlikely , however , due to the weakness of the h@xmath1 emission . finally , our detection of [ s ii ] 4068,4076    is tentative but would be consistent with the sn  1980k spectrum .","summary":"a may 1993 mmt spectrum of sn  1979c ( t = 14.0 yr ) shows a somewhat different spectrum from that of sn  1980k .","abstract":"a low - dispersion keck i spectrum of sn  1980k taken in august 1995 ( t = 14.8 yr after explosion ) and a november 1997 mdm spectrum ( t = 17.0 yr ) show broad 5500 km s emission lines of h , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  . weaker but similarly broad lines detected include [ fe  ii ] 7155  , [ s  ii ] 4068,4072  , and a blend of [ fe  ii ] lines at 50505400  . the presence of strong [ s  ii ] 4068,4072   emission but a lack of [ s  ii ] 6716,6731   emission suggests electron densities of 10 . from the 1997 spectra , we estimate an h flux of erg s indicating a 25% decline from 19871992 levels during the period 1994 to 1997 , possibly related to a reported decrease in its nonthermal radio emission .    a may 1993 mmt spectrum of sn  1979c ( t = 14.0 yr ) shows a somewhat different spectrum from that of sn  1980k . broad , 6000 km s emission lines are also seen but with weaker h , stronger [ o  iii ] 4959,5007  , more highly clumped [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph , near - uv spectrum ( 2200  4500  ) shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weak [ ne  iii ] 3969  , [ s  ii ] 4068,4072   and [ o  iii ] 4363   emissions . the uv emission lines show a double - peak profile with the blueward peak substantially stronger than the red , suggesting dust extinction within the expanding ejecta ( e[b  v ] = mag ) . the lack of detectable [ o  ii ] 3726,3729   emission together with [ o  iii ] ( 4959 + 5007)/4363 4 imply electron densities 10 .    these new sne ii - l spectra show general agreement with the lines expected in a circumstellar interaction model , but the specific models that are available show several differences with the observations . high electron densities ( 10 ) result in stronger collisional de - excitation than assumed in the models , thereby explaining the absence of several moderate to strong predicted lines such as [ o  ii ] 3726,3729  , [ n  ii ] 6548,6583  , and [ s  ii ] 6716,6731  . interaction models are needed that are specifically suited to these supernovae . we review the overall observed range of late - time sne ii - l properties and briefly discuss their properties relative to young , ejecta dominated galactic snrs ."}
{"article_id":"astro-ph9810407","section_id":"c","document":"to date , five papers have been published on the late - time optical spectrum of sn  1980k plus one each on sn  1970 g , sn  1979c , and sn  1986e . none of these , however , presented spectra of sufficient s / n or covered a wide enough wavelength range to constrain several basic physical parameters such as densities or internal extinction , or test current late - time emission models . the new sn  1979c and sn  1980k spectra do provide some of this information and give a much clearer picture for late - time optical and uv properties of sne ii - l . in addition , because sn  1979c and sn  1980k were observed at comparable ages , they can be used to gauge the spread of sn ii - l late - time emission properties . table 1 lists the observed emission properties of four type ii - l sne having detected late - time optical emission . they can be seen to exhibit several spectral similarities . from @xmath11 8 yr and extending at least to 17 yr , the strongest optical emission lines in sne ii - l are h@xmath1 , [ o  i ] 6300,6364 , [ o  ii ] 7319,7330 , and [ o  iii ] 4959,5007 . these lines show similar expansion velocities , @xmath11 5000  6000 km s@xmath0 , often with roughly equal line strengths . several of these lines also have emission profiles showing evidence for dust formation by virtue of diminished flux from the receding emission portions . the presence of this dust extinction creates both blueshifted line centers and asymmetric blue line profiles . in addition , all four sne show narrow emission lines ( e.g. , h@xmath1 and [ o  iii ] ) which could imply similar interstellar environments for the progenitors such as local h  ii regions .    however , significant spectral differences also exist . luminosities cover more than an order of magnitude , with a factor of six difference between objects of similar age ( e.g. , 79c and 80k ) . sn  1970 g and sn  1986e exhibit little if any broad [ o  iii ] emission , sn  1980k some , while in sn  1979c [ o  iii ] is stronger than h@xmath1 . conversely , sn  1980k has fairly strong [ fe  ii ] emission , both at 7155   and the blend at 51005300  , whereas sn  1979c and the other two do not . in addition , the very broad , unidentified emission near 5750   in sn  1979c is not seen in sn  1980k . bright optical emission appears correlated with the presence of strong late - time radio nonthermal emission and inferred high mass loss rates ( see table 1 ) in the sense that h@xmath1 luminosity tracks fairly well the peak 6 cm radio luminosity and the derived mass loss rate from late - time radio data . for example , sn  1979c is the brightest radio and optical sn and has the largest estimated mass loss rate while sn  1970 g is optically the faintest with the lowest estimated mass loss rate . however , this correlation is not a particularly tight one . sn  1986e is nearly as bright optically as sn  1979c , yet it is quite faint in the radio . moreover , strong radio emission is also not always a predictor of bright optical emission . two of us ( fesen & filippenko ) have been unsuccessful in detecting late - time optical emission from sn  1968d in ngc 6946 ( the same parent galaxy as sn  1980k ) as a follow - up to its late - time radio emission recovery ( hyman et al . the lack of detectable optical emission may be related to sn  1968d s location closer to ngc  6946 s center and in a dustier region ( see @xcite and @xcite ) which may be attenuating faint , late - time optical emission below the detection threshold . late - time , optical emission lines from sne ii - l appear surprisingly steady over time spans of many years . our 1993 spectrum of sn  1979c indicated no decrease in h@xmath1 flux compared to 1990/1991 data ( fm93 ) and actually showed a slight increase as does a comparison of 1991/1998 [ o  i ] images . recent radio measurements indicate a flattening of its radio light curve ( van dyk et al . 1998b ) and new optical measurements should be undertaken . sn  1980k s h@xmath1 flux remained nearly constant from 1987 through 1994 , decreasing only recently . in figure 7 , we show the h@xmath1 light curve over one decade : from 1987 through 1997 . the data indicate no change between 1987 and 1992.5 . spectra taken in 1991.4 and 1992.5 , though indicating possibly a slow fading , were of lower quality than one obtained in 1992.6 which indicated no significant drop in h@xmath1 strength ( fm94 ) . moreover , broadband photometric studies covering the years 1990  1992 indicated sn 1980k s optical flux level remained virtually unchanged from that seen in 1987 , especially in the r band which is sensitive to h@xmath1 emission ( r = 21.9 @xmath57 0.1 mag ; leibundgut et al . 1993 ) .    a more recent spectrum taken in 1994 , however , showed an h@xmath1 emission flux of @xmath58 erg @xmath5 s@xmath0 ( fhm95 ) , about 25% less than the @xmath59 erg @xmath5 s@xmath0 found earlier . our 1997 measurement of @xmath60 erg @xmath5 s@xmath0 supports a fading h@xmath1 strength which may have started during the last several years , possibly in 1994 with the fhm95 reported decline . while this optical fading would roughly coincide with a drop in radio emission ( montes et al . 1998 ) , we can not completely rule out a small , steady decline in h@xmath1 over the 19871997 period from the spectroscopic data .    during t = 10  20 yr , sn  1980k s broad h@xmath1 line profile gradually narrowed , changing from a fwhm = 220   in 1988.6 to 190   in 1997.9 ( see fig . this trend has been noted earlier ( fm94 ) and is predicted by sn  csm interaction models ( cf94 ) . however , h@xmath1 appears to be the line most affected , with the [ o i ] 6300,6364 line profile changing little during this time interval .    with the notable exception of h@xmath1 , all the broad emission lines exhibit a spiky profile suggestive of clumpy emission regions at particular velocities . this is perhaps most clearly seen in sn  1979c where emission peaks at @xmath41 and @xmath61 km s@xmath0 can be seen in the [ o  i ] 6300 , [ o  ii ] 2470 , [ o  ii ] 7325 , c  ii ] 2324 , and mg  ii lines . the less blueshifted emission peaks are always weaker in the uv lines compared to the red or near infrared lines , consistent with the presence of internal extinction . in a similar fashion , sn  1980k also exhibits strong emission peaks in the [ o  i ] 6300 and [ o  ii ] 7325 lines . the fact that the h@xmath1 profile in both sn  1979c and sn  1980k does not show such emission peaks suggests that the o , c , mg - rich emitting material is coming mostly from ejecta and is physically separate from the dominant h@xmath1 emitting material which includes the swept - up shell . our new spectra also allow one to get a handle on the electron density and temperature . in sn  1980k , we detected [ s  ii ] 4068,4076   lines but not [ s  ii ] 6716,6731   emission . the [ s  ii ] 4068,4072 lines have a critical density , n@xmath62 , of @xmath63 @xmath3 , whereas the 6731   line has n@xmath62 = @xmath64 @xmath3 . this suggests collision de - excitation of the [ s  ii ] 6716,6731 lines due to electron densities near 10@xmath2 @xmath3 . an upper limit of @xmath11 10@xmath65 @xmath3 is suggested by the presence of strong [ o  i ] 6300,6364   emission ( n@xmath62 = @xmath66 @xmath3 ) and [ o  ii ] 7319,7330 (n@xmath62 = @xmath67 @xmath3 ) , although [ o  i ] 6300,6364   emission can be strong even at high densities because it is an important coolant for low ionization gas . for example , [ o  i ] emission is an important for the cool shell in the cf94 models even though @xmath68 @xmath3 . if sn  1979c s densities were similar to those of sn  1980k , we would predict little [ o  ii ] 3726,3729   emission which has n@xmath62 = @xmath69 @xmath3 , and this agrees with observation . indeed , the fos spectrum of sn  1979c reveals strong [ o  ii ] 2470   emission but virtually no [ o  ii ] 3727   emission . as shown in table 2 , only those emission lines with critical densities above 10@xmath70 @xmath3 are detected in both 79c and 80k . consequently , we conclude that all lines with critical densities below 10@xmath70 @xmath3 are collisionally suppressed relative to lines having higher critical densities . electron densities of @xmath71 @xmath3 would also explain the observed low ratio of [ o  iii ] ( 4959 + 5007)/4363 . the [ o  iii ] 4959,5007   lines have n@xmath62 = @xmath72 @xmath3 . if the electron densities were a bit above @xmath73 @xmath3 , then the normally strong [ o  iii ] lines would be suppressed relative to [ o  iii ] 4363    line intensity ( n@xmath62 = @xmath74 10@xmath65 @xmath3 ) . furthermore , the [ o  iii ] electron temperature must be greater than @xmath11 15,000 k ( i.e. , i(4959 + 5007)/i(4363 ) @xmath7 4 assuming n = @xmath75 @xmath3 ) in order to generate sufficient 4363   emission to be detected given the s / n of the data .    a very broad emission feature seen in sn 1979c s spectrum near 5800   may be partially due to the temperature sensitive [ n  ii ] 5755 line . if correct , this would also indicate a [ n  ii ] temperature above 10@xmath76 k. the overall weaker [ o  iii ] emission seen in the sn  1980k spectrum might be due to low ejecta ionization as indicated by the presence of of strong [ fe  ii ] 50505400   and 7155   emission . late - time optical observations of sne ii - l can be used to test emission predictions in cf94 s recent sn  csm models . in table 1 , we list cf94 s predicted relative line intensities for t = 10 and 17.5 yr arising from sn  csm interactions assuming either a power law or red supergiant ( rsg ) density gradient . there is a general agreement with the observed line list , although there are significant differences with the relative line intensities . the observed line widths are approximately those expected and the general picture of emission from circumstellar interaction is supported , but cf94 present two detailed models that appear not to be well matched to the conditions in sn 1980k and sn 1979c . the models are based on the explosion of a @xmath77 red supergiant with two variations for the outer density profile . although not ideal , these models do provide a starting point for discussing the current observations . the rsg model predicts about the right h@xmath1 luminosity but weaker [ o  i ] and stronger [ o  iii ] ( relative to h@xmath1 ) than observed in all four cases . on the other hand , the 10 and 17.5 yr old power law models predict about the right h@xmath1/[o  i ] ratio , but less [ o  ii ] 7319,7330   emission , too much [ o  iii ] 4959,5007 , and much weaker h@xmath1 luminosity than observed . larger discrepancies between observations and models are seen for several uv lines . both rsg and power law models predict mg  ii 2800   to be the dominant uv / optical line ( after ly@xmath1 ) at a strength @xmath78 times more than h@xmath1 . however , the sn  1979c spectrum shows mg  ii to be slightly weaker than h@xmath1 , with the strongest line actually being c  ii ] 2324,2325 . likewise , mg  i ] 4571   is predicted to be about half the strength of h@xmath1 yet is not seen in either 79c or 80k . large differences between observed and predicted mg ii intensities are a problem common in young , o - rich snrs ( blair et al . 1994 ; sutherland & dopita 1995 ) and may simply be indicating an incorrect assumed mg abundance . however , large differences exist for other uv lines , such as c  ii ] 2324,2325 which is about twice the predicted strength , and this difference grows somewhat larger if internal sn dust extinction is considered . other notable differences involve the [ o  ii ] lines . we find strong [ o  ii ] 7319,7330   emission in both sn  1979c and sn  1980k and suspect its presence in sn  1986e where it may have been mis - identified as [ ca  ii ] 7291,7330 ( @xcite ) . but [ o  ii ] 7319,7330   emission is weak in all cf94 models , due to the high excitation energy of the upper [ o  ii ] level and its small collision strength . because of this cf94 argued that [ ca  ii ] was the chief source of line emission observed near 7300  . however , in view of the new spectra , it now appears quite likely that the majority of the 7300   emission is due to [ o  ii ] . the presence of strong [ o  ii ] 2470 supports this conclusion . since cf94 do not predict a 2470   line strength we can not do a direct comparison . but based upon the theoretical [ o  ii ] 2470/7325 ratio of 0.78 , the model prediction should be about an order of magnitude too low . although [ o  ii ] 7319,7330   lines are weak in most photoionized nebulae , the presence of strong [ o  ii ] emission in young snrs is not uncommon . in almost all young , o - rich snrs such as cas a ( sn 1680 ) , as well as in sn 1957d ( cappellaro et al . 1995 ) and sn  1986j ( leibundgut et al . 1991 ) , one finds strong [ o  ii ] 7325   emission which is equal to or stronger than the other forbidden oxygen line emissions . strong [ o  ii ] emission has been successfully modeled by sutherland and dopita ( 1995 ) using a mixture of shock and photoionized emissions zones in o - rich ejecta . additional model - observation differences involve the the ca  ii ir triplet and the [ s iii ] 9069,9531   lines . these emission lines are predicted to be strong in the power law models but are not detected in the published near - ir spectrum of sn 1980k ( fhm95 ) . finally , the favored power law models predict a steady decline of the h@xmath1 emission and a rapid increase of [ o  iii ] 4959,5007   ( cf94 ) . many model - observation differences appear to be related to higher electron and gas densities than the cf94 models assume . as noted above , the presence of strong [ o  iii ] 4363   emission indicates densities of @xmath79 @xmath3 . high oxygen gas densities would also account for the lack of any [ o  iii ] 4959 and 5007 line discrimination in the [ o  iii ] profile for sn  1979c . at densities above 10@xmath56 @xmath3 , several lines predicted to be observable in the models , like [ o  ii ] 3727 , [ n  ii ] 6548,6583   and [ s  ii ] 6716,6731  , will be strongly de - excited ( see table 2 ) . the differences indicate that the cf94 stellar model is not the best one to model sn 1979c or sn 1980k . their assumed circumstellar density may also be a factor . models for the light curves of these supernovae suggest a h envelope mass of @xmath80 ( swartz , wheeler , & harkness 1991 ; blinnikov & bartunov 1993 ; arnett 1996 ) , much lower than the mass assumed in cf94 . with the low envelope mass , processed core material may not be strongly decelerated and could be moving at @xmath81 km s@xmath0 . some deceleration of the core material could lead to hydrodynamic instabilities and clumping of the gas , which is consistent with the spiky profiles seen in the spectral lines of o , c , and mg . if the gas is h - depleted core material , strong differences can be expected with the models of cf94 who assumed cosmic abundances .    the models presented in cf94 also assumed a circumstellar density determined by a mass loss rate @xmath82 for a wind velocity of @xmath83 . however , the analysis of the radio turn - on by lundqvist & fransson ( 1988 ) leads to @xmath84 for sn 1979c for the same wind velocity . there is new evidence for a high circumstellar density around sn 1979c . immler , pietsch , & aschenbach ( 1998 ) have detected x - ray emission from the supernova with _ rosat _ and determined a @xmath85 kev x - ray luminosity of @xmath86 . the summed luminosity of the observed lines listed in table 1 is @xmath87 and this figure is likely to be substantially increased when unobserved lines such as l@xmath1 are included ( cf94 ) . in the circumstellar interaction model , the optical and ultraviolet lines are excited by the x - ray radiation , so the implication is that the x - rays from the reverse shock wave are being absorbed by the cool circumstellar shell . this would explain the observed constancy of the line emission because the x - ray emission at the reverse shock should decline slowly if the reverse shock is a cooling shock ( cf94 ) . application of eq . ( 2.17 ) of cf94 shows that the circumstellar shell can still be optically thick at 1 kev at the time of the observations if the density power law for the supernova is @xmath88 , where @xmath89 , or if the circumstellar density is about twice that quoted above . in the cf94 power law density model at an age of 10 years , the supernova h density just inside the reverse shock front is @xmath90 @xmath3 . for sn 1979c , the density may be several times higher , but it still falls short of the density implied by the [ o iii ] line ratio . the implication is that the [ o iii ] lines are formed inside of the reverse shock , which is consistent with the lack of narrowing of the lines with time .","summary":"these new sne ii - l spectra show general agreement with the lines expected in a circumstellar interaction model , but the specific models that are available show several differences with the observations . high electron densities ( 10 ) result in stronger collisional de - excitation than assumed in the models , thereby explaining the absence of several moderate to strong predicted lines such as [ o  ii ] 3726,3729  , [ n  ii ] 6548,6583  , and [ s  ii ] 6716,6731  .","abstract":"a low - dispersion keck i spectrum of sn  1980k taken in august 1995 ( t = 14.8 yr after explosion ) and a november 1997 mdm spectrum ( t = 17.0 yr ) show broad 5500 km s emission lines of h , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  . weaker but similarly broad lines detected include [ fe  ii ] 7155  , [ s  ii ] 4068,4072  , and a blend of [ fe  ii ] lines at 50505400  . the presence of strong [ s  ii ] 4068,4072   emission but a lack of [ s  ii ] 6716,6731   emission suggests electron densities of 10 . from the 1997 spectra , we estimate an h flux of erg s indicating a 25% decline from 19871992 levels during the period 1994 to 1997 , possibly related to a reported decrease in its nonthermal radio emission .    a may 1993 mmt spectrum of sn  1979c ( t = 14.0 yr ) shows a somewhat different spectrum from that of sn  1980k . broad , 6000 km s emission lines are also seen but with weaker h , stronger [ o  iii ] 4959,5007  , more highly clumped [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph , near - uv spectrum ( 2200  4500  ) shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weak [ ne  iii ] 3969  , [ s  ii ] 4068,4072   and [ o  iii ] 4363   emissions . the uv emission lines show a double - peak profile with the blueward peak substantially stronger than the red , suggesting dust extinction within the expanding ejecta ( e[b  v ] = mag ) . the lack of detectable [ o  ii ] 3726,3729   emission together with [ o  iii ] ( 4959 + 5007)/4363 4 imply electron densities 10 .    these new sne ii - l spectra show general agreement with the lines expected in a circumstellar interaction model , but the specific models that are available show several differences with the observations . high electron densities ( 10 ) result in stronger collisional de - excitation than assumed in the models , thereby explaining the absence of several moderate to strong predicted lines such as [ o  ii ] 3726,3729  , [ n  ii ] 6548,6583  , and [ s  ii ] 6716,6731  . interaction models are needed that are specifically suited to these supernovae . we review the overall observed range of late - time sne ii - l properties and briefly discuss their properties relative to young , ejecta dominated galactic snrs ."}
{"article_id":"astro-ph9810407","section_id":"c","document":"from keck and mdm optical spectra of sn 1980k and optical mmt and uv _ hst _ spectra of sn 1979c , we find the following :    \\1 ) the optical spectrum of sn  1980k taken at 15 and 17 yr shows continued strong and broad 5500 km s@xmath0 emission lines of h@xmath1 , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  , with weaker but similarly broad lines of [ s  ii ] 4068,4072  , h@xmath26 , [ fe  ii ] 7155  , and a [ fe  ii ] blend at 50505400  . the presence of [ s  ii ] 4068,4072   but a lack of [ s  ii ] 6716,6731   emission suggests collisional de - excitation of the [ s  ii ] 6716 and 6731   lines due to electron densities of 10@xmath2 @xmath3 . the 1997 mdm spectra indicates a h@xmath1 flux of @xmath4 erg @xmath5 s@xmath0 , suggesting a 25% drop from 19871992 levels sometime during the period 1994 to 1997 , possibly simultaneously with an observed decrease in nonthermal radio emission . \\2 ) like sn  1980k , sn  1979c s optical spectrum at t = 14.0 yr shows @xmath11 6000 km s@xmath0 wide emission lines but weaker h@xmath1 , strong [ o  iii ] 4959,5007  , clumpy [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph spectrum covering the range 2200  4500   shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weaker [ ne  iii ] 3969  , [ s  ii ] 4068,4072  , and [ o  iii ] 4363  . a lack of [ o  ii ] 3726,3729   emission together with a [ o  iii ] ( 4959 + 5007)/4363 @xmath7 4 indicates electron densities @xmath11 10@xmath8 @xmath3 . furthermore , the [ o  iii ] temperature must be greater than @xmath11 15,000 k in order to generate sufficient 4363 emission to be so easily detected ( i.e. , i(4959 + 5007)/i(4363 ) @xmath7 4 assuming n = @xmath75 @xmath3 ) . a very broad emission feature seen in sn  1979c s spectrum near 5800  may be partially due to the [ n  ii ] line at 5755  . \\3 ) in both sn  1979c and sn  1980k , several lines show one or more sharp emission peaks . the blueward peak(s ) are substantially stronger than those toward the red indicating internal dust extinction with the expanding ejecta . the amount of internal extinction in sn1979c is estimated to be e(b  v ) = @xmath91 mag . the line profile differences exhibited between h@xmath1 and the oxygen lines suggests that we are seeing emission from two or more separate regions , possibly the shell ( h@xmath1 ) and the inner sn ejecta ( o lines ) . \\4 ) comparison of these observations to late - time sn model predictions indicates several areas of significant differences , many of which can be attributed to model electron densities being several orders of magnitude too low . for example , [ o  ii ] 3727 emission is predicted to be moderately strong in the models but is not seen due to densities well above the [ o  ii ] critical density of @xmath92 10@xmath93 @xmath3 . in other cases , such as mg  ii 2800 which arises chiefly from the swept - up shell , the observed emission is far weaker than predicted . the parameters for future models will have to be more closely adapted to the conditions in these supernovae .    it should be noted that other sne  ii besides type ii - l can exhibit bright , late - time optical emission , most notably the type  iin objects sn  1986j ( @xcite ) and sn  1988z ( @xcite ; @xcite ; and @xcite ) . these objects show quite a different optical spectrum from the sne  ii - l discussed above and are believed to be encountering dense , clumpy csm ( @xcite ; @xcite ) . the current , single type ii - p detection of sn  1923a in m83 in the radio ( @xcite , @xcite ) together with the lack of any reported late - time optical detections of sne ii - p suggests significant mass loss differences between sne ii - l and ii - p . it will be interesting to see if sn  1923a can be recovered optically and how its uv and optical emission properties compare to those of sne ii - l .    into what kind of young remnants will these sn ii - l emission nebulae evolve ? except for the higher densities and the presence of strong hydrogen emission , the observed late - time spectra of sne ii - l bear some resemblance to galactic and lmc o - rich snrs such as cas a and 1e0102 - 7219 ( @xcite ; @xcite ) . their o , s , and c emission - line dominated spectrum with expansion velocities around 5000 km s@xmath0 is not unlike that seen in 10@xmath94 yr old o - rich snrs . the weakness of [ o  iii ] 4959,5007 emission and the absence of lines like [ o  ii ] 3727  , [ ne  iv ] 2425  , and [ ne v ] 3426   can be attributed to higher filament densities and lower ionization levels . however , it is not at all clear if the progenitors of these older , metal - rich remnants are related to sne ii - l events . in the case of cas a , the progenitor may have been a wn star , quite different from the rsg progenitor usually assumed for sne ii - l . moreover , the cas a supernova appears to have been subluminous and thus very different from the super - luminous sn ii - l events sn  1979c and sn  1980k . this all raises the issue of whether sne of different types can yet leave similar looking young remnants at ages 10 to 100 yr . if sn  1979c and sn  1980k remain luminous for several more decades , we may be able to address this question directly . we are grateful to the keck , mmt , and mdm observatory staffs for their excellent observing assistance , and k. weiler and m. montes for generously communicating their radio study results on sn  1980k prior to its publication . financial support for this work was provided by nasa through grant nos . go-6043 and go-6584 from the space telescope science institute , which is operated by aura , inc . , under nasa contract no . nas 5 - 26555 . we also acknowledge nsf grants ast-9529232 to r.a.f . and ast-9417213 to a.v.f . lccccccc age at observation ( yr ) & 8 & 14 - 15 & 1214 & 22 & 10 & 10 & 17.5 + distance    ( mpc ) & 16.8 & 7.5 & 17 & 7 & & & + e(b  v )    ( mag ) & 0.02 & 0.40 & 0.23 & 0.15 & & & + mass loss rate@xmath95 & 4.7 & 2.0 & 19 & 2 & & & + h@xmath1 luminosity@xmath96 & 8.9 & 2.5 & 15 & 1 & 4.8 & 0.9 & 0.5 + peak radio luminosity@xmath97 & 1.1 & 1.0 & 26 & 1.5 & & & + relative line fluxes & & & & & & & +    h@xmath1 6563 & 10  10 & 10  10 & 10  10 & 10  10 & 10 & 10 & 10 +    [ o i ] 6300,6364 &  9  9 &  7  7 &  9  9 &  6  6 & 1 & 5 & 7 +    [ o ii ] 2470,2470 & & &  2  6 & & & & +    [ o ii ] 7319,7330 &  3  3 & 10  9 & 12  11 & & & 1 & 1 +    [ o iii ] 4363 & &  1  2 &  2  3 & & & & +    [ o iii ] 4959,5007 &  @xmath983  @xmath985  &  2  3 &  9  11 &  @xmath986  @xmath987  & 34 & 23 & 46 +    c ii 2324,2325 & & &  6  25 & & 11 & 15 & 10 +    mg ii 2796,2803 & & &  4  9 & & 49 & 79 & 57 +    [ ne iii ] 3868,3869 & & &  2  3 & & 3 & 4 & 5 +    [ s ii ] 4068,4076 & &  2  4 &  1  2 & & & 2 & 3 +    [ fe ii ] 7155 &  @xmath983  @xmath983  &  3  3 &  @xmath985  @xmath985  & & & & + & & & & & & & + detection upper limits & & & & & & & +    [ o ii ] 3726,3729 & & & @xmath99  @xmath982  & & @xmath981 & 2 & 5 +    mg i ] 4571 & &  @xmath982  @xmath984  &  @xmath982  @xmath984  & & 3 & 6 & 4 +    [ na i ] 5890,5896 &  @xmath983 @xmath984  &  @xmath982  @xmath982  & ? &  @xmath985  @xmath986  & 2 & 10 & 13 +    [ n ii ] 6548,6583 &  @xmath983  @xmath983  &  @xmath985  @xmath985  &  @xmath985  @xmath985  &  @xmath985  @xmath985  & @xmath981 & 5 & 7 +    [ c i ]  8729 & &  @xmath982  @xmath982  & & & 0 & 2 & 4 +    [ s iii ] 9069,9531 & &  @xmath983  @xmath983  & & & 2 & 11 & 13 + & & & & & & & + expan . velocity  ( km s@xmath0 ) & & & & & & & +    h@xmath1 6563 ( blue)&@xmath100 & @xmath37&@xmath39 & @xmath101 & & & +          ( red ) & @xmath102 & @xmath103&@xmath104 & @xmath105 & & & +    [ o i ] 6300,6364 ( blue)&@xmath106 & @xmath100&@xmath39 & @xmath107 & & & +    [ o ii ] 7319,7330 ( blue ) & & @xmath41&@xmath39 & & & & +               ( red)&&@xmath108&@xmath109 & & & & +    [ s ii ] 4068,4076 ( blue ) & & @xmath31 & & & & & +               ( red ) & & @xmath110 & & & & & + h@xmath1 line asymmetry & red ? & blue & blue & blue & & & + clumpy [ o i ] emission ? & yes ? & yes & yes & yes & & & + narrow nebular lines ? & yes & yes & yes & yes & & & +    llccc n@xmath111 @xmath112 10@xmath70 @xmath3 & & & & +  [ n ii ] 6548,6583 & @xmath113 & absent & absent & strong +  [ o ii ] 3726,3729 & @xmath114 , @xmath115 & absent & absent & moderate +  [ s ii ] 6716,6731 & @xmath116 , @xmath64 & absent & absent & weak +  [ ne iv ] 2422,2425 & @xmath117 , @xmath118 & & absent & weak + & & & & + n@xmath111 = 10@xmath2 @xmath3 & & & & +  [ o iii ] 4959,5007 & @xmath119 & weak & moderate & v. strong +  [ s iii ] 9069,9531 & @xmath120 & absent ? & & strong + & & & & + n@xmath111 @xmath27 10@xmath56 @xmath3 & & & & +  [ o i ] 6300,6364 & @xmath121 & strong & strong & strong +  [ o ii ] 2470,2470 & @xmath122 , @xmath123 & & strong & +  [ o ii ] 7319,7330 & @xmath123 & strong & strong & weak +  [ o iii ] 4363 & @xmath124 & weak ? & weak & +  [ s ii ] 4069,4076 & @xmath125 , @xmath126 & weak & weak & moderate +  [ ne iii ] 3868,3869 & @xmath127 & & moderate & moderate +  [ ne v ] 3346,3426 & @xmath128 & & absent & moderate +  c ii ] 2324,2325 & @xmath129 , @xmath130 & & strong & strong +    arnett , w. d. 1996 , supernovae and nucleosynthesis , ( princeton : princeton university press ) barbieri , c. , bonoli , c. , & cristiani , s. 1982 , , 114 , 216 barbon , r. , ciatti , f. , & rosino , l. 1979 , , 72 , 287 barbon , r. , cappellaro , e. , & turatto , m. 1989 , , 81 , 421 blair , w. p. , raymond , j. c. , danziger , j. , & matteucci , f. 1989 , , 338 , 812 blair , w. p. , raymond , j. c. , & long , k. s. 1994 , , 334 blinnikov , s. i. , & bartunov , o. s. 1993 , , 273 , 106 burstein , d. , & heiles , c. h. 1982 , , 54 , 33 cappellaro , e. , danziger , i. j. , & 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, 144 , p.357 weaver , t. a. , & woosley , s. e. 1980 , ann . , 336 , 335 weiler , k. w. , panagia , n. , sramek , r. a. , van der hulst , j. m. , roberts , m. s. , & nguyen , l. 1989 , , 336 , 421 weiler , k. w. , sramek , r. a. , panagia , n. , van der hulst , j. m. , & salvati , m. 1986 , , 301 790 weiler , k. w. , van dyk , s. d. , panagia , n. , sramek , r. a. , & discenna , j. l. 1991 , , 380 , 161 weiler , k. w. , van dyk , s. d. , panagia , n. , & sramek , r. a. 1993 , in massive stars : their lives in the interstellar medium , ed . cassinelli & e.b . churchwell , asp conf . series , 104 , p.436 young , t. r. , & branch , d. 1989 , , 342 , l79 weiler , k. w. , van dyk , s. d. , montes , m. , panagia , n. , & sramek , r. a. 1998 , 500 , 51","summary":"a low - dispersion keck i spectrum of sn  1980k taken in august 1995 ( t = 14.8 yr after explosion ) and a november 1997 mdm spectrum ( t = 17.0 yr ) show broad 5500 km s emission lines of h , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  . weaker but similarly broad lines detected include [ fe  ii ] 7155  , [ s  ii ] 4068,4072  , and a blend of [ fe  ii ] lines at 50505400  . the presence of strong [ s  ii ] 4068,4072   emission but a lack of [ s  ii ] 6716,6731   emission suggests electron densities of 10 . from the 1997 spectra , we estimate an h flux of erg s indicating a 25% decline from 19871992 levels during the period 1994 to 1997 , possibly related to a reported decrease in its nonthermal radio emission .    broad , 6000 km s emission lines are also seen but with weaker h , stronger [ o  iii ] 4959,5007  , more highly clumped [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph , near - uv spectrum ( 2200  4500  ) shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weak [ ne  iii ] 3969  , [ s  ii ] 4068,4072   and [ o  iii ] 4363   emissions . the uv emission lines show a double - peak profile with the blueward peak substantially stronger than the red , suggesting dust extinction within the expanding ejecta ( e[b  v ] = mag ) . the lack of detectable [ o  ii ] 3726,3729   emission together with [ o  iii ] ( 4959 + 5007)/4363 4 imply electron densities 10 .   ","abstract":"a low - dispersion keck i spectrum of sn  1980k taken in august 1995 ( t = 14.8 yr after explosion ) and a november 1997 mdm spectrum ( t = 17.0 yr ) show broad 5500 km s emission lines of h , [ o  i ] 6300,6364  , and [ o  ii ] 7319,7330  . weaker but similarly broad lines detected include [ fe  ii ] 7155  , [ s  ii ] 4068,4072  , and a blend of [ fe  ii ] lines at 50505400  . the presence of strong [ s  ii ] 4068,4072   emission but a lack of [ s  ii ] 6716,6731   emission suggests electron densities of 10 . from the 1997 spectra , we estimate an h flux of erg s indicating a 25% decline from 19871992 levels during the period 1994 to 1997 , possibly related to a reported decrease in its nonthermal radio emission .    a may 1993 mmt spectrum of sn  1979c ( t = 14.0 yr ) shows a somewhat different spectrum from that of sn  1980k . broad , 6000 km s emission lines are also seen but with weaker h , stronger [ o  iii ] 4959,5007  , more highly clumped [ o  i ] and [ o  ii ] line profiles , no detectable [ fe  ii ] 7155   emission , and a faint but very broad emission feature near 5750  . a 1997 _ hst _ faint object spectrograph , near - uv spectrum ( 2200  4500  ) shows strong lines of c  ii ] 2324,2325  , [ o  ii ] 2470  , and mg  ii 2796,2803   along with weak [ ne  iii ] 3969  , [ s  ii ] 4068,4072   and [ o  iii ] 4363   emissions . the uv emission lines show a double - peak profile with the blueward peak substantially stronger than the red , suggesting dust extinction within the expanding ejecta ( e[b  v ] = mag ) . the lack of detectable [ o  ii ] 3726,3729   emission together with [ o  iii ] ( 4959 + 5007)/4363 4 imply electron densities 10 .    these new sne ii - l spectra show general agreement with the lines expected in a circumstellar interaction model , but the specific models that are available show several differences with the observations . high electron densities ( 10 ) result in stronger collisional de - excitation than assumed in the models , thereby explaining the absence of several moderate to strong predicted lines such as [ o  ii ] 3726,3729  , [ n  ii ] 6548,6583  , and [ s  ii ] 6716,6731  . interaction models are needed that are specifically suited to these supernovae . we review the overall observed range of late - time sne ii - l properties and briefly discuss their properties relative to young , ejecta dominated galactic snrs ."}
{"article_id":"1206.0291","section_id":"i","document":"the determination of the masses ( or equivalently mass - to - light ratios ) of gas - poor galaxies has been an important issue since the discovery that galaxies are stellar systems like the milky way , with mass being a strong driver of many of their properties . dynamical modelling methods of increased sophistication have been developed over the past decades , all based on the assumption that galaxies can be described as stationary systems . the first attempt at measuring dynamical masses of galaxies were based on the spherical virial equations @xcite . these methods have the disadvantage that , for accurate results , they need to assume self - similarity in the galaxy light and mass distribution . more accurate methods allow for axisymmetry and take the galaxy light distribution into account . the first detailed axisymmetric models of real galaxies were based on the @xcite equations and assumed a distribution function that depends on two ( out of three ) integrals of motion ( e.g * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but special classes of three - integral models were also used . axisymmetric methods were developed to allow for a general orbital distribution , based on @xcite numerical orbital superposition method ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? currently the most general available models assume galaxies can be approximated by a stationary triaxial shape ( e.g. * ? ? ? * ; * ? ? ? the above modelling techniques were developed under the assumption that gas - poor galaxies can be well described by stationary axisymmetric or triaxial spheroidal systems . however a key initial result of the atlas@xmath9  survey ( * ? ? ? * hereafter paper  i ) is the fact that nearby gas - poor galaxies are actually dominated ( 86 per cent of them ) by fast rotators ( * ? ? ? * ; * ? ? ? * hereafter paper  ii and paper  iii ) , often with significant disk components and resembling spiral galaxies with the dust removed ( * ? ? ? * paper vii ) , 30% of which at least are barred . the presence of these bars is a difficult problem for all modelling methods and therefore motivates the present study . bars are density waves which results in a tumbling potential : this figure rotation is often ignored in the popular dynamical modelling methods described above . dynamical models of barred galaxies have been constructed in the past ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? however , the existence of intrinsic degeneracies in the dynamical modelling of bars make the determination of mass quite uncertain even for such models . in fact even the full amount of information one can obtain today for external galaxies , namely the full line - of - sight velocity distribution ( losvd ) at every position on the sky , is not sufficient to uniquely constrain the two free parameters ( @xmath0 and inclination ) of a simple self - consistent axisymmetric model @xcite . a barred model requires at least two extra parameters ( the position angle ( pa ) and pattern speed of the bar ) and dramatically increases the complexity of the orbital structure and the associated degeneracy of the problem , instead of improving the accuracy of the mass estimate : a broad range of parameters space may well fit the data equally well . moreover , assuming a galaxy is barred also increases the degeneracy in the mass deprojection problem ( e.g. * ? ? ? * ) , which is already mathematically non unique in the simple axisymmetric case @xcite . the application of sophisticated barred models to large samples would be computationally challenging , but feasible exploiting the trivial parallelism of the problem . however , this brute - force approach does not remove the intrinsic degeneracies so it is not expected to increase the accuracy of the mass determinations , and for this reason does not seem justified . an alternative approach consists of using some a priori information on the galaxy structure and make empirically - motivated restrictive assumption on the models . this is the approach we are using in the systematic determination of the masses of the 260 early - type galaxies of the atlas@xmath9  survey @xcite . we are applying the multi - gaussian expansion ( mge ) technique @xcite to accurately describe the photometry of all galaxies in the survey ( scott et al . in prep ) and use the jeans anisotropic mge ( jam ) modelling method @xcite to measure masses . the jam method is based on a simple and very efficient solution of the jeans equations which allows for orbital anisotropy @xmath10 . this approach provides good descriptions of the integral - field kinematics of the fast rotator early - type galaxies @xcite , which constitute the large majority of the atlas@xmath9  sample ( see paper  ii and paper  iii ) . a key motivation for our use of the jam method is that it was shown , using 25 real galaxies @xcite , to agree well within the model uncertainties in the mass determination obtained with the more general axisymmetric schwarzschild approach . the use of an axisymmetric dynamical modelling method to measure the mass of barred galaxies raises the obvious question of what errors in the mass determination are introduced by the approach . answering this question is the goal of this paper . our work is in its spirit an extension to barred disk galaxies of the work by @xcite , which explored the biases introduced by the use of axisymmetric models , when extracting masses of triaxial and prolate simulated spheroidal galaxy remnants . the paper is structured as follows : in section  [ sec : model ] we briefly describe the multi - gaussian expansion parametrization from @xcite , the semi - isotropic jeans equations and the method used to create the n - body galaxy models . in section  [ sec : jammodel ] , we give an overview of the input models used for the jam modeling in our investigation , and in section  [ sec : results ] we compare the original and recovered values of the corresponding dynamical parameters . section  [ sec : sum ] summarizes all results .","summary":"[ firstpage ]    methods : n - body simulations  galaxies :  kinematics and dynamics  galaxies :  elliptical and lenticular , cd  galaxies :  structure","abstract":"we investigate the accuracy in the recovery of the stellar dynamics of barred galaxies when using axisymmetric dynamical models . we do this by trying to recover the mass - to - light ratio ( ) and the anisotropy of realistic galaxy simulations using the jeans anisotropic multi - gaussian expansion ( jam ) method . however , given that the biases we find are mostly due to an application of an axisymmetric modeling algorithm to a non - axisymmetric system and in particular to inaccuracies in the de - projected mass model , our results are relevant for general axisymmetric modelling methods . we run n - body collisionless simulations to build a library with various luminosity distribution , constructed to mimic real individual galaxies , with realistic anisotropy . the final result of our evolved library of simulations contains both barred and unbarred galaxies . the jam method assumes an axisymmetric mass distribution , and we adopt a spatially constant and anisotropy distributions . the models are fitted to two - dimensional maps of the second velocity moments of the simulations for various viewing angles ( position angle of the bar and inclination of the galaxy ) . we find that the inclination is generally well recovered by the jam models , for both barred and unbarred simulations . for unbarred simulations the is also accurately recovered , with negligible median bias and with a maximum one of just% when the galaxy is not too close to face on . at very low inclinations ( ) the can be significantly overestimated ( 9% in our tests , but errors can be larger for very face - on views ) . this is in agreement with previous studies . for barred simulations the is on average ( when pa ) essentially unbiased , but we measure an over / under estimation of up to% in our tests . the sign of the bias depends on the position angle of the bar as expected : overestimation occurs when the bar is closer to end - on , due to the increased stellar motion along the line - of - sight , and underestimation otherwise . for unbarred simulations , the jam models are able to recover the mean value of the anisotropy with bias , within the region constrained by the kinematics . however when a bar is present , or for nearly face - on models , the recovered anisotropy varies wildly , with biases up to .    [ firstpage ]    methods : n - body simulations  galaxies :  kinematics and dynamics  galaxies :  elliptical and lenticular , cd  galaxies :  structure"}
{"article_id":"1110.0764","section_id":"i","document":"let @xmath0 be a surface of negative euler characteristic together with a pants decomposition @xmath9 . kra s plumbing construction endows @xmath0 with a projective structure as follows . replace each pair of pants by a triply punctured sphere and glue , or ` plumb ' , adjacent pants by gluing punctured disk neighbourhoods of the punctures . the gluing across the @xmath10 pants curve is defined by a complex parameter @xmath11 . the associated holonomy representation @xmath12 gives a projective structure on @xmath0 which depends holomorphically on the @xmath13 . in particular , the traces of all elements @xmath14 , are polynomials in the @xmath13 . in @xcite the author and series proved a formula , called _ top terms relationship _ , which is theorem [ top ] in section [ ssub2.1 ] , giving a simple linear relationship between the coefficients of the top terms of @xmath15 , as polynomials in the @xmath13 , and the dehn  thurston coordinates of @xmath16 relative to @xmath9 , see section [ ssub2.1 ] for the definitions . this result generalises the previous results proved by keen and series in @xcite in the case of the once punctured torus @xmath17 and by series in @xcite for the twice punctured torus @xmath18 . these formulas were used in the case @xmath19 to determine the asymptotic directions of pleating rays in the maskit embedding of @xmath0 as the bending measure of the ` top ' surface in the boundary of the convex core tends to zero , see section [ sec : background ] for the definitions . in the present article we will use the general top terms relationship to generalise the description of asymptotic directions of pleating rays to the case of an arbitrary hyperbolic surface @xmath0 , see theorem [ ta ] in section [ sec3 ] . the maskit embedding @xmath1 of a surface @xmath0 is the space of geometrically finite groups on the boundary of quasifuchsian space for which the ` top ' end is homeomorphic to @xmath0 , while the ` bottom ' end consists of triply punctured spheres , the remains of @xmath0 when the pants curves have been pinched . as such representations vary in the character variety , the conformal structure on the top side varies over the teichmller space @xmath20 , see section [ sub : maskit ] for a detailed discussion . let @xmath21 , and suppose we have a geometrically finite free and discrete representation @xmath22 for which @xmath23 . denote @xmath24 the complexity of the surface @xmath0 . fix disjoint , non - trivial , non - peripheral and non - homotopic simple closed curves @xmath25 which form a maximal pants decomposition of @xmath0 . we consider groups for which the conformal end @xmath26 is a union of triply punctured spheres glued across punctures corresponding to @xmath25 , while @xmath27 is a marked riemann surface homeomorphic to @xmath0 . kra s plumbing construction gives us an explicit parametrisation of a holomorphic family of representation @xmath28 such that , for certain values @xmath29 of the parameters , @xmath30 has the above geometry , see section [ sub2.2 ] for the definition of this construction . the maskit embedding is the map which sends a point @xmath31 to the point @xmath29 for which the group @xmath32 has @xmath33 . denote the image of this map by @xmath34 . note that , with abuse of notation , we will also call _ maskit embedding _ the image @xmath4 of the map @xmath35 just described . we investigate @xmath1 using the method of pleating rays . given a projective measured lamination @xmath2 $ ] on @xmath0 , the _ pleating ray _ @xmath3}$ ] is the set of groups in @xmath4 for which the bending measure @xmath5 of the top component @xmath6 of the boundary of the convex core of the associated @xmath7-manifold @xmath8 is in the class @xmath2 $ ] . it is known that @xmath36 is a real 1-submanifold of @xmath1 . in fact we can parametrise this ray by @xmath37 , where @xmath38 , so that we associate to @xmath39 the group @xmath40 such that @xmath41 , see theorem 6 in @xcite for the case @xmath42 . note that this result relies on thurston s bending conjecture which is solved for rational lamination by work of otal and bonahon and in the case of punctured tori by work of series . for a general ( irrational ) lamination , anyway , we can only conjecture that the real dimension of the associated pleating ray is 1 . our main result is a formula for the asymptotic direction of @xmath36 in @xmath1 as the bending measure tends to zero , in terms of natural parameters for the representation space @xmath43 and the dehn  thurston coordinates of the support curves to @xmath2 $ ] relative to the pinched curves on the bottom side . this leads to a method of locating @xmath1 in @xmath43 . we restrict to pleating rays for which @xmath2 $ ] is _ rational _ , that is , supported on closed curves , and for simplicity write @xmath44 in place of @xmath45}$ ] , although noting that @xmath44 depends only on @xmath2 $ ] . from general results of bonahon and otal  @xcite , for any pants decomposition @xmath46 such that @xmath47 are mutually non - homotopic and fill up @xmath0 ( see section [ ssub : manifolds ] for the definitions ) , and any pair of angles @xmath48 , there is a unique group in @xmath4 for which the bending measure of @xmath6 is @xmath49 . ( this extends to the case @xmath50 for @xmath51 provided @xmath52 fill up @xmath0 and also to the case @xmath53 . ) thus given @xmath54 , there is a unique group @xmath55 with bending measure @xmath56 for any sufficiently small @xmath57 . let @xmath58 denote the set of homotopy classes of multiple loops on @xmath0 , and let the pants curves defining @xmath9 be @xmath59 . the _ dehn  thurston coordinates _ of @xmath60 are @xmath61 , where @xmath62 is the geometric intersection number between @xmath16 and @xmath63 and @xmath64 is the twist of @xmath16 about @xmath65 . for a detailed discussion about this parametrisation see section [ ssub2.1 ] below or section 3 of @xcite . if @xmath66 , the above condition of bonahon and otal on @xmath47 is equivalent to ask @xmath67 . we call such laminations _ admissible_. the main result of this paper is the following . we will state this result more precisely , as theorem [ ta ] in section 3 . [ thma ] suppose that @xmath66 is admissible . then , as the bending measure @xmath68 $ ] tends to zero , the pleating ray @xmath69 approaches the line @xmath70    we should note that , in contrast to series statement , we were able to dispense with the hypothesis ` @xmath71 non exceptional ' ( see @xcite for the definition ) , because we were able to improve the original proof . in addition , the definition of the line is different because we have corrected a misprint in @xcite . one might also ask for the limit of the hyperbolic structure on @xmath72 as the bending measure tends to zero . the following result is an immediate consequence of the first part of the proof of theorem  [ thma ] . [ thmc ] let @xmath73 be as above . then , as the bending measure @xmath74 $ ] tends to zero , the induced hyperbolic structure of @xmath6 along @xmath75 converges to the barycentre of the laminations @xmath76 in the thurston boundary of @xmath77 . this should be compared with the result in  @xcite , that the analogous limit through groups whose bending laminations on the two sides of the convex hull boundary are in the classes of a fixed pair of laminations @xmath78 $ ] , is a fuchsian group on the line of minima of @xmath78 $ ] . it can also be compared with theorem 1.1 and 1.2 in @xcite .    finally , we wanted to underline that the result achieved in theorem [ disj ] about the relationship between the thurston s symplectic form and the dehn  thurston coordinated for the curves is very interesting in its own . it tells us that given two loops @xmath79 which belongs to the same chart of the standard train track , see section [ ssub : sympl ] for the definition , then @xmath80 where the vector @xmath81 are the dehn  thurston coordinates of the curves @xmath82 . the plan of the paper is as follows . section [ sec : background ] provides an overview of all the background material needed for understanding and proving the main results which we will prove in section [ sec3 ] . in particular , in section [ sec : background ] we will discuss issues related to curves on surfaces ( for example we will recall the dehn  thurston coordinates of the space of measured laminations , thurston s symplectic structure , and the curve and the marking complexes ) . in the same section we will also review kra s plumbing construction which endows a surface with a projective structure whose holonomy map gives us a group in the maskit embedding , and we will discuss the top terms relationship . then we will recall the definition of the maskit embedding and of the pleating rays . in section [ sec3 ] , on the other hand , after fixing some notation , we will prove the three main results stated above . we will follows series method @xcite : we will state ( without proof ) the theorems which generalise straightforwardly to our case , but we will discuss the results which require further comments . in particular , many proofs become much more complicated when we increase the complex dimension of the parameter space from 1 or 2 to the general @xmath83 . it is worth noticing that , using a slightly different proof in theorem [ thma ] , we were able to extend series result to the case of ` non - exceptional ' laminations , see section [ sec3 ] for the definition . we also corrected some mistakes in the statement of theorem [ thma ] .","summary":"this article was born as a generalisation of the analysis made by series in  where she made the first attempt to plot a deformation space of kleinian group of more than 1 complex dimension . we use the top terms relationship proved by the author and series in  to determine the asymptotic directions of pleating rays in the maskit embedding of a hyperbolic surface as the bending measure of the ` top ' surface in the boundary of the convex core tends to zero . the maskit embedding of a surface is the space of geometrically finite groups on the boundary of quasifuchsian space for which the ` top ' end is homeomorphic to , while the ` bottom ' end consists of triply punctured spheres , the remains of when the pants curves have been pinched . given a projective measured lamination $ ] on , the _ pleating ray _ }$ ] is the set of groups in for which the bending measure of the top component of the boundary of the convex core of the associated-manifold is in the class $ ] .    * msc classification : * 30f40 , 30f60 , 57m50    = 1","abstract":"this article was born as a generalisation of the analysis made by series in  where she made the first attempt to plot a deformation space of kleinian group of more than 1 complex dimension . we use the top terms relationship proved by the author and series in  to determine the asymptotic directions of pleating rays in the maskit embedding of a hyperbolic surface as the bending measure of the ` top ' surface in the boundary of the convex core tends to zero . the maskit embedding of a surface is the space of geometrically finite groups on the boundary of quasifuchsian space for which the ` top ' end is homeomorphic to , while the ` bottom ' end consists of triply punctured spheres , the remains of when the pants curves have been pinched . given a projective measured lamination $ ] on , the _ pleating ray _ }$ ] is the set of groups in for which the bending measure of the top component of the boundary of the convex core of the associated-manifold is in the class $ ] .    * msc classification : * 30f40 , 30f60 , 57m50    = 1"}
{"article_id":"1409.3905","section_id":"i","document":"the number of perfect matchings in a bipartite graph is given by the permanent of the bipartite adjacency matrix of the graph . since computing the permanent is generally computationally hard @xcite , various algorithms have been proposed to compute it approximately . we mention in particular the mcmc algorithm of jerrum  sinclair  vigoda @xcite , the linial  wigderson rescaling algorithm @xcite ( denoted lsw in the sequel ) , and the barvinok  godsil  gutman algorithm @xcite ; the analysis of the latter algorithm was the subject of the previous work @xcite . a more general ( and hence hard ) combinatorial problem is that of computing the number of perfect matchings in a graph with an even number of vertices . let @xmath0 denote the adjacency matrix of such a graph with @xmath1 vertices . the relevant combinatorial notion here is the _ hafnian _ @xcite , defined as @xmath2 where @xmath3 denotes the symmetric group on @xmath4 $ ] . it is immediate to check ( see , e.g. ,  @xcite ) that @xmath5 thus , the interest in an efficient computation of @xmath6 . as for the permanent , the exact computation of @xmath6 is computationally expensive . this problem of estimating the hafnian seems to be harder to attack than the corresponding problem for the permanent since many algorithms known for permanent approximation break down when extended to hafnians . in particular , the lsw rescaling algorithm @xcite transforms the adjacency matrix of a graph to an almost doubly stochastic one . yet , a nontrivial lower estimate of the hafnian of a doubly stochastic matrix is impossible ; see @xcite . also , in contrast with the computation of the permanent , @xcite points out that the proof of convergence of the mcmc algorithm breaks down for the approximate computation of the hafnian ( unless the minimal degree is at least @xmath7 , see @xcite ) . we consider in this paper the computation of @xmath6 for symmetric matrices with nonnegative entries . note that the diagonal entries play no role in the computation of @xmath6 and , therefore , in the rest of this paper we always assume that @xmath8 for all @xmath9 .    in his seminal paper @xcite discussing the godsil  gutman estimator for the permanent , barvinok also introduces a probabilistic estimator of @xmath10 for a symmetric matrix @xmath0 possessing nonnegative entries . let @xmath11 be a real skew symmetric matrix with independent centered normal entries @xmath12 above the diagonal satisfying @xmath13 . in other words , let @xmath14 denote a skew symmetric matrix with independent @xmath15 entries above the main diagonal . let @xmath16 denote the skew symmetric matrix with @xmath17 and write @xmath18 , where @xmath19 denotes the element - wise square - root of @xmath0 , that is , @xmath20 . then @xmath21 thus , @xmath22 , which is an easily computable quantity , is a consistent estimator for @xmath6 , and barvinok @xcite proceeds to prove that for any matrix @xmath0 , @xmath23 with high probability , where @xmath24 is euler s constant . other approaches to computing the hafnian include @xcite ( which however does not apply to adjacency matrices of nontrivial graphs ) , @xcite , where a deterministic algorithm of subexponential complexity is constructed and analyzed , and @xcite , where a random algorithm is analyzed but the precision of the algorithm depends in a complicated way on the number of perfect matchings . our goal in this paper is to analyze the performance of the barvinok estimator for the hafnian . as in @xcite , establishing the concentration of a random determinant hinges on bounding the singular values of the gaussian matrix @xmath11 . this crucial step , however , essentially differs from @xcite as @xmath11 is skew - symmetric , and thus has less independence than the unrestricted matrix in @xcite . handling these dependences required different arguments for the smallest and the intermediate singular values . in the first case , we employ a conditioning argument tailored to take into account the structure of the graph ( lemmas  [ l : tree ] , [ l : moderately compressible individual ] ) . the fact that the entries of @xmath11 are real , and thus the @xmath25 main minors of it are degenerate plays a central role here . on the other hand , instead of developing a estimate for intermediate singular values as in @xcite ( a difficult task here due to the skew - symmetry ) , we use the fact that the imaginary - valued matrix @xmath26 is hermitian , which allows us to use estimates from recent work @xcite on the local semi - circle law . to formulate our results , we introduce a notion of strong expansion for graphs . this notion strengthens the standard notion of vertex expansion assuming that sets having many connected components expand faster . for a set @xmath27 $ ] of vertices , denote by @xmath28 the set of the connected components of @xmath29 , and by @xmath30 the boundary of @xmath29 , that is , @xmath31\\setminus j : \\exists j\\in j , ( i , j)$ ] is an edge@xmath32 . [ def-1 ] let @xmath33 , and let @xmath34 . we say that the graph @xmath35 is strongly expanding with parameter @xmath36 up to level @xmath37 if for any set @xmath27 $ ] of vertices with @xmath38 , @xmath39    in this definition and below , we use the following notational convention . important parameters which appear in definitions and theorems are denoted by greek letters . unimportant constants whose value may change from line to line are denoted @xmath40 , etc . the simplest form of our results is in case @xmath0 is the adjacency matrix of a @xmath41-regular graph . [ thm-3 ] fix @xmath42 . let @xmath0 be the adjacency matrix of a @xmath41-regular graph @xmath43 with @xmath44 . assume that @xmath45 ( 1 ) then for any @xmath46 and @xmath47 , @xmath48 where @xmath49 . \\(2 ) fix @xmath50 . if , in addition to the above assumptions , the matrix @xmath51 possesses a spectral gap @xmath52 , then for any @xmath47 , @xmath53 where @xmath54 . [ the assumption in ( 2 ) means that the modulus of the eigenvalues of @xmath51 is either @xmath55 or smaller than @xmath56 . ] theorem  [ thm-3 ] is an immediate consequence of our more general theorem  [ thm-2 ] below . we discuss the definition of strongly expanding graphs in remark  [ r : example ] below . the extension of theorem  [ thm-3 ] to irregular graphs requires the notion of doubly stochastic scaling of matrices . we also need the notion of spectral gap for stochastic matrices . [ def - ds ] a matrix @xmath0 with nonnegative entries is said to possess a doubly stochastic scaling if there exist two diagonal matrices @xmath57 with positive entries such that the matrix @xmath58 is doubly stochastic , that is , @xmath59 for all @xmath60 . we call such @xmath61 a doubly stochastic scaling of @xmath0 . [ def - spectralgap ] a symmetric stochastic matrix @xmath0 is said to possess a _ spectral gap _ @xmath52 if there do not exist eigenvalues of @xmath0 in @xmath62 . we will show below ( see corollary  [ cor : matching exists ] ) that the adjacency matrix of a strongly expanding graph with appropriate lower bound on its minimal degree possesses a unique doubly stochastic scaling , with @xmath63 . we use this fact in the following theorem , where the required lower bound on the minimal degree is satisfied . [ thm-3bis ] fix @xmath64 . let @xmath0 be the adjacency matrix of a graph @xmath43 whose minimal degree satisfies @xmath44 . assume that @xmath65 and @xmath66    \\(1 ) then for any @xmath46 and @xmath47 , @xmath67 with @xmath49 . \\(2 ) fix @xmath50 . if , in addition to the above assumptions , @xmath61 possesses a spectral gap @xmath52 , then for any @xmath47 , @xmath68 where @xmath69 .    condition ( [ eq - dsadj ] ) can be readily checked in polynomial time by applying the lsw scaling algorithm , stopped when its error is bounded above by @xmath70 . indeed , at such time , the lsw algorithm output is a matrix @xmath71 which is almost doubly stochastic in the sense that , with @xmath72 denoting the doubly stochastic scaling of @xmath0 , one has @xmath73 . because the maximal entry of @xmath61 is at least @xmath70 , this implies that the maximal entries of @xmath61 and of @xmath74 are of the same order . note also that the spectral gap condition in point ( 2 ) of theorem [ thm-3bis ] , which depends only on the eigenvalues of @xmath61 , can also be checked in polynomial time . we note that for a given @xmath75 , there exist stronger expansion conditions on the graph @xmath43 which ensure that the maximal element in the doubly stochastic scaling of its adjacency matrix is of size at most @xmath76 . that is , if @xmath43 satisfies these stronger properties , condition ( [ eq - dsadj ] ) is automatically satisfied . we refer to section  [ sec : doubly stochastic ] , proposition  [ prop : not - large ] , for details .    conditions ( [ eq - sethm12bis ] ) and ( [ eq - dsadj ] ) play different roles in the proof . the first one is needed to establish the lower bound on the smallest singular value of @xmath11 , and the second one guarantees that most of the singular values are greater than @xmath77 . [ r : example ] the definition of strongly expanding graphs ( definition  [ def-1 ] above ) reminds one of that of a vertex expander . yet , it is stronger in two senses . first , the strong expansion property takes into account the geometry of the set , requiring more rapid expansion for more `` spread out '' sets . second , we want this expansion property to hold for all sets of size relatively close to @xmath78 , while for the classical expanders , the corresponding property is required only for sets with at most @xmath7 vertices . this may look unnatural at first glance . however , one may construct an example of a graph that can have the strong expansion property up to a level arbitrary close to @xmath55 , and yet the matrix corresponding to it may be degenerate with probability  1 . further , in proposition [ p : bias ] below , we construct a graph whose adjacency matrix barely misses the condition in definition  [ def-1 ] and yet @xmath79 with high probability for an appropriate @xmath80 . [ p : bias ] let @xmath50 . for any @xmath81 , there exists a graph @xmath35 with @xmath82 vertices such that @xmath83 \\qquad{\\vert}j{\\vert}\\le m/2\\quad \\rightarrow \\quad \\bigl{\\vert}\\partial(j ) \\bigr{\\vert}- ( 1-\\delta ) \\bigl{\\vert}\\operatorname{con}(j ) \\bigr{\\vert}\\ge\\kappa { \\vert}j{\\vert}\\ ] ] and @xmath84 here , @xmath85 are constants depending on @xmath52 . our theorems on adjacency matrices are based on a general result pertaining to doubly stochastic symmetric matrices @xmath61 with nonnegative entries . we will consider matrices which have many relatively large entries . to formulate this requirement precisely , we introduce the notion of large entries graph . [ def : large entries ] let @xmath0 be a symmetric matrix with nonnegative entries . for a parameter @xmath86 , define the _ large entries graph _ @xmath87 by connecting the vertices @xmath88 $ ] whenever @xmath89 . if @xmath0 is the matrix of variances of entries of a skew symmetric matrix @xmath11 , we will also refer to @xmath90 as the _ large variances graph _ of  @xmath11 . we will now formulate two theorems on the concentration of the hafnian of a skew symmetric matrix whose large variances graph satisfies a strong expansion condition . [ thm-1 ] fix @xmath91 . let @xmath61 be a symmetric stochastic matrix of even size @xmath78 with nonnegative entries , let @xmath92 be as ( [ wdef ] ) ( with @xmath61 replacing  @xmath0 ) and let @xmath93 denote its large variances graph . assume that :    the minimal degree of a vertex of @xmath35 is at least @xmath94 . @xmath35 is @xmath95 strongly - expanding up to level @xmath96 . @xmath97 . then , for any @xmath46 and @xmath47 there exists @xmath98 so that @xmath99    somewhat tighter bounds are available if the matrix @xmath61 possesses a spectral gap . [ thm-2 ] assume the conditions of theorem  [ thm-1 ] and in addition assume that the matrix @xmath61 has a spectral gap @xmath52 . then , for any @xmath47 , @xmath100 the constant @xmath74 here depends on all relevant parameters @xmath101 and @xmath102 . the structure of the paper is as follows . in section [ sec : compressible ] , we consider unit vectors that are close to vectors with small support and derive uniform small ball probability estimates for their images under the action of @xmath11 . these estimates are used in section  [ sec : smallest singular ] to obtain a lower bound for the smallest singular values of @xmath11 . in section  [ sec : local bounds ] , we provide local estimates for the empirical measure of eigenvalues of @xmath11 . section  [ sec : proof thm 1 2 ] is devoted to the proof of theorems  [ thm-1 ] and  [ thm-2 ] . section  [ sec : doubly stochastic ] is devoted to the proof of a combinatorial lemma concerning the doubly stochastic scaling of adjacency matrices of strongly expanding graphs , which then is used in the proof of theorem  [ thm-3bis ] ; in the section we also present sufficient conditions that ensure that  ( [ eq - dsadj ] ) holds . finally , in section [ sec : strong expansion ] we present the construction of the graph discussed in proposition  [ p : bias ] , and provide the proof of the latter .","summary":"we analyze the behavior of the barvinok estimator of the hafnian of even dimension , symmetric matrices with nonnegative entries . that hafnians count the number of perfect matchings in graphs , we conclude that barvinok s estimator gives a polynomial - time algorithm for the approximate ( up to subexponential errors ) evaluation of the number of perfect matchings .    ./style / arxiv - general.cfg    ,","abstract":"we analyze the behavior of the barvinok estimator of the hafnian of even dimension , symmetric matrices with nonnegative entries . we introduce a condition under which the barvinok estimator achieves subexponential errors , and show that this condition is almost optimal . using that hafnians count the number of perfect matchings in graphs , we conclude that barvinok s estimator gives a polynomial - time algorithm for the approximate ( up to subexponential errors ) evaluation of the number of perfect matchings .    ./style / arxiv - general.cfg    ,"}
{"article_id":"1404.1209","section_id":"i","document":"jets from radio - loud agn show two characteristic morphologies , associated with the fri and frii classes defined by @xcite . jets in fri sources ( e.g. , 3c  31 , * ? ? ? * ) expand rapidly on kiloparsec scales , whereas those in the more powerful frii sources ( e.g. , cyg  a , * ? ? ? * ) are highly collimated until they terminate in compact hot - spots . fri and frii jets appear morphologically similar on parsec scales and both show evidence for relativistic speeds , although the former appear to be somewhat slower and to have significant velocity gradients @xcite . the current paradigm for fri jets is that , unlike frii jets , they are decelerated by entrainment of gas @xcite . whether this susceptibility to entrainment is solely a function of the power of the jet and its external environment or is due to a more fundamental difference is currently a matter of debate . two main processes have been invoked to explain entrainment in fri jets : ( i ) mixing in a turbulent shear layer between the jet and the ambient @xcite , and ( ii ) injection from stellar mass loss @xcite . concerning the process of entrainment through a turbulent shear layer , ( * ? ? ? * hereafter pm07 ) showed , via a 2d axisymmetric simulation , that a recollimation shock in a light jet formed in reaction to steep interstellar density and pressure gradients may trigger nonlinear perturbations that lead to jet disruption and mixing with the external medium . @xcite and @xcite discussed the deceleration of fri jets at discontinuities in the ambient medium and by the growth of helical instabilities in a jet propagating through a homogeneous ambient medium , respectively . the influence of mass loading by stellar winds in fri jets was studied by @xcite , who showed that this problem can be treated as a hydrodynamical one , as the gyroradii of the particles are much smaller than the size of the interaction region between the jet and the stellar wind . thus , this problem can be reduced to that of a distributed source of mass that is injected into and thereafter advected with the jet flow . * hereafter blk ) studied the effect of mass loading by a typical stellar population on jets with different properties by solving the equations of evolution in steady state . in particular , they focused on light and hot electron / proton jets . they concluded that these jets can be efficiently decelerated by this mechanism , with some differences depending on the thermodynamical properties of the jets : hotter jets cool down due to entrainment of the cold wind particles , whereas relatively colder jets gain temperature in the entrainment region due to dissipation . @xcite studied the different ranges of stellar mass - loss rates and jet powers that could imply efficient jet deceleration within the host galaxy , and concluded that the stellar wind from a single wolf - rayet star could be enough to decelerate a weak fri jet . @xcite constructed a one - dimensional model of the jet in 3c  31 using the basic conservation laws and the velocity field inferred by @xcite , which includes a substantial deceleration of the jet within the flaring region , located at 13 kpc from the central engine . close to the outer boundary of this region , at @xmath1kpc , @xcite found maxima in the mass entrainment rate ( per unit length of the jet ) both for their reference model and for the stellar mass input . however , the latter is much smaller . although the expected mass injection by stellar winds seems to be enough to counterbalance the effects of adiabatic expansion and to keep the velocity fairly constant at the beginning of the flaring region , the continuous deceleration in the jet indicated by @xcite s results requires a monotonic increase of the entrainment rate at large distances this can not be the result of mass loss from stars , whose density falls rapidly with increasing radius . @xcite concluded that entrainment from the galactic atmosphere across the boundary layer of the jet is the dominant mass input process far from the nucleus in this powerful ( @xmath2ergs@xmath3 ) fri jet , but that stellar mass loss might also contribute near the flaring point . @xcite have recently presented observations and kinematic models for ten fri radio galaxies . they concluded that the deceleration of fri jets after the flaring point is a gradual process in which the transverse velocity profile evolves from constant to slower at the edges than on - axis . mass loading by stars is distributed throughout the jet volume and is therefore not expected to create large transverse velocity gradients . it is therefore unlikely to be the dominant cause of deceleration on these scales : boundary - layer entrainment is more plausible . a contribution from stellar mass loading , particularly on smaller scales , is not excluded , however . this conclusion was based on models for the six sources with adequately determined transverse velocity profiles . it is consistent with , but not required by the models for the remaining four . all of the cases with well - determined profiles are powerful fri sources . it remains possible that weaker sources such as m84 and ngc193 , for which the models do not show conclusive evidence for velocity gradients , are decelerated primarily by stellar mass loading .    in pm07 the deceleration and decollimation of the jet was produced by the development of a recollimation shock formed at a few kiloparsecs from the central engine due to the density decrease in the ambient igm . the expansion caused by the jet overpressure as it propagated outwards and the subsequent recollimation shock effectively decelerated the jet after the shock , triggering the development of kelvin - helmholtz ( kh ) instabilities and enhancing the mass entrainment beyond this point . the main purposes of this paper are to extend the analysis of pm07 to include the combined effects of the mass loading of the jet by stellar winds and the recollimation shock , to compare with the earlier results and to cover a larger range of jet powers . we also investigate the effects of changing the boundary conditions of the simulations . we present simulations of jets with typical fri powers , including source terms in the equations of relativistic hydrodynamics that account for the mass entrainment by winds from the stellar populations expected for typical host galaxies . our aim is to understand the conditions under which fri jets can be decelerated by this type of entrainment and those for which either another process or a different stellar population are required . the paper is structured as follows . the setup of the simulations , together with the parameters used are presented in section  [ s : sim ] , and the results are given in section  [ s : res ] . section  [ disc ] discusses the implications . a summary and the conclusions of this work are given in section  [ conc ] .","summary":"several mechanisms have been proposed to explain this effect , including strong reconfinement shocks and the growth of instabilities ( both leading to boundary - layer entrainment ) and mass loading from stellar winds or molecular clouds . the jets show larger opening angles and decollimate at smaller distances , but the overall structure and dynamics of the bow - shock are similar to those of unloaded jets with the same power and thrust . according to our results , the flaring observed on kpc scales is initiated by mass loading in the weaker fri jets and by reconfinement shocks or the growth of instabilities in the more powerful jets . [ firstpage ]    galaxies : active  galaxies : jets  hydrodynamics  stars : winds , outflows","abstract":"jets in low - luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub - relativistic speeds on kiloparsec scales . several mechanisms have been proposed to explain this effect , including strong reconfinement shocks and the growth of instabilities ( both leading to boundary - layer entrainment ) and mass loading from stellar winds or molecular clouds . we have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code _ _ r__atpenat . we study the evolution of fanaroff - riley class i ( fri ) jets , with kinetic powers , within the first 2  kpc of their evolution , where deceleration by stellar mass loading should be most effective . mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak fri jets within the first kiloparsec . however , powerful fri jets are not decelerated significantly . in those cases where the mass loading is important , the jets show larger opening angles and decollimate at smaller distances , but the overall structure and dynamics of the bow - shock are similar to those of unloaded jets with the same power and thrust . according to our results , the flaring observed on kpc scales is initiated by mass loading in the weaker fri jets and by reconfinement shocks or the growth of instabilities in the more powerful jets . the final mechanism of decollimation and deceleration is always the development of disruptive pinching modes .    [ firstpage ]    galaxies : active  galaxies : jets  hydrodynamics  stars : winds , outflows"}
{"article_id":"1404.1209","section_id":"r","document":"we first describe the effects resulting from the change of boundary conditions from open ( as used in pm07 ) to reflecting . reflecting boundary conditions mimic the presence of a counter - jet with the same properties as the simulated jet and are therefore likely to be more realistic . [ fig : po - pr ] shows the last frames of both simulations at @xmath83  yr . the images reveal the main differences due to the boundary condition : the shape of the bow - shock ( the forward shock driven into the ambient by the injection of the jet ) , the width of the jet and the prominence of jet pinching . in pr , the reflecting boundary condition causes both the bow - shock and the inner cocoon ( the region with mixed shocked ambient and jet material surrounding the jet ) to be wider . the jet in po is broader and shows stronger recollimation ( conical ) shocks , which in turn make the head of the jet broader . the jet in pr remains more collimated . the choice of boundary condition only affects some aspects of the simulations . for example , the advance speeds of the jet terminal shock and the head of the bow - shock are very similar in pr and po , whereas the cocoon pressure and density in pr are larger : by almost an order of magnitude in the density ( @xmath84 compared with @xmath85  g  @xmath6 ) and a factor of two in the pressure ( @xmath86 compared with @xmath87  erg  @xmath6 ) by the end of the simulations . the pressure is basically determined by the injected energy divided by the volume of the shocked region , implying that the pressure in the shocked ambient and jet material ( i.e.  the whole volume within the bow - shock , excluding the jet ) will decrease with time as it expands . the pressure in the cocoon follows the same power - law @xmath88 in both cases , but with a larger constant of proportionality for pr . the radius of the bow - shock also increases faster with time for pr : by the end of the simulation the mean radius of the shocked region is @xmath89  pc compared with @xmath90  pc in po . another consequence of the higher pressure in pr is that the opening angle of the jet is smaller ( @xmath91 versus @xmath92 in po ) . the recollimation shocks are therefore stronger in po . po also shows a broader and faster backflow component than pr , since backflowing material can escape through the open boundary . in both simulations , the backflow decelerates with the distance travelled from the terminal shock . typical velocities close to the terminal shock ( @xmath93 ) are similar in both cases : @xmath94 in pr and @xmath95 in po . in pr , the velocity drops to values @xmath96 at @xmath97 and @xmath98 at @xmath99 , finally reaching zero at @xmath100 , close to the reflecting boundary . in po , the backflow velocity is typically @xmath101 at @xmath102 and drops to values @xmath98 at @xmath100 .    as the jet in both simulations has the same injection conditions , we expect that the jet and shock structures seen in pr and po should be very similar if they are compared at the same cocoon pressure . in other words , pr at a given time will look quite similar to po seen at some earlier time . in particular , the pressure in the cocoon has a direct influence on the position of a possible recollimation shock , and the appearance of strong shocks in simulations with reflecting boundaries will occur at later times than in simulations with open boundaries . we thus conclude that the shock in the jet in pm07 ( which used an open boundary ) would correspond to an older jet simulated with a reflecting boundary condition , in which the bow shock would have propagated to larger distances than the 15  kpc found in that work .    as the use of a reflecting boundary condition is likely to give a better approximation to the true bipolar case , we use it for the remaining simulations in this paper . the differences introduced by the change of boundary conditions should be borne in mind when comparing with the simulations of pm07 . yr ) for simulations po ( upper panel ) and pr ( lower panel ) . [ fig : po - pr],scaledwidth=45.0% ]    yr ) for simulations po ( upper panel ) and pr ( lower panel ) . [ fig : po - pr],scaledwidth=45.0% ]        neither of the simulations of powerful , mass - loaded jets show signs of strong deceleration over distances of 2kpc , but there is slow deceleration due to a combination of mass loading and dissipation of kinetic energy at internal shocks . the jet flow heats up at the shocks , increasing its temperature by an order of magnitude ( to @xmath103k ) between injection and the terminal shock . the role of mass loading is revealed by a decrease in the jet mass fraction from 1 to around 0.9 on the axis ( slightly larger for pr and smaller for po ) and a decrease in the mean value over the jet cross section to about 0.6 before the jet terminal shock in both simulations . the mean jet flow velocity before the terminal shock is around 80% of the injection value . the jet can only be slowed efficiently by mass loading when the kinetic energy required to accelerate the loaded mass to the flow velocity of the jet ( @xmath104 per unit time , where @xmath105 is the jet lorentz factor , and @xmath106 is the mass - loading rate ) is of the order or larger than the kinetic luminosity , @xmath107 @xcite . if we assume a constant mass - loading rate per unit volume @xmath70 and a jet of constant radius @xmath108 , the characteristic length for jet deceleration is @xmath109 even if we use a constant mass - loading rate equal to the maximum at the centre of the galaxy , @xmath110 ( table  [ tab1 ] ) , we still obtain deceleration lengths of the order of hundreds of kpc . such values are only indicative , since : ( i ) part of the jet kinetic energy will be used to heat the loaded material ; ( ii ) the mass loaded per unit time rises as the jet gets longer and ( iii ) the true value of the mass - loading rate per unit volume decreases very fast with increasing distance from the galaxy centre ( for @xmath111 in our models ) , so the approximation @xmath112 is only valid over distances @xmath1131kpc . whereas ( i ) and ( ii ) tend to decrease the deceleration length , ( iii ) tends to increase it . nevertheless , this simple computation clearly explains the lack of deceleration in models po and pr within the first 2kpc . it is interesting to compare po and pr with the simulation presented in pm07 ( which has the same boundary condition as po ) . note that the flow parameters at injection are quite different , even though the jet power is the same in all three cases . in pm07 , the jet was injected at 500  pc , with a radius of 60  pc , a velocity @xmath114 and an overpressure factor of 7.8 with respect to the ambient value . the jets in po and pr were injected at 80  pc , with a radius of 10  pc , a velocity @xmath115 and an overpressure factor of 17.6 .    in pm07 , the first recollimation shock appeared at @xmath116 after @xmath117 . the jet was injected close to the core radius of the galactic gas , and thus expanded into an ambient medium in which the density and pressure fall rapidly with distance . within this environment the pressure of the cocoon evolves as @xmath118 . in the case of po and pr , the simulations covered much smaller durations ( @xmath119 ) and distances from the nucleus than that in pm07 . the cocoon pressure evolves following a flatter slope @xmath120 , primarily because the jets in po and pr are entirely within the galactic core , where the ambient density falls very slowly with distance . this results in a slower expansion : the jets in po and pr would need to be followed to larger distances and times to be directly compared with the simulation in pm07 . [ fig : a0sequence ] displays a series of snapshots of the rest mass density of model a0 , in which there is no mass loading . the sequence shows the propagation of the shock generated by the jet through the ambient . the weakness of the jet is reflected in the almost spherical shape of this shock at very early times ( fig . [ fig : a0sequence ] , first panel ) , the low mach number of the jet ( @xmath1213 at the beginning of the simulation ) and the clear detachment of the shock from the cocoon . the contact discontinuity between the cocoon and the shocked ambient soon develops a prominent ` nose - cone ' and the bow - shock becomes more extended in the axial direction . the beam shows a series of internal conical shocks produced by the pressure mismatch between it and the cocoon . [ fig : a0final ] shows the distributions of pressure , rest - mass density , temperature and axial flow velocity at the end of the simulation . the protrusion of the bow shock caused by the impact of the beam on the originally spherical shock is clearly seen in the first three panels . conical shocks within the beam are apparent in the pressure , rest - mass density and axial velocity panels . these eventually evolve into planar disrupting shocks . the supersonic beam ends at a terminal shock where the beam flow decelerates , compresses and heats . in fig . [ fig : a0final ] , this shock is located at about @xmath78 kpc from the injection point . the region between this shock and the bow shock forms the so - called head of the jet , a very dynamic structure that governs the propagation of the jet through the ambient . in model a0 , the region is quite broad with no substantial enhancement of the internal energy density ( fig . [ fig : a0final ] ; pressure panel ) ; the terminal shock , and hence the jet , are still propagating at the end of the simulation , and have not stalled . the dynamics of the jet head is discussed in more detail in section  [ ss : head_dyn ] . the cocoon is essentially isobaric , since the time - scale for the pressure to become constant is much shorter than the propagation time - scale . the density and temperature distributions display a clear transition between the almost homogeneous values of the old jet material in the cocoon ( made colder and denser due to mixing with the shocked ambient gas through the contact discontinuity ) and the hot and dilute material newly injected at the nose cone . finally , a hot shear layer develops between the beam and cocoon material ( this is not seen in the temperature panel of fig . [ fig : a0final ] due to its limited resolution ) . we emphasize that the end - points of all of the simulations presented here correspond to very early stages of the evolution of low - power radio galaxies . this is the main reason why the nearly spherical region of gas surrounding the base of the jet in model a0 ( @xmath121700pc in radius in fig . [ fig : a0final ] ) appears much hotter and less dense than the cool cores revealed by x - ray observations in the host galaxies of fri sources @xcite , and indeed included in the initial conditions for the simulations . the hot cocoons will dilute and mix with the cooler ambient material as the jet becomes transonic and the bow shock disappears . the spherical shape that we find for the cocoon close to the injection is due to the low advance velocity of the head of the jet and the action of gravity : the dynamical time - scale of the gravitational field that maintains the atmosphere in hydrostatic equilibrium is in the range @xmath122 to @xmath123 in the simulated region ; this is smaller than the simulation time , where @xmath124 is the gravitational constant and @xmath125 is the density of dark matter within the simulated region . ] . +          figs  [ fig : asequence ] and [ fig : afinal ] are the equivalents for model a of figs  [ fig : a0sequence ] and [ fig : a0final ] for model a0 . the times of the snapshots in figs  [ fig : a0sequence ] and [ fig : asequence ] are almost identical , allowing a direct comparison of the density panels for the two models . the main structural and dynamical features of the cocoon / shocked ambient system found in model a0 ( an almost spherical cocoon , detachment of the bow shock from the cocoon and formation of a nose cone at the head of the jet ) also apply to model a. comparison between the two sequences also shows very similar speeds for the propagation of the jet head and the expansion of the cocoon . these similarities persist until the ends of the simulations ( figs  [ fig : a0final ] and [ fig : afinal ] ) . the reasons for them are discussed in section  [ ss : cocoon ] . however , qualitative differences in the evolution of a0 and a appear as a result of the accumulated effect of mass loading . in particular , the mass loading causes an efficient deceleration of the plasma within the beam in model a , which leads to expansion . the increase of the beam cross section reduces the momentum transfer per unit area to the ambient and causes the jet to decelerate . as a result , the beam in model a is denser , cooler and shorter than the one in model a0 and expands with an almost constant half - opening angle of @xmath126 until its disruption at about 900pc from the nucleus ( fig .  [ fig : afinal ] ) . whereas the beam in model a0 propagates at almost constant speed , the terminal shock in model a decelerates with time and nearly stalls by the end of the simulation ( see section  [ ss : head_dyn ] ) . mass loading and the accompanying jet expansion appear to reduce pinching along the jet in model a relative to model a0 , so the conical shocks are weaker in the former case ( compare the pressure panels of figs  [ fig : a0sequence ] and [ fig : asequence ] ) . however , pinching is more disruptive at the jet head in model a and is the main cause of the flaring . +          models a , b and c ( see table  [ tab1 ] ) form a sequence along which the density at injection decreases by a factor of one hundred and the specific internal energy increases by the same amount , keeping the same power ( and thrust ) for the jets . we do not show the early evolution of models b and c ( very similar to that of model a ) , and concentrate on the distributions of pressure , rest - mass density , temperature and axial flow velocity at the end of simulation c ( fig . [ fig : cfinal ] ) , which show the largest differences compared with a. the differences in the overall structure of the jet / cocoon / shocked ambient system between models a ( fig . [ fig : afinal ] ) and c are very small ( section  [ ss : cocoon ] ) . the similarity between these two models extends to the beam structure , with very similar distributions of density , pressure and flow velocity . the obvious conclusion ( analysed in detail in section  [ ss : beam ] ) is that the dynamics of the beams in models a , b and c are dominated by the process of mass loading with the thermodynamical properties playing a secondary role . +          model d has the same jet injection conditions as model c but a central mass - loading rate per unit volume , @xmath25 , one order of magnitude smaller ( table  [ tab1 ] ) . [ fig : dfinal ] shows the distributions of pressure , rest - mass density , temperature and axial flow velocity of model d at the end of the simulation . the gross morphology of the jet / cocoon / shocked ambient ensemble is again almost identical to that of models a , b and c ( and a0 ) , as explained in sect . [ ss : modela ] . in spite of two orders of magnitude difference in the beam density ( and temperature ) , model d resembles model a0 more than models a and c : the beam remains fast and well - collimated , with strong conical shocks . this result proves again the sensitivity of the beam structure and dynamics to the mass loading rate and the secondary role of the jet thermodynamics , within the range of parameters used in these simulations .","summary":"the final mechanism of decollimation and deceleration is always the development of disruptive pinching modes .   ","abstract":"jets in low - luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub - relativistic speeds on kiloparsec scales . several mechanisms have been proposed to explain this effect , including strong reconfinement shocks and the growth of instabilities ( both leading to boundary - layer entrainment ) and mass loading from stellar winds or molecular clouds . we have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code _ _ r__atpenat . we study the evolution of fanaroff - riley class i ( fri ) jets , with kinetic powers , within the first 2  kpc of their evolution , where deceleration by stellar mass loading should be most effective . mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak fri jets within the first kiloparsec . however , powerful fri jets are not decelerated significantly . in those cases where the mass loading is important , the jets show larger opening angles and decollimate at smaller distances , but the overall structure and dynamics of the bow - shock are similar to those of unloaded jets with the same power and thrust . according to our results , the flaring observed on kpc scales is initiated by mass loading in the weaker fri jets and by reconfinement shocks or the growth of instabilities in the more powerful jets . the final mechanism of decollimation and deceleration is always the development of disruptive pinching modes .    [ firstpage ]    galaxies : active  galaxies : jets  hydrodynamics  stars : winds , outflows"}
{"article_id":"1404.1209","section_id":"c","document":"the parameters defining the ambient medium , the mass - loss rates and the jets in models a , b , c and d are similar to those in blk , allowing a comparison between the two sets of simulations . in particular , the central mass - loss rate of the two reference models in blk ( @xmath127 ) lies between those for models a , b and c ( @xmath128 ) , and model d ( @xmath129 ) . the kinetic luminosity per unit area at injection of our models is about four times smaller than that of the cold reference model in blk , and just a bit larger than that of their hot model . finally , the lorentz factor of the flow at injection is 3 in models a , b , c and d , and 5 in blk s reference models . the deceleration lengths , @xmath130 , predicted by equation  ( [ eq : ld ] ) are therefore in the ratios : @xmath131 . this prediction is in qualitative agreement with our results and those of blk . our models a , b and c all show deceleration , as do the hot and cold reference models of blk , with the former having a shorter stopping distance ( their figs 3 and 4 ) . model d , by comparison , shows little deceleration . the bulk parameters governing the propagation of the jets in our simulations are similar to those of blk , but differences are expected from the disparity in the composition and thermodynamic properties between the models and from the natures of the two kinds of simulation . our jets are composed of electron - positron pairs ; those of blk contain electron - proton plasma . thus , although the temperatures of the two sets of models cover the same range ( @xmath132 k ) , all of our models are thermodynamically hot . the simulations in blk assume steady flows . they are therefore best suited to describe a long , isolated jet propagating through a prescribed ( and undisturbed ) ambient medium . our simulations are dynamical and allow us to study the complex head of the jet , the formation of a cocoon and the process of flaring and disruption . they are , however , restricted to the early evolutionary phases of fri radio sources .      the gross morphological and dynamical properties of the shocked ambient and cocoon in models a , b , c , d and a0 are all very similar . the explanation is that all of the models have the same kinetic power and thrust ( @xmath133 dyn ) and propagate through the same ambient medium , so the differences between their gross dynamical properties are small . [ fig : cavity_evol ] shows the evolution of the length and width of the shocked region with time for all of the models . the differences among the models are tiny , particularly for the sideways expansion . the axial expansions fall in two groups ( although with a difference in expansion speed of only a few percent ) , with models a0 and d ( not affected by the mass loading ) undergoing the faster expansion . in models a , b and c , second - order effects related to the mass loading of the jet slow the expansion slightly ( e.g.  the increase in the jet cross section reduces the jet thrust per unit area ) . although limited in duration , our simulations allow us to study the principal effects of mass loading on the beam evolution because the jet head is followed out to a distance of @xmath77  kpc , well beyond the stellar break radius @xmath134  pc . the internal structure of the jets is dominated by oblique shocks ( conical shocks in axisymmetric models ) . their origin is the pressure mismatch between the beam and its surroundings ( i.e. , the cocoon ) and this produces periodic variations of the beam structure around some state of equilibrium . the wavelength of these variations is given approximately by @xmath135 , where @xmath136 is the relativistic mach number and @xmath137 is the beam radius @xcite . at the incident shock , the beam flow recollimates and decelerates whereas at the reflected shock , the flow is first compressed and then expands and accelerates , helped by the pressure gradient in the post - shock gas . the expansion continues until the pressure drops below the ambient value , when a new incident shock is initiated . [ fig : sketch ] shows a sketch of a conical shock . if the initial jet overpressure is large or the fall in the ambient pressure is steep enough , the shock can produce a planar mach disk , as observed in pm07 . the series of oblique shocks left behind by the jet head is present in all of the models but is especially prominent in models a0 ( fig . [ fig : a0final ] ) and d ( fig . [ fig : dfinal ] ) . it is apparently unaffected by the small amount of mass loading in the latter case . in the more heavily mass loaded models a , b and c , the internal shocks are weaker ( and the amplitudes of the pressure jumps are therefore smaller than in models a0 or d ) .    a simple analysis of the beam properties can be done by assuming stationarity from the injection point to the terminal shock . this is a fair assumption as long as the beam remains supersonic ( which is certainly the case up to the terminal shock ) and the injection boundary conditions and the mass loading are also stationary . the external pressure around the jet ( the cocoon pressure ) is quite homogeneous and varies slowly with time . the evolution of the averages across the beam of different relevant quantities along the axial direction can then be evaluated . to this end , the beam is defined as the domain encompassing all of the plasma with axial velocity larger than @xmath138 . the radius of this region is plotted against axial distance , @xmath139 , in fig .  [ fig : beam_mean_values](a ) . the value of @xmath138 represents a compromise that gives a well - defined beam profile up to the terminal shock at the cost of including a fraction of cocoon material accelerated by shear at the beam / cocoon surface in the analysis . as noted in section  [ ss : modelbc ] , the beam profiles are remarkably similar for models a , b and c. this is primarily a consequence of mass loading dominating the beam structure , with the detailed thermodynamics of the different beam models playing a secondary role . the beam radius profile in model d remains close to that of model a0 and this confirms that the mass - load rate in model d is not strongly affecting the dynamics of the jet . the primary effect of mass loading on the beam is the deceleration and cooling of the flow as a result of the momentum transfer from the original beam fluid to the newly incorporated material and the reduction of the mean specific internal energy . figs  [ fig : beam_mean_values](b ) and ( c ) show , respectively , the averages of the flow velocity and the specific internal energy across the beam as functions of axial distance for models a , a0 , b , c and d at the end of the simulations . the deceleration of the beam flow in models a , b and c is clear . despite the differences in initial specific internal energy and density ( two orders of magnitude between the extreme cases ) , the deceleration rate in these models is roughly the same this is because these initial values have been chosen so that all three models have the same initial internal energy per unit volume and the same thrust ( table  [ tab1 ] ) . the density profiles are dominated by stellar mass input ( except very close to the injection point ) and are also very similar ( fig . [ fig : beam_mean_values]e ) . the deceleration rate depends on the initial momentum of the beam and the mass - loading rate , which are both the same in all three models . similarly , the models all have the same amount of internal energy to share with the cooler stellar wind plasma , so the profiles of specific internal energy along the beam are also almost identical . we conclude that the dissipation of kinetic energy into internal energy along the beam is essentially the same in all three mass - loaded models . finally , the similarity of the velocity and specific internal energy profiles implies that the relativistic beam mach number , @xmath136 must vary in the same way for models a , b and c. it adjusts during the first @xmath140 pc after the injection to a value around @xmath141 , thereafter decreasing along the beam ( fig . [ fig : beam_mean_values]f ) .    in the contrasting case of low or zero mass loading ( models a0 and d ) , the average beam density profiles are dominated by cocoon material accelerated by shear at the interface . a comparison between the profiles for the beam in model a0 ( shown in fig . [ fig : beam_mean_values ] ) and the values of the same quantities at injection ( table  [ tab1 ] ) allows us to quantify the effects of this boundary - layer entrainment . the average flow velocity of the beam is @xmath142 , reduced by @xmath143 from its value of @xmath144 at injection . the density however increases by a factor of @xmath145 since the shear layer material included in the jet by our definition ( cells with axial velocity larger than @xmath138 ) dominates the average . the opposite happens in the case of the specific internal energy , which is several orders of magnitude larger in the beam than in the cocoon . the average is dominated by the beam and shows a reduction of about @xmath146 from the injection value . increasing the velocity cut - off in the definition of the beam reduces the beam radius and produces averages closer to the values at injection . a comparison between the density profiles for models a0 and a ( fig . [ fig : beam_mean_values]e ) , confirms that mass loading by stellar winds dominates over that from shear entrainment in models a , b and c ( but not in d ) . we also note that the plasma in all of our models cools down along the jets because our jets are initially thermodynamically hot . this cooling is most pronounced in models a , b and c and least in a0 , with d being intermediate between them . thus , the effect of thermal dilution between the original beam plasma and the entrained stellar wind plasma dominates over the heating produced by dissipation . this is not what happens in some of the cases considered by blk , notably their ` cold ' reference model . we can gain more insight into the behaviour of the jet radius and internal density from the constraints set by mass conservation and pressure balance . time independence of the equation of continuity requires that @xmath147 along the beam , where @xmath148 is the beam cross section and @xmath57 , @xmath70 , @xmath149 and @xmath60 are respectively the averages across the beam of the rest - mass density , the mass - entrainment rate , the flow velocity and the lorentz factor . hence , the product @xmath150 must grow fast enough to balance the deceleration and still give a positive derivative in eq . ( [ eq : cont_steady ] ) . as a result , @xmath57 , @xmath148 or both must increase along the beam . the pressure in the beam is governed by pressure balance with the cocoon . since the cocoon is almost isobaric , the beam pressure profile ( averaged over fluctuations due to shocks ) is almost constant ( fig . [ fig : beam_mean_values]d ) . this panel also shows the smaller amplitude of the internal shocks in models a , b and c , mentioned at the beginning of this section . to counterbalance the effect of the decrease in the specific internal energy and keep the pressure constant , the density must increase along the beam ( fig . [ fig : beam_mean_values]e ) . in practice , both @xmath57 and @xmath148 increase to ensure pressure equilibrium and to satisfy the equation of continuity . note that beam expansion leads to further mass loading , which in turn leads to further deceleration and cooling . the final result is an effective deceleration of the jet head in models a , b and c , and associated decollimation and flaring of the jet beyond this point ( see section  [ ss : head_dyn ] ) . on the other hand , the triggering of this runaway process occurs only for high enough mass - loading rates : model d ( with a mass - loading rate only one order of magnitude lower than that of models a , b and c ) evolves in essentially the same way as the unloaded model a0 . +     +          the supersonic beam ends at a terminal shock where the beam flow decelerates and transfers part of its momentum to the ambient . in powerful jets , the head of the jet ( the region between the terminal shock and the bow shock ) forms a hot - spot . in the models presented here , due to the weakness of the jet , the region is quite broad and there is no substantial enhancement of the internal energy density . [ fig : terminal_shock_with_time ] shows the position of the terminal shock as a function of time for all of the simulations in this paper . by the end of the simulations , the terminal shock in models a , b and c has nearly stalled at about @xmath151 pc , but those in models a0 and d are still propagating .    in these axisymmetric simulations , the growth of kh pinching modes also helps to trigger jet disruption via the process of external mass loading . although the pressure oscillations along the jet ( fig . [ fig : beam_mean_values]d ) are larger in models a0 and d , the growth of the pinch mode surface amplitude is slower than in models a , b and c. these modes are manifest for the latter group in the large - amplitude oscillations of the averaged flow variables ( beam axial flow velocity , specific internal energy , pressure , rest - mass density and mach number ) at distances between @xmath121500pc and disruption ( fig . [ fig : beam_mean_values ] ) . the effects of pinching modes can also be seen for all of the simulations in the colour pressure panels of figs . [ fig : a0final ] and [ fig : afinal]-[fig : dfinal ] . from linear relativistic kh theory , @xcite and @xcite showed that the growth lengths ( i.e.  the @xmath152-folding lengths of the growing modes ) increase with increasing @xmath135 . in the absence of deceleration due to mass loading , we would expect similar growth lengths for the beams of models a , b , c , d and a0 , since they have roughly the same values of @xmath135 at injection . however , the continuous deceleration and dissipation in models a , b and c cause @xmath135 to decrease with distance , even though the beams expand , so the growth lengths also decrease . moreover , at low values of @xmath135 , the simple supersonic scaling breaks down and growth lengths drop rapidly . thus , we conclude that the main cause of the relative increase in the growth rates and the earlier disruption of the jets in models a , b and c is the deceleration of the flow compared with that in a0 and d.    in order to quantify the further deceleration after jet disruption , fig .  [ fig : mean_velocity ] shows plots of average axial velocity against distance continuing as far as the contact discontinuity with the shocked ambient gas . we can not adopt the definition of the beam used earlier ( axial velocity @xmath153 ) , as the velocities in the jet head region are too low , and have held the radius of the averaging region fixed at its value immediately before disruption . the plots therefore represent the on - axis velocity in the head region . the models with zero or low mass loading ( a0 and d ; fig . [ fig : mean_velocity ] left panel ) decelerate from @xmath154 just before disruption to a mean speed of @xmath155 over a distance of @xmath156pc , with large fluctuations . for the models including mass loading ( a , b and c : fig . [ fig : mean_velocity ] right panel ) , the beams decelerate from @xmath157 to @xmath158 before disruption and the final speed is @xmath159 . as noted in section  [ intro ] , @xcite asserted that the development of a centrally - peaked transverse velocity profile was not consistent with mass input distributed throughout the jet volume , as would be expected for stellar mass loading . in agreement with this statement , our simulations show that , although mass load by stellar winds produces an expansion of the jet and a wide shear - layer , the inner region of the jet preserves a flat transverse velocity profile until the jet is disrupted . profiles at 80 and 540pc for models a and b show this effect clearly ( fig . [ fig : velocity_profiles ] ) . after disruption , the transverse profiles become centrally peaked , but here the deceleration is primarily due to interactions with the ambient medium rather than to stellar mass loading , and the profiles are therefore similar ( although with higher central values ) for models a0 and d , which have zero and low mass loading , respectively ( fig . [ fig : velocity_profiles ] ) . another interesting difference observed between the simulations with and without mass loading relates to the backflow , with models a , b and c showing small backflow velocities , @xmath160c , whereas models a0 and d show regions with velocities @xmath161c . the cause of this difference is related to the strength of the terminal shock , which ultimately depends on the flow velocity immediately upstream of the shock . the powerful jet simulation pr is a more extreme case , with backflow velocities @xmath162 close to the shock ( section  [ ss : boundary ] ) . in all cases , mass - loading at the contact discontinuity with the shocked ambient produced by kh instability decelerates the backflow . recently , @xcite have claimed the detection of backflows with velocities in the range of @xmath163c in two low - luminosity radio galaxies . if this result is confirmed , it could be concluded from our results that the jet flow velocity at the terminal shock is still large in those radio galaxies . it is not clear , however , that the situations are analogous , since the backflows modelled by @xcite are seen around the outer regions of the jets , well downstream of the flaring region and initial deceleration .      over the years , a model for the jets in fri radio sources has emerged in which the main actors producing jet deceleration within the first kiloparsec are ( internal ) mass loading and/or strong recollimation shocks . in both cases , instabilities with post - linear or non - linear amplitudes develop farther downstream and trigger external entrainment at the edges of the jets ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * blk , pm07 ) . the important new result from the simulations presented here is that a low - power ( @xmath164 ) fri jet can be decelerated efficiently as a result of mass loading from the winds of the old stellar populations which dominate the low - excitation radio galaxies typically associated with fri radio sources , whereas a high - power jet ( @xmath165 ) can not . there must be a range of variation between individual galaxies , depending on the precise stellar distribution and population , but the basic result should be robust . a corollary is that low - power fri jets can not be magnetically dominated on kiloparsec scales : the stellar mass loading will completely change the nature of the outflow within a few hundred pc . there are also important implications for the lobe dynamics of weak fri sources and their ability to act as sources of ultra - high energy cosmic rays : @xcite have recently suggested that the pressure in the lobes of centaurus a is dominated by heated plasma originating from stellar mass input . other types of host galaxy may generate higher mass input rates , however . for example , high - excitation radio galaxies typically have lower stellar masses , but younger stellar populations with higher average mass - loss rates ( e.g.  @xcite ) . individual young , massive stars and starbursts may also be important @xcite . the high - excitation radio galaxies also have broad- and narrow - line regions , which could provide mass loading sources for jets if the filling factors are large enough to cause frequent encounters between the jets and ionized gas clouds @xcite . entrainment of molecular clouds into the jets is another possibility @xcite . these sources of mass input may be able to decelerate more powerful jets , and should be investigated in future simulations . recollimation shocks ( section  [ ss : beam ] ) result from the response of the jet to a large pressure imbalance with its surroundings and have been studied in the context of the collimation and structure of extragalactic jets in both classical @xcite and relativistic regimes @xcite . if the jet is instead under - pressured or only slightly over - pressured with respect to the environment , small amplitude pinching will be induced , as observed in models a0 and d. this pinching could then couple to a kh unstable mode and grow with distance , triggering mixing and deceleration . the spatial scale at which this process develops depends on the jet and ambient properties but , in general , will be longer than the kiloparsec scale . the most interesting case is , however , when a recollimation shock reflects on the axis in a mach reflection rather than a regular reflection . in this case , a planar mach disk shock is formed , decelerating the flow very efficiently and leading to a subsonic flow in the shock rest frame . based on the significant overpressure at the flaring point in their models for 3c31 , @xcite proposed that the flaring point is associated with a stationary shock system , even though efficient mach disks are only formed for jets with opening angles much larger than the 8.5@xmath166 found by @xcite for the inner region of 3c  31 . in pm07 , the authors tested such a possibility based on axisymmetric numerical simulations of the 3c  31 jet and environment . three small mach disks were produced within the 2kpc length of the flaring region in the model jet . although the jet simulated in pm07 was injected with a large overpressure factor of 7.8 compared with the ambient , jets generate their own environment ( the cocoon ) , which is also overpressured . the jet was in fact only marginally overpressured with respect to its immediate surroundings and had a relatively small 13.8@xmath166 opening angle close to injection . nevertheless , the series of recollimation shocks was able to decelerate the flow to subsonic speeds .    with the caveats noted in section  [ intro ] , kinematic models of fri jets @xcite imply that deceleration from @xmath167 to sub - relativistic speeds is a fairly gradual process , involving the development of transverse velocity gradients and therefore associated with instabilities and boundary - layer entrainment . this leaves open the question of whether recollimation shocks provide the initial trigger for deceleration . the high - resolution observations summarized by @xcite present a challenge to the idea that deceleration is initiated by recollimation shocks , at least in the two best - resolved cases , 3c296 and ngc315 ( their fig . 17d and i ) . firstly , neither of these jets show bright features crossing the jets at the start of their flaring regions that might plausibly be identified with strong reconfinement shocks . instead , the brightness enhancements in the flaring region are complex , non - axisymmetric and restricted to the central parts of the jets . secondly , the expansion rates of the jets increase monotonically with distance after the flaring point , with no sign of recollimation until much larger distances . on the other hand , the bright knot at the base of the flaring region in 3c31 ( * ? ? ? * their fig . 17e ) could still plausibly be associated with a recollimation shock . higher - resolution observations are needed to decide whether such shocks are present in fri jets . another option considered to explain the deceleration of the flow is the development of instabilities that grow to nonlinear amplitudes and could give rise to the flaring of emission . @xcite suggested that the growing modes have to be high - order because the observed jets flare without disruption . all that is really necessary , however , is that they have short wavelengths . the process of slow deceleration could , instead , be related to the type 2 unstable flows ( ust2 ) classified by @xcite . these occupy a characteristic location in the relativistic mach number - lorentz factor plane and were confirmed using three - dimensional simulations by @xcite . this type of deceleration corresponds to a slow and progressive mixing , expansion and deceleration of jets that is caused by short - wavelength , but low - order , body modes . @xcite showed that this mechanism can be relevant in hot jets , because the linear solutions give high growth - rates and short wavelengths for the resonant values of kh body - modes , as opposed to the solutions obtained for colder jets . interestingly , @xcite conclude that the jets in their sample could be formed by hot , low - mach - number flows . further work is needed to establish whether this mechanism is effective for the parameter range applicable to fri jets . the resolution used in our simulations is not high enough to allow for the development of short - wavelength unstable modes . however , the goal of this paper is to determine the range of jet powers over which mass - loading by stars could be relevant . our simulations allow us to achieve this goal and also to demonstrate the development of longer wavelength unstable modes . a detailed study to compare the effects of the growth of short - wavelength modes and mass - loading by stars would require specific high - resolution simulations . it is important to note that the growth of instabilities from the linear regime requires pressure equilibrium with the ambient : if the jet is overpressured and expands , the expansion dominates the interaction between the jet and the ambient , making it difficult for a growing instability to become dynamically important . in addition , the wavelength of the fastest - growing modes changes proportionally to the jet radius and the growth rates are reduced ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? +     +    we stress that our simulations have followed the evolution of the propagating jets for @xmath168  yr after they are initiated . although we believe that the simulations capture several important aspects of jet propagation , the resulting morphologies are very different from those observed in old fri sources . although the head of the jet in the decelerated models advances at a very low velocity by the end of the simulation , the shape and structure of the cocoon are likely to change radically when the bow - shock expands in the strong pressure gradient beyond the galactic core . the spherical structure observed around the injection region is expected to cool and become denser as the surrounding material falls back towards the galactic centre and is entrained across the contact discontinuity . this spherical cocoon might be observable in young , low - power radio sources , but it is likely to disappear at later times due to mixing with the colder and denser material that surrounds it . three - dimensional , long - term simulations should be performed to study the transition between the early stage studied here and the evolution of the whole structure when the bow - shock propagates out of the galactic core and becomes transonic .","summary":"jets in low - luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub - relativistic speeds on kiloparsec scales .","abstract":"jets in low - luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub - relativistic speeds on kiloparsec scales . several mechanisms have been proposed to explain this effect , including strong reconfinement shocks and the growth of instabilities ( both leading to boundary - layer entrainment ) and mass loading from stellar winds or molecular clouds . we have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code _ _ r__atpenat . we study the evolution of fanaroff - riley class i ( fri ) jets , with kinetic powers , within the first 2  kpc of their evolution , where deceleration by stellar mass loading should be most effective . mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak fri jets within the first kiloparsec . however , powerful fri jets are not decelerated significantly . in those cases where the mass loading is important , the jets show larger opening angles and decollimate at smaller distances , but the overall structure and dynamics of the bow - shock are similar to those of unloaded jets with the same power and thrust . according to our results , the flaring observed on kpc scales is initiated by mass loading in the weaker fri jets and by reconfinement shocks or the growth of instabilities in the more powerful jets . the final mechanism of decollimation and deceleration is always the development of disruptive pinching modes .    [ firstpage ]    galaxies : active  galaxies : jets  hydrodynamics  stars : winds , outflows"}
{"article_id":"1404.1209","section_id":"i","document":"we have performed a series of axisymmetric simulations of the early evolution ( up to @xmath169  yr ) of fri jets in a realistic galactic environment to investigate the effects of mass loading by stellar winds . the simulations presented here allow us to capture the effects of mass loading on beam evolution within the host galaxy and are precise enough to discriminate between models differing by a factor of ten in the mass entrainment rate . our results are consistent with previous steady state simulations ( blk ) and theoretical estimates @xcite . the overall structure and dynamics of the cocoon - shocked ambient system is very similar for all models with the same power and thrust . slight differences in long - term evolution result from differences in the dynamics of the jet head ( which are affected by the mass loading ) . the mass load carried by the beam affects its internal structure ( internal shocks , pinching , beam radius and jet opening angle ) and properties ( increase in the rest mass density , cooling and deceleration ) . we find that mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies lead to deceleration of the beam plasma and effective decollimation of weak ( @xmath170 ) fri jets on scales of about 1 kpc . deceleration is accompanied by expansion and , in axisymmetric simulations , the development of disruptive pinch modes that lead to the decollimation and further deceleration of the jet due to external entrainment . the composition of the jet is also completely changed by the process of mass loading , ruling out a dominant magnetic field on kiloparsec scales in low - power fri jets . however , stellar mass loading seems to be unable to decelerate the most powerful ( @xmath171 ) fri jets . in these powerful jets , the formation of strong recollimation shocks when the pressure in the environment drops well below that of the jet or continuous mass entrainment produced by short - wavelength kh body modes , are more plausible mechanisms for deceleration , entrainment and mixing ( see also * ? ? ? future work should include high - resolution three - dimensional simulations to allow for a detailed comparison between the different proposed mechanisms of deceleration . our conclusions can also be tested observationally by modelling larger samples of weak and powerful fri jets using the techniques developed by @xcite . we would expect transverse velocity gradients to develop in the powerful jets , but the weak jets should maintain their initial transverse velocity profiles as they decelerate .","summary":"we have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code _ _ r__atpenat . mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak fri jets within the first kiloparsec .","abstract":"jets in low - luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub - relativistic speeds on kiloparsec scales . several mechanisms have been proposed to explain this effect , including strong reconfinement shocks and the growth of instabilities ( both leading to boundary - layer entrainment ) and mass loading from stellar winds or molecular clouds . we have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code _ _ r__atpenat . we study the evolution of fanaroff - riley class i ( fri ) jets , with kinetic powers , within the first 2  kpc of their evolution , where deceleration by stellar mass loading should be most effective . mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak fri jets within the first kiloparsec . however , powerful fri jets are not decelerated significantly . in those cases where the mass loading is important , the jets show larger opening angles and decollimate at smaller distances , but the overall structure and dynamics of the bow - shock are similar to those of unloaded jets with the same power and thrust . according to our results , the flaring observed on kpc scales is initiated by mass loading in the weaker fri jets and by reconfinement shocks or the growth of instabilities in the more powerful jets . the final mechanism of decollimation and deceleration is always the development of disruptive pinching modes .    [ firstpage ]    galaxies : active  galaxies : jets  hydrodynamics  stars : winds , outflows"}
{"article_id":"1303.3762","section_id":"i","document":"density functional theory ( dft ) is considered one of the best and most reliable condensed - matter tools for non - empirical studies of molecular , surface , bulk and compound properties.@xcite standard implementations , using the local density approximation ( lda ) or the generalized gradient approximation ( gga ) for the exchange - correlation energy , provide an accurate description of the binding in regions characterized by high electron density . an even more widespread dft usage will follow from an ability to address soft- and sparse - matter systems , structures that have internal voids or low - electron - density regions dominated by the van der waals ( vdw ) forces , also called the london dispersion forces.@xcite while neither lda nor gga capture the truly nonlocal correlation effects that underpin those forces,@xcite the last decade has seen development of both vdw - extended dft@xcite and of regular nonlocal exchange - correlation functionals.@xcite the first class of methods are often atom centered and require use of a damping function or equivalent , while the second class of methods fits inside the regular dft framework . both types of sparse - matter dft can describe , for example , vdw forces between molecules . the van der waals density functional ( vdw - df ) method@xcite is a framework for approximating the exchange - correlation energy @xmath0 $ ] . the method , summarized below , yields efficient general - purpose sparse - matter functionals@xcite that are non - empirical . the method employs the coulomb gauge ( with green function @xmath1 ) and a scalar dielectric function @xmath2 . in its most general form,@xcite the vdw - df method is a reformulation of the adiabatic connection formula@xcite ( acf ) and assumes that a plasmon - pole approximation@xcite for @xmath2 can satisfy @xmath3 + e_{{\\mbox{\\scriptsize self } } } , \\label{eq : acfepsilondefine}\\ ] ] where @xmath4 denotes the complex frequency and where @xmath5 is the internal coulomb self - energy of each electron . this equation summarizes an , in principle , exact description of the ( longitudinal ) electrodynamics in the inhomogeneous electron gas and reflects the use of a dyson equation for handling screening . like the ggas , the vdw - df method further uses physics - based constraints@xcite to approximate the plasmon - pole response and thus defines the functional form of a nonlocal correlation term , @xmath6 . in the recent explicit functional versions , called vdw - df1@xcite and vdw - df2,@xcite the nonlocal energy @xmath7 $ ] is expressed as a double integral over the density , weighted by a kernel . however , the plasmon basis still allows it to capture a collectivity that reflects the broader density variation.@xcite the vdw - df method also involves picking a gradient - corrected exchange that reflects prespecified criteria , e.g. , good all - round molecular - system performance@xcite or improved bulk - system properties.@xcite the vdw - df shares the plasmon - pole emphasis with its lda and gga relatives , and the functionals `` vdw - df # '' have both seamless integration in the homogeneous limit and a build - in conservation of the exchange - correlation hole.@xcite the non - empirical design suggests that the vdw - dfs can achieve a good transferability across systems , length scales , charging states , and binding morphologies . the vdw - df method has been and is being tested for many systems . it delivers a parameter - free atomic - scale characterization of the binding in complex sparse - matter systems . selfconsistent ( sc ) vdw - df calculations can be used to calculate stress within periodic unit cells@xcite and guide atomic optimization ( relaxation ) . there are performance tests for bulk,@xcite layered@xcite absorption,@xcite molecule and atom adsorption,@xcite surface self - assembly,@xcite and molecular systems.@xcite the development of effective algorithms@xcite has allowed sc vdw - df calculations that have today little or no additional costs over gga calculations.@xcite for very large systems , typical of biomolecular - interaction problems , the set of real - space vdw - df evaluation schemes@xcite effectively permits an order-@xmath8 scaling in the evaluation of @xmath7 $ ] , as discussed for example in ref .  .    nevertheless , the feasibility of sparse - matter dft calculations for large molecular matter is still limited by the huge number of atoms that are usually involved in interacting molecular systems . the problem is confounded by the fact that ( especially in biochemically relevant problems ) we are often forced to address nonperiodic systems where size - convergence of the model unit - cell size becomes important.@xcite molecular transport studies,@xcite and many molecular - crystal problems,@xcite further exemplify the general need to address vdw binding in big systems . the challenge for typical sparse - matter dft is increasingly becoming that of computing the steric hindrance effects that are described by the dft kinetic - energy repulsion . when we reach thousands of atoms , all first - principle and vdw - extended dft calculations are simply limited by memory requirements and computational costs of the wavefunction evaluation . in this paper we propose and test an adaption of the harris scheme@xcite to perform non - selfconsistent ( nsc ) vdw - df calculations for sparse matter . the aim is to explore possibilities for reducing the computational cost of the wavefunction - evaluation bottleneck that could be impeding an even broader vdw - df usage in , for example , biochemistry.@xcite the approach consists of using a superposition of the fragment ( electron ) densities , and is here termed sfd - vdw - df . it can be seen as an alternative to the more costly nsc - vdw - df or even sc - vdw - df evaluations.@xcite it is just the regular vdw - df harris scheme if the fragment densities are based on vdw - df calculations . however , the sfd framework also works without a vdw - df implementation of the underlying dft code , and we reserve the term sfd - vdw - df to cases where the fragment densities are obtained from gga calculations . the method uses our code for real - space vdw - df evaluation based on the charge densities from the underlying dft code.@xcite    we present formal analysis and a testing of the sfd - vdw - df computational scheme for molecular systems . as an interesting aside , the analysis also identifies conditions for expecting significant vdw - induced changes in the bandstructure or electron dynamics for a given binding morphology . we separately test how well the sfd framework faithfully reproduces interaction effects that arise from the semi - local part of the vdw - df functional . we test the performance of the sfd - vdw - df scheme across the s22 benchmark set@xcite and for systems with a varying degree of static polarizations . we observe that while a vdw - df harris scheme ( evaluated with vdw - df fragment densities ) is correct to second order in binding - induced density changes , @xmath9 , the proposed scheme is formally only correct to linear order in these density changes . however , we also find that the linear term @xmath10 is weighted by the changes in the effective kohn - sham ( ks ) potential that result from the shift from the gga to the vdw - df functional . the sfd - vdw - df scheme may thus be broadly applicable in the absence of large static dipoles . the paper is organized as follows . in section ii we summarize the case for developing an accelerated ( but approximate ) vdw - df description of biomolecular interaction . in section iii we present some details of the lda , gga , and vdw - df family of constraint - based density functionals to facilitate a formal analysis and our proposal for the sfd - vdw - df scheme in section iv . section v provides a brief summary of computational ( and implementation ) details . section vi presents the results of the performance testing that we have carried out for the proposed sfd - vdw - df scheme , while sec . vii contains a discussion . finally , section viii contains summary and outlook .","summary":"that is , they are formed from components that are mutually separated by low - electron - density regions where dispersive forces contribute significantly to the cohesion and behavior . the introduction of , for example , the van der waals density functional ( vdw - df ) method [ prl * 92 * , 246401 ( 2004 ) ] has addressed part of this sparse - matter system challenge . however , while a vdw - df study is often as computationally efficient as a study performed in the generalized gradient approximation , the scope of large - sparse - matter dft is still limited by computer time and memory . we propose and evaluate an adaption of the harris scheme [ prb * 31 * , 1770 ( 1985 ) ] .","abstract":"large biomolecular systems , whose function may involve thousands of atoms , can not easily be addressed with parameter - free density functional theory ( dft ) calculations . until recently a central problem was that such systems possess an inherent sparseness , that is , they are formed from components that are mutually separated by low - electron - density regions where dispersive forces contribute significantly to the cohesion and behavior . the introduction of , for example , the van der waals density functional ( vdw - df ) method [ prl * 92 * , 246401 ( 2004 ) ] has addressed part of this sparse - matter system challenge . however , while a vdw - df study is often as computationally efficient as a study performed in the generalized gradient approximation , the scope of large - sparse - matter dft is still limited by computer time and memory . it is costly to self - consistently determine the electron wavefunctions and hence the kinetic - energy repulsion . in this paper we propose and evaluate an adaption of the harris scheme [ prb * 31 * , 1770 ( 1985 ) ] . this is done to speed up non - selfconsistent vdw - df studies of molecular - system interaction energies . also , the harris - type analysis establishes a formal link between dispersion - interaction effects on the effective potential for electron dynamics and the impact of including selfconsistency in vdw - df calculations [ prb * 76 * , 125112 ( 2007 ) ] ."}
{"article_id":"1303.3762","section_id":"i","document":"in a related work@xcite we report a vdw - df mapping of the vdw attraction in a dna dimer ( two periodic double - helix strands ) . that pilot study illustrates that general conclusions can be made for the important biomolecular - interaction problem from computing merely how @xmath6 depends on the interaction geometry . the nonempirical nature and the regular - density - functional basis ( no external parameters ) makes vdw - df well suited to pursue investigations of biomolecular interactions . the full dna interaction problem touches on two general challenges for refining a computational description of life processes . first , it illustrates the workings of molecular recognition ( the matching by weak forces of the genes or just the packing of our genome in its environment ) . second , it reminds us of the challenge of characterizing these effects in a solution that contains counter ions . since the counter ions , per se , can be expected to play a smaller role in the overall interfragment vdw attraction , it is natural to focus a sparse - matter dft study on the charged biomolecular structures themselves . however , for this approach to become meaningful , we must be able to also characterize the vdw bonding at various charging states . being a regular ( parameter free ) nonlocal density functional , vdw - df has an inherent advantage for computational studies of biomolecular interactions . the prospect of vdw - df studies of biomolecular systems is as promising in terms of computational cost ( and , currently , as restrained ) as it is for other sparse - matter dft approaches . the evaluation of the nonlocal correlation , @xmath11 , causes no relevant slow down or bottlenecks thanks to the order-@xmath8 scaling in the real - space evaluation approach for large systems.@xcite in fact , our mapping of dna attraction@xcite demonstrates that vdw - df has , in practice , an efficiency similar to that of dft - d for large biomolecular problems . there are for the dna - dimer attraction problem@xcite no memory bottlenecks and essentially a linear scaling at least up to 1000 + cores for the @xmath11 evaluation . it is already today possible to bring that functional evaluation to about ten minutes wall time . while this evaluation of @xmath11 does cost more than adding the dispersion term in dft - d,@xcite neither of these descriptions of the vdw attraction cause limitations : the computing expense is irrelevant when compared to the cost of converging the density in even one dna ( one periodically repeated coil of a dna double helix ) in dft . with such a promise , it is frustrating that a full dft study of the dna dimer is today impossible without an allocation at a petaflop facility . there is a need to accelerate the dft determination of large - system wavefunctions and for sparse matter investigations in general . here we explore an approach that focuses on accelerating the evaluation of the kinetic - energy repulsion , and which can , in principle , reduce the wavefunction - solution stage to just a single electronic iteration , as is possible with the regular harris scheme.@xcite         +     figure [ fig : s22_dimer ] illustrates the feasibility of using the sfd - vdw - df for accelerated vdw - df studies of biomolecular interactions . it reports a comparison of binding in an ammonia dimer and shows that the sfd - vdw - df2 description is in excellent agreement with the binding predicted by sc - vdw - df2 ( indicated by a cross ) . figure [ fig : milky ] summarizes our overall assessment , further detailed in sec . it testifies to a high degree of robustness across the s22 benchmark set@xcite and for other molecular - interaction problems . the important observation for developing a biomolecular computational strategy in dft is that the sfd - vdw - df scheme can be as reliable as the often - used nsc - vdw - df evaluation@xcite even if it bypasses the need for a sc determination of the wavefunctions . the sfd framework could thus be one approach to speed up vdw - df studies of large biomolecular interaction problems at a limited cost in accuracy . the ( regular ) harris scheme works within a fixed functional choice and takes the following steps : first , self - consistent calculations of the densities @xmath12 for each individual building block ` @xmath13 ' ; second , construction of a density @xmath14 as a superposition of the building blocks , and of the effective single - particle potential @xmath15(\\mathbf{r})$ ] that corresponds to @xmath16 ; and third a nsc , that is , no - density update , calculation of the eigenvalues corresponding to the potential @xmath17 . these eigenvalues help provide an estimate of the kinetic energy term in the harris scheme.@xcite the harris scheme is traditionally pursued in a lda or gga framework starting , e.g. , from sc gga input densities . it is today often used when pursuing bandstructure calculations in dft ( and therefore provides very accurate wavefunctions for a given @xmath17 ) . however , it is also possible to use it for its original purpose , namely for providing efficient but approximate dft studies of interactions .    pursuing a regular vdw - df harris scheme represents one alternative for accelerating vdw - df studies . we point out that the original study by harris@xcite ( working with lda ) shows that the scheme works reasonably well also for describing the formation of covalent bonds between atoms in some molecules . it should be even better suited to describe the weaker vdw bonding . the overall criteria for the applicability of a harris - type scheme is that the fully sc density solution @xmath18 should not differ significantly from the input superposition density @xmath16 . it can work also when we consider systems , like biomolecules in solution , where the charging from the surrounding counter ions must be considered when providing the input densities ( and hence @xmath16 and @xmath17 ) . a vdw - df harris scheme can be expected to work well for a study of supramolecular systems as long as the _ binding - induced _ charge relocations remain small . a regular harris vdw - df scheme is , however , not the focus here . this is because we do not yet have the ability to both perform vdw - df calculations and allow an externally - defined superposition of input density in the same code . we have chosen to build on the dacapo@xcite code ( for input densities and for the nsc kinetic - energy evaluation@xcite ) and on the vdw - df postprocessing@xcite that we have previously used extensively for vdw - df studies . a benefit of introducing sfd - vdw - df as a supplement to a regular vdw - df harris scheme is that we thus provide a computational framework that can take input densities from an arbitrary code ( through an adaption of any of the real - space strategies for evaluation vdw - df@xcite ) .","summary":"this is done to speed up non - selfconsistent vdw - df studies of molecular - system interaction energies .","abstract":"large biomolecular systems , whose function may involve thousands of atoms , can not easily be addressed with parameter - free density functional theory ( dft ) calculations . until recently a central problem was that such systems possess an inherent sparseness , that is , they are formed from components that are mutually separated by low - electron - density regions where dispersive forces contribute significantly to the cohesion and behavior . the introduction of , for example , the van der waals density functional ( vdw - df ) method [ prl * 92 * , 246401 ( 2004 ) ] has addressed part of this sparse - matter system challenge . however , while a vdw - df study is often as computationally efficient as a study performed in the generalized gradient approximation , the scope of large - sparse - matter dft is still limited by computer time and memory . it is costly to self - consistently determine the electron wavefunctions and hence the kinetic - energy repulsion . in this paper we propose and evaluate an adaption of the harris scheme [ prb * 31 * , 1770 ( 1985 ) ] . this is done to speed up non - selfconsistent vdw - df studies of molecular - system interaction energies . also , the harris - type analysis establishes a formal link between dispersion - interaction effects on the effective potential for electron dynamics and the impact of including selfconsistency in vdw - df calculations [ prb * 76 * , 125112 ( 2007 ) ] ."}
{"article_id":"1303.3762","section_id":"i","document":"to accelerate large - scale vdw - df characterization of biomolecular systems it seems useful to adapt the ideas of the harris scheme@xcite as is indicated and explored here . a harris - type approximation which works reasonably well for describing the kinetic - energy effects of forming covalent bonds of atoms in some molecules should have a good chance of describing the simpler kinetic - energy repulsion ( steric hindrance ) of molecules in supramolecular systems .    here , we have put this expectation to the test . our results indicate that this scheme is promising for describing supramolecular systems bonded primarily by vdw forces . however , if one or more fragments are highly polar , this comes at the cost of accuracy . the pair of papers suggest a possible computational strategy for the study of binding in large supramolecular systems . the suggestion is to _ begin _ the structure and interaction - morphology search by essentially cost - free evaluations of the @xmath6 variation . that @xmath6 step is available simply from relatively cheap calculations of fragment electron densities . one can in turn search for relevant binding motifs , given the linking to the here - proposed and tested sfd - vdw - df scheme . this strategy eventually leads to a complete vdw - df estimate of the variation in total interaction energy . the strategy exists as an alternative to implementing a real - space vdw - df version in a code that realizes genuine order-@xmath8 scaling for large systems . having established the promise of the sfd scheme for systems bound by vdw forces , the next step would be to investigate if the scheme can be further accelerated , in particular for large supramolecular systems . to this end , implementations for a full sfd - vdw - df scheme for other dft codes ( beyond dacapo ) are being tested . the authors thank pieremanuele canepa and timo thonhauser for discussions and kuyho lee for supplying atomic coordinates for a full range of 14 various separations for each of the dimers in the s22 benchmark set . partial support from the swedish research council ( vr ) ( two grants ) and the chalmers area of advance ` materials ' is gratefully acknowledged . the computations were performed on high - performance computing resources provided by the swedish national infrastructure for computing ( snic ) at the c3se and hpc2n metanodes . langreth , b.i . lundqvist , s.d . chakarova - kck , v.r . cooper , m. dion , p. hyldgaard , a. kelkkanen , j. kleis , l. kong , s. li , p.g . moses , e. murray , a. puzder , h. rydberg , e. schrder , and t. thonhauser , j. phys . matter * 21 * , 084203 ( 2009 ) . a.  tkatchenko and m.  scheffler , phys . * 102 * , 073005 ( 2009 ) ; v.g . ruiz , w.  liu , e.  zojer , m.  scheffler , and a.  tkatchenko , phys . lett .  * 108 * , 146103 ( 2012 ) ; a.  tkatchenko , r.a . distasio , jr . , r.  car , and m.  scheffler , * 108 * , 236402 ( 2012 ) . h. rydberg , _ nonlocal correlations in density functional theory _ , ph.d . thesis ( chalmers university of technology , 2001 ) ; also unpublished by p. hyldgaard , k.  berland , h.  rydberg , e.  schrder , and b.i . lundqvist . n.  nijem , l.  kong , y.  zhao , h.  wu , j.  li , d.c . langreth , and y.j . chabal , j. am . * 133 * , 4782 ( 2011 ) ; n.  nijem , p.  canepa , l.  kong , h.  wu , j.  li , t.  thonhauser and y.j . chabal , j.  phys . : condens . matter  * 24 * , 424203 ( 2012 ) . n.  nijem , j .- f . veyan , l.  kong , k.  li , s.  pramanik , y.  zhao , j.  li , d.c . langreth , and y.j . chabal , j. am . soc . * 132 * , 1654 ( 2010 ) ; q.  li and t.  thonhauser , j.  phys . : condens . matter  * 24 * , 424204 ( 2012 ) . k.  berland , t.l . einstein , and p. hyldgaard , phys . b * 80 * , 155431 ( 2009 ) ; k.  toyoda , y.  nakano , i.  harmada , k.  lee , s.  yanagisawa , and y.  morikawa , surf . sci .  * 609 * , 2912 ( 2009 ) ; k.  lee , y.  morikawa , and d.c . langreth , phys . b * 82 * , 155461 ( 2010 ) . k.  lee , a.k . kelkkanen , k.  berland , s. andersson , d.c . langreth , e.  schrder , b.i . lundqvist , and p.  hyldgaard , phys . b * 84 * , 193408 ( 2011 ) ; k.  lee , k.  berland , m.  yoon , s.  andersson , e.  schrder , p. hyldgaard , and b.i . lundqvist , j. phys . : condens . matter * 24 * , 424213 ( 2012 ) . open - source tool junolo for real - space and fast - fourier transform non - selfconsistent vdw - df total - energy evaluation ; p.  lazi , n. atodiresei , m.  alaei , v. caciuc , s.  blgel , and r. brako , comp . phys . comm . * 181 * , 371 ( 2010 ) . open - source tool for real - space non - selfconsistent vdw - df total - energy evaluation , a python package nscvdwdf ( available upon request ) from the chalmers vdw - df groups , http://fy.chalmers.se/@xmath115schroder/vdwdf                          a single electronic iteration is here taken to mean an evaluation stage during which the external potential is kept fixed . in most dft codes , there are several wavefunction evaluation steps in each such electronic iteration . when pursuing a standard sc dft determination , the requested accuracy on the wavefunction solution remains moderate . for bandstructure calculations , the dft code is formally performing a harris - type evaluation , but a code like dacapo then forces many wavefunction - evaluation steps to deliver a higher accuracy on the wave functions . however , that is not the spirit of the original harris scheme , nor do we intend this here with the proposed sfd - vdw - df scheme . beef , an approach to select the exchange choice for vdw - df calculations to a specific target application , based on baysean logic and training , j.  wellendorff , k.t . lundgaard , a.  mgelhj , v.  petzold , d.d . landis , j.k . nrskov , t.  bligrd , and k.w . jacobsen , phys . b * 85 * , 235149 ( 2012 ) .    one can of course evaluate the ks and the harris schemes as well as the sfd - vdw - df approximation for a general specification of the fragment orientation , motif - alignment , and arbitrary choice of displacement vector .","summary":"it is costly to self - consistently determine the electron wavefunctions and hence the kinetic - energy repulsion . in this paper","abstract":"large biomolecular systems , whose function may involve thousands of atoms , can not easily be addressed with parameter - free density functional theory ( dft ) calculations . until recently a central problem was that such systems possess an inherent sparseness , that is , they are formed from components that are mutually separated by low - electron - density regions where dispersive forces contribute significantly to the cohesion and behavior . the introduction of , for example , the van der waals density functional ( vdw - df ) method [ prl * 92 * , 246401 ( 2004 ) ] has addressed part of this sparse - matter system challenge . however , while a vdw - df study is often as computationally efficient as a study performed in the generalized gradient approximation , the scope of large - sparse - matter dft is still limited by computer time and memory . it is costly to self - consistently determine the electron wavefunctions and hence the kinetic - energy repulsion . in this paper we propose and evaluate an adaption of the harris scheme [ prb * 31 * , 1770 ( 1985 ) ] . this is done to speed up non - selfconsistent vdw - df studies of molecular - system interaction energies . also , the harris - type analysis establishes a formal link between dispersion - interaction effects on the effective potential for electron dynamics and the impact of including selfconsistency in vdw - df calculations [ prb * 76 * , 125112 ( 2007 ) ] ."}
{"article_id":"1505.03910","section_id":"i","document":"last decade has witnessed an ever - growing interest of the scientific and engineering communities in atomically thin two - dimensional ( 2d ) materials @xcite . this is due to both the unique properties of such materials from the basic science perspective @xcite , as well as their tremendous technological potential @xcite . while graphene - a flagship of this class of materials - has attracted most of the attention to date , it lacks an electronic bandgap and is thus unsuitable `` as is '' for multiple applications including photovoltaics and electronics @xcite . the realization of this fact has led to significant efforts spent during the last few years on searching for `` graphene with a bandgap '' , i.e. , atomically thin _ semiconductor _ materials . of many materials identified as potential semiconductor alternatives to graphene , one of the most promising classes of materials is monolayer transition metal dichalcogenides ( ml - tmdc ) @xcite . other possible candidates include phosphorene @xcite , stanene @xcite and ultrathin organic - inorganic perovskite crystals @xcite . a prominent feature of 2d semiconductors ( 2ds ) is the strong coulomb interaction between charge carriers , as compared to their parent 3d materials ( e.g. , bulk tmdc ) . this effect arises from the so called _ dielectric confinement _ - the dielectric screening of the coulomb interaction between two point charges within a 2d material becomes weak at distances larger than some effective thickness of the material @xcite . in other words , the strength of dielectric screening becomes distance - dependent , i.e. , spatially _ non - local_. for example , this effect is pronounced in ml - tmdc , leading to the formation of tightly - bound excitons with binding energies up to @xmath0 @xcite . this is very different from conventional 3d semiconductors , where the optical response at room temperature is dominated by independent charge carriers @xcite . such large exciton binding energies in 2ds suggest the possibility of existence of other stable bound states consisting of a larger number of charge carriers ( e.g. , trions , biexcitons ) at near - room temperatures @xcite . indeed , trions - bound states of a single exciton and an extra charge carrier - with binding energies on the order of @xmath1 in ml - tmdc and up to @xmath2 in few - layer phosphorene have been recently observed @xcite . very recent evidence of stable bound states of two electrons and two holes - biexcitons - with binding energies of @xmath3 in ml - tmdc has been reported in refs . @xcite . the term  excitonic effects \" has been traditionally applied to features of the optical properties of semiconductors , which go beyond the simple picture of non - interacting charge carriers . in particular , the coulomb interaction between carriers leads to the formation of multi - carrier bound states out of free charge carriers . theoretically , excitonic effects have mostly been studied at the level of a single exciton using electronic structure theory tools @xcite . experimentally observed large exciton binding energies were largely reproduced and the detailed structure of excitonic states was studied . in particular , it has been demonstrated that even without any external dielectric screening ( e.g. , due to a solvent or substrate ) the size of an exciton in ml - tmdc is much larger than the size of a single unit cell @xcite . under these conditions , quasimomenta of interacting electrons and holes are distributed very close to the positions of the respective band edge extrema in the brillouin zone , see for example the inset of fig . 3(b ) in ref .  @xcite . this observation justifies the use of the effective mass approximation in the analysis of excitonic effects in ml - tmdc @xcite .    despite enormous interest , however , theoretical and computational studies of multi - carrier bound states beyond a single exciton ( e.g. , trions , biexcitons ) in 2ds are rather sparse to date . to the best of our knowledge , the first theoretical analysis of single excitons and trions in novel 2ds explicitly taking into account the spatially _ non - local _ character of dielectric screening was performed in ref . @xcite , followed by refs .  @xcite . in particular , trion binding energies were found by means of a simple few - parameter variational wave function @xcite . trion excitations in these systems have also been studied by means of the fractional dimensional space approach @xcite , and the time - dependent density - matrix functional theory @xcite , but no non - local screening effects were explicitly taken into account in these works . finally , an accurate analysis of single exciton and trion binding energies in the limit of a very strong non - local 2d screening has been reported very recently @xcite . the goal of the present work is to accurately study the excitonic effects in 2ds at the _ arbitrary _ strength of the non - local 2d screening . within the effective mass approximation , we demonstrate how a general problem of finding the energy of a bound state of a specific number of charge carriers can be reduced to finding an unknown function of two parameters : the electron - to - hole mass ratio and the screening length . we then evaluate this function numerically using the path integral monte carlo ( pimc ) methodology @xcite . this specific flavor of the broad class of quantum monte carlo methods is among the most general methods to study interacting quantum many - body systems . it does not require the assumption of positivity of a wave function ( diffusion quantum monte carlo ) @xcite , or choosing a wave function ansatz ( variational quantum monte carlo ) @xcite , and has been successfully applied to analyze the electronic structure of low - dimensional semiconductors @xcite . in particular , binding energies of excitons , trions and biexcitons in gaas / algaas quantum wells have been accurately evaluated @xcite . using pimc , we evaluate the exciton , trion and biexciton binding energies for a range of values of the screening length assuming identical isotropic electron and hole effective masses . this constitutes the main result of the paper , since a straightforward interpolation and rescaling of the obtained numerical results ( compiled in table  [ tab : energies ] ) can be used to evaluate binding energies of single excitons , trions and biexcitons in _ arbitrary _ 2ds with not too different isotropic effective masses ( e.g. , ml - tmdc or stanene ) . to the best of our knowledge , this work is the first to numerically exactly treat trions and biexcitons in 2ds , albeit within the effective mass approximation . numerical results , obtained here , can be directly used to analyze experimental data and benchmark other theoretical and computational approaches to excitonic effects in 2ds . the paper is organized as follows . the general hamiltonian of the system of interacting charge carriers is introduced in sec . [ sec : gtheory ] . the dependence of the energy of a multi - carrier bound state on the electron to hole effective mass ratio and the strength of 2d screening is discussed in sec . [ sec : gprop ] . brief description of the pimc technique and its application to finding energies of multi - carrier bound states is given in sec . [ sec : pimc ] . section  [ sec : res ] contains the discussion of the numerical results . an example of how these numerical results could be applied in a realistic situation is given in section  [ sec : example ] . section  [ sec : conclusion ] contains the conclusion .","summary":"one of the most striking features of novel 2d semiconductors ( e.g. , transition metal dichalcogenide monolayers or phosphorene ) is a strong coulomb interaction between charge carriers resulting in large excitonic effects . in particular specifically , we have accurately investigated and tabulated the dependence of single exciton , trion and biexciton binding energies on the strength of dielectric screening , including the limiting cases of very strong and very weak screening .","abstract":"one of the most striking features of novel 2d semiconductors ( e.g. , transition metal dichalcogenide monolayers or phosphorene ) is a strong coulomb interaction between charge carriers resulting in large excitonic effects . in particular , this leads to the formation of multi - carrier bound states upon photoexcitation ( e.g. , excitons , trions and biexcitons ) , which could remain stable at near - room temperatures and contribute significantly to optical properties of such materials . in the present work we have used the path integral monte carlo methodology to numerically study properties of multi - carrier bound states in 2d semiconductors . specifically , we have accurately investigated and tabulated the dependence of single exciton , trion and biexciton binding energies on the strength of dielectric screening , including the limiting cases of very strong and very weak screening . the results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models ."}
{"article_id":"1505.03910","section_id":"r","document":"pimc - generated radial distribution functions for a single exciton , trion and biexciton at @xmath59 and @xmath124 are plotted fig . [ fig : rdf ] . rdfs for inter - carrier distances within an exciton ( black ) , trion ( red ) and biexciton ( blue ) for @xmath59 and @xmath124 . electron - hole and hole - hole rdfs are shown in solid and dashed lines , respectively . distance ( horizontal coordinate ) is given in atomic units . rdfs are normalized so that @xmath146.,width=307 ]    radial distribution function ( rdf ) for two particles ( @xmath147 and @xmath77 ) is introduced as @xmath148 where @xmath149 is the wave function of the ground state of the hamiltonian in eq . ( [ eq : genh ] ) . so introduced radial distribution function is normalized as @xmath150 , and since the wave function is finite everywhere , the radial distribution functions demonstrate the standard 2d behavior as they become linearly proportional to @xmath151 at small distances .    of all the rdfs in fig . [ fig : rdf ] , the excitonic one ( black line ) is seen to result in the smallest mean electron - hole distance . this is of course expected as trions and biexcitons are supposed to be much `` looser '' bound states with larger mean inter - carrier distances @xcite . if we assume that @xmath124 is large enough so that the strong 2d screening limit is valid and eq . ( [ eq : hlog_org ] ) is accurate , then we can estimate the excitonic size as @xmath152 . furthermore , since all the parameters in @xmath153 in eq . ( [ eq : hxi ] ) are on the order of @xmath154 at @xmath59 , we can estimate the exciton size in @xmath155-coordinates as @xmath156 . this results in @xmath157 , which is in a rather good agreement with the position of the maximum of the excitonic rdf in fig . [ fig : rdf ] . binding energies of a trion and biexciton are conventionally introduced as @xmath158 and @xmath159 that is the binding energy of trion is defined as the energy released upon adding one more carrier to an exciton . the biexciton binding energy is defined as the energy released upon the formation of a bound state of two single initially isolated excitons . at @xmath73 , @xmath160 and @xmath161 are typically much smaller in magnitude than the single exciton binding energy @xmath120 ( @xmath162 in this work ) @xcite . below we demonstrate that this qualitative picture remains true at arbitrary @xmath49 . as a result , carriers can be thought to form isolated excitons within the zeroth - order picture . consequently , the first - order correction to this picture consists of accounting for weak interactions of these neutral bound electron - hole pairs between each other and with uncompensated charge carriers ( e.g. , in a trion ) @xcite . for instance , an electron in a positive trion is expected to `` see '' one of the two holes being `` excitonic '' with characteristic electron - hole distances being comparable to the size of a single isolated exciton . the other hole is farther away as it forms a much more weakly bound hole - exciton complex . these heuristic considerations are in agreement with what can be deduced from the electron - hole rdfs for a trion ( solid red line ) and biexciton ( solid blue line ) in fig . [ fig : rdf ] . indeed , each of these two lines has two prominent features : ( _ i _ ) a maximum very close to the excitonic one ( solid black line ) , thus representing the `` excitonic '' hole , and ( _ ii _ ) a heavy shoulder at larger distances , representing the other more weakly bound hole . the coulomb repulsion between carriers of the same charge results in the maxima of the hole - hole rdfs ( dashed red and blue lines ) being displaced toward larger distances , as compared to those of the electron - hole rdfs . dimensionless energy of an exciton , trion and biexciton , @xmath47 , as a function of @xmath49 at @xmath59 is shown in fig . [ fig : e - x - t - xx ] .     dimensionless energy of an exciton , trion and biexciton , @xmath163 , as a function of @xmath49 at @xmath59 . thin dashed black line represents the results of the grid - based calculations of the single exciton energy . energy of a dissociated biexciton ( i.e. , two isolated excitons ) , obtained from grid - based calculations , is shown by the thin dashed blue line . pimc results for the exciton energy are shown by the thick dashed line . red circles and blue squares represent the pimc calculations for trion and biexciton energies , respectively.,width=307 ]    the results of the grid - based calculations of the single exciton energy are given by a thin dashed black line and seen to be in excellent agreement with the corresponding pimc results ( thick dashed black line ) . red circles and blue squares represent pimc results for trion and biexciton energies , respectively . as can be seen , the trion energies ( red circles ) are very close to the single exciton ones ( thick dashed black line ) . similarly , biexciton energies ( blue squares ) are very close to the energies of two isolated excitons ( thin blue dashed line ) . pimc results in fig . [ fig : e - x - t - xx ] constitute the main result of this paper since , with the appropriate rescaling using eq . ( [ eq : eg_univ ] ) , they can be straightforwardly used to evaluate the exciton , trion and biexciton energies for an _ arbitrary _ 2d semiconductor if the electron and the hole effective masses are isotropic and not too different from each other . to facilitate the use of this data in analysis of experimental results or benchmarking of theoretical models , we also provide this same data in table  [ tab : energies ] . .[tab : energies ] pimc results for dimensionless energies of single excitons ( @xmath120 ) , trions ( @xmath164 ) and biexcitons ( @xmath165 ) calculated for a range of @xmath49 at @xmath59 . error bars for these energies are given by @xmath166 , @xmath167 and @xmath168 , respectively . the first column is the dimensionless 2d screening length @xmath49 . at vanishing 2d screening ( @xmath73 ) , the trion and biexciton energies are obtained from refs . @xcite and @xcite , respectively . the analytical solution for the exciton binding energy at @xmath73 is @xmath169 @xcite . [ cols=\"^,^,^,^,^,^,^\",options=\"header \" , ]     binding energies of trions , eq .  ( [ eq : ebt ] ) , and biexcitons , eq .  ( [ eq : ebxx ] ) , are compared to the single exciton binding energy , @xmath120 , in fig . [ fig : eb ] . binding energies for single excitons ( black ) , trions ( red ) and biexcitons ( blue ) vs @xmath49 at @xmath59 . pimc results are shown as solid lines with error bars . large-@xmath49 asymptotics , eq .  ( [ eq : e_xi ] ) , are shown by dashed lines . red and blue filled circles represent the trion and biexciton binding energies at @xmath73 obtained from refs . @xcite.,width=307 ]    specifically , binding energies of single excitons , trions and biexcitons as a function of @xmath49 ( at @xmath59 ) are depicted by black , red and blue solid lines , respectively . the lowest 2d screening length for which we have performed pimc calculations is @xmath170 . pimc calculations with even smaller @xmath49 become increasingly difficult because the coulomb potential becomes more singular at vanishing inter - particle distances @xcite . fortunately , the numerical results for the trion and biexciton binding energy at exactly @xmath171 were obtained previously by other methods @xcite . these energies are depicted in fig . [ fig : eb ] by red and blue filled circles , respectively . the analytical solution for the 2d exciton , @xmath172 , is depicted by a black filled circle . as can be seen , our numerical results for a few smallest @xmath49 come quite close to the @xmath171 limit , so that a relatively smooth interpolation is possible and there is no need for explicit pimc calculations with very small 2d screening lengths .    at very large @xmath49 , eq .  ( [ eq : e_xi ] ) is expected to become accurate at describing energies of multi - carrier bound states in 2d semiconductor materials . we performed pimc calculations for the ground states of @xmath153 , eq . ( [ eq : hxi ] ) , for the exciton , trion and biexciton at @xmath59 . the numerical results are @xmath173 up to numerical accuracy and notation , @xmath174 obtained here coincides with the one obtained recently in ref . @xcite . using these constants in eq . ( [ eq : e_xi ] ) , we plot the resulting asymptotic dependencies of binding energies as dashed lines in fig . [ fig : eb ] . as can be seen , a good agreement between the exact pimc results for the single exciton binding energy and the asymptotic dependence , eq . ( [ eq : assy_exc ] ) , is already reached at @xmath175 , and becomes progressively better at larger @xmath49 . on the other hand , the asymptotic dependence deviates significantly from the exact solution at @xmath176 , finally becoming unphysically negative at @xmath95 . evaluation of the trion and biexciton binding energies in the limit of large @xmath49 is done via combining eq . ( [ eq : e_xi ] ) with eqs . ( [ eq : ebt ] ) and ( [ eq : ebxx ] ) . this produces @xmath177 and @xmath178 , i.e. , the @xmath179-independent terms in eq . ( [ eq : e_xi ] ) cancel each other out when @xmath180 and @xmath181 are evaluated . consequently , these expressions yield two straight red and blue dashed lines for trions and biexcitons , respectively , when plotted in the log - log axes in fig .  [ fig : eb ] . the pimc results for a trion and biexciton are seen to converge slower with @xmath49 to their corresponding large-@xmath49 asymptotics , than those for a single exciton . the rationale is that the inter - carrier distances within trions and biexcitons are larger than those within single excitons ( see fig . [ fig : rdf ] ) , so @xmath49 has to be larger to provide the same extent of agreement between the finite-@xmath49 and asymptotic @xmath74 results .    in fig . [ fig : eb ] , the dependence of binding energies on @xmath49 is qualitatively the same decaying function for excitons , trions and biexcitons except for a slowly varying prefactor seen as an almost constant vertical shift in the log - log axes when going from single excitons to trions or biexcitons . to focus on this prefactor it is convenient to introduce the so called trion ( biexciton ) haynes factor @xcite as the binding energy of a trion ( biexciton ) normalized by the binding energy of a single exciton taken at the same @xmath49 @xmath182 and @xmath183 the haynes factors for a trion ( solid red line ) and a biexciton ( solid blue line ) are plotted in fig . [ fig : tri_xx_bind](a ) at @xmath59 .     ( a ) pimc results for the haynes factor - binding energy of a trion ( solid red line ) or biexciton ( solid blue line ) normalized by the exciton binding energy - as a function of screening length @xmath49 at @xmath59 . dashed lines of respective colors are the large-@xmath49 asymptotics , eq . ( [ eq : e_xi ] ) . red and blue filled circles represent the trion and biexciton haynes factors at @xmath73 obtained in refs . red triangles are the trion haynes factors , obtained in ref . @xcite for a series of ml - tmdc materials . insets show schematically the energy ordering of single exciton , trion and biexciton peaks in a photoluminescence spectrum for weak ( left ) and strong ( right ) 2d screening.(b ) the ratio of biexciton and trion haynes factors as a function of screening length @xmath49 . the black dashed line is a guide for the eye for @xmath184 . the blue filled circle represents the ratio of haynes factors at @xmath73 @xcite . , width=307 ]    dashed red and blue lines correspond to the large-@xmath49 asymptotic behavior , eq . ( [ eq : e_xi ] ) , for trions and biexcitons , respectively . red triangles represent trion haynes factors for a series of four ml - tmdc materials , calculated in ref . @xcite by means of a simple variational ansatz approximation for a trion wave function . as expected , these variational results underestimate the exact binding energy ( solid red line ) , but by no more than @xmath185 . on the other hand , it is seen that in the range of @xmath49 corresponding to the red triangles , the large-@xmath49 asymptotics ( red dashed line ) can overestimate the exact trion binding energy ( red solid line ) by up to a factor of @xmath186 . the dielectric screening by the environment is expected to decrease @xmath49 even further @xcite , thus potentially making the large-@xmath49 limit even less accurate when applied to realistic ml - tmdc . numerical results shown in figs .  [ fig : eb ] and [ fig : tri_xx_bind](a ) can be used to obtain the relative spectral positions of photoluminescence ( pl ) peaks pertaining to a single exciton , trion and biexciton . indeed , if one assumes that the final state of a radiative recombination of a trion is a single charge carrier occupying the lowest - energy band edge state , then the spectral energy gap between single exciton and trion pl peaks , @xmath187 , is identical to the trion binding energy . , is then higher than the binding energy , the difference being the fermi energy of the partially occupied band . the binding energy can then be defined as the dissociation energy in the limit of vanishing charge doping @xcite . zero charge doping is assumed in this work , so the dissociation and binding energies are equal here . ] similarly , assuming that the final state of a biexciton radiative recombination is a single exciton in its lowest energy configuration , @xmath188 is identical to the biexciton binding energy . [ fig : eb ] and [ fig : tri_xx_bind](a ) suggest that the binding energy of a trion is larger than that of a biexciton at small @xmath49 , while the opposite is true at large @xmath49 . the crossover , i.e. , where the trion and biexciton binding energies become identical , occurs at @xmath189 . this crossover is further highlighted in fig . [ fig : tri_xx_bind](b ) , where the ratio of haynes factors for a biexciton and trion is plotted as a function of @xmath49 . left and right insets in fig . [ fig : tri_xx_bind](a ) show schematically the relative position of @xmath145 , @xmath190 and @xmath16 pl peaks at small and large @xmath49 , respectively . the former ( left ) pl spectrum is typical for semiconductor quantum wells where the effects of dielectric confinement are weak and the the dielectric screening of the coulomb interaction is local ( @xmath191 ) @xcite . on the other hand , note that the biexciton binding energy can in principle be smaller than that of a trion , as has been demonstrated both experimentally and theoretically for semiconductor carbon nanotubes @xcite . in particular , a crossover very similar to that in figs .  [ fig : eb ] and [ fig : tri_xx_bind ] has been theoretically observed in ref . @xcite for single - wall semiconductor carbon nanotubes . the crossover has been attributed to non - local screening effects , which is again very similar to what is observed in the present work . all the calculations above were performed assuming identical effective masses of electrons and holes , i.e. , @xmath192 . this is because the electron and hole effective masses are similar in ml - tmdc , @xmath193 @xcite , which is presently one of the most important classes of 2ds . in what follows we show that the variation of binding energies of multi - carrier bound states is typically not very strong at @xmath63 . under these conditions , a binding energy at @xmath194 could be a reasonable approximation for binding energies at @xmath193 . the weak variation of biexciton energies with @xmath48 at @xmath63 and arbitrary @xmath49 was already suggested in sec . [ sub : sigma_dep ] on the basis of vanishing derivative @xmath195 . single exciton energy @xmath196 does not depend on the mass ratio whatsoever . that trion energies also vary weakly with @xmath48 at @xmath63 is not known a priori , thus calling for direct numerical testing . figure  [ fig : sigma_dep ] shows the pimc results for @xmath48-dependences of multi - carrier bound state energies normalized to the respective energies at @xmath59 , i.e. , @xmath197 , @xmath54 , @xmath15 and @xmath16 . the dependence of the positive trion ( solid red line ) , negative trion ( dashed red line ) and biexciton ( solid blue line ) energies on @xmath48 at @xmath124 . the energies @xmath198 are normalized by @xmath199 . inset shows the same data , emphasizing the weak variation of @xmath198 with @xmath48 at @xmath63 . , width=307 ]    the 2d screening length is set to @xmath124 . as can be seen , the deviations of the biexciton and trion energies from those at @xmath59 do not exceed @xmath200 for @xmath193 ( see the inset ) . similarly weak variations of trion energies at @xmath63 were previously observed in the limit of the vanishing ( @xmath73 ) and very strong ( @xmath74 ) 2d screening @xcite . it is thus not unreasonable to expect a universally weak variation of @xmath47 with @xmath48 at arbitrary @xmath49 if @xmath201 . it has to be emphasized , however , that the absolute energy of a multi - carrier bound state , eq . ( [ eq : eg_univ ] ) , does depend on effective masses not only through @xmath42 , but also through the reduced mass @xmath202 . consequently , the absolute energies can vary strongly with masses even if @xmath48 remains the same . however , these variations are `` trivial '' in a sense that no new numerical analysis is needed since @xmath62 enters eq . ( [ eq : eg_univ ] ) algebraically .    the dependence of @xmath47 on @xmath48 becomes stronger at @xmath203 for trions and biexcitons . this is especially noticeable for a positive trion and a biexciton , where two holes become very heavy at @xmath71 . under these conditions , the adiabatic born - oppenheimer approximation can be applied , so that the first finite-@xmath48 corrections to @xmath204 and @xmath205 can be calculated as a zero - point energy of vibrational motion of the two holes relative to each other , eq . ( [ eq : zpe_corr ] ) . resulting non - analytical dependence , @xmath206 , is consistent with the rapid growth of the positive trion and biexciton energies when @xmath48 approaches zero . the emergent `` classicality '' of heavy holes can also be seen in fig . [ fig : rdf_sigma ] where the hole - hole rdf becomes progressively narrower when the effective hole mass increases . biexciton hole - hole rdf for a range of @xmath48 at @xmath124 . , width=307 ]    in the limit of @xmath71 , the two holes would become classical particles and , therefore , the hole - hole rdf would be a delta - function localized at finite @xmath207 at zero temperature .","summary":"the results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models .","abstract":"one of the most striking features of novel 2d semiconductors ( e.g. , transition metal dichalcogenide monolayers or phosphorene ) is a strong coulomb interaction between charge carriers resulting in large excitonic effects . in particular , this leads to the formation of multi - carrier bound states upon photoexcitation ( e.g. , excitons , trions and biexcitons ) , which could remain stable at near - room temperatures and contribute significantly to optical properties of such materials . in the present work we have used the path integral monte carlo methodology to numerically study properties of multi - carrier bound states in 2d semiconductors . specifically , we have accurately investigated and tabulated the dependence of single exciton , trion and biexciton binding energies on the strength of dielectric screening , including the limiting cases of very strong and very weak screening . the results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models ."}
{"article_id":"1202.5195","section_id":"i","document":"magnetic helicity is an important topological property of solar active regions ( ars ) and is a measure of twist and writhe of the field lines @xcite . it is gauge invariant for a closed volume of space . the sun s outer atmosphere is dominated by magnetic field at all scales . dynamic phenomena , such as , energetic flares and coronal mass ejections ( cmes ) occur due to the loss of equilibrium during the evolution of magnetic fields in solar ars . magnetic helicity has become an important physical parameter in the context of solar transient phenomena . it is one of the few global quantities which is conserved even in resistive magneto - hydrodynamics on a timescale less than that of the global diffusion . there exists no absolute measure of helicity within a sub - volume of space if that sub - volume is not bounded by a magnetic surface . however , a topologically meaningful and gauge invariant relative helicity for such volumes can be defined . there are several methods for estimating helicity in solar ars . by the force - free field assumption of coronal magnetic field , we have :    @xmath5    where @xmath6 is the force - free parameter , also known as helicity or twist parameter . assuming @xmath6 to be constant for the whole ar , we can fit observed vector magnetograms to deduce the value of @xmath6 @xcite . latitudinal variation of helicity of photospheric magnetic fields , and statistical significance of the observed temporal variations of the ars hemispheric helicity rule , as measured by the latitudinal gradient of the best - fit linear force - free parameter @xmath6 , etc . , have been discussed by @xcite . the poynting - like theorem for helicity in an open volume as derived by @xcite is given by :    @xmath7    where @xmath8 is the vector potential of the potential magnetic field , @xmath9 , which is uniquely specified by the observed flux distribution on the surface(x - y plane ) as    @xmath10    where @xmath11 refers to unit vector along vertical direction of cartesian - geometry . equation  [ eq_heli_ber ] shows that the helicity of magnetic fields in an open volume may change by the passage of helical field lines through the surface ( first term ) and/or by photospheric footpoint motions of the field lines ( second term ) . the temporal evolution of magnetic helicity flux across the photosphere characterizes the injection of magnetic helicity from the sub - photospheric layers into the solar atmosphere , horizontal flux motions , and the changes in the coronal magnetic field configurations related to eruptive events , such as the cmes , propagating into the interplanetary medium .    during the past years , several attempts have been made to estimate magnetic helicity from suitable solar observations . @xcite developed a method for determining the helicity flux ( the second term in equation  [ eq_heli_ber ] ) passing through the photosphere . they used a time series of photospheric line - of - sight ( los ) magnetograms to determine horizontal velocities by local correlation tracking ( lct ) technique @xcite . using this method , vector potential @xmath8 was constructed by using photospheric los field ( as an approximation to @xmath12 field ) as boundary conditions with coulomb gauge in terms of fourier transform ( ft ) as : @xmath13   \\\\ p , y}&=&ft^{-1}\\left[\\frac{-jk_x}{k_{x}^{2}+k_{y}^{2}}ft\\left(b_{\\rm z}\\right)\\right ] \\label{eq_fou_sol}\\end{aligned}\\ ] ]    where @xmath14 , @xmath15 are spatial frequencies in the x , y directions , respectively . later , this method was applied to many ars by several authors @xcite . however , @xcite showed that this method of calculation introduced artificial polarities of both signs in the helicity flux density maps with many flow patterns . therefore , they suggested to use relative velocities for calculating the helicity injection rate :    @xmath16_n}{|\\mathbf{x}-\\mathbf{x'}|^2}b'_z(\\mathbf{x ' } ) b_z(\\mathbf{x } ) ds'ds \\label{eq_par}\\ ] ]    where @xmath17 is the foot - point velocity at the position vector @xmath18 , and @xmath12 is the vertical component of the observed magnetic field . this equation shows that the helicity injection rate can be understood as the summation of relative rotation rates of all the pairs of elementary fluxes weighted with their magnetic flux . furthermore , @xcite has shown that the lct method is inconsistent with the magnetic induction equation , which governs the temporal evolution of the photospheric magnetic fields . tracking methods have serious practical limitations that might result in the failure of detecting significant shear velocity fields and hence in the underestimate of the amount of helicity injected by such velocity fields . @xcite reported that the magnetic energy and helicity fluxes should be computed only from the horizontal motions deduced by tracking the photospheric cross - section of magnetic flux tubes . these authors contend that the apparent horizontal motions include the effect of both the emergence and the shearing motions . they analyzed the observational difficulties involved in deriving such fluxes and in particular , the limitations of the correlation tracking methods . one of the main limitations in the previous studies has been the coarse spatial resolution of the available observations which limits the deduced velocities to the velocity corresponding to the group motion of an unresolved bunch of thin flux tubes covered by a pixel . also , tracking motions faced difficulties in the areas lacking sufficient contrast , such as in the sunspot umbrae . several alternative , improved methods have been developed for inferring plasma velocities consistent with the induction equation at the photospheric level , based on the los , as well as , vector magnetograms . the induction method ( i m ; @xcite ) , induction local correlation tracking(ilct ; @xcite ) , minimum energy fit ( mef ; @xcite ) , differential affine velocity estimator ( dave ; @xcite ) and differential affine velocity estimator for vector magnetograms ( dave4vm ; @xcite ) have been developed for the determination of horizontal component of motion . in contrast , the normal component of velocity can be determined from the doppler observations of ars located near the disk center . dave4vm method requires vector magnetograms . the performance of different techniques has been examined in @xcite which showed that the mef , dave , flct , i m , and ilct algorithms performed comparably . furthermore , they reported that while the dave estimated the magnitude and direction of velocities slightly more accurately than the other methods , mef s estimates of the fluxes of magnetic energy and helicity were more accurate . time series data of photospheric magnetograms have been extensively used to derive magnetic helicity and its evolution in order to examine its role in the level of transient activity of the ars . @xcite reported impulsive variations of helicity during some m and x - class flares . in a survey , @xcite revealed that x - flaring ars have a higher net helicity change with peak helicity rate @xmath19mx@xmath1s@xmath20 with weak hemispheric preference . @xcite have also studied the solar flare productivity in relation to the helicity injection using a large sample of 378 active regions . using soho - mdi magnetograms , they reported variation of helicity injection rates and a significant helicity accumulation of @xmath21 mx@xmath1 over several days around the time of flares above m5.0 . most of the previous studies that used data from michelson doppler imager ( mdi ) onboard soho had the time resolution of 96 minutes . the rather coarse time resolution between two consecutive observations has been a matter of concern in the above calculations because the contribution from the motion of short lived magnetic features in small intervals is difficult to be accounted suitably ( _ e.g. _ , @xcite ) . this underlines the need for observations of magnetic fields with higher temporal resolution . the above mentioned issues can now be addressed with the availability of a better cadence of 12 minutes by the recently launched helioseismic and magnetic imager ( hmi ) onboard _ solar dynamics observatory _ ( sdo ) . our main objective in the present work is to reinvestigate the role of helicity injection in relation with flares and cmes using the high - resolution data obtained from sdo - hmi . we intend to utilize this opportunity to revisit some of the previous studies involving computations of helicity rate for two ars , noaa 11158 and noaa 11166 , that appeared during february and march 2011 , respectively , in the ascending phase of the current solar cycle 24 . using the high quality hmi data obtained for the two ars , we intend to examine whether the variations as reported by @xcite and @xcite for energetic flares occurred also during the flares of lower magnitude . it is of particular interest to investigate if such changes were associated with the cmes as well . for our analysis , we use dave technique for retrieving horizontal foot - point velocity from the los magnetograms . thereafter , using equation  [ eq_par ] we determine helicity injection rates and the accumulated helicity in the two ars due to foot - point shearing motions during their disk transit . it has been inferred from the previous studies that most of the helicity injection corresponds to magnetic flux emergence in the ars@xcite . we , therefore , attempt to interpret the variations found in these physical parameters in relation to the occurrence of flares and cmes . in particular , we investigate whether the transport of magnetic helicity plays a role in solar eruptions . we organize this paper as follows . description of the data used in this study and the procedures of the data processing are given in section  [ data ] . results obtained for the two selected ars are presented in section  [ results ] and the following discussions in section  [ disc ] . the summary of the work presented in this article is given in section  [ sum ] .","summary":"we derived the horizontal velocities in the active regions from the differential affine velocity estimator(dave ) technique . this study suggests that flux motions and spatial distribution of helicity injection are important to understand the complex nature of magnetic flux system of the active region leading to conditions favorable for eruptive events .","abstract":"an investigation of helicity injection by photospheric shear motions is carried out for two active regions(ars ) , noaa 11158 and 11166 , using line - of - sight magnetic field observations obtained from the helioseismic and magnetic imager on - board solar dynamics observatory . we derived the horizontal velocities in the active regions from the differential affine velocity estimator(dave ) technique . persistent strong shear motions at the maximum velocities in the range of 0.60.9km / s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed in the two active regions . the helicities injected in noaa 11158 and 11166 during their six days evolution period were estimated asmx andmx , respectively . the estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min , and increased up to 9% by decreasing the dave window size from to pixel , resulting in 10% variation in the accumulated helicity . in both ars , the flare prone regions ( r2 ) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of cme prone regions had almost homogeneous distribution of helicity flux dominated by single sign . the temporal profiles of helicity injection showed impulsive variations during some flares / cmes due to negative helicity injection into the dominant region of positive helicity flux . a quantitative analysis reveals a marginally significant association of helicity flux with cmes but not flares in ar 11158 , while for the ar 11166 , we found marginally significant association of helicity flux with flares but not cmes , providing evidences of the role of helicity injection at localized sites of the events . these short - term variations of helicity flux are further discussed in view of possible flare - related effects . this study suggests that flux motions and spatial distribution of helicity injection are important to understand the complex nature of magnetic flux system of the active region leading to conditions favorable for eruptive events ."}
{"article_id":"1202.5195","section_id":"m","document":"for our study , we have used high resolution los magnetograms at a cadence of 12 minutes obtained from the helioseismic magnetic imager ( hmi ; @xcite ) on board _ solar dynamic observatory _ ( sdo ) . hmi observes the full solar disk in the fe i 6173   spectral line with a spatial resolution of 1 arc - second . hmi provides four main types of data : dopplergrams ( maps of solar surface los velocity ) , continuum filtergrams ( broad - wavelength maps of the solar photosphere ) , los and vector magnetograms ( maps of the photospheric magnetic field ) . noaa 11158 ( 19@xmath22s ) and 11166 ( 10@xmath22n ) appeared on the disk during february 11 - 20 , 2011 and march 03 - 16 2011 respectively . these ars were very active , and produced some intense x - class flares associated with cmes in addition to many m- and c- class flares during their disk transits . from the aia observations , intermittent mass expulsions were seen , many of which turned into large , fast moving cmes as further confirmed by stereo . table  [ tabflcm ] gives a list of flares ( as recorded by goes ) and cmes . l l l l + ar & date & flares & cmes + ( noaa ) & dd / mm / yyyy & magnitude(time ut ) & ( time ut ) +   + 11158 & 11/02/2011 & no flares & no cmes + & 12/02/2011 & no flares & no cmes + & 13/02/2011 & c1.1(12:29),c4.7(13:44),m6.6(17:28 ) & 21:30,23:30 + & 14/02/2011 & c1.6(02:35),c8.3(04:29),c7.1(06:51 ) & 02:40,07:00,12:50,17:30,19:20 + & & c1.8(08:39),c1.7(11:51),c9.4(12:41 ) & + & & c7.0(13:47),m2.2(17:20)*,c6.6(19:23 ) & + & & c1.2(23:14 ) , c2.7(23:40 ) & + & 15/02/2011 & x2.2(01:44),c2.7(00:31 ) & 00:40,02:00*,03:00,04:30,05:00 + & & c4.8(04:27),c4.8(14:32),c1.7(18:07 ) & 09:00 + & & c6.6(19:30),c1.3(22:49 ) & + & 16/02/2011 & c2.0(00:58),c2.2(01:56),c5.9(05:40 ) & 14:35 + & & c2.2(06:18),c9.9(09:02),c3.2(10:25 ) & + & & c1.0(11:58),m1.0(01:32),m1.1(07:35 ) & + & & m1.6(14:19),c7.7(15:27),c1.3(19:29 ) & + & & c1.1(20:11),c4.2(21:06),c2.8(23:02 ) & +   + 11166 & 06/03/2011 & c5.1(11:56),c3.9(15:21 ) & 02:00,15:20 + & 07/03/2011 & m1.9(13:45 ) & 14:25,22:10 + & 08/03/2011 & c7.7(23:10 ) & 14:30,19:00 + & 09/03/2011 & c9.4(08:23),m1.7(10:35),m1.7(13:17 ) & 06:40,10:40,21:45 + & & c9.4*(22:03),x1.5(23:13 ) & + & 10/03/2011 & c2.9(03:50),c6.2(07:03),c4.2(13:19 ) & + & & c4.7(13:42),c2.0(14:21 ) & 04:50,07:10 + & & c4.0(19:00),m1.1(22:34 ) & + & 11/03/2011 & c1.4(00:29),c1.1(01:46),c2.8(02:24 ) & 00:50 + & & c5.5(04:15),c4.3(07:22),c1.1(08:13 ) & + & & c2.0(11:10),c3.6(11:43),c1.1(16:04 ) & + & & c1.0(22:20),c1.0(22:50 ) & +   +     + _ note : _ all flares(cmes ) associated to source region r2(r1 ) of respective ars except those marked by * [ tabflcm ]    magnetograms obtained at different times were aligned by the method of @xcite . in this method , an image of the ar taken at the central meridian is considered as the reference image . all other images , in time accounted for differential rotation @xcite along with the latitudinal difference of center of reference image from the ephemeris information , were remapped on to the disk center . this method is intended to reduce errors due to geometrical foreshortening and the ar is transformed to the disk center . since at disk center , normal and vertical components of magnetic fields are same , the difference between the normal and los component was corrected by cosine of the distance of the ar center from the disk center by assuming the horizontal field contribution for the transformation to be negligible @xcite . we followed the transits of the two selected ars from east to west on the solar disk . in order to have negligible errors in geometric correction , we restricted ourselves to a region within @xmath2340@xmath22 longitude from the central meridian . with this constraint , we confined our study of the temporal evolution of the ars to six days s period around their central meridian passage . we derived the horizontal velocities of foot - points on the photosphere by using dave technique @xcite . the dave technique is essentially a local optical flow method that determines the magnetic footpoint velocities within the windowed region . further , it adopts an affine velocity profile specifying velocity field in the windowed region about a point and constrains that profile to satisfy the induction equation . any tracking method depends on two parameters , _ viz . _ , the window size and the time interval . for a given time interval @xmath24 t , the window should be large enough so that tracked features remain confined within the window . also , it should be small enough to be consistent with an affine velocity profile . @xcite presented a way to select an optimal window objectively , using the degree of consistency between change in the observed magnetic field ( @xmath25 ) and the expected magnetic field change based on the flow estimated with several trial windows . they found the best performance of this method at approximately a square window of pixels . since the ars evolved rapidly , we chose a window size of 21@xmath2618 pixel@xmath1 after a careful verification of the physical flux motions and directions of estimated flows . the dependence of helicity injection rate on window size and time difference between the tracked maps using this method were investigated . moreover , as the hmi magnetic field measurement precision is 10 g @xcite , we have set this as the threshold to avoid errors while retrieving velocities . further details of this method are given in a recent work of @xcite . computation of the helicity rate using the method ( direct integration ) proposed by @xcite at each pixel of the ar map ( _ cf . _ , equation [ eq_par ] ) is a tedious , time consuming process . however , we chose to use this method for reducing the effect of fake polarities of helicity flux . restricting the calculations at pixels with magnetic field above the threshold ( @xmath2710 g ) helps to reduce the computation time typically by 15 - 25% . parallelization in integrand computation further reduces the time approximately by a factor of the number of processors used . the same equation as rewritten by @xcite to suit the convolution algorithm by fourier transform is faster than the direct integration method . the intrinsic problem of fourier transform with periodicity could be overcome by padding the array corresponding to the data points with rows and columns of zeros to get results as obtained by direct integration method . in this study , we have implemented the former approach ( direct integration ) to get sufficiently accurate results .","summary":"an investigation of helicity injection by photospheric shear motions is carried out for two active regions(ars ) , noaa 11158 and 11166 , using line - of - sight magnetic field observations obtained from the helioseismic and magnetic imager on - board solar dynamics observatory .","abstract":"an investigation of helicity injection by photospheric shear motions is carried out for two active regions(ars ) , noaa 11158 and 11166 , using line - of - sight magnetic field observations obtained from the helioseismic and magnetic imager on - board solar dynamics observatory . we derived the horizontal velocities in the active regions from the differential affine velocity estimator(dave ) technique . persistent strong shear motions at the maximum velocities in the range of 0.60.9km / s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed in the two active regions . the helicities injected in noaa 11158 and 11166 during their six days evolution period were estimated asmx andmx , respectively . the estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min , and increased up to 9% by decreasing the dave window size from to pixel , resulting in 10% variation in the accumulated helicity . in both ars , the flare prone regions ( r2 ) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of cme prone regions had almost homogeneous distribution of helicity flux dominated by single sign . the temporal profiles of helicity injection showed impulsive variations during some flares / cmes due to negative helicity injection into the dominant region of positive helicity flux . a quantitative analysis reveals a marginally significant association of helicity flux with cmes but not flares in ar 11158 , while for the ar 11166 , we found marginally significant association of helicity flux with flares but not cmes , providing evidences of the role of helicity injection at localized sites of the events . these short - term variations of helicity flux are further discussed in view of possible flare - related effects . this study suggests that flux motions and spatial distribution of helicity injection are important to understand the complex nature of magnetic flux system of the active region leading to conditions favorable for eruptive events ."}
{"article_id":"1202.5195","section_id":"i","document":"we have studied the evolution of magnetic fluxes , horizontal flux motions , helicity injection and their relationship with the eruptive transient events in two recent flare ( cme ) productive ars , noaa 11158 and noaa 11166 of 2011 february and march , respectively . we have used high resolution , high cadence data provided by sdo - hmi for these ars which were in their emerging and active phases . the emerging ar consisted of rotating sunspots with increasing flux indicating emergence of twisted flux from the sub - photospheric layers . this indicated the transfer of twist or helicity injection through the photosphere to the outer atmosphere . we suggest that strong shear motions that include rotational and proper motions played significant role in most of the events in addition to the flux emergence . such motions are crucial in twisting or shearing the magnetic field lines and for further flux interactions . ar noaa 11158 consisted of a cme - prone site of rotating main sunspot along with emerging flux of opposite sign and moving magnetic feature . it also had a flare - prone site consisting of self - rotating sunspot(sp2 ) moving about a sunspot of opposite sign(sn2 ) , leading to flux interaction . these motions are likely to form the sigmoidal structures , which are unstable , and more likely to produce eruptive events . a huge expulsion as cme on 2011 february 14/17:30ut occurred in the former site and a white light , energetic x2.2 flare on 2011 february 15/01:44ut occurred in the later site . the other case , ar noaa 11166 was already in its active phase with further increasing content of flux as it evolved . group motions of diffused fluxes merging to form a bigger sunspot manifested major shear motions in addition to outward flows from sunspot . a large cme on 2011 march 09/21:45ut , followed by an x1.5 flare , was one of the major events in this ar . ar noaa 11158 injected @xmath0mx@xmath1 while ar noaa 11166 injected @xmath2mx@xmath1 helicity during the six days period of their evolution . these are consistent with the previously reported order of helicity accumulation ( _ e.g. _ , * ? ? ? it appears that due to the presence of rotational motions , the former ar accumulated larger amount of helicity accounting for its greater activity in the form of flares and cmes . it is also evident that flux emergence is necessary and their motions are crucial in additionally accounting for the accumulated amount of helicity to the emergence term . in both ars , x - class flares with associated cmes were observed in the decreasing phase of helicity accumulation by the injection of opposite helicity . apart from the instrumental and computational errors , the estimation of helicity injection rates are also affected by the choice of dave parameters used to track the motion of the fluxes . helicity injection rates are found to decrease up to 13% by increasing the time interval between magnetograms from 12 to 36 min whereas an increasing trend upto 9% resulted by decreasing the window size from @xmath3 to @xmath4 pixel@xmath1 , with a total variation of 10% in the deduced value of accumulated helicity . the time profile of helicity rate exhibited sudden sharp variations during some flare events due to injection of opposite helicity flux into the existing system of helicity flux . in both ars , the flare prone regions ( r2 ) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of cme prone regions had almost homogeneous distribution of helicity flux dominated by single sign . a quantitative analysis was carried out to show the association of these variations to the timings of flares / cmes . for the ar 11158 , we find a marginally significant association of helicity flux with cmes but not flares , while for the ar 11166 , we find marginally significant association of helicity flux with flares but not cmes . moreover , these variations of helicity flux may not reflect true transfer ; there exists flare - related transient effects and theoretical uncertainties resulting to these variations . we believe the helicity transfer in the cases of c7.0 on 14 february , c4.2 at 13:19ut , c4.7 at 13:42ut on 10 march to be true , without flare - related transient effect but with theoretical uncertainty in the approach .    therefore , to further strengthen the above evidences of true helicity transfer , it would be worthwhile to scrutinize more flare / cmes cases using 3 min cadence magnetic observations , over a period of a day or so . this will enable one to find detectable changes in helicity flux signal during smaller magnitude flares with less transient - flare effects . interpreting the physical significance of such variations using the information of coronal connectivities will be another important aspect to add further to the present knowledge of helicity physics . our study reveals that the spatial information of helicity injection is a key factor to understand its role in the flares / cmes . the data have been used here courtesy of nasa / sdo and hmi science team . we thank dr . etienne pariat for checking our helicity program with comments and suggestions . the author expresses his gratitude to prof . p. venkatakrishnan for some useful discussions on the concept of helicity . we thank an anonymous referee for carefully reading the manuscript and making valuable comments which led to improved clarity and readability of the manuscript .","summary":"the helicities injected in noaa 11158 and 11166 during their six days evolution period were estimated asmx andmx , respectively . the estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min , and increased up to 9% by decreasing the dave window size from to pixel , resulting in 10% variation in the accumulated helicity . in both ars , the flare prone regions ( r2 ) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of cme prone regions had almost homogeneous distribution of helicity flux dominated by single sign . the temporal profiles of helicity injection showed impulsive variations during some flares / cmes due to negative helicity injection into the dominant region of positive helicity flux . a quantitative analysis reveals a marginally significant association of helicity flux with cmes but not flares in ar 11158 , while for the ar 11166 , we found marginally significant association of helicity flux with flares but not cmes , providing evidences of the role of helicity injection at localized sites of the events .","abstract":"an investigation of helicity injection by photospheric shear motions is carried out for two active regions(ars ) , noaa 11158 and 11166 , using line - of - sight magnetic field observations obtained from the helioseismic and magnetic imager on - board solar dynamics observatory . we derived the horizontal velocities in the active regions from the differential affine velocity estimator(dave ) technique . persistent strong shear motions at the maximum velocities in the range of 0.60.9km / s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed in the two active regions . the helicities injected in noaa 11158 and 11166 during their six days evolution period were estimated asmx andmx , respectively . the estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min , and increased up to 9% by decreasing the dave window size from to pixel , resulting in 10% variation in the accumulated helicity . in both ars , the flare prone regions ( r2 ) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of cme prone regions had almost homogeneous distribution of helicity flux dominated by single sign . the temporal profiles of helicity injection showed impulsive variations during some flares / cmes due to negative helicity injection into the dominant region of positive helicity flux . a quantitative analysis reveals a marginally significant association of helicity flux with cmes but not flares in ar 11158 , while for the ar 11166 , we found marginally significant association of helicity flux with flares but not cmes , providing evidences of the role of helicity injection at localized sites of the events . these short - term variations of helicity flux are further discussed in view of possible flare - related effects . this study suggests that flux motions and spatial distribution of helicity injection are important to understand the complex nature of magnetic flux system of the active region leading to conditions favorable for eruptive events ."}
{"article_id":"quant-ph9702031","section_id":"i","document":"the potential use of quantum computers for solving certain classes of problems has recently received a considerable amount of attention ( for a review see , _ e.g. _ , @xcite ) . a major obstacle in the building of quantum computers , however , is the coupling of the computer with its environment or the _ decoherence _ , which rapidly destroys the quantum superposition at the heart of quantum algorithms . an essential element in the realization of such quantum computers is therefore the use of quantum error - correcting codes , which have been shown to ensure protection against decoherence  @xcite . quantum codes are similar in many respects to classical codes . in classical coding theory , logical words ( of @xmath0 bits ) are encoded into codewords ( of @xmath1 bits ) . the latter are suitably chosen among the set of all @xmath2 possible words of @xmath3 bits so that the alteration because of noise of say @xmath4 bits ( at most ) can be recovered . a specific set of codewords then constitutes an @xmath5 $ ] code , encoding @xmath0 bits into @xmath3 bits and correcting all patterns of @xmath4 ( or fewer ) errors among those @xmath3 bits . the simplest example of a classical code with @xmath6 , @xmath7 , and @xmath8 is the repetition code where a logical bit 0 ( or 1 ) is encoded into 000 ( or 111 ) ; decoding is simply performed using the majority rule , which is enough to recover @xmath8 errors . in classical coding theory , corrupted data is thus restored by introducing redundancy ( @xmath1 ) , that is by duplicating part of the information that must be preserved . ( in the above  very inefficient  example , information is triplicated . ) in quantum coding theory , the central issue is to find a set of @xmath9 quantum codewords ( of @xmath3 qubits ) such that _ quantum information _ can be protected against the alteration due to coupling with an environment ( _ i.e. _ , such that the quantum system survives decoherence ) . at first sight , it seems that , since the duplication of an arbitrary quantum state is forbidden by the quantum _ no - cloning _ theorem@xcite , `` quantum redundancy '' is impossible . however , after the pioneering work of shor@xcite , it has been realized that quantum coding is achievable in spite of the no - cloning theorem , and a great deal of work has recently been devoted to this issue  @xcite . it has been shown that quantum information can be distributed over many qubits through a suitable encoding and subsequently recovered after partial alteration , without violating the no - cloning theorem . in this paper , we aim at clarifying some aspects of quantum coding from a perspective centered on quantum entropies . it has been shown recently that classical and quantum entropies can be described within a unified information - theoretical framework involving negative conditional entropies  @xcite , as briefly outlined in appendix  [ sect_app ] . here , we apply this framework to quantum error - correcting codes , paralleling the classical description of error correction in shannon theory . we show that , for an arbitrary entanglement between the logical words and a `` reference '' system to be preserved , the quantum _ mutual _ entropy between this `` reference '' and any `` interacting '' part of the codewords must be vanishing prior to decoherence . in other words , an entropic condition for perfect quantum error correction is that the `` reference '' system is statistically _ independent _ of any arbitrarily chosen part of the codewords that might interact with the environment . this condition relies on the conservation of quantum mutual entropies implied by unitarity , along with the property of strong subadditivity of quantum entropies ( see appendix  [ sect_app ] ) . it expresses the fact that the environment can not become _ directly _ entangled with the `` reference '' system ( entanglement may arise only via the codewords ) , or , roughly speaking , that the environment can not extract information about the logical words . we continue by deriving the analogue of the singleton bound for quantum codes  @xcite , _ i.e. _ , @xmath10 , using simple arguments based on this entropic approach . such an information - theoretic description of coding sheds new light on the interpretation of this bound in terms of `` weak '' cloning . while the quantum bits that are altered as a result of any error are statistically independent of the reference ( or the encoded logical word ) , the quantum information stored in the entire codeword remains unaffected . this results from the fact that the _ ternary _ mutual entropy vanishes for any entangled tripartite system in a pure state , a property which has no classical counterpart  @xcite . the central point is that , in contrast with classical codes , no duplicating  or full cloning  is achieved by _ quantum _ error - correcting codes . rather , a `` weak '' quantum cloning is achieved , such that any part of the codeword susceptible to decohere appears independent of the reference although the entire codeword remains entangled with it . this purely quantum situation is forbidden in classical information theory due to the non - negativity of shannon conditional entropies , and reflects a fundamental difference between classical and quantum error correcting codes .","summary":"quantum error - correcting codes are analyzed from an information - theoretic perspective centered on quantum conditional and mutual entropies . this approach parallels the description of classical error correction in shannon theory , while clarifying the differences between classical and quantum codes . more specifically , it is shown how quantum information theory accounts for the fact that `` redundant '' information can be distributed over quantum bits even though this does not violate the quantum `` no - cloning '' theorem .","abstract":"quantum error - correcting codes are analyzed from an information - theoretic perspective centered on quantum conditional and mutual entropies . this approach parallels the description of classical error correction in shannon theory , while clarifying the differences between classical and quantum codes . more specifically , it is shown how quantum information theory accounts for the fact that `` redundant '' information can be distributed over quantum bits even though this does not violate the quantum `` no - cloning '' theorem . such a remarkable feature , which has no counterpart for classical codes , is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state . this information - theoretic description of quantum coding is used to derive the quantum analogue of the singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors .    2 [ ]"}
{"article_id":"quant-ph9702031","section_id":"c","document":"before concluding , let us discuss the relation between the quantum no - cloning theorem and quantum erasure - correcting codes . the main point is to note that , if we can erase @xmath35 qubits while being able to recover the codeword , it means that the @xmath38 remaining qubits contain all the information , so that the @xmath35 qubits apparently contain a ( partial ) duplication of the logical word . clearly , it is forbidden to erase half ( or more ) of the @xmath3 qubits , since then the two halves of the codeword could be mapped on the logical word , enabling quantum cloning . thus , one must have @xmath208 ( a constraint equivalent to the condition that the dimension of @xmath37 must exceed the dimension of @xmath36 ) . however , eq .  ( [ eq_klerasure ] ) is actually more restrictive , implying that it is possible to quantify the impossibility of cloning ( to be more precise than a yes - or - no theorem ) . we will see that the singleton bound expresses that a `` weak '' cloning is allowed , up to a certain extent . let us define the number of clones ( the _ fractional _ number of copies of the logical word ) as : @xmath209 where the @xmath38 qubits constitute the `` original '' ( necessary to fully recover the logical state ) while the @xmath35 erased qubits make the partial and @xmath210 . however , the outputs unavoidably share a common piece @xmath189 which can not be reduced to zero for @xmath186 and @xmath193 to hold simultaneously . ] clone . it is easy to see from eq . ( [ eq_klerasure ] ) that the fractional number of clones is restricted to the range @xmath211 this somehow extends the standard no - cloning theorem to `` weak '' ( @xmath212 ) cloning . the no - cloning theorem  @xcite states that it is forbidden to make one full clone , _ i.e. _ , @xmath213 , while eq . ( [ eq_weakclone ] ) provides an upper bound on weak cloning . in the limiting case where @xmath214 , the number of clones is strictly zero . this simply means that , if the codewords span the full @xmath2-dimensional hilbert space ( _ i.e. _ , if no coding is actually used ) , then no cloning at all is achieved ( @xmath215 ) . the same is obviously true for a classical code , since , using eq . ( [ eq_class_singleton ] ) , the equivalent condition on `` weak '' cloning is @xmath216 . when quantum coding uses only part of the hilbert space , _ i.e. _ , the space of codewords is some @xmath9-dimensional subspace of the full space ( @xmath217 ) , the logical states may then be viewed as partially cloned by the encoding process , the fractional number of clones being limited to @xmath218 . the latter increases as a smaller subspace is used ( @xmath0 decreases ) , and tends to one ( full cloning ) when @xmath219 . the case @xmath220 corresponds to perfect cloning of a _ fixed _ ( _ i.e. _ , non - arbitrary ) pure state . therefore , whatever the apparent `` replication factor '' @xmath221 of the logical words achieved by the encoding process , the allowed number of clones @xmath222 ( for a non - vanishing @xmath0 ) . for a classical code , however , no such limit exists on the number of clones , as @xmath223 when @xmath219 . we have shown that some new insight into quantum coding can be gained by use of an information - theoretic approach paralleling the one used to describe classical coding . such an analysis displays explicitly the similarities between classical and quantum codes , but also emphasizes the major differences . the entropic condition for a quantum erasure - correcting code is that the quantum mutual entropy between a reference and the erased part of the codeword is vanishing prior to decoherence . such a statistical independence between the reference and the erased qubits ( interacting with the environment ) guarantees that the entanglement of the logical word with respect to this reference is preserved by the quantum code . this is to be compared with the corresponding entropic condition for a classical erasure - correcting code , _ i.e. _ , that the mutual information between the logical bits and the erased bits of the codewords , _ conditional _ on the remaining unchanged bits of the codewords , is vanishing . such a classical condition , however , does _ not _ imply that the erased bits are independent of the logical bits . on the contrary , there must be correlations between them , and this duplication ( or `` cloning '' ) of classical information is at the heart of classical codes . such a classical redundancy has no quantum counterpart , as a consequence of the purely quantum property that the _ ternary _ mutual entropy vanishes for any entangled tripartite system in a pure state . in a quantum code , only a `` weak '' cloning is achieved , up to the extent allowed by the quantum singleton bound , so that the erased qubits are _ unentangled _ with the reference although the entire codeword remains entangled with it . this reflects a major difference between classical and quantum coding . we acknowledge c. adami and j. preskill for very useful discussions . we thank the organizers of the itp program on quantum computers and decoherence for their invitation in santa barbara , where this work has been performed . this research was supported in part by the national science foundation under grant nos . phy 94 - 12818 , phy 94 - 20470 and phy 94 - 07194 , and by a grant from darpa / aro through the quic program ( # daah04 - 96 - 1 - 3086 ) .","summary":"such a remarkable feature , which has no counterpart for classical codes , is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state .","abstract":"quantum error - correcting codes are analyzed from an information - theoretic perspective centered on quantum conditional and mutual entropies . this approach parallels the description of classical error correction in shannon theory , while clarifying the differences between classical and quantum codes . more specifically , it is shown how quantum information theory accounts for the fact that `` redundant '' information can be distributed over quantum bits even though this does not violate the quantum `` no - cloning '' theorem . such a remarkable feature , which has no counterpart for classical codes , is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state . this information - theoretic description of quantum coding is used to derive the quantum analogue of the singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors .    2 [ ]"}
{"article_id":"1201.1414","section_id":"c","document":"we investigated the origin and evolution of the small gas cloud g2 that has been detected approaching the galactic smbh on a highly eccentric orbit . the cloud has an observationally inferred density and temperature that during the first years of detection around 2003 indicates that it was in pressure equilibrium with its surrounding . our analytical estimates and numerical simulations show that it must have formed close to pressure equilibrium . a cloud with a significant lower pressure would be destroyed by implosion while a highly overpressured cloud would go through a phase of rapid expansion , forming a diffuse , extended and tidally elongated structure that is not in agreement with the observations . the `` in situ '' cloud scenario which assumes that the cloud formed as a spheroidal clump in pressure equilibrium in the year 1995 , shortly before it was detected , provides an excellent match to all the observations , dating back to 2002 till today . in this case , our numerical simulations indicate that the cloud will be tidally stretched into a very elongated filament till 2013.5 which shortly after pericenter passage will begin to loose gas as a result of kelvin - helmholtz instabilities . this gas might fall into the inner accretion zone of sgr a@xmath0 , forming a hot luminous accretion disk . over the next 80 years the debris of the tidally destroyed cloud will fuel the smbh , maybe leading to an extended period of nuclear activity .    the main caveat of the `` in situ '' model is the fact that we have not been able to identify any physical mechanism that could have formed g2 in 1995 . we did not find any known star that was close to its birth place at that time . in addition , the cloud could also not have formed by a cooling instability of the hot gas as its cooling timescale is much longer than the dynamical timescale ( burkert & lin 2000 ) . it is intriguing that the assumption of g2 having formed at apocenter leads to several interesting correlations that should be reproduced by any theoretical model of its formation . g2 s orbital plane coincides with the plane of the clockwise rotating stellar disk and its apocenter agrees with the inner disk edge . in addition , g2 s sound crossing timescale , evaporation timescale and orbital timescale are all equal at apocenter . if this is not a coincidence it provides several important constraints on its formation . first of all , g2 obviously did not form very recently ( e.g. 1995 ) by some condensation processes but came from apocenter . it also means that g2 has been in pressure equilibrium at apocenter , either as a result of its formation or due to re - adjustment . it is reasonable to assume that a cloud that is subject to distortions when interacting with a turbulent environment can only maintain coherence if it can react and re - adjust to them . this requires that the cloud s sound crossing timescale , which is the timescale on which information is transported through the cloud , is smaller than the timescale of the perturbation . clouds that can not react will break up into subunits that are smaller than this characteristic timescale . the origin of these perturbation is not clear up to now . the inner hot bubble is probably highly turbulent and might even be convective . for a kolmogoroff spectrum , the largest fluctuations which are of order the size of the region and which interact with the cloud on timescales of order the dynamical time would dominate and might regulate its size . in this case , g2 might represent a piece of a larger dusty cold region that disintegrated into smaller clumps by its interaction with the turbulent environment . as the timescale for such a region to break up is at least equal to an orbital period , the cold gas inside g2 must be older than that . g2 should then have completed at least one full orbit . the massive progenitor cloud might already have been on a highly eccentric orbit at that time . another possibility is that it was on a circular orbit . within the stellar disk region , where it experienced a collision or violent interaction e.g. with a stellar wind shell this destroyed the cloud while at the same time deflected some of its parts onto highly eccentric orbits like g2 . one of the problems with all formation scenarios that start at apocenter is the fact that g2 will become very elongated with a strong velocity gradient around 2011 that is not in agreement with the observations . as our simulations show , one possible solution is that g2 is actually part of a larger shell . this scenario could explain the observed extended tail of lower surface brightness br@xmath2 emission that is seen on about the same orbit as that of g2 . the shell s origin is not clear . it might represent a clumpy wind shell , ejected from one of the luminous blue variable or wolf - rayet stars in the stellar disk . we investigated which of the known high - mass stars in the stellar disk was close to g2 s apocenter in the year 1944 and found one candidate , s91 which appears to be an o6.5ii star with a mass loss rate of order @xmath168 m@xmath4/yr and a wind velocity of 2000 @xmath169 km / s ( puls & kudritzki , private information ) . winds of this kind are usually believed to generate hot plasma with temperatures of order @xmath23 k ( hall , kleinmann & scoville 1982 ; cuadra et al . 2005 ) . whether a cooling instability in the expanding wind bubble could also have generated a ring of cold gas is not clear yet . if the diffuse cloud scenario of g2 fails we are left with the possibility that g2 actually is the visible diffuse gas atmosphere of an unresolved , dense object in its center ( murray - clay & loeb 2012 ) . this would keep the cloud spheroidal , despite the external gravitational force of the smbh , first of all because gas is continuously replenished from the probably spherical radial outflow and secondly , because the gravitational force of the central object inside the roche volume can balance the destructive and deforming gravitational force of the smbh . a crucial test of this scenario is , whether it can explain the close agreement between the sound crossing , evaporation and dynamical timescales , that we discussed earlier . in this case , one also would expect a tail of stripped material , trailing g2 . its structure and especially its velocity distribution might however differ significantly from the shell scenario . for example , it is not clear whether its downstream end would be bright . in addition , it is unlikely that the trailing stripped gas will have the observed offset towards large infall velocities compared to the orbital velocity . we would instead expect smaller infall velocities due to the deceleration by the ram pressure which is not observed . detailed observations of the diffuse environment of g2 and additional numerical simulations would be helpful in distinguishing between the diffuse cloud and compact source scenario . we have presented and discussed a first set of simplified simulations , adopting a hydrostatic atmosphere and an isothermal cloud . already these simulations reveal a very complex , non - linear evolution . future papers should add the effects of compressional heating of the cloud , especially close to pericenter where gillessen et al . ( 2012 ) estimate compression to significantly increase the temperature and by that the luminosity of the cloud . first test simulations demonstrate however that this effect does not significantly alter the cloud s evolution as the gravitational force of the smbh close to pericenter is much stronger than the increase in gas pressure due to tidal heating . after pericenter the cloud material will actually cool again due to expansion . it is also important to investigate the effects of gas evaporation and magnetic fields . in the long run one should replace the currently hydrostatic atmosphere by a turbulent and probably convective , inhomogeneous and rotating hot gas bubble that might strongly affect the cloud evolution . the problem of the origin and evolution of the tiny gas cloud g2 , falling into the accretion zone of sgr a@xmath0 represents an exciting challenge for numerical and theoretical models of the complex multi - phase gas physics in the galactic center . we are in a unique situation where theoretical models and numerical simulations of g2 s evolution will be tested directly by observations within the next couple of years . for the next decades g2 s journey through the galactic nucleus and its evolution will provide detailed information about this fascinating and extreme environment of the milky way and the processes that feed its central smbh . llllllll & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 & @xmath176 + & yr ad & @xmath177 & @xmath178 & @xmath179 & @xmath179 & @xmath180 & @xmath180 + cc01 & @xmath181 & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 & @xmath187 + cc02 & @xmath188 & @xmath189 & @xmath190 & @xmath191 & @xmath192 & @xmath192 & @xmath193 + cc03 & @xmath188 & @xmath194 & @xmath195 & @xmath191 & @xmath192 & @xmath192 & @xmath193 + ss01 & @xmath196 & @xmath197 & @xmath198 & @xmath199 & @xmath192 & @xmath192 & @xmath200 +     the left panel shows the orbit and location of g2 in the orbital plane . g2 s apocenter coincides with the inner edge of the clockwise rotating stellar disk ( shaded area ) . the cloud will pass the smbh ( cross ) in 2013 at a distance of merely @xmath201 times the event horizon . due to its highly eccentric orbit , the cloud spends most of its time in the outer regions . the right panel shows the velocity of g2 as function of its distance r from the smbh . for comparison , the dashed line shows a parabolic , unbound orbit with total energy e=0 . the dotted line shows the local sound speed of the diffuse , hot environment ( equation 3).,scaledwidth=100.0% ]       ( black , horizontal dotted line ) , the evaporation timescale @xmath202 ( black dashed line ) , the sound crossing timescale @xmath121 ( shaded red region ) , adopting @xmath111 ( upper limit ) and @xmath203 ( lower limit ) , respectively , the pressure timescale @xmath204 ( black solid line ) and the infall timescale @xmath135 ( blue solid line ) that measures the time it takes g2 to reach pericenter from radius r. the two vertical dashed lines correspond to the apocenter and the location of g2 in 2011.3 , respectively . [ fig : three ] , scaledwidth=100.0% ]       emission of g2 , obtained with sinfoni on the vlt ( gillessen et al . colors correspond to the total mass of gas as predicted by the simulation in each position - velocity bin with the values given by the color bar . the dashed line shows the ballistic orbit of a point particle in the gravitational potential of the smbh , centered on g2 . the dotted lines show the distribution if each gas element of the cloud would move on a balistic orbit . in 2008.5 the cloud is still compact . over the next 3 years its develops a strong velocity shear . overall the calculations are in excellent agreement with the observations . the predicted structure of g2 in the pv - diagram for the year 2012.5 is shown in the right panel . [ fig : five ] , scaledwidth=100.0% ]                    * acknowledgments : * the research of a.b . is supported by a max planck fellowship and by the dfg cluster of excellence `` origin and structure of the universe '' . we thank chris mckee , eliot quataert , avi loeb , joachim puls and rolf kudritzki for helpful discussions . alexander , r.d . , smedley , s.l . , nayakshin , s. & king , a.r . 2011 , , in press alig , c. , burkert , a. , johansson , p.h . & schartmann , m.  2011 , , 412 , 469 baganoff , f.k . , et al . 2001 , , 413,45 baganoff , f.k . , et al . 2003 , , 591 , 891 bartko , h. et al . 2009 , , 697 , 1741 burkert , a. & lin , d.  2000 , , 537 , 270 burkert , a. & tremaine , s.  2010 , , 720 , 516 bonnell , i.a . & rice , w.k.m . 2008 , sci , 321 , 1060 bower , g.c . , wright , m.c.h . , falcke , h. & backer , d.c . 2003 , , 588 , 331 cheng , k .- s . , chernyshov , d.o . , dogiel , v.a . , ko , c .- m . & ip , w .- h . 2011 , , 731 , l17 clnet , y. , roun , d. , gratadour , d. , marco , o. , lna , p. , ageorges , n. & gendron , e.  2005 , , 439 , 9 cowie , l.l . & mckee , c.f . 1977 , , 211 , 135 cuadra , j. , nayakshin , s. , springel , v. & di matteo , t.  2005 , , 360 , l55 cuadra , j. , nayakshin , s. , springel , v. & di matteo , t.  2006 , , 366 , 358 cuadra , j. , nayakshin , s. & martins , f.  2008 , , 383 , 458 field , g.b . , goldsmith , d.w . & habing , h.j . 1969 , , 155 , l49 genzel , r. et al . 2003 , , 594 , 812 genzel , r. , eisenhauer , f. & gillessen , s.  2010 , _ reviews of modern physics _ , 82 , 3121 ghez , a.m. , salim , s. , hornstein , s.d . , tanner , a. , lu , j.r . , morris , m. , becklin , e.e . & duchne , g.  2005 , , 620 , 744 ghez , a.m. , et al . 2008 , , 689 , 1044 gillessen , s. , et al . 2009 , , 692 , 1075 gillessen , s. , et al . 2012 , , in press gltekin , k. , et al . 2009 , , 698 , 198 hall , d.n.b . , kleinmann , s.g . & scoville , n.z . 1982 , , 260 , l53 hawley , j.f . & balbus , s.a . 2002 , , 573 , 738 heckman , t.m . , kauffman , g. , brinchmann , j. , charlot , s. , tremonti , c. & white , s.d.m . 2004 , , 613 , 109 hobbs , a. & nayakshin , s.  2009 , , 394 , 191 johnson , b.m . & quataert , e.  2007 , , 660 , 1273 king , a.r . & pringle , j.e . 2007 , , 377 , l25 klein , r.i . , mckee , c.f . & colella , p.  1994 , , 420 , 213 kormendy , j. , bender , r. & cornell , m.e . 2011 , , 469 , 7330 koyama , k. et al . 1996 , , 48 , 249 koyama , k. , senda , a. , murakami , h. & maeda , y.  2003 , chjas , 3 , 297 koyama , k. et al . 2009 , , 61 , 255 krabbe , a. , genzel , r. , drapatz , s. & rotaciuc , v.  1991 , , 382 , l19 loeb , a.  2004 , , 350 , 725 marrone , d.p . , moran , j.m . , zhao , j .- h . & rao , r.  2007 , , 654 , l57 martins , f. , genzel , r. , hillier , d.j . , eisenhauer , f. , paumard , t. , gillessen , s. , ott , t. & trippe , s.  2007 , , 468 , 233 melia , f.  1992 , , 387 , l25 mignone , a. et al . 2007 , , 170 , 228 murray , s.d . & lin , d.n.c . 2004 , , 615 , 586 murray - clay , r.a . & loeb , a.  2012 , astro - ph/1112.4822 najarro , f. et al . 1997 , , 325 , 700 narayan , r. & yi , i.  1994 , , 428 , l13 narayan , r.  2002 , in lighthouses of the universe , ed . m. gilfanov et al . 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{"article_id":"astro-ph0211421","section_id":"i","document":"the x - ray emission from radio - quiet active galactic nuclei ( agn ) shows persistent variability that is stronger and more rapid than in any other waveband . this rapid x - ray variability provided early support for the black hole / accretion disc model of agn ( e.g. rees 1984 ) and suggested that the x - ray emission is produced in the inner regions of the central engine ( see mushotzky , done & pounds 1993 for a review ) . the x - ray fluctuations appear erratic and random , with variability occurring on a range of timescales ( e.g. m@xmath3hardy 1989 ) .    in the study of time - variable processes one of the most widely used statistical tools is the variability power spectrum ( e.g. priestley 1981 ; bloomfield 2000 ) . the power spectral density ( psd ) describes the amount of variability power ( i.e. amplitude@xmath7 ) as a function of temporal frequency ( timescale@xmath8 ) . the long , uninterrupted observations provided by  allowed for the measurement of the first accurate x - ray psds for seyfert 1 galaxies . these  psds were shown to rise at lower frequencies as a power - law : @xmath9 , where @xmath10 is the power at frequency @xmath11 and @xmath12 is the psd slope , found to be @xmath13 over the frequencies @xmath14 to @xmath15  hz ( green , m@xmath3hardy & lehto 1993 ; lawrence & papadakis 1993 ) . this type of broad - band variability , rising to lower frequencies with a power spectral slope @xmath16 , is usually called `` red noise '' ( for an introduction to red noise in astronomy and elsewhere see press 1978 ) . the red noise psds of seyfert 1s are similar to those observed in galactic black hole candidates ( gbhcs , see e.g. van der klis 1995 ) on much shorter timescales , and suggests the x - ray emission mechanisms may be the same in these objects that differ in black hole mass by factors of @xmath17 ( m@xmath3hardy 1989 ) . the psd of the best studied gbhc , cygnus x-1 in its low / hard state , can be approximated by a doubly - broken power - law with a steep slope at high frequencies ( @xmath18 above @xmath19  hz ) , breaking to a flatter slope at intermediate frequencies ( @xmath1 in the range @xmath20  hz ) then breaking to a flat ( `` white '' ) spectrum at low frequencies ( @xmath21 below @xmath22  hz ) . see nowak ( 1999a ) and belloni & hasinger ( 1990 ) for more details of cyg x-1 . other gbhcs such as gx 3394 show similar behaviour ( nowak , wilms & dove 2002 ) . the position of the breaks in the psd represent `` characteristic timescales '' of the system , but these timescales have no clear physical interpretation at present ( e.g. belloni , psaltis & van der klis 2002 and references therein ) . the featureless  psds of seyfert 1s provided no such timescales . such breaks must exist , however , or the total power would diverge at low frequencies ( for psd slopes @xmath23 ) . indeed , in recent years dedicated x - ray monitoring programmes with  have revealed deviations from the power - law psd in a few seyfert 1 galaxies ; at low frequencies the psd breaks to a flatter slope ( edelson & nandra 1999 ; uttley , m@xmath3hardy & papadakis 2002 ; markowitz 2002 ) . the timescale of this break frequency is consistent with the idea that the psd of agn and gbhcs are essentially the same , with the characteristic timescales scaling linearly with the black hole mass . such a linear scaling of timescales with black hole mass might be expected if the characteristic timescales are related to e.g. a light - crossing timescale or an orbital timescale . this linear scaling also means that a 100  ks light curve of a seyfert galaxy ( such as presented here ) is comparable to a @xmath24  s light curve of cyg x-1 . on these timescales a bright seyfert 1 galaxy provides many more photons ( by more than two orders of magnitude ) than the gbhc , i.e. seyferts have a higher count rate per characteristic timescale . this means that intensive monitoring of seyferts can provide a view of the very high frequency variations in accreting black holes that is difficult to access even in bright gbhcs . not only do agn and gbhcs show similar psds , but they display other striking similarities in their x - ray timing properties . uttley & m@xmath3hardy ( 2001 ) showed that both x - ray binary and agn light curves show a tight , linear correlation between flux and rms variability amplitude ( see also edelson 2002 ) . the variability properties of gbhcs such as cyg x-1 are a function of photon energy . the psd shape above the high frequency break is energy - dependent , with the harder energy bands showing flatter psd slopes ( e.g. nowak 1999a ; lin 2000 ) . in addition the variations between different bands are highly coherent ( well correlated at each fourier frequency ) and show time delays , with variations at softer energies leading those at harder energies ( miyamoto & kitamoto 1989 ; cui 1997 ; nowak 1999a ) . the magnitude of the time delay is frequency dependent , with the delay increasing at lower frequencies . to date these properties have only been measured in one agn , ngc 7469 ( nandra & papadakis 2001 ; papadakis , nandra & kazanas 2001 ) , and in this object the energy - dependence of the psd slope , the coherence and time delay properties appeared remarkably similar to those seen in cyg x-1 . these similarities re - enforce the idea that the x - ray emission mechanisms are the same in gbhcs and agn . this paper presents a detailed analysis of the x - ray continuum variability of the bright , variable seyfert 1 galaxy ( @xmath25 ) using a long  observation . the large collecting area , wide band - pass and long orbit ( @xmath26 day ) of  make it ideal for examining the high frequency ( @xmath27  hz ) timing properties of seyfert galaxies . the analysis concentrates on frequency domain ( i.e. fourier ) time series analysis techniques , as these are used extensively in the analysis of gbhc data . the rest of this paper is organised as follows . in section  [ sect : data ] the data reduction procedures are outlined . in section  [ sect : timing ] the basic properties of the light curves are discussed , followed by an analysis of the psd in section  [ sect : pds ] . spectral variability is then examined in detail by measuring the coherence and time lags between different energy bands , as discussed in section  [ sect : cross ] . as these analyses are relatively new to agn studies we discuss the methodology in some detail . finally , the implications of these results are discussed in section  [ sect : disco ] and some concluding remarks are given in section  [ sect : conc ] .","summary":"this paper presents a comprehensive examination of the x - ray continuum variability of the bright seyfert 1 galaxy . the magnitude of the lag is small (  s for the frequencies observed ) and is most likely frequency dependent . these properties are remarkably similar to the temporal properties of the galactic black hole candidate cygnus x-1 .","abstract":"this paper presents a comprehensive examination of the x - ray continuum variability of the bright seyfert 1 galaxy . the source clearly shows the strong , linear correlation between rms variability amplitude and flux first seen in galactic x - ray binaries . the high frequency power spectral density ( psd ) of  is examined in detail using a monte carlo fitting procedure and is found to be well represented by a steep power - law at high frequencies ( with a power - law index ) , breaking to a flatter slope ( ) below  hz , consistent with the previous results of uttley , mhardy & papadakis . the slope of the power spectrum above the break is energy dependent , with the higher energies showing a flatter psd . at low frequencies the variations between different energy bands are highly coherent while at high frequencies the coherence is significantly reduced . time lags are detected between energy bands , with the soft variations leading the hard . the magnitude of the lag is small (  s for the frequencies observed ) and is most likely frequency dependent . these properties are remarkably similar to the temporal properties of the galactic black hole candidate cygnus x-1 . the characteristic timescales in these two types of source differ by ; assuming that these timescales scale linearly with black hole mass then suggests a black hole mass  for . we speculate that the timing properties of  may be analogous to those of cyg x-1 in its high / soft state and discuss a simple phenomenological model , originally developed to explain the timing properties of cyg x-1 , that can explain many of the observed properties of .    [ firstpage ]    galaxies : active  galaxies : seyfert : general  galaxies : individual :   x - ray : galaxies"}
{"article_id":"astro-ph0211421","section_id":"c","document":"this paper presents an analysis of the x - ray continuum variability of . a strong , linear correlation is found between the rms variability amplitude and the source flux ( section  [ sect : rms - flux ] ) . the psd was examined by fitting model power spectra to the data after allowing for the distorting effects of sampling using a monte carlo procedure ( section  [ sect : pds ] ) . however , the excellent sampling of the light curves means that these biases are in any case minimised and so there was a minimum of information lost from the psd . the psd is well represented by a power - law of slope @xmath100 at low frequencies , breaking to a slope of @xmath101 at a frequency @xmath102  hz . however , it should be re - iterated that these psd results are model - dependent , and that parameterising the psd using a different model yields slightly different results . the psd is energy dependent , with the variations in the higher energy band showing a flatter psd slope ( above the break frequency ) than variations in the softer bands . there is no evidence for any energy dependence of the break frequency . [ fig : unfolded ] illustrates the psd shape and energy dependence . fitting the psd as a function of energy revealed tentative hints of energy - dependent , high - frequency structure in the psd ( section  [ sect : e - psd ] ) . this could be due to subtle instrument effects or may represent low - amplitude structure intrinsic to the source psd ( see also nandra & papadakis 2001 ) . these timescales ( @xmath103  hz ) are comparable to the dynamical timescale at innermost stable orbit around the black hole . however , further progress on the very high frequency variability of relatively faint sources such as seyfert galaxies must await future high - throughput missions such as  and . the variations observed in different energy sub - bands are highly coherent at low frequencies ( long timescales ) but the coherence falls significantly below unity above @xmath96few @xmath95  hz , close to the break in the psd ( section  [ sect : coherence ] ) . the high coherence between soft and hard bands at low frequencies means that the two bands are linked by a single , linear transfer function . the direction and magnitude of the time lag shows that the hard photons lag the soft photons , on average , by @xmath104  s at a frequency @xmath105  hz ( section  [ sect : phase ] ) . it is not possible to reliably constrain the frequency dependence of the time lags , but the data seem consistent with an approximately @xmath106 dependence of the lag ( i.e. constant phase difference @xmath107 ) similar to that seen in the seyfert galaxy ngc 7469 ( papadakis 2001 ) and in gbhcs ( nowak 1999a ; pottschmidt 2000 ) . on shorter timescales the coherence falls well below unity implying there is no simple transfer function relating soft and hard bands . uttley ( 2002 ) presented an analysis of long timescale monitoring of  using . the psd was found to be best described by a broken power - law with slope of @xmath108 at low frequencies , breaking to @xmath109 at a frequency @xmath110  hz . using the same psd model , the break frequency found from the high - frequency  data is @xmath111  hz , consistent with the  result . the slope of the psd above the break is different , but this is most likely an effect of the energy dependence of the psd . indeed , using the 210  kev  data ( i.e. the same energy range used by uttley 2002 ) the slope of the high frequency psd is @xmath112 , which is consistent with the  result . the break frequency presented here ( and in uttley 2002 ) is model dependent . this is because a model psd had to be assumed and fitted to the data to derive the appropriate parameters . however , the broken power - law model ( with a break to @xmath108 at low frequencies ) provides consistent results when applied to the long timescale  monitoring and the short timescale  observation . this , and the similarity of the observed psd to those of gbhcs ( see section  [ sect : comparison ] ) suggests that the chosen model ( and therefore the derived break frequency ) is reasonable . nowak & chiang ( 2000 ) used  and  data to measure the psd of . they found the psd to break from @xmath21 to @xmath1 at a frequency @xmath14  hz and then break again to @xmath18 in the range @xmath113  hz , the position of the high frequency break , as well as the psd slopes , are roughly consistent with those found from the  data . however , as noted by uttley ( 2002 ) , the method employed by nowak & chiang ( 2000 ) did not account for distorting effects of sampling ( see section  [ sect : bias ] ) and underestimated the errors at low frequencies . once these effects are included the low - frequency flattening found by is no longer significant ( section  6.2 of uttley 2002 ) . nowak & chiang ( 2000 ) also place a limit on any time delay between soft ( 0.52.0  kev ) and hard ( 815  kev ) bands of @xmath114  s , consistent with the time lag results presented here .    hayashida ( 1998 ) also estimated the psd of , this time using  data . they found a broken power - law to be a good fit to the data . however , these authors also did not account for the biases in the periodogram , which will be significant due to the patchy sampling of the  light curves . the unusually flat low - frequency slope ( @xmath115 ) found by these authors is most likely a result of bias in the low - frequency periodogram , and therefore the position of their claimed break frequency should be considered with some caution . the only other agn for which detailed cross spectral analysis has been performed is ngc 7469 ( nandra & papadakis 2001 ; papadakis 2001 ) . in this object the psd does not show any significant breaks , but does show the same energy dependence as found in . the present analysis shows that the energy dependence of the psd is due to the slope of the psd becoming flatter at higher energies , rather than a change in the break frequency . in addition , ngc 7469 shows time lags between energy bands in the same direction ( soft leading hard ) and with the similar relative magnitude ( @xmath97 per cent ) as in . papadakis & lawrence ( 1995 ) showed that in ngc  4051 the harder band showed a flatter psd than the softer band . recently , m@xmath3hardy ( in prep . ) used  data of ngc 4051 and also found this energy dependence of the pds .      since  first showed the medium timescale psds of seyfert galaxies to have a power - law form , their timing properties have been compared to those of gbhcs . now , with long timescale monitoring available from  ( edelson & nandra 1999 ; nandra & papadakis 2001 ; uttley 2002 ) and short timescale observations possible with  ( this paper ) it is possible to re - assess this comparison . the best studied gbhc , cyg x-1 , when in its low / hard state shows a psd with an approximately broken power - law form . the psd breaks from a low frequency slope of @xmath21 to @xmath1 and then to @xmath18 at high frequencies . the position of the high frequency break is typically @xmath116  hz ( belloni & hasinger 1990 ; nowak 1999a ) . the comparable break in the psd of  occurs at @xmath102  hz . this suggests the characteristic timescales in these two systems differ by a factor @xmath117 . under the assumption that the timescales scale linearly with mass of the central black hole , and assuming cyg x-1 to contain a @xmath118  black hole ( herrero 1995 ) , then suggests the mass of the black hole in  is @xmath119  ( in the range 1.55.0 @xmath120  using the 90 per cent limits on the break frequency in ) . assuming a bolometric luminosity of @xmath121  erg s@xmath8 for  ( reynolds 1997 ; converting to @xmath122  km s@xmath8 mpc@xmath8 ) then implies that is radiating at the eddington luminosity . however , since independent mass estimates ( such as from reverberation mapping ) are not available for  it remains possible that this mass estimate is inaccurate if the relevant timescales do not scale linearly with black hole mass ( as assumed above ) . if the frequency of the psd break is related to the orbital frequency of matter close to where the peak emissivity of the accretion disc occurs , @xmath123 , then it will depend on @xmath124 , where @xmath125 is the inner radius of the disc . for a standard disc , @xmath126 . this will also introduce a dependence on @xmath127 ( where @xmath128 is the gravitational radius of the black hole ) and thus the spin parameter of the black hole @xmath129 . if the black hole in  has a higher spin parameter than that in cyg x-1 then the mass deduced from the above scaling could be increased . the other temporal characteristics seen in  are remarkably similar to those observed in cyg x-1 , implying there is indeed a strong connection between these two types of source . the psd ( above the break frequency ) is flatter in harder energy bands in both and cyg x-1 ( nowak 1999a ; lin 2000 ) . the strong rms - flux correlation first seen in x - ray binaries ( uttley & m@xmath130hardy 2001 ) is exhibited by  ( see section  [ sect : rms - flux ] ) .  also displays a loss of coherence between hard and soft bands at high temporal frequencies ( i.e. above the break in the psd ) very similar to that seen in cyg x-1 ( nowak 1999a ) and time lags between these bands that appear similar ( in direction and relative magnitude ) to those observed in cyg x-1 . in particular , the time lags measured in  between soft and hard bands is @xmath98  s in the lowest frequency bin , where the coherence is near unity . in cyg x-1 the shortest time lags observed are @xmath131  s ( nowak 1999a ; pottschmidt 2000 ) at frequencies just below where the coherence falls significantly below unity . the ratio of these two time lags is @xmath5 , similar to the ratio between the psd break timescales . it should also be noted that it is not yet clear whether seyfert galaxies more closely resemble the low / hard or high / soft states of gbhcs ( see also the discussion in uttley 2002 ) . in the high / soft state the psd of cyg x-1 is steep at high frequencies ( @xmath132 ) and flattens to @xmath1 at @xmath133  hz , with no further flattening evident at lower frequencies ( cui 1997 ; churazov & gilfanov & revnivtsev 2001 ; reig , papadakis & kylafis 2002 ) . this ratio of characteristic timescales in this case is @xmath134 and the corresponding mass estimate for  is @xmath135  , implying a luminosity @xmath136 per cent of the eddington limit . this high ( but nevertheless sub - eddington ) accretion rate might be expected if  is indeed in a state similar to the high / soft state seen in cyg x-1 . it is interesting to note that the best - fitting linear model to the rms - flux correlation observed in  is consistent with passing through the zero - flux origin ( section  [ sect : rms - flux ] ) . the simplest explanation of this is if there is no significant constant component to the light curve . a strong constant component ( @xmath137 per cent of the source flux ) is observed from the rms - flux correlation in cyg x-1 ( uttley & m@xmath3hardy 2001 ) , but only when the source is in the low / hard state ( gleissner 2002 ) . this is perhaps also indicating that the variability properties of  are more similar to the high / soft state than the low / hard state of cyg x-1 . ( the time delay properties of cyg x-1 when in its high / soft state are rather similar to those seen in its low / hard state , see e.g. pottschmidt 2000 ) . the x - ray emission mechanism operating in seyfert galaxies is usually thought to be inverse - compton scattering of soft photons in a hot corona ( e.g. sunyaev & titarchuk 1980 ; haardt & maraschi 1991 ) . in the simplest models the harder photons are expected to lag behind the softer photons due to the larger number of scatterings required to produce harder photons , and the delay should be of order the light - crossing time of the corona . the longest observed time delay in  between soft and hard bands is @xmath98  s. assuming a black hole mass of @xmath138  , this lag corresponds to a light - crossing distance of @xmath139 ( @xmath140 ) . thus the direction and magnitude of the observed lag in  are consistent with an origin in a comptonising corona . however , if the lags are frequency dependent ( as expected by analogy with cyg x-1 and also seen in ngc  7469 ; papadakis 2001 ) the lags at lower temporal frequencies would become much longer than expected for a compact corona ( see discussion in nowak 1999b ) . indeed , the simplest such models predict the time delay between soft and hard photons to be independent of fourier frequency ( miyamoto 1988 ) , contrary to what is observed . in addition , some models of compton scattering coronae predict the high frequency psd should be steeper for higher energy photons , due to the high - frequency fluctuations being washed out by multiple scatterings ( hua & titarchuk 1996 ; nowak & vaughan 1996 ) , again contrary to the observations .    alternatively , the time delay between soft and hard bands could be due to the spectral evolution of individual x - ray events . if the spectrum of the event becomes harder as the event unfolds this can lead to an average lag between soft and hard bands . such models have been discussed by bttcher & liang ( 1998 ) and poutanen & fabian ( 1999 ) . another alternative is that the delay between soft and hard bands could be due to a propagation effect , i.e. a `` trigger '' signal reaching the soft emission region before the hard emission region . in this scenario the magnitude of the lag is related to the propagation speed and the distance between soft and hard emission regions . the following section describes a model based on this kind of signal propagation .    at higher temporal frequencies the coherence falls well below unity , meaning there is no longer a simple transfer function between the soft and hard band emission . as a static corona should maintain a transfer function ( whatever the physical mechanism ) , on timescales longer than the break in the psd ( @xmath141  s ) , where the coherence is high , the corona may be effectively static ( i.e. it maintains its average properties on these timescales ) . on shorter timescales the corona may be dynamic and so the steep psd above the break and the loss of coherence may be due to changes in the corona itself . the timescale of the break in the psd from @xmath142 to a steeper slope is @xmath143  s , which corresponds to a light - crossing distance of @xmath144 . the orbital timescale at @xmath145 around a @xmath138  black hole is @xmath146  s , while the thermal timescale for a standard , thin accretion disc is @xmath147  s ( assuming a viscosity parameter @xmath148 ) , which is of the same order as the timescale of the break in the psd . the viscous timescale in such a disc is many orders of magnitude larger than these other timescales ( see the discussion of accretion disc timescales in section 5.8 of frank , king & raine 1985 ) . however , if that part of the accretion flow responsible for modulating the x - ray emission is geometrically thick , the break in the psd could correspond to a viscous timescale ( which depends on the ratio of disc height @xmath149 to radius @xmath150 as @xmath151 ) . various models have been considered to explain the variability of gbhcs and seyfert galaxies . these include : various examples of `` shot noise '' ( e.g. terrell 1972 ; lehto 1989 ; merloni & fabian 2001 ) ; rotating `` hot spots '' on the surface of an accretion disc ( abramowicz 1991 ; abramowicz 1992 ; bao & stgaard 1995 ) ; occultation by moving clouds ( abrassart & czerny 2000 ) ; self - organised criticality in an accretion disc ( mineshige , ouchi & nishimori 1994 ) ; fluctuations in the accretion rate propagating through the disc ( lyubarskii 1997 ; churazov 2001 ; kotov , churazov & gilfanov 2001 ) and magnetohydrodynamic instabilities in the inner accretion disc ( hawley & krolik 2001 ) . most of these models were developed to explain only one aspect of the variations ( e.g. its red noise nature ) . now , however , it is possible to compare the predictions of these models with the well - determined timing properties of . a viable physical model has to be able to reproduce not only the correct psd shape and timescales but also the other temporal characteristics such as the rms - flux correlation , the energy dependence of the psd , the time lags and the coherence . it is not clear whether any of the above mechanism can explain all the observations , and indeed some models ( e.g. the obscuration model of abrassart & czerny 2000 ) seem to offer little hope of explaining properties such as the coherence and time lags . a simple phenomenological model has been developed by lyubarskii ( 1997 ) , churazov ( 2001 ) , and kotov ( 2001 ) that seems to explain ( qualitatively , at least ) the temporal properties of cyg x-1 . as the timing properties of  discussed above are very similar to those of cyg x-1 , it is worth discussing this model as a possible explanation for the behaviour of seyfert galaxies .    in its high / soft state , cyg x-1 shows a @xmath142 psd over several decades in frequency ( cui 1997 ; churazov 2001 ; reig 2002 ) , down to timescales far longer than would normally be associated with the x - ray emitting region itself ( which is assumed to be compact ) . the model put forward by lyubarskii ( 1997 ) to explain this very broad range in timescale has variations in accretion rate occurring over a large range of radii from the central black hole and propagating in towards the x - ray emitting region ( assumed to extend over only a few tens of gravitational radii ) . if the viscosity parameter of the accretion flow is varying randomly and with the same amplitude at all radii , variations in mass accretion rate at much smaller radii will have an @xmath142 psd . the accretion rate at the x - ray emitting region ( assumed to be concentrated at small radii ) is thus being modulated by variations produced over a large range in radius . if the x - ray emission emerging from this region is proportional to the local accretion rate then the x - ray variations will also have an @xmath142 psd extending down to low frequencies . each radius produces variations at a characteristic timescale comparable to the timescale for inward propagation , hence long - timescale fluctuations are produced at large radii and shorter - timescale fluctuations are produced closer in . this works because any variations on timescales shorter than the propagation timescale are damped as they move through the disc ( see lyubarskii 1997 , and churazov 2001 ) . this naturally explains both the @xmath142 part of the psd ( i.e. below the high frequency break ; churazov 2001 ) and the rms - flux correlation ( uttley & m@xmath130hardy 2001 ) . once these variations reach the inner regions , where accretion energy is released as x - ray emission , variations on shorter timescales are further suppressed , leading to a steepening of the psd . thus the high frequency break in the psd from @xmath142 to a steeper slope ( as seen in ) is due to suppression of fluctuations within the x - ray emitting region , and the timescale of the break in the psd corresponds to the characteristic timescale at the outer radius of the x - ray emitting region ( churazov 2001 ) . the emissivity as a function of radius defines a green s function for the incoming @xmath142 fluctuations . in frequency terms , the radial extent of the x - ray producing region makes it act as a `` low - pass filter '' for the incident @xmath142 fluctuations , resulting in a break in the psd , to a steeper slope , at high frequencies . the specific model described by churazov ( 2001 ) has a relatively stable , optically thick , geometrically thin accretion disc sandwiched by an optically thin , geometrically thick corona . the disc produces relatively slowly varying thermal emission ( which would emerge presumably in the optical / ultraviolet for a seyfert galaxy ) while it is the variations within the corona that propagate inwards to produce the x - ray variability . the timescale of the high frequency break thus corresponds to the accretion timescale ( @xmath96the viscous timescale ) of the geometrically thick corona at the outer edge of the x - ray emitting region . kotov ( 2001 ) extended this model by adding the simple condition that the spectrum of the x - ray emitting region is a function of radius , with the outer regions producing a softer spectrum than the inner regions . this model can then reproduce the observed time lags between soft and hard emission . accretion rate variations propagating inwards reach the softer emitting region ( larger radii ) before the harder emitting region ( smaller radii ) , explaining why the soft emission leads the hard . this can explain the energy dependence of the time lags ( as delay increases with the separation between energy bands ) as well as the frequency dependence ( since different radii correspond to different characteristic frequencies as well as different energy spectra ) . in addition , this model explains the energy dependence of the psd above the high frequency break . the harder emission is produced from smaller radii , which can be modulated by high frequency fluctuations , hence the harder emission will have more high frequency power than the softer emission ( i.e. the hard band psd will be flatter ) , as observed ( see fig . [ fig : unfolded ] ) . also , as the variations on short timescales are occurring within the x - ray emitting region , i.e. are a result of the dynamic corona , the coherence between bands will fall off at high frequencies , as mentioned in section  [ sect : physics ] ( see also the discussion in nandra & papadakis 2001 ) . such phenomenological models require that variations occurring at large radii can be fed into much smaller radii and so influence the psd . the observed iron line profile of  from this observation ( fabian 2002 ) indicates that the disc extends down to less than @xmath152 , and , from the steep inferred emissivity profile , that much of the x - ray power is generated very close to the black hole . this presents a challenge for all such models , given that the dynamical timescale of this innermost region is @xmath118@xmath153  s , whereas the timescales measured ( e.g. the psd break timescale ) are orders of magnitude longer . if the @xmath142 psd of  is similar to that in the high / soft state of cyg x-1 ( reig 2002 ) then the variability timescales will extend to many orders of magnitude longer still . indeed , the total power in @xmath142 spectra diverges so slowly that the psd could in principle continue as @xmath142 until very low frequencies without the total power becoming large . ( for example , model 2 from section  [ sect : pds_results ] could continue down to the unphysically low frequency @xmath154  hz without the integrated power exceeding @xmath155 ! )","summary":"the source clearly shows the strong , linear correlation between rms variability amplitude and flux first seen in galactic x - ray binaries . the high frequency power spectral density ( psd ) of  is examined in detail using a monte carlo fitting procedure and is found to be well represented by a steep power - law at high frequencies ( with a power - law index ) , breaking to a flatter slope ( ) below  hz , consistent with the previous results of uttley , mhardy & papadakis . the slope of the power spectrum above the break is energy dependent , with the higher energies showing a flatter psd . at low frequencies the variations between different energy bands are highly coherent while at high frequencies the coherence is significantly reduced . time lags are detected between energy bands , with the soft variations leading the hard . the characteristic timescales in these two types of source differ by ; assuming that these timescales scale linearly with black hole mass then suggests a black hole mass  for . we speculate that the timing properties of  may be analogous to those of cyg x-1 in its high / soft state and discuss a simple phenomenological model , originally developed to explain the timing properties of cyg x-1 , that can explain many of the observed properties of .    [ firstpage ]    galaxies : active  galaxies : seyfert : general  galaxies : individual :   x - ray : galaxies","abstract":"this paper presents a comprehensive examination of the x - ray continuum variability of the bright seyfert 1 galaxy . the source clearly shows the strong , linear correlation between rms variability amplitude and flux first seen in galactic x - ray binaries . the high frequency power spectral density ( psd ) of  is examined in detail using a monte carlo fitting procedure and is found to be well represented by a steep power - law at high frequencies ( with a power - law index ) , breaking to a flatter slope ( ) below  hz , consistent with the previous results of uttley , mhardy & papadakis . the slope of the power spectrum above the break is energy dependent , with the higher energies showing a flatter psd . at low frequencies the variations between different energy bands are highly coherent while at high frequencies the coherence is significantly reduced . time lags are detected between energy bands , with the soft variations leading the hard . the magnitude of the lag is small (  s for the frequencies observed ) and is most likely frequency dependent . these properties are remarkably similar to the temporal properties of the galactic black hole candidate cygnus x-1 . the characteristic timescales in these two types of source differ by ; assuming that these timescales scale linearly with black hole mass then suggests a black hole mass  for . we speculate that the timing properties of  may be analogous to those of cyg x-1 in its high / soft state and discuss a simple phenomenological model , originally developed to explain the timing properties of cyg x-1 , that can explain many of the observed properties of .    [ firstpage ]    galaxies : active  galaxies : seyfert : general  galaxies : individual :   x - ray : galaxies"}
{"article_id":"1510.09129","section_id":"i","document":"the first paper about a universal cellular automaton in the pentagrid , the tessellation @xmath0 of the hyperbolic plane , was @xcite . this cellular automaton was also rotation invariant , at each step of the computation , the set of non quiescent states had infinitely many cycles : we shall say that it is a truly planar cellular automaton . but , the neighbourhood was _  la von neumann _ and it had 22  states . this result was improved by a cellular automaton with 9  states in  @xcite . recently , i improved this result with 5  states , see  @xcite . a bit later , i proved that in the heptagrid , the tessellation @xmath1 of the hyperbolic plane , there is a weakly universal cellular automaton with three states which is rotation invariant and which is truly planar , @xcite . in a paper under printing , see  @xcite , i proved that there is such a cellular automaton in the tessellation @xmath2 of the hyperbolic plane .    in the heptagrid and in the tessellation @xmath2 , there is no difference between a von neumann neighbourhood and a moore neighbourhood . in both case , a cell has 7  immediate neighbours in the heptagrid and 11  of them in the tessellation @xmath2 : a neighbour which shares a vertex also shares an edge . the reason lies in the interior angle of the basic polygons : it is @xmath3 in both cases . in the pentagrid , the situation is different because the interior angle is a right angle . in the pentagrid , a cell has five neighbours which share an edge with it , and it also have five new neighbours which only share a vertex with it . in the euclidean plane , there is a difference between cellular automaton with von neumann or moore neighbourhoods . remember that the game of life cellular automaton requires moore neighbourhoods . and so the question was , to which point is it possible to reduce the number of states for a weakly universal , rotation invariant and truly planar cellular automaton in the pentagrid if we allow moore neighbourhoods ? this time we have ten neighbours , more than the seven neighbours in the heptagrid , but less than the eleven ones in the tessellation @xmath2 . but we have the inconvenience of the right angle and we also have a slight advantage : we have ten neighbours but only five admissible rotations . indeed , rotating the sides induces a similar rotation on the vertices and conversely . in fact , i could prove the following result , which is stated in the abstract :    [ letheo ] there is a weakly universal cellular automaton on the pentagrid with moore neighbourhoods which is rotation invariant , truly planar and which has three states . the paper is devoted to the proof of the theorem . the minimal introduction to hyperbolic geometry needed to understand the paper can be found in  @xcite . in order to understand the constructions of the paper , it is important to remember that in the pentagrid , there are lines of the hyperbolic plane that we call * lines of the pentagrid * because they support the sides of infinitely many pentagons which pairwise share a side which is orthogonal to that line . such a situation is trivial in the euclidean plane with a grid made of squares . the difference , here is that two lines of the pentagrid may be both perpendicular to the same side of a pentagon , but they are not parallel at all : they go in different directions , on both sides of the considered edge . we shall use the fact that the tiling is generated by a tree , see  @xcite , without further explanation .    in section  [ hyprailway ] , we sketchily remind the reader the model which is simulated by our cellular automaton . in section  [ scenar ] , we describe how we implement the model on order to observe the constraints of the three states . in section  [ rules ] , we give the rules of the automaton , together with the figures illustrating the motion of the device performing the computation of the automaton . that section will complete the proof of theorem  [ letheo ] .","summary":"in this paper , we prove that there is a weakly universal cellular automaton on the pentagrid with three states which is rotation invariant and which uses _  la moore _ neighbourhood . moreover , at each step of the computation , the set of non quiescent states has always infinitely many cycles .","abstract":"in this paper , we prove that there is a weakly universal cellular automaton on the pentagrid with three states which is rotation invariant and which uses _  la moore _ neighbourhood . moreover , at each step of the computation , the set of non quiescent states has always infinitely many cycles ."}
{"article_id":"1110.3976","section_id":"i","document":"one of theoretical problems of the standard model ( sm ) is that it does not describe gravitational interaction in a renormalizable form . string theory is a strong candidate for a theory of quantum gravity . there is another theoretical problem so - called hierarchy problem . if the fundamental energy scale of gravitational interaction , _ i.e. _ , the planck scale , is considered as a fundamental scale of the sm , a large hierarchy between the planck scale @xmath6 and the weak scale @xmath7 can not be understood . it is proposed that the string scale @xmath8 which is the fundamental scale in string theory could be much lower than the planck scale due to the existence of _ large extra dimensions _ this is a solution to the hierarchy problem in the framework of string theory with the string scale @xmath9 . such string models with the low string scale are called _ low - scale string models _ ( for review , see ref.@xcite ) .    in low - scale string models , the planck scale is described as @xmath10 where @xmath11 is string coupling and @xmath12 is the volume of six - dimensional compactified space . note that closed strings which mediate gravitational interaction propagate in whole ten - dimensional space - time . if it is assumed that @xmath11 is small for perturbative theory , @xmath13 is required with @xmath9 . imagine a d@xmath14-brane whose @xmath14-dimensional space contains our three - dimensional space . open strings on the d@xmath14-brane give gauge symmetry , and the gauge coupling constant in our four - dimensional space - time is given by @xmath15 where @xmath16 is the volume of @xmath17-dimensional compactified space parallel to the d@xmath14-brane . for appropriately large gauge coupling , @xmath16 should not be very large : @xmath18 . with the above condition for large @xmath19 , the volume of @xmath20-dimensional compactified space , @xmath21 , should be large as much as @xmath22 , because @xmath23 . gravity escapes to large transverse directions to the d@xmath14-brane and the strength of gravity on the d@xmath14-brane becomes weak . it has been shown in ref.@xcite that this type of anisotropic compactification is possible in string theory . a gauge symmetry u@xmath24 is realized on a stack of @xmath25 d - branes . we consider models in which such stacks of d - branes relevant to the sm are localized in compactified space , _ i.e. _ ,  local models \" in ref.@xcite . we need , for example , four stacks of d - branes to realize u@xmath26u@xmath27u@xmath28u@xmath29 gauge symmetry . since u@xmath30 su@xmath31u@xmath32 , there is an u@xmath32 symmetry on each stack of d - branes . the massless modes of open strings on u@xmath33 branes are identified as gluons and an additional u@xmath34 gauge boson , and the massless modes of open strings on u@xmath35 branes are identified as weak bosons and an additional u@xmath36 gauge boson . the u@xmath37 gauge symmetry in the sm is an independent linear combination of four u@xmath32 symmetries . symmetries are usually  anomalous \" , and these gauge bosons are massive . ] the chiral matter for the sm is realized by open strings whose two ends attach on two different stacks of d - branes intersecting with each other @xcite . space of the intersection between the two different stacks contains our three - dimensional space and the open strings are localized on that space . for example , left - handed quark doublets @xmath38 are realized by the massless modes of open strings between u@xmath39 and u@xmath40 branes , right - handed up - type quarks @xmath41 are realized by the massless modes of open strings between u@xmath39 and u@xmath32 branes , and so on . in addition to the sm particles , there are many massive states :  string excited states \" as massive modes of open strings , kaluza - klein ( kk ) states of the sm particles and string excited states , and various closed string states .    in this paper , we explore a possibility to observe signatures of low - scale string models in dijet events at the lhc . as it is reviewed in the rest of this section , there are some model - independent features in parton two - body scattering amplitudes . we investigate dijet events including contributions of string models by monte carlo simulations . we concentrate on the following two distinct properties .    * a resonance in the dijet invariant mass distribution by  string excited states \" consists many degenerated states with various spins . an analysis of the dijet angular distribution at the resonance must be very important to have a signature of low - scale string models @xcite . * string @xmath42th excited states have masses of @xmath43 . a second resonance at a place @xmath44 times far from the place of the first resonance in the dijet invariant mass distribution , is a signature of low - scale string models .    in the rest of this section , we discuss the model independency of predictions to parton two - body scatterings at the lhc by low - scale string models @xcite . we begin with summarizing generally spectra of low - scale string models in four - dimensional space - time . the spectra of excited states of open strings can be understood from open - string two - body scattering amplitudes which are calculated by the world - sheet superconformal field theory in flat space - time . if we consider a d@xmath45-brane where the world volume coincides with our four dimensional space - time , the open - string amplitudes depend only on the string scale @xmath46 , group theoretical factor and gauge coupling constant , and do not depend on the details of model buildings such as the way of compactification and configuration of d - branes . string effects in the open - string two - body scattering amplitudes are described by  string form factors \" which are functions of the mandelstam variables @xmath47 , @xmath48 and @xmath49 ( with @xmath50 ) @xcite . a typical form of the form factor function is @xmath51 in a low - energy limit @xmath52 , the string effects disappear as @xmath53 , and the string amplitudes become equal to the sm amplitudes ( see appendix [ sec : amplitude_and_width ] for details ) . in case of a finite value for @xmath46 , the form factor function is expanded by a sum over infinite @xmath47-channel poles , @xmath54 this expansion is a good approximation , near each of @xmath42th pole @xmath55 . these poles correspond to string excited states which have masses @xmath43 . they are degenerated with different spins from @xmath56 to @xmath57 for each @xmath42th pole , where @xmath58 is an original spin of initial states in the two - body scattering processes . these string excited states are exchanged as virtual states in @xmath47-channel and are experimentally observed as resonances in these processes of the sm particles . signals by the string excited states at colliders were originally pointed out in ref.@xcite .    if open strings have momenta and windings around in the direction of extra dimensions with general d@xmath14-branes ( @xmath59 ) , kk modes and winding modes of open strings appear in our four - dimensional space - time . the masses and the ways to contribute to amplitudes of kk and winding modes depend on the details of the way of compactification . typical masses of quantized kk modes and winding modes are @xmath60 and @xmath61 , respectively . their masses approximate @xmath62 and they are different from the masses of @xmath42th string excited states , @xmath43 . since closed string states interact only at one - loop level with the sm particles due to open - closed string duality , we do not consider these states . black holes may also be produced because of the low string scale , namely , the low fundamental gravitational scale . however , since these produced black holes are expected to be evaporated by hawking radiation , they do not give contributions to dijet events . we do not consider black holes also . we concentrate on dijet events which are caused by parton two - body scattering processes at the lhc . since a target is the physics on resonances in the dijet invariant mass distribution , we may only discuss model independency of states which give @xmath47-channel poles in the scattering amplitudes . if momenta in the direction of extra dimensions are conserved at interaction vertices , states of kk modes ( winding modes ) can appear only in pair and do not contribute to @xmath47-channel poles . momenta in the direction transverse to d - branes are non - conserved and momenta in the direction parallel to d - branes are conserved . therefore , even if d - branes contain extra dimensions , there are no @xmath47-channel exchanges of single kk modes ( winding modes ) in scattering processes of open strings on the d - branes . in scattering processes of open strings connecting two different stacks of d - branes , however , there are @xmath47-channel exchanges of single kk modes ( winding modes ) due to non - conservation of momenta . diagram1.eps ( 45,15)@xmath63 ( 165,15)@xmath63 ( 285,15)@xmath63 ( 405,15)@xmath64    diagram2.eps ( 50,-5)@xmath65 ( 50,62)@xmath65    diagram3.eps ( 45,15)@xmath63 ( 170,15)@xmath65    the processes of @xmath66 , @xmath67 and @xmath68 are model independent . in these processes , only string excited states of gluons can contribute to @xmath47-channel poles as shown in fig.[fig:2-parton_scattering_process_model_independent ] , and kk modes ( winding modes ) of gluons can appear only in pair as shown in fig.[fig : kk_gluon_pair_exchange ] . the process of @xmath69 is also model independent with string excited states of quarks in @xmath47-channel as shown in fig.[fig:2-parton_scattering_process_model_independent ] , because momenta on the intersection plane where open strings of chiral fermions are localized are conserved . on the other hand , the process of @xmath70 is model dependent , since both of kk modes ( winding modes ) of gluons and gluon excitations are exchanged in @xmath47-channel as shown in fig.[fig:2-parton_scattering_process_model_dependent ] . fortunately , cross sections of this process are suppressed by the effect of parton distribution functions ( pdfs ) at the lhc as a proton - proton collider . we concentrate on the above model - independent processes at the lhc , and discuss leading string signals which do not depend on the details of model buildings .    in section [ sec:1st_resonance ] , the appearance of the resonance in the dijet invariant mass distribution due to first string excited states is reviewed . in section [ sec : angular_analysis ] , it is shown that spin degeneracy at the resonance can be observed by analyzing the dijet angular distribution . in section [ sec:2nd_resonance ] , it is shown that the second resonance can be observed at rather close to the first resonance in the dijet invariant mass distribution . in section [ sec : conclusion ] , we give a summary of our results and some discussions . some detailed properties of amplitudes and widths of first and second string excited states are summarized in appendix [ sec : amplitude_and_width ] .","summary":"we investigate a possibility to observe these evidences of low - scale string models by monte carlo simulations with a reference value of at . it is shown that spin degeneracy at the dijet resonance can be observed by looking the-distribution with integrated luminosity of . it is shown that the second resonance can be observed at rather close to the first resonance in the dijet invariant mass distribution with integrated luminosity of .","abstract":"low - scale string models , in which the string scale is of the order of tev with large extra dimensions , can solve the problems of scale hierarchy and non - renormalizable quantum gravity in the standard model . string excited states of the standard model particles are possibly observed as resonances in the dijet invariant mass distribution at the lhc . there are two properties to distinguish whether the resonances are due to low - scale string or some other  new physics \" . one is a characteristic angular distribution in dijet events at the resonance due to spin degeneracy of string excited states , and the other is an appearance of the second resonance at a characteristic mass of second string excited states . we investigate a possibility to observe these evidences of low - scale string models by monte carlo simulations with a reference value of at . it is shown that spin degeneracy at the dijet resonance can be observed by looking the-distribution with integrated luminosity of . it is shown that the second resonance can be observed at rather close to the first resonance in the dijet invariant mass distribution with integrated luminosity of . these are inevitable signatures of low - scale string models .    ut - komaba/11 - 10    * signatures of low - scale string models + at the lhc *    manami hashi and noriaki kitazawa    _ institute of physics , university of tokyo , + komaba 3 - 8 - 1 , meguro - ku , tokyo 153 - 8902 , japan + e - mail : hashi@hep1.c.u-tokyo.ac.jp_ +    _ department of physics , tokyo metropolitan university , + hachioji , tokyo 192 - 0397 , japan + e - mail : kitazawa@phys.se.tmu.ac.jp_"}
{"article_id":"1110.3976","section_id":"c","document":"we have investigated phenomenology of low - scale string models at the lhc . since in low - scale string models , the string scale @xmath185 is of the order of tev with large extra dimensions , it is expected some string excited states as well as kk states may be observed at the lhc . it has been known that parton two - body scattering processes at the lhc is highly model independent , namely independent from the way of compactification of extra dimensions , and processes with single kk state in @xmath47-channel are highly suppressed . therefore , dijet events at the lhc are that should be focused to observe string excited states . the string excited states appear as resonances in the dijet invariant mass distribution . since several string excited states with different spins are degenerated in mass of @xmath185 , dijet events on the resonance exhibit special angular distributions which are not realized in any other `` new physics '' with a single heavy state . we have investigated the @xmath3-distribution on the resonance by monte carlo simulations and shown that main contributions of two kinds of string excited states of quarks with spin @xmath108 and @xmath109 can be confirmed with 20 fb@xmath186 of integrated luminosity at @xmath2 .    another inevitable prediction of low - scale string models is emergence of a second resonance in the dijet invariant mass distribution due to second string excited states of quarks and gluons . a distinct property is the place of the second resonance , namely the mass of second string excited states . the masses should be @xmath187 which should be compared with that masses of second kk states is twice that of first kk states . we have shown by monte carlo simulations that the second resonance in the dijet invariant mass distribution due to second string excited states can be observed with 50 fb@xmath186 of integrated luminosity at @xmath2 . though these are necessary and inevitable signatures of low - scale string models , more information is necessary to establish low - scale string . for example , confirmation of special angular distributions of dijet events on the second resonance , and emergence of light anomalous u@xmath32 gauge bosons with special interactions related with anomalous structures ( though this is rather highly model dependent ) should be worth to investigate in future .","summary":"low - scale string models , in which the string scale is of the order of tev with large extra dimensions , can solve the problems of scale hierarchy and non - renormalizable quantum gravity in the standard model . there are two properties to distinguish whether the resonances are due to low - scale string or some other  new physics \" . these are inevitable signatures of low - scale string models .    ut - komaba/11 - 10    * signatures of low - scale string models + at the lhc *    manami hashi and noriaki kitazawa    _ institute of physics , university of tokyo , + komaba 3 - 8 - 1 , meguro - ku ,","abstract":"low - scale string models , in which the string scale is of the order of tev with large extra dimensions , can solve the problems of scale hierarchy and non - renormalizable quantum gravity in the standard model . string excited states of the standard model particles are possibly observed as resonances in the dijet invariant mass distribution at the lhc . there are two properties to distinguish whether the resonances are due to low - scale string or some other  new physics \" . one is a characteristic angular distribution in dijet events at the resonance due to spin degeneracy of string excited states , and the other is an appearance of the second resonance at a characteristic mass of second string excited states . we investigate a possibility to observe these evidences of low - scale string models by monte carlo simulations with a reference value of at . it is shown that spin degeneracy at the dijet resonance can be observed by looking the-distribution with integrated luminosity of . it is shown that the second resonance can be observed at rather close to the first resonance in the dijet invariant mass distribution with integrated luminosity of . these are inevitable signatures of low - scale string models .    ut - komaba/11 - 10    * signatures of low - scale string models + at the lhc *    manami hashi and noriaki kitazawa    _ institute of physics , university of tokyo , + komaba 3 - 8 - 1 , meguro - ku , tokyo 153 - 8902 , japan + e - mail : hashi@hep1.c.u-tokyo.ac.jp_ +    _ department of physics , tokyo metropolitan university , + hachioji , tokyo 192 - 0397 , japan + e - mail : kitazawa@phys.se.tmu.ac.jp_"}
{"article_id":"0901.4396","section_id":"i","document":"evidence for the @xmath1 meson was first seen in 1981 @xcite . for the next two decades , the argus experiment operating at desy in hamburg , germany and the cleo experiment operating at cesr at cornell university studied the properties of these mesons and made many important discoveries including the discovery of  mixing . the first examples of charmless hadronic @xmath1 decays were seen by cleo @xcite . starting in 2000 , there have been many measurements of these decays with increasing precision by the babar experiment operating at pep - ii at slac in california and the belle experiment operating at kek in japan . there are now nearly 100 of these decays that have been observed with a statistical significance of at least four standard deviations . while the early measurements by cleo were groundbreaking , the errors are sufficiently large that they have little weight in the present world averages . the cdf experiment at fnal also has measurements for these decays . while they are nearly as precise as babar and belle , there are only measurements for four decay channels . thus in tables throughout this review , we concentrate on the copious measurements from belle and babar . the theoretical study of weak nonleptonic decays of a heavy meson is difficult and involved due to the interplay of short- and long - distance qcd effects . the effective weak hamiltonian at the quark level @xmath2 is theoretically well under control , where @xmath3 are four - quark operators and @xmath4 are the wilson coefficients which incorporate strong - interaction effects above the scale @xmath5 . however , it is a difficult task to evaluate the hadronic matrix elements of the local operator @xmath3 reliably due to the nonperturbative qcd effects involved . a simple and widely employed approach is based on the valence quark assumption and the vacuum - insertion ( or factorization ) approximation in which the hadronic matrix elements of two quark bilinear operators are saturated by the vacuum intermediate states . due to the experimental and theoretical efforts in the past decade , qualitative understanding of nonleptonic charmless @xmath1 decays has become possible . since the @xmath1 meson is heavy , it is possible to describe the dynamics of hadronic decays by theories motivated by qcd rather than by phenomenological models . a central aspect of those theories is the factorization theorem which allows us to disentangle short - distance qcd dynamics from nonperturbative hadronic effects . in the heavy quark limit , matrix elements can be expressed in terms of certain nonperturbative input quantities such as light cone distribution amplitudes and transition form factors . power corrections beyond the heavy quark limit generally give the major theoretical uncertainties .    in this article we give an overview of the experimental measurements and the theoretical understanding of the branching fractions and @xmath0-violating asymmetries of charmless @xmath1-meson decays . we begin with the theoretical and experimental tools necessary for the study of hadronic @xmath1 decays . this is followed with a discussion of 2-body , 3-body , quasi-2-body , and baryonic @xmath1 decays , and the status of time - dependent @xmath0-violation measurements and predictions . we discuss the puzzles that remain unsolved .","summary":"we give an overview of the experimental measurements and the theoretical understanding of the branching fractions and-violating asymmetries of charmless-meson decays .","abstract":"we give an overview of the experimental measurements and the theoretical understanding of the branching fractions and-violating asymmetries of charmless-meson decays . most experimetal results are from the babar and belle experiments during the past decade . the global features of these experimental results are typically well described by the qcd - motivated theories such as qcd factorization , pqcd and soft - collinear effective theory . the agreement between theory and experiment is generally satisfactory , though there remain some unsolved puzzles that pose a great challenge to both theorists and experimentalists .    hadronic decay , cp violation , factorization , polarization , b meson"}
{"article_id":"0901.4396","section_id":"c","document":"in this review , we have summarized branching fraction results for more than 100 charmless @xmath1-meson decays . many of these decays have significant experimental signals . we also have shown results for @xmath0-violating asymmetry measurements for nearly 50 of these decays . this represents a truly impressive body of work , most of which have come from the belle and babar experiments in the last decade . the global features of the branching fractions and cp asymmetries of these charmless @xmath1 decays are generally well described by the qcd - motivated theories such as qcdf , pqcd and scet . the agreement between theory and experiment is generally satisfactory . however , there remains some unsolved puzzles : ( i ) @xmath117 cp puzzle : it is naively expected that @xmath424 and @xmath87 have similar direct cp asymmetries , while they differ by 5.3 @xmath108 experimentally , @xmath425 ; ( ii ) the abnormally large @xmath147 rates : while the qualitative picture of the enormously large rate of @xmath188 over @xmath186 is understood , a precise quantitative prediction is still lacking ; ( iii ) branching fractions of @xmath426 : theory usually predicts too small rates for them and a reasonable one for @xmath363 ; ( iv ) the polarization puzzle in penguin - dominated @xmath207 decays : the transverse polarization fraction is not as small as naively anticipated ; ( v ) mixing - induced @xmath0 asymmetries : the predicted values of the effective @xmath427 for most of the @xmath158 induced decays are above the one obtained from @xmath352 , whereas experimentally the value of @xmath354 from the bulk of the decay modes is systematically below that of @xmath352 ; ( vi ) the angular correlation enigma in three - body baryonic @xmath1 decays : the short - distance picture of @xmath340 can not explain or accommodate the observed angular distributions in penguin - dominated decays such as @xmath428 and @xmath429 . the aforementioned puzzles pose a great challenge to the @xmath1-physics community and their solutions need efforts from both theorists and experimentalists . either these enigmas can be resolved within the framework of the standard model provided that the hadronic matrix elements are under fair control or new physics effects already manifest themselves in some of the puzzles .","summary":"most experimetal results are from the babar and belle experiments during the past decade . the global features of these experimental results are typically well described by the qcd - motivated theories such as qcd factorization , pqcd and soft - collinear effective theory . the agreement between theory and experiment is generally satisfactory , though there remain some unsolved puzzles that pose a great challenge to both theorists and experimentalists .   ","abstract":"we give an overview of the experimental measurements and the theoretical understanding of the branching fractions and-violating asymmetries of charmless-meson decays . most experimetal results are from the babar and belle experiments during the past decade . the global features of these experimental results are typically well described by the qcd - motivated theories such as qcd factorization , pqcd and soft - collinear effective theory . the agreement between theory and experiment is generally satisfactory , though there remain some unsolved puzzles that pose a great challenge to both theorists and experimentalists .    hadronic decay , cp violation , factorization , polarization , b meson"}
{"article_id":"1102.0936","section_id":"i","document":"in the riemannian geometry influenced discourse on lorentzian geometry , the causal structure @xmath1 of a spacetime @xmath2 is viewed as a derivative construction which relies on the underlying differentiable structure of @xmath3 , with the causal relation @xmath4 between events on @xmath3 being obtained from the local lightcone structure provided by @xmath5 . @xmath1 is , however , itself rich with information about the spacetime geometry , and it has been the focus of several investigations over the years to endow it with a more primitive role in lorentzian geometry @xcite . we will concern ourselves in this work only with the causal structure of _ causal _ spacetimes , i.e. , those that harbour no closed causal curves . for such spacetimes @xmath1 is a partially ordered set , i.e. , @xmath4 is ( i ) _ acyclic _ : for @xmath6 , @xmath7 and ( ii ) _ transitive _ : for @xmath8 @xmath9 and @xmath10 @xmath11 . it is important to note that the set of events @xmath3 in @xmath1 does not carry with it the attendant differentiable structure of its spacetime avatar . @xmath1 has no analog in riemannian geometry , and it is therefore of very general interest to understand the role it plays in lorentzian geometry @xcite . a set of results due to malament and hawking - mccarthy - king @xcite ( mhkm ) provides an important relationship between @xmath1 and @xmath2 in spacetimes that are _ future and past distinguishing _ ( fpd ) . these are spacetimes in which the chronological ( time - like ) past and future sets are unique for every spacetime event . mhkm address the general question : what aspects of the spacetime geometry are left invariant under a causal structure preserving bijection between two spacetimes ? such a map is called a _ causal bijection_.    a _ causal bijection _ @xmath12 is a bijection between the set of events @xmath13 and @xmath14 which , in addition , preserves the causal relations @xmath15 and @xmath16 : for @xmath17 , @xmath18 and for @xmath19 , @xmath20 . malament s original results were restricted to chronological bijections , i.e. , those that preserve only the chronological relation , but as shown by levichev @xcite causal bijections , themselves imply chronological bijections . we can summarise these results as    * malament - hawking - king - mccarthy - levichev(mhkml ) * + if a causal bijection @xmath21 exists between two n - dimensional spacetimes which are both future and past distinguishing , then these spacetimes are conformally isometric when @xmath22 . [ mhkmlth ]    here , a _ conformal isometry _ between @xmath23 and @xmath24 is a bijection @xmath25 such that @xmath21 and @xmath26 are smooth and @xmath27 for some real , smooth , non - vanishing function @xmath28 . importantly , this implies that @xmath13 and @xmath14 have the same topology . the power of the mhkml theorem is evident . it tells us that the causal structure @xmath1 of an @xmath29-dimensional spacetime which is future and past distinguishing determines its conformal geometry and its topology . the _ only _ remaining geometric degree of freedom not determined by the causal structure is the conformal factor @xmath28 . this suggests an alternative , non - riemannian approach to lorentzian geometry in which a partially ordered set @xmath1 plays a primitive rather than a derivative role . indeed , the mhkml theorem provides a strong motivation for the causal set approach to quantum gravity in which a locally finite partially ordered set replaces the spacetime continuum @xcite . can the mhkml theorem be generalised to include spacetimes of different dimensions ? equivalently , are causal bijections rigid enough to constrain the spacetime dimension ? let us consider for the moment a special subclass of fpd spacetimes , namely those that are strongly causal . for such spacetimes , the alexandrov topology @xmath30 is a causal topology which is equivalent to the manifold topology @xmath31 ( theorem 4.24 in @xcite ) , so that @xmath1 determines the manifold topology and hence dimension . since a causal bijection @xmath21 preserves the chronological relation @xcite and hence the topology @xmath30 , this implies :    [ cor - one ] if there is a causal bijection between two strongly causal spacetimes then they both have the same manifold dimension and topology . this generalises the mhkml theorem when applied to strongly causal spacetimes . however , since @xmath30 is known to be strictly coarser than @xmath31 for spacetimes that are not strongly causal , it is an interesting question whether causal bijections impose topological constraints in such spacetimes . in this work , we show that corollary [ cor - one ] can be generalised to spacetimes satisfying weaker causality conditions , i.e. , those that are either past _ or _ future distinguishing :    [ claim - two ] if there is a causal bijection between two future ( or past ) distinguishing spacetimes then they are of the same dimension . this gives us a genuine generalisation of the mhkml theorem to fpd spacetimes for spacetime dimension @xmath22 . thus for an fpd spacetime @xmath1 encodes the manifold topology and hence its dimension . this begs the question  what is the causal topology for fpd spacetimes that corresponds to the manifold topology ? we define a new causal topology @xmath32 derived from a convergence condition on sequences of _ chain intervals _ which are order theoretic analogs of null geodesic segments . we show that @xmath32 is equivalent to the manifold topology @xmath31 for an fpd spacetime in which the regions of strong causality violation satisfy a certain local achronality condition . in section [ prelims ] we briefly review some of the standard material on causal structure , in the process formalising many of the concepts and definition given in this section . we also define and discuss the properties of _ chain intervals _ which we use throughout our paper , not only to construct the new topology @xmath32 but also to give a _ local _ characterisation of strong causality and future and past distinguishability . in section [ mal ] we investigate the properties of fpd spacetimes in some detail and find some new and generic features . lemma [ claim - two ] follows from this analysis .    in section [ newtop ] we define a new convergence criterion on sequences of chain intervals from which we derive the causal topology @xmath32 . we show that for fpd spacetimes which satisfy an additional local achronality condition for the regions of strong causality violation , @xmath32 is equivalent to the manifold topology . this construction is inspired by the work of @xcite , where null geodesic segments are used instead of chain intervals , albeit with an entirely different motivation . indeed , a convergence condition using null geodesic segments instead of chain intervals always gives the manifold topology for fpd spacetimes , but since null geodesic segments are nt order theoretically defined , this does not give rise to a purely _ causal _ topology . the construction of @xmath32 via a convergence criterion however does not give us a causal basis . finding such a basis has proved difficult and we end this section with some speculative remarks .    in section [ other ] we examine another candidate for a causal topology inspired by a causal convergence criterion defined in @xcite . the convergence criterion used in @xcite gives rise to a causal topology @xmath33 which is strictly finer than @xmath31 and is hausdorff and equivalent to the path topology constructed by hawking - mccarthy - king @xcite ) iff the spacetime is past and future distinguishing . @xmath33 can alternatively be defined in terms of its basis elements , obtained from `` doubled '' chronological intervals and this makes it attractive to work with . we show that a natural extension of the convergence condition of @xcite gives rise to yet another distinct causal topology @xmath34 which is strictly coarser than @xmath33 and also strictly finer than @xmath31 when the spacetime is fpd . it is thus tempting to conclude that the the topological content of @xmath1 is far richer than one might have imagined and that further work could yield valuable insights .","summary":"the causal structure of a strongly causal spacetime is particularly well endowed . not only does it determine the conformal spacetime geometry when the spacetime dimension , as shown by malament and hawking - king - mccarthy ( mhkm ) , but also the manifold dimension . the mhkm result , however , applies more generally to spacetimes satisfying the weaker causality condition of future and past distinguishability(fpd ) , and it is an important question whether the causal structure of such spacetimes can determine the manifold dimension . in this work we show that the answer to this question is in the affirmative . we investigate the properties of future or past distinguishing spacetimes and show that their causal structures determine the manifold dimension . this gives a non - trivial generalisation of the mhkm theorem and suggests that there is a causal topology for fpd spacetimes which encodes manifold dimension and which is strictly finer than the alexandrov topology . we show that such a causal topology does exist . we construct it using a convergence criterion based on sequences of `` chain - intervals '' which are the causal analogs of null geodesic segments . we show that when the region of strong causality violation satisfies a local achronality condition , this topology is equivalent to the manifold topology in an fpd spacetime .","abstract":"the causal structure of a strongly causal spacetime is particularly well endowed . not only does it determine the conformal spacetime geometry when the spacetime dimension , as shown by malament and hawking - king - mccarthy ( mhkm ) , but also the manifold dimension . the mhkm result , however , applies more generally to spacetimes satisfying the weaker causality condition of future and past distinguishability(fpd ) , and it is an important question whether the causal structure of such spacetimes can determine the manifold dimension . in this work we show that the answer to this question is in the affirmative . we investigate the properties of future or past distinguishing spacetimes and show that their causal structures determine the manifold dimension . this gives a non - trivial generalisation of the mhkm theorem and suggests that there is a causal topology for fpd spacetimes which encodes manifold dimension and which is strictly finer than the alexandrov topology . we show that such a causal topology does exist . we construct it using a convergence criterion based on sequences of `` chain - intervals '' which are the causal analogs of null geodesic segments . we show that when the region of strong causality violation satisfies a local achronality condition , this topology is equivalent to the manifold topology in an fpd spacetime ."}
{"article_id":"cond-mat0002133","section_id":"i","document":"in view of understanding a particular phenomenon in condensed matter , theory is supposed to identify the corresponding relevant degrees of freedom and to provide the effective interaction between them by , approximately , integrating out the remaining ones so that one is left with a manageable model . it is a major challenge to determine the effective interactions because that requires to calculate the partition function of the whole system under the constraint of a fixed configuration of the relevant degrees of freedom . the benefit for carrying out this constrained calculation , which in general is more difficult than the original full problem , is twofold . first , there is a gain in transparency by describing the system in terms of relevant degrees of freedom . secondly , it is typically less risky to apply approximations for the partial trace because they only concern the less relevant degrees of freedom . the determination of the phase behavior and of the structural properties of multi - component fluids represents a case study for this general approach . if the composing particles of the mixture are of comparable size and shape their degrees of freedom have to be treated on equal footing . the well developed machinery of liquid state theory  @xcite offers various techniques to cope with this problem . however , these techniques fail to yield reliable results if , e.g. , one component is much larger than the others ; in this case numerical simulations become inefficient and integral theories lose their accuracy . colloidal suspensions are a paradigmatic case for such highly asymmetric solutions . for their description these difficulties can be overcome by resorting to the general scheme laid out at the beginning with the positions of the colloidal particles as the relevant degrees of freedom . accordingly the degrees of freedom of the small solvent particles are to be integrated out for a fixed configuration of the colloidal particles which we assume to be smooth , monodisperse spheres . at sufficiently low concentrations of the suspended particles this leads to an effective pair potential between them . in many cases the effective potential resembles the bare one , i.e. , the one in the absence of the solvent , but with modified , effective interaction parameters which depend on the thermodynamic variables of the system such as pressure and temperature .    the effective pair potential acquires additional new features if the solvent is enriched with particles of medium size such as , e.g. , polymers . if the colloidal particles come close to each other the depletion zones around them , generated by the finite size of the medium particles , overlap leading to an entropically driven attraction of the colloidal particles  @xcite . correlation effects can modify the form and the range of these depletion forces considerably  @xcite . these effective potentials have indeed turned out to be successful in describing the phase behavior of colloidal suspensions  @xcite . qualitatively new aspects arise if the solvent particles exhibit a strong cooperative behavior of their own such as a phase transition which proliferates to the effective potential between the large particles . if the solvent undergoes a continuous phase transition , thermal casimir forces between the large particles are induced due to the geometrical constraint they pose for the critical fluctuations  @xcite . such forces are long - ranged and have a strong influence on the phase behavior of the colloidal particles  @xcite . if the solvent is thermodynamically close to a first - order phase transition , wetting phenomena  @xcite can occur at the surfaces of the dissolved particles ( see ref . @xcite and references therein ) . if the bulk phase of the solvent is the vapor phase of a one - component fluid , the surfaces of the large spheres can be covered by a liquidlike wetting film . this situation corresponds to aerosol particles floating in a vapor . if the bulk phase of the solvent is the a - rich liquid phase of a binary liquid mixture composed of ( small ) a and b molecules , the dissolved colloidal particles can be coated by the b - rich liquid phase of the mixture . if the wet spheres approach each other , at a critical distance the two wetting films snap to a bridgelike structure . this morphological phase transition is expected to yield a nonanalytic form of the effective interaction potential between the large spheres . this nonanalyticity demonstrates that cooperative phenomena among those degrees of freedom which are integrated out can leave clearly visible fingerprints on the effective interaction between the remaining relevant degrees of freedom . the study of this kind of profileration is not only of theoretical interest in its own right but seems to play an important ( albeit not exclusive  @xcite ) role for the experimentally observed flocculation of colloidal particles dissolved in a binary liquid mixture close to its demixing transition into an a - rich and a b - rich liquid phase  @xcite . this observation has triggered numerous theoretical efforts devoted to various possible explanations of it . since they are reviewed in sec . i of ref . @xcite and more recently in ref . @xcite the interested reader is referred to there and we refrain from repeating this discussion here .    in our present analysis of this problem we apply density functional theory  @xcite which offers two advantages . first , this technique is particularly well suited to calculate , as required here , free energies under constraints . secondly , it allows one to keep track of the basic molecular interaction potentials of the system . we focus our interest on thermodynamic states of the solvent which are sufficiently far away from its critical point so that the emerging liquid - vapor interfaces of the wetting films exhibit only a small width . therefore we can apply the so - called sharp - kink approximation which considers only steplike variations of the solvent density distribution and thus leaves the interface position as the main statistical variable . this approximation has turned out to be surprisingly accurate for the description of wetting phenomena  @xcite . our analysis extends and goes beyond previous efforts  @xcite which are based on a similar interface displacement model grounded on a phenomenological ansatz . whereas refs . @xcite and @xcite are aimed at mapping out the phase diagram in terms of interaction parameters for the bridging transition mentioned above , we focus on the effective interaction potentials between the wet spheres , which are not presented in refs . @xcite and @xcite , and on their microscopic origin . inter alia , this allows us to compare the effective interaction potential between the colloidal particles with the bare one , i.e. , in the absence of the solvent , and thus to comment on the quantitative relevance of the solvent - mediated interaction . moreover , we present the phase diagram of the system in terms of the thermodynamic variables temperature and chemical potential which is also not contained in refs . @xcite and @xcite .    in sec . [ s : theory ] we describe the implementation of a simple version of density functional theory for the present problem . for reasons of simplicity we confine our analysis to liquid - vapor coexistence of a one - component solvent ; the generalization to a binary solvent is straightforward . in sec . [ s : morphology ] we present some examples for the numerically calculated wetting film morphologies and discuss a phase diagram for the aforementioned morphological transition , and in sec . [ s : eip ] we analyze the effective wetting - induced interaction potential between the spheres as a function of the distance between the spheres and the undersaturation . the experimental relevance of our model calculations is discussed in sec . [ s : discussion ] and sec . [ s : summary ] summarizes our main results . the appendix contains some technical details .","summary":"using a density functional based interface displacement model we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one - component substance or the a - rich liquid phase of a binary liquid mixture composed of a and b particles . if this solvent is thermodynamically close to a first - order fluid - fluid phase transition , the spheres are covered with wetting films of the incipient bulk phase , i.e. , the liquid phase or the b - rich liquid , respectively . below a critical distance between the spheres their wetting films snap to a bridgelike configuration . we determine phase diagrams for this morphological transition and analyze its repercussions on the effective interaction potential .","abstract":"using a density functional based interface displacement model we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one - component substance or the a - rich liquid phase of a binary liquid mixture composed of a and b particles . if this solvent is thermodynamically close to a first - order fluid - fluid phase transition , the spheres are covered with wetting films of the incipient bulk phase , i.e. , the liquid phase or the b - rich liquid , respectively . below a critical distance between the spheres their wetting films snap to a bridgelike configuration . we determine phase diagrams for this morphological transition and analyze its repercussions on the effective interaction potential . our results are accessible to force microscopy and may be relevant to flocculation in colloidal suspensions ."}
{"article_id":"cond-mat0002133","section_id":"c","document":"the bare dispersion interaction between the two spheres is not included in eq .  ( [ e : ldafunc ] ) . according to hamaker  @xcite this contribution is given by @xmath237 as the dispersion interaction between two identical spheres of radius @xmath0 at center - of - mass distance @xmath1 . in the limit @xmath238 , where @xmath239 ( see fig . [ f : system](a ) ) is the smallest separation between the surfaces of the spheres , eq . ( [ e : vdwbetwsph ] ) reduces to @xmath240 which corresponds to the derjaguin approximation whereas @xmath241 . thus except for the @xmath1-independent bulk contribution @xmath54 the total grand canonical potential of the system is @xmath242 where @xmath243 is given by the minimum value @xmath244)$ ] for given @xmath1 and @xmath0 ( eqs . ( [ e : decomp ] ) and ( [ e : gcpismin ] ) ) ; in analogy to @xmath199 we define the excess total free energy @xmath245 . @xmath246 is the hamaker constant appertaining to the bare dispersion interaction between the particles in the spheres . in the case of pairwise additivity of the molecular interactions and in the absence of retardation effects one has @xmath247 if the interaction potential between two individual molecules in the spheres is given by a lennard - jones potential ( eq .  ( [ e : ljsphere ] ) ) with the parameters @xmath248 and @xmath249 . typically @xmath246 is of the order of @xmath250j or , equivalently , @xmath251 . if the vacuum between the spheres is replaced by a medium of condensed matter the interaction between the spheres is screened  @xcite . in our present model this medium is the bulk vapor phase modified by the presence of the liquidlike films adsorbed on the spheres and the screening effect is described microscopicly by the functional @xmath252 $ ] .    in refs . @xcite and @xcite this additional screening effect , due to spherical shells of adsorbed , homogeneous layers surrounding spherical particles , on the dispersion interaction between the latter immersed in another homogeneous medium has been calculated macroscopicly . beyond molecular scales these results should closely correspond to the configuration without liquid bridge discussed herein because the deviation of the spherical shape of one wetting layer due to the presence of the second sphere is very small . indeed , the interaction energy calculated in refs . @xcite and @xcite is practically the same as the sum of the @xmath1-dependent contributions in @xmath81 ( eq .  ( [ e : omegaei ] ) ) and @xmath56 ( eq .  ( [ e : omegasl ] ) ) for the configurations without bridge  for these configurations @xmath86 and @xmath62 do not contribute to the dependence of @xmath102 on @xmath1  and the direct dispersion interaction @xmath21 . in ref . @xcite the total dispersion interaction is shown to be always attractive if the hamaker constants @xmath253 corresponding to the interaction between any two media @xmath254 and @xmath255 are chosen such that @xmath256 . although the effective interaction induced by the wetting layers shown in figs . [ f : eipforexample1](b ) and [ f : eipforexample1plusbare ] for the configuration without bridge is repulsive , we note that the sum @xmath257 of this interaction and of the bare dispersion potential @xmath21 is also _ attractive _ if we choose the hamaker constant in eq . ( [ e : vdwbetwsph ] ) accordingly , i.e. , @xmath258 ( fig . [ f : eipforexample1plusbare ] ) . therefore our results are consistent with those obtained in ref .  @xcite . since only effective interactions between finite volumes enter into the total excess interaction potential @xmath259 and these effective interactions decay as @xmath91 in the limit of large separations @xmath1 , the same holds for @xmath259 . figure  [ f : eipforexample1 ] shows that as soon as the wetting films snap to a liquidlike bridge , whether it is stable or metastable , there is an attractive wetting - layer - induced force @xmath260 that pulls the spheres together . from fig . [ f : eipforexample1 ] one can infer that this attractive force is of the order of @xmath261 in the range between @xmath262 ( i.e. , @xmath263 for @xmath103 discussed in this figure ) and @xmath264 ( @xmath265 ) where the effective potential varies almost linearly . at the small separation @xmath266 the effective potential @xmath199 induced by the bridgelike wetting layer is minimal and the wetting - induced force is zero . finally , at smaller separations the interaction is repulsive leading to a stabilization of the spheres at @xmath267 . within the range @xmath268 the bare , direct dispersion interaction between the spheres ( eqs .  ( [ e : vdwbetwsph ] ) and ( [ e : barevdw_smalla ] ) ) gives rise to a force @xmath269 . the estimate @xmath270 for the case of pairwise additive interactions without retardation follows from the ansatz @xmath271 , so that the bare dispersion force in our example with @xmath103 is @xmath272 . therefore in the range where the bridge - induced force is almost constant ( @xmath273 ) the direct , bare dispersion force decays from approximately @xmath274 ( which is of the same order of magnitude as the bridge - induced force ) to approximately @xmath275 , whereas for smaller separations it becomes the dominant force . our model calculations can be tested experimentally by force microscopy . this can be done by suitably fixing one sphere in the fluid and by attaching the second one to the tip of a force microscope . alternatively , both spheres can be positioned by optical tweezers and the force law can be inferred by monitoring optically their dynamics after switching off the tweezers . at separations between the spheres which are comparable with the diameter @xmath186 of the solvent particles the actual effective interaction potential will exhibit an additional oscillatory contribution due to packing effects which decays exponentially on the scale @xmath186  @xcite . in order to obtain these oscillations one would have to resort to density functional theories which are more sophisticated than the one in eq . ( [ e : ldafunc ] ) . this , in turn , would make it much more difficult to obtain the bridgelike configuration , to map out the complete phase diagram , and to obtain results for large spheres . according to subsec . [ ss : eipforlargespheres ] , for @xmath187 and at two - phase coexistence @xmath104 the bridging transition occurs at distances @xmath120 which are proportional to @xmath0 . in this case , due to @xmath187 , the effective interaction potential will be practically unaffected by this oscillatory contribution for the vast portion @xmath276 of the range of the effective interaction potential .      whereas the kinds of experiments considered in the previous subsection are focused on two individual spherical particles , we discussed in the introduction that the effective interaction potential enters into the collective behavior of colloidal suspensions such that the bridging transition may trigger flocculation . if colloidal suspensions would be governed by dispersion forces alone , most of them would flocculate even in the absence of the wetting - induced forces discussed here because the dispersion forces generate the so - called primary minimum in the effective interaction potential close to contact . since this minimum is much deeper than @xmath277 the colloidal particles would simply stick together permanently . this effect , which is undesired for many applications , can be avoided by endowing the particles with electrical charges which adds a screened coulomb repulsion between the charged particles . as a result , such charge stabilized colloidal suspensions are characterized by effective interaction potentials in which a substantial energy barrier separates the aforementioned primary minimum from a second , much more shallow minimum at larger distances . since this potential barrier is typically large compared with @xmath277 the phase behavior of the colloidal particles is practically independent of the primary minimum formed by the dispersion forces and determined by the shape of the potential _ outside _ the barrier . as demonstrated by figs . [ f : eipforexample1 ] and [ f : eipforexample1plusbare ] the range of the wetting - induced forces is about @xmath278 , in good agreement with @xmath279 ( see eqs . ( [ e : dbt ] ) and ( [ e : lambda ] ) ) . on the other hand the position ( and height ) of the aforementioned energy barrier depends sensitively on the size of the total charge on the spheres , the amount of salt in the solvent , and the dispersion forces and can be varied over a wide range . with a high salt concentration the barrier position can be as small as a few tens of nm . thus under such circumstances the wetting - induced interaction potentials would be relevant even for colloidal particles whose radii are only a few tens of nm . there is another class of colloidal suspensions for which the wetting - induced forces can be of practical importance . by coating the colloidal particles with polymers and by matching the refractive indices of the colloidal particles and the bulk fluid ( in our case study the vapor phase or , more realisticly in the present context , the a - rich liquid phase of a binary liquid mixture acting as the solvent ) the colloidal particles behave effectively like hard spheres ( see , e.g. , refs . @xcite and @xcite ) . through this index matching the sum of the bare interaction potential @xmath21 and the effective interaction potential @xmath280 , which would arise if the spheres were immersed in the homogeneous and unperturbed bulk solvent , vanishes . within our model @xmath280 is given by the expression in eq . ( [ e : omegasl ] ) with @xmath40 replaced by @xmath41 , which is the density of the bulk phase . since the index matching works for the bulk phase , it does not work for the wetting phase . as a consequence the wetting - induced forces appear against a background effective potential of hard spheres . therefore for this class of colloidal suspensions the wetting phenomena discussed here are expected to have a pronounced effect on their phase behavior . within our model , for _ _ i__ndex-__m__atched suspensions the _ total _ effective interaction potential is given by @xmath281 and in analogy to @xmath199 and @xmath259 we define @xmath282 with @xmath283 for the unbridged solutions . figure  [ f : indexmatch ] displays @xmath284 and @xmath285 as function of @xmath286 for the same system as in figs . [ f : eipforexample1 ] and [ f : eipforexample1plusbare ] . @xmath280 is about @xmath287 smaller than @xmath102 for the unbridged solution and also approaches its asymptote @xmath288 from above . as before ( see the discussion of fig .  [ f : eipforexample1plusbare ] above ) , the resulting total effective interaction between spheres in an index - matched bulk fluid for the state with liquid bridge is still attractive and of the same order of magnitude as the bare dispersion interaction between the spheres , i.e. , in the absence of the solvent .","summary":"our results are accessible to force microscopy and may be relevant to flocculation in colloidal suspensions .","abstract":"using a density functional based interface displacement model we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one - component substance or the a - rich liquid phase of a binary liquid mixture composed of a and b particles . if this solvent is thermodynamically close to a first - order fluid - fluid phase transition , the spheres are covered with wetting films of the incipient bulk phase , i.e. , the liquid phase or the b - rich liquid , respectively . below a critical distance between the spheres their wetting films snap to a bridgelike configuration . we determine phase diagrams for this morphological transition and analyze its repercussions on the effective interaction potential . our results are accessible to force microscopy and may be relevant to flocculation in colloidal suspensions ."}
{"article_id":"1301.3538","section_id":"i","document":"mott metal - insulator transitions and their associated spin and charge ordering appear throughout the physics of transition metal oxides , and present many puzzles of interpretation and modeling . since electrons in the regime of a mott transition may possess both localized and itinerant character , ambiguity may arise as to an appropriate model hamiltonian : hubbard , heisenberg , or @xmath2-@xmath3 ? anderson or kondo model ? in multi - orbital systems , the choices are even more numerous . such a situation arises in the pseudo - cubic perovskite nickelates , _ _ r__nio@xmath0 , where _ r _ is a rare earth ion , which have been studied for many years for their interesting mott metal - insulator transitions.@xcite a @xmath4 transition occurs to an insulating state for all members of the series save the case _ _ r__=la , which is metallic at all temperatures , to a low temperature state with complex structural symmetry breaking  denoted `` charge order '' in the literature  and antiferromagnetism . nominally , in this material the nickel valence is @xmath5 , i.e. @xmath6 , which would suggest a model with a single electron in the cubic @xmath7 doublet , a two - fold orbital degeneracy . however , another interpretation is that the nickel valence is actually @xmath8 , with an additional hole per nickel spread out among the oxygen ions,@xcite analogous to the zhang - rice singlet in cuprates.@xcite in this `` ligand hole '' scenario there is no orbital degeneracy , but rather an @xmath1 spin on the nickel site , corresponding to a half - filled @xmath7 doublet . the difference between these two scenarios ( which we termed the `` nickel valence controversy '' ) is well defined only in the ionic limit where the charge on the nickel site does not fluctuate significantly , which might be the case in the ligand - hole picture . a third , compromise view is that the valence fluctuates significantly due to hybridization , making the distinction between ni@xmath9 and ni@xmath10 moot ; in this case one might build a theory in terms of the low energy bands near the fermi energy . though such a compromise exists , it seems to be unpopular , and strong opinions in favor of the ligand - hole picture are often voiced.@xcite going further , sawatzky has proposed a picture for the observed `` charge '' ordering in terms of local kondo screening of half the ni@xmath9 spins.@xcite a recent dmft paper seems to suggest a similar scenario.@xcite a physical understanding of _ how _ such kondo screening might come about , and whether it can account for the observed charge / spin order , is , however , still lacking .    in this paper , we study a concrete model motivated by the ligand - hole scenario using the numerically exact density matrix renormalization group ( dmrg ) method.@xcite we write down the simplest model incorporating a sharply defined ni@xmath10 valence , and holes on the oxygen sites . because each nickel thereby has an @xmath1 spin and is accompanied by only a single oxygen hole with @xmath11 , this takes the form of an underscreened kondo lattice model.@xcite to enable the dmrg analysis , we take this model to be one dimensional . though this is obviously a drastic approximation , our model retains the underscreened kondo physics , and has the symmetries to allow charge ordering of the same type observed in the nickelate materials . we obtain the numerically exact full zero temperature phase diagram for this model , which contains several magnetic states . however , we _ do not _ find the charge ordered state seen in the nickelates , which is nickel site - centered , but instead a complementary type of charge ordering which is bond - centered , i.e. ordered on the oxygen sites . we will discuss the implications of this result for the nickelates in sec . [ sec : conclude ] .    beyond the context of the nickelates , our model is of interest on its own as a problem in one - dimensional physics , and of the underscreened kondo effect . recent work has shown the possibility of gapless one - dimensional `` spin liquid '' phases , which are strikingly even more non - quasiparticle in nature than the usual luttinger liquid . such phases , have been found in rather exotic models with very large ring exchange interactions.@xcite remarkably , we find evidence for such a spin liquid - like phase in our rather simple and physically motivated kondo lattice model ( technically , we obtain a phase which appears to be proximate to the `` spin bose metal '' phase of ref .  , rather than this phase itself ) . this suggests an intriguing prospect of observing quantum spin liquid states in two and three dimensional kondo lattice systems appropriate to real materials . again , this idea has already been suggested in the literature,@xcite but connections do not seem to have been made to realistic model hamiltonians .    the remainder of this paper is organized as follows . in sec . [ sec : h_tjj ] we introduce our model hamiltonian as well as a simple semi - classical treatment that would guide our intuition about the quantum case . in sec . [ sec : dmrg ] we present our dmrg results , which includes the quantum ground - state phase diagram and various correlation function in each phase . in sec . [ sec : mf ] we introduce a mean - field picture , which , together with degenerate perturbation theory , explains most phases in the dmrg phase diagram . in sec . [ sec : spiral ] we focus on the one phase that can not be explained in the previous section , which we argue is a phase in proximity to the spin bose metal phase in ref .  . further discussions and conclusions are presented in sec . [ sec : conclude ] .","summary":"motivated by the nickel valence controversy in the perovskite nickelate _ _ importantly , for a certain range of parameters the model exhibits a quasi - long - range spiral ( qs ) order . to understand the dmrg results , we construct a mean - field theory based on a schwinger fermion decomposition of the spins , from which we argue that the qs phase corresponds to a phase in proximity to the spin bose metal state proposed by d. n. sheng , o. i. motrunich , and m. p. a. fisher [ phys . rev . notably , we find no evidence for a phase with the symmetry of `` nickel''-centered charge order , which has been argued to arise due to site - selective kondo screening of half the spins , and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions , not present in this model .","abstract":"motivated by the nickel valence controversy in the perovskite nickelate _ _ r__nio , we consider a one - dimensional underscreened kondo chain consisting of alternating spin-1 ( `` nickel '' ) and electron ( `` oxygen '' ) sites , which in addition to the usual electron hopping and spin - spin interaction between the spin and the electron also contains a spin mediated electron hopping term . using the density - matrix renormalization group ( dmrg ) , we obtained the zero temperature phase diagram of the model , as well as various correlation functions in each phase . importantly , for a certain range of parameters the model exhibits a quasi - long - range spiral ( qs ) order . to understand the dmrg results , we construct a mean - field theory based on a schwinger fermion decomposition of the spins , from which we argue that the qs phase corresponds to a phase in proximity to the spin bose metal state proposed by d. n. sheng , o. i. motrunich , and m. p. a. fisher [ phys . rev . b * 79 * , 205112 ( 2009 ) ] . notably , we find no evidence for a phase with the symmetry of `` nickel''-centered charge order , which has been argued to arise due to site - selective kondo screening of half the spins , and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions , not present in this model ."}
{"article_id":"1301.3538","section_id":"r","document":"we determine the quantum ground - state phase diagram of the @xmath2-@xmath3-@xmath12 hamiltonian , eq . ( [ eq : h_tjj ] ) , by large - scale density - matrix renormalization group ( dmrg)@xcite calculations . we consider systems with up to @xmath48 unit cells , each consisting of one oxygen and one nickel site ( see fig . [ fig : unitcells ] for illustration ) . for a fixed number of states kept , we found that this `` super - block '' configuration produces better convergence than the usual practice of alternating blocks of oxygen and nickel sites . in our dmrg calculation , we use open boundary conditions ( obc ) , and keep up to @xmath49 states in each dmrg block . this is found to give excellent convergence in the measurements such as the ground state energy and various correlation functions with a total error of the order of or less than @xmath50 . the phase boundaries in the ( @xmath51 , @xmath52 ) parameter space are determined by extensive scans of the derivatives of the ground state energy and by monitoring the correlation functions , as well as the corresponding order parameters .    to determine the properties of the ground states , we calculate the nickel spin - spin correlation @xmath53 , the electron spin - spin correlation @xmath54 , the electron density @xmath55 , the electron density - density correlation @xmath56 ( @xmath57 is defined in position space by @xmath58 ) , and the nearest - neighbor nickel - oxygen spin - spin correlation @xmath59 . to determine whether the phase is conducting , we also calculate the charge gap @xmath60/2 $ ] . finally , we also obtain the central charge @xmath61 by calculating the von neumann entanglement entropy @xmath62 for a partition of the system into two halves of length @xmath63 , @xmath64 , with varying length @xmath63 of the sub system @xmath65 . a universal logarithmic dependence of @xmath62 on @xmath63 is expected in the thermodynamic limit with a prefactor depending on @xmath61 , and accurate results can usually be obtained using finite - size scaling formulas derived from conformal field theory , see refs . , . the calculation of the von neumann entropy is computationally expensive and generally the most difficult of all physical quantities to converge , especially in highly entangled states . therefore our results for @xmath61 are more limited than for the other quantities discussed above . ( color online ) dmrg block used in the calculations . ] our main result is the phase diagram presented in fig . [ fig : dmrg_phases ] , in which we find four distinct phases as @xmath3 and @xmath12 are varied . in addition , the correlation functions at characteristic points in parameter space are shown in fig . [ fig : correlations ] and [ fig : ss_dmrg ] . note that we have only shown the @xmath66-components of the spin - spin correlation functions . we remark that the phases labeled as qaf , cd , and qs ( detailed below ) possess spin @xmath67 invariance , and thus the other components of the spin - spin correlations are essentially identical to the ones we showed . for the ferromagnetic ( f ) phase , the @xmath68-axis in spin space is constrained to @xmath69 , and thus the magnetization axis is perpendicular to the @xmath68-axis . ( color online ) phase diagram from the dmrg calculation . here f stands for the ferromagnetic phase , qaf stands for the quasi - long - range antiferromagnetic phase , cd stands for the charge - density ordered phase , and qs stands for the quasi - long - range spiral phase . the dashed line within the cd phase represents the boundary in which the peak in @xmath70 changes from @xmath71 to @xmath72 . ]     ( color online ) ( a ) nickel spin - spin correlation @xmath70 , ( b ) electron spin - spin correlation @xmath73 , and ( c ) electron density - density correlation @xmath56 for ( orange , filled circular symbols ) @xmath74 and @xmath75 , ( green , empty square symbols ) @xmath76 and @xmath77 , ( blue , empty diamond symbols ) @xmath78 and @xmath77 , and ( purple , greek cross symbols ) @xmath79 and @xmath80 . the insets of panels  ( a ) and ( b ) show the details of the respective correlation for @xmath79 and @xmath80 in the range @xmath81 . ] ( color online ) the nearest - neighbor nickel - oxygen spin - spin correlation @xmath59 for the characteristic points in parameter space used in table  [ tbl : d_and_c ] , with system size @xmath82 . the two correlations are combined and the index @xmath19 now labels the bond center of the correlation . the positions of the nickel and the oxygen sites are indicated by the labels above the curves . the inset shows finite size scaling of the oscillation amplitude in @xmath59 for @xmath83 and @xmath84 using a second order polynomial fit . ] .[tbl : d_and_c ] charge gap @xmath85 and central charge @xmath61 for characteristic parameter values within each phase of the phase diagram fig . [ fig : dmrg_phases ] . for the cd phase , `` com . '' indicates peak in @xmath70 at @xmath71 while `` incom . '' indicates peak in @xmath70 at incommensurate wavevectors . [ cols=\"^,^,^,^,^,^ \" , ]     for @xmath86 the system exhibits ferromagnetic order with magnetization @xmath87 per unit cell . this is consistent with previous works in the literature on the alternating spin-1spin-1/2 chain,@xcite which can be thought of as the @xmath88 limit of the present model . for @xmath3 and @xmath12 both small and @xmath89 , the system exhibits quasi - long - range antiferromagnetic ( qaf ) order characterized by a sharp peak in @xmath70 at @xmath71 , while @xmath90 and @xmath56 remain largely featureless . as @xmath12 further increases such that @xmath91 , the system develops a charge - density ( cd ) order with period 2 as shown in inset ( a ) in fig . [ fig : cdw ] , and the sharp singularity in @xmath70 in the qaf phase becomes a broad peak . as @xmath3 increases within this cd phase , the peak originally located at @xmath71 splits into two peaks at @xmath72 , with @xmath92 increasing as @xmath3 increases . most interestingly , when @xmath3 and @xmath12 are both large and @xmath89 the system seems to exhibit quasi - long - range spiral ( qs ) order characterized by sharp singularities in _ both the nickel spin - spin correlation @xmath70 and the _ electron _ spin - spin correlations @xmath90 at incommensurate vectors @xmath72 _ , while the electron density correlation @xmath56 remains largely featureless , and no signs of cd order are found . moreover , when the correlation functions are examined more carefully near @xmath93 , a tiny broad peak can be discerned at wavevector roughly equal to @xmath94 in @xmath70 , while no such features are found in @xmath90 . it should be remarked that the value of @xmath92 evolves continuously as @xmath12 and @xmath3 changes and connects across the phase boundaries into the ferromagnetic and the cd phases , as shown in fig . [ fig : peak_location ] . in addition , from fig .  [ fig : ss_dmrg ] we see that in the qaf and the qs phases , the nearest - neighbor spin - spin correlation @xmath59 is essentially uniform in the thermodynamic limit if not already in finite - size systems , while in the cd phase @xmath59 has a significant two - unit - cell oscillation centered at the oxygen site , which is consistent with the symmetry of the cd order . note that the oscillations of @xmath59 in the cd phase have larger amplitudes than the corresponding oscillations in @xmath95 , and that in general @xmath96 increases as the parameters @xmath97 increase . ( color online ) the development of charge - density wave order parameter @xmath98 as @xmath52 increases while @xmath99 is fixed . the inset ( a ) shows @xmath95 as function of unit - cell index @xmath19 for ( black , filled square symbols ) @xmath100 and @xmath101 and ( blue , filled diamond symbols ) @xmath100 and @xmath77 , with system size @xmath102 . the inset ( b ) shows examples of finite - size scaling of @xmath103 at different @xmath12 using second - order polynomials . ] ( color online ) locations of the singularity ( resp . peak ) in the ferromagnetic and qs phases ( resp . cd phase ) as function of @xmath52 when @xmath104 is fixed . ] ( color online ) finite size scaling of the charge gap for the characteristic points in parameter space used in table  [ tbl : d_and_c ] . ] ( color online ) the lower branch of the von neumann entanglement entropies , obtained from the lower envelope of the full entropy shown in the inset , as a function of the conformally - transformed length@xcite @xmath105 of the subsystem @xmath65 for the characteristic points in parameter space in table  [ tbl : d_and_c ] ( @xmath106 is the system size ) . the solid lines are linear fits using @xmath107 , which determines the central charge @xmath61 . ]    to shed further light into the phases we obtained in dmrg , we show the charge gap @xmath85 and central charge @xmath61 for characteristic parameter values within each phase in table  [ tbl : d_and_c ] ( computational details are illustrated in figs .  [ fig : finite_size_d ] and [ fig : ee_scaling ] ) . from the table it can be seen that all phases have finite charge gaps . moreover , the values of the central charges suggest that one bosonic degree of freedom remains gapless in the qaf phase , while no degree of freedom remains gapless in the cd and f phase . unfortunately , owing to the large ( twelve ) internal dimension of the unit cell , we can not accurately determine the central charge of the qs phase .","summary":"b * 79 * , 205112 ( 2009 ) ] .","abstract":"motivated by the nickel valence controversy in the perovskite nickelate _ _ r__nio , we consider a one - dimensional underscreened kondo chain consisting of alternating spin-1 ( `` nickel '' ) and electron ( `` oxygen '' ) sites , which in addition to the usual electron hopping and spin - spin interaction between the spin and the electron also contains a spin mediated electron hopping term . using the density - matrix renormalization group ( dmrg ) , we obtained the zero temperature phase diagram of the model , as well as various correlation functions in each phase . importantly , for a certain range of parameters the model exhibits a quasi - long - range spiral ( qs ) order . to understand the dmrg results , we construct a mean - field theory based on a schwinger fermion decomposition of the spins , from which we argue that the qs phase corresponds to a phase in proximity to the spin bose metal state proposed by d. n. sheng , o. i. motrunich , and m. p. a. fisher [ phys . rev . b * 79 * , 205112 ( 2009 ) ] . notably , we find no evidence for a phase with the symmetry of `` nickel''-centered charge order , which has been argued to arise due to site - selective kondo screening of half the spins , and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions , not present in this model ."}
{"article_id":"1301.3538","section_id":"c","document":"in this manuscript we considered a 1d underscreened kondo chain with alternating spin-1 and electron sites , which in addition to the familiar electron hopping and kondo term also contained a spin - dependent hopping term . we analyzed the model numerically using dmrg and found that the phase diagram consists of a ferromagnetic ( f ) phase , a quasi - long - range antiferromagnetic ( qaf ) phase , a charge - density ( cd ) ordered phase , and , importantly , a quasi - long - range spiral ( qs ) phase , in which singularities in the spin - spin correlation are observed at incommensurate wavevectors . the phases in our model can in principle be distinguished experimentally by many experimental means . for example , the charge order can be observed by x - ray scattering , or by its effect on the crystal structure . the magnetic order is readily probed by neutron scattering , susceptibility measurements , and nuclear magnetic resonance .    to interpret the dmrg results , we introduced a slave - particle representation of the spin-1 spins , from which we obtained a mean - field hamiltonian . taking the simplest class of mean - field anstze and making use of second - order degenerate perturbation theory , we were able to map the mean - field hamiltonian to an effective spin-1/2 model , from which follows a quantum mean - field phase diagram that resembles the one obtained from dmrg , with the exception of the qs phase . we then focused on the qs phase , by extending our class of mean - field anstze and considering the bosonized interacting theory that arose from them . by considering various possible interactions at the four - fermion level , we argued that the qs phase is best reproduced by an interacting bosonized theory with one charge and one spin degree of freedom ( `` c1s1 '' ) , in which the spin fields carry an incommensurate wavevector . this particular interacting bosonized theory is proximate to the spin bose metal phase proposed by sheng , motrunich , and fisher@xcite . consequently , our results point to a possible route to obtain gapless quantum spin liquids with singularities at incommensurate wavevectors that does not involve the `` ring - exchange '' terms , @xcite and might pave the way for realizing such states in 1d as well as constructing similar states in higher dimensions . while we believe that the current work presents a coherent and comprehensive analysis of the system we considered , we also mention a few opportunities for further study . on the numerical side , it is clearly desirable to obtain the central charge of the qs phase from dmrg and check against the @xmath316 prediction from mean - field theory . this requires either further computation resources or improvements of the methodology . moreover , it would be helpful to check the _ projected _ energetics of the mean - field anstze we proposed , and compare them against the energy obtained from dmrg , via variation monte carlo ( vmc ) . unfortunately , because the slave - particle representation we used requires additional constraints on top of the local conservation of spinon number [ c.f . .  [ eq : constraints ] ] , such a calculation is challenging . on the analytic side , it would be desirable to develop a method that can _ directly _ obtain the cd phase from the slave - particle representation without appealing to an indirectly argument based on symmetry . we also note that there is an alternative slave - particle representation of the spin-1 spins in the literature,@xcite and it would be good to check whether results similar to those we obtained can be derived in this alternative slave - particle representation . finally , we return to the nickel valence controversy that motivated this work , which in the simplest case can be considered as a three - dimensional ( 3d ) extension of the present model . from our mean - field analysis and from general arguments on kondo problems we are quite convinced that the low - energy physics of such 3d model will still be described by an effective spin-1/2 model , which tends to exhibit static spin orders . however , the dimer phase in the effective spin-1/2 model , which we argue to correspond to the oxygen - centered charge - density order , is a special feature in 1d , and is unlikely to persist to 3d . in any case , our dmrg phase diagram shows no sign of nickel - centered charge order ( or its symmetry - equivalent order  we do not insist upon any significant charge accumulation ) , which has been interpreted as due to local kondo singlet formation . thus , the direct extension of our model to 3d is unlikely to exhibit any charge order , whether it is oxygen - centered or nickel - centered . in our opinion this points to the necessity of including explicit coupling to oxygen motions in the mechanism of charge ordering . it would be interesting to explore this directly by explicitly including lattice degrees of freedom in a model similar to ours . we leave this topic for future study . we acknowledge useful discussions with george sawatzky , andy millis , susanne stemmer , jim allen , patrick lee , matthew fisher , and olexei motrunich . this work was supported by the aro through grant w911-nf-09 - 1 - 0398 ( h .- c . j. ) , the nserc of canada ( j.g.r . ) , the mrsec program of the nsf under award no . dmr-1121053 ( l.b . ) , and the kitp s nsf grant , phy-11 - 25915 ( w .- h.k . and l.b . ) . we also acknowledge support from the center for scientific computing at the cnsi and mrl : an nsf mrsec ( dmr-1121053 ) and nsf cns-0960316 .","summary":"r__nio , we consider a one - dimensional underscreened kondo chain consisting of alternating spin-1 ( `` nickel '' ) and electron ( `` oxygen '' ) sites , which in addition to the usual electron hopping and spin - spin interaction between the spin and the electron also contains a spin mediated electron hopping term . using the density - matrix renormalization group ( dmrg ) , we obtained the zero temperature phase diagram of the model , as well as various correlation functions in each phase .","abstract":"motivated by the nickel valence controversy in the perovskite nickelate _ _ r__nio , we consider a one - dimensional underscreened kondo chain consisting of alternating spin-1 ( `` nickel '' ) and electron ( `` oxygen '' ) sites , which in addition to the usual electron hopping and spin - spin interaction between the spin and the electron also contains a spin mediated electron hopping term . using the density - matrix renormalization group ( dmrg ) , we obtained the zero temperature phase diagram of the model , as well as various correlation functions in each phase . importantly , for a certain range of parameters the model exhibits a quasi - long - range spiral ( qs ) order . to understand the dmrg results , we construct a mean - field theory based on a schwinger fermion decomposition of the spins , from which we argue that the qs phase corresponds to a phase in proximity to the spin bose metal state proposed by d. n. sheng , o. i. motrunich , and m. p. a. fisher [ phys . rev . b * 79 * , 205112 ( 2009 ) ] . notably , we find no evidence for a phase with the symmetry of `` nickel''-centered charge order , which has been argued to arise due to site - selective kondo screening of half the spins , and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions , not present in this model ."}
{"article_id":"quant-ph0605218","section_id":"i","document":"one of the most striking advances in quantum computing was made by shor @xcite in 1994 . by exploring the power of quantum parallelism , he discovered a polynomial - time algorithm on quantum computers for prime factorization of which the best known algorithm on classical computers is exponential . in 1996 , grover @xcite offered another apt killer of quantum computation , and he found a quantum algorithm for searching a single item in an unsorted database in square root of the time it would take on a classical computer . since both prime factorization and database search are central problems in computer science and the quantum algorithms for them are highly faster than the classical ones , shor and grover s discoveries indicated that quantum computation offers a way to accomplish certain computational tasks much more efficiently than classical computation and thus stimulated an intensive investigation on quantum computation . after that , quantum computation has been an extremely exciting and rapidly growing field of research . in particular , a substantial effort has been made to find new quantum algorithms and to exploit the techniques needed in building functional quantum computers . currently , quantum algorithms are expressed mainly in the very low level of quantum circuits . in the history of classical computation , however , it was realized long time ago that programming languages provide a technique which allows us to think about a problem intended to solve in a high - level , conceptual way , rather than the details of implementation . recently , in order to offer a similar technique in quantum computation , some authors begun to study the design and semantics of quantum programming languages . in the pool of imperative languages , the earliest proposal for quantum programming language was made by knill in  @xcite , where a set of basic principles for writing quantum pseudo - code was outlined and an imperative pseudo - code suitable for implementation on a quantum random access machine was defined . the first real quantum programming language , qcl , was proposed and a simulator for this language was implemented by mer  @xcite . a quantum programming language in the style of dijkstra s guarded - command language , qgcl , is designed by sanders and zuliani in  @xcite . a probabilistic predicate transformer semantics of qgcl was given , a refinement calculus for it was introduced , and a compiler from qgcl to a simple quantum architecture was defined . a quantum extension of c++ was also proposed by bettelli et al  @xcite , and it was implemented in the form of a c++ library . in the functional programming style , the first quantum language , qfc , was defined by selinger  @xcite based on the idea of classical control and quantum data . programs in the language qfc are represented via a functional version of flow charts , and qfc has a denotational semantics in terms of complete partial orders of super - operators . in addition , quantum process calculus cqp ( communicating quantum processes ) was introduced by gay and nagarajan  @xcite , and qpalg ( quantum process algebra ) was proposed by jorrand and lalire  @xcite in order to support the formal specification and verification of quantum cryptographic protocols . also , feng et al @xcite defined a model qccs of quantum processes , which is a natural quantum extension of classical value - passing ccs with the input and output of quantum states , and unitary transformations and measurements on quantum systems . semantic techniques for quantum computation have also been investigated in some abstract , language - independent ways . for example , a notion of quantum weakest precondition is introduced and a stone - type duality between the state transition semantics and the predicate transformer semantics for quantum programs is established by dhondt and panangaden @xcite , and proof rules for probabilistic programs were generalized by feng et al  @xcite to purely quantum programs . there are already two excellent surveys on quantum programming languages and related researches  @xcite    loop is a powerful program construct in classical computation @xcite . in the area of quantum computation , looping technique has also attracted a few authors attention . for example , bernstein and vazirani  @xcite introduced some programming primitives including looping in the context of quantum turing machines ; some high - level control features such as loop and recursion are provided in selinger s functional quantum programming language qfc . however , the full power of quantum loop programs is still to be exploited . the exploitation of such power definitely requires a deep understanding of the mechanism of quantum loops . the purpose of this paper is to examine thoroughly mechanism of quantum loops in a language - independent way , and to give some convenient criteria for deciding termination of a general quantum loop on a given input . this paper is organized as follows . section 2 is a preliminary section in which some basic notions from quantum mechanics needed in this paper are reviewed . in section 3 , a general scheme of quantum loop programs is introduced , the computational process of a quantum loop is described , and the essential difference between quantum loops and classical loops is analyzed . in addition , we introduce the notions of termination and almost termination of a quantum loop . the function computed by a quantum loop is also defined . quantum walks are considered to show the expressive power of quantum loops . in section 4 , we find a necessary and sufficient condition under which a quantum loop program terminates on a given mixed input state ( theorem  [ prop : 5.1 ] ) . in section 5 , a similar condition is given for almost termination ( theorem  [ thm : 2 ] ) . furthermore , we prove that a quantum loop is almost terminating if and only if it is uniformly almost terminating ( theorem  [ thm : teralter ] ) , and a small disturbance either on the unitary transformation in the loop body ( theorem  [ thm : disturbu ] ) or on the measurement in the loop guard ( theorem  [ thm : disturbm ] ) can make any quantum loop ( almost ) terminating . in section 6 , a representation of the function computed by a quantum loop is presented in terms of finite summations of complex matrices ( theorem  [ prop : 6.4 ] ) . to illustrate the notions and results presented in the previous sections , sections 7 is devoted to some examples which observe the computational behavior of two simplest classes of quantum loops : one qubit loops , and two qubit loops defined by controlled operations . section 8 is the concluding section in which we draw the conclusion and point out some problems for further studies .","summary":"loop is a powerful program construct in classical computation , but its power is still not exploited fully in quantum computation . quantum loops are applied in describing quantum walks . we show that a quantum loop is almost terminating if and only if it is uniformly almost terminating . it is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop ( almost ) terminating . moreover , a representation of the function computed by a quantum loop is given in terms of finite summations of matrices . to illustrate the notions and results obtained in this paper , two simplest classes of quantum loop programs , one qubit quantum loops , and two qubit quantum loops defined by controlled gates , are carefully examined .","abstract":"loop is a powerful program construct in classical computation , but its power is still not exploited fully in quantum computation . the exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs . in this paper , we introduce a general scheme of quantum loops and describe its computational process . the notions of termination and almost termination are proposed for quantum loops , and the function computed by a quantum loop is defined . to show their expressive power , quantum loops are applied in describing quantum walks . necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented . a quantum loop is said to be ( almost ) terminating if it ( almost ) terminates on any input state . we show that a quantum loop is almost terminating if and only if it is uniformly almost terminating . it is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop ( almost ) terminating . moreover , a representation of the function computed by a quantum loop is given in terms of finite summations of matrices . to illustrate the notions and results obtained in this paper , two simplest classes of quantum loop programs , one qubit quantum loops , and two qubit quantum loops defined by controlled gates , are carefully examined ."}
{"article_id":"quant-ph0605218","section_id":"c","document":"exploitation of the full power of loop construct in quantum computation requires a deep understanding of the computational mechanism of quantum loop programs . in this paper , we introduced a general scheme of quantum loop programs , the behaviors of quantum loops are carefully analyzed , including termination , almost termination , and sensitivity , and a matrix - summation representation of the function computed by a quantum loop is found . this paper is merely an initial step toward a thorough understanding of quantum loop programs , and many important problems remain open . first , the bodies of quantum loops that we considered are unitary transformations . if a quantum loop is allowed to be embedded into another quantum loop , then as was observed in section 3 , the body of the latter loop is not a unitary operator but a super - operator in general . therefore , it is an interesting topic for further studies to find conditions for termination and almost termination of quantum loops in which the loop bodies are super - operators . second , we demonstrated the expressive power of quantum loops by presenting a loop description of quantum walks . it would be very interesting to find more computational problems that can not be expressed or solved without quantum loops . in general , the study of loop programs is a very important area of computer programming methodology . reconsideration of some fundamental problems from this area , say loop invariants and proof rules , in the quantum setting is a great challenge .","summary":"the exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs . in this paper , we introduce a general scheme of quantum loops and describe its computational process . the notions of termination and almost termination are proposed for quantum loops , and the function computed by a quantum loop is defined . to show their expressive power ,","abstract":"loop is a powerful program construct in classical computation , but its power is still not exploited fully in quantum computation . the exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs . in this paper , we introduce a general scheme of quantum loops and describe its computational process . the notions of termination and almost termination are proposed for quantum loops , and the function computed by a quantum loop is defined . to show their expressive power , quantum loops are applied in describing quantum walks . necessary and sufficient conditions for termination and almost termination of a general quantum loop on any mixed input state are presented . a quantum loop is said to be ( almost ) terminating if it ( almost ) terminates on any input state . we show that a quantum loop is almost terminating if and only if it is uniformly almost terminating . it is observed that a small disturbance either on the unitary transformation in the loop body or on the measurement in the loop guard can make any quantum loop ( almost ) terminating . moreover , a representation of the function computed by a quantum loop is given in terms of finite summations of matrices . to illustrate the notions and results obtained in this paper , two simplest classes of quantum loop programs , one qubit quantum loops , and two qubit quantum loops defined by controlled gates , are carefully examined ."}
{"article_id":"1406.1358","section_id":"i","document":"the epoch of reionization ( eor ) is the time period in the history of the universe when the first sources of light formed and ionized the intergalactic medium ( igm ) . observations of quasar spectra indicate that this process must have been largely completed around @xmath5 @xcite , but the exact details beyond this redshift  both in terms of the timing of reionization and the sources responsible  are still not well known . some additional observational constraints come from the polarisation of the cosmic microwave background @xcite and temperature measurements @xcite . however , these observations are still consistent with a great range of reionization scenarios @xcite .    during the past decade , ly@xmath1emitters have attracted considerable attention as potential probes of the latest stages of the eor ( e.g.  @xcite ) . since ly@xmath1photons are resonantly scattered by neutral hydrogen , the ly@xmath1luminosity from a galaxy is suppressed if the galaxy is surrounded by a neutral igm . therefore , we would expect the statistics and number counts of ly@xmath1emitters to change at redshifts where reionization is not yet completed . in principle , it should be possible to use this change to measure how neutral the igm is at a certain redshift . while some earlier studies saw no evidence of evolution in the ly@xmath1luminosity function of ly@xmath1emitters at redshifts @xmath6 @xcite , in the past few years several observational studies have established that there is in fact a rapid evolution in the population of ly@xmath1emitters . @xcite and @xcite showed that the luminosity function drops in amplitude between @xmath7 and @xmath3 , after being roughly constant in the interval @xmath8 . this drop appears to continue at even higher redshifts @xcite . in a similar vein , @xcite , @xcite , @xcite , @xcite and @xcite all find that the fraction of drop - out selected galaxies that show ly@xmath1emission decreases rapidly between @xmath9 . it is tempting to view these observations as evidence of an increase in the igm neutral fraction at @xmath10 . however , simulations that try to quantify how high the igm neutral fraction needs to be to account for this evolution at @xmath0 typically require very late and rapid reionization scenarios , with neutral fractions as high as 40 per cent at @xmath3 @xcite . such high neutral fractions are hard to justify physically , and seem incompatible with measurements of the igm temperature @xcite and ly@xmath1line profile measurements @xcite . several ways of easing this tension between simulations and observations have been proposed , including intrinsic evolution in the ly@xmath1emitters @xcite , sample variance in the observations @xcite and the presence small - scale high - density structures @xcite . while measurements of the luminosity function and the ly@xmath1emitter fraction can not distinguish between intrinsic evolution and igm evolution , the additional clustering of ly@xmath1emitters due to a partially ionized igm could be used as a much more robust probe of the ionization state of the igm @xcite . as seen in @xcite , this method requires sample sizes of several thousand objects to put meaningful constraints on reionization . such large samples are not available today , but upcoming observations with the hyper - suprime cam ( hsc ) on the subaru telescope , will observe some 5500 narrow - band selected ly@xmath1emitters over a total of 30 deg@xmath11 at @xmath3 ( m. ouchi 2013 , private communication ) . furthermore , the james webb space telescope ( jwst ) will perform deep spectroscopic surveys of ly@xmath1emitters at high redshifts . however , to date , few systematic investigations have been performed regarding what new information about reionization that will be possible to extract from these observations , besides better measurements of quantities like the ly@xmath1luminosity function and ly@xmath1emitter fraction . this paper is a first step towards providing such study . we investigate the extent to which the next generation of large - field ly@xmath1emitter surveys  such as the hsc survey  and deep spectroscopic surveys  for example with the jwst  may be able to distinguish between intrinsic galaxy evolution and a neutral igm , focusing mainly on clustering measurements , which are beyond the reach of today s surveys . furthermore , we explore the possibilities of using such large ly@xmath1samples to perform `` bubble - mapping '' , i.e. determining the positions and shapes of the largest h@xmath12iiregions . the paper is structured as follows : in section [ sec : methods ] we describe our simulations and physical assumptions . we also discuss how the clustering of ly@xmath1emitters is affected by a partially neutral igm and how this clustering can be quantified . in section [ sec : results ] , we present our predictions , first for the hsc survey and then for the jwst survey . here , we also comment briefly on the recent observational results of @xcite and @xcite . finally , in section [ sec : summary ] , we summarize and discuss our results .    for the simulations , we have assumed a flat @xmath13cdm model with @xmath14 , consistent with the 9 year wmap results @xcite .","summary":"we make predictions for the upcoming subaru hyper suprime - cam ( hsc ) lysurvey and a hypothetical spectroscopic survey performed with the james webb space telescope ( jwst ) . considering various scenarios where the observed evolution of the lyluminosity function of lyemitters at is explained partly by an increasingly neutral igm and partly by intrinsic galaxy evolution , we show how clustering measurements will be able to distinguish between these scenarios . [ firstpage ]    cosmology : dark ages , reionization , first stars  methods : numerical","abstract":"we study the prospects for constraining the ionized fraction of the intergalactic medium ( igm ) at with the next generation of large lyemitter surveys . we make predictions for the upcoming subaru hyper suprime - cam ( hsc ) lysurvey and a hypothetical spectroscopic survey performed with the james webb space telescope ( jwst ) . considering various scenarios where the observed evolution of the lyluminosity function of lyemitters at is explained partly by an increasingly neutral igm and partly by intrinsic galaxy evolution , we show how clustering measurements will be able to distinguish between these scenarios . we find that the hsc survey should be able to detect the additional clustering induced by a neutral igm if the global igm neutral fraction is greater than per cent at . if measurements of the lyequivalent widths ( ews ) are also available , neutral fractions as small as 10 per cent may be detectable by looking for correlation between the ew and the local number density of objects . in this case , if it should turn out that the igm is significantly neutral at and the intrinsic ew distribution is relatively narrow , the observed ews can also be used to construct a map of the locations and approximate sizes of the largest ionized regions . for the jwst survey , the results appear a bit less optimistic . since such surveys probe a large range of redshifts , the effects of the igm will be mixed up with any intrinsic galaxy evolution that is present , making it difficult to disentangle the effects . however , we show that a survey with the jwst will have a possibility of observing a large group of galaxies at , which would be a strong indication of a partially neutral igm .    [ firstpage ]    cosmology : dark ages , reionization , first stars  methods : numerical"}
{"article_id":"1406.1358","section_id":"m","document":"our goal is to produce mock observational samples that incorporate different combinations of intrinsic galaxy evolution and evolution of the igm ionized fraction . to do this , we start with a large cosmological simulation of the igm . we then assign intrinsic ly@xmath1emission properties to the dark matter haloes in the simulation and calculate the ly@xmath1emission through the igm at various global ionized fractions . the methods used here are essentially identical to those described in detail in @xcite , although we use a much larger simulation volume here .      to simulate the reionization of the igm we start with a ( 607  cmpc)@xmath15 @xmath16-body simulation produced with the cubep@xmath15mcode @xcite . based on pmfast @xcite , cubep@xmath15mworks by calculating gravitational forces on a particle - to - particle basis at short distances , and on a grid at long distances . for this simulation , we used 5488@xmath15 particles on a 10976@xmath15 grid , which was eventually down - sampled to 504@xmath15 grid points . the particle mass was @xmath17 . after identifying haloes with a spherical - overdensity halo finder , we simulate the reionization of the igm using the c@xmath11-raycode @xcite . c@xmath11-rayis a photon - conserving ray - tracing code that uses short - ray characteristics to solve the equation for the evolution of the ionization fraction of hydrogen by iterating over all sources and grid points until convergence .    in this simulation , we assigned all haloes an ionizing flux @xmath18 proportional to the halo mass @xmath19 : @xmath20 where @xmath21 is the proton mass and @xmath22 is a source efficiency coefficient that effectively incorporates the star formation efficiency , the initial mass function and the escape fraction . the haloes identified with the halo finder had masses down to @xmath23 ; these were assigned a source efficiency of @xmath24 . in addition to this , we also added smaller sources with @xmath19 down to @xmath25 using a subgrid recipe ( ahn et al . , in preparation ) . these were assumed to have a @xmath26 , to account for a lower metallicity and a more top - heavy initial mass function . on the other hand , since small haloes lack the gravitational potential to keep accreting matter in a highly ionized environment ( e.g.  @xcite ) , these low - mass sources were turned off when the local ionization fraction exceeded 10 per cent . these source efficiencies were chosen to give a reionization history that is consistent with observational results for the electron - scattering optical depth and quasar spectra . for more information about these codes and this particular simulation run and the assumptions behind the simulation parameters , see @xcite . the next step is to simulate the observed ly@xmath1emission from the haloes from the previous step . we use the same two - step model as in @xcite , where we model the ly@xmath1line shape emerging from the circum - galactic medium , @xmath27 , using a recipe based on high - resolution simulations , and then trace sight - lines through the igm , calculating the optical depth due to scatterings out of the line - of - sight . the division between the circum - galactic and extragalactic parts was taken to be at @xmath28 , where @xmath29 is the virial radius of the halo . this value is motivated by @xcite , whose simulations show that at @xmath3 , 80 per cent of ly@xmath1photons have experienced their last scattering into the line - of - sight . the line shape recipe we use is the gaussian - minus - gaussian ( gmg ) model introduced in @xcite . this recipe is a fit to high - resolution hydrodynamical+ly@xmath1radiative transfer simulations . while there is no physical justification for this recipe , it has turned out to match the high - resolution simulations well . the gmg model gives double - peaked line shapes that are symmetric on the blue and red sides of the line centre , and widen as the halo mass increases . such a line shape gives a slightly weaker dependence on igm neutral fraction for the igm transmission of ly@xmath1than models where a big part of the emission comes from the line centre ( e.g.  @xcite ) . this will tend to make our predictions here somewhat on the conservative side . in reality , far from all observed ly@xmath1lines show a double - peaked structure . however , at the redshifts considered here , the blue peak will almost always be absorbed by the igm , and will only affect the normalization of the intrinsic ly@xmath1luminosity ( see below ) . for a more in - depth discussion about other line - shape models , both analytical and simulated , see @xcite .    for the igm part of the ly@xmath1radiative transfer , we use the same modified version of igmtransfer @xcite as described in @xcite . the optical depth for ly@xmath1photons is summed over all cells along the sight - line : @xmath30 where @xmath31 is the length of each step , @xmath32 is the local neutral hydrogen density , @xmath33 is the neutral hydrogen cross section to ly@xmath1scattering and @xmath34 is the gas velocity component of the cell along the line of sight , including the hubble flow . using this method , we calculate the transmission of ly@xmath1through the igm for sightlines along the three coordinate axes for all haloes with @xmath35 . by multiplying the line profile with @xmath36 we then get the observed line profile . the fraction @xmath37 of ly@xmath1photons that are transmitted through the igm is then : @xmath38    a weakness of this method is that the division between the circum - galactic and extragalactic part ( which we put at @xmath39 virial radii ; see discussion above ) in reality depends on the amount of neutral hydrogen . while our value appears reasonable for a fairly ionized medium , it is probably less realistic for a more neutral case . ideally , one would carry out the full radiative transfer of ly@xmath1for every galaxy out to a distance where no more photons scatter into the line - of - sight . however , this would require a very high resolution and is computationally unfeasible . in practice , all studies of the effect of the igm on ly@xmath1emitters have to make some simplified assumptions . here , we therefore use the same division and line model for all ionization fractions , but note that this may cause us to underestimate the effects of the igm somewhat . we also need a model for the intrinsic ly@xmath1and uv continuum luminosities of the galaxies ( here , we use the word _ intrinsic _ to mean the luminosity of the light as it exits the galaxies at @xmath28 ) . since we are interested only in the evolution of the observables due to the igm neutral fraction , we make no attempt to construct a physically motivated model for the intrinsic properties . instead , we simply calibrate the luminosities to observations at @xmath7 .    in our model for the intrinsic properties , each dark matter halo with mass @xmath19 from the @xmath16-body simulations is assigned a ly@xmath1luminosity randomly drawn from a log - normal distribution with a standard deviation of @xmath40 dex and a mean that is proportional to @xmath19 . the normalisation of the luminosities is simply a fit to observations and has no influence on our results , since we are only interested in the changes of various properties . for example , the normalisation of the intrinsic ly@xmath1luminosity is degenerate with our line shape model . had we assumed a line shape with no red peak , the intrinsic ly@xmath1luminosities would have been a factor 2 lower . the change in luminosity with an increasing igm neutral fraction , however , would be the same . the more important quantity here is @xmath41 , which gives us the amount of random scatter in the distributions of luminosities . more random scatter leads to a weaker correlation between galaxy mass and luminosity , which , as we shall see , makes methods that rely on the spatial clustering of ly@xmath1emitters less viable for constraining reionization . the value of @xmath41 was chosen based on the same set of high - resolution simulations that we used for the ly@xmath1line shape model ( see @xcite for more details ) . as we shall see in the next section , our ly@xmath1luminosity model results in luminosity functions with rather shallow slopes compared to observations . since higher values of @xmath41 give shallower slopes , this indicates that if anything , we are over - estimating the random scatter in the ly@xmath1luminosities . this would make our predictions for clustering somewhat conservative , since more randomness tends to make luminosity - selected galaxies appear less clustered .    through the igm . ]    for the ly@xmath1ew  essentially the ratio between ly@xmath1and uv continuum luminosity  we use a similar approach , assigning each dark matter halo an ew drawn from a probability distribution ( for the remainder of the paper , we will use `` ew '' to mean restframe ew ) . the exact shape of the intrinsic ew distribution at @xmath3 is not well known , but observations from lower redshifts suggest that a log - normal distribution is reasonable ( e.g.  @xcite ) . our fiducial ew distribution is shown as the blue histrogram in fig .  [ fig : rew_distribution ] . in this model , 65 per cent of all galaxies have ly@xmath1ews lower than 25  , which is consistent with the ew distribution of lyman - break selected galaxies observed by @xcite . later on in the paper , we also consider a more narrow ew model , shown as a green histogram in fig . [ fig : rew_distribution ] . in the narrow model , approximately 25 per cent of all galaxies have a ly@xmath1ew lower than 25  . this is only marginally consistent with the least luminous galaxies of @xcite , and thus represents a bit of an extreme case . for the rest of the paper , if nothing else is stated , results are shown for the fiducial ew model . for both models , we assume that the ew distribution is valid at @xmath7 for 50 per cent igm transmission , and that any change in the ew at higher @xmath42 is due to the igm only . further , we assign the ews completely randomly to our galaxies , assuming that there is no correlation between ly@xmath1luminosity and ew . this seems to be supported by observations , at least for objects with detectable ews @xcite . a large part of our focus in this paper is on the change in the ly@xmath1emitter population between @xmath7 and @xmath3 , since these are the highest redshifts where the hsc survey will obtain substantial samples . previous observations have indicated that the ly@xmath1luminosity function of ly@xmath1emitters changes between these two redshifts @xcite , but it is not clear whether this is due to an increasingly neutral igm , a change in the intrinsic properties of ly@xmath1emitters or a combination of the two . luminosity functions for the physical scenarios considered in the first part of this paper . the blue dots are observations by ouchi et al at @xmath7 . red dots are observations by ouchi et al 2010 at @xmath3 . all the different simulated scenarios give luminosity functions that are indistinguishable from each other . ]    for this paper , we will make the assumption that the luminosity function at @xmath3 from @xcite holds true . for the mock hsc observations in the first part of the paper , we consider a number of different scenarios where there are varying degrees of change in the igm ionized fraction and the intrinsic properties of the ly@xmath1emitters . there are several possible mechanisms that could change the intrinsic properties of ly@xmath1emitters , including changes in dust content and star formation rate @xcite . here , we do not specify the mechanism responsible . instead , we simply model intrinsic evolution by dimming / brightening all objects in our mock samples by some constant amount . effectively , this means that we dim / brighten the objects both in ly@xmath1and uv continuum luminosity so that their intrinsic ews are unchanged . one could also imagine intrinsic processes that would alter ly@xmath1and uv luminosities in different ways . however , this distinction is unlikely to have any major effects on the statistical observables we discuss here , i.e.  clustering of galaxies . we label our scenarios `` @xmath43 '' , where @xmath44 is the global mass - averaged ionized fraction of the universe at @xmath3 . our most extreme scenario is `` @xmath45 '' ( i.e.  the igm is only 60 per cent ionized at @xmath3 ) . this is the ionized fraction we need in order to explain the change in the luminosity function without any intrinsic galaxy evolution between @xmath7 and @xmath3 . apart from this scenario , we also consider 70 , 80 and 90 per cent ionization at @xmath3 . in these scenarios , the rest of the luminosity evolution is due to intrinsic evolution ( which we model by simply dimming all haloes by a constant factor ) . later on , in section [ sec : jwst ] , we will take a slightly different approach , and instead compare a scenario with simulated igm evolution to two different models for intrinsic evolution . since we have only one reionization simulation , we have to construct these scenarios from simulation volumes that are nominally at different redshifts . for example , for the @xmath46 scenario , we use the c@xmath11-rayoutput from @xmath47 and increase all the halo masses so that the intrinsic luminosity function matches the one at @xmath7 . this is of course not entirely self - consistent , but since many studies have shown that the reionization topology is much more dependent on global ionized fraction than on redshift  at least if the relative contribution of high - mass and low - mass sources is similar  this method should still be reasonable @xcite . to verify that the different redshifts do not have an appreciable impact on the intrinsic properties of our galaxies , we have calculated both the ly@xmath1luminosity functions and the counts - in - cells variances ( see sec .  [ sec : clustering ] ) for the samples with the effects of the igm removed . we found the differences between the samples to be negligible .    . here , we construct 10 samples along each coordinate axis . the right box ( b ) shows the jwst skewers , which have a field - of - view of 220 arcmin@xmath11 , and a depth of @xmath48 . we construct a total of 256 such skewers from our full volume . ]    for each of the scenarios , we construct a number of mock hsc samples by first selecting all objects with ew @xmath49    , and then selecting the ones with the highest ly@xmath1luminosities to give the same number density of ly@xmath1emitters as the planned hsc survey ( i.e.  5500 objects per 30 deg@xmath11 ) . this gives similar effective luminosity cutoffs as those expected for the hsc survey , but we chose to specify exact number densities instead of exact cutoffs to make clustering comparisons easier . since the redshift depth of the hsc survey is approximately one tenth of our simulation volume , we are able to construct ten mock observations for each coordinate axis for each scenario . each such mock observation will have roughly half the area of the full hsc survey , so for some statistical predictions we combine two separate mock observations [ fig : lfs_scenario ] shows the ly@xmath1luminosity functions of all these mock samples along with the observations of @xcite at @xmath7 and @xmath3 . by design , they are indistinguishable when looking only at the luminosity functions . in fig .  [ fig : lae_boxes ] we show a schematic illustration of how the mock samples compare to our full simulation volume and to the mock samples for the jwst survey that we consider in section [ sec : jwst ] . as can clearly be seen in fig . [ fig : lfs_scenario ] , observations of luminosity functions alone are not useful for telling intrinsic galaxy evolution apart from igm evolution . however , by looking at the spatial clustering of ly@xmath1emitters , it may be possible to separate the two effects . when doing this , it is important to distinguish the clustering that comes from the topology of the ionized bubbles ( which is what we are interested in here ) from other sources of clustering . in addition to the intrinsic clustering of galaxies due to density fluctuations in the universe , a partially neutral igm will affect the clustering of ly@xmath1emitters in two ways @xcite . first , if one considers two observed samples with the same luminosity cutoff but different igm ionized fractions , the sample with the most neutral igm will have a higher clustering of sources . this is mainly because only the most massive sources will be seen through the more neutral igm , and these are also the ones that are found in the densest regions . second , if one considers two samples again with different igm ionized fraction , but with the same number of observed sources ( implying different luminosity cutoffs ) , then the clustering of sources will also be increased since ly@xmath1emitters are easier to observe if they are located deep inside an ionized region . high - luminosity ly@xmath1emitters that happen to lie at the edge of an ionized region may be obscured , while slightly lower - luminosity sources that are in the middle of an ionized region may be observable . however , since the ionized regions are not located at random , but are localized around the largest clusters of galaxies , this effect is fairly weak and requires large samples to observe . the first of these two effects is simply due to the decrease in number density , and can not be used to separate intrinsic galaxy evolution from igm evolution . the second one , on the other hand , is a signature of a partially ionized igm . therefore , we consider only samples with a fixed number density . a visual illustration of the igm - induced clustering for a fixed sample size is shown in fig . [ fig : observed_samples ] , where we show the detected ly@xmath1emitters in four of our scenarios scenarios for the mock hsc survey . there are several ways to quantify the spatial clustering of galaxies . one of the most common methods is the two - point correlation function , @xmath50 , which is the excess probability of finding two galaxies at a separation @xmath51 , compared to a uniform random distribution . the two - point correlation function contains a lot of information since it measures the clustering over a range of scales . however , comparing two different correlation functions is usually done by fitting a parameterized functional shape , which requires implicit assumptions about the statistics of the objects in the sample . furthermore , the two - point correlation function is awkward to calculate for fields with complicated shapes .    here , we consider instead a related statistic called _ counts - in - cells_. the counts - in - cells method works by simply dividing the observed field into a number of cells of equal size and counting the number of galaxies @xmath52 that fall into each cell @xmath53 . typically , one then calculates the variance of the counts : @xmath54 where @xmath16 is the total number of cells . the counts - in - cells variance gives us a single , easy to calculate , number that measures the clustering without any assumptions of the statistics of the objects  higher variance means more clustered objects . in fact , @xmath55 can be shown to be proportional to the integral of the two - point correlation function ( see e.g.  @xcite and @xcite for more details ) . the two major drawbacks of the method are that the results depend on the choice of the cell size , and that it contains no information about the clustering on different spatial scales ( as opposed to the correlation function ) . the counts - in - cells method discussed above requires only that we know the positions of ly@xmath1emitters . however , if we know also the ew of the galaxies in our sample , we can use this to learn more about the igm . since the uv luminosity is not affected by neutral hydrogen in the igmline will be subject to igm absorption , but at redshifts @xmath56 , this absorption is essentially a complete gunn - peterson trough , and can be corrected for . the presence of a ly@xmath1damping wing will introduce a slight uncertainty to the correction , but for a broad - band measurement , this uncertainty will be small . ] , the ew  i.e .  the ratio between the ly@xmath1and the uv continuum luminosity  will be a measure of @xmath37 , the fraction of ly@xmath1flux that is transmitted through the igm .    for an individual galaxy , calculating @xmath37 from the ew is fairly meaningless , since the random scatter is very large ( cf . [ fig : rew_distribution ] ) . however , with a sample containing thousands of galaxies , it becomes possible to look for trends in the observed ew in different regions on the sky . we would expect the ew to be higher on average in regions where the igm is highly ionized . by studying the mean ew in different regions , it may be possible to reconstruct the ionization structure of the igm and measure the locations and sizes of the largest ionized regions ( or `` bubbles '' ) . such `` bubble mapping '' may give valuable insights into the topology of reionization . this approach is different from so - called ly@xmath1intensity mapping @xcite in that it only deals with galaxies , not the diffuse emission from the igm itself .","summary":"the results appear a bit less optimistic .","abstract":"we study the prospects for constraining the ionized fraction of the intergalactic medium ( igm ) at with the next generation of large lyemitter surveys . we make predictions for the upcoming subaru hyper suprime - cam ( hsc ) lysurvey and a hypothetical spectroscopic survey performed with the james webb space telescope ( jwst ) . considering various scenarios where the observed evolution of the lyluminosity function of lyemitters at is explained partly by an increasingly neutral igm and partly by intrinsic galaxy evolution , we show how clustering measurements will be able to distinguish between these scenarios . we find that the hsc survey should be able to detect the additional clustering induced by a neutral igm if the global igm neutral fraction is greater than per cent at . if measurements of the lyequivalent widths ( ews ) are also available , neutral fractions as small as 10 per cent may be detectable by looking for correlation between the ew and the local number density of objects . in this case , if it should turn out that the igm is significantly neutral at and the intrinsic ew distribution is relatively narrow , the observed ews can also be used to construct a map of the locations and approximate sizes of the largest ionized regions . for the jwst survey , the results appear a bit less optimistic . since such surveys probe a large range of redshifts , the effects of the igm will be mixed up with any intrinsic galaxy evolution that is present , making it difficult to disentangle the effects . however , we show that a survey with the jwst will have a possibility of observing a large group of galaxies at , which would be a strong indication of a partially neutral igm .    [ firstpage ]    cosmology : dark ages , reionization , first stars  methods : numerical"}
{"article_id":"1406.1358","section_id":"i","document":"using a large - scale simulation of the igm during reionization combined with ly@xmath1radiative transfer simulations , we have explored the new types of statistical measurements of the ionization state of the igm at @xmath56 that will become possible with the next generation of large ly@xmath1emitter surveys . surveys with instruments such as the hsc and jwst / nirspec will provide improved measurements of many important properties of high - redshift ly@xmath1emitters , such as their luminosity function , their typical sizes , ages , star formation rates etc . however , such measurements only give indirect information about the history of reionization . in this paper , we have instead focused mainly on methods to break the degeneracy between neutral igm and intrinsic galaxy evolution . clustering measurements such as counts - in - cells provide a way of separating the effects of a neutral igm from intrinsic galaxy evolution . while changes in star formation rate , escape fraction or dust content may all help explain the apparent decrease of ly@xmath1emitters between @xmath59 and @xmath3 , it is unlikely that any of these processes would produce a clustering signal that could be confused with a neutral igm . we find that , if only ly@xmath1luminosities are available , the subaru hyper - suprime cam ( hsc ) survey should be able to distinguish an igm that is @xmath98 per cent neutral from one that is completely ionized at @xmath3 by measuring the clustering of ly@xmath1emitters , for example using the counts - in - cells method .    if the uv continuum luminosities can also be measured , several new possibilities open up . we have shown that by measuring the correlation between the mean ew of all the close neighbours of a galaxy and the number of such close neighbours , it is possible to detect a neutral fraction with a sensitivity similar to counts - in - cells measurements . if the two methods are combined , a neutral fraction as small as 10 per cent may be detectable at @xmath3 using hsc .    in this more optimistic case , it may also become possible to use the ly@xmath1ews to directly map the locations , sizes and shapes of the largest ionized regions . regardless of the availability of data , such bubble mapping is of course only possible if there actually is a substantial amount of neutral hydrogen at @xmath3 . in most reionization simulations , at an ionized fraction somewhere around 70 per cent or so , the ionized bubbles are overlapping to such a large extent that one can no longer speak of individual ionized regions . additionally , we have seen that the feasibility of a bubble mapping measurement depends strongly on the intrinsic ew distribution  if there is a large amount of random scatter in the ews , the correlation between local ionized fraction and observed ew is weak . if , however , such a bubble mapping measurement could be made , it could give unique insights into the topology of reionization . it would also provide great synergies with upcoming 21-cm experiments such as lofar and the ska , for example for cross - correlating the ly@xmath1emitter density with the 21-cm signal @xcite . we have also investigated the prospects for using the jwst to constrain the igm ionization state . the statistical methods we used to look for clustering in the hsc data do not work very well for the type of data produced by a deep spectroscopic survey . first of all , the sample size will be considerably smaller than for the hsc , even for a very ambitious survey . second , such a survey will contain objects from a wide range of redshifts , so that any effect from an increasingly neutral igm will be mixed up with whatever intrinsic galaxy evolution effects are present . nevertheless , we have shown that there is a chance that such a survey will detect a group containing a large number of galaxies in a small redshift interval at high @xmath42 . finding such a group would be a strong indication of a neutral igm where galaxies reside in ionized bubbles , especially if the group contains one or more high - ew objects . however , even a detection like this would not be a conclusive proof of a neutral igm , since similar groups can occur also in the other evolution scenarios considered here , albeit with much lower probability . it is also interesting to compare our simulations to the recent observations by @xcite and @xcite , who performed spectroscopic observations of ly@xmath1emitters at @xmath10 and both found that the ew distribution at high redshifts is better explained by a patchy evolution model  where some objects are completely turned off and some are left as is  than a smooth model , where all galaxies are dimmed by a constant factor . the patchy model is intended as a toy model of reionization , where galaxies are either inside or outside ionized bubbles . however , in our simulations , galaxies are always located inside ionized bubbles , and the distribution of igm transmission fractions , @xmath37 , is not bimodal . the same result is found in most similar simulations ( see e.g.  @xcite and @xcite ) . with a unimodal @xmath37 distribution , the ew distribution looks almost indistinguishable from the smooth evolution model , but very different from the patchy evolution model . interestingly , this implies that the results of @xcite and @xcite actually argue _ against _ the reionization scenarios produced by most simulations . it is not obvious what kind of scenario could produce the observed results , which show a strong deficit of intermediate - ew objects . it is conceivable that a situation like this could be produced in a scenario like that proposed by @xcite , in which the igm at high @xmath42 is highly ionized , but ly@xmath1emitters are obscured by small , high - density clumps of neutral gas . if there are relatively few clumps , there could be some galaxies that are unobscured and others that are hidden behind clumps , leading to a bimodal @xmath37 distribution . it is also possible that some change in the intrinsic properties of galaxies ( such as evolution in the escape fraction ; @xcite ) is strong in some group of galaxies , and weak in the rest . observations with the jwst will provide much better statistics on the ew distribution of high-@xmath42 ly@xmath1emitters . regardless of whether the results of @xcite and @xcite are verified or not , this will teach us something about the evolution of galaxies in the early universe . while our results overall look rather promising , at least for the hsc , there are a few caveats to bear in mind . first , the observations we are considering are all very challenging , and some of our assumptions about them are somewhat optimistic . for example , obtaining uv luminosities for all the objects in the hsc survey may not be possible . second , there are a number of uncertain parameters in our model for ly@xmath1emitters , as discussed in more detail in section [ sec : lya_only ] . performing accurate simulations of ly@xmath1production and radiative transfer through the circum- and intergalactic medium is a highly challenging task with many pitfalls . our aim in this study has been to investigate the types of measurements that may become possible with the next generation of ly@xmath1emitter surveys , rather than to explore every possible model uncertainty . we have therefore attempted to construct a model with reasonable assumptions that tend to lie on the conservative side .    in any case , the results from the next generation of ly@xmath1emitter surveys will doubtless be of great value for studying reionization , regardless of what is actually observed . if a clustering signal can be seen in the hsc observations at @xmath3 , this will be strong evidence that reionization was still ongoing at this redshift . conversely , if no clustering is seen , this will indicate that reionization is already almost completely finished by this redshift , and instead the intrinsic properties of ly@xmath1change rapidly between @xmath59 and @xmath3 . for the jwst , if a large group of galaxies could be detected at high redshift , this would be a strong indication of a partially neutral igm . however , even without such luck , a deep spectroscopic survey with the jwst would put unprecedented constraints on the evolution of the ew distribution , which contains valuable information about the first galaxies in the universe .","summary":"we study the prospects for constraining the ionized fraction of the intergalactic medium ( igm ) at with the next generation of large lyemitter surveys . we find that the hsc survey should be able to detect the additional clustering induced by a neutral igm if the global igm neutral fraction is greater than per cent at . if measurements of the lyequivalent widths ( ews ) are also available , neutral fractions as small as 10 per cent may be detectable by looking for correlation between the ew and the local number density of objects . in this case , if it should turn out that the igm is significantly neutral at and the intrinsic ew distribution is relatively narrow , the observed ews can also be used to construct a map of the locations and approximate sizes of the largest ionized regions . for the jwst survey , since such surveys probe a large range of redshifts , the effects of the igm will be mixed up with any intrinsic galaxy evolution that is present , making it difficult to disentangle the effects . however , we show that a survey with the jwst will have a possibility of observing a large group of galaxies at , which would be a strong indication of a partially neutral igm .   ","abstract":"we study the prospects for constraining the ionized fraction of the intergalactic medium ( igm ) at with the next generation of large lyemitter surveys . we make predictions for the upcoming subaru hyper suprime - cam ( hsc ) lysurvey and a hypothetical spectroscopic survey performed with the james webb space telescope ( jwst ) . considering various scenarios where the observed evolution of the lyluminosity function of lyemitters at is explained partly by an increasingly neutral igm and partly by intrinsic galaxy evolution , we show how clustering measurements will be able to distinguish between these scenarios . we find that the hsc survey should be able to detect the additional clustering induced by a neutral igm if the global igm neutral fraction is greater than per cent at . if measurements of the lyequivalent widths ( ews ) are also available , neutral fractions as small as 10 per cent may be detectable by looking for correlation between the ew and the local number density of objects . in this case , if it should turn out that the igm is significantly neutral at and the intrinsic ew distribution is relatively narrow , the observed ews can also be used to construct a map of the locations and approximate sizes of the largest ionized regions . for the jwst survey , the results appear a bit less optimistic . since such surveys probe a large range of redshifts , the effects of the igm will be mixed up with any intrinsic galaxy evolution that is present , making it difficult to disentangle the effects . however , we show that a survey with the jwst will have a possibility of observing a large group of galaxies at , which would be a strong indication of a partially neutral igm .    [ firstpage ]    cosmology : dark ages , reionization , first stars  methods : numerical"}
{"article_id":"math-ph0702094","section_id":"i","document":"this paper is a survey of some author s results related with the maslov  shvedov method of complex germ [ 2 ] and with perturbative quantum field theory . these results are , shortly , the following . firstly , the results from the theory of quantum mechanical schrodinger equation . the maslov  shvedov method makes it possible to give a simple exposition of the method of canonical operator on a lagrangian manifold with complex germ [ 25 ] of asymptotic solution of the cauchy problem for the schrodinger equation . it turns out that many maslov  shvedov s formulas become more simple and get a natural mathematical interpretation if in the schrodinger equation one chooses the weyl ( symmetric ) ordering of multiplication and differentiation operators . in particular , the transport equation describes the transport of half - forms along the classical trajectory , and the transport of maslov  shvedov wave packets is given by the action of the operator of the weil representation of the metaplectic group corresponding to the tangent symplectic transformation to the hamiltonian flow . besides that , one obtains a simple and natural definition of the maslov index modulo 4 , related with the complex germ method at a point , which seemingly did not appear in the literature . a closed exposition of these results is given in  1 . secondly , the results from perturbative quantum field theory . here introducing the infinite dimensional analog of the weyl algebra allows one not only to interpret the quantum field theory maslov  shvedov complex germ obtained in [ 2 ] by complicated computations ( or , more precisely , to obtain a result close to that result of [ 2 ] ) , but , generally , it allows one to give an exposition of the main results of perturbative quantum field theory not using subtraction of infinities from the hamiltonian of a free field and normal ordering of operators . the weyl algebra plays the role of an extended algebra of operators in the fock space , where the @xmath0-product corresponds to the composition of operators , while the usual commutative product of functions corresponds to normally ordered product of operators . this result seems very important for understanding free and perturbative quantum field theory . a closed exposition of these results on the simplest example of the @xmath1 model of quantum field theory in four - dimensional space - time is contained in  2 . the author is grateful to v.  v.  dolotin , yu .  a.  neretin , and i.  v.  tyutin for helpful discussions .","summary":"the paper is a survey of some author s results related with the maslov  shvedov method of complex germ and with quantum field theory . the main idea is that many results of the method of complex germ and of perturbative quantum field theory can be made more simple and natural if instead of the algebra of ( pseudo)differential operators one uses the weyl algebra ( operators with weyl symbols ) with the moyal-product .","abstract":"the paper is a survey of some author s results related with the maslov  shvedov method of complex germ and with quantum field theory . the main idea is that many results of the method of complex germ and of perturbative quantum field theory can be made more simple and natural if instead of the algebra of ( pseudo)differential operators one uses the weyl algebra ( operators with weyl symbols ) with the moyal-product ."}
{"article_id":"1408.5182","section_id":"i","document":"a pump converts an external bias into work . we need the average bias to get the work from a macroscopic mechanical pump , but it is known that the average bias to get a pumping current is not necessary in mesoscopic systems . when a mesoscopic system , thus , is slowly and periodically modulated by several control parameters such as chemical potentials , gate voltages , and tunneling barriers , there exists a net average current without dc bias . this phenomenon is known as adiabatic pumping , and has been observed in various processes such as quantized charge transport@xcite , spin pumping@xcite , and qubit manipulation@xcite . the first proposal of adiabatic pumping was given by thouless@xcite for a closed quantum system . the idea of quantum pumping for closed systems has been extended to open systems@xcite . such adiabatic pumping processes have been experimentally realized in mesoscopic transport processes@xcite . it is recognized that the mechanism of adiabatic pumping originates from the geometrical effect of the berry phase in quantum mechanics@xcite , where a circular operation in a parameter space creates a non - zero geometrical quantity associated with the pumping current . similar phenomena have been studied in stochastic systems described by classical master equations@xcite and quantum master equations@xcite . as indicated in the analysis of classical master equations@xcite , adiabatic pumping is also characterized by a berry - phase - like quantity , the so - called berry - sinitsyn - nemenman ( bsn ) phase@xcite . the bsn phase has been extended to the quantum master equation case@xcite . it is remarkable that the bsn phase is directly related to the path - dependent entropy under strong nonequilibrium conditions@xcite , which is an interesting extension of the equilibrium thermodynamics to a nonequilibrium thermodynamics .    most of the previous studies , however , assume that the pumping process is only modulated adiabatically , where the validity of the approximation is ensured if the modulation speed is zero . this situation is practically useless , because the pumping current under adiabatic modulation is zero in the strict sense . it is , thus , important to ( i ) clarify the limitation of the adiabatic approximation and ( ii ) analyze the pumping process without the introduction of the adiabatic approximation to get a finite pumping current under a finite speed modulation . although there exist some papers discussing non - adiabatic pumping effects based on a stochastic equation with weak noise@xcite , the master equation@xcite , the floquet scattering theory@xcite , and the green function@xcite , it is unclear how non - adiabatic effects affect the pumping current . indeed , it is known that a non - adiabatic process can cause a phase transition through the analysis of a simple quantum mechanical model@xcite . we may ask another non - trivial question associated with the non - adiabatic pumping process besides the pumping current . although there exists the heat fluctuation theorem@xcite , for adiabatic dynamics of open markovian processes , at least , the heat fluctuation theorem seems to be violated under some situations such as the dynamics under modulated external fields@xcite , non - gaussian noise@xcite , or dry friction@xcite . we have to clarify the reason why the heat fluctuation theorem seems to be violated .    in this paper , we systematically study non - adiabatic pumping effects within the framework of the quantum master equation under the markovian approximation . for this purpose , similar to ref.@xcite , we analyze the simplest spin - boson model under the weak coupling condition between surrounding environments and the system . we continuously control the temperatures in the environments with the modulation frequency @xmath3 , and clarify the initial condition dependence of the pumping current and the essential non - adiabatic effects on the pumping current . we also extend the steady heat fluctuation theorem to cases of slowly modulated temperatures and high transferred energy limits . the organization of this paper is as follows . in sect .  2 , we introduce the model of the spin - boson system and the methods of the generalized quantum master equation with the full counting statistics ( fcs ) . section 3 is the main part of this paper , and consists of three parts . in sect . 3.1 , we derive general expressions for the non - adiabatic pumping current . in sect . 3.2 , we apply our formulation to the spin - boson system introduced in sec .  2 , and present the results for the pumping current to clarify the non - adiabatic effects . in sect .  3.3 , we discuss whether the heat fluctuation theorem is still valid . finally , we discuss and summarize our results in sect . 4 . in appendix a , we briefly summarize the properties of the cumulant - generating function and the first moment . in appendix b , we derive the master equation with parameter modulation in the context of fcs . in appendix c , we reproduce the adiabatic markovian pumping current obtained in ref.@xcite within our framework . in appendix d , we summarize the relationship between our formulation and that in ref.@xcite . in appendix e , we derive the asymptotic expansion of the density matrices and the non - adiabatic pumping current . in appendix f , we explain the detailed derivation of the extended heat fluctuation theorems showed in sect .","summary":"we clarify the role of non - adiabatic effects in quantum pumping for a spin - boson system . the validity of the analytic expression is verified by our numerical calculation . moreover , we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies .","abstract":"we clarify the role of non - adiabatic effects in quantum pumping for a spin - boson system . when we sinusoidally control the temperatures of two reservoirs with phase difference , we find that the pumping current strongly depends on the initial condition , and thus , the current deviates from that predicted by the adiabatic treatment . we also analytically obtain the contribution of non - adiabatic effects in the pumping current proportional to where is the angular frequency of the temperature control . the validity of the analytic expression is verified by our numerical calculation . moreover , we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies ."}
{"article_id":"1408.5182","section_id":"c","document":"we have successfully extended the theory of adiabatic pumping to non - adiabatic pumping for finite speed modulations within the framework of the markovian quantum master equation . we have applied our formulation to the spin - boson system and found that ( i ) the pumping current strongly depends on the initial condition , and ( ii ) the contribution of the non - adiabatic pumping current is relevant for relatively large @xmath172 if the contribution of the initial relaxation is eliminated . ( iii ) the contribution of the non - adiabatic effect is analytically reproducible in terms of the technique of the asymptotic expansion . ( iv ) the extended fluctuation theorems for slowly modulated temperatures and large transferred energies are derived . our master equation in a weak coupling limit does not have any contribution from the off - diagonal elements of the density matrix . therefore , our master equation is reduced to the classical rate equation@xcite . to extract the off - diagonal contributions , we may consider a strong coupling regime or more complicated model such as a three - level system . this will be our future work . although our system is equivalent to that analyzed in ref.@xcite , there are various differences in the analysis between two papers . indeed , ref.@xcite uses discretized time evolution under the finite interval @xmath173 when the master equation is solved , while we have obtained both numerical and analytic solutions under continuous time evolution . moreover , we have explicitly obtained the analytic form for the pumping current whose validity is quantitatively verified through comparison with the numerical calculation . furthermore , the discussion on the extended fluctuation theorems in sect . 3.3 is completely new . therefore , we believe that there exist several merits for the publication of our paper besides ref.@xcite .    we have derived an analytic expression for the non - adiabatic pumping current @xmath174 corresponding to the geometrical phase in the adiabatic limit . we should note , however , that @xmath174 is no longer geometric quantity as in the adiabatic case because the curvature depends on time . such a time - dependent quantity may be interpreted by the aharonov - anandan phase method@xcite . we have also derived the fluctuation theorem with the temporal change of parameters in the case of @xmath158 or @xmath175 . this is a natural extension of the steady fluctuation theorem to the time - dependent fluctuation theorems . we expect floquet theory to be applicable to our system because we study periodic modulations to the system . in future work we will compare our analysis with that based on floquet theory . we only analyze the case of continuous modulation of the temperature ( [ t(t ) ] ) under the assumption that both environments are always in equilibrium . it is straightforward to apply our formulation to fermion systems such as the impurity anderson model@xcite . it should be noted that our theory can not be applied to either discontinuous changes in temperature or fast modulation . although it is possible to apply our formulation to non - markovian processes , we are suspicious of whether the analysis within this framework is meaningful , because non - markovian processes may affect the state of the environments . we also note that the distinction between two current terms is no longer valid for non - markovian processes , because @xmath176 sometimes takes positive values . we will discuss the non - markovian pumping process elsewhere .","summary":"when we sinusoidally control the temperatures of two reservoirs with phase difference , we find that the pumping current strongly depends on the initial condition , and thus , the current deviates from that predicted by the adiabatic treatment .","abstract":"we clarify the role of non - adiabatic effects in quantum pumping for a spin - boson system . when we sinusoidally control the temperatures of two reservoirs with phase difference , we find that the pumping current strongly depends on the initial condition , and thus , the current deviates from that predicted by the adiabatic treatment . we also analytically obtain the contribution of non - adiabatic effects in the pumping current proportional to where is the angular frequency of the temperature control . the validity of the analytic expression is verified by our numerical calculation . moreover , we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies ."}
{"article_id":"1504.03527","section_id":"i","document":"a random variable has a phase - type ( ph ) distribution if it corresponds to the time until absorption of a transient markov chain with one absorbing state . ph distributions , introduced in the early 1980 s by neuts ( * ? ? * chapter 2 ) , form a class of distributions with considerable modelling versatility , which results from attractive probabilistic properties . the set of ph distributions is closed under convolutions and finite mixtures , and is dense in the class of all distributions with non - negative support . ph distributions have therefore been extensively used in practice , in particular for modelling lifetime distributions , see for instance @xcite , @xcite , and @xcite .    the question addressed in this paper arose initially when modelling the lifetime reproductive success of the black robin _ petroica traversi _ , which is an endangered songbird species endemic to the chatham islands , an isolated archipelago located 800 km east of new zealand . by 1980 , the population of black robins had declined to five birds , including a single successful breeding pair , on mangere island  @xcite . through intensive conservation efforts in 1980 - 1989 by the new zealand wildlife service ( now the department of conservation ) , the population recovered to 93 birds by spring 1990 @xcite . over the next decade ( 1990 - 1998 ) , the population was closely monitored , but without human intervention . nevertheless the population continued to grow rapidly to 197 adults by 1998 , but after this period , the population growth slowed considerably and it only reached 239 adults in 2011 @xcite . the black robin population is modeled in a parallel studys . hautphenne , m. massaro , e. s. kennedy , and r. sainudiin . modelling of the chatham island black robin _ petroica traversi _ populations using branching processes : informed management strategies for reintroduction of endangered species . in preparation ] using a special class of branching processes called the markovian binary tree ( mbt ) , in which an underlying transient markov chain controls the reproduction and death events of each individual in the population . a direct consequence of this model is that each bird lives for a random time which has a ph distribution , in which it progresses through states ( also called phases ) of a continuous - time markov chain and dies when the chain moves to an absorbing state . in this application , the phases do not have any particular physical interpretation , their role is to increase the accuracy and realism of the mbt model , as opposed to the simplest linear birth - and - death model . in other real - world applications , the phases may have a physical meaning , such as in @xcite where they model physiological ages , which can be interpreted as relative health indices , as opposed to chronological age . mbts have proved to be powerful stochastic models in population biology and demography @xcite . having fitted an mbt to real data , we can calculate properties of the population , such as the probability that it will become extinct in some time interval @xmath0 $ ] , and the distribution of the population size at time @xmath1 . in particular , the model allows us to compute the expected number of birds in phase @xmath2 at time @xmath1 , and the asymptotic frequency of phase @xmath2 in the population . however , the latter two quantities may not have significance for biologists , who are likely to be interested in age - specific , rather than phase - specific , properties of individuals . we therefore need to be able to translate information about the phase distribution into information about the age distribution ; that is , we need to answer the question `` _ _ what is the age distribution of a bird , given its phase _ _ '' ? note that the reverse exercise of translating information about age into information about phase is much easier since the distribution of the phase at any given age is well known . the main difference is that age is deterministic , while phase is random and an individual stays in a given phase for an exponentially distributed amount of time . in fact , defining the event that an individual is in phase @xmath2 is already not trivial . it is necessary to describe in more detail how the individual is sampled . we suggest three sampling schemes according to which an observer looks at the phase of an individual :    * first , we assume that individuals are born according to a poisson process which started infinitely far in the past , and one observes the phase of a randomly selected individual at time 0 ; * second , no assumption is made on the birth process , and the observations of individuals occur according to a poisson process , in which case we allow a single or multiple observation(s ) ; * third , a single observation occurs at a uniformly distributed random time within some time window .    for each observation scheme , we compute the conditional age distribution given the observed phase , as well as related quantities . we show that the age distribution conditional on a single rare poisson phase observation coincides with the age distribution conditional on a single rare uniform phase observation . moreover , this age - distribution also corresponds to the age distribution of a randomly selected bird in a given phase at time 0 in the process where individuals are born according to a poisson process . the questions addressed in this paper , and their proposed answers , are not restricted to the context of ph distributions and ageing processes ; they have a wider interest in markov chain theory . indeed , if @xmath3 is the generator of a continuous - time markov chain @xmath4 , then it is well known that @xmath5=[\\exp(qt)]_{ij}$ ] , but the conditional distribution of the time @xmath1 elapsed since the start of the markov chain , given that the chain is observed in phase @xmath2 is much less explored . as we observed above , the nature of this observation event needs to be described carefully . the paper is organised as follows . in the next section , we provide some background on ph distributions used to model the ageing process of individuals . in section 3 , we compute the conditional age distribution at time 0 in the poisson birth process , given the observed phase . in section 4 , we consider the poisson phase observation scheme and provide the conditional age distribution with a single or multiple observation(s ) . in section 5 , we consider a uniform observation scheme , and in section 6 we discuss the rare observation limit of the results obtained in sections 4 and 5 . finally , in section 7 , we illustrate our results on a toy example first , and then on the computation of the age pyramid for the black robin population .","summary":"in this paper , we use a finite - state continuous - time markov chain with one absorbing state to model an individual s lifetime . under this model , the time of death follows a phase - type distribution , and the transient states of the markov chain are known as _ + _ keywords : _ phase - type distribution ; transient markov chain ; age distribution ; _ petroica traversi _","abstract":"in this paper , we use a finite - state continuous - time markov chain with one absorbing state to model an individual s lifetime . under this model , the time of death follows a phase - type distribution , and the transient states of the markov chain are known as _ phases_. we then attempt to provide an answer to the simple question `` _ _ what is the conditional age distribution of the individual , given its current phase _ _ '' ? we show that the answer depends on how we interpret the question , and in particular , on the phase observation scheme under consideration . we then apply our results to the computation of the age pyramid for the endangered chatham island black robin _ petroica traversi _ during years of intensive conservation efforts in 1980 - 1989 . + _ keywords : _ phase - type distribution ; transient markov chain ; age distribution ; _ petroica traversi _"}
{"article_id":"0809.2073","section_id":"i","document":"xz tauri ( hbc 50 , haro 6 - 15 ) is a pre - main sequence binary system located in the l1551 molecular cloud at a distance of 140 pc . both components of the 03 binary have strong emission lines that are characteristic of classical t tauri stars ( hartigan & kenyon 2003 ; white & ghez 2001 ) . these studies have determined spectral types of m3-m3.5 for the southern component and m1.5-m2 for the northern one . the spectrum of the s component in our data ( hereafter xz tau a ) indicates that it is a typical t tauri star , while the n component ( xz tau b ) has large amount of spectral veiling and numerous emission lines , especially ca  ii ( hartigan & kenyon 2003 ) . the relative brightnesses of the two components fluctuates at optical wavelengths , with the s component 12 mags brighter in 1995 and 1997 _ hubble space telescope _ ( _ hst _ ) images ( krist et al . 1997 ; white & ghez 2001 ) and the n component brighter in 1996 and 2000 ( white & ghez 2001 ; hartigan & kenyon 2003 ) . the xz tau system is an x - ray source with strong variability and a hard spectrum ( carkner et al . 1996 ; knig et al . 2001 ; giardino et al . it is also a 3.6 cm radio continuum source ( rodriguez et al . 1994 ) . xz tau was identified by mundt et al . ( 1990 ) as the source of a bipolar , collimated outflow ( hh 152 ) along a position angle of @xmath3 with radial velocities of up to @xmath4 km s@xmath1 , and the blueshifted lobe to the n. welch et al . ( 2000 ) found an expanding shell of @xmath5co emission @xmath6 pc across and centered on xz tau , which may be related to this outflow . krist et al . ( 1997 , 1999 ) resolved the inner parts of the outflow using psf - subtracted _ hst _ images , finding an unusual bubble of emission nebulosity within 5of the star . marked changes were seen in this bubble over 1995  1998 : the onset of limb brightening , the dissipation of a bright knot within the bubble , and large outward proper motions ( @xmath2 150 km s@xmath1 ) indicative of a dynamical age of only 20 years . however , they were unable to determine if the bubble energetics were dominated by the energy of an initial blast or the ongoing input of energy from a continuous jet .    to measure flow accelerations and monitor the growth and decay of emission knots , multiple epochs and high spatial resolution are needed . _ hst _ is a particularly valuable tool for the study of herbig - haro flows such as xz tau s . for sources at 140 pc distance , its @xmath2005 resolution corresponds to linear scales of @xmath7 m , small enough to resolve the cooling zones of radiative shocks . this resolution is also sufficient to measure proper motions of @xmath2100 km s@xmath1 on temporal baselines of only one year . we report here the results of an imaging campaign spanning 1995  2005 that monitored the evolution of the xz tau outflow . the new data include emission line images that reveal the excitation structure of the xz tau bubble , and deeper , wider - field images taken with the _ hst _ advanced camera for surveys ( acs ) . some of our data has also been discussed by coffey et al .","summary":"our data monitors the system from 1995  2005 and includes emission line images of the flow . the bubble emission nebulosity has a low excitation overall , as traced by the [ s  ii]/h line ratio , requiring a nearly comoving surrounding medium that has been accelerated by previous ejections or stellar winds .    within the broad bubbles future evolution of the flow should see the outer bubble structures fade from view , and the emergence of a more typical herbig - haro jet / bowshock morphology . we present a preliminary numerical model of a pulsed jet to illustrate this scenario .","abstract":"we present nine epochs of _ hubble space telescope _ optical imaging of the bipolar outflow from the pre - main sequence binary xz tauri . our data monitors the system from 1995  2005 and includes emission line images of the flow . the northern lobe appears to be a succession of bubbles , the outermost of which expanded ballistically from 1995  1999 but in 2000 began to deform and decelerate along its forward edge . it reached an extent of 6from the binary in 2005 . a larger and fainter southern counterbubble was detected for the first time in deep acs images from 2004 . traces of shocked emission are seen as far as 20south of the binary . the bubble emission nebulosity has a low excitation overall , as traced by the [ s  ii]/h line ratio , requiring a nearly comoving surrounding medium that has been accelerated by previous ejections or stellar winds .    within the broad bubbles there are compact emission knots whose alignments and proper motions indicate that collimated jets are ejected from each binary component . the jet from the southern component , xz tau a , is aligned with the outflow axis of the bubbles and has tangential knot velocities of 70  200 km s . knots in the northern flow are seen to slow and brighten as they approach the forward edge of the outermost bubble . the knots in the jet from the other star , xz tau b , have lower velocities of 100 km s .    to explain the observations of the outer bubble , we propose that the xz tau a stellar jet underwent a large velocity pulse circa 1980 . this ejection quickly overtook older , slower - moving ejecta very near the star , producing a 70 km s shock in a hot ( t 80,000 k ) , compact `` fireball '' . the initial thermal pressure of this gas parcel drove the expansion of a spherical bubble . subsequent cooling caused the bubble to transition to ballistic expansion , followed by slowing of its forward edge by mass - loading from the pre - shock medium . repeated pulses may explain the multiple bubbles seen in the data . collimated jets continue to flow through the bubble s interior , and with the fading of the original fireball they are becoming the primary energizing mechanism for the emission line structures . future evolution of the flow should see the outer bubble structures fade from view , and the emergence of a more typical herbig - haro jet / bowshock morphology . we present a preliminary numerical model of a pulsed jet to illustrate this scenario ."}
{"article_id":"0809.2073","section_id":"c","document":"the nine epochs of hst imaging reveal a complex combination of outflows from both stars and their interaction with the surrounding medium . each star has a collimated , bipolar jet . large bubbles are aligned along the xz tau a jet axis . knots in the xz tau a jet move through these bubbles and are seen catching up with the apex of the outer bubble , a few arcseconds n of the binary . the s side of the flow shows a faint counterpart to the outermost n bubble , and two interior , compact , bow - shaped knots that suddenly appeared in 2004 . evidence for a more extended flow to the n is seen in ground - based images , and to the s extending to distances of 20where the h@xmath0-a structure is found oriented perpendicular to the jet . in comparison , the visible portion of the xz tau b jet consists of only knots n4 and s4 that show proper motions about half those of the fastest xz tau a knots . it is clear that xz tau a is the dominant outflow source in the system , which is suprising given that xz tau b is much more photometrically variable and has a more prominent emission line spectrum . the xz tau bubbles are unlike the large bowshocks seen in other herbig - haro flows and numerically modeled by various workers . a prototypical bowshock represents the interaction region where a narrow , fast - moving jet impacts material along the flow axis . the impacted gas can be either ambient interstellar material , or slower - moving ejecta output previously by the source . the brightest emission and highest excitation is found at the bowshock apex , where normal incidence of the flow along the jet axis creates the largest shock velocity difference . lower shock velocities at oblique angles along the sides of the bowshock produce fainter emission and weaker excitation along the trailing bowshock wings . examples include the hh 1 and hh 34 systems ( hester et al . 1998 ; reipurth et al . 2002 ) , and the h@xmath0 emission structures at northern limit of the hl tau jet in figure 2 . in comparison , the xz tau bubbles lack the characteristic peak brightness and excitation at their apex ; the outer bubble becomes limb - brightened , fades , decelerates , and deforms along its leading edge over a period of less than 10 years ; and the flow has a large opening angle @xmath230near the source . taken together , these features suggest that the outer bubble is largely `` coasting '' on the initial momentum with which it formed , with little ongoing energy deposition from the flow of a continuous jet . we now sketch out a scenario for the origin and evolution of the n outer bubble in the xz tau outflow . it can not be the result of a wide - angle , ballistic ejection from the star given that it appears limb - brightened in 1998 - 1999 along more than just its forward edge . instead , the spherical symmetry of the bubble in the early epochs suggests radial expansion of an initially hot , compact gas parcel carried along in the general outward flow from xz tau a. the observed transverse proper motions of the bubble ( 70 km s@xmath1 ; see table 6 ) suggest a characteristic initial energy for the bubble . we postulate that the xz tau a stellar jet underwent a large velocity pulse circa 1980 . this ejection quickly overtook older , slower - moving ejecta very near the star , producing a @xmath2 70 km s@xmath1 shock in a hot ( t@xmath2 80,000 k ) , compact `` fireball '' . the initial pressure of this gas parcel created a expanding hot bubble within the flow , but rapid cooling terminated this early inflationary stage and left a ballistically expanding cloud carried along at the mean longitudinal velocity of the flow . surrounding material swept up in the radial expansion of the bubble led to the formation of a shell , which took on the appearance of a limb - brightened emission bubble when the shell became dense enough for enhanced cooling and/or enough time had elapsed for the post - shock h@xmath0/[s  ii ] cooling zone to form . the forward edge of the bubble has preferentially slowed and deformed as it encounters higher downstream densities found in the wakes of previous ejections along the flow axis . subsequent jet velocity pulses have led to the formation of additional shells trailing the bright outer bubble . the southern bubble , seen only in 2004 , is sufficiently similar to the n one in appearance to suggest a common origin in a symmetric velocity pulse in bipolar jets . the s bubble is slightly larger and centered further from the binary than the n one , and is much fainter . it lacks the complex internal knots seen within the n bubble . because the s bubble is detected at only one epoch , it is unknown if it transitioned from an internally - brightened to limb - brightened nebula as the n bubble did . it is clear that the n bubble has encountered material dense enough to decelerate and deform its forward edge , creating the cusps . the faintness and relative simplicity of the s bubble suggest that it is expanding into a more rarified and uniform medium than the northern one . coffey et al . ( 2004 ) studied the 1995  2001 epochs from our dataset and suggested that xz tau b was an eruptive , exor - type star based on its spectral lines and photometric variability and thus was the likely source of the bubbles . without using psf - subtracted images or tracing knot motions through later epochs , they did not recognize that both stars have jets and that the bubbles are aligned with the xz tau a jet . they modeled the formation of the outer bubble as the result of a 250 km s@xmath1 stellar wind with an opening angle of 22 , with the collimated jet having no significant effect . this scenario , however , does not suitably explain the appearance of the bubble in 1995 , the multiple bubbles and their curvatures , or the finite apparent length of the northern outflow . the interaction of slow and fast moving knots from xz tau a seem to better explain these characteristics . the extended emission bubbles of xz tauri enclose multiple compact emission knots which attest to the continued flow of bipolar jets after the bubble ejection events . the position and proper motions of knots n4 and s4 point to xz tau b as their source and a flow pa of 36 . both steadily brightened by a factor of @xmath25 between 2000 and 2004 . all of the other observed knots are associated with the jet from xz tau a along pa 15 , and show more transient brightness variation . on timescales of just a year or two , knots n1 , n2 , n3 , and s3 completely faded from view . this requires relatively high gas densities within the knots so that rapid cooling and recombination can take place . conversely , s5 and s6 appeared suddenly in 2004 as the brightest and fastest - moving knots in the entire outflow , but were entirely absent two years previously . the jet s encounter with a sharp density discontinuity in the pre - shock medium at this epoch ( likely a structure in the wake of prior ejections ) would account for this . s5 appears the most bowshock - like of all the jet knots , showing both extended curved wings and a bright spot at its apex . numerical simulations of herbig - haro jets tend to focus on the structure of the classical jet / bowshock working surface at large propagation distances from the outflow source . for comparision to the xz tau bubbles , simulations of a very young pulsed jet are needed in the region very close to the outflow source . we have begun to explore such models using a third - order weno ( weighted essentially non - oscillatory ) method ( shu 1995 ) for supersonic astrophysical flow simulations ( ha et al . 2005 ) . weno schemes are high - order finite difference methods designed for nonlinear hyperbolic conservation laws with piecewise smooth solutions containing sharp discontinuities like shock waves and contacts . locally smooth stencils are chosen via a nonlinear adaptive algorithm to avoid crossing discontinuities whenever possible in the interpolation procedure . the weighted eno ( weno ) schemes use a convex combination of all candidate stencils , rather than just one as in the original eno method . lccc gas density & h atoms @xmath105 & 500 & 50 + gas velocity & km s@xmath1 & 200 & 0 + gas temperature & k & 1000 & 10000 + sound speed & km s@xmath1 & 3.8 & 12 +    we simulated an approximation to the northern jet outflow and a pair of expanding bubbles , including the effects of radiative cooling using the cooling function from figure 8 of schmutzler & tscharnuter ( 1993 ) . two - dimensional simulations were performed on a @xmath106 grid spanning @xmath107 km on each side . the jet has a width of @xmath108 km , and inflows at mach 15 with respect to the sound speed in the light ambient gas and mach 55 with respect to its own internal soundspeed . other flow parameters of the simulation are summarized in table 8 , and atomic gas ( @xmath109 ) is assumed . the leading edge of the resulting outer bubble propagates initially at 150 km s@xmath1 , decaying to 90 km s@xmath1 at 24 years , with an average velocity over this period of 120 km s@xmath1 . the jet was pulsed : a first pulse was turned on for 0.4 yr , and then the jet inflow was turned off for 8.6 yr while the first pulse propagated . next a second pulse was turned on for 0.4 yr creating a second bubble , and then the jet inflow was turned off for 5.6 yr . figure 12a depicts the flow after the two initial pulses . a third pulse was turned on for 0.4 yr , and the jet inflow was turned off for 5.6 yr ; finally a fourth pulse was turned on for 0.4 yr , and then the jet inflow was turned off for 2.6 yr . figure 12b depicts the flow after the fourth pulse . the third and fourth pulses create internal shocks _ within _ the bubbles that formed from the first and second bubbles . the third pulse has almost merged with the second pulse and the third pulse has just propagated into the first bubble at 24 yr . these simulations produce limb - brightened bubbles and internal knots like those seen on the n side of the outflow from xz tau a , supporting the idea that a jet pulsed by strong velocity variations is the basic underlying mechanism of the flow . the diameter of the simulated bubbles agrees with the hubble images : roughly @xmath110 km ( @xmath2 3 ) . a wide - angle wind is not necessary to match the morphology of the imaged flows . several model details remain unoptimized , however : the initially static ambient medium makes the shock in the outer bubble stronger and less spherically symmetric than seen in xz tau ; the jet width in the simulations is oversized compared to the knots observed in the hst images ; and we do not yet have specific predictions for the optical emission line fluxes .","summary":"we present nine epochs of _ hubble space telescope _ optical imaging of the bipolar outflow from the pre - main sequence binary xz tauri . this ejection quickly overtook older , slower - moving ejecta very near the star , producing a 70 km s shock in a hot ( t 80,000 k ) , compact `` fireball '' . the initial thermal pressure of this gas parcel drove the expansion of a spherical bubble . repeated pulses may explain the multiple bubbles seen in the data . collimated jets continue to flow through the bubble s interior , and with the fading of the original fireball they are becoming the primary energizing mechanism for the emission line structures .","abstract":"we present nine epochs of _ hubble space telescope _ optical imaging of the bipolar outflow from the pre - main sequence binary xz tauri . our data monitors the system from 1995  2005 and includes emission line images of the flow . the northern lobe appears to be a succession of bubbles , the outermost of which expanded ballistically from 1995  1999 but in 2000 began to deform and decelerate along its forward edge . it reached an extent of 6from the binary in 2005 . a larger and fainter southern counterbubble was detected for the first time in deep acs images from 2004 . traces of shocked emission are seen as far as 20south of the binary . the bubble emission nebulosity has a low excitation overall , as traced by the [ s  ii]/h line ratio , requiring a nearly comoving surrounding medium that has been accelerated by previous ejections or stellar winds .    within the broad bubbles there are compact emission knots whose alignments and proper motions indicate that collimated jets are ejected from each binary component . the jet from the southern component , xz tau a , is aligned with the outflow axis of the bubbles and has tangential knot velocities of 70  200 km s . knots in the northern flow are seen to slow and brighten as they approach the forward edge of the outermost bubble . the knots in the jet from the other star , xz tau b , have lower velocities of 100 km s .    to explain the observations of the outer bubble , we propose that the xz tau a stellar jet underwent a large velocity pulse circa 1980 . this ejection quickly overtook older , slower - moving ejecta very near the star , producing a 70 km s shock in a hot ( t 80,000 k ) , compact `` fireball '' . the initial thermal pressure of this gas parcel drove the expansion of a spherical bubble . subsequent cooling caused the bubble to transition to ballistic expansion , followed by slowing of its forward edge by mass - loading from the pre - shock medium . repeated pulses may explain the multiple bubbles seen in the data . collimated jets continue to flow through the bubble s interior , and with the fading of the original fireball they are becoming the primary energizing mechanism for the emission line structures . future evolution of the flow should see the outer bubble structures fade from view , and the emergence of a more typical herbig - haro jet / bowshock morphology . we present a preliminary numerical model of a pulsed jet to illustrate this scenario ."}
{"article_id":"0809.2073","section_id":"i","document":"our multiepoch _ hst _ observations of the young xz tau binary reveal a more complex system of outflows than was previously suspected . both stars have collimated , bipolar jets as shown by the motions of compact knots . the knots in the xz tau a jet , which is oriented along pa=15 , have tangential velocities of 80  200 km sec@xmath1 . this jet is assumed to be inclined by @xmath227from the plane of the sky . it can be traced to 19  to the south where it apparently impacts the edge of an interstellar cloud , creating a broad shock ( h@xmath0-a ) that travels at 100 km sec@xmath1 . the xz tau a jet knots show a surprising variety of forms , including fans , bow shocks , and shells , some of which suddenly appear and then fade away with a year or two . the more sedate xz tau b jet is defined by a pair of knots aligned along pa=36with velocities of 40  125 km sec@xmath1 . although xz tau b is more photometrically variable and has richer spectral features than xz tau a , it is not the primary outflow driver as was previously assumed . the most unusual aspect of the xz tau outflow is the series of bipolar bubbles that are aligned with the xz tau a jet . the outermost bubble in the northern outflow extended to 61 from the star and was 45 wide in early 2005 . the tangential velocity of its forward edge was @xmath2130 km sec@xmath1 prior to 1999 , and it slowed to @xmath293 km sec@xmath1 by 2002 , presumably due to interaction with the surrounding medium . at later epochs the outer edge became deformed and fragmented . its transverse velocity of 46  76 km sec@xmath1 is probably indicative of the true expansion velocity from its center , which by derivation has a forward velocity of @xmath265 km sec@xmath1 along the jet . the bubble was dominated by interior emission in 1995 , but in later epochs it appeared limb brightened due to cooling and the resulting recombination emission . the northern extension of the xz tau a jet appears to terminate at the forward edge of the bubble where it brightens due to the impact with the same ism material that is slowing the bubble . two additional bubbles trail the outer one and appear to overlap it . the one closest to the stars appears as a nearly circular shell with strong limb brightening , while the intermediate bubble is fainter with strong brightening along its forward edge . another , more circular and more uniformly illuminated bubble appears on the southern side of the stars in the 2004 acs images . the bubbles do not appear similar to the typical bow shocks seen in the jets of other young stars and must have a different origin . notably , the outer bubble was a filled volume of emitting gas in 1995 , not a limb - brightened bow shock . the form and expansion velocity of the outer bubble suggests that it may have been created by a very hot and dense shock generated close to the star . the shock may have rapidly expanded until it transitioned to a ballistically expanding bubble . recombination within the cooling interior would cause the emission seen in 1995 . density enhancement along the outer boundary may have accelerated the cooling , creating additional emission seen along the limb after then . additional interactions of the xz tau a jet with the bubble material may have created the trailing bubbles . the southern bubble may have formed at the same time in a bipolar outburst , but because of a possibly less - dense external medium it appears more uniform . xz tau presents a unique collection of unusual outflow phenomena that vary considerably on timescales and distances that can be observed using the capabilities of _ hst_. it represents a test of the ability of current methods of jet modeling .","summary":"subsequent cooling caused the bubble to transition to ballistic expansion , followed by slowing of its forward edge by mass - loading from the pre - shock medium .","abstract":"we present nine epochs of _ hubble space telescope _ optical imaging of the bipolar outflow from the pre - main sequence binary xz tauri . our data monitors the system from 1995  2005 and includes emission line images of the flow . the northern lobe appears to be a succession of bubbles , the outermost of which expanded ballistically from 1995  1999 but in 2000 began to deform and decelerate along its forward edge . it reached an extent of 6from the binary in 2005 . a larger and fainter southern counterbubble was detected for the first time in deep acs images from 2004 . traces of shocked emission are seen as far as 20south of the binary . the bubble emission nebulosity has a low excitation overall , as traced by the [ s  ii]/h line ratio , requiring a nearly comoving surrounding medium that has been accelerated by previous ejections or stellar winds .    within the broad bubbles there are compact emission knots whose alignments and proper motions indicate that collimated jets are ejected from each binary component . the jet from the southern component , xz tau a , is aligned with the outflow axis of the bubbles and has tangential knot velocities of 70  200 km s . knots in the northern flow are seen to slow and brighten as they approach the forward edge of the outermost bubble . the knots in the jet from the other star , xz tau b , have lower velocities of 100 km s .    to explain the observations of the outer bubble , we propose that the xz tau a stellar jet underwent a large velocity pulse circa 1980 . this ejection quickly overtook older , slower - moving ejecta very near the star , producing a 70 km s shock in a hot ( t 80,000 k ) , compact `` fireball '' . the initial thermal pressure of this gas parcel drove the expansion of a spherical bubble . subsequent cooling caused the bubble to transition to ballistic expansion , followed by slowing of its forward edge by mass - loading from the pre - shock medium . repeated pulses may explain the multiple bubbles seen in the data . collimated jets continue to flow through the bubble s interior , and with the fading of the original fireball they are becoming the primary energizing mechanism for the emission line structures . future evolution of the flow should see the outer bubble structures fade from view , and the emergence of a more typical herbig - haro jet / bowshock morphology . we present a preliminary numerical model of a pulsed jet to illustrate this scenario ."}
{"article_id":"astro-ph0611328","section_id":"i","document":"early - type galaxies are known to follow well defined empirical scaling laws relating their global observational properties , such as total luminosity @xmath1 , effective radius @xmath2 , and central velocity dispersion @xmath3 . among others we recall the faber & jackson ( 1976 , hereafter fj ) , kormendy ( 1977 ) , fundamental plane ( djorgovski & davis 1987 ; dressler et al . 1987 ; hereafter fp ) , the color-@xmath3 ( bower , lucey & ellis 1992 ) , and the mg@xmath4 ( e.g. , guzman et al . 1992 ; bernardi et al . 2003c ) relations . in addition , it is now believed that all elliptical galaxies host a central supermassive black hole ( smbh ; e.g. , see de zeeuw 2001 ) , whose mass @xmath5 scales with the stellar mass @xmath6 and velocity dispersion @xmath3 of the host galaxy ( magorrian et al . 1998 ; ferrarese & merritt 2000 ; gebhardt et al . 2000 ; tremaine et al . clearly , these scaling relations provide invaluable information about the formation and evolution of early - type galaxies , and set stringent constraints to galaxy formation models . the two major formation models for ellipticals that have been proposed so far are the monolithic ( eggen , lynden - bell & sandage 1962 ) , and the merging ( toomre 1977 ; white & frenk 1991 ) scenarios . each of them scores observational and theoretical successes and drawbacks ( e.g. , see ostriker 1980 , renzini 2006 ) . for instance , we list here three observational and theoretical evidences in favour of a fast and dissipative monolithic - like collapse . first , the observed color - magnitude and mg@xmath7-@xmath3 relations , and the increase of the @xmath8 $ ] ratio with @xmath3 in the stellar population of elliptical galaxies ( e.g. , see jrgensen 1999 , thomas , greggio & bender 1999 saglia et al . 2000 ; bernardi et al . 2003c , and references therein ) , suggest that star formation in massive ellipticals was not only more efficient than in low mass galaxies , but also that it was a faster process ( i.e. , completed before snia explosions take place ) , with the time scales of gas consumption and ejection shorter or comparable to the galaxy dynamical time ( e.g. , see matteucci 1994 , pipino & matteucci 2004 ) , and decreasing for increasing galaxy mass . second , structural and dynamical properties of ellipticals are well reproduced by cold dissipationless collapse , a process which is expected to dominate the last stages of highly dissipative collapses , in which the gas cooling time of the forming galaxy is shorter than its dynamical time , so that stars form ` in flight ' , and the subsequent dynamical evolution is a dissipationless collapse . it is now well established that the end - products of cold and phase - space clumpy collapses have projected density profiles well described by the @xmath9 de vaucouleurs ( 1948 ) law , radially decreasing line - of - sight velocity dispersion profiles , and radially increasing velocity anisotropy , in agreement with what observed in elliptical galaxies ( e.g. , see van albada 1982 ; may & van albada 1984 ; mcglynn 1984 ; aguilar & merritt 1990 ; londrillo , messina & stiavelli 1991 ; udry 1993 ; hozumi , burkert , & fujiwara 2000 ; trenti , bertin & van albada 2005 ) . third , the current and remarkably succesful cosmological scenario for structure formation predicts that well defined scaling laws are imprinted in the dark matter halos ; in particular , the virial velocity dispersion of dm halos increases as @xmath10 . this because virialized dm halos are the _ collapse _ end - products of negative energy ( inhomogeneous ) density distributions , in which the absolute value of the binding energy per unit mass increases with the halo mass ( peebles 1980 ) . on the contrary , in a parabolic merging @xmath11 would not increase with halo mass . thus the observed scaling laws of elliptical galaxies could be originated by the fast collapse of inhomogeneous gas and star distributions in pre - existing dm halos , rather than by parabolic merging processes ( e.g. , see lanzoni et al . note that high resolution n - body simulations ( nipoti , londrillo & ciotti 2006 ) have shown that cold ( dissipationaless ) collapses in pre - existing dm halos nicely reproduce the weak homology of elliptical galaxies ( e.g. , see caon , capaccioli & donofrio 1993 ; prugniel & simien 1997 ; bertin , ciotti & del principe 2002 , hereafter bcd02 ; graham & guzmn 2003 ) and the central break radius in their surface brightness profile ( ferrarese et al . 1994 ; lauer et al . 1995 ; graham et al . 2003 ; trujillo et al . 2004 ) . the last point above is particularly puzzling because the available observations seem to indicate that mergers may happen in the life of elliptical galaxies , with dissipative ( wet ) mergers dominating at high redshift , and gas - free ( dry ) merging mainly affecting massive ellipticals at @xmath12 ( e.g. , see bell et al . 2004 , 2006 ; van dokkum 2005 ; faber et al . 2005 ; conselice 2006 ) . this picture is also suggested by the available information on the star formation history of the universe and the redshift evolution of the quasar luminosity function ( see , e.g. , haehnelt & kauffmann 2000 ; burkert & silk 2001 ; yu & tremaine 2002 ; cavaliere & vittorini 2002 ; haiman , ciotti & ostriker 2004 ) . in addition , parabolic orbits seem to be quite relevant in the hierarchical merging picture ( e.g. , see benson 2005 ; khochfar & burkert 2006 ) . to get insights on this issue , in the present paper we will focus on the remarkable homogeneity and regularity of the family of early - type galaxies ( testified by their scaling laws ) , and we explore the consequences of galaxy merging on them .    the impact of dry merging on the scaling laws of early - type galaxies has been already investigated in several works ( e.g. , capelato , de carvalho & carlberg 1995 ; pentericci , ciotti & renzini 1996 ; haehnelt & kauffmann 2000 ; ciotti & van albada 2001 , hereafter cva01 ; evstigneeva , reshetnikov & sotnikova 2002 ; nipoti , londrillo & ciotti 2003 , hereafter nlc03 ; gonzlez - garca & van albada 2003 ; dantas et al . 2003 ; evstigneeva et al . 2004 ; boylan - kolchin , ma & quataert 2005 , 2006 ) . in particular , the simple approach of cva01 and the n - body simulations of nlc03 showed that repeated , parabolic merging of gas - free galaxies is unable at reproducing the observed scaling laws , because the merger - products are characterized by unrealistically large effective radius and mass - independent velocity dispersion ( see also shen et al . however , simple physical arguments show that gas dissipation should be able to mitigate the problems posed by dry merging to the explanation of the observed scaling laws ( e.g. , see cva01 ; kazantzidis et al . 2006 ; robertson et al . 2006ab ; dekel & cox 2006 ) . unfortunately , numerical simulations with gas dissipation are considerably more complicate than pure n - body simulations ( e.g. , see siz , domiguez - tenreiro & serna 2004 ; oorbe et al . 2005 , 2006 ; robertson et al . 2006ab ) , and , in particular , very few of them have been done from realistic cosmological initial conditions ( e.g. , see naab et al . 2006 , and references therein ) . for these reasons , by generalizing the approach presented in cva01 to the dissipative case , we further investigate with monte - carlo simulations the compatibility of galaxy merging with the formation and evolution of early - type galaxies , focusing in particular on 1 ) the effects of gas dissipation on the merger end - products ( wet merging ) , and 2 ) the effects of parabolic dry and wet merging on the scaling laws followed by elliptical galaxies in the local universe . we argue that parabolic merging of low - mass seed galaxies alone can not be at the origin of the scaling laws , even though wet mergers lead to early - type galaxies following the observed scaling laws better than the end products of dry merging . we also show that galaxy scaling laws , such as the fj , kormendy and fp relations , once in place , are robust against merging . thus , our results reinforce the idea that monolithic - like collapse at early times and subsequent merging could just represent the different phases of galaxy formation ( collapse ) and evolution ( merging , in addition to the aging of the stellar populations and related phenomena ) . the paper is organized as follows . in section [ sec : models ] we derive the recursive equations describing the evolution of galaxy properties after dry and wet parabolic mergers , and in section 3 we discuss in detail the case of equal - mass merging . in section [ sec : simu ] we use the derived relations in monte - carlo investigations of merging of elliptical galaxy populations , and the main results are finally summarized and discussed in section [ sec : concl ] .","summary":"with the aid of a simple yet robust approach we investigate the influence of dissipationless and dissipative merging on galaxy structure , and the consequent effects on the scaling laws followed by elliptical galaxies .","abstract":"with the aid of a simple yet robust approach we investigate the influence of dissipationless and dissipative merging on galaxy structure , and the consequent effects on the scaling laws followed by elliptical galaxies . our results suggest that ellipticals can not be originated by parabolic merging of low mass spheroids only , even in presence of substantial gas dissipation . however , we also found that scaling laws such as the faber - jackson , kormendy , fundamental plane , and the relations , when considered over the whole mass range spanned by ellipticals in the local universe , are robust against merging . we conclude that galaxy scaling laws , possibly established at high redshift by the fast collapse in pre - existing dark matter halos of gas rich and clumpy stellar distributions , are compatible with a ( small ) number of galaxy mergers at lower redshift ."}
{"article_id":"astro-ph0611328","section_id":"c","document":"with the aid of a scheme based on very simple physical arguments we investigated the influence of dry and wet merging on the formation and evolution of elliptical galaxies , focusing on the origin and robustness of some of their scaling laws . in particular , by using analytical arguments and numerical simulations we showed that massive elliptical galaxies can not be formed by ( parabolic ) merging of low mass spheroidal galaxies , even in presence of substantial gas dissipation , and allowing for the helpful effects of structural weak homology . however the observed scaling laws of elliptical galaxies , once established by galaxy formation , are robust against merging . more specifically , our findings can be summarized as follows :    \\1 ) parabolic dry merging in a population of low mass spheroids leads to massive ellipticals that can not be simultaneously placed on the kormendy , fj and edge - on fp relations . for example , forcing the end - products to stay on the edge - on fp , the fj and kormendy relations are failed by massive galaxies , with deviations increasing with galaxy mass . this behavior was predicted in cva01 and confirmed by high resolution numerical simulations ( nlc03 , boylan - kolchin et al . 2005 , 2006 ) . for example boylan - kolchin et al . ( 2006 ) , in a series of dissipationless merging simulations of galaxies in cosmologically motivated orbits , found that the merging end - products , while preserving the edge - on view of the fp , can present significant differences in the fj and kormendy relations . this because the variations in the resulting @xmath186 are compensated by corresponding variations in the @xmath187 relation , so that the _ projections _ of the fp - but not the edge - on fp itself - should provide a powerful way to investigate the assembly history of massive elliptical galaxies . \\2 ) parabolic wet merging in the same population of low mass progenitors lead to galaxies in much better agreement with the observed scaling relations , as long as enough gas for dissipation is available . in particular , the resulting @xmath5-@xmath3 relation is in better agreement with the observed one , also in the case of significant mass loss ( via gravitational waves ) of the coalescing bhs . significant deviations from the observed scaling laws are however expected for massive galaxies . similar conclusions were reached by sophisticated @xmath83-body plus hydrodynamical simulations of merging of disk galaxies . for example , kazantzidis et al . ( 2005 ) found that merging disk galaxies constructed to obey the @xmath161 relation move relative to it depending on whether they undergo a dissipational or dissipationless merger . in particular , remnants of dry mergings tend to move away from the mean relation , showing the role of gas - poor mergers as a possible source of scatter . in addition , robertson et al ( 2006b ) studied the development of the @xmath161 over cosmic time with a large set of hydrodynamical simulations of galaxy mergers that include star formation and feedback from the growth of the central bh , and found that the @xmath161 relation is created through coupled bh and spheroid growth ( via star formation ) in galaxy mergers . \\3 ) parabolic dry mergers in a population of galaxies following the observed scaling laws over the full mass range populated today by stellar spheroids ( or following the scaling laws of dark matter halos predicted by the current cosmological scenario ) , preserve the kormendy , fj , and edge - on fp remarkably well . the reason of this behavior is rooted in the availability in the merger population of galaxies with velocity dispersion increasing with galaxy mass . remarkably , robertson et al . ( 2006a ) found evidences that dry merging of spheroidal galaxies at low redshift is expected to maintain the fp relation _ imprinted by gas - rich merging during the epoch of rapid spheroid and central bh growth at high redshift _ , when the progenitors were characterized by gas fractions @xmath188 and efficient gas cooling was allowed in the simulations . thus , points 1 ) and 2 ) above suggest that ellipticals can not be originated by parabolic merging of low mass spheroids only , even in presence of substantial gas dissipation . in addition , point 3 ) , when considered together the cosmologically imprinted scaling laws of dark matter halos , and the several appealing features of dissipationless collapse end - products ( see introduction ) , support the idea that elliptical galaxies formed in a process similar to the monolithic collapse , even though their structural and dynamical properties are compatible with a limited number of dry mergers ( we note that the same conclusion has been reached also from the study of color profiles in early - type galaxies , as described in wu et al . 2005 ) . the possibility that monolithic collapse and successive merging are just the leading physical processes at different times in galaxy evolution , and that they are both important for galaxy formation , is perhaps indicated also by a `` contradictory '' and often overlooked peculiarity of massive ellipticals in fact , while the kormendy relation dictates that the mean stellar density of galaxies decreases for increasing galaxy mass ( a natural result of parabolic dry merging ) , the normalized light profiles of elliptical galaxies becomes steeper and their metallicity increases at increasing galaxy mass ( as expected in case of significant gas dissipation ) . thus , the present - day light profiles of ellipticals could represent the fossil evidence of the impact of both the processes ; quite obviously , this problem can not be addressed in the framework adopted in this paper . it would be very interesting to extend the robertson et al . ( 2006a ) and naab et al . ( 2006 ) analysis to the study of dissipative collapses in cosmologically motivated dark matter halos , thus extending the investigation of nipoti et al . 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tenreiro , r. , & serna , a. 2004 , , 601 , l131 srsic , j.l . 1968 , atlas de galaxias australes . observatorio astronomico , cordoba shen , s. , mo , h.j . , white , s.d.m . , et al . 2003 , , 343 , 978 taffoni , g. , mayer , l. , colpi , m. , & governato , f. 2003 , , 341 , 434 thomas , d. , greggio , l. , & bender , r. 1999 , , 302 , 537 toomre , a. 1977 , in evolution of galaxies and stellar populations , ed . tinsley & r.b . larson ( new haven : yale university observatory ) , p.401 trenti , m. , bertin , g. , & van albada , t.s . 2005 , a&a , 433 , 57 treu , t. 2001 , phd thesis , scuola normale superiore di pisa , italy trujillo , i. , erwin , p. , asensio ramos , a. , & graham , a.w . 2004 , , 127 , 1917 udry , s. 1993 , a&a , 268 , 35 van albada , t.s . 1982 , , 201 , 939 van dokkum , p.g . 2005 , , 130 , 264 volonteri , m. , haardt , f. , & madau , p. 2003 , , 582 , 559 white , s.d.m . , & frenk , c.s . 1991 , , 379 , 52 wu , h. , shao , z. , mo , h.j . , xia , x. , & deng , z. 2005 , , 622 , 244 yu , q. , & tremaine , s. 2002 , , 335 , 965","summary":"our results suggest that ellipticals can not be originated by parabolic merging of low mass spheroids only , even in presence of substantial gas dissipation .","abstract":"with the aid of a simple yet robust approach we investigate the influence of dissipationless and dissipative merging on galaxy structure , and the consequent effects on the scaling laws followed by elliptical galaxies . our results suggest that ellipticals can not be originated by parabolic merging of low mass spheroids only , even in presence of substantial gas dissipation . however , we also found that scaling laws such as the faber - jackson , kormendy , fundamental plane , and the relations , when considered over the whole mass range spanned by ellipticals in the local universe , are robust against merging . we conclude that galaxy scaling laws , possibly established at high redshift by the fast collapse in pre - existing dark matter halos of gas rich and clumpy stellar distributions , are compatible with a ( small ) number of galaxy mergers at lower redshift ."}
{"article_id":"1605.06149","section_id":"i","document":"when in 2007 the new york times published an article suggesting that plants were quantum computers , quantum information scientists exploded into laughter @xcite . their concern was , of course , decoherence which is believed to be one of the fastest and most efficient processes in nature . the laughter is over and quantum biology is firmly established , but the mechanism which sets decoherence apart is still under debate . + the experiments by engel et al . show that long lasting coherence in photosynthetic pigment - protein complexes is observed at physiological temperatures @xcite . quantum coherence over hundreds of femtoseconds in the initial steps of photosynthesis , the tranfer of light quanta towards the reaction centers , in green and purple bacteria @xcite at room temperature @xcite , algae at ambient temperature of 294 k @xcite and even in living cells of purple bacterium @xcite warrant the high efficiency of the light - harvesting process . it has even been suggested that the high efficiency of photosynthesis may be associated with coherent energy and charge transfer on a long timescale @xcite . + citing hildner et al . :  ... quantum coherence is the central aspect connecting fields as diverse as quantum computing and light - harvesting  @xcite . + in 2011 the first commercially available quantum computer was presented by the company d - wave consisting of an array of more than thousand flux qubits ( june , 2015 ) , which solves optimization problems with many free parameters @xcite . it works as a quantum computer of the quantum annealing type for minutes and even for half an hour . however , a single flux qubit in a ramsey interference experiment shows coherent oscillations between the two supercurrents for time of the order of 20 ns , which is 8 orders of magnitude shorter than the coherence time of the d - wave computer @xcite . the amplitude of the oscillations decays to @xmath3 after 20 - 25 ns . it is often said that the flux qubit loses coherence within 20 ns , or it dephases , or it is decohered , or it is driven by noise or experimental imperfections . the experimental observation is that the probability for the oscillatory state change decreases exponentially , achieving some non - zero final value , which does not change with time any more . + this was a noteworthy result as a flux qubit is a macroscopic device with dimensions of the order of @xmath4  . but not less noteworthy was the experimental observation of a coherent quantum behaviour of the fenna - matthews - olson pigment - protein complex not only at low temperature but even at 277 k and the coherent behaviour of the light harvesting complex in the purple bacterium living cell in a dense , wet noisy environment @xcite . the time of coherent development of the fmo - complex is picoseconds , i.e. 4 orders of magnitude shorter than that of a single flux qubit . with the help of 2d fourier transfrom electronic spectroscopy @xcite-@xcite the amplitude of a photon echo signal as a function of the waiting time between the first two laser pulses , which excite the fmo electronically , and the third laser pulse , which stimulates the photon emission from the exciton , shows beats . the beats , the oscillations in the time development of the photon echo signal , are due to the coherent superposition of two lowest energy excitons shared by all chlorophyll molecules and indicate coherent time development of the fmo - complex during the waiting time . in contrast to the experimental observation , an exponential decay of the photon signal with time would be expected , if decoherence due to interaction with the noisy environment ( phonons ) of the fmo - complex were effective , as it is generally believed that electronic coherence decays on 10 - 100 fs timescales @xcite . + why is the beating between exciton states observed for picoseconds instead of a fast exponentially decaying signal without oscillations , as decoherence theory suggests ? why is no decay to zero amplitude of the photon signal observed , if decoherence due to interaction with the noisy environment ( phonons ) of the fmo - complex were effective ? the expected question is : why does decoherence not take over and reduce the photon signal of the fmo complex , which is in an environment of many degrees of freedom at high temperature ? decoherence theory aims to calculate the time development of the reduced density matrix of a subsystem and thereby tries to demonstrate that the reduced density matrix very rapidly approaches a quasi - diagonal form . the diagonal matrix elements are then interpreted as probabilities of finding the subsystem in the respective state . calculations for realistic models are scarce . notable are those by joos and zeh @xcite , zurek @xcite and , applying to the present investigation , by lloyd et al . + in contrast to expectations based on the decoherence concept , both the molecular system fmo and the macroscopic flux qubit show long time coherence . the major question is : why does decoherence in both cases play no role ? the damping of the ramsey fringes in the experiment with the single flux qubit can not be due to decoherence , because otherwise the d - wave quantum computer , with an array of 1000 flux qubits , would not be able to function as a quantum computer for minutes . + semi - classical diffusive models based on stochastic dynamics have been extensively applied to study energy and charge transport in biological systems @xcite . within a quantum master equation approach the time development of the reduced density matrix is evaluated @xcite , the effect of the phonon environment is simulated by an additive redfield term , which is dropped for the study of the time development . with a very special selection of the phonon environment ( coloured noise ) the beats of the photon amplitude are reproduced , but the finite final value of the photon amplitude is not explained . furthermore the 2d fourier transform experiment shows that no special phonons are involved in the damping of the signal , changing the fmo phonon spectrum does not influence the results @xcite . + theoretical attempts based on the electron incoherent hopping process @xcite between pigment molecules in the photosynthetic unit have been suggested @xcite . + a discussion topic is the nature of the superimposed coherent states in the protein - pigment complexes . vibrational , electronic or vibronic states may be involved , with indications from experiment favouring their vibronic character ( @xcite , @xcite-@xcite ) . + we focus on the experimental observation in the 2d fourier transform electronic spectroscopy which demonstrates coherence by the fenna - matthews - olson protein - chlorophyll complex of green sulfur bacteria over times longer than 1000 fs and even at high temperature ( 277 k ) . the amplitude of the measured photon echo signal oscillates with time , which is an indication of coherent behaviour , suggested as the basis for the extreme efficiency of the photon transfer towards the reaction center and hence of the photosynthetic processes in the depth of the black sea . the expectation that decoherence due to the chaotic molecular environment , considered to be very fast , on the timescale of @xmath5 s , in the bacterium cell at physiological temperatures will destroy coherence , is not confirmed experimentally . the issues we will address in the present article refer to :    * why is decoherence not effective and not fast enough to destroy coherence ? * despite that the photon amplitude beats are exponentially damped with time , the final value is finite , larger than zero even at high temperature . what is the reason for this ? * missing isotope effect , random exchanges of @xmath1h atoms or of @xmath6 with their isotopes do not change the picture . random hydrogen exchange with deuterium and exchange of all @xmath6 with @xmath7 or even the whole hydrocarbon side chain of the pigment by a different one do not affect the coherent behaviour @xcite . this procedure certainly changes the phonon spectrum , but the results on the coherent quantum beats are not influenced . coherence is experimentally shown in bacteria @xcite , algae @xcite and green plants @xcite . the structure of their protein backbones differ and hence the protein scaffolds can not serve as the ubiquitous protection of electronic coherence , as it is suggested in refs . @xcite . * a discusion issue is the nature of the coherent states and the role of the environment . our results are in favour of vibronic states , many - particle states involving electron exciton components and local vibrations of the protein backbone . the dying out of the oscillations between the two supercurrents in the single flux qubit was explained in a coherent picture solving shrdinger s time dependent equation in high dimensional spacetime @xcite . the decisive features of the theory are summarized in the next section together with the description of a simple model of the physical picture of the processes in fmo 2d fourier transform electronic spectroscopy . the results are presented in section [ results ] , followed by a summary and conclusions .","summary":"long lasting coherence in photosynthetic pigment - protein complexes has been observed even at physiological temperatures . experiments have demonstrated quantum coherent behaviour in the long - time operation of the d - wave quantum computer as well . quantum coherence is the common feature between the two phenomena . however , the decoherence time of a single flux qubit , the component of the d - wave quantum computer , is reported to be on the order of nanoseconds , which is comparable to the time for a single operation and much shorter than the time required to carry out a computation on the order of seconds . an explanations for the factor of discrepancy between the single flux qubit coherence time and the long - time quantum behaviour of an array of thousand flux qubits + explanations for the quantum beats observed in 2d fourier transform electronic spectroscopy of the fenna - matthews - olson ( fmo ) protein complex in the green sulfur bacteria are presently sought in constructing transport theories based on quantum master equations where good molecular vibrations ( coloured noise ) in the chlorophyll and the surrounding protein scaffold knock the exciton oscillations back into coherence . these good vibrations are claimed to have developed in three billion years of natural selection . these theories , however , face the discomforting experimental observation that `` attempts to scramble vibrational modes or to shift resonances with isotopic substitution miserably failed to affect the beating signals '' . as a possible way out of this dilemma we adopted the formalism of the quantum computation to the quantum beats in the fmo protein complex . + keywords : long - living coherence , quantum biology , green sulfur bacteria , emergent quantum mechanics    * how can the green sulfur bacteria use quantum computing for light harvesting ? *    _ d drakova and g doyen _ +    state university of sofia , faculty of chemistry , sofia , bulgaria + ludwig - maximilians - university , munich , germany","abstract":"long lasting coherence in photosynthetic pigment - protein complexes has been observed even at physiological temperatures . experiments have demonstrated quantum coherent behaviour in the long - time operation of the d - wave quantum computer as well . quantum coherence is the common feature between the two phenomena . however , the decoherence time of a single flux qubit , the component of the d - wave quantum computer , is reported to be on the order of nanoseconds , which is comparable to the time for a single operation and much shorter than the time required to carry out a computation on the order of seconds . an explanations for the factor of discrepancy between the single flux qubit coherence time and the long - time quantum behaviour of an array of thousand flux qubits was suggested within a theory where the flux qubits are coupled to an environment of particles called gravonons of high density of states . the coherent evolution is in high dimensional spacetime and can be understood as a solution of schrdinger s time - dependent equation . + explanations for the quantum beats observed in 2d fourier transform electronic spectroscopy of the fenna - matthews - olson ( fmo ) protein complex in the green sulfur bacteria are presently sought in constructing transport theories based on quantum master equations where good molecular vibrations ( coloured noise ) in the chlorophyll and the surrounding protein scaffold knock the exciton oscillations back into coherence . these good vibrations are claimed to have developed in three billion years of natural selection . these theories , however , face the discomforting experimental observation that `` attempts to scramble vibrational modes or to shift resonances with isotopic substitution miserably failed to affect the beating signals '' . as a possible way out of this dilemma we adopted the formalism of the quantum computation to the quantum beats in the fmo protein complex . + keywords : long - living coherence , quantum biology , green sulfur bacteria , emergent quantum mechanics    * how can the green sulfur bacteria use quantum computing for light harvesting ? *    _ d drakova and g doyen _ +    state university of sofia , faculty of chemistry , sofia , bulgaria + ludwig - maximilians - university , munich , germany"}
{"article_id":"hep-ph9601375","section_id":"i","document":"the dynamics of a second order , or weakly first order , phase transition is governed by long wavelength fluctuations of the order parameter . these fluctuations , whose length scale is much larger than the inverse temperature of the system , are essentially classical , since the probability of a quantum fluctuation over such scales is highly suppressed . for this reason , the details of the microscopic theory are not relevant to the description of the critical behaviour of the system , which can be successfully studied by using classical models , such as the ising model for ferromagnets or the ginsburg - landau theory for superconductors .    in these models , a free energy can be defined as a functional of a macroscopic order parameter , which is allowed to vary only on large length scales . the effect of the short wavelength ( quantum and thermal ) fluctuations is incorporated by the parameters appearing in the free energy ( masses , coupling constants , etc . ) , which are usually treated as phenomenological parameters but should in principle be computable , starting from the underlying theory .    the wilson renormalization group ( rg ) @xcite provides the natural framework in which this procedure can be systematically carried out . the main idea is to start from a microscopic theory , the parameters of which are supposed to be known , and then progressively integrate out the high frequency modes of the order parameter down to some infra - red cutoff @xmath2 . in this way one obtains a coarse - grained order parameter and the corresponding effective action , which can be used as the relevant tool to describe the system .    in this paper , we will apply this idea to quantum field theory at finite temperature . our approach will be the following . first , we will assume that we `` know '' the zero - temperature renormalized quantum field theory , which means that there exists some reliable approximation method ( perturbation theory , lattice simulations , etc . ) to compute the zero - temperature renormalized green functions . in this way , the renormalization constants can be fixed by the experimental measurements and all the parameters of the theory are known . in a rg language , we assume that all the quantum fluctuations have already been integrated out . second , we will integrate out thermal modes only , for frequencies higher than the infrared cutoff @xmath2 . for non - vanishing values for @xmath2 , we will obtain coarse - grained order parameter and free energy , which are the appropriate objects to study the dynamics of long wavelength thermal fluctuations . in the limit @xmath3 , we will obtain the finite temperature quantum field theory in thermal equilibrium .    in this approach , since all the quantum fluctuations are integrated out from the beginning , it will be possible to relate the thermal field theory and the physical ( renormalized ) quantum field theory at zero temperature in a transparent way .    the ideal framework to perform this program of coarse - graining of thermal fluctuations is the real time ( rt ) formulation of thermal field theories @xcite , in which the thermal part in the free propagators is well separated from the zero - temperature quantistic one . as is well known , the price to pay for this is a doubling of the number of degrees of freedom . these `` ghost '' fields are necessary to cancel the so - called pinch singularities , which are due to the fact that the thermal fluctuations are on - shell . because of these technical complications matsubara s imaginary time ( it ) approach @xcite is more popular in the literature . in particular , the coarse - graining procedure can be precisely formulated in the so - called closed - time - path ( ctp ) formalism @xcite ( see refs . @xcite for a clear presentation ) . indeed , the description of a system in which only the short wavelength fluctuations are in thermal equilibrium can be achieved by modifying the density matrix with respect to the thermal one , and the ctp was designed just to describe systems with a generic density matrix . anyway , the reader not familiar with the ctp formalism should not worry too much about it . as we will discuss in appendix a , the modification of the density matrix that we will consider is equivalent to working in the more familiar rt formulation of niemi and semenoff @xcite with a modified distribution function , given by the bose - einstein distribution function ( or the fermi - dirac , for fermions ) multiplied by the cutoff function .    as a first stage of this program , in this paper we illustrate our method by considering the well - studied self - interacting real scalar theory . as is well known , this model belongs to the universality class of the ising model , and then it has a second order phase transition . however , perturbation theory fails to reproduce this result even after the resummation of daisy and super - daisy diagrams @xcite , unless the gap equations are solved to @xmath4 , @xmath5 being the quartic coupling constant @xcite . we derive the `` exact '' wilson rg equation for the effective potential and approximate it by expanding in powers of space - time derivatives of the field . as we will discuss , even after our approximations , the effective potential computed in this approach includes more contributions than the super - daisy resummed one in @xcite and the prediction of a second order phase transition will emerge in a clear way . in particular , we will see that the running of the coupling constant , which is neglected in perturbation theory , has a very strong effect . at the critical temperature , the effective coupling constant vanishes together with the thermal mass , and this cures the severe infra - red problems encountered in perturbation theory . the paper is organized as follows . in section 2 we define the cutoff thermal field theory and discuss its relationship with other rg approaches . in section 3 we derive the rg flow equations for the quantities of interest . in section 4 the evolution equation for the cutoff effective potential is approximated in various ways in order to perform the numerical analysis . section 5 contains the results of our numerical study and section 6 some conclusions and further comments . in appendix a we briefly describe the closed time path method and how it applies to our case . appendix b contains a discussion of the problem of pinch singularities appearing in the kernel of rg flow equations .","summary":"we apply renormalization group techniques to the real time formulation of thermal field theory . due to the separation between the and the parts of the propagator in this formalism = 2ex         # 1([#1 ] )    ii    cern - th/96 - 23 + shep 96 - 05 +    * wilson renormalization group formulation *    * of real time thermal field theories *    m. dattanasio    _ department of physics , university of southampton , united kingdom _    _ and infn gruppo collegato di parma , italy _    m. pietroni    _ theory division , cern _    _ ch-1211 geneva 23 , switzerland _    cern - th/96 - 23 + february 1996","abstract":"we apply renormalization group techniques to the real time formulation of thermal field theory . due to the separation between the and the parts of the propagator in this formalism , one can derive exact evolution equations for the green functions describing the effect of integrating out thermal fluctuations of increasing wavelengths , the initial conditions being the renormalized green functions of the theory . as a first application , we study the phase transition for the real scalar theory , computing the order of the transition , the critical temperature , and critical exponents , in different approximations to the evolution equations for the scalar potential .    = 2ex         # 1([#1 ] )    ii    cern - th/96 - 23 + shep 96 - 05 +    * wilson renormalization group formulation *    * of real time thermal field theories *    m. dattanasio    _ department of physics , university of southampton , united kingdom _    _ and infn gruppo collegato di parma , italy _    m. pietroni    _ theory division , cern _    _ ch-1211 geneva 23 , switzerland _    cern - th/96 - 23 + february 1996"}
{"article_id":"hep-ph9601375","section_id":"r","document":"we have solved the system in eq . ( [ syst ] ) at different orders of truncation and for different values of @xmath47 . in this way we are able to reconstruct the shape of the tadpole , and then of the effective potential . since we are mainly interested in the study of the phase transition , we will solve the evolution equations for @xmath47 close to the origin , and running from @xmath85 ( in practice @xmath115 will be enough , see fig .  [ 1 ] ) down to @xmath56 . as initial condition in @xmath55 we use the 1-loop effective potential at @xmath0 , v__0 ( ) = - ^2 ^2 + ^4 + , where @xmath116 and the potential has been renormalized in the @xmath117 scheme with @xmath118 . in principle , different approximation schemes to the @xmath0 effective potential could also be used , as given for instance by the polchinski rg or by lattice computations . however , due to universality , the results for the critical theory should be almost insensitive to the details of the initial conditions , and the 1-loop approximation will be enough for our present purposes .    in fig . [ 2 ] we show the tadpole @xmath119 as a function of @xmath47 at the critical temperature , when the system has been truncated to the second line . as we see the potential has three stationary points ( the zeros of @xmath119 ) , i.e. there are two minima , so that it describes a ( weakly ) first - order phase transition . in this case , we have fixed the temperature in such a way that the two minima are degenerate . this result agrees with the one obtained in 1-loop resummed perturbation theory , see for instance ref . @xcite . however as soon as we turn the evolution for the third and fourth coupling on , as we did in fig . [ 3 ] , we see that things change dramatically . in this case the tadpole has only one zero in @xmath120 for temperatures higher than a critical value and two zeros for lower temperatures . there is no temperature interval in which a third zero is present , in other words the effective potential develops no barrier between the symmetric and the asymmetric phases . the critical temperature @xmath121 has been determined by requiring that the second derivative of the potential vanished . so , as soon as the running of the coupling is taken into account , the transition turns out to be of second - order , as would be expected from universality . the continuous and dash - dotted lines in this plot represent the results obtained by truncating to the fourth and sixth orders , respectively . the running of the coupling is indeed a strong effect , in particular close to the critical temperature , as we read from fig . the @xmath0 value for the coupling in this picture is chosen to be @xmath122 , and we see that , while for @xmath12 far from @xmath121 the running is an @xmath123 effect , for @xmath124 the coupling vanishes . the expansion parameter of the super - daisy resummation is given by @xmath114 , where @xmath125 is the mass scale of the theory , in this case the thermal mass @xmath126 . as @xmath124 the thermal mass vanishes , and @xmath127 diverges . this is the source of the wild infra - red problems of resummed perturbation theory , which prevent computations for temperatures close to the critical one . including the running of the coupling , which is also vanishing at @xmath121 , @xmath127 tends to a finite value , and the infrared problems are , if not cured , at least domesticated . this observation was already made in ref . @xcite . looking at the evolution equations , we see that the range of @xmath48 for which there is a sizeable running of the parameters is determined by the function @xmath128 . for @xmath129 the distribution function is exponentially suppressed and the running is negligible , as we read from fig . high energy modes are boltzmann suppressed .    on the other hand , for small @xmath48 , the function goes approximately as @xmath130 , and so there is running as long as @xmath131 . we can then define a correlation length as the inverse of @xmath132 , such that _c^2=v__c . since there are no thermal modes at wavelengths larger than the correlation length , integrating over @xmath133 gives a negligible effect .    at the critical temperature we have @xmath134 , and the correlation length diverges . we can define critical indices in the usual way ( see for instance ref . @xcite ) and see how their computation is improved with respect to perturbation theory in the present approach .    at the lowest order in the derivative expansion , we have computed the critical exponent @xmath135 , governing the scaling of the renormalized mass near the critical temperature , m_=0 ~|t - t_c|^ , and @xmath136 , describing how the magnetization at the critical temperature , @xmath137 , scales with the magnetic field @xmath138 , m(h , t = t_c)=~|h|^1/ = ( v_)^1/.    .results for the order of the phase transition , the critical temperature , and the critical exponents @xmath135 , @xmath136 , and @xmath139 at different orders of approximations to the evolution equations ( see text ) . the last row contains the best values in the literature . [ cols=\"^,^,^,^,^,^,^\",options=\"header \" , ]     in table  [ tab1 ] we summarize our results for the order of the phase transition , the critical temperature , and the critical exponents @xmath135 and @xmath136 obtained at the lowest order in the derivative expansion , and truncating the system in eq . ( [ syst ] ) at second , fourth , and sixth order respectively .    in the last row we have listed the best results for the critical exponents obtained in the literature @xcite . we see that passing from the fourth to the sixth order of truncation we have a sizeable improvement in the result for @xmath135 and @xmath136 .    including the corrections of @xmath140 , keeping also the third and fourth terms in the expansion in ( [ derexp ] ) , we can compute the critical exponent @xmath139 , which describes the scaling of the two - point renormalized green function with respect to @xmath48 for @xmath141 at @xmath142 : ^(2)_(0 ) = m^2_(1+z_ ) ~^2- . taking again derivatives with respect to the field @xmath47 , we obtain a system of first order differential equations for @xmath143 , @xmath144 , @xmath108 , @xmath51 , @xmath145 , @xmath108 , @xmath96 , @xmath146 , @xmath108 . we have truncated this system at the fourth derivative for @xmath95 and at the second one for @xmath51 and @xmath96 . due to the @xmath46 symmetry of the model , and using the fact that the initial condition for @xmath96 ( which corresponds to its zero - temperature value ) is zero , the effect of @xmath96 and its derivatives is negligible for values of @xmath47 close to the origin , and can be neglected with respect to that of @xmath51 . moreover , we have still neglected the imaginary part of the self - energy on - shell , which is only a two - loop effect in standard perturbation theory @xcite . the result is reported in the fourth row of table  [ tab1 ] . as we can read , the effect of wave function renormalization is very small , as may be expected since in perturbation theory it arises at two loops . so , in this model , the derivative expansion turns out to be a very efficient approximation scheme . the accuracy of our results for the critical exponents is generally a lot better than the one obtained in other approaches to the four - dimensional theory , such as perturbation theory or the it formulation of the rg @xcite , both predicting @xmath147 . nevertheless , the best way to compute the critical exponents remains the study of the three - dimensional critical theory ( see refs . @xcite and , for a rg computation , @xcite ) . once one has established that the effective potential solution of eq .   describes a second order phase transition , the universal quantities ( the critical exponents ) can be obtained studying the evolution around the fixed points of the critical ( @xmath142 ) theory at large length - scales ( @xmath148 ) . for @xmath149 one expects that the theory becomes scale invariant . this is what indeed happens , as can be seen by rescaling @xmath95 and @xmath47 according to @xmath150 and @xmath151 ( notice that the temperature enters as expected by dimensional reduction arguments ) . in terms of the new variables , eq . becomes @xmath152\\,,\\qquad t=\\log\\left(\\frac{t_c}{\\l}\\right)\\,.\\ ] ] as @xmath153 the explicit @xmath32-dependence in the rhs disappears , and we obtain the scale - invariant equation ( dropping tildes and changing variables to absorb the factor in front of the logarithm ) [ lpa ] v_+v_-3 v_=(1+v_ ) . this is the rg flow equation for the zero temperature potential in @xmath154 space - time dimensions at the lowest order in the derivative expansion and for a sharp momentum cutoff @xcite . we see than that the critical behaviour of is effectively described by a three dimensional @xmath0 theory . the fixed points and the corresponding critical indices of eq .   can be computed numerically without truncations and the result for @xmath135 is ( see @xcite for details ) @xmath155 on the other hand , if one is interested in studying the theory out of the critical regime , or in the case of a first order phase transition , the three - dimensional approach is no longer suited , and the full four - dimensional theory has to be addressed . in this case , as we have discussed at the end of sect .  3 , the present formulation of the real time rg provides a clear connection between the theory at finite temperature and the theory at @xmath0 , which we are supposed to test in the laboratory .","summary":", we study the phase transition for the real scalar theory , computing the order of the transition , the critical temperature , and critical exponents , in different approximations to the evolution equations for the scalar potential .   ","abstract":"we apply renormalization group techniques to the real time formulation of thermal field theory . due to the separation between the and the parts of the propagator in this formalism , one can derive exact evolution equations for the green functions describing the effect of integrating out thermal fluctuations of increasing wavelengths , the initial conditions being the renormalized green functions of the theory . as a first application , we study the phase transition for the real scalar theory , computing the order of the transition , the critical temperature , and critical exponents , in different approximations to the evolution equations for the scalar potential .    = 2ex         # 1([#1 ] )    ii    cern - th/96 - 23 + shep 96 - 05 +    * wilson renormalization group formulation *    * of real time thermal field theories *    m. dattanasio    _ department of physics , university of southampton , united kingdom _    _ and infn gruppo collegato di parma , italy _    m. pietroni    _ theory division , cern _    _ ch-1211 geneva 23 , switzerland _    cern - th/96 - 23 + february 1996"}
{"article_id":"1406.5065","section_id":"i","document":"characterization and quantification of quantum correlation  @xcite play a central role in quantum information . entanglement , in particular , has been successfully identified as a useful resource for different quantum communication protocols  @xcite and computational tasks  @xcite . moreover , it has also been employed to study cooperative quantum phenomena like quantum phase transitions in many - body systems  @xcite . however , in the recent past , several quantum phenomena of shared systems have been discovered in which entanglement is either absent or does not play any significant role . locally indistinguishable orthogonal product states  @xcite  ( c.f . @xcite ) is a prominent example where entanglement does not play an important role . the role of entanglement is also unclear in the model of deterministic quantum computation with one quantum bit  @xcite . such phenomena motivated the search for concepts and measures of quantum correlation independent of the entanglement - separability paradigm . introduction of quantum discord  @xcite is one of the most important advancements in this direction and has inspired a lot of research activity  @xcite . it has thereby emerged that quantum correlations , independent of entanglement , can also be a useful ingredient in several quantum information processing tasks @xcite . other measures in the same direction include quantum work deficit  @xcite , measurement - induced nonlocality  @xcite , and quantum deficit  @xcite ( see also @xcite ) . these measures can be generally considered to be quantum correlation measures within an `` information - theoretic paradigm '' . in classical as well as quantum information theory , one of the most important pillars is the framework of entropy  @xcite , which quantifies the ignorance or lack of information in the relevant physical system . moreover , it helps to understand information theory from a thermodynamic perspective . almost all the quantum correlation measures incorporate entropic functions in various forms . and , most of the quantum correlation measures are defined by using the von neumann entropy  @xcite . the operational significance of von neumann entropy has been widely recognized in numerous scenarios in quantum information theory . nonetheless , there are classes of generalized entropies like the rnyi  @xcite and tsallis  @xcite entropies , which are also operationally significant in important physical scenarios . both the rnyi and tsallis entropies reduce to the von neumann entropy when the entropic parameter @xmath0 @xmath1 . for @xmath2 the relative rnyi entropy appears in the quantum chernoff bound which determines the minimal probability of error in discriminating two different quantum states in the setting of asymptotically many copies  @xcite . in ref . @xcite , it was shown that the relative rnyi entropy is relevant in binary quantum state discrimination , for the same range of @xmath0 . the concept of rnyi entropy has also been found to be useful in the context of holographic theory  @xcite . it has also been found useful in dealing with several condensed matter systems  @xcite . the significance of the tsallis entropy in quantum information theory has been established in the context of quantifying entanglement  @xcite , local realism  @xcite , and entropic uncertainty relations  @xcite ( see also @xcite ) . both the rnyi and tsallis entropies have important applications in classical as well as quantum statistical mechanics and thermodynamics  @xcite .    while there are important interpretational and operational breakthroughs that have been obtained by using the concept of quantum discord , there are also several intriguing unanswered questions and thriving controversies  @xcite . it is therefore interesting and important to look back upon the conceptual foundations of quantum discord and inquire whether certain changes , subtle or substantial , in those concepts lead us to a better understanding of the controversies and the unanswered questions . towards this aim , we introduce measures of the total , classical , and quantum correlations of a bipartite quantum state in terms of the entire class of relative rnyi and tsallis entropy distances . we show that the measures satisfy all the required properties of bipartite correlations . we then evaluate the quantum correlation measure for several paradigmatic classes of states . as an application , we find that the quantum correlation measures , via relative rnyi and tsallis entropies , can indicate quantum phase transitions and give better finite - size scaling exponents than the other known order parameters . importantly , we show that the conceptualization of the measures in terms of rnyi and tsallis entropies solves an incommodious feature regarding the behavior of nearest - neighbor quantum discord in a second order phase transition .    there are at least two distinct ways in which the relative rnyi and tsallis entropies are defined , and are usually referred to as the `` traditional ''  @xcite and `` sandwiched ''  @xcite varieties . the sandwiched varieties incorporate the noncommutative nature of density matrices in an elegant way , and it is therefore natural to expect that it will play an important role in fundamentals and applications . indeed , the sandwiched relative rnyi entropy has been used to show that the strong converse theorem for the classical capacity of a quantum channel holds for some specific channels  @xcite . moreover , an operational interpretation of the sandwiched relative rnyi entropy in the strong converse problem of quantum hypothesis testing is noted for @xmath3  @xcite . on the other hand , the sandwiched relative tsallis entropy has recently been shown to be a better witness of entanglement @xcite than the traditional one @xcite . the relative min- and max - entropies @xcite , which can be obtained from the sandwiched relative rnyi entropy for specific choices of @xmath0 , play significant roles in providing bounds on errors of one - shot entanglement cost  @xcite , on the one - shot classical capacity of certain quantum channels  @xcite , and in several scenarios in non - asymptotic quantum information theory  @xcite . in ref . @xcite , connection of max- relative entopy with frustration in quantum many body systems has been established . the paper is organized as follows . in sec . [ gre ] , we discuss the relative rnyi and tsallis entropies . in sec . [ qd ] , we talk about the usual quantum discord . the rnyi and tsallis quantum correlations are defined in sec . [ gqd ] , where we also derive their properties and evaluate them for paradigmatic classes of bipartite quantum states . some special cases like the `` linear '' , `` min- '' , and `` max- '' quantum discord are also formulated and discussed there . the quantum correlation measure is then applied for detecting quantum phase transition in a quantum many - body system in sec . we present a conclusion in sec . [ conclu ] .","summary":"it is conceptualized by using the von neumann entropy as a measure of disorder . we introduce a class of quantum correlation measures as differences between total and classical correlations , in a shared quantum state , in terms of the sandwiched relative rnyi and tsallis entropies . we find that the measures satisfy all the plausible axioms for quantum correlations . we show that the measures can faithfully detect the quantum critical point in the transverse quantum ising model and find that they can be used to remove an unquieting feature of nearest - neighbor quantum discord in this respect . furthermore , the measures provide better finite - size scaling exponents of the quantum critical point than the ones for other known order parameters , including entanglement and information - theoretic measures of quantum correlations .","abstract":"quantum discord is a measure of quantum correlations beyond the entanglement - separability paradigm . it is conceptualized by using the von neumann entropy as a measure of disorder . we introduce a class of quantum correlation measures as differences between total and classical correlations , in a shared quantum state , in terms of the sandwiched relative rnyi and tsallis entropies . we compare our results with those obtained by using the traditional relative entropies . we find that the measures satisfy all the plausible axioms for quantum correlations . we evaluate the measures for shared pure as well as paradigmatic classes of mixed states . we show that the measures can faithfully detect the quantum critical point in the transverse quantum ising model and find that they can be used to remove an unquieting feature of nearest - neighbor quantum discord in this respect . furthermore , the measures provide better finite - size scaling exponents of the quantum critical point than the ones for other known order parameters , including entanglement and information - theoretic measures of quantum correlations ."}
{"article_id":"1611.06275","section_id":"i","document":"white dwarfs ( wd ) are the endpoint of stellar evolution for stars lighter than 8  10  @xmath7 @xcite , or greater than 97% of galactic stars . as the direct remnants of earlier star formation , wds are an important tool in studying the evolution of our galaxy . the basic observable when studying star formation history with wds is the distribution of wds in luminosity , or the luminosity function ( lf ; see @xcite for a recent review of both the observational and theoretical work on the white dwarf luminosity function ) . in particular , for a given stellar population , the location and shape of the peak and turnover in the lf at the faint end can be used to constrain the age of that population @xcite . the bright end ( @xmath8 ) of the white dwarf luminosity function ( wdlf ) is populated by hot wds whose optical colors are distinct from other stellar populations , allowing clean samples of hot wds to be found based on photometry alone . thus , even the earliest lfs for hot wds contained hundreds of stars , including those produced from the palomar - green @xcite and kiso @xcite ultraviolet excess surveys . lfs generated from modern large - scale spectroscopic surveys have been based on samples of thousands of hot wds , including those from the sdss @xcite and the anglo - australian 2df qso redshift survey @xcite . thus , the bright end of the wdlf is defined with high statistical significance . the majority of wds however are fainter , with colors indistinguishable from subdwarfs , making their selection using photometry alone impossible . the first study to resolve the peak of the lf and obtain samples of wds fainter than the turnover was @xcite , based on a sample of 43 cool wds selected from the luyten half - second catalog @xcite to have @xmath9 ( and later reanalyzed with additional spectroscopy and photometry by @xcite ) . subsequent proper - motion based studies had similar sample sizes @xcite . the first major increase in sample size was that of ( * ? ? ? * hereafter h06 ) , which used sloan digital sky survey ( sdss ; * ? ? * ; * ? ? ? * ; * ? ? ? * ) photometry and proper motions from a combined catalog @xcite of sdss and usno - b @xcite astrometry to generate a sample of 6000 reduced - proper - motion selected wds . * hereafter rh11 ) similarly used reduced proper motions to select 10,000 wds from the supercosmos sky survey @xcite . both surveys provide a galactic disk wdlf with high statistical significance in the luminosity range @xmath10 , and clearly define the peak of the disk wdlf at @xmath11 . however , neither provides many stars fainter than the turnover , with only 4 stars in h06 and 48 in rh11 with @xmath12 ( in their @xmath13 samples ) . both surveys are dependent on the classic schmidt telescope photographic surveys for one or both epochs , and thus are limited to the depth of the photographic surveys , @xmath14 . a hydrogen atmosphere wd one magnitude fainter than the turnover has @xmath15 , which at a faint limit of @xmath14 corresponds to only 50  pc . thus the small surveyed volume severely limits the number of wds detectable past the turnover . rh11 detected more such wds as their sky coverage is nearly six times as great as that for h06 ( roughly 30,000  deg@xmath16 for rh11 versus 5300  deg@xmath16 for h06 ) . both papers also present a lf for clean samples of galactic halo wds , defined kinematically by requiring @xmath17 . h06 detect only 18 such halo wds , while rh11 with their greater sky coverage detect 93 . the sample sizes of halo wds are limited by the much smaller density of halo stars within the solar neighborhood . the rh11 sample is by far the largest sample of halo wd candidates to date . note that , unlike many of the other samples discussed above , most of the wds in the h06 and rh11 samples lack spectroscopic confirmation , though contamination by non - wds is thought to be both understood and small @xcite . recent work has concentrated on producing nearly complete samples of wds in the local volume . lfs have been produced using wds within 20 @xcite , 25 @xcite , and 40  pc @xcite of the sun , with sample sizes of 147 , 232 , and 501 wds , respectively . the 40  pc lf has 22 stars fainter than the turnover ( @xmath12 ) . no halo wds were found in any of the samples , with three possible candidates in the 40  pc sample .    in order to address the paucity of both disk wds fainter than the turnover and halo wds in our earlier work in h06 , in 2009 we started a survey to re - observe parts of the sdss imaging footprint , obtaining a second epoch which , combined with sdss astrometry , would yield proper motions roughly 2 magnitudes fainter than that obtainable using the schmidt surveys @xcite . this paper presents a catalog of wd candidates selected from that survey , and the resultant disk and halo wdlfs . individual objects with additional follow - up observations have been presented in previous papers @xcite . section  [ section - sample ] describes the sample selection . section  [ section - model - fits ] describes the fitting of atmospheric models to sdss photometry to derive distances , effective temperatures , and bolometric luminosities for the sample wds . section  [ section - luminosity - function ] presents the luminosity functions , section  [ section - catalog ] presents the catalog , and section  [ section - summary ] summarizes our results .","summary":"the wdlf for the halo is also constructed , using a sample of 135 halo wds with .","abstract":"a catalog of 8472 white dwarf ( wd ) candidates is presented , selected using reduced proper motions from the deep proper motion catalog of . candidates are selected in the magnitude range over 980 square degrees , and over an additional 1276 square degrees , within the sloan digital sky survey ( sdss ) imaging footprint . distances , bolometric luminosities , and atmospheric are derived by fitting sdss photometry to pure hydrogen and helium model atmospheres . the disk white dwarf luminosity function ( wdlf ) is constructed using a sample of 2839 stars with , with statistically significant numbers of stars cooler than the turnover in the luminosity function . the wdlf for the halo is also constructed , using a sample of 135 halo wds with . we find space densities of disk and halo wds in the solar neighborhood of and , respectively . we resolve the bump in the disk wdlf due to the onset of fully convective envelopes in wds , and see indications of it in the halo wdlf as well ."}
{"article_id":"1611.06275","section_id":"i","document":"we have presented a reduced - proper - motion selected sample of 8472 wd candidates from a deep proper motion catalog , covering 2256 square degrees of sky to faint @xmath20 limits of 21.3  21.5 . sdss @xmath2 photometry has been fit to pure hydrogen and helium atmosphere model wds to derive distances , bolometric luminosities , effective temperatures , and atmospheric compositions . the disk wdlf has been presented , with statistically significant samples of stars cooler than the lf turnover , a region of the lf particularly important in applying the wdlf to the determination of the age of the disk . that determination remains hampered by the unknown atmospheric composition and masses of most stars fainter than the turnover , and likely wo nt be resolved until parallaxes for significant samples of faint wds are available . the halo wdlf has also been presented , based on a sample of 135 stars . both the disk and halo wdlfs have been compared to those of h06 and rh11 , which are similar in technique , the portion of the lf studied , and sample size . the shape of the disk lf is in broad agreement with both h06 and rh11 brighter than the turnover . we find a higher density of wds fainter than the turnover , though only at the 2  3 @xmath25 level . our halo wdlf agrees with the h06 lf within their errors , but the rh11 lf gives densities about 40% larger ( after scaling to match our disk lfs ) . the turnover in the halo wdlf remains undetected . we detect with high statistical significance the bump in the disk lf due to the onset of fully convective envelopes in wds , a feature first seen by h06 , and see indications of it in the halo lf as well . while these are the largest samples to date of disk wds fainter than the turnover , as well as of halo wds , the imminent release of the the panoramic survey telescope and rapid response system 3pi survey data will allow for both deeper and much larger samples , with improved photometric accuracy that should help in distinguishing between hydrogen and helium atmosphere wds for those wds cooler than the turnover in the disk lf . in about a year we anticipate the revolution in wd research that data release 2 of will offer , and in just a few years the second revolution that the large synoptic survey telescope will deliver . in a field that has long been challenged by insufficiently small samples , the next few years are going to be rewarding . we thank n. rowell and n. c. hambly for providing us with the data for their luminosity functions . this material is based on work supported by the national science foundation under grant ast 06 - 07480 . mk , kd , and ag gratefully acknowledge the support of the nsf and nasa under grants ast-1312678 and nnx14af65 g . kw gratefully acknowledges the support of the nfs under grant ast-0602288 . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . the digitized sky surveys were produced at the space telescope science institute under u.s . government grant nag w-2166 . the images of these surveys are based on photographic data obtained using the oschin schmidt telescope on palomar mountain and the uk schmidt telescope . the plates were processed into the present compressed digital form with the permission of these institutions .","summary":"a catalog of 8472 white dwarf ( wd ) candidates is presented , selected using reduced proper motions from the deep proper motion catalog of . the disk white dwarf luminosity function ( wdlf ) is constructed using a sample of 2839 stars with , with statistically significant numbers of stars cooler than the turnover in the luminosity function . we resolve the bump in the disk wdlf due to the onset of fully convective envelopes in wds , and see indications of it in the halo wdlf as well .","abstract":"a catalog of 8472 white dwarf ( wd ) candidates is presented , selected using reduced proper motions from the deep proper motion catalog of . candidates are selected in the magnitude range over 980 square degrees , and over an additional 1276 square degrees , within the sloan digital sky survey ( sdss ) imaging footprint . distances , bolometric luminosities , and atmospheric are derived by fitting sdss photometry to pure hydrogen and helium model atmospheres . the disk white dwarf luminosity function ( wdlf ) is constructed using a sample of 2839 stars with , with statistically significant numbers of stars cooler than the turnover in the luminosity function . the wdlf for the halo is also constructed , using a sample of 135 halo wds with . we find space densities of disk and halo wds in the solar neighborhood of and , respectively . we resolve the bump in the disk wdlf due to the onset of fully convective envelopes in wds , and see indications of it in the halo wdlf as well ."}
{"article_id":"gr-qc9907010","section_id":"i","document":"the radiative era of cosmic evolution comprises the period from the end of primeval nucleosynthesis to the decoupling of matter and radiation ( see refs @xcite to @xcite ) . a gross description of cosmological matter sources in this period is given by an interactive mixture of ideal relativistic and non relativistic gases ( `` radiation '' and `` matter '' ) in local thermal equilibrium ( lte ) . the standard approach to this type of matter source is either a flrw spacetime whith equilibrium kinetic theory distributions@xcite , @xcite , @xcite , gauge invariant perturbations on a flrw background @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and various types of hydrodynamical models , @xcite , @xcite , @xcite which , in general , fail to incorporate a physically plausible description of the interaction between matter and radiation . even if we argue that the universe is `` almost flrw '' or `` almost in thermal equilibrium '' , the small deviations from equilibrium are extremely important , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , to account for most interesting phenomena of cosmic evolution : nucleosynthesis , structure formation , abundance of relic gases , etc . models with perfect fluid sources , whether hydrodynamic , @xcite , @xcite , or based on kinetic theory , @xcite , necessarily assume a quasi - static adiabatic and reversible evolution and thus , fail to incorporate into the resulting picture even small deviations from equilibrium . dissipative sources have been incorporated numerically within a purely flrw geometry @xcite or following a perturbative approach @xcite . however , the literature still lacks an alternative hydrodynamical treatment , based on inhomogeneous exact solutions of einstein s equations with dissipative sources and fully complying with the thermodynamics of a radiative gas within a transient regime . ideally , such exact models should include all dissipative agents ( heat flux , bulk and shear viscosity ) and should be consistent with the theoretical framework of extended irreversible thermodynamics ( see refs @xcite to @xcite ) , thus satisfying suitable transport equations complying with causality , with phenomenological coefficients given by kinetic theory for this type of source . since this general treatment would be mathematically untractable , we aim at the best possible approach based on exact solutions of einstein s equations . therefore , we have made the following simplifying assumptions : ( a ) the matter source is a fluid with shear viscosity but without heat conduction nor bulk viscosity , ( b ) the equilibrium state variables satisfy the equation of state of a mixture of relativistic and non - relativistic ideal gases , where the internal energy and pressure of the latter have been neglected , ( c ) the particle numbers of each mixture components is independently conserved , ( d ) we exclude dark matter and/or exotic particles and assume instead a tight coupling between photons ( radiation ) and baryons and electrons ( matter ) , hence there is a common temperature for the mixture ( lte ) , while the microscopical interaction models are the various processes of radiative transfer , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite : thomson scattering , brehmstrallung , free - free absortion , etc . although this type of interactions involve mostly photons and electrons , the dynamics of the matter component is governed by the baryons since the latter provide most of the rest mass content of non - relativistic matter ( without dark matter ) .    restrictions ( b ) and ( c ) are easy to justify : since the ratio of photons to baryons is such a large number ( @xmath6 ) , we can truly ignore the pressure of non - relativistic matter . also , after nucleosynthesis , in the temperature range @xmath7 , matter creation and anhilitation processes balance each other and effectively cease to be dynamically important @xcite , @xcite . on the other hand , the lack of heat conduction ( restriction ( a ) ) is more difficult to justify . it can be associated with an adiabatic ( zero heat flux ) but still irreversible evolution ( nonzero viscosity ) , and can be a reasonable approximation on specific conditions . for example , for a radiative gas at higher temperatures shear viscosity dominates over heat conduction , but the latter becomes significant as the mixture cools@xcite . the lack of bulk viscosity is a better approximation : it is negligible for a radiative gas in the temperature range @xmath8 that we are interested , @xcite , @xcite , @xcite , @xcite , @xcite , becoming important for higher temperatures ( the mid relativistic regime where @xmath9 @xcite , @xcite , @xcite ) . however , we accept that ignoring these dissipative fluxes weakens the scope and validity of the models , but we argue that this is compensated by the simplification of the field equations , leading to exact forms for the equilibrium state variables and shear viscosity that still satisfy ( under the restrictions mentioned ) thermodynamically consistent relations . the models we present are based on the spherically symmetric lematre - tolman - bondi metrics , usually associated with dust sources @xcite , @xcite . however , this metric is compatible with a comoving fluid source with zero heat flux but with anisotropic stresses , which we describe as shear viscosity . obviously , the lack of heat flux and 4-acceleration necessarily implies a very special shear viscous tensor whose divergence exactly balances the nonzero spatial gradient of the equilibrium pressure . considering this metric and this source , we impose on the equilibrium state variables the equation of state for a mixture of ideal gases ( under the restriction ( b ) ) . the field equations can be solved up to a quadrature , without having to make any assumption on the form of the shear viscous pressure . the latter , as well as all equilibrium state variables can be determined from the solution of the quadrature , up to two initial value functions that can be identified with the initial energy densities of the matter and radiation components . we consider only the case that would be equivalent to spacelike sections of zero curvature . a generalization of this class of exact solutions to the more general szekeres - szafron metrics admitting no isometries has been published recently @xcite , while the study of a non - relativistic ideal gas is considered in @xcite . once the field equations have been integrated , we define a set of initial value functions that gauge the deviation from homogeneity of the average of initial density contrasts . the terms involving various gradients of metric functions can be given in terms of these gauges , so that in the limit when the latter vanish a flrw spacetime can always be obtained as the homogeneous ( and reversible ) subcase . in section vii we derive the conditions that the models must satisfy in order to be consistent with the theoretical framework of irreversible extended thermodynamics , in the case where shear viscosity is the only dissipative agent and the coefficient of shear viscosity is that given by kinetic theory for the radiative gas @xcite , @xcite , @xcite , @xcite , @xcite , @xcite . this leads to an entropy balance law and a suitable transport equation for shear viscosity that is satisfied for a specific functional form of the relaxation time . conditions are given so that the latter quantity behaves as a relaxation parameter for an interactive cosmological mixture of matter and radiation . these conditions of thermodynamical consistency are then explicitly tested on the models , leading to a set of restrictions on the initial conditions ( the latter given in terms of the gauges of initial density constrasts ) . the most relevant result is that thermodynamical consistency constrains an initial value adimensional function , @xmath0 , which in the limit of small density contrasts is approximately the average gradient of the photon entropy per baryon along the initial hypersurface @xmath10 . an analogy is provided with the theory of perturbations on a flrw background , whereby @xmath11 is formally analogous to the definition of initialy adiabatic perturbations in the sincronous gauge @xcite , @xcite , @xcite , @xcite . the constraints on the observed anisotropy of the microwave cosmic background , as well as the condition that decopling occurs at @xmath12 , leads to the estimated value @xmath4 . since initial conditions of the radiative era should be traced to previous periods of cosmic evolution , this constraint can be related to maximal bounds on entropy fluctuations in primordial perturbations . finally , we compute the jeans mass associated with the thermodynamically consistent models , leading to a value similar to that obtained for baryon dominated perturbation models : @xmath13 .","summary":"the solutions are characterized by the lematre - tolman - bondi metric with a viscous fluid source , subjected to the following conditions : ( a ) the equilibrium state variables satisfy the equation of state of a mixture of an ultra - relativistic and a non - relativistic ideal gases , where the internal energy of the latter has been neglected , ( b ) the particle numbers of the mixture components are independently conserved , ( c ) the viscous stress is consistent with the transport equation and entropy balance law of extended irreversible thermodynamics , with the coefficient of shear viscosity provided by kinetic theory . the fulfilment of ( a ) , ( b ) and ( c ) restricts initial conditions in terms of an initial value function , , which in the limit of small density contrasts becomes the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface . for and choosing the phenomenological coefficients of the `` radiative gas '' model constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at k yield an estimated value : which can be associated with a bound on promordial entropy fluctuations . the jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models ( ) .","abstract":"we derive a new class of exact solutions of einstein s equations providing a physically plausible hydrodynamical description of cosmological matter in the radiative era , between nucleosynthesis and decoupling . the solutions are characterized by the lematre - tolman - bondi metric with a viscous fluid source , subjected to the following conditions : ( a ) the equilibrium state variables satisfy the equation of state of a mixture of an ultra - relativistic and a non - relativistic ideal gases , where the internal energy of the latter has been neglected , ( b ) the particle numbers of the mixture components are independently conserved , ( c ) the viscous stress is consistent with the transport equation and entropy balance law of extended irreversible thermodynamics , with the coefficient of shear viscosity provided by kinetic theory . the fulfilment of ( a ) , ( b ) and ( c ) restricts initial conditions in terms of an initial value function , , which in the limit of small density contrasts becomes the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface . for and choosing the phenomenological coefficients of the `` radiative gas '' model , we have an interactive photon - baryon mixture under local thermal equilibrium , with radiation dominance and temperatures characteristic of the radiative era ( ) . constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at k yield an estimated value : which can be associated with a bound on promordial entropy fluctuations . the jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models ( ) ."}
{"article_id":"gr-qc9907010","section_id":"c","document":"we have derived a new class of exact solutions of einstein s equations providing a physically plausible hydrodynamic description of a radiation - matter ( photon - baryon ) interacting mixture , evolving along adiabatic but irreversible thermodynamic processes . the conditions for these models to be consistent with the transport equation and entropy balance law of eit ( when shear viscosity is the only dissipative agent ) have been provided explicitly , and their effect on initial conditions have been given in detail , briefly discussing the analogy of these conditions with gauge invariant initial perturbations in the isochronous gauge . as far as we are aware , and in spite of their limitations mentioned in the introduction , we believe these models are the first example in the literature of a self consistent hydrodynamical approach to matter - radiation mixtures that : ( a ) is based on inhomogeneous exact solutions of einstein s field equations , and ( b ) is thermodynamically consistent . we believe these models can be a useful theoretical tool in the study of cosmological matter sources , providing a needed alternative and complement to the usual approaches based on perturbations or on numerical methods . the solutions have an enormous potential as models in applications of astrophysical and cosmological interest . consider , for example , the following possibilities : ( a ) _ structure formation in the acoustic phase_. there is a large body of literature on the study of acoustic perturbations in relation to the jeans mass of surviving cosmological condensations . equations of state analogous to ( 2 ) are often suggested in this context @xcite , @xcite , @xcite , @xcite , @xcite , @xcite . since practically all work on this topic has been carried on with perturbations on a flrw background , the exact solutions derived and presented here may be viewed as an alternative treatment for this problem . ( b ) _ comparison with perturbation theory_. the models presented in this paper are based on exact solutions of einstein s field equations , but their initial conditions and evolution can be adapted for a description of `` exact spherical perturbations '' on a flrw background . it would be extremely interesting , not only to compare the results of this approach with those of a perturbative treatment , but to provide a physically plausible theoretical framework to examine carefully how much information is lost in the non - linear regime that falls beyond the scope of linear perturbations . we have studied in this paper only the case @xmath355 in ( 11 ) , thus restricting the evolution to the `` growing mode '' since all fluid layers expand monotonously . the study of the more general case , where @xmath356 in ( 11 ) is an arbitrary function that could change sign , would allow a comparison with perturbations that include also a `` decaying mode '' related to condensation and collapse of cosmological inhomogeneities . ( c ) _ inhomogeneity and irreversibility in primordial density perturbations_. the initial conditions of the models with @xmath1 are set for a hypersurface with temperature @xmath357 . these initial conditions can be considered the end product of processes characteristic of previous cosmological history , and so the estimated value @xmath4 , related to the spatial variation of photon entropy fluctuations , can be used as a constraint on the effects of inhomogeneity on primordial entropy fluctuations that might be predicted by inflationary models at earlier cosmic time . also , the deviation from equilibrium in the initial hypersurface ( proportional to @xmath256 ^ 2\\approx      this work has been partially supported by the spanish ministry of education and the national university of mexico ( unam ) , under grants pb94 - 0718 and dgapa - in-122498 , respectively . one of us ( ras ) wishes to acknowledge inspiration from the feline wisdom of tontina , chiquita and pintita . g. efstathiou , _ cosmological perturbations_. in _ physics of the early universe _ , proceedings of the thirty sixth scottish universities summer school in physics . peacock , a.f . heavens and a.t . iop publishing ltd , bristol , u.k . , ( 1990 ) . ellis et al . , _ gen . _ , * 10 * , 931 ( 1883 ) ; g.r.f ellis and s.r . matravers , _ class . quantum grav . _ , * 7 * , 1869 ( 1990 ) ; r. maartens and f.p . wolvaardt , _ class . quantum grav . _ , * 11 * , 203 ( 1994 ) .","summary":"we derive a new class of exact solutions of einstein s equations providing a physically plausible hydrodynamical description of cosmological matter in the radiative era , between nucleosynthesis and decoupling .","abstract":"we derive a new class of exact solutions of einstein s equations providing a physically plausible hydrodynamical description of cosmological matter in the radiative era , between nucleosynthesis and decoupling . the solutions are characterized by the lematre - tolman - bondi metric with a viscous fluid source , subjected to the following conditions : ( a ) the equilibrium state variables satisfy the equation of state of a mixture of an ultra - relativistic and a non - relativistic ideal gases , where the internal energy of the latter has been neglected , ( b ) the particle numbers of the mixture components are independently conserved , ( c ) the viscous stress is consistent with the transport equation and entropy balance law of extended irreversible thermodynamics , with the coefficient of shear viscosity provided by kinetic theory . the fulfilment of ( a ) , ( b ) and ( c ) restricts initial conditions in terms of an initial value function , , which in the limit of small density contrasts becomes the average of spatial gradients of the fluctuations of photon entropy per baryon in the initial hypersurface . for and choosing the phenomenological coefficients of the `` radiative gas '' model , we have an interactive photon - baryon mixture under local thermal equilibrium , with radiation dominance and temperatures characteristic of the radiative era ( ) . constraints on the observed anisotropy of the microwave cosmic radiation and the condition that decoupling occurs at k yield an estimated value : which can be associated with a bound on promordial entropy fluctuations . the jeans mass at decoupling is of the same order of magnitude as that of baryon dominated perturbation models ( ) ."}
{"article_id":"1306.5719","section_id":"c","document":"let us consider a `` scattering '' where a strongly interacting and dense system ( intensive scale @xmath2 , with a global energy @xmath78 ) is produced from a pure state , but then expands and decays into a `` many''-particle system of typical momenta @xmath70 ( hence , there will be @xmath208 particles at the end ) . a good example of this is an expanding and hadronizing quark - gluon plasma , but any `` large bag of particles '' will do . crucially , a black hole of mass @xmath209 gev formed from a `` pure '' quantum state and evaporating should also fall into this category . the crucial question is : to what extent can an eft , valid for @xmath49 , be used to describe the final state of the system . as the previous sections argued , if the system is strongly interacting ( as in quantum gravity at momentum scales @xmath210 gev , or qcd with momentum scales @xmath211 mev ) , or even a weakly coupled theory where the typical state occupancy number @xmath212 ( of the type studied in @xcite ) , it is natural to assume that en evolution described by eq . [ evolrho],[evolrho2 ] will result in very complicated correlations of a large ( @xmath213 ) numbers of particles . if an `` ideal '' detector accepts all particles produced in the event , _ and _ enough `` identically prepared systems '' are available ] to measure correlations of _ all _ produced particles , than , provided the black hole or fireball was produced within a pure state , the experiment could measure only a `` modest '' increase in entropy , reflecting information lost via the coarse - graining barrier ( panel ( c ) in fig . [ eftcoarse ] ) . such reactions are kinematically allowed , but strongly suppressed , since they require @xmath214 .    if , however , such a precision is not available , then the `` realistic detector '' will find that the original pure state produced a large amount of entropy in its evolution : the number of particles most likely increased , as the initial kinetic energy went into particle production , and the correlations which balance the increased number of degrees of freedom ( @xmath215 negative entropy @xmath90 terms in eq . [ ineq ] ) are invisible to the detector . this increase in entropy will be interpreted by the `` effective theorist '' , with only the effective field theory at their disposal , as a violation of unitarity , for such a theorist can only calculate correlations of up to @xmath216 particles reliably . the `` fundamental theorist '' , with access to the full strongly interacting fundamental theory will be able to predict , from fundamental theory and particle averages , the necessary @xmath22particle correlations which will , to a good approximation , restore unitarity . an `` ideal detector '' , capable of measuring correlations between @xmath213 produced particles , will however be necessary to verify these predictions . the near - thermal particle distributions observed so far in _ all _ hadronic collisions are therefore natural , for realistic experiments are very far away from the `` ideal detector '' limit described above . it is therefore not surprising that , as known for a long time , thermal model describe very well a closed quantum system such as a hadronic collision , even for systems much smaller than those where kinetic thermalization is required  @xcite , as long as the observables considered are final - state particle averages . the distinction between `` fake thermalization '' and `` real thermalization '' , if such a thing is meaningful , however , requires measuring higher and higher particle momentum distribution cumulants and comparing them to statistical mechanics expectations . we do not know how realistic is such a program . measurements of this type have been performed for other reasons in the past @xcite , but for obvious reasons they fall far short of the `` ideal detector '' standard described above . note that to reach the conclusions above we just needed to assume that the final state is described by an eft ( the typical momentum is @xmath49 ) , but the system itself is `` large '' w.r.t . @xmath0 and exhibits a `` strongly interacting '' phase . the above discussion , from an eft point of view , is therefore similar to the `` scattering '' of a pure quantum system into a black hole , which eventually evaporates into hawking radiation : general relativity , coupled to quantum field theory , can be considered as an effective field theory to a hitherto unknown uv - complete quantum theory of gravity , which is relevant for momentum exchanges of order @xmath14 gev . the black hole evaporation process , similar to its sonic counterpart @xcite and the schwinger pair production mechanism in a strong field @xcite , is a semiclassical but non - perturbative process involving an `` infinite '' ( @xmath217 ) number of ingoing and outgoing states . infinite , here , simply means that backreaction of evaporated particles on the parent system can safely be neglected . semiclassical means that quantum fluctuations around the action extremum can be neglected . quantitatively , the two assumptions are connected since such corrections will carry @xmath218 `` units of action '' ( @xmath219 in natural units , @xmath220 in other unit systems ) while the system as a whole carries @xmath221 units . this picture is intuitively clear in the laboratory `` analogue of hawking radiation '' , the sonic black hole @xcite ; in this case , the physical picture , and the analogy with @xcite , is clearly that of a mean - field condensate amenable to a coarse - grained description ( the `` fluid '' ) and an effective quantum theory of perturbations ( the `` phonons '' ) . the unitarity violation implicit `` hawking sound '' is clearly of the same type as that of @xcite , and can be accounted for by going further than the semiclassical approach . to what extent a `` real black hole '' is analogous to its sonic counterpart of course remains to be seen , but certainly this scenario is the simplest one . [ bhdiagram ] top panel summarizes the situation of a black hole formed by a coherent quantum state which evaporates into a `` many '' particle system . we are bothered by a `` black hole information paradox '' due to our conviction that , even though we lack a uv - complete theory of quantum gravity , the _ effective theory _ of quantum gravity relevant to an evaporating black hole is quantum field theory on a schwarzchild background . the effective theory before and after the black hole exists is , of course , the same quantum field theory on a flat background . corrections to these efts will necessarily come in factors of @xmath222 and lower . the essence of the `` black hole information problem '' is that we believe that we can calculate all observables using only the eft . the eft tells us that `` before the black hole formed '' , entropy was zero , because we have a pure quantum state , and `` after the black hole formed '' entropy is non - zero because the momentum distribution function seems to be a thermal distribution . going from one to another is forbidden in a unitary quantum evolution . however , the `` non - unitarity of the black hole evolution '' is a necessary artifact of using effective field theory . the energy of each evaporated particle @xmath223 , but @xmath224 , where @xmath16 is the total number of evaporated particles . hence , one can not a priori assume that @xmath16 particle terms of the density matrix carry an amount of negentropy smaller than 1-particle terms ( which set the form of the thermal distribution ) . if the theory of gravity that holds close to the singularity is strongly coupled , as dimensional analysis suggests , the overwhelming fraction of the entropy needs terms at order @xmath225 to be calculated . even if this theory is not strongly coupled , the time required for the black hole to emit most of its entropy @xmath226 , so plenty of time should be available for correlations between many many hawking radiation particles to form . such correlations , therefore , will most likely be non - negligible and calculating them _ can not be done _ using a semiclassical theory with a cutoff , since this theory s approximation _ is equivalent to assuming these terms be zero _ ( fig . [ bhdiagram ] bottom panel ) . for average occupation numbers such terms are suppressed , but not for high - order correlations . asking `` where the entropy is '' with only the effective theory at our disposal , therefore , is somewhat analogous to asking why the coupling constant of qed runs without having computed a single qed loop diagram , or to take a more everyday example , cooling hot vapor down to ice , and asking why one can not describe the entropy of the system by an effective theory of phonons propagating in ice . in all these cases , we simply are not using the tools capable of addressing the problem . `` experimentally '' , there might well be non - trivial correlations between `` many '' ( @xmath213 ) particles emitted from black hole evaporation , which decrease the overall entropy of the @xmath22particle final state . each correlated state is `` unlikely '' ( suppressed by powers of @xmath222 ) , but the number of possible correlations ( enhanced by @xmath227 ) beats this unlikelihood . their exact nature is only accessible to a theory capable of calculating @xmath228 corrections , which of course is lacking at the moment .    in the same way , the resolution of the firewall paradox pointed out in @xcite might well be that assumption ( ii ) ( as in the abstract of @xcite ) is invalid . an eft of n - particle correlations is not expected to conserve unitarity in the ir because entanglement of many final - state particles is only visible beyond the 1-particle eft currently at our disposal . these particles could have been emitted at any time during the black hole evaporation , before or after the absorption of an entangled pair , and still contribute to the correlations balancing the negentropy measured `` long after '' the black hole in question evaporated @xcite . an infalling `` classical '' observer will most likely not see anything special happening at the horizon because , by definition , such a `` classical observer '' does not contain many entangled quantum particles ; as the previous section shows , a correlated quantum pair , of the type examined in works such as @xcite might well get its entanglement entropy transferred into very complicated correlations of @xmath75 particles . conversely , if the observer is some sort of quantum computer with @xmath229 entangled particles , and is governed by dynamics where such many - particle correlations quickly cascade into 1-particle correlations , they might be able to observe effects similar to what @xcite call a firewall . such carefully prepared , or highly non - linear systems , however , are very far from what we usually consider to be `` an observer '' . indeed , at present , it is difficult to see , even at the gedankenlevel , what kind of system would be needed to see the effects required to resolve `` firewall effect '' . our conclusion is , therefore , very similar to the one suggested in @xcite : the black hole entropy is almost entirely an entropy of entanglement , which will be encoded in complicated inter - particle correlations . this conclusion ( which , as argued by @xcite , also preserves the equivalence principle ) , is unavoidable when the problem is considered from an eft point of view . the analysis contained in this work was , by necessity , qualitative and general . we have made no attempt to describe how `` slow '' quantum dynamics and coarse - graining combine into an effective dynamics which incorporates both unitary and dissipative effects . in particular , our arguments can not as yet be used to isolate the regime where `` fast local thermalization '' can be developed into an effective coarse grained theory of thermalized `` small '' volume elements , i.e. hydrodynamics @xcite . we have just guessed what the results might look like in certain limits . however , as already noted @xcite , the macroscopic gradient expansions usually used to generate effective theories ( such as hydrodynamics ) from fundamental theories have not one expansion parameter but two : one , well explored , is the `` knudsen number '' , the ratio of the mean free path to the system size . the other , the `` microscopic scale '' @xcite ( the mean particle separation @xmath230 in the boltzmann equation , @xmath231 in systems with classical gravity duals such as those described in section [ secplanar ] ) is supposed to be parametrically smaller than the mean free path , something which ensures the convergence of the bbgky expansion . the conclusions of this work are similar : the number of expansion parameters here is also not one but two : the is the coarse - graining scale , @xmath4 and the state quantum occupancy number @xmath232 , where @xmath182 is the total system volume and @xmath233 the microscopic degeneracy . if we interpret @xmath0 as the inverse mean free path , we can understand the above two scales in terms of the density matrix picture . only when @xmath234 does the effective theory converge to a boltzmann equation . if @xmath235 , as we saw , the quantum analogue of the bggky hierarchy diverges and non - trivial correlations cascade between `` microscopic '' and `` macroscopic '' degrees of freedom . a `` quantum turbulent '' fluid @xcite , or a weakly coupled plasma of the type studied in @xcite , might be examples of such systems . these phenomena are much less studied than the gradient expansion , as we are very far from having analytical tools capable of describing them . they might , however , be more appropriate for systems with a comparatively small number of degrees of freedom ( hadronic collisions , ultracold atoms ) than approaches based on either the boltzmann equation or large @xmath199 expansions .    in conclusion , we have argued that effective field theories are inadequate for describing multi - particle correlations even when the `` fundamental scale '' is well - separated from the probed scale . we have also argued that , when the theory in the uv is strongly coupled , negentropy is likely to be dominated by such multi - particle correlations . these arguments must be kept in mind when large non - equilibrium systems are described with effective field theory tools . we acknowledge the financial support received from the helmholtz international centre for fair within the framework of the loewe program ( landesoffensive zur entwicklung wissenschaftlich - konomischer exzellenz ) launched by the state of hesse . gt also acknowledges support from doe under grant no . de - fg02 - 93er40764 . this manuscript started as an effort to put down my point of view after some interesting and illuminating discussions with bill zajc . any misunderstandings in it are however entirely my own doing . i would also like to thank mohammed mia for helpful discussions . s.  weinberg , arxiv:0903.0568 [ hep - th ] . s.  weinberg , in * boston 1996 , conceptual foundations of quantum field theory * 241 - 251 [ hep - th/9702027 ] . s.  weinberg , pos cd * 09 * , 001 ( 2009 ) [ arxiv:0908.1964 [ hep - th ] ] . j.  preskill , in * houston 1992 , proceedings , black holes , membranes , wormholes and superstrings * 22 - 39 , and caltech pasadena - calt-68 - 1819 ( 92,rec.oct . ) 17 p [ hep - th/9209058 ] . h.  nastase , hep - th/0501068 . p.  castorina , d.  kharzeev and h.  satz , eur . j.  c * 52 * , 187 ( 2007 ) [ arxiv:0704.1426 [ hep - ph ] ] . b.  muller and a.  schafer , int . j.  mod . e * 20 * , 2235 ( 2011 ) [ arxiv:1110.2378 [ hep - ph ] ] . a.  andronic , f.  beutler , p.  braun - munzinger , k.  redlich and j.  stachel , phys . b * 675 * , 312 ( 2009 ) [ arxiv:0804.4132 [ hep - ph ] ] . goldstein , poole and safko , classical mechanics , 3rd edition , addison wesley ( 2000 )      n. n. bogoliubov . `` kinetic equations '' . journal of physics ussr * 10 * 223 - 274 . ( 1946 ) n. n. bogoliubov , k. p. gurov ( 1947 ) journal of experimental and theoretical physics * 17 * 614 - 628 . j. yvon actual . * 203 * ( paris , hermann ) . t.  -j . chen , m.  fasiello , e.  a.  lim and a.  j.  tolley , jcap * 1302 * , 042 ( 2013 ) [ arxiv:1209.0583 [ hep - th ] ] . john g. kirkwood.the journal of chemical physics * 14 ( 3 ) * 180 ( 1946 ) john g. kirkwood the journal of chemical physics * 15 ( 1 ) * : 72 ( 1947 ) m. born and h. s. green , proc . a * 188 * 10 - 18            s.  hegyi , nucl . suppl .   * 92 * , 122 ( 2001 ) [ hep - ph/0011301 ] . a.  bilandzic , r.  snellings and s.  voloshin , phys . c * 83 * , 044913 ( 2011 ) [ arxiv:1010.0233 [ nucl - ex ] ] . m.  m.  aggarwal _ et al . _ [ star collaboration ] , phys . * 105 * , 022302 ( 2010 ) [ arxiv:1004.4959 [ nucl - ex ] ] . k.  dusling , t.  epelbaum , f.  gelis and r.  venugopalan , nucl . a * 850 * , 69 ( 2011 ) [ arxiv:1009.4363 [ hep - ph ] ] . for a few examples of such systems see a.  zee , `` quantum field theory in a nutshell , '' princeton , uk : princeton univ . ( 2010 ) 576 p g.  t hooft , nucl . b * 72 * , 461 ( 1974 ) . + e.  witten , nucl . b * 160 * , 57 ( 1979 ) . s.  w.  hawking and d.  n.  page , commun . phys .   * 87 * , 577 ( 1983 ) . g.  policastro , d.  t.  son and a.  o.  starinets , phys . * 87 * , 081601 ( 2001 ) [ hep - th/0104066 ] . s.  caron - huot , p.  m.  chesler and d.  teaney , phys . d * 84 * , 026012 ( 2011 ) [ arxiv:1102.1073 [ hep - th ] ] . j.  s.  schwinger , phys . rev .   * 82 * , 664 ( 1951 ) . s.  l.  braunstein , s.  pirandola and k.  yczkowski , physical review letters 110 , * 101301 * ( 2013 ) [ arxiv:0907.1190 [ quant - ph ] ] . a.  almheiri , d.  marolf , j.  polchinski and j.  sully , jhep * 1302 * , 062 ( 2013 ) [ arxiv:1207.3123 [ hep - th ] ] . xiao - song ma _ et al _ , nature physics * 8 * , 480 - 485 ( 2012 ) , [ arxiv:1203.4834 [ hep - th ] ] b. reznik , a. retzker , j. silman phys . rev . * a * 71 , 042104 ( 2005 ) [ arxiv : quant - ph/0310058 [ hep - th ] ]    p.  kovtun , g.  d.  moore and p.  romatschke , phys .  rev . d * 84 * , 025006 ( 2011 ) [ arxiv:1104.1586 [ hep - ph ] ] . p.  kovtun , j.  phys . a * 45 * , 473001 ( 2012 ) [ arxiv:1205.5040 [ hep - th ] ] . g.  torrieri , phys . d * 85 * , 065006 ( 2012 ) [ arxiv:1112.4086 [ hep - th ] ] . t.burch , g.  torrieri , `` quantum fluids on the lattice '' , to be submitted","summary":"hence , an effective field theory will be grossly inadequate for describing multi - particle correlations and related observables , even far away from the fundamental scale .","abstract":"we discuss the treatment , in an effective field theory , of multi - particle correlations within a `` large '' system . we show that the act of coarse - graining necessarily introduces violations of unitarity in the evolution of states where the particle number is not defined . for an interacting system , such unitarity violations can cascade from the ultraviolet scale to the infrared in a `` short '' time . hence , an effective field theory will be grossly inadequate for describing multi - particle correlations and related observables , even far away from the fundamental scale . we furthermore argue that if the system is strongly coupled at , than its final state _ in the effective field theory _ ( eft ) will appear as the highest entropy state if only low cumulants and correlations of the eft degrees of freedom are measured . heuristically , this can serve as an explanation of how `` entropy '' is created in a microscopically unitary evolution of a quantum field theory ( qft ) . we conclude by discussing how these considerations might provide a clue to the apparent thermalization in a hadronic collision even in comparatively small systems , as well as the so - called black hole information paradox ; we argue the `` paradoxes '' are likely to be artifacts of using an effective theory beyond its domain of validity ."}
{"article_id":"nlin0011026","section_id":"i","document":"turbulent flows are often forced in an anisotropic fashion . the anisotropy has a significant effect on a variety of measured turbulence characteristics . we are interested in the effect of anisotropy on statistical quantities , especially the low - order structure functions of velocity differences across a scale @xmath1 . in perfectly isotropic systems such objects are expected to display pure scaling behavior in the limit of high reynolds number . we have suggested recently @xcite that in the presence of anisotropy , the structure functions are no longer pure power laws . instead , components of the structure functions that belong to different irreducible representations ( sectors ) of the so(@xmath2 ) group possess different scaling exponents . each of these sectors is characterized by the angular momentum indices @xmath0 and @xmath3 . by projecting the structure function onto the different sectors , we could measure @xcite the universal scaling exponents in each sector separately . the spectrum of anisotropic exponents is particularly accessible in _ linear _ problems like passive scalar @xcite and passively advected magnetic fields @xcite . in both the models , the equations of motion are isotropic and as a result the existence of universal anisotropic exponents can be proven @xcite . additionally the isotropy of the equations implies that the scaling exponents depend on @xmath0 but not on @xmath3 . one of the important results of the analysis is that the discrete spectrum of anisotropic exponents is strictly increasing as a function of @xmath0 . this explains the isotropization of the statistics as smaller and smaller scales are observed . since the scaling exponents @xmath4 appear in power laws of the type @xmath5 , with @xmath6 being some typical outer scale and @xmath7 , the larger is the exponent , the faster is the decay of the contribution as the scale @xmath1 diminishes . therefore the gap between the leading , isotropic exponent , and the next available exponent governs the rate of isotropization . experiments and simulations on navier - stokes ( ns ) turbulence also indicate that anisotropic sectors possess larger scaling exponents than the isotropic sector @xcite . however , to date , the exponents for @xmath8 were not determined with sufficient accuracy . we thus do not know whether the higher sectors are characterized by an ever increasing exponents , or whether the exponents _ saturate_. this issue is theoretically puzzling because of the effects of pressure . the inversion of the pressure in terms of the green s function of the laplacian operator introduces integrals over the domain of turbulence . these integrals manifest the nonlocality of the problem , and are present in both the dynamical equation , and in the equations for the correlation functions . when considering a spatially homogeneous turbulence , the turbulent domain is usually taken to be infinite . the physical boundary conditions at scale @xmath6 , are mimicked by employing a homogeneous forcing that acts at that scale . in this case , the integrals that result from the pressure term are over all @xmath9 , and their convergence has to be guaranteed . the question that we want to address in this paper is the following : does the requirement of the convergence of the integrals necessarily bound the spectrum of the scaling exponents from above ? since the correlation functions appear in the integrand , an unbounded spectrum implies a rapidly increasing integrand as a function of the length scale . on the face of it , at some point the integrals must diverge in the infrared . it would appear therefore that either there must be a limit to the magnitude of the scaling exponents , or that the integrals converge due to an infrared crossover in the correlation functions . the latter scenario looks physically reasonable , yet in the presence of pressure integrals , seems to break scale invariance in the inertial range . to demonstrate that , consider a typical integral term of the form , @xmath10 here @xmath11 is the infinite domain green function of the laplacian operator , and @xmath12 is some statistical object , which is expected to be scale invariant in the inertial range . if @xmath12 has an infrared crossover at scale @xmath6 ( or equivalently , the integral has an infrared cutoff at scale @xmath6 ) , then the above expression will not be a pure power law of @xmath13 , not even inside the inertial range . then how is it possible that such an expression will cancel out a local term of @xmath12 , as is required by the typical equations of motion ? this puzzle has led in the past to the introduction of the concept of `` window of locality '' @xcite . the window of locality is the range for the scaling exponents in which no divergence occurs , even if the crossover length @xmath6 is taken to infinity . for these exponents , integrals of type ( [ eq : ex ] ) are dominated by the range of integration @xmath14 and are therefore termed  local \" . in a  local \" theory no infrared cutoff is called for .    in this paper we show that scaling behavior of the correlation functions together with finite integrals over an infinite domain _ do not _ necessarily imply a bounded spectrum of anisotropic exponents . our strategy in this paper is to come up with a tractable example of a _ linear _ model with pressure , see eq . ( [ eq : v - p ] ) . we refer to this model as the  linear pressure model \" . we approach the solutions of this model in two steps . first we distill yet another , simpler , exactly solvable model , which still poses the riddle of the navier - stokes problem . the exact solution reveals that the spectrum of scaling exponents is unbounded , and the convergence of the integrals is nevertheless not compromised . in the second step we find the scaling exponents of the  zero modes \" @xcite of the linear pressure model , and use the conclusions of the simpler model to relate them to the full solution . we show that also in this case the spectrum does not saturate in the anisotropic sectors . the linear pressure model and its simplified version reveal two mechanisms that allow an unbounded spectrum of scaling exponents . first , a careful analysis of the window of locality in the anisotropic sectors shows that it widens as @xmath0 increases . we always have a leading scaling exponent within the window of locality . second , there is a more subtle mechanism that comes to play when subleading exponents exist outside the window of locality . in these cases we show that there exist counter - terms in the exact solution ( not the zero modes ! ) that maintain the locality of the integrals . the bottom line is that in these models the anisotropic exponents are unbounded from above leading to a fast decay of the anisotropic contributions in the inertial range .    in sec . [ sec : linearp ] we introduce the linear pressure model and derive the equations for the two - point correlation function . we arrive at the form containing the dangerous integrals , and discuss again the fundamental riddle . in sec . [ sec : toy ] we construct a simpler , exactly solvable model with the same riddle . in sec . [ sec : solution ] we display the exact solution of the model , and discuss the windows of locality and the existence of an unbounded spectrum . in sec .  [ sec : zeromodes ] we go back to the linear pressure model and offer a solution of its zero modes . section [ sec : summary ] offers a summary and a discussion .","summary":"one could argue that the requirement of convergence of these integrals bounds the exponents from above . we show that the spectrum of scaling exponents can increase with without bounds , while preserving finite integrals . the conclusion is that contributions from higher and higher anisotropic sectors can disappear faster and faster upon decreasing the scales also in systems with pressure .   ","abstract":"we discuss the scaling exponents characterizing the power - law behavior of the anisotropic components of correlation functions in turbulent systems with pressure . the anisotropic components are conveniently labeled by the angular momentum index of the irreducible representation of the so(3 ) symmetry group . such exponents govern the rate of decay of anisotropy with decreasing scales . it is a fundamental question whether they ever increase as increases , or they are bounded from above . the equations of motion in systems with pressure contain nonlocal integrals over all space . one could argue that the requirement of convergence of these integrals bounds the exponents from above . it is shown here on the basis of a solvable model ( the  linear pressure model \" ) , that this is not necessarily the case . the model introduced here is of a passive vector advection by a rapidly varying velocity field . the advected vector field is divergent free and the equation contains a pressure term that maintains this condition . the zero modes of the second - order correlation function are found in all the sectors of the symmetry group . we show that the spectrum of scaling exponents can increase with without bounds , while preserving finite integrals . the conclusion is that contributions from higher and higher anisotropic sectors can disappear faster and faster upon decreasing the scales also in systems with pressure .    .#1#1    2"}
{"article_id":"nlin0011026","section_id":"i","document":"the main question raised and answered in this paper is whether the existence of the pressure terms necessarily leads to a saturation of the scaling exponents associated with the anisotropic sectors . such terms involve integrals over all space , and seem to rule out the existence of an unbounded spectrum . we have discussed a mechanism that allows an unbounded spectrum without spoiling the convergence of the pressure integrals . the mechanism is demonstrated fully in the context of the simple toy model and we proposed that it also operates in the case of the linear pressure model . the mechanism is based on two fundamental observations . the first one is that the window of locality widens up linearly in @xmath0 due to the angular integration . the second , and more important , is that a scaling solution with an unbounded spectrum can exist _ as a part of a full solution , which decays at infinity_. indeed pure scaling solutions can not solve by themselves the zero - modes equation if their scaling exponent is out of the window of locality . however , the zero - modes are always part of the full solution that decays to zero once @xmath172 and we have shown that if such a solution solves a differential version of the full equation , it must also solve the original equation . therefore by differentiating the full equation sufficiently many times , we can always reach a differential equation with a window of locality as high as we wish . in that equation we can find zero - mode solutions with arbitrarily high exponents ( notice that in the toy model , it was sufficient to differentiate once to get rid of all integrals , thus obtaining an `` infinitely wide '' window of locality ) . but since these zero - modes are part of a full solution that decays at infinity , then this solution is also valid for the original equation , hence showing that in the full solution there can be power laws with arbitrarily high exponents .    finally , we want to comment about the relevance of our calculations to navier - stokes turbulence . if we substitute blindly @xmath331 in our results , we predict the exponents 2/3 , 1.252  26 , 2.019  22 , 4.048  43 , 6.068  60 and 8.083  37 for @xmath332 , and 10 , respectively . it would be tempting to propose that similar numbers may be expected for navier - stokes and indeed for @xmath77 and 2 this is not too far from the truth . we can not , however , state with confidence that the genuine nonlinearity of navier - stokes does not change these numbers significantly . more work is needed before we can draw final conclusions on the rate of decay of the high sectors of anisotropy in navier - stokes turbulence . we thank luca biferale , yoram cohen and massimo vergassola for many helpful discussions and suggestions . we would also like to thank anna pomyalov for her help in the numerical calculations . this work has been supported in part by the israel science foundation , the german - israeli foundation , the european commission under contract no . hprn - ct-2000 - 00162 (  nonideal turbulence \" ) , and the naftali and anna backenroth - bronicki fund for research in chaos and complexity .","summary":"such exponents govern the rate of decay of anisotropy with decreasing scales .","abstract":"we discuss the scaling exponents characterizing the power - law behavior of the anisotropic components of correlation functions in turbulent systems with pressure . the anisotropic components are conveniently labeled by the angular momentum index of the irreducible representation of the so(3 ) symmetry group . such exponents govern the rate of decay of anisotropy with decreasing scales . it is a fundamental question whether they ever increase as increases , or they are bounded from above . the equations of motion in systems with pressure contain nonlocal integrals over all space . one could argue that the requirement of convergence of these integrals bounds the exponents from above . it is shown here on the basis of a solvable model ( the  linear pressure model \" ) , that this is not necessarily the case . the model introduced here is of a passive vector advection by a rapidly varying velocity field . the advected vector field is divergent free and the equation contains a pressure term that maintains this condition . the zero modes of the second - order correlation function are found in all the sectors of the symmetry group . we show that the spectrum of scaling exponents can increase with without bounds , while preserving finite integrals . the conclusion is that contributions from higher and higher anisotropic sectors can disappear faster and faster upon decreasing the scales also in systems with pressure .    .#1#1    2"}
{"article_id":"0802.4288","section_id":"i","document":"in recent years , the evolution of massive galaxies in the universe has received much attention because of the possible tension between observations of the abundance and clustering of such galaxies , as a function of redshift , and predictions from popular hierarchical models of galaxy evolution . naively , in a cold dark matter ( cdm ) dominated universe , one would expect the most massive galaxies to form last through the hierarchical merging of smaller galaxies . this behaviour is illustrated in the recent high resolution simulations of @xcite , which include the latest semi  analytical formalism and account for feedback from active galactic nuclei ( agns ) . in these simulations , the stars in the most massive galaxies are formed at high redshifts , but their stellar mass is only assembled into a single system at relatively late times through  dry mergers \" , i.e. , major mergers of gas  poor galaxies with little or no associated star  formation . for example , in figures 4 and 5 of @xcite , the simulations shows that for low redshift elliptical galaxies , with masses @xmath14 , 80% of their stars are formed at a median redshift of @xmath15 , but 80% of the stellar mass is only put in place by @xmath16 . likewise , the simulations show that galaxies with masses @xmath14 have multiple large progenitors and can not be formed through a single major merger of two large galaxies . these recent agn  feedback models of galaxy evolution ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) solve the apparent inconsistency of the old ages of stars in massive galaxies ( both in and outside galaxy clusters ) and the late assembly of such galaxies in a @xmath17dominated cdm universe . however , they appear to be in conflict with recent observations of the luminosity function and clustering of massive ellipticals as a function of redshift . for example , @xcite showed that the lack of evolution of the luminosity function of luminous red galaxies ( lrgs ; as defined in * ? ? ? * ; * ? ? ? * ) put an upper limit on the amount of allowed evolution in these massive galaxies , i.e. , at least half of the lrgs at low redshift ( @xmath18 ) must already have been well assembled ( with more than half their stellar mass in place ) by @xmath19 . this is in excellent agreement with other luminosity function studies . for example , @xcite used data from the noao deep wide - field survey ( ndwfs ) and the spitzer irac shallow survey to show that  @xmath20 of the stellar mass contained within today s @xmath21 red galaxies was already in place at @xmath22 \" . these observational constraints are barely consistent with the semi - analytical cdm simulations discussed above . the clustering of massive ellipticals provides an additional test of the models . @xcite argue that the small  scale clustering of lrgs from the sloan digital sky survey ( sdss ; * ? ? ? * ) suggest that lrg  lrg mergers ( i.e. a major merger of two equally massive systems ) were not important for the mass growth of lrgs below @xmath23 . more recently , @xcite used the lrg  galaxy cross  correlation function to study the small  scale clustering of lrgs at @xmath24 and concluded that lrgs grow in stellar mass at most by @xmath25 between @xmath26 ( or approximately half the age of the universe ) . @xcite interpretted the evolution in the clustering of luminous red galaxies in the ndwfs using the halo model - they argue that a third of all satellite galaxies ( in a halo ) disappear over the redshift range @xmath27 . since the satellite fraction in their models is of order 20% , only about 7% of the galaxies have merged . however , if these mergers increase the stellar mass of the central object , then this increase can be 25% or even larger . @xcite report rapid evolution in the stellar mass of red galaxies since @xmath28 . this apparent discrepancy is probably due to the differences in the luminosity distributions of the samples , as it is known in clusters that most of the evolution on the so  called  red sequence \" is at magnitudes fainter than @xmath29 ( see * ? ? ? * ; * ? ? ? * and references therein ) .    in this paper , we expand our earlier study of the evolution of the lrg luminosity function ( * ? ? ? * paper i ) to include an investigation of the two  point auto - correlation function of these galaxies . the key difference of this work to that in the literature is the combination of two large samples of lrgs from the sdss and the 2df  sdss lrg and qso ( 2slaq ) survey @xcite . as in paper i , we are careful to ensure the colour selection of lrgs is consistent between these two surveys , thus allowing a study of this unique population of massive ellipticals across the redshift range of @xmath30 . in addition , this paper uses the halo model to understand the evolution of the clustering of galaxies and constrain the merger rates of lrgs . although the logic is similar to the @xcite analysis of ndwfs , our halo model is entirely analytic , rather than entirely simulation - based . our analysis is complementary to that of @xcite who study the redshift space correlation function of the 2slaq sample , binned in pair separation parallel and perpendicular to the line of sight , and fit both biasing and cosmological parameters to this data . @xcite conclude that  lrgs have a constant space density and their clustering evolves purely under gravity \" , which is consistent with the results of paper i. here we wish to test if this conclusion remains true under a more precise comparison of the evolution of the correlation function of lrgs where we accurately account for the changing definition of an lrg with redshift ..    in section [ sec : data ] , we describe the sdss and 2slaq data used in this paper , while in section [ sec : samp ] we provide details of the sample selection used to ensure a consistent definition of an lrg across the two samples . in section [ sec:2ptcalc ] , we present our measurements of the two  point correlation function in both real and redshift  space . section [ sec : halo ] presents a halo model analysis of our measurements and discuss constraining the merger rate in the halo model framework in section [ sec : hodmerge ] . we discuss our findings in the context of recent work in section [ sec : comp ] and conclude in section [ sec : discuss ] . throughout this paper , we assume a flat @xmath17dominated cosmology with @xmath31 , @xmath32 km s@xmath33mpc@xmath13 , and @xmath34 unless otherwise stated .","summary":"we study the spatial two  point auto - correlation function in both redshift - space ( ) and real  space ( ) of a combined sample of over 10,000 lrgs , which represent the most massive galaxies in the universe with stellar masses and space densitiesmpc . we compare our measurements with the predicted evolution of dark matter clustering and use the halo model to interpret our results . [ firstpage ]    surveys  cosmology : observations  cosmology : large - scale structure of universe  galaxies : elliptical and lenticular , cd  galaxies : evolution  galaxies : haloes","abstract":"we present an analysis of the small  to  intermediate scale clustering of samples of luminous red galaxies ( lrgs ) from the sloan digital sky survey ( sdss ) and the 2df - sdss lrg and qso ( 2slaq ) survey carefully matched to have the same rest - frame colours and luminosity . we study the spatial two  point auto - correlation function in both redshift - space ( ) and real  space ( ) of a combined sample of over 10,000 lrgs , which represent the most massive galaxies in the universe with stellar masses and space densitiesmpc . we find no significant evolution in the amplitude ( ) of the correlation function with redshift , but do see a slight decrease in the slope ( ) with increasing redshift over and scales ofmpc . we compare our measurements with the predicted evolution of dark matter clustering and use the halo model to interpret our results . we find that our clustering measurements are inconsistent ( significance ) with a passive model whereby the lrgs do not merge with one another ; a model with a merger rate of 7.5.3% from to ( i.e. an average rate of 2.4% gyr ) provides a better fit to our observations . our clustering and number density measurements are consistent with the hypothesis that the merged lrgs were originally central galaxies in different haloes which , following the merger of these haloes , merged to create a single brightest cluster galaxy ( bcg ) . in addition , we show that the small scale clustering signal constrains the scatter in halo merger histories . when combined with measurements of the luminosity function , our results suggest that this scatter is sub - poisson . while this is a generic prediction of hierarchical models , it has not been tested before .    [ firstpage ]    surveys  cosmology : observations  cosmology : large - scale structure of universe  galaxies : elliptical and lenticular , cd  galaxies : evolution  galaxies : haloes"}
{"article_id":"0802.4288","section_id":"i","document":"we present here a detailed analysis of the clustering of luminous red galaxies ( as defined by @xcite and @xcite ) as a function of redshift using samples of lrgs matched to have the same intrinsic colours and luminosities assuming passive evolution of their stellar populations . these galaxies represent the most massive in the universe with stellar masses lager than @xmath140 and space densities of @xmath141mpc@xmath4 . we find that :    * the amplitude of the clustering ( @xmath5 ) does not significantly evolve with redshift over @xmath142 , whereas there is a marginally significant decrease in the slope ( @xmath6 ) with increasing redshift . + * the lack of evolution in the clustering amplitude on large - scales is inconsistent with a picture in which the lrgs have purely passive evolution undergoing no major mergers over this time period , and rules out this passive model at @xmath143 significance . + * a hod where the fraction of haloes which host central galaxies @xmath144 and only haloes which host centrals can host satellites where the satellites are drawn from a poisson distribution with mean @xmath145 is able to accurately reproduce the clustering and space density of our lrg samples . within this framework the lrgs are predicted to be hosted in haloes with a typical mass close to @xmath146 which increases by @xmath134 50% from @xmath11 to @xmath77 , and to have satellite fractions increasing from @xmath134 5 to 10% over this time . the lrgs are found to have a bias @xmath147 and which decreases with redshift at a much greater rate than would be predicted for the passive no merger case . + * we introduce an analytic approach to describe the evolution of the hod with redshift , and demonstrate that this guarantees that the comoving density remains constant and the large scale bias evolves in accordance with the continuity equation . we use this approach to further demonstrate that the passive evolution of the lrg hod from _ z _ = 0.55 is inconsistent with the measurements at _ z _ = 0.19 at greater than 99.9% significance , predicting far too many satellite galaxies at _ z _ = 0.19 and greatly over estimating the clustering strength on all scales . + * we introduce a model in which high - redshift centrals are allowed to merge with other high - redshift centrals occupying the same halo at low - redshift . this choice is motivated by the fact that centrals are likely to be more massive than satellites , so dynamical friction may be more effective at making these objects merge with the true low - redshift central . this model is able to accurately match the large - scale clustering evolution of the lrgs . we demonstrate that the small scale clustering is dependent on the parametrisation of the scatter in halo merger histories . we investigate three models for this scatter and find that both the sub - poisson and poisson models are able to match the small - scale clustering evolution . however , the poisson model requires a much larger lrg - lrg merger rate ( 20% ) which is not favoured by either the evolution of the lrg luminoisty function @xcite or other independent measures of the lrg - lrg merger rate @xcite . we therefore favour the best motivated sub - poisson scatter giving observational support to this generic prediction of hierarchical models . + * in order to match the clustering evolution we require an lrg - lrg merger rate of 7.5@xmath102.3% from _ z _ = 0.55 to _ z _ = 0.19 corresponding to 2.4% gyr@xmath13 . this is probably consistent with other measurements of the merger rate of massive red galaxies given the uncertainties in how the merger rate depends on the mass of the galaxy and evolves with redshift . + * although some merging is required to match the clustering evolution , the merger rate is sufficiently small that it is entirely compatible with the low rate of evolution in the luminosity function of lrgs found in @xcite . + * we compare in detail the measured hod for one of the lrg samples to that predicted by the latest semi - analytic models of galaxy formation for a very similar sample of lrgs which matches both the luminosity function and clustering as described in @xcite . the model hod is very different to our fit , and would not be reproducible by the functional form of the hod we assume . in particular the model has many haloes that contain lrg satellites where the central is not an lrg . this suggests that a more sophisticated form of the hod may be required for galaxy samples selected by colour in addition to luminosity , although caution is required as the semi - analytic model is still unable to accurately reproduce the evolution of the lrg population . + * our halo model analysis of the relation between the low- and high - redshift populations is similar in spirit to those of @xcite and @xcite . however , whereas their work used numerical simulations , our approach is entirely analytic . this means that our analysis relies heavily on the accuracy of current models of @xmath87 , the conditional mass function . these models are not particularly accurate for small redshift intervals @xcite , so we hope that our analysis will generate interest in improving these models . + * our analysis also highlights the need for a better understanding of the stochasticity in halo merger histories .","summary":"we find no significant evolution in the amplitude ( ) of the correlation function with redshift , but do see a slight decrease in the slope ( ) with increasing redshift over and scales ofmpc . we find that our clustering measurements are inconsistent ( significance ) with a passive model whereby the lrgs do not merge with one another ; a model with a merger rate of 7.5.3% from to ( i.e. an average rate of 2.4% gyr ) provides a better fit to our observations . our clustering and number density measurements are consistent with the hypothesis that the merged lrgs were originally central galaxies in different haloes which , following the merger of these haloes , merged to create a single brightest cluster galaxy ( bcg ) . in addition , we show that the small scale clustering signal constrains the scatter in halo merger histories . when combined with measurements of the luminosity function , our results suggest that this scatter is sub - poisson . while this is a generic prediction of hierarchical models , it has not been tested before .   ","abstract":"we present an analysis of the small  to  intermediate scale clustering of samples of luminous red galaxies ( lrgs ) from the sloan digital sky survey ( sdss ) and the 2df - sdss lrg and qso ( 2slaq ) survey carefully matched to have the same rest - frame colours and luminosity . we study the spatial two  point auto - correlation function in both redshift - space ( ) and real  space ( ) of a combined sample of over 10,000 lrgs , which represent the most massive galaxies in the universe with stellar masses and space densitiesmpc . we find no significant evolution in the amplitude ( ) of the correlation function with redshift , but do see a slight decrease in the slope ( ) with increasing redshift over and scales ofmpc . we compare our measurements with the predicted evolution of dark matter clustering and use the halo model to interpret our results . we find that our clustering measurements are inconsistent ( significance ) with a passive model whereby the lrgs do not merge with one another ; a model with a merger rate of 7.5.3% from to ( i.e. an average rate of 2.4% gyr ) provides a better fit to our observations . our clustering and number density measurements are consistent with the hypothesis that the merged lrgs were originally central galaxies in different haloes which , following the merger of these haloes , merged to create a single brightest cluster galaxy ( bcg ) . in addition , we show that the small scale clustering signal constrains the scatter in halo merger histories . when combined with measurements of the luminosity function , our results suggest that this scatter is sub - poisson . while this is a generic prediction of hierarchical models , it has not been tested before .    [ firstpage ]    surveys  cosmology : observations  cosmology : large - scale structure of universe  galaxies : elliptical and lenticular , cd  galaxies : evolution  galaxies : haloes"}
{"article_id":"astro-ph0309096","section_id":"i","document":"the barred - spiral galaxy ngc3783 ( @xmath3 mag . , @xmath4 ) hosts a well - studied , type - i active galactic nucleus ( agn ) with prominent broad emission lines and strong x - ray absorption features . the object has been observed extensively with almost all x - ray instruments , most recently by  ( kaspi et al . 2002 , hereafter paper i ) and  ( blustin et al 2002 ) . the 210 kev flux of ngc3783 varies in the range @xmath5@xmath6  ^-2s^-1 ergs@xmath2s@xmath7 , and its mean 210 kev luminosity is @xmath8  ^-1 ergs s@xmath7  ( for @xmath9  kms@xmath7mpc@xmath7 and @xmath10 ) . paper i gives an extensive list of references and a comprehensive summary of historical observations , including ground - based and uv ( hst ) observations . it also discusses the unique  data set obtained in 20002001 . these observations consist of a relatively short observation performed in 2000 january , and five longer observations performed in 2001 february  june , separated by various intervals from 2 to 120 days ( see  2 ) . paper  i contains numerous illustrations of the mean spectrum , absorption line profiles and detailed measurements of many absorption and emission lines . two other papers ( gabel et al . 2003a , b ) discuss the _ hst _ and _ fuse _ data obtained as part of this multi - waveband campaign . there have been several previous attempts to model the characteristics of the x - ray absorbing gas along the line of sight to ngc3738 . here we comment only on the more detailed works . a very detailed work kaspi et al ( 2001 ) attempted to fit the spectrum obtained with  in 2000 . the kaspi et al . most successful model consists of two absorbing shells , both outflowing from the central source with a velocity of @xmath11 ^-1 kms@xmath7 . the gas in both shells was assumed to be turbulent with internal turbulent motion of @xmath12 ^-1 kms@xmath7 . the two shells had similar column densities , but different ionization parameters . the model is consistent with the intensity and equivalent width ( ew ) of many ( but not all ) emission and absorption lines observed in the spectrum . a major limitation of the kaspi et al . ( 2001 ) work was the limited signal - to - noise ( s / n ) of the spectrum , which results in large uncertainties on the model parameters . in addition , the limited duration of the only observation then available did not allow a meaningful analysis of any time - dependence . a new paper , by krongold et al . ( 2003 , hereafter k03 ) , discussing the full  data set , was accepted for publication after the submission of our paper . some results of that work are relevant to our study and are discussed in the various sections below . this paper discusses the complete spectroscopic  data of ngc3783 . we present our modeling of this material , with emphasis on the properties of the absorber(s ) along the line of sight . in  2 we describe the two x - ray spectral states discovered using the new observations . in  3 we explain the various ways we measured and modeled the spectrum .  4 contains a discussion of the new findings , and  5 summarizes our new results .","summary":"this analysis , along with the measured equivalent widths of a large number of x - ray lines and photoionization calculations , lead us to the following results and conclusions .","abstract":"we present a detailed spectral analysis of the data obtained from ngc3783 during the period 20002001 using . the data were split in various ways to look for time- and luminosity - dependent spectral variations . this analysis , along with the measured equivalent widths of a large number of x - ray lines and photoionization calculations , lead us to the following results and conclusions . 1 ) ngc3783 fluctuated in luminosity by a factor during individual observations ( most of which were of 170 ks duration ) . these fluctuations were not associated with significant spectral variations . 2 ) on a longer time scale ( 20120 days ) , we found the source to exhibit two very different spectral shapes . the main difference between these can be well - described by the appearance ( in the `` high state '' ) and disappearance ( in the `` low state '' ) of a spectral component that dominates the underlying continuum at the longest wavelengths . contrary to the case in other objects , the spectral variations are not related to the brightening or the fading of the continuum at short wavelengths in any simple way . ngc3783 seems to be the first agn to show this unusual behavior . 3 ) the appearance of the soft continuum component is consistent with being _ the only _ spectral variation , and there is no need to invoke changes in the opacity of the absorbers lying along the line of sight . indeed , we find all the absorption lines which can be reliably measured have the same equivalent widths ( within the observational uncertainties ) during high- and low - states . 4 ) photoionization modeling indicates that a combination of three ionized absorbers , each split into two kinematic components , can explain the strengths of almost all the absorption lines and bound - free edges . these three components span a large range of ionization , and have total column of about 4 . moreover , all three components are thermally stable and seem to have the same gas pressure . thus all three may co - exist in the same volume of space . this is the first detection of such a multi - component , equilibrium gas in an agn . 5 ) the only real discrepancy between our model and the observations concerns the range of wavelengths absorbed by the iron m - shell uta feature . this most likely arises as the result of our underestimation of the poorly - known dielectronic recombination rates appropriate for these ions . we also note a small discrepancy in the calculated column density of and discuss its possible origin . 6 ) the lower limit on the distance of the absorbing gas in ngc3783 is between 0.2 and 3.2 pc , depending on the component of ionized gas considered . the assumption of pressure equilibrium imposes an upper limit of about 25 pc on the distance of the least - ionized component from the central source ."}
{"article_id":"astro-ph0309096","section_id":"c","document":"this section discusses the main results of the new analysis of all the observations of ngc3783 performed to date . the reader is referred also to an appendix where we give a detailed comparison with the recent work of krongold et al . ( 2003 ) . the main new findings of our work are the large increase in flux between the low- and high - states , which is _ not _ accompanied by any significant changes in the properties of the absorption . the central source in ngc3783 fluctuates between two such flux states on a 20120 days time scale , and the best description of the observed variations is the appearance and disappearance of a `` soft excess '' , low energy continuum component . these lead to important conclusions regarding the nature of the continuum source . other important conclusions are the multi - component nature of the absorber and the large range of ionization . below we discuss some interpretations . we found that three ionization components with different properties and a large range of ionization , are required to fit the spectrum of ngc3783 . each of those components is split into two kinematic components , as implied by the observed line profiles reported in paper  1 . the three `` generic absorbers '' of our model are listed in table 4 and shown in figs . 5 & 6 . as explained above , the number of real components and the exact values of @xmath59 and @xmath58 are not very meaningful since several somewhat different combinations of ionization components give equally good fits . rather , the values chosen here are representative , `` average '' ionization parameters , and the total column densities required . our modeling of the low - state spectrum assumes the underlying x - ray continuum is a single power - law . however , the s / n of the long wavelength spectrum is not high enough to completely rule out the presence of an additional softer continuum component , similar to the one seen during the high states but of much lower luminosity . we also note that there is little ( if any ) response of the absorbing gas to the short ( @xmath142 days ) time scale continuum variations . thus our measurements are models represent some time - averaged spectral properties . ccc low ionization & -2.4 & 21.9 + intermidiate ionization & -1.2 & 22.0 + high ionization & -0.6 & 22.3 +    the main difference between the present model and the one given by kaspi et al . ( 2001 ) is the presence of the lowest ionization component . only the first  observation ( obtained in 2000 january ) was available to kaspi et al . , and hence was insufficient to reveal the two spectral states . furthermore , this relatively short observation resulted in the s / n at @xmath143  which was insufficient to reveal the true shape of the continuum . hence kaspi et al . naturally ( but incorrectly ) assumed the underlying continuum was a single power - law for this high - state spectrum . as a result , their preferred model contained a component with a strong bound - free edge , but very little absorption at longer wavelengths ( i.e. at @xmath143  the underlying continuum was `` recovered '' ) . our new observations do not show such a recovery . in fact , the absorption in the long wavelength region is dominated by features of k - shell carbon and nitrogen and l - shell nitrogen and oxygen . the presence of a lower ionization component is also a key point in the k03 work . in their study they assume two absorbers with log@xmath144 ( i.e. a factor of about two lower than our lowest ionization component ) and log@xmath145 ( very similar to our imtermediate ionization component ) . their fit does not require a third , very ionized component . our reason for suggesting this higest - ionization ( log@xmath146 ) component is based on the fit to the lines of , and . when this component is not included , the discrepancy in column densities of these ions is a factor 23 . several of the lines of these ions are in fact missing from the k03 analysis . moreover , some of the highest -ionization lines are badly saturated , ( e.g. @xmath147 ) . thus a comparison of the observed and the calculated ews of those lines , as performed by k03 , is not sufficient for evaluating the ionic column densities .    perhaps the largest observed discrepancy between model and observation is due to absorption by the iron m - shell uta . this feature has been observed in several other agn ( steenbrugge et al . 2003 and references therein ) with similar shape and central wavelength . its smooth shape is due to the large number of absorption lines of many iron ions and the wavelength of largest absorption is ionization dependent . our modeling of this spectral region includes all the lines in the behar et al . ( 2001 ) calculations ( i.e. not only the shorter published list of lines ) . the central observed wavelength of the feature in ngc3783 is at around 16.4  suggesting that most of the contribution is due to . for the assumed sed , this corresponds to gas whose dominant oxygen ions are . in our modeling , most long wavelength absorption is due to the component with log@xmath148 ( fig . the dominant ions in this components are  and . this corresponds to peak uta opacity at around 16.1 . as shown in fig . 7 , the model fits the observed oxygen lines and continua reasonably well but badly misses the position of the uta absorption . we have experimented with various other models to try to eliminate this discrepancy . for example , an overabundance of iron relative to oxygen may decrease the level of ionization of iron due to the increased iron opacity . experimenting with iron abundance which is three times larger resulted with changes that are not large enough to explain the observed discrepancy . we have also experimented with models that include several low ionization components , instead of the single low @xmath59 component shown here . this , again , gave very little improvement . it seems that the apparent conflict between the oxygen and iron ionization can not be resolved by these models and we suggest two alternative explanations .    1 .   the absorbing gas in ngc3783 may not be in ionization equilibrium due to its low density and the rapid flux variations on time scales that are shorter than the recombination and ionization time scales . this is probably not very important for the short wavelength flux since its variability time scale is short and the amplitude not very large . the gas responding to this continuum is probably at some mean level of ionization . this however is not the case for the soft excess continuum which varies on a much longer time scale with a much larger amplitude . this can contribute , significantly , to the ionization of the lower ionization species . different ions react on different time scales and the gas may never reach an equilibrium . since all our models assume steady state gas , they may not be adequate to describe the absorbing gas properties . in particular , the iron and oxygen recombination times may be different enough to result in gas where iron is less ionized or oxygen is more ionized compared to the equilibrium situation . the complicated issue of time dependent ionization is beyond the scope of this paper . 2 .   the ionization balance of iron depends critically on low temperature dielectronic recombination ( dr ) rates that are not well known for the iron m - shell ions . experience with l - shell iron ions , whose dr rates have been measured and computed recently ( savin et al . 2002 and references therein ) , shows that in almost all cases the previous low temperature dr rates were consistently smaller than the newly calculated values . assuming a similar effect in the m - shell ions , we can envisage a situation where , in the absence of realistic dr rate , the entire ionization balance of iron is shifted toward higher ionization . thus , more realistic low temperature dr rates may bring models to better agreement with the observations . we note that low temperature dr rates are also not available for the magnesium and silicon ions that we have modeled . for some of these ions ( and ) these are probably not very important and for others ( the relevant silicon ions ) the situation is less clear ( d. savin , private communication but see also gu 2003 ) . nevertheless , since we do obtain good agreement between the calculated ews of these lines and the ews of other lines observed in the spectrum , we did not consider changing those rates in the calculations . it is interesting to note that the k03 model assumes a lower level of ionization for all elements , including iron , and hence provides a better fit to the uta . however , their lower ionization component fails to fit the and lines around 6.8 . our model was designed to give a very good fit over the 57   wavelength range and hence produces a lower quality fit to the uta feature . thus , there seem to be no satisfactory solution based on a single low - ionization component that explains all these features . an interesting and somewhat problematic issue is the abundance of , which can also be clearly observed in the far uv ( gabel et al . 2003a ; gabel et al . , 2003b ) . paper i found even the k@xmath136 line of undetectable with the current s / n . however , revisiting this measurement more carefully , and with more accurate atomic data , we can now detect several lines . from two such lines , both of which are probably saturated , we have obtained a lower limit of @xmath149 @xmath2 on the column density of . this is much higher than the value ( @xmath150 @xmath2 ) obtained from the  rgs spectrum ( behar et al . moreover , the values predicted from our model ( @xmath151 @xmath2 ) is even larger . such a large value is problematic for several reasons . it may be in contradiction with the uv observations of the source ( see below ) , it is much larger than the values obtained from the rgs observations , and it results in a prediction of a strong absorption line at around 21.87    which is not seen in the spectrum ( fig . 7 , the absorption line underneath the intercombination line ) . an explanation of the discrepancy between the values for the column density measured by  and   is the crowded region of the spectrum where k@xmath136 resides . in particular , the lower spectral resolution of the  rgs makes it extremely difficult to resolve the weak absorption line at 22.01    in the presence of the bright forbidden emission line ( 22.10   ) . we also wish to note that with the lack of laboratory measurements for the wavelengths , high - resolution astrophysical spectra such as the present one constitute the best determination of these wavelengths currently available . the  data , along with the assumption that is outflowing at the same velocity as , places the k@xmath136 line at a rest - wavelength of 22.01  @xmath152  0.01   . this value is in agreement with our model wavelength of 22.005   , calculated with the hullac atomic code , as well as with the value measured in ngc  5548 ( steenbrugge et al . , 2003 ) , but is somewhat different from the value of 22.05    calculated by pradhan ( 2000 ) using the r - matrix method . for more information see behar and kahn ( 2002 ) . a column density less than @xmath153 @xmath2 is also inconsistent with theoretical predictions based on modelling the abundances of , and . this is illustrated in fig . 10 where we show calculations for the fractional abundance of oxygen , silicon and magnesium ions as a function of @xmath59 assuming an incident continuum similar to the one used here . the diagram shows the very similar fractional abundance of , and as a function of ionization parameter . using the measured ew of the @xmath154 line , which is an unblended , easy - to - measure feature , we can use fig . 10 , and the assumed silicon - to - oxygen abundance ratio , to derive an estimate for the column density of . this number is very close to the model prediction . the situation is more complicated regarding magnesium since several of the relevant lines ( around 9.4 ) are blended with neon lines . however , we could obtain an estimate of the ew of the @xmath155 lines that are good enough to constrain the column density . the column density based on this measurement is , again , much larger than @xmath153 @xmath2 and in good agreement with the model prediction . a comparison with the k03 work shows a disagreement by a factor of two in the total ( hydrogen ) column density of the lowest - ionization absorber . one reason for the difference is that k03 analyse the combined ( high- and low - state ) spectrum , which is then interpreted in terms of a different amount of bound - free absorption . another reason is the somewhat larger oxygen abundance assumed by k03 ( the oxygen column densities of the low - ionization components in the two papers actually differ only by a factor 1.35 ) . we also note that the inner - shell lines that we have used to determine the limit on the column density of this ion are missing from the k03 model . this makes a noticeable difference in the spectral fitting at around 21 . finally , we have looked for the lowest column density allowed by the observations if we remove the constraint imposed by the short wavelength continuum slope (  3.2.4 ) and keep the ionization parameter unchanged . this means finding the lowest column density for the log(@xmath59)=-2.4 component which is still consistent with the measured ews of the 57.1    silicon and sulphur lines . we found this limit to be log(@xmath156 for the low - state spectrum , and log(@xmath157 for the high - state spectrum . these lower limits on the column densities are consistent with the uncertainties given in table 1 . under these assumptions , the column density of in the low - state spectrum can be as low as @xmath158 @xmath2 . this column is large enough to produce saturated lines at 21.01 and 21.87   . it also requires a much harder continuum ( @xmath159 ) . some of the parameters our model are based on measured profiles of several absorption lines that were shown in paper i to include at least two components with different ouflow velocities . the measurements in paper i also show that the relative ews of the two components seems to be ionization independent and that most of the lines used for the profile analysis were heavily saturated . this suggests that the apparent optical depths of those lines are determined by the covering factor rather than the line opacity , and hence similar to the case seen in many uv absorption systems in agn ( e.g. barlow , hamann & sargent 1997;arav et al . the covering factor of the lower - velocity components of the , and lines is in the range 0.81.0 . the covering factor of the larger - velocity component of the same lines , assuming saturated profiles , is 0.60.8 . we also note that the large number of iron lines near the uta center gives an independent estimate of the covering factor which is at least 0.85 . 8 shows that models with a covering factor less than unity provide fits to the data of similar quality . using the silicon and sulphur lines ( as in  3.2.3 ) , we find three ionization components are again required , each with parameters similar to those listed in table 4 . the only difference is the need to assume a somewhat harder ionizing continuum . the fit to the long wavelength lines is in fact somewhat better than that produced by the full covering models . however given the low s / n at those wavelengths , this is not a strong conclusion . thus , the data - model comparison can not constrain covering factor beyond the actual observations . the most important conclusion is that the covering factor is similar in low ( e.g. and the iron uta ) and in high ( e.g. , ) ionization lines . our measurements and analysis are consistent with no variations in the absorbers properties on time scales of 14 days . there are also indications for no spectral changes over much longer periods , perhaps a few months . for instance we find no evidence for any significant , narrow ( @xmath160 1   ) spectral features in the high- to low - state spectral ratio shown in fig.9 . the reason we can not constrain the variability of the absorbers on short time - scales are the fast , relatively - small amplitude fluctuations in the luminosity of the central source ( maximum amplitude of about a factor 2 ) . as a result of these variability characteristics of the illuminating continuum , the lack of significant spectral variations may be due to the ionization level of the gas reflecting the _ time averaged _ ionizing luminosity , rather than very long ionization or recombination times . this conclusion therefore depends primarily on the direct comparison between the low and the high state spectra , and thus on the s / n in the lower - quality spectrum used for the comparison ( the high state spectrum ) .    to further examine this point , we have calculated the theoretical spectrum appropriate for the high state continuum under the assumption that the absorbing gas responds instantly to changes in the ionizing continuum . this would be the case if the gas along the line - of - sight gas were of very high density . the initial conditions are those assumed for the low - state continuum , and the change in the sed as described earlier : a two component x - ray continuum , where the long - wavelength component is assumed to extrapolate down to 40  ev . the increase in flux between the low- and high states was assumed to be a factor 1.5 at 4    ( see fig . 3 ) . fig . 11 shows two theoretical spectra : the low - state spectrum ( in blue ) is the same model shown in fig . 7 , the high state spectrum ( in red ) is the result of these new calculations . the two are clearly different . in particular the , and lines are are much weaker for the high - state model . this is due to the large increase in flux at longest wavelengths , with the largest consequences for the lowest ionization component ( @xmath59 has increased by a factor close to 2 and @xmath60 by a factor of 6.6 ) . the variations predicted by this theoretical exercise are much larger than those observed ( table 1 and fig . 4 ) . this illustrates the gas did not simply react to the differences in the illuminating continuum between the low- and high - states . an even stronger conclusion is obtained from the fact that at long wavelengths the differences observed between the two states are much larger than can be explained by simple variations in opacity . given the above findings , we can place limits on the electron density ( @xmath161 ) and the distance from the central source ( @xmath162 ) for each absorption component . we used the temperatures derived from the models , average recombination times for the dominant oxygen and silicon ions , and assuming there is no response to continuum variations on a time scale of 10 days . we find @xmath163 @xmath57 and @xmath164 pc for the log@xmath148 component , @xmath165 @xmath57 and @xmath166 pc for the log@xmath167 component , and @xmath168 @xmath57 and @xmath169 pc for the log@xmath146 component . the corresponding masses are @xmath170 , 390@xmath171 and 64@xmath171 solar masses , respectively , where @xmath171 is the absorption ( @xmath172 ) covering factor . the mass outflow rate is dominated by the lowest ionization component and is approximately @xmath173 solar masses per year , where @xmath174 is the radial filling factor of the flow . the very large number suggests a short duration outburst rather than continuous ejection . we also note that the covering factor can be small , of order 0.1 . the above distances are in agreement with the findings of behar et al . ( 2003 ) , who have suggested the outflow is located at a distance of a few pc and is extended beyond 10  pc based on a comparison between the soft x - ray emission and absorption characteristics of the  data . a significant new aspect of our model is that the product @xmath175 is similar ( within a factor @xmath162 ) for all three absorption components . this raises the interesting possibility that all the components are in pressure equilibrium ( assuming gas pressure dominates the total pressure , i.e. radiation pressure and turbulent pressure are not important ) , and they all occupy the same volume of space . to test this idea , we have calculated thermal stability curves ( log@xmath176 vs. log@xmath177 ) for the low - state continuum and our assumed composition ( table 2 ) under various assumptions . we have kept the uv sed unchanged and varied @xmath135(0.150 kev ) over a wide range . we have also investigated the possibility of a line - of - sight attenuation by the absorbing gas . this can be relevant for the situation under study since , even in the simplest geometry , two of the absorbers do not have a clear view of the central radiation source . screening by the lowest - ionization component ( log@xmath178 is the most important since this gas modifies the transmitted spectrum much more than the other components ( see fig . three such stability curves are shown in fig . 12 , along with the location of the three ionization components . the exact location depends on the details of the assumed sed , the gas metallicity and opacity . the interesting feature of the stability diagram is that all radiation fields considered here result in extended , almost vertical parts between @xmath179k and @xmath180k . the curve for @xmath140 has a more extended vertical part since the higher mean energy of the radiation field results in a compton temperature . screening by the lowest - ionization component in ngc3783 is indeed important , but does not change the main result that , given the uncertainties on the sed and composition , all three ionization components lie on the stable part of the curve . we also note that , while here we only considered gas with a single composition , the details of the stability curve are abundance dependent . needless to say , very different curves will be obtained for significantly different seds . we note that k03 reach similar conclusions regarding the pressure equilibrium of their two ionization components . however , in our model all components are situated on stable branches of the thermal stability curve ( fig . 12 ) while according to k03 , their high - ionization component is situated on the unstable branch ( their fig . we suspect that the difference is in part due to the different sed and metalicity assumed by k03 , and in part due to the method they used to calculate the curve . the existence of an additional stable - region along the curve of thermal - equilibrium ( intermediate between the cold and the hot branches ) where `` warm '' ( @xmath181k ) can survive is not a new idea . it has been discussed by marshall et al . ( 1993 ) in their study of the multi - phase medium in ngc1068 , and later by many others . reynolds & fabian ( 1995 ) discussed the stability criteria and noted the narrow range of ionization parameter allowed for warm absorbers . hess et al ( 1997 ) discussed the various parameters governing the stability curve ( metallicity and more ) . komossa and collaborators ( e.g. komossa & fink , 1997 ; komossa & meerschweichen 2001 ) calculated many such curves , for different seds and metallicities , and discussed the location of warm absorbers as well as the possible link between the nlr and the x - ray gas . krolik & kriss ( 2001 ) considered multi - phase , warm - absorber winds and noted the various locations of stable , over - heated and over - cooled gas . kinkhabwala et al . ( 2002 ) re - visited the thermal stability issue in ngc1068 and showed that a wide range of @xmath59 is needed to account for the observed x - ray emission lines . chelouche & netzer ( 2003 ) investigated the changes in the stability criteria for clouds with large internal line radiation pressure . most of these earlier works focused either on the allowed parts of the curve from general stability conditions , or on the location of a certain absorber observed in a certain source . our work shows that three very different aborbers in a source can all occupy extended , stable parts of the curve where the gas pressure is roughly the same . this means there may well be more than three absorbers spread over the vertical branch of the curves in fig . the three ionization parameters considered here may therefore represent some volume - averaged properties of the entire cloud ensemble . the column densities are therefore the total column densities of a large number of such clouds . moreover , the most - ionized component may provide the confining medium for the two other ionization components . needless to say , real confined outflowing clouds are characterised by a more complicated density and pressure structure than with the simplified , constant density clouds considered here ( e.g. see chelouche & netzer 2001 ) .    the pressure equilibrium between all three absorbers in ngc3783 suggest they occupy the same general location . this allows additional constraints to be placed on their density and location . specifically , we require that the distance of this region is at least 3.2 pc ( the minimum distance of the lowest ionization component ) . however , this zone can not be much further away because of total size and volume considerations . under the assumed conditions , the highest - ionization parameter component has the lowest density , and hence the largest dimension . however , its radial extent can not exceed about 500 pc ( the approximate radius of the narrow - line region ) , and thus its mean density can not fall below about 10 @xmath57 . pressure equilibrium then dictates the density of the lowest - ionization component , and a maximum distance of about 25 pc . this limitation is only imposed on discrete clouds  i.e. on the mean properties of the gas . real absorbers may not be `` clouds '' , they can cover a large range of distances , and can have properties which depend on location . the detailed investigation of such models is beyond the scope of the present paper . there is no indication for flux variation in any of the observed emission lines . however the measurement uncertainty on these line is rather large since the strongest lines are observed at the long wavelengths where the s / n is poor . we obtain satisfactory fits for most lines by assuming that the emission  line gas has the same column density and ionization parameter as the absorbing gas . the covering factors required for the emitting gas are 0.20.3 for the log@xmath148 component , 0.10.2 for the log@xmath167 component , and @xmath134 for the log@xmath146 component . the large range is due to the uncertainties in the continuum placement and in estimating the fraction of the and emission lines that are being absorbed by the line - of - sight gas ( the model shown in figs . 7 and 8 assumes that _ all _ the emitted photons are seen through the absorbers ) . a clear shortcoming of the model is the fitting of the intercombination line . the intensity predicted for this line is too small by a large factor ( 2 - 4 ) . a large part of the discrepancy is due to the  @xmath182    absorption line situated close to this emission ( fig . this may be related to the problem discussed earlier . alternatively it may be a consequence of our assumption that all emission - line photons are seen through the absorbers . indeed , a model that assumes no absorption of the emitted photons by the line - of - sight gas ( not shown here ) would give a much better agreement to the absorption complex . this would also required a smaller emission covering factor . obviously we can not determine the exact geometry using current observations , and the real case may well be intermediate between those two extremes . we also note on the difference between the absorption covering factor ( 0.81.0 ) and the emission covering factor ( 0.10.3 ) . given the uncertain geometry and the fact that the first is a line - of - sight covering factor and the secong a globel ( @xmath172 ) property , the two are perhaps consistent with each other . we did not investigate all possibilities and can not comment in detail on special cases like biconical flows or a torus geometry ( e.g. krolik & kriss 2001 ) .    finally , comparing our method with that of k03 we note that those authors do not calculate the emission line flux and profile in a self - consistent way . instaed , they add gaussian shaped emission profiles to their calculated absorption profiles ( e.g. their fig . this can result in significant differences regarding the line flux and ew . for example , our default approach assumes that all emission lines are seen through the absorber . in such a case , the entire `` blue '' wing of many emission lines is absorbed . clearly this affects the ew of the emission lines , but has almost no effect on the ew of the absorption features . in contrast , the approach adopted in k03 always results in a decrease of the ew of the absorption lines . ngc3783 contains time - variable absorbers in the uv that have been described in various earlier publications ( gabel et al . 2003a and references therein ) . our analysis clearly indicates that at least one x - ray component contains gas which is of sufficiently low ionization so as to produce strong absorption lines of , and in the uv . the predicted ews of these uv lines depend on two factors that have been given little attention in this work : the exact shape of the uv continuum , and covering factor appropriate for the uv absorbers . a uv continuum which is softer than that assumed here can result in higher levels of ionization for carbon , nitrogen and oxygen , with little effect on most x - ray lines . this is very important for the @xmath183  and @xmath184    lines , but less so for the uv lines of that are directly linked to the column density discussed here .    as for the covering factors , the size of the uv continuum source is likely to be much larger than the size of the central x - ray source . thus the covering factor appropriate in the uv can be different to that appropriate in the x - ray . this will result in saturated uv absorption lines whose ews are smaller than the ones indicated by the column densities derived here . however , our upper limit on the density of the low - ionization component , combined with its column density , suggest a very large line - of - sight dimension ( @xmath185 cm ) . assuming lateral dimension of the same size or large , we conclude that the physical dimension of this component is much larger than the expected dimension of any likely uv source ( e.g. the surface of a thin accretion disk ) . a combined analysis of the uv and x - ray results , taking these such points into consideration , is in progress    uv absorbers are also uv emitters , and the low - ionization component can also contribute to the observed uv emission lines . our photoionization calculations show that this contribution is very small . for example , an emission covering factor of 0.1 , similar to the one deduced from the x - ray emission lines , will produce @xmath186 line with emission ew of about 1 . perhaps the most interesting result of this study is the appearance and disappearance of the soft excess component . this broad - band continuum source was seen in two of the six observations . on average , these are the two observations with the highest luminosity . an increase in softness ratio with increasing source luminosity is well known and well documented in a number of agn ( e.g. magdziarz et al . , 1998 ; chiang et al . , 2000 ; markowitz & edelson 2001 ) . however we are not aware of a softness ratio increase that is _ not correlated _ with a short wavelength flux increase . ngc3783 seems to be the first agn to show this phenomenon , but we suspect that careful spectroscopic monitoring will reveal the same or a similar behavior in other sources . this has important consequences to the continuum production mechanism , as well as for the modeling of the warm x - ray gas around the center . we do not know the origin of the soft continuum source . in particular , we do not have information on its flux at wavelengths @xmath187   ( the source was not in a high - state in any of the published  observations ) . it may be related to a broad - band phenomenon ( e.g. due a flaring accretion disk ) , or a component covering a narrower band ( e.g. a single temperature black body ) . simple global energy consideration show that this phenomenon is unrelated to the appearance of broad emission features like those claimed to be seen in at least two sources and interpreted as due to relativistic disk lines ( branduardi et al 2001 ; mason et al . 2002 ; but see also lee et al . 2002 ) . finally , we must comment on the possibility of a more complex behavior . our analysis is based on the fitting of a single powerlaw continuum at low - state and the addition of a soft x - ray component during the high - state . however , an equivalent analysis could be carried out in the reverse order  i.e. starting from a pure powerlaw for the high - state and _ subtracting _ a continuum component to explain the low - state spectrum . however , as argued earlier , the observed spectral changes at long wavelengths are too large to be explained by pure opacity variations and it is not at all clear what other mechanism could explain an agn continuum with flux deficit at long wavelengths .","summary":"ngc3783 seems to be the first agn to show this unusual behavior . thus all three may co - exist in the same volume of space . this most likely arises as the result of our underestimation of the poorly - known dielectronic recombination rates appropriate for these ions . 6 ) the lower limit on the distance of the absorbing gas in ngc3783 is between 0.2 and 3.2 pc , depending on the component of ionized gas considered . the assumption of pressure equilibrium imposes an upper limit of about 25 pc on the distance of the least - ionized component from the central source .","abstract":"we present a detailed spectral analysis of the data obtained from ngc3783 during the period 20002001 using . the data were split in various ways to look for time- and luminosity - dependent spectral variations . this analysis , along with the measured equivalent widths of a large number of x - ray lines and photoionization calculations , lead us to the following results and conclusions . 1 ) ngc3783 fluctuated in luminosity by a factor during individual observations ( most of which were of 170 ks duration ) . these fluctuations were not associated with significant spectral variations . 2 ) on a longer time scale ( 20120 days ) , we found the source to exhibit two very different spectral shapes . the main difference between these can be well - described by the appearance ( in the `` high state '' ) and disappearance ( in the `` low state '' ) of a spectral component that dominates the underlying continuum at the longest wavelengths . contrary to the case in other objects , the spectral variations are not related to the brightening or the fading of the continuum at short wavelengths in any simple way . ngc3783 seems to be the first agn to show this unusual behavior . 3 ) the appearance of the soft continuum component is consistent with being _ the only _ spectral variation , and there is no need to invoke changes in the opacity of the absorbers lying along the line of sight . indeed , we find all the absorption lines which can be reliably measured have the same equivalent widths ( within the observational uncertainties ) during high- and low - states . 4 ) photoionization modeling indicates that a combination of three ionized absorbers , each split into two kinematic components , can explain the strengths of almost all the absorption lines and bound - free edges . these three components span a large range of ionization , and have total column of about 4 . moreover , all three components are thermally stable and seem to have the same gas pressure . thus all three may co - exist in the same volume of space . this is the first detection of such a multi - component , equilibrium gas in an agn . 5 ) the only real discrepancy between our model and the observations concerns the range of wavelengths absorbed by the iron m - shell uta feature . this most likely arises as the result of our underestimation of the poorly - known dielectronic recombination rates appropriate for these ions . we also note a small discrepancy in the calculated column density of and discuss its possible origin . 6 ) the lower limit on the distance of the absorbing gas in ngc3783 is between 0.2 and 3.2 pc , depending on the component of ionized gas considered . the assumption of pressure equilibrium imposes an upper limit of about 25 pc on the distance of the least - ionized component from the central source ."}
{"article_id":"astro-ph0309096","section_id":"c","document":"our detailed measurements and analysis of the 900 ks data set of ngc3783 lead to the following results :    1 . the source fluctuates in luminosity , by a factor @xmath0 , during individual 170 ks observations . the fluctuations are not associated with significant spectral variations . 2 .   on time scales of 20120 days , the source exhibits two very different spectral shapes denoted here as the high- and low - states . the two are associated with different softness ratios that seem unrelated to the total x - ray luminosity . the observed changes in the underlying continuum can be described as due to the appearance ( in the high - state ) and disappearance ( in the low - state ) of a soft excess component . the origin of this continuum component is not clear . to the best of our knowledge , ngc3783 is the first agn to show such a behavior . the appearance of the soft continuum component can explain all spectral variations observed within the measurement uncertainties . there is no need to invoke opacity changes between the high- and low - states . this conclusion depends mostly on the s / n in the high state spectrum . 4 .   a combination of three ionization components , each split into two kinematic components , provides a good description of the intensity of almost all the absorption lines and bound - free edges observed . the components span a large range of ionization , and have a total column of about 4@xmath1 @xmath2 . the only real discrepancy between the observed and theoretical spectra are for the iron m - shell uta feature at 1616.5 . this is most likely due to inadequate dielectronic recombination rates currently available to use in our calculations . the largest other uncertainty is in the column density of . the three generic absorbers discussed in this work have very similar values of @xmath175 . we speculate that the absorbers may be in pressure equilibrium with each other , occupying the same volume in the nucleus . this is the first confirmation of the location of several x - ray absorbers on the vertical part of the log@xmath176 vs. log@xmath177 ) stability curve of agn . we have obtained thee lower limits on the gas distance from the center , corresponding to our three generic absorbers . the limits are 3.2 pc , 0.6 pc and about 0.2 for the low ionization , intermediate ionization and high ionization absorbers , respectively . the pressure equilibrium assumption implies distances in the range 325  pc . this work is supported by the israel science foundation grant 545/00 , h.n . thanks s. kahn and the astrophysics group at columbia university for hospitality and support during a summer visit in 2002 . e.b . was supported by the yigal - alon fellowship and by the gif foundation under grant # 2028 - 1093.7/2001 . we gratefully acknowledge the financial support of cxc grant go1 - 2103 ( s. k. , w. n. b. , i. m. g. ) , nasa ltsa grant nag  5 - 13035 ( w. n. b. ) and the alfred p. sloan foundation ( w. n. b. ) ,","summary":"1 ) ngc3783 fluctuated in luminosity by a factor during individual observations ( most of which were of 170 ks duration ) . these fluctuations were not associated with significant spectral variations . 2 ) on a longer time scale ( 20120 days ) , we found the source to exhibit two very different spectral shapes . the main difference between these can be well - described by the appearance ( in the `` high state '' ) and disappearance ( in the `` low state '' ) of a spectral component that dominates the underlying continuum at the longest wavelengths . 3 ) the appearance of the soft continuum component is consistent with being _ the only _ spectral variation , and there is no need to invoke changes in the opacity of the absorbers lying along the line of sight . 4 ) photoionization modeling indicates that a combination of three ionized absorbers , each split into two kinematic components , can explain the strengths of almost all the absorption lines and bound - free edges . these three components span a large range of ionization , and have total column of about 4 . 5 ) the only real discrepancy between our model and the observations concerns the range of wavelengths absorbed by the iron m - shell uta feature .","abstract":"we present a detailed spectral analysis of the data obtained from ngc3783 during the period 20002001 using . the data were split in various ways to look for time- and luminosity - dependent spectral variations . this analysis , along with the measured equivalent widths of a large number of x - ray lines and photoionization calculations , lead us to the following results and conclusions . 1 ) ngc3783 fluctuated in luminosity by a factor during individual observations ( most of which were of 170 ks duration ) . these fluctuations were not associated with significant spectral variations . 2 ) on a longer time scale ( 20120 days ) , we found the source to exhibit two very different spectral shapes . the main difference between these can be well - described by the appearance ( in the `` high state '' ) and disappearance ( in the `` low state '' ) of a spectral component that dominates the underlying continuum at the longest wavelengths . contrary to the case in other objects , the spectral variations are not related to the brightening or the fading of the continuum at short wavelengths in any simple way . ngc3783 seems to be the first agn to show this unusual behavior . 3 ) the appearance of the soft continuum component is consistent with being _ the only _ spectral variation , and there is no need to invoke changes in the opacity of the absorbers lying along the line of sight . indeed , we find all the absorption lines which can be reliably measured have the same equivalent widths ( within the observational uncertainties ) during high- and low - states . 4 ) photoionization modeling indicates that a combination of three ionized absorbers , each split into two kinematic components , can explain the strengths of almost all the absorption lines and bound - free edges . these three components span a large range of ionization , and have total column of about 4 . moreover , all three components are thermally stable and seem to have the same gas pressure . thus all three may co - exist in the same volume of space . this is the first detection of such a multi - component , equilibrium gas in an agn . 5 ) the only real discrepancy between our model and the observations concerns the range of wavelengths absorbed by the iron m - shell uta feature . this most likely arises as the result of our underestimation of the poorly - known dielectronic recombination rates appropriate for these ions . we also note a small discrepancy in the calculated column density of and discuss its possible origin . 6 ) the lower limit on the distance of the absorbing gas in ngc3783 is between 0.2 and 3.2 pc , depending on the component of ionized gas considered . the assumption of pressure equilibrium imposes an upper limit of about 25 pc on the distance of the least - ionized component from the central source ."}
{"article_id":"0904.4623","section_id":"i","document":"in this work we are interested in the study of the regularized benjamin - ono equation ( rbo equation henceforth ) @xmath3 where @xmath4 is a real - valued function and @xmath5 denotes the hilbert transform defined via the fourier transform as @xmath6 where @xmath7 the regularized benjamin - ono equation is a model for the time evolution of long - crested waves at the interface between two immiscible fluids . some situations in which the equation is useful are the pycnocline in the deep ocean , and the two - layer system created by the inflow of fresh water from a river into the sea , see @xcite . this equation is formally equivalent to the benjamin - ono equation @xmath8 which was first introduced by benjamin @xcite and later by ono @xcite as a model equation for the same situation as the rbo . being more specific , for suitably restricted initial conditions , the solutions @xmath4 of ( [ ecuabasica ] ) and @xmath9 of ( [ boequation ] ) are nearly identical at least for values of @xmath10 in @xmath11 $ ] where @xmath12 is quite large , see @xcite for more details . see also @xcite for a more detail discussion about the advantages and disadvantages of using equation ( [ boequation ] ) or ( [ ecuabasica ] ) for modelling the propagation of small - amplitude long waves . + as far as we know in the periodic setting there does not exist any result about the well - posedness problem for the equation ( [ ecuabasica ] ) . we prove that the periodic initial value problem @xmath13 with initial data in periodic sobolev spaces @xmath14)$ ] is locally wellposed if @xmath15 and globally wellposed if @xmath16 these results on existence , uniqueness and continuous dependence on the initial data of solutions to ( [ probperiod ] ) have no special difficulty , and we were able to established them almost in the same way as in bona and kalisch @xcite , where they were obtained on the real line . local well - posedness can be proved using a contraction argument in the space @xmath17;h^s_{per})$ ] and global solution is obtained via _ a priori _ estimates . + the rbo equation possesses three conservation laws : @xmath18 and @xmath19 this suggests that the space @xmath20 ( or @xmath21 ) is a good candidate for a global well - posedness theory of the cauchy problem associated to ( [ ecuabasica ] ) . this problem is open in @xmath22 ( or @xmath23 ) with @xmath24 and one of the goals of this paper is to present some obstructions to its solution by iteration methods . more precisely , we prove that the flow map data - solution can not be @xmath25 for @xmath26 in both , periodic and non - periodic case . this kind of ill - posedness was studied by bourgain in @xcite and tzvetkov in @xcite for the kdv equation ; molinet , saut and tzvetkov in @xcite and @xcite did the same for the benjamin - ono equation and the kadomsev - petviashvili i ( kpi ) equation , respectively . as far as we know , there does not exist any result about ill - posedness for the rbo on the periodic and non - periodic cases . + the last part of the paper is dedicated to another important qualitative aspect of nonlinear dispersive equations , the travelling wave solutions , which depending on the specific boundary conditions on the wave s shape can be either solitary or periodic waves . the existence , nonlinear stability and instability of solitary wave solutions have been discussed in the past two decades from several points of view . many techniques have been created to find solutions and sufficient conditions have been obtained to insure the stability or instability of this kind of waves , see for example @xcite , @xcite,@xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite . in contrast to the study of solitary waves , the periodic travelling wave solutions has received less attention . in recent years some papers in this subject have appeared , see for instance @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite . + in this paper we are interested in giving a stability theory of periodic travelling wave solutions for the nonlinear dispersive equation ( [ ecuabasica ] ) . the periodic travelling wave solutions to be considered here will be of the general form @xmath27 where @xmath28 is a smooth @xmath29periodic function and @xmath30 so , by replacing these permanent wave form into ( [ ecuabasica ] ) , integrating and considering the constant of integration equal to zero , we obtain @xmath31 in the framework of travelling waves of solitary type , it is known the existence of solutions for ( [ ecuaordina ] ) in the form @xmath32 where @xmath33 the stability theory for this solitary wave was established by albert , bona and henry in @xcite . additionally , kalisch in @xcite exhibited a periodic family of travelling wave solutions ( depending of the speed ) with period @xmath34 for the rbo and used it to test the rate of convergence of a numerical scheme , which was introduced in @xcite to prove that the equation ( [ ecuabasica ] ) does not constitute an _ infinite - dimensional completely integrable system . _ + for @xmath35 and @xmath36 we prove the existence of a smooth curve of even periodic travelling wave solutions for ( [ ecuabasica ] ) . the construction of this solutions is based on the poisson summation theorem ( as in angulo and natali @xcite ) . the family of solutions is given by @xmath37 with @xmath38 satisfying @xmath39 concerning the nonlinear stability of this family of periodic solutions we extend the classical approach developed by benjamin @xcite , bona @xcite and weinstein @xcite to the periodic case . more precisely , we use the conservations laws ( [ prisegley ] ) to prove that the orbit @xmath40 generated by the wave @xmath41 is orbitally stable in @xmath42)$ ] with regard to the periodic flow of the rbo equation . + in order to get the spectral conditions required to prove the nonlinear stability , we use the recent theory developed by angulo and natali @xcite . although their theory was established for another kind of equations we still can apply it to obtain an specific spectral structure associated to the non - local operator @xmath43    in the last section of the paper the theory established for the rbo equation is extended for a general family of regularized equations . we study a class of equations of the form @xmath44 where @xmath45 is an integer and @xmath46 is a differential or pseudo - differential operator in the context of periodic functions . note that a considerable range of equations arise in practice . for instance , if you consider @xmath47 you get the generalized benjamin - bona - mahony equation and if @xmath48 we obtain the generalized regularized benjamin - ono equation , so the stability issues for the generalized class ( [ formagen ] ) are not just of mathematical interest . + we give sufficient conditions to get the nonlinear stability of periodic wave solutions associated to equations of the type ( [ formagen ] ) , and as example we prove that the cnoidal wave solutions of the bbm equation , with fundamental period @xmath49 are orbitally stable in @xmath50),$ ] for speeds @xmath51 + this kind of generalization in the context of solitary waves have been studied before , see for example @xcite and @xcite . in the periodic setting hrgu in @xcite proved the spectral stability of periodic travelling wave solutions , for the generalized bbm , which are small perturbations of the constant solution @xmath52 in both @xmath53 and @xmath54 if @xmath55 she proved spectral stability for @xmath56 and for @xmath57 there exists a critical speed @xmath58 such that the periodic waves are spectrally stable for @xmath59 , and unstable for @xmath60 if @xmath61 also it is worth to note that hakkaev , iliev and kirchev in @xcite studied the orbital stability of a type of generalized bbm and camassa holm equations . the family of bbm equations that they investigated were of the form @xmath62 they proved the existence solutions of the cnoidal type , but they only proved the orbital stability of this solutions in the case @xmath63 + finally , this paper is organized as follows : in section 2 we introduced some notations to be used throughout the whole article ; in section 3 , we prove the global well - posedness result in the periodic setting ; in section 4 , the ill - posedness result is obtained ; in section 5 , we show the existence of periodic travelling waves using the poisson summation theorem , in section 6 , the spectral properties needed to obtain the nonlinear stability are gotten , in section 7 , we get the stability of the waves based on the ideas in @xcite,@xcite , @xcite and @xcite , in section 8 , we present the extension of the theory , then we used it to proved the stability of cnoidal waves associated to the bbm equation .","summary":"it is also shown that these solutions are nonlinearly stable in the energy space by perturbations of the same wavelength .","abstract":"this paper has various goals : first , we develop a local and global well - posedness theory for the regularized benjamin - ono equation in the periodic setting , second , we show that the cauchy problem for this equation ( in both periodic and non - periodic case ) can not be solved by an iteration scheme based on the duhamel formula for negative sobolev indices , third , a proof of the existence of a smooth curve of periodic travelling wave solutions , for the regularized benjamin - ono equation , with fixed minimal period , is given . it is also shown that these solutions are nonlinearly stable in the energy space by perturbations of the same wavelength . finally , an extension of the theory developed for the regularized benjamin - ono equation is given and as an example it is proved that the cnoidal wave solutions associated to the benjamin - bona - mahony equation are nonlinearly stable in ."}
{"article_id":"cond-mat9807093","section_id":"i","document":"spin - peierls systems have been the subject of a renewed interest because of the discovery of several inorganic quasi - one dimensional ( q1d ) spin - peierls compounds . a very well studied example is cugeo@xmath0 . this q1d compound made of weakly coupled cuo@xmath1 chains has a spin - peierls transition at @xmath2 @xcite , as revealed by diffraction measurements , showing a dimerization below @xmath3 , and by susceptibility data , which indicate the opening of a spin gap at @xmath3 . cugeo@xmath0 can be doped in a controlled fashion , giving the unique opportunity to study the role of impurities in a spin - peierls system . doping is done in two different ways . one possibility is to directly affect the spin degrees of freedom within each cuo@xmath1 chain by substituting some of the cu atoms ( whose spin is @xmath4 ) with magnetic ( ni @xcite , which has @xmath5 , or co @xcite , @xmath6 ) or non - magnetic ( zn @xcite , mg @xcite ) impurities . another way is by substituting ge with si @xcite , which is expected to modify the strength of the exchange couplings among the magnetic ions . for all these compounds , even a small amount of doping strongly enhances the magnetic fluctuations , leading in most cases to a lower temperature nel phase coexisting with the peierls s distorted phase . for instance , in 0.3% si - doped compounds , free spins are released which contribute with a curie - like behavior below @xmath7 ( which is slightly reduced with respect to the undoped sample ) , and finally get frozen below the nel temperature @xmath8 @xcite . the same behavior has been reported in a @xmath9 zn - doped compound , where magnetization measurements can be interpreted as if approximately one spin-1/2 per zn atom is released @xcite . in all cases but co - doped samples @xcite , the low doping @xmath10 phase diagram seems to have universal features @xcite : @xmath3 decreases almost linearly with @xmath11 , while no critical concentration for the appearance of the nel phase has till now been revealed down to the lowest accessible impurity concentrations ( e.g. 0.12% zn for which @xmath12 @xcite ) .    at larger doping , the situation is still not fully established . however , most of the data indicate that over some critical @xmath13 , the spin - peierls long - range order disappears , although short - range correlations seem to persist . for mg - doped samples , it is claimed that at @xmath14 a first order phase transition takes place which is signaled by a jump of @xmath15 @xcite . manabe _ et al . _ @xcite have reported an antiferromagnetic ( af ) ordering with zn concentrations as low as 0.11% . their analysis of the variation of the nel temperature versus doping concentration has shown the absence of a critical doping concentration for af ordering at zero temperature ( @xmath16 ) . the goal of the present article is to understand this onset of long range af order at such low doping . this experimental observation questions the validity of existing theories in a much more drastic way than the coexistence of af order and dimerization . several distinct theories describe this coexistence of dimerization and antiferromagnetism . @xcite first proposed a model showing that the two orders can coexist , and another model was proposed by mostovoy _ two of the present authors have proposed another model for the coexistence of af ordering and dimerization @xcite . all these theories successfully describe the coexistence of dimerization and af order upon doping , and they also show that the effect of doping amounts to generate states inside the spin - peierls gap , in agreement with susceptibility experiments ( for example @xcite ) . a similar behavior is reported in spin - ladder systems , which , in spite of having a large spin gap , undergo a nel transition upon very small doping . for instance srcu@xmath1o@xmath0 , with a spin gap of @xmath17 , has a finite @xmath18 already at @xmath19 zn doping @xcite . in these ladder compounds the low energy spin excitations induced by doping have also been revealed by a finite specific heat coefficient @xcite .    in their article , manabe _ et al . _ pointed out that one energy scale emerging from our model ( denoted by @xmath20 , see sections [ sec : sus ] and [ sec : mean - field ] for its definition ) was many orders of magnitude lower than the nel temperature ( for instance at @xmath21 , @xmath22k whereas @xmath23mk has been measured @xcite ) . on the basis of the analysis of af fluctuations in the 1d model , we already suggested @xcite that this apparent inconsistence can be avoided if one makes a proper treatment of disorder averaging . in the present article , we push further this analysis by estimating the nel temperature in the presence of interchain coupling , which turns the quasi - long - range af fluctuations of the 1d model into a longer range order . we prove by two different methods ( a mean field treatment of the interchain coupling , and a decimation procedure of the 2d disordered problem ) that the resulting nel temperature has the right order of magnitude . moreover , under both treatments , we show that there is no critical concentration for the establishment of af order . as it was shown by mostovoy _ _ , this is not the case in their model , and we believe that this is not the case either in the approach by fukuyama _ _ , further extended by yoshioka and suzumura @xcite . the paper is organized as follows . we introduce the model in section [ sec : themodel ] , and discuss the experiments by manabe _ the problem of interchain coupling is first solved in section [ sec : mean - field ] at the mean field level . section [ sec : renor ] is devoted to the decimation approach that goes beyond the mean field treatment of interchain interactions , and is more relevant for the extremely low doping situation . the picture of griffith - like antiferromagnetism emerges from this treatment : large af correlated clusters are formed when the temperature is decreased below the spin - peierls temperature , without infinite range ordering . a summary of our results is presented in section [ sec : conclusion ] together with a comparison with the approaches by mostovoy _ @xcite , fukuyama _ et al . _ @xcite , and yoshioka and suzumura @xcite . we argue that these approaches would fail to properly describe the low doping behavior , whereas our description leads to af ordering at infinitesimal doping . since the analysis of the work by fukuyama _ is more technically involved , we have kept the qualitative features for the concluding section while the technical aspects are left for the appendices .","summary":"the phase diagram is investigated by two methods : ( i ) in a mean field treatment of the interchain coupling and ( ii ) in a real space decimation procedure in a two dimensional model of randomly distributed moments . both methods lead to similar results , in a qualitative agreement with experiments .","abstract":"the phase diagram of a model describing doped cugeo is derived . the model emphasizes the role of local moments released by the impurities and randomly distributed inside the gaped singlet background . the phase diagram is investigated by two methods : ( i ) in a mean field treatment of the interchain coupling and ( ii ) in a real space decimation procedure in a two dimensional model of randomly distributed moments . both methods lead to similar results , in a qualitative agreement with experiments . in particular , a transition to an inhomogeneous nel phase is obtained for arbitrary small doping . from the decimation procedure , we interpret this phase at very low doping as a _ griffith antiferromagnet_. namely , it does not have a true long range order down to zero temperature . nonetheless , large magnetically ordered clusters appear already at relatively high temperatures . this demonstrates the role of disorder in the theoretical description of doping in cugeo . a detailed comparison with other approaches is also given .    16.8cm-.4cm-1 cm    plus 0.2pt minus 0.1pt"}
{"article_id":"cond-mat9807093","section_id":"c","document":"let us summarize the proposal we have presented for the onset of the nel long range order in doped cugeo@xmath0 . we first want to stress that , in our opinion , the real difficulty in the subject is not the coexistence of dimerization and antiferromagnetism , since the two order parameters are not incompatible . instead , what is puzzling is the appearance of antiferromagnetism at such low impurity concentration as @xmath171 , with a reasonably high transition temperature . we have shown that this behavior might depend on the peculiar properties of the disorder in this system , as well as in other spin gaped systems . we believe that the most important effect of disorder , at low doping , is to induce randomly distributed localized free moments . these moments are weakly coupled by an exchange constant exponentially decaying upon the distance , see eq.([j ] ) , caused by the virtual polarization of the singlet background . we have shown that even a single chain does develop quasi long range nel order , _ i.e. _ a power law decaying staggered correlation function , which , we believe , does imply a low temperature transition to an af phase as soon as the interchain exchange is taken into account . moreover , we argued that the exponential dependence on the distance of the exchange between those randomly distributed moments implies that rare events in which the impurity released spins are closer than the average distance ( and therefore get strongly coupled ) , dominate the physics at low doping , in a griffith - like scenario . this picture was fully confirmed by an investigation of the 2d disordered problem using a decimation method . the formation of these griffith - like clusters , together with the finite staggered susceptibility of the singlet background , may explain why ordered domains larger that the neutron coherence length do appear at temperatures much larger than the temperature @xmath20 ( the exchange between two moments at a distance equal to the average one ) . some consequences can be drawn from this scenario :    * a nel transition is expected for any arbitrary small impurity concentration . * at relatively large doping concentrations , the mean field picture is expected to hold since the inhomogeneities of the af order are weak . in this concentration range , the nel temperature behaves like @xmath172 , where @xmath29 is the exchange constant in the @xmath27-direction , and @xmath108 the correlation length in the pure cugeo@xmath0 . * for low impurity concentrations , the nel state becomes highly inhomogeneous and the decimation method is more suited than the mean field theory . instead of a single transition temperature we find a quite broad distribution of @xmath15 s . we have indications that a true long range order is never established , so that the low temperature phase might be rather interpreted as a griffith - like antiferromagnet . we have shown that , for small coherence volumes , the nel temperature behaves like @xmath173 . by increasing the coherence volume , this behavior does not rigorously hold . however , as it is visible on fig . [ fig - manabe ] , the behavior of the nel temperature for @xmath163 can hardly be discriminated from the @xmath155 calculation , and a fit of our results to a @xmath173 behavior would be equally satisfactory . * a very long correlation length in the c - axis direction , extending well above @xmath108 , may be observed in a wide temperature range . this can be measured in nmr experiments at very low doping . for instance , the nmr linewidth in the ladder compound sr(cu@xmath52zn@xmath53)@xmath1o@xmath0 at a zn concentration @xmath174 , at which no nel transition has been observed down to the lowest accessible temperature , is two orders of magnitude larger than the correlation length of the undoped compound @xcite , which indicates that a similar behavior might well occur in the doped cugeo@xmath0 . we now compare our results with other theoretical proposals . we first compare our work to the one by mostovoy _ @xcite , and next to the work by fukuyama _ @xcite , and yoshioka and suzumura @xcite . the technicalities involved in the discussion of these last two works are left in the appendices [ ap : scha ] and [ ap : solitons ] , and we focus here in the concluding section on more qualitative aspects . mostovoy _ et al . _ @xcite have recently investigated the effects of interchain coupling at a mean field level in an antiferromagnetic heisenberg chain with random dimerization , modeled by a @xmath35-correlated in space gaussian - distribution peaked around a finite average value . in order to make contact with their work , we make the following comments :    * the microscopic modeling of doping in a spin - peierls system is quite different in our model and in ref . @xcite . as we showed in ref . @xcite , our model is more related to a dimerization with a random telegraph noise of zero average distribution , with the low temperature physics dominated by the localized spins around the domain walls . * the physics of the 1d limit of both models is different . this can be seen by considering the rg flow @xcite . the 1d limit of the model by mostovoy _ _ has been solved by hyman _ @xcite , and flows to a fixed point with power - law griffith singularities . by contrast , the 1d limit of our model flows to the random singlet fixed point @xcite with logarithmic singularities @xcite . * more importantly , the random dimerized heisenberg chain , which is the starting point of the description in ref . @xcite , does _ not _ develop quasi long range af fluctuations , as it is the case in our proposal . this allows to understand why a finite critical concentration of impurities is required in ref . @xcite to generate an af - dimerized phase . as we show in the present article , this is not the case in our model , and it seems that this is not the case in experiments either @xcite .    a proposal similar to the one by mostovoy _ _ was previously put forward by fukuyama , tanimoto and saito ( fts ) @xcite , who also worked out a model showing a coexistence of antiferromagnetism and dimerization , as well as the onset of antiferromagnetism for arbitrary small doping . as we discussed , we have started our analysis by assuming that the main effect of the impurities is the release of free spins out of the singlet background , which is in agreement with the magnetic susceptibility data on the doped compounds , showing an almost curie like component at low temperature which seems to scale linearly with doping ( see for instance ref . @xcite and @xcite ) . instead , fts assume , as mostovoy _ , that the main effect of disorder is the local reduction of the dimerization @xmath175 close to each impurity , hence of the spin gap . for instance , they can fit the experimental reduction of the scattering intensity from the dimerized lattice in the @xmath176 si doped compound , by taking @xmath177 . this leads to a rough estimate of the local reduction of the spin gap @xmath178 . obviously , for smaller impurity concentrations , one should expect an even smaller reduction of the spin gap . however , to explain within this model the almost curie like behavior of the low temperature susceptibility at low doping , one should assume a much stronger suppression of the spin gap down to @xmath179 close to each impurity , not just a small reduction as the fit to the neutron scattering data would imply . this is one reason why we believe that our approach is more relevant . the other is that we do not believe that a local reduction of the dimerization might explain the appearance of antiferromagnetism at such low concentration as @xmath180 of zn doping . in fact , a more realistic modeling of disorder in cugeo@xmath0 should include both disorder effects , the local reduction of dimerization as well as the appearance of free spins . essentially , the main difference between our approach and the fts one is in the different emphasis placed on the two effects . we believe that the main role at low doping in establishing the nel phase is played by the free moments induced by disorder , while fts seem to favor the other mechanism of a local reduction of the dimerization . apart from this comment on the grounds of the model proposed in ref . @xcite , we also have some more technical criticisms . to analyze their model , fts use the so - called self consistent harmonic approximation ( scha ) applied to the bosonized version of a dimerized heisenberg chain . this approximation is a mean field theory , or saddle point approximation , plus random phase fluctuations . by this technique , they show the existence of a mean field solution having both a finite dimerization parameter and a finite nel order parameter . essentially , close to the impurity , where the dimerization parameter is assumed to be reduced , a staggered magnetic moment in the @xmath181-direction arises . we believe that this approach is not fully consistent , as we explain in detail in appendix a.    an alternative variational approach has recently been developed by yoshioka and suzumura @xcite for the zn doping case . they have rigorously shown that in bosonization the spin - lattice coupling does change sign crossing a non magnetic impurity , as it was proposed in ref . @xcite . with this disorder modeling they have proved the existence of a variational action which does again describe a state where the dimerization gets reduced around an impurity and at the same time a static staggered moment appears in the @xmath181-direction . we believe that this variational approach gives a reasonable description of the nel ordered phase , very close to what we propose , but does not allow a description of how the af ordering occurs , which we did in the present work . we postpone to appendix [ ap : solitons ] a detailed discussion of this point , and we end - up with two simple comments on these semiclassical analyzes .    the dimerized phase breaks translational invariance like a nel phase does , which , in addition , also breaks spin symmetry . if one analyzes the role of defects in a dimerized state within a scheme which breaks su(2 ) symmetry ( what is implicitly done in those semiclassical approaches , as shown in appendix [ ap : solitons ] ) , it is not a surprise that a finite staggered magnetization comes out of the calculation ( without spin anisotropy or an applied staggered magnetic field ) , since the dimerized state already breaks translational symmetry .    finally , one can work out a model in the spirit of the fts scenario . this can be done by considering a dimerization distributed as a telegraph noise , and taking a value @xmath35 in the dimerized background ( large segments ) , and @xmath182 close to the impurities ( short segments ) . the resulting disordered model can be exactly solved in the xx limit along the lines in ref . this would result in a model with power - law griffith singularities , equivalent to the model by mostovoy _ @xcite , and inequivalent to our model where the dyson singularities are power - law . this model would not flow to the random singlet fixed point @xcite , would have much weaker af fluctuations than our model , and , as in the case of the model by mostovoy _ , a critical concentration would be expected for the appearance of af order .","summary":"the model emphasizes the role of local moments released by the impurities and randomly distributed inside the gaped singlet background .","abstract":"the phase diagram of a model describing doped cugeo is derived . the model emphasizes the role of local moments released by the impurities and randomly distributed inside the gaped singlet background . the phase diagram is investigated by two methods : ( i ) in a mean field treatment of the interchain coupling and ( ii ) in a real space decimation procedure in a two dimensional model of randomly distributed moments . both methods lead to similar results , in a qualitative agreement with experiments . in particular , a transition to an inhomogeneous nel phase is obtained for arbitrary small doping . from the decimation procedure , we interpret this phase at very low doping as a _ griffith antiferromagnet_. namely , it does not have a true long range order down to zero temperature . nonetheless , large magnetically ordered clusters appear already at relatively high temperatures . this demonstrates the role of disorder in the theoretical description of doping in cugeo . a detailed comparison with other approaches is also given .    16.8cm-.4cm-1 cm    plus 0.2pt minus 0.1pt"}
{"article_id":"1608.05058","section_id":"i","document":"rankings of the elements of a set is a common daily decision making activity , such as , voting for a political candidate , choosing a consumer product , etc . so there is a huge literature concerning the analysis and interpretation of preference rankings data . however , if we trace back in time , we find that de borda ( 1781 ) was the first author , who outlined a simple well thought method based on a solid argument . borda , as a member of the french academy of sciences , criticised the plurality method of choosing a new academy member and suggested , what is known as the borda count(bc ) rule , to fully rank order ( seriate ) the @xmath0 candidates based on the preferences of the @xmath1 judges . bc has generated a large litterature , and this paper makes full use of it as much needed . let @xmath2 denote a set of @xmath0 alternatives / candidates / items , and @xmath3 a set of @xmath1 voters / individuals / judges . in this paper we consider the linear orderings / rankings / preferences , in which all @xmath0 objects are rank - ordered according to their levels of desirability by the @xmath1 voters . we denote a linear order by a sequence @xmath4 , where @xmath5 means that the alternative @xmath6 is preferred to the alternative @xmath7 let @xmath8 be the set of all linear orders on @xmath9 the cardinality of @xmath8 is @xmath10 . a _ voting profile _ is a function @xmath11 from @xmath3 to @xmath8 , that is , @xmath12    we denote by @xmath13 the set of permutations of the elements of the set @xmath14 the borda score is a function @xmath15 from @xmath8 to @xmath16 where for a linear ordering @xmath17 @xmath18 , borda assigned to the element @xmath19the score of @xmath20 , because @xmath19 is preferred to ( @xmath21 other alternatives , or equivalently it is the @xmath22th most preferred alternative . we denote @xmath23 , where @xmath24 is a matrix having @xmath1 rows and @xmath25 columns , and @xmath26 designates the borda score of the @xmath27th judge s preference of the @xmath22th alternative . the average borda score of the elements of @xmath28 is @xmath29 where @xmath30 is a column vector of @xmath31 s having @xmath1 coordinates . borda s count rule ( bc ) seriates / orders the @xmath0 elements of the set @xmath28 according to their average scores : @xmath32 means alternative @xmath22 is preferred to alternative @xmath27 . we define the reverse borda score to be a function @xmath33 from @xmath18 to @xmath16 where for a linear order @xmath17 @xmath34 , we assign to the element @xmath19the score of @xmath35 we denote @xmath36 , where @xmath37 is a matrix having @xmath1 rows and @xmath0 columns , and @xmath38 designates the reverse borda score of the @xmath27th judge s preference of the @xmath22th alternative . the average reverse borda score of the elements of @xmath28 is @xmath39    we note that @xmath40and @xmath41      this example has two aims : first to make the notation clear ; second to show that traditional well established methods for rank data , such as distance and latent class based , may mask groups of small sizes in mixture models . table 1 introduces a well known data set first analyzed by croon ( 1989 ) ; the data derive from a german survey of 2262 rankings of four political items concerning inglehart ( 1977 ) s theory of postmodernism . the four items are : ( @xmath42 ) maintaining order in the nation ; ( @xmath43 ) giving people more to say in important government decisions ; ( @xmath44 ) fighting rising prices ; ( @xmath45 ) protecting freedom of speech . inglehart advanced the thesis that there is a shift in political culture in europe ; that is , some younger europeans have different political values than their fathers : he named the elder europeans as materialists , because after the first and second world wars , they valued mostly material security item ( @xmath44 ) and domestic order item ( @xmath28 ) ; while he named some of the younger generation as postmaterialists , because they valued much more human rights and political liberties item ( @xmath45 ) and democracy item ( @xmath43 ) . so in this example @xmath46 , @xmath47 , and the voting profile is displayed in the first two columns of table 1 ; similarly , table 1 displays the borda scores @xmath48 and the reverse borda scores @xmath49 . the average bc score @xmath50 and the average reverse bc score @xmath51 show that , the 2262 voters generally rank materialist items @xmath52  postmaterialist items @xmath53 .      + item & observed & & + ordering & & & b & c & d & & b & c & d + a@xmath54b@xmath54c@xmath54d & & & 2 & 1 & 0 & & 1 & 2 & 3 + a@xmath54b@xmath54d@xmath54c & & & 2 & 0 & 1 & & 1 & 3 & 2 + a@xmath54c@xmath54b@xmath54d & & & 1 & 2 & 0 & & 2 & 1 & 3 + a@xmath54c@xmath54d@xmath54b & & & 0 & 2 & 1 & & 3 & 1 & 2 + a@xmath54d@xmath54b@xmath54c & & & 1 & 0 & 2 & & 2 & 3 & 1 + a@xmath54d@xmath54c@xmath54b & & & 0 & 1 & 2 & & 3 & 2 & 1 + b@xmath54a@xmath54c@xmath54d & & & 3 & 1 & 0 & & 0 & 2 & 3 + b@xmath54a@xmath54d@xmath54c & & & 3 & 0 & 1 & & 0 & 3 & 2 + b@xmath54c@xmath54a@xmath54d & & & 3 & 2 & 0 & & 0 & 1 & 3 + b@xmath54c@xmath54d@xmath54a & & & 3 & 2 & 1 & & 0 & 1 & 2 + b@xmath54d@xmath54a@xmath54c & & & 3 & 0 & 2 & & 0 & 3 & 1 + b@xmath54d@xmath54c@xmath54a & & & 3 & 1 & 2 & & 0 & 2 & 1 + c@xmath54a@xmath54b@xmath54d & & & 1 & 3 & 0 & & 2 & 0 & 3 + c@xmath54a@xmath54d@xmath54b & & & 0 & 3 & 1 & & 3 & 0 & 2 + c@xmath54b@xmath54a@xmath54d & & & 2 & 3 & 0 & & 1 & 0 & 3 + c@xmath54b@xmath54d@xmath54a & & & 2 & 3 & 1 & & 1 & 0 & 2 + c@xmath54d@xmath54a@xmath54b & & & 0 & 3 & 2 & & 3 & 0 & 1 + c@xmath54d@xmath54b@xmath54a & & & 1 & 3 & 2 & & 2 & 0 & 1 + d@xmath54a@xmath54b@xmath54c & & & 1 & 0 & 3 & & 2 & 3 & 0 + d@xmath54a@xmath54c@xmath54b & & & 0 & 1 & 3 & & 3 & 2 & 0 + d@xmath54b@xmath54a@xmath54c & & & 2 & 0 & 3 & & 1 & 3 & 0 + d@xmath54b@xmath54c@xmath54a & & & 2 & 1 & 3 & & 1 & 2 & 0 + d@xmath54c@xmath54a@xmath54b & & & 0 & 2 & 3 & & 3 & 1 & 0 + d@xmath54c@xmath54b@xmath54a & & & 1 & 2 & 3 & & 2 & 1 & 0 + @xmath50 & & & 1.10 & 2.05 & 0.88 & & & & + @xmath51 & & & & & & & 1.90 & 0.95 & 2.12 +    table 2 provides a statistical summary of four methods of data analysis of table 1 . the first method suggested by inglehart is _ deductive and supervised _ ; it opposes to the other three methods , which are _ inductive , unsupervised and aim to validate inglehart s theory of postmaterialism , _ see also moors and vermunt ( 2007 ) . the other three methods are mixture models and they attempt to see if this data set confirms inglehart s theory of postmaterialism . the first one is by croon ( 1989 ) , who used a stochastic utility ( su ) based latent class model ; the second one by lee and yu ( 2012 ) , who used a weighted distance - based footrule mixture model ; and the third one is based on taxicab correspondence analysis ( tca ) , which is the topic of this paper . here , we provide some details on the statistics displayed in table 2 . \\a ) inglehart ( 1977 ) _ apriori _ classified the respondents into three groups : materialists , postmaterialists and mixed . his method of classification is based on partial rankings based on the first two preferred choices . here , we discuss each group separately . materialists are defined by their response patterns @xmath55 @xmath56 @xmath57 @xmath58 , where the pair of materialist items @xmath59 are always ranked above the pair of postmaterialist items @xmath60 ; they make @xmath61 of the voters . in the ideal case we expect to have the average bc scores for the four items to be : @xmath62 and @xmath63 the corresponding observed values , displayed in table 2 , are ( very near to the ideal ones ) : @xmath64 and @xmath65    postmaterialists are defined by response paterns ( @xmath66 @xmath67 @xmath68 @xmath69 ) , where the pair of postmaterialist items @xmath60 are always ranked above the pair of materialist items @xmath59 ; they make @xmath70 of the voters . the comparison of ideal and observed average bc scores , displayed in table 2 , show that : @xmath71 is very near to @xmath72 while @xmath73 is somewhat near to @xmath74 @xmath75 . the last group is named mixed by inglehart and is composed of the remaining sixteen response patterns ; they make @xmath76 of the voters . in the ideal case we expect to have the average bc scores for the four items to be : @xmath77 @xmath78 the corresponding observed values , displayed in table 2 , are ( somewhat near to the ideal ones ) : @xmath79 @xmath80 @xmath81 and @xmath82    furthermore , based on the global homogeneity coefficient ghc in % : @xmath83 and @xmath84 inglehart s mixed group is not globally homogenous ; that is why we did not calculate its ghc index . the development of the ghc index and its interpretation will be done in section 3 . it is important to note that , the underlying hypothetical conceptual - structural model for this data is a mixture composed of three specific groups ( materialist , postmaterialist and mixed ) , which are explicitly characterized by inglehart . b , c ) given that , croon s su model and lee and yu s weighted distance - based footrule mixture model produced globally very similar groups , we present them together . a summary of croon s analysis can also be found in skrondal and rabe - hesketh ( 2004 , p.404 - 406 ) , lee and yu ( 2012 ) and in alvo and yu ( 2014 , p.228 - 232 ) . sections b and c of table 2 are taken from alvo and yu ( 2014 , p. 230 ) , who present a summary and a comparison of results from croon ( 1989 ) and lee and yu ( 2012 ) . the interpretation of the estimated parameters of the su model in table 2 is similar to the average borda score : for each group the score @xmath85 shows the intensity of the preference for that item in an increasing order . there are two kinds of estimated parameters in lee and yu s weighted distance - based footrule mixture model : the modal response pattern for each group is shown in the last column ; and the weight of an item @xmath86 , which reflects our confidence in the ranked position of the item in the modal response pattern , the higher value representing higher confidence . both methods find a mixture of three groups similar in contents : the first two groups represent materialists with @xmath87 and @xmath88 of the voters for the weighted footrule mixture model , and @xmath89 and @xmath90 of the voters for the su mixture model ; and the third group represents postmaterialists with @xmath91 of the voters for the weighted footrule mixture model , and @xmath92 for the su mixture model . lee and yu ( 2012 ) s conclusion is :  _ based on our grouping , we may conclude that inglehart s theory is not appropriate in germany_. this assertion shows that , the two well established traditional methods masked the existence of the mixed group as put forth by inglehart . \\d ) our approach , based on taxicab correspondence analysis ( tca ) , which is an l@xmath93 variant of correspondence analysis ( ca ) , discovers a mixture of three globally homogenous groups as advocated by inglehart : materialists with @xmath94 of the voters , postmaterialists with @xmath95 , and mixed with @xmath70 of the voters . furthermore , there is an outlier response pattern ( @xmath96 ) representing @xmath97 of the voters . so contrary to lee and yu ( 2012 ) s assertion , _ our results validates inglehart s theory of postmodernism for this data set_. probably , this is due mainly to the fact that tca is a directional method specially useful for spherical data : rank data with all its permutations is spherical by nature ( graphically , it is represented by a permutahedron ; see marden ( 2005 , figure 2.4 , page 11 ) or benzcri ( 1980 , p.303 ) . furthermore , based on the global homogeneity coefficient ghc in % : @xmath98 , @xmath99 and @xmath100 we see that the materialist voters form much more globally homogenous group than the voters in the mixed group ; and the voters in mixed group are much more homogenous than the voters in the postmaterialist group . furthermore , our analysis clearly shows why the postmaterialists ( they have three poles of attractions as defined by marden ( 1995 , ch . 2 ) or benzcri ( 1966 , 1980 ) ) are much more heterogenous than the materialists ( they have two poles of attractions ) . more details on the local heterogeneities of each group will be presented later on in section 4 . +   + group & sample% & @xmath101 & @xmath102 & @xmath103 & @xmath104 & + materialist & @xmath105 & @xmath106 & @xmath107 & @xmath108 & @xmath109 & + postmaterialist & @xmath110 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & + mixed & @xmath115 & @xmath116 & @xmath117 & @xmath118 & @xmath119 & +   + group & sample% & @xmath120 & @xmath121 & @xmath122 & @xmath123 & + materialist 1 & @xmath124 & @xmath125 & @xmath126 & @xmath127 & @xmath128 & + materialist 2 & @xmath129 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & + postmaterialist & @xmath134 & @xmath135 & @xmath136 & @xmath137 & @xmath138 & +   + group & sample% & @xmath139 & @xmath140 & @xmath141 & & + materialist 1 & @xmath142 & @xmath143 & @xmath144 & @xmath145 & & + materialist 2 & @xmath146 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & + post - materialist & @xmath151 & @xmath152 & @xmath145 & @xmath153 & & +   + group & sample% & @xmath101 & @xmath102 & @xmath103 & @xmath104 & + materialist & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath158 & + postmaterialist & @xmath159 & @xmath160 & @xmath161 & @xmath162 & @xmath163 & + mixed & @xmath110 & @xmath164 & @xmath165 & @xmath166 & @xmath167 & + outlier & @xmath168 & @xmath169 & @xmath145 & @xmath31 & @xmath170 & +      the traditional methods of finding mixture components of rank data are mostly based on distance and latent class models ; these models may mask groups of small sizes ; probably due to the spherical nature of rank data . in this paper , our apparoach diverges from the traditional methods , because we discuss the concept of a mixture for rank data essentially in terms of its globally homogenous group components . we use the law of contradiction to identify globally homogenous components . for instance , by tca we were able to discover that the data set in table 1 is a mixture of three globally homogenous group components ( materialist , postmaterialist and mixed ) ; furthermore , each group component can be summarized by its average borda count ( bc ) score as its consensus ranking ; this is the first step in our procedure . in the second step , we look at local heterogeneities if there are any , given the globally homogenous component . this two step procedure produces finer visualization of rank data ; it is done via the exploratory analysis of rank data by taxicab correspondence analysis with the nega coding . also we introduce a new coefficient of global homogeneity , ghc . ghc is based on the first taxicab dispersion measure : it takes values between 0 and 100% , so it is easily interpretable . ghc measures the extent of crossing of scores of voters between 2 or 3 blocks seriation of the items where the borda count statistic provides consensus ordering of the items on the first axis . furthermore , to our knowledge , this is the first time that a tangible method has been proposed that identifies explicitly outliers in a rank data : neither the recently written monograph by alvo and yu ( 2014 ) , nor the much cited monograph of marden ( 1995 ) discuss the important problem of identification of outliers in rank data . we mention two publicly available written packages in r , that we used , _ rankclustr _ by jacques , grimonprez and biernacki ( 2014 ) , and _ pmr _ ( probability models for ranking data ) by lee and yu ( 2013 ) .    the contents of this paper are organized as follows : section 2 reviews the tca approach for rank data ; section 3 develops the new global homogeneity coefficient ghc ; section 4 presents the analysis of some well known rank data sets by tca ; and finally in section 5 we conclude with some remarks . we just want to mention that there is a large litterature in social choice theory or social welfare theory studying the properties of the bc . here , we mention some important contributions according to our personal readings . young ( 1974 ) presents a set of four axioms that characterize uniquely bc ; see also among others , saary ( 1990a ) and marchant ( 1998 ) . saari ( 1990b ) distinguishes two levels of susceptiblity of manipulation of voting theories : _macro_- where a large percentage of voters- , and _micro_- where a small percentage of voters - attempt to change the results of the elections . in data analysis , a macro manipulation is equivalent to the existence of a mixture of groups of voters . while , a micro manipulation is equivalent to the existence of few outliers in the globally homogenous set of voters @xmath3 . further , saari concludes that among all positional voting systems , bc is the least susceptible to micro manipulation ; this assertion seems fully true in this paper . saari ( 1999 ) proves that bc is the only positional voting method that satisfies the property of _ reversal symmetry , _ which states that if everyone reverses all their preferences , then the final outcome should also be reversed . this property plays an important role in the nega coding of a rank data set before the application of tca . choulakian ( 2014 ) incorporates the bc to interpret the first principal factor of taxicab correspondence analysis ( tca ) of a nega coded rank data , see theorem 1 in the next section . additionally , this essay further extends and complements the ideas of global homogeneity and local heterogeneities for rank data .","summary":"the traditional methods of finding mixture components of rank data are mostly based on distance and latent class models ; these models may exhibit the phenomenon of masking of groups of small sizes ; probably due to the spherical nature of rank data . our approach diverges from the traditional methods ; it is directional and uses a logical principle , the law of contradiction . we discuss the concept of a mixture for rank data essentially in terms of the notion of global homogeneity of its group components . this is done via the exploratory analysis of rank data by taxicab correspondence analysis with the nega coding : if the first factor is an affine function of the borda count , then we say that the rank data are globally homogenous , and local heterogeneities may appear on the consequent factors ; otherwise , the rank data either are globally homogenous with outliers , or a mixture of globally homogenous groups . also we introduce a new coefficient of global homogeneity , ghc . ghc is based on the first taxicab dispersion measure : it takes values between 0 and 100% , so it is easily interpretable . ghc measures the extent of crossing of scores of voters between two or three blocks seriation of the items where the borda count statistic provides consensus ordering of the items on the first axis . key words : preferences ; rankings ; borda count ; global homogeneity coefficient ; nega coding ; law of contradiction ; mixture ; outliers ; taxicab correspondence analysis ; masking .","abstract":"the traditional methods of finding mixture components of rank data are mostly based on distance and latent class models ; these models may exhibit the phenomenon of masking of groups of small sizes ; probably due to the spherical nature of rank data . our approach diverges from the traditional methods ; it is directional and uses a logical principle , the law of contradiction . we discuss the concept of a mixture for rank data essentially in terms of the notion of global homogeneity of its group components . local heterogeneities may appear once the group components of the mixture have been discovered . this is done via the exploratory analysis of rank data by taxicab correspondence analysis with the nega coding : if the first factor is an affine function of the borda count , then we say that the rank data are globally homogenous , and local heterogeneities may appear on the consequent factors ; otherwise , the rank data either are globally homogenous with outliers , or a mixture of globally homogenous groups . also we introduce a new coefficient of global homogeneity , ghc . ghc is based on the first taxicab dispersion measure : it takes values between 0 and 100% , so it is easily interpretable . ghc measures the extent of crossing of scores of voters between two or three blocks seriation of the items where the borda count statistic provides consensus ordering of the items on the first axis . examples are provided .    key words : preferences ; rankings ; borda count ; global homogeneity coefficient ; nega coding ; law of contradiction ; mixture ; outliers ; taxicab correspondence analysis ; masking ."}
{"article_id":"1608.05058","section_id":"c","document":"here we conclude with a summary of some aspects of tca of nega coded rank data . we note that the rank data is spherical by nature , they are represented on a permutahedron ; so a directional method , like tca of the nega coded rank data , is able to discover some other aspects of the data , which are eclipsed or masked by well established methods , such as distance or latent class based methods . like occam s razor , step by step , tca peels the essential structural layers ( globally homogenous groups ) of rank data ; it can also identify outliers in a group . we presented a new coefficient , @xmath399 , that measures the global homogeneity of a group . ghc is based on the first taxicab dispersion measure : it takes values between 0 and 100% , so it is easily interpretable . ghc takes into account the following two aspects of rank data : a ) how the items are partitioned into blocks by the first axis . b ) the extent of crossing of scores of voters among the partitioned blocks , where the borda count statistic provides consensus ordering of the items on the first axis . @xmath418 means that the partition of the set of items into 2 or 3 blocks is faithful and for all voters their orderings of the items are intra block permutations with no crossings between the blocks . for fully ranked data , the lower bound of @xmath399 is positive but unknown being an open problem . as is well known , a coefficient in itself does not show important local details in a data set . we named these important local details , local heterogeneity ; and they appear in the higher dimensions of tca outputs : so it is important to examine the sequence of tca dispersion measures and the graphical displays as expounded and professed by benzcri . benzcri , j.p . geometric representation of preferences and correspondence tables . in _ pratique de lanalyse des donnes _ , vol . 2 , by bastin , ch . , benzcri , j.p . , bourgarit , ch . and cazes , p. p : 299 - 305 , dunod , paris .            choulakian v. ( 2013 ) . the simple sum score statistic in taxicab correspondence analysis . in _ advances in latent variables _ ( ebook ) , eds . brentari e.and carpita m. , vita e pensiero , milan , italy , isbn 978 88 343 2556 8 , 6 pages . de leeuw , j ( 2006 ) . nonlinear principal component analysis and related techniques . in mj greenacre , j blasius ( eds . ) , _ multiple correspondence analysis and related methods _ , chapter 4 , 107134 , chapman & hall / crc , boca raton . van deun , k. , heiser , w.j . and delbeke , l. ( 2007 ) multidimensional unfolding by nonmetric multidimensional scaling of spearman distances in the extended permutation polytope . _ multivariate behavioral research _ , 42(1 ) , 103132 . _ proof _ : using the same notation as in choulakian ( 2014 ) , we designate@xmath527first , by ( 12 ) we have @xmath528from which we get,@xmath529second , by triangle inequality of the l@xmath93 norm we have@xmath530              \\c ) the vector containing the first and only factor scores of the columns is @xmath536 where @xmath537  for @xmath352 in particular , we see that @xmath538 @xmath539 and @xmath379 for @xmath280 are equispaced . so for an odd number of items @xmath380 for @xmath540 , we have @xmath541    _ proof _ : a ) a _ faithfully homogenous group _ consists of one response pattern , and its borda score values for a complete linear order of @xmath0 items , without loss of generality by relabeling of the items , will be @xmath542 . then the nega coded correspondence table will have only two rows and @xmath0 columns@xmath364and @xmath543 will be of rank 1 ; that is , there is only one principle factor , for which we note the taxicab dispersion measure by @xmath367 for a fixed finite integer value of @xmath366by ( 18 ) the elements of @xmath318 are@xmath544and@xmath545so@xmath546the value of @xmath367 by theorem 1 b is@xmath547                          \\a ) necessary condition . we have @xmath567 , \\end{aligned}\\]]where @xmath568 and @xmath569 for  @xmath340 given that @xmath570 is a sum of @xmath571 positive terms , it is easy to see that * u*@xmath572 is the first tca principal axis , where @xmath573 is the characteristic function of @xmath574 that is , it has the value of 1 if @xmath575 and 0 otherwise . so for @xmath368 and @xmath383 the first tca axis divides the set of items @xmath28 into 2 blocks such that @xmath384 with @xmath576 and @xmath577 that is , the partition of the set of items @xmath28 is _ faithful . _ furthermore , _  _ the borda scores of all voters are intra block permutations by definition of @xmath578 and @xmath579 . \\b ) sufficient condition . we suppose that the partition of @xmath580 is faithful and there are no crossings between the 2 blocks @xmath581 and @xmath582 this implies that for @xmath583 @xmath584 for @xmath585 and @xmath586 for @xmath587 thus we get @xmath588 as in the proof of the necessary condition .","summary":"local heterogeneities may appear once the group components of the mixture have been discovered .","abstract":"the traditional methods of finding mixture components of rank data are mostly based on distance and latent class models ; these models may exhibit the phenomenon of masking of groups of small sizes ; probably due to the spherical nature of rank data . our approach diverges from the traditional methods ; it is directional and uses a logical principle , the law of contradiction . we discuss the concept of a mixture for rank data essentially in terms of the notion of global homogeneity of its group components . local heterogeneities may appear once the group components of the mixture have been discovered . this is done via the exploratory analysis of rank data by taxicab correspondence analysis with the nega coding : if the first factor is an affine function of the borda count , then we say that the rank data are globally homogenous , and local heterogeneities may appear on the consequent factors ; otherwise , the rank data either are globally homogenous with outliers , or a mixture of globally homogenous groups . also we introduce a new coefficient of global homogeneity , ghc . ghc is based on the first taxicab dispersion measure : it takes values between 0 and 100% , so it is easily interpretable . ghc measures the extent of crossing of scores of voters between two or three blocks seriation of the items where the borda count statistic provides consensus ordering of the items on the first axis . examples are provided .    key words : preferences ; rankings ; borda count ; global homogeneity coefficient ; nega coding ; law of contradiction ; mixture ; outliers ; taxicab correspondence analysis ; masking ."}
{"article_id":"astro-ph0006194","section_id":"i","document":"we are motivated by the steep evolution of the bright quasar ( qs ) population ; out to @xmath3 their number exceeds the local value by some @xmath4 ( schmidt & green 1983 , schmidt 1989 ) . around @xmath5 the evolution culminates , and farther out it goes into a decline ( osmer 1982 , shaver et al . 1996 ) .    our work will be based on two widely shared notions . first , the qss are powered by massive black holes ( bhs ) accreting gas from their host galaxies ; thus e.m . outputs @xmath6 obtain when the baryonic mass @xmath7 is accreted over the time @xmath8 with conversion efficiency up to @xmath9 ( rees 1984 ) . second , the structures surrounding the bhs develop after the hierarchical clustering ( see peebles 1993 ) ; this envisages the galaxies as baryonic cores within heavier halos of cold dark matter ( dm ) . before @xmath3 galactic halos are built up through merging of smaller units ; thereafter the galaxies begin to assemble into small groups of dynamical mass @xmath10 , which in turn merge into richer groups and eventually into clusters . by such a hierarchical development , the numbers of structures in each mass range undergo a fast increase followed by a slow demise .    on these grounds , the high qs luminosities in the optical , ir or x - ray bands may be expected to signal out to @xmath11 environmental conditions conducive to accretion . in fact , the decline ( a rise in cosmic epoch ) of the early qss is widely held to be geared to galaxy formation . specifically , their environment is held to be constituted by protogalactic spheroids being built up hierarchically through major , chaotic merging events between dense , very gas - rich subunits . in these events the gravitational potential is strongly distorted , while the baryons are lumped and shocked ; so the angular momentum @xmath12 of the gas orbiting at kpc distances in the host is efficiently transferred to the heavier dm substructures , and the gas can begin an inward course toward pc or smaller scales . from the plenty of gas so made available , central massive bhs collapse and/or accrete rapidly ; they can accrete at their full _ self - limiting _ rate , and easily attain eddington luminosities @xmath13 erg@xmath14 . this is indicated by eq . ( 1.1 ) , when the bhs double their mass and make @xmath15 over short dynamical scales @xmath8 that match the effective eddington time @xmath16 gyr . in sum , the number of early qss ought to track the galaxy formation , and _ rise _ together with the number of host galactic halos exceeding some @xmath17 . such a direct connection of qss with newly forming galaxies has been represented with models developing over the years from the first attemps by cavaliere & szalay ( 1986 ) and efstathiou & rees ( 1988 ) , to haehnelt & rees ( 1993 ) , haiman & loeb ( 1998 ) , haehnelt , natarajan & rees ( 1998 ) , cavaliere & vittorini ( 1998 , henceforth cv98 ) . concurring evidence is being provided by observations such as those by fontana et al . ( 1998 ) , and in djorgowski ( 1998 ) . here we focus on the dramatic _ fall _ of the bright qs population later than @xmath3 , where more features can be observed and the picture is more complex . the time scale involved is around @xmath18 gyr , fast compared with the gentle demise of the galaxy formation envisaged by the hierarchical clustering . the behavior of the optical luminosity function ( lf ) is dominated by luminosity evolution ( le , see boyle , shanks & peterson 1988 ; hatziminaoglou , van waerheke & mathez 1998 ) , a trend also shared by the lfs in x - rays ( della ceca et al . 1994 , boyle et al . 1994 ) and in the radio band ( dunlop & peacock 1990 ) . additional features appear in the optical data toward low @xmath19 . first , a minor component of density evolution ( de ) has been discerned at blue magnitudes @xmath20 by boyle et al . ( 1988 ) , and confirmed by maloney & petrosian ( 1999 ) . second , la franca & cristiani ( 1997 ) , and goldschmidt & miller ( 1998 ) found an excess of bright qss over previous surveys ; from these observations and those by khler et al . ( 1997 ) the lfs appear to be stretched out into a generally smoother shape on approaching low @xmath19 . finally , faint x - ray emissions and liner - type activity are increasingly found to be widespread among otherwise normal galaxies , see ho , filippenko & sargent ( 1997 ) ; miyaji , hasinger & schmidt ( 1998 ) ; giommi , fiore & perri ( 1998 ) . on the other hand , sharp imaging of a number of bright qss at intermediate @xmath19 has revealed host galaxies which are not really newly forming , but rather are surrounded by a complex environment . some still exhibit morphological marks of a recent tidal interaction , in spite of the low surface brightness and short duration ( @xmath21 gyr ) of such features ; others are found in close association with comparable or fainter companions ; a fraction even appear to harbor secondary nuclei ( see hutchings & neff 1992 ; hutchings , crampton & johnson 1995 ; rafanelli , violato & baruffolo 1995 ; hasinger et al . 1997 ; bahcall et al . 1997 ; boyce et al . 1998 ; mclure et al . 1998 ; ridgway et . al . 1999 ) . in addition , recent statistical evidence ( fisher et al . 1996 ; jaeger , fricke & heidt 1998 ; wold et al . 1999 ) points toward a poor group environment also for radio - quiet qss , perhaps poorer than for the radio - loud objects ( yee & green 1987 , lehnert et al . 1999 ) .    but the issue is not settled . other observers detect at most marginal evidence that the environments of the bright qs are richer than the field ( see smith , boyle & maddox 1995 ; teplitz , mclean & malkan 1999 ; croom & shanks 1998 ) , and find low incidence of peculiarities in galaxies active at the levels of the seyfert nuclei ( malkan , gorjian & tam 1998 ) . many point out the need to enlarge and complete the qs samples , and to compare them with proper controls .    such a complex data situation warrants exploring what predictions follow from pursuing the physical connection of bright qs activity with host interactions . our guideline ( taking up cavaliere & padovani 1989 , small & blandford 1992 , cv98 ) will be that later than @xmath3 the accretion feast ought to cease turning the qs rise into a descent , due to a gradual _ change _ in their environment . in fact , toward lower @xmath19 major merging events ( with the associated gas imports into the host ) become rarer and rarer at galactic scales ; the prevailing dynamical events are best described as _ interactions _ between developed galaxies , occurring mainly in the small groups which then begin to virialize . these events do not necessarily increase the dark halo masses , yet they can _ destabilize _ the gas in the hosts and trigger limited accretion episodes ; these draw from the gas reservoirs in the hosts , and concur with starbursts in progressively exhausting them . but as exhaustion is approached other , lesser gas supplies become relevant for lower level activity , such as those provided from accretion of satellite galaxies that occours even in low density environments or in the field . we intend to single out and address directly the astrophysical processes involved , rather than base upon numerical and phenomenological treatments as in kauffmann & haehnelt ( 1999 ) . specifically , we shall simplify the dynamical history of the dm , to focus on the consumption and depletion of the gas reservoirs in the host galaxies . first , in  2 and  3 we will examine the outcomes of encounters of the host with sizeable companions , occurring mainly in poor _ groups_. then in  4 we examine accretion of satellite galaxies with their additional but small gas supplies , and consider also other processes that can occur in the _ field_. finally , in  5 we summarize and discuss our conclusions , stressing implications and predictions .","summary":"we derive quantitative predictions of the optical and x - ray luminosity functions for quasars in the redshift range . the host encounters with companions drive onto already existing holes further but meager accretion ; these consume the gas reservoirs in the hosts , and cause supply - limited emissions which are intermittent , go progressively sub - eddington and peter out","abstract":"we derive quantitative predictions of the optical and x - ray luminosity functions for quasars in the redshift range . based on accreting black holes as primary sources for the quasar outputs , we investigate how the accretion is controlled by the surrounding structures , as these grow hierarchically from the formation of the host galaxies to their assemblage into poor and eventually into rich groups . we argue that for efficient black hole fueling is triggered by the encounters of a gas - rich host with its companions in a group ; these destabilize the gas and induce accretion , giving rise to the following features . the dispersion of the dynamical parameters in the encounters produces luminosity functions with the shape of a double power - law . strong luminosity evolution is produced as these encounters deplete the gas supply in the host ; an additional , milder density evolution obtains since the interactions become progressively rarer as the groups grow richer but less dense . we carry out these arguments to derive a specific model for the evolving luminosity functions . from the agreement with the optical and the x - ray data , we conclude that the evolution of the bright quasars is driven by the development of cosmic structures in two ways . earlier than the gas - rich protogalaxies grow by merging , which also induces parallel growth of central holes accreting at their full eddington rates . in the later era of group assemblage the host encounters with companions drive onto already existing holes further but meager accretion ; these consume the gas reservoirs in the hosts , and cause supply - limited emissions which are intermittent , go progressively sub - eddington and peter out . then other fueling processes occurring in the field come to the foreground ; we specifically discuss the faint emissions , especially noticeable in x - rays , which are expected when hosts in the field cannibalize satellite galaxies with their meager gas contents ."}
{"article_id":"astro-ph0006194","section_id":"c","document":"we have shown that a steep qs fall for @xmath232 is to result from the effects of the hierarchical _ growth _ of structures around accreting bhs , amplified by the exhaustion of the gas available for the accretion . the hierarchical clustering envisages the era of galaxy formation to go over to an era of group assemblage for @xmath233 . in a group , the settled host galaxies keep on evolving for a while , no longer by major merging events but rather via _ encounters _ which occur at rates @xmath234 gyr@xmath166 .    these are milder events , yet able to destabilize the host gas , specifically by causing considerable _ loss _ of angular momentum as tackled in  2 . we have shown how they trigger intermittent and _ supply - limited _ accretion episodes onto the central bh , yielding blue luminosities @xmath235 erg / s for some @xmath37 gyr in large , gas - rich galaxies . but we have additionally shown in  2.2 how such substantial gas discharges , which also fuel simultaneous starbursts activity , _ deplete _ the host reservoirs and cause the gaseous mass to decrease substantially following @xmath236 on average . thus the encounters not only turn rarer ( @xmath237 ) as the clustering proceeds toward groups richer but less dense , and so produce a later , _ weak _ de ; but they also become less and less effective in terms of triggered accretion , and this causes _ strong _ le with the luminosities scaling down close to @xmath238 . the result we predict for bright qss in the range @xmath233 is outlined in eq . ( 2.6 ) , is derived and shown in more details in  3 to yield eq . ( 3.6 ) , and is represented in full by fig . this agrees not only with the observations by boyle et al . 1988 , but also with the recent re - analysis of variuos samples by maloney & petrosian 1999 , and with the greatly extended samples being provided at @xmath239 by shanks at al . 2000 .    as to the shape of the lfs , we have shown in  2.1 that the statistics of the encounters naturally yields a double power - law _ broken _ from about @xmath240 toward the faint end , to @xmath241 and _ steeper _ at the bright end , in accord with the above data . but toward low @xmath19 a _ smoother _ overall shape is produced by the changing tilt @xmath171 given by eqs . ( 3.6 ) ; this concurs with the enhancement of the bright end at @xmath242 erg / s provided by the additional feeding processes in the field discussed in  4 and shown in fig . 2 . our result accords with the observations by la franca & cristiani ( 1997 ) and by goldschmidt & miller ( 1998 ) , which are confirmed by a recent survey being analyzed by cristiani and collaborators ( see grazian et al . 2000 ) . the above values and behaviors are given for the critical universe , see fig.2a ; but fig . 2b shows that similar or better results obtain in a flat , low density cosmology .    from a different path , we agree with cattaneo , haehnelt & rees 1999 and kauffmann & haehnelt 1999 that strong qs evolution down to very low @xmath19 implies destabilization of substantial fractions of the gas stockpiled in the hosts . only a minor part of such gas ends up into accretion episodes ; the major part is likely to be heated and/or ejected , or used up to produce  over and above the quiescent star formation  star bursts specifically in the bright host galaxies , mostly ellipticals . but we see reasons why the le evolution component may be expected to slow down on approaching @xmath243 . for example , when interactions cause outright galaxy aggregations the host mass @xmath244 grows appreciably while its internal density @xmath245 decreases ; then it is easily checked that the scaling of @xmath162 includes the factors @xmath246 , giving rise to @xmath247 with @xmath248 . correspondingly , from eq . ( 2.4 ) the late evolution @xmath249 brakes into a softening exponential at low @xmath99 and @xmath19 . on the other hand , when it comes to faint agns at @xmath250 the situation becomes more complex , since the underlying bhs may be fed at low levels by various processes which superpose . we have explored in  4 and in fig . 3 one such process , namely , the _ accretion _ of satellites with the associated gas supplies ; this contributes many more but weaker sources , in the range of the seyfert galaxies and below . these sources undergo a strong @xmath99-dependent de , similar to that observed in x - rays by miyaji , hasinger & schmidt ( 1998 ) ; many , in fact , will be more easily pinpointed in x - rays at @xmath251 erg / s or fainter . other feeding processes are conceivably provided by the self - destruction of giant nuclear star clusters ( see norman & scoville 1988 ) , and by internal instabilities and bar formation in disk galaxies ( see heller & shlosman 1994 , merritt 1998 , sellwood & moore 1998 ) . it will be interesting to see what specific shape and evolution are predicted for the lfs of agns fed in this latter fashion . here we focussed on _ dynamic _ losses of the gas angular momentum @xmath12 as primary triggers of the inflow eventually leading to bh accretion ; the gas may undergo other adventures before actually fueling the central bh , see e.g. siemiginowska & elvis ( 1997 ) . but the straight prediction from our study substantiating the outline by cavaliere & padovani ( 1989 ) , is that the emissions from the average qs or agn should go progressively _ sub - eddington _ later than @xmath22 , even at constant @xmath214 ; this accords with the data trend taking shape from various observational lines , see sun & malkan ( 1989 ) , haiman & menou ( 1998 ) , salucci et al . ( 1998 ) , wandel ( 1998 ) . our specific prediction for the average eddington ratio is @xmath252^{3 } \\ , m_{bh}(2.5)/ m_{bh}(z)~ , \\eqno(5.1)\\ ] ] which goes down to about @xmath203 by @xmath253 . this is based on the intrinsically _ depleted _ accretion onto already existing , massive bhs which yields @xmath254 as discussed above ; the other factor is the related mass growth by the ratio @xmath255 , see cv98 . in fact , as outlined there and expanded elsewhere , by all episodes of rekindled accretion in the range @xmath256 the central bhs now dormant in most galaxies grow by an average factor @xmath257 . this will be lower for hosts which are disk dominated at radii of a few kpcs , based on the values of @xmath258 indicated in  2.1 by case @xmath94 compared with case @xmath92 . otherwise , the factor will be limited by the bound @xmath259 set when a large central condensation enforces axial symmetry despite the dynamical perturbations . correspondingly , the local density of baryons collapsed into bhs amounts to @xmath260 gpc@xmath261 . these findings agree with the observational estimates of the central bh masses in many local galaxies given by richstone et al . 1998 , and with the upper bounds set by magorrian et al . 1998 .    toward a comprehensive picture , we point out that the losses of @xmath12 during galaxy - galaxy interactions as here analyzed go back to dynamically generated _ asymmetries _ of the gravitational potential . compared with the major merging events during the build up of the spheroids , these do not differ in kind , but only as for the lesser strength and as for their falling rate and decreasing gas amounts involved . so we conclude that most of the bright qs evolution can be understood in terms of _ one _ engine ( the accreting bh ) and _ one _ trigger ( dynamical destabilization of the gas ) , which however operate under _ two _ adjoining regimes geared to the development of cosmic structures . such regimes are related to the early , violent merging events when the gas - rich spheroids form ; and to the later , dwindling interactions of host galaxies in groups or even in the field , with the slow demise of galaxy formation magnified by the fast depletion of the gas supplies . we thank for helpful exchanges b. guiderdoni , b. liberti , p. rafanelli and m. ramella . early stimulating discussions with g. hasinger and c. norman are gratefully ackowledged . thanks are due to our referee for stimulating us to clarify our presentation throughout the ms . work supported by partial grants from asi and murst .","summary":"we argue that for efficient black hole fueling is triggered by the encounters of a gas - rich host with its companions in a group ; these destabilize the gas and induce accretion , giving rise to the following features . we conclude that the evolution of the bright quasars is driven by the development of cosmic structures in two ways . earlier than the gas - rich protogalaxies grow by merging , which also induces parallel growth of central holes accreting at their full eddington rates . in the later era of group assemblage . then other fueling processes occurring in the field come to the foreground ; we specifically discuss the faint emissions , especially noticeable in x - rays , which are expected when hosts in the field cannibalize satellite galaxies with their meager gas contents .","abstract":"we derive quantitative predictions of the optical and x - ray luminosity functions for quasars in the redshift range . based on accreting black holes as primary sources for the quasar outputs , we investigate how the accretion is controlled by the surrounding structures , as these grow hierarchically from the formation of the host galaxies to their assemblage into poor and eventually into rich groups . we argue that for efficient black hole fueling is triggered by the encounters of a gas - rich host with its companions in a group ; these destabilize the gas and induce accretion , giving rise to the following features . the dispersion of the dynamical parameters in the encounters produces luminosity functions with the shape of a double power - law . strong luminosity evolution is produced as these encounters deplete the gas supply in the host ; an additional , milder density evolution obtains since the interactions become progressively rarer as the groups grow richer but less dense . we carry out these arguments to derive a specific model for the evolving luminosity functions . from the agreement with the optical and the x - ray data , we conclude that the evolution of the bright quasars is driven by the development of cosmic structures in two ways . earlier than the gas - rich protogalaxies grow by merging , which also induces parallel growth of central holes accreting at their full eddington rates . in the later era of group assemblage the host encounters with companions drive onto already existing holes further but meager accretion ; these consume the gas reservoirs in the hosts , and cause supply - limited emissions which are intermittent , go progressively sub - eddington and peter out . then other fueling processes occurring in the field come to the foreground ; we specifically discuss the faint emissions , especially noticeable in x - rays , which are expected when hosts in the field cannibalize satellite galaxies with their meager gas contents ."}
{"article_id":"1605.03448","section_id":"i","document":"the representation theory of the symmetric group , @xmath0 , is governed by its associated branching graph @xmath1 ( also known as young s lattice ) . the set of vertices on the @xmath2th level this graph , @xmath3 , is given by the set of partitions of @xmath2 ; the edges connect partitions which differ by a single node . the first few levels of this graph are depicted in [ asdhjkdsf ] . given @xmath4 a vertex on the @xmath2th level of this graph , there is an associated @xmath5-module , @xmath6 , called a specht module . this module has an integral basis indexed by the set of paths in the branching graph which begin at @xmath7 and terminate at @xmath4 ; we refer to such paths as standard tableaux of shape @xmath4 . the specht modules @xmath8 provide a complete set of simple @xmath5-modules . @xmath9            \\begin{scope }         \\draw ( 0,3 ) node {    $ \\varnothing $   } ;                   \\draw ( 0,0 ) node { $   \\yboxdim{6pt}\\gyoung ( ; ) $   } ;         \\draw ( -2,-3 ) node    {   $ \\yboxdim{6pt}\\gyoung ( ; ; )   $ }       ;          \\draw ( + 2,-3 ) node    {    $ \\yboxdim{6pt}\\gyoung(;,;)$     }        ;         \\draw ( 0,-6 ) node     {      \\yboxdim{6pt}\\gyoung ( ; ; , ; ) }        ;        \\draw ( -4,-6 ) node     {     \\yboxdim{6pt}\\gyoung ( ; ; ; ) }      ;              \\draw ( 4,-6 ) node     {     \\yboxdim{6pt}\\gyoung ( ; , ; , ; ) }       ;       \\draw ( 0.0,1 ) -- ( 0,2 ) ;                              \\path ( -1.5,-2 ) edge[decorate ]   node[auto ] { \\ } ( -0.5,-1 ) ;                                        \\path ( 0.5,-1 ) edge[decorate ]   node[auto ] { \\ } ( 1.5,-2 ) ;                              \\path ( -0.5,-8.2 + 3 )   edge[decorate ]   node[auto ] { \\ } ( -1.5,-6.8 + 3 ) ;                           \\path ( 1.5,-6.8 + 3 ) edge[decorate ]   node[auto ] { \\ } ( 0.5,-8.2 + 3 ) ;    \\path ( -3.5,-8.2 + 3 )   edge[decorate ]   node[auto ] { \\ } ( -2.5,-6.8 + 3 ) ;         \\path ( 2.5,-6.8 + 3 ) edge[decorate ]   node[auto ] { \\ } ( 3.5,-8.2 + 3 ) ;                  \\end{scope}\\end{tikzpicture}\\ ] ]    for @xmath10 , we consider @xmath11 as a subgroup of @xmath0 under the embedding @xmath12 . in other words , @xmath13 is the subgroup of permutations of the set @xmath14 . generalising the above , for any two vertices @xmath15 and @xmath16 , we may define the skew specht module @xmath17 the skew specht module @xmath18 has an integral basis indexed by the set of paths in the branching graph which begin at the vertex @xmath19 and terminate at the vertex @xmath20 ; we refer to such paths as skew tableaux of shape @xmath21 . skew specht modules carry the structure of simple modules for affine hecke algebras @xcite and play an important role in the graded representation theory of the symmetric groups and their affine analogues , see @xcite . most importantly for us , one obtains a particularly natural interpretation of the skew - kostka and littlewood  richardson coefficients as the multiplicities @xmath22 respectively ( here @xmath23 ) . we have a natural map @xmath24 and so we can immediately deduce that @xmath25 . in @xcite , james shows that @xmath26 has a basis indexed by the set of semistandard skew tableaux of shape @xmath21 and weight @xmath27 . james then shows that the homomorphisms which factor through the map @xmath28 are indexed by the subset of these skew tableaux which satisfy the lattice permutation property . this provides a concrete combinatorial interpretation of the coefficients @xmath29 and @xmath30 . the purpose of this article is to generalise the classical construction of skew specht modules for the symmetric group to the setting of diagram algebras ( such as the brauer , walled brauer , temperley  lieb , birman  wenzl , and partition algebras ) over a field @xmath31 . the representation theory of these diagram algebras is again controlled by their associated branching graphs . each vertex @xmath4 of the branching graph labels a cell module @xmath32 and the paths in the branching graph index integral bases of these cell modules . given two fixed points @xmath4 and @xmath20 in the branching graph , we provide an explicit construction of an associated skew cell module @xmath33 . we show that these skew cell modules possess integral bases indexed by skew tableaux ( paths between the two fixed vertices in the graph ) exactly as in the classical case . we expect the skew cell modules to play an important role in the graded representation theory of these algebras ( which has only recently begun to be explored , see @xcite ) and provide a link between finite dimensional diagrammatic algebras and their affine analogues . the partition algebra over the rational numbers , @xmath34 , will provide the motivating example of a diagram algebra throughout this paper . precisely as in the classical case , one can define the multiplicities @xmath35 ( here @xmath36 ) and @xmath37 as before . in this paper we prove that the coefficients @xmath38 are equal to the stable kronecker coefficients . these coefficients have been described as ` perhaps the most challenging , deep and mysterious objects in algebraic combinatorics ' @xcite . on the other hand , the coefficients @xmath39 do not seem to have been studied anywhere in the literature . motivated by the classical case , we ask the following questions :    1 . can one interpret the coefficients @xmath39 and @xmath40 in terms of the combinatorics of skew - tableaux for the partition algebra ? 2 .   do there exist natural generalisations of the semistandard and lattice permutation conditions in this setting ? do the coefficients @xmath41 provide a first step towards understanding the stable kronecker coefficients @xmath40 ? we shall address these questions in an upcoming series of papers . the paper is structured as follows . in section 1 we recall the axiomatic framework for diagram algebras due to enyang , goodman , and graber . we focus on the construction of murphy bases of these diagram algebras which are encoded via the branching graph . in section 2 we consider the restriction of a cell module down the tower of algebras ; we construct filtrations of these restricted modules which will be essential in sections 3 and 4 . in section 3 we recall the definitions of jucys  murphy elements and seminormal forms of diagram algebras , following goodman  graber and mathas . we use the results of section 2 in order to improve upon these results ( these stronger statements will then be used in section 4 ) . section 4 contains the main results of the paper . given a cell module for a diagram algebra , we examine the action of certain young subalgebras on the murphy basis . we hence construct integral bases for the skew modules which are indexed by skew tableaux . the authors are grateful for the financial support received from the royal commission for the exhibition of 1851 and epsrc grant ep / l01078x/1 .","summary":"we provide an explicit construction of skew cell modules for diagram algebras .","abstract":"we provide an explicit construction of skew cell modules for diagram algebras ."}
{"article_id":"astro-ph9702239","section_id":"i","document":"oxygen burning in a convective shell is one of the last , dominant burning stages before core collapse of a massive star . its importance lies not just in the nucleosynthesis occurring by the nuclear burning itself , but also in the structure left by convection which might affect subsequent supernova evolution ( @xcite , @xcite , @xcite ) . for instance , the division between the proto - neutron star and supernova ejecta , known as the  mass cut , \" is expected to appear somewhere near the `` edge '' of the convective zone . convection generated perturbations in density , velocity , entropy , and y@xmath2 ( or neutron excess @xmath3 ) could alter the nature of core collapse as compared to spherically symmetric , one - dimensional calculations ( @xcite , @xcite , @xcite , @xcite ; see @xcite for extensive discussion and references ) . the bottom of the oxygen convective shell is expected to be the region where explosive nucleosynthesis occurs . most iron peak isotopes are thought to be produced here . the most important individual product of this region would be @xmath4ni , which is responsible for powering supernova light curves and ( after decay to co ) is the source of the 847 and 1208 kev @xmath5-ray lines seen in sn1987a ( @xcite , @xcite , @xcite , @xcite , @xcite ) . the explosive o- and si - burning which produces @xmath4ni also produces other @xmath5-ray emitting radionuclides such as @xmath6ti and @xmath7ni ( @xmath7co ) . perturbations in y@xmath2 , density , and temperature , left by convective o - burning , will _ greatly _ affect the relative abundances of individual isotopes , due to the sensitivity of nuclear statistical equilibrium ( nse ) and quasiequilibrium to these parameters ( @xcite , @xcite , @xcite ) . studies of nse have shown a neutron excess @xmath8 best recreates the relative abundances of iron - peak nuclei , with slight changes in @xmath3 altering relative abundances by large factors . a change in @xmath9 from 0.499 to 0.4995 changes the relative abundance of @xmath7fe to @xmath4fe by roughly a factor of 2 . we know from observations of sn 1987a that significant mixing of newly synthesized material thoughout the envelope must occur ( @xcite , @xcite , @xcite , @xcite ) . the only physical explanation that agrees with our understanding of massive star evolution is that significant density perturbations must appear at the interfaces of composition discontinuities and these result in rayleigh - taylor ( and richtmeyer - meshkov ) mixing in the ejecta ( @xcite , @xcite ) . this hypothesis has been tested with various fluid hydrodynamics codes by adopting ad hoc distributions of initial perturbation amplitude and length scale ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . on the whole , calculated @xmath4ni velocities were in agreement with observations for the bulk of the matter , but not for the highest speeds . not enough ni could be mixed to velocities as high as 3,000 km @xmath10 , which the observations imply . we believe that convective shell o - burning has a major effect on all of these phenomena .    in almost all hydrostatic stellar models , convection is treated by enforcing an adiabatic gradient , or better , some version of mixing length theory ( @xcite , @xcite , @xcite ; hereafter mlt ) . the basic tenets of mlt are that ( 1 ) convection occurring deep in stellar interiors results in an almost completely adiabatic structure , and that ( 2 ) excess energy flux ( above that of radiative diffusion at the adiabatic gradient ) is a function of the local superadiabatic gradient . the mixing of chemical species is approximated either by complete homogenization , or the use of a radial diffusion equation ( when mlt formalism is applied ) . the concept of penetrative convection ( overshoot from convective regions into adjacent radiative zones ) is not a natural outcome of mlt , due to the local nature of the theory ( @xcite ) . various ad hoc approaches to overshoot have been applied to stellar evolution ; in most the overshoot distance is scaled to some multiple of the local pressure scale height . multi - dimensions simulations of turbulent compressible convection have revealed both the successes and shortcomings of mlt . one dynamical feature of convection , which has been present in every multi - dimensional simulation , is the asymmetry between up and down motions . upward moving elements are typically broader in extent and slower than downward moving elements , although the degree of asymmetry is very dependent on the density contrast of the unstable region ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . as density contrast increases , so does the asymmetry ( @xcite ) . pressure fluctuations ( the compressible nature of the fluid ) can assist in driving descending motions , lead to buoyancy braking in ascending motions , and satisfy a bernoulli relation with horizontal velocities ( @xcite ) . the basic notion of buoyancy driven motions throughout most of the convective zone has been upheld , but at the boundaries , dissipation and compressibilty are the dominant factors in the flow . in the more complex case , in which convective regions have nuclear timescales comparable to the mixing timescale , a kinetic ( rather than steady state ) description becomes crucial . there are hints that the basic tenet in mlt regarding _ energy _ flux still holds true in multidimensional simulations . in both 2- and 3-d  large eddy \" simulations , in which a sub - grid scale turbulence formalism ( sgs ) has been applied , vertical motions have been seen to breakup in less than the simulation dimension ( @xcite , @xcite , @xcite , @xcite ) . in fact , the autocorrelation of vertical velocity along vertical direction is a function of the difference in logarithmic pressure , but symmetric with a similar full width - half maximum ( fwhm ) across the entire computational regime ( @xcite , @xcite ) . this means that the convective flux should be a function of the local pressure scale height . amazingly , vertical velocities seem to be correlated over about one pressure scale height ( @xcite ) , which is the range used for the past 30 years in stellar evolution models . however , even these positive indications are faulty . there seems to be a numerical dependence to these results : the correlation is no longer constant over an entire grid when the aspect ratio is increased ( @xcite ) and the correlation length is dependent on the magnitude of the sgs turbulence included in the model . indeed , in models where sgs turbulent viscosity has been omitted in favor of ordinary dynamical viscosity , no breakup of vertical motions has been observed ( @xcite , @xcite ) . penetrative convection has also been modelled in multi - dimensions . in what follows , we will use a nomenclature in which _ penetration _ refers to mixing ( in formally stable zones ) that is efficient enough to weaken thermal stratification . otherwise , edge mixing is referred to as _ overshooting _ ( @xcite ) . fast downward plumes are responsible for extensive mixing of composition and energy from the unstable region into the lower stable region through gravity waves ( @xcite ) , although a rapid increase in the stability of adjacent regions reduces the ability of plumes to penetrate ( @xcite ) . composition is advected across the stability boundary to a `` penetration depth , '' on the timescale for plume transit . in the case of true penetration , the region adjacent to the convective zone can be described by two layers : ( 1 ) where peclet number @xmath11 , adiabatic structure exists , and motions decelerate due to buoyancy breaking and ( 2 ) where peclet number @xmath12 , temperature perturbations damp out from radiative damping ( @xcite , @xcite ) . note that the peclet number is the ratio of the velocity scale @xmath13 times the length scale @xmath14 , to the thermal conductivity @xmath15 , @xmath16 , and a large peclet number implies ineffective thermal energy transport relative to mass transport ; see @xcite . our case , in which cooling is by @xmath17 emission instead of radiative diffusion , does not seem to have been considered by the hydrodynamic community . shell oxygen burning differs from the canonical problem addressed by most previous multidimensional convection simulations . the convective regions of zams a and f stars ( @xcite , @xcite ) and generic convection with ionization ( @xcite ) are most comparable . however , such convective regions do not contain nuclear energy sources and neutrino energy sinks within the flow . it seems that local thermal effects , such as heating from ionization , can significantly affect convective flows . the treatment of convection affects neutrino cooled regions , since the efficiency of convection determines which adiabat a convective region can achieve . this in turn feeds back upon the neutrino emission ( @xcite , @xcite ) .    in previous work ( @xcite , @xcite ) , we used our piecewise parabolic method fluid dynamics code prometheus ( @xcite ) to begin an examination of the problem of the evolution of a o - burning shell in a 20 m@xmath0 , z = 0.007 star , prior to core collapse . significant density perturbations ( of the order of 7% ) were found to occur at the boundaries of the convective region , along with non - uniform mixing of chemical species within the shell . here , we present more extensive results of models of the same star , with different boundary conditions , grid sizes , and grid resolutions , and for a longer evolutionary time . we compare results for different boundary conditions to see the effects on the dynamics ( @xcite ) . computational domains are varied in order to see the effects of sound waves on the system . calculations with different grid resolutions are performed to estimate the role of scale lengths on the problem . a detailed analysis of the simulations and their astronomical implications is given .","summary":"by direct hydrodynamic simulation , using the piecewise parabolic method ( ppm ) code prometheus , we study the properties of a convective oxygen burning shell in a sn 1987a progenitor star ( 20 m ) prior to collapse . the convection is too heterogeneous and dynamic to be well approximated by one - dimensional diffusion - like algorithms which have previously been used for this epoch . density perturbations ( up to 8 % ) occur at the  edges \" of the convective zone and are the result of gravity waves generated by interaction of penetrating flows into the stable region . runs of different resolution , and angular extent , were performed to test the robustness of these simulations .","abstract":"by direct hydrodynamic simulation , using the piecewise parabolic method ( ppm ) code prometheus , we study the properties of a convective oxygen burning shell in a sn 1987a progenitor star ( 20 m ) prior to collapse . the convection is too heterogeneous and dynamic to be well approximated by one - dimensional diffusion - like algorithms which have previously been used for this epoch . qualitatively new phenomena are seen .    the simulations are two - dimensional , with good resolution in radius and angle , and used a large ( 90-degree ) slice centered at the equator . the microphysics and the initial model were carefully treated . many of the qualitative features of previous multi - dimensional simulations of convection are seen , including large kinetic and acoustic energy fluxes , which are not accounted for by mixing length theory . small but significant amounts ofc are mixed non - uniformly into the oxygen burning convection zone , resulting in hot spots of nuclear energy production which are more than an order of magnitude more energetic than the oxygen flame itself . density perturbations ( up to 8 % ) occur at the  edges \" of the convective zone and are the result of gravity waves generated by interaction of penetrating flows into the stable region . perturbations of temperature and y ( or neutron excess ) at the base of the convective zone are of sufficient magnitude to create angular inhomogeneities in explosive nucleosynthesis products , and need to be included in quantitative estimates of yields . combined with the plume - like velocity structure arising from convection , the perturbations will contribute to the mixing ofni throughout supernovae envelopes . runs of different resolution , and angular extent , were performed to test the robustness of these simulations ."}
{"article_id":"astro-ph9702239","section_id":"c","document":"convection in oxygen shells of massive stars is not driven in quite the same manner as convection in stellar envelopes or terrestrial phenomena . the equations to be solved look much like those of other compressible convection simulations , @xmath33 where @xmath34 is given by , @xmath35 and @xmath36 is the radiative conductivity . notice , however , that there are source and sink terms for nuclear energy release and neutrino losses . thus , we must solve a set of continuity equations for composition as well , @xmath37 where , except for the factor of @xmath22 , the right side is a system of reaction network equations . this means that convection in oxygen shells involves energy production and loss which is directly in the flow .    to our knowledge , the most physically similar system to have been examined previously with multi - dimensional simulations is the core helium flash ( @xcite , @xcite , @xcite ) . the oxygen shell differs in that ( 1 ) the reaction rates involved have even more extreme temperature dependencies ( roughly @xmath38 ) , ( 2 ) the equation of state is dominated by radiation and electron thermal pressures rather than degeneracy and thermal pressures , and ( 3 ) convection is driven by the competition between heating by nuclear burning and cooling by expansion and by neutrino emission ( rather than cooling by radiative diffusion , as is the normal assumption in convective systems ) . the timescales of the problem portray this connection between convective mixing and energetics . figure 1 shows the various timescales estimated from the mlt solution from the initial one - dimensional , hydrostatic stellar evolution model . the upper plot shows that the convective turnover time across a given radial grid zone , @xmath39 is very much shorter than either the nuclear energy timescale , @xmath40 where @xmath41 is the thermal component of the specific energy , or the kelvin - helmholtz timescale , @xmath42 where @xmath43 if the gravitational potential energy and @xmath44 the luminosity ( radiative and convective ) . this means that local convective response is fast enough to control heating and cooling . however , using mlt velocities , the integrated convective turnover time across the whole oxygen convective region is long ( 10@xmath24 seconds , or 550 sound travel times ) , so that the time to move material across the whole region is approaching both the nuclear timescale at the base of the convective shell ( 10@xmath45 seconds ) , and the neutrino kelvin - helmholtz timescale ( 10@xmath46 seconds ) through the oxygen shell . this implies heterogeneity and significant nonspherical variation . the timescale for energy flow by radiative diffusion , @xmath47 is orders of magnitude larger than all of these timescales , and , thus , is not important in this stage of evolution . for this reason , we need not calculate the effects of radiative diffusion in these simulations . [ fig.1 ]    the lower plot shows the various abundance timescales , for nucleus @xmath48 , where @xmath49 the burning timescale of oxygen is of the same order as the fastest convective timescale across a given grid zone , but orders of magnitude less than the turnover time across the convective region . notice that many other nuclei have short timescales as well . the magnitudes of these timescales lead us to several conclusions . first , _ composition will not be homogeneous . _ this will feed back into the structure via the energy source terms . second , _ the system has strong fluctuations in space and in time . _ because the thermal energy timescale is of the order of both the kelvin - helmholtz timescale and full convective mixing timescale , the dynamics of convection and evolution of the star will be strongly varying . this hardly satisfies the requirements of mlt which mandate that the dynamics of convection reach a statistical steady state . the energy supply changes as fast as convection can move energy across the region .      even at the beginning of our simulations , we see that mlt does not correctly represent the dynamics of convection in oxygen shells . because the fluid transport timescales are initially longer than the oxygen burning time in the flame zone , the oxygen flame undergoes a initial thermal pulse , much like an agb star ( but faster ) , and a sound wave is emitted . this sound wave takes 18 seconds to cross the oxygen shell and effectively erases the mlt velocity field which we imposed initially . this allows the shell to establish dynamical structures from very low noise levels and reduces any worry that the initial perturbations somehow determine the final dynamical state . this pulse is not due to a faulty mapping of the initial model onto the 2d grid , but to an inconsistency between the assumed mlt physics of the convective shell , and the actual 2d hydrodynamics with heating and cooling . it is due to a thermal inconsistency involving assumed and actual convective cooling , not an error in overall hydrostatic balance . [ fig.2 ]    figure  2 shows snapshots of velocity evolution after times of 100 , 200 , 300 , and 400 seconds . before about 100 seconds , the dynamics are dominated by rising and descending plumes , which are driven by simple buoyancy . small eddies ( scale length @xmath20 pressure scale height ) form at the base of the shell and form / merge like those in most two dimensional convection simulations ( @xcite ) . by 200 seconds ( 11 sound travel times across the original oxygen convective zone ) , the region is fully convective and buoyancy braking is readily apparent as a retarding force to upward motions , causing swirls . a large eddy dominates the upper two - thirds of the convective region , and one eddy dominates in the lower third . at 300 seconds , a single downward plume spans the upper 2/3 of the zone , and buoyancy still dominates the flow dynamics . by 400 seconds , buoyancy braking affects the dynamics not only at the boundaries , but also throughout the zone . these simulations exhibit many of the generic traits of multidimensional compressible turbulent convection simulations . a comparison of these vortices with other two - dimensional convection simulations ( @xcite , @xcite ) shows that they are qualitatively similar in dimension ( length / width @xmath50 ) , and that a few large eddies dominate . @xcite showed that this is to be expected , as two - dimensional simulations exhibit the merging of counterrotating eddies into larger ones . earlier in our simulations , the lower @xmath51 of the domain was populated by small eddies . velocity magnitudes in these eddies are typically at mach numbers of 0.1 to 0.2 , which is more than a factor of ten higher than mlt would predict . the spatial extent of these eddies is on the order of 3 pressure scale heights . the simulation at this epoch is still time dependent so that its structures should not be compared to the mixing length used in mlt . only the radial velocity correlation length of a statistical steady state ( @xcite , @xcite , @xcite ) should be used as some measure of a mixing length . as we explain later , the dynamical coupling of the energy generation to the kinematical mixing , as well as the limited number of convective turnover times involved in the entire stage of shell oxygen burning , prevents a statistical steady state from ever being attained in this stellar evolution stage .    in light of these results , _ we view the details of one dimensional stellar evolution calculations of the structure of the oxygen shell with skepticism . _ the smooth , steady flow assumed in those simulations appears to be a phenomenon which does not survive in more realistic calculations . the convective energy fluxes in this stage show both similarities and differences in comparison to previous compressible convection simulations . figure 3 shows the azimuthally averaged enthalpy , kinetic , acoustic , and radiative fluxes after 400 seconds . the top panel shows the inner part of the o convective shell ; the bottom panel gives the outer part , on different scales . notice that the fluxes in the outer region are smaller in amplitude by more than a factor of 20 . the enthalpy flux pictured here is _ negative _ through much of the schwarzschild unstable region ; mlt assumes it is positive . the formal convective boundaries are indicated as vertical dashed lines . the convective fluxes extend beyond these limits . [ fig.3 ]    as in previous convection simulations , we find a non - zero flux of energy to be carried in the form of sound waves , @xmath52 and kinetic energy , @xmath53 mlt conventions require that the net radial kinetic energy flux be zero and that pressure equilibrium is always in effect . however , compressible convection simulations ( @xcite , @xcite , @xcite , @xcite , @xcite ) , reveal a finite kinetic energy flux due to cool , dense material being compressed into plumes . since these plumes occupy a filling fraction at constant radius which conserves mass flux relative to slower , upward moving material , the kinetic energy flux must be nonzero . in this particular model , the kinetic energy flux can reach as much as 20 % of the enthalpy flux , which is less than the peak values of 60 % seen in previous `` box '' simulations . one explanation for this difference might be that simulations of convection in a box are governed by the competition between convective instability and viscous dissipation by radiative ( or thermal ) diffusion . here , convective motion competes with neutrino losses , as well as numerical dissipation . the estimated radiative flux is at least 4 orders of magnitude less than the enthalpy flux at all points in the simulation . this fact was emphasized in early stellar evolution studies of massive stars ( @xcite ) , where mlt theory yielded the result that the luminosity at the boundary of such convective zones would be zero . [ fig.4 ]    figure 4 shows the enthalpy and kinetic fluxes and their sum at the top , middle , and bottom of the convective shell as a function of time . the dot - dashed curve is the kinetic flux , the dashed curve the convective flux , and the solid curve their sum . at no time during the simulation is the total luminosity equal to zero in the formally stable region . we note in passing that it is fortunate that neutrino losses govern the extent of this convection , since the numerical dissipation of the ppm method at this resolution ( @xcite ) , while yielding effective reynolds numbers ranging from 10@xmath54 at the base of the shell to 10@xmath55 at the top , also imply prandtl numbers ranging from 200 at the base to 1000 at the top . the small numerical dissipation is still larger than the tiny radiative dissipation . this suggests that we would need at least a tenfold increase in resolution before the radiative diffusion could be quantitatively evaluated , if at this tiny level it were still important . an important component of the energy flow is the acoustic flux . this quantity measures the energy carried in the form of sound waves and is relevant to the kinetic energy flux in flows of significant mach number ( @xcite ) . in places the acoustic flux is a significant fraction of the kinetic flux . thus , _ any attempt to model systems such as these with implicit or anelastic methods will miss the significant contribution to energy transport by sound waves_.    the enthalpy flux distribution is negative through much of the schwarzschild unstable domain . this is because the neutrino losses are dominant globally , causing contraction . after the first sound crossing time , the simulation adjusts to a state representative of the physics involved . the negative enthalpy flux implies that the energy arising from the oxygen burning flame zone is insufficient to suppport the structure predicted by mlt , and energy is being drawn from above . neutrino - cooled matter is contracting down on the flame zone . we find that there is a time dependance in many quantities throughout the duration of the simulation . for example , significant deviations in flux about an average value are seen in figure  4 . however , there may be a trend toward to a roughly constant amplitude for each of the three regions after 200s . there are several reasons for the time variability in the simulation , and for it to continue until the time of core collapse . first of these are the similarities of both the nuclear and convective turnover timescales to the time left before core collapse . we estimate that there should be no more than 12 turnovers from the birth of the convective oxygen shell until core collapse , as estimated from our one - dimensional model . previous box models of convection certainly required more turnovers before reaching a time - independent state ( @xcite , @xcite ) . the other reason for time dependence in the simulation has to do with the density contrast and the aspect ratio . previous work stressed that for density contrasts of 21 , a minimum aspect ratio ( horizontal /vertical dimensions ) of about 3 was necessary for a static state to be reached in 80 turnover timescales ( @xcite ) . in fact , since our simulation covers such a large spherical geometric area , the aspect ratio ranges from @xmath56 at the base to @xmath57 at the upper edge of the convective zone . even for a @xmath58 simulation in @xmath59 and @xmath60 , rather than @xmath59 and @xmath61 , the ratio is only four times this value . simulations still should be performed to see if these trends still hold in arbitrary geometries ( cylindrical + spherical ) as the effects of adiabatic cooling on individual mass elements is more enhanced in a curvilinear coordinate system than a cartesian system . nevertheless , assuming the trends from the cartesian simulations roughly hold true in a spherical system , and that a density contrast of about 200 exists across the convective zone , and the values of our aspect ratios , our simulations suggest that _ we can hardly expect this convective oxygen burning shell to ever reach a dynamical steady state before core collapse _ and that _ the application of mixing length theory in convective shell oxygen burning is unjustified . _      we now consider the presence of overshoot in these calculations . the structure below and above the unstable region is not changed much from the initial state , hence the designation of _ overshoot _ and not _ penetration_. as figure 3 showed , thermal energy is transported out of the stable region while kinetic energy is transported into the region , apparently not in quantities sufficient to alter the structure in these regions . however , the structure of the temperature and density at the lower boundary is significantly altered . most of this has to do with the mixing timescale being slower than the local oxygen burning timescale , in which case the oxygen is depleted and y@xmath2 drops locally due to electron capture on the oxygen burning products . this , in turn causes changes in the entropy and composition , which then feeds back into the temperature and density . [ fig.5 ]    _ while these mass motions ( reynolds stresses ) are not sufficient to alter the stellar structure significantly , they do allow mixing of composition from the convectively stable region into the unstable region . _ figure 5 shows the composition profiles of @xmath1c . the @xmath1c abundance in this oxygen - burning convective shell is purely the result of undershoot from the upper , @xmath1c - rich regions . a blob of @xmath62 rich matter sinks down through the oxygen shell , finally halted by its own rapid burning . this is a new effect , not seen in one - dimensional simulations . we will discuss the consequences below .    unlike the box simulations ( @xcite , @xcite ) , we find that overshoot is more vigorous at the upper rather than the lower edge of the unstable region . this seems to be related to the relative stability of our upper and lower zones ( @xcite ) . the presence of a nuclear shell at the bottom of the zone leads to a value of @xmath5 which changes faster as a function of position than it does at the top of the shell . this means that the @xmath63 stability of the bottom of the zone is higher than the top of the convective zone . the early appearance of @xmath5-lines from decay of @xmath4ni , as well as its effects on the light curve of sn 1987a , left theorists with the idea that mixing occurred , so that density and/or velocity perturbations must exist in the progenitor models ( @xcite , @xcite , @xcite , @xcite ) . as hydrodynamical simulations have shown ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) , these perturbations facilitate the mixing of @xmath4ni toward the surface through rayleigh - taylor instabilities . the exact details of the perturbations , such as scale distribution and amplitude , have not been self consistently examined , but linear analysis indicates that instabilities are likely at composition interfaces ( @xcite , @xcite ) .    because of the behavior of the equation of state , as seen in its linearized form : @xmath64 the nonspherical perturbations are correlated , and show a strong temperature dependence due to the radiation pressure . [ fig.6 ]    figure  6 shows the different contributions to the pressure , as a function of radius . electron degeneracy and thermal ion pressure contribute little to the total . roughly 60 % is from thermal electrons , while almost all of the remaining 40 % is radiation pressure . this simplifies the above expression to one of the form : @xmath65 this expression is a good description of the fluctuations in the flows . [ fig.7 ]    in figure  7 , we show the density perturbation structure in and around the oxygen shell at the end of the calculation . the perturbation contours range over @xmath66 . the largest perturbations are in the flame zone ( the inner convective boundary ) , and at the outer convective boundary , as may be seen in the right - hand panel . notice that the thin flame zone , which lies near the leftmost arc in the left panel , has large perturbations in its small physical volume . the perturbations at the top of the convective zone have a much larger length scale , although their angular scales are similar to those in the flame zone . the `` perturbation amplitudes '' implied by the convection in the oxygen shell easily exceed the minimum needed to give significant mixing in supernova ejecta models ( i.e. a few percent ) . not surprisingly , the highest amplitude perturbations are found at the point where the linear analysis indicated : at the composition interfaces . this may be sufficient to explain the mixing of most of the @xmath4ni observed in sn1987a , but apparently _ not _ that at highest velocity ( @xmath67 3,000 @xmath68 ; see @xcite , @xcite ) . the production of this high velocity material may be related to the passage of the explosion shock , and explosive oxygen burning in this inhomogeneous shell ( @xcite , bazan and arnett , in preparation ) . it might also be due to mixing outward by overshoot of @xmath69 just prior to explosion ( @xcite ) . this would require very high temperature oxygen burning ; the silicon burning core has too large a neutron excess to produce @xmath69 . we have seen no evidence for such high temperature oxygen burning ; probably the best chance would be at the very onset of core collapse . [ fig.8 ]    as with previous convection simulations ( @xcite , @xcite ) , we conclude that gravity waves are responsible for the generation of the perturbations . a fourier analysis of the power in vertical velocities at different frequencies @xmath70 , was made for the time interval from 200 to 400s . figure  8 shows the power as a function of frequency just above the convective zone ( top panel ) , in the middle of the zone , and just below the convective zone ( bottom panel ) ; compare with figure  4 of @xcite . the solid , dashed , and dot - dashed lines were taken at @xmath71 of the angular domain . in the lower panel , we see the signature of a complex series of modes . the local brunt - vaisala frequency is @xmath72 , which is much higher than most of the power . as did @xcite , we interpret this as a time variation due to internal gravity waves , recalling that such waves have frequencies less than the buoyancy frequency . however , just above the convective zone ( top panel ) , we find that the power is also at frequencies just below the local brunt - vaisala frequency , @xmath73 . the level of power here is larger , unlike @xcite , where the power above the convection zone was smaller than the power just below the convection zone . the difference seems to be in the nature of the driving and damping . in our simulation , the driving energy flux from the oxygen burning flame zone varies by factors of two at the base of the schwarzschild unstable region . in addition , the energy release rate in the @xmath74-rich plume exceeds that from the oxygen flame . it has already been inferred that g - mode waves of high radial wave - number can appear at the interfaces between convectively stable and unstable regions ( @xcite , @xcite ) , and in this case we seem to have preferential driving of these modes .    while the appearance of g - mode wave interactions in this simulation is consistent other studies ( @xcite , @xcite ) , the details are different . thermal diffusion is not present in this calculation , so that any damping of linear internal waves is the result of numerical dissipation ( shocks ) . pressure waves generated within the convective zone should have a constant horizontal wavenumber as their source . these internal waves are known to undergo internal reflection when n(r ) = @xmath75 , where n(r ) is the brunt - vissala frequency at radius @xmath59 ( @xcite ) . we note that the detailed coupling of acoustic and gravity waves to the convection also depends on boundary conditions ( @xcite ) . the greatest power in the middle of the convective zone occurs at zero frequency ( center panel ) , as found by @xcite . however , despite our significantly better numerical resolution , our peaks are less well developed . we attribute this to the fact that our convection is much further from statistical relaxation . this is a physical feature of the epoch of oxygen shell burning , not a limitation of the simulation , as our previous discussion shows . [ fig.9 ]    figure  9 shows the power spectrum of density perturbations versus angular separations @xmath76 , at 400s . three radii are indicated : a solid line indicates a radius above the convective zone , a dot - dashed line the convective zone , and a dashed line a radius below the convective zone . there is a fall off at low angular separations , @xmath77 . the zoning is much finer than that , and will allow clumping on a much smaller scale ( @xmath78 ) . this fall off could be taken as a measure of the scale length of the perturbations to eventually be compared with observations , and as such is an important quantity , but two dimensional simulations such as these are biased . because the vortices are pinned on the grid  their angular momentum vectors stay perpendicular to the plane of computation  cascading to smaller scales is inhibited . thus we expect clumping down _ at least _ to scales this size ; this issue must be addressed with fully three dimensional simulations . we mentioned that the asymmetry in the upflows and downflows has direct consequences for convective mixing . in figure  6 , we showed a time history of @xmath1c abundance . in the initial model , @xmath1c exists at the 10@xmath79 abundance level in the oxygen convective zone , and up to the 0.4 level above the zone . as rising material overshoots into the high @xmath1c abundance area , @xmath1c - rich matter is entrained . eventually , cooling causes fast moving downward plumes to mix @xmath1c deep into the convective zone . these fingers terminate at the point where @xmath1c burns faster than it can be advected . nuclear energy hot spots appear at these points , and by the end of the simulation the energy output from these hotspots are a factor of 30 higher than the oxygen flame zone itself . even @xmath24he , which exists still farther away from the mlt convection boundary , is brought down into the convective shell , albeit at a low level . [ fig.10 ]    an interesting phenomenon is the mixing of higher y@xmath2 into the convective shell . figure  10 shows the perturbation structure of the neutron excess @xmath80 at the end of the calculation . the non - uniform distribution at both the upper and lower boundaries is readily apparent . since the ` mass cut ' between the proto - neutron star and supernova ejecta is expected to occur within this convective zone , the presence of a non - uniform distribution of y@xmath2 may alter core collapse ( @xcite , @xcite ) . a larger effect could be from the coupling of the electron capture with hydrodynamics , which would change the entropy and the size of the core ( @xcite , @xcite ) . furthermore , once the delineation between neutron star and ejecta is made , explosive nucleosynthesis in the ejecta will reflect the distribution of neutron excess @xmath3 . the differences of @xmath81 that we find here will radically alter the details of the quasi - statistical equilibrium ( qse ) nuclear burning process ( @xcite , @xcite , @xcite ) so that a non - uniform distribution of isotopes is produced . this may be a welcome result , as one dimensional models of explosive burning in massive stars have usually produced too many neutron - rich isotopes ( @xcite , @xcite ) , unless the mass cut was carefully chosen ( e.g. , @xcite ) . most significantly , this extensive mixing by plumes may indicate that our concept of convection is too narrow to properly describe the neutrino cooled stages of massive star evolution . if this stage is so drastically altered , why not earlier stages as well ? we have found that the results of our two - dimensional computations are inconsistent with 1d hydrostatic mlt results in many ways . as yet the evolution has proceeded about 10  % of the time from oxygen shell ignition to core collapse ( for the 1d evolution of this initial model ) . what can we infer about 2d effects on evolution ?    in 1d models , under mlt conventions , the o - burning region is wholly contained within the convective zone . this determines the evolution : the convective region burns until it changes its fuel to ashes , and there is little ingestion of new fuel or loss of ashes . thus , at the exhaustion of fuel in the convective region , this layer of ashes is added to the underlying core . contraction follows , and a new shell generally ignites just above the old , now defunct convective shell , and the process is repeated . this behavior has long been known ( @xcite ) ; see @xcite ,  10.1 for details . @xcite noted its possibly non - physical nature , contrasted it to the case of a radiatively cooled shell , and also considered an alternative in which the convective region both lost ashes and ingested new fuel , so that it burned out in mass coordinate as a `` wave . '' however , we are aware of no published evolutionary sequences of neutrino cooled shells except those calculated with the implicit assumption that the first picture is correct . this distinction involves the nature of the _ boundaries _ of the convective region .    in these 2d simulations , within the first 25 seconds of evolution time , the flame zone ` flashed ' and changed its thermodynamic state from convective instability to stability , thereby removing itself from the convective zone , as mlt would define it . the resulting sound wave does not develop into a shock as it moves down the density gradient . no structure changes occur by the passage of this wave . [ fig.11 ]    the upper panel of figure  11 shows the azimuthally averaged values of energy production , temperature , density , and convective speed , as a function of mass coordinate , for the initial and final state in this simulation ( that is , at 0 and 400s ) . the variables of the initial model are represented by solid lines ; those of the final model by dashed and by dotted lines . the most obvious difference is in the convective speed . in the initial ( mlt ) model , the velocities are significant only in the convective oxygen burning shell and the convective helium burning shell . they are separated by a stable region containing c , ne , mg , and mostly o. in the final model , the convective speed is larger , and does not go to zero in this intermediate region . while in mlt the convective speed is a slowly varying quantity , in 2d simulations it fluctuates strongly . this additional mixing has affected the composition structure , which is shown in the lower panel of figure  11 . this is especially noticeable in the range @xmath82 . it is interesting that the he burning shell , which is broadened by radiative diffusion , widens more due to convection . a second important difference is in the thin flame zone , which is strongly compressed in the mass coordinate , and therefore less obvious in figure  11 . consider the temperature and density structure . just above the inner boundary , the temperature has a small hole and the density a corresponding peak . at first sight , the run of both variables is almost idential between the initial and final models , but in fact the _ boundary _ has changed . the steep abundance gradient below the oxygen flame zone is becoming shallower , and the oxygen flame is no longer in the most convectively active region . similarly , the outer edge of the temperature `` hole '' is smoothed out . [ fig.12 ]    figure  12 shows a closeup of the heating rate in the flame region . there is one velocity vector for each 25 zones . the 20 density contours are logarithmically spaced between @xmath83 and @xmath84 . the oxygen burning shell is burning at @xmath85 , and so is barely discernable as an inner ledge . the oxygen burning is not uniform , having several peaks . most of the energy release comes from carbon and neon burning , as blobs having @xmath86 of a few percent burn vigorously . these conditions ( @xmath87 and @xmath88 ) , occurring on a hydrodynamic time scale , are typical of `` explosive nucleosynthesis '' of carbon and neon . notice that the `` hot spots '' correspond to downward moving matter . the width of the whole flame zone is about 5 times wider that of just @xmath89 , and much more uneven . the velocities in the fastest burning zones ( both oxygen and carbon ) are relatively small , so the ashes are not immediately swept out into the most active convection . this situation is drastically different from the conventional picture suggested by 1d models . it causes worry that the 2d evolution would have diverged from the 1d at a time even earlier than that for our initial model . we are currently attempting to push this sequence to later times ( core collapse ) .      two dimensional simulations such as these clearly are more realistic than one dimensional simulations with ad hoc prescriptions for convection and mixing . hydrodynamic flow is simulated self - consistently , and heterogeneity in space and time may be examined . nevertheless , the assumed `` rotational '' symmetry ( not presumed due to rotation but simply enforced by limitations in computational resources ) , is simply not valid . simulation of a 3d sector , for example by extending the 460x128 by 64 zones in @xmath60 , is feasible on a massively parallel supercomputer . we are currently continuing this calculation with a pvm version of prometheus , and will to extend the simulations to three dimensions by the time of publication . it is unclear at this time what physical state will be described by a three dimensional simulation . it is well known that the energy cascade in two dimensional turbulence ( lower to higher scales ) is opposite that in three dimensions ( higher to lower scales ) . this effect can be seen quite easily in our and other ppm - based simulations ( @xcite ) , where small eddies disappear in favor of larger scale eddies . a recent comparison of two- and three - dimensional simulations of convection in a proto - neutron star ( @xcite ) also show an increase of small scale features in the three - dimensional simulation relative to the two - dimensional simulations , with an overall lower kinetic energy in the three - dimensional case . thus , the overall convective iand composition fields are expected to be more homogeneous in a three - dimensional case .    however , the effects of a third dimension on overshoot are not at all clear . this is critical for the oxygen shell evolution in light of what we mentioned previously concerning carbon brought into the oxygen shell by overshoot and the inhomogeneous energy release . on the one hand , we know that overshoot is the result of individual plumes creating gravity waves at convective stability@xmath90instability boundaries . such plumes are known to be more energetic in three dimensions than two due to a reduced drag effect ( two dimensional ` plumes ' are tori in realty ) if starting from the same initial conditions . we know , though , that the initial underdensity which characterizes a plume is a function of the kinetic environment , which , from the supernova simulation mentioned above and turbulence studies , should be reduced from its two dimensonal analog . just which effect will predominate requires a three dimensional simulation . more insight can be obtained from laser experiments for related hydrodynamic problems , where rayleigh - taylor instabilities in 2d and 3d are examined experimentally within the context of inertial confinement fusion ( @xcite ) . testing of prometheus against icf codes and nova laser experiments is beginning ( @xcite ) .","summary":"qualitatively new phenomena are seen .    the simulations are two - dimensional , with good resolution in radius and angle , and used a large ( 90-degree ) slice centered at the equator . the microphysics and the initial model were carefully treated . small but significant amounts ofc are mixed non - uniformly into the oxygen burning convection zone , resulting in hot spots of nuclear energy production which are more than an order of magnitude more energetic than the oxygen flame itself . perturbations of temperature and y ( or neutron excess ) at the base of the convective zone are of sufficient magnitude to create angular inhomogeneities in explosive nucleosynthesis products , and need to be included in quantitative estimates of yields . combined with the plume - like velocity structure arising from convection , the perturbations will contribute to the mixing ofni throughout supernovae envelopes .","abstract":"by direct hydrodynamic simulation , using the piecewise parabolic method ( ppm ) code prometheus , we study the properties of a convective oxygen burning shell in a sn 1987a progenitor star ( 20 m ) prior to collapse . the convection is too heterogeneous and dynamic to be well approximated by one - dimensional diffusion - like algorithms which have previously been used for this epoch . qualitatively new phenomena are seen .    the simulations are two - dimensional , with good resolution in radius and angle , and used a large ( 90-degree ) slice centered at the equator . the microphysics and the initial model were carefully treated . many of the qualitative features of previous multi - dimensional simulations of convection are seen , including large kinetic and acoustic energy fluxes , which are not accounted for by mixing length theory . small but significant amounts ofc are mixed non - uniformly into the oxygen burning convection zone , resulting in hot spots of nuclear energy production which are more than an order of magnitude more energetic than the oxygen flame itself . density perturbations ( up to 8 % ) occur at the  edges \" of the convective zone and are the result of gravity waves generated by interaction of penetrating flows into the stable region . perturbations of temperature and y ( or neutron excess ) at the base of the convective zone are of sufficient magnitude to create angular inhomogeneities in explosive nucleosynthesis products , and need to be included in quantitative estimates of yields . combined with the plume - like velocity structure arising from convection , the perturbations will contribute to the mixing ofni throughout supernovae envelopes . runs of different resolution , and angular extent , were performed to test the robustness of these simulations ."}
{"article_id":"1210.1088","section_id":"i","document":"the notion of quantum entanglement is one of the main current research subjects in quantum information theory as well as quantum physics , where the fundamental question is , of course , how to distinguish entangled states from separable ones @xcite . one of useful criteria is to use the notion of partial transpose , as it was observed by choi @xcite and peres @xcite : the partial transpose of a separable state is still positive , that is , positive semi - definite , but the converse is not true . even though we have a more complete criterion using positive linear maps @xcite , it is not so easy to apply this criterion due to the current stage of poor understanding on positive linear maps . we denote by @xmath4 the convex set of all separable states on @xmath5 , where @xmath6 denotes the algebra of all @xmath7 matrices over the complex field . a state is called separable if it is a convex combination of pure product states . therefore , every separable state is of the form @xmath8 with unit product vectors @xmath9 and positive numbers @xmath10 satisfying @xmath11 . a non - separable state is called entangled . the partial transpose @xmath12 of a state @xmath13 is obtained by taking the transpose in the first component . then the partial transpose of a separable state in ( [ sep ] ) is given by @xmath14 which is still positive , where @xmath15 denotes the vector whose entries are the complex conjugates of the corresponding entries of the vector @xmath16 . the product vector @xmath17 is called the partial conjugate of @xmath18 . we denote by @xmath19 the convex set of all states whose partial transposes are positive . the positive partial transpose ( ppt ) criterion tells us that the relation @xmath20 holds . these two convex sets coincide if and only if @xmath21 , as it was shown by woronowicz @xcite , choi @xcite and horodecki s @xcite . we note that the boundary between separable states and entangled ones consists of faces of the convex set @xmath4 , and so it is very important to understand the whole facial structures of @xmath22 . first of all , we note that every extreme point of @xmath4 is a pure product state @xmath23 . the next step to understand the facial structures of @xmath4 is naturally to find faces of @xmath4 which are affinely isomorphic to simplices . we call those _ simplicial faces_. we recall that a convex subset @xmath24 of a convex set @xmath25 is said to be a face of @xmath25 is the following property hold : @xmath26 we note that every point @xmath27 in a convex set determines a unique face in which @xmath27 is an interior point with respect to the relative topology given by the affine manifold generated by the face . this is the smallest face containing the point @xmath27 . by definition of face , it is clear that the following two statements for a separable state @xmath13 of the form ( [ sep ] ) are equivalent :    * @xmath13 determines a simplicial face . * the decomposition ( [ sep ] ) of @xmath13 is unique . it was shown by kirkpatrick @xcite that if @xmath28 is pairwise distinct up to constant multiplications and @xmath29 is linearly independent then the decomposition ( [ sep ] ) is unique . this result was also found by alfsen and shultz @xcite independently in the context of facial structures . see also @xcite for further progresses . recently , chen and djokovi @xcite extended this result to show that if product vectors in ( [ sep ] ) with @xmath30 satisfy a suitable linear independence condition for each subsystem then they are linearly independent and @xmath31 are the only product vectors in the span of them . this clearly implies that the separable states determined by these vectors have unique decompositions . we note that this result covers the cases when the ranks of separable states do not exceed @xmath32 . the main purpose of this paper is to search for separable states with unique decompositions whose ranks exceed the number @xmath32 .    in the two - qutrit case , it is well known that generic five dimensional subspaces of @xmath33 have exactly six product vectors @xmath34 , and their orthogonal complements have no product vectors . we show that these six product vectors give rise to a simplicial face isomorphic to the @xmath35-simplex @xmath36 whose interior consists of separable states of rank five . the interiors of the six maximal faces , isomorphic to the @xmath37-simplex @xmath38 , also consist of separable states of rank five . the interiors of the next fifteen maximal faces , isomorphic to the @xmath39-simplex @xmath40 , consist of separable states of rank four , and so on . we consider the set @xmath24 of all ppt states whose ranges are contained in the span of @xmath34 such that the ranges of partial conjugates are contained in the span of @xmath41 . this is a face of the convex set @xmath19 consisting of all ppt states @xcite . if the partial conjugates of six product vectors also span the @xmath35-dimensional space , then we see that the face @xmath36 ( we use the same notion with the simplex itself ) is inscribed in @xmath24 so that fifteen faces @xmath40 are located on the boundary of @xmath24 . with a mild additional condition , we also show that the interior of six maximal faces @xmath38 are contained in the interior of @xmath24 . remaining boundary of @xmath24 consists of ppt entangled edge states of rank four , which are extreme points of @xmath24 . we also show that every edge state of rank four arises in this way . from this , we see that every ppt entangled edge state of rank four is the difference of scalar multiples of two separable states with rank five . we have another byproducts with this picture . we see that if we take two boundary points of @xmath24 so that they are outside   of different maximal faces , then the convex sums of these two points intersect separable states in @xmath36 . this gives an affirmative answer to the problem 1 in @xcite which asks if a sum of two extreme ppt entangled states may be separable . for a given entangled state , it is an important problem to find the nearest separable state . see @xcite . for generic @xmath0 ppt entangled states of rank five , our picture gives a simple method to find the nearest separable state within the face of ppt states determined by @xmath13 .    in the above discussion , it may happen that the partial conjugates of six product vectors span the @xmath42-dimensional space . in this case , we also have a simplicial face isomorphic to the @xmath35-simplex @xmath36 . it is interesting to note that the interior points @xmath13 of this face have unique decompositions but have asymmetric ranks : @xmath43 . it turns out that the convex combinations of them and the edge states of rank five constructed in @xcite give rise to ppt states @xmath13 of type @xmath44 , that is , @xmath45 and @xmath46 . ppt states of such type were missing in a numerical search @xcite , but the existence has been noticed in @xcite . we give explicit examples of such states . the _ length _ of a separable state @xmath13 is defined by the minimum number @xmath47 for which the expression ( [ sep ] ) is possible . horodecki @xcite showed that the length of an @xmath48 separable state does not exceed @xmath49 . the notion of length was defined in @xcite , where it was shown that the length is invariant under the operation of partial transpose , and so the length may be strictly greater than the rank of the state . see also @xcite . our picture also gives concrete examples . any separable state @xmath13 in the interior of @xmath36 has length six , while rank of @xmath13 is five . the rank of @xmath12 may be five or six . therefore , there exists a state @xmath13 whose length is greater than the rank of the state even in the case of @xmath50 . but the lengths of these examples do not exceed @xmath51 . now , it is natural to ask if there exists an @xmath48 separable state of length exceeding the number @xmath51 . in a recent paper @xcite , chen and djokovi showed that such a separable state exists when @xmath52 , and conjectured ( * ? ? ? * conjecture 10 ) that a certain number may be the maximum length . by this conjecture , the length of @xmath0 separable states do not exceed @xmath53 . we note that the face @xmath36 of @xmath4 is induced by the face @xmath24 of @xmath19 , in the sense that @xmath36 is the intersection of @xmath4 and a face @xmath24 of @xmath19 . we call such faces of @xmath4 _ induced _ ones , as it was introduced in @xcite . note that the maximal faces @xmath38 are not induced . we construct a simplicial face isomorphic to the @xmath53-simplex @xmath54 with ten extreme points . this face is turned out to be non - induced . our construction gives an example of a @xmath55 separable state whose length is @xmath56 , to disprove the conjecture mentioned above . we note that a face of a face is again a face . therefore , we have simplicial faces with arbitrary affine dimensions less than @xmath56 , considering faces of @xmath54 ,    in the @xmath57 cases , the results in @xcite give us simplicial faces isomorphic to the @xmath58-simplex . we show for @xmath59 that @xmath60 choices of vectors in @xmath61 also give rise to simplicial faces isomorphic to the @xmath62-simplex @xmath63 , under suitable linear independence assumption . in this case , we do not have the pictures as in the @xmath0 case , since there is no ppt entangled states outside of @xmath64 . we note that the convex hull of @xmath65 is a simplex if and only if they are linearly independent in the _ real _ vector space of all hermitian matrices . it should be noted that this convex hull need not to be a face . in this context , we begin this paper to search for conditions on the family @xmath34 for which @xmath66 is linearly independent in the next section . in section [ sec : qutrit ] , we consider the @xmath0 case to describe the picture explained above , and construct separable states with unique decompositions which have asymmetric ranks in section [ spa ] . we explain the notion of induced faces of @xmath4 in section [ indeced_face ] , and construct a @xmath0 separable state which determines the face isomorphic to the @xmath53-simplex @xmath54 . finally , we consider the @xmath67 cases in section [ sec : qubit - qudit ] , and discuss briefly higher dimensional cases and related problems in the final section .","summary":"we search for faces of the convex set consisting of all separable states , which are affinely isomorphic to simplices , to get separable states with unique decompositions . in the two - qutrit case , we found that six product vectors spanning a five dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six vertices , under suitable linear independence assumption . if the partial conjugates of six product vectors also span a 5-dimensional space , then this face is inscribed in the face for ppt states whose boundary shares the fifteen 3-simplices on the boundary of the 5-simplex . the remaining boundary points consist of ppt entangled edge states of rank four . we also show that every edge state of rank four arises in this way . if the partial conjugates of the above six product vectors span a 6-dimensional space then we have a face isomorphic to 5-simplex , whose interior consists of separable states with unique decompositions , but with non - symmetric ranks . we also construct a face isomorphic to the 9-simplex . as applications , we give answers to questions in the literature , and construct ppt states of type ( 9,5 ) . for the qubit - qudit cases with , we also show that-dimensional subspaces give rise to faces isomorphic to the-simplices , in most cases","abstract":"we search for faces of the convex set consisting of all separable states , which are affinely isomorphic to simplices , to get separable states with unique decompositions . in the two - qutrit case , we found that six product vectors spanning a five dimensional space give rise to a face isomorphic to the 5-dimensional simplex with six vertices , under suitable linear independence assumption . if the partial conjugates of six product vectors also span a 5-dimensional space , then this face is inscribed in the face for ppt states whose boundary shares the fifteen 3-simplices on the boundary of the 5-simplex . the remaining boundary points consist of ppt entangled edge states of rank four . we also show that every edge state of rank four arises in this way . if the partial conjugates of the above six product vectors span a 6-dimensional space then we have a face isomorphic to 5-simplex , whose interior consists of separable states with unique decompositions , but with non - symmetric ranks . we also construct a face isomorphic to the 9-simplex . as applications , we give answers to questions in the literature , and construct ppt states of type ( 9,5 ) . for the qubit - qudit cases with , we also show that-dimensional subspaces give rise to faces isomorphic to the-simplices , in most cases .    6.0 truemm 1.5 true pc"}
{"article_id":"1301.0119","section_id":"i","document":"to understand the role of space in ecological communities in which individuals compete for resources , kang and the author @xcite recently introduced a stochastic spatial model of producer - consumer systems on the lattice . based on their numerical simulations of this spatial model and their analytical results for its nonspatial deterministic mean - field approximation , they concluded that the inclusion of space drastically affects the outcome of such biological interactions . their results for the models with two species are reminiscent of the ones found in @xcite for the spatially explicit lotka - volterra model and in @xcite for a non mendelian diploid model : in the parameter region where the nonspatial model displays bistability , there is a dominant type that wins regardless of its initial density in the spatial model , while the inclusion of space also translates into a significant reduction of the parameter region where both species coexist . in the presence of three species , other disagreements between the spatial and nonspatial models appear . the main purpose of this paper is to give rigorous proofs of some of the results stated in @xcite for the stochastic spatial model with two species , which we now describe in detail . each point of the @xmath0-dimensional square lattice is occupied by exactly one individual which is characterized by one of two possible types , say type 1 and type 2 . each individual is thought of as a producer and consumer of resources , and we described the dynamics based on four parameters @xmath1 that denote the ability of an individual of type @xmath2 to consume the resource produced by an individual of type @xmath3 , that we call resource @xmath3 . to avoid degenerate cases , we also assume that each resource can be consumed by at least one type : @xmath4 . each individual dies at rate one , i.e. , the type at each vertex is updated at rate one , with the new type being chosen at random from a certain neighborhood according to probabilities proportional to the ability of the neighbors to consume the resource produced by the individual to be updated . more precisely , the state space consists of all functions @xmath5 that map the square lattice into the set of types @xmath6 and the dynamics are described by the markov generator @xmath7\\ ] ] where @xmath8 denotes the number of type @xmath2 neighbors @xmath9 and where the configuration @xmath10 is obtained from the configuration @xmath5 by assigning type @xmath2 to vertex @xmath11 and leaving the type of all the other vertices unchanged . to avoid cumbersome notations , we will write later @xmath12 to indicate that vertices @xmath11 and @xmath13 are neighbors , i.e. , @xmath14 the positive integer @xmath15 is referred to as the range of the interactions . the fraction in means that the conditional probability that the new type is chosen to be type @xmath2 given that vertex @xmath11 is of type @xmath3 at the time of an update is equal to the overall ability of the neighbors of type @xmath2 to consume resource @xmath3 divided by the overall ability of all the neighbors to consume resource @xmath3 . note that the assumption on the parameters , @xmath4 for @xmath16 , allows to define @xmath17 \\qquad \\hbox{and } \\qquad a_2 \\ : = \\ a_{22 } \\ ( a_{12 } + a_{22})^{-1 } \\in \\,[0 , 1]\\ ] ] and to rewrite the markov generator in the form @xmath18\\ ] ] indicating that our model reduces to a two - parameter system . note also that if one of the original parameters in equation is equal to zero then the denominator in @xmath19 may be equal to zero , in which case the numerator is equal to zero as well . when this happens , we have the following alternative and define as follows :    1 .   @xmath20 . in this case , motivated by the fact that there is no neighbor of type @xmath2 , we define the probability at which vertex @xmath11 becomes type @xmath2 to be zero . @xmath21 . in this case , motivated by the fact that there are only neighbors of type @xmath2 , we define the probability at which vertex @xmath11 becomes type @xmath2 to be one . we point out that , in addition to be the most natural from a biological point of view , the two assumptions above also make the transition probability continuous with respect to the parameters , which is a key to some of our proofs .      as pointed out in @xcite , one of the most interesting aspects of the spatial model is that it results in predictions that differ significantly from its nonspatial deterministic mean - field approximation , thus indicating that the spatial component plays a key role in these interactions . we recall that the mean - field model is obtained by assuming that the population is well - mixing , and refer to durrett and levin @xcite for more details . this assumption results in a system of coupled differential equations for the densities of each type , and since the densities sum up to one , the mean - field model of reduces to the one - dimensional system @xmath22 where @xmath23 denotes the density of type @xmath2 individuals . interestingly , the limiting behavior of the mean - field model depends on whether the parameters @xmath24 and @xmath25 are smaller or larger than one half , which has a biological interpretation in terms of altruism and selfishness . more precisely ,    1 . type @xmath2 is said to be * altruistic * whenever @xmath26 since in this case the resources it produces are more beneficial for the other type than for its own type , 2 . type @xmath2 is said to be * selfish * whenever @xmath27 since in this case the resources it produces are more beneficial for its own type than for the other type . the mean - field model has two trivial equilibria given by @xmath28 and @xmath29 , respectively . by setting the right - hand side of equation equal to zero and assuming , in order to study the existence of nontrivial interior fixed points , that the product @xmath30 , we find @xmath31 from which it follows that @xmath32 is the unique fixed point that may differ from zero and one . to analyze the global stability of the fixed points , we observe that the sign of the derivative is given by @xmath33 which leads to the following three possible regimes for the mean - field model . + 1  a selfish type always wins against an altruistic type . +    without loss of generality , we may assume that @xmath34 indicating that type 1 is altruistic whereas type 2 is selfish . in this case , the first line of equation implies that the derivative of @xmath35 is always negative when @xmath36 hence there is no fixed point in @xmath37 , and the trivial equilibrium @xmath38 is unstable while the trivial equilibrium @xmath39 is globally stable . + 2  in the presence of two selfish types , the system is bistable . +    since @xmath40 and @xmath41 we have @xmath42 . the second line of equation implies that the derivative of @xmath35 has the same sign as @xmath43 so the interior fixed point is unstable and the boundary equilibria locally stable : the system converges to @xmath38 if the initial density of type 1 is strictly larger than @xmath44 , and to @xmath39 if the initial density of type 1 is strictly smaller than @xmath44 . + 3  in the presence of two altruistic types , coexistence occurs . +    since @xmath45 and @xmath46 the fixed point @xmath44 again belongs to @xmath37 as in the presence of two selfish types . however , the second line in equation now implies that the derivative of @xmath35 has the same sign as @xmath47 so the interior fixed point is globally stable whereas the two boundary equilibria @xmath38 and @xmath39 are unstable .      in order to state our results for the spatial model , we start by defining some of the possible regimes the spin system can exhibit .     for the stochastic spatial model , we say that    1 . type @xmath2 * wins * if starting from any configuration with infinitely many type @xmath2 , @xmath48 2 . the system * clusters * if starting from any translation invariant configuration , @xmath49 3 . type @xmath2 * survives * if starting from any configuration with infinitely many type @xmath2 , @xmath50 4 .   both types * coexist * if they both survive .    as pointed out above , the analytical results for the spatial and the nonspatial models differ in many aspects , which reveals the importance of the spatial component in the interactions . these disagreements are more pronounced in low dimensions and emerge when both types are selfish or both types are altruistic , while in the presence of one selfish type and one altruistic type the analytical results for both the spatial and nonspatial models agree . to begin with , we focus on the one - dimensional nearest neighbor process . in this case , one obtains a complete picture of the phase diagram based on a simple analysis of the interfaces of the process which almost evolve according to a system of annihilating random walks , whereas the more challenging study in higher dimensions and for larger ranges of interactions relies on very different techniques . we point out that the one - dimensional nearest neighbor process appears as a degenerate case in which coexistence is not possible while increasing the spatial dimension or the range of the interactions may result in coexistence of altruistic types .  [ th : spatial-1d ] assume that @xmath51 . then ,    1 .   except for the case @xmath52 , the process clusters . assuming in addition that @xmath53 , type 2 wins . the exclusion of the case @xmath52 is simply due to the fact that , under this assumption , a vertex may flip to a new type if and only if all its neighbors already have this type , which implies that the process has infinitely many absorbing states . while in the absence of space one type wins regardless of the initial densities only in selfish - altruistic systems , theorem [ th : spatial-1d ] indicates that the most selfish / least altruistic type always wins in the one - dimensional nearest neighbor case . in particular , coexistence no longer occurs even in altruistic systems . although this case is pathological , it is also symptomatic of the general behavior of the spatial model for which the existence of a dominant type that always wins may occur even when both types are altruistic . the next result shows that , in any spatial dimension and for any dispersal range , selfish - altruistic interactions result in the same outcome in the spatial and nonspatial mean - field models .  [ th : invasion ] assume that @xmath34 . then , type 2 wins .    even though its rigorous proof is not straightforward , the result is predictable since , when one type is selfish and the other type is altruistic , regardless of the type of the vertex to be updated and the spatial configuration , each of the selfish neighbors is individually more likely to be selected to determine the new type than each of the altruistic neighbors . in contrast , in the case of selfish - selfish interactions covered by theorem [ th : pure - birth ] below , the spatial and nonspatial models disagree in all dimensions and for all dispersal ranges . recall that in this case the mean - field model is bistable , indicating that the long - term behavior is determined by both the parameters and the initial densities . the next result shows on the contrary that , including local interactions , even if both types are selfish , enough asymmetry in the parameters implies that the most selfish type wins .     [ th : pure - birth ] for all @xmath54 there is @xmath55 such that type 2 wins when @xmath56 . numerical simulations in two dimensions indicate more generally that , when type 2 is selfish , it wins whenever @xmath53 . in the neutral case , the obvious symmetry of the evolution rules implies that none of the types wins , but simulations indicate that the population again clusters , with boundaries getting sharper as the common value of @xmath57 increases . this suggests that , in the presence of two selfish types , the long - term behavior of the one - dimensional nearest neighbor process occurs in two dimensions as well , a property that we believe is true in any spatial dimension and for any range of interactions . looking finally at altruistic - altruistic interactions , recall that coexistence always occurs in the mean - field approximation whereas the least altruistic type always wins in the one - dimensional nearest neighbor process . our last two results show that the long - term behavior of the process in higher spatial dimensions and/or for larger dispersal ranges is intermediate between these two extreme behaviors .     [ th : coexistence ] for all @xmath58 , there is @xmath55 such that coexistence occurs when @xmath59    in words , sufficiently strong mutual altruism translates into coexistence of both types . numerical simulations of the two - dimensional system suggest in addition that two altruistic types coexist in the neutral case @xmath60 therefore the coexistence region of the spatial model stretches up to the parameter point corresponding to voter model interactions . interestingly , our last result shows that there exists a parameter region for which even altruistic types can not coexist , thus indicating that the inclusion of local interactions translates into a reduction of the coexistence region in general and not only in the one - dimensional nearest neighbor case .     [ th : reduction ] there exists @xmath55 such that type 2 wins whenever @xmath61    we note that , even though the inclusion of local interactions always translate into a reduction of the coexistence region , numerical simulations indicate that this reduction becomes less pronounced while increasing the spatial dimension or the range of the interactions . the results for the mean - field model and spatial model when @xmath58 are summarized in figure [ fig : diagrams ] . in the phase diagram of the spatial model , the dashed regions are the ones that are covered by our theorems , while the thick lines are the critical curves suggested by simulations . for a detailed analysis of the nonspatial model and additional results based on numerical simulations for the spatial model in the presence of three species , we refer the reader to the companion paper @xcite . the rest of this paper is devoted to the proofs . to avoid cumbersome notations and messy calculations , we prove all our results , with the exception of theorem [ th : coexistence ] , when the range of the interactions is equal to one . however , we point out that all the techniques used in the proofs easily extend to larger dispersal ranges . the reason for excluding theorem [ th : coexistence ] from this rule is that it is the only result that shows a disagreement between the one - dimensional nearest neighbor case and the other cases , thus indicating that the range of the interactions plays a specific role in the presence of strong altruistic - altruistic interactions .","summary":"the objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer - consumer systems that has been recently introduced by kang and the author to understand the role of space in ecological communities in which individuals compete for resources . each point of the square lattice is occupied by an individual which is characterized by one of two possible types , and updates its type in continuous time at rate one . each individual being thought of as a producer and consumer of resources , the new type at each update is chosen at random from a certain interaction neighborhood according to probabilities proportional to the ability of the neighbors to consume the resource produced by the individual to be updated . in addition to giving a complete qualitative picture of the phase diagram of the spatial model , our results indicate that the nonspatial deterministic mean - field approximation of the stochastic process fails to describe the behavior of the system in the presence of local interactions . in particular , we prove that , in the parameter region where the nonspatial model displays bistability , there is a dominant type that wins regardless of its initial density in the spatial model , and that the inclusion of space also translates into a significant reduction of the parameter region where both types coexist .","abstract":"the objective of this paper is to give a rigorous analysis of a stochastic spatial model of producer - consumer systems that has been recently introduced by kang and the author to understand the role of space in ecological communities in which individuals compete for resources . each point of the square lattice is occupied by an individual which is characterized by one of two possible types , and updates its type in continuous time at rate one . each individual being thought of as a producer and consumer of resources , the new type at each update is chosen at random from a certain interaction neighborhood according to probabilities proportional to the ability of the neighbors to consume the resource produced by the individual to be updated . in addition to giving a complete qualitative picture of the phase diagram of the spatial model , our results indicate that the nonspatial deterministic mean - field approximation of the stochastic process fails to describe the behavior of the system in the presence of local interactions . in particular , we prove that , in the parameter region where the nonspatial model displays bistability , there is a dominant type that wins regardless of its initial density in the spatial model , and that the inclusion of space also translates into a significant reduction of the parameter region where both types coexist ."}
{"article_id":"0803.2052","section_id":"i","document":"in this paper we consider the problem of deciding whether an algebraic curve @xmath1 over a number field @xmath2 has any @xmath2-rational points . we assume that @xmath1 is complete and non - singular . a necessary condition for @xmath3 to be non - empty is that @xmath1 has a rational point over every extension of @xmath2 . in particular , for any place @xmath4 of @xmath2 , the curve @xmath1 should have a rational point over the completion @xmath5 of @xmath2 at @xmath4 .    for curves of genus @xmath6 , this is sufficient as well : if a genus @xmath6 curve @xmath1 has a rational point over every completion @xmath5 of @xmath2 , then @xmath3 is non - empty . a @xmath5-point of @xmath1 is referred to as a _ local _ point of @xmath1 at @xmath4 and a @xmath2-point of @xmath1 is called a _ global _ point . for a genus @xmath6 curve @xmath1 , having a local point everywhere ( at all places of @xmath2 ) implies having a global point . genus @xmath6 curves are said to obey the _ local - to - global _ principle for points . the local - to - global principle is important from a computational point of view . one can decide in finite time whether a curve has points everywhere locally : for any curve @xmath1 over a number field @xmath2 , the set @xmath7 is nonempty for all places @xmath4 outside an explicitly determinable finite set @xmath8 . for the remaining places @xmath9 , one can decide in finite time if @xmath7 is non - empty as well . see @xcite for some algorithms , in particular a quite efficient algorithm for hyperelliptic curves . thus , whether a curve has points everywhere locally can actually be decided in finite time . it is well known that curves of genus greater than @xmath6 do not always obey the local - to - global principle . most proofs of this phenomenon are based on the fact that curves of positive genus can have unramified galois - covers . in fact , if a curve  @xmath1 of positive genus has a rational point  @xmath10 , then the abel - jacobi map allows us to consider @xmath1 as a non - singular subvariety of its jacobian variety  @xmath11 . since the map @xmath12 is unramified , the pull - back @xmath13 yields an unramified cover of @xmath1 that has a rational point mapping to  @xmath10 . more generally , an _ @xmath14-cover _ of  @xmath1 is a cover that is isomorphic to one of this form over an algebraic closure @xmath15 of  @xmath2 . thus , if one can show that an algebraic curve @xmath1 does not have @xmath14-covers that have a rational point , then it follows that @xmath1 has no rational points . even though @xmath1 may have points everywhere locally , it is possible that on every cover , rational points can be ruled out by local conditions . the major content of this paper is inspired by the following well - known observation . let @xmath16 be an unramified cover of a curve @xmath1 over a number field @xmath2 that is galois over an algebraic closure @xmath15 of  @xmath2 . it is a standard fact , going back to chevalley and weil @xcite that there is a finite collection of twists @xmath17 of the given cover @xmath18 such that any rational point on @xmath1 has a rational pre - image on one of the covers @xmath19 . we call such a set of covers a _ covering collection_. furthermore , at least in principle , such a finite collection of covers is explicitly computable given a cover @xmath16 . thus , one approach for testing solvability of a curve @xmath1 that has points everywhere locally is :    1 .   fix @xmath20 . 2 .   construct an @xmath14-cover @xmath21 of @xmath1 . if no such covers exist , then @xmath3 is empty . 3 .   determine a covering collection associated to @xmath22 . test each member of the covering collection for local solvability . if none of the members has points everywhere locally then no curve in the covering collection has any rational points , and @xmath1 has no rational points either . each of the covers might have a local obstruction to having rational points , while the underlying curve @xmath1 has none . thus the procedure sketched above can actually prove that a curve does not obey the local - to - global principle for points . see @xcite for a detailed discussion , including the theoretical background and some links to the brauer - manin obstruction against rational points .    in the present article we discuss a relatively efficient way of carrying out the procedure sketched above for hyperelliptic curves . we consider unramified covers @xmath23 over  @xmath2 such that for an algebraic closure @xmath15 of @xmath2 we have that @xmath24({\\overline{k}})$ ] as @xmath25-modules . these are exactly the _ two - covers _ of @xmath1 over @xmath2 . we write @xmath26 for the set of isomorphism classes of two - covers of @xmath1 over @xmath2 . our claim to efficiency stems from the fact that we avoid explicitly constructing a covering collection . in fact , the method can be described without any reference to unramified covers , see section  [ sec : definition ] . instead , we determine an abstract object that ( almost ) classifies the isomorphism classes of two - covers . see section  [ sec : geom ] for how to construct the covers explicitly from the information provided by the algorithm . we observe that for any field extension @xmath27 there is a well - defined map @xmath28 by sending a point to the two - cover that has an @xmath29-rational point above it . for completions @xmath30 , we show that this map is locally constant : if two points @xmath31 lie sufficiently close , then they lift to the same two - cover . this allows us to explicitly compute the @xmath5-isomorphism classes of two - covers that have points locally at @xmath4 . we can then piece together this information to obtain the global isomorphism classes of two - covers that have points everywhere locally . we define @xmath32 to be the set of everywhere locally solvable two - covers of @xmath1 . the algorithm computes a related object , that we denote by @xmath33 , which is a quotient of @xmath34 . it classifies everywhere locally solvable two - covers , up to an easily understood equivalence . since any curve @xmath1 with a rational point admits a globally and hence everywhere locally solvable two - cover , @xmath35 implies that @xmath3 is empty .    a priori , the elements of @xmath33 represent two - covers that have a model of a certain form ( described in section  [ sec : geom ] ) , but we will prove that every two - cover that has points everywhere locally does have such a model , see theorem  [ thm : twocovers ] below .    in section  [ sec : noratpoints ] we illustrate how the algorithm presented in sections  [ sec : localmu ] , [ sec : real ] , and [ sec : selfake ] can be used to show that a hyperelliptic curve has no rational points . this method was also used in a large scale project @xcite to determine the solvability of all genus @xmath36 curves with a model of the form @xmath37 in section  [ sec : statistics ] we describe some statistics that illustrate how frequently one would expect that @xmath35 for curves of genus @xmath36 . section  [ sec : ratpoints ] shows how information obtained on @xmath33 can be used for determining the rational points on curves if @xmath3 is non - empty . this complements chabauty - methods as described in @xcite . in earlier articles , the selection of the covers requiring further attention was done by ad - hoc methods . here we describe a systematic and relatively efficient approach . in section  [ sec : genus1 ] we describe the results of applying the method to curves of genus @xmath0 . we find ( unsurprisingly ) that we recover well - known algorithms for performing @xmath36-descents and second @xmath36-descents on elliptic curves @xcite . a practical benefit of this observation is that to our knowledge , nobody has bothered to implement second two - descent over arbitrary number fields , whereas our implementation in magma @xcite ( which is available for download at @xcite ) can immediately be used . we give an example by exhibiting an elliptic curve over @xmath38 with a non - trivial tate - shafarevich group .","summary":"we describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve , with the property that any rational point will lift to one of the covers . in particular , if the algorithm returns an empty set , then the hyperelliptic curve has no rational points . this provides a relatively efficiently tested criterion for solvability of hyperelliptic curves .","abstract":"we describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve , with the property that any rational point will lift to one of the covers . in particular , if the algorithm returns an empty set , then the hyperelliptic curve has no rational points . this provides a relatively efficiently tested criterion for solvability of hyperelliptic curves . we also discuss applications of this algorithm to curves of genus and to curves with rational points .    = 0.1pt"}
{"article_id":"astro-ph0605530","section_id":"r","document":"in fig .  [ fig : sed ] , we show the seds constructed for knots a , b1 , c1 , c2 , and d1 . since the interpretation of multiple knots ( b2/b3 and d2/h3 ) could be misleading , the  summed \" spectra for b2/b3 and d2/h3 have been omitted in fig . [ fig : sed ] and in the spectral modeling described below . the overall spectral appearance of the _ inner knots _ ( a and b1 ) has strikingly different characteristics as compared to the _ outer knots _ ( c1 , c2 , and d1 ) . first , the _ inner knots _ radiate strongly in the x - ray ( or even beyond ) with hard spectra while the _ outer knots _ radiate predominantly in the mid - infrared . second , and most importantly , the seds of the _ inner knots _ have a concave shape from the mid - infrared to optical band , indicating that two spectral components cross over at optical wavelengths . figure  [ fig : ir - opt ] gives a close - up version of fig . [ fig : sed ] highlighting the mid - infrared to near - ultraviolet part of the spectrum . we emphasize here that the irac fluxes fill a critical region in the seds , making it possible to identify unambiguously the spectral structures present in the infrared to optical wavelengths .    in the seds of the _ inner knots _ , we identify two spectral components , namely ( 1 ) the low - energy synchrotron spectrum extending from radio to infrared with a spectral cutoff at @xmath102 hz , and ( 2 ) the high - energy component arising in the optical and smoothly connecting to the x - ray flux . tentatively , we suggest that the high - energy component is likely _ of synchrotron origin _ , because the optical polarization is consistent with the radio polarization in degree and orientation . in   [ sec : syn2 ] and [ sec : ic ] we discuss the origin of the high - energy spectral component and its implications to particle acceleration in the jet . in explaining the broadband spectrum of knot a , a single power - law continuum all the way from radio to x - ray has been proposed in prior studies @xcite , but this picture does not correctly describe the present , more extensive data .    in the _ outer knots _ , the seds also show the two components but with different relative strengths . the low - energy part becomes more dominant with increasing distance from the quasar core . at first glance the entire infrared - optical spectrum may be attributed to the falling part of synchrotron emission . however , careful inspection shows a slight spectral - flattening in the optical and near - ultraviolet , which suggests a contribution from the second component responsible for the x - ray emission , as already proposed by @xcite . this idea is further strengthened by the observation that the radio brightening in d1 ( relative to c1/c2 ) accompanies infrared brightening while the near - ultraviolet and x - ray fluxes remain at similar levels ( see fig . [ fig : ir - opt ] ) .    to visualize the spectral transition from the _ inner _ to the _ knots along the jet , we present a three - color image of the jet in fig .  [ fig : truecolor ] based on the data taken with _ , _ hst _ , and _ , with the _ vla _ contours from fig . [ fig : image ] overlaid . the colors are coded as follows : _ spitzer _ @xmath46 ( _ red _ ) , _ hst _ @xmath103 ( _ green _ ) , _ chandra _ 0.46 kev ( _ blue _ ) . the _ spitzer _ image is a  deconvolved \" irac image , which represents the results of our infrared photometry via psf - fitting in  [ sec : irphoto ] . specifically , the best - fit image obtained with two - dimensional fitting is artificially shrunk to match the effective resolution of the _ hst _ image . the _ hst _ image is an  uv excess \" map [ determined as @xmath103 based on the data in @xcite ] representing the dominance of near - ultraviolet light over the near - infrared . it is clear that the inner knots are luminous in both the uv excess and x - rays ( the high - energy component ) , while the outer knots are bright in the mid - infrared ( the low - energy component ) . cccccccc parameter & a & b1 & c1 & c2 & d1 & h2 & h1 + @xmath104 & 0.76 & 0.73 & 0.63 & 0.68 & 0.75 & 0.9 & 0.9 + @xmath105 ( hz ) & @xmath106 & @xmath106 & @xmath107 & @xmath106 & @xmath108 & @xmath106 & @xmath107 + @xmath109 & 0.8 & 0.8 & 0.8 & 0.8 & 0.8 & 0.8 & 0.8 + @xmath110 & 0.7 & 0.8 & 1.0 & 1.0 & 1.0 & & +    we describe the radio - to - x - ray spectra with the following double power - law models ( one with an exponential cutoff ) : @xmath111 +   \\kappa_2 \\nu^{-\\alpha_2}.\\ ] ] the first term of the right - hand - side accounts for the low - energy spectrum and the second pure power - law describes the high - energy part . ( for the second component , @xmath112 , we set an artificial low - energy turn - over below @xmath113 hz . ) we introduced a parameter @xmath109 in the exponential part because particle acceleration models generally do not provide a robust prediction concerning the electron spectrum in the cutoff region . we adopt a common value of @xmath114 ; the choice has little influence on other parameters . table [ tbl-2 ] lists the spectral parameters that well describe the knot seds shown in fig . [ fig : sed ] . also , in fig . [ fig : ir - opt ] we show the relative contribution of the second component , namely @xmath115 , in the infrared to ultraviolet part . it should be noted that the second component is dominant ( @xmath116 ) already in the @xmath117 band flux and therefore the  optical \" jet traces the high - energy radiation . for knot a , the first component has a luminosity of @xmath118 ( in the frequency range @xmath119 hz ) without taking account of relativistic beaming . the minimum luminosity in the second component of knot a is @xmath120 ( @xmath121 hz ) , and can be much higher if the spectrum extends well beyond the x - ray domain . the spectral index of the low - energy component is in the range of @xmath122 , as determined from the radio spectra . remarkably , the cutoff frequency is quite similar among the knots , @xmath123 hz , which differs from previous modeling that deduced a progressive decrease of the cutoff frequencies ( see * ? ? ? * and references therein ) . the difference in the deduced cutoff frequency results from our inclusion of the irac fluxes into the modeling . the second spectral index for knots a and b1 is @xmath124 ; for knots c1 , c2 and d1 , the second index is steeper , @xmath125 . it should be emphasized that the second index of knot a agrees well with the local spectral index determined by x - rays alone , in other words @xmath126 . interestingly , the steepness of the index seems to increase with decreasing x - ray intensity of the knots . there are some caveats for the interpretation of the seds that we constructed . as mentioned earlier , knot b1 in the optical shows a different morphology as compared to the radio one . therefore , the first and second components should originate in different emission volumes . also , the x - ray flux assigned for knot b1 could be contaminated by adjacent , bright knots . the cutoff frequency of the low - energy synchrotron emission that we determined in the previous section represents the maximum energy of the associated electron population . according to standard synchrotron theory ( e.g. , * ) , the maximum energy can be estimated as @xmath127^{0.5 }   \\left ( \\frac{b}{0.1\\ \\rm mg}\\right)^{-0.5 }   \\left ( \\frac{\\nu_{\\rm c}}{10^{14}\\ \\rm hz } \\right)^{0.5 }   \\ \\rm tev,\\ ] ] where @xmath128 is the doppler factor , @xmath10 is the redshift , and @xmath129 is the comoving magnetic field strength . the doppler factor is defined as @xmath130^{-1}$ ] with @xmath131 the velocity of the jet , @xmath132 the bulk lorentz factor of the jet , and @xmath133 the observing angle with respect to the jet direction . it is difficult to determine the doppler factor , and therefore to what extent the observed jet radiation is enhanced by doppler beaming . furthermore , the jet may be decelerating along the observed jet portion resulting in a declining doppler factor @xcite . a likely range is @xmath134 ( see however  [ sec : ic ] ) . if equipartition between the radiating electrons and magnetic fields is assumed , without taking into account any relativistic motion ( i.e. , @xmath135 ) , one can obtain an estimate of @xmath136 @xcite . therefore , given the cutoff frequencies of @xmath137 hz , the maximum energy can be deduced as @xmath138 , where @xmath139 . according to the prescription given in @xcite , the equipartition condition yields @xmath140 ( see , * ? ? ? * for slightly different scaling ) . then , an estimate of @xmath141 is rather robust being nearly independent of both @xmath128 and @xmath129 . synchrotron cooling in the source should affect the spectral shape provided that the cooling time is shorter than the formation timescale of the radiating knots . the synchrotron cooling time ( in the jet comoving frame ) for electrons with energy @xmath142 emitting on average at a frequency @xmath21 ( observed ) can be expressed as @xmath143^{0.5 }   \\left ( \\frac{b}{0.1\\ \\rm mg}\\right)^{-1.5 }   \\left ( \\frac{\\nu}{10^{14}\\ \\rm hz } \\right)^{-0.5 }    \\rm yr , \\end{aligned}\\ ] ] where @xmath144 is the thomson cross section , and @xmath145 is the energy density of the magnetic field . equation  ( [ eq : emax ] ) was used in relating @xmath146 with @xmath21 , by replacing @xmath147 with @xmath148 and @xmath149 with @xmath150 . the source age , though quite uncertain , would be @xmath151 . therefore , the observed synchrotron spectra from the radio to optical frequencies are likely to be formed in the  cooling regime \" , namely @xmath152 , which means that a continuous injection of electrons with an acceleration spectrum of @xmath153 ( in the power - law part ) over the timescale @xmath154 gives rise to the energy distribution of synchrotron - emitting electrons @xmath155 . in this case , according to the relation @xmath156 , the observed index of @xmath157 is translated into the electron acceleration index of @xmath158 , which is coincident with the hardest possible index ( @xmath159 ) in the nonlinear shock acceleration theory @xcite . we implicitly assumed particle acceleration taking place in each knot @xcite , where relativistic electrons are accumulated without escaping . a similar treatment was applied to the hotspot of 3c  273 by @xcite to incorporate a shock - acceleration theory into the emerging radiation spectrum . there may be occasions for which the above argument is not applicable ; for example , in the case of significant beaming , the synchrotron cooling time would be much longer ( @xmath160 for the equipartition field ) and the realization of the cooling regime would not be justified for radio - emitting electrons .      for the inner knots ( a and b ) we have found that the optical and x - ray fluxes can be modeled as a common power - law spectrum of spectral index @xmath161 . also , the optical to x - ray slope agrees with the x - ray spectral index , especially for knot a , @xmath126 . one implication of this finding is that the optical and x - ray fluxes must be explained by the same emission mechanism . in  [ sec:3c273 ] we mentioned that both the radio and optical jet emission are linearly polarized to a similar degree of @xmath162 @xcite , which has been taken as evidence for a synchrotron origin for the optical radiation in the inner knots . now this in turn would imply a synchrotron origin for the x - ray radiation as well . therefore we first discuss the optical - x - ray component in terms of synchrotron radiation produced by high - energy electrons .    according to the prescription in  [ sec : syn1 ] , the power - law slope of the energy distribution of the _ accelerated _ electrons is @xmath163 in the synchrotron - cooling regime . then the spectral index of the high - energy component , @xmath161 for the inner knots , yields @xmath164 . interestingly , the index of acceleration is almost same between the low- and high - energy synchrotron components : @xmath165 ( because of @xmath166 ) . on the other hand , the two indices differ in the outer knots : @xmath167 , corresponds to @xmath168 . the apparent difference in the cutoff frequency between the low- and high - energy components likely reflects a difference in the maximum energy of electron acceleration . the cutoff frequency associated with the high - energy component is not constrained by the current data , but must be greater than @xmath169 hz ( @xmath170 kev ) . consequently , from equation  ( [ eq : emax ] ) , the lower limit to the maximum electron energy is @xmath171 . the presence of two different cutoff energies suggests two acceleration modes that can be characterized by different acceleration rates in the knots . the acceleration timescale can be expressed as @xmath172 , with a gyroradius @xmath173 . the rate of acceleration is parametrized by the factor @xmath174 which is , as frequently assumed , taken to be energy independent . by equating @xmath175namely , balancing the acceleration and synchrotron loss rates  one obtains the maximum attainable energy limited by synchrotron losses : @xmath176 using equation  ( [ eq : emax ] ) this can be translated into the corresponding cutoff frequency , @xmath177   \\frac{\\delta}{1+z }   \\ \\rm hz.\\ ] ] therefore , for the second synchrotron component to extend beyond @xmath169 hz , the condition @xmath178 should be fulfilled . on the other hand , for the low - energy synchrotron component , an extremely large value of @xmath179 can be inferred via a similar argument . interestingly , a study of multiwavelength spectra of small - scale blazar emission also gives large @xmath180 @xcite . in the theory of diffusive shock acceleration , for relativistic shocks , the factor @xmath180 corresponds roughly to the ratio of the energy density of regular magnetic fields to that of turbulent fields which resonantly scatter accelerating relativistic particles . then a different value of @xmath180 means a different development of turbulent magnetic fields near the shock . the inferred large value of @xmath181 , following a discussion in @xcite , may be understood in terms of steep turbulence spectra , e.g. , of kolmogorov - type @xmath182 [ where @xmath183 is the magnetic energy density per wavenumber @xmath184 in the turbulent field ] , though it should be noted that @xmath185 was silently assumed above to obtain energy - independent @xmath180 for simplicity . there may be two distinct types of shocks characterized by different @xmath180 in the knots giving rise to their  double - synchrotron \" nature . alternatively , another acceleration mechanism may be operating , accounting in a natural way for a different acceleration rate for the second component . for instance , turbulent acceleration may occur in the shear of jet boundary layers @xcite , generating the second synchrotron component @xcite . in highly turbulent shear layers , the acceleration rate can be estimated as @xmath186 , where @xmath187 denotes the alfvn velocity in units of @xmath188 . provided that the jet is composed of electron - proton plasma with the comoving number density @xmath189 @xcite , the alfvn velocity in the jet can be written as @xmath190 the condition @xmath178 needed to produce the x - rays can be fulfilled if @xmath191 , which seems reasonable for the typical jet parameters .    an intriguing implication of interpreting the x - ray emission as being due to a synchrotron process would be the possibility that protons in the jet can be accelerated to very high energies . in the case of protons , synchrotron losses do not limit the acceleration process unless they reach ultra - high energies . instead , a condition set by @xmath192 , where @xmath193 is the light - crossing timescale of the knot along the jet ( typically @xmath194 kyr ) , would give a conservative estimate of the maximum attainable energy of protons . here we use a light - crossing time rather than the  age \" of the jet , probably @xmath195 , to conservatively account for an escape loss which takes at least longer than a light - crossing time . this condition leads to @xmath196 and consequently @xmath197 for @xmath198 and typical values of @xmath129 and @xmath193 . remarkably , if @xmath199 ( close to the so - called bohm diffusion in the framework of diffusive shock acceleration ) , ultra - high - energy protons with energies @xmath200 can be accelerated in the jet of 3c  273 ( see * ? ? ? * ; * ? ? ? * for detailed theoretical arguments ) . even with a large value of @xmath180 ( @xmath201 ) , the shear acceleration would still be capable of generating @xmath200 , since the turbulent acceleration in the shear layer may be available for much longer timscales . the fraction of jet power that goes to high energy protons depends on the particle content of the jet and the details of the physics of particle acceleration , both of which are not well known . it is interesting to note that if protons are indeed accelerated in the jet to very high energies , @xmath202 , the second synchrotron component can be produced directly by _ protons _ , i.e. , proton synchrotron radiation @xcite , rather than by electrons . for the same particle energy , the characteristic frequency of proton synchrotron radiation , @xmath203 , is less than that of electron synchrotron radiation by a factor of @xmath204 . therefore , by using equation  ( [ eq : emax ] ) , the spectrum of proton synchrotron has a cutoff frequency of @xmath205 \\left ( \\frac{b}{\\rm mg}\\right )   \\left ( \\frac{e_{\\rm p , max}}{10^{18}\\ \\rm ev } \\right)^2\\   \\rm hz,\\ ] ] which is located above the x - ray domain . thus protons rather than a second population of electrons , may explain the second synchrotron component . unlike the electron - synchrotron case , the diffuse nature of the emission ( at least in the optical ) can be understood more easily thanks to much longer cooling timescale for protons . a magnetic field strength of @xmath206 is needed in order to keep the power spent to accelerate protons at a reasonable level , and at the same time to render the acceleration timescale shorter and the diffusion timescale longer @xcite . by adopting @xmath207 , @xmath208 , an escape loss timescale of @xmath209 , and a continuous proton injection over @xmath210 , @xcite obtained the acceleration power for protons of @xmath211 to explain the optical - x - ray spectrum of knot a in 3c  273 in terms of proton synchrotron radiation . previous explanations of the second , x - ray - dominated component of the sed for jet knots have emphasized the beamed ic scenario @xcite . specifically , relativistically beamed ic emission in the cmb photon field has been invoked to model the x - ray emission in 3c  273 @xcite , as well as in other quasar jets . this model requires a highly relativistic bulk velocity of the jet , with a doppler factor @xmath6 out to nearly megaparsec distances . a direct connection between the optical and x - ray fluxes in the inner knots a and b1 and also between the ultraviolet and x - ray fluxes in the outer knots ( see fig .  [ fig : sed ] ) led us to consider that the same mechanism should be responsible for the optical and x - ray emissions , forming a distinct high - energy component . if one adopts the beamed ic model for the x - rays , the optical fluxes in the inner knots and the ultraviolet fluxes in the outer knots should be explained also by the beamed ic radiation . this implies that the energy distribution of electrons has to continue down to very low energies of @xmath212 without a cutoff or break .    in this scenario , one still should account for the optical polarization . in the case of  cold \" electrons in the jet , compton up - scattering off the cmb by an ultrarelativistic jet ( so - called  bulk comptonization \" ) can yield in principle a high degree of polarization for the standard choice of @xmath213 @xcite . however , for relativistic electrons with @xmath214 as appropriate for the optical ic emission in this jet , the degree of polarization should be significantly reduced @xcite . the present data of the radio and optical polarization @xcite may require a tuned set of physical conditions to reconcile with the beamed ic scenario .    in this respect , a possible caveat would be that in addition to the cmb , the synchrotron radiation of the jet itself might serve as seed photons for compton up - scattering ; if the highly relativistic jet accompanies slowly moving outer portions , the synchrotron radiation that comes from the slowing part can be relativistically enhanced in the fast moving jet , providing the effective photon fields for comptonization ( * ? ? ? * as discussed for small - scale jets ) . if the observed radio flux is largely contributed by a slow , non - relativistic layer , the energy density of the synchrotron photons ( as measured in the observer s frame ) could reach @xmath215 , being comparable to the cmb energy density . this possibility introduces a complication to the polarization argument .    within the framework of the beamed ic radiation , the physical parameters that can reproduce the seds of the 3c  273 jet have been obtained ( e.g. , * ? ? ? * ; * ? ? ? compared to a typical value of @xmath216 in the previous work ( e.g. , * ? ? ? * ) , a smaller minimum energy of the electron distributions , say @xmath212 , is required by the present data . note that this increases the estimate of the jet kinetic power by an order of magnitude if the jet power is dynamically dominated by cold protons . let us model the sed of knot a with a synchrotron plus beamed ic model of @xcite assuming @xmath217 and a knot radius of 1 kpc ( in the jet frame of reference ) . for a doppler factor of @xmath218 and magnetic field @xmath219 g as roughly corresponding to an equipartition condition , we obtain a jet kinetic power of @xmath220 , if the number of the observed electrons is balanced by the number of cold protons in the jet . however , such a large doppler factor of @xmath218 seems problematic , since relatively large contributions from the un - beamed components are observed in the core emission , such as an ultraviolet bump ( see * ? ? ? * and references therein ) , and the accretion - disk emission comparable to the jet emission in the x - ray regime @xcite . instead , if we adopt a smaller doppler factor of @xmath221 ( together with @xmath222 to account for the optical emission ) , the energy density of electrons exceeds that of magnetic fields more than three orders of magnitude , and the jet kinetic power reaches an uncomfortable level of @xmath223 . to summarize , the beamed ic model , in its simple form , does not easily find a satisfactory set of parameters , particularly for the case of knot a.    finally , the upper limit to the infrared fluxes from the quiet portion of the jet upstream of knot a is important to constrain the structure of the jet in the context of the beamed ic model @xcite . unfortunately , we need additional irac observations to derive a reliable upper limit there because of the large systematic uncertainty in psf subtraction in the region close to the quasar core .      in fig . [ fig : sed2 ] , we show the seds obtained for h1 and h2 in the head region . note that no significant x - ray emission was found in this region . we have modeled the seds using a power law with an exponential - type cutoff , namely by equation  ( [ eq : fnu ] ) with @xmath224 , as drawn in fig . [ fig : sed2 ] . the spectral parameters used for the model are indicated in table [ tbl-2 ] . interestingly , the spectrum of h2 shows a notable flattening at the optical and ultraviolet wavelengths , as first reported by @xcite . the radio spectra are steeper than those of the upstream knots , with @xmath225 . it is likely that particle acceleration acting in the head region would be terminal shocks that have different properties as compared to upstream shocks . as argued by @xcite , if the effect of synchrotron cooling is taken into account , the index seems consistent with an acceleration spectrum of @xmath226 , which is the standard spectrum of diffusive shock acceleration . within the picture proposed by @xcite , however , the excess fluxes at optical and ultraviolet wavelengths seen in the spectrum of h2 can not be easily understood . these excesses may represent a second synchrotron component just as in the case of the upstream knots .","summary":"we have performed infrared imaging of the jet of the quasar 3c  273 at wavelengths 3.6 and with the infrared array camera ( irac ) on the _ spitzer space telescope_. when combined with the radio , optical and x - ray measurements , the irac photometry of the x - ray - bright jet knots clearly shows that the optical emission is dominated by the high - energy emission component of the jet , not by the radio synchrotron component , as had been assumed to date . the high - energy component , represented by a power - law from the optical through x - ray , may be due to a second synchrotron component or to inverse compton scattering of ambient photons . in the former case , we argue that the acceleration of protons exceeding energies of or possibly even to would be taking place in the jet knots of 3c  273 assuming that the acceleration time is proportional to the particle gyroradius . in contrast , the inverse compton model , into which highly relativistic doppler beaming has to be incorporated , requires very low - energy electrons of in the jet knots . the present polarization data in the radio and optical would favor the former interpretation in the case of the 3c  273 jet .","abstract":"we have performed infrared imaging of the jet of the quasar 3c  273 at wavelengths 3.6 and with the infrared array camera ( irac ) on the _ spitzer space telescope_. when combined with the radio , optical and x - ray measurements , the irac photometry of the x - ray - bright jet knots clearly shows that the optical emission is dominated by the high - energy emission component of the jet , not by the radio synchrotron component , as had been assumed to date . the high - energy component , represented by a power - law from the optical through x - ray , may be due to a second synchrotron component or to inverse compton scattering of ambient photons . in the former case , we argue that the acceleration of protons exceeding energies of or possibly even to would be taking place in the jet knots of 3c  273 assuming that the acceleration time is proportional to the particle gyroradius . in contrast , the inverse compton model , into which highly relativistic doppler beaming has to be incorporated , requires very low - energy electrons of in the jet knots . the present polarization data in the radio and optical would favor the former interpretation in the case of the 3c  273 jet . sensitive and detailed measurements of optical polarization are important to establish the radiation mechanism responsible for the high - energy emission . the present study offers new clues as to the controversial origin of the x - ray emission seen in many quasar jets ."}
{"article_id":"astro-ph0605530","section_id":"c","document":"we have presented results from our _ spitzer _ irac observation of the 3c  273 jet at wavelengths 3.6 and @xmath0 , combined with the photometry with the _ vla _ radio , _ hst _ optical , and _ chandra _ x - ray data . our multiwavelength analysis led us to conclude that the flat optical emission in the x - ray - dominated knots originates in the high - energy power - law component , which also accounts for the x - ray emission . the agreement between the optical - x - ray slope ( @xmath110 ) and the x - ray spectral index ( @xmath227 ) throughout the jet supports this picture . on the other hand , the radio to infrared spectra can be expressed by a power law with an exponential cutoff at @xmath102 hz . the two distinct radiation components , namely low - energy ( radio - infrared ) and high - energy ( optical - x - ray ) emission , have similar power of @xmath228 for the entire jet volume ( without a beaming correction ) ; the power in the second component becomes noticeably higher if its peak position is located far beyond the x - ray domain . the relative importance of the two components changes along the jet ( see fig .  [ fig : truecolor ] ) . in the inner , x - ray - dominated knots , the high - energy component overwhelms the low - energy one . the second component can be attributed to either synchrotron radiation by a second population of high - energy electrons ( or protons ) , or the beamed ic emission by the radio - emitting electrons . in the first case , the double synchrotron nature may arise from the presence of distinctively different acceleration processes ( e.g. , shock and turbulent acceleration ) . in the context of the origin of extragalactic cosmic - rays , it is interesting that a faster acceleration mechanism producing the second component is capable of accelerating cosmic - ray protons to energies @xmath229 . on the comptonization interpretation of the high - energy emission , we argued that the present polarization data seems problematic . future sensitive measurements of polarization are quite important to draw firmer conclusions about the origin of the high - energy emission .    the identification of the synchrotron component peaking at @xmath230 in the x - ray - dominated knots of the 3c  273 jets calls for a follow - up deep observation with the _ spitzer _ irac with better configurations . our _ spitzer _ cycle-3 proposal ( pi : uchiyama ) requesting follow - up deep observations of 3c  273 , as well as the observations of 10 other jets , has recently been approved . ultimately , the _ james webb space telescope _ , a future large infrared - optimized space telescope , will have an excellent capability to explore the jet emission in the irac band with much improved resolution and sensitivity . an interesting implication of this work is that a number of optical jets in radio - loud quasars discovered so far may be directly related to the x - ray emission rather than to the radio emission , as in the 3c  273 jet . for example , in @xcite , we have associated the optical flux of the jet knot in the quasar pks 0637@xmath4752 with the highest energy part of the synchrotron component . however , the optical flux could be attributed equally to the low energy part of the second component , given the result presented here . this issue should be addressed in future analyses based on multiwavelength observations of _ chandra_-detected quasar jets . [ in this context , we note that our discussions are not concerned with low - luminosity fr i jets such as m  87 ( e.g. , * ? ? ? * ) , in which the x - ray emission appears to lie on the extrapolation of the emission at lower frequencies , and is widely believed to be of synchrotron origin . ] it is clear from our results that the measurements over as wide a wavelength coverage as possible in the infrared - optical domain are of great importance in studying the particle acceleration mechanisms in the large - scale jets of powerful quasars . unfortunately , quasar jet emission in the optical region of the spectrum is very faint , and only a few optical slopes for the powerful quasars have been measured @xcite . further _ observations are therefore particularly helpful even though the spatial resolution is not optimal for the study of jet emissions . also , a careful measurement of x - ray spectral index and its comparison with the optical fluxes is valuable to progress toward the understanding of the dominant x - ray emission mechanism operating in the quasar jets . we wish to thank felix aharonian for invaluable discussion . we also thank the anonymous referee for constructive comments and suggestions . this work was supported in part by nasa grant nag5 - 12873 . this work is based on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under nasa contract 1407 . support for this work was provided by nasa through contract number rsa 1265389 issued by jpl / caltech . the national radio astronomy observatory is operated by associated universities , inc .  under a cooperative agreement with the national science foundation . aharonian , f. a. 2002 , , 332 , 215 albert , c. e. , blades , j. c. , morton , d. c. , lockman , f. j. , proulx , m. , & ferrarese , l. 1993 , , 88 , 81 atoyan , a. m. , & dermer , c. d. 2001 , , 87 , 221102 atoyan , a. m. , & dermer , c. d. 2003 , , 586 , 79 atoyan , a. m. , & dermer , c. d. 2004 , , 613 , 151 bahcall , j. n. , kirhakos , s. , schneider , d. p. , davis , r. j. , muxlow , t. w. b. , garrington , s. t. , conway , r. g. , & unwin , s. c. 1995 , , 452 , l91 begelman , m. c. , & sikora , m. 1987 , , 322 , 650 biermann , p.  l. , & strittmatter , p.  a.  1987 , , 322 , 643 celotti , a. , ghisellini , g. , & chiaberge , m. 2001 , , 321 , l1 chartas , g. , et al . 2000 , , 542 , 655 cheung , c.  c.   2002 , , 581 , l15 conway , r. g. , garrington , s. t. , perley , r. a. , & biretta , j. a. 1993 , , 267 , 347 courvoisier , t. j. -l . 1998 , , 9 , 1 dermer , c. d. , & atoyan , a. m. 2002 , , 568 , l81 davis , r. j. , muxlox , t. w. b. , & conway , r. g. 1985 , , 318 , 343 fazio , g. , et al.2004 , , 154 , 10 fruchter , a. s. , & hook , r. n. 2002 , , 114 , 144 georganopoulos , m. , & kazanas , d. 2004 , , 604 , l81 georganopoulos , m. , kazanas , d. , perlman , e. , & stecker , f. w. 2005 , , 625 , 656 ghisellini , g. , tavecchio , f. , & chiaberge , m. 2005 , , 432 , 401 ginzburg , v.  l. , & syrovatskii , s.  i.  1965 , , 3 , 297 grandi , p. , & palumbo , g. g. c. 2004 , science , 306 , 998 hao , l. , et al.2005 , , 625 , l75 hardcastle , m.2006 , , 366 , 1465 harris , d. e. , & krawczynski , h. 2002 , , 565 , 244 harris , d. e. , mossman , a. e. , & walker , r. c. 2004 , , 615 , 161 harris , d. e. , & stern , c. p. 1987 , , 313 , 136 honda , y.  s. , & honda , m.   2004 , , 613 , l25 inoue , s. , & takahara , f. 1996 , , 463 , 555 jester , s. , rser , h .- j . , meisenheimer , k. , & perley , r. a. 2002 , , 385 , l27 jester , s. , rser , h .- j . , meisenheimer , k. , & perley , r. a. 2005 , , 431 , 477 jester , s. , rser , h .- j . , meisenheimer , k. , perley , r. a. , & conway , r. g. 2001 , , 373 , 447 kataoka , j. , & stawarz ,  . 2005 , , 622 , 797 makovoz , d. , & marleau , f. r. 2005 , , 117 , 1113 malkov , m. a. , & drury ,  l.  oc.2001 , rep . phys . , 64 , 429 marshall , h. l. , et al.2001 , , 549 , l167 marshall , h. l. , et al.2005 , , 156 , 13 martel , a. r. , et al.2003 , , 125 , 2964 mcleod , k. k. , & rieke , g. h. 1994 , , 431 , 137 meisenheimer , k. , & heavens , a. f. 1986 , , 323 , 419 neronov , a. , semikoz , d. , aharonian , f. , kalashev , o. 2002 , , 89 , 051101 - 1 neumann , m. , meisenheimer , k. , & rser , h .- j . 1997 , , 326 , 69 ostrowski , m. 2000 , , 312 , 579 perlman , e.  s. , & wilson , a.  s.   2005 , , 627 , 140 poutanen , j.   1994 , , 92 , 607 reach , w. t. , et al.2005 , , 117 , 978 ridgway , s.  e. , & stockton , a.1997 , , 114 , 511 rser , h .- j . , conway , r. g. , & meisenheimer , k. 1996 , , 314 , 414 rser , h .- j . , & meisenheimer , k. 1991 , , 252 , 458 rser , h .- j . , meisenheimer , k. , neumann , m. , conway , r. g. , & perley , r. a. 2000 , , 360 , 99 robson , e. i. , gear , w. k. , brown , l. m. j. , courvoisier , t. j. -l . , smith , m. g. , griffin , m. j. , & blecha , a. 1986 , , 323 , 134 sambruna , r. m. , gambill , j. k. , maraschi , l. , tavecchio , f. , cerutti , r. , cheung , c. c. , urry , c. m. , & chartas , g. 2004 , , 608 , 698 sambruna , r. m. , urry , c. m. , tavecchio , f. , maraschi , l. , scarpa , r. , chartas , g. , & muxlow , t. w. b. 2001 , , 549 , l161 scarrott , s. m. , & rolph , c. d. 1989 , , 238 , 349 schmidt , m. 1963 , , 197 , 1040 schwartz , d. a. , et al.2000 , , 540 , l69 sikora , m. , & madejski , g. 2000 , , 534 , 109 spergel , d. n. , et al.2003 , , 148 , 175 stawarz ,  . 2004 , , 613 , 119 stawarz ,  . , & ostrowski , m. 2002 , , 578 , 763 stawarz ,  . , sikora , m. , & ostrowski , m. 2003 , , 597 , 186 tavecchio , f. , maraschi , l. , sambruna , r. m. , gliozzi , m. , cheung , c. c. , wardle , j. f. c. , urry , c. m. 2006 , , 641 , 732 tavecchio , f. , maraschi , l. , sambruna , r. m. , urry , c. m. 2000 , , 544 , l23 trler , m. , et al.1999 , , 134 , 89 uchiyama , y. , urry , c. m. , van duyne , j. , cheung , c.  c. , sambruna , r.  m. , takahashi , t. , tavecchio , f. , & maraschi , l.   2005 , , 631 , l113 wilson , a.  s. , & yang , y.   2002 , , 568 , 133","summary":"sensitive and detailed measurements of optical polarization are important to establish the radiation mechanism responsible for the high - energy emission . the present study offers new clues as to the controversial origin of the x - ray emission seen in many quasar jets .","abstract":"we have performed infrared imaging of the jet of the quasar 3c  273 at wavelengths 3.6 and with the infrared array camera ( irac ) on the _ spitzer space telescope_. when combined with the radio , optical and x - ray measurements , the irac photometry of the x - ray - bright jet knots clearly shows that the optical emission is dominated by the high - energy emission component of the jet , not by the radio synchrotron component , as had been assumed to date . the high - energy component , represented by a power - law from the optical through x - ray , may be due to a second synchrotron component or to inverse compton scattering of ambient photons . in the former case , we argue that the acceleration of protons exceeding energies of or possibly even to would be taking place in the jet knots of 3c  273 assuming that the acceleration time is proportional to the particle gyroradius . in contrast , the inverse compton model , into which highly relativistic doppler beaming has to be incorporated , requires very low - energy electrons of in the jet knots . the present polarization data in the radio and optical would favor the former interpretation in the case of the 3c  273 jet . sensitive and detailed measurements of optical polarization are important to establish the radiation mechanism responsible for the high - energy emission . the present study offers new clues as to the controversial origin of the x - ray emission seen in many quasar jets ."}
{"article_id":"0912.1315","section_id":"i","document":"the main result of this paper shows there are closed orientable 3-manifolds which have distinct distance three genus two heegaard splittings . on the other hand , it is shown in @xcite , which corrects an omission in the 1998 paper @xcite in which rubinstein and scharlemann applied their powerful method of sweepouts to the problem of classifying genus two heegaard splittings of closed orientable 3-manifolds , that all of the constructions of potential alternate genus two heegaard splittings described in @xcite yield splittings of distance no more than two . it follows that the constructions of @xcite must be augmented by those of @xcite in order to obtain all possible alternate genus two splittings of a closed orientable 3-manifold .","summary":"we describe an example of a closed orientable 3-manifold with distinct distance three genus two heegaard splittings .","abstract":"we describe an example of a closed orientable 3-manifold with distinct distance three genus two heegaard splittings . this demonstrates that the constructions of alternate genus two heegaard splittings of closed orientable 3-manifolds described by rubinstein and scharlemann in their 1998 paper , _ genus two heegaard splittings of orientable 3-manifolds _ , does not yield all alternate genus two splittings , and must therefore be augmented by the constructions described in ."}
{"article_id":"1003.0998","section_id":"i","document":"in recent times major advances in the experimental techniques have led to the realization of experiments in which quantum systems in a single particle regime are studied under their controlled interaction with some environment . a paradigmatic example in this context is given by the motion of a massive test particle in an interferometric setup , which gives rise to interference fringes as typical quantum signatures . when the coupling with the environment becomes of relevance , such interference fringes are gradually washed out , and a classical dynamics is eventually recovered . this phenomenon goes under the name of decoherence @xcite . its understanding and theoretical description require on the one hand a control over the environment , on the other hand a microscopic model for the interaction and the ensuing dynamics .    for the case of a tracer particle immersed in a dilute gas such a microscopic description has been obtained considering the centre of mass degrees of freedom only . the reduced dynamics is given by a master equation in lindblad form which has been called quantum linear boltzmann equation , since it provides the natural quantum counterpart of the classical linear boltzmann equation ( see @xcite for a recent review and references therein ) . the microscopic input is given by the complex scattering amplitudes describing the collisions between gas and test particle , while the gas is characterized by its density and momentum distribution . in this paper we consider an extension of this result , which includes internal degrees of freedom of the tracer particle . the microscopic derivation is performed along the lines of a general strategy for the derivation of markovian master equations , which relies on a scattering description of the interaction events @xcite . besides the gas properties , this approach takes as basic input the multichannel complex scattering amplitudes , which describe the influence of the internal states on the scattering events . indeed , when the scattering cross section does not only depend on the relative motional state between tracer and gas particle , such an extension becomes mandatory in order to correctly describe the dynamics . according to the markovian approximation , the obtained master equation is in lindblad form . this derivation confirms the structure of the dissipative term , which has been heuristically obtained in @xcite , further determining the coherent contribution to the dynamics due to forward scattering . the latter becomes relevant in the determination of the index of refraction for matter waves . when either type of degrees of freedom can be described in classical terms , a markovian quantum classical master equation is obtained . such a result , corresponding to a classical treatment of the motional degrees of freedom , has been considered in @xcite . in that context the name bloch - boltzmann equation was proposed for the equation , since for a two - level system an extension of the optical bloch equations to include a boltzmann - like collision term is obtained . in the same spirit , the name quantum bloch - boltzmann equation can be used to indicate a master equation , which gives a quantum description of both internal and centre of mass state . an interesting situation appears when in the final detection the internal state of the test particle is not resolved at the output of the interferometer . in this case the internal degrees of freedom become part of the environment . then a non - markovian dynamics for the motional state appears , which can be described in terms of a coupled set of lindblad equations for the unnormalized statistical operators corresponding to specific internal channels . this type of non - markovian dynamics can be considered as a generalized non - markovian lindblad structure . it arises as a mean over a classical index , which can take place e.g. as a consequence of the interaction with a structured reservoir @xcite . this situation is here considered in the study of the loss of visibility of the interference fringes in an interferometric setup . the ensuing decoherence effect is generally not described as an exponential loss of visibility depending on the strength of the interaction , as in the usual markovian case . the paper is organized as follows . in sect . [ sec : ms ] we consider the expression of the master equation , pointing to the main steps necessary for its derivation and putting into evidence the microscopic quantities determining its explicit form . a detailed microscopic derivation of the master equation is performed in appendix  [ sec : micr - deriv - mast ] . the master equation is given both in terms of matrix elements of the statistical operator in the momentum and internal energy eigenstates basis , as well as an explicit operator expression , which makes its lindblad structure manifest . this also allows to easily recover under suitable limits previously considered master equations , which describe either only one of the two kind of degrees of freedom or a hybrid quantum classical description of both . in sect . [ sec : decoh ] we show how the interplay between internal and motional states can influence the visibility in an interferometric setup for the study of decoherence , leading to a non - markovian behaviour in the reduction of the visibility of the interference fringes .","summary":"if in an interferometric setup the internal degrees of freedom are not detected at the output , the equation can be recast in the form of a generalized lindblad structure , which describes non - markovian effects .","abstract":"we address the microscopic derivation of a quantum master equation in lindblad form for the dynamics of a massive test particle with internal degrees of freedom , interacting through collisions with a background ideal gas . when either internal or centre of mass degrees of freedom can be treated classically , previously established equations are obtained as special cases . if in an interferometric setup the internal degrees of freedom are not detected at the output , the equation can be recast in the form of a generalized lindblad structure , which describes non - markovian effects . the effect of internal degrees of freedom on centre of mass decoherence is considered in this framework ."}
{"article_id":"1003.0998","section_id":"c","document":"we have derived the master equation describing the dynamics of a test particle with both translational and internal degrees of freedom , interacting through collisions with a low density background gas . this has been done building on the so - called monitoring approach @xcite , and confirms a previous heuristic argument put forward by one of us in @xcite . the present microscopic derivation further allows to determine the energy shift . as we have checked , the result reduces to known equations in suitable limits : the quantum linear boltzmann equation if the internal degrees of freedom are neglected @xcite , the master equation for an immobile test particle if the translational degrees of freedom are not relevant @xcite , as well as quantum classical markovian master equations if one or both kind of degrees of freedom can be treated as classical . note that the natural bases in the derivation was given by momentum for the motional degrees of freedom and energy for the internal ones , the latter corresponding to the channel basis of scattering theory . in these cases different channels are only coupled through the collision term . if another internal basis can be of interest , also coherent tunnelling effects appear . + we have further focused on the situation in which the internal degrees of freedom , in spite of influencing the collisional scattering cross section , are not probed by the measuring apparatus and therefore have to be averaged out from the set of the observed dynamical variables , thus effectively becoming part of the environment . the equation obtained in this situation is no more of lindblad type , but rather takes the form of a generalized lindblad structure @xcite . it can therefore describe behaviour quite different from that characterizing a markovian dynamics . solving these equations in the position representation for an initial factorized state , we have obtained an explicit expression for the visibility reduction in interferometric experiments when internal degrees of freedom are involved . the behaviour of the visibility can indeed be quite different from the exponential decay corresponding to a markovian dynamics , showing up e.g. oscillations and revivals . + the interplay between different degrees of freedom in a bipartite system is a natural source of non - markovian behaviour , when either degrees of freedom can not be controlled , thus acting as an environment . this scenario has here been studied in a concrete setting , assuming a factorized initial state , and describing the dynamics in terms of a generalized lindblad structure . such a choice of initial condition is relevant for the considered interferometric setting , it would be however of great importance to consider initially correlated states , which naturally appear when considering a non - markovian dynamics in a strong coupling regime . it would further be of interest to study whether , instead of using this generalized lindblad structure , one can obtain a closed description of the reduced system dynamics in terms of a master equation with a memory kernel , at least in some simplified situations . we plan to address these topics in future research work .","summary":"we address the microscopic derivation of a quantum master equation in lindblad form for the dynamics of a massive test particle with internal degrees of freedom , interacting through collisions with a background ideal gas .","abstract":"we address the microscopic derivation of a quantum master equation in lindblad form for the dynamics of a massive test particle with internal degrees of freedom , interacting through collisions with a background ideal gas . when either internal or centre of mass degrees of freedom can be treated classically , previously established equations are obtained as special cases . if in an interferometric setup the internal degrees of freedom are not detected at the output , the equation can be recast in the form of a generalized lindblad structure , which describes non - markovian effects . the effect of internal degrees of freedom on centre of mass decoherence is considered in this framework ."}
{"article_id":"1110.1613","section_id":"i","document":"if the hierarchy problem is solved by strong dynamics we expect resonances to appear around the tev scale which will be hopefully within the reach of the lhc . producing these states would allow to determine precious informations about the symmetries and dynamics of the strong sector . for example in technicolor theories the electro - weak symmetry is spontaneously broken by strong dynamics according to the pattern @xmath1 and the dynamics of the techni - resonances plays an important role .    due to the notorious difficulties of theories without a higgs , a logical possibility is that the higgs doublet itself is a composite state , as in this case the scale of strong dynamics could be larger , alleviating phenomenological problems . this can be most naturally realized if the higgs is a goldstone boson ( gb ) associated to the spontaneous breaking of a symmetry @xmath2 to @xmath3 , an idea which goes back to the 80s @xcite . one important ingredient of modern realizations is the mechanism of partial compositeness where the sm fermions and gauge fields mix to the composite states analogously to the photon-@xmath4 mixing in qcd . the simplest example based on the symmetry pattern @xmath5 was considered in @xcite in the context of randall - sundrum scenarios . these models are also dual to strongly coupled 4d theories through the ads / cft correspondence @xcite . in this paper we provide a general 4d effective description of composite higgs models ( chm ) with partial compositeness ( see @xcite for a review and refs . ) . our starting point will be the @xmath6model @xmath7 describing the low energy interactions of gbs . spin-1 resonances non - linearly realizing the symmetry can be very simply included by introducing an additional @xmath6model @xmath8 and gauging the diagonal subgroup of @xmath9 and @xmath2 . proceeding in the same way a tower of resonances can be included at will . fermionic resonances can be treated in a similar way . differently from other constructions we find it natural and economic to include complete @xmath2 multiplets . couplings to the elementary fields are simply accounted by adding kinetic terms for the sources associated to the operators of the composite sector . the motivation of our work is two - fold . given that the 5d theories under consideration are effective theories with a cut - off , it is natural to write an effective 4d lagrangian containing only the degrees of freedom below the cut - off : up to cut - off dependent effects the two theories will coincide . this is particularly useful because in phenomenologically relevant models only very few resonances lie below the cut - off . the same idea was considered in @xcite in the context of 5d models for qcd . moreover only the lowest resonances have a chance to be produced at the lhc , so for collider applications it is useful to write a truncation of the theory to the first multiplet of resonances . one practical advantage is that in this limit very simple , explicit formulas can be derived which are well suited for simulating the model at the lhc . our philosophy is here similar to the one of @xcite . in this ref . an effective lagrangian capturing the essential features of partial compositeness was considered but the full gb structure of the theory was not incorporated . this was also done recently in @xcite with a different construction from ours . since our framework is based on general symmetry principles it is also interesting to consider a fully 4d point of view and treat our effective theory with one set of @xmath2 multiplets on its own . this can be interesting because terms not obtained from the 5d theory can be added to the action compatibly with the symmetries which could be relevant phenomenologically . we will show in particular that they contribute to the @xmath0parameter allowing to reduce it for appropriate choice of the parameters . the paper is organized as follows . in section [ sec:2 ] we develop the general formalism to include an arbitrary tower of spin-1 and spin-1/2 resonances in a theory with global symmetry @xmath2 spontaneously broken to @xmath3 . various limits are considered which reproduce in particular higher dimensional theories and the ccwz construction @xcite . in section [ sec:3 ] we apply our tools to the minimal composite higgs @xmath5 focusing on the case where a single @xmath10 multiplet of resonances is included . all the results can be conveniently expressed in terms of 2-point functions of the composite sector which are collected in appendix [ sec : a ] . the higgs potential is discussed in section [ sec:4 ] and appendix [ sec : b ] . in section [ sec:5 ] we study the effect of non - minimal terms in the effective action . conclusions are in section [ sec:6 ] . couplings and decay widths of spin-1 resonances can be found in appendix [ appwidth ] .","summary":"our setup captures all the relevant features of 5d models and more in general of composite higgs models with partial compositeness . we focus on the minimal scenario where we include a single multiplet of resonances of the composite sector , as these will be the only degrees of freedom which might be accessible at the lhc . moreover our simplified approach is well adapted to simulate these models at the lhc .","abstract":"we propose a four dimensional description of composite higgs models which represents a complete framework for the physics of the higgs as a pseudo - nambu - goldstone boson . our setup captures all the relevant features of 5d models and more in general of composite higgs models with partial compositeness . we focus on the minimal scenario where we include a single multiplet of resonances of the composite sector , as these will be the only degrees of freedom which might be accessible at the lhc . this turns out to be sufficient to compute the effective potential and derive phenomenological consequences of the theory . moreover our simplified approach is well adapted to simulate these models at the lhc . we also consider the impact of non - minimal terms in the effective lagrangian which do not descend from a 5d theory and could be of phenomenological relevance , for example contributing to theparameter ."}
{"article_id":"1110.1613","section_id":"c","document":"in this note we have presented a simplified 4d description of composite higgs models with partial compositeness . our formalism allows to introduce an arbitrary tower of resonances , bosonic and fermionic , in a theory where the higgs is a gb . as a particular case one can reproduce the physics of higher dimensional models .    for phenomenological applications we focused on the minimal model with only the lowest lying resonances which provides a self - contained framework reproducing all the relevant features of composite higgs models at the lhc . for example our theoretical setup already allows to compute the higgs potential with a minimal number of degrees of freedom . we believe that this is the most natural and economic setup , being dictated by the symmetries of theory . as an example we considered in detail the chm@xmath117 scenario of @xcite with results comparable to the 5d scenario for similar choices of parameters .    while our construction was inspired by 5d models one can consider the truncation of the theory to the lowest resonances on its own . based on the symmetries of the theory more terms can be added to the lagrangian which do not follow from the discretization of the 5d theory . in particular we have shown that , as for the @xmath4 in qcd , these terms modify the coupling of the resonances to the gbs and could be of phenomenological relevance changing their decays and possibly reducing the @xmath0parameter . our work is the starting point for a study of the model at lhc . the simplified lagrangian allows to capture all the effects of compositeness and is simple enough to be implemented on an event generator . we hope to return to this in future work . we would like to thank roberto contino , leandro da rold and andrea wulzer for useful discussions . at would like to thank cern for partial support and hospitality .","summary":"we propose a four dimensional description of composite higgs models which represents a complete framework for the physics of the higgs as a pseudo - nambu - goldstone boson . we also consider the impact of non - minimal terms in the effective lagrangian which do not descend from a 5d theory and could be of phenomenological relevance , for example contributing to theparameter .","abstract":"we propose a four dimensional description of composite higgs models which represents a complete framework for the physics of the higgs as a pseudo - nambu - goldstone boson . our setup captures all the relevant features of 5d models and more in general of composite higgs models with partial compositeness . we focus on the minimal scenario where we include a single multiplet of resonances of the composite sector , as these will be the only degrees of freedom which might be accessible at the lhc . this turns out to be sufficient to compute the effective potential and derive phenomenological consequences of the theory . moreover our simplified approach is well adapted to simulate these models at the lhc . we also consider the impact of non - minimal terms in the effective lagrangian which do not descend from a 5d theory and could be of phenomenological relevance , for example contributing to theparameter ."}
{"article_id":"0705.4066","section_id":"c","document":"the conclusion of this paper is : the weakly charged spherically symmetric dust distribution considered here ( @xmath17 at @xmath118 and @xmath367 at @xmath119 ) must contain at least one of the following features :    \\1 . a big bang / big crunch singularity ;    \\2 . a permanent central singularity ;    \\3 . a shell crossing singularity in a vicinity of the center    \\4 . a finite time interval around the bounce instant in which the energy density becomes negative , and a transient momentary singularity of infinite energy density at a single point on the world line of the center of symmetry a fully nonsingular bounce is possible for a strongly charged configuration , @xmath368 , which can exist only with @xmath64  see the comments after ( [ 2.14 ] ) . this would be a collapse followed by a single bounce and re - expansion to infinite size . this phenomenon occurs also in the newtonian limit  the bounce here is caused by the prevalence of electrostatic repulsion over gravitational attraction . such an example was reportedly found , but never published , by ori and coworkers @xcite . a permanently nonsingular pulsating configuration of spherically symmetric charged dust does not exist . at most , a single full cycle of nonsingular bounce can occur , and shell crossings will necessarily appear during the second collapse phase . the nonsingular bounce occurs at @xmath46 , but the momentary isolated singularity at the center of symmetry is still there .    the possibility of @xmath2 going negative in the presence of electric charges does not seem to have been noticed and may need further work on its interpretation . if the negative energy density region existed permanently in some part of the space , with comoving boundary , then we might suspect that this is a consequence of a bad choice of parameters that implies unphysical properties in that region . however , here we have the case in which the energy density is positive for some time , and then these same matter particles acquire negative energy density in a time - interval around the bounce instant . this suggests that there is some physical process involved in this , which should be further investigated . a question arises now . the uncharged limit of the family of configurations defined by eqs . ( [ 2.1 ] )  ( [ 2.10 ] ) , @xmath41 , is the lematre  tolman ( l  t ) model @xcite . for the latter , shell crossings can be avoided , as is well - known since long ago @xcite . why , then , are they unavoidable with @xmath369 ? the answer is this : in the l  t model , the big bang ( bb ) or big crunch ( bc ) are unavoidable ( both are present when @xmath7 ) . in the cases that are colloquially called `` free of shell crossings '' , in reality the shell crossings are not removed , but shifted to the epoch before the bb or after the bc , or both . thus , the shell crossings are no longer in the domain of physical applicability of the model . when the bb / bc singularities are replaced with a smooth bounce in charged dust , the shell crossings that were hidden on the other side of bb / bc become physically accessible , and they terminate the evolution of the configuration .","summary":"a singularity of infinite energy density does exist  it is a point singularity situated on the world line of the center of symmetry .","abstract":"in a previous paper we formulated a set of necessary conditions for the spherically symmetric weakly charged dust to avoid big bang / big crunch , shell crossing and permanent central singularities . however , we did not discuss the properties of the energy density , some of which are surprising and seem not to have been known up to now . a singularity of infinite energy density does exist  it is a point singularity situated on the world line of the center of symmetry . the condition that no mass shell collapses to if it had initially thus turns out to be still insufficient for avoiding a singularity . moreover , at the singularity the energy density is direction - dependent : when we approach the singular point along a const hypersurface and when we approach that point along the center of symmetry . the appearance of negative - energy - density regions turns out to be inevitable . we discuss various aspects of this property of our configuration . we also show that a permanently pulsating configuration , with the period of pulsation independent of mass , is possible only if there exists a permanent central singularity .    n. copernicus astronomical center , polish academy of sciences    bartycka 18 , 00 716 warszawa , poland    email : akr@camk.edu.pl"}
{"article_id":"0801.2172","section_id":"i","document":"despite their old age and low metal content , galactic globular clusters ( gcs ) are now known to be dust factories @xcite . this has important implications for our understanding of mass loss from low - mass and metal - poor stars and for the replenishment of the interstellar medium ( ism ) within old , metal - poor stellar systems , such as gcs , dwarf spheroidal ( dsph ) galaxies , and galactic halos . all stars more massive than @xmath6 lose a significant fraction of their mass before they deflagrate or leave a compact remnant ( see reviews by * ? ? ? * ; * ? ? ? in the final stages of evolution , most stars enter higher stages of nuclear burning , and the products of this nucleosynthesis are transported to the stellar surface through convection or rotation . the chemically enriched mass that is recycled ( with some delay ) into the ism has a significant impact on any further star formation , and drives the chemical evolution within galaxies . in particular , the enrichment of the ism by dust is of great importance , as grains play important roles in many ism processes , including the formation of molecular hydrogen @xcite and planet formation . the winds of low and intermediate - mass stars on the upper red giant and asymptotic giant branches ( rgb and agb ) and massive red supergiants are prolific dust producers @xcite . the dust is an integral part of the driving mechanism of the most massive winds ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and our understanding of red giant mass loss relies heavily on the details of the dust condensation process ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * )  which is poorly understood in particular at low metallicity ( for a review , see * ? ? ? gcs are exquisite laboratories in which to study stellar winds because they represent the closest match to a single stellar population at metallicities that span over two orders of magnitude down to @xmath7 1% solar ( cf . mass loss remains important throughout the history of a gc @xcite ; even in old gcs , stars lose @xmath830% of their mass , most or all of which is removed from the cluster via a host of mechanisms including ram - pressure stripping during galactic plane crossings . rgb mass loss may be responsible for the blue horizontal branches observed in metal - poor gcs @xcite , and evidence for mass loss is seen in the line profiles of chromospherically active or pulsating red giants in gcs @xcite . there is mounting evidence for mass loss from gc red giants in the form of dusty winds @xcite . the first spectroscopic identifications of silicate dust are in the tip - agb star v1 in the massive gc 47tucanae @xcite and subsequent identification of minerals in other agb stars in 47tuc with _ spitzer _ irs observations @xcite . with [ fe / h ] @xmath9 , 47tuc is a metal - rich gc , providing an environment similar to that found , for instance , in the small magellanic cloud . to probe uncharted terrain , it is important to study dust in gcs at lower metallicity . the surprising detection of both interstellar and circumstellar dust and gas in the metal - poor gc m15 @xcite demonstrates that dust forms even in extremely metal - deficient environments . the most massive galactic gc , @xmath0centauri , contains enough stars in the dusty wind phase for an empirical reconstruction of the evolution of mass loss . its gravitational well ( @xmath10 km s@xmath3 ; * ? ? ? * ) could retain interstellar matter if winds are slow . @xmath0cen is located approximately 15 out of the galactic plane at a distance of @xmath115 kpc @xcite , so it is possible to probe the stellar population to the cluster core . the bulk of the stars in @xmath0cen have [ fe / h ] @xmath12 @xcite , a metallicity much lower than the environments in which circumstellar dust has traditionally been studied . complications arise because @xmath0cen also harbors a small fraction of stars up to an order of magnitude more metal - rich @xcite and an intermediate population of stars with an abnormally high helium content @xcite . red giants in @xmath0cen display a range in surface abundances , from oxygen - rich , m - type stars with titanium oxides , stars enhanced in ch or in cyanide ( cn ) , to genuine carbon stars with molecular carbon ( c@xmath13 ; * ? ? ? these disparate populations cause difficulties in stellar evolution studies of @xmath0cen , but since stars from the metal - rich and metal - poor populations can be distinguished by means of optical spectroscopy , @xmath0cen presents us with a unique opportunity to study the dust and mass loss within a single environment as a function of atmospheric chemistry . consensus has yet to be reached regarding the formation history of the different subpopulations @xcite . the spread and peculiarities in elemental abundances in @xmath0cen have been interpreted as evidence that this gc may be the remnant nucleus of a tidally disrupted dsph @xcite . if so , @xmath0cen may offer us insight into the mass loss and chemical enrichment in the much more distant nucleated dsphs , and perhaps dsphs in general .    here , we present nasa _ spitzer space telescope _ @xcite images of @xmath0cen and a catalog including the magnitudes of over 40,000 point - sources from 3.6 to 70  . the 24   mosaic , which enables reliable detection of individual circumstellar dust shells near the peak wavelength of their spectral energy distributions ( seds ) , provides the most dramatic improvement over previous data . we make use of proper motion @xcite and radial velocity @xcite measurements to separate cluster members from the substantial foreground stellar and background galaxy populations . optical spectroscopic information permits us to compare the contributions from stars of different composition and evolutionary status to their infrared ( ir ) emission and dust production . our observations are discussed in  [ sec : obs ] , photometry and the @xmath0cen point - source catalog are described in  [ sec : phot ] . the color - magnitude diagrams ( cmds ) , stellar populations , mass loss , and the intracluster medium ( icm ) dust are discussed in  [ sec : disc ] , and our conclusions are presented in  [ sec : concl ] .","summary":"we present a _ spitzer space telescope _ the survey covers approximately 3.2 the cluster half - mass radius at 3.6 , 4.5 , 5.8 , 8 , and 24  , resulting in a catalog of over 40,000 point - sources in the cluster .","abstract":"we present a _ spitzer space telescope _ imaging survey of the most massive galactic globular cluster ,centauri , and investigate stellar mass loss at low metallicity and the intracluster medium ( icm ) . the survey covers approximately 3.2 the cluster half - mass radius at 3.6 , 4.5 , 5.8 , 8 , and 24  , resulting in a catalog of over 40,000 point - sources in the cluster . approximately 140 cluster members ranging 1.5 dex in metallicity show a red excess at 24  , indicative of circumstellar dust . if all of the dusty sources are experiencing mass loss , the cumulative rate of loss is estimated at 2.9  4.2 10 yr , 63%  66% of which is supplied by three asymptotic giant branch stars at the tip of the red giant branch ( rgb ) . there is little evidence for strong mass loss lower on the rgb . if this material had remained in the cluster center , its dust component ( 1 10 ) would be detectable in our 24 and 70   images . while no dust cloud located at the center ofcen is apparent , we do see four regions of very faint , diffuse emission beyond two half - mass radii at 24  . it is unclear whether these dust clouds are foreground emission or are associated withcen . in the latter case , these clouds may be the icm in the process of escaping from the cluster ."}
{"article_id":"0801.2172","section_id":"c","document":"figure  [ fig : cmd1 ] displays the optical @xcite , the near - ir @xcite , and our mid - ir cmds . the cmds are corrected for reddening , as discussed in   [ sec : phot ] , with @xmath32 values from @xcite , but the effect of reddening on the mid - ir magnitudes is minimal . the irac and mips cmds shows very little structure aside from the rgb , and at longer wavelengths , a very broad , faint red plume . mid - ir isochrones that include all known rgb / agb properties , molecular bands , and dust considerations have yet to be developed . for reference , the brightest irac sources are labeled with large filled circles in figure  [ fig : cmd1 ] , and the three brightest m - type stars are also labeled with their leid numbers . bright irac sources that are not labeled are not cluster members . figure  [ fig : cmd2 ] shows the same cmds with different source types labeled in color . black points are confirmed cluster members ( confirmed non - members are not plotted ) and gray points , which are mostly located at the faint end of the rgb , do not have matches in the proper motion catalog . absorption in molecular bands may be responsible for some of the spread towards red colors on the rgb , but can not cause colors as red as those of the dustiest stars . however , while many of the very red stars on the mid- to lower - rgb in figure  [ fig : cmd1 ] may be dusty , it is very likely that some of the these sources are red due either to mismatches across bands , photometric errors , or contamination from cluster non - members . the @xmath33  [ 3.6 ] cmd clearly displays the rgb , agb , and hb . also visible as a sparsely populated branch to the red of the rgb is the rgb - a ( magenta points ) . the plume of stars that falls intermediate to the rgb and the hb is mostly due to foreground contamination @xcite , however the brighest cluster members in this plume ( @xmath34 13 , 1 @xmath35  [ 3.6 ] @xmath4 3 ) include post - agb stars such as leid 16018 , 30020 , 32015 , 32029 , and 43105 . note that while @xcite found that 16018 and 32029 are cluster non - members , @xcite determined through optical spectroscopy that they do in fact belong to @xmath0cen . as such , their membership probabilities have been set to 100% in the _ spitzer _ catalog . we identified hb stars ( blue points ) by their positions on the optical cmd @xcite . at ir wavelengths , the hb becomes indistinct from the rgb . the stellar density profile shown in figure  [ fig : denprof ] shows a paucity of hb stars in the center of the cluster . the non - central peak of the hb density profile is explained by the dominance of the cluster luminosity by bright agb and rgb stars in the most crowded regions . rgb - a stars are those located on the red branch of the rgb in optical and near - ir cmds ( see fig . 5 of * ? ? ? the offset of the rgb - a from the main rgb in optical and near - ir cmds has been attributed to a metallicity difference between the rgb - a and the regular rgb @xcite . except for a slight blue excess in the [ 3.6 ]  [ 4.5 ] colors , no metallicity separation is evident in the _ spitzer _ cmds . inspection of the luminosity functions ( fig . [ fig : lumfnc ] ) suggests that the stellar count begins to decrease at an accelerated rate near an absolute magnitude of @xmath255 at each wavelength . we chose this magnitude as the divide at all _ spitzer _ wavelengths between mass - losing agb candidates and the rest of the stellar population . we identify 75 mass - losing agb candidates , several of which have a red excess , although mass - loss can occur even without a dusty circumstellar envelope @xcite . the agb population is slightly more centrally concentrated than the total stellar population ( fig . [ fig : denprof ] ) , which is probably due to decreasing completeness of fainter sources towards the core . the locations on the cmd of stars that are identified as cn- and super - ba - rich by optical spectroscopy @xcite are marked in figure  [ fig : populations]a . the term super - ba - rich distinguishes stars with enhanced ba through pre - enrichment from those that are enriched beyond this , probably due to internal mixing processes . the super - ba - rich stars dominate the stars brighter than [ 24 ] @xmath11 8.5 , supporting the suggestion by @xcite that these stars are enriched in barium due to third - dredge up , and therefore delineate the thermal pulsating agb . the super - ba - rich stars may also be enriched in carbon , but not so much as to warrant their classification as genuine carbon stars . figure  [ fig : indiv ] shows the [ 8 ]  [ 24 ] cmd for cluster members , non - members , and sources without proper motion measurements . sources affected by blending at 24   are not plotted . the location on the cmd of the majority of sources without proper motion measurements suggests that most are likely galaxies . stars brighter than [ 24 ] @xmath11 10 with [ 8 ]  [ 24 ] @xmath22 0.1 likely harbor dust , while sources fainter than [ 24 ] @xmath11 10 are dusty if [ 8 ]  [ 24 ] @xmath22 0.2 . also marked in figure  [ fig : indiv ] and listed in table  [ tab : type ] are 16 stars of interest , identified by @xcite as six m - type stars ( open squares ) , five carbon stars that show c@xmath13 bands ( open triangles ) , and five post - agb stars ( closed circles ) , including fehrenbach s star @xcite near [ 24 ] = 9.25 . @xcite obtained optical spectra for five of the extremely red faint cluster members ( [ 24 ] @xmath22 10 and [ 8 ]  [ 24 ] @xmath22 0.8 ) ; these stars range from [ fe / h ] @xmath17 @xmath251.5 to [ fe / h ] @xmath17 @xmath252 , and two of the stars are abnormally hot ( @xmath36 7000 k ) . the remaining three stars appear to be normal rgb stars . visual inspection suggests that none of these five sources are affected by blending at 24  , however , it is possible that hb stars or rgb stars that have little or no emission at 24   are spatially coincident with background galaxies , causing them to appear to have red colors . this may also be the case for the other @xmath1110 faint , extremely red stars that are matched to cluster members . _ spitzer _ studies of gcs that do not have proper motion or radial velocity unambiguous confirmation of membership will suffer from contamination from red field stars mistaken for dusty cluster stars . many of the bright 24   sources in our images are field stars , including a variable m - type star with a period of 509 days ( leid 34041 ) . proper motion measurements allowed us to identify almost all bright and red cluster members in figure  [ fig : indiv ] against field stars , with only one bright star remaining for which no proper motion information is available . this bright source is most likely leid 55017 , which is a confirmed cluster non - member . the proper motion of leid 55017 is large enough that the _ spitzer _ coordinates are @xmath114 different from the @xcite coordinates . it is expected that metal - rich stars form more dust in their winds than their low metallicity counterparts due to the higher abundance of condensable material . we have metallicity information from @xcite for 32 of the @xmath11140 dusty stars in figure  [ fig : indiv ] . the brightest potentially dusty stars in the cluster range @xmath252.25 @xmath37 [ fe / h ] @xmath37 @xmath251.25 , i.e.  nearly the entire breadth of metallicities encountered in @xmath0cen . in fact , of this small sample , the reddest stars have [ fe / h ] @xmath38 @xmath251.5 ( fig . [ fig : dusty ] ) and two of the three brightest dusty stars ( leid 33062 , 44262 , 35250 ) have [ fe / h ] @xmath38 -2.0 , which suggests that dust production is not inhibited at these low metallicities .      since mass - loss rates ( @xmath39 ) scale directly with dust optical depth ( @xmath40 ) , all dusty stars have the potential to drive a wind @xcite . however , the value for @xmath39 derived from the optical depth also scales with the square root of the luminosity , so the brightest stars contribute a larger fraction of the cluster s cumulative mass - loss rate than the fainter stars . of the @xmath11140 red cluster members that remain after eliminating blends and non - members such as leid 34041 , which , as a bright m - type star with a period of 509 days , would dominate the cumulative mass - loss rate of the cluster if included . we used the agb models computed by @xcite to determine the mass - loss rates corresponding to the color of the red member stars with 0.15 @xmath4 [ 8 ]  [ 24 ] @xmath4 3.1 . luminosities were determined by scaling to the @xcite mass - loss tracks for agb stars with temperatures of 3297 and 3850  k and with silicate and alo@xmath41 dust compositions , however differing bolometric corrections for stars with different temperatures and metallicities are not taken into account . for reference , the colors corresponding to two sample optical depths are marked on the cmd in figure  [ fig : indiv ] and listed in table  [ tab : tau ] . the final mass - loss rates ( @xmath42 ) were scaled according to the following relationship :    @xmath43    where @xmath44 is the unscaled mass - loss rate from @xcite , @xmath45 is the wind velocity , @xmath46 is the dust - to - gas mass ratio ( @xmath47 0.005 at solar metallicity ) , and @xmath48 is the luminosity . following @xcite and @xcite , the velocity scales approximately as :    @xmath49    from equation ( 2 ) , the wind velocities of even the strongest mass - losing stars in @xmath0cen are slow ( @xmath50 ) . winds this slow may have difficulty driving a massive wind ; it is possible that the wind is driven by some other mechanism and that the dust is a by - product . @xcite suggest wind velocities of 5  10  km  s@xmath3 for agb stars in gcs ; if wind velocities are 5@xmath1 higher , the mass - loss rates would increase by the same factor . the @xcite models were calculated assuming spherical circumstellar dust shells , a constant mass - loss rate , and photospheres with solar metallicity . the last of these assumptions affects the stellar colors , which we used to determine the mass - loss rates . while we do take metallicity into account in the dust - to - gas ratio , increasing the mass - loss rates by a factor of seven , the metallicity dependence is not yet well established . the mass - loss rates computed using the @xcite models should therefore be considered a rough estimate . bolometric luminosities of the @xmath0cen sources can be estimated through fitting the sed or spectrum of each star , facilitating a better estimate of the real mass - loss rates ( i. mcdonald et al . , in preparation ) . assuming that all stars have the metallicity that comprises the majority of the population and that @xmath51 scales with metallicity ( * ? ? ? * ; * ? ? ? * @xmath52}$ ] = 1.7 , @xmath51 @xmath8 10@xmath53 ) , we find that the three brightest m - type stars ( fig .  [ fig : indiv ] ) contribute a total of @xmath39(gas @xmath54 dust ) @xmath17 1.8  2.8 @xmath1 10@xmath55 @xmath27 yr@xmath3 , depending on the temperature and dust composition . the combined mass - loss rate of these three stars is an order of magnitude less than the mass - loss rate measured for v1 in 47 tuc with ir spectroscopy @xcite , suggesting either that we have underestimated the mass - loss rates or that the variance of @xmath39 with metallicity is not a linear relation . figure  [ fig : mlr ] and table  [ tab : mlr ] shows that the cumulative mass - loss rate ( @xmath56 ) of the @xmath11140 dusty stars together is less than twice the combined mass - loss rate of the three brightest m - type stars ( leid 33062 , 44262 , 35250 ) . however , the fainter stars may be contributing more to the total mass - loss rate of the cluster if their dust - to - gas ratios are smaller . to compare @xmath56 to the number of dusty stars present at each magnitude , we also plot the percentage of stars that are dusty ( @xmath57 ) in figure  [ fig : mlr ] , binned by half magnitudes . @xmath57 remains roughly constant at 10%  20% for [ 24 ] @xmath22 9.5 , causing the cumulative mass - loss rate to slowly increase at [ 24 ] @xmath22 8 . the increase in @xmath56 at [ 24 ] @xmath11 11 is due to the very red sources ( [ 8 ]  [ 24 ] @xmath22 1.0 ) at these magnitudes . it is possible that many of the faint stars with red excess are not truly dusty ( see  [ sec : agb ] ) . since the cumulative mass - loss rate does not increase much over more than 2 magnitudes on the upper - rgb , it is unlikely that even fainter stars , which are generally warmer and do not pulsate strongly , contribute significantly to the dust - traced mass loss .    in a _ study of 47 tuc , @xcite find that red stars occupy the cmd from the trgb down to the hb and conclude that mass - loss is occurring at a significant rate along the entire rgb . however , at least 25% of the red sources in @xmath0cen have proven to have red colors because of blending effects at 24   ( see   [ sec : catalog ] ) . figure  [ fig : mlr ] shows that these blended sources can increase the cumulative mass - loss rate by up to 17% . in more crowded clusters like 47 tuc , blending will affect an even larger percentage of red stars . indeed , it is evident in figure 2 of @xcite that the cmd covering the central region of the cluster is affected by blending , since the many red sources claimed to exist between 2 @xmath58 @xmath37 0 have no equivalent in the cmd for the outer regions of the cluster . by eliminating these blends , we find that significant dusty mass loss occurs only at or near the trgb . two previous mid - ir studies of gcs detected several very red , faint sources @xcite . both studies offer the possibility that these sources are dusty , mass - losing stars . while the nature of the sources has yet to be established , we find that after weeding out pesky field stars and background galaxies via proper motion information , very few of the confirmed @xmath0cen cluster members reside in this region of the cmd ( fig . [ fig : indiv ] ) , and significant dusty mass loss occurs only near the very tip of the rgb or agb . in the case of ngc 362 @xcite , these faint , red sources may be background agb stars belonging to the small magellanic cloud , however in other gcs , these sources are more likely to be background galaxies .    if the current population in @xmath0cen is representative of the cluster s population at all times , then the cluster has lost at least 1  2 @xmath27 of material ( 1  2 @xmath1 10@xmath59 of dust ) through stellar mass loss since its last galactic plane crossing , which occurred more than 3.4 @xmath1 10@xmath60 years ago @xcite . @xcite find a few post - agb stars in @xmath0cen . assuming a post - agb lifetime of several @xmath61 yr and 0.1 @xmath27 of mass shed on the agb , this could have produced up to 100 @xmath27 of lost mass . this comparison suggests that either these agb stars lose on average less than 0.1 @xmath27 on the agb , or that our mass - loss rate estimates are too low ( for instance because the wind velocity is actually higher and/or the dust - to - gas ratio is lower than assumed here ) . background galaxies ( green points in fig .  [ fig : cmd1 ] ) dominate the faint , red plume in the [ 3.6 ]  [ 8 ] cmd due to strong pah emission at 8   @xcite . the coverage overlap between the 3.6   and 8   mosaics is @xmath110.3 deg@xmath62 , yielding a density of 2823 galaxies / deg@xmath62 . this number increases to 3174 galaxies / deg@xmath62 if we consider undetected galaxies behind the cluster center ( an area of @xmath1111 arcmin@xmath62 , see fig .  [ fig : denprof ] ) . the red and faint region of the [ 3.6 ]  [ 24 ] cmd is also heavily populated with sources . if these 24   sources are all background galaxies , the galaxy density derived from this cmd is 2681 galaxies / deg@xmath62 , which increases to 3015 galaxies / deg@xmath62 when considering sources located behind the cluster core . when including all sources with very red colors and faint magnitudes at all wavelengths , we find a total background galaxy density of @xmath111  @xmath1  10@xmath63 galaxies / deg@xmath62 ( fig . [ fig : denprof ] ) .    to determine the expected background galaxy density , we queried the swire extragalactic database @xcite for sources located in the same region of the cmd as our galaxy candidates . in the six swire fields , there are @xmath11900  2200 sources / deg@xmath62 in the [ 3.6 ]  [ 8 ] cmd and 900  1900 sources / deg@xmath62 in the [ 3.6 ]  [ 24 ] cmd . our images are slightly more sensitive than the swire data , but when comparing identical regions of the cmd , the galaxy densities in our cmds fall within the range of the swire galaxy densities , strengthening the argument that the sources we have identified as galaxy candidates are indeed background galaxies . it is also possible that the faintest sources in the red [ 3.6 ]  [ 8 ] and [ 3.6 ]  [ 24 ] plumes are either stellar blends or regular rgb stars whose fluxes are poorly determined due to their proximity to the completion limit , causing them to have a non - zero color . nine point - sources appear in the 70   mosaic , although none are the red , possibly dusty cluster members discussed in  [ sec : agb ] and  [ sec : mlr ] . one of these sources is resolved at the shorter wavelengths and appears to be a background spiral galaxy ( 2masx j132726214746042 ; fig . [ fig : gal ] ) . this galaxy shows a ring of pah emission at 8   that is reminiscent of the famous star - forming `` ring of fire '' , seen in m31 @xcite . two of 70   sources are near confirmed cluster members @xcite ; source 1 is 3.7 from leid 27094 , a distance that is within the half - width , half - maximum of the 70   psf , and source 4 is 1.0 from leid 46055 . optical spectra for both leid stars are reported by @xcite and reveal that both stars have [ fe / h ] @xmath64 1.25 and @xmath65 @xmath64 5000  k. leid 27094 is ch strong and appears to be a normal rgb star , while leid 46055 is ch and cn strong , and is ba - rich , suggesting that it may be enriched in carbon from third dredge - up . despite the proximity in position between these two leid sources and sources 1 and 4 , the leid sources may be associated with warmer stars that appear in the irac mosaics as secondary stars blended with sources 1 and 4 , and not with the corresponding 70   source . the remaining six 70   sources are not near any known cluster members . we measured 70   fluxes for the eight point - sources with the aperture feature of _ imexamine _ in version 2.12.2 of iraf . aperture radii were initially set to 3@xmath1 the fwhm of each source and three iterations were performed to find the optimal radius . the median of the background was subtracted from the flux and the appropriate mips aperture correction was applied . fluxes are listed in table  [ tab:70flux ] and the 3.6 to 70   seds are shown in figure  [ fig:70sed ] . aside from sources 1 and 4 , all of the sources appear to be unaffected by blends at all irac wavelengths .    for each 70   source , we performed a reduced-@xmath66 fit of a two - component blackbody curve that include 2mass @xmath67 fluxes to better define the warmer blackbody . source 8 falls off of our irac images , so its irac fluxes were determined by using an earlier epoch of data from the gehrz guaranteed time observing program with _ spitzer _ ( pid 132 ) with data reduction identical to that described in  [ sec : obs ] . the fits take the photometric errors into account . sources 3 , 5 , 7 , and 8 are underconstrained for this fitting technique when we exclude the anomalously bright 5.8 and 8   points from the fit ; for these sources , we decreased the number of fitting parameters by fixing the temperatures to 1000 to 14,000  k and 40 to 90  k for the blue and red blackbodies , respectively , and choosing the temperatures that gave the best reduced-@xmath66 . the irac and mips color corrections were applied by iterating the fit until the corrections remained constant within 1% . while a dual - blackbody fits well with most of the 70   sources , we point out that the dust around these sources may be emitting over a range of temperatures . better fits were obtained by excluding the 8   point , which is above the blue blackbody for all eight sources . to a lesser degree , the 5.8   point is also systematically brighter than the blue blackbody component , suggesting that there is a range of dust temperatures causing warm dust to radiate above the blackbody at 5.8   and perhaps also at 8  . however , the 5.8   points are still included in the fit for source 3 in order to keep the fit properly constrained . the resulting blackbodies are overplotted in figure  [ fig:70sed ] and fitting results are shown in table  [ tab : bb70 ] . the emission features at 5.8 and 8  , where pah emission dominates , and the relatively flat seds of the non - blended sources suggests that all or most of these sources are background galaxies ( for examples of _ spitzer _ galaxy seds , see * ? ? ? * ) . for comparison , an sed of the resolved spiral galaxy is shown in figure  [ fig : galsed ] . we determined the flux by placing square apertures of roughly 45 @xmath1 50 on the galaxy and subtracting the median background . as with source 8 , the galaxy falls off of our irac coverage , so data from pid 132 is used to determine its irac fluxes . this sed is similar to the other eight , except that it lacks the slight excess emission at 5.8   that many of the other sources exhibit . the cold dust component of the blackbody fits for the eight unidentified sources range in temperature from @xmath1150  k to 68  k  a temperature commensurate with these objects being post - thermal pulse stars , stars suffering from episodic mass loss on the rgb , or post - agb stars . however , the temperatures of all eight sources are also consistent with dust in star forming regions that dominate the galactic far - ir emission . at a temperature of 48.8 @xmath31 0.8  k , the cold blackbody component of the resolved galaxy is colder than the other eight 70   sources , which may suggest that the warmer sources are of a different nature . although , with so few constraints in the blackbody fits , one might argue that the temperatures of all nine sources are consistent with each other . if the 70   sources are dusty agb stars , the flux at 8   may be included in the wing of a broad emission feature centered at 9.5   due to amorphous silicate grains that overlaps with the irac 8   bandpass . the 9.5   feature is also detected in the 8  13   spectrum of a particularly red , large - amplitude variable star in 47  tuc @xcite . the positions of the 70   sources on the [ 8 ]  [ 24 ] cmd are marked in figure  [ fig : populations]b . all sources lie redward of the rgb and near the brighter end of the cmd . however , the 3.6 and 4.5   magnitudes of sources 2 , 3 , 6 , 7 , and 8 ( triangles ) are fainter than 12.5 magnitudes , suggesting that these sources are indeed galaxies . sources 1 and 4 lie on the brighter end of the rgb , but they are blended with the aforementioned leid sources at the shorter wavelengths , which will cause an artificial increase in brightness . while near - ir redshift measurements or radial velocity measurements would conclusively determine the nature of these sources , analysis of the _ spitzer _ data strongly suggests that they are all background galaxies .      despite ongoing stellar mass loss in @xmath0cen , there are no known detections of any phase of icm material in the cluster . the wind velocities discussed in  [ sec : mlr ] are @xmath68 10 km s@xmath3 for metal - poor , dust - driven winds from low - mass agb stars . such velocities are much less than the escape velocity of @xmath0cen at 1 r@xmath69 ( @xmath70 @xmath17 44 km s@xmath3 ; * ? ? ? * ) , but if the dust and gas are not well coupled , then the dust velocity may be higher . rgb and agb wind velocities measured from h@xmath71 emission wings can be as high as the cluster escape velocity , however it is likely that h@xmath71 wings are due to pulsation and/or chromospheric activity instead of the circumstellar shells of stars . core velocities originate in the chromospheres and are typically lower ( @xmath37 15 km s@xmath3 ) , but there have been at least two observations of high velocities from the ir line @xcite . if the winds are indeed slow and the total mass - loss rate discussed in  [ sec : mlr ] has been constant since the last galactic plane crossing , then , barring any icm removal mechanisms and assuming that all stars belong to the population with the lowest metallicity , 1  2 @xmath27 of material should have accumulated in the cluster . this mass estimate includes only dusty mass loss on the rgb and agb ; mass loss from non - dusty stars on the rgb and from stars that lose significant mass in such a brief period of time that it may easily have been missed ( e.g. , associated with the formation of a planetary nebula ) may cause this estimate to increase by a factor of two or three . based on the total amount of agb mass loss , which is the only source of dust , we expect a dust mass of @xmath72 = @xmath73 @xmath8 1  2 @xmath1 10@xmath53 @xmath27 of dust . since the estimate of the time since the last galactic plane crossing is a lower limit ( @xmath22 3.4 @xmath1 10@xmath60 yr ; * ? ? ? * ) , the predicted icm dust mass may be higher . the average 1 @xmath18 sensitivity of our 24   mosaic is @xmath112.5 @xmath1 10@xmath74 mjy / str . following @xcite , the relationship between the dust mass and the expected ir flux density is :    @xmath75    where @xmath76 is the distance to @xmath0cen , @xmath77 is the dust absorption coefficient ( cm@xmath62 g@xmath3 ) , @xmath79 is the dust temperature ( k ) , and @xmath80 ) is the planck function in cgs units . assuming a standard mathis - rumpl - nordsieck dust distribution @xcite and an ism - type dust composition of graphite and silicate grains , @xmath77 is taken to be 56 @xmath31 11 cm@xmath62 g@xmath3 @xcite , although this value could be up to a decade larger . a cloud with 1  2 @xmath1 10@xmath53 @xmath27 of dust and an equilibrium temperature of 70 k would yield a 24   flux density of 23  45 mjy . with our sensitivity , we are capable of detecting 23 mjy to the 3 @xmath18 level in our 24   mosaic if all of the dust is uniformly distributed within an area of 2 @xmath1 2 , or a radius of @xmath81 a small , centrally located cloud at the 3 @xmath18 level would be detectable over the background stellar emission in the 24 and 70   mosaics . however , unlike in m15 @xcite , our mips images do not show a large dust cloud located at the center of @xmath0cen .    while there is no central icm dust cloud in @xmath0cen , there is faint , diffuse emission covering nearly the entire 24   image to the south of the cluster center , including several small regions of concentrated extended emission on the outskirts of the cluster that appear near the 3 @xmath18 limit ( figs . [ fig : icm ] and  [ fig : abcd ] ) . feature a ( fig . [ fig : icma ] ) appears at 8 , 24 , and 70  , features b and c appear at 8 and 24  , and feature d appears only at 24  , as the coverage is not identical across all bands . the probability that these features are artefacts is quite low as they each appear in more than 95% of the bcd images at various array positions .    it is uncertain whether features a  d are associated with the cluster or are part of the foreground . the morphology of feature a provides the strongest evidence for cluster association , as the warmer 8   emission lies closer to the cluster center than the cooler 24 and 70   emission ( figs .  [ fig : abcd ] and  [ fig : icma ] ) . moreover , the warmer portion is approximately perpendicular to the direction towards the cluster center . this configuration suggests the possibilities that either a warm wind is pushing the icm out of the cluster or that the 8   arc is optically thick and is being irradiated by the cluster s stellar radiation field with cold dust in its shadow . a determination of the dust temperature would aid in ascertaining the origin of feature a. unfortunately , only very small portions of feature a are present in the _ spitzer _ mosaics at all wavebands ( fig . [ fig : icma ] ) , and the limited coverage makes it impossible to reliably determine the temperature of the dust from an sed .    the case for an icm origin for features a  d is strengthened by our discovery of an unreported cloud near the velocity of @xmath0cen ( fig . [ fig : hipass ] ) in public data from the parkes all - sky survey ( hipass ; * ? ? ? * ) , which may have also been detected by @xcite in earlier observations . the center of this feature is not spatially coincident with any of the dust features , but rather lies @xmath1115 to the southeast of the cluster center , just on the edge of the coverage of our mips mosaic ( fig . [ fig : icm ] ) . the velocity of the feature ( @xmath82 190 km s@xmath3 ) suggests a connection to @xmath0cen ( @xmath83 230 km s@xmath3 ) . @xcite argue instead that , because the feature is detected on only one side of the cluster , it is more likely to be a small high - velocity cloud that is part of the magellanic stream ( * ? ? ? * @xmath84 = 200 km s@xmath3 ) . while an association between the feature and the magellanic stream is a possibility , similar offset clouds have been discovered in larger dsph galaxies @xcite , so finding a cloud that is associated with @xmath0cen may not come as a surprise . in m15 , dust and trace each other in the icm @xcite . therefore , if the feature is indeed associated with @xmath0cen , it is reasonable to assume that dust is also present . since both the dust and the feature are located well outside 1 @xmath16 , it is possible that we are seeing the icm in the process of escaping the cluster .","summary":"if this material had remained in the cluster center , its dust component ( 1 10 ) would be detectable in our 24 and 70   images . while no dust cloud located at the center ofcen is apparent , we do see four regions of very faint , diffuse emission beyond two half - mass radii at 24  .","abstract":"we present a _ spitzer space telescope _ imaging survey of the most massive galactic globular cluster ,centauri , and investigate stellar mass loss at low metallicity and the intracluster medium ( icm ) . the survey covers approximately 3.2 the cluster half - mass radius at 3.6 , 4.5 , 5.8 , 8 , and 24  , resulting in a catalog of over 40,000 point - sources in the cluster . approximately 140 cluster members ranging 1.5 dex in metallicity show a red excess at 24  , indicative of circumstellar dust . if all of the dusty sources are experiencing mass loss , the cumulative rate of loss is estimated at 2.9  4.2 10 yr , 63%  66% of which is supplied by three asymptotic giant branch stars at the tip of the red giant branch ( rgb ) . there is little evidence for strong mass loss lower on the rgb . if this material had remained in the cluster center , its dust component ( 1 10 ) would be detectable in our 24 and 70   images . while no dust cloud located at the center ofcen is apparent , we do see four regions of very faint , diffuse emission beyond two half - mass radii at 24  . it is unclear whether these dust clouds are foreground emission or are associated withcen . in the latter case , these clouds may be the icm in the process of escaping from the cluster ."}
{"article_id":"0801.2172","section_id":"c","document":"our _ spitzer _ multi - wavelength and dual - epoch study of the most massive galactic globular cluster , @xmath0cen , and the resulting point - source catalog provide the most complete mid- to far - ir atlas of any gc to date . despite @xmath0cen s rather unusual stellar population , the _ spitzer _ cmds show little structure beyond the division between the rgb stars belonging to the cluster and background galaxies . the hb stars and rgb - a stars are not separated from the rgb , except for a slightly blue [ 3.6 ]  [ 4.5 ] color for the rgb - a . nine sources are detected at 70  , one of which is a resolved spiral galaxy , and two of which are spatially coincident with optical sources that are known cluster members . if emission at 5.8 and 8   in the seds of the eight point sources is pah emission , then these sources are background galaxies .    by cross - referencing with a catalog of optical spectra @xcite , we confirm that super - ba - rich stars delineate the tip of the agb , likely due to a third dredge - up , and find that three m - type stars not only have strong red excess , but are brighter than the 24   trgb . attributing the excess ir luminosity to dust suggests that the three bright m - type stars dominate the cluster s cumulative mass - loss rate ( gas @xmath54 dust ) of 2.9  4.2 @xmath1 10@xmath55 @xmath27 yr@xmath3 . if the cluster mass - loss rate has remained constant since the last galactic plane crossing , then the cluster has lost at least 1  2 @xmath27 of dust - traced material over the last 3.4 @xmath1 10@xmath85 years .    the dusty stars in our sample range over @xmath111.5 dex in metallicity , suggesting that dust production is not inhibited even in stars with very low metal contents . in addition , our results show that , in @xmath0cen , significant dusty mass loss occurs near the very tip of the rgb or agb , concentrated in only a few individual stars , with little evidence for such mass loss lower on the rgb .    while our images are sensitive enough to detect the amount of dust expected in @xmath0cen based on the current mass - loss rate , no obvious icm dust clouds are apparent in the cluster center at 24 or 70  . we do find several regions of faint extended 24   emission on the outskirts of the cluster , but it is unclear whether these clouds are associated with the icm or are in the foreground . if the dust features are associated with the cluster , they are well outside the cluster half - mass radius , and could therefore be icm material that is in the process of escaping the cluster . we thank the anonymous referee for his / her careful reading of the manuscript and his / her valuable comments , which much improved the presentation of these data . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . m.  .l . b. is supported in part by the university of minnesota louise t. dosdall fellowship . m.  l.  b. , c.  e.  w. , and r.  d.  g. are supported in part by nasa through _ spitzer _ contracts 1276760 , 1256406 , and 1215746 issued by jpl / caltech to the university of minnesota . i.  m. is supported by a stfc / pparc studentship . a.  k.  d. acknowledges research support from _ contract 1279224 . @xmath86 ( ) & 3.6 , 4.5 , 5.8 and 8 & & 24 and 70 + program i d & 20648 & & 20648 + date ( ut ) & 2006 mar 26 & & 2006 feb 22 and mar 02 + aorkey & 14955264 & & ( 1495)5520 , 5776 , 6032 , 6288 , + & & & 6544 , and 6800 + coverage & 35 @xmath1 35 & & 24  : 35 @xmath1 55 + & & & 70  : 21 @xmath1 55 + single frame exposure time ( s ) & 10.4 & & 24  : 9.96 + & & & 70  : 10.49 + average depth ( no . frames ) & 10 & & 24  : 67 + & & & 70  : 36 + pixel size ( arcsec pixel@xmath3 ) & 1.22 & & 24  : 1.25 @xmath1 1.30 + & & & 70  : 4.93 @xmath1 5.03 + psf size & 3.6  : 1.7 @xmath1 1.6 & & 24  : 5.3 @xmath1 5.9 + & 4.5  : 1.6 @xmath1 1.6 & & + & 5.8  : 1.6 @xmath1 1.7 & & + & 8  : 1.8 @xmath1 1.8 & & +      3.6 & 16.7 @xmath31 0.1 & 15.9 @xmath31 0.1 + 4.5 & 16.7 @xmath31 0.1 & 15.9 @xmath31 0.1 + 5.8 & 16.0 @xmath31 0.1 & 14.5 @xmath31 0.1 + 8 & 15.8 @xmath31 0.1 & 14.3 @xmath31 0.1 + 24 & 11.9 @xmath31 0.1 & 11.6 @xmath31 0.1 +      18562&j132626.28@xmath25472520.06 & 8.49(05 ) & 8.52(06 ) & 8.53(04 ) & 8.47(04 ) & 8.48(05 ) & 100 & & cn & 35090 + 18563&j132626.28@xmath25473229.59&14.04(09)&14.16(07)&14.24(07)&14.32(07 ) & & & & & + 18564&j132626.28@xmath25471144.58&16.58(08)&16.37(09)&15.86(13 ) & & & & & & + 18565&j132626.28@xmath25474102.18&16.77(09)&16.68(16)&16.33(18 ) & & & & & & + 18566&j132626.29@xmath25473737.68&17.51(12)&17.71(46 ) & & & & & & & + 18567&j132626.29@xmath25471200.23&17.20(11)&17.13(20 ) & & & & & & & + 18568&j132626.29@xmath25473049.11&13.59(05)&13.58(07)&13.68(06 ) & & & 100 & hb & & 47097 + 18569&j132626.29@xmath25472651.06&13.23(05)&13.20(06)&13.18(05)&13.16(10 ) & & 98 & & & 39111 + 18570&j132626.30@xmath25471915.97&17.04(09)&17.00(22 ) & & & & & & & + 18571&j132626.30@xmath25473515.89&17.30(14)&17.55(27 ) & & & & & & & + 18572&j132626.30@xmath25471416.24&16.00(06 ) & & 16.21(19 ) & & & & & & + 18573&j132626.30@xmath25474159.18&13.22(06)&13.24(06)&13.28(04 ) & & & 86 & & cn & 72019 + 18574&j132626.31@xmath25471627.20 & 9.34(04 ) & 9.28(06 ) & 9.31(05 ) & 9.29(04 ) & 9.30(06 ) & 18 & & p & 16018 + 18575&j132626.31@xmath25473111.71&14.94(08)&15.06(11 ) & & & & & & & + 18576&j132626.31@xmath25472320.08&13.98(06)&13.99(05)&14.00(05)&14.02(06 ) & & & & & + 18577&j132626.31@xmath25474246.15&17.80(20)&17.95(52 ) & & 16.08(35 ) & & & galaxy & & + 18578&j132626.32@xmath25473543.47&13.12(04)&13.18(09)&13.11(08)&13.18(08 ) & & & & & + 18579&j132626.32@xmath25472534.32&10.13(05)&10.15(06)&10.15(05)&10.16(04)&10.18(09 ) & 100 & & & 36061 + 18580&j132626.32@xmath25474718.12 & & 15.72(08 ) & & 15.67(26 ) & & & & & + 18581&j132626.33@xmath25473132.57&12.23(08)&12.28(07)&12.24(06)&12.02(06 ) & & 100 & rgb - a & & 49082 +      14043&j132750.37@xmath25471542.79 & 11.75(06 ) & & 11.77(04 ) & & & carbon star + 16018&j132626.31@xmath25471627.20 & 9.34(04 ) & 9.28(06 ) & 9.31(05 ) & 9.29(04 ) & 9.30(06)&post - agb + 30020&j132549.95@xmath25472259.76 & 12.62(05 ) & 12.62(06 ) & 12.61(06 ) & 12.66(04 ) & & post - agb + 32015&j132538.44@xmath25472401.79 & 10.26(05 ) & 10.23(07 ) & 10.22(07 ) & 10.27(04 ) & 10.27(09)&post - agb + 32029&j132605.17@xmath25472342.43 & 9.11(05 ) & 8.96(05 ) & 8.82(04 ) & 8.81(04 ) & 8.48(05)&post - agb + 32059&j132628.13@xmath25472340.56 & 8.45(05 ) & 8.52(06 ) & 8.52(04 ) & 8.40(05 ) & 8.40(05)&carbon star + 33062&j132630.19@xmath25472427.89 & 6.96(05 ) & 6.88(06 ) & 6.74(05 ) & 6.27(04 ) & 4.98(05 ) & m - type + 35094&j132628.81@xmath25472523.60 & 8.43(05 ) & 8.56(07 ) & 8.48(05 ) & 8.50(05 ) & 8.43(05 ) & m - type + 35250&j132737.72@xmath25472517.37 & 7.39(05 ) & 7.45(06 ) & 7.35(05 ) & 7.23(04 ) & 6.61(05 ) & m - type + 35252&j132738.29@xmath25472505.60 & 14.21(04 ) & 14.07(10 ) & 14.49(08 ) & 14.15(10 ) & & m - type + 41071&j132614.42@xmath25472805.39 & 9.82(04 ) & 9.93(06 ) & 9.89(05 ) & 9.81(04 ) & 9.97(08)&carbon star + 42044&j132605.35@xmath25472820.80 & 7.59(04 ) & 7.74(06 ) & 7.67(04 ) & 7.55(05 ) & 7.33(05 ) & m - type + 43105&j132627.22@xmath25472847.47 & 9.56(04 ) & 9.54(06 ) & 9.46(04 ) & 9.44(04 ) & & post - agb + 44262&j132646.37@xmath25472930.35 & 7.05(05 ) & 6.85(05 ) & 6.68(04 ) & 6.42(04 ) & 5.85(05 ) & m - type + 44484&j132726.37@xmath25472916.93 & 8.44(06 ) & 8.63(05 ) & 8.53(05 ) & 8.51(05 ) & 8.44(05 ) & m - type + 52030&j132601.59@xmath25473306.08 & 7.40(05 ) & 7.48(06 ) & 7.44(05 ) & 7.32(04 ) & 7.33(05)&carbon star + 53019&j132544.03@xmath25473324.79 & 13.03(05 ) & 13.07(06 ) & 13.03(04 ) & 12.77(10 ) & & carbon star +          33062&sstocen j132630.19@xmath25472427.89 & 1.7 @xmath1 10@xmath55 & 1.3 @xmath1 10@xmath55 & 2.1 @xmath1 10@xmath55 & 1.5 @xmath1 10@xmath55 + 44262&sstocen j132646.37@xmath25472930.35 & 3.4 @xmath1 10@xmath89 & 2.8 @xmath1 10@xmath89 & 4.4 @xmath1 10@xmath89 & 3.5 @xmath1 10@xmath89 + 35250&sstocen j132737.72@xmath25472517.37 & 2.3 @xmath1 10@xmath89 & 1.8 @xmath1 10@xmath89 & 2.8 @xmath1 10@xmath89 & 2.2 @xmath1 10@xmath89 + & total @xmath39 for all dusty members & 3.4 @xmath1 10@xmath55 & 2.9 @xmath1 10@xmath55 & 4.2 @xmath1 10@xmath55 & 3.4 @xmath1 10@xmath55 +      1&sstocen j132723.86@xmath25472130.00 & 15.94(0.32 ) & 10.23(0.20 ) & 6.66(0.13 ) & 5.59(0.11 ) & 2.42(0.05 ) & 75.79(17.31 ) + 2&sstocen j132521.01@xmath25472623.43 & 1.96(0.04 ) & 1.49(0.03 ) & 1.96(0.04 ) & 12.33(0.25 ) & 14.33(0.29)&226.70(8.18 ) + 3&sstocen j132523.57@xmath25472813.61 & & 0.17(0.00 ) & 0.16(0.00 ) & 0.79(0.02 ) & 2.82(0.06)&246.73(18.94 ) + 4&sstocen j132615.23@xmath25473024.56 & 46.46(0.93 ) & 30.02(0.60 ) & 19.52(0.39 ) & 11.56(0.23 ) & 10.74(0.47)&158.02(7.96 ) + 5&sstocen j132426.26@xmath25473905.88 & & & & & 0.74(0.05 ) & 82.01(9.44 ) + 6&sstocen j132714.06@xmath25474112.83 & 0.93(0.02 ) & 0.63(0.01 ) & 0.60(0.01 ) & 2.60(0.05 ) & 3.54(0.07 ) & 53.04(11.19 ) + 7&sstocen j132655.87@xmath25474445.02 & 0.12(0.01 ) & 0.11(0.01 ) & 0.12(0.01 ) & 0.69(0.01 ) & 3.81(0.08)&131.46(23.81 ) + 8&sstocen j132712.89@xmath25474739.59 & 0.07(0.01 ) & 0.05(0.01 ) & 0.05(0.01 ) & 0.06(0.01 ) & 0.75(0.02)&107.50(23.54 ) + 9&2masx j13272621@xmath254746042 & 2.92(0.07 ) & 3.38(0.09 ) & 3.06(0.08 ) & 9.27(0.21 ) & 5.20(0.21)&617.08(73.84 ) +      1 & sstocen j132723.86@xmath25472130.00&35.8 & 4664 @xmath31 19 & 58.5 @xmath31 1.7 + 2 & sstocen j132521.01@xmath25472623.43 & 3.3 & 2688 @xmath31 25 & 67.5 @xmath31 0.5 + 3 & sstocen j132523.57@xmath25472813.61&199.7 & 1100 @xmath31 200 & 55.0 @xmath31 10 + 4 & sstocen j132615.23@xmath25473024.56&40.1 & 4329 @xmath31 16 & 66.5 @xmath31 0.8 + 5 & sstocen j132426.26@xmath25473905.88&75.0 & & 50.0 @xmath31 10 + 6 & sstocen j132714.06@xmath25474112.83&15.4 & 2901 @xmath31 28 & 68.0 @xmath31 2.0 + 7 & sstocen j132655.87@xmath25474445.02&52.2 & 1800 @xmath31 200 & 60.0 @xmath31 10 + 8 & sstocen j132712.89@xmath25474739.59&15.7 & 4000 @xmath31 200 & 50.0 @xmath31 10 + 9 & 2masx j13272621@xmath254746042&2.5 & 1084 @xmath31 29 & 48.8 @xmath31 0.8 +","summary":"imaging survey of the most massive galactic globular cluster ,centauri , and investigate stellar mass loss at low metallicity and the intracluster medium ( icm ) . approximately 140 cluster members ranging 1.5 dex in metallicity show a red excess at 24  , indicative of circumstellar dust . if all of the dusty sources are experiencing mass loss , the cumulative rate of loss is estimated at 2.9  4.2 10 yr , 63%  66% of which is supplied by three asymptotic giant branch stars at the tip of the red giant branch ( rgb ) . there is little evidence for strong mass loss lower on the rgb . it is unclear whether these dust clouds are foreground emission or are associated withcen . in the latter case , these clouds may be the icm in the process of escaping from the cluster .","abstract":"we present a _ spitzer space telescope _ imaging survey of the most massive galactic globular cluster ,centauri , and investigate stellar mass loss at low metallicity and the intracluster medium ( icm ) . the survey covers approximately 3.2 the cluster half - mass radius at 3.6 , 4.5 , 5.8 , 8 , and 24  , resulting in a catalog of over 40,000 point - sources in the cluster . approximately 140 cluster members ranging 1.5 dex in metallicity show a red excess at 24  , indicative of circumstellar dust . if all of the dusty sources are experiencing mass loss , the cumulative rate of loss is estimated at 2.9  4.2 10 yr , 63%  66% of which is supplied by three asymptotic giant branch stars at the tip of the red giant branch ( rgb ) . there is little evidence for strong mass loss lower on the rgb . if this material had remained in the cluster center , its dust component ( 1 10 ) would be detectable in our 24 and 70   images . while no dust cloud located at the center ofcen is apparent , we do see four regions of very faint , diffuse emission beyond two half - mass radii at 24  . it is unclear whether these dust clouds are foreground emission or are associated withcen . in the latter case , these clouds may be the icm in the process of escaping from the cluster ."}
{"article_id":"astro-ph0308064","section_id":"i","document":"following the commissioning of scuba on jcmt(holland et al . 1999 ) , sub - mm surveys of distant universe have rapidly increased the number of sub - mm selected galaxies ( hughes et al . 1998 ; eales et al . 1999 ; barger et al . 1998 ; smail et al . 1997 , 2002a ; chapman et al . 2002a ; fox et al . 2002 ; scott et al . the advantages of selecting high - redshift objects based on a sub - mm wavelength are not only their negative _ k_-correction up to @xmath9 ( blain et al . 2002 ) but also their high sensitivity to very dusty objects , which are believed to be undergoing vigorous star formation at high redshift [ their median redshift is revealed to be @xmath52.4(smail et al . 2002a ; chapman et al . 2003 ) ] . they are one of the candidates of forming giant elliptical galaxies based on the current observational and theoretical predictions ( lilly et al . although a very limited number of optical counterparts have been identified spectroscopically , they show notable diversity in their morphology ( extended and/or merging ) , agn possessions , dust temperatures , and so on ( smail et al . to study the mechanisms of galaxy formations , such as merging and/or gravitational collapses , we need to clarify the nature and the environments of these faint sub - mm sources . clearly , we need a much larger sample of faint sub - mm sources than we currently have . it also helps for comparing their features with nearby analogous objects , such as ultra - luminous iras galaxies and/or some other dusty populations detected by iso , mambo , etc . these populations might be missed by the popular  lyman break galaxy surveys \" [ there are only few cases of lyman break galaxies with sub - mm detection ( e.g. chapman et al . 2002c ) ] . on the other hand , as firstly reported by cimatti et al.(1998 ) , there is some evidence that many of the sub - mm sources are associated with eros(extremely red objects)(cimatti et al . 1998 ; blain et al . 2002 ; smail et al . 2002a ; ivison et al . 2002 ; wehner et al . 2002 ; frayer et al . eros have red colors , which is consistent with elliptical galaxies at high redshift , and they are separated into two categories of dusty starburst population and passively evolved stellar systems . the former are believed to be young high - redshift objects with a large star - formation rate , and their features are consistent with forming elliptical galaxies based on theoretical predictions . therefore , searching for eros associated with faint scuba sources is one of the most effective methods for detecting obscured ( dusty ) star - forming galaxy at high redshift , though it may be limited only for z@xmath103 , because of large extinction of their optical(rest uv ) light by their internal dust . there have been several studies ( smail et al . 1999 ; ivison et al . 2000 ; frayer et al . 2000 ; barger et al . 2000 ; lutz et al . 2001 ; frayer et al . 2003 ) which identified the ero counterparts of the sub - mm sources . furthermore , ivison et al.(2000 ) succeeded to obtain the redshifts of scuba sources at @xmath11 and @xmath12 in the a 1835 region , and there are some lower redshift samples with spectroscopically determined redshifts(e.g . smith et al . the lack of a suitable sample is partly because of their optical faintness . thus , it is needed to search for ero counterparts to those sub - mm sources that are optically bright enough for detailed spectroscopic studies .    using the gravitational lensing effect as a natural telescope , which amplifies the brightness of distant objects behind the lens , is one of the most powerful methods for obtaining detailed information on intrinsically faint objects . there have been many successful results in observing various types of high redshift galaxies using this effect , such as lyman break galaxies(pettini et al . 2000 ; franx et al . 1997 ) , faint scuba sources(ivison et al . 2000 ; ivison et al . 2001 ; ledlow et al . 2002 ) and eros(g.p . smith et al . the advantages of using the lensing effect is not only its photometric , but also spatial magnification , which will provide enlarged images of smaller distant objects , corresponding to a very high effective spatial resolution , which could not be achieved by the usual ground based observations . by using these effects , we could investigate the detailed structures and also the environmental status of distant objects .    in order to search for bright counterparts of scuba sources and to investigate their surrounding environments in detail , we performed ero search observations behind 2 massive clusters of galaxies , ms @xmath1 ( @xmath2 ) and ms @xmath3 ( @xmath4 ) . these clusters were discovered in the einstein medium sensitivity survey(emss)(gioia et al . 1990 ) , and were covered by a scuba mapping observation by chapman et al.(2002a ) and smail et al.(1998 ; 2002a ) .    in the next section , we describe our data collection , including our observations . in section 3 , we address the result of our imaging surveys and the various features of the candidates of the scuba source counterparts . a discussion is given in section 4 . in this paper we use the cosmological parameters @xmath1360.0 km s@xmath14 mpc@xmath14 , @xmath15 , and @xmath16 . all magnitudes without any notice are given in vega magnitude . we used the values in fukugita et al . ( 1996 ) for converting between the ab and vega scale magnitudes .","summary":"many of their optical and near - infrared colors are consistent with dusty star - forming galaxies at high redshifts(z.04.0 ) , and they may be constituting a cluster of dusty starburst galaxies and/or lensed star - forming galaxies at high redshift . their red colors and faint optical magnitudes suggest they are relatively old massive stellar systems with ages( mega years ) suffering from dust obscuration .","abstract":"we performed deep-band imaging observations of 2 massive clusters , ms at and ms at , for searching counterparts of the faint sub - mm sources behind these clusters , which would provide one of the deepest extremely red object(ero ) samples . comparing our near - infrared images with optical images taken by the hubble space telescope and by the subaru telescope , we identified 13 eros in these fields . the sky distributions of eros are consistent with the previous results , that there is a sign of strong clustering among detected eros . also , the surface density with corrected lensing amplification factors in both clusters are in good agreement with that derived from previous surveys . we found 7 eros and 3 additional very red objects in a small area ( 0.6 arcmin ) of the ms field around an extended scuba source . many of their optical and near - infrared colors are consistent with dusty star - forming galaxies at high redshifts(z.04.0 ) , and they may be constituting a cluster of dusty starburst galaxies and/or lensed star - forming galaxies at high redshift . their red colors and faint optical magnitudes suggest they are relatively old massive stellar systems with ages( mega years ) suffering from dust obscuration . we also found a surface - density enhancement of eros around the scuba source in the ms field ."}
{"article_id":"astro-ph0308064","section_id":"i","document":"we performed deep near - infrared and optical imaging of two massive clusters of galaxy fields . by combining this data with photometric information taken from the deep wfpc2/f702w image , we identified eros in each field , 8 in ms @xmath1 and 5 in ms @xmath3 with @xmath113 5.3 , and @xmath11422.0 , in a 2@xmath262field of view . our sample provide one of the deepest sample of eros ever reported . the surface density of our whole - area sample shows good agreement with other previous samples at the bright part . at the faint end , the number of eros is slightly deficient compared to the previous work , though it is within the error bars . we identified 7 eros ( @xmath1135.3 ) and 3 red objects ( @xmath115 ) with @xmath116 20.6 within 0.6 arcmin@xmath6 of an extended scuba source in the ms @xmath1 field . our investigation using a lens model provided a value of surface density of eros of @xmath546 arcmin@xmath36 for @xmath117 , showing a surface - density enhancement of extremely red galaxies , even after a correction of the lensing effect . it is possible that 4 sources , named `` a1 '' to `` a4 '' , constitute an extremely red - giant arc , and that the best - fit redshift by our model is @xmath99 . the photometric redshift for a sub - mm source , derived based on the sub - mm to radio index , does not give consistent redshift . we also investigated the optical and near - infrared photometric features for the 6 red sources , and identified that 4 of them have seds which are typical of high - redshift objects . their extinctions are typical , or slightly higher , values compared to those of lyman break galaxies at @xmath107 . our redshift estimation for `` a4 '' based on an sed fitting is consistent with that from sub - mm to radio index , and it is possible to consider that `` a1 '' to `` a4 '' are lensed extremely red sources at @xmath118 , and a counterpart of an extended sub - mm source . one source with severe extinction is identified at a lower redshift(@xmath119 ) , and is one of the candidates of contributors to the extended sub - mm flux . for revealing their clustering properties and the relation with extended sub - mm emission , a spectroscopic follow - up observation in the optical and/or near - infrared wavelength is essential . this study is based mainly on data collected at subaru telescope , and that obtained from the data archive at the astronomical data analysis center , which is operated by the national astronomical observatory of japan . the authors thank an anonymous referee for valuable comments and suggestions for improving the manuscript . we are grateful to all subaru staff members for their enormous help during our observations . thanks to dr . kentaro motohara and dr . chris simpson for their enormous help during the observation and data reduction , dr . yoshitomo maeda for giving instructions on the ciao software for reducing the chandra image . t.t . also thanks the staff of the archive system of the space telescope science institute for their help in retrieving the hst data . this work is partly supported by the ministry of education , culture , sports , science and technology in japan under grant no . 12740126 . k.n . has been financially supported by a jsps fellowship . adelberger , k.l . , & steidel , c.c . 2000 , apj , 544 , 218 alexander , d.m . , et al . 2003 aj , 125 , 383 baba , h. et al . 2002 , rep . japan , 6 , 23 ( in japanese ) barger , a.j . , cowie , l.l . , sanders , d.b . , fulton , e. , taniguchi , y. , sato , y. , kawara , k. , & okuda , h.  1998 , nature , 394 , 248 barger , a.j . , cowie , l.l . , & richards , e.a . 2000 , aj , 119 , 2092 bertin , e. , & arnouts , s.  1998 , a&as , 117 , 393 blain , a. w. , smail , i. , ivison , r.j . , kneib , j .- p . , & frayer , d.t . 2002 , physics report , 369 , 111 blain , a.w . , barnard , v.e . & chapman , s.c . 2003 , mnras , 338 , 733 bolzonella , m , miralles , j - 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( a ) @xmath0 vs @xmath48 plot for ms @xmath1 . color of @xmath120 5.3 and 6.0 , which represent those for eros , are shown by the dashed and dash - dotted line , respectively . the line indicating the 2@xmath18 limit of the @xmath19-band image is also shown . ( b ) same figure for ms @xmath3 . + * figure 2 . true - color @xmath121 image of ms @xmath1 ( using @xmath19 and @xmath20 data by focas and a @xmath0 image by cisco ) . this is a 2@xmath262field of view . we identify several very red objects mainly detected in @xmath0 image . + * figure 3 . sky distributions of eros in the regions of ( a ) ms @xmath1 and ( b ) ms @xmath3 . filled red circles , filled orange stars , filled orange circles represent ero with @xmath41 6.0 , ones with 5.3 @xmath122 6.0 with and without upper limit value of @xmath19 magnitudes , respectively . triangles represent other sources detected in @xmath0-band image for those fields . regions encircled by dotted lines are showing the area we used for surface density calculations . the dashed line in ( b ) is showing the edge of f702w image . central coordinates in j2000.0 for both fields are denoted at the top of the panels . + * figure 4 . @xmath0 image of the area around smm j @xmath42 with an overplotted scuba contour map by chapman et al . ( 2002a ) . the contour levels represent the 2@xmath18 to 4@xmath18 detection levels . eros around the scuba source are represented as `` a1 '' to `` a4 '' and `` e '' , `` f '' , and `` g '' with red rectangles , and optically bright red objects(@xmath47 5 ) `` b '' , `` c '' , and `` d '' are also shown along with purple ones . the arc , which is clearly visible in the optical images , is denoted as `` blue arc '' . + * figure 5 . @xmath48 vs @xmath7 diagram for the objects with red colors in the ms @xmath1 region . the dotted lines indicate the boundary between passively evolved galaxies ( left side ) and dusty starbursts ( right side ) with an extremely red color(@xmath123 ) . the objects which are identified near the extended scuba source are denoted as in figure 4 . the curves indicate the track of elliptical galaxies(solid line ) and dusty starbursts(dashed line ) with a redshift range of 1 to 4 ( redshifts 1.0 , 2.0 , 3.0 are denoted for each track ) . the details can be referred to in the text . + * figure 6 . focas @xmath19 and @xmath20 band and suprimecam @xmath21 and @xmath22 images around smm j @xmath43 in ms @xmath1 . the field sizes are 30@xmath2630 arcsec@xmath86 . a contour map of scuba detection is overplotted on the @xmath19 band image with the same levels as in figure 4 . + * figure 7 . f702w and @xmath0 images around smm j @xmath69 in ms @xmath3 . eros are denoted as `` a '' , `` b '' , and `` c '' . `` b '' is the optical counterpart of the sub - mm source(``n4 '' in frayer et al . 2003 ) at @xmath124 . field sizes are 30@xmath2630 arcsec@xmath86 . a bright galaxy neighboring `` b '' is `` n1 '' in smail et al . the overplotted contours in @xmath0 band image are 850 @xmath44 m map in smail et al . ( 1998 ) . + * figure 8 . cumulative area of the source plane in our survey at @xmath125 that experiences magnification greater than @xmath44 . + * figure 9 . amplification - corrected surface densities of eros for surveyed regions . the corrections were applied assuming a single source plane at @xmath95 , as discussed in the text . the triangles indicate the cumulative surface densities for ms @xmath3 , the filled pentagons and circles for ms @xmath1 within a small region as shown in figure  [ fig : fig3 ] , and for the whole region , respectively . the open circles show the results of g.p . smith et al.(2002 ) , and the open squares represent those by wehner et al.(2002 ) . we also plotted the results of field ero searches by daddi et al . ( 2000 ) , moustakas et al . ( 1997 ) , and roche et al . we plotted them without any correction for the data with @xmath126 or @xmath127 . the uncertainties for our data are 1@xmath18 , based on the poisson distribution . + * figure 10 . @xmath0 image of ms @xmath1 with the contour of soft ( 0.21.5 kev ) x - ray image taken by chandra with a 10 ks exposure overplotted . the levels show between 1.0@xmath2610@xmath128 to 5.0@xmath2610@xmath128 photons cm@xmath36s@xmath14pix@xmath14 with the same interval . the critical curves for the source at @xmath741.2 , 1.5 , 2.0 , 2.5 , and 3.0 are also shown as dotted blue , light blue , green , orange and red lines , respectively . the objects denoted in figure 4 are all shown encircled by squares ( red rectangles represent eros . ) . + * figure 11 . fitted seds for 6 ( extremely ) red objects around smm j @xmath42 .","summary":"we found 7 eros and 3 additional very red objects in a small area ( 0.6 arcmin ) of the ms field around an extended scuba source .","abstract":"we performed deep-band imaging observations of 2 massive clusters , ms at and ms at , for searching counterparts of the faint sub - mm sources behind these clusters , which would provide one of the deepest extremely red object(ero ) samples . comparing our near - infrared images with optical images taken by the hubble space telescope and by the subaru telescope , we identified 13 eros in these fields . the sky distributions of eros are consistent with the previous results , that there is a sign of strong clustering among detected eros . also , the surface density with corrected lensing amplification factors in both clusters are in good agreement with that derived from previous surveys . we found 7 eros and 3 additional very red objects in a small area ( 0.6 arcmin ) of the ms field around an extended scuba source . many of their optical and near - infrared colors are consistent with dusty star - forming galaxies at high redshifts(z.04.0 ) , and they may be constituting a cluster of dusty starburst galaxies and/or lensed star - forming galaxies at high redshift . their red colors and faint optical magnitudes suggest they are relatively old massive stellar systems with ages( mega years ) suffering from dust obscuration . we also found a surface - density enhancement of eros around the scuba source in the ms field ."}
{"article_id":"astro-ph0309041","section_id":"i","document":"it is becoming clear that a proper understanding of galaxy formation and evolution must address the role played by the supermassive black holes ( sbh ) now suspected to be present in most galaxy nuclei ( e.g. , magorrian et al . 1998 ) and responsible for the agn phenomenon . in the local universe , the importance of the sbh  host - galaxy relationship has been highlighted recently by the tight correlation of sbh mass with the host bulge velocity dispersion ( gebhardt et al . 2000 ; ferrarese & merritt 2000 ) and concentration index ( graham et al .  2001 ) . it is of great interest to probe the agn  host - galaxy relationship out to higher redshifts , where , for example , the strong evolution observed at the low end of the agn luminosity function by _ rosat _ deep x - ray surveys ( hasinger et al . 1999 ; miyaji et al . 2000 ) has been associated with an increased rate of galaxy interactions and distorted / irregular morphologies in the early universe ( lilly et al . 1998 ; abraham et al .  1999 ) . the recent _ chandra x - ray observatory _ ( _ cxo _ ) deepest field surveys have extended the _ rosat _ results to fainter fluxes and harder x - ray energies ( cowie et al . 2003 ; giacconi et al . 2002 ; brandt et al .  2001 ; hornschemeier et al .  2001 ; mushotzky et al . 2000 ; tozzi et al . these studies have also confirmed that the cosmic x - ray background is largely attributable to moderate - luminosity agn ( @xmath4 erg s@xmath5 ) at moderate to high redshifts ( @xmath6 ) , many with significant obscuration by the host galaxy . this underscores the desirability of studying the agn  host connection with samples detected at hard x - ray energies , where there is much less bias against the dust obscuration that segregates agn into type  1 ( unobscured ) and type  2 ( obscured ) in the standard unified model ( e.g. , urry & padovani 1995 ) . although much has been learned from studies of agn and their hosts at low redshift , and from comparisons of the evolution of higher - luminosity agn and field galaxies at high redshifts , the fundamental question of whether nuclear activity drives galaxy evolution , or vice versa , can only be fully addressed by obtaining high - resolution multi - wavelength observations of _ typical _ agn _ and _ their hosts over a _ wide range _ of redshifts . the combination of _ hubble space telescope _ ( _ hst _ ) and _ cxo _  deep imaging offers a unique opportunity to satisfy these requirements : the _ chandra _ deepest fields contain the requisite large , unbiased sample of distant low- to moderate - luminosity agn with the high positional accuracy ( @xmath7 ) necessary for unambiguous association with their faint host galaxies ; subsequent high - resolution _ hst _  images of these regions then permit the detailed investigation of their host galaxy morphologies and environments .    to this end , we obtained the first _ imaging within the chandra deep field south ( hereafter cdfs ; giacconi et al . 2002 ) : three moderately - deep exposures using the wide field planetary camera  2 ( wfpc2 ) in @xmath8 and @xmath9 . in paper i of this series ( schreier et al . 2001 ) , we identified unambiguous _ hst _ counterparts for @xmath10% of the 26 cdfs sources in the initial 300  ksec exposure ( tozzi et al .  2001 ) , and discussed the heterogeneous nature of this population as indicated by the joint x - ray and optical photometry . paper ii ( koekemoer et al .  2002 ) extended this analysis to the larger population of 40 cdfs sources revealed at the 1  ms _ cxo _  depth , which is still current at the time of this writing . again we found a @xmath10% fraction with unambiguous _ _  counterparts , and the combined x - ray and optical properties of this expanded sample largely reinforced the conclusions of paper i : the optical counterparts to the x - ray sources are divided into two distinct populations , namely 1 )  an optically faint group with relatively blue colors , similar to the faint blue field galaxy population , and 2 )  an optically brighter group , including resolved galaxies with average colors significantly redder than the corresponding bright field galaxy population . the brighter objects comprise a wide range of types , including early and late type galaxies , starbursts , and agn , most at moderate redshifts ( @xmath111.0 ; szokoly et al . , in prep . ) . the faint blue x - ray population is consistent with expected numbers and characteristics of low- to moderate - luminosity type  2 agn at the quasar epoch ( @xmath123 ) .    in the present paper , we undertake a detailed morphological analysis of the cdfs optical counterparts introduced in papers i and ii . in  [ obsrcsec ] we review the _ hst _  and _ cxo _  imaging of the cdfs , introduce the full _ hst_/wfpc2 source list , and review the matching of sources common to both sets of observations . we then present a variety of morphological analyses of the _ hst _  data in  [ morphansec ] , including isophotal ellipse fitting and point - spread function ( psf ) convolved two - dimensional surface - brightness modeling of the _ cxo _ counterparts , as well as determinations of asymmetry and concentration indices for the entire _ hst _  source list in order to contrast the _ cxo _  counterparts with the much more numerous field population in our wfpc2 frames . we discuss the implications of these findings in  [ discsec ] and conclude in  [ concsec ] . throughout this paper we adopt a cosmology with @xmath13 , @xmath14 , and @xmath15  km  s@xmath16  mpc@xmath16 .","summary":"we present quantitative morphological analyses of 37 _ moreover , the frequency of near neighbors around the cdfs counterparts is not significantly different from the field sample .","abstract":"we present quantitative morphological analyses of 37 _ hst_/wfpc2 counterparts of x - ray sources in the 1 ms chandra deep field  south ( cdfs ) . we investigate : 1 ) one - dimensional surface brightness profiles via isophotal ellipse fitting ; 2 ) two - dimensional , psf - convolved , bulge+disk+nucleus profile - fitting ; 3 ) asymmetry and concentration indices compared with all sources in our three wfpc2 fields ; and 4 ) near - neighbor analyses comparing local environments of x - ray sources versus the field control sample . significant nuclear point - source optical components appear in roughly half of the resolved _ hst_/wfpc2 counterparts , showing a narrow range of consistent with the several _ hst_-unresolved x - ray sources ( putative type  1 active galactic nuclei [ agns ] ) in our fields . we infer roughly half of the _ hst_/wfpc2 counterparts host unobscured agn , comparable to analogous low - redshift agn samples and suggesting no steep decline in the type  1/type  2 ratio out to the redshifts typical of our sources . the concentration indices of the cdfs counterparts are clearly larger on average than those of the field distribution , at 5-sigma , suggesting that the strong correlation between central black hole mass and host galaxy properties ( including concentration index ) observed in nearby galaxies is already evident by . by contrast , the asymmetry index distribution of the 21 resolved cdfs sources at is indistinguishable from the field . moreover , the frequency of near neighbors around the cdfs counterparts is not significantly different from the field sample . these results , combined with previous similar findings for local samples , suggest that recent merger / interaction history is not a good indicator of agn activity over a substantial range of look - back time ."}
{"article_id":"astro-ph0309041","section_id":"c","document":"examining the isophotal fitting results for the 22 resolved @xmath49 _ cxo_counterparts ( fig .  1 ) , we find that about half of the objects have a relatively flat color profile all the way into the nucleus , while a slightly smaller fraction display a nucleus that is at least half a magnitude bluer at its core than the average color across the rest of the galaxy . three objects display nuclei that are redder by at least half a magnitude than their average global color . we have searched for correlations between color gradient results and the x - ray properties of the galaxies . the three redder - centered objects appear to have somewhat harder x - ray spectra , while the flat - color objects are softer and in particular include all objects detected solely in the _ cxo _  soft band ( 0.52  kev ) . the bluer - centered objects have hardness ratios that are intermediate in value , covering the entire range from soft to hard . there is also some suggestion that the bluer - centered objects have a slightly higher @xmath118 on average than the flat - color and redder - centered objects . the correlation between higher @xmath118 and blue central color gradient is expected since the bluer - centered objects are probably all type  1 agn and are therefore detected at somewhat higher distances on average . this is confirmed by the optical spectroscopy that we have so far : all 3 of the 8 bluer - centered objects for which we have spectroscopic classifications ( szokoly et al . 2003 , in prep . ) are type  1 s ; all 4 of the spectroscopic classifications available for the 16 flat - color and redder - centered objects suggest that they are type  2 s . finally , the bluer - centered objects are found mostly in elliptical hosts ( according to our morphological classifications ) , while the flat - centered objects are found in both spiral and elliptical hosts . most of the optically brighter _ cxo _  counterparts for which we estimated the nuclear point - source flux ( [ twodfitdesc ] ) also have measured redshifts ( szokoly et al . , in prep . ) which imply @xmath120 . such large x - ray luminosities are associated with agn or intense starbursts  in either case the x - ray output of the host galaxy is dominated by the nuclear regions . thus we can use our estimates of the unresolved nuclear flux in the cdfs counterparts to provide a much cleaner investigation of x - ray sources @xmath121 . figure [ ptsrcfig ] shows two plots of 210  kev @xmath122 versus  @xmath123 for the 1  ms cdfs sources in our fields : the top panel shows @xmath124 of the entire host ( including nucleus ) , analogous to figure  8 of paper  i for the 300  ksec cdfs sources ; the bottom panel shows @xmath125 of the counterparts which are either unresolved ( filled star symbols ) or resolved but with finite unresolved nuclear flux ( open star symbols ) . in the bottom panel , we also pair each @xmath126 with the corresponding @xmath124 ( dotted symbols ) for comparison with the top panel . here and throughout the rest of the discussion , we focus on the @xmath9-band data in preference to the @xmath8-band , since only the former samples rest - frame optical light ( @xmath127 ) at the substantial redshifts ( @xmath1281 ) of even the brighter resolved _ cxo _  counterparts . it is immediately obvious from figure [ ptsrcfig ] that the scatter in @xmath129 is greatly reduced when considering only the optical flux originating from an unresolved nucleus  most have @xmath130 . in particular , we see that the @xmath131 values for the resolved cdfs sources are now consistent with the narrow range of @xmath129 of the several _ hst_-unresolved counterparts  all spectroscopically - confirmed type  1 agn ( szokoly et al . , in prep . ) . we may therefore infer that we are seeing type  1 agn in these additional resolved hosts , bringing the total fraction of brighter cdfs counterparts with unobscured agn to @xmath132% . even these brighter optical cdfs counterparts are at substantial distances ( @xmath1191 ; szokoly et al . , in prep . ) , yet their type  1 fraction is comparable with recent measures of unbiased agn samples at lower redshift ( wilkes et al . the hard - x - ray sensitivity of _ cxo _  can detect even highly - obscured agn ( @xmath133  cm@xmath52 ) of moderate luminosities ( @xmath135 erg s@xmath5 ) in the 1  ms cdfs out to @xmath136 , leading us to conclude that our current sample , albeit modest , does not support a steep redshift evolution in the type  2/type  1 ratio as favored by recent agn synthesis models ( e.g. ,  gilli et al . 2001 ) . having measured the asymmetry and concentration indices of all sources appearing in our three wfpc2 pointings (  [ asymconcsec ] ) , we can make statistical comparisons of these morphological indicators between the _ cxo_-detected and the _ cxo_-undetected sources . figure [ asymcdffig ] shows the cumulative distribution of asymmetry index @xmath43 for the 21 _ cxo_-detected and _ hst_-resolved sources with @xmath3 ( heavy solid line ) and for the remaining 267 galaxies with @xmath3 but undetected by _ cxo_. the two distributions are statistically indistinguishable according to the kolmogorov - smirnov ( k - s ) test , which gives a 56% probability of the null hypothesis that they are drawn from the same underlying distribution . our finding that the brighter resolved cdfs sources , almost all at moderate redshifts @xmath1281 , have a strikingly similar asymmetry distribution to the @xmath3 field may be compared with earlier morphological studies of the _ local _ agn population . for example , corbin  ( 2000 ) finds that the 45 galaxies in the seyfert and liner subsets of the bjc00 sample do not show significant asymmetry index differences compared with the 60 galaxies among the non - active subsets . @xmath137-body simulations of galaxy interactions ( walker , mihos & hernquist 1996 ) suggest that even minor mergers induce sufficient morphological disturbances to be detectable via the asymmetry index up to @xmath138  gyr after the onset of the merger . on this basis , corbin  ( 2000 ) concludes that minor mergers either have _ no _ role in the triggering of lower - luminosity agn , or that the agn manifests only in the late stages of the mergers  implying that the nuclei in his nearby sample have only been active within the last @xmath139  gyr . inasmuch as the hard x - ray sensitivity of the cdfs provides a near - complete census of both obscured and unobscured agn at @xmath140 down to modest luminosities , similar to the bjc00 sample , the cdfs counterparts unexceptional asymmetries and paucity of obvious merger candidates ( @xmath141 ; c.  conselice 2003 , private comm . ) now suggest that very recent merger history is not a good indicator of agn activity over a substantial range of lookback time . if galaxy mergers are indeed a primary driver of agn fueling , as has been commonly hypothesized ( e.g.  gunn  1979 , dahari  1984 , roos  1985 , taniguchi  1999 ) , then the epoch of agn activity can not closely coincide with that of merger - induced morphological disturbance  @xmath142 yr .      as a further check into the merger  agn connection , we took a census of near neighbors to the cdfs counterparts . in figure [ nnfig ] we plot a histogram of the number of @xmath3 galaxies appearing within 8  of the @xmath3 cdfs counterparts ( heavier solid line ) . for comparison , we also plot the histogram of @xmath3 galaxies appearing within 8  of the _ cxo_-undetected @xmath3 population ( lighter solid line ) . we adopt an angular separation threshold rather than a projected linear distance because we currently lack redshift information for most of the field galaxy control sample . however we note that 8  corresponds to a narrow range of angular diameter distance , @xmath14365  kpc , over a broad redshift range @xmath144 in our adopted cosmology . this redshift range includes almost all the cdfs counterparts at @xmath3 , whose redshift survey is virtually complete ( szokoly et al . , in prep . ) , and presumably the majority of the @xmath3 field galaxies . if the @xmath3 galaxies were not clustered , an 8  radius would on average contain 1.1 such objects given their source density over the @xmath145  arcmin@xmath146 of our three wfpc2 fields . we show the corresponding poisson distribution in figure [ nnfig ] ( dotted line ) for reference .    compared with the x - ray - undetected @xmath3 population , the cdfs counterparts show an enhancement in the fraction with a single near neighbor and a corresponding deficit of isolated systems ; the fraction with multiple companions is almost identical between the two populations . while it is obvious that the near - neighbor frequency histogram ( fig . [ nnfig ] ) shows greater discrepancy between the x - ray host and field populations than the asymmetry parameter , nonetheless the @xmath93 statistic between the two histograms gives only a modest rejection of the null hypothesis ( prob@xmath147 ) that the nearest - neighbor frequencies are consistent . larger samples are clearly needed to establish the significance of a bias against isolated cdfs sources ( see  [ concsec ] ) . as the current data do not support a significant enhancement in the fraction of cdfs sources with near neighbors , this reinforces our interpretation from the asymmetry analysis (  [ asymdisc ] ) that there is no strong association between low- to moderate - luminosity agn at moderate redshifts and recent / ongoing merger activity of the host galaxies . similar conclusions at low redshift have emerged from recent studies of the agn fractions among close pairs versus the field ( barton , geller , & kenyon  2000 ) , and of the companion fractions of agn versus non - agn ( schmitt  2001 ) . figure [ conccdffig ] shows the cumulative distribution of concentration index @xmath44 for the 21 _ cxo_-detected and _ hst_-resolved sources with @xmath3 ( heavier line ) and for the remaining 267 galaxies with @xmath3 but undetected by _ cxo _  ( lighter line ) . in marked contrast to the result for the asymmetry index , the two distributions of @xmath44 are clearly distinct and have a low k - s probability of @xmath148 for the null hypothesis .    even though we have restricted this comparison to the _ hst_-resolved cdfs counterparts , i.e.  those whose optical flux is not dominated by the central engine , one may still worry that their concentration indices may be biased by the presence of optical flux from the agn . indeed we have found several of the cdfs host galaxies to be best - fit with a nuclear point source comprising @xmath149% of the total flux ( fig . [ ptsrcfig ] ) .    in theory , our two - dimensional modeling could be used to refine the @xmath44 estimates by removing nuclear point - source bias . for example , one may consider computing @xmath44 from a galaxy image _ after _ subtracting the best - fit nuclear point source . the model psf does not precisely match the shape of the true psf , however , and scaled psf subtraction leaves relatively large - amplitude residuals in the host s central pixels which hamper @xmath44 estimation via sextractor . alternately , one may consider computing @xmath44 from a model galaxy image constructed from the other , non - point - source , parameters in the two - dimensional fit . in practice this approach also fails , as our simulations indicate the two - dimensional fitting robustly recovers the point - source flux but not the input bulge and disk shape parameters . furthermore , a proper comparison with the field control sample in either case would require extending the two - dimensional modeling and `` nuclear point - source correction '' to the whole population , which is beyond the scope of the current study . fortunately , our calculations below suggest that any enhancement of @xmath44 from nuclear point - source flux is at most a small fraction of the observed @xmath44 discrepancy ( fig . [ conccdffig ] ) between _ cxo _  hosts and field . the effect of added point - source flux to a galaxy s concentration index is not straightforward , since the near - gaussian _ hst_psf is significantly less concentrated than an exponential or @xmath53 profile . small additions of nuclear flux will cause @xmath44 to rise as @xmath150 shrinks faster than @xmath151 , but when the point - source becomes sufficiently dominant the concentration will peak and then collapse to the lower @xmath44 of the psf . we have attempted to quantify this effect by creating a suite of model galaxies based on a fiducial galaxy profile typical of our @xmath3 cdfs counterparts : a psf - convolved , @xmath152 devaucouleurs profile with @xmath153  pixels ( 0.25 ) . we then steadily increase the flux fraction in the point - source nucleus , and measure @xmath44 as a function of the point - source fraction . the result is plotted in figure [ concbiasplot ] , where we see that the peak increase of @xmath44 is only @xmath139 . over the range corresponding to our measured point - source fractions , the deviation is @xmath154 . this is only @xmath155 of the discrepancy seen in figure  [ conccdffig ] , from which we conclude that the agn host concentration bias is truly related to differences in the host galaxy structure , and not to the possibility of nuclear point - source flux contribution . graham et al . ( 2001 ) have found a tight correlation between sbh mass and host galaxy concentration index exists among the nearby galaxy samples which previously established the close correlation between sbh mass and host bulge velocity dispersion ( ferrarese & merritt  2000 , gebhardt et al . although our initial analysis reveals little correlation between @xmath118 ( as a proxy for sbh mass ) and @xmath44 for the @xmath3 cdfs host galaxies , it is likely that our sample  almost all with hard x - ray luminosities indicative of agn ( @xmath156 ergs s@xmath5 )  harbor sbhs at the high end of the sbh mass function relative to the x - ray undetected galaxies in our fields . our wfpc2 findings therefore suggest , for the first time , that the close linkage between sbh mass and host galaxy properties extends to the substantial look - back times ( @xmath157 ) typical of the @xmath3 cdfs x - ray sources .","summary":"we investigate : 1 ) one - dimensional surface brightness profiles via isophotal ellipse fitting ; 2 ) two - dimensional , psf - convolved , bulge+disk+nucleus profile - fitting ; 3 ) asymmetry and concentration indices compared with all sources in our three wfpc2 fields ; and 4 ) near - neighbor analyses comparing local environments of x - ray sources versus the field control sample . we infer roughly half of the _ hst_/wfpc2 counterparts host unobscured agn , comparable to analogous low - redshift agn samples and suggesting no steep decline in the type  1/type  2 ratio out to the redshifts typical of our sources . by contrast , the asymmetry index distribution of the 21 resolved cdfs sources at is indistinguishable from the field .","abstract":"we present quantitative morphological analyses of 37 _ hst_/wfpc2 counterparts of x - ray sources in the 1 ms chandra deep field  south ( cdfs ) . we investigate : 1 ) one - dimensional surface brightness profiles via isophotal ellipse fitting ; 2 ) two - dimensional , psf - convolved , bulge+disk+nucleus profile - fitting ; 3 ) asymmetry and concentration indices compared with all sources in our three wfpc2 fields ; and 4 ) near - neighbor analyses comparing local environments of x - ray sources versus the field control sample . significant nuclear point - source optical components appear in roughly half of the resolved _ hst_/wfpc2 counterparts , showing a narrow range of consistent with the several _ hst_-unresolved x - ray sources ( putative type  1 active galactic nuclei [ agns ] ) in our fields . we infer roughly half of the _ hst_/wfpc2 counterparts host unobscured agn , comparable to analogous low - redshift agn samples and suggesting no steep decline in the type  1/type  2 ratio out to the redshifts typical of our sources . the concentration indices of the cdfs counterparts are clearly larger on average than those of the field distribution , at 5-sigma , suggesting that the strong correlation between central black hole mass and host galaxy properties ( including concentration index ) observed in nearby galaxies is already evident by . by contrast , the asymmetry index distribution of the 21 resolved cdfs sources at is indistinguishable from the field . moreover , the frequency of near neighbors around the cdfs counterparts is not significantly different from the field sample . these results , combined with previous similar findings for local samples , suggest that recent merger / interaction history is not a good indicator of agn activity over a substantial range of look - back time ."}
{"article_id":"astro-ph0309041","section_id":"i","document":"the deep fields observed with the _ chandra x - ray observatory _ have produced the first large uniform catalogs of x - ray sources down to modest agn luminosities ( @xmath158  erg  s@xmath5 ) at substantial redshift . given the good hard - x - ray sensitivity of the cdfs observations , this catalog is expected to provide a near - complete census of both obscured and unobscured agn at @xmath140 , whose redshifts appear to be concentrated in the range @xmath157 ( rosati et al .  2002 ; szokoly et al . , in prep . ) . we have presented this first quantitative morphological study of many optical counterparts of these distant agn based on our deep _ hst _ observations of three wfpc2 fields in the cdfs . we have compared the asymmetry indices of @xmath3 agn hosts with the much larger population of similarly bright x - ray - undetected field galaxies . we find a very good agreement between the asymmetry distributions of the two populations ( fig . [ asymcdffig ] ) . furthermore , the _ cxo _ counterparts show only a modest difference from the field population in the frequency of nearby companions ( fig . [ nnfig ] ) . these findings are similar to studies of comparable low - redshift populations , and now suggest that recent merger history is not a good indicator of agn activity over a substantial range of lookback time .    our psf - convolved two - dimensional profile fitting of the _ hst_-resolved _ cxo_counterparts shows that over a third have significant nuclear point - source emission . the @xmath129 of these unresolved nuclear sources is consistent with the narrow @xmath129 range of the several _ hst_-unresolved counterparts ( fig . [ conccdffig ] ) . we therefore infer that the total fraction of @xmath49 cdfs counterparts harboring type  1 agn is @xmath132% , consistent with recent findings for unbiased agn samples at lower redshift ( wilkes et al . if the large type  1 fraction inferred from our modest sample were representative of the overall @xmath1191 agn population , this would be problematic for recent agn synthesis models ( e.g.  gilli et al . 2001 ) which favor a sharp rise in the type  2/type  1 ratio out to @xmath159 . our comparison of the concentration indices of _ cxo _  counterparts with the field reveals a clear bias toward higher @xmath44 among the _ cxo _  host galaxies ( fig . [ conccdffig ] ) . this @xmath160 result does not appear to be an artifact of heightened optical flux from the cdfs hosts nuclei , and may represent the first evidence that the locally - observed correlation between sbh mass and host - galaxy properties , including concentration index , is already in place by @xmath161 .    to press upon these results regarding the merger  agn connection and sbh  host - galaxy connection at moderate- to high - redshift , we are undertaking extensive _ hst_/advanced camera for surveys ( acs ) multicolor imaging of the two _ chandra _ deepest fields as part of the great observatories origins deep survey ( goods , dickinson & giavalisco  2003 ) . the goods data will both increase by @xmath162 times the available number of _ hst_-imaged agn hosts and comparison field galaxies in _ cxo _ @xmath163  ms fields and also will provide extensive spectroscopic and photometric redshift coverage to complement the acs morphologies . with @xmath164 counterparts of @xmath165  ms _ cxo _  sources , we will solidly verify the morphological and environmental conclusions we have drawn from the 37 cdfs host galaxies in the present work . furthermore , the large sample in combination with multicolor imaging and redshift information will allow us to track the _ evolution _ of agn versus  non - agn environment and rest - frame @xmath101 morphology out to @xmath166 ( grogin et al . 2003 ) . we thank c.  conselice for insightful discussions and for graciously providing his asymmetry - index code for our use . we thank r.  gilli and the anonymous referee for comments which strengthened the manuscript . we gratefully acknowledge the award of _ hst _  director s discretionary time in support of this project . we also acknowledge support for this work which was provided by nasa through go grants go-08809.01-a and go-07267.01-a from the space telescope science institute , which is operated by aura , inc . , under nasa contract . brandt , w.  n. , alexander , d.  m. , hornschemeier , a.  e. , garmire , g.  p. , schneider , d.  p. , barger , a.  j. , bauer , f.  e. , broos , p.  s. , cowie , l.  l. , townsley , l.  k. , burrows , d.  n. , chartas , g. , feigelson , e.  d. , griffiths , r.  e. , nousek , j.  a. , & sargent , w.  l.  w.  2001 , aj , 122 , 2810    casertano , s. , de mello , d. , dickinson , m. , ferguson , h.  c. , fruchter , a.  s. , gonzalez - lopezlira , r.  a. , heyer , i. , hook , r.  n. , levay , z. , lucas , r.  a. , mack , j. , makidon , r.  b. , mutchler , m. , smith , t.  e. , stiavelli , m. , wiggs , m.  s. , williams , r.  e.  2000 , aj , 120 , 2747                  gebhardt , k. , kormendy , j. , ho , l.  c. , bender , r. , bower , g. , dressler , a. , faber , s.  m. , filippenko , a.  v. , green , r. , grillmair , c. , lauer , t.  r. , magorrian , j. , pinkney , j. , richstone , d. , & tremaine , s.  2000 , apj , 539 , 13    giacconi , r. , zirm , a. , wang , j.  x. , rosati , p. , nonino , m. , tozzi , p. , gilli , r. , mainieri , v. , hasinger , g. , kewley , l. , bergeron , j. , borgani , s. , gilmozzi , r. , grogin , n. , koekemoer , a. , schreier , e. , zheng , w. & norman , c.  2002 , apj , 139 , 369        grogin , n.  a. , conselice , c.  j. , chatzichristou , e. , alexander , d.  m. , bauer , f.  e. , hornschemeier , a.  e. , jogee , s. , koekemoer , a.  m. , laidler , v.  g. , lucas , r.  a. , paolillo , m. , ravindranath , s. , schreier , e.  j. , simmons , b.  d. , & urry , c.  m.  2003 , apjl , submitted        hornschemeier , a.  e. , brandt , w.  n. , garmire , g.  p. , schneider , d.  p. , barger , a.  j. , broos , p.  s. , cowie , l.  l. , townsley , l.  k. , bautz , m.  w. , burrows , d.  n. , chartas , g. , feigelson , e.  d. , griffiths , r.  e. , lumb , d. , nousek , j.  a. , ramsey , l.  w. , & sargent , w.  l.  w.  2001 , apj , 554 , 742    koekemoer , a.  m. , grogin , n.  a. , schreier , e.  j. , giacconi , r. , gilli , r. , kewley , l. , norman , c. , zirm , a. , bergeron , j. , rosati , p. , hasinger , g. , tozzi , p. , & marconi , a.  2002 , apj , 567 , 657 ( paper ii )                  rosati , p. , tozzi , r. , giacconi , r. , gilli , r. , hasinger , g. , kewley , l. , mainieri , v. , nonino , m. , norman , c. , szokoly , g. , wang , j.  x. , zirm , a. , bergeron , j. , borgani , s. , gilmozzi , r. , grogin , n. , koekemoer , a. , schreier , e. , & zheng , w.  2002 , apj , 566 , 667          tozzi , p. , rosati , p. , nonino , m. , bergeron , j. , borgani , s. , gilli , r. , gilmozzi , r. , hasinger , g. , grogin , n. , kewley , l. , koekemoer , a. , norman , c. , schreier , e. , shaver , p. , szokoly , g. , wang , j.  x. , zheng , w. , zirm , a. & giacconi , r.  2001 , apj , 562 , 42              rrrrrrrrrr 53.007162 & @xmath167 & 27.53 & @xmath168 & 0.16 & 0.02 & 0.63 & @xmath169 & 1.89 & 1.81 + 53.007943 & @xmath170 & 26.43 & 25.16 & 0.24 & 0.00 & 0.00 & @xmath171 & 2.47 & 2.82 + 53.008016 & @xmath172 & 27.34 & 26.07 & 0.20 & 0.80 & 0.01 & @xmath173 & 3.34 & 2.88 + 53.008110 & @xmath174 & 27.01 & 25.96 & 0.16 & 0.01 & 0.05 & @xmath175 & 2.13 & 2.43 + 53.008349 & @xmath176 & 24.52 & 22.73 & 0.29 & 0.02 & 0.02 & @xmath177 & 2.28 & 2.63 + 53.008414 & @xmath178 & 27.24 & @xmath168 & 0.09 & 0.01 & 0.63 & @xmath179 & 2.56 & 1.83 + 53.008675 & @xmath180 & 26.00 & 25.35 & 0.11 & 0.00 & 0.00 & @xmath181 & 2.60 & 2.20 + 53.009305 & @xmath182 & 23.18 & 21.12 & 0.56 & 0.00 & 0.00 & @xmath183 & 2.25 & 2.39 + 53.009428 & @xmath184 & 27.34 & @xmath168 & 0.07 & 0.53 & 0.56 & @xmath185 & 2.04 & 1.74 + 53.009442 & @xmath186 & 24.83 & 23.08 & 0.38 & 0.00 & 0.02 & @xmath187 & 2.43 & 2.13 + 53.009653 & @xmath188 & 26.48 & 25.89 & 0.13 & 0.00 & 0.00 & @xmath189 & 3.02 & 2.76 + 53.009702 & @xmath190 & 26.01 & 24.66 & 0.16 & 0.02 & 0.01 & @xmath191 & 3.16 & 2.89 + 53.009772 & @xmath192 & 27.15 & 25.55 & 0.12 & 0.00 & 0.00 & @xmath193 & 2.89 & 2.16 + 53.009885 & @xmath194 & 23.37 & 21.91 & 0.38 & 0.00 & 0.00 & @xmath169 & 2.46 & 2.60 + 53.009959 & @xmath195 & 26.23 & 25.24 & 0.14 & 0.00 & 0.00 & @xmath196 & 2.24 & 2.09 + 53.010116 & @xmath197 & @xmath198 & 26.05 & 0.10 & 0.06 & 0.01 & @xmath199 & 1.67 & 2.29 + 53.010253 & @xmath200 & 26.04 & 24.24 & 0.37 & 0.00 & 0.00 & @xmath201 & 3.85 & 3.02 + 53.010534 & @xmath202 & 26.10 & 25.84 & 0.14 & 0.00 & 0.00 & @xmath203 & 2.12 & 1.86 + 53.010582 & @xmath204 & 24.37 & 22.94 & 0.38 & 0.00 & 0.00 & @xmath205 & 2.04 & 2.42 + 53.010584 & @xmath206 & 24.71 & 22.73 & 0.18 & 0.02 & 0.04 & @xmath207 & 3.12 & 3.15 + 53.010590 & @xmath208 & 24.21 & 23.29 & 0.38 & 0.00 & 0.00 & @xmath209 & 2.33 & 2.23 + 53.010664 & @xmath210 & 27.41 & @xmath168 & 0.10 & 0.02 & 0.00 & @xmath211 & 1.61 & 1.86 + 53.010679 & @xmath212 & 27.25 & 25.65 & 0.15 & 0.00 & 0.00 & @xmath196 & 2.09 & 2.86 + 53.010681 & @xmath213 & @xmath198 & 25.99 & 0.12 & 0.01 & 0.00 & @xmath214 & 1.62 & 1.79 + 53.010846 & @xmath215 & 23.13 & 21.56 & 0.18 & 0.03 & 0.03 & @xmath216 & 2.69 & 2.82 + 53.010918 & @xmath217 & 27.12 & 25.53 & 0.12 & 0.03 & 0.00 & @xmath183 & 2.07 & 2.77 + 53.011001 & @xmath218 & 27.28 & 25.93 & 0.19 & 0.01 & 0.00 & @xmath219 & 2.35 & 1.97 + 53.011020 & @xmath220 & 26.36 & 24.87 & 0.20 & 0.00 & 0.00 & @xmath216 & 3.73 & 2.55 + 53.011088 & @xmath221 & 27.15 & 25.91 & 0.17 & 0.00 & 0.01 & @xmath222 & 3.68 & 2.87 + 53.011158 & @xmath223 & 27.71 & 25.53 & 0.14 & 0.00 & 0.00 & @xmath224 & 3.14 & 1.91 + 53.011179 & @xmath225 & 27.19 & @xmath168 & 0.08 & 0.04 & 0.02 & @xmath226 & 1.92 & 2.48 + 53.011219 & @xmath227 & @xmath198 & 25.54 & 0.21 & 0.05 & 0.00 & @xmath209 & 2.48 & 1.91 + 53.011291 & @xmath228 & 25.41 & 23.88 & 0.56 & 0.00 & 0.00 & @xmath203 & 2.69 & 2.08 + 53.011320 & @xmath229 & 26.56 & 25.36 & 0.44 & 0.00 & 0.00 & @xmath230 & 2.56 & 3.10 + 53.011347 & @xmath231 & @xmath198 & @xmath168 & 0.10 & 0.01 & 0.02 & @xmath232 & 1.86 & 2.25 + 53.011536 & @xmath233 & 26.01 & 24.25 & 0.16 & 0.00 & 0.01 & @xmath234 & 2.36 & 2.44 + 53.011569 & @xmath235 & 24.62 & 23.56 & 0.25 & 0.00 & 0.00 & @xmath236 & 2.42 & 2.56 + 53.011587 & @xmath237 & 27.52 & 26.39 & 0.15 & 0.00 & 0.01 & @xmath211 & 2.22 & 1.78 + 53.011632 & @xmath238 & 26.61 & 25.32 & 0.21 & 0.00 & 0.00 & @xmath239 & 3.27 & 2.63 + 53.011753 & @xmath240 & 26.00 & 24.80 & 0.38 & 0.00 & 0.00 & @xmath234 & 3.24 & 2.21 + 53.011806 & @xmath241 & 26.97 & 26.31 & 0.10 & 0.01 & 0.00 & @xmath183 & 2.04 & 1.86 + 53.011876 & @xmath242 & 26.96 & @xmath168 & 0.20 & 0.01 & 0.48 & @xmath243 & 1.98 & 1.17 +      36 & j033233.1@xmath72274548 & @xmath244 & @xmath245 & 22.95 & 21.08 & 0.71 & 0.00 & 0.00 & @xmath246 & @xmath247 & @xmath248 & @xmath249 & in compact group + 38 & j033230.3@xmath72274505 & @xmath250 & @xmath251 & 22.18 & 20.87 & 0.16 & 0.69 & 0.03 & @xmath138 & @xmath138 & @xmath252 & @xmath253 & + 39 & j033230.1@xmath72274530 & @xmath254 & @xmath255 & 21.34 & 20.45 & 0.14 & 0.87 & 0.15 & @xmath138 & @xmath138 & @xmath256 & @xmath257 & + 52 & j033217.2@xmath72274304 & @xmath258 & @xmath259 & 21.57 & 19.91 & 0.25 & 0.03 & 0.03 & @xmath260 & @xmath261 & @xmath262 & @xmath263 & + 56 & j033213.3@xmath72274241 & @xmath264 & @xmath265 & 20.83 & 19.16 & 0.35 & 0.03 & 0.03 & @xmath266 & @xmath267 & @xmath268 & @xmath269 & + 58 & j033211.8@xmath72274629 & @xmath270 & @xmath271 & 25.95 & 24.42 & 0.19 & 0.00 & 0.02 & & & @xmath272 & @xmath273 & + 60 & j033211.0@xmath72274415 & @xmath274 & @xmath275 & 22.39 & 21.04 & 0.13 & 0.54 & 0.41 & @xmath138 & @xmath138 & @xmath276 & @xmath277 & + 61 & j033210.6@xmath72274309 & @xmath278 & @xmath279 & 25.09 & 22.51 & 0.20 & 0.83 & 0.73 & @xmath138 & @xmath138 & @xmath280 & @xmath281 & + 62 & j033209.5@xmath72274807 & @xmath282 & @xmath283 & 20.87 & 19.63 & 0.12 & 0.91 & 0.89 & @xmath138 & @xmath138 & @xmath284 & @xmath285 & + 63 & j033208.7@xmath72274735 & @xmath286 & @xmath287 & 19.21 & 17.86 & 0.15 & 0.93 & 0.88 & @xmath138 & @xmath138 & @xmath288 & @xmath289 & + 64 & j033208.1@xmath72274658 & @xmath290 & @xmath291 & 25.32 & 24.27 & 0.14 & 0.02 & 0.01 & & & @xmath292 & @xmath293 & + 66 & j033203.7@xmath72274604 & @xmath294 & @xmath295 & 21.40 & 19.29 & 0.37 & 0.03 & 0.03 & @xmath296 & @xmath267 & @xmath297 & @xmath298 & + 67 & j033202.5@xmath72274601 & @xmath299 & @xmath300 & 24.71 & 22.73 & 0.18 & 0.02 & 0.04 & @xmath301 & @xmath302 & @xmath303 & @xmath304 & + 78 & j033230.1@xmath72274524 & @xmath305 & @xmath259 & 23.04 & 21.45 & 0.26 & 0.37 & 0.03 & @xmath306 & @xmath307 & @xmath308 & @xmath309 & + 81 & j033226.0@xmath72274515 & @xmath310 & @xmath311 & 26.41 & 25.26 & 0.10 & 0.13 & 0.13 & & & @xmath312 & @xmath313 & + 83 & j033215.0@xmath72274225 & @xmath314 & @xmath315 & 23.80 & 22.01 & 0.25 & 0.03 & 0.03 & @xmath316 & @xmath317 & @xmath318 & @xmath319 & + 86 & j033233.9@xmath72274521 & @xmath320 & @xmath283 & 25.32 & 24.13 & 0.31 & 0.00 & 0.00 & & & @xmath321 & @xmath322 & + 89 & j033208.3@xmath72274153 & @xmath323 & @xmath279 & 25.23 & 24.24 & 0.12 & 0.10 & 0.04 & & & @xmath324 & @xmath325 & + 149 & j033212.3@xmath72274621 & @xmath326 & @xmath327 & 23.85 & 21.76 & 0.32 & 0.03 & 0.03 & @xmath328 & @xmath329 & @xmath330 & @xmath331 & + 155 & j033208.0@xmath72274240 & @xmath332 & @xmath333 & 23.06 & 21.11 & 0.47 & 0.00 & 0.03 & @xmath334 & @xmath335 & @xmath336 & @xmath337 & + 173 & j033216.8@xmath72274327 & @xmath338 & @xmath339 & 22.88 & 21.11 & 0.22 & 0.03 & 0.03 & @xmath340 & @xmath341 & @xmath342 & @xmath343 & + 185 & j033211.0@xmath72274343 & @xmath344 & @xmath345 & 22.39 & 20.54 & 0.62 & 0.00 & 0.03 & @xmath346 & @xmath347 & @xmath348 & @xmath349 & truncated by chip edge + 224 & j033228.8@xmath72274621 & @xmath350 & @xmath339 & 22.97 & 20.76 & 0.27 & 0.03 & 0.03 & @xmath351 & @xmath352 & @xmath353 & @xmath354 & + 266 & j033214.0@xmath72274249 & @xmath332 & @xmath355 & 22.29 & 20.35 & 0.69 & 0.00 & 0.03 & @xmath356 & @xmath356 & @xmath357 & @xmath358 & + 515 & j033232.2@xmath72274652 & @xmath359 & @xmath360 & 27.78 & 25.41 & 0.19 & 0.01 & 0.00 & & & @xmath361 & @xmath362 & + 532 & j033214.2@xmath72274231 & @xmath363 & @xmath191 & 24.81 & 23.64 & 0.13 & 0.22 & 0.04 & @xmath364 & @xmath365 & @xmath366 & @xmath367 & + 535 & j033211.5@xmath72274650 & @xmath368 & @xmath369 & 22.69 & 20.82 & 0.31 & 0.03 & 0.03 & @xmath370 & @xmath371 & @xmath372 & @xmath373 & + 536 & j033210.9@xmath72274235 & @xmath320 & @xmath374 & 19.97 & 18.17 & 0.59 & 0.03 & 0.03 & @xmath375 & @xmath246 & @xmath376 & @xmath377 & double nucleus , 03 sep . + 538 & j033208.6@xmath72274649 & @xmath378 & @xmath327 & 19.90 & 18.19 & 0.85 & 0.03 & 0.03 & @xmath379 & @xmath380 & @xmath381 & @xmath382 & truncated by chip edge + 560 & j033206.3@xmath72274537 & @xmath383 & @xmath339 & 23.05 & 20.65 & 0.27 & 0.03 & 0.03 & @xmath384 & @xmath385 & @xmath386 & @xmath387 & + 563 & j033231.5@xmath72274624 & @xmath388 & @xmath339 & 23.64 & 22.31 & 0.26 & 0.02 & 0.03 & @xmath389 & @xmath390 & @xmath391 & @xmath392 & + 593 & j033214.8@xmath72274403 & @xmath388 & @xmath339 & 26.27 & 24.51 & 0.47 & 0.00 & 0.00 & & & @xmath393 & @xmath394 & + 594 & j033209.8@xmath72274249 & @xmath395 & @xmath339 & 22.93 & 20.30 & 0.44 & 0.02 & 0.03 & @xmath396 & @xmath397 & @xmath398 & @xmath399 & + 623 & j033228.6@xmath72274659 & @xmath400 & @xmath339 & 26.95 & 26.35 & 0.12 & 0.00 & 0.00 & & & @xmath401 & @xmath402 & + 624 & j033229.3@xmath72274708 & @xmath383 & @xmath339 & 22.68 & 20.36 & 0.33 & 0.03 & 0.03 & @xmath403 & @xmath404 & @xmath405 & @xmath406 & + 626 & j033209.5@xmath72274758 & @xmath383 & @xmath339 & 25.44 & 24.20 & 0.21 & 0.01 & 0.00 & & & @xmath407 & @xmath408 & + 631 & j033215.2@xmath72274335 & @xmath350 & @xmath339 & 25.13 & 22.93 & 0.23 & 0.00 & 0.03 & @xmath409 & @xmath410 & @xmath411 & @xmath412 & +","summary":"the concentration indices of the cdfs counterparts are clearly larger on average than those of the field distribution , at 5-sigma , suggesting that the strong correlation between central black hole mass and host galaxy properties ( including concentration index ) observed in nearby galaxies is already evident by . these results , combined with previous similar findings for local samples , suggest that recent merger / interaction history is not a good indicator of agn activity over a substantial range of look - back time .","abstract":"we present quantitative morphological analyses of 37 _ hst_/wfpc2 counterparts of x - ray sources in the 1 ms chandra deep field  south ( cdfs ) . we investigate : 1 ) one - dimensional surface brightness profiles via isophotal ellipse fitting ; 2 ) two - dimensional , psf - convolved , bulge+disk+nucleus profile - fitting ; 3 ) asymmetry and concentration indices compared with all sources in our three wfpc2 fields ; and 4 ) near - neighbor analyses comparing local environments of x - ray sources versus the field control sample . significant nuclear point - source optical components appear in roughly half of the resolved _ hst_/wfpc2 counterparts , showing a narrow range of consistent with the several _ hst_-unresolved x - ray sources ( putative type  1 active galactic nuclei [ agns ] ) in our fields . we infer roughly half of the _ hst_/wfpc2 counterparts host unobscured agn , comparable to analogous low - redshift agn samples and suggesting no steep decline in the type  1/type  2 ratio out to the redshifts typical of our sources . the concentration indices of the cdfs counterparts are clearly larger on average than those of the field distribution , at 5-sigma , suggesting that the strong correlation between central black hole mass and host galaxy properties ( including concentration index ) observed in nearby galaxies is already evident by . by contrast , the asymmetry index distribution of the 21 resolved cdfs sources at is indistinguishable from the field . moreover , the frequency of near neighbors around the cdfs counterparts is not significantly different from the field sample . these results , combined with previous similar findings for local samples , suggest that recent merger / interaction history is not a good indicator of agn activity over a substantial range of look - back time ."}
{"article_id":"1203.3638","section_id":"i","document":"in this paper we consider the analysis of longitudinal data that arise in the form of a small number of long sequences . our interest in this problem is motivated by the naturalistic teenage driving study ( ntds ) , an observational study of teenage driving performance and characteristics [ simons - morton et al . ( @xcite ) ] . in the study , 42 newly licensed teenage drivers in virginia were monitored continuously during their first 18 months of independent driving using in - vehicle data recording systems . the instrumentation included accelerometers , video cameras , a global positioning system , a front radar and a lane tracker . the ntds is a first of its kind , at least for teenage drivers in the united states . the study provides valuable information on risky driving behavior , which can be assessed in terms of elevated gravitational force ( @xmath0-force ) events ( rapid start , hard stop , hard turn and yaw ) . counts of @xmath0-force events are available for each trip ( defined as ignition on to ignition off ) , and their incidence rates represent different aspects of risky driving behavior . the ntds data set comprises more than 68,000 trips by the 42 teen subjects , with an average of 1,626 trips per subject . figure [ fig1 ] provides a summary of the ntds data by subject in terms of the number of trips made and the total number of miles driven . an important goal in our analysis of the ntds data is to understand how risky driving is associated with subject - level covariates ( i.e. , individual characteristics such as gender ) as well as trip - level or time - dependent covariates ( e.g. , time since licensure , presence of passengers ) . there is an extensive literature on longitudinal data analysis ; see , for example , @xcite , @xcite and @xcite . common approaches to longitudinal data analysis include random effect models [ @xcite , @xcite ] and generalized estimating equations ( gee ) [ @xcite , @xcite , @xcite ] . in general , the two approaches have different interpretations ( subject - specific versus marginal ) , although that distinction is not important when the log link is used for count data . for analyzing the ntds data , it is natural to consider generalized linear mixed models ( glmm ) with appropriate random effects to account for population heterogeneity , serial correlation and/or possible overdispersion [ @xcite , @xcite , @xcite ] . however , a realistic glmm for the ntds data would involve several random components , including a latent process that induces serial correlation ( see section [ analysis ] ) , and the computational demand of such a glmm analysis can be prohibitive with thousands of trips per subject . even if the computation is feasible , the resulting inference may be sensitive to modeling assumptions that are difficult to verify . the computational burden can be reduced by resorting to a marginal analysis using the gee approach , especially under a working independence assumption . the gee approach only requires specification of the first two moments and not the entire distribution . the robust variance estimate can be used to make asymptotically valid inference that only requires correct specification of the mean structure , assuming that the number of subjects is large relative to the number of observations per subject . the exact opposite situation occurs in the ntds , and @xcite have shown that the robust variance estimate can perform poorly in such a situation and that the model - based variance estimate may be preferable . numerous methods have been proposed to improve upon the robust variance estimate , including jackknife [ @xcite , @xcite ] , bias correction [ @xcite ] and window subsampling techniques [ @xcite , @xcite ] . given the well - known advantages and potential issues of the gee approach , it is natural to ask how to perform a simple and valid marginal analysis of the ntds data with reasonable efficiency and robustness . we attempt to address this question in the present paper by examining some existing methods and developing new ones . we find that it is generally helpful to include a fixed effect for each subject in the gee model . once the subject effects are estimated , they can be treated as the response variable in a subsequent linear regression analysis for estimating the effects of subject - level covariates . these fixed effects also help with trip - level covariates by removing the correlation due to population heterogeneity . if the counts are large ( with a marginal mean of 1 , say ) , the effects of trip - level covariates can be estimated from a conventional gee analysis using an estimated covariance matrix together with the robust variance estimate . for small counts ( with a marginal mean of 0.1 ) , the conventional approach is not satisfactory , and we explore a within - cluster resampling ( wcr ) approach [ @xcite , @xcite ] . the wcr approach was originally proposed to deal with informative cluster sizes , which is not of concern in the ntds . our motivation for considering wcr is to improve the performance of gee methods by altering the data structure . to this end , we consider extensions of wcr that reduce serial correlation within clusters or increase the number of ( approximately ) independent clusters . this leads to a wcr method involving separated blocks which performs better than the conventional methods . the rest of the paper is organized as follows . in the next section we set up the notation , formulate the problem , and discuss potential issues . then we examine the standard gee methods in section [ gee ] and explore some wcr methods in section  [ mo ] . the ntds data are analyzed in section [ analysis ] using the appropriate methods . the paper concludes with a discussion in section [ disc ] .","summary":"for this situation , we explore a within - cluster resampling ( wcr ) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples . this leads to a novel wcr method which operates on separated blocks within subjects and which performs better than all of the previously considered methods .","abstract":"most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small . motivated by the naturalistic teenage driving study ( ntds ) , which represents the exact opposite situation , we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences . we consider standard methods based on generalized estimating equations , under working independence or an appropriate correlation structure , and find them unsatisfactory for dealing with time - dependent covariates when the counts are low . for this situation , we explore a within - cluster resampling ( wcr ) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples . this leads to a novel wcr method which operates on separated blocks within subjects and which performs better than all of the previously considered methods . the methods are applied to the ntds data and evaluated in simulation experiments mimicking the ntds .    ,    ."}
{"article_id":"1203.3638","section_id":"c","document":"even with a great variety of methods available for longitudinal data analysis , it can still be difficult to analyze longitudinal data in long sequences , especially when the serial correlation is strong and long - lived . in this paper , we examine standard gee methods and propose new ones for marginal analysis of longitudinal count data in a small number of very long sequences . the methods are evaluated and compared in simulation experiments mimicking the ntds , and the main findings can be summarized as follows . we consider the use of fse in this particular situation , a  simple technique with important practical implications . it allows the effects of subject - level covariates to be estimated easily from a linear regression analysis for the estimated fse , and it also helps with trip - level covariates by removing the correlation due to population heterogeneity . for trip - level covariates , we find that a standard gee analysis under working independence can lead to inefficient estimates and serious undercoverage , and that both problems can be alleviated by incorporating a properly specified correlation structure . the latter approach works well for large counts but not for small counts , mainly because the serial correlation is hard to estimate with small counts . we therefore explore an alternative approach ( wcr ) for the case of small counts . the original version of wcr and an extension to simple random sampling seem unsatisfactory , however , because of numerical instability in repeated analyses of small samples and a bias magnification effect of wcr that results in variance underestimation . to address these issues , we propose an wcr - sb approach that involves separated blocks and that performs better than all of the previously considered methods ( wcr and standard gee ) .    in table [ tb6 ] the wcr - sb analyses are not dramatically different from the other analyses . this is reassuring to the scientists , but it also suggests that the ntds data set is not ideal for demonstrating the advantage of the wcr - sb approach . to put the latter point in perspective , we note that better performance in the frequentist sense does not imply better results in every realization . the performance of the wcr - sb approach has been evaluated in simulation experiments which are , in fact , designed to mimic the ntds . most of the uncertainty in designing the simulation experiments is associated with the length of the serial correlation , which is very difficult to estimate with small counts , as shown in table [ tb3 ] . it is certainly possible that the serial correlation in the ntds is not sufficiently long - lived for the new method to make a material difference . in that case , a better example than the ntds might be a proposed follow - up study that involves 100 teenage drivers to be followed for at least 3 years . the larger amount of data from the latter study will afford a better understanding of both the nature and the length of the serial correlation . furthermore , as teenage drivers gain experience and perspective over time , their driving behavior may become less haphazard and more stable , in which case the serial correlation will gradually become longer - lived toward the end of the ( longer ) study duration . thus , in terms of the length of the serial correlation , the follow - up study will provide a better opportunity than the ntds to demonstrate the advantage of the wcr - sb approach . the wcr - sb approach is designed for longitudinal data in a small number of long sequences . the strength of this approach relative to standard gee methods is the ability to handle strong and long - lived serial correlation when the mean count is low . the weaknesses of the wcr - sb approach include increased computational demand ( relative to standard gee methods ) and the need for information about the length of the serial correlation ( in order to specify the separation size @xmath84 ) . because @xmath36 can be very difficult to estimate , one may need to consult the subject - matter scientist or perform a sensitivity analysis with different values of @xmath84 , as we did in analyzing the ntds data ( see section [ analysis ] ) .    as mentioned earlier at the end of section [ wind ] , we have actually explored several existing alternatives to the robust variance estimate in the present situation . no appreciable improvement has been achieved using a standard bootstrap procedure ( i.e. , sampling subjects with replacement ) and jackknife methods [ @xcite , @xcite ] . a  block bootstrap procedure [ @xcite ] appears to work well for short - lived serial correlation but not for long - lived serial correlation . in a simple setting that permits closed - form calculations of the finite - sample target of the robust variance estimate ( with sample quantities replaced by their population counterparts ) under working independence , we have found that the target can be far below the sampling variance of the point estimate observed in simulations , suggesting that the asymptotic theory may not provide a reasonable approximation in this situation . given that , it seems unlikely that a substantial improvement can be made using the available bias correction methods [ e.g. , @xcite ] . another possible approach to variance estimation is window subsampling [ @xcite , @xcite , @xcite ] . a practical difficulty with this approach is specification of the window size , which has been found to have a  large impact on the variance estimate . @xcite have suggested taking the maximum among variance estimates based on several window sizes , but it remains unclear how to choose the set of window sizes for the maximization . maximizing over a large set of window sizes can lead to a very conservative variance estimate , as the maximum among several underestimators need not be an underestimator itself .    under the wcr approach , we have considered various sampling schemes based on time . an interesting possibility , suggested by a referee , is to sample trips using a mechanism that involves other covariates than time and possibly the outcome . in the latter case , appropriate adjustments will be necessary to account for the outcome - dependent nature of the subsample . further research is needed to explore the potential benefits of the more sophisticated sampling schemes . this article has been focused on valid inference in the sense of ( nearly ) correct coverage . we have not discussed the issue of generalization from a sample of subjects to the target population , which is always important and especially so when the number of subjects is small . such generalizations should be easier to justify when the within - subject variability is large relative to the between - subject variability , which appears to be the case in the ntds .","summary":"most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small . motivated by the naturalistic teenage driving study ( ntds ) , which represents the exact opposite situation , we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences . the methods are applied to the ntds data and evaluated in simulation experiments mimicking the ntds .    ,    .","abstract":"most of the available methods for longitudinal data analysis are designed and validated for the situation where the number of subjects is large and the number of observations per subject is relatively small . motivated by the naturalistic teenage driving study ( ntds ) , which represents the exact opposite situation , we examine standard and propose new methodology for marginal analysis of longitudinal count data in a small number of very long sequences . we consider standard methods based on generalized estimating equations , under working independence or an appropriate correlation structure , and find them unsatisfactory for dealing with time - dependent covariates when the counts are low . for this situation , we explore a within - cluster resampling ( wcr ) approach that involves repeated analyses of random subsamples with a final analysis that synthesizes results across subsamples . this leads to a novel wcr method which operates on separated blocks within subjects and which performs better than all of the previously considered methods . the methods are applied to the ntds data and evaluated in simulation experiments mimicking the ntds .    ,    ."}
{"article_id":"1501.07616","section_id":"i","document":"in many single molecule experiments beads that are attached to molecular motors are used to infer properties of the motor protein from the analysis of the trajectory of these probe particles . in particular , external forces can be exerted on the motor via such a probe particle @xcite . in the theoretical analysis of such assays , the motor is usually modelled as a particle hopping on a discrete state space with transitions governed by a master equation @xcite . alternatively , the so called ratchet models combine continuous diffusive spatial motion with stochastic switching between different potentials corresponding to different chemical states @xcite . these approaches often comprise only one particle explicitly , representing the motor . the contribution of external forces which in the experiments act on the motor only via the probe are then included in the transition rates @xcite ( or langevin equation for the spatial coordinate @xcite ) of the motor particle directly . however , theoretical models that are used to reproduce the experimental observations should comprise at least two ( coupled ) degrees of freedom , one for the motor and one for the probe particle . such models consisting of one degree of freedom hopping on a discrete state space representing the motor coupled to a continuously moving degree of freedom representing the probe are discussed in @xcite . while multi - particle models are more precise and better represent the actual experimental setup , one - particle models are widely - used toy models often applied to illustrate basic ideas .    simplifying the description of systems consisting of many degrees of freedom with a concomitant large state space while still maintaining important properties is commonly known as coarse - graining . in the context of stochastic thermodynamics @xcite , various coarse - graining methods have been applied , e.g. , lumping together states of a discrete state space among which transitions are fast @xcite , averaging over states for discrete @xcite or continuous processes @xcite , eliminating single states from a network description @xcite or eliminating slow ( invisible ) degrees of freedom @xcite . it was found that , in general , coarse - graining has implications on the entropy production and , in particular @xcite , dissipation . in the context of biological systems and especially molecular motors , coarse - graining procedures mostly focus on eliminating selected states of the motor @xcite or on reducing continuous ( ratchet ) models to discrete - state models @xcite .    in the present paper , we introduce a coarse - graining procedure that allows to reduce molecular motor - bead models to effective one - particle models with discrete motor states with the external force acting directly on the effective motor particle . we eliminate the explicit dynamics of the probe particle completely still maintaining the correct local detailed balance condition for the effective motor transition rates and preserving the average currents of the system . as a main result , we find that the coarse - grained rates show a more complex force dependence than the usually assumed exponential behaviour and a more complex concentration dependence than mass action law kinetics . the paper is organized as follows . in section [ sec : onestate ] , we introduce our coarse - graining method on the basis of a simple motor - bead model with only one motor state and apply it to a model for the @xmath0-atpase @xcite . in section [ sec : multistate ] , we generalize the procedure to motor models with several internal states and apply it to both a refined model for the @xmath0-atpase and to a kinesin model . a possible experimental implementation of our method is presented in section [ sec : exp ] . we show that entropy production and efficiency remain invariant under this coarse - graining procedure in section [ sec : entropy ] , discuss implications on the stall conditions in section [ sec : stall ] and conclude in section [ sec : conc ] .","summary":"many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it . the theoretical analysis of these assays , however , often takes into account only the degrees of freedom representing the motor . we present a coarse - graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one - particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way .","abstract":"many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it . the theoretical analysis of these assays , however , often takes into account only the degrees of freedom representing the motor . we present a coarse - graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one - particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way . the coarse - grained rates obey a local detailed balance condition and reproduce the net currents . moreover , the average entropy production as well as the thermodynamic efficiency is invariant under this coarse - graining procedure . our analysis reveals that only by assuming unrealistically fast probe particles , the coarse - grained transition rates coincide with the transition rates of the traditionally used one - particle motor models . additionally , we find that for multicyclic motors the stall force can depend on the probe size . we apply this coarse - graining method to specific case studies of the-atpase and the kinesin motor ."}
{"article_id":"1501.07616","section_id":"c","document":"most experiments on molecular motors comprise some kind of probe particle . therefore , any theoretical modelling with parameters estimated from experimental data will explicitly or implicitly contain characteristics of the probe particle .    in this paper , we have introduced a systematic coarse - graining method that allows to reduce motor - bead models to effective one - particle motor models . this coarse - graining procedure provides a compromise between a one - particle description that is simple to handle and a detailed model comprising the dynamics of the full system . it yields an effective one - particle model maintaining the true motor network , where the influence of the probe is naturally incorporated without any additional assumptions since the simplification of the description takes place a posteriori . any external force acting on the probe is then acting on the effective motor directly . the coarse - grained rates obey a ldb condition and yield the correct net currents . fixing the marginal distribution and the average currents , there is still freedom on how to choose the rates . only with the ldb condition the effective rates are determined uniquely .    applying the coarse - graining procedure to motor - bead models , we find that in general the coarse - grained rates do not show a single exponential dependence on the external force in contrast to what is often assumed for mechanical transition rates in one - particle models . only in the often unrealistic limit of fast bead relaxation , the coarse - grained rates reduce to the corresponding one - particle rates .    in the absence of external forces , in general the coarse - grained rates are not proportional to the atp concentration even if the motor rates obey mass action law kinetics . this feature originates from the drag effect of probe ( due to friction ) that is incorporated in the coarse - grained rates . for the same reason , the average velocity shows a sub - linear dependence on the atp concentration even for a one - state motor model . assuming an a priori one - state model with external force acting directly on the motor , one would have either to use a rather counterintuitive complex force - dependence of the transition rates or to introduce additional motor states in order to obtain a sublinearly growing velocity caused by the drag of the probe . in a one - particle description , the effect of large probe particles on the dwell time distributions could also be mistaken as signature of additional motor states thus leading to an overly complex motor network @xcite . considering the influence of the coarse - graining procedure on the stochastic thermodynamics of the system , we show that the total entropy production remains invariant under coarse - graining . this is due to the fact that , on the one hand , the state space of the eliminated degree of freedom contains no entropy producing cycles . on the other hand the design of the coarse - graining procedure is also important . it has to conserve the motor network as well as the net currents and provide transition rates fulfilling a ldb condition . likewise , the thermodynamic efficiency remains invariant in our scheme . our coarse - graining method conserves average quantities like the entropy production or operational currents although eliminating the dynamics of the probe particle strongly affects the cycle structure of the full system . in order to preserve also fluctuations of current observables in the long - time limit it was found that coarse - graining methods should conserve the cycle structure of the full system @xcite .    from the experimental point of view , in order to obtain the simpler effective model , the underlying mesoscopic modelling need not to be known since all these quantities enter the coarse - grained description via the net currents and the marginal distributions which , in principle , can be extracted from the experimental data as we have demonstrated using a two step model for the @xmath0-atpase . the main advantage of the coarse - graining procedure introduced here is that once the rates have been obtained from experimentally accessible quantities , they automatically fulfill a ldb condition and provide the correct average currents , i.e. , velocity , entropy production , hydrolysis rate etc ..    for multicyclic motors , the coarse - graining procedure can yield rates that can have poles and become ( piecewise ) negative . if this scenario occurs , the coarse - grained rates lack a physical interpretation as transition probabilities in this range but they can still be used to calculate average quantities . for this class of motors the stall force typically depends on the size of the probe particle , i.e. , the friction coefficient . applying naively a one - particle model to such an experimental setup would not allow to determine the energy transduction mechanism of the motor correctly . for one - state motors , the coarse - grained rates are always positive . so far , we have discussed coarse - graining only under ness conditions . in principle , the coarse - graining procedure as introduced in sections [ sec : cg - one ] and [ sec : cg - mult ] can also be applied to non - stationary states , e.g. , if the nucleotide concentrations are not constant and @xmath260 decreases with time @xcite . such a scenario would yield time - dependent @xmath119 s , net currents , ldb conditions and therefore also time - dependent coarse - grained rates . further generalizations might include other types of models representing the full system . while developed here for discrete motor models , the coarse - graining procedure should be also applicable to continuous motors moving in a tilted periodic potential where the potential minima will become the discrete states of the coarse - grained effective motor . the introduction of the index @xmath105 in principle also accounts for more involved potentials or free energy surfaces that depend on both the motor and the probe state . thanks p. pietzonka for valuable hints concerning numerical implementations .","summary":"the coarse - grained rates obey a local detailed balance condition and reproduce the net currents .","abstract":"many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it . the theoretical analysis of these assays , however , often takes into account only the degrees of freedom representing the motor . we present a coarse - graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one - particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way . the coarse - grained rates obey a local detailed balance condition and reproduce the net currents . moreover , the average entropy production as well as the thermodynamic efficiency is invariant under this coarse - graining procedure . our analysis reveals that only by assuming unrealistically fast probe particles , the coarse - grained transition rates coincide with the transition rates of the traditionally used one - particle motor models . additionally , we find that for multicyclic motors the stall force can depend on the probe size . we apply this coarse - graining method to specific case studies of the-atpase and the kinesin motor ."}
{"article_id":"0904.1087","section_id":"i","document":"one of the key features expected in quantum theories of gravity is fluctuation of the classical lightcone and possible effects on signal propagation . this possibility has been discussed in several contexts by numerous authors  @xcite . one approach is to study variations in the flight times of light pulses between a source and a detector  @xcite . this approach was used in ref . @xcite to study the effects of boundaries and periodic compactification of one space dimension . in particular , it was found that the fluctuation in flight time of a pulse propagating parallel to a plane boundary , or in a direction transverse to the compactified dimension , will tend to grow as the flight distance increases . this growth can be viewed as a cumulative effect of spacetime geometry fluctuations modified by the boundary or the compactification . this effect is analogous to the local casimir effect , whereby a boundary modifies the two - point function of the quantized electromagnetic field . this modification can produce observable effects , such as a force on an atom . this force was predicted theoretically by casimir and polder  @xcite in 1948 , and measured experimentally by sukenik  _ et al _ @xcite in 1993 . another effect of modified electromagnetic vacuum fluctuations can be brownian motion of charged test particles  @xcite . the presence of a boundary can alter the mean squared velocity or position of the particle . this modification is analogous to the effects of lightcone fluctuations when spacetime geometry fluctuations are modified .    in the present paper , we will be concerned with modification of lightcone fluctuations due to compact extra dimensions . theories with extra dimensions were introduced into physics by kaluza  @xcite and klein  @xcite , and have been the topic of many papers in recent years  @xcite . we wish to address the question of whether compact extra dimensions can give rise to observable effects on the propagation of light rays in the uncompactified directions . such an effect could be a potential test for the existence of extra dimensions . a secondary purpose of this paper is to discuss quantization of linearized gravity in arbitrary numbers of flat spacetime dimensions and to give explicit expression for the graviton two - point functions in the transverse tracefree gauge . in effect , we are searching for modifications of quantum effects in the uncompactified dimensions due to the presence of the extra dimensions . a somewhat different effect , whereby extra dimensions lead to changes in casimir forces has recently been discussed by cheng and others  @xcite . the outline of this paper is as follows : in sect . [ sec : lc_flucts ] , we review how quantized linear metric perturbations may give rise to variations in flight times of pulses . in sect .  [ sec : two - point ] , we discuss quantization of linearized metric perturbations and compute the graviton two - point function in the transverse , tracefree gauge for flat spacetime of arbitrary dimension . in particular , in sect . [ sec : del_t ] we give a new derivation of the formula for @xmath0 , the mean flight time variation . this result is used in sect . [ sec:5dkk ] to study lightcone fluctuations in a five dimensional spacetime with one compact dimension . some results for more than one compact dimension are also summarized . we also examine the issue of the correlation of successive pulses in this model in sect . [ sec : corr ] . we turn to a different measure of lightcone fluctuations , the possible broadening of spectral lines , in sect . [ sec : red ] . our results are discussed in sect . [ sec : diss ] . appendix  [ sec:2pt ] provides a detailed treatment of the graviton two - point functions .","summary":"we treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity . the mean variation in flight time can grow logarithmically with the flight distance .","abstract":"we treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity . we find that the flight times of pulses can fluctuate due to modification of the graviton vacuum by the compactification . in the case of a five dimensional kaluza - klein theory , the mean variation in flight time can grow logarithmically with the flight distance . this effect is in principle observable , but too small to serve as a realistic probe of the existence of extra dimensions . we also examine the effect of the compactification on the widths of spectral lines , and find that there is a small line narrowing effect . this effect is also small for compactification well above the planck scale , but might serve as a test of the existence of extra dimensions ."}
{"article_id":"0904.1087","section_id":"c","document":"we have treated the effects of compact extra flat spacetime dimensions on quantum lightcone fluctuations . one measure of lightcone fluctuations is variations in the flight times of pulses . we found in a five dimensional model that this variation will grow as the logarithm of the flight distance . in principle this is an observable effect , but it is too small to be a realistic test of extra dimensions . we also examined the correlations of successive pulses . this correlation weakens as the pulse separation increases , but is always nonzero . this nonzero correlation is presumably responsible for the result that effect of geometry fluctuations on the width of spectral lines does not increase with increasing flight distance . in fact , we find a weak line narrowing effect in which the spacetime geometry fluctuations slightly reduce the natural line width . the fractional line narrowing effect is = = c , where @xmath159 is a constant of order unity . the analysis in this paper assumes gravitons on a fixed background spacetime and is presumable only valid when the compactification scale is well above the planck scale , @xmath160 . nonetheless , this suggests a possible observational signature of the existence of extra dimensions : a small , systematic narrowing of all spectral line from what would otherwise be expected . this work was supported in part by the national natural science foundation of china under grants no . 10375023 , 10775050 , the srfdp under grant no . 20070542002 , the national science foundation under grant phy-0555754 and by conselho nacional de desenvolvimento cientifico e tecnologico do brasil ( cnpq ) . lhf would like to thank the institute of physics at academia sinica in taipei , national dong hwa university in hualien , taiwan and the kavali institute for theoretical physics china for hospitality while this manuscript was completed . hy thanks the kavali institute for theoretical physics china for hospitality in the final stages of this work .","summary":"this effect is in principle observable , but too small to serve as a realistic probe of the existence of extra dimensions . we also examine the effect of the compactification on the widths of spectral lines , and find that there is a small line narrowing effect . this effect is also small for compactification well above the planck scale , but might serve as a test of the existence of extra dimensions .","abstract":"we treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity . we find that the flight times of pulses can fluctuate due to modification of the graviton vacuum by the compactification . in the case of a five dimensional kaluza - klein theory , the mean variation in flight time can grow logarithmically with the flight distance . this effect is in principle observable , but too small to serve as a realistic probe of the existence of extra dimensions . we also examine the effect of the compactification on the widths of spectral lines , and find that there is a small line narrowing effect . this effect is also small for compactification well above the planck scale , but might serve as a test of the existence of extra dimensions ."}
{"article_id":"astro-ph0504604","section_id":"i","document":"a connection between galaxy - galaxy mergers and the onset of nuclear activity in classical optical and radio - selected active galactic nuclei ( agn ) has been inferred over the last 20 years . many classical radio galaxies and qsos have been observed at optical and near - infrared wavelengths to have double - nuclei , tidal bridges / tails , and close companions consistent with them being the mergers of disk galaxies ( e.g. stockton & mackenty 1983 ; heckman et al . 1986 ; smith & heckman 1990a , b ; mcleod & rieke 1994 ; surace , sanders & evans 2001 ) . further evidence of the agn - merger connection has resulted from multiwavelength surveys of luminous infrared - selected galaxies , which have shown these galaxies to be merging / interacting disk galaxies and have shown an increasing fraction of infrared galaxies with optical , near - infrared , and x - ray signatures of imbedded agn as a function of increasing luminosity ( e.g. , sanders et al . 1988a , b ; veilleux , sanders , & kim 1997 , 1999 ; veilleux et al 1999 ; vignati et al . 1999 ) . star formation appears to be a component of the activity occuring in the host galaxies of agn  a growing number of radio galaxies and qsos have detectable amounts of molecular gas and young uv - luminous knots indicative of recent star formation ( philips et al . 1987 ; sanders , scoville , & soifer 1988c ; lazareff et al . 1989 ; mirabel , sanders , & kazs 1989 ; mazzarella et al . 1993  hereafter , paper 1 ; reuter et al . 1993 ; evans et al . 2001 ; allen et al . 2002 ; scoville et al . 2003 ) . in addition , the fraction of classical agn with dust in their host galaxies is substantial ( e.g. , golombek et al . 1988 ; sanders et al 1989 ) , with @xmath6 50% of 3c radio galaxies and @xmath6 70% of palomar - green ( pg : schmidt & green 1983 ) qsos at @xmath13 having iras detections at 60@xmath14 m . the infrared space observatory ( iso ) detected thermal dust emission in a larger fraction of radio galaxies and qsos ( meisenheimer et al . 2001 ; haas et al . 2003 , 2004 ) , providing further proof of rich isms in the host galaxies of radio galaxies and qsos . this dust is most likely a combination of dust intrinsic to the progenitor galaxies , as well as dust produced through stellar mass loss from a recent / ongoing starburst . the importance of star formation in agn host galaxies is also inferred via recent black hole surveys in nearby galaxies . these observations have shown that the massive spheroidal component of many nearby normal galaxies contain quiescent supermassive nuclear black holes ( @xmath15 m@xmath4 : e.g. magorrian et al . a key result that has come from these surveys is the scaling of black hole mass with stellar bulge mass ( e.g. , magorrian et al . such a correlation may indicate that the formation of stars in the bulge component of galaxies is intimately associated with the building of supermassive black holes . while the molecular gas properties of infrared - selected galaxies have been studied in detail , co observations of large samples of radio galaxies and qsos have lagged behind . thus , conclusions about the co properties of classical agn and their host galaxies is often based on small number statistics or incomplete data sets . the present study focusses on the global molecular gas properties of a sample of low - redshift radio galaxies , and it serves as an extension of the survey presented in paper 1 . the primary issues to be addressed with this survey are _ ( a ) _ whether low-@xmath5 radio - selected agn reside in molecular gas - rich host galaxies and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn . to address the latter issue , the millimeter data are complemented by infrared , radio , and x - ray data to allow a comparison between the available amount of fuel for star formation ( and perhaps agn activity ) and the energy emitted from the agn and/or host galaxy at these wavelengths . the analysis presented here builds primarily upon similar analysis done of low - redshift , infrared - selected galaxies over the last twenty years ( e.g. , sanders & mirabel 1996 and references therein ; franceschini et al . 2003 ; trentham et al . 2005 ) and recent analysis of a sample of co - detected pg qso host galaxies ( evans et al . these galaxies , which may emanate from the same parent population as the radio galaxies or be linked via evolution , will serve as the primary comparison samples . in addition , optical imaging of a radio galaxy subsample will be briefly discussed . parts of this extended millimeter survey have been presented elsewhere ( evans 1996 ; sanders & mirabel 1996 ; evans 1998 ; evans et al . 1999a , b ) . this paper is divided into six sections . the selection criteria of the radio galaxy sample is discussed in  2 . section 3 is a summary of the observations and data reduction . in  4 , the co(@xmath16 ) emission - line properties are presented , along with the method of calculating the molecular gas mass . section 5 contains a brief summary of the optical imaging data and an extended discussion of the infrared , radio , co , and x - ray properties of the radio galaxies relative to those of infrared - selected galaxies , pg qsos , and elliptical galaxies . section 6 is a summary . throughout the paper , @xmath17 km s@xmath1 mpc@xmath1 , @xmath18 , and @xmath19 are assumed .","summary":"the iras flux - limited sample contains 33 radio galaxies with different radio morphologies and a broad range of infrared luminosities ( l ) , allowing for an investigation of _ ( a ) _ whether low- radio - selected agn reside in molecular gas - rich host galaxes , and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn .","abstract":"this paper reports the latest results from a millimeter - wave ( co ) spectroscopic survey of iras - detected radio galaxies with w hz in the redshift range . the iras flux - limited sample contains 33 radio galaxies with different radio morphologies and a broad range of infrared luminosities ( l ) , allowing for an investigation of _ ( a ) _ whether low- radio - selected agn reside in molecular gas - rich host galaxes , and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn . all of the radio galaxies in mazzarella et al . ( 1993 ) and mirabel et al . ( 1989 ) have been reobserved . three new co detections have been made , raising the total number of co detections to nine and setting the survey detection rate at 25% . many of the co lines have double - peaked profiles , and the co line widths are broad ( average km s ) , exceeding the average co widths of both ultraluminous infrared galaxies ( km s ) and palomar - green qsos ( km s ) , and thus being indicative of massive host galaxies . the co luminosities translate into molecular gas masses of m , however , the 3 co upper limits for nondetections do not rule out a molecular gas mass as high as that of the milky way ( m ) . optical images of eight out of nine molecular gas - rich radio galaxies show evidence of close companions and/or tidal features . finally , there is no obvious correlation between radio power and molecular gas mass . however , it is notable that only one f - r ii galaxy out of 12 is detected in this co survey ; the remaining detections are of galaxies hosting f - r i and compact radio jets ."}
{"article_id":"astro-ph0504604","section_id":"r","document":"table 3 is a summary of the co emission - line properties of the 31 radio galaxies observed as part of this survey . all of the radio galaxies observed for paper 1 were reobserved , as well as two additional radio galaxies previously detected in co ( 3c 84 : lazareff et al . 1989 ; mirabel et al . 1989 ; reuter et al . 1993 , pks 1345 + 12 : mirabel et al . 1989 ) . in one case ( txs 1506 + 345 ) , the pointing was shifted by @xmath37 from that used in paper 1 in order to center the galaxy in the beam . nine radio galaxies are detected in co(@xmath16 ) , including three new detections ( 3c 31 , pks 0502 - 10 , 3c 293 ) . however , the previously reported detection of co emission in b2 0648 + 27 was not confirmed . the radio galaxy pks 1345 + 12 was the weakest co detection in the sample , thus independent co observations of the galaxy were also obtained with the iram 30 m telescope to improve the determination of the co flux and line shape ( figure 1b ) . the average full width at half the maximum intensity velocity , @xmath38 , of the detected galaxies is 500 km s@xmath1 . several of the galaxies have double - peaked profiles . table 3 lists the measured co intensities and luminosities . the co luminosities of 3c 120 , b2 0722 + 30 , b2 1318 + 34 , and txs 1506 + 345 agree with the values in paper 1 to within @xmath6 20% , and the values of @xmath38 for all except txs 1506 + 345 are similar ( txs 1506 + 345 is reported as having a 2-component co emission line profile in paper 1 ) . there is a major discrepancy between the new co measurements of perseus a and pks 1345 + 12 and those in the literature . for perseus , the line width of co luminosity are in agreement with the measurements of lazareff et al . 1989 and reuter et al . ( 1993 ) , but @xmath39 is a factor of two higher than the value determined by mirabel et al . the discrepancy with the mirabel et al . ( 1989 ) measurements results from what appears to be extended emission in the wings of the line in figure 1  if this emission is ignored , then the co luminosity is @xmath40 k km s@xmath1 pc@xmath41 , within 22% of the value reported by mirabel et al . ( 1989 ) . the pks 1345 + 12 co luminosity comparison is more difficult to rectify  the co luminosity is a factor of two lower than measured by mirabel et al . note , however , that the errors associated with the mirabel et al . ( 1989 ) data are not known . the present pks 1345 + 12 co measurements are correct to within the error of those reported in evans et al . ( 1999 ) if a 20% calibrated error on the present observations is assumed . many of the observations resulted in non - detections . for each of these galaxies , upper limits to the co intensity were calculated via ,    @xmath42 , \\eqno(1)\\ ] ]    where @xmath43 is the main beam temperature , @xmath38 is the average fwhm velocity for the detected radio galaxies (= 500 km s@xmath1 ) , and @xmath44 is the root - mean - squared main beam temperature of the spectral data for a velocity resolution of @xmath45 .    to calculate the co luminosity , the luminosity distance for a source at a given redshift and a @xmath46 universe was first calculated using the equation    @xmath47 @xmath48 . \\eqno(2)\\ ] ]    given the measured co flux , @xmath49 [ jy km s@xmath1 ] , the co luminosity of a source at redshift @xmath5 is    @xmath51 @xmath52 , \\eqno(3)\\ ] ]    ( solomon , downes , & radford 1992 ) where @xmath53 [ km s@xmath1 ] is the speed of light , @xmath54 [ j k@xmath1 ] is the boltzmann constant , and @xmath55 [ hz ] is the observed frequency . in terms of useful units , @xmath56 can be written as    @xmath57 @xmath58 . \\eqno(4)\\ ] ]    to estimate the mass of molecular gas in these radio galaxies , the reasonable assumption that the co emission is optically thick and thermalized , and that it originates in gravitationally bound molecular clouds , is made . thus , the ratio of the h@xmath59 mass and the co luminosity is given by    @xmath60 @xmath61 , \\eqno(5)\\ ] ]    where @xmath62h@xmath63 and @xmath64 are the density of h@xmath59 and brightness temperature for the co(1@xmath650 ) transition ( scoville & sanders 1987 ; solomon , downes , & radford 1992 ) . multitransition co surveys of molecular clouds in the milky way ( e.g. sanders et al . 1993 ) , and in nearby starburst galaxies ( e.g. gsten et al . 1993 ) have shown that hotter clouds tend to be denser such that the density and temperature dependencies cancel each other . the variation in the value of @xmath66 is approximately a factor of 2 for a wide range of kinetic temperatures , gas densities , and co abundance ( e.g. @xmath67 [ k km s@xmath1 pc@xmath68^{-1}$ ] : radford , solomon , & downes 1991 ) . solomon et al . ( 1997 ) and downes & solomon ( 1998 ) have made use of dynamical mass estimates of a low - redshift infrared galaxy sample observed in co with the plateau de bure interferometer to argue that @xmath66 may , in some cases , be as low as 1 @xmath69 ( k km s@xmath1 pc@xmath70 .    for the present sample of galaxies , an @xmath71 ( k km s@xmath1 pc@xmath70 is adopted , which is the approximate value derived for luminous and ultraluminous infrared galaxies ( solomon et al . 1997 ; downes & solomon 1998 ; evans et al . 2002 ) . however , note that @xmath66 for some , or all , of these galaxies may be a factor of @xmath72 higher ( i.e. , the approximate value derived for bulk of the molecular gas in the disk of the milky way : scoville & sanders 1987 ; strong et al . the derived molecular gas masses are listed in table 3 . taking these masses and comparing them with the dust masses , @xmath73 , which are calculated via    @xmath74 @xmath75 \\eqno(6)\\ ] ]    ( see young et al . 1989 ) where the dust temperature , @xmath76 is calculated from the 60@xmath21 and 100@xmath21 flux densities via    @xmath77\\ ] ] @xmath78 , \\eqno(7)\\ ] ]    yields an average molecular gas - to - dust mass ratio of @xmath79 ( see table 4 ) . by comparison , the gas - to - dust ratio is @xmath80 ( @xmath81 [ k km s@xmath1 pc@xmath68^{-1}$ ] ) for iras - detected spiral and luminous infrared galaxies ( young & scoville 1991 and references therein ) . note that the estimated dust masses in table 4 are likely lower limits ; the bulk of the dust in these galaxies may be in a colder ( @xmath82k ) dust component ( young & scoville 1991 ; devereux & young 1990 ) .    given the adopted value of @xmath66 , it is worthwhile to make a conservative estimate of the dynamical mass in order to determine the percentage of the total mass in the form of molecular gas . the dynamical mass within the region of the galaxies containing molecular gas and dust can be calculated via    @xmath83 @xmath84 , \\eqno(8)\\ ] ]    where @xmath38 is the full co velocity width at half the maximum flux density ( table 3 ) and @xmath85 is the radius of the co distribution . the quantity @xmath85 is estimated by assuming optically thick , thermalized gas with a unity filling factor and a blackbody temperature , @xmath86 , equal to that of the dust . thus , the radius of the co distribution is calculated via    @xmath87 \\eqno(9)\\ ] ]    ( see table 4 ) . the resultant size estimates yield @xmath88 m@xmath4 and thus @xmath89 with a mean value of @xmath90 . note that the values of @xmath85 are likely to be underestimated , and thus the derived values of @xmath91 are lower limits . for example , the column densities derived from @xmath85 and @xmath92(h@xmath59 ) are in the range @xmath93 @xmath94 . in contrast , the x - ray column densities estimated from x - ray observations of 3c 120 and pks 1345 + 12 are in the range of @xmath95 @xmath94 ( sambruna et al . 1999 ; odea et al . 2000 ) . further , the co disks in 3c 293 ( evans et al . 1999a ) and 3c 31 ( okuda et al . 2005 ) are extended @xmath6 6 kpc and 1 kpc , respectively , which are 612 times the sizes of the respective co distributions listed in table 4 . this issue will be addressed further in a follow - up paper containing co interferometric maps of the sample ( evans et al .","summary":"all of the radio galaxies in mazzarella et al . ( 1993 ) and mirabel et al .","abstract":"this paper reports the latest results from a millimeter - wave ( co ) spectroscopic survey of iras - detected radio galaxies with w hz in the redshift range . the iras flux - limited sample contains 33 radio galaxies with different radio morphologies and a broad range of infrared luminosities ( l ) , allowing for an investigation of _ ( a ) _ whether low- radio - selected agn reside in molecular gas - rich host galaxes , and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn . all of the radio galaxies in mazzarella et al . ( 1993 ) and mirabel et al . ( 1989 ) have been reobserved . three new co detections have been made , raising the total number of co detections to nine and setting the survey detection rate at 25% . many of the co lines have double - peaked profiles , and the co line widths are broad ( average km s ) , exceeding the average co widths of both ultraluminous infrared galaxies ( km s ) and palomar - green qsos ( km s ) , and thus being indicative of massive host galaxies . the co luminosities translate into molecular gas masses of m , however , the 3 co upper limits for nondetections do not rule out a molecular gas mass as high as that of the milky way ( m ) . optical images of eight out of nine molecular gas - rich radio galaxies show evidence of close companions and/or tidal features . finally , there is no obvious correlation between radio power and molecular gas mass . however , it is notable that only one f - r ii galaxy out of 12 is detected in this co survey ; the remaining detections are of galaxies hosting f - r i and compact radio jets ."}
{"article_id":"astro-ph0504604","section_id":"c","document":"the present co survey has increased the number of radio galaxies observed in paper 1 by a factor of four . three new co detections have been made , yielding a 25% detection efficiency for the sample with the 12 m telescope . the co detections translate into molecular gas masses of @xmath96 m@xmath4 , with 3@xmath11 upper limits for nondetections in the range of @xmath97 m@xmath4 for a @xmath98 galaxy to @xmath99 m@xmath4 for a @xmath100 galaxy . thus , while only a quarter of the sample was detected , the upper limits of the more distant members of the sample do not rule out molecular gas mass as high as that of the milky way ( @xmath12 m@xmath4 ) . there are two notable features in the co spectra shown in figure 1 . the first is the broad linewidth  the average @xmath38 of the present sample of radio galaxies is @xmath101 km s@xmath1 , which exceeds the average value for both pg qsos ( 260@xmath102 km s@xmath1 : evans et al . 2005b ) and ultraluminous infrared galaxies ( 300@xmath103 km s@xmath1 : solomon et al . 1997 ) detected in co to date . this result likely indicates that the host galaxies of molecular gas - rich radio galaxies are extremely massive . the second notable feature is the double - peaked co emission line profiles in many of the spectra . interferometric co observations of two of these galaxies are in the literature and show this feature to be present for ( at least ) two different reasons . in the case of 3c 293 , the `` double - peak '' appearance is caused by a co absorption feature at the systemic velocity of the galaxy ( evans et al . 1999a ) . in the case of 3c 31 , the molecular gas is distributed in a ring ( okuda et al . 2005 ) . figure 4 shows optical images of 7 of the nine radio galaxies detected in co ; two of the nine radio galaxies ( b2 1318 + 34 and pks 1345 + 12 ) are well - studied systems that have been imaged by several groups ( e.g. sanders et al . 1988b ; bushouse & stanford 1992 ; surace et al . 1998 ; evans et al . 1999b ; scoville et al . 2000 ; kim , veilleux , & sanders 2003 ) , and thus have not been reobserved by us . most of these molecular gas - rich galaxies have nearby companions ( 3c 31 ; pks 1345 + 12 ) and/or show clear evidence of being involved in a recent merger ( 3c 84 ; 3c 120 ; pks 0502 - 10 ; 3c 293 ; pks 1345 + 12 ; b2 1318 + 34 ) . the one exception is b2 0722 + 30 , an edge - on spiral galaxy . while the images in figure 4 support the possibility that interaction and merger events may be a primary trigger for radio - loud agn activity , it is notable that many low - redshift radio galaxies are elliptical galaxies ( e.g. , sandage 1966 ; martel et al . thus , unless the elliptical galaxies are advanced mergers , other mechanisms must play an important role in igniting the agn activity observed in these galaxies . given the results of the present survey and recent co surveys of low - redshift pg qsos ( evans et al . 2001 ; scoville 2003 ) , there is sufficient data to begin a comparison of the molecular gas properties and the global energy output ( measured at infrared , radio , and x - ray wavelengths ) of classical uv and radio - selected agn with infrared - selected galaxies and elliptical galaxies . before exploring such comparisons , it is worth first considering two issues which have direct relevance to the interpretation of the data . the first issue is the infrared bias in the sample . while the sample was selected based on the 60@xmath14 m and 100@xmath14 m flux densities , it is important to realize that _ ( a ) _ the flux density limits are extremely low , and thus the infrared luminosity range of the sample spans several decades ( i.e. , @xmath104 l@xmath4 ) , and that _ ( b ) _ 55% , 33% , and 24% of @xmath105 3c , b2 and pks galaxies , respectively , were detected at 60@xmath14 m by iras . the fraction for pg qsos is even higher , with 69% of pg qsos out to @xmath106 ( the redshift limit of the qso co survey ) having 60@xmath14 m detections . thus , infrared excesses in agn host galaxies from radio - selected ( and uv - selected ) surveys are quite common . the second issue of relevance to the interpretation of the data is the nature of the radio emission from the galaxies in the sample ; i.e. , whether the radio emission from all of the galaxies in the sample is due to agn jet emission , or whether some of the galaxies are actually nearby starburst galaxies luminous enough in the radio to have been detected by the 3c , b2 or pks surveys . to address this issue , iras and 1.4 ghz data have been compiled for the radio galaxies , along with complementary data sets for infrared galaxies with both warm and cool 25-to-60@xmath14 m colors ( note that classical agn typically have warm colors , @xmath107 ) , pg qsos , and elliptical galaxies . figure 5 shows the result of the compilation ; plotted is the 1.4 ghz - to - infrared luminosity ratio , @xmath108 , versus the infrared luminosity , @xmath109 . the `` radio - infrared '' correlation ( see condon 1992 ) is clearly visible in this figure ; the radio - to - infrared ratio for infrared - selected galaxies is relatively constant with increasing infrared luminosity . this has led to speculation that the same population of massive stars responsible for heating the dust is also responsible for the radio emission ( through , for example , the production of supernovae ) . lonsdale , smith , & lonsdale ( 1995 ) showed that qsos follow the same bolometric luminosity  radio correlation as infrared galaxies . similarly , the qsos follow the infrared  radio correlation in figure 5 , indicating , perhaps , that a significant fraction of their radio and infrared emission is associated with massive stars , or that agn - related processes in radio - quiet sources yield the proper @xmath110 ratio to place qsos on the relation . in contrast , the data points for all but one of the radio galaxies are above this correlation ; their excess radio emission is associated with agn jets . only the galaxy b2 1318 + 34 ( aka ic 883 ) , which is classified optically as a liner galaxy , has a @xmath111 ratio consistent with the infrared - radio correlation . the liner classification is commonly an indication of ionization of an agn with a shallow power law , however , the spatial coincidence between the radio ( condon et al . 1991 ) and co ( downes & solomon 1998 ) emission in the disk of ic 883 is evidence in favor of the radio emission being associated with a starburst population . given this , b2 1318 + 34 will be denoted by a symbol different from the other radio galaxies in figures 6 and 8 . figure 6 shows two common plots of infrared and co luminosity for extragalactic sources . the first plot is the co luminosity versus the infrared luminosity of the radio galaxies and pg qsos , plotted with infrared galaxies and elliptical galaxies with co detections . in addition , arrows have been plotted to represent 3@xmath11 @xmath39 upper limits for the radio galaxies with co nondetections in the present survey . there are two noteworthy features in figure 6a . first , the pg qso population appear to have low co luminosities for their infrared luminosity relative to infrared galaxies ( see also evans et al . second , by contrast , the radio galaxies are well distributed throughout the area of the plot occupied by infrared and elliptical galaxies , with the three newly detected radio galaxies ( 3c 31 , pks 0502 - 10 , and 3c 293 ) having high co luminosities for their infrared luminosity . these features are better represented in figure 6b , which is a plot of the @xmath112 versus the infrared luminosity . the ratio @xmath113 is commonly referred to as the star formation efficiency , i.e. , it is the measure of energy from massive stars heating the dust normalized by the amount of molecular gas available to form new stars . thus , for highly efficient starbursts ( i.e. , high @xmath113 ) , a large number of massive stars are produced from the available gas . the qsos have high @xmath113 , indicating that either they are producing massive stars with extremely high efficiency , or that there is significant heating of the dust by the agn ( evans et al . most of the radio galaxies have @xmath113 similar to those of giant molecular clouds ( gmcs : sanders & mirabel 1996 ) in the galaxy . exceptions to this include pks 1345 + 12 , which has a @xmath114 similar to the pg qsos , and the three newly detected radio galaxies , which have @xmath115 ) similar to the global value for local spiral galaxies ( see also evans et al . 1999a ) . it thus appears that while some radio galaxies have significant amounts of molecular gas , the rate of massive star formation is extremely low . indeed , if the assumption is made that the infrared luminosity in 3c 31 , pks 0502 - 10 , and 3c 293 is due entirely to star formation , then the star formation rates are roughly a few solar masses per year . note also that the dust temperatures of 3c 31 , pks 0502 - 10 , and 3c 293 are lower ( 3045 k ) than that of the previously detected radio galaxies ( 5590 k ) , also consistent with the idea that current massive star formation rates in these three radio galaxies is low . given the amount of molecular gas in the radio galaxies detected in co to date , and the diversity in the apparent levels of active star formation ( as traced by @xmath109 and @xmath113 ) , it is worth examining their hard ( 210 kev ) x - ray properties to determine _ ( a ) _ whether these radio galaxies have x - ray emission indicative of agn , and _ ( b ) _ whether any of the radio galaxies have sufficient column densities of molecular gas to be significantly x - ray absorbed . the @xmath116-to-@xmath117 ratio provides a straight - forward way of addressing these issues  the ratio is constant in starburst galaxies , indicating that the starburst responsible for heating the dust in hii region galaxies produces a constant fraction of massive x - ray binary pairs ( grimm et al . 2003 ; ranalli et al . ` excesses ' in @xmath116 / @xmath117 arise from the contribution of agn to the x - ray emission , making the ratio a powerful agn vs. starburst diagnostic . however , in objects that contain large columns of gas and dust , the x - ray emission can be suppressed , lowering the observed @xmath118 .    for the purposes of the present discussion , the available radio galaxy data of our sample have been compiled from the literature and added to the @xmath116 vs. @xmath117 plot of trentham et al . ( 2005 ) , which is a compilation of data of local liners , seyferts , hii - region galaxies , infrared galaxies , and pg qsos . the result is plotted in figure 7 ; figure 7a shows the data plotted in the manner typically done by other authors , i.e. , @xmath116 vs. @xmath117 , and figure 7b shows the data plotted in terms of the @xmath119 versus @xmath117 . a least - squares fit has been applied to the hii region galaxy data . several of the infrared galaxies , which are rich in molecular gas , are below the fit and thus compton thick . in terms of the radio galaxies data , the figures show that , _ ( a ) _ the agn dominates the x - ray emission from the radio galaxies in a manner consistent with pg qsos and lower luminosity seyferts and liners , and _ ( b ) _ the x - ray emission from the agn does not seem to be significantly suppressed , and thus these radio galaxies do not reside in compton - thick environments . indeed , several of the radio galaxies have measured column densities in the literature  the derived column densities from these x - ray observations are @xmath6 @xmath120 @xmath94 ( leighly et al . 1997 ; sambruna et al . 1999 ; and odea et al . 2000 ) . another issue relevant to the present sample of galaxies is whether the molecular gas properties are correlated with the radio output of the radio galaxies . i.e. , if molecular gas fuels agn activity , there may be a correlation between @xmath39 and the energy emitted by these agn at radio wavelengths . figure 8a is a plot of @xmath39 versus @xmath121 of the sample of radio galaxies ; comparative samples of infrared galaxies , pg qsos , and ellipticals are also plotted . the infrared galaxy and pg qso data are correlated , with higher @xmath39 corresponding to higher @xmath108 . such a correlation can be understood , for example , if a significant fraction of the 1.4 ghz emission is generated via star formation  the higher the molecular gas content , the higher the number of supernovae generating radio emission . the radio galaxies occupy a different location on this plot , having high @xmath108 for their @xmath39 relative to infrared galaxies and qsos . it is also clear from the radio galaxy data that no obvious correlation exists between @xmath108 and @xmath39 . this result may simply illustrate the fact that , if a correlation between the agn radio output and molecular gas mass exists , it may only exist for the component of the molecular gas in the nuclear region ( near the agn ) , and not the global molecular gas mass measured by these observations . figure 8b is a plot of @xmath113 versus @xmath121 . in terms of the distribution of infrared galaxies and qso data , the plot is reminiscent of figure 6b  @xmath113 increases with increasing @xmath108 , and the qsos and warm infrared galaxies reside primarily at high @xmath113 and @xmath121 relative to cool infrared galaxies . the radio galaxies occupy a different location on the plot , having high @xmath108 for their @xmath113 , but no obvious correlation among the radio galaxy data exists . thus , regardless of whether stars or agn in the host galaxy of these radio galaxies are heating the dust , the fueling efficiency factor @xmath113 is not correlated with the total radio output . all but one of the radio galaxies detected as part of this survey have molecular gas masses in excess of @xmath122 m@xmath4 , indicating that there are large fuel reservoirs for star formation and possibly agn activity . the presence of molecular gas , in itself , is not evidence of active star formation . high mass star formation in the milky way occurs in the cores of giant molecular clouds ( gmcs ) where the molecular gas densities exceed @xmath123 @xmath124 . preliminary observations have been done of pks 0502 - 10 and b2 0722 + 30 to provide additional information about the state of the molecular gas . the first observations are of the co(@xmath30 ) emission line ; the @xmath125 ratios of pks 0502 - 10 and b2 0722 + 30 are 0.6 and 0.7 , respectively . such low values of @xmath126 are suggestive of subthermally excited co , i.e. , low molecular gas temperatures and densities . the second set of preliminary observations designed to probe the state of the gas in these radio galaxies are of the high density tracer hcn . hcn is seen in abundance when the molecular gas densities are on the order of @xmath127 @xmath124 , and thus is found in the cores of gmcs where massive star formation is commencing . gao & solomon ( 2004 ) have presented an hcn survey of infrared galaxies , and have calculated an average @xmath128 ratio of @xmath129 . the hcn(@xmath16 ) observations of two radio galaxies yielded only upper limits , translating into @xmath128 lower limits of @xmath6 550 and 3700 for pks 0502 - 10 and b2 0722 + 30 , respectively . thus , while the @xmath128 of pks 0502 - 10 does not provide a useful constraint , the high @xmath128 of b2 0722 - 30 is suggestive of either highly efficient massive star formation or significant heating of dust by the agn . one of the goals of this survey was to obtain detections of co emission from radio galaxies of all morphological types . this survey yielded a co detection in only one fanaroff - riley ii ( edge - brightened radio morphology : fanaroff & riley 1974 ) radio galaxy , 3c 293 . however , in terms of its radio properties , 3c 293 is not a representative f - r ii . the galaxy has a low radio power ( @xmath130 w m@xmath131 hz@xmath1 ) relative to the bulk of f - r ii radio galaxies . in addition , 3c 293 has a complex steep spectrum core which shows evidence of a previous radio outburst ( akujor et al . 1996 ) .    the low co detection rate of f - r ii galaxies ( @xmath6 8% ) relative to f - r i and compact radio source galaxies ( @xmath6 35% ) may be a simple consequence of larger distances of f - r ii galaxies , on average , relative to lower radio power radio galaxies in the sample . this explanation is unlikely ; figure 6a shows the @xmath39 of the detected radio galaxies and the @xmath39 upper limits of the undetected galaxies . the upper limits of all of the non - detected f - r ii galaxies are below @xmath132 k km s@xmath1 pc@xmath41 , and three out of seven ( excluding b2 1318 + 34 ) of the co - detected f - r i and compact radio galaxies are above this line . thus , though the f - r ii galaxies comprise 36% of the sample , there are no additional f - r ii galaxies in the sample with molecular gas masses comparable to either 3c 293 , or the most gas - rich f - r i and radio compact galaxies ( pks 0502 - 10 , txs 1506 + 345 , and pks 1345 + 12 ) in the sample . this result , of course , relies on the assumption that f - r ii radio galaxies have co emission line widths of @xmath133 km s@xmath1 ; if the line widths are sufficiently broad , then the limited velocity bandwidth ( i.e. , @xmath6 1400 km s@xmath1 at 3 mm ) available with single - dish telescopes such as the 12 m telescope would make the co detections difficult . the present co survey has focussed on a sample of iras - detected radio galaxies using a fairly moderate size single - dish millimeter telescope . the results presented here can be improved upon in the following ways : _ ( i ) _ co surveys of larger samples of iso and spitzer space telescope - detected radio galaxies using larger single - dish millimeter - wave telescopes or interferometers . _ ( ii ) _ volume - limited co surveys of radio galaxies ( and qsos ) similar to those initiated by lim et al . ( 1999 ) and scoville et al . such surveys will provide a more complete view of the molecular gas properties of radio ( and uv - selected ) agn . _ ( iii ) _ interferometric observations of the co - detected radio galaxies to measure the extent , surface density , and kinematics of the molecular gas relative to the stellar population and the ionized / neutral gas ( inoue et al . 1996 ; evans et al . 1999a , b ; okuda et al . 2005 ; evans et al . finally , continued investigations of star formation in radio galaxies using diagnostics at multiple wavelengths will provide a more complete picture of the putative starburst - agn connection . recent optical spectroscopy of three of the galaxies in the sample ( 3c 293 , 3c 305 , and pks 1345 + 12 : tadhunter et al . 2005 ) have provided encouraging results .","summary":"this paper reports the latest results from a millimeter - wave ( co ) spectroscopic survey of iras - detected radio galaxies with w hz in the redshift range . ( 1989 ) have been reobserved . three new co detections have been made , raising the total number of co detections to nine and setting the survey detection rate at 25% . the co luminosities translate into molecular gas masses of m , however , the 3 co upper limits for nondetections do not rule out a molecular gas mass as high as that of the milky way ( m ) . finally , there is no obvious correlation between radio power and molecular gas mass . however , it is notable that only one f - r ii galaxy out of 12 is detected in this co survey ; the remaining detections are of galaxies hosting f - r i and compact radio jets .","abstract":"this paper reports the latest results from a millimeter - wave ( co ) spectroscopic survey of iras - detected radio galaxies with w hz in the redshift range . the iras flux - limited sample contains 33 radio galaxies with different radio morphologies and a broad range of infrared luminosities ( l ) , allowing for an investigation of _ ( a ) _ whether low- radio - selected agn reside in molecular gas - rich host galaxes , and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn . all of the radio galaxies in mazzarella et al . ( 1993 ) and mirabel et al . ( 1989 ) have been reobserved . three new co detections have been made , raising the total number of co detections to nine and setting the survey detection rate at 25% . many of the co lines have double - peaked profiles , and the co line widths are broad ( average km s ) , exceeding the average co widths of both ultraluminous infrared galaxies ( km s ) and palomar - green qsos ( km s ) , and thus being indicative of massive host galaxies . the co luminosities translate into molecular gas masses of m , however , the 3 co upper limits for nondetections do not rule out a molecular gas mass as high as that of the milky way ( m ) . optical images of eight out of nine molecular gas - rich radio galaxies show evidence of close companions and/or tidal features . finally , there is no obvious correlation between radio power and molecular gas mass . however , it is notable that only one f - r ii galaxy out of 12 is detected in this co survey ; the remaining detections are of galaxies hosting f - r i and compact radio jets ."}
{"article_id":"astro-ph0504604","section_id":"i","document":"the survey presented here is a follow - up to the mazzarella et al . ( 1993 ) study of iras - detected radio galaxies , which yielded new co detections in three radio galaxies . the survey has increased the number of low - redshift radio galaxies observed in the prior survey by a factor of four . the following conclusions have been reached :    \\(1 ) three additional radio galaxies ( 3c 31 , pks 0502 - 10 , 3c 293 ) have been detected in co(@xmath16 ) , yielding a total of 9 detections out of 33 radio galaxies . the co detections translate into molecular gas masses of @xmath96 m@xmath4 , with 3@xmath11 upper limits for nondetections in the range of @xmath97 m@xmath4 for a @xmath134 galaxy to @xmath99 m@xmath4 for a @xmath100 galaxy ( @xmath66 = 1.5 @xmath69 [ k km s@xmath1 pc@xmath68^{-1}$ ] . thus , the upper limits of the more distant members of the sample do not rule out molecular gas mass as high as that of the milky way ( @xmath12 m@xmath4 ) . \\(3 ) the co line widths are extremely broad . the average velocity dispersion of the co - detected radio galaxies is @xmath135 km s@xmath1 , which exceeds the average line width of both ultraluminous infrared galaxies (= @xmath8 km s@xmath1 ) and pg qsos (= @xmath9 km s@xmath1 ) . this is an indication that the co - luminous radio galaxies are massive . \\(4 ) with the exception of the edge - on spiral galaxy b2 0722 + 30 , optical images show the molecular gas - rich radio galaxies to have close companions and/or tidal features consistent with those of infrared - luminous interacting and merging galaxy systems . \\(5 ) most of the radio galaxies have @xmath113 similar to gmcs . exceptions to this include _ ( i ) _ pks 1345 + 12 , which has a @xmath136 ) comparable to the pg qsos , likely an indication of highly efficient massive star production or of significant dust heating by the agn , and ( _ ii ) _ 3c 31 , pks 0502 - 10 , and 3c 293 , which have low @xmath113 ( @xmath137 30 ) consistent with the global @xmath113 of spiral galaxies . \\(6 ) all of the radio galaxies have measured values of @xmath138 significantly higher than the average for hii - region like galaxies . thus , the agn is the major contributor to the x - ray emission , and the agn do not reside in compton - thick environments . \\(8 ) only one f - r ii radio galaxy ( 3c 293 ) was detected , yielding an 8% co detection rate for f - r ii galaxies . by comparison , @xmath139% of the f - r i and compact radio source galaxies were detected . the @xmath39 upper limits of the undetected f - r ii galaxies are sufficiently small to support the conclusion that either low - redshift f - r ii galaxies are gas - poor compared with f - r i and radio compact galaxies , or that the co line widths of the undetected f - r ii galaxies are broad enough to make their detection difficult with a single - dish telescope . we thank the telescope operators and staff of the nrao 12 m and iram 30 telescopes for their support both during and after the observations were obtained , and the anonymous referee for many useful comments and suggestions . ase also thanks n. trentham for useful discussions and assistance . ase was supported by nsf grant ast 02 - 06262 and the 2002 nasa / asee faculty fellowship . dtf , jmm , and jas were supported by the jet propulsion laboratory , california institute of technology , under contract with nasa . d.b.s . gratefully acknowledges the hospitality of the max - plank institut fur extraterrestrische physik and the alexander von humboldt stiftung for a humboldt senior award , and partial financial support from nasa grant go-8190.01 - 97a . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . ( a ) nrao 12 m and iram 30 m co(1@xmath650 ) spectrum of 31 of the 33 radio galaxies in the survey . the intensity scale is in units of main beam brightness temperature . a linear baseline has been subtracted from each spectrum ; the baseline subtraction is performed outside of the velocity range of emission lines when they are present . with the exception of pks 0502 - 10 , the zero velocity corresponds to the redshift of the radio galaxy listed in table 1 . the zero velocity redshift of pks 0502 - 10 is 0.0396 . ( b ) iram 30 m co(1@xmath140 ) spectrum of pks 1345 + 12 . the spectrum confirm the general features of the 12 m spectrum of figure 1a , but with significantly higher signal - to - noise . jcmt 15 m and iram 30 m telescope co(@xmath30 ) spectra of pks 0502 - 10 , b2 0722 + 30 , and cygnus a. the intensity scale is in units of main beam brightness temperature ( iram ) and antenna temperature corrected for aperture losses ( jcmt ) . a linear baseline has been subtracted from each spectrum ; the baseline subtraction is performed outside of the velocity range of emission lines when they are present . zero velocity corresponds to the redshift of the radio galaxy listed in table 3 . iram 30 m hcn(@xmath16 ) spectra of pks 0502 - 10 and b2 0722 + 30 . the intensity scale is in units of main beam brightness temperature . a linear baseline has been subtracted from each spectrum ; the baseline subtraction is performed outside of the velocity range where the hcn emission line is expected to be . zero velocity corresponds to the redshift of the radio galaxy listed in table 3 . false - color _ u@xmath32 _ , _ b _ , and _ i_-band images of seven of the radio galaxies detected in co(@xmath16 ) . _ b _ , and _ i_-band data are displayed as blue , green , and red , respectively . north is up , and east is to the left . the ratio of 1.4 ghz to infrared luminosity versus the infrared luminosity of infrared luminous radio galaxies , a sample of infrared galaxies , pg qsos and elliptical galaxies detected in co. references for the infrared data are as follows : infrared galaxies , mazzarella et al . ( 1993 ) ; pg qsos , sanders et al . ( 1989 ) and haas et al . ( 2003 ) ; elliptical galaxies ( moshir et al . 1990 ) . references for the 1.4 ghz data are as follows : infrared galaxies , condon et al . ( 1990 , 1991 , 1992 ) ; elliptical galaxies ( white & becker 1992 ; becker et al . 1995 ; condon et al . 1998 ) ; radio galaxies ( white & becker 1992 ; becker et al . 1995 ) ; pg qsos ( white & becker 1992 ; barvainis , lonsdale , & antonucci 1996 ; condon et al . 1998 ) . ( a ) co vs. infrared luminosity plot of infrared luminous radio galaxies , a sample of infrared galaxies , pg qsos and elliptical galaxies detected in co. references for co data are as follows : infrared galaxies , mazzarella et al . ( 1993 ) ; pg qsos , sanders et al . ( 1988c ) , barvainis et al . ( 1989 ) , evans et al . ( 2001 ) , and scoville et al . ( 2003 ) ; elliptical galaxies : wiklind & combes ( 1997 ) . ( b ) the ratio of infrared to co luminosity vs. infrared luminosity for the same sample of galaxies as in 6(a ) . in both figures , the galaxy b2 1318 + 34 is denoted by an unfilled triangle . ( a ) hard ( 2 - 10 kev ) x - ray luminosity vs. far - infrared luminosity plot of the infrared luminous radio galaxies and a comparison sample of infrared galaxies , pg qsos , and less luminous galaxies classified as hii region - like galaxies , seyferts , and liners . the far - infrared luminosities have been calculated using data in ned . the radio galaxies in the figure are ngc 315 , 3c 84 , 3c 111 , 3c 120 , pks 0634 - 20 , hydra a , m87 , pks 1345 + 12 , 3c 293 , 3c 321 , ngc 6251 , 3c 390.3 , and 3c 405 . references for the x - ray data are as follows : hii , seyferts , and liners , terashima et al . ( 2002 ) and grimm et al . ( 2003 ) ; infrared luminous galaxies , iwasawa & comastri ( 1998 ) , boller ( 2002 ) , dalla ceca ( 2002 ) , franceschini et al . ( 2003 ) , and sanders et al . ( 2005 ) ; radio galaxies , churazov et al . ( 2003 ) ; di matteo et al . ( 2003 ) ; leighly et al . ( 1997 ) ; mcnamara et al . ( 2000 ) ; odea et al . ( 2000 ) ; and sambruna et al . ( 1999 ) . the x - ray luminosity of 3c 293 ( @xmath141 erg s@xmath1 ) was calculated by us from archival asca data . ( b ) ratio of the x - ray to far - infrared luminosity versus the far - infrared luminosity for the same sample of galaxies as in figure 7(a ) . in both ( a ) and ( b ) , radio galaxies and pg qsos with co detections are encircled . adapted from trentham et al . ( 2005 ) . ( a ) the co luminosity vs. the radio power of the infrared luminous radio galaxies and a comparison sample of infrared galaxies , pg qsos , and elliptical galaxies . ( b ) @xmath113 vs. the radio power for the same sample of galaxies plotted in 8a . in both figures , the galaxy b2 1318 + 34 is denoted by an unfilled triangle . lrcccrrllc ngc 315 & 00h57m48.85s & + 30d21m08.63s & 0.0165 & i & 368 & 460 & 7.2@xmath142 & 2.3@xmath142 & 1.6@xmath143 3c 31 & 01h07m24.98s & + 32d24m44.77s & 0.0167 & i & 435 & 1675 & 7.4@xmath142 & 4.7@xmath142 & 2.5@xmath143 4c 31.04 & 01h19m35.00s & + 32d10m50.03s & 0.0590 & c & 150 & 524 & 3.7@xmath144 & 1.9@xmath144 & 1.7@xmath145 ngc 741 & 01h56m21.05s & + 05d37m44.17s & 0.0185 & c & 214 & 777 & 7.0@xmath142 & 2.7@xmath142 & 6.0@xmath146 3c 84 & 03h19m48.09s & + 41d30m42.47s & 0.0176 & i & 7427 & 8267 & 1.6@xmath147 & 5.1@xmath144 & 7.3@xmath143 3c 88 & 03h27m54.17s & + 02d33m41.85s & 0.0302 & ii & 180 & 816 & 1.7@xmath144 & 7.0@xmath142 & 8.5@xmath143 3c 111 & 04h18m21.07s & + 38d01m32.59s & 0.0485 & ii & 321 & @xmath1372250 & 9.0@xmath144 & 2.8@xmath144 & 6.5@xmath145 3c 120 & 04h33m11.09s & + 05d21m16.03s & 0.0331 & i & 1383 & 1937 & 1.2@xmath147 & 3.6@xmath144 & 9.0@xmath143 pks 0502 - 10 & 05h04m52.99s & -10d14m52.18s & 0.0410 & ? & 688 & 1370 & 6.1@xmath144 & 3.0@xmath144 & 4.6@xmath143 pks 0634 - 20 & 06h36m32.24s & -20d34m52.92s & 0.0544 & ii & 484 & 1150 & 9.5@xmath144 & 4.3@xmath144 & 3.3@xmath145 b2 0648 + 27 & 06h42m02.82s & + 27d28m21.69s & 0.0414 & c & 2633 & 1529 & 2.2@xmath147 & 8.7@xmath144 & 4.9@xmath146 b2 0722 + 30 & 07h25m37.35s & + 29d57m14.71s & 0.0188 & i & 3108 & 4999 & 5.2@xmath144 & 2.8@xmath144 & 8.2@xmath148 4c 29.30 & 08h40m02.44s & + 29d49m02.87s & 0.0650 & i & 472 & 595 & 1.1@xmath147 & 4.7@xmath144 & 3.3@xmath146 hydra a & 09h18m05.69s & -12d05m45.45s & 0.0538 & i & 155 & 416 & 2.8@xmath144 & 1.4@xmath144 & 2.5@xmath149 3c272.1 & 12h25m03.78s & + 12d53m13.1s & 0.0035 & i & 556 & 1024 & 5.6@xmath150 & 1.8@xmath150 & 1.0@xmath146 m 87 & 12h30m49.35s & + 12d23m28.06s & 0.0047 & i & 546 & 559 & 1.1@xmath142 & 2.6@xmath150 & 7.2@xmath143 b2 1318 + 34 & 13h20m35.20s & + 34d08m13.56s & 0.0233 & i & 16070 & 20682 & 3.4@xmath147 & 2.0@xmath147 & 8.9@xmath148 3c 285 & 13h21m17.78s & + 42d35m14.23s & 0.0789 & ii & 253 & 637 & 1.8@xmath147 & 5.0@xmath144 & 2.6@xmath145 pks 1345 + 12 & 13h47m33.38s & + 12d17m24.18s & 0.1224 & c & 2098 & 1738 & 1.5@xmath151 & 6.7@xmath147 & 1.5@xmath149 3c 293 & 13h52m17.86s & + 31d26m46.67s & 0.0450 & ii & 233 & 621 & 2.9@xmath144 & 1.5@xmath144 & 1.7@xmath145 oq 208 & 14h07m00.39s & + 28d27m14.73s & 0.0768 & c & 753 & 1029 & 4.1@xmath147 & 1.1@xmath147 & 8.3@xmath143 3c 305 & 14h49m21.46s & + 63d16m16.14s & 0.0410 & i & 298 & 450 & 2.4@xmath144 & 1.2@xmath144 & 9.4@xmath143 txs 1506 + 345 & 15h08m05.64s & + 34d23m22.75s & 0.0449 & i & 2647 & 3956 & 2.3@xmath147 & 1.3@xmath147 & 4.5@xmath146 pks b1518 + 045 & 15h21m22.61s & + 04d20m29.21s & 0.0513 & ? & @xmath137120 & 968 & 4.6@xmath144 & 1.8@xmath144 & 2.1@xmath145 3c 321 & 15h31m43.45s & + 24d04m18.70s & 0.0960 & ii & 1067 & 961 & 5.0@xmath147 & 2.1@xmath147 & 6.2@xmath145 3c 327 & 16h02m27.39s & + 01d57m55.70s & 0.1048 & ii & 670 & 371 & 4.1@xmath147 & 1.4@xmath147 & 1.9@xmath149 ngc 6251 & 16h32m31.97s & + 82d32m16.46s & 0.0249 & i & 188 & 600 & 5.7@xmath142 & 2.7@xmath142 & 2.6@xmath143 b2 1707 + 34 & 17h09m38.37s & + 34d25m53.76s & 0.0808 & ii & 464 & 841 & 2.0@xmath147 & 8.2@xmath144 & 8.4@xmath143 3c 390.3 & 18h42m08.92s & + 79d46m17.27s & 0.0561 & ii & 250 & 340 & 1.3@xmath147 & 1.9@xmath144 & 7.2@xmath145 3c 402 & 19h41m46.00s & + 50d35m44.86s & 0.0254 & ii & 257 & 1052 & 1.1@xmath144 & 6.6@xmath142 & 3.1@xmath143 3c 403 & 19h52m15.36s & + 02d30m28.14s & 0.0590 & ii & 441 & @xmath137500 & 1.5@xmath147 & 3.0@xmath144 & 3.9@xmath145 3c 405 & 19h59m28.51s & + 40d44m01.70s & 0.0556 & ii & 2847 & @xmath1371800 & 4.0@xmath147 & 1.6@xmath147 & 9.4@xmath152 3c 433 & 21h23m44.53s & + 25d04m09.99s & 0.1016 & i & 299 & @xmath1371200 & 2.9@xmath147 & 8.8@xmath144 & 2.3@xmath143    lrlcrc ngc 315 & 12 m & co(1@xmath140 ) & oct-97 & 3.0 & 420 3c 31 & 12 m & co(1@xmath140 ) & jan-96 & 17.4 & 272 & 12 m & co(1@xmath140 ) & jun-97 & 18.4 & 333 & 12 m & co(1@xmath140 ) & oct-97 & 4.6 & 273 4c 31.04 & 12 m & co(1@xmath140 ) & jan-96 & 29.6 & 199 ngc 741 & 12 m & co(1@xmath140 ) & jun-97 & 12.4 & 371 3c 84 & 12 m & co(1@xmath140 ) & jun-97 & 4.8 & 318 3c 88 & 12 m & co(1@xmath140 ) & oct-97 & 7.2 & 248 3c 111 & 12 m & co(1@xmath140 ) & sep-95 & 10.2 & 260 3c 120 & 12 m & co(1@xmath140 ) & oct-97 & 19.6 & 259 pks 0502 - 10 & 12 m & co(1@xmath140 ) & sep-95 & 14.8 & 369 & 12 m & co(1@xmath140 ) & jan-96 & 9.4 & 256 & 15 m & co(2@xmath153 ) & sep-95 & 4.0 & 411 & 30 m & hcn(1@xmath140 ) & dec-03 & 1.8 & 120 pks 0634 - 20 & 12 m & co(1@xmath140 ) & jun-97 & 5.2 & 372 & 12 m & co(1@xmath140 ) & oct-97 & 12.6 & 256 b2 0648 + 27 & 12 m & co(1@xmath140 ) & sep-95 & 24.6 & 319 & 12 m & co(1@xmath140 ) & jan-96 & 2.6 & 237 b2 0722 + 30 & 12 m & co(1@xmath140 ) & oct-97 & 6.6 & 299 & 15 m & co(2@xmath153 ) & sep-95 & 1.8 & 469 & 30 m & hcn(1@xmath140 ) & dec-03 & 1.8 & 83 4c 29.30 & 12 m & co(1@xmath140 ) & jan-96 & 12.2 & 220 & 12 m & co(1@xmath140 ) & jun-97 & 30.8 & 232 & 12 m & co(1@xmath140 ) & oct-97 & 8.2 & 196 hydra a & 12 m & co(1@xmath140 ) & jun-97 & 5.2 & 288 & 12 m & co(1@xmath140 ) & oct-97 & 9.4 & 224 m 87 & 12 m & co(1@xmath140 ) & dec-92 & 21.9 & 368 b2 1318 + 34 & 12 m & co(1@xmath140 ) & oct-97 & 1.8 & 256 3c 285 & 12 m & co(1@xmath140 ) & jan-96 & 49.6 & 210 pks 1345 + 12 & 12 m & co(1@xmath140 ) & jun-97 & 30.1 & 256 & 12 m & co(1@xmath140 ) & jun-00 & 4.3 & 200 3c 293 & 12 m & co(1@xmath140 ) & jan-96 & 17.6 & 240 oq 208 & 12 m & co(1@xmath140 ) & sep-95 & 12.8 & 261 3c 305 & 12 m & co(1@xmath140 ) & oct-97 & 16.0 & 261 txs 1506 + 345 & 12 m & co(1@xmath140 ) & oct-97 & 8.4 & 211 pks b1518 + 045 & 12 m & co(1@xmath140 ) & jun-97 & 9.4 & 269 3c 321 & 12 m & co(1@xmath140 ) & sep-95 & 23.6 & 276 & 12 m & co(1@xmath140 ) & jun-97 & 16.4 & 249 3c 327 & 12 m & co(1@xmath140 ) & oct-97 & 5.6 & 321 & 12 m & co(1@xmath140 ) & jun-00 & 16.2 & 205 b2 1707 + 34 & 12 m & co(1@xmath140 ) & jun-97 & 13.0 & 252 & 12 m & co(1@xmath140 ) & oct-97 & 12.0 & 208 3c 390.3 & 12 m & co(1@xmath140 ) & jun-97 & 16.4 & 356 & 12 m & co(1@xmath140 ) & oct-97 & 5.2 & 464 3c 402 & 12 m & co(1@xmath140 ) & oct-97 & 6.0 & 248 3c 403 & 12 m & co(1@xmath140 ) & jun-97 & 11.4 & 254 3c 405 & 30 m & co(1@xmath140 ) & nov-95 & 5.9 & 186 & 30 m & co(2@xmath153 ) & nov-95 & 3.3 & 321 3c 433 & 12 m & co(1@xmath140 ) & jan-96 & 11.6 & 200 & 12 m & co(1@xmath140 ) & oct-97 & 13.0 & 179                                                                              lllrrlcc 3c 31 & 33 & @xmath155 & 160 & 75 & @xmath156 & 0.10 & @xmath157 3c 84 & 64 & @xmath158 & 1084 & 154 & @xmath159 & 0.83 & @xmath157 3c 120 & 55 & @xmath160 & 884 & 112 & @xmath161 & 0.23 & @xmath162 pks 0502 - 10 & 46 & @xmath163 & 1075 & 185 & @xmath164 & 0.32 & @xmath165 b2 0722 + 30 & 50 & @xmath166 & 525 & 105 & @xmath167 & 0.24 & @xmath168 b2 1318 + 34 & 58 & @xmath169 & 572 & 222 & @xmath170 & 0.68 & @xmath171 pks 1345 + 12 & 91 & @xmath172 & 802 & 194 & @xmath173 & 0.94 & @xmath174 3c 293 & 40 & @xmath175 & 1807 & 222 & @xmath176 & 0.26 & @xmath177 txs 1506 + 345 & 54 & @xmath178 & 860 & 227 & @xmath179 & 0.46 & @xmath180 average & & & @xmath79 & & & @xmath90 &","summary":"many of the co lines have double - peaked profiles , and the co line widths are broad ( average km s ) , exceeding the average co widths of both ultraluminous infrared galaxies ( km s ) and palomar - green qsos ( km s ) , and thus being indicative of massive host galaxies . optical images of eight out of nine molecular gas - rich radio galaxies show evidence of close companions and/or tidal features .","abstract":"this paper reports the latest results from a millimeter - wave ( co ) spectroscopic survey of iras - detected radio galaxies with w hz in the redshift range . the iras flux - limited sample contains 33 radio galaxies with different radio morphologies and a broad range of infrared luminosities ( l ) , allowing for an investigation of _ ( a ) _ whether low- radio - selected agn reside in molecular gas - rich host galaxes , and _ ( b ) _ whether the co properties are correlated with the properties of the host galaxy or the agn . all of the radio galaxies in mazzarella et al . ( 1993 ) and mirabel et al . ( 1989 ) have been reobserved . three new co detections have been made , raising the total number of co detections to nine and setting the survey detection rate at 25% . many of the co lines have double - peaked profiles , and the co line widths are broad ( average km s ) , exceeding the average co widths of both ultraluminous infrared galaxies ( km s ) and palomar - green qsos ( km s ) , and thus being indicative of massive host galaxies . the co luminosities translate into molecular gas masses of m , however , the 3 co upper limits for nondetections do not rule out a molecular gas mass as high as that of the milky way ( m ) . optical images of eight out of nine molecular gas - rich radio galaxies show evidence of close companions and/or tidal features . finally , there is no obvious correlation between radio power and molecular gas mass . however , it is notable that only one f - r ii galaxy out of 12 is detected in this co survey ; the remaining detections are of galaxies hosting f - r i and compact radio jets ."}
{"article_id":"1505.07977","section_id":"i","document":"last decade was quite fruitful in the field of heavy baryon spectroscopy . at present , all baryons containing heavy charm and bottom quarks , except @xmath8 baryon , as well as several heavy baryons with negative parity , have been observed by a number of collaborations ( for a review see @xcite ) . these progresses stimulated further theoretical studies , and experimental researches on heavy baryons at the existing facilities , especially at lhc . heavy baryons are well recognized to represent a rich  laboratory \" for theoretical investigations . the properties of heavy baryons have been studied in framework of the various methods such as , relativistic quark model @xcite , variational approach @xcite , constituent quark model @xcite , lattice qcd model @xcite , qcd sum rules method @xcite . recent progress on this subject can be found in @xcite . study of the electromagnetic properties of baryons constitutes very important source of information in understanding their internal structure , and can provide valuable insight about the nonperturbative aspects of qcd . one of the most crucial quantities in this respect is the magnetic moments of baryons . magnetic moments of the ground state @xmath9 heavy baryons have widely been studied in literature . furthermore , magnetic moments of the heavy baryons have been investigated in the naive quark model in @xcite , phenomenological quark model @xcite , relativistic three - quark model @xcite , variational approach @xcite , nonrelativistic quark model with screening and effective quark mass @xcite , nonrelativistic hypercentral model@xcite , chiral constituent quark model @xcite , chiral bag model @xcite , chiral perturbation theory @xcite , traditional qcd sum rules @xcite , and light cone qcd sum rules ( lcsr ) @xcite , respectively .    in the present work , we calculate the diagonal and transition magnetic moments of the negative parity , spin-1/2 heavy baryons in framework of the light cone qcd sum rules method . the body of the paper is organized as follows . in section 2 , we construct the light cone qcd sum rules for the diagonal and transition magnetic moments of the negative parity , heavy baryons . section 3 is devoted to the numerical analysis of these sum rules for the magnetic moments ; and contains discussion of the obtained results and conclusion .","summary":"diagonal and transition magnetic moments of the negative parity , spin-1/2 heavy baryons are studied in framework of the light cone qcd sum rules . by constructing the sum rules for different lorentz structures ,","abstract":"diagonal and transition magnetic moments of the negative parity , spin-1/2 heavy baryons are studied in framework of the light cone qcd sum rules . by constructing the sum rules for different lorentz structures , the unwanted contributions coming from negative ( positive ) to positive ( negative ) parity transitions are removed . it is obtained that the magnetic moments of all baryons , except , and , are quite large . it is also found that the transition magnetic moments between neutral negative parity heavy and baryons are very small . magnetic moments of the and transitions are quite large and can be measured in further experiments .    # 1#2#3           # 1#2#3           0^*0 5_5 q 5_5    o _ ^0 _    pacs numbers : 11.55.hx , 13.40.em , 14.20.lq , 14.20.mr"}
{"article_id":"1409.8156","section_id":"i","document":"the _ kepler _ mission ( borucki et al .  2010 ) was designed to determine , for the first time , the frequency of earth - sized planets in the classical habitable zone of sun - like stars . by combining quasi - continuous photometric monitoring of @xmath3 stars in the _ kepler _ search field with the high level of photometric precision obtained by _ kepler _ , it also allows us an unprecedented statistical overview of the size - distribution of exoplanets . it has been shown by borucki et al . ( 2011 ) and batalha et al . ( 2012 ) that the vast majority of planets that _ finds are small planets in the radius range from 1 to 4  r@xmath2 and that the hot jupiters , gas giant planets with radii similar to jupiter and with orbital periods of a few days , are a very small minority of the overall planet population in the kepler field . howard et al .  ( 2012 ) estimate the frequency of hot jupiter candidates in the the _ kepler _ search volume as 0.5@xmath40.1% . interestingly , this is only about half the occurrence rate of this type of planets derived from precise radial velocity ( rv ) surveys of the solar neighborhood . wright et al .  ( 2012 ) estimate a local hot jupiter frequency of 1.2@xmath40.38% based on the lick and keck rv survey results . an interesting aspect of the class of hot jupiter planets is their apparent lack of additional , nearby planetary companions . these jupiters are `` lonely '' in the sense that searches in the _ kepler _ photometry and using transit - timing - variations ( ttvs ) do not find any other nearby planets in these systems ( steffen et al . this is in stark contrast to smaller and lower mass planets which are very often found in multi - planet systems ( e.g. latham et al . 2011 , rowe et al . 2014 ) , sometimes in mean - motion resonances . one hypothesis for the formation of such systems is that the migration of the inner planet is caused by planet - planet scattering ( e.g. rasio & ford  1996 ) rather than by disk - driven tidal migration ( e.g. goldreich & tremaine  1980 ) . the large eccentricity of the inner planet s orbit , pumped up by a close encounter with a massive second giant planet in the system , is subsequently circularized by tidal forces at small separations to the host star and establishes the hot jupiter orbit . the outer planet s orbit remains eccentric since tidal interactions are too weak at these separations . however , the planet - planet scattering process might be quite violent and potentially could lead more often to the loss of the inner planet by falling into the star than by forming a hot jupiter . conversely , the strong planet - planet interactions could also lead to the ejection of the outer planet , leaving behind a single hot jupiter planet . observational footprints of planet - planet interactions include moderate to high eccentricities of the outer planet ( if one exists ) , an inclined orbital plane of the inner planet with respect to the stellar spin axis , and significant non - zero mutual inclinations . interestingly , mcarthur et al .  ( 2010 ) measured a mutual inclination of @xmath5 of the orbits of @xmath1  and c ( @xmath6  d ) and d ( @xmath7  d ) . while the inclination of @xmath1  and  b ( @xmath8  d ) remains unknown , this could indicate a very dynamical past of this system . moreover , hot jupiter planets appeared to rarely have outer giant planets at longer periods found by rvs ( e.g. discussion in bryan et al . this paucity of additional planets in hot jupiter systems was usually interpreted as evidence for a significant dynamical evolution in the past , that cleared out all or most of the other ( detectable ) planets . systems where a hot jupiter is found in a multi - planet system ( e.g. the @xmath1  andromedae system ) are therefore ideal testbeds to search for evidence for dynamical evolution of the system . knutson et al .  ( 2014 ) presented first results of their rv survey of hot jupiter systems to detect additional massive companions that could dynamically effect the close - in giant planets . they estimate a frequency of @xmath9% for high - mass companions ( from giant planets to brown dwarfs ) at larger orbital separations . they also did not find a difference in the occurrence rates of systems with misaligned or eccentric orbits and well - aligned and circular orbits . in this paper we present the data and their analysis performed by members of the _ kepler _ team and follow - up observers at mcdonald observatory ( het & 2.7  m telescope ) , la palma ( not ) , mauna kea ( keck i ) and kitt peak ( wiyn ) for five kepler - object - of - interest ( koi ) : koi-22 , koi-127 , koi-135 , koi-183 , and koi-214 . we highlight the kepler-424 (= koi-214 ) system , a new 2-planet system , where we have found a second ( outer ) giant planet in this system using precise rv measurements .","summary":"hot jupiter systems provide unique observational constraints for migration models in multiple systems and binaries . we report on the discovery of the kepler-424 ( koi-214 ) two - planet system , which consists of a transiting hot jupiter ( kepler-424b ) in a 3.31-d orbit accompanied by a more massive outer companion in an eccentric ( ) 223-d orbit . the outer giant planet , kepler-424c , is not detected to transit the host star . hot jupiters are predominantly found to be lacking any nearby additional planets , the appear to be `` lonely '' ( e.g. steffen et al .  2012 ) . this might be a consequence of a highly dynamical past of these systems . the kepler-424 planetary system is a system with a hot jupiter in a multiple system , similar to  andromedae . 2012 ) , and kepler-423 ( koi-183 ) .","abstract":"hot jupiter systems provide unique observational constraints for migration models in multiple systems and binaries . we report on the discovery of the kepler-424 ( koi-214 ) two - planet system , which consists of a transiting hot jupiter ( kepler-424b ) in a 3.31-d orbit accompanied by a more massive outer companion in an eccentric ( ) 223-d orbit . the outer giant planet , kepler-424c , is not detected to transit the host star . the masses of both planets and the orbital parameters for the second planet were determined using precise radial velocity ( rv ) measurements from the hobby - eberly telescope ( het ) and its high resolution spectrograph ( hrs ) . in stark contrast to smaller planets , hot jupiters are predominantly found to be lacking any nearby additional planets , the appear to be `` lonely '' ( e.g. steffen et al .  2012 ) . this might be a consequence of a highly dynamical past of these systems . the kepler-424 planetary system is a system with a hot jupiter in a multiple system , similar to  andromedae . we also present our results for kepler-422 ( koi-22 ) , kepler-77 ( koi-127 ; gandolfi et al .  2013 ) , kepler-43 ( koi-135 ; bonomo et al .  2012 ) , and kepler-423 ( koi-183 ) . these results are based on spectroscopic data collected with the nordic optical telescope ( not ) , the keck 1 telescope and het . for all systems we rule out false positives based on various follow - up observations , confirming the planetary nature of these companions . we performed a comparison with planetary evolutionary models which indicate that these five hot jupiters have a heavy elements content between 20 and 120  m ."}
{"article_id":"1409.8156","section_id":"c","document":"two of the hot jupiters presented here , koi-127.01 and koi-135.01 , have been confirmed previously by other groups in the astronomical community . koi-127.01 was confirmed as kepler-77b by gandolfi et al . their spectroscopic data were obtained with the sandiford spectrograph at the otto struve 2.1 m telescope at mcdonald observatory and with fies at the nordic optical telescope on la palma . in general , their results are in good agreement with our work . one discrepancy is the host star metallicity , where we find [ fe / h]@xmath59 while gandolfi et al . determined an [ m / h ] of @xmath60 . they also estimated a somewhat cooler effective temperature of @xmath61k , which is almost consistent with our value of @xmath62k . the largest difference is the planetary mass ( and thus also planet density ) : they obtain @xmath63 compared to our value of @xmath64 . this discrepancy is due to a smaller rv semi - amplitude of @xmath65ms@xmath66 measured from the sandiford and fies rvs . in contrast , the @xmath36 value that we have determined from our hrs and fies rvs is @xmath67ms@xmath66 . koi-135.01 was confirmed as kepler-43b by bonomo et al . ( 2012 ) using spectroscopic observations with the sophie spectrograph on the 1.93 m telescope at the observatoire de haute provence . in this case , the results from both of our studies are fully consistent within the quoted uncertainties .    of these five systems , the kepler-424 system stands out as a multi - planet system that also contains a hot jupiter . the second companion resides on a moderately eccentric orbit and is many times more massive than the inner planet ( mass ratio of @xmath68 ) . given the large separation between the two planets in the kepler-424 system , intuition suggests their orbits should be dynamically stable over long timescales . however , as evidenced by the @xmath1 and system ( mcarthur et al . 2010 ) , giant planets with mutually inclined orbital planes may exhibit important dynamical interactions , even when the orbits are well separated . to test whether this is the case for kepler-424 , we have performed some very simple dynamical simulations of the system using the systemic console ( meschiari et al . 2009 ) .    in our simulations , the planets are initially configured with the orbital solution given in table[214 t ] . we left the inclination of planet b fixed , while setting c to a range of mutual inclinations in steps of 5 degrees . at each mutual inclination we simulated the orbits over 100,000 years , or until a collision occurred . the simulations were computed using a gragg - burlisch - ster integrator with a time step of 1 day . the effect of planet c s inclination on the system stability can best be visualized by its impact on the eccentricity of planet b. in figure[paul ] , we show the planets eccentricities as a function of simulation time for a representative set of mutual inclination values . even for coplanar orbits , the eccentricity of b undergoes low - amplitude periodic oscillations , but the amplitude of the oscillations increases greatly for higher mutual inclinations . most notably , when the mutual inclination reaches 45 degrees , @xmath69 abruptly increases to levels inconsistent with our orbital solution . this sudden increase of planet b s eccentricity is caused by the lidov - kozai mechanism ( lidov 1962 , kozai 1962 ) . while it is conceivable that the system is highly mutually inclined and we are observing it during a period of low eccentricity , this possibility becomes less likely as the inclination of planet c decreases and the mean eccentricity of planet b increases . we therefore conclude that the inclination of planet c is most likely greater than 45 degrees . the results of our dynamical analysis are particularly useful because they allow us to place an upper limit on the mass of planet c. if we require @xmath70 , then the actual mass of planet c is @xmath71 . this limit places planet c comfortably within the planetary mass regime , ruling out the possibility that it is a stellar or brown dwarf companion in a face - on configuration . a more sophisticated dynamical study of this system , that also includes tidal dissipation , could lead to a more robust upper mass limit for planet c.    observing the rossiter - mclaughlin effect for kepler-424b will be an interesting test . if planet - planet scattering is the physical mechanism that caused the inward migration , it could also lead to a high inclination of the planet s orbit with respect to the stellar equator . it is a challenging observation for a @xmath72  magnitude star , that we plan to carry out with the newly upgraded and high - efficiency hrs at the het , once it will become available in early 2015 . funding for this discovery mission is provided by nasa s science mission directorate . we thank the entire _ kepler _ team , a wonderful group of people who make this mission so successful . we also thank the anonymous referee , her / his comments helped to improve this paper . me and dh acknowledge support by nasa under grants nnx14ab86 g ( me ) and nnx14ab92 g ( dh ) issued through the kepler participating scientist program . we are grateful to geoff marcy and andrew howard for their help in obtaining the keck / hires observations . the hobby - eberly telescope ( het ) is a joint project of the university of texas at austin , the pennsylvania state university , stanford university , ludwig - maximilians - universitt mnchen , and georg - august - universitt gttingen . the het is named in honor of its principal benefactors , william p. hobby and robert e. eberly . based in part on observations made with the nordic optical telescope , operated on the island of la palma jointly by denmark , finland , iceland , norway , and sweden , in the spanish observatorio del roque de los muchachos of the instituto de astrofisica de canarias . some of the data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w.m . keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . almenara , j.  m. ; bouchy , f. ; gaulme , p. et al . 2013 , , 555 , a118 baraffe , i. ; chabrier , g. ; barman , t. 2008 , , 482 , 315 barclay , t. ; rowe , j.  f. , lissauer , j.  j. ; huber , d. ; et al . 2013 , nature , 494 , 452 batalha , n. ; borucki , w. ; bryson , s. et al . 2011 , , 729 , 27 batygin , k. ; stevenson , d.  j. ; bodenheimer , p.  h. 2011 , , 738 , 1 bonomo , a.  s. ; hebrard , g. ; santerne , a. et al . 2012 , , 538 , 96 borucki , w.  j. ; et al . 2010 , science , 327 , 977 bressan , a. ; marigo , p. ; girardi , l. ; salasnich , b. ; dal cero , c. ; rubele , s. ; nanni , a. 2012 , mnras , 427 , 127 bryson , s.  t. ; jenkins , j.  m. ; gilliland , r.  l. ; et al . 2013 , , 125 , 889 buchhave , l.  a. ; bakos , g.  a. ; hartman , j.  d. ; et al.2010 , , 720 , 1118 deleuil , m. ; almenara , j .- m . ; santerne , a. et al . 2014 , , 564 , a56 djupvik , a.  a. , & andersen , j.  2010 , in `` highlights of spanish astrophysics v '' eds . j.  m.  diego , l.  j.  goicoechea , j.  i.  gonzlez - 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[ gen ] ]       of 22.8ms@xmath66 ( kepler-422 ) and 14.8ms@xmath66 ( kepler-77 ) from the highest probability models from the mcmc analysis . [ 22_127],title=\"fig : \" ]   of 22.8ms@xmath66 ( kepler-422 ) and 14.8ms@xmath66 ( kepler-77 ) from the highest probability models from the mcmc analysis . [ 22_127],title=\"fig : \" ]     of 32.7ms@xmath66 ( kepler-43 ) and 25.1ms@xmath66 ( kepler-423 ) from the highest probability models from the mcmc analysis . [ 135_183],title=\"fig : \" ]   of 32.7ms@xmath66 ( kepler-43 ) and 25.1ms@xmath66 ( kepler-423 ) from the highest probability models from the mcmc analysis . [ 135_183],title=\"fig : \" ]         planet with a time - averaged equilibrium temperature of 1120k . text labels indicate the amount of heavy elements in the planet ( its core mass , in earth masses ) . dashed lines represent planetary evolution models for which 0.25% of the incoming stellar flux ( @xmath74 ) is dissipated into the core of the planet , whereas plain lines do not account for this dissipation ( standard models ) . ]             of the planetary orbits . the high eccentricities of the orbit of planet b induced by @xmath76 are inconsistent with the observed low or zero eccentricity of the hot jupiter orbit . this would correspond to an estimated upper mass limit for planet c of @xmath77 . [ paul ] ]    lrrr 2455390.7061 & -11651.2 & 46.0 & hrs / het + 2455398.6922 & -11817.6 & 22.2 & hrs / het + 2455399.6872 & -11941.0 & 24.2 & hrs / het + 2455400.8879 & -11678.4 & 24.0 & hrs / het + 2455405.6585 & -11965.6 & 50.5 & hrs / het + 2455408.9012 & -12021.4 & 25.1 & hrs / het + 2455409.8791 & -12013.0 & 29.3 & hrs / het + 2455476.7011 & -11925.9 & 39.7 & hrs / het + 2455502.6109 & -11960.1 & 51.3 & hrs / het + 2455515.5966 & -11965.6 & 29.4 & hrs / het + 2455518.5628 & -11992.1 & 51.2 & hrs / het + 2455674.9104 & -12097.2 & 80.0 & hrs / het + 2455677.9101 & -12183.7 & 74.5 & hrs / het + 2455689.8917 & -11948.8 & 38.5 & hrs / het + 2455710.8406 & -12120.4 & 44.0 & hrs / het + 2455718.8050 & -11820.5 & 30.6 & hrs / het + 2455729.7733 & -11903.3 & 26.8 & hrs / het + 2455734.7532 & -11877.7 & 19.5 & hrs / het + 2455739.7648 & -11902.4 & 24.0 & hrs / het + 2455745.7485 & -11704.1 & 23.7 & hrs / het + 2455883.5846 & -12142.2 & 49.3 & hrs / het + 2455884.5760 & -11959.3 & 25.8 & hrs / het + 2455886.5792 & -12240.8 & 25.3 & hrs / het + 2455887.5533 & -12004.1 & 26.5 & hrs / het + 2455889.5618 & -12230.1 & 30.4 & hrs / het + 2456033.9355 & -11507.4 & 30.8 & hrs / het + 2456043.9233 & -11456.5 & 36.4 & hrs / het +    lrrr 2455014.9026 & 13.9 & 17.7 & keck / hires + 2455017.0576 & 15.8 & 17.7 & keck / hires + 2455041.9829 & -22.4 & 18.2 & keck / hires + 2455042.8107 & -30.7 & 18.0 & keck / hires + 2455044.0113 & -54.7 & 18.2 & keck / hires + 2455045.0133 & -27.9 & 18.0 & keck / hires + 2455048.8795 & 85.8 & 18.8 & keck / hires + 2455074.8224 & -20.0 & 17.4 & keck / hires + 2455075.8558 & -6.9 & 17.4 & keck / hires + 2455078.8808 & 108.6 & 17.6 & keck / hires + 2455084.8208 & -34.0 & 17.4 & keck / hires + 2455437.8116 & -28.2 & 4.0 & keck / hires + 2455465.8030 & 18.6 & 4.0 & keck / hires + 2455789.8189 & 20.2 & 3.6 & keck / hires + 2455792.9381 & -37.2 & 3.8 & keck / hires +    lrrr 2455432.7847 & -43.2 & 20.8 & het / hrs + 2455442.7527 & 27.5 & 6.4 & het / hrs + 2455476.6646 & -86.6 & 35.3 & het / hrs + 2455481.6440 & 74.9 & 19.0 & het / hrs + 2455483.6388 & -73.9 & 26.7 & het / hrs + 2455507.5791 & -41.9 & 31.1 & het / hrs + 2455508.5783 & -69.6 & 21.7 & het / hrs + 2455512.5673 & -17.6 & 22.7 & het / hrs + 2455674.8853 & 102.3 & 35.5 & het / hrs + 2455379.6416 & -44.9 & 15.1 & not / fies + 2455380.5392 & 105.6 & 24.6 & not / fies + 2455382.5104 & -8.0 & 18.0 & not / fies + 2455383.6729 & -22.4 & 18.4 & not / fies + 2455384.5210 & 118.3 & 17.5 & not / fies + 2455428.3972 & 91.8 & 16.6 & not / fies + 2455429.4562 & -24.6 & 24.7 & not / fies + 2455431.3953 & 119.5 & 17.2 & not / fies + 2455480.4322 & 21.0 & 21.4 & not / fies + 2455486.4220 & 0.0 & 15.1 & not / fies +    lrrr 2455382.6432 & -3.3 & 14.7 & not / fies + 2455383.6244 & -493.3 & 13.0 & not / fies + 2455384.6123 & 97.8 & 12.9 & not / fies + 2455424.5139 & 223.4 & 15.8 & not / fies + 2455425.6033 & -502.4 & 14.9 & not / fies + 2455426.4740 & -221.5 & 13.3 & not / fies + 2455427.4796 & 185.7 & 18.9 & not / fies + 2455428.4842 & -417.0 & 19.3 & not / fies + 2455430.4280 & 165.6 & 21.7 & not / fies + 2455480.4818 & -471.4 & 23.0 & not / fies + 2455482.3520 & 0.4 & 14.5 & not / fies + 2455486.4697 & -522.0 & 15.8 & not / fies + 2455488.4282 & -37.7 & 27.1 & not / fies + 2455490.3694 & 79.6 & 20.8 & not / fies +    lrrr 2455398.6748 & 30.5 & 43.5 & het / hrs + 2455400.8711 & 146.0 & 16.4 & het / hrs + 2455405.8708 & 83.0 & 26.6 & het / hrs + 2455448.7528 & 100.9 & 15.6 & het / hrs + 2455451.7393 & 47.4 & 46.5 & het / hrs + 2455452.7287 & -60.7 & 11.7 & het / hrs + 2455476.6827 & -67.6 & 34.8 & het / hrs + 2455487.6378 & -106.9 & 13.2 & het / hrs + 2455511.5646 & -66.3 & 26.5 & het / hrs + 2455513.5558 & 52.1 & 20.0 & het / hrs + 2455515.5707 & 121.7 & 21.5 & het / hrs + 2455520.5452 & -40.2 & 14.4 & het / hrs + 2455521.5509 & 98.6 & 29.8 & het / hrs + 2456088.7878 & -71.9 & 29.2 & het / hrs + 2456104.7149 & 0.8 & 18.9 & het / hrs + 2456219.6414 & 80.0 & 9.1 & het / hrs +    lrrrrr 22 & 9631995 & 13.435 & 13.642 & 18:50:31.11 & 46:19:24.10 + 127 & 8359498 & 13.938 & 14.197 & 19:18:25.92 & 44:20:43.52 + 135 & 9818381 & 13.958 & 14.082 & 19:00:57.78 & 46:40:05.70 + 183 & 9651668 & 14.290 & 14.499 & 19:31:25.36 & 46:23:28.24 + 214 & 11046458 & 14.256 & 14.497 & 19:54:29.99 & 48:34:38.82 +    lrrrrrl 22 & 5972@xmath484 & 4.50@xmath78 & 2.2@xmath41.3 & 0.23@xmath40.09 & ... & sme + 127 & 5668@xmath477 & 4.53@xmath78 & 1.8@xmath41.0 & ... & 0.43@xmath40.1 & spc + 135 & 6019@xmath482 & 4.54@xmath78 & 4.9@xmath41.0 & ... & 0.43@xmath40.1 & spc + 183 & 5790@xmath4116 & 4.57@xmath79 & ... & 0.26@xmath40.12 & ... & moog + 214 & 5460@xmath481 & 4.49@xmath80 & 0.5@xmath41.0 & 0.44@xmath40.14 & ... & moog / spc / sme +    lrrrr @xmath81 [ @xmath82 & 1.01 & + 0.054 & -0.054 & isochrone fit + @xmath83 [ @xmath84 & 0.94 & + 0.056 & -0.056 & isochrone fit + log(g ) & 4.50 & + 0.05 & -0.05 & isochrone fit + @xmath85 [ @xmath86 & 0.71 & + 0.11 & -0.11 & isochrone fit + @xmath87 [ g@xmath88 & 1.73 & + 0.29 & -0.29 & isochrone fit + @xmath87 [ g@xmath88 & 1.74 & + 0.44 & -0.34 & transit model + planet b : & & & & + @xmath89 [ days ] & 3.3118644 & @xmath90 & -3.9@xmath91 & + @xmath92 [ bjd ] & 2454964.7427 & + 0.00023 & -0.00017 & + @xmath93 & 0.934 & + 0.065 & -0.053 & + @xmath94 & 0.0961 & + 0.0065 & -0.0033 & + @xmath19 [ @xmath95 & 0.89 & + 0.08 & -0.06 & + @xmath36 [ ms@xmath66 ] & 140.0 & + 12.0 & -13.0 & + @xmath33 & 0.001 & + 0.043 & -0.029 & + @xmath32 & 0.002 & + 0.061 & -0.066 & + @xmath97 [ @xmath98 & 1.03 & + 0.13 & -0.13 & + @xmath99 [ au ] & 0.044 & + 0.005 & -0.004 & + @xmath100 [ g@xmath88 & 1.94 & + 0.25 & -0.25 & + planet c : & & & & + @xmath89 [ days ] & 223.3 & + 2.1 & -2.1 & + @xmath92 [ bjd ] & 2455403.4 & + 2.1 & -2.0 & + @xmath36 [ ms@xmath66 ] & 246.0 & + 17.0 & -17.0 & + @xmath33 & 0.018 & + 0.052 & -0.052 & + @xmath32 & 0.318 & + 0.057 & -0.061 & + @xmath101 [ @xmath98 & 6.97 & + 0.62 & -0.62 & + @xmath99 [ au ] & 0.73 & + 0.08 & -0.07 & + rv@xmath102 [ ms@xmath66 ] & 8.0 & + 13.0 & -6.0 & +    lrrrr @xmath81 [ @xmath82 & 1.15 & + 0.06 & -0.06 & isochrone fit + @xmath83 [ @xmath84 & 1.24 & + 0.12 & -0.12 & isochrone fit + log(g ) & 4.31 & + 0.073 & -0.073 & isochrone fit + @xmath85 [ @xmath86 & 1.75 & + 0.37 & -0.37 & isochrone fit + @xmath87 [ g@xmath88 & 0.86 & + 0.22 & -0.22 & isochrone fit + @xmath87 [ g@xmath88 & 0.87 & + 0.22 & -0.22 & transit model + planet : & & & & + @xmath89 [ days ] & 7.8914483 & + 5.0@xmath103 & -5.1@xmath103 & + @xmath92 [ bjd ] & 2455010.25005 & + 0.00011 & -9.4@xmath104 & + @xmath93 & 0.416 & + 0.045 & -0.045 & + @xmath94 & 0.0957 & + 0.00048 & -0.00055 & + @xmath19 [ @xmath95 & 1.15 & + 0.11 & -0.11 & + @xmath36 [ ms@xmath66 ] & 40.0 & + 11.0 & -10.0 & + @xmath33 & 0.013 & + 0.096 & -0.063 & + @xmath32 & -0.009 & + 0.07 & -0.096 & + @xmath97 [ @xmath98 & 0.43 & + 0.13 & -0.13 & + @xmath99 [ au ] & 0.082 & + 0.011 & -0.010 & + @xmath100 [ g@xmath88 & 0.38 & + 0.11 & -0.11 & + rv@xmath102 [ ms@xmath66 ] & 26.8 & + 9.4 & -7.0 & +    lrrrr @xmath81 [ @xmath82 & 1.08 & + 0.034 & -0.034 & isochrone fit + @xmath83 [ @xmath84 & 0.99 & + 0.053 & -0.053 & isochrone fit + log(g ) & 4.48 & + 0.036 & -0.036 & isochrone fit + @xmath85 [ @xmath86 & 0.90 & + 0.13 & -0.13 & isochrone fit + @xmath87 [ g@xmath88 & 1.6 & + 0.22 & -0.22 & isochrone fit + @xmath87 [ g@xmath88 & 2.7 & + 1.05 & -1.05 & transit model + planet : & & & & + @xmath89 [ days ] & 3.5787806 & + 1.6@xmath103 & -1.6@xmath103 & + @xmath92 [ bjd ] & 2454967.0304 & + 4.4@xmath104 & -4.3@xmath104 & + @xmath93 & 0.291 & + 0.05 & -0.05 & + @xmath94 & 0.0997 & + 0.00069 & -0.00075 & + @xmath19 [ @xmath95 & 0.96 & + 0.05 & -0.05 & + @xmath36 [ ms@xmath66 ] & 89.0 & + 11.0 & -10.0 & + @xmath33 & -0.030 & + 0.034 & -0.027 & + @xmath32 & 0.23 & + 0.15 & -0.10 & + @xmath97 [ @xmath98 & 0.71 & + 0.10 & -0.10 & + @xmath99 [ au ] & 0.047 & + 0.007 & -0.008 & + @xmath100 [ g@xmath88 & 1.07 & + 0.15 & -0.15 & + rv@xmath102 [ ms@xmath66 ] & 17.6 & + 8.0 & -6.1 & +    lrrrr @xmath81 [ @xmath82 & 1.23 & + 0.04 & -0.04 & isochrone fit + @xmath83 [ @xmath84 & 1.34 & + 0.055 & -0.055 & isochrone fit + log(g ) & 4.27 & + 0.029 & -0.029 & isochrone fit + @xmath85 [ @xmath86 & 2.12 & + 0.22 & -0.22 & isochrone fit + @xmath87 [ g@xmath88 & 0.71 & + 0.078 & -0.078 & isochrone fit + @xmath87 [ g@xmath88 & 0.74 & + 0.067 & -0.067 & transit model + planet : & & & & + @xmath89 [ days ] & 3.0240922 & + 1.6@xmath103 & -1.6@xmath103 & + @xmath92 [ bjd ] & 2454965.4169 & + 6.7@xmath104 & -7.5@xmath104 & + @xmath93 & 0.631 & + 0.025 & -0.027 & + @xmath94 & 0.0862 & + 0.00048 & -0.00058 & + @xmath19 [ @xmath95 & 1.12 & + 0.047 & -0.047 & + @xmath36 [ ms@xmath66 ] & 372.0 & + 12.0 & -13.0 & + @xmath33 & -0.005 & + 0.011 & -0.017 & + @xmath32 & 0.005 & + 0.033 & -0.017 & + @xmath97 [ @xmath98 & 3.03 & + 0.18 & -0.18 & + @xmath99 [ au ] & 0.044 & + 0.002 & -0.002 & + @xmath100 [ g@xmath88 & 2.87 & + 0.17 & -0.17 & + rv@xmath102 [ ms@xmath66 ] & 30.0 & + 11.0 & -8.0 & +    lrrrr @xmath81 [ @xmath82 & 1.07 & + 0.05 & -0.05 & isochrone fit + @xmath83 [ @xmath84 & 0.99 & + 0.054 & -0.054 & isochrone fit + log(g ) & 4.48 & + 0.04 & -0.04 & isochrone fit + @xmath85 [ @xmath86 & 0.96 & + 0.16 & -0.16 & isochrone fit + @xmath87 [ g@xmath88 & 1.58 & + 0.22 & -0.22 & isochrone fit + @xmath87 [ g@xmath88 & 1.65 & + 0.36 & -0.21 & transit model + planet : & & & & + @xmath89 [ days ] & 2.68432848 & + 8.2@xmath105 & -8.2@xmath105 & + @xmath92 [ bjd ] & 2454966.3548 & + 2.6@xmath104 & -2.7@xmath104 & + @xmath93 & 0.11 & + 0.10 & -0.08 & + @xmath94 & 0.1242 & + 0.00089 & -0.00037 & + @xmath19 [ @xmath95 & 1.20 & + 0.065 & -0.065 & + @xmath36 [ ms@xmath66 ] & 101.0 & + 13.0 & -14.0 & + @xmath33 & -0.002 & + 0.039 & -0.048 & + @xmath32 & -0.010 & + 0.043 & -0.068 & + @xmath97 [ @xmath98 & 0.72 & + 0.12 & -0.12 & + @xmath99 [ au ] & 0.0396 & + 0.003 & -0.003 & + @xmath100 [ g@xmath88 & 0.55 & + 0.09 & -0.09 & + rv@xmath102 [ ms@xmath66 ] & 30.0 & + 11.0 & -8.0 & +","summary":"these results are based on spectroscopic data collected with the nordic optical telescope ( not ) , the keck 1 telescope and het .","abstract":"hot jupiter systems provide unique observational constraints for migration models in multiple systems and binaries . we report on the discovery of the kepler-424 ( koi-214 ) two - planet system , which consists of a transiting hot jupiter ( kepler-424b ) in a 3.31-d orbit accompanied by a more massive outer companion in an eccentric ( ) 223-d orbit . the outer giant planet , kepler-424c , is not detected to transit the host star . the masses of both planets and the orbital parameters for the second planet were determined using precise radial velocity ( rv ) measurements from the hobby - eberly telescope ( het ) and its high resolution spectrograph ( hrs ) . in stark contrast to smaller planets , hot jupiters are predominantly found to be lacking any nearby additional planets , the appear to be `` lonely '' ( e.g. steffen et al .  2012 ) . this might be a consequence of a highly dynamical past of these systems . the kepler-424 planetary system is a system with a hot jupiter in a multiple system , similar to  andromedae . we also present our results for kepler-422 ( koi-22 ) , kepler-77 ( koi-127 ; gandolfi et al .  2013 ) , kepler-43 ( koi-135 ; bonomo et al .  2012 ) , and kepler-423 ( koi-183 ) . these results are based on spectroscopic data collected with the nordic optical telescope ( not ) , the keck 1 telescope and het . for all systems we rule out false positives based on various follow - up observations , confirming the planetary nature of these companions . we performed a comparison with planetary evolutionary models which indicate that these five hot jupiters have a heavy elements content between 20 and 120  m ."}
{"article_id":"0708.2357","section_id":"i","document":"soliton and hairy black hole solutions of einstein - yang - mills ( eym ) theory and its variants have been the subject of extensive research since the discovery of non - trivial , spherically symmetric solitons @xcite and ` colored ' black holes @xcite in @xmath5 eym in asymptotically flat space - time . these black holes are ` hairy ' in the sense that they have no magnetic charge , and are therefore indistinguishable at infinity from a standard schwarzschild black hole . there are discrete families of solutions , indexed by the event horizon radius @xmath6 ( with @xmath7 for solitons ) and @xmath8 , the number of zeros of the single gauge field function @xmath9 , each pair @xmath10 identifying a solution of the field equations . a key feature of the solutions is that @xmath11 , so that the gauge field function must have at least one zero ( or ` node ' ) . these solutions , while they violate the ` letter ' of the no - hair conjecture , may be thought of as not contradicting its ` spirit ' , since they are found to be unstable to classical , linear , spherically symmetric perturbations @xcite . there is also a large literature concerning analytic studies of the asymptotically flat @xmath5 eym field equations @xcite , proving the existence of the above numerical solutions and detailed properties of the phase space of solutions . since these initial discoveries a plethora of new soliton and black hole solutions have been found ( see @xcite for a review ) . the present work combines two natural extensions of these initial studies : the generalization to @xmath0 eym , and the inclusion of a negative cosmological constant . we now briefly review each of these generalizations in turn . firstly , in asymptotically flat space , both charged and neutral numerical solutions of the @xmath0 eym field equations have been found @xcite . we consider in this paper only purely magnetic solutions , which , in the asymptotically flat case , are described by @xmath2 gauge field functions @xmath12 . as in asymptotically flat @xmath5 eym , solutions exist at discrete points in the parameter space , and can be indexed by the radius of the event horizon ( if there is one ) and the number of nodes of the @xmath12 ( all @xmath12 having at least one zero ) . once again , there is a general result @xcite that all these solutions must be unstable . the @xmath0 eym field equations are considerably more complicated than those for @xmath5 and correspondingly less analytic work has been done . local existence of solutions of the field equations near the origin ( for solitons ) , black hole event horizon ( if there is one ) and at infinity has been established @xcite . there is a heuristic proof ( following @xcite ) of the existence of black hole solutions for general @xmath13 @xcite , but more rigorous work exits only for the case of @xmath3 @xcite . the second generalization of asymptotically flat @xmath5 eym that we consider in this paper is the inclusion of a non - zero cosmological constant @xmath14 . when the cosmological constant is positive , soliton @xcite and black hole @xcite @xmath5 solutions have been found . these solutions possess a cosmological horizon and approach de sitter space at infinity ( for a complete classification of the possible space - time structures , see @xcite ) . the phase space of solutions is again discrete , and the single gauge field function @xmath9 must have at least one zero . unsurprisingly , these solutions again turn out to be unstable @xcite . the inclusion of a negative cosmological constant ( so that the space - time is asymptotically anti - de sitter ( ads ) ) may be motivated by recent progress in string theory , particularly the ads / cft correspondence @xcite . it is found @xcite that the solutions of @xmath5 eym in ads possess quite different properties compared with their asymptotically flat or asymptotically de sitter cousins . in particular , solutions for which the gauge field function @xmath9 has no zeros exist for sufficiently large @xmath15 . solutions exist in continuous open subsets of the parameter space , rather than at discrete points . in addition , for sufficiently large @xmath15 , at least some of these solutions are stable under linear , spherically symmetric perturbations @xcite ( this was subsequently extended to cover non - spherically symmetric linear perturbations in @xcite ) . therefore , while black holes can not be given stable ym hair in either asymptotically flat or asymptotically de sitter space , in asymptotically anti - de sitter space , stable gauge field hair is possible . we are thus led to the following natural question : are there stable solutions of the @xmath0 eym solutions with a negative cosmological constant ? in this paper we will present the first soliton and hairy black hole solutions of @xmath0 eym in ads , for @xmath16 . we consider only purely magnetic gauge fields , so that the ym field is described by @xmath2 functions @xmath12 . we make a detailed study of the phase space of solutions and their general properties in the particular cases @xmath17 , @xmath18 . of particular interest is the existence , for sufficiently large @xmath15 , of solutions in which all the @xmath12 have no zeros . we anticipate that at least some of these solutions will be stable under linear , spherically symmetric perturbations , and will examine their stability in detail elsewhere . the outline of this paper is as follows . in section [ sec : equations ] we discuss the field equations , our ansatze for the fields and the boundary conditions that must be satisfied , considering the cases of black holes and solitons separately . our new solutions are discussed in detail in section [ sec : solutions ] , focussing particularly on the phase space of solutions . finally , our conclusions can be found in section [ sec : conc ] . throughout this paper , the metric has signature @xmath19 and we use units in which @xmath20 .","summary":"we present new soliton and hairy black hole solutions of einstein - yang - mills theory in asymptotically anti - de sitter space . these solutions are of particular interest because we anticipate that at least some of them will be linearly stable .","abstract":"we present new soliton and hairy black hole solutions of einstein - yang - mills theory in asymptotically anti - de sitter space . these solutions are described by independent parameters , and have gauge field degrees of freedom . we examine the space of solutions in detail for and solitons and black holes . if the magnitude of the cosmological constant is sufficiently large , we find solutions where all the gauge field functions have no zeros . these solutions are of particular interest because we anticipate that at least some of them will be linearly stable ."}
{"article_id":"0708.2357","section_id":"c","document":"in this paper we have presented new soliton and hairy black hole solutions of @xmath0 einstein - yang - mills theory with a negative cosmological constant . our solutions are purely magnetic , so that the gauge field functions are in general described by @xmath2 functions , giving @xmath2 independent degrees of freedom . this gives , in total , @xmath1 parameters ( @xmath2 from the gauge fields , plus the cosmological constant @xmath14 and the event horizon radius @xmath6 , the latter being zero for soliton solutions ) which characterize the solutions . we have developed the formalism for finding solutions for arbitrary @xmath13 , and have discussed in some detail the properties of the solution space for @xmath17 , @xmath18 . 1 .   solutions exist in continuous open subsets of the phase space ; 2 .   as @xmath267 , the solution space fragments and approaches the discrete solution space in asymptotically flat space ; 3 .   for sufficiently large @xmath15 , we have solutions in which all @xmath2 gauge field functions have no zeros . the last item is of particular interest . the existence of these solutions , for sufficiently large @xmath15 , can be proved analytically @xcite . in the @xmath5 case , it is known that at least some of the solutions in which the gauge field function has no zeros , for sufficiently large @xmath15 , are linearly stable , both under spherically symmetric @xcite and non - spherically symmetric @xcite linear perturbations . we have seen how @xmath5 solutions can be embedded into @xmath0 eym , and the first question is whether those solutions which are stable as solutions of @xmath5 eym remain stable when considered as solutions of @xmath0 eym . we will show in a separate publication that this is indeed the case @xcite , and , furthermore , that there are genuinely @xmath0 solutions , in a neighborhood of these embedded @xmath5 solutions , which are also stable under linear , spherically symmetric perturbations . the analysis is rather involved so we do not describe it further here . the question of non - spherically symmetric perturbations remains open at this stage . other interesting open questions remain . firstly , there is evidence @xcite that solutions to @xmath268 exist in ads , at least for sufficiently large @xmath15 . the field equations for @xmath268 are rather different in structure from those for @xmath0 , with the infinite number of ordinary differential ym equations being replaced by a partial differential equation @xcite . therefore different numerical techniques will be required to solve the field equations . however , the fact ( to be proved in @xcite ) that there are soliton and hairy black hole solutions in @xmath0 eym for any @xmath13 suggests that non - trivial solutions of @xmath268 eym may indeed exist . this leaves open the interesting possibility of giving a black hole infinite amounts of gauge field hair . secondly , we have not examined the question of whether there are topological black hole solutions of @xmath0 eym , generalizing the topological @xmath5 black holes found in @xcite , but we anticipate that such solutions exist . all @xmath269 @xmath5 eym topological black holes are known to be stable as are at least some of the @xmath270 solutions @xcite , so the stability of any @xmath0 eym topological black holes would also be of particular interest . finally , there is the question of the implication of our solutions for the ads / cft correspondence @xcite . a black hole with a particular mass and magnetic charge measured at infinity in ads can now be either an abelian , magnetically - charged , reissner - nordstrom - ads black hole or any one of a number of @xmath0 eym black holes with different @xmath13 . we would expect that , in analogy with the @xmath5 case @xcite , there are @xmath0 solutions in some super - gravity theories , which will be even more puzzling in the context of ads / cft . it would also be interesting to study the corresponding picture in higher dimensions @xcite . we hope to return to these issues in the near future . we are grateful to eugen radu for innumerable enlightening discussions . the work of jeb is supported by uk epsrc , and the work of ew is supported by uk pparc , grant reference number ppa / g / s/2003/00082 . n.  straumann and z.  h.  zhou , phys . lett . * b237 * , 353 ( 1990 ) ; 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+ y.  brihaye , a.  chakrabarti and d.  h.  tchrakian , class . quant . grav . * 20 * , 2765 ( 2003 ) ; + y.  brihaye , a.  chakrabarti , b.  hartmann and d.  h.  tchrakian , phys b561 * , 161 ( 2003 ) ; + y.  brihaye , f.  clement and b.  hartmann , phys . rev . * d70 * , 084003 ( 2004 ) ; + y.  brihaye and t.  delsate , phys . rev . * d75 * , 044013 ( 2007 ) ; + y.  brihaye and b.  hartmann , class . * 22 * , 183 ( 2005 ) ; + y.  brihaye , e.  radu and d.  h.  tchrakian , phys . rev . * d75 * , 024022 ( 2007 ) ; preprint ; + b.  hartmann , y.  brihaye and b.  bertrand , phys . b570 * , 137 ( 2003 ) ; + n.  okuyama and k .- maeda , phys . rev . * d67 * , 104012 ( 2003 ) ; + e.  radu , c.  stelea and d.  h.  tchrakian , phys . rev . * d73 * , 084015 ( 2006 ) ; + e.  radu and d.  h.  tchrakian , phys . rev . * d73 * , 024006 ( 2006 ) ; + m.  s.  volkov , preprint .","summary":"these solutions are described by independent parameters , and have gauge field degrees of freedom .","abstract":"we present new soliton and hairy black hole solutions of einstein - yang - mills theory in asymptotically anti - de sitter space . these solutions are described by independent parameters , and have gauge field degrees of freedom . we examine the space of solutions in detail for and solitons and black holes . if the magnitude of the cosmological constant is sufficiently large , we find solutions where all the gauge field functions have no zeros . these solutions are of particular interest because we anticipate that at least some of them will be linearly stable ."}
{"article_id":"0902.0043","section_id":"i","document":"one of the key questions of automated reasoning is the following : `` when does a set @xmath0 of sentences have a model ? '' in fact , given reasonable assumptions about calculi , most inference problems can be reduced to determining ( un)-satisfiability of a set @xmath0 of sentences . since building models for @xmath0 is hard in practice , much research in computational logic has concentrated on finding sufficient conditions for satisfiability , e.g. whether there is a hintikka set @xmath1 extending @xmath0 .    of course in general the answer to the satisfiability question depends on the class of models at hand . in classical first - order logic , model classes are well - understood . in impredicative higher - order logic , there is a whole landscape of plausible model classes differing in their treatment of functional and boolean extensionality . satisfiability then strongly depends on these classes , for instance , the set @xmath2 is unsatisfiable in a model class where the universes of booleans are required to have at most two members ( see property @xmath3 below ) , but satisfiable in the class without this restriction .    in we have shown that certain ( i.e. _ saturated _ ) hintikka sets always have models and have derived syntactical conditions ( so - called _ saturated _ abstract consistency properties ) for satisfiability from this fact . the importance of abstract consistency properties is that one can check completeness for a calculus @xmath4 by verifying proof - theoretic conditions ( checking that @xmath4-irrefutable sets of formulae have the saturated abstract consistency property ) instead of performing model - theoretic analysis ( for historical background of the abstract consistency method in first - order logic , cf . unfortunately , the saturation condition ( if @xmath0 is abstractly consistent , then for all sentences @xmath5 one of @xmath6 or @xmath7 is as well ) is very difficult to prove for machine - oriented calculi ( indeed as hard as cut elimination as we will show ) .    in this paper we investigate further the relation between the lack of the subformula property in the saturation condition ( we need to `` guess '' whether to extend @xmath0 by @xmath5 or @xmath8 on our way to a hintikka set ) and the cut rule ( where we have to `` guess , '' i.e. `` search for '' in an automated reasoning setting the cut formula @xmath5 ) . an important result is the insight that there exist `` cut - strong '' formulae which support the effective simulation of cut in calculi for impredicative logics . prominent examples of cut - strong formulae are leibniz equations and the axioms for comprehension , extensionality , induction , description and choice . the naive addition of any of these cut - strong formulae to any calculus for an impredicative logic is a strong threat for effective automated proof search , since these formulae in a way introduce the cut rule through the backdoor ( even if the original calculus is cut - free and thus appears appropriate for proof automation at first sight ) . cut - strong formulae thus introduce additional sources for breaking the subformula property and therefore they should either be avoided completely or treated with great care in calculi designed for automated proof search . consider the following formula of higher - order logic representing boolean extensionality : @xmath9 for a theorem prover to make use of this formula , it must instantiate @xmath10 and @xmath11 with terms of type @xmath12 . in other words , the theorem prover must synthesize two arbitrary formulas . requiring a theorem prover to synthesize these formulas is just as hard ( and unrealistic ) as requiring a theorem prover to synthesize cut formulas . an alternative to including the formula for boolean extensionality is to include a rule in the search procedure which allows the theorem prover to reduce proving @xmath13 to the subgoal of proving @xmath14 . using this rule does not require the prover to synthesize any terms . simply adding such a rule is not enough to obtain a complete calculus . we will explore what additional rules are required to obtain completeness and argue that these rules are appropriate for mechanized proof search . in section [ sec : hol ] , we will fix notation and review the relevant results from . we define in section  [ sec : seq - calc ] a basic sequent calculus and study the correspondence between saturation in abstract consistency classes and cut - elimination . in section  [ sec : cut - simulation ] we introduce the notion of `` cut - strong '' formulae and sequents and show that they support the effective simulation of cut . in section  [ sec : prominent - cut - strong ] we demonstrate that the pertinent extensionality axioms are cut - strong . we develop alternative extensionality rules which do not suffer from this problem . further rules are needed to ensure henkin completeness for this calculus with extensionality . these new rules correspond to the acceptability conditions we propose in section  [ sec : acceptability ] to ensure the existence of models and the existence of saturated extensions of abstract consistency classes .","summary":"we investigate cut - elimination and cut - simulation in impredicative ( higher - order ) logics .","abstract":"we investigate cut - elimination and cut - simulation in impredicative ( higher - order ) logics . we illustrate that adding simple axioms such as leibniz equations to a calculus for an impredicative logic  in our case a sequent calculus for classical type theory  is like adding cut . the phenomenon equally applies to prominent axioms like boolean- and functional extensionality , induction , choice , and description . this calls for the development of calculi where these principles are built - in instead of being treated axiomatically ."}
{"article_id":"0902.0043","section_id":"c","document":"we have shown that adding cut - strong formulae to a calculus for an impredicative logic is like adding cut . for machine - oriented automated theorem proving in impredicative logics  such as classical type theory  it is therefore not recommendable to naively add cut - strong axioms to the search space . in addition to the comprehension principle and the functional and boolean extensionality axioms as elaborated in this paper the list of cut - strong axioms includes :    formulas @xmath358 are @xmath359-cut - strong in @xmath244 where @xmath360 is @xmath361 ( cf . the argument is similar to examples  [ ex1]-[ex4 ] ; here we the crucial step is to instantiate @xmath362 with @xmath363 . the _ axiom of induction _ for the naturals @xmath364 is @xmath365-cut - strong in @xmath244 . ( other well - founded ordering axioms are analogous . ) the crucial step in the proof is to instantiate @xmath270 with @xmath366 for some parameter @xmath306 . @xmath367 is @xmath249-cut - strong in @xmath244 . the crucial step is to instantiate @xmath362 with @xmath368 . @xmath369 , the _ description axiom _ ( see  @xcite ) , where @xmath370 stands for @xmath371 is @xmath372-cut - strong in @xmath244 . the crucial step in the proof is to instantiate @xmath362 with @xmath373 for some parameter @xmath374 .    as we have shown in example  [ ex4 ] , comprehension axioms can be cut - strong . church s formulation of type theory ( cf . @xcite ) used typed @xmath15-calculus to build comprehension principles into the language . one can view church s formulation as a first step in the program to eliminate the need for cut - strong axioms . for the extensionality axioms a start has been made by the sequent calculi in this paper ( and ) , for resolution in  @xcite and for sequent calculi and extensional expansion proofs in  @xcite . the extensional systems in  @xcite also provide a complete method for using primitive equality instead of leibniz equality . for improving the automation of higher - order logic our exploration thus motivates the development of higher - order calculi which directly include reasoning principles for equality , extensionality , induction , choice , description , etc . , without using cut - strong axioms .","summary":"we illustrate that adding simple axioms such as leibniz equations to a calculus for an impredicative logic  in our case a sequent calculus for classical type theory  is like adding cut . the phenomenon equally applies to prominent axioms like boolean- and functional extensionality , induction , choice , and description .","abstract":"we investigate cut - elimination and cut - simulation in impredicative ( higher - order ) logics . we illustrate that adding simple axioms such as leibniz equations to a calculus for an impredicative logic  in our case a sequent calculus for classical type theory  is like adding cut . the phenomenon equally applies to prominent axioms like boolean- and functional extensionality , induction , choice , and description . this calls for the development of calculi where these principles are built - in instead of being treated axiomatically ."}
{"article_id":"astro-ph9711174","section_id":"i","document":"early investigations of the galaxy s emission revealed that it extends well past the solar circle , and that , in the outer galaxy , the emission is warped systematically from its midplane in the inner galaxy ( @xcite ; @xcite ; @xcite ; oort , kerr , & westerhout  1958 ) . more recent stellar ( @xcite ) , infrared ( @xcite ; @xcite ) , and molecular ( @xcite ) observations have shown that these disk constituents also extend well past the solar circle and are warped similar to the layer . ionized gas occupies potentially 10% or more of the volume of the interstellar medium ( ism ) near the solar circle and is probably a dynamically important constituent ( e.g. , @xcite ; @xcite ) , but its radial extent is poorly constrained . h@xmath1 measurements are limited to distances of a few kiloparsecs by interstellar absorption ( @xcite ) . the frequency at which the galactic plane becomes optically thick because of free - free absorption can indicate the extent of the disk , but for plausible disk sizes ( see below ) this frequency is less than 10  mhz and so is difficult to observe . few pulsars are known in the anticenter direction . less than ten have dispersion - measure  independent distance estimates ( @xmath3 ) and the estimated distances are less than 2  kpc ( @xcite ) ; the remainder have dms of 30125  pc  @xmath4 , consistent with distances of a few kiloparsecs ( taylor , manchester , & lyne  1993 ; @xcite ) . fluctuations in the ionized gas produce radio - wave scattering which manifests itself as angular broadening of compact sources ( see @xcite for a review of the full variety of interstellar radio wave propagation effects ) . scattering measurements have been biased toward the inner galaxy , even for surveys of angular broadening of extragalactic sources ( e.g. , fey , spangler , & mutel  1989 ; fey , spangler , & cordes  1991 ) . only one angular broadening survey has been conducted toward the outer galaxy ( @xcite ) , and , as we illustrate below , most of the sources in that survey had galactic latitudes too large to provide effective constraints on the radial extent of the ionized galactic disk . measurements of interplanetary scintillation determine source diameters indirectly , but in general do not have sufficient resolution to provide stringent constraints . though the radial extent of the ionized gas is poorly constrained , a number of lines of evidence suggest that its radial extent may equal or exceed that of the :    * savage , sembach , & lu  ( 1995 ) find absorption along the line of sight to h  1821@xmath5643 ( @xmath6 ) . among the velocity components contributing to this absorption is low - density ( @xmath7  @xmath4 ) , warm ( @xmath8  k ) gas at a velocity of @xmath9  km  s@xmath10 , corresponding to a kinematic galactocentric distance of 25  kpc . * the disks of nearby galaxies are truncated at radii of order 2550  kpc , at which the surface density drops to @xmath11  @xmath12 ( corbelli , schneider , & salpeter  1989 ; @xcite ; @xcite ) . this truncation is observed even for galaxies without nearby companions and likely occurs where the disks become optically thin to the intergalactic ionizing flux ( @xcite ; @xcite ) . bland - hawthorn , freeman , & quinn  ( 1997 ) have reported the detection of ionized gas beyond the observed disk of ngc  253 . charlton , salpeter , & hogan  ( 1992 ) have proposed that at least some of the low - redshift ly@xmath1 clouds seen in quasar spectra may be due to residual in extended , nearly fully ionized disks of normal spiral galaxies . our galaxy would then be a prototypical , @xmath13 absorber . * material blown out of the galactic disk by the action of clustered supernovae may account for a fraction of high - velocity clouds and later return to the disk forming a galactic fountain ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . models of high - velocity clouds often require the material to be supported by gas pressure at large galactocentric radii , @xmath14  kpc ( e.g. , @xcite ) . taylor & cordes  ( 1993 , hereinafter @xcite ) modelled the galactic distribution of ionized gas with three global components :    1 . an extended component with scale height of approximately 1  kpc and @xmath15 radial scale length of order 20  kpc ; 2 . an inner galaxy component with scale height of 0.15  kpc and radial scale length of 3.5  kpc ; and 3 . spiral arms , the number and shape of which were determined by appeal to radio and optical observations of regions and radio observations of and non - thermal emission . the data available to constrain the model parameters consisted of 74 pulsars with dm - independent distances , 223 scattering measurements toward pulsars , masers , and extragalactic sources , and the galactic longitude distribution for 553 pulsar dms .    because of the paucity of measurements summarized above , @xcite could place only a lower bound on the scale length of the extended component , @xmath16 . they adopted @xmath17  kpc , though @xmath18  kpc produced comparable fits to the data . moreover , they modelled the extended component as planar ; if the ionized disk does extend to 20  kpc or more , it is likely to be warped similarly to the other outer galaxy disk constituents . figure  [ fig : angle ] demonstrates that angular broadening measurements of extremely low - latitude , @xmath19 , extragalactic sources toward the galactic anticenter have the potential of constraining @xmath16 . the line of nodes of the disk is fairly constant with galactocentric radius and is near a galactic longitude of 170 , so sources toward the anticenter probably provide the longest path length through the ionized disk . extremely low - latitude sources are required because the scale height of the extended component near the solar circle is 0.88  kpc and only for sources with @xmath19 does the line of sight remain within one scale height for path lengths of 50  kpc or more . only three of the sources in dennison et al.s  ( 1984 ) survey meet this criterion ; of these , one may show excessive scattering due to an region along the line of sight and another shows complex structure making it difficult to estimate a scattering diameter . we have carried out a program of multifrequency very long baseline array ( vlba ) observations of twelve anticenter sources , seven of which have @xmath20 ( lazio & cordes  1997 , hereinafter @xcite ) . we detected all but one of the sources at one or more of our observation frequencies0.3 , 1.6 , and 5  ghz . [ fig : angle ] illustrates , the nominal resolutions of the vlba are such that 18  cm observations are sensitive to scale lengths of @xmath21  kpc and  90  cm observations should detect scattering even if @xmath22  kpc . figure  [ fig : angle ] also shows the nominal resolution of the space vlbi satellite halca , and thereby illustrates another important aspect of improving our knowledge of the galactic distribution of scattering . at low galactic latitudes , interstellar scattering will determine the limiting resolution for baselines in excess of the earth s diameter at frequencies near 1  ghz . if the disk flares or warps similarly to the disk , interstellar angular broadening could be non - negligible at much higher latitudes ( e.g. , @xmath23 ) .    in this paper we combine the sources from our survey with other radio - wave scattering measurements from the literature and use a likelihood analysis to constrain the distribution of ionized gas in the outer galaxy . in  [ sec : outerdisk ] we describe our model for the distribution of ionized gas in the outer galaxy , in  [ sec : analyze ] we extract scattering diameters from our measured angular diameters and develop a likelihood analysis of scattering in the outer galaxy , and in  [ sec : conclude ] we discuss our results and present our conclusions .","summary":"we use radio - wave scattering data for extragalactic sources and pulsars to constrain the distribution of ionized gas in the outer galaxy . like previous models , in addition , we have used the known distribution in the outer galaxy in constructing our model , and we allow the disk to warp and flare . our analysis favors an unwarped , non - flaring disk with a scale height of 1  kpc , though this may reflect the non - uniform and coarse coverage of the anticenter provided by the available data .","abstract":"we use radio - wave scattering data for extragalactic sources and pulsars to constrain the distribution of ionized gas in the outer galaxy . like previous models , our model for the disk includes parameters for the radial scale length and scale height of the ionized gas . in addition , we have used the known distribution in the outer galaxy in constructing our model , and we allow the disk to warp and flare . we also include the perseus arm in our model . we use a likelihood analysis on 18 anticenter sources with measured scattering observables : 11 extragalactic sources and 7 pulsars . we find that the strength of scattering in the perseus arm is no more than 60% of the level contributed by spiral arms in the inner galaxy and is equivalent to a scattering diameter of 1.5  mas at  1  ghz . our analysis favors an unwarped , non - flaring disk with a scale height of 1  kpc , though this may reflect the non - uniform and coarse coverage of the anticenter provided by the available data . one extragalactic source has a size a factor of two smaller than predicted by our model , possibly indicating the existence of holes in the scattering material . the lack of a warp in the scattering material indicates that vlbi observations near 1  ghz with an orbiting station having baseline lengths of a few earth diameters will not be affected by interstellar scattering at moderate galactic latitudes , . the radial scale length is 1520  kpc , but the data can not distinguish between a gradual decrease in the electron density and a truncated distribution . we favor a truncated one , because we associate the scattering with massive star formation , which is also truncated near 20  kpc . a radial extent of 20  kpc is also comparable to the radial extent of h emission observed for nearby spiral galaxies . we find that the distribution of electron density turbulence must decrease more rapidly with galactocentric distance than the distribution of hydrogen . alternate ionizing and turbulent agents  the intergalactic ionizing flux and the passage of satellite galaxies through the disk  are unlikely to contribute significant amounts to scattering in the anticenter . we can not exclude the possibility that a largely ionized , but quiescent disk extends to  kpc , similar to that inferred for some ly absorbers ."}
{"article_id":"astro-ph9711174","section_id":"c","document":"our likelihood results indicate that @xmath180  kpc if the fluctuating part of the electron density distribution exhibits a gradual decrease in the outer galaxy or @xmath193  kpc if the disk is truncated . the apparent decrease in the rms @xmath25 could result if sites of turbulence became less numerous while the mean @xmath25 remained constant or it could result from decreases in the mean @xmath25 itself . in this section we assess the extent to which our inferred value for @xmath16 can distinguish between these possibilities .    to discuss variations in the electron density , we recast equation  ( [ eqn : sm ] ) in terms of the density and ionization and integrate over a path length @xmath32 , @xmath194 in this form , it is clear that there are three means by which the amount of scattering in the outer galaxy could be limited :    1 . @xmath195it is well known that the distribution of decreases at large galactocentric radii ( @xcite ) . outer galaxy scattering could be limited because there is simply not enough gas to be ionized and produce scattering . @xmath196this factor is the product of the fractional ionization , @xmath197 , and the volume filling factor , @xmath198 , of the ionized gas . if the number density of ionization sources , e.g. , regions and supernovae , decreases faster than does @xmath195 , the scattering would be limited by a lack of ionized gas , even though there would be sufficient amounts of neutral gas . we treat the product @xmath196 rather than @xmath198 and @xmath197 separately because our measurements can not distinguish between the two . changes in @xmath198 can be balanced by changes in @xmath199 so as to keep the product constant . 3 .   @xmath37this factor is a measure of the level of turbulence . since the rate of star formation does fall off toward the outer galaxy , unless alternate or additional sources of ionization are present in the outer galaxy , e.g. , the intergalactic ionizing flux , the scattering could be limited by a lack of turbulent energy input into the medium rather than the ionization . our motivation for assuming that sm is separable in this manner is to consider ionization and energy input mechanisms from sources not generally thought to be operative in the inner galaxy . we consider each of these factors in turn .      outside the solar circle atomic hydrogen dominates molecular hydrogen ( @xcite ) and we take @xmath200 . comparison of the emission measure ( @xmath201 ) and dm toward high - latitude pulsars suggest @xmath202 and @xmath203 ( @xcite ) . because we are assuming the strength of scattering in the outer galaxy is dominated by the decrease in the density , we take @xmath198 , @xmath197 , and @xmath37 to be constant as a function of @xmath67 . we estimate the quantity @xmath204 toward the anticenter using the mass models of dehnen & binney  ( 1997 ) . we are required to use a model to estimate this quantity because the self - opacity of toward the anticenter means that the column density is not an observable ( @xcite ) . our estimate is @xmath205  @xmath206  kpc . assuming that @xmath207 , the resulting sm is @xmath208 . this sm produces a 1  ghz scattering diameter of 40  mas , approximately 25 times larger than what we observe . we conclude that the distribution of electron density turbulence must decrease more rapidly with galactocentric distance than the distribution of hydrogen . this decrease may be due to an overall decrease in ionized gas or to a diminution of turbulence in the ionized gas . interior to @xmath209  kpc , the surface density is greater than @xmath210  @xmath12 ( @xcite ; @xcite ) and the disk is optically thick to the intergalactic ionizing flux . consequently , @xmath196 should increase with @xmath67 as the surface density and the disk s optical depth decrease . patchiness in the outer galaxy distribution would also increase @xmath196 .    as the previous section showed , if @xmath211 and is constant as a function of @xmath67 , the distribution overpredicts the scattering diameters . allowing @xmath196 to increase with @xmath67 would increase the size of this discrepancy . further , the scale length of the scattering is smaller than the galactocentric distance at which the disk becomes optically thin , indicating that the intergalactic ionizing flux does not play a significant role in the scattering in the outer galaxy . we favor star formation in the outer galaxy as the more likely source of ionization . wouterloot et al . ( 1990 ) showed that the distribution of molecular clouds with embedded massive star formation terminates at 20  kpc . this truncated distribution has an extent comparable to what our likelihood functions imply for the radial extent of scattering . the limited radial extent of the molecular clouds is also the reason we favor the truncated disk model to describe the radial dependence of scattering . figure  [ fig : ac.summary ] illustrates schematically the spatially coincident distributions of molecular clouds and turbulent gas in the outer galaxy . the factoring of the scattering measure into separate ionization and turbulent contributions , equation  ( [ eqn : sm_ii ] ) , ignores possible correlations between these factors : many of the same sources responsible for the ionization of the gas can also serve to produce turbulence , e.g. , regions and supernovae . we utilize this factoring in order to consider an alternate source of turbulence not associated with massive star formation . we conclude that turbulence is in fact associated with star formation . the orbits of the magellanic clouds cause them to cross the midplane of the disk . as these and other satellite galaxies cross the disk , they generate mixing layers and wakes . the eddy turnover time , which is related to the energy dissipation rate , is @xmath212 ( @xcite ) where @xmath213 is the outer scale of the turbulence and @xmath214 is a characteristic velocity . for @xmath215 pc ( @xcite ; @xcite ; and references within ) and @xmath216  km  s@xmath10 , @xmath217  yr . since the orbital period of a typical satellite galaxy is of order @xmath218  yr , the passage of a satellite galaxy through the outer disk will provide only a transitory source of turbulence . the distribution of molecular clouds with embedded massive star formation extends to 20  kpc ( @xcite ) , comparable to the extent of the extended ionized component . the stars embedded in these molecular clouds have spectral types of early b ( wouterloot , brand , & henkel  1988 ) . these stars are probably sufficiently powerful to produce turbulence : the pulsar b0611@xmath522 exhibits strong interstellar scintillation and the line of sight to it passes near several late o and early b stars ( @xcite ) . diffuse ionized gas in external galaxies has been detected in h@xmath1 emission ( @xcite and references within ) . this diffuse gas is presumably the equivalent of the galaxy s warm ionized medium ( @xcite ) . spangler & reynolds  ( 1990 ) showed that the scattering diameters for extragalactic sources are correlated with h@xmath1 emission , suggesting that the same ( warm ionized ) gas responsible for the h@xmath1 emission is also responsible for the scattering . in this section we compare the radial extent of the galaxy as inferred in our likelihood analysis with that determined for other galaxies . table  [ tab : external ] presents a subset of h@xmath1 measurements extracted from the literature . we restrict the list to those galaxies for which the published observations include images large enough that radial extents can be estimated reliably . the last entry in table  [ tab : external ] is our estimate , based on the likelihood results , for the radial extent of the galaxy as it would appear to an external observer . we have obtained this estimate in the following manner . the ( @xmath219 ) sensitivities for the h@xmath1 observations are typically @xmath220  @xmath206  pc . we integrated @xmath221 to produce the modelled em , @xmath222 , along a line of sight appropriate for an external observer seeing the galaxy edge on , i.e. , along the path parallel to the @xmath55-axis ( the discussion following eqn . [ [ eqn : ne ] ] describes the coordinate system ) . trial and error was sufficient to determine that , for a truncated disk , @xmath223 at @xmath224 . the radial extent of the galaxy is comparable to the radial extent of these other galaxies .    a measure of the star formation rate of the galaxy is provided by @xmath225 , the far - infrared luminosity within the optical isophotal diameter at @xmath226 magnitude . this is an imperfect measure of the star formation rate , however , as low - mass stars heating `` cirrus '' clouds can contribute to the far infrared luminosity ( @xcite ) and the optical and infrared luminosities may have different extents . although the star formation rate , as measured by @xmath225 , is a good predictor of the amount of extraplanar gas ( @xcite ) , it is not well correlated with the radial extent of h@xmath1 . for instance , the radial extent of ngc  4217 is only 25% ( 4  kpc ) smaller than that of ugc  10288 even though the star formation rate is at least a factor of three higher in ugc  10288 ; ngc  5746 has a radial extent larger than that of the galaxy even though its star formation rate is an order of magnitude less than the galaxy s . more likely , the star formation rate is determined by a quantity like the or h@xmath227 surface density .    further support for our proposal that our measurements trace the extent of the turbulent ionized disk is found by comparing the h@xmath1 emission in external galaxies ( @xcite , figs . 19 ) with the molecular cloud distribution in the outer galaxy ( @xcite , fig .  4 ) . the h@xmath1 emission is concentrated toward the galaxies centers with a gradient to large radial distances . near the edge of the h@xmath1 disk , the emission becomes patchy . the molecular cloud distribution in the outer galaxy has a similar appearance  it display a strong galactocentric gradient and , for @xmath22820  kpc , the distribution is patchy .    high latitude structure in the extended component could influence our estimates for the various model parameters , in particular @xmath86 ,  [ sec : ac.results ] . the morphology of the extraplanar diffuse gas in external galaxies shows considerable variety : ngc  891 shows diffuse gas up to 4  kpc off the plane with many vertical filaments ( rand , kulkarni , & hester  1992 ) ; ugc 10288 shows vertical filaments but no diffuse gas ( @xcite ) ; ngc  4278 shows patchy emission ( @xcite ) ; and ngc  4565 shows little halo diffuse gas ( @xcite ) . h@xmath1 observations of the diffuse gas in the solar neighborhood show filamentary structure ( @xcite ) and the vertical morphology of the extended component could be quite complex . we have modified the outer galaxy portion of the taylor - cordes model for the global distribution of ionized gas . our modifications are motivated by the observed warping and flaring of the , h@xmath227 , and stellar constituents of the outer galaxy . the data available to constrain the model consist of 18 sources , 9 extragalactic sources from a survey we conducted ( @xcite ) and 7 pulsars and 2 extragalactic source extracted from the literature ( table  [ tab : literature ] ) . we used a likelihood analysis to constrain the model parameters . the two most important parameters are the radial scale length of the ionized disk , @xmath16 and the strength of scattering in the perseus arm . the adopted model parameters are summarized in table  [ tab : params ] . the scattering in the perseus arm is , at most , 60% of the level seen in the inner galaxy spiral arms . this upper limit assumes that all of the scattering for sources toward @xmath229 is due to the perseus arm . our analysis favors a level of scattering less than this upper limit . we adopt a value 25% that in the inner galaxy ; the equivalent scattering diameter is 1.5  mas at  1  ghz . we considered two different radial dependences for the electron density , a smooth decrease of the electron density with galactocentric distance , equation  ( [ eqn : radial1 ] ) , and a truncated distribution , equation  ( [ eqn : radial2 ] ) . the current data can not distinguish between these two forms . the radial scale length for the ionized disk is @xmath18020  kpc , comparable to the extent that @xcite adopted with fewer anticenter measurements . we favor the truncated disk because the radial extent inferred for sites of massive star formation also appears truncated at approximately 20  kpc , as indicated schematically in fig . [ fig : ac.summary ] . h@xmath1 observations of external galaxies show that they have radial extents comparable to that which we infer for the galaxy . the observed scattering diameter of one extragalactic source ( 87 gb  0600@xmath52957 ) is a factor of two smaller than the modelled scattering diameter , suggesting the possibilities of holes in the scattering material . the h@xmath1 emission in the outer portions of the disks of these external galaxies also appears patchy , similar to the distribution of molecular clouds in the outer galaxy . a patchy distribution of massive star formation sites would allow the possibility of holes in the scattering material . we conclude that scattering in the outer galaxy traces star formation , as it does in the inner galaxy . the intergalactic ionizing flux and turbulence generated by satellite galaxies passing through the disk contribute little to the scattering . however , the ionized disk of the galaxy could extend to much larger radii ( @xmath230  kpc ) , comparable to that inferred from ly@xmath1 absorption systems ( e.g. , @xcite ) , if the extreme outer disk is quiescent and contributes little scattering . we thank p.  goldsmith , d.  chernoff , and t.  herter for helpful conversations . we thank the referee for a suggestion that led to fig .  [ fig : decon ] . this research has made use of the simbad database , operated at the cds , strasbourg , france . this research was supported by nasa gro grants nag  5 - 2436 and nag  5 - 3515 and nsf grant ast-9528394 . 87 gb  0433@xmath54706 & 157.3 & @xmath2310.0 & @xmath2324887 gb  0451@xmath54309 & 162.5 & @xmath2310.1 & @xmath2325.1 87 gb  0512@xmath52627 & 178.5 & @xmath2316.6 & @xmath2326.8 87 gb  0537@xmath53059 & 177.9 & 0.2 & @xmath2323.7 87 gb  0547@xmath53044 & 178.9 & 1.8 & @xmath2326.1    87 gb  0558@xmath52325 & 186.5 & 0.3 & 3.7@xmath2330.8 87 gb  0600@xmath52957 & 180.9 & 4.0 & 1.5@xmath2330.4 87 gb  0621@xmath51219 & 198.8 & @xmath2310.4 & 2.8@xmath2330.1 87 gb  0622@xmath51153 & 199.4 & @xmath2310.3 & @xmath23218      psr  b0301@xmath519 & 161.14 & @xmath23133.27 & 9.55@xmath2332.4 & 0.29@xmath2330.097 & 0.94 & 1 psr  b0320@xmath539 & 152.18 & @xmath23114.33 & 2.291@xmath2330.77 & 0.46@xmath2330.15 & 1.47 & 1 psr  b0450@xmath555 & 152.62 & 7.54 & 9.55@xmath2332.4 & 0.29@xmath2330.097 & 0.78 & 1 psr  b0525@xmath521 & 183.86 & @xmath2316.89 & 0.62@xmath2330.2 & 0.72@xmath2330.24 & 2.27 & 1 psr  b0531@xmath521 & 184.60 & @xmath2315.80 & & 0.50@xmath2330.05 & 2.0 & 4    psr  b0540@xmath523 & 184.36 & @xmath2313.31 & 0.11@xmath2330.03 & 1.4@xmath2330.47 & 3.53 & 1 psr  b0611@xmath522 & 188.79 & 2.39 & 0.04@xmath2330.01 & 2.0@xmath2330.67 & 4.72 & 1 psr  b0626@xmath524 & 188.82 & 6.22 & 0.08@xmath2330.02 & 1.4@xmath2330.47 & 4.69 & 1 psr  b0656@xmath514 & 201.11 & 8.25 & 8.51@xmath2332.1 & 0.34@xmath2330.11 & 0.76 & 1 psr  b0823@xmath526 & 196.96 & 31.74 & 9.55@xmath2332.4 & 0.29@xmath2330.097 & 0.37 & 1","summary":"we find that the strength of scattering in the perseus arm is no more than 60% of the level contributed by spiral arms in the inner galaxy and is equivalent to a scattering diameter of 1.5  mas at  1  ghz . one extragalactic source has a size a factor of two smaller than predicted by our model , possibly indicating the existence of holes in the scattering material . the radial scale length is 1520  kpc , but the data can not distinguish between a gradual decrease in the electron density and a truncated distribution . we favor a truncated one , because we associate the scattering with massive star formation , which is also truncated near 20  kpc . a radial extent of 20  kpc is also comparable to the radial extent of h emission observed for nearby spiral galaxies . we find that the distribution of electron density turbulence must decrease more rapidly with galactocentric distance than the distribution of hydrogen . alternate ionizing and turbulent agents  the intergalactic ionizing flux and the passage of satellite galaxies through the disk  are unlikely to contribute significant amounts to scattering in the anticenter . we can not exclude the possibility that a largely ionized , but quiescent disk extends to  kpc , similar to that inferred for some ly absorbers .","abstract":"we use radio - wave scattering data for extragalactic sources and pulsars to constrain the distribution of ionized gas in the outer galaxy . like previous models , our model for the disk includes parameters for the radial scale length and scale height of the ionized gas . in addition , we have used the known distribution in the outer galaxy in constructing our model , and we allow the disk to warp and flare . we also include the perseus arm in our model . we use a likelihood analysis on 18 anticenter sources with measured scattering observables : 11 extragalactic sources and 7 pulsars . we find that the strength of scattering in the perseus arm is no more than 60% of the level contributed by spiral arms in the inner galaxy and is equivalent to a scattering diameter of 1.5  mas at  1  ghz . our analysis favors an unwarped , non - flaring disk with a scale height of 1  kpc , though this may reflect the non - uniform and coarse coverage of the anticenter provided by the available data . one extragalactic source has a size a factor of two smaller than predicted by our model , possibly indicating the existence of holes in the scattering material . the lack of a warp in the scattering material indicates that vlbi observations near 1  ghz with an orbiting station having baseline lengths of a few earth diameters will not be affected by interstellar scattering at moderate galactic latitudes , . the radial scale length is 1520  kpc , but the data can not distinguish between a gradual decrease in the electron density and a truncated distribution . we favor a truncated one , because we associate the scattering with massive star formation , which is also truncated near 20  kpc . a radial extent of 20  kpc is also comparable to the radial extent of h emission observed for nearby spiral galaxies . we find that the distribution of electron density turbulence must decrease more rapidly with galactocentric distance than the distribution of hydrogen . alternate ionizing and turbulent agents  the intergalactic ionizing flux and the passage of satellite galaxies through the disk  are unlikely to contribute significant amounts to scattering in the anticenter . we can not exclude the possibility that a largely ionized , but quiescent disk extends to  kpc , similar to that inferred for some ly absorbers ."}
{"article_id":"cond-mat0101256","section_id":"i","document":"in 1996 m. isobe and y. ueda@xcite published magnetic susceptibility measurements of @xmath0-nav@xmath1o@xmath2  powder samples , proposing the existence of linear antiferromagnetic spin-1/2 chains and a possible spin - peierls transition at a critical temperature , t@xmath6  =  34  k. the original picture of the charge ordering in this mixed valence ladder compound was that of alternating legs of v@xmath7 and v@xmath8 ions.@xcite however , a recent determination of the crystal structure using single crystal x - ray diffraction at room temperature@xcite yielded only one symmetrically inequivalent vanadium ( v@xmath9 ) position . due to the observed one - dimensional character of the spin and charge system at room temperature - which was by that time also confirmed by inelastic neutron scattering@xcite and angle - resolved photoemission experiments@xcite - the picture of linear chains of v - o - v rungs containing a single @xmath10-electron in a molecular orbital - like state with antiferromagnetic alignment along the ladders has increasingly won recognition . below t@xmath6 charge ordering has been observed in @xmath11v nmr studies,@xcite but the ordering pattern has not yet been defined . calculations of the electronic ground state@xcite have predicted a zig - zag charge ordering along the ladders and only lately , with the support of the most recent experimental data@xcite does the evidence for zig - zag order appear to outweigh that for more complicated order patterns.@xcite nevertheless , there remain a number of important , open questions such as the nature of the correlations between the charges and spins which are the driving force for the observed charge ordering and which make the system insulating .    the electronic structure of @xmath0-nav@xmath1o@xmath2  has been intensively studied experimentally by means of optical absorption@xcite and reflectivity,@xcite as well as theoretically within the framework of bandstructure calculations @xcite and exact diagonalization techniques.@xcite nevertheless , there is a controversial discussion about the origin of the electronic excitations in this system . for example , concerning the absorption peak occurring at about 1  ev in optics , transitions between bonding and antibonding combinations of v  3@xmath4 states,@xcite transitions between vanadium states of different symmetry@xcite as well as on - site @xmath12 transitions between crystal - field - split vanadium 3@xmath10 states@xcite have been proposed as the origin of this feature . furthermore , the information from the experiments still appears to be insufficient to enable the definition of a unique parameter set for the description of the electronic structure of @xmath0-nav@xmath1o@xmath2 . in particular , independent of which theoretical model was used , significantly different values for the on - site coulomb repulsion u , the inter - site coulomb repulsion @xmath13 between electrons on legs of adjacent ladders and the hopping parameter @xmath14 have been discussed in the literature ( for a comparison see table  [ parameters ] ) . since the charge ordering as well as the charge transport properties strongly depend on the energies described by these parameters , a more exact determination of their values could lead to a better understanding of the electronic properties of @xmath0-nav@xmath1o@xmath2 .    in this contribution , we present a joint experimental and theoretical investigation of the electronic excitations and their momentum dependence in @xmath0-nav@xmath1o@xmath2 measured using high resolution electron energy - loss spectroscopy in transmission . the comparison of the data with models based both on the lsda+u formalism , as well as a cluster approach , enable the construction of a consistent theoretical description of the electronic structure of @xmath0-nav@xmath1o@xmath2 and result in the determination of a double - checked parameter set . the paper is organized as follows . in sec . ii the experimental and theoretical methods are introduced . section iii contains the presentation and discussion of the experimental and theoretical results and is split into sub - sections dealing with the different aspects of the data . lastly , sec . iv is a summary .","summary":"we have studied the electronic properties of the ladder compound-navo adopting a joint experimental and theoretical approach . the momentum - dependent loss function was measured using electron energy - loss spectroscopy in transmission . in addition , we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model .","abstract":"we have studied the electronic properties of the ladder compound-navo adopting a joint experimental and theoretical approach . the momentum - dependent loss function was measured using electron energy - loss spectroscopy in transmission . the optical conductivity derived from the loss function by a kramers - kronig analysis agrees well with our results from lsda+ band- structure calculations upon application of an antiferromagnetic alignment of the v  3 spins along the legs and an on - site coulomb interaction of between 2 and 3  ev . the decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the dos reveals the origin of the observed anisotropy of the optical conductivity . in addition , we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model . good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band - structure and moderate coulomb interactions between the electrons within the plane ."}
{"article_id":"cond-mat0101256","section_id":"m","document":"single crystals of @xmath0-nav@xmath1o@xmath2  were grown from the melt . the detailed procedure is described elsewhere.@xcite @xmath0-nav@xmath1o@xmath2  crystallizes in an orthorhombic unit cell with lattice constants , and .@xcite the vanadium atoms and their five nearest neighbor oxygen atoms build slightly distorted vo@xmath2 pyramids which are connected by their corners along the * b * direction as well as by their corners and edges along the * a * direction , as shown in fig . [ structure]a . the resulting pyramid layers in the ab - plane are separated by sodium atoms . the weak interactions between the vanadium oxide layers and the sodium layers are the reason for the good cleavage behavior of this system along the plane perpendicular to the * c * direction . the projection of the vanadium and the oxygen atoms of a single pyramid layer onto the @xmath5 plane , excluding the oxygen atoms on the apices of the pyramids , delivers the atomic configuration as illustrated in fig . [ structure]b . this approach emphasizes the ladder structure in which adjacent ladders are shifted with respect to each other by half of the lattice parameter b in the * b * direction ( see dashed lines in fig .  [ structure]b ) .    for the measurements using electron energy - loss spectroscopy in transmission , thin films of about 1000   thickness were cut from the single crystals with a diamond knife using an ultramicrotome . because of the good cleavage behavior , the crystallinity remains conserved after cutting parallel to the @xmath5 plane . the high quality and orientation of the single crystalline samples were checked by _ in  situ _ electron diffraction . eels in transmission with a primary beam energy of 170 kev was performed on free standing films at room temperature ( for experimental details see ref . ) . the energy and momentum transfer ( q ) resolution were chosen to be 110 mev and 0.05 @xmath15 for q @xmath16 0.4 @xmath15 , and 160 mev and 0.06 @xmath15 for q @xmath17 0.4 @xmath15 , in order to compensate for the decrease of the cross section at higher momentum transfer . eels in transmission provides us with the momentum and energy dependent loss function im(- 1/@xmath18(@xmath19 , @xmath20 ) ) , from which , by means of the kramers - kronig relations , the real part of the negative inverse dielectric function and thus all the optical properties such as , for example , the optical conductivity @xmath21 can be calculated . for small momentum transfer only dipole transitions are allowed , and for the limit q = 0 the transition matrix elements are the same as in optics . for the kramers - kronig analysis the loss spectra closest to the optical limit ( q = 0.1 @xmath15 ) were used in order to derive the optical conductivity spectra . the band structure of @xmath0-nav@xmath1o@xmath2  was calculated self - consistently using the scalar - relativistic lmto method @xcite in the atomic sphere approximation with the combined correction taken into account ( asa+cc ) . the von barth - hedin parameterization @xcite was used for the exchange - correlation potential constructed in the local spin density approximation . the brillouin zone ( bz ) integrations in the self - consistency loop were performed using the improved tetrahedron method . @xcite the experimental lattice parameters and atomic positions as determined for the high temperature phase ( ref .  ) were used in the calculations . the angular momentum expansion of the basis functions included @xmath22 for vanadium and sodium and @xmath23 for oxygen and the empty spheres.@xcite the o  3@xmath10 and the v  4@xmath24 states were included in the basis , as they give a significant contribution to the dipole matrix elements of the optical transitions .    in order to account for the strong electronic correlation at the v sites , we used the lsda+@xmath3 method in the band structure calculations @xcite , which has been shown to be very helpful for the description of the electronic structure of transition metal oxides , in which the 3@xmath10 orbitals hybridize quite strongly with the oxygen 2@xmath25 orbitals ( for a review see ref .  ) . in this method a hubbard - like term is added to the lsda total energy functional : @xmath26 where @xmath27 is the lsda energy functional , @xmath28 takes into account the on - site coulomb and exchange interactions , and @xmath29 is necessary to avoid the double counting of the averaged coulomb and exchange interactions already included in @xmath27.@xcite if non - spherical contributions to the on - site coulomb and exchange integrals @xmath3 and @xmath30 are neglected , the @xmath28 term can be written as : @xmath31 where @xmath32 is the occupancy of the @xmath33-th localized orbital with the spin projection @xmath34 . the localized orbitals used in ( [ eq : eu ] ) are constructed in such a way that they diagonalize the charge density matrix @xmath35 . then , the expression for the orbital dependent one - electron potential corresponding to ( [ eq : ldau ] ) is given by : @xmath36 where @xmath37 is the projector onto the localized orbital . the absorptive part of the optical conductivity tensor components was computed from the lmto energy bands and eigenvectors on the basis of the linear - response expressions,@xcite whereas the dispersive part was obtained via the kramers - kronig transformation . the finite - lifetime effects and the experimental resolution were simulated by broadening the calculated dielectric tensor spectra with a lorentzian width of 0.2  ev . as mentioned in the introduction , @xmath0-nav@xmath1o@xmath2  can be considered as composed of linear chains of v - o - v rungs containing a single @xmath10- electron in a molecular orbital - like state with antiferromagnetic alignment along the ladders . for the lsda+@xmath3 calculations presented here , initially an antiferromagnetic ( afm ) order of each of the v spins along the leg of the ladder is assumed . we have also carried out a brief analysis of the influence of deviations from this afm order upon the calculated dos and optical conductivities by means of spin - waves . the band structure calculations for non - collinear magnetic structures including constrained moment directions were performed using the formalism developed in the refs .   and . the magnetization direction in the atomic sphere surrounding the site @xmath38 , where @xmath39 is its position in the unit cell and @xmath40 is a real space lattice vector , is defined by two polar angles @xmath41 and @xmath42 . if @xmath41 does not depend on @xmath40 and @xmath42 is given by @xmath43 ( @xmath44 determines the relative orientation of the magnetization directions for different sublattices ) , the calculations can be performed without an enlargement of the unit cell for an arbitrary vector @xmath45 , which defines a spiral magnetic structure in real space . ( in the present paper we adopted the notation @xmath46 instead of the usually used character @xmath19 to distinguish the vector of a spiral structure from the momentum transfer vector in the eels measurements ) . the details of the @xmath3 calculations for spiral magnetic structures will be given elsewhere.@xcite here we only mention that in this case the effective orbital dependent potential is still given by equation ( [ eq : vldau ] ) but with the spin part of a localized orbital @xmath47 centred at a given atomic site being defined in the local coordinate system with the @xmath48 axis parallel to the magnetization direction in the corresponding atomic sphere .      we have studied the dynamic dielectric response using a quarter - filled @xmath49-@xmath30-@xmath50 model @xmath51 where @xmath52 are constrained electron creation operators , @xmath53 is the occupation - number operator , and @xmath54 denotes the spin-@xmath55 operator at site @xmath33 . the expression @xmath56 denotes the summation over all pairs of nearest neighbors . the hopping parameters @xmath57 , intersite coulomb interactions @xmath58 , and exchange interactions @xmath59 are defined in fig . [ ebene ] . the loss function measured in eels experiments is directly proportional to the dynamic density - density correlation function.@xcite by including the long - range coulomb interaction in the model within a random - phase approximation ( rpa ) one finds for the loss function @xmath60,\\label{lost}\\end{aligned}\\ ] ] where @xmath61|0      \\rangle e^{i\\omega t}\\end{aligned}\\ ] ] is the response function at zero temperature for the short - range interaction model described by eq . ( [ hamilton ] ) . @xmath62 depends on the energy loss @xmath20 and momentum transfer @xmath19 . @xmath63 is the ground state , @xmath64 denotes the fourier transform of @xmath65 , and @xmath66 is the long - range coulomb potential with unit cell volume @xmath67 . furthermore , @xmath68 is the number of electrons per unit cell , @xmath69 is the permittivity , and @xmath70 is the real part of the dielectric function . we evaluated eq . ( [ lost ] ) by direct diagonalization using the standard lanczos algorithm.@xcite as this method is limited to small clusters , the maximum cluster size in our calculations was restricted to 16 vanadium sites . however , calculations for a cluster consisting of two adjacent ladders , each containing four rungs , showed strong finite - size effects . we have solved this problem by using two different clusters for momentum transfer parallel to * a * and * b * direction , as denoted in fig . [ ebene ] by the filled circles . in the * a * direction we chose an array of double rungs extending over four adjacent ladders , whereas in the * b * direction the cluster consisted of a single ladder with eight rungs . the separation into these two clusters is justified by the small value of the interladder hopping amplitude @xmath71  ev ( details will be given elsewhere@xcite ) . this value of @xmath14 has also been found by previous lda calculations@xcite , as well as from a tight binding fit to our own lda results.@xcite additional evidence for a small @xmath14 follows from the weak magnetic dispersion along the * a * direction as observed in neutron scattering experiments.@xcite    for the calculation of the loss function we chose open boundary conditions , and for momentum transfer parallel to the * a * direction we used renormalized intersite coulomb interactions @xmath72 and @xmath73 . these values follow from a straightforward analysis of the influence of adjacent rungs of the same ladder on the electronic states.@xcite furthermore , in the case of open boundary conditions one has to make sure that electrons on the edges of the cluster are still embedded in the local coulomb potential that results from a zig - zag charge ordered state . thus , sites on the edge of the cluster for momentum transfer parallel to the * a * direction are assigned an additional on - site energy @xmath13 . by analogy , sites on the edges of the cluster for * q * parallel to the * b * direction need an additional on - site energy @xmath74 , if they are not occupied in a zig - zag charge ordered state .","summary":"the optical conductivity derived from the loss function by a kramers - kronig analysis agrees well with our results from lsda+ band- structure calculations upon application of an antiferromagnetic alignment of the v  3 spins along the legs and an on - site coulomb interaction of between 2 and 3  ev .","abstract":"we have studied the electronic properties of the ladder compound-navo adopting a joint experimental and theoretical approach . the momentum - dependent loss function was measured using electron energy - loss spectroscopy in transmission . the optical conductivity derived from the loss function by a kramers - kronig analysis agrees well with our results from lsda+ band- structure calculations upon application of an antiferromagnetic alignment of the v  3 spins along the legs and an on - site coulomb interaction of between 2 and 3  ev . the decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the dos reveals the origin of the observed anisotropy of the optical conductivity . in addition , we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model . good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band - structure and moderate coulomb interactions between the electrons within the plane ."}
{"article_id":"cond-mat0101256","section_id":"r","document":"we have measured the energy dependent loss functions for different momentum transfers * q * parallel to the crystallographic * a * and * b * direction in an energy range between 0.5  ev and 70  ev . due to the contribution of the elastic line and surface losses it is not possible to measure at zero momentum transfer but close to the optical limit ( q  =  0.1  @xmath15 ) . in fig . [ optlim ] the loss functions with momentum transfer * q *  =  0.1  @xmath15 parallel to the * a * ( solid line ) and the * b * direction ( dashed line ) are shown . both spectra are dominated by a broad feature at around 23  ev which represents the volume plasmon - a collective excitation of the valence electrons . while the feature at 50  ev results from local excitations between the v  3@xmath25 and the v  3@xmath10 states , the features emerging below the volume plasmon energy can be assigned to transitions of the valence electrons into the conduction band . as fig . [ optlim ] shows , an anisotropic behavior is only visible in the low energy regime ( @xmath16  22  ev ) .    in order to compare the spectra with results derived from our lsda+@xmath3 calculations , we have calculated the optical conductivity , @xmath34 , by performing a kramers - kronig analysis ( kka ) . the comparison with the optical conductivity of the structurally related v@xmath1o@xmath2 ( d@xmath75 configuration ) obtained with the same method,@xcite shows that above @xmath765  ev the spectra of both compounds look very similar ( not shown ) . in ref . , the anisotropy of the loss function and of the optical conductivity of v@xmath1o@xmath2 are discussed in detail . as a result , the features above 5  ev can be assigned to transitions from occupied bands with mainly oxygen character into unoccupied bands which are dominated by the v  3@xmath10 states . from the resemblance of the spectra and the related crystal structures of both compounds we conclude that the same holds for @xmath0-nav@xmath1o@xmath2 . thus , in this work we focus on the energy range below 5  ev where the loss functions and , consequently , the optical conductivities of @xmath0-nav@xmath1o@xmath2  differ strongly from those of v@xmath1o@xmath2 .      in comparison to v@xmath1o@xmath2 , which has a similar network of linked vo@xmath2 pyramids , the na atom in @xmath0-nav@xmath1o@xmath2  donates an additional electron to the valence band . since in v@xmath1o@xmath2 the bands formed by the o 2@xmath25 states are essentially completely filled and the energetically lowest lying unoccupied bands are formed by the v  3@xmath4 states , @xcite the additional electron in @xmath0-nav@xmath1o@xmath2  goes into the rather localized v  3@xmath4 states . these states determine , to a great extent , the fascinating properties of this compound . due to the localized nature of the v  3@xmath10 electrons , the coulomb correlations between them are rather strong and , as a consequence , conventional l(s)da calculations fail to describe properly the electronic structure of @xmath0-nav@xmath1o@xmath2 . in the unit cell corresponding to the centrosymmetric @xmath77 structure of the high temperature phase , a non - magnetic metallic solution is obtained , in contradiction to the experimental data . one way to overcome this discrepancy is to introduce an antiferromagnetic ( afm ) order of v magnetic moments along the * b * direction . this leads to a doubling of the unit cell and the opening of an energy gap in the lsda band structure . however , the value of the energy gap is still strongly underestimated . it should , however , be borne in mind there is no experimental evidence for the existence of afm order in @xmath0-nav@xmath1o@xmath2  even at low temperatures .    an efficient way to take the strong correlations in the v  3@xmath10 shell into account is to use the lsda+@xmath3 approach . however , this method is usually applied to ordered compounds and thus an additional assumption has to be made in order to study the electronic structure and the optical properties of the high temperature phase of @xmath0-nav@xmath1o@xmath2 . since , according to the experimental data , there is no charge ordering above @xmath78 and all v sites are equivalent,@xcite we have assumed that the effective one electron potential at each v site is the same and equal to the average of the lsda+@xmath3 potentials for v@xmath7 and v@xmath8 ions . in other words , the orbital dependent potential is calculated using the occupation numbers averaged formally over the v@xmath7 and v@xmath8 orbital occupation numbers . on application of @xmath3 , the partially occupied v @xmath4 orbitals are the most affected . the average occupation of the majority - spin @xmath4 orbitals is close to 0.5 and their energy position remains unchanged as compared to lda , whereas the unoccupied minority - spin @xmath4 orbitals are shifted upwards by @xmath79 . as a result , an insulating behavior - with the magnetic moment of 0.5 @xmath80 per v atom - or 1 @xmath80 per rung - is immediately obtained , which is independent of the kind of magnetic order which is assumed along the * b * axis . one can say that the on - site coulomb repulsion effectively suppresses the occupation of the @xmath4 orbitals with the opposite spin at each rung .    the effect of the absence , in reality , of long range afm order in the high temperature phase of @xmath0-nav@xmath1o@xmath2  on the electronic structure and optical properties was modelled by performing calculations for spin waves defined by a vector @xmath81 with @xmath82 varying from 0.5 ( corresponding to afm order of v magnetic moments along the * b * direction ) , to 0 at which all v magnetic moments are ferromagnetically aligned . in these calculations all @xmath83 were set to zero , whereas the @xmath44 were chosen in such a way that the v ions situated at the same rung had the same magnetization direction . we found that the relative orientation of the magnetization at v sites of neighbouring ladders , which is also determined by @xmath44 , has only minor effect on the calculated band structure . the calculations were iterated to self - consistency for @xmath84 and then one iteration was performed for spin waves with other values of @xmath82 . the comparison of the band energies confirmed that the ground state of the system is antiferromagnetic , in accordance with previous estimates for the exchange coupling constants between v spins in the * b * direction . the densities of the v  3@xmath10 and o  2@xmath25 states , calculated for @xmath85  =  3  ev and an afm order of the v magnetic moments along the * b * direction are shown in fig . [ dos ] . in fig . [ dos]b , the density of v  3@xmath10 states calculated for @xmath86 ( dashed lines ) is also shown . here , and in the following , we assume that the magnetic moments of the v ions situated at the same rung are ferromagnetically ordered . the overall structure of the dos is similar to that of v@xmath1o@xmath2.@xcite the states in the energy range from -6.5 to -2  ev are formed mainly by the o  2@xmath25 states ( fig . [ dos]a ) with a bonding hybridization with the v  3@xmath10 states . the v  @xmath87 states dominate in the 1.83  ev range , while the states with v  @xmath88 and v  @xmath89 character are shifted to higher energies due to the comparatively strong hybridization with o  2@xmath25 states and form the upper part ( @xmath90  ev ) of the conduction band , shown in fig . the main differences in the structure of the dos as compared to v@xmath1o@xmath2 are caused by the additional electrons occupying the v  @xmath4 bands which are empty in the case of v@xmath1o@xmath2 . since the change in the occupation of the v  @xmath4 states is the main source of the differences between the optical spectra and other physical properties of these compounds , in the following we will focus our attention on the states originating from the v  @xmath4 orbitals . the narrow peak in the majority - spin v  3@xmath10 dos just below the fermi level ( fig .  [ dos]b ) originates from a combination of the 3@xmath4 orbitals of the two v atoms on the same rung which is orthogonal to the 2@xmath91 orbital of the o@xmath92 atom in the center of the rung . the corresponding antibonding v  3@xmath4o@xmath92  2@xmath91 states are responsible for the dos peak at 1  ev . in terms of the effective v  v hopping these two peaks result from the bonding and antibonding combination of the v  3@xmath4 states , respectively , and the energy separation between them is determined by @xmath93  =  0.38  ev acting across the rung . here , for the effective v  v hopping terms we use the values obtained from a tight binding fit to the lda band structure calculated with the lmto method , @xcite which were found to be very close to the hopping parameters determined in ref .  . the minority spin @xmath94 states of bonding character are shifted to higher energy by the effective coulomb repulsion and lie above the antibonding @xmath95 peak . while the energy of the latter is governed by @xmath93 and thus does not depend on @xmath85 , the relative position of the minority spin @xmath94 states does depend on the exact value of @xmath85 . finally , the peak at @xmath762.5  ev arising from the antibonding @xmath94 states is almost lost in the contributions from the other states of the conduction band , mainly formed by the remaining v  3@xmath10 states hybridized with o  2@xmath25 states . it should be noted that for both spin directions the width of the bonding @xmath4 peaks in the lsda+@xmath3 calculations is much smaller than 0.7  ev , the value obtained from lda calculations , because the relatively strong hybridization along the * b * direction governed by @xmath96  =  0.17  ev is suppressed due to the afm order . however , as @xmath82 - which defines the magnetic structure along the * b * direction - decreases , the width of the peaks increases and reaches the lda value when the v magnetic moments are ordered ferromagnetically . as for the antibonding @xmath4 states , the dispersion of the corresponding bands along the @xmath97@xmath98 direction is much weaker already in lda @xcite and the width of their dos does not depend on @xmath82 .      in order to verify our theoretical results we turn our attention to the optical data . in fig . [ th+exp ] , the optical conductivity , derived by means of a kramers - kronig analysis of the eels spectra measured at low momentum transfer ( * q * = 0.1   ) , aligned either parallel to the crystallographic * a * or * b * direction ( figs . [ th+exp]a and [ th+exp]b ) is shown , together with @xmath99 and @xmath100 calculated for @xmath84 using the lsda ( @xmath101 ) and lsda+@xmath3 with @xmath102 and 3  ev ( figs . [ th+exp]c and [ th+exp]d ) . our experimental spectra agree well with the previous results derived from reflectivity@xcite and absorption@xcite measurements of @xmath0-nav@xmath1o@xmath2 . comparing @xmath99 with the * q*@xmath103*a * experimental data ( figs . [ th+exp]a and [ th+exp]c ) , one can see that for this polarization the theoretical spectra are only weakly affected by @xmath3 and thus that the lsda curve agrees well with the experimental one . the calculated position of the low energy peak in @xmath99 centred at 1  ev does not depend on @xmath3 , and coincides almost perfectly with the position of the corresponding experimental maximum . however , the calculations overestimate the magnitude of the peak and fail to reproduce accurately its asymmetric shape . the peak corresponding to the experimental feature at 3.4  ev lies at slightly lower energy in the lsda calculations and shifts upwards to @xmath763.7  ev with increasing @xmath3 .    for @xmath100 ( figs . [ th+exp]b and [ th+exp]d ) , the situation is quite different . in this case the lsda calculations result in an optical gap of 0.2  ev , which is significantly smaller than the experimental value ( 0.7  ev ) . in contrast to @xmath99 , the position of the low energy peak in @xmath100 is sensitive to @xmath3 , and gets close to the experimental value for @xmath104  ev . a less strong but still noticeable dependence on @xmath3 can be found in the energy range between 2.5 and 4  ev . comparing the theoretical spectra calculated with different values of @xmath85 to the experimental ones , one can conclude that the best overall agreement between the theory and the experiment is achieved for @xmath85 lying in the range between 2 and 3  ev . this range for @xmath85 derived from the lsda+u calculations gives an important guideline for the u value taken in the cluster model calculations which will be presented later in the paper . the observed correspondence between the calculated and the experimental spectra allows us to draw additional information from the detailed analysis of the theoretical spectra . in order to understand better the origins of the features of the optical conductivity and the reasons for their different dependence on the value of @xmath3 , we analyzed the contributions to the optical conductivity originating from the interband transitions between the initial and final states of v  3@xmath4 character . in fig . [ sigmas ] we show the results of a decomposition of @xmath99 and @xmath100 , calculated with @xmath85  =  3  ev . in each case , the thin solid line marks the sum of all the contributions - i.e. the total optical conductivity . figs . [ sigmas]a and [ sigmas]c show the calculations for @xmath99 , and figs . [ sigmas]b and [ sigmas]d for @xmath100 . starting with the top two panels ( figs . [ sigmas]a and [ sigmas]b ) , the areas shaded grey indicate spectral weight connected with transitions starting from the occupied v  3@xmath4 bands . thus , it is clear that the lowest lying peaks in both @xmath99 and @xmath100 are derived from transitions involving v  3@xmath4 _ initial _ states . the higher lying spectral weight , however , involves transitions starting from o  2@xmath25 states ( i.e. the majority of the total @xmath34 at higher energy is unshaded ) . we turn now to an analysis of the final states involved ( see figs .  [ sigmas]c and [ sigmas]d ) . in the lower panels of the figure we code the various final state characters with different shading : ( i ) the antibonding v  3@xmath95 final states are depicted as light grey ; ( ii ) the bonding v  3@xmath94 final states are depicted as dark grey and ( iii ) the hatched areas show the contributions from interband transitions into higher lying v  3@xmath10 states .    on comparing the top and bottom panels of fig . [ sigmas ] we can therefore conclude the following about the transitions giving rise to the optical conductivity . firstly , the 1 ev peak in @xmath99 is due to a transition between bonding and antibonding hybrids involving the v  @xmath4 levels of equal spin direction . as was mentioned above , the bonding  antibonding splitting of @xmath4 states is determined only by the hybridization within a rung and is thus _ not _ affected by @xmath3 .    secondly , for momentum transfer parallel to the * b * direction , the matrix elements for the bonding - antibonding transitions are zero . in this case , transitions between bonding v  @xmath4 levels with opposite spin become active . the energy position of these transitions is sensitive to the strength of the on - site coulomb interaction , which naturally explains the strong dependence of the position of the low energy peak in @xmath100 on the value of @xmath3 observed in fig . [ th+exp ] . in the language of a many - body approach , the @xmath105 transitions can be thought of as excitations which lead to the creation of doubly occupied rungs.@xcite    having dealt with the low - lying features of the optical conductivity , we now turn our attention to the energy range between 3 and 4  ev . in this context , the lack of grey shaded weight in figs . [ sigmas]a and [ sigmas]b illustrates that the initial states of the transitions responsible for @xmath34 in this energy range have o  2@xmath25 character . consideration of figs . [ sigmas]c and [ sigmas]d reveals that the peak in @xmath99 at 3.7  ev and the small hump in @xmath100 at the same energy are dominated by transitions into the @xmath94 bands ( dark grey shaded spectral weight ) . the initial and final states of the transitions giving rise to @xmath99 between 3 and 4 ev are , in fact , of the same character as those which determine the shape of the @xmath99 spectrum in v@xmath1o@xmath2 just above the absorption threshold.@xcite the dipole transitions from the o  2@xmath25 valence band states into the antibonding @xmath95 states are completely suppressed for a polarization parallel to * a * ( @xmath99 ) , while for @xmath100 they play an important role in the formation of the shoulder in this energy range ( shaded light grey in fig . [ sigmas]d ) .    finally , we mention that transitions from the occupied @xmath4 bands to that part of the conduction band originating from the v  @xmath87 states give rise to the non - vanishing intensity in the calculated spectra in the energy range between the main features ( i.e. between 1.5 and 3 ev ) . the experimental @xmath34 s ( see figs .  [ th+exp]a and [ th+exp]b ) confirm the accuracy of the theoretically predicted optical conductivity in this regard .    in order to summarize the detailed information won in this section as regards the character of the states involved in the transitions giving rise to both @xmath99 and @xmath100 in a concise form , table  [ dec ] shows a breakdown including the respective initial and final states behind each spectral feature .    the level to which the detailed breakdown of the calculated optical conductivity has been carried out in fig . [ sigmas ] is justified by the fact that the theoretical curves ( for example the solid line ) in fig . [ th+exp ] are able not only to reproduce the main features in @xmath99 and @xmath100 quite well , but also the weaker , double peak structure in @xmath100 in the 3 - 4 ev range in our experimental data ( see fig .  [ th+exp]b ) . we note that the spectra derived from optical measurements did not resolve this double - peak feature.@xcite    despite the quite good agreement between the calculated and measured optical conductivity on the qualitative level , the absolute magnitude and strongly asymmetric shape of the low energy peaks in @xmath99 and @xmath100 are not accurately reproduced by the calculations ( see fig . [ th+exp ] ) . we point out two possible sources for these discrepancies : ( i ) an oversimplified treatment of the charge fluctuations in the high temperature phase using an averaged one - electron potential and ( ii ) the assumption that the v magnetic moments are antiferromagnetically aligned along the * b * direction . dealing firstly with the issue of the charge fluctuations , we note that a more rigorous treatment of the charge disorder on the v sublattice of @xmath0-nav@xmath1o@xmath2  is beyond the capabilities of the lsda+@xmath3 approach in its present formulation . we therefore return to this question later in the paper in the context of the cluster calculations which will be described in detail in the next but one sub - section . as regards the influence of deviations from long range afm order on the optical spectra , we point out that the strength of such effects can be estimated by performing calculations for a spin - wave structure along the b - axis . the optical conductivity spectra calculated for @xmath85  =  3  ev and for different values of the vector describing the spiral magnetic structure in real space , @xmath82 , are shown in fig . [ spirals ] . since the change of the magnetic structure affects the bands formed from the v  @xmath4 bonding states most strongly ( see fig .  [ dos ] ) , the spectral features originating from the transitions in which these bands are involved demonstrate the strongest dependence on @xmath82 . in particular , the change in shape and intensity of the peak at 1  ev in @xmath99 ( fig .  [ spirals]a ) is the most noticeable result of including spiral spin structures along the b - axis . as can be seen from the figure , as @xmath82 decreases , the peak becomes less intensive and its maximum shifts to higher energy . since the final states for the corresponding transitions ( i.e. the antibonding v  @xmath4 states ) remain very narrow independent of the nature of the magnetic order along the * b * direction , the increase in the width of the peak reflects the change of the density of the occupied v  @xmath4 states ( i.e the initial states ) . the shape of the low energy peak in @xmath100 ( fig . [ spirals]b ) does not change with increasing @xmath82 but its intensity rapidly decreases as @xmath82 decreases , and vanishes completely for @xmath106 at which point the v magnetic moments order ferromagnetically . the drop of intensity of the low lying feature in @xmath100 is caused by the decrease of the weight of majority - spin states in the final state wave functions . for @xmath106 the initial and final states are formed by pure majority and minority - spin states , respectively , and the corresponding transitions are forbidden ( since the relativistic effects were not included in the calculations ) . the spectral features in the energy range between 3 and 4  ev are also influenced by @xmath82 , but the changes are less pronounced than for the low lying features . the comparison of the calculated optical conductivity with inclusion of the spin spiral structures ( fig .  [ spirals ] ) with the experimental spectra ( figs . [ th+exp]a and [ th+exp]b ) indicates that an improved agreement between the theoretical and experimental magnitude of the low energy peaks of @xmath99 and @xmath100 can be achieved if deviations from pure afm order along the * b*-axis are taken into account . however , even including spin - waves , the lsda+u results are unable to fully account for the asymmetric shape of the low energy peaks in the experimental optical conductivities .    to try to overcome this weakness , we have also calculated the optical conductivity for different relative orientations of the magnetization at neighbouring ladders ( not shown ) . the changes of the calculated spectra were found to be very small , which is in keeping with the size of the inter - ladder hopping term ( @xmath107  ev ) which couples v ions belonging to neighboring ladders .    to bring this section on the data from band structure calculations to a close , the lsda+@xmath3 results regarding the optical properties of @xmath0-nav@xmath1o@xmath2  can be summarized as follows . \\(a ) the optical conductivities @xmath99 and @xmath100 calculated with @xmath85 in the range between 2 and 3  ev are able to reproduce the main features of the experimental spectra , as well as the observed optical anisotropy quite well . this fact indicates the relevance and accuracy of the parameters determined both from the fit to the band structure ( the transfer integrals , or t s ) or from the comparison with the experiment ( @xmath3 ) . \\(b ) the analysis of the contributions to @xmath34 coming from interband transitions with different initial and final states allows us to determine the electronic states responsible for the formation of the peaks in the experimental optical conductivity . table  [ dec ] summarizes this information for each spectral feature in @xmath99 and @xmath100 . \\(c ) however , the remaining discrepancy between the theory and the experiment as regards the shape of the low energy peaks ( even despite going beyond the afm approximation for the spin order along * b * ) indicates that the subtle details of the electronic structure of the high temperature phase of @xmath0-nav@xmath1o@xmath2are beyond the approximations inherent to the lda , and thus are most likely sensitive to effects more suitably treated within the framework of models in which electronic correlation is dealt with at a more fundamental level .    before going on to the @xmath108 model cluster calculations presented in the last sub - section of the results and discussion part of the paper , the next sub - section deals with the first eels spectra of @xmath0-nav@xmath1o@xmath2  recorded beyond the optical limit . here we exploit the strength of eels in transmission as a measure of the bulk optical properties ( in this case of @xmath0-nav@xmath1o@xmath2 ) for finite momenta , thus giving additional insight into the nature of the two - particle excitations in this complex system .      in the left panels of fig . [ lossf ] , we show the eels loss function of @xmath0-nav@xmath1o@xmath2  recorded for different values of * q * , either parallel to the crystallographic * a * ( fig . [ lossf]a ) or * b * ( fig .  [ lossf]a ) direction . the spectra are normalized at higher energy ( ca . 7 ev ) where the shape of the spectra does not change either with the absolute value or with the direction of the momentum transfer ( see also fig . [ optlim ] ) . for clarity the spectra are incrementally off - set in the y - direction .    for * q * parallel to both the * a * and * b * directions the spectra show strong intensity between the spectral onset at 0.7  ev up to 2  ev , as well as additional weaker features located between 3 and 4.5  ev . for small * q * the corresponding plasmon excitations are related to the same dipole transitions which are responsible for the peaks at around 1 and 3.5  ev in the optical conductivities whose origin was discussed in detail above . in the following , we concentrate our attention on the fine structure of the low energy peaks , as well as on the dependence of the shape and position of the peaks on the increasing momentum transfer .    first , we focus on the features below 2  ev . the intensities in the * a * direction are about two times larger than those with the same momentum transfer in the * b * direction . for * q*@xmath103*a * , the maximum lies at 1.55  ev compared with 1.45  ev for * q*@xmath103*b*. at high momentum transfers the fine structure of the feature around 1.5  ev in the * a * direction indicates the presence of transitions into more than a single final state . one can distinguish between essentially three features , whereby the intensity of the component with its maximum at 1.55  ev decreases more rapidly with q than the features at 1.2 and 1.7  ev , the latter pair being visible as weak shoulders only for high momentum transfers . in the * b * direction the low energy feature is also composed of more than one component - at least at high * q*. the energetically lowest lying feature ( at @xmath76  0.9  ev ) - which can be seen as a shoulder at q  @xmath109  0.4  @xmath15 - looses intensity only slowly with increasing q. the second component , which one can relate to the main intensity maximum ( ca . 1.3 ev ) decreases more strongly in intensity at higher q. lastly , for q@xmath110  @xmath15 , a third component is visible at higher energy ( ca . 1.7 ev ) .    finally , we turn to the features in the loss function at energies above 3  ev , which , as in the data recorded at the low - q limit , are clearly separated from the lower energy features by a strong drop of spectral weight between 2 and 3  ev . in the * a * direction a steep increase of spectral weight occurs at 3  ev , which evolves into a maximum at 3.5  ev . with increasing momentum transfer the peak position of this feature does not change and the intensity decreases slowly . a peak at the same energy position with a similar shape was observed for the * a * as well as for the * b * direction in the loss functions of v@xmath1o@xmath2 , and is assigned to transitions from the o  2@xmath25 states into the lowest unoccupied v  3@xmath4 states.@xcite however , in the eels spectra of @xmath0-nav@xmath1o@xmath2 , the shape of the corresponding feature in the * b * direction differs by the presence of a double - peaked structure with maxima at 3.5  ev and 5.1  ev . the two peaks merge together with increasing momentum transfer , and for q  @xmath109  0.7  @xmath15 a further feature becomes visible at @xmath763.8  ev . since in electron energy - loss spectroscopy the cross section for dipole transitions decreases and that for dipole forbidden transitions increases with increasing momentum transfer , the latter 3.8 ev feature is most likely related to monopole or quadrupole transitions . having described the experimental loss functions as a function of momentum , we now discuss the results of the cluster model calculations aimed at their simulation .      in fig . [ lossf ] the results of our cluster calculations ( see section [ clustercal ] ) are compared with the experimental spectra.@xcite such cluster calculations require , naturally , input parameters which in turn describe the essentials of the physics of the system in question . in this case , for the transfer integrals we take the values @xmath111  ev , @xmath112  ev , @xmath113  ev from our tight - binding fit to the band structure calculations mentioned earlier . these values are identical to those of ref .  . a further , vital parameter is the on - site coulomb repulsion , @xmath3 . here we take a value of 2.8 ev - a choice which is guided by the range of @xmath114 which came out of the lsda+@xmath3 calculations presented and discussed above .    at this stage we can have faith in these parameters for two reasons . firstly , it is well known that lda does a good job in describing the charge distribution , and hence the hybridisation / transfer integrals , even in systems with strong electronic correlation . secondly , the good basic agreement between the optical conductivity calculated within lsda+@xmath3 with experiment ( see sec .  [ optcon ] ) not only lends support to the @xmath49 s , but underpins the chosen @xmath3 value . the exchange interactions were parametrized as @xmath115 and the values of the intersite coulomb interactions @xmath116  ev and @xmath117ev fulfill the condition for the system to be close to a quantum critical point caused by charge ordering , as described by cuoco et al .. @xcite the inter - ladder coulomb interaction @xmath118  ev has been adjusted within the model to obtain the correct peak positions with respect to the experimental loss functions . to allow a direct comparison with experiment , the calculated data were broadened with a gaussian function of 0.3  ev width . the unbroadened spectra for @xmath119    are also shown as vertical lines in figs . [ lossf]b and [ lossf]d . as the cluster model contains only v sites , we only attempt to simulate the loss function in the low energy range ( i.e. for @xmath120  3ev ) . at higher energies - as we know from our combined analysis of the experimental and theoretical optical conductivities ( sec . [ optcon ] ) - excitations from o  2@xmath25 to v  3@xmath10 orbitals play a role . thus this spectral weight can not be described within the present cluster model . we find a good agreement between theory and experiment for the low energy part of the loss function for * q*@xmath103*a * , in particular for the data recorded at higher q ( see fig . [ lossf]a and [ lossf]b ) . specifically , the intensity reduction and increasing width of the experimentally observed structure between @xmath121 and @xmath122  ev for q  @xmath17  0.5  @xmath15 is well reproduced in the cluster calculation , a characteristic which eluded our best efforts within the lsda+@xmath3 approach . for the calculated loss function with * q*@xmath103*b * ( fig .  [ lossf]d ) , the experimental q - dependent reduction in intensity is also well reproduced . however , in this case the simulation fails to reproduce accurately the large width of the low - energy feature - a shortcoming which becomes increasingly apparent for higher q.    in order to enable a discussion of the origin of the individual features underlying the calculated spectra , one should note that since @xmath0-nav@xmath1o@xmath2  is close to a charge order transition,@xcite one can describe the nature of the excitations using a zig - zag ordered ground state . in this context , we mention that excitations with momentum transfer parallel to the * a * direction lead to a disturbance of the charge ordering as they involve hopping of electrons from one side of a rung to the other . note that this process can also be interpreted as a transition from a bonding to an antibonding state of a singly occupied rung , in agreement with the results from recent calculations using the heitler - london model.@xcite since the net inter - ladder coulomb interaction , @xmath13 , remains unchanged after the hopping on the rung in the charge ordered state , the excitation energy is dominated by @xmath74 . in addition to the one electron hopping discussed above , there are also collective processes that involve two or three neighboring rungs on different ladders .    as the unbroadened theoretical results presented in fig .  [ lossf]b show , the theoretical spectra consist of three main features , each of which can be attributed to a density oscillation ( plasmon ) with energies between @xmath121 and @xmath122  ev . for * q*@xmath103*a * , the spectral weight shifts from the plasmon at @xmath123  ev to the one at @xmath124  ev with increasing @xmath19 , which makes it appear as if the low lying feature as a whole disperses to higher energy , which is not , in fact , the case . the three excitations differ in their degree of delocalization . the excitation at @xmath125  ev is related to rather delocalized transitions involving more than one electron in the cluster . the higher lying plasmons , however , result from more localized processes .    for momentum transfer parallel to the * b * direction , the excitations contributing to the low lying spectral weight ( see fig . [ lossf]d ) can be interpreted as transitions from a state in which two rungs are singly occupied to one in which one rung is empty and the other doubly occupied . due to the finite hopping amplitude @xmath126  ev , the unoccupied and the occupied rung are able to move along the ladder independently from each other . thus , many more final states are available in the * b * direction than in the * a * direction . the energies of the transitions into these final states depend on the distance between the unoccupied and the doubly occupied rung . however , since we can observe only localized excitations by the direct diagonalization of small clusters , we are unable to capture fully the dynamics of these excitations and thus we miss some spectral weight ( in the form of spectral breadth ) in the theoretical spectra ( fig . [ lossf]d ) compared to the experimental data ( fig . [ lossf]c ) . this explanation is supported by a further reduction of spectral weight in the cluster calculation when we adopt a four - rung ladder , in place of the eight rung cluster from which the results are presented here . thus , in contrast to the good description of the strongly localized excitations in the * a * direction described earlier , for * q*@xmath103*b * we find that the theory significantly underestimates the spectral weight , due to finite size effects in the cluster calculation . that these differences also persist in the high q regime illustrates that the cluster size imposes limitations even in the case where the excitations have shorter wavelength . nevertheless , it should be pointed out that the cluster calculations do provide a qualitative description of both position and the q - dependent decrease of intensity of the experimental features . the optical conductivity can also be calculated using the same , cluster - based method . with the same model parameters we obtain a qualitative agreement with the optical conductivity , either as derived from eels or optical measurements @xcite ( not shown ) . however - as was the case for the lsda+@xmath3 data - the asymmetric line shape in @xmath34 could not be fully reproduced in the cluster calculation . we ascribe this to the delocalized character of some of the final states , which at * q *  =  0 ( i.e. at infinite wavelength ) therefore elude our calculations based upon a finite cluster . we note here that a similar type of calculation has been carried out recently,@xcite and a good agreement between theory and the ( q  =  0 ) optical conductivity was found , albeit with a rather high value of the inter - ladder hopping integral @xmath127  ev . the momentum - dependent eels data presented here allow a further test of the theoretical parameters beyond the optical limit . we have found that adopting @xmath127  ev in our @xmath49-@xmath30-@xmath50 model calculations yields a significantly worse agreement with the experimental data than does the value of @xmath113  ev , which also comes out of the tight binding fit to the band structure . consequently , it appears as if a large value of the interladder hopping is not a requirement for an accurate description of the charge excitations in @xmath0-nav@xmath1o@xmath2 .    to summarize , one can say that while the small inter - ladder hopping gives a rationale for the quasi one - dimensional character of the dynamics of the v  3@xmath10 electrons ; the fact that all three inter - site coulomb interactions ( @xmath128 , @xmath129 and @xmath13 ) are of similar size is consistent with the two - dimensional nature of the charge ordering occurring at low temperatures in this system .","summary":"the decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the dos reveals the origin of the observed anisotropy of the optical conductivity . good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band - structure and moderate coulomb interactions between the electrons within the plane .","abstract":"we have studied the electronic properties of the ladder compound-navo adopting a joint experimental and theoretical approach . the momentum - dependent loss function was measured using electron energy - loss spectroscopy in transmission . the optical conductivity derived from the loss function by a kramers - kronig analysis agrees well with our results from lsda+ band- structure calculations upon application of an antiferromagnetic alignment of the v  3 spins along the legs and an on - site coulomb interaction of between 2 and 3  ev . the decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the dos reveals the origin of the observed anisotropy of the optical conductivity . in addition , we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model . good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band - structure and moderate coulomb interactions between the electrons within the plane ."}
{"article_id":"1504.04995","section_id":"i","document":"plasma turbulence has been analyzed extensively using in - situ measurements of magnetic field and velocity fluctuations in the solar wind @xcite . the statistical properties of these fluctuations are usually interpreted by means of power spectral density @xmath10 as a function of frequency in spacecraft frame . power spectral densities ( psd ) derived from these in - situ measurements of single spacecraft are generally obtained in a one - dimensional reduced form . this means that fluctuations associated with various wave vectors are observed at the same frequency in spacecraft frame and thus contribute to the spectral density @xmath10 at a certain frequency @xmath11 . however , turbulence models are commonly formulated in three - dimensional wave vector space , where each wave vector @xmath0 is assigned a certain energy . under the assumption of taylor s hypothesis and statistical homogeneity , the observable power spectrum @xmath10 can be obtained from the energy distribution in @xmath0-space by a two - dimensional integration . although this fact is very well known ( e.g. * ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , there is currently no application , where several plasma scales in @xmath0-space have been considered simultaneously . we provide here a numerical tool , which we use to study the effects of various @xmath0-space distributions .- space distributions by the interested reader . ] note , that for the calculation of reduced power spectral densities in frequency space , the applicability of taylor s hypothesis and homogeneity needs to be justified for each physical system under investigation , e.g. , the solar wind or magnetospheric plasmas . we will return to this issue when we compare observations in the solar wind and saturn s magnetosphere with our model results . the transformation from @xmath0-space to the observed frequency space taken in a rest frame moving with respect to the turbulent media is unique . in contrast , the observations taken in the moving frame do not allow to uniquely determine the spatio - temporal turbulent structure in the rest frame of the media ( e.g. * ? ? ? * ) . thus interpretation of observed single spacecraft frequency spectra can only test whether certain @xmath0-space distributions of turbulence are consistent with observations or not , but they can not uniquely identify one certain @xmath0-space structure . the statistical properties of turbulent fluctuations have led to the understanding that turbulent fluctuations in plasmas are anisotropic with respect to a background magnetic field @xmath12 . @xcite observed anisotropy with a composite slab and 2-d model consisting of wave vectors parallel and perpendicular to the mean magnetic field , respectively . @xcite successfully explained the relative ratios of turbulence power in different magnetic field components of helios measurements with a 85% 2-d and 15% slab model . @xcite found that low frequency turbulent fluctuations in the solar wind could be explained with a combination of 2-d and a radial slab model . to explain the anisotropic cascading process , @xcite proposed a critical balance between alfvn wave period and nonlinear time , which leads to spectral anisotropy of the measured power spectral densities . although there have been recent results that seem to confirm the critical balance theory @xcite , it is an ongoing debate if critical balance is an inherent property of plasma turbulence . @xcite , e.g. , found no dependence of the spectral index on the field - to - flow angle @xmath4 , i.e. , the angle between @xmath12 and plasma flow @xmath13 ( relative to the observing spacecraft ) , using a global background magnetic field in their analysis and @xcite recently found a @xmath4-independent range , which they claim contradicts the critical balance assumption .    in this paper , we analyze in detail the spectral form of one - dimensional reduced psd based on critical balance in the mhd and kinetic range of scales . the psd are modeled for the first time for oblique angles @xmath14 from mhd to electron scales based on a three - dimensional energy distribution . in section [ sec : de ] , we discuss the diagonal elements of the spectral tensor , which depend on two scalar functions for toroidal and poloidal fluctuations and we show how the tensor reduces to a one - dimensional spectrum if taylor s hypothesis holds . in section [ sec : models ] , we introduce our model for the energy distribution in @xmath0-space based on a critically balanced cascade on mhd , ion kinetic , and electron kinetic scales . further , we discuss potential anisotropic damping terms . in a comparative study in section [ sec : results ] , we analyze if the results published by @xcite in the mhd regime and @xcite in the kinetic regime of the solar wind can be explained by a critically balanced or slab/2-d model . in addition to @xcite , who made a similar analysis for the results of @xcite , we include kinetic scalings and damping effects . in section [ sec : satmod ] , we investigate how spectra observed by @xcite in saturn s magnetosphere are consistent with a critically balanced cascade and damping processes . we like to point out that our analysis is also relevant to modeling cosmic ray transport in turbulent media ( e.g. , jokipii , 1966 ; engelbrecht & burger , 2014 , 2015 ) . cosmic rays are traveling with very large velocities through turbulent plasma fields while being scattered by time - variable fields , which are seen in a lagrangian frame by the moving particles commonly described in an appropriate guiding center . thus , cosmic rays are subject to the same sampling effects of anisotropic wave vector distribution as the time - dependent spacecraft measurements commonly also taken at large velocities with respect to the turbulent plasma . the effect of field - to - flow angle on cosmic ray properties has for example been studied by @xcite .","summary":", we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity . given a critically balanced turbulent cascade with and the spectra are obtained under the assumption of taylor s hypothesis . we further investigate the functional dependence of the spectral index on the field - to - flow angle between plasma flow and background magnetic field from mhd to electron kinetic scales .","abstract":"we present results from a numerical forward model to evaluate one - dimensional reduced power spectral densities ( psd ) from arbitrary energy distributions in-space . in this model , we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity . given a critically balanced turbulent cascade with and , we explore the implications on the reduced psd as a function of frequency . the spectra are obtained under the assumption of taylor s hypothesis . we further investigate the functional dependence of the spectral index on the field - to - flow angle between plasma flow and background magnetic field from mhd to electron kinetic scales . we show that critically balanced turbulence asymptotically develops toward-independent spectra with a slope corresponding to the perpendicular cascade . this occurs at a transition frequency , which is analytically estimated and depends on outer scale , critical balance exponent and field - to - flow angle . we discuss anisotropic damping terms acting on the-space distribution of energy and their effects on the psd . further , we show that the spectral anisotropies as found by and in the solar wind are in accordance with a damped critically balanced cascade of kinetic alfvn waves . we also model power spectra obtained by in saturn s plasma sheet and find that the change of spectral indices inside can be explained by damping on electron scales ."}
{"article_id":"1504.04995","section_id":"r","document":"in this section , we introduce a @xmath0-space turbulence model ranging from mhd to electron scales based on commonly discussed models in the literature . with this model we calculate one - dimensional reduced psd for arbitrary measurement geometries . we focus on the theory of a strong critically balanced turbulent cascade as originally proposed by @xcite for alfvnic turbulence . it has been further developed to include the ion kinetic range @xcite and the electron kinetic range @xcite . observations indicate that it is suited to describe solar wind turbulence @xcite , although these observations have not been explicitly compared with reduced spectra rigorously derived from three - dimensional @xmath0-space models . however , with the forward model derived here , we are able to perform such an explicit test and are able to check if the observations are truly in agreement with critical balance and other suggested properties of three - dimensional @xmath0-space .      according to @xcite , the ( kinetic ) energy distribution on mhd scales can be described as @xmath61 where @xmath62 is the alfvn speed with @xmath63 the mass density of the plasma , @xmath6 the outer scale , and `` _ _ @xmath64 is a positive , symmetric function of @xmath65 , that becomes negligibly small , when @xmath66 _ _ '' @xcite . it is this function @xmath64 , which contains the critical balance relation of wave vectors on mhd scales @xmath67 the energy is supposed to be isotropically injected into the system on the outer scale @xmath6 , where the excitation is assumed to be strong @xmath68 . this relation leads to spectral anisotropy , i.e. , different scalings depending on the field - to - flow angle @xmath4 . @xcite find that the function that best explains the magnetic fluctuations in their simulation of incompressible mhd turbulence , is @xmath69 according to equation  ( [ eq : gs95 ] ) , this indicates that the magnetic fluctuations on the outer scale @xmath6 are strong , @xmath70 . however , @xcite find from fits to solar wind data that @xmath71 overestimates the energy of the turbulent fluctuations by a factor of @xmath72 . therefore , the energy level of the modeled power spectra can not be obtained unambiguously . the energy distribution given by equation  ( [ eq : emhd ] ) describes the alfvnic fluctuations and we thus set @xmath73 on mhd scales . according to equation  ( [ eq : tp ] ) , this constrains the poloidal function to @xmath74 . next to the exponential function used in equation  ( [ eq : emhd ] ) , there are several different possibilities to describe @xmath64 , e.g. , dirac delta , heaviside or gauss functions . the particular choice of @xmath64 , however , results in similar spectral anisotropies as found in the case of mhd scales by @xcite and @xcite . for @xmath75 , the one - dimensional psd scales as @xmath76 and for @xmath77 as @xmath78 in the inertial range . exact power - laws in frequency space only occur for these two extreme cases . in the literature , however , it is often implicitly assumed that the spectra in the intermediate range @xmath79 also follow power - laws with spectral slopes @xmath80 and that the spectral index @xmath3 of the reduced spectra is  similar to the spectral index of three - dimensional @xmath0-space  independent of frequency . in this paper , we will see that these assumptions are incorrect . when the observed doppler - shifted frequencies reach scales close to the characteristic ion scales , such as the ion gyro radius @xmath81 or the ion inertial length @xmath82 , the mhd approximation breaks down and one needs to take into account kinetic effects to describe the plasma dynamics . for the remainder of this paper , we use the gyro radius as the controlling kinetic scale with an associated critical balance on ion kinetic scales @xmath83 according to @xcite . here , we drop the factor @xmath84 , where @xmath85 is the ion plasma beta and @xmath86 and @xmath87 the temperatures of ions and electrons , respectively , because the factor is of order unity in the solar wind and saturn s magnetosphere . note , that our forward model can similarly be formulated for other theories or with the inertial length as the controlling scale . we model the transition from mhd to kinetic scales as an abrupt change in the function @xmath88 at @xmath89 without energy loss , e.g. , due to ion resonances . let us denote the function @xmath90 , given in equation  ( [ eq : emhd ] ) , as the one applicable for @xmath91 and @xmath92 as the one applicable for @xmath93 . at @xmath89 , both energy distributions are equal , @xmath94 . also , the kinetic energy distribution , @xmath92 , is assumed to scale as @xmath95 for @xmath75 @xcite . these requirements are fulfilled in the expression @xmath96 for the parallel cascade ( @xmath77 ) , this leads to a scaling of @xmath97 .    at even smaller scales , we approach the electron gyro radius @xmath98 and the energy distribution changes once again from @xmath92 to an electron or dissipation range distribution @xmath99 . here , landau damping is assumed to weaken the cascade so that there is no more parallel transfer of energy @xcite . the electron or dissipation range fluctuations are modeled with an associated critical balance @xcite of @xmath100 a functional form that satisfies the equality of @xmath92 and @xmath99 at @xmath101 can be given by @xmath102 it can be shown that this leads to a scaling of @xmath103 for the perpendicular cascade ( @xmath75 ) and an exponential decay @xmath104 for the parallel cascade . the energy distribution in @xmath0-space according to our model is shown in figure [ fig : kspa ] for the parameters given in table [ tab : sw ] . it shows logarithmically equidistant iso - contours of energy densities according to equations ( [ eq : emhd ] ) , ( [ eq : ekaw ] ) and ( [ eq : ed ] ) in a double - logarithmic plot as a function of @xmath105 and @xmath106 normalized by the ion gyro radius @xmath81 . the characteristic slopes of the critical balance relations , @xmath107 , @xmath108 , and @xmath109 in the mhd , kaw , and ed regime , respectively , can be seen as the boundary , where the energy becomes negligible ( dark blue ) . note , that the energy density decreases with @xmath110 and @xmath111 , which leads to a seemingly negative slope in the electron dissipation range . recall from equation  ( [ eq : trafo ] ) and subsequent discussion that the reduced one - dimensional spectrum is calculated by integrating over a plane given by @xmath112 projections of these planes into the @xmath113 plane are shown as dashed lines in figure [ fig : kspa ] for an angle @xmath114 at logarithmically equidistant frequencies @xmath115hz . for @xmath77 , these dashed lines would be horizontal and parallel to the @xmath105-axis , and for @xmath75 , they would be vertical and parallel to the @xmath106-axis . however , due to the double - logarithmic nature of the plot , the dashed lines for intermediate angles @xmath4 are curved . note , that even for a very small angle @xmath114 , the plane of integration turns quasi - perpendicular to the @xmath105-axis , i.e. , lies parallel to planes expected from integration for @xmath116 , for sufficiently large @xmath105 .      while equation  ( [ eq : pfull ] ) can be integrated analytically for angles @xmath77 and @xmath75 , it can only be numerically evaluated for intermediate angles @xmath79 . here , we carry out this numerical integration for the first time considering all scales from the mhd to the electron kinetic regime . results of this calculation using the parameters given in table [ tab : sw ] are shown in figure [ fig : psd_theta ] . we plot the resulting psd for several field - to - flow angles as a function of frequency @xmath11 in spacecraft frame . note , that frequency can be transformed into normalized wave number according to @xmath117 , particularly for parameters in table [ tab : sw ] : @xmath118 . for @xmath75 the spectral breaks of the psd , which mark the transition from mhd to kaw and kaw to ed range , are located at the doppler - shifted frequencies corresponding to @xmath81 and @xmath98 ( denoted by vertical dashed lines ) . here , the spectral slope of the reduced psd steepens from @xmath119 to @xmath120 and from @xmath120 to @xmath121 , respectively . for smaller angles @xmath122 these spectral breaks are less pronounced and occur at lower frequencies . the expected spectral slopes for @xmath77 and @xmath75 are shown as black lines in figure [ fig : psd_theta ] to guide the eye . here and throughout this paper , we use plasma parameters characteristic of the solar wind at @xmath123au as given in table [ tab : sw ] , which we adopt from the work of @xcite , @xcite , and @xcite . l c parameter & value + background magnetic field @xmath124 & @xmath125nt + outer scale @xmath6 & @xmath126 km + plasma speed @xmath37 & @xmath127km@xmath41s@xmath42 + alfvn speed @xmath128 & @xmath129km@xmath41s@xmath42 + ion gyro radius @xmath81 & @xmath130 km + electron gyro radius @xmath98 & @xmath131 km +    we note a particular interesting feature in figure [ fig : psd_theta ] : the spectra for oblique angles are steepened in a short frequency range around the first spectral break at @xmath132 and then flatten out toward a slope of @xmath120 at higher frequencies . the smaller the angle @xmath4 , the longer the range , where psd are steeper than @xmath120 . such an asymptotic behavior has been predicted for the mhd range by @xcite , however , without specifying the frequency range , where this transition could be expected . here , we show for the first time that this transition happens on a short frequency range around the spectral break in the solar wind . we emphasize the importance of this result as it contradicts the commonly assumed constancy of the spectral index with frequency . also , it implies that psd in the kinetic range are almost exclusively observed with their perpendicular slope ( here @xmath120 and @xmath121 ) if not subject to damping . in the remainder of this section , we explain this feature as a geometrical or sampling effect . the flattening of the psd , although puzzling at first , can be explained with the anisotropic distribution of energy in @xmath0-space . because of the linear relation between @xmath105 and @xmath106 in equation  ( [ eq : plane ] ) , the point of maximum curvature of the integration plane in figure  [ fig : kspa ] grows faster than the critical balance relations @xmath1 in the mhd ( @xmath133 ) , kaw ( @xmath134 ) , and ed ( @xmath135 ) range . hence , for increasing frequencies @xmath11 , the plane of integration given by equation  ( [ eq : plane ] ) effectively has only contributions from the part quasi - perpendicular to the @xmath105-axis in the double - logarithmic plot of figure [ fig : kspa ] . therefore , at frequencies above a transition frequency @xmath136 , the power spectrum at a given field - to - flow angle @xmath4 will have a slope within a small error @xmath137 to that at @xmath75 appropriate to mhd ( @xmath119 ) , kaw ( @xmath120 ) , or ed ( @xmath121 ) . the transition frequency @xmath136 thus marks the boundary , where the anisotropy of the @xmath0-space energy distribution becomes so large that it is indistinguishable from a 2d - distribution in the reduced psd within measurement error @xmath137 . it is this feature that causes the spectral slope of the psd to asymptotically approach its perpendicular value at high frequencies . a derivation of an analytically approximated expression @xmath138 ( see equation  ( [ eq : fmax ] ) ) can be found in appendix [ app ] . the frequencies , where the psd turn quasi - perpendicular , are shown in figure [ fig : psd_theta ] as colored dots assuming a pure kaw cascade . note , that the transition frequency @xmath138 , in contrast to the spectral break , shifts to higher frequencies for smaller angles @xmath4 . assuming a plain mhd cascade , the approximate transition frequency from equation  ( [ eq : fmax ] ) gives @xmath139hz . the corresponding transition frequencies for @xmath140 $ ] reach into the kinetic range of scales . the transition to quasi - perpendicular scaling is always found at frequencies below the electron spectral break , @xmath141 , which is why frequencies @xmath138 are not shown in the ed range . we find that the transition for kaw toward a quasi - perpendicular cascade for almost all field - to - flow angles ( namely @xmath142 , see figure [ fig : fmax ] in the appendix ) occurs already below @xmath123hz , where the spectral break is observed at typical solar wind conditions @xcite . we conclude that spectra of a critically balanced kaw cascade without damping on kinetic scales will almost exclusively be observed with spectral indices close to @xmath120 and @xmath121 in the ion and electron kinetic range , respectively . only for small angles and in a short frequency range between the first spectral break and @xmath123hz a measurably steeper slope might be observed in the solar wind . we stress the importance of this result : we have shown that the spectral index in a critically balanced cascade for oblique field - to - flow angles @xmath79 is not constant with growing frequency . instead , it evolves toward a quasi - perpendicular slope as a function of frequency . therefore , we can not expect to observe significantly steeper slopes than @xmath120 and @xmath121 over a broad frequency range in the kaw and ed range , respectively , for a critically balanced cascade in the solar wind . indeed , we see in section  [ sec : damp ] that such slopes only appear if the fluctuations are additionally subject to damping . this transition of reduced psd toward quasi - perpendicular spectra contrasts a common understanding in the literature , where it is often implicitly assumed that the psd have a power - law shape with a constant spectral index that only depends on the field - to - flow angle . it is interesting to note that a three - dimensional direct numerical simulation with strong guide field by @xcite produced a qualitatively similar transition toward a perpendicular cascade with a @xmath4-independent slope , although the flattening of their spectra does not follow equation  ( [ eq : fmax ] ) . several mechanisms have been proposed to explain the dissipation of fluctuations on small scales , e.g. , ion - cyclotron damping , landau damping and current sheet formation @xcite . most of the proposed mechanisms are anisotropic with regards to the background magnetic field . in this section , we analyze how possible anisotropic damping terms that act on the energy distribution in three - dimensional @xmath0-space change the characteristics of reduced one - dimensional spectra . here , we assume that damping leads to an exponential decay of the energy in @xmath0-space associated with the damped wave vectors .    from our assumption of critical balance , it follows that @xmath143 . therefore , damping at a fixed scale affects the turbulent cascade first through perpendicular wave vectors and only later through wave vectors parallel to the mean magnetic field . it has been argued that the ion - cyclotron resonance at @xmath144 , where @xmath145 is the ion - cyclotron frequency , has only minor influence on a critically balanced cascade as it is reached only at very high perpendicular wave numbers @xmath111 , where landau damping already dominates @xcite . with our synthetic spectra , we are now able to test this argument quantitatively .      for the ion - cyclotron resonance , the damping rate is low for @xmath146 and increases rapidly as @xmath147 approaches unity @xcite . we may therefore model the ion - cyclotron resonance as an exponential decay according to @xmath148 to quantify the effective damping , we model damped spectra @xmath149 using the parameters in table [ tab : sw ] and find only minor changes compared to their undamped counterparts @xmath150 .    in figure [ fig : icr_diff ] , we show the ratio @xmath151 as a function of normalized wave number for several angles @xmath4 . both @xmath150 and @xmath149 cover all three ranges from mhd to kaw to electron kinetic scales . for quasi - parallel spectra ( @xmath114 ) , a peak factor of @xmath152 is observed around the spectral break . power spectra @xmath149 for larger field - to - flow angles @xmath153 only differ a factor of @xmath154 from psd without damping . on electron scales , the difference between damped and undamped spectra remains constant as there is no more parallel transfer along the cascade . the asymptotic factor @xmath151 for @xmath155 and @xmath75 can be calculated by integration of equation  ( [ eq : ed ] ) over @xmath106 according to @xmath156 this shows that the influence of cyclotron damping on the spectral shape can be neglected in the solar wind for critically balanced turbulence . however , one might think of systems , in which the ion - cyclotron resonance _ does _ change the form of the psd significantly . such systems could be characterized by ( 1 ) low plasma density , which leads to large alfvn speeds ; ( 2 ) a critical balance exponent @xmath7 close to unity ; and/or ( 3 ) a much smaller outer scale than the @xmath157 m found in the solar wind @xcite , so that high @xmath110 values are reached earlier in the cascade . an enhanced ion - cyclotron damping then leads to a visible decrease of spectral power around the spectral break . let us now turn to damping of perpendicular wave vectors . @xcite found that reduced power spectra measured in the solar wind can empirically be described by @xmath158 with a spectral index of @xmath159 . this result is consistent with numerical gyrokinetic simulations @xcite and we may treat the exponential damping term of equation  ( [ eq : damp1d ] ) as a proxy for electron landau damping . note , that we apply the damping term of equation  ( [ eq : damp1d ] ) to three - dimensional @xmath0-space according to @xmath160 the corresponding distribution in @xmath0-space is shown in figure [ fig : kspa_damp ] , where both damping of parallel and perpendicular wave vectors ( equations ( [ eq : dampic ] ) and ( [ eq : damp ] ) ) is included . while the power at a certain frequency is obtained by integration over a two - dimensional plane , the damping term depends on @xmath111 and is therefore axisymmetric with respect to @xmath106 . this means that the integration along @xmath161 includes perpendicular wave numbers larger than @xmath162 . consequently , the effect of the exponential damping term is stronger when applied to three - dimensional @xmath0-space compared to a reduced one - dimensional spectrum . therefore , we are able to produce similar results to those of equation  ( [ eq : damp1d ] ) with @xmath159 , although we apply a less steep spectral index of only @xmath120 in the ion kinetic range ( see figure [ fig : psd_theta_damp ] ) . figure [ fig : psd_theta_damp ] shows damped psd according to equations  ( [ eq : dampic ] ) and ( [ eq : damp ] ) with the same plasma parameters ( table [ tab : sw ] ) as in figure [ fig : psd_theta ] . as expected , the high frequency part is strongly affected and the damping leads to a characteristic exponential decay . the spectra are dominated by damping of perpendicular wave vectors and the damping terms are found to be generally more effective at small angles @xmath4 . the latter can be understood considering the plane of integration given by equation  ( [ eq : plane ] ) . the power at a certain frequency primarily stems from perpendicular wave numbers @xmath111 . for small angles @xmath4 , this involves larger @xmath111 , which are more strongly damped than a corresponding spectrum with angles close to @xmath163 .    although strong damping sets in not before electron scales in wave vector space , the kaw range of the psd , @xmath164 , is already affected : figure [ fig : psd_theta_damp ] shows the undamped spectrum for @xmath75 as black dashed line and it is fairly visible that the spectrum subject to damping is steeper . in fact , we measure a spectral slope of @xmath165 ( shown by black dashed line ) in the ion kinetic range , @xmath166 for @xmath167 , although the corresponding energy in @xmath0-space scales with @xmath120 . if @xmath168 decreases or the electron gyro radius increases , the exponential decay moves to lower frequencies and further steepens the spectra . the two opposed mechanisms , flattening toward perpendicular slope and damping , can cancel each other and may lead to a range of seemingly constant slope . this shows that an approximate power - law of the measured psd is not equivalent to the absence of damping . further , it shows that the observed spectral slope of the reduced spectrum on ion kinetic scales is not necessarily the spectral index predicted for this range by the underlying theory .","summary":", we explore the implications on the reduced psd as a function of frequency . we discuss anisotropic damping terms acting on the-space distribution of energy and their effects on the psd .","abstract":"we present results from a numerical forward model to evaluate one - dimensional reduced power spectral densities ( psd ) from arbitrary energy distributions in-space . in this model , we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity . given a critically balanced turbulent cascade with and , we explore the implications on the reduced psd as a function of frequency . the spectra are obtained under the assumption of taylor s hypothesis . we further investigate the functional dependence of the spectral index on the field - to - flow angle between plasma flow and background magnetic field from mhd to electron kinetic scales . we show that critically balanced turbulence asymptotically develops toward-independent spectra with a slope corresponding to the perpendicular cascade . this occurs at a transition frequency , which is analytically estimated and depends on outer scale , critical balance exponent and field - to - flow angle . we discuss anisotropic damping terms acting on the-space distribution of energy and their effects on the psd . further , we show that the spectral anisotropies as found by and in the solar wind are in accordance with a damped critically balanced cascade of kinetic alfvn waves . we also model power spectra obtained by in saturn s plasma sheet and find that the change of spectral indices inside can be explained by damping on electron scales ."}
{"article_id":"1504.04995","section_id":"c","document":"we present results from a numerical forward model to evaluate reduced psd from from an arbitrarily distributed energy density in three - dimensional @xmath0-space . given a critically balanced @xmath0-space distribution of energy , we investigate the functional dependence of the reduced spectra on several parameters , such as the field - to - flow angle or the outer scale . such an analysis has been carried out for the first time covering the complete range from mhd to electron kinetic scales . we show that for intermediate field - to - flow angles @xmath4 , the spectral slope of undamped critically balanced turbulence is not constant , i.e. , the reduced psd is not an exact power - law ( see figure  [ fig : psd_theta ] ) . instead , the reduced spectra evolve with frequency in the undamped case toward a quasi - perpendicular spectrum . this is a pure sampling effect of highly doppler - shifted measurements at any angle @xmath262 caused by the anisotropy @xmath25 increasing with frequency . power spectra in this quasi - perpendicular cascade range have a spectral slope corresponding to the spectral index of the perpendicular cascade @xmath263 . for psd that are additionally subject to damping ( figure [ fig : psd_theta_damp ] ) , this transition to quasi - perpendicular spectra is masked by landau damping on electron kinetic scales . here , the spectra become steeper and steeper at higher frequencies . the transition frequency , where the change of slope to @xmath264 is reached for the undamped cascade , can be approximated by a simple expression @xmath138 given in equation  ( [ eq : fmax ] ) . under typical solar wind conditions , @xmath138 for the ion kinetic regime is smaller than or on the same order of the observed spectral break at @xmath265hz . therefore , significantly steeper slopes than the perpendicular spectra on kinetic scales can only be explained by additional damping effects . we find that an empirical damping term at electron scales of the form @xmath266 @xcite already affects the spectral index in the ion kinetic range @xmath164 of the reduced spectrum and steepens it measurably . we apply our model to in - situ measurements in the solar wind and show that turbulent fluctuations measured by @xcite are in good agreement with a critically balanced cascade and less so with a combined slab+2-d turbulence . in the kinetic range we find good agreement with the results of @xcite , which can be explained by a damped critically balanced kaw cascade . while the spectral break and damping terms have only minor influence on the fit to the observations of @xcite , the inclusion of a damping term is essential to explain the results in the kinetic range . indeed , spectral slopes for an undamped cascade differ strongly from the @xcite results and are approximately @xmath120 for nearly all field - to - flow angles in the ion kinetic regime . this is caused by the transition toward a quasi - perpendicular slope . this means that damping is an integral part of the kinetic range cascade and the dominating factor in the observed spectral anisotropy . the forward modeling technique is further applied to observations of turbulent magnetic field fluctuations in saturn s magnetosphere . here , we show that the measured reduced spectra are qualitatively in agreement with a critically balanced kinetic alfvn wave cascade , which further corroborates the interpretation of @xcite . the observation of shallower spectra inside @xmath9 can be reproduced by damping on electron scales controlled by the hot electron population . this indicates that the dissipation of turbulent magnetic fluctuations predominantly heats the hot electron population at saturn . this additional insight on magnetic turbulence in saturn s magnetosphere shows the advantage of applying a first principles forward modeling technique to determine the shape of reduced spectra .","summary":"we present results from a numerical forward model to evaluate one - dimensional reduced power spectral densities ( psd ) from arbitrary energy distributions in-space . in this model as found by and in the solar wind are in accordance with a damped critically balanced cascade of kinetic alfvn waves . we also model power spectra obtained by in saturn s plasma sheet and find that the change of spectral indices inside can be explained by damping on electron scales .","abstract":"we present results from a numerical forward model to evaluate one - dimensional reduced power spectral densities ( psd ) from arbitrary energy distributions in-space . in this model , we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity . given a critically balanced turbulent cascade with and , we explore the implications on the reduced psd as a function of frequency . the spectra are obtained under the assumption of taylor s hypothesis . we further investigate the functional dependence of the spectral index on the field - to - flow angle between plasma flow and background magnetic field from mhd to electron kinetic scales . we show that critically balanced turbulence asymptotically develops toward-independent spectra with a slope corresponding to the perpendicular cascade . this occurs at a transition frequency , which is analytically estimated and depends on outer scale , critical balance exponent and field - to - flow angle . we discuss anisotropic damping terms acting on the-space distribution of energy and their effects on the psd . further , we show that the spectral anisotropies as found by and in the solar wind are in accordance with a damped critically balanced cascade of kinetic alfvn waves . we also model power spectra obtained by in saturn s plasma sheet and find that the change of spectral indices inside can be explained by damping on electron scales ."}
{"article_id":"1006.2373","section_id":"i","document":"what are the natural `` random loop ensemble '' analogs of the schramm - loewner evolution sle@xmath4 when the paths are simple ( i.e. , @xmath7 ) ? this is a natural question , as such families of loops should describe the scaling limits of the collection of interface loops appearing in various critical two - dimensional lattice models in statistical physics . one way to address the above question is to use the sle curves themselves . in this approach , which appears in @xcite , one chooses a point @xmath8 on the boundary of a simply connected domain @xmath9 and launches from @xmath8 a branching sle@xmath10 process ( for @xmath5 in @xmath11 $ ] ) . the sle@xmath12 process is a natural variant of sle@xmath4 with a target - independence property ( see @xcite ) that allows one to construct a branching tree of such processes in a canonical way . using this `` exploration tree '' , one can define a random collection of loops , which was called a _ conformal loop ensemble _ with parameter @xmath5 ( cle@xmath4 ) in @xcite . these loop ensembles are the conjectured scaling limits for various random models from statistical physics . for example , cle@xmath13 appears as the scaling limit of spin cluster boundaries of the critical ising model ( see @xcite ) . we note that some features of these cle@xmath4 loop - ensembles are not easy to derive via this branching sle definition . for instance , the general question of whether their law is independent of the choice of the starting point @xmath8 ( the `` root '' of the branching - tree ) i.e. , whether these cle@xmath4 are invariant under all conformal maps from @xmath9 onto itself , remained open . a completely different approach , proposed in @xcite , is based on the brownian loop - soup . the brownian loop - soup is a random poissonian collection of brownian loops in a domain @xmath9 that inherits nice properties from brownian motion , including conformal invariance . it was introduced in @xcite , motivated by questions concerning restriction properties of sle processes in @xcite . in a loop - soup , the brownian loops can intersect and therefore create clusters . the outer boundaries of these clusters are random conformally invariant curves . the way the laws of these curves vary when the boundary of the domain changes is related to the way the laws of sle curves vary ( these are the `` restriction properties '' of the curves ) , and it is therefore natural to think they are actually sle - type loops . the authors of the present paper recently showed in @xcite that any random collection of loops satisfying the so - called _ conformal restriction axioms _ must be one of the cle@xmath4 defined via the branching sle@xmath10 tree with @xmath5 in @xmath11 $ ] ( and that it could also be constructed via a poisson point process of sle@xmath4 excursions ) . in that paper , the term cle was used to refer to any simple loop ensemble satisfying the conformal restriction axioms . there , as here , the scope was limited to simple loop ensembles ( where loops are disjoint and simple loops ) . it was not shown in either @xcite or @xcite ( and remained far from obvious ) that the cle@xmath4 actually satisfy the axioms ( in part because of the starting - point independence problem ) . in other words , it was proved that _ if _ any cle exist , then they must have the form cle@xmath4 for some @xmath5 in @xmath11 $ ] , but it was not proved that any cle exist , so the result was a rather conditional one . however , it becomes very useful when combined with the results of the present paper .    here , we will study properties of the brownian loop - soup clusters . we will describe properties of its `` subcritical phase '' and of its phase transition : a property of the decay rate of the size of clusters at the critical point , and the fact that the collection of `` loop - soup cluster outer boundaries '' satisfies the conformal restriction axioms introduced in @xcite . this will allow us to apply the results of that paper to deduce that these loup - soup boundaries are cle@xmath4 s . furthermore , this enables us to identify precisely the phase transition point of the loop - soup percolation , and to show that all cle@xmath4 s for @xmath14 $ ] can be constructed via brownian loop - soups . this therefore completes the program of @xcite , and in particular implies that the cle@xmath4 _ do _ in fact satisfy the conformal restriction axioms and that they are root - independent for all @xmath5 in @xmath6 $ ] . hence , we now have two remarkably different explicit constructions of these conformal loop ensembles cle@xmath4 for each @xmath5 in @xmath11 $ ] . this is useful , since many properties that seem very mysterious from one perspective are easy from the other . for example , the ( expectation ) fractal dimensions of the individual loops and of the set of points not surrounded by any loop can be explicitly computed with sle tools @xcite , while many monotonicity results and fkg - type correlation inequalities are immediate from the loop - soup construction @xcite . one illustration of the interplay between these two approaches is already present in this paper : one can use sle tools to determine exactly the value of the critical intensity that separates the two percolative phases of the brownian loop - soup ( and to our knowledge , this is the only self - similar percolation model where this is the case ) . another consequence of this identity between cle@xmath4 and brownian loop soup cluster boundaries , is the `` additivity property '' of cle s that we will describe in more detail later in the introduction : the union of two independent cle s defines another cle . the introductions of the papers @xcite contain additional history and motivation , and we refer the interested reader to them . let us also mention that the present paper gives an interpretation of the _ central charge _ @xmath0 of models ( as usually defined in theoretical physics ) for @xmath0 in @xmath15 $ ] as the intensity of the underlying brownian loop - soup . the brownian loop - soup , as defined in @xcite , is a poissonian random countable collection of brownian loops contained within a fixed simply - connected domain @xmath9 . we will actually only need to consider the outer boundaries of the brownian loops , so we will take the perspective that a loop - soup is a random countable collection of simple loops ( outer boudaries of brownian loops can be defined as sle@xmath16 loops , see @xcite ) . let us stress that the conformal loop ensembles cle@xmath4 , with @xmath17 $ ] , are also random collections of simple loops , but that , unlike the loops of the brownian loop - soup , the loops in a cle are almost surely disjoint from one another . random collections of loops can be formally defined using the notational framework of @xcite , which we briefly review here : a simple loop in the complex plane @xmath18 is the image of the unit circle in @xmath18 under a continuous injective map . a simple loop @xmath19 separates @xmath18 into two connected components that we call its interior @xmath20 ( the bounded one ) and its exterior ( the unbounded one ) . we endow the space @xmath21 of simple loops with the @xmath22-field @xmath23 generated by all the events of the type @xmath24 when @xmath25 spans the set of open sets in the unit plane . note that this @xmath22-field is also generated by the events of the type @xmath26 where @xmath27 spans a countable dense subset @xmath28 of the plane ( recall that we are considering simple loops so that @xmath29 as soon as @xmath30 ) . it is not hard to see that @xmath23 is equivalent to the borel @xmath22-algebra of the hausdorff metric on @xmath21 . thus , the following extension is also natural : let @xmath31 be the set of _ all _ closed bounded subsets of @xmath18 and @xmath32 the borel @xmath22-algebra of the hausdorff metric on @xmath31 . a countable collection @xmath33 of simple loops can be identified with a point - measure @xmath34 . the space @xmath35 of countable collections of elements of @xmath36 is naturally equipped with the @xmath22-field @xmath37 generated by the sets @xmath38 , where @xmath39 . similarly , there is an obvious extension : the space @xmath40 of countable collections of elements of @xmath41 is naturally equipped with the @xmath22-field @xmath42 generated by the sets @xmath38 , where @xmath43 . the loops of the _ brownian loop - soup _ @xmath44 in the unit disk @xmath45 are the points of a poisson point process with intensity @xmath46 , where @xmath0 is an _ intensity _ constant , and @xmath47 is the _ brownian loop measure in @xmath45 _ on @xmath48 . the brownian loop - soup measure @xmath49 is the corresponding probability measure on @xmath50 . when @xmath51 and @xmath52 are two closed bounded subsets of a bounded domain @xmath9 , we denote by @xmath53 the @xmath47-mass of the set of loops that intersect both sets @xmath51 and @xmath52 , and stay in @xmath9 . when the distance between @xmath51 and @xmath52 is positive , this mass is finite @xcite . similarly , for each fixed positive @xmath54 , the set of loops that stay in the bounded domain @xmath9 and have diameter larger than @xmath54 , has finite mass for @xmath47 .    the conformal restriction property of the brownian loop measure @xmath47 ( which in fact characterizes the measure up to a multiplicative constant ; see @xcite ) implies the following two facts ( which are essentially the only features of the brownian loop - soup that we shall use in the present paper ) :    1 . conformal invariance : the measure @xmath55 is invariant under any moebius transformation of the unit disc onto itself . this invariance makes it in fact possible to define the law @xmath56 of the loop - soup in any simply connected domain @xmath57 as the law of the image of @xmath58 under any given conformal map @xmath59 from @xmath45 onto @xmath9 ( because the law of this image does not depend on the actual choice of @xmath59 ) . restriction : if one restricts a loop - soup in @xmath45 to those loops that stay in a simply connected domain @xmath60 , one gets a sample of @xmath61 .    we will work with the usual definition ( i.e. , the usual normalization ) of the measure @xmath47 ( as in @xcite  note that there is often some confusion about a factor @xmath62 in the definition , related to whether one keeps track of the orientation of the brownian loops or not ) . since we will be talking about some explicit values of @xmath0 later , it is important to specify this normalization . for a direct definition of the measure @xmath47 in terms of brownian loops , see @xcite . we now describe the axioms introduced in @xcite . we say that @xmath63 is a simple loop configuration in the unit disc @xmath45 if it is a collection of simple loops in @xmath45 that are _ disjoint _ ( for all @xmath64 , @xmath65 ) and _ non - nested _ ( for all @xmath66 in @xmath67 , @xmath68 ) and that is _ locally finite _ ( for each @xmath69 , only finitely many loops @xmath70 have a diameter greater than @xmath71 ) . we say that a non - empty random simple loop configuration @xmath72 in the unit disc @xmath45 ( or rather its law @xmath73 ) satisfies the _ conformal restriction axioms _ ( introduced in @xcite ) if the following hold :    1 . conformal invariance : the law of @xmath74 is invariant under any conformal transformation from @xmath45 onto itself . as for the loop - soup , this enables us to define the law @xmath75 of the loop - ensemble in any simply connected domain @xmath57 . we can also define @xmath75 if @xmath9 has several connected components by taking independent samples in each of the connected components restriction : we want to describe the law of the loops on the loop - ensemble that stay in a simply connected subset @xmath76 of @xmath45 . to state this natural property for random families @xmath74 of _ disjoint loops _ , we need to introduce some notation . define @xmath77 to be the set obtained by removing from @xmath76 all the loops and interiors of loops of @xmath74 that do not stay in @xmath76 . this set @xmath78 is an open subset of @xmath45 ( because of the local finiteness condition ) . the restriction property is that ( for all @xmath76 ) , given @xmath77 , the conditional law of the set of loops in @xmath74 that _ do _ stay in @xmath76 ( and therefore in @xmath77 ) is @xmath79 . +   is the rectangle and @xmath80 is darkened , title=\"fig:\",width=192 ]   is the rectangle and @xmath80 is darkened , title=\"fig:\",width=192 ]      as mentioned above , @xcite pointed out a way to relate brownian loop - soups clusters to sle - type loops : two loops in @xmath58 are said to be adjacent if they intersect . denote by @xmath81 the set of clusters of loops under this relation . for each element @xmath82 write @xmath83 for the closure of the union of all the loops in @xmath84 and denote by @xmath85 the family of all @xmath83 s . we write @xmath86 for the _ filling _ of @xmath84 , i.e. , for the complement of the unbounded connected component of @xmath87 . a cluster @xmath84 is called _ outermost _ if there exists no @xmath88 such that @xmath89 . the _ outer boundary _ of such an outermost cluster @xmath84 is the boundary of @xmath86 . denote by @xmath74 the set of outer boundaries of outermost clusters of @xmath58 . let us now state our main results :    [ loopsoupsatisfiesaxioms ] suppose that @xmath58 is the brownian loop - soup with intensity @xmath0 in @xmath45 . * if @xmath90 $ ] , then @xmath74 is a random countable collection of disjoint simple loops that satisfies the conformal restriction axioms . * if @xmath2 , then there is almost surely only one cluster in @xmath81 . it follows immediately from this result and @xcite that @xmath74 is a cle@xmath4 ( according to the branching sle@xmath91 based definition in @xcite , see also @xcite for alternative descriptions ) for _ some _ @xmath17 $ ] . we will derive the following correspondence :    [ kappacorrespondence ] fix @xmath90 $ ] and let @xmath58 be a brownian loop - soup of intensity @xmath0 on @xmath45 . then @xmath74 is a cle@xmath4 where @xmath17 $ ] is determined by the relation @xmath92 .    since every @xmath17 $ ] is obtained for exactly one value of @xmath90 $ ] , this implies the following :    the random simple loop configurations satisfying the conformal restriction axioms are precisely the cle@xmath4 where @xmath17 $ ] . recall from @xcite that the hausdorff dimension of an sle@xmath4 curve is almost surely @xmath93 . our results therefore imply that the boundary of a loop - soup cluster of intensity @xmath94 has dimension @xmath95 note that just as for mandelbrot s conjecture for the dimension of brownian boundaries @xcite , this statement does not involve sle , but its proof does . in fact the result about the dimension of brownian boundaries can be viewed as the limit when @xmath96 of this one . furthermore we may define the _ carpet _ of the cle@xmath4 to be the random closed set @xmath97 , and recall that sle methods allowed @xcite to compute its `` expectation dimension '' in terms of @xmath5 . the present loop - soup construction of cle@xmath4 enables to prove ( see @xcite ) that this expectation dimension is indeed equal to its almost sure hausdorff dimension @xmath98 , and that in terms of @xmath0 , @xmath99 the critical loop - soup ( for @xmath3 ) corresponds therefore to a carpet of dimension @xmath100 . another direct consequence of the previous results is the `` additivity property '' of cle s : if one considers two independent cle s in the same simply connected domain @xmath9 with non - empty boundary , and looks at the union of these two , then either one can find a cluster whose boundary contains @xmath101 , or the outer boundaries of the obtained outermost clusters in this union form another cle . this is simply due to the fact that each of the cle s can be constructed via brownian loop soups ( of some intensities @xmath102 and @xmath103 ) so that the union corresponds to a brownian loop - soup of intensity @xmath104 . this gives for instance a clean direct geometric meaning to the general idea ( present on various occasions in the physics literature ) that relates in some way two independent copies of the ising model to the gaussian free field in their large scale limit : the outermost boundaries defined by the union of two independent cle@xmath13 s in a domain ( recall @xcite that cle@xmath13 is the scaling limit of the ising model loops , and note that it corresponds to @xmath105 ) form a cle@xmath106 ( which corresponds to level lines of the gaussian free field , see @xcite and to @xmath107 ) . this paper is structured as follows : we first study some properties of the brownian loop - soup and of the clusters it defines . the main result of section [ s.2 ] is that when @xmath0 is not too large ( i.e. is subcritical ) , the outer boundaries of outermost brownian loop - soup clusters formally a random collection of disjoint simple loops that does indeed satisfy the conformal restriction axioms . by the main result of @xcite , this implies that they are cle@xmath4 ensembles for some @xmath5 . in section [ s.3 ] , we compare how loop - soups and sle@xmath4 curves behave when one changes the domain that they are defined in , and we deduce from this the relation between @xmath5 and @xmath0 in this subcritical phase . in section [ s.4 ] , we show that if the size of the clusters in a brownian loop - soup satisfy a certain decay rate property , then the corresponding @xmath0 is necessary _ strictly _ subcritical . this enables to show that the loop - soup corresponding to @xmath108 is the only possible critical one , and completes the identification of all cle@xmath4 s for @xmath14 $ ] as loop - soup cluster boundaries . the present paper is closely related to various other work on sle and cle , but it will in fact directly use sle results on only three distinct occasions : we use the main result of @xcite at the begining of section [ s.3 ] , we use the standard sle restriction properties from @xcite and the description of cle in terms of sle excursions derived in @xcite in section [ s.3 ] , and finally an estimate about the size of an sle@xmath4 excursion borrowed from @xcite in section [ s.4 ] .","summary":"the two - dimensional brownian loop - soup is a poissonian random collection of loops in a planar domain with an intensity parameter . when , we show that the outer boundaries of the loop clusters are disjoint simple loops ( when there is a.s .  only one cluster ) that satisfy certain conformal restriction axioms . we prove various results about loop - soups , cluster sizes , and the phase transition .    combining this with the results of another paper of ours on the markovian characterization of simple _ conformal loop ensembles _ more generally , it completes the proof of the fact that the following three descriptions of simple cles ( proposed in earlier works by the authors ) are equivalent :    1 .   the random loop ensembles traced by branching schramm - loewner evolution ( sle ) curves for in $ ] . 2 .   the outer - cluster - boundary ensembles of brownian loop - soups for . 3 .   the ( only ) random loop ensembles satisfying the _ conformal restriction axioms_.","abstract":"the two - dimensional brownian loop - soup is a poissonian random collection of loops in a planar domain with an intensity parameter . when , we show that the outer boundaries of the loop clusters are disjoint simple loops ( when there is a.s .  only one cluster ) that satisfy certain conformal restriction axioms . we prove various results about loop - soups , cluster sizes , and the phase transition .    combining this with the results of another paper of ours on the markovian characterization of simple _ conformal loop ensembles _ ( cle ) , this proves that these outer boundaries of clusters of brownian loops are in fact sle loops for in $ ] . more generally , it completes the proof of the fact that the following three descriptions of simple cles ( proposed in earlier works by the authors ) are equivalent :    1 .   the random loop ensembles traced by branching schramm - loewner evolution ( sle ) curves for in $ ] . 2 .   the outer - cluster - boundary ensembles of brownian loop - soups for . 3 .   the ( only ) random loop ensembles satisfying the _ conformal restriction axioms_."}
{"article_id":"0905.2287","section_id":"i","document":"since its introduction in a centralized context  @xcite , the minimum spanning tree ( or mst ) construction problem gained a benchmark status in distributed computing thanks to the influential seminal work of  @xcite . given an edge - weighted graph @xmath0 , where @xmath1 denotes the edge - weight function , the mst problem consists in computing a tree @xmath2 spanning @xmath3 , such that @xmath2 has minimum weight among all spanning trees of @xmath4 . one of the most versatile technique to ensure forward recovery of distributed systems is that of _ self - stabilization _  @xcite . a distributed algorithm is self - stabilizing if after faults and attacks hit the system and place it in some arbitrary global state , the system recovers from this catastrophic situation without external ( _ e.g. _ human ) intervention in finite time . a recent trend in self - stabilizing research is to complement the self - stabilizing abilities of a distributed algorithm with some additional _ safety _ properties that are guaranteed when the permanent and intermittent failures that hit the system satisfy some conditions . in addition to being self - stabilizing , a protocol could thus also tolerate a limited number of topology changes  @xcite , crash faults  @xcite , nap faults  @xcite , byzantine faults  @xcite , and sustained edge cost changes  @xcite . this last property is specially relevant when building spanning trees in dynamic networks , since the cost of a particular edge is likely to evolve through time . if a mst protocol is _ only _ self - stabilizing , it may adjust to the new costs in such a way that a previously constructed mst evolves into a disconnected or a looping structure ( of course , in the abscence of new edge cost changes , the self - stabilization property guarantees that _ eventually _ a new mst is constructed ) . of course , if edge costs change unexpectedly and continuously , a mst can not be maintained at all times . now , a packet routing algorithm is _ loop free _ @xcite if at any point in time the routing tables are free of loops , despite possible modification of the edge - weights in the graph ( _ i.e. _ , for any two nodes @xmath5 and @xmath6 , the actual routing tables determines a simple path from @xmath5 to @xmath6 , at any time ) . the _ loop - free _ property  @xcite in self - stabilization guarantees that , a spanning tree being constructed ( not necessarily a mst ) , then the self - stabilizing convergence to a `` minimal '' ( for some metric ) spanning tree maintains a spanning tree at all times ( obviously , this spanning tree is not `` minimal '' at all times ) . the consequence of this safety property in addition to that of self - stabiization is that the spanning tree structure can still be used ( e.g. for routing ) while the protocol is adjusting , and makes it suitable for networks that undergo such very frequent dynamic changes . [ [ related - works ] ] related works + + + + + + + + + + + + +    gupta and srimani  @xcite have presented the first self - stabilizing algorithm for the mst problem . it applies on graphs whose nodes have unique identifiers , whose edges have integer edge weights , and a weight can appear at most once in the whole network . to construct the ( unique ) mst , every node performs the same algorithm . the mst construction is based on the computation of all the shortest paths ( for a certain cost function ) between all the pairs of nodes . while executing the algorithm , every node stores the cost of all paths from it to all the other nodes . to implement this algorithm , the authors assume that every node knows the number @xmath7 of nodes in the network , and that the identifiers of the nodes are in @xmath8 . every node @xmath5 stores the weight of the edge @xmath9 placed in the mst for each node @xmath10 . therefore the algorithm requires @xmath11 bits of memory at node @xmath5 . since all the weights are distinct integers , the memory requirement at each node is @xmath12 bits . higham and lyan  @xcite have proposed another self - stabilizing algorithm for the mst problem . as  @xcite , their work applies to undirected connected graphs with unique integer edge weights and unique node identifiers , where every node has an upper bound on the number of nodes in the system . the algorithm performs roughly as follows : every edge aims at deciding whether it eventually belongs to the mst or not . for this purpose , every non tree - edge @xmath13 floods the network to find a potential cycle , and when @xmath13 receives its own message back along a cycle , it uses information collected by this message ( _ i.e. _ , the maximum edge weight of the traversed cycle ) to decide whether @xmath13 could potentially be in the mst or not . if the edge @xmath13 has not received its message back after the time - out interval , it decides to become tree edge . the core memory of each node holds only @xmath14 bits , but the information exchanged between neighboring nodes is of size @xmath15 bits , thus only slightly improving that of @xcite .    to our knowledge , _ none _ of the self - stabilizing mst construction protocols is loop - free . since the aforementioned two protocols also make use of the knowledge of the global number of nodes in the system , and assume that no two edge costs can be equal , these extra hypoteses make them suitable for static networks only . relatively few works investigate merging self - stabilization and loop free routing , with the notable exception of  @xcite . while  @xcite still requires that a upper bound on the network diameter is known to every participant , no such assumption is made in  @xcite . also , both protocols use only a reasonable amount of memory ( @xmath14 bits per node ) . however , the metrics that are considered in  @xcite are derivative of the shortest path ( _ a.k.a . _ sp ) metric , that is considered a much easier task in the distributed setting than that of the mst , since the associated metric is _ locally optimizable _  @xcite , allowing essentially locally greedy approaches to perform well . by contrast , some sort of _ global optimization _ is needed for mst , which often drives higher complexity costs and thus less flexibility in dynamic networks . [ [ our - contributions ] ] our contributions + + + + + + + + + + + + + + + + +    we describe a new self - stabilizing algorithm for the mst problem . contrary to previous self - stabilizing mst protocols , our algorithm does not make any assumption about the network size ( including upper bounds ) or the unicity of the edge weights . moreover , our solution improves on the memory space usage since each participant needs only @xmath14 bits , and node identifiers are not needed . in addition to improving over system hypotheses and complexity , our algorithm provides additional safety properties to self - stabilization , as it is loop - free . compared to previous protocols that are both self - stabilizing and loop - free , our protocol is the first to consider non - monotonous tree metrics .    the key techniques that are used in our scheme include fast construction of a spanning tree , that is continuously improved by means of a pre - order construction over the nodes . the cycles that are considered over time are precisely those obtained by adding one edge to the evolving spanning tree . considering solely that type of cycles reduces the memory requirement at each node compared to @xcite because the latter consider all possible paths connecting pairs of nodes . moreover , constructing and using a pre - order on the nodes allows our algorithm to proceed in a completely asynchronous manner , and without any information about the size of the network , as opposed to  @xcite . the main characteristics of our solution are presented in table  [ tableresume ] , where a boldface denotes the most useful ( or efficient ) feature for a particular criterium .","summary":"the minimum spanning tree ( mst ) construction is a classical problem in distributed computing for creating a globally minimized structure distributedly . self - stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner . the loop - free property provides interesting safety assurance in dynamic networks where edge - cost changes during operation of the protocol .    we present a new self - stabilizing mst protocol that improves on previous known approaches in several ways . second , it is loop - free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new mst .","abstract":"the minimum spanning tree ( mst ) construction is a classical problem in distributed computing for creating a globally minimized structure distributedly . self - stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner . the loop - free property provides interesting safety assurance in dynamic networks where edge - cost changes during operation of the protocol .    we present a new self - stabilizing mst protocol that improves on previous known approaches in several ways . first , it makes fewer system hypotheses as the size of the network ( or an upper bound on the size ) need _ not _ be known to the participants . second , it is loop - free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new mst . finally , time complexity matches the best known results , while space complexity results show that this protocol is the most efficient to date ."}
{"article_id":"0708.1788","section_id":"i","document":"the reionization of cosmic hydrogen , which is commonly believed to have been due to ultraviolet photons produced by the first stars and quasars ( barkana & loeb  2001 ) , was an important milestone in the history of the universe . the recent discovery of very distant quasars has enabled detailed studies of the ionization state of the high redshift igm to be made at a time when the universe was less than a billion years old ( fan et al . 2006 ; white et al . several studies have used the evolution of the ionizing background inferred from these spectra to argue that the reionization of cosmic hydrogen was completed just beyond @xmath10 ( white et al . 2003 ; fan et al . 2006 ; gnedin & fan  2006 ) . however other authors have claimed that the evidence for this rapid change becomes significantly weaker for a different choice density distribution in the igm ( becker et al  2007 ) . one reason for the ambiguity in interpreting these absorption spectra is that ly@xmath0   absorption can only be used to probe neutral fractions that are larger than @xmath2 , owing to the large cross - section of the ly@xmath0   resonance . several of the most distant quasars exhibit complete gunn - peterson troughs , the red edges of which do not extend as far as the redshifted ly@xmath0 wavelength . a possible interpretation of the observation of a gunn - peterson trough which does not extend all the way to the ly@xmath0 wavelength is the presence of an h   region in a partially neutral igm ( e.g. cen & haiman  2000 , madau & rees  2000 ) . this interpretation has been used in different ways to argue that there is a significant fraction of neutral hydrogen in the igm beyond @xmath1 ( wyithe & loeb  2004 ; mesinger & haiman  2004 ; wyithe , loeb & carilli  2005 ) , with a lower limit on the hydrogen neutral fraction that is as much as two orders of magnitude larger than constraints available from direct absorption studies . bolton & haehnelt ( 2007a ) , maselli et al . ( 2007 ) and lidz et al . ( 2007 ) , however , have argued that this interpretation is uncertain and that these observed regions of transmission could either be due to an h   region or due to a classical proximity zone . given this uncertainty , and in order to connect the evolution of the igm ionization state at redshifts both above and below those where the gunn - peterson troughs have been observed , fan et al . ( 2006 ) proposed defining the sizes of these regions of transmission as the distance where the smoothed spectrum first drops below the level where 10 per cent of the flux is transmitted . bolton & haehnelt ( 2007a ) refer to this region as the highly ionized near - zone , and fan et al . ( 2006 ) argued that its size should reflect the ionization state of the igm in a simple way . using this definition , fan et al . ( 2006 ) found a rapid trend of near - zone size with redshift , from which they inferred an order of magnitude increase in the neutral fraction of the igm over the observed range of @xmath11 . however bolton & haehnelt  ( 2007a ) demonstrated that the near - zone size becomes independent of the neutral hydrogen fraction when the igm is highly ionized . in this paper we shall address two points regarding the interpretation of the near - zones observed in high redshift quasar absorption spectra . as pointed out recently by lidz et al . ( 2007 ) and alvarez & abel ( 2007 ) , the quasars observed prior to @xmath1 are likely to have formed in regions substantially preionized by nearby clustered galaxies . we therefore first discuss the extent to which regions of the igm observed close to high redshift quasars in absorption spectra are representative of the universe on average , using a density dependent semi - analytic model for the reionization history . this model is carefully calibrated to be consistent with the current observational data , and as such provides a consistent theoretical framework for modeling quasar near - zones in highly biased regions of the igm . we then use this model to predict the sizes of quasar near - zones and their evolution with redshift , both semi - analytically and using detailed simulations of radiative transfer . we begin by describing our density dependent semi - analytic model for the reionization history (   [ models ] ) , including our procedures for the calculation of the ionizing background . we then present results for the bias of reionization near quasars in   [ results ] , before discussing the evolution of the observed high redshift quasar near - zones using the semi - analytic model in   [ nearzones ] . we then explore this model in more detail with full radiative transfer simulations in  [ sec : sims ] . we present our conclusions in   [ conclusions ] . throughout the paper we adopt the set of cosmological parameters determined by _ wmap _ ( spergel et al . 2007 ) for a flat @xmath12cdm universe .","summary":"however , the interpretation of these spectra is complicated by the fact that the ly optical depth is already large for neutral hydrogen fractions in excess of , and also because quasars are expected to reside in dense regions of the igm . [ firstpage ]    cosmology : theory - galaxies : formation - intergalactic medium","abstract":"absorption spectra of high redshift quasars exhibit an increasingly thick ly forest , suggesting the fraction of neutral hydrogen in the intergalactic medium ( igm ) is increasing towards . however , the interpretation of these spectra is complicated by the fact that the ly optical depth is already large for neutral hydrogen fractions in excess of , and also because quasars are expected to reside in dense regions of the igm . we present a model for the evolution of the ionization state of the igm which is applicable to the dense , biased regions around high - redshift quasars as well as more typical regions in the igm . we employ a cold dark matter ( cdm ) based model in which the ionizing photons for reionization are produced by star formation in dark matter halos spanning a wide range of masses , combined with numerical radiative transfer simulations which model the resulting opacity distribution in quasar absorption spectra . with an appropriate choice for the parameter which controls the star formation efficiency , our model is able to simultaneously reproduce the observed ly   forest opacity at , the ionizing photon mean - free - path at and the rapid evolution of highly ionized near - zone sizes around high - redshift quasars at . in our model , reionization extends over a wide redshift range , starting at and completing as hii regions overlap at . we find that within 5 physical mpc of a high redshift quasar , the evolution of the ionization state of the igm precedes that in more typical regions by around 0.3 redshift units . more importantly , when combined with the rapid increase in the ionizing photon mean - free - path expected shortly after overlap , this offset results in an ionizing background near the quasar which exceeds the value in the rest of the igm by a factor of . we further find that in the post - overlap phase of reionization the size of the observed quasar near - zones is not directly sensitive to the neutral hydrogen fraction of the igm . instead , these sizes probe the level of the background ionization rate and the temperature of the surrounding igm . the observed rapid evolution of the quasar near - zone sizes at can thus be explained by the rapid evolution of the ionizing background , which in our model is caused by the completion of overlap at the end of reionization by .    [ firstpage ]    cosmology : theory - galaxies : formation - intergalactic medium"}
{"article_id":"0708.1788","section_id":"i","document":"absorption spectra of high redshift quasars show an increasingly thick ly@xmath0 forest , suggesting an increase in the fraction of neutral gas in the igm approaching @xmath1 , culminating in the complete lack of detected flux in the gunn - peterson trough blueward of the ly@xmath0   line . however the meaning of the complete gunn - peterson troughs remains controversial , having been interpreted both as the completion of the reionization epoch , and as merely a gradual thickening of the ly@xmath0 forest . the inconclusive nature of the observations has its root in the very large cross - section for absorption of ly@xmath0   photons , which allow a direct probe of the neutral hydrogen content of the igm only down to volume averaged neutral fractions of around @xmath2 . the fact that quasars reside in massive halos places them in overdense and strongly biased regions of the igm . this presents an additional challenge for the interpretation of regions in quasar absorption spectra close to the quasars intrinsic redshift , since one is using results from these biased regions to infer the properties of the mean igm . in this work we have presented a model for the evolution of the emissivity of ionizing photons and the ionization state of the igm that takes such a reionization bias in the environment of bright , high - redshift quasars into account . in our cdm based model the ionizing photons for reionization are produced by star formation in dark matter halos spanning a wide mass range . at redshifts both prior to , and post overlap , our model allows us to calculate values for the volume and mass - averaged neutral fractions , the ionizing photon mean - free - path and the evolution of the ionizing background . with appropriate choices for the parameters controlling the star formation efficiency , we are able to reproduce the ionizing emissivity at @xmath3 and the ionizing photon mean - free - path at @xmath4 inferred from the observed opacity distribution in ly@xmath0forest absorption spectra . in our model the comoving ionizing emissivity is roughly constant with redshift and the volume filling factor of ionizing regions increases slowly from 10 to 90 per cent between @xmath213 and @xmath7 , where reionization completes following the overlap of cosmological hii regions . within 5 physical mpc of a high redshift quasar , we find the evolution of the ionization state of the igm precedes that of the mean universe by around 0.3 redshift units . during the period shortly after overlap the mean - free - path is seen to increase rapidly in the model . the offset in the redshift of overlap between overdense regions and the mean igm therefore results in an ionizing background near high redshift quasars ( excluding the flux of ionizing radiation from the quasar itself ) that exceeds the value in the mean igm by a factor of @xmath8 for a short period of time .    high redshift quasar spectra also show evidence for a highly ionized region immediately surrounding the quasar . using our semi - analytic prescription for biased reionization , we model the evolution of these quasar near - zones . we find near - zone sizes which exhibit a redshift dependence which is qualitatively consistent with the current observational data . the model indicates that the rapid evolution in the near - zone sizes in the redshift range @xmath5 is due to the increasing background ionization rate originating from an almost constant galactic emissivity . within our model , this rise in the background ionization rate is therefore due to the rapid rise in the mean free path for ionizing photons , which is expected near the tail - end of the reionization epoch as h   regions overlap .    in order to model the opacity distribution in spectra of bright high - redshift quasars in more detail we have combined our model for the evolution of the metagalactic ionization rate in the biased environment surrounding quasars with detailed line - of - sight radiative transfer simulations in the inhomogeneous high - redshift igm . in this way we were able to reproduce the sizes of the observed near - zones and their rapid evolution in the redshift range @xmath5 very well . our numerical modeling also suggests that the rapid evolution is not due directly to large changes in the neutral hydrogen fraction of the igm . instead , as suggested by bolton & haehnelt ( 2007a ) , the near - zone sizes probe the evolution of the background ionization rate , which results in modest changes to an already very small neutral fraction . we furthermore find that the absolute sizes of the near - zones are rather sensitive to the igm temperature in the near - zones , due to the temperature dependence of the recombination rate . the observed near - zone sizes are reproduced given the observed quasar ionizing luminosities if the temperature of the surrounding igm is high ( @xmath202 ) . heating to such high temperatures at distances of up to @xmath214 proper mpc may be plausible if the hydrogen and helium in the near - zone has been highly ionized by a hard spectrum prior to the completion of reionization in the igm as a whole . this requires the continuous or intermittent emission of a hard spectrum for an extended period of time . if the igm temperature is not as hot as @xmath215 , the differences found between modeled and observed near - zone sizes could be explained as at least partially being due to a continuum on the observed spectra which has been placed too low , or perhaps a quasar sed which is different to the one we have assumed . there are still several issues to address regarding the sizes and redshift evolution of high redshift quasar near - zones . larger samples will clarify the significance of the evolution observed in the current data and hopefully constrain the evolution at even higher redshift . a more detailed modeling of the quasar accretion history and the ensuing flux of ionizing photons may be required to self - consistently model near - zone sizes . the detection of strongly broadened absorption lines within quasar near - zones would lend support to a scenario in which igm temperatures within quasar near - zones are increased by the reionization of hydrogen and helium by a hard spectrum . however , in this work we have presented a simple reionization model with a roughly constant ionizing emissivity , in which reionization ends following a rapid increase in the ionizing photon mean - free - path as h   regions overlap at @xmath7 . this scenario successfully reproduces the gross features present in high redshift quasar absorption spectra , both within and outside of the quasar near - zones .","summary":"absorption spectra of high redshift quasars exhibit an increasingly thick ly forest , suggesting the fraction of neutral hydrogen in the intergalactic medium ( igm ) is increasing towards . we present a model for the evolution of the ionization state of the igm which is applicable to the dense , biased regions around high - redshift quasars as well as more typical regions in the igm . we employ a cold dark matter ( cdm ) based model in which the ionizing photons for reionization are produced by star formation in dark matter halos spanning a wide range of masses , combined with numerical radiative transfer simulations which model the resulting opacity distribution in quasar absorption spectra . with an appropriate choice for the parameter which controls the star formation efficiency , our model is able to simultaneously reproduce the observed ly   forest opacity at , the ionizing photon mean - free - path at and the rapid evolution of highly ionized near - zone sizes around high - redshift quasars at . in our model , reionization extends over a wide redshift range , starting at and completing as hii regions overlap at . we find that within 5 physical mpc of a high redshift quasar , the evolution of the ionization state of the igm precedes that in more typical regions by around 0.3 redshift units . more importantly , when combined with the rapid increase in the ionizing photon mean - free - path expected shortly after overlap , this offset results in an ionizing background near the quasar which exceeds the value in the rest of the igm by a factor of .","abstract":"absorption spectra of high redshift quasars exhibit an increasingly thick ly forest , suggesting the fraction of neutral hydrogen in the intergalactic medium ( igm ) is increasing towards . however , the interpretation of these spectra is complicated by the fact that the ly optical depth is already large for neutral hydrogen fractions in excess of , and also because quasars are expected to reside in dense regions of the igm . we present a model for the evolution of the ionization state of the igm which is applicable to the dense , biased regions around high - redshift quasars as well as more typical regions in the igm . we employ a cold dark matter ( cdm ) based model in which the ionizing photons for reionization are produced by star formation in dark matter halos spanning a wide range of masses , combined with numerical radiative transfer simulations which model the resulting opacity distribution in quasar absorption spectra . with an appropriate choice for the parameter which controls the star formation efficiency , our model is able to simultaneously reproduce the observed ly   forest opacity at , the ionizing photon mean - free - path at and the rapid evolution of highly ionized near - zone sizes around high - redshift quasars at . in our model , reionization extends over a wide redshift range , starting at and completing as hii regions overlap at . we find that within 5 physical mpc of a high redshift quasar , the evolution of the ionization state of the igm precedes that in more typical regions by around 0.3 redshift units . more importantly , when combined with the rapid increase in the ionizing photon mean - free - path expected shortly after overlap , this offset results in an ionizing background near the quasar which exceeds the value in the rest of the igm by a factor of . we further find that in the post - overlap phase of reionization the size of the observed quasar near - zones is not directly sensitive to the neutral hydrogen fraction of the igm . instead , these sizes probe the level of the background ionization rate and the temperature of the surrounding igm . the observed rapid evolution of the quasar near - zone sizes at can thus be explained by the rapid evolution of the ionizing background , which in our model is caused by the completion of overlap at the end of reionization by .    [ firstpage ]    cosmology : theory - galaxies : formation - intergalactic medium"}
{"article_id":"cond-mat9609015","section_id":"i","document":"study of the coulomb blockade and charging effects in the transport properties of semiconductor systems is peculiarly suitable to investigation through self - consistent electronic structure techniques . while the orthodox theory @xcite , in parameterizing the energy of the system in terms of capacitances , is strongly applicable to metal systems , the much larger ratio of fermi wavelength to system size , @xmath3 , in mesoscopic semiconductor devices , requires investigation of the interplay of quantum mechanics and charging .    in the first step beyond the orthodox theory , the `` constant interaction '' model of the coulomb blockade supplemented the capacitance parameters , which were retained to characterize the gross electrostatic contributions to the energy , with non - interacting quantum levels of the dots and leads of the mesoscopic device @xcite this theory was successful in explaining some of the fundamental features , specifically the periodicity , of coulomb oscillations in the conductance of a source - dot - drain - gate system with varying gate voltage . other effects , however , such as variations in oscillation amplitudes , were not explained .    in this paper we employ density functional ( df ) theory to compute the self - consistently changing effective single particle levels of a lateral @xmath0 quantum dot , as a function of gate voltages , temperature @xmath4 , and dot electron number @xmath5 @xcite . we also compute the total system free energy from the results of the self - consistent calculation . we are then able to calculate the device conductance in the linear bias regime without any adjustable parameters . here we consider only weak ( @xmath6 ) magnetic fields in order to study the effects of breaking time - reversal symmetry . we will present results for the edge state regime in a subsequent publication @xcite . we include donor layer disorder in the calculation and present results for the statistics of level spacings and partial level widths due to tunneling to the leads . recently we have employed monte - carlo variable range hopping simulations to consider the effect of coulomb regulated ordering of ions in the donor layer on the mode characteristics of split - gate quantum _ wires _ @xcite . the results of those simulations are here applied to quantum dot electronic structure . a major innovation in this calculation is our method for determining the two dimensional electron gas ( 2deg ) charge density . at each iteration of the self - consistent calculation , at each point in the @xmath7 plane we determine the subbands @xmath8 and wave functions @xmath9 in the @xmath10 ( growth ) direction . the full three dimensional density is then determined by a solution of the multi - component 2d schrdinger equation and/or 2d thomas - fermi approximation .    among the many approximation in the calculation are the following . we use the local density approximation ( lda ) for exchange - correlation ( xc ) , specifically the parameterized form of stern and das sarma @xcite . while the lda is difficult to justify in small ( @xmath11 ) quantum dots it is empirically known to give good results in atomic and molecular systems where the density is also changing appreciably on the scale of the fermi wavelength @xcite .    in reducing the 3d schrdinger equation to a multi - component 2d equation we cutoff the expansion in subbands , often taking only the lowest subband into account . we also cutoff the wavefunctions by placing another artificial @xmath12 interface at a certain depth ( typically @xmath13 ) away from the first interface , thereby ensuring the existence of subbands at all points in the @xmath7 plane . generally the subband energy of this bare square well is much smaller than the triangular binding to the interface in all but those regions which are very nearly depleted .    the dot electron states in the zero magnetic field regime are simply treated as spin degenerate . for @xmath14 an unrenormalized land g - factor of @xmath15 is used . we employ the effective mass approximation uncritically and ignore the effective mass difference between @xmath16 and @xmath12 ( @xmath17 ) . similarly we take the background dielectric constant to be that of pure @xmath16 ( @xmath18 ) thereby ignoring image effects ( in the @xmath12 ) . we ignore interface grading and treat the interface as a sharp potential step . these effects have been treated in other calculations of self - consistent electronic structure for @xmath0 devices @xcite and have generally been found to be small . we mostly employ effective atomic units wherein @xmath19 and @xmath20 . the structure of the paper is as follows . in section ii we first discuss the calculation of the electronic structure , focusing on those features which are new to our method . further subsections then consider the treatment of discrete ion charge and disorder , calculation of the total dot free energy from the self - consistent electronic structure results , calculation of the source - dot - drain conductance in the linear regime and calculation of the dot capacitance matrix . section iii provides new results which are further subdivided into basic electrostatic properties , properties of the effective single electron spectra , statistics of level spacings and widths and conductance in the coulomb oscillation regime . section iv summarizes the principal conclusions which we derive from the calculations .","summary":"the schrdinger equation is reduced from 3d to multi - component 2d and solved via an eigenfunction expansion in the dot . we present details of our derivation of the total dot - lead - gates interacting free energy in terms of the electronic structure results , which is free of capacitance parameters .","abstract":"we employ density functional theory to calculate the self consistent electronic structure , free energy and linear source - drain conductance of a lateral semiconductor quantum dot patterned via surface gates on the 2deg formed at the interface of a heterostructure . the schrdinger equation is reduced from 3d to multi - component 2d and solved via an eigenfunction expansion in the dot . this permits the solution of the electronic structure for dot electron number . we present details of our derivation of the total dot - lead - gates interacting free energy in terms of the electronic structure results , which is free of capacitance parameters . statistical properties of the dot level spacings and connection coefficients to the leads are computed in the presence of varying degrees of order in the donor layer . based on the self - consistently computed free energy as a function of gate voltages , , and n , we modify the semi - classical expression for the tunneling conductance as a function of gate voltage through the dot in the linear source - drain , coulomb blockade regime . among the many results presented , we demonstrate the existence of a shell structure in the dot levels which ( a ) results in envelope modulation of coulomb oscillation peak heights , ( b ) which influences the dot capacitances and should be observable in terms of variations in the activation energy for conductance in a coulomb oscillation minimum , and ( c ) which possibly contributes to departure of recent experimental results from the predictions of random matrix theory .    2 [    ]"}
{"article_id":"cond-mat9609015","section_id":"r","document":"we consider only a small subspace of the huge available parameter space . for the results presented here we have fixed the nominal 2deg density to @xmath128 and the aluminum concentration of the barrier to @xmath129 . the lithographic gate pattern is shown in figure [ fig1 ] , as is the growth profile ( including our artificial second barrier ) . some results are presented with a variation of the total thickness @xmath32 of the algaas ( fig . [ fig1 ] ) .    to interpret the results we note the following considerations . hohenberg - kohn - sham theory provides only that the ground state energy of an interacting electron system can be written as a functional of the density @xcite . the single particle eigenvalues @xmath130 have , strictly speaking , no physical meaning . however , as pointed out by slater @xcite , the usefulness of df theory depends to some extent on being able to interpret the energies and wave functions as some kind of single particle spectrum . in the coulomb blockade regime it is particularly important to be clear what that interpretation , and its limitations , are . a distinction is commonly made between the addition spectrum and the excitation spectrum for quantum dots @xcite . differences between our effective single particle eigenvalues represent an approximation to the excitation spectrum . as a specific example , in the absence of depolarization and excitonic effects the first single particle excitation from the @xmath5-electron ground state with gate voltages @xmath2 is @xmath131 . the addition spectrum , on the other hand , depends on the energy difference between the ground states of the dot _ interacting with its environment _ at two different @xmath5 . thus , in our formalism , the addition spectrum is given by differences in @xmath132 at neighboring @xmath5 , possibly further modulated by excitations , i.e. differences in the occupation numbers @xmath133 . in contrast to experiment , the electronic structure can be determined for arbitrary @xmath5 and @xmath2 ( so long as the dot is closed ) . this includes both non - integer @xmath5 as well as values which are far from equilibrium ( differing chemical potential ) with the leads . the `` resonance curve '' @xcite is given by the @xmath5 which minimizes @xmath134 at each @xmath103 ( gates other than the plunger gate are assumed fixed ) . this occurs when the chemical potential of the dot equals those of the leads ( which are taken as equal to one another and represent the energy zero ) and gives the most probable electron number . results presented below as a function of varying gate voltage , particularly the spectra in figs . [ fig10 ] and [ fig14 ] , are assumed to be along the resonance curve . figure [ fig3]a shows an example of a potential profile along with a corresponding density plot for a quiet dot containing @xmath135 electrons . the basic potential / density configuration , as well as the capacitances are highly robust . these data are computed completely in the 2d thomas - fermi approximation , single @xmath10-subband , at @xmath136 . solution of schrdinger s equation or variation of @xmath4 result in only subtle changes . the depletion region spreading is roughly @xmath137 . figure [ fig3]b shows a set of potential and density profiles along the y - direction ( transverse to the current direction ) in steps of @xmath138 in @xmath60 , from the qpc saddle point to the dot center . note that the density at the dot center is only about @xmath139 of the ungated 2deg    density . correspondingly the potential at the center is above the floor of the ungated 2deg ( @xmath140 ) . we discuss a simple model for the potential shape of a circular quantum dot below ( sec . iii.b.1 ) . here we note only that the radial potential can be regarded as parabolic to lowest order with quartic and higher order corrections whose influence increases near the perimeter . in thomas - fermi studies on larger dots @xcite with a comparable aspect ratio we find that the potential and density achieve only @xmath141 of their ungated 2deg value nearly @xmath142 from the gate . regarding classical billiard calculations for gated structures therefore @xcite even in the absence of impurities it is difficult to see how the `` classical '' hamiltonian at the 2deg level can be even approximately integrable unless the lithographic gate pattern is azimuthally symmetric @xcite . the importance of the remote ionized impurity distribution is demonstrated in figure [ fig4 ] which shows a quantum dot with randomly placed ionized    donors on the left and with ions which have been allowed to reach quasi - equilibrium via variable range hopping , on the right . in both cases the total ion number in the area of the dot is fixed . the example shown here for the ordered case assumes , in the variable range hopping calculation , one ion for every five donors ( @xmath143 ) . as in ref . @xcite we have , for simplicity , ignored the negative @xmath144 model for the donor impurities ( dx centers ) , which is still controversial @xcite . if the negative @xmath144 model , at some barrier aluminum concentration , is correct , the most ordered ion distributions will occur for @xmath145 , as opposed to the neutral dx picture employed here , where ordering increases monotonically as @xmath72 decreases @xcite . for these assumptions figure [ fig5 ] indicates that ionic ordering substantially reduces the potential fluctuations relative to the completely disordered case , even for relatively large @xmath72 . here , using ensembles of dots with varying @xmath72 we compare the effective 2d potential with a quiet dot ( jellium donor layer ) at the same gate voltages and same dot electron number . the distribution of the potential deviation is computed as : @xmath146)\\ ] ] where @xmath147 labels samples ( different ion distributions ) , typically up to @xmath148 , @xmath5 is the total number of @xmath60 or @xmath61 grid points in the dot ( @xmath149 ) , and `` qd '' stands for quiet dot . the distributions for all @xmath72 are asymmetric ( fig . [ fig5 ] ) . although the means are indistinguishably close to zero , the probability for large potential hills resulting from disorder is greater than for deep depressions . also , the distributions for points above the fermi surface ( dashed lines ) are broader by an order of magnitude ( in standard deviation ) than below , due to screening . finally , saturation as @xmath150 ( inset fig . [ fig5 ] ) shows that even if the ions are arranged in a wigner crystal ( the limiting case at @xmath151 ) , potential fluctuations would be expected in comparison with ionic jellium . the success of the capacitance model in describing experimental results of charging phenomena in mesoscopic systems has been remarkable @xcite . for our calculations as well , even the simplest formulations for the capacitance tend to produce smoothly varying results when gate voltages or dot charge are varied . figure [ fig6 ] shows the trend of the dot self - capacitances with @xmath103 . also shown are the equilibrium dot electron number @xmath5 and the minimum of the dot potential @xmath152 as functions of @xmath103 . note here that @xmath152 is the minimum of the 3d electrostatic potential rather than the effective 2d potential which is presented elsewhere ( such as in figs . [ fig3 ] and [ fig4 ] ) .    that @xmath123 generally decreases as the dot becomes smaller is not surprising and has been discussed elsewhere @xcite . all three forms of @xmath123 are roughly in agreement giving a value @xmath153 ( the capacitance as calculated from the free energy is not shown ) . the fluctuations result from variations in the quantized level energies as the dot size and shape are changed by @xmath103 . note that _ numerical _ error is indiscernible on the scale of the figure . the pronounced collapse of @xmath154 near @xmath155 , which is expanded in the upper panel , shows the presence of a region where the change of @xmath5 with @xmath156 is greatly suppressed . since the change of @xmath152 with @xmath156 is similarly suppressed there is no corresponding anomaly in @xmath123 . interestingly , the capacitance computed from the free energy also reveals no deep anomaly . the anomaly at @xmath155 and also the fluctuation in the electrostatic properties near @xmath157 are related to a shell structure in the spectrum which we discuss below .    a frequently encountered model for the classical charge distribution in a quantum dot is the circular conducting disk with a parabolic confining potential @xcite . it can be shown ( solving , for example , poisson s equation in oblate spheroidal coordinates ) that for such a model the 2d charge distribution in the dot goes as @xmath158 where @xmath159 is the dot radius and @xmath160 is the density at the dot center . the `` external '' confining potential is assumed to go as @xmath161 and @xmath159 is related to @xmath5 through @xmath162 where @xmath110 is the dielectric constant @xcite .    to justify this model , the authors of ref . @xcite claim that the calculations of kumar _ @xcite show that `` the confinement ... has a nearly parabolic form for the external confining potential ( _ sic _ ) . '' this is incorrect . what kumar _ s calculations shows is that ( for @xmath163 ) the _ self - consistent _ potential , which includes the potential from the electrons themselves , is approximately cutoff parabolic . the _ external _ confining potential , as it is used in ref . @xcite , would be that produced by the donor layer charge and the charge on the surface gates only . we introduce a simple model ( see iii.b.1 below ) wherein this confining potential charge is replaced by a circular disk of positive charge whose density is fixed by the doping density and whose radius is determined by the number of electrons _ in the dot_. the gates can be thought of as merely cancelling the donor charge outside that radius . the essential point , then , is this : adding electrons to the dot decreases the ( negative ) charge on the gates and therefore increases the radius . one can make the assumption , as in ref . @xcite , that the external potential is parabolic , but it is a mistake to treat that parabolicity , @xmath164 , as independent of @xmath5 . this is illustrated in figure [ fig7 ] where we have plotted contours for the _ change _ in the 2d density , as @xmath156 is incrementally increased ,    as determined self - consistently ( thomas - fermi everywhere , left panel ) and as determined from eq . [ eq : circ ] . the white curves display the density change profiles across the central axis of the dot . the total change in @xmath5 is the same in both cases , but clearly the model of eq . [ eq : circ ] underestimates the degree to which new charge is added mostly to the perimeter . recently the question of charging energy renormalization via tunneling as the conductance @xmath165 through a qpc approaches unity has received much attention @xcite . in a recent experiment employing two dots in series a splitting of the coulomb oscillation peaks has been observed as the central qpc ( between the two dots ) is lowered @xcite . perturbation theory for small @xmath165 and a model which treats the decaying channel between the dots as a luttinger liquid for @xmath166 lead to expressions for the peak splitting which is linear in @xmath165 in the former case and goes as @xmath167 in the latter case .    a crucial assumption of the model , however , is that the `` bare '' capacitance , specifically that between the dots @xmath168 , remains approximately independent of the height of the qpc , even when an open channel connects the two dots . thus the mechanism of the peak splitting is assumed to be qualitatively different from a model which predicts peak splitting entirely on an electrostatic basis when the inter - dot capacitance increases greatly @xcite . the independence of @xmath168 from the qpc potential is plausible insofar as most electrons , even when a channel is open , are below the qpc saddle points and hence localized on either one dot or the other . further , if the screening length is short and if the channel itself does not accommodate a significant fraction of the electrons , there is little ambiguity in retaining @xmath168 to describe the gross electrostatic interaction of the dots , even when the dots are _ connected _ at the fermi level .    in figure [ fig8 ] we present evidence for this theory by showing the capacitance between a dot and the _ leads _ as the qpc voltage is reduced . in the figure @xmath169 is the effective 2d potential of the left ( right ) saddle point as the left qpc gate voltages @xmath170 only are varied . the dot is nearly open when the qpc voltages ( both pins on the left ) reach @xmath171 . the results here use the full quantum mechanical solution ( without the lda exchange - correlation energy ) , however the electrons in the lead continue to be treated with a 2d tf approximation . the dot `` reconstruction '' seen in figure  [ fig5 ] is visible    here also around @xmath172 . note that the right saddle point is sympathetically affected when we change this left qpc . while the effect is faint , @xmath173 of the change of the left saddle , the sensitivity of tunneling to saddle point voltage ( see also below ) has resulted in this kind of cross - talk being problematical for experimentalists . the figure also shows that the capacitance between the dot and one lead exceeds that to a ( single ) qpc gate or even to a plunger gate . however the most important result of the figure is to show that the dot to lead capacitance is largely insensitive to qpc voltage . when the left qpc is as closed as the right ( @xmath174 ) the capacitances to the source and drain are equal . but even near the open condition the capacitance to the left lead ( arbitrarily the `` source '' ) only exceeds that to the drain ( which is still closed ) minutely . therefore the assumptions of a `` bare '' capacitance which remains constant even as contact is made with a lead ( or , in the experiment , another dot ) seems to be very well founded . as noted above , the interaction between a gate and the 2deg depends upon the distance of the gates from the 2deg , i.e. , the @xmath12 thickness @xmath32 . in figure [ fig9 ] we show that , as we decrease @xmath32 , simultaneously changing the gate voltages such that @xmath5 and the saddle point potentials remain constant , the total dot capacitance also decreases , but the distribution of the dot capacitance between leads , gates and ( not shown ) back gate change only moderately . that gates closer to the 2deg plane should produce dots of lower capacitance is made clear in the upper panel of the figure , which shows the potential and density profile ( using tf ) near a depletion region at the side of the dot at varying @xmath32 and constant gate voltage . for smaller @xmath32 the depletion region is widened but the density achieves its ungated 2deg value ( here @xmath175 ) more quickly ; a potential closer to hard walled is realized . in the presence of stronger confinement the capacitance decreases and the charging energy increases .    the profile of the tunnel barriers and the barrier penetration factors are also dependent on @xmath32 . however we postpone a discussion of this until the section on tunneling coefficients . the bulk electrostatic properties of a dot are , to first approximation , independent of whether a thomas - fermi approximation is used or schrdinger s equation is solved . a notable exception to this is the fluctuation in the capacitances . figure [ fig10 ] shows the plunger gate voltage dependence of the energy levels . the fermi level of the dot is kept constant and equal to that of the leads ( it is the energy zero ) . hence as the gate voltage increases ( becomes less negative ) @xmath5 increases . since the qpcs lie along the @xmath60-axis , the dot is never fully symmetric with respect to interchange of @xmath60 and @xmath61 , however the most symmetric configuration occurs for @xmath176 , towards the right side of the plot . the levels clearly group into quasi - shells with gaps between . the number of states per shell follows the degeneracy of a 2d parabolic potential , i.e. 1,2,3,4 , ... degenerate levels per shell ( ignoring spin ) . there is a pronounced tendency for the levels to cluster at the fermi surface , here given by @xmath177 , which we discuss below . shell structure in atoms arises from the approximate constancy of individual electron angular momenta , and degeneracy with respect to @xmath10-projection . since in two dimensions the angular momentum @xmath178 is fixed in the @xmath10 ( transverse ) direction , the isotropy of space is broken and the only remaining manifest degeneracy , and this only for azimuthally symmetric dots , is with respect to @xmath179 . a two dimensional parabolic potential , in the absence of magnetic field , possesses an accidental degeneracy for which a shell structure is recovered . we have shown above that modelling a quantum dot as a classical , conducting layer in an _ external _ parabolic potential @xmath180 , where @xmath164 is independent of the number of electrons in the dot , ignores the image charge in the surface gates forming the dot and therefore fails to properly describe the evolving charge distribution as electrons are added to the dot . a more realistic model , which _ explains _ the approximate parabolicity of the _ self - consistent _ potential , and hence the apparent shell structure , is illustrated in figure [ fig11 ] . the basic electrostatic structure of a quantum dot , in the simplest approximation , can be represented by two circular disks , of radius @xmath159 and homogeneous charge density @xmath181 , separated by a distance @xmath182 . the positive charge outside @xmath159 is assumed to be cancelled by the surface gates . this approximation will be best for surface gates very close to the donor layer ( i.e. small @xmath32 ) . larger @xmath12 thicknesses will require a non - abrupt termination    of the positive charge . in either case , the electronic charge is assumed in the classical limit to screen the background charge as nearly as possible . this is similar to the postulate in which wide parabolic quantum wells are expected to produce approximately homogeneous layers of electronic charge @xcite . a simple calculation for the radial potential ( for @xmath183 ) in the electron layer ( @xmath42 ) gives , for the first few terms : @xmath184 \\label{eq : phi}\\end{aligned}\\ ] ] where @xmath185 and @xmath110 is the background dielectric constant . while the coefficient of the quartic term is comparable to that of the parabolic term , the dependences are scaled by the dot radius @xmath159 . hence , the accidental degeneracy of the parabolic potential is broken only by coupling via the quartic term near the dot perimeter . this picture clearly agrees with the full self - consistent results wherein the parabolic degeneracy is observed for low lying states and a spreading of the previously degenerate states occurs nearer to the fermi surface . comparison ( not shown ) of the potential computed from eq . [ eq : phi ] and the radial potential profile ( lowest curve , fig . [ fig3]b ) from the full self - consistent structure , shows good agreement for overall shape . however the former is about @xmath186 smaller ( same @xmath5 ) indicating that the sharp cutoff of the positive charge is , for these parameters , too extreme . however eq . [ eq : phi ] improves for larger @xmath5 and/or smaller @xmath32 . the wavefunction moduli squared associated with the fig . [ fig10 ] quiet dot levels for @xmath176 , @xmath187 are shown schematically for levels @xmath188 through @xmath189 in figure [ fig12 ] , and for levels @xmath190 through @xmath191 in figure [ fig13 ] . the lowest level in a shell is , for the higher shells , typically the most circularly symmetric . when the last member of a shell depopulates with @xmath103 the inner shells expand outward , as can be seen near @xmath155 ( fig . [ fig10 ] ) where level @xmath192 depopulates . since to begin filling a new shell requires the inward compression of the other shells and hence more energy , the capacitance decreases in a step when a shell is depopulated . the shell structure should have two distinct signatures in the standard ( electrostatic ) coulomb oscillation experiment @xcite . first , since the self - capacitance drops appreciably ( figure [ fig6 ] ) when the last member of a shell depopulates , here @xmath5 goes from @xmath193 to @xmath194 , a concomitant discrete rise in the activation energy in the minimum between coulomb oscillations can be predicted . second , envelope modulation of peak heights @xcite occurs when excited dot states are thermally accessible as channels for transport , as opposed to the @xmath89 case where the only channel is through the first open state above the fermi surface ( i.e. the @xmath195 state ) . when @xmath5 is in the middle of a shell of closely spaced , spin degenerate levels , the entropy of the dot , @xmath196 , where @xmath197 is the number of states accessible to the dot , is sharply peaked . for example , for six electrons occupying six spin degenerate levels ( i.e. twelve altogether )    all within @xmath198 of the fermi surface , the number of channels available for transport is @xmath199 . for eleven electrons in the shell , however , the number of channels reduces to @xmath200 . consequently , minima and peaks of envelope modulation ( see also figure [ fig22 ] below ) of cb oscillations which are frequently observed are clear evidence of level bunching , if not an organized shell structure .    recently experimental evidence has accumulated for the existence of a shell structure as observed by inelastic light scattering @xcite and via coulomb oscillation peak positions in transport through extremely small ( @xmath201 ) vertical quantum dots @xcite . interestingly , a _ classical _ treatment , via monte - carlo molecular dynamics simulation @xcite also predicts a shell structure . here , the effect of the neutralizing positive background are assumed to produce a parabolic confining potential . a similar assumption is made in ref . @xcite which analyzes a vertical structure similar to that of ref . we believe that continued advances in fabrication will result in further emphasis on such invariant , as opposed to merely statistical , properties of dot spectra . as noted above , there is a strong tendency for levels at the fermi surface to `` lock . '' such an effect has been described by sun _ @xcite in the case of subband levels for parallel quantum wires . in dots , the effect can be viewed as electrostatic pressure on the individual wavefunctions thereby shifting level energies in such a way as to produce level _ occupancies _ which minimize the total energy . insofar as a given set of level occupancies is electrostatically most favorable , level locking is a temperature dependent effect which increases as @xmath4 is lowered . this self - consistent modification of the level energies can also be viewed as an excitonic correction to excitation energies . the difference between the cases of a quantum dot and that of parallel wires is one of localized versus extended systems . it is well known that , unlike hartree - fock theory , wherein self - interaction is completely cancelled since the direct and exchange terms have the same kernel @xmath202 , in hartree theory and even density functional theory in the lda , uncorrected self - interaction remains @xcite . while it is reasonable to expect that excited states will have their energies corrected downward by the remnants of an excitonic effect , we expect that lda and especially hartree calculations will generally overestimate this tendency to the extent that corrections for self - interaction are not complete . the panel labelled `` xc '' in figure [ fig10 ] illustrates the preceding point . in contrast to the large panel ( on the left ) these results have had the xc potential in lda included . the differences between hartree and lda are generally subtle , but here the clustering of the levels at the fermi surface is clearly mitigated by the inclusion of xc . the approximate parabolic degeneracy is evidently not broken by lda , however , and the shell structure remains intact . similarly for xc , the capacitances also show anomalies near the same gate voltages , where shells depopulate , as in figure [ fig5 ] , which is pure hartree . the two remaining panels in figure [ fig10 ] illustrate the effects of disorder and ordering in the donor layer ( xc not included ) . as with the `` xc '' panel , @xmath103 is varied between @xmath203 and @xmath204 . the `` disorder '' panel represents a single fixed distribution of ions placed at random in the donor layer as discussed above . similarly , the `` order '' panel represents a single ordered distribution generated from a random distribution via the monte - carlo simulation @xcite ; here @xmath205 ( cf . two panels of fig . [ fig4 ] ) .    the shell structure , which is completely destroyed for fully random donor placement ( see also fig . [ fig15 ] ) , is almost perfectly recovered in the ordered case . in both cases the energies are uniformly shifted upwards relative to the quiet dot by virtue of the discreteness of donor charge ( cf . also discussion of fig . [ fig5 ] above ) . closer examination of the disordered spectrum shows considerably more level repulsion than the other cases . the application of a small magnetic field , roughly a single flux quantum through the dot , has a dramatic impact on both the spectrum , figure [ fig14 ] , and the wave functions , figure [ fig15 ] , top . the magnetic field dependence of the levels ( not shown ) up to @xmath206 exhibits shell splitting according to azimuthal quantum number as    well as level anti - crossing . by @xmath207 level spacing ( fig . [ fig14 ] ) is substantially more uniform than @xmath208 , fig . [ fig10 ] . furthermore , while the @xmath208 quiet dot displays reconstruction due to the depopulation of shells at @xmath209 and @xmath157 , the @xmath210 results show a similar pattern , a step in the levels , repeated    many times in the same gate voltage range . the physical meaning of this is clear . the magnetic field principally serves to remove the azimuthal dependence of the mod squared of the wave functions ( fig . [ fig15 ] ) . in a magnetic field , the states at the fermi surface also tend to be at the dot perimeter . depopulation of an electron in a magnetic field , like depopulation of the last member of a shell for @xmath208 , therefore removes charge from the perimeter of the dot and a self - consistent expansion of the remaining states outward occurs . the statistical spectral properties of quantum systems whose classical hamiltonian is chaotic are believed to obey the predictions of random matrix theory ( rmt ) @xcite . arguments for this conjecture however invariably treat the hamiltonian as a large finite matrix with averaging taken only near the band center . additionally , an often un - clearly stated assumption is that the system in question can be treated _ semi - classically _ , that is , in some sense the action is large on the scale of planck s constant and the wavelength _ of all relevant states _ is short on the scale of the system size . clearly , for small quantum dots these assumptions are violated . rmt predictions apply to level spacings @xmath211 and to transition amplitudes ( for the `` exterior problem , '' level widths @xmath212 ) @xcite . rmt is also applied to scattering matrices in investigations of transport properties of quantum wires @xcite . ergodicity for chaotic systems is the claim that variation of some external parameter @xmath213 will sweep the hamiltonian rapidly through its entire hilbert space , whereupon energy averaging and ensemble ( i.e. @xmath213 ) averaging produce identical statistics . in our study @xmath213 is either the set of gate voltages , the magnetic field or the impurity configuration and we consider the statistics of the lowest lying @xmath214 levels ( spin is ignored here ) . care must also be taken in removing the secular variations of the spacings or widths with energy , the so - called unfolding . according to rmt level repulsion leads to statistics of level spacings which are given by the `` rayleigh distribution : '' @xmath215 where @xmath216 is the mean local spacing @xcite . figure [ fig16 ] shows the calculated histogram for the level spacings for the quiet dot as well as for disordered , ordered and ordered with @xmath210 cases . statistics are generated from ( symmetrical ) plunger gate variation , in steps of @xmath217 , over a range of @xmath218 , employing the spacings between the lowest @xmath214 levels ; thus about @xmath219 data points . deviation from the rayleigh distribution is evident . an important feature of our dot is symmetry under inversion through both axes bisecting the dot . it is well known that groups of states which are    un - coupled will , when plotted together , show a poisson distribution for the spacings rather than the level repulsion of eq . [ eq : stat ] . thus we have also plotted ( white bars ) the statistics for those states which are totally even in parity . while the probability of degeneracy decreases , a @xmath220 test shows that the distribution remains substantially removed from the rayleigh form . in contrast to this , the disordered case shows remarkable agreement with the rmt prediction . as with the spectrum in figure [ fig10 ] we use a single ion distribution . however we also find ( not shown ) that fixing the gate voltage and varying the random ion distributions results in nearly the same statistics . when the ions are allowed to order the level statistics again deviate from the rmt model . this is somewhat surprising since fig . [ fig5 ] shows that , even for @xmath221 , the standard deviation of the effective 2d potential below the fermi surface from the quiet dot case , @xmath222 , is still substantially greater than the mean level spacing @xmath223 . we have recently shown that , as @xmath72 goes from unity to zero , a continuous transition from the level repulsion of eq . [ eq : stat ] to a poisson distribution of level spacings results @xcite . finally , the application of a magnetic field strong enough to break time - reversal symmetry clearly reduces the incidence of very small spacings , but the distribution is still significantly different from rmt .      in eq . [ eq : tun ] we defined @xmath109 as the barrier penetration factor from the classically accessible region of the lead to the matching point in the barrier , for the @xmath108 channel . the penetration factor _ completely _ through the barrier , @xmath224 where @xmath225 is the classical turning point on the dot side of the barrier , is plotted as a function of qpc voltage in figure [ fig17 ] . @xmath226 is simply the wkb penetration for a given channel with a given self - consistent barrier profile , and can be computed at any energy . here we have computed it at energies coincident with the dot levels . therefore the dashes recapitulate the level structure , spaced now not in energy but in `` bare '' partial width . the _ actual _ width of a level depends upon the wave function for that state ( cf . [ eq : tun ] ) . for energies above the barrier @xmath227 . the solid lines represent @xmath228 _ at the fermi surface _ computed for three different @xmath12 thicknesses @xmath32 ( as in figure [ fig9 ] ) and for both @xmath229 and @xmath230 ( the dashes are computed for @xmath231 ) . the qpc voltage is given relative to values at which @xmath228 for @xmath229 is the same for all three @xmath32 ( hence the top three solid lines converge at @xmath232 ) . quite surprisingly @xmath32 has very little influence on the trend of @xmath228 with qpc voltage . note that the ratio of barrier penetration between the second and first channels @xmath233 decreases substantially with increasing @xmath32 since the saddle profile becomes wider for more distant gates . even for @xmath234 however , penetration via the second channel is about a factor of five smaller than via @xmath229 . figure [ fig18 ] shows the partial width for tunneling via @xmath229 through the barrier , now using the full eq . [ eq : tun ] , for the quiet dot . the barriers here are fairly wide . while this strikingly coherent structure is quickly destroyed by discretely localized donors even when donor ordering is allowed , the pattern is nonetheless highly informative . the principal division between upper and lower states is based on parity . states which are odd with respect to the axis bisecting the qpc should in fact have identically zero partial width ( that they do nt is evidence of numerical error , mostly imperfect convergence ) .    note that _ this _ division is largely preserved for discrete but ordered ions . the widest states ( largest @xmath212 ) are labelled with their level index for comparison with their wave functions in figs . [ fig13 ] and [ fig14 ] . comparison shows they represent the states which are aligned along the direction of current flow . thus in each shell there are likely to be a spread of tunneling coefficients , that is , two members of the same shell will not have the same @xmath212 . statistics of the level partial widths are shown in figure [ fig19 ] , here normalized to their local mean values . while the statistics for the quiet dot are in substantial disagreement with rmt it is clear that discreteness of the ion charge , even ordered , largely restores ergodicity . the rmt prediction , the `` porter - thomas '' ( pt ) distribution , is also plotted . for non - zero @xmath235 , panels ( b ) and ( c ) , the predicted distribution is @xmath236 rather than pt . even the completely disordered case ( e ) retains a fraction of vanishing partial width states . since in our case the zero width states result from residual reflection symmetry , it would be interesting to compare the data from references @xcite and @xcite , which employ nominally symmetric and non - symmetric dots respectively , to see if the incidence of zero width states shows a statistically significant difference . one further statistical feature which we calculate is the autocorrelation function of the level widths as an external parameter @xmath213 is varied : @xmath237 where @xmath238 , and where @xmath239 is again the _ local _ average , over levels at fixed @xmath213 , of the level widths . note that the sum on @xmath240 is over levels and the sum on @xmath241 is over starting values of @xmath213 .    in figure [ fig20 ] we show the autocorrelation function for varying magnetic field ( cf . ref . @xcite , figure [ fig4 ] ) . the sample is ordered , @xmath143 . our range of @xmath235 only encompasses @xmath242 \\ ; t$ ] in steps of @xmath243 , so we have here averaged over all levels ( i.e. @xmath244 ) . the crucial feature , which has been noted in refs . @xcite and , for conductance correlation in open dots in @xcite , is that the correlation function becomes negative , in contradiction with a recent prediction based on rmt @xcite . indeed , as noted by bird _ @xcite , an oscillatory structure seems to emerge in the data . comparison with calculation here is hampered since the statistics are less good as @xmath235 increases .    nonetheless , the rmt prediction is clearly erroneous . we speculate that the basis of the discrepancy is in the assumption @xcite that @xmath245 . given this assumption @xcite the correlation becomes positive definite . physically this means that , regardless of whether @xmath235 is positive or negative , the self - correlation of a level width will be independent of whether @xmath246 is positive or negative . this implies that the level widths should be independent of the absolute value of @xmath235 , or any even powers of @xmath235 , at least to lowest order in @xmath247 . for real quantum dot systems this assumption is inapplicable . similar behaviour is observed with @xmath213 taken as the ( plunger ) gate voltage , for which we have considerably more calculated results , fig . [ fig21 ] . the upper panel is the analogue of fig . [ fig20 ] , only we have broken the average on levels into separate groups of fifteen levels centered on the level listed on the figure ( e.g. , the `` @xmath248 '' denotes a sum in equ . [ eq : auto ] of @xmath249 ) . the lower panel shows the autocorrelation as a grey scale for the individual levels ( averaging performed only over starting @xmath103 ) . the very low lying levels , up to @xmath250 , remain self - correlated across the entire range of gate voltage . this simply indicates that the correlation field is level dependent . however , rather than becoming uniformly grey in a lorentzian fashion , as predicted by rmt @xcite , individual levels tend to be strongly correlated or anti - correlated with their original values , and the disappearance of correlation only occurs as an average over levels . again we expect that the explanation for this behaviour lies in the shell structure . coulomb interaction prevents states which are nearby in energy from having common spatial distributions . thus in a given range of energy , when one state is strongly connected to the leads , other states are less likely to be . further , the ordering of states appears to survive at least a small amount of disorder in the ion configuration . the final topic we consider here is the coulomb oscillation conductance of the dot . we will here focus on the temperature dependence @xcite , although statistical properties related to ion ordering are also interesting . we have shown in ref . @xcite that detailed temperature dependence of coulomb oscillation amplitudes can be employed as a form of quantum dot spectroscopy . roughly , in the low @xmath4 limit the peak heights give the individual level connection coefficients and , as temperature is raised activated conductance _ at the peaks _ depends on the nearest level spacings at the fermi surface . in this regard we have explained envelope modulation of peak heights , which had previously not been understood , as clear evidence of thermal activation involving tunneling through excited states of the dot @xcite .    figure [ fig22]a shows the conductance as a function of plunger gate voltage for the ordered dot at @xmath251 . note that the magnitude of the conductance is small because the coupling coefficients are evaluated with relatively wide barriers for numerical reasons . over this range the dot @xmath5 depopulates from @xmath135 ( far left ) to @xmath252 . the level spacings and tunneling coefficients are all changing with @xmath103 . at low temperature a given peak height is determined mostly by the coupling to the first empty dot level ( @xmath253 ) and by the spacings between the @xmath254 level and the nearest other level ( above or below ) . the relative importance of the @xmath212 s and the level spacings can obviously vary . in this example , figs . [ fig22]a and [ fig22]b suggest that peak heights correlate more strongly with the level spacings . the double envelope coincides with the fermi level passing through two shells . in general , the dos fluctuations embodied in the shell structure and the observation ( above ) that within a shell a spreading of the @xmath212 s ( with a most strongly coupled level ) results from coulomb interaction provide the two fundamental bases of envelope modulation . finally , we typically find that , when peak heights are plotted as a function of temperature ( not shown ) some peaks retain activated conductance down to @xmath255 . since the dot which we are modelling is small on the scale of currently fabricated structures , this study suggests that claims to have reached the regime where all coulomb oscillations represent tunneling through a single dot level are questionable .","summary":"this permits the solution of the electronic structure for dot electron number .","abstract":"we employ density functional theory to calculate the self consistent electronic structure , free energy and linear source - drain conductance of a lateral semiconductor quantum dot patterned via surface gates on the 2deg formed at the interface of a heterostructure . the schrdinger equation is reduced from 3d to multi - component 2d and solved via an eigenfunction expansion in the dot . this permits the solution of the electronic structure for dot electron number . we present details of our derivation of the total dot - lead - gates interacting free energy in terms of the electronic structure results , which is free of capacitance parameters . statistical properties of the dot level spacings and connection coefficients to the leads are computed in the presence of varying degrees of order in the donor layer . based on the self - consistently computed free energy as a function of gate voltages , , and n , we modify the semi - classical expression for the tunneling conductance as a function of gate voltage through the dot in the linear source - drain , coulomb blockade regime . among the many results presented , we demonstrate the existence of a shell structure in the dot levels which ( a ) results in envelope modulation of coulomb oscillation peak heights , ( b ) which influences the dot capacitances and should be observable in terms of variations in the activation energy for conductance in a coulomb oscillation minimum , and ( c ) which possibly contributes to departure of recent experimental results from the predictions of random matrix theory .    2 [    ]"}
{"article_id":"1109.0159","section_id":"i","document":"in this section , i summarize the basic features of entangled states and reduced density matrices and illustrate them with examples . for further details , see e.g. the short review @xcite . entanglement is a notion which goes back to 1935 when it was introduced by schrdinger in a series of three articles ( in german , the german word is `` verschrnkung '' ) @xcite . at the same time einstein , podolski and rosen discussed their famous `` gedankenexperiment '' , in which they considered two particles with fixed total momentum and relative distance . nowadays this is usually formulated with two spins , and this is also where one encounters entanglement first . entanglement has to do with the features of quantum states and the information contained in wave functions . for a long time , it was a topic discussed mostly in quantum optics and for systems with few degrees of freedom .    in the last 25 years , however , it has seen a revival with input from very different areas , namely    * the theory of black holes * the numerical investigation of quantum chains * the field of quantum information    in these cases one always deals with large systems and many degrees of freedom .    in entanglement investigations , one asks the following _ question _ :    * given a total system in a certain quantum state @xmath0 * divide it ( in space , or in hilbert space ) in two parts ( bipartition ) * how are the two parts coupled in @xmath0 ? this is more general than looking at , say , a two - point correlation function . and there is a general way to answer this question , namely one can bring @xmath0 into a standard form , which displays the coupling . this is the _ schmidt decomposition _ which we will discuss in a moment . to obtain it in practice , one uses quantities which determine all properties of a subsystem , namely _ reduced density matrices _ ( rdm s ) . they also contain the information on the entanglement and will be the basic _ tool _ throughout the lectures . the _ states _ we will study are the ground states of models which , on the one hand , are solvable and , on the other hand , have a physical significance , like tight - binding ( hopping ) models or spin chains . as in other contexts , they serve as points of orientation which allow to study the features of the problem and to develop a feeling and an overall picture . my own interest arose in connection with the dmrg , where the entanglement turned out to be crucial for the performance of the method . entanglement continues to play a role also in other algorithms and their design , and in this respect it has quite practical implications . but in these lectures , we shall be concerned essentially with the theory . consider a quantum system in state @xmath0 and divide it into two parts 1 and 2 . then one can write @xmath1 where the @xmath2 and @xmath3 are orthonormal bases in the two hilbert spaces . + note that one has a double sum and that the matrix @xmath4 is in general rectangular , since the dimensions of the hilbert spaces can differ . nevertheless one can obtain a diagonal form via the so - called singular - value decomposition @xmath5 where @xmath6 is square and unitary , @xmath7 diagonal and @xmath8 rectangular with orthonormal rows . this gives @xmath9 combining @xmath2 with @xmath6 and @xmath10 with @xmath8 one obtains with @xmath11 @xmath12 this is called the schmidt decomposition ( schmidt 1907 ) @xcite . for the history see section 1.7 . it has the following features    * single sum , limited by the smaller hilbert space * new orthonormal sets @xmath13 in both parts * @xmath14 if @xmath0 is normalized * entanglement encoded in the @xmath15 * limiting cases + @xmath16 for @xmath17 : only one term , product state , no entanglement + @xmath18 for all @xmath19 : all terms equal weight , maximal entanglement    this refers to a particular bipartition and one can investigate different partitions to obtain a complete picture . some standard bipartitions for one - dimensional systems are shown in fig . [ fig : geometries ] . we give here examples for the schmidt decomposition in three different systems . \\(a ) _ two spins one - half _ @xmath20 @xmath21 \\hspace{1.0 cm } \\mathrm{product\\,\\,\\ , state } \\label{spins2}\\end{aligned}\\ ] ] @xmath22 all these states are already in schmidt form . however @xmath23 +                        c |-\\rangle |+\\rangle \\label{spins4}\\end{aligned}\\ ] ] is entangled , but not in schmidt form , because the two states in subsystem 2 are not orthogonal . \\(b ) _ two large spins _ @xcite    consider the ferromagnetic spin one - half heisenberg chain with @xmath24 sites @xmath25 all eigenstates can be written as @xmath26 with total spin @xmath27 and @xmath28-component @xmath29 . in the ground state all spins are parallel , @xmath30 , and @xmath29 can be chosen . choose @xmath31 and divide the chain in two halves . then one can use angular momentum addition as illustrated in fig . [ fig : clebsch - gordan ] +     obtained from states in the subsystem . ]    to obtain @xmath32 with the clebsch - gordan coefficients @xmath33 this is the schmidt form for this state . its features are    * only ( s+1 ) terms , while dimension of hilbert space is @xmath34 * for large @xmath27 , @xmath35 , gaussian * analogous formulae for arbitrary @xmath29 * special case @xmath36 , all spins in the @xmath28-direction . then @xmath37 is a product state @xmath38    \\(c ) _ two coupled oscillators _ @xcite    consider the hamiltonian ( @xmath39 ) @xmath40 the eigenfrequencies are @xmath41 and @xmath42 with corresponding normal coordinates @xmath43 in these coordinates , the ground state is the product of two gaussians @xmath44\\ , ) \\label{two - osc2}\\ ] ] then the following formula holds @xmath45 where @xmath46 and the @xmath47 are oscillator states for a frequency @xmath48 , i.e. in between @xmath49 and @xmath50 . _ features _    * schmidt states are `` squeezed '' states * coefficients decay exponentially , @xmath51 * weak coupling @xmath52 : @xmath53 @xmath54 @xmath55 small , @xmath56 large , rapid decay , weak entanglement * strong coupling @xmath52 : @xmath57 @xmath54 @xmath55 large , @xmath56 small , slow decay , strong entanglement    these features are also found for one oscillator in a whole assembly . the schmidt structure just discussed can be found from the density matrices associated with the state @xmath0 . this is also the standard way to obtain it . starting from the total density matrix @xmath58 one can , for a chosen division , take the trace over the degrees of freedom in one part of the system . this gives the reduced density matrix for the other part , i.e. @xmath59 these hermitian operators can be used to calculate arbitrary expectation values in the subsystems . as to the entanglement , assume that @xmath0 has the schmidt form ( [ schmidt ] ) . then @xmath60 taking the traces with the @xmath13 gives @xmath61 and @xmath62 this means that    * @xmath63 and @xmath64 have the same non - zero eigenvalues * these eigenvalues are given by @xmath65 * their eigenfunctions are the schmidt functions @xmath13    therefore the eigenvalue spectrum of the @xmath66 gives directly the weights in the schmidt decomposition and a glance at this spectrum shows the basic entanglement features of the state , for the chosen bipartition . for this reason , it has also been termed `` entanglement spectrum '' @xcite . _ remarks _    * the @xmath66 describe mixed states . an expectation value in subsystem @xmath67 is given by @xmath68 * since the @xmath66 are hermitian and have non - negative eigenvalues , one can write @xmath69 where @xmath70 is a normalization constant and the operator @xmath71 has been termed `` entanglement hamiltonian '' . this form will be encountered permanently in the following . * the @xmath66 should not be confused with e.g. the one - particle density matrices , which are simple correlation functions . usually , one starts in a basis where @xmath0 has the form ( [ state ] ) . then @xmath72 and taking the trace with the @xmath3 gives @xmath61 and @xmath73 thus @xmath74 contains the square hermitian matrix @xmath75 and similarly @xmath76 contains @xmath77 . the form ( [ rhodiag ] ) is then obtained by diagonalizing these matrices . this is the general approach . _ example _ : two spins one - half + a general normalized state is @xmath78 where @xmath79 . the matrix @xmath80 is then @xmath81 and one obtains @xmath82 since the trace is one , the eigenvalues are given by @xmath83 the state is entangled if @xmath84 , i.e. if @xmath85 . this includes the state @xmath86 in section 1.3 , where @xmath87 and @xmath88 . the density - matrix renormalization group method ( dmrg ) is a numerical procedure , which was introduced by steven white in 1992 @xcite and makes direct use of the schmidt decomposition and the reduced density matrices . for a review , see @xcite . consider a quantum chain , e.g. a spin one - half model , with open ends . then in the simplest variant , the following steps take place , compare fig . [ fig : dmrg ] . \\(0 ) start + begin with a small system of 5 - 10 sites . + calculate the ground state _ exactly_. + ( 1 ) schmidt decomposition + divide into two halves . + calculate the rdm s . + diagonalize them and obtain the schmidt coefficients and schmidt states . + ( 2 ) approximation + keep only the @xmath89 schmidt states with largest weights @xmath90 . + truncation error : sum of the discarded weights @xmath91 . + ( 3 ) enlargement + insert ( two ) additional sites in the center . + form new hamiltonian in the basis of kept and additional states . + calculate ground state . + go back to ( 1 ) and repeat . +        for this procedure , the form of the schmidt spectra is crucial . to have a good performance , a rapid drop of the @xmath90 is necessary such that only a small number of schmidt states has to be kept . in terms of entanglement , the state must be _ weakly entangled_. this is satisfied for non - critical chains . for an ising model in a transverse field , such a small number as 16 schmidt states gives already a fantastic accuracy for the ground - state energy . it is therefore important to understand the features of rdm spectra and this leads directly to the study of solvable cases , which is the topic of these lectures . the full rdm spectra give the clearest impression of the entanglement in a bipartite system . but it is also desirable to have a simple measure through one number . since the eigenvalues of the rdm s can be viewed as probabilities , one can take the usual entropy , as used in probability theory , to characterize the @xmath90 . this gives the ( von neumannn ) entanglement entropy @xmath92 which is the common entanglement measure for bipartitions . it has the following properties    * @xmath93 since the spectra are equal . one can talk of _ the _ entanglement entropy . * @xmath94 for product states . * @xmath27 is maximal if all @xmath90 are equal . + if @xmath95 for @xmath96 then @xmath97 . the last property leads to a simple interpretation of @xmath27 . write @xmath98 then @xmath99 is an effective number of states in the schmidt decomposition . a related measure is the rnyi entropy @xmath100 where @xmath19 can also be non - integer . @xmath101 has similar properties as @xmath27 and the same extremal values @xmath94 and @xmath102 . for @xmath103 write @xmath104 \\label{renyi_limit}\\ ] ] and expand the exponential function to obtain @xmath105 . the rnyi entropy is somewhat simpler to calculate , since it contains only a power of @xmath66 . the important point is that both entropies measure a _ mutual connection _ and will , in general , _ not _ be proportional to the size of a subsystem as usual thermodynamic entropies are . erhard schmidt ( 1876 - 1959 ) obtained his phd in 1905 with hilbert in gttingen and was professor at the berlin university 1917 - 1950 . he is most widely known by the orthogonalization procedure bearing his name . the work linking him to the quantum problems discussed here , appeared in 1907 in the prestigeous journal `` mathematische annalen '' @xcite . it was based on his thesis and dealt with coupled integral equations with a non - symmetric kernel @xmath106 .    in abstract notation , and changing his parameter @xmath107 to @xmath108 , the equations were @xmath109 he deduced a spectral representation for @xmath110 @xmath111 where @xmath112 and @xmath113 are the eigenfunctions of the symmetric kernels @xmath114 and @xmath115 with common eigenvalue @xmath116 @xmath117 one sees that the kernel @xmath106 corresponds to the total wave function , which for two degrees of freedom is @xmath118 . moreover , one sees that he already worked with the quantities which in the present context are called reduced density matrices . and finally , he discussed best approximations for the kernel based on keeping the terms with largest weights , which is the same recipe as used in the dmrg . the representation of a wave function @xmath118 in this way was discussed in a paper by schrdinger in 1935 @xcite . at that time , unsymmetric kernels were already well - known in mathematics , so he referred not to schmidt but to the textbook by courant and hilbert . the specialists will notice that the equations ( [ hist1 ] ) , ( [ hist3 ] ) with @xmath119 and @xmath120 are just the ones appearing in the famous paper by lieb , schultz and mattis ( 1961 ) @xcite where they diagonalize a quadratic form in fermions .","summary":"this is done using a thermodynamic formulation in which the eigenvalue spectrum of a certain hamiltonian determines the entanglement properties . preface *    entanglement in many - particle quantum states has been a topic of intense research in recent years with applications in numerics and interesting links to statistical physics . it is therefore excellently suited for an advanced course in a summer school . they are based on a recent review article , but the material has been properly adapted to the purpose . the style is lecture - like with itemized statements . references are only given in direct connection with the problem at hand , show a preference of own work and should not be regarded as an exhaustive list . compared to the version handed out in natal , additional figures have been included and some editing took place .    * contents *    \\1 . background and basics + 2 . entanglement entropies + 5 .","abstract":"lecture notes for the brazilian school on statistical mechanics + natal , brazil , july 18 - 22 , 2011 . + the five lectures introduce to the description of entanglement in many - particle systems and review the ground - state entanglement features of standard solvable lattice models . this is done using a thermodynamic formulation in which the eigenvalue spectrum of a certain hamiltonian determines the entanglement properties . the methods to obtain it are discussed and results , both analytical and numerical , for various cases including time evolution are presented .    * preface *    entanglement in many - particle quantum states has been a topic of intense research in recent years with applications in numerics and interesting links to statistical physics . it is therefore excellently suited for an advanced course in a summer school . the following notes correspond closely to five lectures given in july 2011 at the international institute of physics in natal , brazil . they are based on a recent review article , but the material has been properly adapted to the purpose . thus they contain more introductory examples and certain topics are presented in more detail . on the other hand , new material from the last two years , as well as supplementary notes have been added . throughout the notes , the style is lecture - like with itemized statements . references are only given in direct connection with the problem at hand , show a preference of own work and should not be regarded as an exhaustive list . compared to the version handed out in natal , additional figures have been included and some editing took place .    * contents *    \\1 . background and basics + 2 . free - particle models + 3 . integrable models + 4 . entanglement entropies + 5 . quenches and miscellaneous"}
{"article_id":"0806.4553","section_id":"i","document":"many problems in mathematics and computer science can be reduced to proving satisfiability of conjunctions of ( ground ) literals modulo a background theory . this theory can be a standard theory , the extension of a base theory with additional functions , or a combination of theories . it is therefore very important to find efficient methods for reasoning in standard as well as complex theories . however , it is often equally important to find local causes for inconsistency . in distributed databases , for instance , finding local causes of inconsistency can help in locating errors . similarly , in abstraction - based verification , finding the cause of inconsistency in a counterexample at the concrete level helps to rule out certain spurious counterexamples in the abstraction . the problem we address in this paper can be described as follows : let @xmath0 be a theory and @xmath1 and @xmath2 be sets of ground clauses in the signature of @xmath0 , possibly with additional constants . assume that @xmath3 is inconsistent with respect to @xmath0 . can we find a ground formula @xmath4 , containing only constants and function symbols common to @xmath1 and @xmath2 , such that @xmath4 is a consequence of @xmath1 with respect to @xmath0 , and @xmath5 is inconsistent modulo @xmath0 ? if so , @xmath4 is a _ ( craig ) interpolant _ of @xmath1 and @xmath2 , and can be regarded as a `` local '' explanation for the inconsistency of @xmath3 .    in this paper we study possibilities of obtaining ground interpolants in theory extensions . we identify situations in which it is possible to do this in a hierarchical manner , by using a prover and a procedure for generating interpolants in the base theory as `` black - boxes '' . we consider a special type of extensions of a base theory  namely local theory extensions  which we studied in @xcite . we showed that in this case hierarchical reasoning is possible . i.e.  proof tasks in the extension can be reduced to proof tasks in the base theory . here we study possibilities of hierarchical interpolant generation in local theory extensions . the main contributions of the paper are summarized below :    1 . first , we identify new examples of local theory extensions . 2 .   second , we present a method for generating interpolants in local extensions of a base theory . the method is general , in the sense that it can be applied to an extension @xmath6 of a theory @xmath7 provided that : a.   @xmath7 is convex ; b.   @xmath7 is @xmath8-interpolating for a specified set @xmath8 of predicates ( cf .  the definition in section  [ examples - sep ] ) ; c.   in @xmath7 every inconsistent conjunction of ground clauses @xmath3 allows a ground interpolant ; d.   the extension is defined by clauses of a special form ( type ( [ general - form ] ) in section  [ examples - sep ] ) . + the method is _ hierarchical _ : the problem of finding interpolants in @xmath6 is reduced to that of finding interpolants in the base theory @xmath7 . we can use the properties of @xmath7 to control the form of interpolants in the extension @xmath6 . third , we identify examples of theory extensions with properties ( i)(iv ) . 4 .   fourth , we discuss application domains such as : modular reasoning in combinations of local theories ( characterization of the type of information which needs to be exchanged ) , reasoning in distributed databases , and verification .    the existence of ground interpolants has been studied in several recent papers , mainly motivated by abstraction - refinement based verification @xcite . in @xcite mcmillan presents a method for generating ground interpolants from proofs in an extension of linear rational arithmetic with uninterpreted function symbols . the use of free function symbols is sometimes too coarse ( cf . the example in section  [ motivation - verif ] ) . here , we show that similar results also hold for other types of extensions of a base theory , provided that the base theory has some of the properties of linear rational arithmetic . another method for generating interpolants for combinations of theories over disjoint signatures from nelson - oppen - style unsatisfiability proofs was proposed by yorsh and musuvathi in @xcite . although we impose similar conditions on @xmath7 , our method is orthogonal to theirs , as it can also handle combinations of theories over non - disjoint signatures . in @xcite a different interpolation property  stronger than the property under consideration in this paper  is studied , namely the existence of ground interpolants for _ arbitrary formulae _  which is proved to be equivalent to the theory having quantifier elimination . this limits the applicability of the results in @xcite to situations in which the involved theories allow quantifier elimination . if the theory considered has quantifier elimination then we can use this for obtaining ground interpolants for arbitrary formulae . the goal of our paper is to identify theories  possibly without quantifier elimination  in which , nevertheless , ground interpolants for ground formulae exist . _ structure of the paper : _ we start by providing motivation for the study in section  [ motivation ] . in section  [ prelim ] the basic notions needed in the paper are introduced . section  [ local ] contains results on local theory extensions . in section  [ hierarchic ] local extensions allowing hierarchical interpolation are identified , and based on this , in section  [ procedure ] a procedure for computing interpolants hierarchically is given . in section  [ appl ] applications to modular reasoning in combinations of theories , reasoning in complex databases , and verification are presented . in section  [ conclusions ] we draw conclusions , discuss the relationship with existing work , and sketch some plans for future work . for the sake of clarity in presentation , all the proofs that are not directly related to the main thread of the paper can be found in the appendix . ( these results concern illustrations of the fact that certain theory extensions are local , or satisfy assumptions that guarantee that interpolants can be computed hierarchically . )","summary":"in this paper we study interpolation in local extensions of a base theory . we identify situations in which it is possible to obtain interpolants in a hierarchical manner , by using a prover and a procedure for generating interpolants in the base theory as black - boxes . we present several examples of theory extensions in which interpolants can be computed this way , and discuss applications in verification , knowledge representation , and modular reasoning in combinations of local theories .","abstract":"in this paper we study interpolation in local extensions of a base theory . we identify situations in which it is possible to obtain interpolants in a hierarchical manner , by using a prover and a procedure for generating interpolants in the base theory as black - boxes . we present several examples of theory extensions in which interpolants can be computed this way , and discuss applications in verification , knowledge representation , and modular reasoning in combinations of local theories ."}
{"article_id":"1202.1229","section_id":"i","document":"if a player , say , bob , receives a message @xmath6 that claims to come from alice , he might wish to know if this is true , or if the message was generated or modified by some adversary . this task is called _ authentication _ , and in their seminal work  @xcite , wegman and carter showed that it can be achieved with informationtheoretic security by appending a tag @xmath7 to the message ( often called a message authentication code or mac ) , where @xmath8 , @xmath9 is a family of almost strongly universal@xmath1 ( asu@xmath1 ) hash functions hashing was only formally defined later by stinson  @xcite . a family of functions is said to be asu@xmath1 if any two different messages are almost uniformly mapped to all pairs of tags . an exact definition is given in on . ] , and @xmath10 is a secret key shared by alice and bob . there exist asu@xmath1 families @xmath11 that require @xmath12 bits of shared secret key  @xcite , where @xmath13 is the message alphabet and @xmath14 the tag alphabet . wegman and carter  @xcite propose a scheme to use even less bits of key when multiple messages are to be authenticated : each tag should be encrypted with a fresh one - time pad ( otp ) , but the same hash function can be used each time . alice thus appends the tag @xmath15 to her message @xmath16 , where @xmath17 is used for all messages and @xmath18 is a fresh key used only in this round . asymptotically this scheme consumes only @xmath19 bits of key per round .    to prove the security of this scheme , wegman and carter show that given any amount of messagetag pairs @xmath20 the secret key @xmath17 is still perfectly uniform . they then argue that the probability of an adversary successfully falsifying any new message is the same in every round , and guaranteed to be small by the properties of the asu@xmath1 hash functions . however , proving that a protocol is secure in a standalone model does not necessarily guarantee that it is still secure when combined with other protocols , not even when combined with itself like wegman and carter s scheme . a lot of research has gone into composability of cryptographic tasks in recent years . a general framework for proving composable security was developed by canetti  @xcite , and dubbed _ universally composable ( uc ) security_. independently , backes , pfitzmann and waidner  @xcite introduced the equivalent notion of _ reactive simulatability_. these security notions have been extended to the quantum setting by ben - or and mayers  @xcite and unruh  @xcite . an essential application of informationtheoretic authentication is in quantum key distribution ( qkd ) protocols . every ( classical ) message exchanged between the two parties generating the key needs to be authenticated with informationtheoretic security in order to guarantee the overall unconditional security of the protocol . recycling the hash function is a practical way to save a large part of the secret key consumed in each round . and as wegman and carter s security proof does not fit in any composable security framework , it raises the question of whether this qkd application is still secure . many works , e.g. ,  @xcite , reuse wegman and carter s authentication scheme with key recycling , and they all sketch the security using the same noncomposable argument as wegman and carter . composable security for key recycling in authentication has been studied in the case of quantum messages by hayden , leung and mayers  @xcite , but to the best of our knowledge has not been treated when the messages are classical . computationally secure variants of wegman and carter s scheme have been proposed  @xcite , but not analysed in a composable framework either . some works @xcite have pointed out that informationtheoretic authentication might not be composable with qkd . they attempt to study this problem by analyzing the security of authentication when the secret keys used are not perfect . in particular , abidin and larsson  @xcite suggest that when qkd and authentication with key recycling are combined recursively , and the ( imperfect ) secret key resulting from qkd is fed back into the next round of authentication and qkd , the total error could increase exponentially in the number of rounds . ben - or et al . @xcite and mller - quade and renner  @xcite provide a detailed treatment of the composability of qkd . in particular , the latter show that if the authentication and qkd schemes are proven to be composable , and if a short initial key is available , a continuous key stream can be generated with arbitrarily small error . we therefore study wegman and carter s authentication scheme with key recycling  @xcite using the uc framework from @xcite . even though we ultimately wish to show that this protocol is composable in a quantum world , it is sufficient to consider classical uc security , since unruh s lifting theorem  @xcite proves that classical uc security of a classical scheme implies quantum uc security . we show that the recycled hash function is gradually leaked to the adversary , even when the key used for the otp is perfect . this leakage is however very small : we prove that this scheme is indeed @xmath0-uc - secure if the hash functions used are @xmath0-asu@xmath1 . since for any good asu@xmath1 hash function construction @xmath0 decreases exponentially fast in the size of the family , @xmath21 , it can easily be made arbitrarily small . as a consequence , the doubts of @xcite are unfounded for all ranges of the parameter @xmath0 . in fact , the hash functions used are slightly weaker than asu@xmath1 hashing , namely almost xor universal@xmath1 ( axu@xmath1 ) hash functions . if the bitwise xor of the hash of any two different messages is almost uniform over the choice of hash function . see on for an exact definition . ] we show that the recycled key is close to perfectly uniform and independent from all other random variables produced throughout the protocol . this means that the recycled key can be reused for any task , not only for subsequent rounds of authentication . an immediate implication of this and the composition theorem  @xcite is that if this authentication scheme is used @xmath2 times in each round of an @xmath5-uc - secure qkd protocol , which is run @xmath3 times , recycling the same hash function throughout , the final key has distance at most @xmath4 from uniform .      in we introduce the elements from the uc framework that we need in this work . we briefly define the security notion and state the universal composition theorem . in we model the uc security for standard authentication without recycling . in we then model authentication with key recycling , and prove that using @xmath0-axu@xmath1 hash functions and a otp results in a scheme which is @xmath0-uc - secure . in we take a closer look at the secret key which is leaked to the environment , and show that an optimal attack over @xmath2 rounds of authentication which takes advantage of this key leakage produces an error of size exactly @xmath22 . and finally in we illustrate the composition theorem by applying it to the case of many rounds of authentication with key recycling and qkd .    in we give a proof of security of standard authentication , as defined in . and in we provide some more details on impersonation attacks .","summary":"in their seminal work on authentication , wegman and carter propose that to authenticate multiple messages , it is sufficient to reuse the same hash function as long as each tag is encrypted with a one - time pad . it turns out that the above argument is insufficient : information about the hash function is in fact leaked in every round to the adversary , and after a bounded finite amount of rounds it is completely known . we show however that this leak is very small , and wegman and carter s protocol is still-secure , if-almost strongly universal hash functions are used . we illustrate this by applying it to quantum key distribution ( qkd ) : if the same hash function is recycled to authenticate the classical communication in every round of a qkd protocol , and used times per round , the total error after rounds is upper bounded by , where is the error of one round of qkd given an authentic channel .","abstract":"in their seminal work on authentication , wegman and carter propose that to authenticate multiple messages , it is sufficient to reuse the same hash function as long as each tag is encrypted with a one - time pad . they argue that because the one - time pad is perfectly hiding , the hash function used remains completely unknown to the adversary .    since their proof is not composable , we revisit it using a universally composable framework . it turns out that the above argument is insufficient : information about the hash function is in fact leaked in every round to the adversary , and after a bounded finite amount of rounds it is completely known . we show however that this leak is very small , and wegman and carter s protocol is still-secure , if-almost strongly universal hash functions are used . this implies that the secret key corresponding to the choice of hash function can be recycled for any task without any additional error than this .    we illustrate this by applying it to quantum key distribution ( qkd ) : if the same hash function is recycled to authenticate the classical communication in every round of a qkd protocol , and used times per round , the total error after rounds is upper bounded by , where is the error of one round of qkd given an authentic channel ."}
{"article_id":"0709.4291","section_id":"i","document":"let @xmath6 denote the symmetric group of permutations of @xmath7:=\\{1,\\ldots , n\\}$ ] . for each @xmath8 , a _ descent _ is an index @xmath9 ( @xmath10 ) such that @xmath11 . we let @xmath12 : w_i > w_{i+1 } \\}|\\ ] ] denote the number of descents in @xmath13 . the corresponding generating function @xmath14 is known as an _ eulerian polynomial _ , although this definition differs from the classical one by a power of @xmath15 . some interesting features of the eulerian polynomials include the facts that they have symmetric and unimodal coefficients and are known to have all real roots . more generally , if @xmath2 is any finite coxeter group with simple reflections @xmath16 ( such as the symmetric group @xmath17 with simple transpositions @xmath18 ) , then a descent in some @xmath19 may be defined as an index @xmath9 such that @xmath20 , where @xmath21 denotes the minimum length of an expression for @xmath13 as a product of simple reflections . thus there is an analogous _ @xmath2-eulerian polynomial _ @xmath22 where @xmath23 is defined to be the number of descents in @xmath13 . note that as a coxeter group , @xmath6 is often denoted @xmath24 , so this notation is consistent with  .    like the classical eulerian polynomials , the @xmath2-eulerian polynomials are known to have symmetric and unimodal coefficients . an elegant explanation of this fact may be based on a topological interpretation of @xmath25 as the @xmath4-polynomial of the coxeter complex of @xmath2 . since every ( finite ) coxeter complex is realizable as the boundary complex of a simplicial polytope , the symmetry and unimodality of the coefficients of @xmath25 may thus be seen as a consequence of the @xmath26-theorem ( e.g. , see section iii.1 of  @xcite ) . recently , several authors ( see for example @xcite ) have identified interesting classes of simplicial complexes whose @xmath4-polynomials have expansions of the form @xmath27 where the coefficients @xmath28 are nonnegative . it is easy to see that each summand in this expansion has symmetric and unimodal coefficients centered at @xmath29 , and thus any @xmath4-polynomial with a nonnegative `` @xmath5-vector '' in this sense necessarily has symmetric and unimodal coefficients . in these terms , the @xmath4-polynomials of all finite coxeter complexes ( i.e. , the @xmath2-eulerian polynomials ) are known to have nonnegative @xmath5-vectors  @xcite . another feature of @xmath5-nonnegativity is that it is a necessary condition for a polynomial to have all real roots , given that the polynomial has nonnegative symmetric coefficients . in this direction , brenti  @xcite has conjectured that the @xmath2-eulerian polynomials have all real roots , a result that remains unproved only for the groups @xmath30 .    in this paper , we study a family of eulerian - like polynomials associated to irreducible affine weyl groups . these `` affine '' eulerian polynomials may be defined as generating functions for `` affine descents '' over the corresponding finite weyl group . an affine descent is similar to an ordinary descent in a weyl group , except that the reflection corresponding to the highest root may also contribute a descent , depending on its effect on length . the affine eulerian polynomials have a number of interesting properties similar to those of the ordinary @xmath2-eulerian polynomials . in particular , we show that they have nonnegative @xmath5-vectors ( theorem  [ thm : gamnonn ] ) , and conjecture that all of their roots are real . perhaps the most interesting similarity is that each affine eulerian polynomial is the @xmath4-polynomial of a naturally associated relative cell complex ( theorem  [ thm : torus ] ) .    to describe this complex , one should start with an irreducible affine coxeter arrangement . such an arrangement induces a simplicial decomposition of the ambient space ; by taking the quotient of this space by the translation subgroup of the associated affine weyl group , one obtains a torus decomposed into simplicial cells . we refer to this cell complex as the _ steinberg torus _ in recognition of the work of steinberg , who gave a beautiful proof of bott s formula for the poincar series of an affine weyl group by analyzing the action of the finite weyl group on the homology of this complex in two different ways ( see section  3 of  @xcite ) . in fact , steinberg also allows the possibility of twisting the entire construction by an automorphism , but we will not consider this variation here .    it is important to note that the steinberg torus is not a simplicial complex ( distinct cells may share the same set of vertices ) , but it is at least a boolean cell complex in the sense that all lower intervals in the partial ordering of cells are boolean algebras . for further information about boolean complexes , see  @xcite and the references cited there .    for our purposes , it is essential to omit the empty cell of dimension @xmath31 from the steinberg torus ; we refer to the resulting relative complex as the _ reduced steinberg torus_. it is this complex whose @xmath4-polynomial is the corresponding affine eulerian polynomial ; i.e. , the generating function for affine descents . it is noteworthy that affine descents in finite weyl groups were first introduced by cellini  @xcite in a construction of a variant of solomon s descent algebra , and developed further for the groups of type @xmath32 and @xmath33 in several follow - up papers on `` cyclic descents '' by cellini  @xcite , fulman  @xcite , and petersen  @xcite . in very recent work , lam and postnikov  @xcite study a weighted count of affine descents ( the `` circular descent number '' ) that coincides with an ordinary count ( only ) in type @xmath32 . the paper is structured as follows . section  [ sec : prelim ] introduces the necessary definitions , including details of the construction of the steinberg torus . in section  [ sec : affe ] we show that the affine eulerian polynomials are the @xmath4-polynomials of reduced steinberg tori ( theorem  [ thm : torus ] ) . although we do not know of any conceptual topological explanation for the nonnegativity of the @xmath4-vector , we do show that reduced steinberg tori are partitionable ( remark  [ rmk : partition ] ) ; this is a weak analogue of shellability that implies @xmath4-nonnegativity .    in section  [ sec : rrgp ] , we present our second main result ; namely , that the affine eulerian polynomials have nonnegative @xmath5-vectors ( theorem  [ thm : gamnonn ] ) . as a corollary , it follows that the @xmath4-vectors of reduced steinberg tori are symmetric and unimodal . in this section , we also present evidence supporting our conjecture that all roots of affine eulerian polynomials are real . the proof of theorem  [ thm : gamnonn ] is case - by - case , and relies on combinatorial expansions for the @xmath5-vectors of affine eulerian polynomials for the classical weyl groups that we provide in section  [ sec : comb ] . in this latter section , we also provide combinatorial expansions for the flag @xmath4-polynomials of reduced steinberg tori , one of which suggests the possibility that a natural class of ( reduced ) polyhedral tori may have nonnegative @xmath34-indices ( see question  [ quest : cd ] ) .    in section  [ sec : ident ] , we present three unexpected identities relating ordinary and affine eulerian polynomials ( two new , one old ) , and use these to derive exponential generating functions for the affine eulerian polynomials for each classical series of weyl groups .","summary":"we also show that the ordinary-polynomial has a nonnegative-vector , and hence , symmetric and unimodal coefficients . in the classical cases , we also provide expansions , identities , and generating functions for the-polynomials of steinberg tori .    0.5","abstract":"let be an irreducible affine weyl group with coxeter complex , where denotes the associated finite weyl group and the translation subgroup . the steinberg torus is the boolean cell complex obtained by taking the quotient of by the lattice . we show that the ordinary and flag-polynomials of the steinberg torus ( with the empty face deleted ) are generating functions over for a descent - like statistic first studied by cellini . we also show that the ordinary-polynomial has a nonnegative-vector , and hence , symmetric and unimodal coefficients . in the classical cases , we also provide expansions , identities , and generating functions for the-polynomials of steinberg tori .    0.5"}
{"article_id":"1102.1586","section_id":"i","document":"metallicity is one of the few progenitor attributes that can affect the luminosity of type ia supernovae ( snia ) , with important consequences for their use as cosmological standard candles @xcite . recently , @xcite analysed the metallicity as a source of dispersion in the light - curve width - luminosity relationship and found that deriving supernova luminosities from light curve shapes without accounting for the supernova metallicity might lead to systematic errors of up to 0.5 mag . from an observational point of view , the dependence of snia luminosities on metallicity might originate a systematic error of @xmath5% in the measurement of the dark energy equation of state @xmath6 @xcite , comparable to the current statistical uncertainties . @xcite proposed to include the host properties ( galaxy mass and metallicity ) into the snia light - curve fitters in order to correct for these systematic errors .    up to now , attempts to measure the metallicity directly from supernova observations have been scarce and their results uncertain @xcite . measuring the metallicity , @xmath7 , from the x - ray emission of supernova remnants is a promising alternative but as yet has been only applied to a single supernova @xcite , although there are prospects to extend this analysis to further remnants @xcite . an alternative venue is to estimate the supernova metallicity as the mean @xmath7 of its environment @xcite - this can be done for statistically significant samples of sne in nearby galaxies by taking advantage of the long evolutionary timescales of their supernova remnants @xcite . excluding these studies based on individual objects or supernova remnants , the vast majority of our knowledge about the metallicity of type ia sn progenitors has been assembled by measuring the bulk properties of their _ entire _ host galaxies . @xcite looked for galactic age or metal content correlations with snia luminosity in star - forming hosts , but their results were ambiguous . @xcite studied the correlations between snia properties and galaxy metallicity or , more precisely , its oxygen abundance as determined from emission lines in the integrated spectra of star - forming hosts . @xcite looked for systematic trends of snia uv spectra with metallicity of the host galaxy , and found that the spectral variations were much larger than predicted by theoretical models . @xcite studied the metallicity of all the star - forming galaxies in the sloan digital sky survey ( sdss ) catalogue with redshifts in the range @xmath8 that hosted sne of some kind and noted that snia occur in a wide range of metallicities , as low as 0.25 solar . @xcite , using data from the sdss and supernova survey concluded that prompt snia are more luminous in metal - poor systems . @xcite and @xcite , using different methodologies to estimate the metallicity of snia hosts , arrived to opposite conclusions with respect to the dependence of supernova luminosity on @xmath7 , although these discrepancies might have been solved recently @xcite . we note that most of the previous work has focused on comparisons between the empirical observationally - determined relationship between the _ metallicity of hosts _ and their snia luminosities on the one hand ( e.g. * ? ? ? * ) and theoretical predictions of correlations between the _ supernova metallicity _ and luminosity on the other hand ( e.g. * ? ? ? * ) , thus assuming implicitly that both metallicities are somehow tied .    estimating the metallicity of an entire galaxy is a complex task , involving many different observational and theoretical challenges . on the observational side , different tracers exist for both gas - phase and stellar metallicities , each with their own advantages and disadvantages @xcite . on the theoretical side , complex modelling of the observations is often required to arrive at a numerical estimate of the metallicity , which introduces biases and uncertainties that depend on the specific technique used ( e.g. * ? ? ? @xcite measured the host metallicity from absorption lines of fe at two wavelengths , thus testing the gas - phase in early - type galaxies , using single - age single - metallicity stellar population models . then , to derive metallicity , they assumed solar elemental ratios in the galactic interstellar medium ( ism ) . @xcite determined the host metallicity indirectly . in a first step , they determined the host mass from spectral energy distribution fits to galaxy photometry . next , they applied the well - known mass - metallicity relationship @xcite , also valid for the gas - phase . the @xcite mass - metallicity relationship was determined in turn through measures of the nebular emission lines of oxygen in star - forming galaxies . @xcite compared the stellar metallicities to those of the gas - phase ( measured through the oxygen abundance ) for several thousand galaxies in the sdss . they found that the relationship between both metallicities is non - linear , with a shallower than linear dependence of the gas - phase oxygen abundance on the stellar metallicity , and a large scatter of data points . the question we want to address in this work is : what is the relationship between the metallicity of a snia and that of its host galaxy ? given the complexity of the problem we want to address it from a statistical point of view , aiming to determine a distribution function for the difference of metallicities between the supernova and its host . our approach is based on calculations of galactic chemical evolution together with the evolution of the supernova rate . in order to understand which the best estimators of snia metallicity are we study the correlations between snia metallicity and different observational tracers of host metallicity : fe vs. o in the gas - phase and stellar vs. gas - phase metallicity . in order to keep simplicity , we use homogeneous one - zone galactic chemical evolution models , disregarding spatial variations within each galaxy . taking into account the spatial variations of metallicity would increase the scatter and corrections modelled in this paper . the plan of the paper is as follows . in section  [ models ] , we describe the theoretical framework we adopt in order to derive the statistical properties of the metallicities of snia compared to that of their host galaxies . in the next section , we analyse the results , with particular emphasis on the reliability of different host metallicity measures as estimators of snia metallicity . among the tracers that we consider , we rank highest the measure of snia metallicity through the gas - phase metallicity of its host . we pay special attention to the influence of the assumed delay time distribution ( dtd ) of snia . it turns out that the metallicity of an average snia is closer to that of its host if the dtd peaks at small time delays , as the dtd of @xcite , than if the snia rate follows the rate of formation of white dwarfs , as proposed by @xcite . in section  [ catalogs ] we explore the possibility of using current galactic catalogues , such as sdss and vespa , to derive the metallicity distribution function of snia . finally , in section  [ toconclude ] we draw our conclusions .","summary":"the efficient use of type ia supernovae ( snia ) for cosmological studies requires knowledge of any parameter that can affect their luminosity in either systematic or statistical ways . catalogues  distance scale  galaxies : abundances  supernovae : general .","abstract":"the efficient use of type ia supernovae ( snia ) for cosmological studies requires knowledge of any parameter that can affect their luminosity in either systematic or statistical ways . observational samples of snia commonly use the metallicity of the host galaxy , , as an estimator of the supernova progenitor metallicity , , that is one of the primary factors affecting snia magnitude . here , we present a theoretical study of the relationship between and . we follow the chemical evolution of homogeneous galaxy models together with the evolution of the supernova rates in order to evaluate the metallicity distribution function , , i.e. the probability that the logarithm of the metallicity of a snia exploding now differs in less than from that of its host . we analyse several model galaxies aimed to represent from active to passive galaxies , including dwarf galaxies prone to experience supernova driven outflows . we analyse as well the sensitivity of the mdf to the most uncertain ingredients of our approach : imf , star - formation law , stellar lifetime , stellar yields , and snia delay - time distribution ( dtd ) . our results show a remarkable degree of agreement between the mean in a galaxy and its when they both are measured as the cno abundance , especially if the dtd peaks at small time delays , while the average fe abundance of host and snia may differ up to 0.4 - 0.6 dex in passive galaxies . the dispersion of in active galaxy models is quite small , meaning that is a quite good estimator of the supernova metallicity . passive galaxies present a larger dispersion , which is more pronounced in low mass galaxies . we present a procedure to generate random snia metallicities , given the host metallicity . we also discuss the use of different metallicity indicators : fe vs. o , and gas - phase metallicity vs. stellar metallicity . finally , the results of the application of our formalism to a galactic catalogue ( vespa ) suggest that snia come , in average , from small metallicity progenitors both at low redshifts ( contrary to expectations ) and in galaxies with high star - formation activity . in spite of large uncertainties in the metallicities derived from the catalogue , the gross trends of vs. obtained from vespa for different galaxy types are roughly consistent with our theoretical estimates .    catalogues  distance scale  galaxies : abundances  supernovae : general ."}
{"article_id":"1102.1586","section_id":"r","document":"in this section , we will present the results obtained with the models including inflow and the models of passive galaxies . unless otherwise stated , we solve eqs . [ eqmg ] and [ eqmj ] from @xmath100 to @xmath101  gyr .      . the different curves are meant to represent typical galaxies : model d in table  [ tab1 ] ( long - dashed magenta ) belongs to an early - type galaxy , while models b ( dotted black ) and c ( short - dashed blue ) are representative of late - type galaxies , and model a ( solid red ) is a transition galaxy characterized by a short infall timescale and a moderately long star formation rate timescale . the vertical axis gives the sfr _ normalized _ by the total mass of the system , @xmath102 ( @xmath102 is also the mass of the halo at @xmath100 and should be much smaller for irregulars and dwarf ellipticals than for normal - size galaxies ) . , width=9 ]    [ cols=\"<,^,^,^,^,^,^,^,^ \" , ]     we start by analysing the behaviour of typical galaxies meant to represent from ellipticals to late - type galaxies . table  [ tab1 ] gives their main parameters together with the final mass fractions of gas and stars with respect to the total mass of the system , the final metallicity ( both as given by all metals and by cno elements ) of the host , and the statistical properties of the corresponding mdf of snia : metallicity correction and standard deviation of the distribution , @xmath103 . we computed all the model galaxies discussed in this subsection with no outflow . models a to c are in good agreement with the models in table 2 of @xcite for galaxies of types e , sc , and sd ( the remaining mass of gas and the mass of stars at @xmath104 of the models , as well as the final metallicities agree reasonably well given that the model of evolution of the rate of snia we use are not the same as their ) . the sfr of model d is more bursty ( fig . [ figsfr ] ) , and we include it here as a representative of the early - type galaxy models used in the rest of the paper ( even though it has @xmath105 , which would correspond to a massive early - type galaxy ) . in this and the next subsection , we present the results obtained with the dtd of p08 , while we delay to section  [ sectdtd ] the discussion of the differences with respect to the dtd of m10b .    in fig . [ figpiap ] , we show the distribution of birth - times for a snia exploding at @xmath104 . the curves peak at the present time because the dtd is strongly biased towards small delay times . this effect is more pronounced in late - type galaxies , for which the star - formation activity is either slightly decreasing or increasing . early - type galaxies display a similar peak at quite early times , belonging to the epoch of intense star - formation activity , but the importance of this initial peak varies according to the duration of the star - formation epoch . thus , snia from early - type galaxy models come from two different populations whose properties can be quite different : an old , predominantly low - mass , population belonging to the star - formation peak , and a young population characterized by larger masses .      +      figure  [ figmdf ] shows the mdf of snia , for the same typical galaxies as those in the left panel of fig . [ figpiap ] , as a function of @xmath3 . as can be deduced from fig . [ figpiap ] , the younger the stellar population of a galaxy is ( as in models b and c ) the smaller the scatter in metallicity of potential snia progenitors . the late - type galaxy distribution is strongly biased towards a zero correction and display a short tail , down to @xmath106  dex for a galaxy that is still in its initial phases of star formation ( @xmath107  gyr , meant to represent an irregular galaxy ) , and @xmath108  dex for a galaxy that has already gone through most of the infall process ( @xmath109  gyr ) . the probability of a snia metallicity differing in less than 0.1  dex ( in absolute value ) from @xmath0 is 75% for the irregular galaxy model and 57% for the model with @xmath109  gyr . , for the same models as in the left panel of fig . [ figpiap ] . , width=9 ]    early - type galaxies show a broader mdf implying that snia from these hosts will have a larger intrinsic metallicity dispersion , even if they come from the same host ! again , this behaviour can be understood from the probability density of snia progenitors shown in fig . [ figpiap ] : models a and d have a substantial contribution of old potential snia progenitors , thus they show a large scatter in their mdf . for the model with @xmath60  gyr and @xmath110 gyr half of the snia have a metallicity differing more than 0.38  dex ( in absolute value ) from @xmath0 , while for the model with @xmath60  gyr and @xmath111  gyr the median of the correction is -0.49  dex .    . , width=9 ]    figure  [ figcnomdf ] shows the mdf of snia when the metallicity is measured as the abundance of cno elements . the main difference with the mdf derived for fe is found in the behaviour of the older galaxy model , i.e. the one with @xmath60  gyr and @xmath111  gyr . the reason of this behaviour can be understood by looking at fig . [ figpiap ] ( bottom right panel ) , where we display the evolution with time of the mass fraction of cno elements in the gas . the long - dashed ( magenta ) curve shows the evolution following the short burst of star formation coincident with the infall epoch . initially the abundance of cno elements grows fast due to the self - enrichment of the gas due to efficient reprocessing driven by massive stars . once the star formation burst is over , there are no more massive stars present , and intermediate and low mass stars enrich the interstellar medium at the end of their lifetime with yields representative of their birth time , on average less rich on cno elements than at the peak of the curve . this causes the cno abundance to decrease rapidly until it reaches a stable value at about 60% of the peak cno mass fraction . therefore , the snia that explode at @xmath112  gyr can have birth metallicites _ larger _ than that of the host , as seen in fig . [ figcnomdf ] .    because snia are observed at different redshifts , it is also interesting to know if their mdf varies with the elapsed time of galactic evolution , @xmath113 . we have integrated again the evolutionary equations with @xmath114 and 13.7  gyr . within this range of @xmath113 the  metallicity correction  changes by less than @xmath115 .      in this section , we use a sample of galactic models with varying @xmath51 , @xmath59 , and @xmath87 to study the statistical properties of the relationship between @xmath1 and @xmath0 . we have built models for early - type galaxies by using small values of the timescales associated to infall and sfr : either @xmath60  gyr or @xmath116  gyr , and either @xmath111  gyr or @xmath116  gyr , and with different degrees of outflow , controlled by the parameter @xmath87 . thus , for each value of @xmath87 we show four models , obtained with the aforementioned combinations of @xmath59 and @xmath51 . in general , the location of these models in the plane @xmath4 vs @xmath0 is driven by @xmath87 , while the variation with @xmath59 and @xmath51 is small .    in order to generate models for late - type galaxies  gyr and @xmath105 . note that this includes models a to c and a to c in table  [ tab1 ] . ] we left the infall and sfr timescales vary in the ranges : @xmath117  gyr and @xmath118  gyr . in order to avoid too extreme or unrealistic galaxy models we have further constrained our sample to have @xmath119 and @xmath120 . figure  [ figziap ] ( left panel : dtd of p08 ) shows the metallicity correction , to be applied to @xmath0 in order to estimate @xmath1 , as a function of the host metallicity . the two kind of galaxies show different behaviour : while there is an approximately linear dependence of the correction on @xmath0 for late - type galaxies , the correction is about constant for early - type galaxies of every metallicity , i.e. the dispersion of the corrections is much smaller than the range of host metallicities . the linear function that fits the late - type galaxies passes as well through the early - type ones with no outflow ( @xmath105 ) . as @xmath87 increases , the final metallicities of the early - type hosts decrease while the metallicity correction remains the same . figure  [ figcnoiap ] shows the metallicity correction belonging to cno abundances . it displays the same gross properties as those seen in fig . [ figziap ] with one important difference concerning early - type galaxies : their metallicity corrections are now among the lowest of all models displayed . the reason for this behaviour is again the peculiar mdf of cno elements in snia from this kind of galaxies as seen in fig . [ figcnomdf ] . the dispersion of their mdf is , however , similar to that of galaxies with a much larger metallicity correction ( compare models a and d in table  [ tab1 ] ) .        in many observational studies , it is necessary to generate a random set of snia with stochastic metallicities in order to compare their statistical properties with those of the observational sample . the linear fit of @xmath13 vs. @xmath121 $ ] shown in fig . [ figziap ] together with the mdf may be used to generate such a random set of snia , with stochastic metallicities related ( but not equal ) to their host metallicities . the simpler way to do this is to approximate the mdf of snia as a straight line in the semi - logarithmic plot shown in fig . [ figmdf ] ,    @xmath122    that determines the probability density ,    @xmath123    the mean metallicity correction ,    @xmath124    and the standard deviation , @xmath103 , of the distribution of @xmath3 :    @xmath125    in table  [ tab1 ] we give the standard deviation of the mdf of our typical galaxy models . as can be seen , the relationship between @xmath13 and @xmath103 derived in eq . [ eqsigma ] approximately holds for all the models , with the exception of the distribution of cno in models d and d , for which a simple proportionality law as that of eq . [ eqfitmdf ] is not a good fit ( see fig . [ figcnomdf ] ) .    to generate a stochastic distribution of snia metallicites in a late - type galaxy of known @xmath0 , one would have first to apply the linear function of fig . [ figziap ] ( or that in fig . [ figcnoiap ] if what is desired is the distribution of mass fractions of the cno elements ) to obtain the metallicity correction @xmath126 and @xmath103 ( @xmath127 ) . for an early - type host the procedure is even simpler , as the metallicity correction takes on a nearly constant value for this kind of galaxies . the delay time distribution is a property specific of snia that has rather small imprint on the galactic chemical evolution of cno elements but affects strongly the temporal distribution of snia , hence it is expected to influence appreciably the mdf . the dtd of snia is a matter of current debate @xcite . p08 proposed a model in which the rate of snia was proportional to the wd formation rate . this model reproduced satisfactorily the trend of snia rates as a function of the specific sfr in galaxies of ages between 1 and 13  gyr . in a recent work , @xcite presented a method to recover the supernova dtd that simultaneously takes into account supernova data and the reconstructed star formation history of the individual galaxies in a survey , and applied this method to the events present in the loss sn survey and in the vespa database . independently , @xcite analyzed light curves and host galaxy spectra of 101 snia from the sdss using vespa algorithms , from which they derived the dtd of snia . @xcite found that their data required a stronger short delay - time component than allowed by the model of p08 , i.e. they called for a higher contribution from large mass progenitors . the vespa database is organized in temporal bins , whose resolution is better at the present epoch and degrades with look - back time ( for further details see section  [ catalogs ] ) , hence the results of @xcite should be more sensitive to the short delay time component of the snia dtd . thus , the discrepancy between the models proposed by p08 and @xcite might be due to the different sensitivities to the time ranges of the snia dtd ( but see m10b ) . anyway , it is necessary to check the imprint that the different dtd have on the mdf of snia . having used a model based on p08 in the previous sections , we now discuss the results obtained with the dtd of m10b , eq . 13 in their paper , @xmath128 where @xmath129 , @xmath19 is measured in gyr , and we have applied a factor 0.7 to the dtd of m10b to convert back from their diet - salpeter imf to ours . models a to d in table  [ tab1 ] were computed using their dtd in eqs .  [ eqria ] and [ eqpia ] . the right panel of fig . [ figpiap ] shows the distribution of birth - times for a snia exploding at @xmath104 for these model galaxies . with respect to the dtd of p08 ( left panel of fig . [ figpiap ] ) the new dtd increases the contribution from young stars ( small delay - time ) with respect to old stars . late - type galaxies are scarcely affected at all , but early - type galaxies display a quite different trend in which the contribution of the population belonging to the initial star - formation peak is dramatically reduced . with this new dtd , the differences between galaxy - types strongly smooth out .    the metallicity correction obtained with the dtd of m10b is shown in the right panel of figs . [ figziap ] and [ figcnoiap ] , for both late - type and early - type galaxies . overall , the correction is significantly smaller than that obtained using the dtd of p08 , as expected given the larger contribution from prompt snia implied by the dtd of m10b .    from these results it is clear that the dtd of snia is the most important factor determining the magnitude of the correction needed to obtain the metallicity of snia from those of their host galaxies . we stress that any of the above dtd models ( p08 vs. m10b ) is subject to a large degree of observational uncertainty . for instance , m10b discuss two possible approaches to determine the power law exponent in eq . [ dtdmaoz ] , based on what they call the optimal - iron constraint and the minimal - iron constraint , which lead to different exponents , @xmath130 , in the range from -1.5 to -0.9 ( in this study , we have adopted in eq . [ dtdmaoz ] the mean , i.e. -1.2 ) . it is interesting to consider how much would change the plots in figs . [ figziap ] and [ figcnoiap ] if @xmath130 covered the full range given by m10b . we have repeated the calculations with @xmath131 and @xmath132 . for the first case , belonging to an extreme case of the optimal - iron constraint , the straight - line fit to our late - type galaxies changes to @xmath133 + 0.06 $ ] while the correction for early - type galaxies changes by @xmath134  dex . for the last case , belonging to an extreme case of the minimal - iron constraint , the fit of the late - type host corrections changes to @xmath135 - 0.16 $ ] , and the corrections for early - type hosts changes by @xmath136  dex . we can see that the uncertainty in the dtd leads to uncertainties in @xmath13 of the same order as the own correction . we conclude that an accurate determination of the dtd of snia is a prerequisite to achieve a good understanding of the differences between the metallicities of these supernovae and those of their host galaxies .      here we discuss the reliability of different host metallicity estimators as for establishing the statistical properties of snia : gas - phase vs. stellar metallicity , @xmath137 , and gaseous cno abundance vs. fe abundance . we have evaluated the mean host stellar metallicity as the mean of the metallicity of the ism at star birth , weighted by the sfr and by the imf , for all the stars whose mean - sequence lifetime is larger than the elapsed time since their formation . the mean stellar metallicity derived by observational studies is weighted by the contribution of stars in different phases of their life , with weights depending on the particular spectral feature used for measuring the metallicity . even though both ways to define a mean stellar metallicity may give different values , we expect that both will follow the same qualitative trends . [ figziazstar ] shows the metallicity correction to apply if the host galaxy metallicity is measured from the stellar population ( and the dtd of m10b is used ) . in comparison with the trend shown in the right panel of fig . [ figziap ] we notice that the corrections to apply to the metallicities of early - type galaxies continues being independent of host metallicity , but now they cluster around @xmath138 . late - type galaxies display also a similar behaviour as in fig . [ figziap ] , with changed sign , but they could not be fitted by a linear function and show larger dispersion for given @xmath0 . thus , if possible , it is advisable to measure the metallicity of snia in late - type hosts as that of their gas . these results can be understood by computing the distribution of birth - times of present - day ( at @xmath101  gyr ) stars . we have calculated the distribution of birth times as the fraction of the mass in present - day stars represented by the stars born at time @xmath19 that are still alive , @xmath139 the distribution of birth - times follows closely the sfr of each model ( see fig .  [ figsfr ] ) because 99% of the stellar mass at birth belongs to stars smaller than @xmath140  m@xmath141 ( for our salpeter imf ) , hence the integral in eq . [ birth ] is always close to @xmath142 . comparing fig . [ figsfr ] with the probability density of birth times of snia shown in fig . [ figpiap ] ( top right ) it is easy to see that the average age of snia progenitors is much less than the average age of the stellar population , especially because the peak of @xmath23 at times close to @xmath113 . in galaxies characterized by a monotonic increase of the metallicity ( models a , b , and c ) the immediate consequence is that the metallicity of snia is larger than the average stellar metallicity . early - type galaxies , like model d , display a non - monotonic evolution of the metallicity , that peaks later than the sfr . for instance , for model d the peak of the sfr occurs at @xmath143  gyr , while the peak of @xmath144 is found at @xmath145  gyr and that of @xmath146 takes place at @xmath147  gyr . thus , the stellar population is chiefly drawn from low - metallicity gas , while snia have an appreciable contribution from times close to present , at which the gas metallicity is much larger .    , instead of the gas metallicity , @xmath0 . here we have used the dtd of m10b . the filled symbols belong to models a , b , c , and d in table  [ tab1 ] ( from top to bottom ) . the error bar at the top left of the figure is the typical uncertainty in observationally determined @xmath148 $ ] ( see discussion at the end of section  [ themostrelevant ] ) . , width=8 ]    in fig . [ figcnoiap ] we show the metallicity correction when the gas - phase metallicity is estimated from the mass fraction of cno elements in the gas . in comparison with fig . [ figziap ] the cno metallicity correction is nearly identical to the fe correction for late - type galaxies but significantly smaller for early - type hosts , for a given dtd . as can be seen in fig . [ figpiap ] ( bottom row ) the chemical evolutions of fe and cno elements in the galaxy models a , b , and c are in close agreement , thus the mdf of both element groups are similar ( compare fig . [ figmdf ] with fig . [ figcnomdf ] ) . thus , the use of fe instead of cno abundances does not seem to represent an improvement in the estimates of snia metallicities obtained from those of their hosts . the host cno abundance of early - type galaxies is in much better agreement with the _ mean _ snia one than are the corresponding total metal abundances , although their dispersions are similar . using again the chemical evolution computed for the prototypical galaxy model d , displayed in the bottom row of fig . [ figpiap ] , and the probability density of snia shown in fig . [ figpiap ] , the reason for this closer agreement between cno abundances in snia and the gas , as compared with fe abundances , is that snia from early - type galaxies have non - negligible contributions from quite early times and near present time . the cno abundances are low at both times , because presently there are no high - mass stars contributing to their synthesis . on the other hand , the fe abundance increases continuously during the last 11 gyr due to the contribution of snia , with the result that young snia progenitors are drawn from gas with high fe abundance while old snia progenitors were born from gas with quite small fe abundance . hence , the average discrepancy between present - day gas fe abundance and that of snia is larger than in the case of the cno abundances .    a meaningful evaluation of the corrections we propose to obtain snia metallicities from the different metallicity measures of their hosts can only be done by considering the observational errors in the galactic metallicity and in the dtd of snia . as discussed in the introduction , galactic metallicities are measured using different methods , all of them subject to a suite of experimental and theoretical uncertainties . @xcite measured the fe abundance of the gas of early - type hosts of snia with quite different errors , depending on the host . an average error in @xmath149 $ ] of 0.1 - 0.2  dex can be deduced from their table  4 and from the comparison they perform with metallicities measured by @xcite and @xcite for a subset of galaxies they have in common . on the other hand , the @xcite mass - metallicity relationship , used by @xcite to measure host metallicity , is sensitive to @xmath150 $ ] in the gas phase . the scatter in this relationship is of order @xmath151  dex . finally , the observational determination of @xmath148 $ ] is subject to systematic biases of order @xmath152  dex @xcite . summarizing , the uncertainty in the measured metallicity of snia hosts is similar for the different metallicity tracers , @xmath153  dex , although it may be substantially larger for a given galaxy . we have drawn in figs . [ figziap ] , [ figcnoiap ] , and [ figziazstar ] an error bar indicative of the typical uncertainty in the measured host metallicity . these uncertainties are not large compared to the range of host metallicities covered in the figures ( horizontal axes ) . one can also compare the host metallicity uncertainty with the correction necessary to obtain @xmath1 , plotted in the same figures ( vertical axes ) . looking at the corrections deduced for the dtd of p08 ( left panels of the same figures ) it can be seen that they are in general much larger than @xmath154 . on the contrary , if the dtd of m10b is used ( right panels of figs . [ figziap ] and [ figcnoiap ] ) , @xmath155 is of the same order as @xmath154 , especially for early - type galaxies . thus , if this last dtd were the correct choice , the error in the determination of snia metallicity would be dominated by the uncertainty in the measurement of the host metallicity rather than the difference between galactic and supernova metallicities .","summary":"our results show a remarkable degree of agreement between the mean in a galaxy and its when they both are measured as the cno abundance , especially if the dtd peaks at small time delays , while the average fe abundance of host and snia may differ up to 0.4 - 0.6 dex in passive galaxies . we present a procedure to generate random snia metallicities , given the host metallicity .","abstract":"the efficient use of type ia supernovae ( snia ) for cosmological studies requires knowledge of any parameter that can affect their luminosity in either systematic or statistical ways . observational samples of snia commonly use the metallicity of the host galaxy , , as an estimator of the supernova progenitor metallicity , , that is one of the primary factors affecting snia magnitude . here , we present a theoretical study of the relationship between and . we follow the chemical evolution of homogeneous galaxy models together with the evolution of the supernova rates in order to evaluate the metallicity distribution function , , i.e. the probability that the logarithm of the metallicity of a snia exploding now differs in less than from that of its host . we analyse several model galaxies aimed to represent from active to passive galaxies , including dwarf galaxies prone to experience supernova driven outflows . we analyse as well the sensitivity of the mdf to the most uncertain ingredients of our approach : imf , star - formation law , stellar lifetime , stellar yields , and snia delay - time distribution ( dtd ) . our results show a remarkable degree of agreement between the mean in a galaxy and its when they both are measured as the cno abundance , especially if the dtd peaks at small time delays , while the average fe abundance of host and snia may differ up to 0.4 - 0.6 dex in passive galaxies . the dispersion of in active galaxy models is quite small , meaning that is a quite good estimator of the supernova metallicity . passive galaxies present a larger dispersion , which is more pronounced in low mass galaxies . we present a procedure to generate random snia metallicities , given the host metallicity . we also discuss the use of different metallicity indicators : fe vs. o , and gas - phase metallicity vs. stellar metallicity . finally , the results of the application of our formalism to a galactic catalogue ( vespa ) suggest that snia come , in average , from small metallicity progenitors both at low redshifts ( contrary to expectations ) and in galaxies with high star - formation activity . in spite of large uncertainties in the metallicities derived from the catalogue , the gross trends of vs. obtained from vespa for different galaxy types are roughly consistent with our theoretical estimates .    catalogues  distance scale  galaxies : abundances  supernovae : general ."}
{"article_id":"1102.1586","section_id":"c","document":"we have calculated the chemical evolution of homogeneous galaxy models together with the evolution of the supernova rates in order to evaluate the metallicity distribution function of snia , @xmath2 , i.e. the probability that the logarithm of the metallicity of a snia exploding now differs in less than @xmath3 from that of its host . we have analysed several model galaxies aimed to represent from active to passive galaxies , including dwarf galaxies prone to experience supernova driven outflows . our results show a remarkable degree of coincidence ( in an statistical sense ) between the mean @xmath1 and @xmath0 . the dispersion of @xmath1 in active galaxy models is quite small , meaning that @xmath0 is a quite good estimator of the supernova metallicity , while passive galaxies present a larger dispersion . we have devised a procedure to correct the difference in metallicity between snia and their hosts ( sect . [ sectstat ] ) , based on a linear fit given in fig .  [ figziap ] . these results are insensitive to the choice of imf , stellar lifetime and stellar yields , within the ranges we have explored . in contrast , the delay time distribution of snia remains one of the main ingredients influencing the difference of metallicity between snia and their hosts . we have discussed the use of different metallicity indicators ( fe vs. o , gas - phase metallicity vs. stellar metallicity ) . using o ( assuming its evolution is representative of that of the cno group ) as a metallicity measure for late - type galaxies does not change appreciable the metallicity correction with respect to using fe ( assuming its evolution is representative of that of all metals ) . it is remarkable that the metallicity correction for early - type galaxies ( @xmath180  gyr ) is quite different for o than for fe . on the other hand , the metallicities of snia are much better represented by those of the gas - phase than by the mean stellar metallicities . thus , when possible , it is advisable to measure the host metallicity through that of its gas - phase .    finally , the results of the application of our formalism to a galactic catalogue ( vespa ) suggest that snia come , in average , from smaller metallicity progenitors both at low redshifts and in galaxies with large star - formation activity . the paucity of metallicities used in the original stellar - population synthesis models used in the construction of the galactic catalogue does not allow us to build a significant mdf of snia based on the galactic histories stored in the database . however , in spite of the large uncertainty in the metallicity derived from the catalogue , the gross trends of @xmath4 vs. @xmath0 obtained from vespa for different galaxy types are roughly consistent with our theoretical estimates . the derivation of improved , observationally based , mdf will be possible in the future if the ssp models include further refinements in their grid of metallicities . one of the main drawbacks of our approach is the use of homogeneous one - zone galactic chemical evolution models . actual galaxies are heterogeneous , and radial gradients of chemical composition are routinely measured within them . a possible improvement of our model would be to divide the galaxy in several non - interacting shells as in , e.g. , @xcite , then computing the galactic mdf accounting for the probability that a snia originates in each shell . then , however , a complication would arise when comparing to observations of far away galaxies for which there is no possibility of measuring the metallicity gradient : what is the meaning of _ the _ galaxy metallicity in a context where each independent shell has its own chemical history ? what is clear is that the derived mdf of snia would be characterized by a larger dispersion than the mdf we have obtained . in some sense , the true mdf of snia reflects a double dependence : in space , i.e. the position of the snia progenitor within its host galaxy , and in time , i.e. the moment in the galactic history when the progenitor was born . it is just this last dependence what we have studied in the present work .","summary":"we follow the chemical evolution of homogeneous galaxy models together with the evolution of the supernova rates in order to evaluate the metallicity distribution function , , i.e. the probability that the logarithm of the metallicity of a snia exploding now differs in less than from that of its host . we analyse several model galaxies aimed to represent from active to passive galaxies , including dwarf galaxies prone to experience supernova driven outflows . the dispersion of in active galaxy models is quite small , meaning that is a quite good estimator of the supernova metallicity . passive galaxies present a larger dispersion , which is more pronounced in low mass galaxies . we also discuss the use of different metallicity indicators : fe vs. o , and gas - phase metallicity vs. stellar metallicity . finally , the results of the application of our formalism to a galactic catalogue ( vespa ) suggest that snia come , in average , from small metallicity progenitors both at low redshifts ( contrary to expectations ) and in galaxies with high star - formation activity . in spite of large uncertainties in the metallicities derived from the catalogue , the gross trends of vs. obtained from vespa for different galaxy types are roughly consistent with our theoretical estimates .   ","abstract":"the efficient use of type ia supernovae ( snia ) for cosmological studies requires knowledge of any parameter that can affect their luminosity in either systematic or statistical ways . observational samples of snia commonly use the metallicity of the host galaxy , , as an estimator of the supernova progenitor metallicity , , that is one of the primary factors affecting snia magnitude . here , we present a theoretical study of the relationship between and . we follow the chemical evolution of homogeneous galaxy models together with the evolution of the supernova rates in order to evaluate the metallicity distribution function , , i.e. the probability that the logarithm of the metallicity of a snia exploding now differs in less than from that of its host . we analyse several model galaxies aimed to represent from active to passive galaxies , including dwarf galaxies prone to experience supernova driven outflows . we analyse as well the sensitivity of the mdf to the most uncertain ingredients of our approach : imf , star - formation law , stellar lifetime , stellar yields , and snia delay - time distribution ( dtd ) . our results show a remarkable degree of agreement between the mean in a galaxy and its when they both are measured as the cno abundance , especially if the dtd peaks at small time delays , while the average fe abundance of host and snia may differ up to 0.4 - 0.6 dex in passive galaxies . the dispersion of in active galaxy models is quite small , meaning that is a quite good estimator of the supernova metallicity . passive galaxies present a larger dispersion , which is more pronounced in low mass galaxies . we present a procedure to generate random snia metallicities , given the host metallicity . we also discuss the use of different metallicity indicators : fe vs. o , and gas - phase metallicity vs. stellar metallicity . finally , the results of the application of our formalism to a galactic catalogue ( vespa ) suggest that snia come , in average , from small metallicity progenitors both at low redshifts ( contrary to expectations ) and in galaxies with high star - formation activity . in spite of large uncertainties in the metallicities derived from the catalogue , the gross trends of vs. obtained from vespa for different galaxy types are roughly consistent with our theoretical estimates .    catalogues  distance scale  galaxies : abundances  supernovae : general ."}
{"article_id":"astro-ph0701049","section_id":"i","document":"when a bright , nearby supernova ( sn ) is discovered , it may be possible to directly identify the progenitor of the sn in deep pre - sn images . analysis of the properties ( e.g. , mass , spectral type ) of such sn progenitors allows a direct comparison to theoretical expectations based on the observed quantities of the sne ( e.g. , light curves , spectral evolution ) .    while observers have had some luck with ground - based observations , such as the identifications of a @xmath8 blue supergiant ( bsg ) star for the peculiar , subluminous type ii sn 1987a in the large magellanic cloud ( gilmozzi et  al . 1987 ; sonneborn et  al . 1987 ) , a @xmath9 red supergiant ( rsg ) , possibly in a binary system , for the type iib sn 1993j in m81 ( aldering et  al .  1994 ; van dyk et  al . 2002 ) , and a 1320  @xmath5 yellow supergiant ( ysg ) for the type ii - p sn 2004et in ngc 6946 ( li et  al .  2005a , 2005b ) , most of the recent progress in this field has been based on the rich archival data of the _ hubble space telescope _ ( _ hst _ ) ( van dyk et  al . 2003a ; smartt et  al . 2004 ; maund & smartt 2005 ; maund et  al . 2005a ; li et al . 2006 ; hendry et  al .  2006 ; gal - yam et  al .  2007 ) . the superior spatial resolution of the _ hst _ images allows the sn progenitors to be isolated from their environments , and the deep limiting magnitude allows the sn progenitors to be detected in more distant ( but still relatively nearby ) galaxies .    in this paper we report the identification of the progenitors on _ hst _ images of two nearby sne in the virgo cluster . k. itagaki , a veteran japanese amateur sn searcher , discovered both of these sne : sn 2006my in ngc 4651 on 2006 nov . 8.82 ( ut dates are used throughout this paper ) and sn 2006ov in m61 ( ngc 4303 ) on 2006 nov . 24.86 ( nakano & itagaki 2006a , 2006b ) . unfortunately , the sn explosions occurred while the galaxies were behind the sun , and were only detected after becoming visible again in the early morning , so the objects were discovered rather late in their evolution . spectra obtained soon after the time of discovery show that both sne are of type ii : sn 2006my is similar to sn ii - p 1999em ( hamuy et  al . 2001 ; leonard et  al .  2002b ; elmhamdi et  al . 2003 ) about 12 months after maximum brightness ( stanishev & nielsen 2006 ) , and sn 2006ov , perhaps reddened , is similar to sn ii - p 2005cs ( pastorello et  al .  2006 ; takts & vink 2006 ) roughly a month after maximum ( blondin et  al .  2006 ) ( see  2 for a more detailed discussion of the age and reddening of both sne ) . we took ground - based images of the sne with the canada - france - hawaii telescope ( cfht ) under good seeing conditions ( figures 1 and 2 ) , and are able to precisely ( to within @xmath10 and @xmath11 , for sne 2006my and 2006ov , respectively ) locate the site of both sne on pre - sn archival _ hst _ images of the host galaxies . we further obtained _ hst_/acs images of sn 2006ov itself and were able to pinpoint the sn site to within 0@xmath202 . we identify a 715  @xmath5 red supergiant ( rsg ) and a 1220 @xmath5 rsg in the error circles of sne 2006my and 2006ov , respectively , and propose these as the progenitors of the sne . we note that ngc 4651 also produced sn 1987k , while m61 produced sne 1926a , 1961i , 1964f , and 1999gn . this paper is organized as follows . in  2 we discuss the properties ( type , age , and reddening ) of both sne , and demonstrate that they are of the type ii variety discovered near the end of the plateau phase . in  3 we report our identification of the progenitors in the pre - sn _ hst_/wfpc2 images . we describe the nature of the progenitors inferred from the _ hst _ photometry in  4 . further discussion is in  5 , and we summarize our conclusions in  6 .","summary":"we obtained high - quality ground - based images of sn 2006my with the canada - france - hawaii telescope , and are able to locate the site of the sn on pre - sn _ hubble space telescope _ ( _ hst _ ) wide field planetary camera 2 images to a high precision ( 1 uncertainty of ) . we detected a red supergiant progenitor for each sn within the error circles , with an inferred zero - age main - sequence mass ( ) of and for the progenitors of sne 2006my and 2006ov , respectively .","abstract":"direct identification of the progenitors of supernovae ( sne ) is rare because of the required spatial resolution and depth of the archival data prior to the sn explosions . here we report on the identification of the progenitors of two nearby sne in the virgo cluster : sn 2006my in ngc 4651 and sn 2006ov in m61 . we obtained high - quality ground - based images of sn 2006my with the canada - france - hawaii telescope , and are able to locate the site of the sn on pre - sn _ hubble space telescope _ ( _ hst _ ) wide field planetary camera 2 images to a high precision ( 1 uncertainty of ) . we pinpoint the site of sn 2006ov to within 0 from _ hst _ advanced camera for surveys images of the sn . we detected a red supergiant progenitor for each sn within the error circles , with an inferred zero - age main - sequence mass ( ) of and for the progenitors of sne 2006my and 2006ov , respectively . the mass estimates for the progenitors of both sne confirm a suggested trend that the most common type ii - plateau sne originate from low - mass supergiants with  ."}
{"article_id":"astro-ph0701049","section_id":"c","document":"we have located the sites of sne 2006my and 2006ov to high precision on pre - sn _ hst_/wfpc2 images , and identified the likely progenitor stars of both sne . as can be seen in figures 1 and 2 , both sne occurred on a spiral arm of their host galaxies , and their immediate environments are heavily contaminated by host - galaxy emission ( more so for sn 2006ov than sn 2006my ) . even at _ hst_/wfpc2 resolution ( figures 5 and 8) , there are many sources in the sn environments . it is thus possible that the objects we identified in the error circles are just rsgs that happened to be close to the sn explosion , but are completely unrelated . the confidence of the progenitor identifications can be strengthened if we put stringent limits on the non - detection of the progenitors . using the limiting magnitudes in table 5 , we place the following mass limits if the progenitors of sne 2006my and 2006ov were not detected in the _ hst_/wfpc2 f814w images : @xmath77 11 @xmath5 or 8 @xmath5 for the sn 2006my progenitor , when @xmath50 mag and @xmath60 mag are adopted for ngc 4651 , respectively ; @xmath77 9 @xmath5 or 13 @xmath5 for the sn 2006ov progenitor , when @xmath53 mag and @xmath78 mag are adopted for m61 , respectively . these mass limits are not very restrictive , unfortunately , as several of the previously identified progenitors for sne  ii - p have masses in the range 813 @xmath5 ( van dyk et  al . 2003a ; smartt et  al .  2004 ; maund et  al . 2005a ; li et al . 2006 ; hendry et  al . hence , there exists the possibility that the progenitors of sn 2006my and/or sn 2006ov were not detected . the probability of a chance coincidence ( that is , the objects we identified are unrelated rsgs that happened to be within the error circles ) can be further assessed by studying the density of rsgs in the sn environments . within a 1@xmath20 radius ( approximately 80 pc at our adopted average vc distance ) , we identified 6 possible rsgs ( 8 possible rsgs ) in the neighborhood of sn 2006my ( sn 2006ov ) by noting their absolute magnitudes and colors on the cmds . the probability of a rsg within the 0@xmath2045 ( 0@xmath202 ) error radius is thus 1.2% ( 0.2% ) . the small probability ( 0.2% ) of a chance coincidence for the progenitor of sn 2006ov solidifies our identification . while the probability of a chance coincidence for the progenitor of sn 2006my is also small ( 1.2% ) , the confidence of our progenitor identification can be further increased if we can significantly reduce the astrometric error radius .    in  3.1 we also mentioned a possible blending issue for the progenitor of sn 2006my . using the rsg density in the environment of sn 2006my , the chance of two rsgs occurring in adjacent wfc pixels ( 0@xmath21 ) is only 0.4% , assuming that massive stars do nt tend to occur in clusters . ( the probability of blending would increase somewhat if the tendency of massive stars to occur in associations were included , but it would still likely be relatively low . )    the two main reasons for the large mass range of our identified progenitors are ( a ) the uncertain distances to the galaxies , and ( b ) the large photometric uncertainty due to the low s / n of the detections . when more accurate distances for the galaxies ( e.g. , cepheid distances ) become available , the masses of the progenitors will be further constrained . the second problem highlights the difficulty in directly identifying progenitors of sne : they are faint beyond the local group , and the pre - sn _ hst _ archival images often do not have the optimal combination of filters and depth because most of them were obtained by various observers for different projects . a dedicated _ hst _ program to image the most nearby galaxies would give observers a chance to identify the progenitors of most core - collapse sne in these galaxies , further advancing our understanding of the death of massive stars . our identified progenitors of sn 2006my and sn 2006ov increase the number of directly detected progenitors for genuine sne from 7 to 9 . the first half of table 6 lists the inferred masses of these progenitors . the progenitors of several probable super - outbursts of luminous blue variables ( lbvs ) misclassified as sne , such as sn 1961v ( zwicky 1964 ) and sn 1997bs ( van dyk et  al . 1999b , 2000 ) , have been identified but are not listed . the second half of table 6 gives the mass limits for the progenitors of several core - collapse sne . for these sne , the progenitors are not directly identified , but a mass limit is derived based on the limiting magnitudes of pre - sn images . in particular , sn 2004dj occurred in a compact star cluster ( csc ) , and the mass of the progenitor is estimated from the properties ( luminosity and color ) of the csc ( maz - apellniz et  al . 2004 ; wang et  al . sn 2005gl is associated with a very luminous ( @xmath79 mag ) source ( gal - yam et  al . 2007 ) , which could be a very massive single star ( e.g. , an lbv ) or a csc . there is also some uncertainty regarding the exact type of the sn : while a very early - time spectrum showed narrow hydrogen lines typical of sne  iin , its later spectral evolution is more typical of normal sne  ii , perhaps a sn  ii - l . it is clear from table 6 that observers have had the most success identifying progenitors for sne  ii - p ( 7 out of 9 ) . the main reason for this is perhaps the relative frequency of different types of sne . a preliminary analysis indicates that out of the 68 core - collapse sne discovered by loss within 30 mpc in the past 9 years , 46 are sne  ii ( most of which are sne  ii - p ) , 18 are sne  ib / c , 1 is a sn  iib , and 3 are sne  iin . sne  ii - p are thus by far the most common type of core - collapse sn . still , it is a bit surprising that no direct progenitor has been detected for a sn  ib / c , given that they are roughly 40% as frequent as sne  ii from the loss statistics . one factor is perhaps the low luminosity of the possible progenitors for sne  ib / c , which also limits the progenitors to be either relatively low - mass stripped stars in binary systems , or single wolf - rayet stars . the inferred masses for the progenitors of sne 2006my and 2006ov are consistent with the trend that sne  ii - p come from low - mass ( 820 @xmath5 ) rsgs , as previously suggested ( li et  al . 2006 ; hendry et  al . 2006 ) . in total , there are now 7 directly identified progenitors for sne  ii - p , all with @xmath80 . the statistics are growing , and suggest that perhaps all sne  ii - p come from low - mass rsgs . if this is true , stars more massive than @xmath8 may have a different evolutionary path , and explode as other types of sne such as sne  ii - l or sne  iin . the possible association of the sn  iin / ii - l 2005gl with a very massive single star ( gal - yam et  al . 2007 ) is in agreement with this speculation . in the future , when a very massive star explodes as a sn in a nearby galaxy ( a rare event ) , observers may have a chance to study both the massive star and the sn in detail . until then , the fate of the very massive stars ( @xmath81 ) still needs to be observationally verified .","summary":"direct identification of the progenitors of supernovae ( sne ) is rare because of the required spatial resolution and depth of the archival data prior to the sn explosions . here we report on the identification of the progenitors of two nearby sne in the virgo cluster : sn 2006my in ngc 4651 and sn 2006ov in m61 .","abstract":"direct identification of the progenitors of supernovae ( sne ) is rare because of the required spatial resolution and depth of the archival data prior to the sn explosions . here we report on the identification of the progenitors of two nearby sne in the virgo cluster : sn 2006my in ngc 4651 and sn 2006ov in m61 . we obtained high - quality ground - based images of sn 2006my with the canada - france - hawaii telescope , and are able to locate the site of the sn on pre - sn _ hubble space telescope _ ( _ hst _ ) wide field planetary camera 2 images to a high precision ( 1 uncertainty of ) . we pinpoint the site of sn 2006ov to within 0 from _ hst _ advanced camera for surveys images of the sn . we detected a red supergiant progenitor for each sn within the error circles , with an inferred zero - age main - sequence mass ( ) of and for the progenitors of sne 2006my and 2006ov , respectively . the mass estimates for the progenitors of both sne confirm a suggested trend that the most common type ii - plateau sne originate from low - mass supergiants with  ."}
{"article_id":"astro-ph0701049","section_id":"c","document":"1 .   both sn 2006my in ngc 4651 and sn 2006ov in m61 are sne  ii - p discovered 34 months after explosion . their spectra show no evidence of strong host - galaxy reddening . we obtained high - quality ground - based cfht images for both sne , and were able to locate the sn sites to high precision on the pre - sn _ hst_/wfpc2 images ( astrometric uncertainty 1@xmath0 = 0@xmath2045 and 0@xmath211 for sne 2006my and 2006ov , respectively ) . we further improved the astrometric solution to 1@xmath0 = 0@xmath202 for sn 2006ov with _ hst_/acs images of the sn . within each error circle , we identified a likely progenitor of each sn . photometric analysis suggests that the progenitor of sn 2006my has @xmath82 , and the progenitor for sn 2006ov has @xmath83 @xmath5 . there is a small probability ( 1.2% and 0.2% , respectively ) that the object we identified as the progenitor is caused by chance coincidence . 4 .   the inferred masses for the possible progenitors of sne 2006my and 2006ov are consistent with the trend that the most common core - collapse sne  ii - p arise from stars with @xmath3 in the range 820 @xmath5 . we thank louis desroches , mohan ganeshalingam , jennifer hoffman , douglas leonard , frank serduke , jeffery silverman , and diane wong for obtaining and reducing the optical spectra of sne used in this paper with the 3-m shane reflector at lick observatory . the work of a.v.f.s group at u. c. berkeley is supported by national science foundation grant ast-0607485 , and by the tabasgo foundation . additional funding is provided by nasa through grants ar-10690 , ar-10952 , and go-10877 from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas  5 - 26555 . kait was made possible by generous donations from sun microsystems , inc . , the hewlett - packard company , autoscope corporation , lick observatory , the national science foundation , the university of california , and the sylvia & jim katzman foundation .    aldering , g. , humphreys , r.  m. , & richmond , m. w. 1994 , , 107 , 662 bessell , m.  s.  1999 , , 111 , 1426 blondin , s. , modjaz , m. , kirshner , r. , challis , p , & berlind , p. 2006 , cbet 757 dolphin , a. e. 2000a , pasp , 112 , 1383 dolphin , a. e. 2000b , pasp , 112 , 1397 elmhamdi , a. , et  al . 2003 , , 338 , 939 filippenko , a. v. 1988 , , 96 , 1941 filippenko , a. v. 1997 , , 35 , 309 filippenko , a. v. 2005 , in the fate of the most massive stars , ed . r. humphreys and k. stanek ( san francisco : asp ) , 33 filippenko , a. v. , li , w. , treffers , r. r. , & modjaz , m. 2001 , in small - 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11 - 23 & 15 & keck i 10-m / lris&30869250 & 1.55&1@xmath20 & 200 + 2006my & 2006 - 12 - 01 & 23 & lick 3-m / kast&331010400 & 1.25&2@xmath20 & 1500 + 2006ov & 2006 - 12 - 01 & 7 & lick 3-m / kast&331010400 & 1.48&2@xmath20 & 1500 +    ccccccr u2dt0901 t & 1994 may 20 & 60 & f555w & 5375 + u2dt0903 t & 1994 may 20 & 300 & f555w & 5375 + u2dt0903 t & 1994 may 20 & 300 & f555w & 5375 + u2dt0904 t & 1994 may 20 & 60 & f814w & 5375 + u2dt0905 t & 1994 may 20 & 300 & f814w & 5375 + u2dt0906 t & 1994 may 20 & 300 & f814w & 5375 + u2ex0f01 t & 1995 mar 4 & 900.0 & f218w & 5419 + u2ex0f02 t & 1995 mar 4 & 900.0 & f218w & 5419 + u2ex0f03 t & 1995 mar 4 & 300.0 & f547 m & 5419 +    ccccccr u29r4d01 t & 1994 jun 6 & 80 & f606w & 5446 + u29r4d02 t & 1994 jun 6 & 80 & f606w & 5446 + u33z0801 t & 1996 mar 15 & 600 & f218w & 6358 + u33z0802 t & 1996 mar 15 & 600 & f218w & 6358 + u6ea6201r & 2001 jul 26 & 230 & f450w & 9042 + u6ea6202r & 2001 jul 26 & 230 & f450w & 9042 + u6ea6203r & 2001 jul 26 & 230 & f814w & 9042 + u6ea6204r & 2001 jul 26 & 230 & f814w & 9042 +    llllll 2006my & 2006 nov 19 & @xmath23 & 60 & @xmath84 & @xmath85 + 2006my & 2006 dec 24 & @xmath23 & 60@xmath305 & @xmath84 & @xmath24 + 2006ov & 2006 nov 27 & @xmath23 & 48@xmath305 & @xmath84 & @xmath25 +      lllllllll 2006my&410.11&158.31 & 409.72 & 158.13 & 5.6 & f814w=24.47(20 ) & @xmath47=24.45(20 ) & @xmath8625.5 + 2006my&410.11&158.31 & @xmath87 & @xmath87 & @xmath87 & f555w@xmath3926.5 & @xmath8826.5&@xmath41@xmath3926.5 + 2006ov&571.12&235.72 & 571.12 & 235.72 & 6.1 & f814w=23.19(18 ) & @xmath47=23.08(18)&@xmath8624.6 + 2006ov&226.94&266.84 & 226.94 & 266.84 & 2.2 & f606w=24.07(50 ) & @xmath41=24.24(50)&@xmath8825.3 + 2006ov&571.12&235.72 & 571.12 & 235.72 & 6.1 & f450w=23.51(18 ) & @xmath55=23.40(18)&@xmath8925.3 +    lllll 1987a & ii - peculiar & @xmath1520 @xmath5 & & 1,2 + 1993j & iib & @xmath1517 @xmath5 & & 3,4 + 1999ev & ii - p & 1518 @xmath5 & & 5 + 2003gd & ii - p & 612 @xmath5 & & 6,7 + 2004a & ii - p & 712 @xmath5 & & 8 + 2004et & ii - p & 1320 @xmath5 & & 9 + 2005cs & ii - p & 713 @xmath5 & & 10,11 + 2006my & ii - p & 715 @xmath5 & & this paper + 2006ov & ii - p & 1220 @xmath5 & & this paper + 2005gl & iin ? ii - l ? & & 4080 @xmath5 lbv ? & 12 + 2004dj & ii - p & & @xmath90 ? ( in csc)&13,14,15 + 1999em & ii - p & & @xmath92 & 16 + 1999gi & ii - p & & @xmath93@xmath94&17 + 2001du & ii - p & & @xmath95@xmath96 & 18,16 + 1999an & ii - p & & @xmath97 & 19 + 1999br & ii - p & & @xmath98 & 19 + 2000ds & ib / c & & @xmath99 rsg ? w - r ? & 19 + 2000ew & ib / c & & low - mass rsg ; w - r ? & 19 + 2001b & ib / c & & @xmath100 rsg ? w - r?&19 + 2004gt & ib / c & & @xmath101@xmath102 ? w - r?&20,21 +","summary":"the mass estimates for the progenitors of both sne confirm a suggested trend that the most common type ii - plateau sne originate from low - mass supergiants with  .","abstract":"direct identification of the progenitors of supernovae ( sne ) is rare because of the required spatial resolution and depth of the archival data prior to the sn explosions . here we report on the identification of the progenitors of two nearby sne in the virgo cluster : sn 2006my in ngc 4651 and sn 2006ov in m61 . we obtained high - quality ground - based images of sn 2006my with the canada - france - hawaii telescope , and are able to locate the site of the sn on pre - sn _ hubble space telescope _ ( _ hst _ ) wide field planetary camera 2 images to a high precision ( 1 uncertainty of ) . we pinpoint the site of sn 2006ov to within 0 from _ hst _ advanced camera for surveys images of the sn . we detected a red supergiant progenitor for each sn within the error circles , with an inferred zero - age main - sequence mass ( ) of and for the progenitors of sne 2006my and 2006ov , respectively . the mass estimates for the progenitors of both sne confirm a suggested trend that the most common type ii - plateau sne originate from low - mass supergiants with  ."}
{"article_id":"cond-mat0601574","section_id":"i","document":"mnas is an extremely promising material for magneto - electronics , since it can grow epitaxially on gaas @xcite and si @xcite forming clean and atomically sharp interfaces . @xcite mnas / gaas heterojunctions have been extensively studied experimentally , @xcite and spin injection from mnas into gaas has been demonstrated.@xcite however one of the major drawbacks for the use of mnas in devices is the fact that bulk mnas has a phase transition at 318  k , where the magnetic state changes from ferromagnetic to paramagnetic . moreover when grown on gaas , this temperature changes depending on the growth direction . this is mainly attributed to the induced strain . @xcite the aim of this paper is to use _ ab initio _ density functional theory ( dft ) calculations to develop a theory of the phase transitions of mnas , which can be compared with experiments and with existing phenomenological models . first a review of the experimental properties of mnas is presented , and a brief description of the existing phenomenological models is given . then the results of our _ ab initio _ calculations are presented and compared to experiments and phenomenological models . within the scope of a heisenberg model the exchange coupling constants are calculated for different distorted unit cells , and the curie temperature and its dependence on the lattice parameters are evaluated in the mean field approximation . the use of the heisenberg model also makes possible the prediction of the ground state volume and lattice structure for the paramagnetic state . it will be shown that the phase transitions of mnas can indeed be explained by _ ab initio _ calculations . in the last section our results are summarized and a simple model for the susceptibility as function of temperature is given . from these a semi - quantitative description of the phase diagram of mnas will emerge .","summary":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model .","abstract":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model . the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells . this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters ."}
{"article_id":"cond-mat0601574","section_id":"r","document":"mnas is a ferromagnetic metal at low temperature , but it becomes paramagnetic at @xmath0 k. at this critical temperature the magnetic moment changes abruptly from a finite value to zero ( figure  [ fig : moft ] ) , the resistivity increases discontinuously , @xcite the volume is reduced by 2.1% , and the lattice structure changes from the hexagonal b@xmath1 ( nias - type ) to the orthorhombic b31 ( mnp - type ) structure . @xcite the b31 structure is obtained by slightly distorting the b@xmath1 structure . associated with this transition there is a latent heat of 7490 j / kg . @xcite furthermore the phase transition shows hysteresis with a critical temperature of 307  k upon cooling and of 318  k upon heating.@xcite all these properties clearly indicate that the phase transition is of first order . magnetization per mn atom @xmath2 as a function of temperature for ferromagnetic mnas below 318 k , and inverse susceptibility @xmath3 for paramagnetic mnas above 318 k ( schematically after reference [ ] ) .,width=302 ]    above @xmath4 the distortion of the crystal structure reduces continuously , until it vanishes at @xmath5 k. @xcite at @xmath6 mnas undergoes another phase transition , where it changes back from the b31 structure to the b@xmath1 structure . the lattice dimensions change continuously and there is no latent heat , but only a discontinuity in the heat capacity of the material . therefore this phase transition is of second order . for temperatures between @xmath4 and @xmath6 the paramagnetic susceptibility of the material has an anomalous behavior . it increases with increasing temperature until it reaches a maximum at @xmath6 . above @xmath6 it decreases and has a curie - weiss behavior ( figure  [ fig : moft ] ) . moreover at @xmath6 there is a lambda point in the specific heat . @xcite application of a magnetic field is found to transform the b31 structure back to the b@xmath1 above a critical field . @xcite table [ tab : propmnaszp ] gives a short summary of the described properties of mnas . * 4l + & @xmath7 & @xmath8 & @xmath9 +   + crystal structure & hexagonal b@xmath1 & orthorhombic b31 & hexagonal b@xmath1 + magnetic order & ferromagnetic & paramagnetic & paramagnetic + magnetic moment & @xmath10 & @xmath11 & @xmath11 + susceptibility @xmath12 & @xmath11 & @xmath13 & @xmath14 +    figure [ fig : phased ] shows the phase diagram of mnas . if pressure is applied to the system , @xmath4 is lowered , while @xmath6 increases . above a critical pressure of 4.6 kbar the ferromagnetic b@xmath1 structure becomes unstable , and the material has the b31 structure for all temperatures below @xmath6 . at high pressures and low temperatures different types of ordered magnetic structures are found , with a reduced saturation magnetic moment with respect to the zero pressure ferromagnetic phase . this , together with the anomalous behavior of the susceptibility between @xmath4 and @xmath6 , led goodenough to the idea that the magnetic moment of the mn atoms changes from a high spin state in the b@xmath1 structure to a low spin state in the b31 structure . @xcite according to his idea in the b31 structure the moment of the mn atoms lies between 1 and 2 @xmath15 . however neutron scattering experiments on mnas samples in the b31 structure have shown that the local magnetic moment of the mn atoms lies between 3 and 3.4 @xmath15 for different temperatures and pressures , @xcite in clear contradiction to the assumption of a low spin state . canted spin structures , similar to the helimagnetic structures of mnp , @xcite are found at a pressure of 4.75 kbar below 210 k , with a local magnetic moment of about 3 @xmath15 . the different saturation magnetic moments for different pressures therefore correspond to different types of canted magnetic alignments . a hysteresis region lies between the ferromagnetic and the canted regions , where both the b8@xmath16 and the b31 structures can be stabilized . when the magnetic order breaks down and the system becomes paramagnetic , it has the b31 structure for all pressures . as the temperature is further increased the structure of the cell continuously changes back towards the b@xmath1 , until at @xmath6 it has again the b@xmath1 structure , with @xmath17 , where @xmath18 is the pressure . the magnetocrystalline anisotropy is quite strong in mnas , with the @xmath19-axis being the hard axis , so that the moments prefer to lie in the hexagonal plane . @xcite measurements on the magnetoelastic coupling @xcite indicate that the coupling is stronger in the hexagonal plane than perpendicular to it . temperature ( @xmath20 ) versus pressure ( @xmath18 ) phase diagram of mnas ( adapted from reference [ ] ) , indicating also @xmath4 and @xmath6 as functions of pressure.,width=321 ]    figure [ fig : uc ] shows the unit cells of mnas in the hexagonal b@xmath1 and in the orthorhombic b31 crystal structures and it defines the unit cell vectors @xmath21 , @xmath22 ( @xmath23 for the b@xmath1 structure ) and @xmath24 . the b@xmath1 structure consists of stacked hexagonal layers of mn and as atoms , and the unit cell contains two mn and two as atoms . the b31 structure has twice the volume of the b@xmath1 due to symmetry lowering and contains four mn and four as atoms . the lattice is nearly hexagonal , and the atoms are moved out of the hexagonal symmetry points along the @xmath22 and @xmath24 directions ( figure [ fig : uc : ortho ] ) .    the mn atoms are mainly displaced in the hexagonal plane along the @xmath22 direction , to form chains of closer mn atoms , separated from the other chains by a larger distance ( figure [ fig : ortho_2d ] ) . the as atoms are mainly displaced along the @xmath24 axis . in each unit cell one of the planar as atoms is moved upwards and the other downwards with respect to the original position in the b8@xmath16 structure , so as to keep the mn - as distance nearly constant . the displacement @xmath25 of the mn atoms in the hexagonal plane lies between 0 and @xmath26 ( @xmath27 ) , depending on the temperature and pressure , and the displacement @xmath28 of the as atoms along the @xmath19-axis lies between 0 and @xmath29 ( @xmath30 ) . the b@xmath1 structure is a special case of the b31 structure , where @xmath31 and @xmath32 . therefore we choose the unit cell vectors in such a way that @xmath21 and @xmath24 have the same direction for both the b8@xmath16 and the b31 structures . in contrast the directions of the vectors @xmath23 ( @xmath33 ) for the hexagonal cell and @xmath22 for the orthorhombic cell are different . represent the various mn - mn distances . the first index @xmath34=2 indicates that all the mn are second nearest - neighbor to each other in the b8@xmath16 structure . the second index @xmath351 , 2 , 3 labels the three distances arising from the b31 distortion . , width=245 ]    the lattice parameters of mnas as function of temperature and magnetic field have been measured in several works [ ] . figure [ fig : acoft ] shows the change of the lattice parameters as a function of temperature for zero pressure.@xcite the lattice parameters increase with temperature due to normal thermal expansion . however the in plane lattice parameter @xmath36 decreases when the temperatures get near @xmath4 , where it jumps from @xmath37   to the lower value of @xmath38  . the perpendicular lattice parameter @xmath19 always increases continuously with temperature . at @xmath6 there is an inflection in the slope of the lattice parameter as a function of temperature , and at about @xmath39 k the slope changes discontinuously . in other measurements the discontinuous change of the slope is found at about 410 k.@xcite    the exact temperature at which the distortion disappears is somewhat uncertain , and fluctuations may play a role for small distortions . the given temperature for the disappearing of the distortion correspond to @xmath40 k , @xcite however measurements for small distortions are difficult and such temperature can only be inferred . as pointed out in reference [ ] the distortion should appear at temperatures slightly above @xmath6 . throughout this work we assume that the disappearing of the distortion occurs at @xmath41 , which the temperature where the thermal expansion coefficient of mnas changes abruptly .          until the fifties it was believed that the first order phase transition at @xmath4 was between a ferromagnetic and an antiferromagnetic state . kittel then proposed a model where the distortion from the b@xmath1 to the b31 structure produces the change in sign of one of the exchange coupling constants , giving rise to antiferromagnetic order.@xcite however there was no experimental evidence of this antiferromagnetic state and experiments demonstrated that the transition is instead to a paramagnetic state . @xcite    therefore bean and rodbell ( br ) proposed a modification of kittel s theory , where the exchange interactions are ferromagnetic for both structures , but they are much weaker in the b31 phase . @xcite the main idea is that the exchange interaction decays strongly as the volume decreases . in order to simplify the model , the analysis was based on the extrapolated curie temperature @xmath42 only , and not on the details of the magnetic interaction at the atomic level . furthermore the model neglected the anisotropic change of the crystal structure , and assumed that it is possible to describe the change from the b@xmath1 to the b31 structure by a change in volume only . the dependence of @xmath42 on the volume @xmath43 was described by the following equation @xmath44~ , \\label{eq : tcbr}\\ ] ] where @xmath45 is the curie temperature at the volume @xmath46 , which is the volume that the system would have in the hypothetical absence of exchange interaction . in this context this corresponds to the volume of the b31 structure above @xmath4 . @xmath47 is a parameter and is determined by fitting the model to experiments . within the br model one can show that for certain values of @xmath47 a first order phase transition between a ferromagnetic and paramagnetic state occurs with a simultaneous change of the volume . however the model does not explain the second order phase transition at @xmath6 . further improvements such as the introduction of a term proportional to @xmath48 do not change the main results.@xcite    later goodenough made an attempt to explain the anomalous behavior of the susceptibility and the second order phase transition at @xmath6 by extending the br model and assuming that the local magnetic moment on the mn atoms depends strongly on the volume . @xcite here the mn atoms are assumed to be in a high spin state in the b@xmath1 structure and in a low spin state in the b31 structure . @xcite however measurements of the local magnetic moment show that the change in the magnetic moment at @xmath4 is very small , therefore the goodenough model is not applicable to this phase transition . this is probably due to the fact that the mnas unit cell volume in any crystalline structure is too big to justify a high - spin to low - spin transition . in fact in mnas@xmath49p@xmath50 the change from high - spin to low - spin state is observed , @xcite however the low spin state is found for unit cell volumes smaller than 120 @xmath51 . in contrast the unit cell of mnas has always a volume of around 130 @xmath51 , and it is always in the high - spin state .    in 1982 kato et al . extended the br model by taking into account not only the change in volume , but also the change of the crystal structure . @xcite furthermore instead of just using @xmath42 for describing the magnitude of the exchange interactions , they consider exchange coupling constants up to second nearest neighbors . the obtained results are similar to those of bean and rodbell . the second order phase transition at @xmath6 is explained by assuming that locally the structure above @xmath6 is still the b31 , but that the distortions from the b@xmath1 are randomly distributed . this assumption is probably not valid , since neutron diffraction experiments clearly indicate that the structure is a regular b@xmath1 above @xmath6 . @xcite    a landau - type phenomenological model , where the free energy @xmath52 is expanded as a function of order parameters , is given in references [ ] and references therein . in reference [ ] just two order parameters are used , the relative magnetization @xmath53 ( @xmath54 for a ferromagnetic state , @xmath55 for a paramagnetic state ) and the orthorhombic distortion @xmath56 . the following equation is used for the free energy : @xmath57 where @xmath58 and @xmath59 are expansion coefficients to be fitted to experiment , @xmath60 is an external magnetic field , @xmath61 is the saturation magnetization , @xmath45 is the extrapolated curie temperate of the low temperature phase , and @xmath62 is a constant . the distortion @xmath56 plays the same role as the relative change in volume @xmath63 of the br model ( equation ) . in equation @xmath42 depends linearly on the change in volume , whereas now it depends quadratically on the distortion @xmath56 , @xmath64 . this is the correct expansion of @xmath42 , since the linear term in @xmath56 disappears due to symmetry ( @xmath65 and @xmath66 correspond to the same distortion ) . the terms in @xmath67 , @xmath68 and @xmath69 appear also in the br model and lead to the first order transition at @xmath4 . the second order phase transition at @xmath70 is generated by the @xmath71 and @xmath72 terms in the expansion . also the variation of the magnetic moment with the distortion is contained in the model , although the authors find that the coefficient @xmath73 is essentially zero . for @xmath45 the curie temperature extrapolated from the high temperature susceptibility above @xmath6 was considered ( @xmath74  k ) , and for @xmath75 the temperature at which the inverse susceptibility has a minimum ( @xmath76  k ) . by construction this model yields the correct thermodynamic behavior , and also predicts the increase of the susceptibility between @xmath4 and @xmath6 by means of the reduction of the distortion with increasing temperature . variations of this model [ ] give similar results . in reference [ ] the full @xmath20-@xmath18-@xmath60 phase diagram of mnas is explained with a landau - type expansion , where more order parameters are used . however also in this case a term equivalent to @xmath77 of equation is used in order to obtain the phase transition at @xmath75 . despite the fact that landau - type expansions give very good agreement between theory and experiments when the right parameters are used , they do not provide insights into the origin of the terms of the expansion , especially of the @xmath77 term . in reference [ ] a basic justification of such term is given from first principles within a spin fluctuation theory constructed from a hubbard hamiltonian . it is shown that for a given volume the minimum of the free energy can lie at @xmath78 for a ferromagnetic state or at @xmath79 for a paramagnetic state .    in 1986 - 87 motizuki and katoh used spin fluctuation theory in order to explain the anomalous behavior of the susceptibility between @xmath4 and @xmath6 . @xcite a hubbard hamiltonian was used , with model density of states obtained from first principle calculations . they could qualitatively show that the susceptibility increases when going from the b31 structure to the b@xmath1 structure , again mainly due to the fact that @xmath42 increases with increasing temperature . more recently various tight binding @xcite as well as first principles@xcite calculations have been performed for mnas in the b@xmath1 structure . the results generally agree and compare well with the experiments . only two studies on mnas in the b31 structure are known to the authors . @xcite in reference [ ] a description of the paramagnetic state of the b31 structure is given by assuming that the paramagnetic state coincides with zero local magnetic moment of the mn atoms . this does not correspond to the usual way of describing paramagnetism , which rather corresponds to constant local magnetic moments , whose directions in space change randomly in time due to spin fluctuations . the present work investigates the magnetic interactions across the various phase transitions of mnas . an explanation of the magnetostructural properties in terms of first - principles calculations is given , thereby illustrating the origin and providing a justification of the parameters used by the different models .","summary":"it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state","abstract":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model . the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells . this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters ."}
{"article_id":"cond-mat0601574","section_id":"r","document":"first principles calculations within density functional theory ( dft ) are performed using the pseudopotential code based on localized atomic orbitals siesta . @xcite the generalized gradient approximation ( gga ) is used for the exchange correlation potential,@xcite since it has been shown to give good structural properties for hexagonal mnas . @xcite in the valence we consider @xmath80 and @xmath81 orbitals for mn , and @xmath82 , @xmath83 and @xmath84 for as . for both mn and as double zeta polarized local orbitals are used for the @xmath85 and @xmath86 angular momenta , whereas for the @xmath56 orbitals double zeta is used . the number of @xmath87-points in the brillouin zone is specified by a grid cutoff of 20  . this corresponds to a 11@xmath8811@xmath888 mesh for the b@xmath1 unit cell , giving approximately 1000 @xmath87-points in the full brillouin zone . for the b31 unit cell such cutoff yields a 8@xmath8811@xmath887 mesh . the real space mesh cutoff , which determines the density of the real space grid , is 300 ry . after full relaxation of the unit cell to a pressure below 0.1 kbar , and of the atomic positions to a force smaller than 0.01 ev /   the b31 unit cell in the ferromagnetic configuration relaxes to a b@xmath1 structure with @xmath89   and @xmath90  . the experimental values at room temperature are @xmath91   and @xmath92  . therefore the relative error is below @xmath93 for @xmath36 and @xmath94% for @xmath19 . the lattice parameters at 110 k can be extracted from figure [ fig : acoft ] and are @xmath95   and @xmath96  . this demonstrates that gga - dft reproduces rather well the zero temperature ground state .    for a fixed @xmath97 ratio of 1.54 , which is close to the experimental value at the first order phase transition , the energy is minimized for @xmath98  , which compares well with the results of other _ ab initio _ calculations . @xcite also the band structure and the density of states are similar to previous calculations . the magnetic moment per mn atom is @xmath99 , and compares well with the measured value of @xmath99.@xcite     symmetry positions.,width=283 ]    the unit cell of the b31 structure contains 4 mn atoms , allowing for 3 possible independent antiferromagnetic configurations of the local moments of the mn atoms . the different antiferromagnetic states are @xmath100 , @xmath101 and @xmath102 . as a matter of notation @xmath100 means that the atoms 1 and 2 in the unit cell have opposite magnetic moment than that of atoms 3 and 4 . the indices of the mn atoms in the unit cell are defined in figure [ fig : uc_ortho_nummn ] . a cell relaxation is performed for those three antiferromagnetic configurations . table [ tab : relaxcell ] lists the obtained relaxed structures together with the total energies per mn atom as compared to the ferromagnetic ground state energy ( @xmath103 ) . the structure remains of the b@xmath1 type if the local moments are ferromagnetically aligned in the hexagonal plane , whereas it changes to the b31 type if the moments are antiferromagnetically aligned , with @xmath25 ( @xmath28 ) of the order of 0.05 @xmath104 ( @xmath19 ) . there is also a slight displacement of the mn atoms along @xmath24 of at most 0.01 @xmath19 , and of the as atoms along @xmath22 of at most 0.01 @xmath104 . generally it can be observed that the in - plane lattice parameters contract and the @xmath19-parameter expands for the antiferromagnetic states , resulting in a reduction of the volume @xmath43 . the calculated values are similar to those given in reference [ ] . the total energy for the ferromagnetic alignment is the lowest , although the @xmath102 configuration is higher of only 17 mev / mn . this indicates that the system should evolve to one of the antiferromagnetic states under pressure , since those have a much smaller volume but only a slightly higher energy . c|*11c &  @xmath105@xmath106 &  @xmath107@xmath106 &  @xmath108@xmath106 &  @xmath109@xmath110 &  @xmath111   &  @xmath112   &  @xmath113( ) &  @xmath114( ) & @xmath115 & @xmath116 & @xmath117 +   + @xmath118   &   3.72 & 6.47 & 5.58 & 134.27 & 0.00 & 0.00 & 3.73 & 3.73 & 3.43 & -0.24 & 0 + @xmath100   &   3.56 & 6.18 & 5.81 & 127.93 & 0.00 & 0.00 & 3.56 & 3.57 & 3.10 &  0.00 & 62 + @xmath101   &   3.55 & 6.24 & 5.62 & 124.54 & 0.05 & 0.05 & 3.10 & 4.10 & 3.01 & -0.08 & 17 + @xmath102   &   3.62 & 6.29 & 5.70 & 129.83 & 0.04 & 0.04 & 3.12 & 4.17 & 3.33 & -0.03 & 35 +    table [ tab : relaxcell ] gives also the distances between the first three nearest neighbor mn atoms in the hexagonal plane @xmath113 , @xmath119 and @xmath114 ( see figure [ fig : ortho_2d ] ) . note that @xmath120 and it is not given explicitly . while these distances are all equal in the hexagonal case , they differ of as much as 1   in the b31 structure . large changes in the distance between the mn atoms are possible since the nearest neighbor mn - mn separation in mnas is well above the inter - atomic distance 2.61   of bulk mn , @xcite which can be regarded as the minimal possible distance between mn atoms . the distance between nearest neighbor mn and as atoms lies between 2.46   and 2.62   for all the different configurations , and changes therefore much less than the mn - mn distance .    the local magnetic moment on the mn ( @xmath121 ) and as ( @xmath122 ) atoms , calculated using the atomic mulliken population , @xcite is also given in table [ tab : relaxcell ] . the local moment on the mn atoms ranges between 3.43 @xmath15 for the ferromagnetic configuration to 3.01 @xmath15 for the @xmath101 configuration . this reduction in the local moment is mainly due to the decrease of the cell volume , and the consequent increase of the hybridization between the mn-@xmath56 and as-@xmath86 orbitals .    in summary these calculations show that the distortion to the b31 structure is caused by an antiferromagnetic alignment of the local magnetic moments in the hexagonal plane .      in order to extract the various exchange parameters , calculations are performed for three different b31 supercells in different local magnetic configurations . these supercells contain 8 mn atoms , and are obtained by doubling the b31 unit cell along the @xmath21 lattice vector ( supercell 1 ) , along @xmath22 ( supercell 2 ) and along @xmath24 ( supercell 3 ) . the calculated total energies are then fitted to a model hamiltonian . the most general form of hamiltonian able to fit all possible energies for a system of @xmath123 collinear magnetic moments is @xmath124 where @xmath125 is the moment at site @xmath126 ( normalized to one ) , and the @xmath127s are coupling parameters . the @xmath128 parameters are symmetric under permutations of the indices , and each of the @xmath128 is zero if any of the indices @xmath34 and @xmath126 are equal . the number of independent parameters is therefore @xmath129 . since time reversal symmetry makes the system invariant under a global spin rotation only @xmath127s with an even number of indices are not zero and equation reduces to @xmath130 here we neglect 4-moment coupling constants @xmath131 and higher thus reducing the model to an ising - type . this approximation neglects the dependence of the moment on each mn atom as well as the small induced magnetic moment of the as atoms on the orientation of the moments of the surrounding mn atoms . furthermore it is assumed that the coupling constants are independent from the angle between the magnetic moments , so that the fit can be extrapolated to vector magnetic moment @xmath132 to give a heisenberg type energy @xmath133 in mean field theory the curie temperature @xmath42 for classical heisenberg exchanged magnetic moments is @xmath134 where @xmath135 is the boltzmann constant . the quantity @xmath136 is the sum of the exchange coupling constants of a given magnetic moment with all the other moments . in the following sections equation is always used to extract curie temperatures , although it is well - known that the mean field approximation overestimates @xmath42 . @xcite    calculations are performed for all the independent spin configurations of the supercell 1 , and for a randomly chosen subset of those of supercells 2 and 3 . 35 different configurations of the magnetic moments are used in total . the energies are then fitted by a least - mean - square fit to the coupling parameters of equation . since the system is metallic with the @xmath56-orbitals having finite density of states at the fermi level , the magnetic interaction is expected to have a long range character . for the chosen supercells it is possible to extract coupling constants up to the ninth nearest neighbor . the lattice parameters used are approximately those for ferromagnetic mnas in the b@xmath1 structure at the phase transition temperature @xmath0 k ( @xmath36=3.71  , @xmath97=1.54 ) .     included in the fit . ( a ) standard deviation @xmath137 of the energies resulting from equation as compared to the calculated dft energies per mn atom . ( b ) @xmath138 per mn atom ( equation ) , where the zero of energy is chosen as the energy of the ferromagnetic state . ( c ) mean field curie temperature @xmath42.,title=\"fig:\",width=302 ] [ fig : numc : tc_nn ]    we have carefully tested the convergence of our results with the range of the heisenberg exchange interaction . figure [ fig : numc ] shows the standard deviation @xmath137 of the energies resulting from equation as compared to the calculated dft energies per mn atom , the value of @xmath138 per mn atom and the mean field curie temperature @xmath42 as a function of the number of coupling coefficients @xmath139 included in the fit . the standard deviation @xmath137 decays monotonically , remains roughly constant for @xmath140 , and then reaches a minimum value of around 5 mev for @xmath141 . this can be considered as the error resulting from neglecting high moment coupling constants . the value of @xmath138 changes less over the whole range . @xmath42 reaches a constant value of approximately 633  k for @xmath142 . this indicates that the main contribution arises from the first three nearest neighbor coupling constants . the experimental value of @xmath42 for the low temperature phase ranges between @xmath0 k and @xmath143 k. this means that our mean field @xmath42 overestimates the experimental one by about a factor 2 . exchange coupling parameters for @xmath144 and @xmath141 as a function of the distance between the magnetic moments.,width=264 ]    figure [ fig : j39hex ] shows the calculated exchange coupling constants as a function of the distance for two different fits counting respectively 3rd and 9th nearest neighbor coupling . the first three exchange constants remain nearly unchanged when going from 3rd to 9th nearest neighbor coupling . interestingly the coupling parameters are positive and therefore ferromagnetic up to @xmath145  ( fifth neighbor interaction ) . in what follows we consider only coupling parameters up to third nearest neighbors , as they give the main contribution to the properties of the material . the b@xmath1 to b31 structural phase transition at @xmath4 is investigated by calculating the heisenberg coupling constants for different distorted cells . we start from the b@xmath1 with the experimental lattice parameters near @xmath4 ( @xmath146  , @xmath31 , @xmath147 , @xmath32 ) and then distort the cell linearly to the b31 structure . the amount of distortion @xmath56 is given in percent , where @xmath1480 % stands for the lattice parameters of the ferromagnetic b@xmath1 cell at @xmath4 , and @xmath149 % for the paramagnetic b31 cell at @xmath4 ( @xmath150  , @xmath151 , @xmath152 , @xmath153 , @xmath154 ) . calculations are done for distortions between 0 % and 220 % . note that the volume decreases with increasing distortion . for these calculations only the supercells 1 and 2 are used with a total of 26 different spin configurations . the standard deviation of the fit is approximately constant for all the distortions and is of the order of 5  mev / mn . figure [ fig : js : hex ] shows the mn atoms of the b8@xmath16 structure coupled by first ( @xmath155 ) , second ( @xmath156 ) and third ( @xmath157 ) nearest neighbor interaction . in the distorted b31 structure the three coupling constants @xmath155 , @xmath156 and @xmath157 are split into six different constants due to symmetry loss . while there is still only one @xmath155 coupling , the in - plane @xmath156 splits into three different coupling constants @xmath158 , @xmath159 and @xmath160 , corresponding to different distances between the mn atoms in the hexagonal plane ( see figure [ fig : ortho_2d ] ) . moreover also the third nearest neighbor coupling @xmath157 splits into three different constants , although two of them are between mn atoms separated by approximately the same distance at @xmath4 , and so they are assumed to be identical . hence @xmath157 effectively splits only into @xmath161 and @xmath162 . figure [ fig : js_od ] shows the calculated values for the exchange parameters as a function of the distortion . for 0% distortion the values of @xmath158 , @xmath159 and @xmath160 are approximately equal reflecting the hexagonal symmetry . the values of @xmath161 and @xmath162 also should be identical although they differ by about 2  mev ( note that in the fit we do not force the b8@xmath16 symmetry when determining the @xmath127s for the undistorted structure ) . this can be assumed to be the error over the fit . additional control fits were also performed for different subsets of the 26 spin configurations . the variation over the individual @xmath127s was of 20% , whereas the variation of @xmath163 was always smaller than 6% . the value of @xmath155 remains approximately constant for all the distortions , reflecting the fact that the distance between the quasi - hexagonal layers remains roughly constant . in contrast the in - plane @xmath127s change and eventually become antiferromagnetic . in particular the coupling becomes strongly antiferromagnetic for @xmath158 , i.e. for those mn atoms that get closer in the hexagonal plane under distortion . also @xmath160 , which couples the mn atoms increasing their separation , is reduced and becomes antiferromagnetic for large distortions . finally the coupling parameters @xmath161 and @xmath162 have only minor changes , with @xmath161 becoming weakly antiferromagnetic for large distortions . the evolution of the coupling constants with the distortion explains why for the @xmath101 and @xmath102 spin configurations ( table [ tab : relaxcell ] ) , where the spins are antiferromagnetically aligned in the hexagonal plane , the lowest energy is found for the b31 structure . in fact the relaxed structure for both spin configurations is similar to a distortion of about 200 % . at this distortion the in - plane coupling constants @xmath158 and @xmath160 become antiferromagnetic , resulting in a reduction of the total energy as compared to the b@xmath1 structure . figure [ fig : tcrel_od ] shows the relative change of the mean field curie temperature @xmath164 for the ferromagnetic state . @xmath42 decreases monotonically with increasing the distortion . for 100  % distortion ( b31 structure at @xmath4 ) @xmath165 , demonstrating that when the phase transition from the b@xmath1 to the b31 structure occurs , the system in the b31 cell is already paramagnetic with very little magnetic order . the experimental curie temperature @xmath166 for the hexagonal cell at @xmath167 is not known , since the structure changes . structure to the b31 structure . @xmath78 % represents the b@xmath1 structure at @xmath0 k , @xmath149 % represents the b31 structure at @xmath4 . a positive ( negative ) value of @xmath127 means ferromagnetic ( antiferromagnetic ) coupling.,width=283 ]    figure [ fig : ene_od ] shows the total energy per b31 unit cell as a function of the distortion in the ferromagnetic ( fm ) and in the @xmath102 antiferromagnetic configurations ( af ) . this latter is the antiferromagnetic configuration giving the lowest total energy at its minimum among all the ones calculated along the considered distortion . the figure also shows the value of @xmath138 , the energy of the paramagnetic state ( see equation ( [ eq : heis ] ) ) . the zero in the energy scale is the energy of the ferromagnetic state for @xmath78  % . the ferromagnetic state has its energy minimum for @xmath78  % , and increases parabolically for increasing distortion . this means that the b8@xmath16 structure is the one with lowest energy in the ferromagnetic state . in contrast the competing antiferromagnetic configuration has a minimum for about 180  % distortion , where the energy is lower than the ferromagnetic phase . the ground state of the system is therefore expected to be ferromagnetic for distortions up to about 100  % , and then to become antiferromagnetic for @xmath168180  % . for distortions in between the ground state is expected to be a non - collinear , canted spin structure . @xmath138 has a very flat minimum for distorted cells , reflecting the fact that the total energy increases for the ferromagnetic state , but decreases on average for the antiferromagnetic states . the minimum is found to be at about @xmath169  % , which corresponds indeed to the lattice parameters of the paramagnetic state above the phase transition . this explains the structural change from the b@xmath1 to the b31 structure when the mnas magnetic state goes from ferromagnetic to paramagnetic . the phase transition at @xmath4 can be seen as a jump from the minimum of the fm curve to the minimum of the @xmath138 curve .      for temperature in between @xmath4 and @xmath6 the mnas crystal structure continuously changes from b31 to b@xmath1 . as mentioned in section [ sec : expprop ] the phase transition temperature @xmath6 is usually identified as the temperature where the susceptibility and the specific heat have a maximum . this is at about 398  k. however , the distortion disappears at slightly higher temperatures as pointed out in reference [ ] . therefore , since the exact temperature for this second order structural phase transition is not known exactly , we introduce an operative definition and assume that the distortion disappears at a temperature @xmath41 , at which the slope of the in - plane lattice constant as function of temperature @xmath170 changes discontinuously ( see figure [ fig : acoft ] ) . according to figure [ fig : acoft ] the lattice constant at @xmath41 is @xmath171  , and @xmath172 . at @xmath6 the same lattice parameter is @xmath1733.697  , so that the difference in @xmath174 is very small . the main reason for the second order phase transition at high temperatures is related to the lattice thermal expansion . the idea is that upon volume expansion , the ground state of the paramagnetic phase moves towards the hexagonal structure . we verify this hypothesis by calculating the minimum of @xmath138 ( @xmath175 ) along a distortion of the cell transforming b@xmath1 to b31 . in the calculation the volume of the cell is kept constant and we repeat the calculation for different volumes . this allows us to evaluate both @xmath175 and the corresponding distortion as a function of the volume . since for @xmath176 mnas is always paramagnetic , then the minimum of @xmath138 corresponds to the stable distortion @xmath177 at a given volume . in practice the change in volume can be described simply by the change in the planar lattice constant @xmath36 , since both @xmath178 and @xmath97 do not deviate much from their value at @xmath4 . thus we always consider @xmath31 and @xmath152 and the phase transition is investigated as a function of @xmath36 only .     for the minimum of the paramagnetic ground state as a function of the lattice constant @xmath36 . the dots are calculated values , the dashed line is a fit with equation .,width=264 ]    the equilibrium distortion @xmath177 as a function of @xmath36 is presented in figure [ fig : d_of_v ] . indeed the distortion decreases with volume and it disappears for @xmath36 between @xmath98   and @xmath146  . moreover we find 100% distortion for @xmath179  . these values agree rather well with the experimental ones , where the distortion disappears at about @xmath180  , and 100% distortion is found at @xmath181  .    in order to interpret these results consider that the distortion is symmetric for @xmath182 ( @xmath183 ) , and therefore @xmath138 can be expanded in even powers of the distortion @xmath184 . here @xmath185 are parameters to fit to the dft calculations . in particular note that @xmath186 corresponds to the energy of the paramagnetic phase when the crystal is undistorted , i.e. it has the hexagonal structure . in this way the minimum of the @xmath187 curve is obtained for @xmath188 . for small distortions the parameters @xmath189 and @xmath190 can be further expanded around @xmath174 as @xmath191 and @xmath192 . the calculated values for the leading terms are @xmath193  , @xmath194 mev /   and @xmath195 mev , ( @xmath56 is given in percent ) . the equilibrium distortion @xmath177 up to first order in @xmath36 is then @xmath196 where @xmath197 is the heaviside function . with the values of @xmath174 , @xmath198 and @xmath199 given above @xmath200 is obtained . the resulting distortion is presented in figure [ fig : d_of_v ] . interestingly if we use the equation ( [ eq : dofa ] ) to fit the experimentally determined distortions at @xmath180  ( @xmath201% ) and @xmath181  ( @xmath202 ) , we obtain @xmath203 and @xmath204 , both in good agreement with our calculated values . this suggests that the main effects of the distortion to the b31 structure arise from the atomic displacement from the symmetry positions , and that small changes of the ratio of the lattice vectors , neglected in our calculations , play only a secondary role . using the values @xmath203 and @xmath204 of the two parameters the evolution of the distortion as a function of temperature @xmath20 can be obtained by inserting the data for @xmath170 from figure [ fig : acoft ] in equation . the result is shown in figure [ fig : d_of_t ] . it agrees well with the experimental result ( see figure 3 in reference ) . the main difference however is that in reference the distortion @xmath177 becomes zero at 398 k , whereas in our results this happens only at 450 k. this is due to our choice of @xmath39 k , which by definition sets the temperature where the distortion disappears . close to the phase transition temperature fluctuations play an important role , so that for very small distortions close to the phase transition the description may not be valid .     for the minimum of the paramagnetic ground state as a function of temperature calculated with equation ( with @xmath203 and @xmath204 ) using @xmath170 taken from figure [ fig : acoft].,width=264 ]    by using the computed values of @xmath186 , @xmath189 and @xmath190 the minimum of @xmath138 ( @xmath205=@xmath206 ) is calculated as a function of the volume of the unit cell , and it is shown in figure [ fig : e0_of_v ] together with @xmath186 . recalling that @xmath186 is the energy of the paramagnetic hexagonal phase , it also can be expanded as function of the lattice constant @xmath207 , where @xmath208 is the equilibrium lattice constant of the hexagonal phase . this , combined with equation , gives an expression for the energy minimum as a function of the lattice constant @xmath36 @xmath209 where @xmath210 and @xmath208 are to be fitted from the calculations of @xmath186 ( figure [ fig : e0_of_v ] ) . the fitted values are @xmath211 mev , @xmath212 mev / @xmath213 and @xmath214  . from the equation ( [ eq : eofa ] ) the energy minimum is easily found @xmath215 and by using the calculated parameters we estimate @xmath216  . since @xmath217 , we derive the important result that the distortion allows the volume to be further reduced as compared to the hexagonal phase . furthermore the curvature of the energy as a function of @xmath36 is @xmath218 which is also reduced by a factor @xmath219 when the structure is distorted . the effect of the thermal expansion on the lattice parameter can now be modeled as a temperature dependent position of @xmath208 , @xmath220 . the change of the lattice constant with temperature for the distorted phase can therefore be written as @xmath221 since @xmath222 is smaller than @xmath223 the lattice expands with temperature faster for the distorted phase than for the undistorted phase . if the calculated values for @xmath223 and @xmath222 are used the ratio @xmath224 is found to be 1.90 , which agrees well with the value of 2.25 extracted from figure [ fig : acoft ] . near the phase transition , i.e. where @xmath225 , phononic effects due to the different curvatures of the energy and fluctuations should be considered . it is especially interesting that the change of the lattice constant with the temperature goes to zero near the phase transition temperature .     and @xmath226 as function of the lattice constant . the dashed line shows @xmath227 , the solid line shows @xmath228 ( see equation ) .,width=264 ]    in the same way as @xmath138 also @xmath42 can be expanded as a function of the lattice constant and of the distortion @xmath229 ,   \\label{eq : tcofa_m1}\\ ] ] where @xmath230 and @xmath231 are parameters , and @xmath232 is the curie temperature for the cell with lattice parameter @xmath174 and where the atoms are in the hexagonal positions . the parameters are fitted by least mean squares to the calculated values of @xmath42 obtained for six lattice constants ranging between 3.656   and 3.78    and for different distortions . we obtain @xmath232=573 k , @xmath233 and @xmath234 . at @xmath235 the relative change of the curie temperature is @xmath236 and corresponds roughly to the value of figure [ fig : tcrel_od ] . in this case it is slightly larger due to the fact that the volume is kept constant , whereas for the calculations of figure [ fig : tcrel_od ] it shrinks with increasing the distortion . next we calculate the dependence of the magnetic moment on the distortion and on the unit cell volume . the dependence is again expanded to lowest order in @xmath36 and @xmath56 @xmath237\\;. \\label{eq : muofa } \\end{split}\\ ] ] we now have different ways of extracting the magnetic moment of the mn atoms from our dft calculations . one possibility is to take the total moment of the cell for the ferromagnetic spin configuration and divide it by the number of mn atoms . in this way however the small induced moments of the as atoms are subtracted from the moment on the mn . a second possibility is to take the average mulliken spin population for the mn atoms . the advantage of this method is that also antiferromagnetic configurations can be used to determine the average moment , and the induced moments of the as atoms are accounted for . the drawback however is that mulliken populations are somewhat arbitrary as they depend on the basis set .    by setting @xmath174 to 3.699  , the values obtained using the cell moment are @xmath238 , @xmath239=3.28 and @xmath240=@xmath241 . similarly from the average mulliken population over all the magnetic configurations we obtain @xmath242=3.42 @xmath15 , @xmath239=3.48 , and @xmath243 . these results are rather similar to each other . our analysis shows that the change of the magnetic moment is mainly due to the change in volume , whereas the distortion has basically no effect .      in this section the dependence of @xmath42 on the individual lattice parameters and on the distances between the atoms is investigated for the b8@xmath16 structure . our approach is to distort the cell orthorhombically but to leave the atoms in their high symmetry positions . apart from a general understanding of the phase diagram of mnas this analysis is useful for predicting the behavior of mnas when grown on a substrate . for instance when grown on gaas(001 ) the substrate induces strain in mnas , and the unit cell is slightly orthorhombically distorted . @xcite this distortion does not correspond to the orthorhombic b31 structure , since the atoms do not move out of the high symmetry positions . moreover different growth orientations are possible , and the curie temperature varies accordingly . @xcite in addition reference [ ] presents experimental results showing that the phase transition temperature @xmath4 changes when strain is applied to the mnas film . in that article we have compared our theoretical predictions for the dependence of @xmath4 on the lattice distortion with the experimental findings . in this section we refine and expand our previous analysis .    when the cell is orthorhombically distorted the first three nearest neighbor coupling constants split into five different constants , corresponding to the ones of the b31 cell ( figure [ fig : js ] ) , and with the only exception that now @xmath244 . the number of total energy calculations for the fit of the coupling parameters is 16 . the change of @xmath42 for each different distortion can be expressed as a function of the change of each single mn - mn and mn - as distance in the unit cell . this gives @xmath245 where the sum goes over all five independent distances in the orthorhombic unit cell as defined in figure  [ figure3 ] . the dependence on the angles between the atoms is neglected . @xmath246 are the multiplicities of each distance @xmath247 within one unit cell , and have the values @xmath248 . for the evaluation of the coefficients @xmath249 , 21 different distortions are considered , including changes of volume , changes of the ratio of the different axes and different displacements of the as atoms . for all the distortions the orthorhombic symmetry however was preserved . the best fit for @xmath249 gives @xmath250 the values of @xmath251 and @xmath252 are almost identical , as one should expect from the symmetry and similarly for @xmath253 and @xmath254 . equation describes the fact that the change of @xmath42 is the result of an interplay between the change of the mn - mn and mn - as distances . the calculated @xmath249 show that , while an increase in the distance between mn atoms increases @xmath42 , an increase of the mn - as distance decreases it . however note that the two distances can not be changed independently , thus the net change in @xmath42 depends on the details of the distortion . @xmath163 can also be expanded over the orthorhombic lattice parameters @xmath255 where @xmath256 , @xmath257 and @xmath258 . the change of the distances between mn and as atoms is not exactly known for the orthorhombic cell . however it is easy to show that to first order the position of the as atom in the cell does not influence @xmath163 , since up to first order @xmath259 when moving the as atom inside the cell . therefore the as atoms can be assumed to remain in the high symmetry position . assuming now @xmath260 and @xmath261 ( as imposed by symmetry ) , the general form of the @xmath262 is @xmath263 where @xmath264 . using the average between @xmath265 and @xmath266 and @xmath267 this gives @xmath268 our results clearly show that stretching the unit cell along the basal plane raises @xmath4 ( since @xmath269 ) , while stretching along the @xmath19-axis lowers @xmath4 ( @xmath270  0 ) . an increase of the volume without distorting the cell results in an increase of the ferromagnetic exchange interactions and therefore of @xmath42 , since @xmath271 is positive and larger in magnitude than @xmath272 . if the cell changes only its volume the expansion corresponds to the one of equation with a factor @xmath273 . these results differ slightly from the ones given in reference [ ] , since in that case we did not constrain @xmath271 to be equal to @xmath274 .","summary":"an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells .","abstract":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model . the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells . this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters ."}
{"article_id":"cond-mat0601574","section_id":"c","document":"it is now possible to analyze two peculiar properties of mnas . the first is the anomalous behavior of the susceptibility @xmath12 as a function of temperature between @xmath4 and @xmath6 . the second is the fact that although the curie temperature for ferromagnetic mnas has to be larger than @xmath4 , the @xmath42 extrapolated from the susceptibility above @xmath6 is only 285 k. @xcite in this section both these features are explained using the dependence of the susceptibility on the curie temperature ( @xmath275 ) , and the strong dependence of the curie temperature on the lattice parameters @xmath276 . @xmath277 and @xmath278 are therefore determined using the experimentally measured temperature dependence of the lattice vectors @xmath279 and @xmath280 and of the distortion @xmath281 . this analysis also provides a tool for extracting the parameters @xmath282 and @xmath283 from experimental data .    by generalizing the equations and the curie temperature @xmath284 can be written as @xmath285 , \\end{split } \\label{eq : tcofadist}\\ ] ] where we use the fact that @xmath286 . we take the values for @xmath271 and @xmath272 from equation , @xmath234 and @xmath287 k are those calculated in section [ sec : disttt ] . the reference lattice parameters are chosen to be the lattice vectors at @xmath41 ( @xmath288@xmath289 .    similarly to the curie temperature also the susceptibility is calculated in the mean field approximation . this is justified for @xmath290 , a condition which is satisfied for paramagnetic mnas . the molar susceptibility @xmath291 is then given by @xmath292 @xmath293 is the avogadro s number , @xmath294 is the lande s factor for the free electron spin , @xmath135 is the boltzmann constant and @xmath85 is the atomic total spin . note that the susceptibility has an additional implicit temperature dependence since @xmath42 and @xmath85 depend on the temperature through the lattice distortion . however in what follows we neglect the dependence of @xmath85 on the lattice parameters so that @xmath295 is constant over all temperature . an analysis performed by relaxing this approximation gives similar results . similarly to section [ sec : disttt ] the model is further simplified by assuming that @xmath178 and @xmath97 are constant above @xmath4 . as indicated in equation @xmath56 then is a function of the lattice constant , @xmath296 . moreover we have shown that the experimental distortion as function of the lattice constant is well reproduced when @xmath203 . therefore it is now possible to express @xmath42 and @xmath3 as a function of the lattice constant @xmath36 only @xmath297 , \\label{eq : susc_of_a } \\end{split}\\ ] ] where @xmath298 . this equation shows that if the lattice expands strongly with temperature @xmath3 decreases . for temperatures between @xmath4 and about 390 k , as well as above @xmath41 , @xmath36 increases approximately linearly with temperature ( see figure [ fig : acoft ] ) and can therefore be written as @xmath299 , \\label{eq : aoft_lin}\\ ] ] where the experimental values for the coefficients are @xmath300 k , @xmath301   and @xmath302 for temperatures above @xmath41 ( the index `` @xmath303 '' denotes the high temperature region above @xmath41 ) , and @xmath304 k , @xmath181 and @xmath305 for temperatures between @xmath4 and about 390 k ( the index `` @xmath306 '' denotes the intermediate temperature region ) . by inserting equation into equation we obtain for the high temperature region above @xmath41 @xmath307 with @xmath308 @xmath309 and @xmath310 are the experimentally accessible quantities for the high temperature susceptibility , and due to the expansion of the lattice they are different from @xmath311 and @xmath295 . the experimentally measured values are @xmath309= 285 k and @xmath312 m@xmath51 k , @xcite which corresponds to an effective magnetic moment of 3.57 @xmath15 . from @xmath310 and @xmath309 the values of @xmath313 and @xmath295 can now be obtained @xmath314 all the variables on the right hand side of equation can be obtained from experiment except @xmath282 . for small @xmath282 the difference between @xmath311 and @xmath309 is proportional to @xmath282 . since @xmath315 is larger than the experimental value of @xmath309 the effect of the thermal expansion of the hexagonal structure is a reduction of the slope of the inverse susceptibility as a function of temperature , as well as a reduction of the extrapolated curie temperature as compared to the real curie temperature .    in the region where linear expansion holds the slope of the inverse susceptibility above @xmath6 is @xmath316 whereas for in the intermediate temperature region above @xmath4 it is @xmath317 in both regions there is a reduction of the slope due to the expansion of the lattice . however the reduction is much larger for @xmath318 than for @xmath319 , since there is the additional term proportional to @xmath283 due to the distortion , and also @xmath320 . as a rough approximation it can be assumed that @xmath321 , so that @xmath322 becomes negative for @xmath323 the values of @xmath324 and @xmath325 are determined experimentally and describe how the structure changes with temperature , whereas @xmath282 and @xmath283 describe how @xmath42 varies for distorted cells . by using our calculated values for @xmath282 and @xmath283 we obtain @xmath326 . this is indeed larger than one . therefore we do predict a negative slope for the inverse susceptibility in the intermediate temperature region . finally we extract the values for @xmath230 and @xmath231 from the experimental behavior of the curie temperature . since the ratio between @xmath271 and @xmath272 can not be obtained from the thermal properties of mnas , it is therefore assumed that @xmath327 is fixed and corresponds to our calculated value . for the hexagonal cell ( @xmath78 ) the equation reads @xmath328,\\ ] ] where @xmath329 and @xmath330 . this has to be valid for all temperatures where the cell is hexagonal , therefore it can not be assumed that the ratio between @xmath19 and @xmath36 is constant since it changes abruptly from 1.533 to 1.556 at @xmath4 . by using the expression for @xmath311 from equation we obtain @xmath282 @xmath331 as reference curie temperature the extrapolated value to room temperature is used , which can be estimated to be about @xmath332  , @xmath333=360 k. by inserting the experimental values for the parameters on the right hand side of the equation ( [ eq : kv ] ) we obtain @xmath334 . this is about twice as big as our predicted value . the disagreement may be due to the fact that the ratio between @xmath272 and @xmath271 has been fixed for our calculated value . by inserting this value for @xmath282 in equation we obtain @xmath335 k , the curie temperature for the lattice parameters at @xmath336 .    in order to extract @xmath283 from experiments we use the relative change in the slope of the inverse susceptibility around @xmath337 . this is , according to the equations and , @xmath338 and increases with increasing @xmath282 and @xmath283 . all the variables in this equation can be derived from the experimental measurements , except @xmath282 and @xmath283 . experimentally different values are found for the relative change of the slope ( left hand side of equation ( [ eq : slope ] ) ) . @xcite these are all of the order of @xmath339 . by using this value for the relative change of the slope and the previously calculated value @xmath334 , @xmath283 is found to be @xmath340 . this value agrees approximately with our predicted value of @xmath341 .    in conclusion the table [ tab : paramdftexp ] summarizes the parameters calculated in this work , by comparing our _ ab initio _ results obtained from the dft calculations and the heisenberg model , with the results obtained by fitting to the experimental data . in general there is a fair agreement , although the the dft results underestimate @xmath282 and overestimate @xmath283 . p1.6cmp0.3cm*8p0.8 cm + & & @xmath342 ( k ) & @xmath283 (  10@xmath343 ) & @xmath282 & @xmath271 & @xmath272 & @xmath325 & @xmath174 (  ) +   + dft & & 579 & 2.62 & 8.8 & 4.9 & -1.0 & 947 & 3.706 + fit & & 311 & 1.78 & 18.1 & 10.1 & -2.1 & 1184 & 3.699 +      it is now possible to draw a qualitative description of the phase diagram of mnas ( see figure [ fig : phased ] ) . since the magnetic interactions are strongly dependent on the volume , the effects of the thermal expansion of the lattice are important . first the state of mnas at zero pressure is considered . for @xmath344 and temperatures below 155  k both ferromagnetic and canted spin structures can be stabilized . the ground state is the ferromagnetic b8@xmath16 structure , however also the b31 structure is stable , because at these low temperatures the thermal energy is not large enough to induce a phase transition from a canted spin structure to a ferromagnetic one . as the temperature increases above 155  k the thermal fluctuation may induce the phase transition , and therefore only the ferromagnetic state survives . as the temperature is further increased and the system becomes paramagnetic , the b31 structure becomes the stable state , as described in section [ disttp ] ( figure [ fig : ene_od ] ) . mnas then remains paramagnetic for all temperatures , but because of the thermal expansion the orthogonal distortion decreases , until it vanishes when a critical volume is reached ( see figure [ fig : d_of_v ] ) . then the volume becomes large enough to stabilize the b@xmath1 structure even for a paramagnetic state , leading to the second structural phase transition at @xmath6 . as pressure is applied to the system the volume is reduced and thus the ferromagnetic exchange interaction decreases . therefore @xmath4 decreases with pressure , while @xmath6 increases . at a temperature of approximately 230  k the ferromagnetic state is stable up to a pressure of 2kbar . for high pressures above 2.5 - 4  kbar the volume is small enough that canted spin structures become the ground state . the temperature at which these states become paramagnetic is approximately 230 k. it increases slightly with pressure , reflecting the fact that the antiferromagnetic interaction increases as the volume is reduced .","summary":"the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters .","abstract":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model . the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells . this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters ."}
{"article_id":"cond-mat0601574","section_id":"c","document":"we have investigated by means of _ ab initio _ electronic structure calculations the magneto - structural properties of mnas . the stable structure for the ferromagnetic state is found to be the b8@xmath16 structure . however if antiferromagnetic alignment in the hexagonal plane is imposed the b31 structure becomes more stable . by fitting the dft total energies of different magnetic configurations to a heisenberg type energy it is shown that the main contributions to the physical properties originate from the exchange coupling parameters up to 3rd nearest neighbor . the curie temperature was calculated in the mean field approximation , with values approximately twice as large as the experimental ones . the main assumption of the phenomenological model of bean and rodbell @xcite that the ferromagnetic exchange coupling parameters increase when the volume is increased has been confirmed ( equation ) using this analysis . however it has been shown that the exchange interactions depend not only on the volume , but that the orthogonal distortion to the b31 structure plays an important role . for the experimentally observed distortions some of the in - plane exchange coupling coefficients become antiferromagnetic . this is the reason for the stability of the b31 structure for those configurations of the magnetic moments that have an antiferromagnetic component in the hexagonal plane . different canted spin structures are expected to minimize the energy for different distortions , since there are both positive and negative exchange coefficients depending on the amount of distortion of the b31 structure . furthermore it has been shown that for paramagnetic states the b31 structure is stable at small volumes , while the b@xmath1 structure is stable above a critical lattice constant of about 3.7  . this explains the second order phase transition at @xmath6 , since at that temperature the lattice constant crosses this critical value . the curie temperature has been expanded as a function of the lattice vectors and of the amount of distortion . an increase in the volume leads to an enhancement of the curie temperature , while an increase of the distortion leads to a reduction . with these results in hand the increase of the susceptibility between @xmath4 and @xmath6 has been explained as the result of the increase of the curie temperature due to the change of the structure from the b31 to the b@xmath1 and to the increase of the volume . by using the experimental variation of the lattice parameters with increasing temperature the susceptibility is indeed found to increase between @xmath4 and @xmath6 . a fit of the dependence of the curie temperature on the lattice parameters to best reproduce the experimental behavior is also given . the calculated values agree within a factor of two with the values obtained by the _ ab initio _ calculations . our results are in agreement with the phenomenological models based on the bean rodbell idea . but now the various parameters used are derived from first principles and therefore validated .","summary":"the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal .","abstract":"the magnetic and structural properties of mnas are studied with _ ab initio _ methods , and by mapping total energies onto a heisenberg model . the stability of the different phases is found to depend mainly on the volume and on the amount of magnetic order , confirming previous experimental findings and phenomenological models . it is generally found that for large lattice constants the ferromagnetic state is favored , whereas for small lattice constants different antiferromagnetic states can be stabilized . in the ferromagnetic state the structure with minimal energy is always hexagonal , whereas it becomes orthorhombically distorted if there is an antiferromagnetic component in the hexagonal plane . for the paramagnetic state the stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7  , above which it remains hexagonal . this leads to the second order structural phase transition between paramagnetic states at about 400 k , where the lattice parameter increases above this critical value with rising temperature due to the thermal expansion . for the paramagnetic state an analytic approximation for the magnitude of the orthorhombic distortion as a function of the lattice constant is given . within the mean field approximation the dependence of the curie temperature on the volume and on the orthorhombic distortion is calculated . for orthorhombically distorted cells the curie temperature is much smaller than for hexagonal cells . this is mainly due to the fact that some of the exchange coupling constants in the hexagonal plane become negative for distorted cells . this is also the reason for the appearance of canted spin structures at low temperatures and high pressures , where the cell is orthorhombic . with these results a description of the susceptibility as function of temperature is given , where the temperature dependence enters via the dependence of the curie temperature on the lattice parameters ."}
{"article_id":"astro-ph0311055","section_id":"i","document":"in its strongest form , gravitational lensing produces unmistakably distorted , amplified , and multiplied images of distant astronomical objects . it is therefore not surprising that the majority of known galaxy - scale gravitational lens systems have been discovered through imaging observations . however , a small number of lenses have been discovered spectroscopically , with the spectrum of a targeted galaxy showing evidence of emission from a background source and follow - up imaging revealing lensing morphology . the three most secure examples are the lensed quasars 2237 + 0305 @xcite and sdss j0903 + 5028 @xcite and the lensed lyman-@xmath0 emitting galaxy 0047@xmath12808 @xcite . several authors have made predictions for the frequency of lensed quasar discoveries in galaxy redshift surveys @xcite . others , inspired by the discovery of 0047@xmath12808 , have undertaken spectroscopic searches for lensed lyman-@xmath0-bright galaxies @xcite . the idea behind such searches is that a massive foreground galaxy should act as an effective gravitational lens of _ any _ object positioned sufficiently far behind it and at small enough impact parameter , and any emission features from such lensed objects should be detectable in the spectra of the foreground galaxy . therefore a search for discrepant emission features in galaxy spectra can potentially lead to a sample of gravitational lens systems that would not be discovered in broadband imaging searches due to faintness of source relative to lens . this `` lenses - looking - for - sources '' approach is complementary to lens searches such as the recently completed cosmic lens all - sky survey ( class ; * ? ? ? * ; * ? ? ? * ) which proceed by targeting sources and looking for evidence of an intervening lens .    with its massive scale and quality of data , the spectroscopic component of the sloan digital sky survey ( sdss ) provides an unprecedented opportunity for spectroscopic galaxy - galaxy gravitational lens discovery . this paper presents the first results of such a search within a sample of @xmath251,000 sdss luminous red galaxy ( lrg ) spectra ( * ? ? ? * hereafter e01 ) : a catalog of candidate lensed star - forming galaxies at intermediate redshift . the lens candidates presented in this paper were detected by the presence of not one but ( at least ) three emission lines in the lrg spectra identified as nebular emission from a single background redshift :  and two out of the three of h@xmath3 @xmath4 , , and ( all emission - line wavelengths in this paper are vacuum values , in angstroms ) . this implies a maximum redshift of @xmath5 for any candidate lensed galaxies : at higher redshifts , [ o  iii ] emission moves off the red end of the sdss spectrograph .    the lensing cross section of a particular foreground galaxy is lower for intermediate - redshift sources than high - redshift sources , and in this sense the lens search we describe here is at a disadvantage relative to searches for lensed high - redshift lyman-@xmath0 emitters however , the identities of the emission lines in the sample we present here are absolutely unambiguous . this can not be said for spectroscopic lyman-@xmath0 lens candidates , which are typically detected as single discrepant emission lines and are difficult to distinguish from lower - redshift emission or ( in the case of a huge survey such as the sdss ) non - astrophysical spectral artifacts . ( a forthcoming paper will present sdss single - line [ o  ii ] and lyman-@xmath0 lens candidates . ) our spectroscopic lens search based on multiple - line detection has further advantages . first , the source redshift of any lensed galaxies will be known from the outset . second , for a given limiting line flux , star - forming galaxies at intermediate redshift are more numerous on the sky than lyman-@xmath0 emitters at high redshift ( see * ? ? ? * ; * ? ? ? * ) , and hence strong lensing events could be more frequent despite decreased lensing cross sections . the non - lensed source population should thus be more amenable to study and characterization ( * ? ? ? * for example ) , facilitating lens statistical analysis . finally , intermediate - redshift lensed galaxies would probe the mass distribution of the lens population in a systematically different manner than do high - redshift sources . the search for new lens systems is motivated by the unique power of gravitational lensing to constrain the mass distribution of the lensing galaxy . @xcite argued that strong galaxy - galaxy gravitational lenses in the optical band should be both ubiquitous and of great scientific interest , but their detection has proved difficult . in addition to the optical einstein ring 0047@xmath12808 mentioned above , @xcite have published one more spectroscopic galaxy - lens candidate . _ hubble space telescope _ ( _ hst _ ) imaging has also had some success in detecting lensed galaxies , as described by @xcite , @xcite , and @xcite , but spectroscopic confirmation remains a challenge in most cases . lensed galaxies are especially useful for investigating the mass distribution of the lensing galaxy because unlike lensed quasars they are spatially resolved sources which provide more detailed constraints ( * ? ? ? * for example ) . as with lensed quasars , the relative angular deflections between multiple images can constrain the total deflecting lens mass . but the relative distortions of multiple images can provide constraints as well , probing the slope of the radial mass profile and allowing more detailed connection with theories of galaxy formation and cold dark matter ( cdm ) . the promise of our candidate sample is enhanced by the fact that lens _ and _ source redshifts for any confirmed lens systems will be known from the outset with great precision ; this is generally not the case for lenses discovered in optical imaging or radio data . the lack of sufficient lensing constraints on the radial slope of the galaxy mass profile in lensed quasar systems is the greatest source of uncertainty in the hubble constant ( @xmath6 ) values derived from the time delays between images @xcite , which remain systematically low compared to the current best @xmath6 values from the distance ladder @xcite and cosmic microwave background @xcite ; @xcite highlights the importance of resolving this discrepancy . any galaxy - galaxy lenses confirmed within our current list of candidates would help to solve this problem by expanding the sample for ensemble lensing studies of early - type galaxy mass profiles like that of @xcite and allowing for the inclusion of distortion information as mentioned above . the generally lower lens and source redshifts of our candidate systems as compared to known lens systems are also of particular interest because the images of any strong lenses within our sample will tend to form at smaller _ physical _ radii within the lens galaxy than in current lens systems ( see * ? ? ? * table 1 ) , thus probing elliptical galaxy mass profiles in a systematically different manner1231 , has @xmath7 @xcite . ] . a large enough sample of strongly lensed star - forming galaxies could even be monitored directly for supernovae . multiple images of the same supernova would give time delays and @xmath6 measurements , as numerous authors have envisioned @xcite . if we assume one supernova per galaxy per century as an order - of - magnitude estimate @xcite , a program to monitor @xmath8 lensed galaxies for several years would have a good chance of success . numerous studies have addressed the inability of standard macroscopic galaxy mass models to predict the flux ratios observed between images of strongly lensed quasars . some authors have suggested that this phenomenon may be due to the effects of substructure in the lensing galaxy on the scale of either cdm sub - halos @xcite or stars @xcite , while others have invoked macroscopically modified lens models as a possible explanation @xcite . a sizeable sample of strongly lensed galaxies would provide valuable insight into this problem : by virtue of the arcsecond - scale intrinsic angular size of the source , galaxy - galaxy lenses will be immune to the lensing effects of any substructure with lensing deflection angles on the scale of microarcseconds ( stars ) or milliarcseconds ( sub - halos ) . if the suppressed saddle point image fluxes seen in many quasar lenses are indeed due to macroscopic inadequacies in the standard lens models , similar effects should be seen in galaxy - galaxy lenses . if on the other hand these effects are due to micro / millilensing by substructure , they should be absent from lensed galaxy systems .","summary":"potentially lensed star - forming galaxies are detected through the presence of background oxygen and hydrogen nebular emission lines in the spectra of these massive foreground galaxies . this multiline selection eliminates the ambiguity of single - line identification and provides a very promising sample of candidate galaxy - galaxy lens systems at low to intermediate redshift , with foreground redshifts ranging from 0.16 to 0.49 and background redshifts from 0.25 to 0.81 .","abstract":"we present a catalog of 49 spectroscopic strong gravitational lens candidates selected from a sloan digital sky survey sample of 50996 luminous red galaxies . potentially lensed star - forming galaxies are detected through the presence of background oxygen and hydrogen nebular emission lines in the spectra of these massive foreground galaxies . this multiline selection eliminates the ambiguity of single - line identification and provides a very promising sample of candidate galaxy - galaxy lens systems at low to intermediate redshift , with foreground redshifts ranging from 0.16 to 0.49 and background redshifts from 0.25 to 0.81 . any lenses confirmed within our sample would be important new probes of early - type galaxy mass distributions , providing complementary constraints to those obtained from currently known lensed high - redshift quasars ."}
{"article_id":"astro-ph0311055","section_id":"c","document":"we have presented a catalog of candidate strong galaxy - galaxy gravitational lens systems detected spectroscopically within the sloan digital sky survey . these systems have known foreground _ and _ background redshifts ; only the detailed spatial alignment of foreground and background galaxies remains unknown . we plan to conduct integral - field spectrographic follow - up observations of these systems , which will allow us to resolve the spatial distribution of the background nebular line emission that we have detected . these observations should confirm a substantial number of lenses within our candidate sample , with many lensed galaxies at lower redshift than any other currently known lensed extra - galactic optical sources . any lenses confirmed within our sample will be of considerable interest for the study of early - type galaxy mass distributions , and could have implications for lens - time - delay @xmath6 measurements and anomalous quasar - lens flux ratios . our sample demonstrates the feasibility of the emission - line - based spectroscopic lens search technique within the sdss and other redshift surveys , and we plan to extend the search to higher source redshifts in the near future . we have also developed and applied a method for abating the influence of night sky emission - line residuals in the 70009000-  range that allows us to detect [ o  iii ] and h@xmath3 emission over the redshift range @xmath85 0.40.8 without an excess of false - positive detections . funding for the creation and distribution of the sdss archive has been provided by the alfred p. sloan foundation , the participating institutions , the national aeronautics and space administration , the national science foundation , the u.s . department of energy , the japanese monbukagakusho , and the max planck society . the sdss web site is http://www.sdss.org/.    the sdss is managed by the astrophysical research consortium ( arc ) for the participating institutions . the participating institutions are the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , university of pittsburgh , princeton university , the united states naval observatory , and the university of washington . the authors thank paul hewett for his constructive referee report . asb thanks paul schechter and hsiao - wen chen for valuable discussion and consultation .","summary":"we present a catalog of 49 spectroscopic strong gravitational lens candidates selected from a sloan digital sky survey sample of 50996 luminous red galaxies . any lenses confirmed within our sample would be important new probes of early - type galaxy mass distributions , providing complementary constraints to those obtained from currently known lensed high - redshift quasars .","abstract":"we present a catalog of 49 spectroscopic strong gravitational lens candidates selected from a sloan digital sky survey sample of 50996 luminous red galaxies . potentially lensed star - forming galaxies are detected through the presence of background oxygen and hydrogen nebular emission lines in the spectra of these massive foreground galaxies . this multiline selection eliminates the ambiguity of single - line identification and provides a very promising sample of candidate galaxy - galaxy lens systems at low to intermediate redshift , with foreground redshifts ranging from 0.16 to 0.49 and background redshifts from 0.25 to 0.81 . any lenses confirmed within our sample would be important new probes of early - type galaxy mass distributions , providing complementary constraints to those obtained from currently known lensed high - redshift quasars ."}
{"article_id":"1312.0285","section_id":"i","document":"the emergence of cloud computing has led to a proliferation of distributed storage solutions that offer high availability , reliability , and excellent performance . for example , open - source distributed object stores that offer these benefits include riak @xcite , swift @xcite , hdfs @xcite , cephfs @xcite and quantcast qfs @xcite . the main idea behind these systems is to replicate and spread the data uniformly across a cluster of servers , in order to increase availability and reliability and take advantage of data declustering ( in other words , process data in parallel across multiple servers ) . these systems make good use of the available cluster resources , but they are targeted towards specific query workloads . in particular , replication and declustering favor mapreduce - style processing , or any processing that can be easily parallelized . on the other hand , declustering hurts the performance of query workloads that perform certain types of joins , the reason being that joins could result in a large volume of data migrations , which can saturate the network and reduce the performance of the underlying distributed data store . for these types of queries , careful placement of data around the cluster is critical for guaranteeing high availability , reliability and high query throughput . for example , in a relational data warehouse , queries include multi - way joins to combine fact tables with multiple dimension tables . materialized views are commonly used to pre - compute query results and must be maintained over time . thus , data placement in a distributed data warehouse is critical for good query performance and efficient view maintenance ; the latter is particularly important in on - line streaming warehouses @xcite , which are continuously updated ( as opposed to being taken down for refresh once a week or once a month ) and must keep up with the incoming data feeds . recent work such as cohadoop @xcite enables the co - location of related data , but places the burden on the user or the database administrator to determine what should be co - located and where . in this paper , we aim to automate this process by proposing algorithms for computing nearly - optimal _ data placement _ strategies for a given workload .    in the simplest version of the problem , we are given a set of base tables , ad - hoc queries and servers with known capacities . the goal is to decide where to store the tables and where to evaluate the queries in order to minimize the data communication cost during query evaluation . we also address other issues that arise in our motivating applications , such as load balancing , replication , materialized views , and complex query plans consisting of sequences of intermediate results that may be computed on different servers . first , not surprisingly , we show that even the simplest formulation of our data placement problem is np - hard . second , and more surprisingly , we reduce the data placement problem without replication to graph partitioning . previous work on distributed data placement relied on _ hypergraph _ partitioning to represents different objectives such as minimizing the number of distributed transactions @xcite . as we will show , hypergraph partitioning fails to capture the data communication cost , but our reduction to graph partitioning can do so _ exactly_. we consider this reduction to be the main contribution of this paper . the reduction to graph partitioning is a desirable result . graph partitioning is an np - hard problem , but it has been studied extensively . in particular , effective and efficient approximation algorithms and a variety of robust libraries are publicly available ( e.g. , metis @xcite and chaco @xcite ) . some problems involving hypergraph partitioning may be approximated by graph partitioning , as was done in @xcite ( see section  [ sec.related ] ) . on the other hand , by reducing our problem to graph partitioning , we can directly use tools such as metis to provide good approximate data placement plans very efficiently in practice . had we needed hypergraph partitioning , we would have had to use _ hypergraph _ partitioning software , which , by solving a more general problem , gives worse performance . third , we present two classes of algorithms for our problem : non - trivial integer program ( ip ) formulations that compute an optimal data placement using an ip solver , and practical approximation algorithms based on our reduction to graph partitioning . we also extend our algorithms to handle load balancing . fourth , we turn our attention to the version of the problem with replication and we present two heuristics that use the reduction to graph partitioning as a subroutine . we also present an ip formulation that can be used to compute an optimal solution . fifth , we present a detailed empirical evaluation of our algorithms using the tpc - ds decision support benchmark . for many parameter settings , it may take an ip solver weeks ( or longer ) to compute an optimal data placement , whereas our reduction produces nearly - optimal solutions in seconds . the remainder of the paper is organized as follows . section [ sec.definition ] formally defines the problem and notation used throughout the paper . section [ sec.related ] presents related work . section [ sec.solution ] presents our reduction to graph partitioning . section [ sec.experiments ] presents an empirical study . finally , section [ sec.conclusion ] concludes the paper .","summary":"with the widespread use of shared - nothing clusters of servers , there has been a proliferation of distributed object stores that offer high availability , reliability and enhanced performance for mapreduce - style workloads . however , relational workloads can not always be evaluated efficiently using mapreduce without extensive data migrations , which cause network congestion and reduced query throughput . we study several practical extensions of the problem : with load balancing , with replication , with materialized views , and with complex query plans consisting of sequences of intermediate operations that may be computed on different servers . we provide integer linear programs ( ips ) that may be used with any ip solver to find an optimal data placement . for the no - replication case , we use publicly available graph partitioning libraries ( e.g. , metis ) to efficiently compute nearly - optimal solutions . for the versions with replication , , it may take an ip solver weeks to compute an optimal data placement , whereas our reduction produces nearly - optimal solutions in seconds .","abstract":"with the widespread use of shared - nothing clusters of servers , there has been a proliferation of distributed object stores that offer high availability , reliability and enhanced performance for mapreduce - style workloads . however , relational workloads can not always be evaluated efficiently using mapreduce without extensive data migrations , which cause network congestion and reduced query throughput . we study the problem of computing data placement strategies that minimize the data communication costs incurred by typical relational query workloads in a distributed setting .    our main contribution is a reduction of the data placement problem to the well - studied problem of graph partitioning , which is np - hard but for which efficient approximation algorithms exist . the novelty and significance of this result lie in representing the communication cost exactly and using standard graphs instead of hypergraphs , which were used in prior work on data placement that optimized for different objectives ( not communication cost ) .    we study several practical extensions of the problem : with load balancing , with replication , with materialized views , and with complex query plans consisting of sequences of intermediate operations that may be computed on different servers . we provide integer linear programs ( ips ) that may be used with any ip solver to find an optimal data placement . for the no - replication case , we use publicly available graph partitioning libraries ( e.g. , metis ) to efficiently compute nearly - optimal solutions . for the versions with replication , we introduce two heuristics that utilize the graph partitioning solution of the no - replication case . using the tpc - ds workload , it may take an ip solver weeks to compute an optimal data placement , whereas our reduction produces nearly - optimal solutions in seconds ."}
{"article_id":"1312.0285","section_id":"c","document":"in this paper , we presented _ practical _ algorithms for minimizing the data communication cost of evaluating a query workload in a distributed setting . we reduced the data communication problem to graph partitioning and showed how to treat arbitrary query execution plans that can involve tables , materialized views , and intermediate results . we also discussed load balancing , and presented two heuristics for handling replication . we implicitly assumed that queries and view updates arrive asynchronously . an interesting direction for future work is to optimize for workloads in which some queries are always executed together , in some pre - specified order . this complicates the data placement problem , but may enable solutions with lower data communication costs . for example , if two views are maintained on the same server and require the same table to be shipped from some other server , then by always updating these two views together we only need to ship said table once per update . load balancing may also be improved by knowing which queries tend to be executed together . for instance , if queries @xmath24 and @xmath64 are always executed together and each consists of two steps , then we may prefer to assign their first steps to two different servers , rather than allocating the first steps of both queries to the same server and having the servers allocated to the second steps sit idle until the first steps are done .    10 . https://www.quantcast.com/engineering/qfs .    . http://basho.com/riak .    . http://docs.openstack.org/developer/swift .    . https://tahoe-lafs.org/trac/tahoe-lafs . s.  agrawal , v.  narasayya , and b.  yang . integrating vertical and horizontal partitioning into automated physical database design . in _ sigmod _ , pages 359370 , 2004 . d.  borthakur . the hadoop distributed file system : architecture and design . http://hadoop.apache.org/docs/r0.18.0/hdfs_design.pdf , 2007 . f.  chang , j.  dean , s.  ghemawat , w.  c. hsieh , d.  a. wallach , m.  burrows , t.  chandra , a.  fikes , and r.  e. gruber . bigtable : a distributed storage system for structured data . in _ osdi _ , pages 1515 , 2006 . s.  chaudhuri . an overview of query optimization in relational systems . in _ pods _ , pages 3443 , 1998 .    c.  curino , e.  jones , y.  zhang , and s.  madden . schism : a workload - driven approach to database replication and partitioning . , 3(1 - 2):4857 , sept . 2010 . g.  decandia , d.  hastorun , m.  jampani , g.  kakulapati , a.  lakshman , a.  pilchin , s.  sivasubramanian , p.  vosshall , and w.  vogels . dynamo : amazon s highly available key - value store . in _ sosp _ , pages 205220 , 2007 . m.  y. eltabakh , y.  tian , f.  zcan , r.  gemulla , a.  krettek , and j.  mcpherson . cohadoop : flexible data placement and its exploitation in hadoop . , 4(9):575585 , june 2011 . s.  ghandeharizadeh and d.  j. dewitt . hybrid - range partitioning strategy : a new declustering strategy for multiprocessor database machines . in _ vldb _ , pages 481492 , 1990 . l.  golab , t.  johnson , s.  j. seidel , and v.  shkapenyuk . stream warehousing with datadepot . in _ sigmod _ , pages 847854 , 2009 . b.  hendrickson and t.  g. kolda . graph partitioning models for parallel computing . , 26(12):15191534 , 2000 . b.  hendrickson and r.  leland . chaco : software for partitioning graphs . http://www.sandia.gov/~bahendr/chaco.html , 1994 . g.  karypis and v.  kumar . metis - unstructured graph partitioning and sparse matrix ordering system , version 2.0 . http://glaros.dtc.umn.edu/gkhome/metis/metis/overview , 1995 . a.  k. kayyoor , a.  deshpande , and s.  khuller . data placement and replica selection for improving co - location in distributed environments . , abs/1302.4168 , 2013 . liu and s.  shekhar . partitioning similarity graphs : a framework for declustering problems . , 21:475496 , 1996 . s.  b. navathe and m.  ra . vertical partitioning for database design : a graphical algorithm . , 18(2):440450 , june 1989 .    r.  v. nehme and n.  bruno . automated partitioning design in parallel database systems . in _ sigmod _ , pages 11371148 , 2011 . j.  rao , c.  zhang , n.  megiddo , and g.  lohman . automating physical database design in a parallel database . in _ sigmod _ , pages 558569 , 2002 . t.  p. p.  c. ( tpc ) . http://www.tpc.org / tpcds/.    d.  c. zilio . . phd thesis , university of toronto , 1998 .","summary":"we study the problem of computing data placement strategies that minimize the data communication costs incurred by typical relational query workloads in a distributed setting .   ","abstract":"with the widespread use of shared - nothing clusters of servers , there has been a proliferation of distributed object stores that offer high availability , reliability and enhanced performance for mapreduce - style workloads . however , relational workloads can not always be evaluated efficiently using mapreduce without extensive data migrations , which cause network congestion and reduced query throughput . we study the problem of computing data placement strategies that minimize the data communication costs incurred by typical relational query workloads in a distributed setting .    our main contribution is a reduction of the data placement problem to the well - studied problem of graph partitioning , which is np - hard but for which efficient approximation algorithms exist . the novelty and significance of this result lie in representing the communication cost exactly and using standard graphs instead of hypergraphs , which were used in prior work on data placement that optimized for different objectives ( not communication cost ) .    we study several practical extensions of the problem : with load balancing , with replication , with materialized views , and with complex query plans consisting of sequences of intermediate operations that may be computed on different servers . we provide integer linear programs ( ips ) that may be used with any ip solver to find an optimal data placement . for the no - replication case , we use publicly available graph partitioning libraries ( e.g. , metis ) to efficiently compute nearly - optimal solutions . for the versions with replication , we introduce two heuristics that utilize the graph partitioning solution of the no - replication case . using the tpc - ds workload , it may take an ip solver weeks to compute an optimal data placement , whereas our reduction produces nearly - optimal solutions in seconds ."}
{"article_id":"1303.6823","section_id":"i","document":"we consider the following reaction - diffusion problem @xmath7 where @xmath8 is the fractional laplacian operator with @xmath9 . we are interested in studying the propagation properties of nonnegative and bounded solutions of this problem in the spirit of the fisher - kpp theory . therefore , we assume that the reaction term @xmath10 satisfies @xmath11)\\text { is a concave function with } f(0)=f(1)=0 , \\quad f'(1)<0<f'(0).\\ ] ] for example we can take @xmath12 our results will depend on the parameters @xmath13 and @xmath14 , according to the ranges @xmath15 , @xmath16 , and @xmath17 , where @xmath18    * 1.1 . . the traveling wave behavior . * the problem with standard diffusion goes back to the work of kolmogorov , petrovskii and piskunov , see @xcite , that presents the most simple reaction - diffusion equation concerning the concentration @xmath19 of a single substance in one spatial dimension , @xmath20 the choice @xmath21 yields fisher s equation @xcite that was originally used to describe the spreading of biological populations . the celebrated result says that the long - time behavior of any solution of , with suitable data @xmath22 that decay fast at infinity , resembles a traveling wave with a definite speed . when considering equation in dimensions @xmath23 , the problem becomes @xmath24 which corresponds to in the case when @xmath25 , the standard laplacian . this case has been studied by aronson and weinberger in @xcite , where they prove the following result .    * theorem aw . *    _ let @xmath19 be a solution of with @xmath26 compactly supported in @xmath27 and satisfying @xmath28 . let @xmath29 . then , _    1 .   if @xmath30 , then @xmath31 uniformly in @xmath32 as @xmath33 . 2 .   if @xmath34 , then @xmath35 uniformly in @xmath36 as @xmath33 . in addition , problem admits planar traveling wave solutions connecting @xmath37 and @xmath38 , that is , solutions of the form @xmath39 with @xmath40    this asymptotic traveling - wave behavior has been generalized in many interesting ways . of concern here is the consideration of nonlinear diffusion . de pablo and vzquez study in @xcite the existence of traveling wave solutions and the property of finite propagation for the reaction - diffusion equation @xmath41 with @xmath17 , @xmath42 , @xmath43 and @xmath44 . similar results hold also for other slow diffusion cases , @xmath17 , studied by de pablo and snchez ( @xcite ) .    * * 1.2 . non - traveling wave behavior . * * departing from these results , king and mccabe examined in @xcite a case of fast diffusion , namely @xmath45 where @xmath46 . they showed that the problem does not admit traveling wave solutions . using a detailed formal analysis , they also showed that level sets of the solutions of the initial - value problem with suitable initial data propagate exponentially fast in time . they extended the results to all @xmath47 .    on the other hand , and independently , cabr and roquejoffre in @xcite studied the case of fractional linear diffusion , @xmath48 and @xmath4 , and they concluded in the same vein that there is no traveling wave behavior as @xmath49 , and indeed the level sets propagate exponentially fast in time . this came as a surprise since their problem deals with linear diffusion . motivated by these two examples of break of the asymptotic tw structure , we study here the case of a diffusion that is both fractional and nonlinear , namely problem in the range @xmath48 and @xmath50 . the initial datum @xmath51 $ ] and satisfies a growth condition of the form @xmath52 where the exponent @xmath53 is stated explicitly in the different ranges , @xmath15 and @xmath54 . in this paper we establish the negative result about traveling wave behaviour , more precisely , we prove that an exponential rate of propagation of level sets is true in all cases . we also explain the mechanism for it in simple terms : the exponential rate of propagation of the level sets of solutions ( with initial data having a certain minimum decay for large @xmath55 ) is a consequence of the power - like decay behaviour of the fundamental solutions of the diffusion problem studied in @xcite . therefore , we obtain two main cases in the analysis , @xmath15 and @xmath56 , depending on that behaviour . main results . * the existence of a unique mild solution of problem follows by semigroup approach . the mild solution corresponding to an initial datum @xmath57 @xmath58 is in fact a positive , bounded , strong solution with @xmath59 regularity . in the appendix we give a brief discussion of these properties . let us introduce some notations . once and for all , we put @xmath60  and @xmath61 the value @xmath62 appears for @xmath15 and then @xmath63 . notice also that @xmath64 for @xmath17 . here is the precise statement of our main results for the solutions of the generalized kpp problem . [ mainthm1 ] let @xmath23 , @xmath48 , @xmath65 satisfying and @xmath66 . let @xmath19 be a solution of , where @xmath28 is measurable , @xmath26 and satisfies @xmath67 then    1 .   if @xmath68 , then @xmath31 uniformly in @xmath69 as @xmath33 . 2 .   if @xmath70 , then @xmath35 uniformly in @xmath71 as @xmath33 .    [ mainthm2 ] let @xmath23 , @xmath48 , @xmath65 satisfying and @xmath72 . let @xmath19 be a solution of , where @xmath28 is measurable , @xmath26 and satisfies @xmath73 then    1 .   if @xmath74 , then @xmath31 uniformly in @xmath69 as @xmath33 . 2 .   if @xmath75 , then @xmath35 uniformly in @xmath71 as @xmath33 .    [ mainthm3 ] let @xmath23 , @xmath48 , @xmath65 satisfying and @xmath17 . let @xmath19 be a solution of , where @xmath28 is measurable , @xmath76 and satisfies @xmath67 then    1 .   if @xmath77 , then @xmath31 uniformly in @xmath69 as @xmath33 . 2 .   if @xmath70 , then @xmath35 uniformly in @xmath71 as @xmath33 . [ figparameters ]   and @xmath14 : we study the cases @xmath78 ; @xmath79 , @xmath80,title=\"fig:\",width=302,height=226 ]    * remarks . * in all ranges of parameters @xmath50 , there appear critical values of @xmath81 with an influence on the behavior of the level sets . @xmath82 in the case @xmath83 , the case @xmath84 is still open . this critical exponent is the same as in the case of the linear diffusion @xmath4 , proved in @xcite . @xmath82 in the range @xmath15 , the case @xmath85 is still open . in particular , for the classical case @xmath3 and @xmath5 we get @xmath86 , which is a critical speed found by king and mccabe @xcite . in this way , we complete their result with rigorous proofs to all @xmath48 . @xmath82 in the case @xmath17 , we do not cover the entire interval @xmath87 $ ] . therefore , we prove that for @xmath17 the nonlinearity has a different influence on the velocity of propagation . @xmath82 the result of theorems [ mainthm1 ] and [ mainthm2 ] is true also in the case @xmath88 , where @xmath89 . the outline of the proof is the same , but there are a number of additional technical difficulties , typical of borderline cases . we have decided to skip the lengthy analysis of this case because of the lack of novelty for our intended purpose . our main conclusion is that exponential propagation is shown to be the common occurrence , and the existence of traveling wave behavior is reduced to the classical kpp cases mentioned at the beginning of this discussion ( see dotted line in figure [ figparameters ] ) . as we have already mentioned , one of the motivations of the work was to make clear the mechanism that explains the exponential rate of expansion in simple terms , even in this situation that is more complicated than @xcite . in fact , due to the nonlinearity , the solution of the diffusion problems involved in the proofs does not admit an integral representation as the case @xmath4 . instead , we will use as an essential tool the behavior of the fundamental solution of the fractional porous medium equation , also called barenblatt solution , recently studied in @xcite . to be precise , the decay rate of the tail of these solutions as @xmath90 is the essential information we use to calculate the rates of expansion . this information is combined with more or less usual techniques of linearization and comparison with sub- and super - solutions . we also need accurate lower estimates for positive solutions of this latter equation , and a further selfsimilar analysis for the linear diffusion problem .    * organization of the proofs . * in section [ subsecconv0 ] , under the assumption of initial datum with the decay , we prove convergence to @xmath37 in the outer set @xmath69 by constructing a super - solution of the linearized problem with reaction term @xmath91 . the arguments hold for @xmath81 larger than the corresponding critical velocity .    in section [ subsecconv1 ] we prove convergence to @xmath38 on the inner sets @xmath71 in various steps . we only assume @xmath92 , @xmath93 we first show that the solution reaches a certain minimum profile for positive times , thanks to the analysis of theorem [ low.par.est1 ] below , we then perform an iterative proof the conservation in time of this minimum level , and finally convergence to @xmath38 is obtained by constructing a super - solution to the problem satisfied by @xmath94 . therefore , we deal with a problem of the form @xmath95 a suitable choice for constructing the super - solution @xmath96 is represented by self - similar solutions of the form @xmath97 of the linear problem @xmath98 with radial increasing initial data . this motivates us to derive a number of properties of the linear diffusion problem , also known as the fractional heat equation . in particular , we need to show that the profile @xmath99 mentioned above has the same asymptotic behavior as the initial data . in order to establish such fact we have to review , section [ sectselfsimlinprob ] , the properties of the fundamental solution of problem @xmath100 we perform a further analysis of the profile @xmath65 by proving that @xmath101    * remark . * as a consequence of the exponential propagation of the level sets , we immediately obtain the non - existence of traveling wave solutions of the form @xmath102 . however , our results amount to the existence of a kind of logarithmic traveling wave behaviour , that is a kind of wave solutions that travel linearly if we measure distance in a logarithmic scale . this whole issue deserves further investigation . new estimates for the fractional diffusion problem . * the study of the sub- and super - solutions is strongly determined by the existence of suitable lower parabolic estimates for the associated diffusion problem , the fractional porous medium equation ( fpme ) @xmath103 in section [ subsectlowerparest ] , we devote a separate study in the case @xmath17 of the behavior of the solution when @xmath104 , more precisely its rate of decay , for small times @xmath105 . our main result says that roughly speaking @xmath106 when @xmath55 is large and @xmath107 small . the precise result is as follows . [ low.par.est1 ] let @xmath108 be a solution of problem with initial data @xmath109 such that @xmath110 in the ball @xmath111 . then there is a time @xmath112 and constants @xmath113 such that @xmath114 if @xmath115 and @xmath116 . the fact that solutions of the fpme with nonnegative initial data become immediately positive for all times @xmath105 in the whole space has been proved in @xcite . such result is true not only for @xmath1 and @xmath17 , but also for @xmath1 and @xmath117 , this lower restriction on @xmath118 aimed at avoiding the possibility of extinction in finite time . precise quantitative estimates of positivity for @xmath105 on bounded domains of @xmath119 have been obtained in the recent paper @xcite . the estimates of that reference are also precise in describing the behavior as @xmath90 when @xmath120 ( fast diffusion ) , but they are not relevant to establish the far - field behavior for @xmath17 . we recall that the limit @xmath121 with @xmath17 fixed we get the standard porous medium equation , where positivity at infinity for all nonnegative solutions is false due to the property of finite propagation , cf . this explains that some special characteristic of fractional diffusion must play a role if positivity is true . we fill the needed gap for some convenient class of initial data that includes continuous nontrivial and nonnegative initial data . we give a quantitative version here since it can be useful in the applications .","summary":"we study the propagation properties of nonnegative and bounded solutions of the class of reaction - diffusion equations with nonlinear fractional diffusion : . for all and , we consider the solution of the initial - value problem with initial data having fast decay at infinity and prove that its level sets propagate exponentially fast in time , in contradiction to the traveling wave behaviour of the standard kpp case , which corresponds to putting , and . the proof of this fact uses as an essential ingredient the recently established decay properties of the self - similar solutions of the purely diffusive equation , .    2000 _ mathematics subject classification . _ 35k57 , 26a33 , 35k65 , 76s05 , 35c06 , 35c07 .    _ keywords and phrases . _ reaction - diffusion equation , fisher - kpp equation , propagation of level sets , nonlinear fractional diffusion .","abstract":"we study the propagation properties of nonnegative and bounded solutions of the class of reaction - diffusion equations with nonlinear fractional diffusion : . for all and , we consider the solution of the initial - value problem with initial data having fast decay at infinity and prove that its level sets propagate exponentially fast in time , in contradiction to the traveling wave behaviour of the standard kpp case , which corresponds to putting , and . the proof of this fact uses as an essential ingredient the recently established decay properties of the self - similar solutions of the purely diffusive equation , .    2000 _ mathematics subject classification . _ 35k57 , 26a33 , 35k65 , 76s05 , 35c06 , 35c07 .    _ keywords and phrases . _ reaction - diffusion equation , fisher - kpp equation , propagation of level sets , nonlinear fractional diffusion ."}
{"article_id":"1110.2934","section_id":"i","document":"the vertical structure of an exoplanetary atmosphere can be derived from transmission and emission spectroscopy when a planet transits its host star . the atmospheric properties of hd 189733b have been extensively investigated using transit spectroscopy observations from both space and ground - based telescopes . transmission spectra acquired during primary transits , where light from the host star is filtered through the upper layers of an exoplanetary atmosphere , have been measured in the near- , mid- and far - infrared ( nir , mir and fir , respectively ) by both the @xmath3 @xmath4 @xmath5 ( @xmath6 ) @xcite and @xmath7 telescope @xcite . @xmath7 mid- and far - infrared ( mir and fir ) broadband photometry was used to deduce a high abundance of h@xmath0o in the terminator region of this planet @xcite . in addition , a strong absorption due to ch@xmath1 was reported in the near - infrared ( nir ) using the nicmos ( near infrared camera and multi - object spectrometer ) spectrophotometry on the @xmath6 @xcite . however , the accuracy of transit spectroscopy and photometry has been called into question ( see the review by * ? ? ? * ) , and most recently @xcite claimed that instrumental systematics limit our ability to constrain atmospheric ch@xmath1 from these @xmath6/nicmos data as well as co@xmath0 and co. a spectral feature at 4.5 @xmath2 m can be explained by either of the carbon bearing molecules co@xmath0 or co , although it is still unclear which due to the degeneracy of the solution @xcite . at visible wavelengths , strong lines of the alkali metal sodium were reported using observations with the high resolution ground spectrograph of the @xmath8@xmath9 telescope @xcite , while featureless spectra detected by the @xmath6/acs @xcite and @xmath6/stis @xcite are thought to be caused by thick atmospheric hazes . observations of secondary transit spectra of hd 189733b by @xmath7 broadband photometry , when emission spectra from the planet s dayside is detected before and after the planet is eclipsed , have suggested that h@xmath0o is also abundantly present in the dayside atmosphere @xcite , forming the main features of the emission spectrum . the h@xmath0o - rich atmosphere was confirmed via @xmath7 irs ( infrared spectrograph ) dayside spectroscopy @xcite . @xmath6/nicmos dayside observations indicated a high abundance of co@xmath0 , co , and ch@xmath1 ( * ? ? ? * hereafter s09 ) , supporting the conclusions of their primary transit spectrophotometry . with all measurements , each of these studies suggested that an atmospheric thermal profile lacking a thermal inversion ( i.e. without a warm stratosphere ) could best explain their observations . finally , a decreasing temperature with altitude between 0.01 - 1.0 bar suggested the presence of a troposphere ( s09 ; * ? ? ? * hereafter ms09 ) . this work revisits the secondary transit spectroscopy of this hot jupiter to assess the family of atmospheric structures consistent with these measurements . various techniques have been used to investigate the atmospheric constituents and structure from transit spectroscopy . infrared dayside spectra during secondary eclipses measure the thermal emission of the dayside of the exoplanet , which depends mostly on the vertical temperature structure , while primary eclipse observations are more sensitive to the absolute temperature at the terminator due to its scale height dependence @xcite . the retrieval of atmospheric properties from remote sensing measurements has been developed over many decades @xcite and has become a common tool for the study of planetary atmospheres . measured radiances ( either photometry or spectroscopy ) can be compared to synthetic spectra from radiative transfer modelling so as to determine the atmospheric structure and composition . based on the bayesian approach , an optimal estimation retrieval model solves an ill - constrained inversion problem using an iterative scheme to maximise the probability of solutions to the available data ( the maximum @xmath10 @xmath11 solution ) @xcite . previous studies of the terminator and dayside spectrum , such as those by @xcite , @xcite and s09 , have utilised forward modelling to determine a best - fitted spectrum to the data , and have constrained the range of molecular abundances of transiting exoplanets by synthesising spectra based on theoretical pressure - temperature ( @xmath12-@xmath13 ) profiles . an alternative forward modelling approach used by a number of studies ( ms09 ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) used freely roaming @xmath12-@xmath13 profiles and molecular abundances in a parameterised space , where calculated spectra were again compared with observations in terms of the goodness - of - fit , and their numerous runs were able to constrain @xmath12-@xmath13 profiles and atmospheric compositions . although these forward modelling techniques provide valuable insights , their methods are based on line - by - line radiative transfer models , which are slow when large numbers of synthetic spectra are to be calculated over a wide wavelength range . moreover , the huge degeneracies between the different model parameters were not explored in detail . the nemesis optimal estimation retrieval algorithm @xcite uses the correlated-@xmath14 technique @xcite in its radiative transfer model , which rapidly integrates synthetic spectra using @xmath14-distribution tables pre - calculated from line databases @xcite . the combination of the correlated-@xmath14 forward model , which is orders of magnitude faster than a standard line - by - line model , with an optimal estimation retrieval scheme @xcite has been used to successfully investigate planetary atmospheres in our own solar system . in this study we apply this rapid retrieval architecture to exoplanets for the first time , which allows us to formally address the uncertainties and degeneracies inherent in previous studies . moreover , we use the covariance matrices calculated via the inversion method to quantify the correlations between the derived @xmath12-@xmath13 profile and atmospheric composition . consequently , this study will show how the characteristics of these extreme exoplanet atmospheres can be deduced from spectroscopic measurements and highlight the limitations of the datasets available today .    in this report , the modelling method used to retrieve the atmospheric properties from the dayside spectroscopy and photometry of hd 189733b is described in section 2 . all available measurements used to constrain atmospheric properties are described in section 3 and the best - fitting solution to these measurements is discussed in section 4 . section 5 demonstrates the validity of the retrieval scheme , and quantifies the degeneracy of the solution . in section 6 we discuss the implications of our results and arrive at our conclusions .","summary":"the development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described , building upon a retrieval algorithm which is extensively used in the study of our own solar system . [ firstpage ]    physical data and processes : radiative transfer  methods : analytical  planetary systems : individual : hd 189733b  planets and satellites : atmospheres","abstract":"recent spectroscopic observations of transiting hot jupiters have permitted the derivation of the thermal structure and molecular abundances of ho , co , co , and ch in these extreme atmospheres . here , for the first time , we apply the technique of optimal estimation to determine the thermal structure and composition of an exoplanet by solving the inverse problem . the development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described , building upon a retrieval algorithm which is extensively used in the study of our own solar system . first , we discuss the plausibility of detection of different molecules in the dayside atmosphere of hd 189733b and the best - fitting spectrum retrieved from all publicly available sets of secondary eclipse observations between 1.45 and 24 m . additionally , we use contribution functions to assess the vertical sensitivity of the emission spectrum to temperatures and molecular composition . over the altitudes probed by the contribution functions , the retrieved thermal structure shows an isothermal upper atmosphere overlying a deeper adiabatic layer ( temperature decreasing with altitude ) , which is consistent with previously - reported dynamical and observational results . the formal uncertainties on retrieved parameters are estimated conservatively using an analysis of the cross - correlation functions and the degeneracy between different atmospheric properties . the formal solution of the inverse problem suggests that the uncertainties on retrieved parameters are larger than suggested in previous studies , and that the presence of co and ch is only marginally supported by the available data . nevertheless , by including as broad a wavelength range as possible in the retrieval , we demonstrate that available spectra of hd 189733b can constrain a family of potential solutions for the atmospheric structure .    [ firstpage ]    physical data and processes : radiative transfer  methods : analytical  planetary systems : individual : hd 189733b  planets and satellites : atmospheres"}
{"article_id":"1110.2934","section_id":"c","document":"-@xmath13 profile ( left ) . the given pressures correspond to the levels covered by the contribution functions . we also display the dry adiabatic lapse rate ( dalr ) in grey , assumed to be a constant over this pressure range.,width=340 ]    the retrieved thermal structure is a useful tool for further understanding of dynamic processes in the atmosphere . as a description of atmospheric stability , the lapse rate ( @xmath67 , the rate of change of temperature with respect to the height ) is shown in fig . an increase in the lapse rate indicates that there is an adiabatic layer beneath the @xmath39100 mbar level ( @xmath391400 km above from the level of 10 bar ) , and that the lapse rate tends to zero for pressure levels above @xmath3930 mbar ( @xmath392100 km ) where the temperature profile tends to an isotherm . moreover , the measured lapse rate is similar to the dry adiabatic lapse rate ( dalr ) below the 300 mbar pressure level , and is overlain by a sub - adiabatic layer extending up to 30 mbar , similar to the atmospheric thermal structures seen in the upper tropospheres of the giants planets of our solar system . the nemesis algorithm uses two novel tools for an efficient retrieval of the atmospheric properties : a non - linear optimal estimation scheme and a fast forward model taking advantage of the correlated-@xmath14 approximation and @xmath14-distribution tables . this rapid retrieval method allows us to infer general atmospheric properties from small datasets . the optimal estimation retrievals permit an extension of previous results and the formal quantification of errors and uncertainties . the functional derivatives , which are analytically computed , enable us to trace the vertical contribution of the different input constituents in each channel , permitting us to move beyond the single best - fitting approach and show the relationship between the features of the data and physical values . we have shown that the current set of observations of the dayside spectrum of hd 189733b are enough to constrain the thermal structure at some pressure levels and the mixing ratios for h@xmath0o and co@xmath0 , albeit with large uncertainties due to molecular degeneracies and the limited number of spectral measurements . on the other hand , we do not find statistically - significant evidence for co and ch@xmath44 in the dayside emission spectra alone , and the present observational set of hd 189733b only allows us to place upper limits on the abundances of these species . furthermore , the ability to calculate the cross - correlation function allows us to assess the degeneracies between the various modelled parameters in our state vector .    with the retrieval method presented here , we derive three major findings from the measurements of the dayside of hd 189733b . firstly , we have produced the first retrieval ( i.e. solution to the inverse problem ) of the vertical temperature structure of the dayside atmosphere of hd 189733b . the retrieved profile shows that the constraints in the nir and mir lead to an adiabatically decreasing temperature between 0.11 bar . in addition , strong constraints from the @xmath7 irs measurements in the 916 @xmath2 m range suggest that the temperature structure in the mid and upper atmosphere ( 1100 mbar ) seems to be isothermal with a uniform temperature ( @xmath391100 k ) . one explanation for the isothermal layer is that super - rotating jets blowing from the night- to dayside play an critical role of an efficient energy re - distribution over the whole planet and may be responsible for maintaining the high temperature in the upper atmosphere @xcite . secondly , the functional derivatives for the molecules show that the measurements at nir ( 1.61.7 and 1.92.2 @xmath2 m ) , mir ( 4.5 @xmath2 m ) , and fir ( 916 @xmath2 m ) spectral ranges constrain the co@xmath0 abundance at @xmath39100 mbar but not in the upper atmosphere . its abundance in the lower atmosphere is responsible for the spectral flatness at 916 @xmath2 m , where previous studies assumed h@xmath0o to be the dominant constituent . we determine the vertical sensitivity of co@xmath0 abundance by comparing the retrievals with abundant ( 2.0@xmath4510@xmath61 ) and scarce co@xmath0 ( 10@xmath47 ) , and height - dependant co@xmath0 profile . the functional derivatives for co@xmath0 show low sensitivity at 0.11 mbar , which implies that the abundance of co@xmath0 in the upper atmosphere remains underconstrained by existing data . thirdly , we have quantified the degeneracies between the atmospheric properties using the cross - correlation functions . the correlations between molecular abundances and temperature exhibit substantial degeneracies , in particular , between temperature and h@xmath0o abundance at 300 mbar . we determine the temperature uncertainty at different pressure levels by calculating the statistics of the retrievals with the variation of each molecular mixing ratio . in the same way , the molecular abundances are also constrained by demonstrating that the uncertainty on retrieved parameters , based on the available measurements and the degeneracy with the temperature profile is considerably larger than previous studies have suggested . therefore , additional data is clearly required to break the degeneracy between temperature and composition , particularly h@xmath0o . as long as the number of retrieval variables for the molecular abundance are kept to a small number , the cross - correlation functions are not significant between molecules . if we were forced to use a more detailed representation of the vertical distributions of the gases and scattering properties , then the degeneracies would become more substantial . this study has shown the benefit of considering a wide spectral range for breaking the degeneracy between different atmospheric parameters . by constraining the overall shape of the infrared spectrum , the @xmath6 and @xmath7 secondary eclipse data allow us to evaluate the vertical temperature structure and to place crude estimates on the molecular abundances in this hot jupiter . studies that focus on smaller wavelength ranges or fewer data points are subject to broader uncertainties than are currently being presented in the literature . future work will permit an extension of this technique into cross - comparison with transmission spectroscopy , including the visible range ( alkali metals , metal oxides , and clouds and hazes ) especially at the terminator regions of this planet .","summary":"the formal uncertainties on retrieved parameters are estimated conservatively using an analysis of the cross - correlation functions and the degeneracy between different atmospheric properties .","abstract":"recent spectroscopic observations of transiting hot jupiters have permitted the derivation of the thermal structure and molecular abundances of ho , co , co , and ch in these extreme atmospheres . here , for the first time , we apply the technique of optimal estimation to determine the thermal structure and composition of an exoplanet by solving the inverse problem . the development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described , building upon a retrieval algorithm which is extensively used in the study of our own solar system . first , we discuss the plausibility of detection of different molecules in the dayside atmosphere of hd 189733b and the best - fitting spectrum retrieved from all publicly available sets of secondary eclipse observations between 1.45 and 24 m . additionally , we use contribution functions to assess the vertical sensitivity of the emission spectrum to temperatures and molecular composition . over the altitudes probed by the contribution functions , the retrieved thermal structure shows an isothermal upper atmosphere overlying a deeper adiabatic layer ( temperature decreasing with altitude ) , which is consistent with previously - reported dynamical and observational results . the formal uncertainties on retrieved parameters are estimated conservatively using an analysis of the cross - correlation functions and the degeneracy between different atmospheric properties . the formal solution of the inverse problem suggests that the uncertainties on retrieved parameters are larger than suggested in previous studies , and that the presence of co and ch is only marginally supported by the available data . nevertheless , by including as broad a wavelength range as possible in the retrieval , we demonstrate that available spectra of hd 189733b can constrain a family of potential solutions for the atmospheric structure .    [ firstpage ]    physical data and processes : radiative transfer  methods : analytical  planetary systems : individual : hd 189733b  planets and satellites : atmospheres"}
{"article_id":"quant-ph9706062","section_id":"i","document":"many of the problems of interest to computation experts are , or are reducible to , decision problems . these are problems that for a given input require the determination of a yes or no answer to a specified question about the input . for example the traveling salesman problem is ( polynomial time ) equivalent to the decision problem that asks whether or not for a given set of intercity distances there is a route passing through all of the cities whose length is less than a given fixed length . another example that we will later use for concreteness in this paper is the @xmath2 integer programming problem called  exact cover\"@xcite . here we are given an @xmath3 by @xmath0 matrix , @xmath4 , all of whose entries are either 0 or 1 . the number of columns @xmath3 is @xmath5 . we are asked if there exists a solution to the @xmath3 equations @xmath6 with the @xmath7 restricted to be 0 or 1 . the brute force approach to this problem is to try the @xmath8 possible choices of @xmath9 . for each choice of @xmath10 , checking to see if eq . ( [ eq:1 ] ) is satisfied takes at most of order @xmath11 operations , which is polynomial in the input size . however , checking all @xmath8 possible choices for @xmath10 is prohibitively time consuming even for moderately large values of @xmath0 .    for the exact cover problem , with a given instance of the input matrix @xmath4 , it is not actually necessary to check all @xmath8 values of @xmath10 to see if eq . ( [ eq:1 ] ) can be satisfied . note that generically @xmath12 can take the values 0 or 1 and @xmath13 can have the values @xmath14 or @xmath15 . however , suppose that for some @xmath16 the matrix @xmath4 has @xmath17 . in this case the choice @xmath18 is eliminated and no @xmath10 of the form @xmath19 need be tried . if we consider @xmath10 s that begin with @xmath20 then if for some @xmath16 we have @xmath21 , then any @xmath10 beginning with @xmath20 is eliminated . we can picture this in terms of a decision tree as follows . before imposing any constraints we construct an underlying branching tree . this tree starts at the top with one starting node that branches to two nodes corresponding to the two choices for @xmath12 . this then branches to the four choices for @xmath13 and so on until we have all @xmath8 choices for @xmath22 at the @xmath23 level . however if we impose the constraints and see that a particular node is eliminated , then we can also eliminate all nodes connected to that node that lie below it in the tree . the decision tree is the underlying branching tree that has been trimmed as a result of the constraints . note that the exact cover problem has a solution if and only if the decision tree has one or more nodes left at the bottom ( @xmath23 ) level . more generally we view decision problems as having an underlying bifurcating branching tree with @xmath0 levels as in fig.[fig : figi ] . the specific form ( or instance ) of the problem imposes constraints that eliminates nodes from the tree as in fig.[fig : figii ] . when a node is excluded the whole branch with that node as its topmost point is also cut from the tree . the decision question we wish to answer is `` are there any nodes left at the @xmath23 level after all constraints have been imposed ? ''    consider a family of decision problems indexed by a size @xmath0 . particular instances of the problem of size @xmath0 give rise to particular decision trees that either have or do not have nodes at the @xmath23 level . the computational concern is how much time , or how many algorithmic steps , are required to answer the decision question as @xmath0 gets big . roughly speaking if the time grows like @xmath24 for fixed @xmath25 , the problem is considered easy whereas if the time grows like @xmath26 with @xmath27 , the problem requires an `` exponential amount of time '' and is considered computationally hard . one approach to solving a decision problem is to systematically check every path that starts at the top of the tree and moves downward through the tree . if a path reaches a dead end you try the next path ( in some list of paths ) until you find a path that has a node at the @xmath23 level or else , after having checked all paths , you discover that the answer to the decision question is  no \" . an alternative to systematically exploring the whole tree is to move through the tree with a probabilistic rule . for example you could use the rule that if you are at a given node you move to the other nodes that are connected to it with equal probability . thus if you are at a node that connects to two nodes below it you have a 1/3 chance of moving back up the tree ; if the node connects to just one below you have a 1/2 chance of moving back up whereas if the node is a dead end you definitely move back . if you start at the top of the tree and move with this probabilistic rule you will eventually visit every node in the tree . consider a family of decision trees that are associated with underlying branching trees that are @xmath0 levels deep . an individual instance of the decision tree either has or does not have nodes at the @xmath23 level . if it does have nodes at the @xmath23 level and we use a probabilistic rule for moving through the tree , then we say that the tree is penetrable if there is a good chance of reaching the @xmath23 level in not too great a time . more precisely we define the family of trees as penetrable if : @xmath28 this means that in polynomial time the probability of reaching the @xmath23 level is at worst polynomially small . if ( p ) is met , then by running the process order @xmath29 times we achieve a probability of order  1 of reaching the @xmath23 level in time @xmath30 . if ( p ) is not met it means that it either takes more than polynomial time to reach the @xmath23 level or the probability of reaching the @xmath23 level is always smaller than @xmath31 to any power . therefore if condition ( p ) is not met instances of the trees with nodes at the @xmath23 level can not practically be distinguished from instances with no nodes at the @xmath23 level . in this case the corresponding decision problem is not solvable in polynomial time by this algorithm . we will divide families of decision trees indexed by @xmath0 into two classes , those that satisfy ( p ) and those that do not , which we call impenetrable . we are interested in using quantum mechanics to move through decision trees . we imagine that nodes of the decision tree correspond to quantum states , which give a basis for the hilbert space . we further imagine constructing a hamiltonian @xmath32 with nonzero off - diagonal matrix elements only between states that are connected in the corresponding decision tree . ( we will be more specific about constructing the hilbert space and @xmath32 later . ) we start the quantum system in the state corresponding to the topmost node and let it evolve with its time evolution determined by @xmath32 so that the unitary time evolution operator  is @xmath33 at any time @xmath34 we have a pure state that can be expressed as a ( complex ) superposition of basis states corresponding to the nodes . given @xmath32 and the initial state , the probability ( the amplitude squared ) of finding the system at the @xmath35 level at time @xmath34 is determined . we then say that a family of trees indexed by size @xmath0 is quantum penetrable if condition @xmath36 is met and it is quantum impenetrable if condition @xmath36 is not met .    in the next section we will give a specific form for the quantum hamiltonian @xmath32 and then prove that any family of trees that is classically penetrable is associated with a closely related family of trees that is quantum penetrable . this will demonstrate that our model for quantum mechanically solving decision problems is at least as powerful as the classical probabilistic method . in section three we will go further and give an example of a family of decision trees that is classically impenetrable but which is quantum mechanically penetrable . this means that the quantum penetration is exponentially faster than the corresponding classical penetration for these trees . however , we have not yet identified general characteristics of a problem that guarantee that its associated decision trees are quantum penetrable . furthermore , for the example considered , the problem associated with the classically impenetrable trees can be reformulated so that it is computationally simple to solve by an alternative , classical method .    in section four we discuss the construction of the hilbert space and the hamiltonian @xmath32 . the usual paradigm for quantum computation@xcite envisages a string of , say , @xmath37 spin-1/2 particles that gives rise to a @xmath38-dimensional hilbert space . each elementary operation is a unitary transformation that acts on one or two spins at a time . we will show that the hilbert space for our system can be constructed using @xmath37 spin 1/2 particles just as in a conventional quantum computer . furthermore , for a large class of problems , the hamiltonian that we construct is a sum of hamiltonians that act on a fixed number of spins . in this sense@xcite our quantum evolution through decision trees lies in the framework of conventional quantum computation .","summary":"a natural classical algorithm is to then run a random walk on the tree , starting at the root , to see if the tree contains a node  levels from the root .","abstract":"many interesting computational problems can be reformulated in terms of decision trees . a natural classical algorithm is to then run a random walk on the tree , starting at the root , to see if the tree contains a node  levels from the root . we devise a quantum mechanical algorithm that evolves a state , initially localized at the root , through the tree . we prove that if the classical strategy succeeds in reaching level in time polynomial in , then so does the quantum algorithm . moreover , we find examples of trees for which the classical algorithm requires time exponential in , but for which the quantum algorithm succeeds in polynomial time . the examples we have so far , however , could also be solved in polynomial time by different classical algorithms .    mit - ctp-2651 ,  quant - ph/9706062    6.5 in -.7 in boxedeps    # 1#2#3#4       # 1"}
{"article_id":"quant-ph9706062","section_id":"c","document":"there is great interest in devising quantum algorithms that improve on classical algorithms , and there have been some notable successes . for example , the well - known shor  @xcite and grover  @xcite algorithms demonstrate remarkable ingenuity . each uses quantum interference , the necessary ingredient for quantum speed - up , in what appears to be a problem - specific way . so far these methods have not been successfully applied to problems very different from the ones for which they were originally devised .    in this paper , we have considered a single time - dependent hamiltonian that evolves a quantum state through the nodes of a decision tree . ( for a related approach , see @xcite . ) this is in contrast to the usual setup consisting of a sequence of unitary operators each acting on a fixed number of bits . ( for many problems , including np - complete ones , our algorithm can be rewritten in the conventional language of quantum computation . ) studying hamiltonian evolution on decision trees is facilitated by the technique of calculating energy - dependent transmission coefficients . the example in section three shows explicitly how interference allows a class of trees to be penetrated exponentially faster by quantum evolution than by classical random walk . however , this example can be quickly solved by a different classical algorithm . the particular hamiltonian we chose allowed us to prove , in section  two , that the quantum algorithm succeeded in polynomial time whenever the corresponding classical random walk on the decision trees succeeded in polynomial time . in searching for more examples where the quantum algorithm outperforms the classical algorithm , one is not restricted to this hamiltonian . we can imagine trying any hamiltonian with nonzero off - diagonal elements where there are links between the nodes on the decision tree . with this flexibility , we hope that the class of trees that can be penetrated quickly by the quantum algorithm is large enough to include classically difficult problems . we thank francis low and mike sipser for their help and insights . we also thank rachel cohen and cindy lewis for latex   assistance , and martin stock for creating figs.[fig : figi][fig : figviii ] and final formatting . 99  computational complexity \" , d.s . johnson and c.h . papadimitriou , p.  37 of _ the traveling salesman problem _ , e.l . lawler , j.k . lenstra , a.h.g . rinnooy kan , and d.b . shmoys , eds . john wiley & sons , 1985 .","summary":"many interesting computational problems can be reformulated in terms of decision trees . we devise a quantum mechanical algorithm that evolves a state , initially localized at the root , through the tree . we prove that if the classical strategy succeeds in reaching level in time polynomial in , then so does the quantum algorithm . the examples we have so far , however , could also be solved in polynomial time by different classical algorithms .   ","abstract":"many interesting computational problems can be reformulated in terms of decision trees . a natural classical algorithm is to then run a random walk on the tree , starting at the root , to see if the tree contains a node  levels from the root . we devise a quantum mechanical algorithm that evolves a state , initially localized at the root , through the tree . we prove that if the classical strategy succeeds in reaching level in time polynomial in , then so does the quantum algorithm . moreover , we find examples of trees for which the classical algorithm requires time exponential in , but for which the quantum algorithm succeeds in polynomial time . the examples we have so far , however , could also be solved in polynomial time by different classical algorithms .    mit - ctp-2651 ,  quant - ph/9706062    6.5 in -.7 in boxedeps    # 1#2#3#4       # 1"}
{"article_id":"astro-ph0601645","section_id":"i","document":"the origin of the stable magnesium isotopes , mg , mg and mg , is of particular interest to astrophysics because mg is one of the few elements for which we can obtain isotopic information from stellar spectroscopy . the ratio mg : mg : mg has been derived from high - resolution spectra of cool dwarfs and giants in the thin and thick disk of the galaxy @xcite , and for giants stars in the globular cluster ( gc ) ngc 6752 @xcite . these observations show that many of the stars , including relatively metal - poor stars ( [ fe / h ] @xmath4 ) , have non - solar mg isotopic ratios with enhancements in the neutron - rich isotopes , mg and mg , compared to what is expected from galactic chemical evolution ( gce ) models . the main stellar nucleosynthesis site for all three stable isotopes is hydrostatic burning in the carbon and neon shells of massive stars that explode as type ii supernovae @xcite . the abundances of the neutron - rich mg isotopes are further enhanced by secondary @xmath5-capture processes operating in the helium shell . the amount of mg produced does not strongly depend on the initial metallicity of the model and is an example of primary nucleosynthesis , whereas secondary production requires some heavier seed nuclei to be present , and the amount produced scales with @xmath6 . ] , whereas the amounts of mg and mg produced scale with the initial metallicity of the star . this means that the mg content of the ejecta of low metallicity supernovae will be mostly mg with very little mg and mg produced , with typical ratios mg : mg : mg @xmath7 99.0:0.50:0.50 from a 25@xmath8 supernova model with metallicity @xmath9 @xcite . previous studies have shown that gce models using ejecta from massive stars match the observational data well for [ fe / h ] @xmath10 but severely underestimate mg / mg at lower metallicities @xcite , indicating that another production site for the neutron - rich mg isotopes at low metallicities is required to account for the observations . recently , @xcite included the predicted stellar yields of mg and mg from asymptotic giant branch ( agb ) stars @xcite along with yields from type ii supernovae @xcite into a gce model of the solar neighborhood . the gce model with the agb contribution could successfully match the mg isotopic ratios of the metal - poor galactic disk stars while the model without an agb contribution could not . this result indicates that low - metallicity intermediate mass agb stars may play an important role in the production of these species in galaxies and stellar systems . the production of the neutron - rich isotopes in agb stars is also of interest in relation to the non - solar mg isotopic ratios observed in giant stars in globular clusters @xcite . the non - solar mg isotopic ratios observed in ngc 6752 have been attributed to agb stars , but @xcite used a gce model with tailor made agb yields from @xcite and failed to match the abundance patterns observed in stars in that cluster . as @xcite have pointed out , there are still many uncertainties that effect the stellar yields , so an agb solution to the globular cluster anomalies can not be ruled out at present . further motivation for the study of the production of the mg isotopes in agb stars is given by their relevance in the important current debate on the apparent variation of the fine - structure constant @xcite , and the origin of pre - solar spinel grains , some of which show enhancements in both mg and mg compared to solar @xcite . briefly , intermediate - mass stars ( initial mass @xmath114 to 8@xmath8 ) will enter the thermally - pulsing phase with a hydrogen ( h)-exhausted core mass ( hereafter core mass ) @xmath12 0.8@xmath8 , after experiencing the second dredge - up ( sdu ) @xcite . the sdu brings the products of h - burning to the stellar surface ( mostly he and n ) , and will slightly alter the composition of the mg isotopic ratios , with an enrichment in mg at the expense of mg . for the massive , @xmath13 models , the sdu is the first time the surface abundances are altered , because there is essentially no first giant branch phase @xcite . following the sdu , the he - burning shell becomes thermally unstable and flashes every few thousand years or so . the energy from the thermal pulse ( tp ) drives a convective pocket in the he - rich intershell , which thoroughly mixes the products of he - nucleosynthesis within this region . following the tp , the convective envelope moves inward in mass and may reach the region previously mixed by the flash - driven convective pocket . this mixing event is known as the third dredge - up ( tdu ) and if it occurs , is responsible for enriching the envelope in material from the h - exhausted core . following the tdu the star contracts and the h - shell is re - ignited and provides nearly all of the surface luminosity for the next interpulse period . the thermal pulse  tdu  interpulse cycle may occur many times during the tp - agb phase ; how many times depends on a number of factors including the convective model which determines the surface luminosity and mass - loss rate and hence the total agb lifetime @xcite . hot bottom burning can also occur when the base of the convective envelope becomes hot enough to sustain proton - capture nucleosynthesis @xcite . if temperature at the base of the envelope is sufficiently hot ( over @xmath14k ) , the nena and mgal chains may operate alongside the cno cycle ; li production is also possible via the cameron - fowler mechanism @xcite , which operates at lower temperatures ( typically @xmath15k ) . @xcite noted that intermediate - mass agb stars may become luminous , optically obscured carbon stars near the end of the tp - agb , when mass loss has removed much of the envelope , extinguishing hbb but allowing dredge - up to continue . @xcite described in detail the various nucleosynthesis processes that alter the mg isotopic ratios in agb stars . to summarize , mg and mg are synthesized in the he - shell during thermal pulses by the reactions ne(@xmath16)mg and ne(@xmath17)mg , when the temperature exceeds about 300@xmath18k . the amount of mg produced depends on the thermodynamic conditions inside the pulse as well as on the composition of the intershell , which will have been altered by previous h and he - burning . neutron captures , in particular the mg(@xmath19)mg reaction , can also alter the mg isotopic ratio in the intershell , where the neutrons come from the ne(@xmath20)mg reaction @xcite . hbb can also significantly alter the surface mg isotopic ratio via the activation of the mgal chain , which can result in the destruction of mg if the temperature exceeds @xmath21k . the stellar yields of mg presented in @xcite and shown in figure  [ fig : mg - previous ] were calculated from models covering a range in mass ( 1@xmath8 to 6@xmath8 ) and metallicity ( [ fe / h ] @xmath22 ) . from this figure we see that the most massive agb models produce the most mg , as a consequence of higher temperatures in the he - shells compared to lower mass stars ; we also notice an increase in production at a given mass with a decrease in metallicity . the computationally demanding nature of agb models precluded a detailed study in that paper of the effect of the major uncertainties ( mass loss , nuclear reaction rates , convection ) . a recent comprehensive study by @xcite demonstrated that the predictive power of agb models is still seriously undermined by these uncertainties . the theory of convection has a significant effect on the structure and nucleosynthesis @xcite , whilst varying the mass - loss rate results in larger changes to the stellar yields than varying the nuclear reaction rates @xcite . however , the magnitude of the errors associated with the relevant nuclear reaction rates is still one of the key questions concerning predictions of magnesium production in intermediate - mass agb models . whilst the rates of the n(@xmath17)f and o(@xmath17)ne reactions are well determined @xcite , the two key @xmath5-capture reaction rates : ne(@xmath16)mg and ne(@xmath17)mg , suffer from large uncertainties at the stellar energies appropriate for agb stars @xcite . for example , at typical he - shell burning temperatures , @xmath23k , the nacre compilation @xcite give an upper limit to the ne(@xmath16)mg reaction rate that is about 47 times larger than the recommended rate . at lower temperatures , the uncertainties are even larger . the aims of this paper are two fold . first , we present new reaction rates for the two key @xmath5-capture reactions , with considerably reduced uncertainties compared to those given by the nacre compilation . second , we use these new rates within models of different metallicities ( [ fe / h ] @xmath24 ) , for a typical mass ( 5@xmath8 ) that produces the mg isotopes during the thermally - pulsing agb ( tp - agb ) phase . for each model we calculate the stellar yields and compare to previous nucleosynthesis calculations using older estimates of these reaction rates , including those by @xcite and @xcite . we also examine the effect of other model uncertainties , in particular the inclusion of a partial mixing zone and mass loss , on the stellar yields . the paper is organized as follows . in  [ section : method ] we discuss the numerical method used for the stellar model calculations , including a discussion of the input physics used . in  [ section : rates ] we present new rates for the ne @xmath3 capture reactions . the results of the calculations are presented in  [ section : results ] and discussed in  [ section : discussion ] .","summary":"we have therefore removed one of the important sources of uncertainty to effect models of agb stars .","abstract":"we present new rates for the ne)mg and ne mg reactions , with uncertainties that have been considerably reduced compared to previous estimates , and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass asymptotic giant branch ( agb ) stars of different initial compositions . all the models have deep third dredge - up , hot bottom burning and mass loss . calculations have been performed using the two most commonly used estimates of the ne rates as well as the new recommended rates , and with combinations of their upper and lower limits . the main result of the present study is that with the new rates , uncertainties on the production of isotopes from mg to p coming from the ne-capture rates have been considerably reduced . we have therefore removed one of the important sources of uncertainty to effect models of agb stars . we have studied the effects of varying the mass - loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure , such as the modeling of convection , the inclusion of a partial mixing zone and the definition of convective borders . these uncertainties are found to be much larger than those coming from ne-capture rates , when using our new estimates . much effort is needed to improve the situation for agb models ."}
{"article_id":"astro-ph0601645","section_id":"m","document":"we calculate the structure first and perform detailed nucleosynthesis calculations afterward , using a post - processing algorithm . the stellar structure models were calculated with the monash version of the mount stromlo stellar structure program ; see @xcite and references therein for details . mass loss on the first giant branch is included using the reimer s mass - loss prescription @xcite with the parameter @xmath25 ; on the agb we use the formulation given by @xcite in all models unless indicated otherwise . we calculate two models ( 5@xmath8 , @xmath26 and @xmath27 ) using reimer s mass loss on the agb with the parameter @xmath28 . here we assume that the @xcite and @xcite mass - loss prescriptions , derived for solar - like metallicities or those appropriate for the magellanic clouds , can be applied to @xmath27 intermediate - mass agb models without modification . the use of either mass - loss law results in a large number of thermal pulses ( up to @xmath29 ) . all models were calculated from the zero - age main sequence to near the end of the tp - agb phase . the occurrence of the third dredge up and hot bottom burning ( hbb ) depend critically upon the convection model used @xcite and the method for determining convective borders . briefly , we use the standard mixing - length theory ( mlt ) for convective regions , with a mixing - length parameter @xmath30 , and determine the border by applying the schwarzschild criterion . hence we do not include convective overshoot , in the usual sense . we do however , search for a neutral border to the convective zone , in the manner described in detail by @xcite and @xcite . we note that this method has been shown to increase the efficiency of the third dredge - up compared to models that strictly use the schwarzschild criterion . we performed detailed nucleosynthesis calculations using a post - processing code which includes 74 species and time - dependent diffusive mixing in all convective zones @xcite . the details of the nucleosynthesis network are outlined in @xcite , but we remind the reader that we include 59 light nuclei and 14 iron - group species . we also add the fictional particle @xmath31 , to count the number of neutron captures occurring beyond ni @xcite . initial abundances are taken from @xcite for the @xmath26 models and we assume scaled - solar for the @xmath27 models . we assume an initially @xmath5-enhanced mixture typical of thin - disk stars @xcite for the 5@xmath8 , @xmath32 models . the initial mg isotopic ratios ( e.g. mg / mg ) are 21.9% and 35.2% less than solar in the @xmath33 and @xmath34 models , respectively . the bulk of the 506 reaction rates are from the reaclib data tables @xcite , based on the 1991 updated version . some of the proton , @xmath5 and neutron capture reaction rates have been updated according to the latest experimental results , see @xcite for details , and we calculate one set of models using these rates . we define this set to be our _ standard _ set and the results from these computations are shown in figure  [ fig : mg - previous ] . in all the other sets of computed models we have updated the proton capture rates for the nena and mgal chains to those recommended by nacre ( see table  [ tab : pcaptures ] in  [ app : rates ] for details of which proton capture rates that have been updated ) . with this new set of updated rates , we study the effect of changing the ne @xmath3 rates : we run models with our standard choice for these rates ( * ? ? ? * without the inclusion of the 633 kev resonance , indicated as k94 in table  [ tab : mgyields ] ) , with the nacre recommended rates ( indicated as nacre in table  [ tab : mgyields ] ) , and with our new recommended rates , as well as using combinations of the new upper and lower limits .","summary":"all the models have deep third dredge - up , hot bottom burning and mass loss . calculations have been performed using the two most commonly used estimates of the ne rates as well as the new recommended rates , and with combinations of their upper and lower limits .","abstract":"we present new rates for the ne)mg and ne mg reactions , with uncertainties that have been considerably reduced compared to previous estimates , and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass asymptotic giant branch ( agb ) stars of different initial compositions . all the models have deep third dredge - up , hot bottom burning and mass loss . calculations have been performed using the two most commonly used estimates of the ne rates as well as the new recommended rates , and with combinations of their upper and lower limits . the main result of the present study is that with the new rates , uncertainties on the production of isotopes from mg to p coming from the ne-capture rates have been considerably reduced . we have therefore removed one of the important sources of uncertainty to effect models of agb stars . we have studied the effects of varying the mass - loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure , such as the modeling of convection , the inclusion of a partial mixing zone and the definition of convective borders . these uncertainties are found to be much larger than those coming from ne-capture rates , when using our new estimates . much effort is needed to improve the situation for agb models ."}
{"article_id":"astro-ph0601645","section_id":"r","document":"we now present the results of the stellar models . unless otherwise stated , we discuss the models computed using the @xcite mass - loss rates . in this section we present some of the structural properties of the stellar models used for the present study in detail , including a brief discussion of the evolution of the cno nuclei during the tp - agb phase . in table  [ table : agbmodels ] we first include the initial mass and metallicity and the mass - loss law adopted for the structure calculation . vw93 refers to models calculated with @xcite mass loss whilst r75 refers to models calculated with @xcite with the parameter @xmath57 . furthermore , we present the core mass at the beginning of the tp - agb , the mass of the envelope when hbb is shutoff and the mass at the end of the calculation , the total number of tps , the number of tdu episodes , the total amount of matter dredged into the envelope @xmath58 , the maximum temperature at the base of the convective envelope , the maximum temperature in the he - shell during a tp and the maximum dredge - up efficiency , @xmath59 . in table [ tab : agb2 ] we present some surface abundances results including the final c@xmath60n@xmath60o value divided by the initial ( see table caption for more details ) . the dredge - up efficiency is defined by @xmath61 , where @xmath62 is the amount of h - exhausted core matter mixed into the envelope and @xmath63 is the amount by which the core mass grew during the previous interpulse period . for all the models considered here , @xmath64 , is reached after a small number ( @xmath65 ) of pulses , similar to behavior observed by @xcite and @xcite for the same mass . the vw93 mass - loss rate depends on the pulsation period until the period reaches 500days , after which the luminosity - driven superwind phase begins . the pulsation period @xcite depends in turn on the radius and total mass and because the lower metallicity models are more compact they take longer ( in time ) to reach the start of the superwind phase and hence experience more tps than the solar metallicity models . in comparison , the r75 mass - loss rate is proportional to both the radius and the luminosity and as we can see from table  [ table : agbmodels ] at the lowest metallicity we consider ( @xmath66 ) the large luminosity at this composition results in fewer tps than using vw93 mass loss , the reverse of the behavior observed at @xmath26 . for all models except the @xmath26 cases , the temperature at the base of the envelope , @xmath67 , increases quickly at the beginning of the tp - agb and exceeds @xmath68k by about the 8@xmath69 pulse . the envelope mass after which hbb is shutoff decreases with a decrease in metallicity , see column  5 in table  [ table : agbmodels ] . for the solar composition vw93 ( r75 ) models , @xmath67 reaches @xmath68k after about the 9@xmath69 tp ( 12@xmath69 tp ) and decreases quickly once the envelope mass drops below @xmath70 , which is when hbb is shutoff . after this , dredge - up continues increasing the c / o ratio above unity in some cases ( see table  [ tab : agb2 ] ) .    for the remainder of this section we summarize the nucleosynthesis of the cno nuclei , because these species are not affected by varying the ne @xmath3 reaction rates . the contribution of many tps with efficient dredge - up means that there is a considerable increase in the amount of c that can be converted to primary n by hbb ( note also the low final c / c ratios shown in table  [ tab : agb2 ] ) . this increase can be best appreciated by comparing the final envelope c@xmath60n@xmath60o abundance ( divided by the initial ) for each model in table  [ tab : agb2 ] . in the lowest @xmath6 models n is the most abundant isotope , and an increase in @xmath6 results in decreasing levels of enrichment , where the final [ n / fe ] models . we use the standard logarithmic notation [ @xmath71 @xmath72 . ] values are 3.9 , 1.9 , 1.5 and 0.6 in the @xmath73 and 0.02 model , respectively . [ c / n ] ratios have been observed in metal - poor stars in the halo , with the finding that @xmath74 [ c / n ] @xmath75 at carbon abundances around [ c / fe ] @xmath76 @xcite . our models overproduce n compared to c , with [ c / n ] @xmath77 in all metal - poor 5@xmath8 computations . the solar - metallicity vw93 model does not become carbon rich , whereas the r75 model becomes a carbon star after the 28@xmath69 tp . from table [ table : agbmodels ] we see that the reason for this is more tdu episodes , resulting in about a factor of two more matter dredged into the envelope . the 5@xmath8 , @xmath33 model does not become a carbon star , whereas the @xmath34 model does . the final [ c / fe ] values for both cases are 0.16 and 0.70 , compared to 0.09 and 0.16 initially . the @xmath34 model has a longer tp - agb phase ( 0.59  myr compared to 0.50  myr ) , leading to more o destroyed by hbb , even though hbb temperatures are similar in both models . the final [ o / fe ] values are 0.02 and 0.04 , compared to the initial enhanced values of 0.16 and 0.24 , respectively . the 5@xmath8 , @xmath27 models ( with vw93 and r75 mass loss ) become carbon stars quickly , after the second tp . this is a consequence of deep third dredge - up and a low initial o envelope abundance . the final [ c / fe ] values are 2.4 and 2.6 , in the vw93 and r75 models . the envelope o abundance is destroyed during the interpulse by hbb at temperatures @xmath78k whereas the many efficient tdus result in an overall increase , leading to a final [ o / fe ] @xmath79 in both cases . this behavior was also observed by @xcite for the equivalent mass and metallicity . the envelope abundances of the mg isotopes are first modified by the operation of the sdu , and the magnitude of such modifications increases with a decrease in the metallicity or an increase increase in the mass . for the 5@xmath8 , @xmath26 , the envelope mg abundance decreases by 4.2% while mg increases by 3.7% after the sdu , whereas in the 5@xmath8 , @xmath34 model we observe a decrease of 9.4% in the mg abundance and an 8.4% increase in mg . for all cases but the 5@xmath8 , @xmath27 model , the mg abundance does not change . for this model , the mg abundance increases by 11% , whereas the mg and mg abundances decrease by 13% and 6.8% respectively . the results quoted above are for the calculations that use the nacre nena and mgal chain reaction rates .    in figure  [ m5z02 ] we show the evolution during the tp - agb phase of the mg ( solid line ) and mg ( dashed line ) abundances at the surface of the 5@xmath8 , @xmath26 model for four different choices of the ne @xmath3 reaction rates . the abundances in figure  [ m5z02 ] are the mole fraction , @xmath80 ( where the mass fraction @xmath81 and @xmath82 is the atomic mass ) , scaled to the total magnesium abundance , mg @xmath83 mg@xmath60mg@xmath60 mg . in figure  [ mg - surf ] we show the surface abundance evolution of the mg isotopes for three different initial compositions , that use the new recommended rates for the ne @xmath3 reactions . in table [ tab : agb2 ] we also present the mg isotope ratios ( in terms of mg : mg : mg ) at the beginning and at the end of the tp - agb phase for each model . figure  [ mg - surf ] and table  [ tab : agb2 ] shows the influence of metallicity on the evolution of the mg isotopes , where the effects of hbb become more significant at lower @xmath6 .    from figure  [ m5z02 ] we see the important result that using the new recommended rates for the ne @xmath2 reactions does not result in large changes to the production of mg compared to the calculations performed using older estimates . for the solar metallicity model , the final surface mg isotopic ratios are 70.8:13.5:15.6 when using nacre compared to 72.2:12.4:15.4 when using the new recommended rates . the only observable change is less mg but about the same amount ( or just slightly less ) mg . these results are consistently observed in the metal - poor agb models , although the trends are stronger at lower metallicity .    to explain the above trends , we need to examine the behavior of the new rates compared to the nacre and k94 rates . we produce less mg because the older estimates for the ne(@xmath20)mg reaction are up to 40% faster at typical he - shell burning temperatures i.e. @xmath84k to @xmath85k . why the production of mg is reduced or remains about the same is not immediately obvious given that the new recommended rate is faster than both the nacre ( by up to 26% ) and k94 ( by 70% to 100% ) rates . the reason is again related to the ( @xmath20 ) reaction which releases neutrons during a tp , some of which are captured to produce mg , a process that is most efficient in the lowest @xmath6 models . in the solar metallicity models the production of mg is less dependent on the neutron flux and we produce about the same when using the new recommended rate for the ne(@xmath17)mg reaction .      in the first row of table  [ tab : mgyields ] we present the stellar yields of mg and mg ( in @xmath8 ) for the 5@xmath8 models of different @xmath6 , computed using the new recommended rates . in other rows we present the percentage difference between yields calculated with a different set of rates ( as noted in the table ) and our reference yields given in the first row yield(ref)]/yield(ref ) multiplied by 100 , where @xmath86 is one of the combinations of reaction rates described in  [ section : method ] ] . in figure  [ yield - compare1 ] we show the percentage difference between the stellar yields calculated using the new recommended rates ( the reference ) , the new upper and lower limits and the nacre recommended rates , for two different metallicities . the @xmath87-axis is atomic mass , and we present percentage differences for ne through to p , with al included at @xmath88 . according to the definition of the percentage difference given above , a positive difference means that that model produced ( or destroyed ) more of a given species compared to our reference case . to compare to the magnitude of the uncertainties associated the nacre rates , in figure  [ yield - compare2 ] we show the percentage difference for models that use the nacre recommended ( the reference ) and the nacre upper and lower limits . we also vary the mg(@xmath19)mg reaction rate by a factor of two each way ( see figure  [ yield - compare2 ] ) . these figures show that using the new rates for the ne @xmath2 reactions results in considerably smaller uncertainties in the production of all isotopes between ne to p compared to models that use the nacre rates . for the mg isotopes , differences of the order @xmath11400% in the case of the 5@xmath8 , @xmath26 model with the nacre upper limits are reduced to less than 30% , when using the new upper limits . for models of lower metallicity , the uncertainties are even smaller ( at most @xmath89% ) . varying the mg(@xmath19)mg reaction rate given by @xcite by a factor of two each way results in differences of at most 33% in the production of p , about 26% in the production of mg and about 15% in the production of mg for all models , regardless of metallicity . note that the abundance of heavier isotopes are affected by neutron captures hence the dependence on these reaction rates . the percentage differences reported in table  [ tab : mgyields ] and shown in figures  [ yield - compare1 ] and  [ yield - compare2 ] illustrate that the computed errors decrease with a decrease in the metallicity of the model . the reason could be that the yields significantly increase with an decrease in @xmath6 , and hence changes to a larger number result in smaller differences than changes to a smaller number ( in the case of the @xmath26 models ) . also , the low @xmath6 models have more tps and more efficient hbb means that the proton - capture mgal chain reactions have a greater overall effect on the stellar yields .      the inclusion of a partial mixing zone ( pmz ) at the deepest penetration of the tdu will mix protons from the envelope into the he - intershell , producing a c pocket . in the pmz neutrons are liberated during the interpulse period by the neutron source reaction c(@xmath16)o and the mg isotopic abundances can be modified because of the activation of the chain of neutron captures starting from the abundant ne and proceeding through na to mg , mg and mg . given the high value of the neutron capture cross section of mg , with respect to those of mg and mg ( see * ? ? ? * ) , neutron captures in the c pocket produce mg and mg , while depleting mg . the details of how the c pocket forms is still unknown although various mechanisms have been proposed ; see @xcite for a wider discussion . in nucleosynthesis studies , the extent of the pocket is usually set as a free parameter with typical values @xmath901/15@xmath69 the mass of the he - intershell @xcite . in intermediate mass stars , the mass of the he - intershell is smaller by about an order of magnitude compared to lower mass stars and hence the importance of the c pocket may be lessened @xcite . as done in previous nucleosynthesis studies @xcite , we artificially include in the post - processing calculation a pmz of constant mass @xmath91 in the 5@xmath8 , @xmath26 model . we chose a proton profile in which the number of protons decreases exponentially with the mass depth below the base of the convective envelope exactly in the same way as described in @xcite . the mass of the he - intershell decreases with evolution and for the solar metallicity model , the final he - shell mass is about 0.001 , so that our pmz region is at maximum 1/10@xmath69 of the he intershell . the inclusion of the pmz produces small percentage differences ( less than @xmath1110% ) for most species , with the exception of p ( 28% ) and the particle @xmath31 ( 104% ) . hence there are no changes to the mg yields with the introduction of a pmz of @xmath91 . this conclusion is consistent with the results obtained by @xcite for the elements si and ti and can be extended to all intermediate - mass elements . there are two reasons for this . first , since elements lighter than iron have very small neutron capture cross sections , as much as 3 orders of magnitude smaller as compared to those of nuclei heavier than iron , their abundances are not strongly affected by the neutron flux in the c pocket . in fact , the changes in the abundances of intermediate mass elements in the c pocket are at maximum of one order of magnitude , while the abundances of heavy elements are produced by up to three orders of magnitudes of their initial values ( see e.g. table 2 of @xcite ) . second , the c pocket is engulfed and diluted ( of factors between 1/20@xmath69 to 1/10@xmath69 ) by the next growing convective pulse , and is thus mixed with material already @xmath5 processed during the previous pulses , and with the ashes of the h - burning shell . during this dilution process the signature on intermediate mass elements of neutron captures in the c pocket is completely lost . as for proton captures occurring in the pmz region just after the mixing of protons has occurred , they are expected to destroy mg only in the upper layer of the pmz where the number of protons is higher than 0.5 ( see figure 1 of @xcite ) . thus they do not produce a strong effect when this region is diluted in the he intershell , unless the proton profile is very different from the one assumed here . we also experiment with varying the mass - loss rate . the results for the @xmath26 case with r75 mass loss are shown in figure  [ m5z02r75 ] . in this figure we observe large differences of a few hundred percent for most species . for the 5@xmath8 , @xmath27 r75 model we use two different choices of the ne @xmath2 reaction rates , as described in figure  [ m5z0001r75 ] . the r75 model has fewer tps than the vw93 case which results in smaller yields , hence the negative values . we see from figure  [ m5z0001r75 ] that changing the reaction rates has only a small effect on the yields , compared to the change induced by varying the mass - loss rate . this was also well demonstrated by @xcite for intermediate mass agb stars of @xmath92 . the species most affected by the change in mass - loss law are na , mg and al , because the abundances of these isotopes depend on the duration of the hbb phase .      with regards to the reaction rates , uncertainties remain related to the proton capture rates for the nena and mgal chains that modify the abundances of these nuclei because of hbb . table  [ tab : mgyields ] shows that updating these proton capture rates from our standard set to those recommended by nacre did not produce any major modifications on the mg isotopes , since variations are only a few percent . the variations are small because the reaction rates in the mgal chain which affect the mg isotopic ratios the most are similar between nacre and our standard choices , with differences typically less than 40% . a detailed study of the impact of the uncertainties of proton capture reactions on the results produced by hot bottom burning on the ne , na , mg and al isotopes is underway ( izzard , lugaro , karakas & iliadis , 2005 , in preparation ) . we discussed in the introduction that major uncertainties are still present in the computation of the stellar models , in particular in relation to the treatment of convection and of convective boundaries . when our results for the 5@xmath8 , @xmath34 model , which are calculated using mlt with @xmath93 , are compared with those produced by a 5@xmath8 , @xmath92 model computed using the `` full spectrum of turbulence '' ( fst ) prescription for convective regions by @xcite , we find that the final abundances of the mg isotopes are lower in the fst case with respect to our case by about 2  dex for mg , 1  dex for mg and 0.4  dex for mg ( including the contribution of radioactive al ) . in particular , in our case , mg and mg are produced in similar abundances by the effect of the ne @xmath2 reactions and deep tdu , while , in the fst case , the production of nuclei of mass a@xmath8326 ( al and mg ) is favored with respect to that of mg by the combined effect of strong hbb and weak tdu ( ventura p. 2005 , private communication ) . these different behaviors should be tested against data from pre - solar grains and , using gce models , against the observations of the mg isotopes in stars , and also the galactic abundance of the radioactive nucleus al , as obtained by the galactic gamma line at 1.809  mev @xcite . @xcite implements a diffusive convective overshoot scheme at all convective borders in his agb models ( see also * ? ? ? * ) , which results in a considerably different stellar structure to our models of the same mass and metallicity . the most significant differences are hotter tps and deeper tdu ( where @xmath94 ) , as well as the mixing of some co core material into the flash - driven convective pocket . if we compare the surface mg mass fractions after the 14@xmath69 tp , we find that these isotopes are enriched by up to 5 times more in herwig s 5@xmath8 , @xmath27 model compared to our equivalent case with the new recommended rates . these differences are much larger than those introduced by the ne @xmath2 capture rates . herwig also reports @xmath95 after 14 tps , whereas after the same number of pulses we find this ratio to be less than unity . this is because hotter tps result in a stronger activation of the ne(@xmath20)mg reaction hence more neutrons are released that are captured by mg to form mg .","summary":"we have studied the effects of varying the mass - loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure , such as the modeling of convection , the inclusion of a partial mixing zone and the definition of convective borders . these uncertainties are found to be much larger than those coming from ne-capture rates , when using our new estimates .","abstract":"we present new rates for the ne)mg and ne mg reactions , with uncertainties that have been considerably reduced compared to previous estimates , and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass asymptotic giant branch ( agb ) stars of different initial compositions . all the models have deep third dredge - up , hot bottom burning and mass loss . calculations have been performed using the two most commonly used estimates of the ne rates as well as the new recommended rates , and with combinations of their upper and lower limits . the main result of the present study is that with the new rates , uncertainties on the production of isotopes from mg to p coming from the ne-capture rates have been considerably reduced . we have therefore removed one of the important sources of uncertainty to effect models of agb stars . we have studied the effects of varying the mass - loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure , such as the modeling of convection , the inclusion of a partial mixing zone and the definition of convective borders . these uncertainties are found to be much larger than those coming from ne-capture rates , when using our new estimates . much effort is needed to improve the situation for agb models ."}
{"article_id":"astro-ph0601645","section_id":"c","document":"the main important result of the present study is that the reduction of the uncertainties on the ne @xmath2 reaction rates has allowed us to considerably reduce the uncertainties coming from these rates on the production of isotopes from mg to p in agb stars of intermediate mass . the uncertainties on the mg yields are now at a level of @xmath96% , much lower than those obtained when using the nacre upper or lower limits . the yields of mg and mg are 20% to 45% and 9% to 16% , respectively , smaller with the new rates , as compared to nacre . the uncertainties have also been reduced for species heavier than mg , where for example , the uncertainty on the production of p in solar metallicity models is now at a level of 35% , much lower than the 400% obtained when using the nacre upper limit . these results are clearly illustrated by figures  [ yield - compare1 ] and  [ yield - compare2 ] and in table  [ tab : mgyields ] . from our analysis it would appear that among the uncertainties related to the stellar models , those coming from the treatment of convection and of the mass loss are the largest . we described earlier that these are enormous when compared to the current uncertainties coming from the ne @xmath2 reaction rates . much effort is needed to improve the situation for agb models , in particular with respect to convection , by trying to evaluate and reduce the uncertainties , perhaps by exploiting all the available observational constraints . our new evaluation of the ne @xmath3 reaction rates will encourage much future work , as these rates are important for many nucleosynthetic processes and sites . the ne(@xmath20)mg reaction is an important source of neutrons both during the final evolutionary stages of massive stars , and during the agb phase of low to intermediate mass stars . it is responsible for the production of heavy s - process elements in these environments @xcite . the new rate and its uncertainties have to be tested in relation to this process . moreover , the smaller uncertainties of the rates presented here with respect to those in nacre , appear to rule out the possibility that the production of the relatively abundant p - only isotopes of mo and ru could be related to a high value of the ne(@xmath20)mg rates @xcite . it is important to study the relative production of mg and mg , as we have done in table  [ tab : mgyields ] , because both spectroscopic observations and the analysis of pre - solar grains are able to separate these two isotopes . also the contribution of radioactive al to the abundance of mg has to be carefully evaluated . in particular , one pre - solar spinel grain ( * ? ? ? * oc2 ) appears to bear the signature of nucleosynthesis in intermediate mass agb stars , with excesses in both mg and mg . a future application of our present work will be to compare our detailed results to the composition of this grain , extending the study to the oxygen isotopic ratios in agb stars and their uncertainties , as these are also measured in the grain .","summary":"we present new rates for the ne)mg and ne mg reactions , with uncertainties that have been considerably reduced compared to previous estimates , and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass asymptotic giant branch ( agb ) stars of different initial compositions . the main result of the present study is that with the new rates , uncertainties on the production of isotopes from mg to p coming from the ne-capture rates have been considerably reduced . much effort is needed to improve the situation for agb models .","abstract":"we present new rates for the ne)mg and ne mg reactions , with uncertainties that have been considerably reduced compared to previous estimates , and we study how these new rates affect the production of the heavy magnesium isotopes in models of intermediate mass asymptotic giant branch ( agb ) stars of different initial compositions . all the models have deep third dredge - up , hot bottom burning and mass loss . calculations have been performed using the two most commonly used estimates of the ne rates as well as the new recommended rates , and with combinations of their upper and lower limits . the main result of the present study is that with the new rates , uncertainties on the production of isotopes from mg to p coming from the ne-capture rates have been considerably reduced . we have therefore removed one of the important sources of uncertainty to effect models of agb stars . we have studied the effects of varying the mass - loss rate on nucleosynthesis and discuss other uncertainties related to the physics employed in the computation of stellar structure , such as the modeling of convection , the inclusion of a partial mixing zone and the definition of convective borders . these uncertainties are found to be much larger than those coming from ne-capture rates , when using our new estimates . much effort is needed to improve the situation for agb models ."}
{"article_id":"astro-ph9902153","section_id":"i","document":"observed samples of galaxy clusters are notoriously contaminated by projection effects ( frenk et al . 1990 ) even when selected with respect to their x - ray emission ( bartelmann & steinmetz 1996 ; van haarlem , frenk & white 1997 ; cen 1997 ) . this is particularly annoying because clusters constitute an important class of cosmological objects , and cleanly defined cluster samples could provide a wealth of cosmological information . not only the definition of clusters within samples , but also observable cluster properties like their richness , x - ray luminosity , gas fraction , degree of substructure , velocity dispersion and the mass estimates derived therefrom can substantially be biased by projection effects . while not solving the principal problem of observing aspherical three - dimensional objects in projection , selection of clusters by mass rather than luminosity might prove a substantial step towards more reliably defined cluster samples . with the advent of weak - lensing techniques and wide - field surveys , mass - selected cluster samples are beginning to come within reach . the tidal field of the total gravitating cluster mass determines the amount of distortion observed in images of background galaxies ( kaiser & squires 1993 ) . a variety of elaborate tools has been developed in the past few years to detect clusters and derive their masses utilising distortions of faint - galaxy samples ( fahlman et al . 1994 ; kaiser 1995 ; kaiser , squires & broadhurst 1995 ; seitz & schneider 1995 ; bartelmann et al .  1996 ; seitz & schneider 1996 ; squires & kaiser 1996 to name just a few ) . in particular , weighted second - order measures of the distortion field in apertures like the _ aperture mass _ statistics ( @xmath1-statistics ) provide means to derive the signal - to - noise ratio @xmath2 of a measurement from the data themselves ( schneider 1996 ) . a possible strategy to use aperture measures like @xmath3 for cluster detection is to move the aperture across a wide data field and monitor @xmath3 and @xmath2 as a function of aperture position . points or regions of high @xmath2 can then be identified as potential clusters , leading to the definition of mass - selected cluster samples . this technique led to a cluster detection in the eso imaging survey ( t.  erben , private communication ) . a further spectacular example of galaxy clusters detected through weak lensing is given by kaiser et al . ( 1998 ) .    strictly speaking , distortions caused by gravitational lensing trace the gravitational tidal field rather than the mass itself . this is due to the fact that a sheet of constant surface mass density added to any given lens does not change the shapes of distorted images , but only their sizes ( the so - called mass - sheet degeneracy ) . therefore , cluster detection techniques based on distortion measurements alone select clusters not by mass , but by the amplitude of their tidal field . keeping this in mind , we will hereafter speak of _ mass - selected _ clusters in that sense . the question then arises , are the cluster samples so obtained any more reliable than , e.g. , cluster samples selected via abell s criterion or x - ray luminosity ? more precisely , what fraction of true three - dimensional clusters is detected that way , and what fraction of the mass - selected samples are spurious detections , either not corresponding to real clusters at all or to clusters outside the desired mass range ? this is the question addressed in this paper using simulated @xmath4-body data , to which we apply for the first time the @xmath3 statistics to construct synthetic cluster samples . we use high - resolution large - scale structure simulations and first identify three - dimensional clusters in real space . we then populate the simulation volume with galaxies , fixing the average mass - to - light ratio . in projection , we apply abell s criterion to construct optically - selected cluster samples for comparison , and the @xmath2-statistics to define mass - selected cluster samples via the gravitational lensing effects of the simulated matter distribution . the quality of the mass - selected samples is then assessed in comparison to that of the optically - selected samples . moreover , we derive masses both from galaxy kinematics and weak lensing to compare the reliability of the different mass estimates .    section  2 details the methods used . section  3 discusses the quality of the cluster samples in terms of completeness and the fraction of spurious detections . in sect .  4 and in the appendix , we give examples for the line - of - sight structure of some representative mass - selected clusters . mass estimates are presented and discussed in sect .  5 , and sect .  6 summarises our conclusions .","summary":"it is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples . we address this question using simulated data , from which we construct synthetic cluster catalogues both with abell s criterion and an aperture - mass estimator sensitive to gravitational tidal effects .","abstract":"selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects . it is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples . we address this question using simulated data , from which we construct synthetic cluster catalogues both with abell s criterion and an aperture - mass estimator sensitive to gravitational tidal effects . the signal - to - noise ratio of the latter allows to some degree to control the properties of the cluster sample . for the first time , we apply the cluster - detection algorithm proposed by schneider to large - scale structure simulations .    we find that selection of clusters through weak gravitational lensing is more reliable in terms of completeness and spurious detections . choosing the signal - to - noise threshold appropriately , the completeness can be increased up to 100% , and the fraction of spurious detections can significantly be reduced compared to abell - selected cluster samples .    we also investigate the accuracy of mass estimates in cluster samples selected by both luminosity and weak - lensing effects . we find that mass estimates from gravitational lensing , for which we employ the-statistics by kaiser et al . , are significantly more accurate than those obtained from galaxy kinematics via the virial theorem ."}
{"article_id":"astro-ph9902153","section_id":"m","document":"in order to study the influence of projection effects on cluster surveys selected by optical and gravitational lensing information , we need simulated data allowing to mimic as accurately as possible the selection of clusters and the determination of their properties , for instance their masses . at the same time , the full phase - space information is required to assess the amount of contamination of selected clusters by intervening matter along the line - of - sight ( hereafter _ los _ ) . for this purpose , we use a large , high - resolution @xmath4-body simulation of a standard cold dark matter ( scdm ) universe . the simulation was carried out within the gif project ( kauffmann et al . 1998 ) using a parallelised version of the hydra code . hydra ( couchman , pearce & thomas 1995 ; couchman , thomas & pearce 1996 ) is an adaptive particle - particle particle - mesh ( ap@xmath5 m ) code . it uses direct force summation in clustered regions , whereas long - range forces and forces within weakly clustered regions are computed on a mesh . the simulation used here transports @xmath6 particles in a periodic comoving cubic volume of @xmath7 , where @xmath8 is the hubble constant in units of @xmath9 . the simulation adopts the approximation to the linear cdm power spectrum ( bond & efstathiou 1984 ) given by @xmath10^{\\nu}]^{2/\\nu}}\\;,\\ ] ] where @xmath11 with the shape parameter @xmath12 , @xmath13mpc , @xmath14mpc , @xmath15mpc , and @xmath16 . the normalisation constant , @xmath17 , is chosen by fixing @xmath18 , the _ rms _ density contrast in spheres of @xmath19mpc radius . it is determined following the procedure outlined by white , efstathiou & frenk ( 1993 ) to meet the present - day local cluster abundance of @xmath20 for rich galaxy clusters . the cosmological parameters are @xmath21 ( i.e.  @xmath22 ) , @xmath23 , @xmath24 , @xmath25 , and @xmath26 . we select a simulation box located at a redshift of @xmath27 to achieve high lensing efficiency on sources at redshifts around unity , where we assume sources to be throughout this paper .    for the analysis of gravitational lensing effects of the simulated matter distribution , namely the @xmath2- and @xmath0-statistics to be introduced below , the high resolution provided by the gif simulations is essential . spatial and mass resolution must be distinguished . the spatial resolution is determined by the comoving force softening length , @xmath28kpc . at one softening length from a particle , the softened force is about half its newtonian value . this limitation is reduced by the high redshift of our simulation box , where the force softening translates to a very small force softening angle , @xmath29 . the mass resolution , which describes the effect of the finite particle number , is given by the particle mass @xmath30 . the finite mass resolution introduces a white noise component into the simulations . this is not negligible for the scdm model because there a higher proportion of the particles is in voids than for models with lower mean density .    since we want to evaluate two different methods for detecting clusters _ in projection _ , we first have to create a sample of _ true _ 3-dimensional ( 3-d ) clusters or groups from the simulation that will serve as a reference set . we extract clusters and groups from the 3-d dark - matter simulation with a friends - of - friends algorithm ( also called group - finder , cf . davis et al .  1985 ) . the friends - of - friends algorithm is based on a percolation analysis : it identifies groups and clusters in the simulation box by linking together all particle pairs separated by less than a fraction @xmath31 of the mean particle separation . each distinct subset of connected particles is then taken as a group or cluster . we have chosen @xmath32 , but the result of group finding does not sensitively depend on the exact choice of @xmath31 .    assuming that the clusters and groups found by the group - finder are completely virialised , we compute their virial masses @xmath33 , defined as the mass enclosed by a sphere with a radius @xmath34 which contains a mean overdensity of 200 times the critical mass density , @xmath35 . for an @xmath23 universe , this radius approximately separates virialised regions from the infall regions of the haloes ( cole & lacey 1996 ) . several reference sets of `` true '' 3-d clusters are then formed by selecting objects with @xmath33 above certain mass thresholds . having dark - matter particles only , we need to populate our simulation with galaxies for optical cluster selection . we employ the following scheme . galaxy luminosities @xmath36 are drawn from a schechter function ( schechter 1976 ) , @xmath37 with parameters @xmath38 and @xmath39 taken from the cfa redshift survey by marzke , huchra & geller ( 1994 ) . the formal divergence for @xmath40 in the number - density integral of the luminosity function is avoided by introducing a lower luminosity cut - off @xmath41 . for the normalisation of the luminosity distribution , we follow the prescription by schechter ( 1976 ) . we calculate a richness estimate by computing the most probable value of the third - brightest absolute magnitude @xmath42 , and then integrate the luminosity distribution from @xmath42 to @xmath43 . frenk et al . ( 1990 ) showed that this yields the dimension - less normalisation factor @xmath44 . the normalisation factor determines the amount of luminous galaxies to be introduced into the simulation . the total mass - to - light ratio of the 3-d clusters turns out to be @xmath45 on average , in qualitative agreement with observations .    assuming that mass follows light in our model universe , galaxies inherit positions and velocities from randomly selected dark - matter particles . in this sense , our constructed galaxy sample is unbiased both in number density and velocity .    transforming luminosities to apparent magnitudes for higher redshifts , we account for the @xmath46 correction . if the spectral energy distribution varies with frequency @xmath47 as a power law with exponent @xmath48 , the additive @xmath46 correction is @xmath49 we choose @xmath50 for the spectral index , which sufficiently well reflects the spectral properties of ordinary galaxies . volume - limited cluster catalogues are then obtained after projecting particle positions onto planes along the three orthogonal axes of the simulation box . groups and clusters in projection are identified with a 2-d version of the friends - of - friends algorithm . we then apply the optical abell criterion ( abell 1958 ) to select galaxy clusters . this widely used cluster detection and classification scheme does not depend on redshift @xmath51 . therefore , it can also be employed at the high redshift of the simulation even though it has traditionally been used only for fairly shallow cluster surveys . briefly , a cluster is classified as an abell cluster if within the abell radius of @xmath52mpc from its centre , and after subtraction of the mean background , the number count of galaxies exceeds a certain value @xmath53 . counting is restricted to the apparent magnitude interval @xmath54 , where @xmath55 denotes the apparent magnitude of the third - brightest cluster galaxy . the actual count @xmath53 is used to assign abell richness classes @xmath56 . for @xmath57 , a cluster has to contain at least @xmath58 galaxies , while @xmath59 and @xmath60 correspond to @xmath61 and @xmath62 , respectively . we also straightforwardly apply abell s criterion to three - dimensional clusters in order to assess the influence of projection effects on richness - class estimates .    for the background subtraction , we follow frenk et al . ( 1990 ) . in order to estimate the background , i.e.  the contamination by foreground and background galaxies in the simulation box , we assume that the number of galaxies contributing to the contamination is proportional to the volume projected onto the cluster . in our case , we expect 8 background galaxies within a cylinder of volume @xmath63 . therefore , a cluster with richness class @xmath64 has to encompass at least 58 galaxies in the appropriate magnitude interval ; 8 background galaxies in addition to the 50 genuine cluster members . since observed column densities towards galaxy clusters will be considerably larger than assumed here , and since the conditions in realistic observations are less controlled than here , projection effects could even be larger in reality . we briefly review in this section relations from gravitational lensing theory important later on . for a derivation cf . schneider , ehlers & falco ( 1992 ) . some remarks on the numerical calculation of lensing properties will also be made . the dimension - less surface mass density @xmath65 ( also called _ convergence _ ) is given by @xmath66 with the critical surface mass density @xmath67 @xmath68 , @xmath69 , and @xmath70 are the angular - diameter distances from the observer to the sources , from the observer to the lens , and from the lens to the sources , respectively . the surface mass density @xmath71 is related to the effective deflection potential @xmath72 through the poisson equation @xmath73 which can be solved for @xmath74 , @xmath75 boundary conditions have to be specified when solving eq . ( [ eqpos ] ) numerically . periodic boundaries are adequate because of the periodicity of the simulation volume .    for numerically computing @xmath74 , the projected particle positions are interpolated on a grid of @xmath76 cells to maintain the high resolution of the @xmath4-body simulation . the resulting surface mass density is scaled with the critical surface mass density ( [ sig_cr ] ) to find the convergence @xmath65 . for a numerically stable and efficient method to convert @xmath65 to @xmath74 , we use a fast poisson solver ( swarztrauber 1984 ) . the efficiency of this method rests on the fast fourier transform ( fft ) leading to an asymptotic operation count of @xmath77 . the algorithm approximates the laplacian on a grid , transforms to fourier space , solves the resulting tri - diagonal system of linear equations , and back - transforms to real space . in contrast to other approaches , the approximation is made here by discretising the equations , which can then be solved exactly by a subsequent discrete fft . having determined the deflection potential @xmath72 , the local properties of the lens , such as the surface mass density @xmath65 and the complex shear @xmath78 , can be expressed in terms of second derivatives of @xmath72 , @xmath79 where indices @xmath80 following commas denote partial derivatives with respect to @xmath81 . galaxy clusters can be selected solely by their mass using the method developed by schneider ( 1996 ) . for detecting dark - matter concentrations through image distortions of faint background galaxies , we define an aperture mass measure @xmath82 as @xmath83 where the integral extends over a circular aperture @xmath84 , and @xmath85 is a continuous weight function depending on the modulus of @xmath86 only , vanishing for @xmath87 . we assume @xmath85 to be a compensated filter function , i.e. @xmath88 for such filter functions , the aperture mass measure @xmath82 can be expressed in terms of the tangential shear component @xmath89 inside a circle with radius @xmath90 ( fahlman et al . 1994 ; schneider 1996 ) @xmath91 where @xmath92 is related to the filter function @xmath93 by @xmath94 in the above equations , the tangential shear @xmath95 at the position @xmath86 relative to position @xmath96 is given by @xmath97\\;,\\ ] ] where @xmath98 is the position angle of @xmath99 . equation  ( [ mapstat ] ) relates the spatially filtered aperture mass @xmath82 to the observable shear field . an estimate for the shear field @xmath100 , and thus for the aperture mass @xmath82 via equation ( [ mapstat ] ) , is provided by the distortions of images of faint background galaxies . the complex ellipticity of galaxy images , @xmath101 , is commonly defined in terms of second moments of the surface - brightness tensor ( schneider & seitz 1995 ) . for sources with elliptical isophotes with axis ratio @xmath102 , the modulus of the source ellipticities is given as @xmath103 , and the phase of the @xmath104 is twice the position angle of the ellipse . it has been demonstrated ( schramm & kaiser 1995 ; seitz & schneider 1997 ) that the ellipticity @xmath101 of a galaxy image is an unbiased estimate of twice the local shear in the case of weak lensing , @xmath105 . if one assumes that the intrinsic orientations of the sources are random , @xmath106 with the average taken over an ensemble of sources , then all average net image ellipticities @xmath107 reflect the gravitational tidal effects of the intervening mass distribution . we draw the source ellipticities from a gaussian probability distribution @xmath108}\\ ,    \\exp\\left(-\\frac{|\\chi^{({\\rm s})}|^2}{\\sigma_\\chi^2}\\right)\\;,\\ ] ] where the width of the distribution is chosen as @xmath109 . we set the number density of the background sources to @xmath110 . the complex image ellipticity @xmath101 can then be calculated in terms of the source ellipticity @xmath104 and the reduced shear @xmath111 by the transformation ( schneider & seitz 1995 ) @xmath112    in analogy to the tangential shear component @xmath113 occurring in ( [ mapstat ] ) , a similar quantity for the image ellipticities can be defined . consider a galaxy image @xmath80 at a position @xmath114 with a complex image ellipticity @xmath115 . the tangential ellipticity @xmath116 of this galaxy relative to the point @xmath96 is then given by schneider ( 1996 ) @xmath117 where @xmath118 and @xmath119 are complex representations of the vectors @xmath120 and @xmath121 . we are now able to estimate the weighted integral ( [ mapstat ] ) as a discrete sum over galaxy images , @xmath122 the dispersion @xmath123 of the aperture mass estimate @xmath82 is found by squaring ( [ map_1 ] ) and taking the expectation value , which leads to @xmath124 finally , the _ signal - to - noise _ ratio @xmath2 at position @xmath96 can be written as @xmath125^{1/2}}\\;. \\label{eq_sn}\\ ] ]      so far , the formalism for aperture mass measures and their signal - to - noise ratios is independent of the choice for the weight function @xmath93 . specialising @xmath93 now , we are led to aperture measures with different merits . two principal choices for the filter function have been suggested in the literature . one leads to the @xmath0-statistics proposed by kaiser ( 1995 ) and first applied by fahlman et al . it gives a lower bound to the average surface mass density @xmath65 within a circle inside an annulus by measuring the distortions of background galaxy images inside the annulus . the @xmath0-statistics will be used in sect . [ zeta ] for constraining the masses of clusters detected through their @xmath2-statistics . the piece - wise constant weight function for the @xmath0-statistics reads ( schneider 1996 ) @xmath126 inserting this weight function into eq . ( [ mapstat ] ) yields @xmath127 where @xmath128 is the distance vector between the point under consideration and @xmath96 , and @xmath129 and @xmath130 are the bounding radii of an annulus around @xmath96 . it can then be shown that @xmath131 is related to the mean convergence @xmath132 in the annulus by @xmath133 @xmath134 being the mean convergence in the circle with radius @xmath129 around @xmath96 . in other words , the @xmath0-statistics constrains the average convergence in a circular aperture through the tangential shear in an annulus surrounding the aperture . since @xmath135 , @xmath131 provides a lower bound to the mean surface mass density enclosed by @xmath129 .    as mentioned before , it is possible to use the image ellipticities @xmath101 of the background galaxies as unbiased estimates of twice the tangential shear , @xmath136 . therefore , the integral in ( [ eq_zeta ] ) can be approximated as a discrete sum over galaxy images , @xmath137    in this study , we want to obtain a lower bound to the total cluster masses . for a meaningful application of the @xmath0-statistics , it is important to include the complete cluster into the measurement . this can be achieved following bartelmann ( 1995 ) . if we apply the @xmath0-statistics to a nested set of annuli with radii @xmath138 , @xmath139 , then the @xmath0-statistics for an annulus with @xmath140 reads @xmath141 where @xmath142 and @xmath143 . on the other hand , the mass @xmath144 in such an annulus is the product of surface mass density times the area , @xmath145 where the area of the annulus is @xmath146 the crucial point is now that the mass contained within a circle of radius @xmath90 is always the sum of the masses contained in annuli with outer radii @xmath147 , irrespective of how the area is decomposed into such rings . keeping this in mind , eqs . ( [ zeta_system ] ) and ( [ mass_rings ] ) can be combined into a system of @xmath148 linear equations with @xmath149 unknowns @xmath150 , where the @xmath150 denote the masses in adjacent rings @xmath151 . the fact that there is one equation less than the number of unknowns reflects the scaling invariance of the surface mass density @xmath65 . assuming that the outermost annulus does not contain any significant convergence , i.e.  @xmath152 , we finally arrive at the following set of equations for the masses @xmath153 enclosed by radii @xmath154 : @xmath155 where @xmath156 is shorthand for @xmath157    of course , a lower bound to the total cluster mass could also be obtained by placing an annulus around the entire cluster and applying the @xmath0-statistics to that annulus only rather than to a set of nested annuli . our approach has two advantages ; first , it yields a profile of @xmath65 which allows to assess the location of the outer cluster boundary , for which we found that @xmath158mpc is an appropriate choice . second , it uses galaxy ellipticity measurements in all annuli rather than the outermost only , thus reducing the noise . however , the errors in the @xmath153 are correlated at successive radii , making an immediate interpretation of the significance at any given radius less transparent . since the @xmath0-statistics is not designed for detecting mass concentrations , its filter function is not optimised for achieving high signal - to - noise ratios , leading to high noise levels in a signal - to - noise map . schneider ( 1996 ) solved this problem by introducing the smooth , continuous weight function @xmath159 in the following , the term @xmath2-statistics refers to the signal - to - noise ratio obtained from eq . ( [ eq_sn ] ) using the filter function @xmath160 , which guarantees low noise in the signal - to - noise ratio map . the parameters @xmath161 , @xmath31 , and @xmath162 are determined once @xmath163 and @xmath164 are specified ; see schneider ( 1996 ) . we choose @xmath165 and @xmath166 in order to achieve high signal - to - noise ratios and evaluate the @xmath2-statistics for an aperture size of 2  arc minutes .","summary":"the signal - to - noise ratio of the latter allows to some degree to control the properties of the cluster sample . for the first time we find that mass estimates from gravitational lensing , for which we employ the-statistics by kaiser et al .","abstract":"selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects . it is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples . we address this question using simulated data , from which we construct synthetic cluster catalogues both with abell s criterion and an aperture - mass estimator sensitive to gravitational tidal effects . the signal - to - noise ratio of the latter allows to some degree to control the properties of the cluster sample . for the first time , we apply the cluster - detection algorithm proposed by schneider to large - scale structure simulations .    we find that selection of clusters through weak gravitational lensing is more reliable in terms of completeness and spurious detections . choosing the signal - to - noise threshold appropriately , the completeness can be increased up to 100% , and the fraction of spurious detections can significantly be reduced compared to abell - selected cluster samples .    we also investigate the accuracy of mass estimates in cluster samples selected by both luminosity and weak - lensing effects . we find that mass estimates from gravitational lensing , for which we employ the-statistics by kaiser et al . , are significantly more accurate than those obtained from galaxy kinematics via the virial theorem ."}
{"article_id":"astro-ph9902153","section_id":"c","document":"we investigated for the first time with simulated data whether mass - selected galaxy cluster samples are more reliable than samples constructed via abell s criterion . selection of clusters by mass is possible through their gravitational lensing effects , in particular through the coherent image distortion patterns imposed on faint galaxies in their background . as mentioned in the introduction , image distortions trace the gravitational tidal field of a lens rather than its mass , and it is in that sense that we speak of `` mass - selected '' cluster samples . the second - order aperture - mass statistics @xmath1 was used which is particularly suitable for detecting dark - matter haloes . the signal - to - noise ratio , @xmath2 , of @xmath3 provides a straightforward detection criterion . we also compared the performance of cluster mass estimators based on cluster - galaxy kinematics and gravitational lensing . our results can be summarised as follows .    1 . as already found in previous studies , abell clusters are severely affected by projection effects . this not only concerns the selection of abell clusters , but also mass estimates based on galaxy kinematics and the virial theorem , indicating that the velocity dispersion is also hampered by projection effects . a second reason for the failure is the fact that the assumption of dynamical equilibrium is not justified in at least some of the clusters . the projection effects are worse for clusters and groups of lower richness class . clusters detected with a high significance @xmath2 of @xmath3 are less affected by projection effects than typical abell - selected clusters . like abell cluster samples , the mass - selected cluster samples are generally incomplete : samples of clusters detected above a certain @xmath2 threshold typically do not encompass all three - dimensional clusters present in the simulation ; some clusters have lower @xmath2 . however , the completeness of the samples can be increased by lowering the @xmath2 threshold . we therefore investigated the effect of varying the @xmath2 threshold on the samples . completeness of @xmath243 can be achieved for massive three - dimensional cluster samples ( @xmath244 ) by varying @xmath245 . then , the samples also contain a substantial fraction of spurious detections , most of which correspond to real clusters with smaller masses . generally , there is a trade - off between completeness and the contamination by spurious detections . more complete cluster samples are more heavily contaminated by spurious clusters , and the balance can be adapted choosing the @xmath2 threshold . it should be noted that the exact thresholds on @xmath2 depend somewhat on the choice of the weight function entering the definition of @xmath2 ( cf .  the discussion in sect .  2 ) . while qualitatively the same trend is also observed in abell - selected cluster samples , the @xmath2-statistics generally performs significantly better than abell s criterion : higher completeness can typically be achieved with a lower fraction of spurious detections . for instance , cluster samples detected at @xmath175 contain all of the most massive clusters in the simulation and 65% spurious detections , while abell samples with richness @xmath174 encompass only about two - thirds of the most massive clusters and 82% spurious detections . 4 .   lensing - based mass estimates are significantly more accurate than mass estimates based on cluster - galaxy kinematics and the virial theorem . virial masses are typically biased high because line - of - sight velocity distributions are broadened by projection effects . lensing also adds up mass in front of and behind the clusters , but the bias is less severe . the standard deviation from the true ( three - dimensional ) mass of the lensing mass estimate is smaller by a factor of three or more than that of the virial mass estimates . it should , however , be noticed that the accuracy of lensing - based mass estimates depends on the depth of the background - galaxy sample and other observational effects . while the mass estimates based on the @xmath0 statistics are accurate to within @xmath246 in our simulations , they may well be less accurate under realistic observational conditions . our study underestimates projection effects because of the limited size of the simulation volume . this affects both the optical and the lensing - based cluster selection . yet it appears that selection of clusters by mass yields more reliable cluster samples than optical cluster selection , and , more importantly , the quality of the samples can be controlled by an objective criterion , namely the signal - to - noise threshold imposed . selection of clusters by their gravitational - lensing effects is comparable to selection by their x - ray luminosity . in essence , both methods measure weighted projections of the newtonian cluster potential along the line - of - sight . however , lensing - based cluster detections only require sufficiently deep imaging of wide fields in optical or near - infrared wave bands , and detection algorithms can then be applied in a straightforward manner . in particular , lensing can detect clusters out to significantly higher redshifts than x - ray surveys . what is more , lensing - based mass estimates do not rely on any assumptions on the composition and physical state of the cluster matter , in contrast to x - ray mass estimates . it can therefore be expected that reliable , mass - selected cluster samples at moderate to high redshifts can be constructed in the near future from upcoming deep , wide - field surveys with a straightforward , well - controlled algorithm , and that the accuracy of cluster mass estimates will generally be substantially improved . lensing - based cluster detection algorithms like that based on the @xmath2-statistics can be utilised for cosmology without reference to actual 3-d clusters . instead , one could define a `` cluster '' operationally as something visible as a sufficiently high peak in an @xmath2 map , and then compare model predictions with observations ( cf . kruse & schneider 1999 ) . if , however , emphasis is laid on clusters as individual entities , it needs to be clarified how well different selection criteria fare in detecting true clusters . our study has shown that selection of clusters by means of gravitational lensing techniques can be adapted such that the resulting samples are superior to abell - selected samples in terms of completeness , spurious detections , and the quality of mass estimates .","summary":"selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects . we find that selection of clusters through weak gravitational lensing is more reliable in terms of completeness and spurious detections . we also investigate the accuracy of mass estimates in cluster samples selected by both luminosity and weak - lensing effects . , are significantly more accurate than those obtained from galaxy kinematics via the virial theorem .","abstract":"selection of galaxy clusters by mass is now possible due to weak gravitational lensing effects . it is an important question then whether this type of selection reduces the projection effects prevalent in optically selected cluster samples . we address this question using simulated data , from which we construct synthetic cluster catalogues both with abell s criterion and an aperture - mass estimator sensitive to gravitational tidal effects . the signal - to - noise ratio of the latter allows to some degree to control the properties of the cluster sample . for the first time , we apply the cluster - detection algorithm proposed by schneider to large - scale structure simulations .    we find that selection of clusters through weak gravitational lensing is more reliable in terms of completeness and spurious detections . choosing the signal - to - noise threshold appropriately , the completeness can be increased up to 100% , and the fraction of spurious detections can significantly be reduced compared to abell - selected cluster samples .    we also investigate the accuracy of mass estimates in cluster samples selected by both luminosity and weak - lensing effects . we find that mass estimates from gravitational lensing , for which we employ the-statistics by kaiser et al . , are significantly more accurate than those obtained from galaxy kinematics via the virial theorem ."}
{"article_id":"0809.2286","section_id":"i","document":"in this paper we discuss the characteristics of the parton bubble model ( pbm)@xcite and connect them to related characteristics of the glasma flux tube model ( gftm)@xcite . we will then proceed to use the pbm to discuss and explain the observed ridge phenomenon by adding appropriate trigger requirements to the pbm . a successful comparison with experimental data is made . we then show how the pbm can be used to search for strong cp violations or chern - simons topological charge@xcite . we develop four charged particle correlations that can be used to detect the presence of these color electric and color magnetic fields . then we show that existing published analyses can be used to already provide strong experimental evidence for the longitudinal color electric fields . our predicted specific four charged particle correlations can be used to search for experimental evidence for the color magnetic fields . our interest in and the eventual development of the pbm goes back many years to the early nineteen eighties . van hove s work@xcite in the early eighties considered the bubbles as small droplets of quark - gluon plasma ( qgp ) assumed to be produced in ultra - relativistic collisions of hadrons and/or nuclei . his work recognized that experimental detectors only see what is emitted in the final state at kinetic freezeout . therefore final state predictions of his string model work on plasma bubbles or any other theory required specific convincing predictions that are observable in the final state which can be measured by experiment . his work predicted that the final state rapidity distribution dn / dy of hadrons would exhibit isolated maxima of width @xmath4 ( single bubble ) or rapidity bumps of a few units ( due to those cases producing a few bubbles ) . these rapidity regions would also contain traditional signals of qgp formation . even this early work by van hove needed his bubbles near the surface of the final state fireball in order to experimentally measure the particles emitted in the final state at kinetic freezeout . we and other searched for these van hove bubbles , but no one ever found any significant evidence for them . our next paper@xcite was our final attempt to make a theoretical treatment of the single bubble case ( similar to the van hove case ) which could be experimentally verified . it is possible that with enough statistics one in principle could find single to a few bubble events . we developed a number of event generators which could possibly provide evidence for striking signals resulting from these bubbles . one should note that in that paper we had included in sec . 11 mathematical expressions describing how charged pions are effected by strong color electric and color magnetic fields which are present and parallel in a cp - odd bubble of metastable vacuum . this section was motivated by the work of kharzeev and pisarski@xcite . for example eq . 3 - 4 of the section show the boosts of the @xmath5 and the @xmath6 we estimated . thus in 2000 we were already interested in and were investigating and publishing predictions for this phenomenon . when we considered the rhic quantum interference data in 2000@xcite it became clear that the fireball surface was rapidly moving outward . this implied a very large phase space region covered by the fireball , and also implied that it would be very unlikely for there to be only one isolated bubble ( small sourcesize ) with a large amount of energy sitting on the surface . it seemed more likely that there would be many bubbles or gluonic hot spots around the expanding surface . this led to a paper@xcite which was our earlier version of ref.@xcite . in that paper we concluded that the behavior of the hanbury - brown and twiss ( hbt ) measurements@xcite should be interpreted as evidence of a substructure of bubbles located on the surface of the final state fireball in the central rapidity region at kinetic freezeout . the hbt radii were decreasing almost linearly with transverse momentum and implying to us a source size of @xmath72 fm radii bubbles were on the surface and could be selected for if we considered transverse momenta above 0.8 gev / c . these momenta would allow sufficient resolution to resolve individual bubbles of @xmath72 fm radii . we further concluded that these hbt quantum interference observations were likely due to phase space focusing of the bubbles pushed by the expanding fireball . thus the hbt measurements of source size extrapolated to transverse momenta above 0.8 gev / c were images of the bubbles . the hbt correlation has the property of focusing these images on top of each other for a ring of bubbles transverse to and centered on the beam forming an average hbt radius . thus our model was a ring of bubbles sitting on the freezeout surface with average size @xmath72 fm radius perpendicular to the beam at mid - rapidity . the phase space focusing would also lead to angular correlations between particles emitted by the bubbles and be observable . 1 of that paper shows such a bubble geometry . for the background particles that account for particles in addition to the bubble particles we used unquenched hijing@xcite with its jets removed . we assumed that most of the jets were eliminated from the central events because of the strong jet quenching observed at rhic@xcite . we investigated the feasibility of using charged particle pair correlations as a function of angles which should be observable due to the phase space focusing of the particles coming from individual bubbles . at that point we fully expected that these correlations would be observable in the star detector@xcite at rhic if one analyzed central au + au collisions . correlation analyses are powerful tools in detecting substructures . historically substructures have played an important role in advancing our understanding of strong ( non perturbative ) interactions . our earlier paper explained the general characteristics of the angular correlation data , and was also consistent with hbt measurements in a qualitative manner . this motivated us to develop a reasonably quantitative model , the parton bubble model@xcite which is discussed in the following .      in this publication@xcite we developed a qcd inspired parton bubble model ( pbm ) for central ( impact parameter near zero ) high energy heavy ion collisions at rhic . the pbm is based on a substructure consisting of a single ring of a dozen adjoining 2-fm - radius bubbles ( gluonic hot spots ) transverse to the collider beam direction , centered on the beam , and located at or near mid - rapidity . the ring resides on the fireball blast wave surface ( see fig . 1 of ref.@xcite ) . we assumed these bubbles are likely the final state result of quark - gluon - plasma ( qgp ) formation since the energy densities produced experimentally are greater than those estimated as necessary for formation of a quark - gluon - plasma . thus this is the geometry for the final state kinetic freezeout of the qgp bubbles on the surface of the expanding fireball treated in a blast wave model . the twelve bubble ring creates the average behavior of bubble formation driven by the energy density near the surface of the expanding fire ball of the blast wave ; that forms the final state surface bubbles that emit the final state particles at kinetic freezeout . one should note that the blast wave surface is moving at its maximum velocity at freezeout ( 3c/4 ) . for central events each of the twelve bubbles have 3 - 4 partons per bubble each at a fixed @xmath8 for a given bubble . the transverse momentum ( @xmath2 ) distribution of the charged particles is similar to pqcd but has a suppression at high @xmath2 like the data . the bubble ring radius of our model was estimated by blast wave , hbt and other general considerations to be approximately 8 fm . the bubbles emit correlated charged particles at final - state kinetic freezeout where we select a @xmath2 range ( 0.8 gev / c @xmath1 @xmath2 @xmath1 4.0 gev / c ) in order to increase signal to background . the 0.8 gev / c @xmath2 cut increases the resolution to allow resolving individual bubbles which have a radius of @xmath72 fm . this space momentum correlation of the blast wave provides us with a strong angular correlation signal . pythia fragmentation functions@xcite were used for the bubbles fragmentation that generate the final state particles emitted from the bubbles . the pbm explained the high precision au + au central ( 0 - 10% ) collisions at @xmath9 200 gev@xcite ( the highest rhic energy ) . the pbm fit to the angular correlation data was reasonably quantitative to within a few percent ( see sec . 4 of ref.@xcite ) . the correlation functions we employed ( like the hbt correlation functions ) have the property that for the difference in angles ( difference of momentum for hbt ) these correlations will image all 12 bubbles on top of each other . this leads to average observed angles of approximately @xmath10 in @xmath11 , @xmath12 in @xmath13 , originating from a source size of about @xmath72 fm radius which is consistent with the hbt correlation . thus the pbm generates @xmath11 vs @xmath13 charged - particle - pair correlations for charged particles with @xmath2 in the range 0.8 gev / c to 4.0 gev / c as displayed in fig . 1 . see sec . 4 of ref.@xcite for a reasonably quantitative successful comparison with data . furthermore the model results were consistent with the hanbury - brown and twiss ( hbt ) observations@xcite that the observed source radii determined by quantum statistical interference were reducing by a considerable factor with increasing transverse momentum ( @xmath2 ) . the hbt radii are interpreted to reduce from @xmath76 fm at @xmath2 @xmath70.2 gev / c to @xmath72 fm at @xmath2 @xmath71 gev / c for our @xmath2 range . the generally accepted explanation for this behavior is that as @xmath2 increases radial flow increasingly focused the viewed region of the final state into smaller volumes . if just one small hbt size bubble were emitting all the correlated particles , this phenomena would lead to large spikes of particles emitted at one limited @xmath8 angular region in individual events . this is definitely not observed in the au + au or other collision data at rhic . therefore , a distributed ring of small sources around the beam as assumed in the pbm is necessary to explain both the hbt results@xcite and the correlation data@xcite . the particles emitted from the same bubble are virtually uncorrelated to particles emitted from any other bubble except for momentum conservation requirements . an away side peak in the total correlation is built up from momentum conservation between the bubbles . the pbm was also recently extended to pbme@xcite which is identical to the pbm for central collisions ( 0 - 5% ) . for centralities running from 30 - 80% jet quenching is not strong enough to make jets negligible therefore , a jet component was added which was based on hijing calculations . this jet component accounts for more of the correlation as one moves toward peripheral bins , and explains all of it for the most peripheral collisions . the pbme explained in a reasonably quantitative manner ( within a few percent ) the behavior of the recent quantitative experimental analysis of charge pair correlations as a function of centrality@xcite . this further strengthened the substantial evidence for bubble substructure . the agreement of the pbm and the pbme surface emission models with experimental analyses strongly implied that at kinetic freezeout the fireball was dense and opaque in the central region and most centralities ( except the peripheral region ) in the intermediate transverse momentum region ( 0.8 @xmath1 @xmath2 @xmath1 4.0 gev / c ) . thus we conclude that the observed correlated particles are both formed and emitted from or near the surface of the fireball . in the peripheral region the path to the surface is always small .    in the pbm and the pbme the bubbles are produced in large numbers , are most symmetric , and have unusual features in the most central collisions that can be related to the gftm . therefore the central region pbm is the model most suitable for comparing to the gftm . the pbm fit to the central production au + au correlation data@xcite which was observed in the star tpc detector reasonably quantitatively fit the data . the average observed angles were approximately @xmath10 in @xmath11 and @xmath12 in @xmath13 , originating from a source size of @xmath72 fm radius . thus the pbm generates @xmath11 vs @xmath13 charged - particle - pair correlations for the charged particles with @xmath2 in the range 0.8 gev / c to 4.0 gev / c as displayed in fig . 1 of the present paper . 4 of ref.@xcite for a reasonably quantitative successful comparison with data ( within a few percent of the observed correlations ) . the ci correlation used in fig . 1 and the pbm@xcite is defined below . the two different types of charged - particle - pair correlations are the unlike - sign charge pairs ( us ) and the like - sign charge pairs ( ls ) . the charge - independent correlation ( ci ) is defined as the correlation made up of charged - particle - pairs independent of what the sign is , which is the average of the us plus the ls correlations . thus ci = ( us + ls)/2 . therefore the ci is the total charge pair correlation observed in the experimental detection system within its acceptance . we utilize a two particle correlation function in the two dimensional ( 2-d ) space where @xmath8 is the azimuthal angle of a particle measured in a clockwise direction about the beam . @xmath14 which is the difference of the psuedorapidity of the pair of particles ] of @xmath11 versus @xmath13 ( see ref.@xcite sec . the pbm generated the two dimensional differences for a pair of particles @xmath11 versus @xmath13 contributing to the correlation function . the sum over all pairs coming from the same event and then summed over all events is our numerator in the correlation function . we then divide this numerator by a sum over all pairs coming from created mixed pairs where , the two particles are produced in different events , and then summed over all mixed events . the sum over all the particle pair entries in the mixed event denominator is normalized to equal the sum over all particle pairs in the numerator . this rescales the ci such that the ratio of the numerator divided by the denominator has a mean of 1 . the ci was generated for @xmath0 = 200 gev central ( 0 - 5% ) au + au collisions in the @xmath2 range 0.8 gev / c to 4.0 gev / c at rhic . when the ci was compared to the corresponding experimental analyses@xcite a reasonably quantitative agreement within a few percent of the observed ci was attained . see ref.@xcite sec . 4.2 , ref.@xcite sec . v , and ref.@xcite sec . vi b. the ci correlation for the 0 - 5% centrality bin is shown in fig . this analysis and our previous work@xcite was done without using a jet trigger . in fact jet production in the central region was negligible due to strong jet quenching@xcite . as one can see in fig . 1 the central ci correlation of @xmath11 on the near side ( @xmath11 @xmath1 @xmath15 ) , is sharp and approximately jetlike at all @xmath13 . in contrast the @xmath13 dependence is relatively flat . in the central production the average observed angles are approximately @xmath10 in @xmath11 and @xmath12 in @xmath13 . it is of interest to note that the sharp jetlike collimation in @xmath11 persists at all centralities ( 0 - 80% ) . the elongation in @xmath13 persists in the 0 - 30% centrality range and then decreases with decreasing centrality becoming jetlike in the peripheral bins . these characteristics are in reasonable quantitative agreement with the fits of the pbm and the pbme to experimental data analyses@xcite . the difference of the us and ls correlations is defined as the charge - dependent ( cd ) correlation ( cd = us - ls ) . the 2-d experimental cd correlation for centralities ( 0 - 80% ) has a jetlike shape which is consistent with pythia jets ( vacuum fragmentation ) for all centralities . this clearly implies that both particle hadroniztion and emission occur from the fireball surface region as explained in ref.@xcite sec . a glasma flux tube model ( gftm)@xcite that had been developed considers that the wavefunctions of the incoming projectiles , form sheets of color glass condensates ( cgc)@xcite that at high energies collide , interact , and evolve into high intensity color electric and magnetic fields . this collection of primordial fields is the glasma@xcite , and initially it is composed of only rapidity independent longitudinal color electric and magnetic fields . an essential feature of the glasma is that the fields are localized in the transverse space of the collision zone with a size of 1/@xmath16 . @xmath16 is the saturation momentum of partons in the nuclear wavefunction . these longitudinal color electric and magnetic fields generate topological chern - simons charge@xcite which becomes a source for particle production . the transverse space is filled with flux tubes of large longitudinal extent but small transverse size @xmath7@xmath17 . particle production from a flux tube is a poisson process , since the flux tube is a coherent state . as the partons emitted from these flux tubes locally equilibrate , transverse flow builds due to the radial flow of the blast wave@xcite . the flux tubes that are near the surface of the fireball get the largest radial flow and are emitted from the surface . as in the parton bubble model these partons shower and the higher @xmath2 particles escape the surface and do not interact . these flux tubes are in the present paper considered strongly connected to the bubbles of the pbm . the method used to connect the pbm and the gftm is described and discussed in the next subsection i d . @xmath16 is around 1 gev / c thus the transverse size of the flux tube is about 1/4 fm . the flux tubes near the surface are initially at a radius @xmath75 fm . the @xmath8 angle wedge of the flux tube is @xmath71/20 radians or @xmath7@xmath18 . thus the flux tube initially has a narrow range in @xmath8 . the large width in the @xmath13 correlation which in the pbm depended on the large spread in @xmath13 of the bubble partons results from the independent longitudinal color electric and magnetic fields that created the glasma flux tubes . how much of these longitudinal color electric and magnetic fields are still present in the surface flux tubes when they have been pushed by the blast wave will be a speculation of this paper for measuring strong cp violation ?    it has been noted that significant features of the pbm that generated final state correlations which fit the experimentally observed correlation data@xcite are similar to those predicted by the gftm@xcite . therefore in the immediately following subsection we assume a direct connection of the pbm and the gtm , give reasons to justify it , and then discuss its consequences , predictions and successes . the successes of the pbm have strongly implied that the final state surface region bubbles of the pbm represent a significant substructure . in this subsection we show that the characteristics of our pbm originally developed to fit the precision star au + au correlation data in a manner consistent with the hbt data ; implies that the bubble substructure we originally used to fit these previous data is closely related to the gftm . a natural way to connect the pbm bubbles to the gftm flux tubes is to assume that the final state at kinetic freezeout of a flux tube is a pbm final state bubble . thus the initial transverse size of a flux tube @xmath71/4 fm has expanded to the size of @xmath72 fm at kinetic freezeout . with this assumption we find consistency with the theoretical expectations of the gftm . we can generate and explain the triggered ridge phenomenon and data ( see sec . ii ) , thus implying the ridge is connected to the bubble substructure . we can predict and obtain very strong evidence for the color electric field of the glasma from comparing our multi - particle charged particle correlation predictions , and existing experimental correlation publications ( see sec . we have also predicted correlations which can be used to search for evidence for the glasma color magnetic field ( sec . of course an obvious question that arises is that since a flux tube is an isolated system does a pbm bubble , that we assume is the final state of a flux tube at kinetic freezeout , also act as an isolated system when emitting the final state particles ? the near side correlations signals since the original pbm@xcite have always come virtually entirely from particles emitted from the same bubble . thus each bubble has always acted as an isolated system similar to the behavior of a flux tube .","summary":"in an earlier paper we developed a parton bubble model ( pbm ) for rhic , high - energy heavy - ion collisions . pbm was based on a substructure of a ring of localized bubbles ( gluonic hot spots ) which initially contain 3 - 4 partons composed of almost entirely gluons . the bubble ring was perpendicular to the collider beam direction , centered on the beam , at midrapidity , and located on the expanding fireball surface of au + au central collisions ( 0 - 10% ) at=200 gev . the bubbles emitted correlated particles at kinetic freezeout , leading to a lumpy fireball surface . for a selection of charged particles ( 0.8 gev / c  4.0 gev / c ) , the pbm reasonably quantitatively ( within a few percent ) explained high precision rhic experimental correlation analyses in a manner which was consistent with the small observed hbt source size in this transverse momentum range . we demonstrated that surface emission from a distributed set of surface sources ( as in the pbm ) was necessary to obtain this consistency . a glasma flux tube model ( gftm ) that formed longitudinal flux tubes in the transverse plane of two colliding sheets of color glass condensate ( cgc ) , which pass through one another had been developed . we consider the equivalent characteristics of the pbm and gftm and connect the two models . when one considers a 3 - 4 gev / c transverse momentum tagged charged particle in combination with another intermediate transverse momentum charged particle in the pbm , the ridge correlation is generated and explained . in the gftm the longitudinal color electric and magnetic fields have a non - zero topological charge density . we also show that from previously published analyses of experimental data there is already strong evidence for the longitudinal color electric fields , and predict correlations which can be used to search for color magnetic field effects .   ","abstract":"in an earlier paper we developed a parton bubble model ( pbm ) for rhic , high - energy heavy - ion collisions . pbm was based on a substructure of a ring of localized bubbles ( gluonic hot spots ) which initially contain 3 - 4 partons composed of almost entirely gluons . the bubble ring was perpendicular to the collider beam direction , centered on the beam , at midrapidity , and located on the expanding fireball surface of au + au central collisions ( 0 - 10% ) at=200 gev . the bubbles emitted correlated particles at kinetic freezeout , leading to a lumpy fireball surface . for a selection of charged particles ( 0.8 gev / c  4.0 gev / c ) , the pbm reasonably quantitatively ( within a few percent ) explained high precision rhic experimental correlation analyses in a manner which was consistent with the small observed hbt source size in this transverse momentum range . we demonstrated that surface emission from a distributed set of surface sources ( as in the pbm ) was necessary to obtain this consistency . a glasma flux tube model ( gftm ) that formed longitudinal flux tubes in the transverse plane of two colliding sheets of color glass condensate ( cgc ) , which pass through one another had been developed . these sheets create boost invariant flux tubes of longitudinal color electric and magnetic fields . a blast wave gives the tubes near the surface transverse flow in the same way it gave transverse flow to the bubbles in the pbm . in this paper we consider the equivalent characteristics of the pbm and gftm and connect the two models . the pbm results discussed above were all obtained without a jet trigger . therefore while investigating the ridge in this paper we add a jet trigger to the pbm . when one considers a 3 - 4 gev / c transverse momentum tagged charged particle in combination with another intermediate transverse momentum charged particle in the pbm , the ridge correlation is generated and explained . in the gftm the longitudinal color electric and magnetic fields have a non - zero topological charge density . these fields cause a local strong cp violation which effects charged particle production coming from quarks and anti - quarks created in the tube or bubble . for investigating these phenomena we use the pbm alone , without a jet trigger . we developed four charged particle correlations which show this strong cp violation effect and accumulate from bubble to bubble independent of whether particles are pushed or pulled ( by the color electric field ) , and rotated in a right or left handed direction ( by the color magnetic field ) . we also show that from previously published analyses of experimental data there is already strong evidence for the longitudinal color electric fields , and predict correlations which can be used to search for color magnetic field effects .    # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )"}
{"article_id":"0809.2286","section_id":"i","document":"in this article we have made a direct connection between our parton bubble model ( pbm@xcite ) and the glasma flux tube model ( gftm)@xcite ) . in the gftm a flux tube is formed right after the initial collision of the au + au system . this flux tube extends over many units of pseudorapidity ( @xmath13 ) . in the pbm this flux tube is approximated by a sum of partons which are distributed over this same large @xmath13 region . a blast wave gives the tubes near the surface transverse flow in the same way it gave flow to the bubbles in the pbm . this means the transverse momentum ( @xmath2 ) distribution of the flux tube is directly translated to the @xmath2 spectrum of the pbm . initially the transverse space is filled with flux tubes of large longitudinal extent but small transverse size @xmath7@xmath17 . the flux tubes that are near the surface of the fireball get the largest radial flow and are emitted from the surface . as in the parton bubble model these partons shower and the higher @xmath2 particles escape the surface and do not interact . @xmath16 is around 1 gev / c thus the size of the flux tube is about 1/4f initially . the flux tubes near the surface are initially at a radius @xmath75 fm . the @xmath8 angle wedge of the flux tube @xmath7 1/20 radians or @xmath7@xmath18 . in sec . i d ( also see sec . i c ) we connect the gftm to the pbm ( see sec . i b ) : by assuming the bubbles are the final state of a flux tube at kinetic freezeout , and discussing evidence for this connection which is further developed in sec . ii and sec . iii .    with the connection of the pbm to the gftm two new predictions become possible for our pbm . the first is related to the fact that the blast wave radial flow given to the flux tube depends on where the tube is initially in the transverse plane of the colliding au + au system . the tube gets the same radial boost all along its longitudinal length . this means that there is correlated @xmath2 among the partons of the bubble . in this paper we consider predictions we can make in regard to interesting topics and comparisons with relevant data which exist by utilizing the parton bubble model ( pbm@xcite ) , and its features related to the glasma flux tube model ( gftm)@xcite ) . topic 1 : the ridge is treated in sec . topic 2 : strong cp violation ( chern - simons topological charge ) is treated in sec . we show in sec . ii that if we trigger on particles with 3 to 4 gev / c and correlate this trigger particle with an other charged particle of greater than 1.1 gev / c , the pbm can produce a phenomenon very similar to the ridge@xcite . ( see figs . 2 - 8 ) . we then selected charged particles inside the ridge and predicted the correlation that one should observe when compared to the average charged particles of the central au + au collisions at @xmath0 = 200 gev@xcite .    in sec . ii d ( comparison to data ) : triggered experimental angular correlations showing the ridge were presented at quark matter 2006@xcite . figure 7 shows the experimental @xmath11 vs. @xmath13 ci correlation for 0 - 10% central au + au collisions at @xmath0 = 200 ; requiring one trigger particle @xmath2 between 3 to 4 gev / c and an associated particle @xmath2 above 2.0 gev / c . the yield is corrected for the finite @xmath13 pair acceptance .    for the pbm generator , we then form a two charged particle correlation between one charged particle with a @xmath2 between 3.0 to 4.0 gev / c and another charged particle whose @xmath2 is geater than 2.0 gev / c . these are the same trigger conditions as in ref.@xcite which is shown in fig . 7 , that shows the corrected pair yield in the central data . 8 shows the correlation function generated by the pbm which does not depend on the number of events analyzed . the two figures were shown to be in reasonable agreement when compared as explained previously in sec . ii d. in fig . 9 we show the ridge signal predicted by the pbm for very similar data but with 0 - 5% centrality . figure 10 shows the extraction of the jet signal . explanations are given in the text . the second prediction is a development of a predictive pionic measure of the strong cp violation . the gftm flux tubes are made up of longitudinal color electric and magnetic fields which generate topological chern - simons charge@xcite through the @xmath3 term that becomes a source of cp violation . the color electric field which points along the flux tube axis causes an up quark to be accelerated in one direction along the beam axis , while the anti - up quark is accelerated in the other direction . so when a pair of quarks and anti - quarks are formed they separate along the beam axis leading to a separated @xmath5 and @xmath6 pair along this axis . the color magnetic field which also points along the flux tube axis ( which is parallel to the beam axis ) causes an up quark to rotate around the flux tube axis in one direction , while the anti - up quark rotates in the other direction . so when a pair of quarks and anti - quarks are formed they will pickup or lose transverse momentum . these changes in @xmath2 will be transmitted to the @xmath5 and @xmath6 pairs . the above pionic measures of strong cp violation are used to form correlation functions based on four particles composed of two pairs which are opposite sign charge - particle - pairs that are paired and binned . these four particle correlations accumulate from bubble to bubble by particles that are pushed or pulled ( by the color electric field ) and rotated ( by the color magnetic field ) in a right or left handed direction . the longitudinal color electric field predicts aligned pairs in a pseudorapidity or @xmath13 measure . the longitudinal color magnetic field predicts anti - aligned pairs in a transverse momentum or @xmath45 measure . the observations of these correlations would be a strong confirmation of this theory . the much larger unlike - sign pairs than like - sign pairs in the pbm and the data ; and the strong dip of the ci correlation at small @xmath13 ( see fig . 1 and sec . iii c for full details ) shows very strong evidence supporting the color electric alignment prediction in the @xmath0 = 200 gev central au + au collision data analyses at rhic@xcite . this highly significant dip ( @xmath7@xmath38 ) means that like - sign pairs are removed as one approaches the region @xmath13 = @xmath11 = 0.0 . thus this is very strong evidence for the predicted effect of the color electric field . the color magnetic anti - aligned pairs in the transverse momentum prediction , treated in sec . iii c as of now has not been observed or looked for . however our predicted specific four charged particle correlations can be used to search for experimental evidence for the color magnetic fields . our success in demonstrating strong experimental evidence for the expected color electric field effects from previously published data suggests that the unique detailed correlations we have presented for searching for evidence for the predicted color magnetic field effects should be urgently investigated . if we are lucky and the predicted color magnetic effects can be confirmed experimentally we would have strong evidence for the following :    \\1 ) cp is violated in the strong interaction in isolated local space time regions where topological charge@xcite is generated . \\2 ) the glasma flux tube model ( gftm ) which was evolved from the color glass condensate ( cgc ) would be found to be consistent with a very significant experimental check . \\3 ) the parton bubble model event generator ( pbm ) is clearly closely connected to the gftm . the bubble substructure strongly supported by the pbm is likely due to the final state of the flux tube at kinetic freezeout .","summary":"these sheets create boost invariant flux tubes of longitudinal color electric and magnetic fields . a blast wave gives the tubes near the surface transverse flow in the same way it gave transverse flow to the bubbles in the pbm . in this paper we developed four charged particle correlations which show this strong cp violation effect and accumulate from bubble to bubble independent of whether particles are pushed or pulled ( by the color electric field ) , and rotated in a right or left handed direction ( by the color magnetic field ) .","abstract":"in an earlier paper we developed a parton bubble model ( pbm ) for rhic , high - energy heavy - ion collisions . pbm was based on a substructure of a ring of localized bubbles ( gluonic hot spots ) which initially contain 3 - 4 partons composed of almost entirely gluons . the bubble ring was perpendicular to the collider beam direction , centered on the beam , at midrapidity , and located on the expanding fireball surface of au + au central collisions ( 0 - 10% ) at=200 gev . the bubbles emitted correlated particles at kinetic freezeout , leading to a lumpy fireball surface . for a selection of charged particles ( 0.8 gev / c  4.0 gev / c ) , the pbm reasonably quantitatively ( within a few percent ) explained high precision rhic experimental correlation analyses in a manner which was consistent with the small observed hbt source size in this transverse momentum range . we demonstrated that surface emission from a distributed set of surface sources ( as in the pbm ) was necessary to obtain this consistency . a glasma flux tube model ( gftm ) that formed longitudinal flux tubes in the transverse plane of two colliding sheets of color glass condensate ( cgc ) , which pass through one another had been developed . these sheets create boost invariant flux tubes of longitudinal color electric and magnetic fields . a blast wave gives the tubes near the surface transverse flow in the same way it gave transverse flow to the bubbles in the pbm . in this paper we consider the equivalent characteristics of the pbm and gftm and connect the two models . the pbm results discussed above were all obtained without a jet trigger . therefore while investigating the ridge in this paper we add a jet trigger to the pbm . when one considers a 3 - 4 gev / c transverse momentum tagged charged particle in combination with another intermediate transverse momentum charged particle in the pbm , the ridge correlation is generated and explained . in the gftm the longitudinal color electric and magnetic fields have a non - zero topological charge density . these fields cause a local strong cp violation which effects charged particle production coming from quarks and anti - quarks created in the tube or bubble . for investigating these phenomena we use the pbm alone , without a jet trigger . we developed four charged particle correlations which show this strong cp violation effect and accumulate from bubble to bubble independent of whether particles are pushed or pulled ( by the color electric field ) , and rotated in a right or left handed direction ( by the color magnetic field ) . we also show that from previously published analyses of experimental data there is already strong evidence for the longitudinal color electric fields , and predict correlations which can be used to search for color magnetic field effects .    # 1#2#3#4#1 * # 2 * , # 3 ( # 4 )"}
{"article_id":"1603.09502","section_id":"i","document":"in the late 1980s the idea of using _ argumentation _ to model nonmonotonic reasoning emerged ( see @xcite as well as @xcite for excellent overviews ) . nowadays argumentation theory is a vibrant subfield of artificial intelligence , covering aspects of knowledge representation , multi - agent systems , and also philosophical questions . among other approaches which have been proposed for capturing representative patterns of inference in argumentation theory @xcite , dung s abstract argumentation frameworks ( afs ) @xcite play an important role within this research area . at the heart of dung s approach lie the so - called _ argumentation semantics _ @xcite for an excellent overview ) . given an af @xmath0 , which is set - theoretically just a directed graph encoding arguments and attacks between them , a certain argumentation semantics @xmath1 returns acceptable sets of arguments @xmath2 , so - called @xmath1-_extensions_. each of these sets represents a reasonable position w.r.t . @xmath0 and @xmath1 .    over the last 20 years a series of abstract argumentation semantics were introduced . the motivations of these semantics range from the desired treatment of specific examples to fulfilling a number of abstract principles . the comparison via abstract criteria of the different semantics available is a topic which emerged quite recently in the community ( @xcite can be seen as the first paper in this line ) . our work takes a further step towards a comprehensive understanding of argumentation semantics . in particular , we study the following question : do we really need the entire af @xmath0 to compute a certain argumentation semantics @xmath1 ? in other words , is it possible to unambiguously determine acceptable sets w.r.t . @xmath1 , given only partial information of the underlying framework @xmath0 . in order to solve this problem let us start with the following reflections :    1 .   as a matter of fact , one basic requirement of almost all existing semantics is that of conflict - freeness , i.e. arguments within a reasonable position are not allowed to attack each other . consequently , knowledge about conflict - free sets is an essential part for computing semantics . 2 .   the second step is to ask the following : which information on top on conflict - free sets has to be added ? imagine the set of conflict - free sets given by @xmath3 . consequently , there has to be at least one attack between @xmath4 and @xmath5 . unfortunately , this information is not sufficient to compute any standard semantics ( except naive extensions , which are defined as @xmath6-maximal conflict - free sets ) since we know nothing precise about the neighborhood of @xmath4 and @xmath5 . the following three afs possess exactly the mentioned conflict - free sets , but differ with respect to other + ( a1 ) at ( -0.6,0 ) [ circle , thick , draw , label = left:@xmath7@xmath4 ; ( b1 ) at ( 0.4,0 ) [ circle , thick , draw]@xmath5 ; + ( a2 ) at ( 2,0 ) [ circle , thick , draw , label = left:@xmath8 @xmath4 ; ( b2 ) at ( 3.0,0 ) [ circle , thick , draw ] @xmath5 ; + ( a3 ) at ( 4.6,0 ) [ circle , thick , draw , label = left:@xmath9 @xmath4 ; ( b3 ) at ( 5.6,0 ) [ circle , thick , draw ] @xmath5 ; + ( a1 ) to [ thick , bend right ] ( b1 ) ; ( b2 ) to [ thick , bend right ] ( a2 ) ; ( a3 ) to [ thick , bend right ] ( b3 ) ; ( b3 ) to [ thick , bend right ] ( a3 ) ; 3 . the final step is to try to minimize the added information . that is , which kind of knowledge about the neighborhood is somehow dispensable in the light of computation ? clearly , this will depend on the considered semantics . for instance , in case of stage semantics @xcite , which requests conflict - free sets of maximal range , we do not need any information about incoming attacks . this information can not be omitted in case of admissible - based semantics since incoming attacks require counterattacks . the above considerations motivate the introduction of so - called verification classes specifying a certain amount of information . in a first step , we study the relation of these classes to each other . we therefore introduce the notion of being _ more informative _ capturing the intuition that a certain class can reproduce the information of an other . we present a hierarchy w.r.t .  this ordering . the hierarchy contains 15 different verification classes only . this is due to the fact that many syntactically different classes collapse to the same amount of information . we then formally define the essential property of a semantics @xmath1 being _ verifiable _ w.r.t .  a certain verification class . we present a general theorem stating that any _ rational _ semantics is exactly verifiable w.r.t . one of the @xmath10 different verification classes . roughly speaking , a semantics is rational if attacks inbetween two self - loops can be omitted without affecting the set of extensions . an important aside hereby is that even the most informative class contains indeed less information than the entire framework by itself . in this paper we consider a representative set of standard semantics . all of them satisfy rationality and thus , are exactly verifiable w.r.t .  a certain class . since the theorem does not provide an answer to which verification class perfectly matches a certain rational semantics we study this problem one by one for any considered semantics . as a result , only @xmath11 different classes are essential to classify the considered standard semantics .    in the last part of the paper we study an application of the concept of verifiability . more precisely , we address the question of strong equivalence for semantics lying inbetween known semantics , so - called intermediate semantics . strong equivalence is the natural counterpart to ordinary equivalence in monotonic theories ( see @xcite for abstract argumentation and @xcite for other nonmonotonic theories ) . we provide characterization theorems relying on the notion of verifiability and thus , contributing to a more abstract understanding of the different features argumentation semantics offer . besides these main results , we also give new characterizations for strong equivalence with respect to naive extensions and strong admissible sets .","summary":"_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ dung s abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations . hereby , the knowledge is represented by so - called argumentation frameworks ( afs ) and the reasoning is done via semantics extracting acceptable sets . we introduce a hierarchy of so - called verification classes specifying the required amount of information . our framework also gives a means to study semantics lying inbetween known semantics , thus contributing to a more abstract understanding of the different features argumentation semantics offer . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _","abstract":"_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ dung s abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations . hereby , the knowledge is represented by so - called argumentation frameworks ( afs ) and the reasoning is done via semantics extracting acceptable sets . all reasonable semantics are based on the notion of conflict - freeness which means that arguments are only jointly acceptable when they are not linked within the af . in this paper , we study the question which information on top of conflict - free sets is needed to compute extensions of a semantics at hand . we introduce a hierarchy of so - called verification classes specifying the required amount of information . we show that well - known standard semantics are exactly verifiable through a certain such class . our framework also gives a means to study semantics lying inbetween known semantics , thus contributing to a more abstract understanding of the different features argumentation semantics offer . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _"}
{"article_id":"1611.07463","section_id":"i","document":"let @xmath0 be a group and @xmath1 be an element of the commutator subgroup @xmath2 $ ] , the _ commutator length _ of @xmath1 , denoted @xmath3 , is the minimal number @xmath4 such that @xmath5[a_2,b_2]\\cdots[a_n , b_n]$ ] for some @xmath6 , and the _ stable commutator length _ of @xmath1 , denoted @xmath7 , is the limit @xmath8 which always exists by subadditivity . it is obvious from the definition that @xmath9 has the following basic properties :    1 . monotone : for any homomorphism @xmath10 and @xmath11 $ ] , we have @xmath12 ; 2 . characteristic : for any @xmath13 and @xmath11 $ ] , @xmath14 . it follows that the _ spectrum _ , the set of values that @xmath15 takes , is invariant under isomorphisms . however , @xmath9 is notoriously difficult to compute if it does not vanish . thus many interesting questions about the spectrum are extremely hard to answer . gromov ( @xcite ) asked whether the spectrum is rational ( or perhaps algebraic ) when @xmath0 is finitely presented . a counter example was found by zhuang ( @xcite ) . on the other hand , calegari showed that @xmath9 is rational and can be computed efficiently in a free group ( @xcite ) by interpreting and studying @xmath9 in terms of surface maps . he later showed that a modification of the geometric argument proves rationality of scl in free products of abelian groups ( @xcite ) . we generalize this latter result , substantially weakening the assumption that the factors are abelian . [ rationality ] let @xmath16 with @xmath17 for each @xmath18 , then @xmath9 is piecewise rational linear in @xmath0 . this holds , for example , when all @xmath19 are amenable . see remark [ vanscl ] for a list groups having vanishing scl . a homomorphism @xmath10 for which @xmath20 for all chains @xmath21 ( see section [ sec2 ] ) is said to be _ isometric _ for scl . injections admitting a retract are isometric . it is shown by calegari - walker ( @xcite ) that random homomorphisms between free groups are isometric for scl . in this paper , we show that isometric embeddings ( injective and isometric ) are preserved under taking free products :    let @xmath22 be a family of isometric embeddings , then so is the induced map @xmath23 .    a spin - off of the techniques used in the proof is a new method to compute scl ; we give examples in section [ app ] . in particular , these techniques give new insights for scl in families . it was proved by calegari - walker that for free products of free abelian groups , certain families of words @xmath24 ( called surgery families ) are eventually a ratio of two quasi - polynomials in @xmath4 . a similar question was studied by walker : for any fixed rational chain @xmath21 in @xmath25 , and any @xmath26 , with @xmath27 , let @xmath28 be the image of @xmath29 under the natural homomorphism @xmath30 , how does @xmath31 vary as a function of @xmath32 ? it was observed experimentally by walker ( @xcite ) that some interesting periodicity comes into @xmath31 , and he conjectured that the result is piecewise quasi - linear in @xmath33 ( see conjecture [ conj ] ) . in section [ wconj ] we give experimental examples to disprove this , but prove a weaker version : @xmath31 is piecewise quasi - rational in @xmath32 ( see theorem [ weakwconj ] ) . it was pointed out by timothy susse after the post of the first version that he had proved the same result earlier in @xcite corollary 4.14 using a different approach . it is worth mentioning that the method in this paper can be used to generalize and give a new approach to the spectral gap theorem by duncan - howie @xcite , which will be discussed in another paper @xcite . we first give basic definitions in section [ sec2 ] . then in section [ sec3 ] we introduce a way , following @xcite , to use a finite dimensional polyhedral cone to encode surface maps into a wedge of spaces with given boundary information . the encoding loses information , so in section [ sec4 ] we study a nonlinear optimization problem on the fibers . this reduces the computation of scl to a lattice point problem , which we solve , deducing theorem [ rationality ] and theorem [ isoemb ] . when scl vanishes in each factor , the non - linearity comes from _ disk vectors _ , which become complicated compared to the abelian case discussed in @xcite . in section [ app ] , we apply our method to give generalizations and new proofs of old results , where we also prove a formula conjectured by alden walker in @xcite . finally in section [ wconj ] we study walker s conjecture and prove a weaker ( correct ) version . the author thanks his advisor danny calegari for insightful introduction to this topic . the author also thanks timothy susse and alden walker for useful conversations .","summary":"we study stable commutator length ( scl ) in free products via surface maps into a wedge of spaces . we further prove that the property of isometric embedding with respect to scl is preserved under taking free products .","abstract":"we study stable commutator length ( scl ) in free products via surface maps into a wedge of spaces . we prove that scl is piecewise rational linear if it vanishes on each factor of the free product , generalizing the main result in . we further prove that the property of isometric embedding with respect to scl is preserved under taking free products . the method of proof gives a way to compute scl in free products which lets us generalize and derive in a new way several well - known formulas . finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasi - rational way when the word is fixed but the orders of factors vary , previously proved by timothy susse , settling a conjecture of alden walker ."}
{"article_id":"1611.07463","section_id":"r","document":"in this section , we apply the isometric embedding theorem and the computational methods we have developed to get generalizations and new proofs of old results . we start with a simple corollary of theorem [ isoemb ] .    [ steal ] let @xmath421 , @xmath16 , and @xmath422 be the inclusion . then the induced map @xmath423 is an isometric embedding . in particular , let @xmath424 , then the spectrum of @xmath15 contains that of @xmath425 if @xmath19 has an element of order @xmath426 ( @xmath427 could be @xmath428 , in which case @xmath429=@xmath430 ) . here the `` spectrum '' could refer to values scl takes on @xmath431 or the commutator subgroup . just note that @xmath359 is an isometric embedding even if @xmath432 ; because the definition of an isometric embedding is that @xmath231 induces an isometric map @xmath433 , and @xmath434 since @xmath429 is abelian . scl in free products of cyclic groups has been studied in @xcite , @xcite and @xcite . the program scallop ( @xcite ) can compute scl on specific chains . this allows us to generalize results about the scl spectrum in free groups ( or free products of cyclic groups ) to general free products . for example , we have    let @xmath16 ( @xmath304 , @xmath435 ) and suppose at least two @xmath19 s contain an element of infinite order . then the image of @xmath2 $ ] under scl contains elements congruent to every element of @xmath436 mod @xmath430 . moreover , it contains a well - ordered sequence of values with ordinal type @xmath437 . this follows from corollary 3.19 in @xcite , which states that the conclusion is true for nonabelian free groups , and our corollary [ steal ] . now we give three examples to illustrate how lemma [ detscl ] works . we first deduce the following product formula , which was originally stated not quite correctly in @xcite ( but the proof is still valid for torsion free elements ) and later corrected and proved in @xcite for the general case . [ prod ] let @xmath74 , and let @xmath438 , @xmath439 be nontrivial elements . suppose @xmath212 and @xmath213 are of order @xmath440 and @xmath441 ( could be @xmath428 , in which case @xmath442 by convention ) , then @xmath443    if the image of @xmath212 in @xmath122 is not zero , then both sides are @xmath428 by convention , and similarly for @xmath213 . now we assume this is not the case . using the notations in previous sections , let @xmath444 , then @xmath86 is just an oriented circle , @xmath445 , and @xmath446 by linearity of scl . if @xmath440 is finite , then @xmath447 , @xmath448 and thus @xmath449 , @xmath450 either by lemma [ chi0scl0 ] or lemma [ chi0gen ] . if @xmath451 , then @xmath452 and @xmath453 , thus @xmath454 by lemma [ chi0gen ] . then @xmath455 is valid in either case . similarly we get @xmath456 . now the `` glue - up '' condition on @xmath457 simply requires @xmath458 for @xmath459 , thus @xmath460 . then the fundamental class @xmath325 corresponds to the chain @xmath206 , thus @xmath461 and @xmath462 . therefore by lemma [ detscl ] , we get @xmath463    the following self - product formula is an analogy of the product formula . when @xmath464 and @xmath465 is the generator , it is proved in @xcite . [ selfprod ] let @xmath75 and @xmath76 be groups , @xmath466 and @xmath467 be torsion free elements . then @xmath468    again both sides are @xmath428 if @xmath469 is not @xmath41 in @xmath119 . thus we assume this does not happen . the result easily follows from the original self - product formula and theorem [ isoemb ] by considering @xmath470 and the inclusion @xmath471 . but we prove it using the computational tool above , which gives a new proof even for the original formula . we apply lemma [ detscl ] to calculate the left hand side . using notations as before , let @xmath472 , then @xmath86 is an oriented circle , @xmath473 consists of vectors of the form @xmath474 where we can think @xmath213 as a @xmath475 matrix with entries @xmath476 . then in the definition of @xmath477 , @xmath478 requires the sum of elements in the @xmath51-th row equals that of those in the @xmath51-th column for all @xmath51 , which is @xmath479 in this case ; @xmath480 requires @xmath481 if @xmath465 is non - zero in @xmath482 and is redundant otherwise . thus it is subtle to determine @xmath477 , but @xmath483 is clear . similarly @xmath484 , where @xmath485 . if @xmath486 , the glue - up condition requires @xmath487 , @xmath488 , @xmath489 and @xmath490 . in other words , @xmath213 is the matrix we get by moving the first column of @xmath212 to the last . finally @xmath491 requires in additional that each row of @xmath213 ( and @xmath212 ) sums up to @xmath142 . together with @xmath478 , this implies that @xmath479 , which implies @xmath480 in any case , compatible with remark [ redun ] .    in summary , @xmath492\\}$ ] where @xmath493 @xmath494 with @xmath495    now @xmath496 since all @xmath465 and @xmath497 will cancel . since @xmath465 is torsion free , @xmath498 , and @xmath499)=\\beta$ ] . thus @xmath500 by lemma [ chi0gen ] . for @xmath302 , it is more straight forward to use equation ( [ chi0 ] ) . thus we have @xmath501    therefore by lemma [ detscl ] , we only need to show @xmath502\\cap\\mathbb{q } } \\{2-\\alpha+\\inf\\{-\\chi(s_a)/n|v(s_a)=nu(\\alpha)\\}\\}.\\ ] ] let @xmath503 , then @xmath504 and thus @xmath505 since @xmath98 has no disk components because @xmath506 and @xmath281 are torsion free . this gives the `` @xmath507 '' direction . conversely , we just need to show @xmath508 always holds . in fact , since @xmath509+n\\alpha[(x , x)+(y , y)]$ ] , there are @xmath510 points on the boundary of @xmath98 that sit in between an @xmath506 and a @xmath281 , where it is from @xmath506 to @xmath281 for half of them ( referred to as a @xmath511 point ) and from @xmath281 to @xmath506 for the other half ( referred to as a @xmath512 point ) . whenever we have a @xmath511 point and a @xmath512 point that lie on the same boundary component , we glue a rectangle to the surface with one edge glued to the @xmath511 point and its opposite edge glued to the @xmath512 point . such a surgery increases @xmath513 by @xmath142 . repeating the process we get a new surface @xmath172 such that @xmath514 and each boundary component either winds around @xmath506 several times or around @xmath281 . this implies that @xmath172 has no disk components since @xmath506 and @xmath281 are torsion free and @xmath173 winds around each of @xmath506 and @xmath281 @xmath4-times in total . thus @xmath515 . this completes the proof . finally we prove the following formula which was conjectured for free product of cyclic groups and proved for @xmath516 by alden walker in @xcite . it was pointed out by timothy susse that in the case of free product of cyclic groups , this is equivalent to proposition 4.1 he proved in @xcite by considering certain amalgams of abelian groups . [ abab ] let @xmath74 , @xmath517 and @xmath518 , then @xmath519)=\\frac{1}{2}-\\frac{1}{k}\\ ] ] where @xmath520 is the minimum of the order of @xmath212 and @xmath213 .    by theorem [ isoemb ] , we may assume @xmath521 and @xmath522 . let @xmath523 and @xmath524 be the order of @xmath212 and @xmath213 respectively . similar to the proof of proposition [ selfprod ] , we have @xmath525\\}$ ] where @xmath493 , @xmath494 with @xmath526 and @xmath527 therefore @xmath528 which has maximum @xmath529 for @xmath530 $ ] , thus @xmath519)=\\frac{1}{2}-\\frac{1}{k}.\\ ] ]","summary":"finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasi - rational way when the word is fixed but the orders of factors vary , previously proved by timothy susse , settling a conjecture of alden walker .","abstract":"we study stable commutator length ( scl ) in free products via surface maps into a wedge of spaces . we prove that scl is piecewise rational linear if it vanishes on each factor of the free product , generalizing the main result in . we further prove that the property of isometric embedding with respect to scl is preserved under taking free products . the method of proof gives a way to compute scl in free products which lets us generalize and derive in a new way several well - known formulas . finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasi - rational way when the word is fixed but the orders of factors vary , previously proved by timothy susse , settling a conjecture of alden walker ."}
{"article_id":"0708.2863","section_id":"i","document":"the @xmath1 a@xmath2 line of methanol at 6.7 ghz is the strongest of the class ii methanol masers . theoretical models ( e.g. @xcite ) , and observational studies ( e.g. @xcite ) suggest that the masers are associated with early phases of massive star formation . the fact that 6.7 ghz methanol masers have not been detected to date towards late type stars or low - mass star forming regions , makes them unique compared to their oh and h@xmath3o counterparts . this , in addition to their high brightness , makes 6.7 ghz methanol masers powerful tools to identify sites of massive star formation across the galaxy , which in turn can probe galactic structure at great distances .    however , some puzzles remain . @xcite found that many relatively weak methanol masers were associated with iras sources with colors different from those expected for ultracompact  regions . they further found that many faint masers had very narrow linewidths . this raises the question of whether faint methanol masers have properties different from that of bright masers . recently , we reported on the sensitive blind survey for 6.7 ghz methanol masers carried out using the arecibo radio telescope ( @xcite ; hereafter paper i ) . the methanol maser sample from this survey is ideal for probing some of the questions above . here , we present an analysis of the properties of the methanol masers discovered in the survey .","summary":"we present an analysis of the properties of the 6.7 ghz methanol maser sample detected in the arecibo methanol maser galactic plane survey . we also find no evidence that faint methanol masers have different properties than those of their bright counterparts .","abstract":"we present an analysis of the properties of the 6.7 ghz methanol maser sample detected in the arecibo methanol maser galactic plane survey . the distribution of the masers in the galaxy , and statistics of their multi - wavelength counterparts is consistent with the hypothesis of 6.7 ghz maser emission being associated with massive young stellar objects . using the detection statistics of our survey , we estimate the minimum number of methanol masers in the galaxy to be 1275 . the diagram of the sample shows the tangent point of the carina  sagittarius spiral arm to be around 49.6 , and suggests occurrence of massive star formation along the extension of the crux  scutum arm . a gaussian component analysis of the maser spectra shows the mean line - width to be 0.38  which is more than a factor of two larger than what has been reported in the literature . we also find no evidence that faint methanol masers have different properties than those of their bright counterparts ."}
{"article_id":"hep-ex9810021","section_id":"i","document":"we describe measurements and searches using a data sample of photonic events with large missing energy collected in 1997 with the opal detector at lep . the events result from @xmath11 collisions at centre - of - mass energies of 130.0 , 136.0 and 182.7  gev with integrated luminosities of 2.35 , 3.37 and 54.5  pb@xmath58 , respectively . the present paper complements our recent publication of results from earlier data samples @xcite consisting of a total of 25  pb@xmath58 at centre - of - mass energies of 130 , 136 , 161 and 172  gev . results on photonic events without missing energy at @xmath59 183  gev are presented in a separate paper@xcite . recent measurements of photonic event production have also been made by the other lep collaborations at centre - of - mass energies above the w pair threshold  @xcite , including new results at @xmath59 183  gev  @xcite . related searches in @xmath60 collisions have been reported in  @xcite . the interest in the 1997 data is twofold . the main motivation is that the large data set at a higher centre - of - mass energy ( 183 gev ) gives discovery potential in a new kinematic regime . additionally , the lower energy data sets allow the experiment at 130 and 136 gev to be repeated leading to a check of our previous results which indicated an excess of events with acoplanar photons  @xcite . the single - photon and acoplanar - photons search topologies presented here are designed to select events with one or more photons and significant missing transverse energy , indicating the presence of at least one neutrino - like invisible particle which interacts only weakly with matter . the event selections for these search topologies are similar to those used in our recent publication@xcite . the main changes are improvements in the rejection of backgrounds from cosmic ray interactions which allow for an increased kinematic acceptance of the single - photon topology . the single - photon search topology is sensitive to neutral events in which there are one or two photons and missing energy which , within the standard model , are expected from the @xmath61 process . the allowance for two observed photons retains acceptance for doubly radiative neutrino pair production . the acoplanar - photons search topology is designed to select neutral events with two or more photons and significant missing transverse energy which , within the standard model , are expected from the @xmath62 process . the selection is designed to retain acceptance for events with three photons , if the system formed by the three photons shows evidence for significant missing transverse energy . these photonic final - state topologies are sensitive to new physics of the type @xmath63 and @xmath64 where @xmath65 is neutral and decays radiatively ( @xmath66 ) and @xmath5 is stable and only weakly interacting . for the general case of massive @xmath65 and @xmath5 this includes conventional supersymmetric processes@xcite @xmath67 . in this context it has been emphasized @xcite that the radiative branching ratio of the @xmath68 may be large . these topologies also have particularly good sensitivity for the special case of @xmath69 . this applies both to the production of excited neutrinos @xmath70 and to supersymmetric models in which the lightest supersymmetric particle ( lsp ) is a light gravitino(kev ) . ] and @xmath71 is the next - to - lightest supersymmetric particle ( nlsp ) which decays to a gravitino and a photon ( @xmath72 ) . for supersymmetric models with a light gravitino , the photonic branching ratio of the @xmath71 is naturally large . such a signature has been discussed in  @xcite and more recently in  @xcite in the context of both no - scale supergravity models and gauge - mediated supersymmetry breaking models . other types of new physics to which these search topologies are sensitive include the production of an invisible particle in association with a photon and the production of invisible particles tagged by initial - state radiation . an example of this is @xmath73@xcite . the acoplanar - photons search topology also has sensitivity to the production of two particles , one invisible , or with an invisible decay mode , and the other decaying into two photons . such events might arise from the production of a higgs - like scalar particle , @xmath74 : @xmath75 , followed by s@xmath76@xmath77 , @xmath78 . opal results from a search for this process at @xmath79 gev , including the hadronic and leptonic @xmath80 decays , are reported in a separate paper@xcite . the results from our previous searches  @xcite for @xmath63 and @xmath64 with @xmath66 have been used to set model - dependent limits on excited neutrinos and neutralinos @xcite . the new results reported here can be used in the same manner . this paper will first briefly describe the detector and the monte carlo samples used . the event selection for each search topology will then be described , followed by cross - section measurements for @xmath61 and @xmath62 and comparisons with standard model expectations . implications of these results on the possibility of new physics processes will be discussed .","summary":"results are presented for event topologies with a single photon and missing transverse energy or with an acoplanar photon pair . are derived for the case of stable and invisible . these limits apply to single and pair production of excited neutrinos ( ) , to neutralino production ( ) and to supersymmetric models in which and is a light gravitino .    plus 1pt minus 1pt plus 1pt    plus 1pt minus 1pt plus 1pt    european laboratory for particle physics    cern - ep/98 - 143 + 08 september 1998    * search for anomalous photonic + events with missing energy in collisions + at = 130 , 136 and 183  *    the opal collaboration    ( submitted to eur . phys . j. * c*. )    the opal collaboration     g.abbiendi , k.ackerstaff , g.alexander , j.allison , n.altekamp , k.j.anderson , s.anderson , s.arcelli , s.asai , s.f.ashby , d.axen , g.azuelos , a.h.ball , e.barberio , r.j.barlow , r.bartoldus , j.r.batley , s.baumann , j.bechtluft , t.behnke , k.w.bell , g.bella , a.bellerive , s.bentvelsen , s.bethke , s.betts , o.biebel , a.biguzzi , s.d.bird , v.blobel , i.j.bloodworth , m.bobinski , p.bock , j.bhme , d.bonacorsi , m.boutemeur , s.braibant , p.bright-thomas , l.brigliadori , r.m.brown , h.j.burckhart , c.burgard , r.brgin , p.capiluppi , r.k.carnegie , a.a.carter , j.r.carter , c.y.chang , d.g.charlton , d.chrisman , c.ciocca , p.e.l.clarke , e.clay , i.cohen , j.e.conboy , o.c.cooke , c.couyoumtzelis , r.l.coxe , m.cuffiani , s.dado , g.m.dallavalle , r.davis , s.de jong , l.a.del pozo , a.de roeck , k.desch , b.dienes , m.s.dixit , j.dubbert , e.duchovni , g.duckeck , i.p.duerdoth , d.eatough , p.g.estabrooks , e.etzion , h.g.evans , f.fabbri , m.fanti , a.a.faust , f.fiedler , m.fierro , i.fleck , r.folman , a.frtjes , d.i.futyan , p.gagnon , j.w.gary , j.gascon , s.m.gascon-shotkin , g.gaycken , c.geich-gimbel , g.giacomelli , p.giacomelli , v.gibson , w.r.gibson , d.m.gingrich , d.glenzinski , j.goldberg , w.gorn , c.grandi , e.gross , j.grunhaus , m.gruw , g.g.hanson , m.hansroul , m.hapke , k.harder , c.k.hargrove , c.hartmann , m.hauschild , c.m.hawkes , r.hawkings , r.j.hemingway , m.herndon , g.herten , r.d.heuer , m.d.hildreth , j.c.hill , s.j.hillier , p.r.hobson , a.hocker , r.j.homer , a.k.honma , d.horvth , k.r.hossain , r.howard , p.hntemeyer , p.igo-kemenes , d.c.imrie , k.ishii , f.r.jacob , a.jawahery , h.jeremie , m.jimack , c.r.jones , p.jovanovic , t.r.junk , d.karlen , v.kartvelishvili , k.kawagoe , t.kawamoto , p.i.kayal , r.k.keeler , r.g.kellogg , b.w.kennedy , a.klier , s.kluth , t.kobayashi , m.kobel , d.s.koetke , t.p.kokott , m.kolrep , s.komamiya , r.v.kowalewski , t.kress , p.krieger , j.von krogh , t.kuhl , p.kyberd , g.d.lafferty , d.lanske , j.lauber , s.r.lautenschlager , i.lawson , j.g.layter , d.lazic , a.m.lee , d.lellouch , j.letts , l.levinson , r.liebisch , b.list , c.littlewood , a.w.lloyd , s.l.lloyd , f.k.loebinger , g.d.long , m.j.losty , j.ludwig , d.liu , a.macchiolo , a.macpherson , w.mader , m.mannelli , s.marcellini , c.markopoulos , a.j.martin , j.p.martin , g.martinez , t.mashimo , p.mttig , w.j.mcdonald , j.mckenna , e.a.mckigney , t.j.mcmahon , r.a.mcpherson , f.meijers , s.menke , f.s.merritt , h.mes , j.meyer , a.michelini , s.mihara , g.mikenberg , d.j.miller , r.mir , w.mohr , a.montanari , t.mori , k.nagai , i.nakamura , h.a.neal , b.nellen , r.nisius , s.w.oneale , f.g.oakham , f.odorici , h.o.ogren , m.j.oreglia , s.orito , j.plinks , g.psztor , j.r.pater , g.n.patrick , j.patt , r.perez-ochoa , s.petzold , p.pfeifenschneider , j.e.pilcher , j.pinfold , d.e.plane , p.poffenberger , j.polok , m.przybycie , c.rembser , h.rick , s.robertson , s.a.robins , n.rodning , j.m.roney , k.roscoe , a.m.rossi , y.rozen , k.runge , o.runolfsson , d.r.rust , k.sachs , t.saeki , o.sahr , w.m.sang , e.k.g.sarkisyan , c.sbarra , a.d.schaile , o.schaile , f.scharf , p.scharff-hansen , j.schieck , b.schmitt , s.schmitt , a.schning , m.schrder , m.schumacher , c.schwick , w.g.scott , r.seuster , t.g.shears , b.c.shen , c.h.shepherd-themistocleous , p.sherwood , g.p.siroli , a.sittler , a.skuja , a.m.smith , g.a.snow , r.sobie , s.sldner-rembold , m.sproston , a.stahl , k.stephens , j.steuerer , k.stoll , d.strom , r.strhmer , b.surrow , s.d.talbot , s.tanaka , p.taras , s.tarem , r.teuscher , m.thiergen , m.a.thomson , e.von trne , e.torrence , s.towers , i.trigger , z.trcsnyi , e.tsur , a.s.turcot , m.f.turner-watson , r.van  kooten , p.vannerem , m.verzocchi , h.voss , f.wckerle , a.wagner , c.p.ward , d.r.ward , p.m.watkins , a.t.watson , n.k.watson , p.s.wells , n.wermes , j.s.white , g.w.wilson , j.a.wilson , t.r.wyatt , s.yamashita , g.yekutieli , v.zacek , d.zer-zion   school of physics and astronomy , university of birmingham , birmingham b15 2tt , ukdipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italyphysikalisches","abstract":"photonic events with large missing energy have been observed in collisions at centre - of - mass energies of 130 , 136 and 183  gev collected in 1997 using the opal detector at lep . results are presented for event topologies with a single photon and missing transverse energy or with an acoplanar photon pair . cross - section measurements are performed within the kinematic acceptance of each selection . these results are compared with the expectations from the standard model process + photon(s ) . no evidence is observed for new physics contributions to these final states . using the data at = 183 gev , upper limits on and are derived for the case of stable and invisible . these limits apply to single and pair production of excited neutrinos ( ) , to neutralino production ( ) and to supersymmetric models in which and is a light gravitino .    plus 1pt minus 1pt plus 1pt    plus 1pt minus 1pt plus 1pt    european laboratory for particle physics    cern - ep/98 - 143 + 08 september 1998    * search for anomalous photonic + events with missing energy in collisions + at = 130 , 136 and 183  *    the opal collaboration    ( submitted to eur . phys . j. * c*. )    the opal collaboration     g.abbiendi , k.ackerstaff , g.alexander , j.allison , n.altekamp , k.j.anderson , s.anderson , s.arcelli , s.asai , s.f.ashby , d.axen , g.azuelos , a.h.ball , e.barberio , r.j.barlow , r.bartoldus , j.r.batley , s.baumann , j.bechtluft , t.behnke , k.w.bell , g.bella , a.bellerive , s.bentvelsen , s.bethke , s.betts , o.biebel , a.biguzzi , s.d.bird , v.blobel , i.j.bloodworth , m.bobinski , p.bock , j.bhme , d.bonacorsi , m.boutemeur , s.braibant , p.bright-thomas , l.brigliadori , r.m.brown , h.j.burckhart , c.burgard , r.brgin , p.capiluppi , r.k.carnegie , a.a.carter , j.r.carter , c.y.chang , d.g.charlton , d.chrisman , c.ciocca , p.e.l.clarke , e.clay , i.cohen , j.e.conboy , o.c.cooke , c.couyoumtzelis , r.l.coxe , m.cuffiani , s.dado , g.m.dallavalle , r.davis , s.de jong , l.a.del pozo , a.de roeck , k.desch , b.dienes , m.s.dixit , j.dubbert , e.duchovni , g.duckeck , i.p.duerdoth , d.eatough , p.g.estabrooks , e.etzion , h.g.evans , f.fabbri , m.fanti , a.a.faust , f.fiedler , m.fierro , i.fleck , r.folman , a.frtjes , d.i.futyan , p.gagnon , j.w.gary , j.gascon , s.m.gascon-shotkin , g.gaycken , c.geich-gimbel , g.giacomelli , p.giacomelli , v.gibson , w.r.gibson , d.m.gingrich , d.glenzinski , j.goldberg , w.gorn , c.grandi , e.gross , j.grunhaus , m.gruw , g.g.hanson , m.hansroul , m.hapke , k.harder , c.k.hargrove , c.hartmann , m.hauschild , c.m.hawkes , r.hawkings , r.j.hemingway , m.herndon , g.herten , r.d.heuer , m.d.hildreth , j.c.hill , s.j.hillier , p.r.hobson , a.hocker , r.j.homer , a.k.honma , d.horvth , k.r.hossain , r.howard , p.hntemeyer , p.igo-kemenes , d.c.imrie , k.ishii , f.r.jacob , a.jawahery , h.jeremie , m.jimack , c.r.jones , p.jovanovic , t.r.junk , d.karlen , v.kartvelishvili , k.kawagoe , t.kawamoto , p.i.kayal , r.k.keeler , r.g.kellogg , b.w.kennedy , a.klier , s.kluth , t.kobayashi , m.kobel , d.s.koetke , t.p.kokott , m.kolrep , s.komamiya , r.v.kowalewski , t.kress , p.krieger , j.von krogh , t.kuhl , p.kyberd , g.d.lafferty , d.lanske , j.lauber , s.r.lautenschlager , i.lawson , j.g.layter , d.lazic , a.m.lee , d.lellouch , j.letts , l.levinson , r.liebisch , b.list , c.littlewood , a.w.lloyd , s.l.lloyd , f.k.loebinger , g.d.long , m.j.losty , j.ludwig , d.liu , a.macchiolo , a.macpherson , w.mader , m.mannelli , s.marcellini , c.markopoulos , a.j.martin , j.p.martin , g.martinez , t.mashimo , p.mttig , w.j.mcdonald , j.mckenna , e.a.mckigney , t.j.mcmahon , r.a.mcpherson , f.meijers , s.menke , f.s.merritt , h.mes , j.meyer , a.michelini , s.mihara , g.mikenberg , d.j.miller , r.mir , w.mohr , a.montanari , t.mori , k.nagai , i.nakamura , h.a.neal , b.nellen , r.nisius , s.w.oneale , f.g.oakham , f.odorici , h.o.ogren , m.j.oreglia , s.orito , j.plinks , g.psztor , j.r.pater , g.n.patrick , j.patt , r.perez-ochoa , s.petzold , p.pfeifenschneider , j.e.pilcher , j.pinfold , d.e.plane , p.poffenberger , j.polok , m.przybycie , c.rembser , h.rick , s.robertson , s.a.robins , n.rodning , j.m.roney , k.roscoe , a.m.rossi , y.rozen , k.runge , o.runolfsson , d.r.rust , k.sachs , t.saeki , o.sahr , w.m.sang , e.k.g.sarkisyan , c.sbarra , a.d.schaile , o.schaile , f.scharf , p.scharff-hansen , j.schieck , b.schmitt , s.schmitt , a.schning , m.schrder , m.schumacher , c.schwick , w.g.scott , r.seuster , t.g.shears , b.c.shen , c.h.shepherd-themistocleous , p.sherwood , g.p.siroli , a.sittler , a.skuja , a.m.smith , g.a.snow , r.sobie , s.sldner-rembold , m.sproston , a.stahl , k.stephens , j.steuerer , k.stoll , d.strom , r.strhmer , b.surrow , s.d.talbot , s.tanaka , p.taras , s.tarem , r.teuscher , m.thiergen , m.a.thomson , e.von trne , e.torrence , s.towers , i.trigger , z.trcsnyi , e.tsur , a.s.turcot , m.f.turner-watson , r.van  kooten , p.vannerem , m.verzocchi , h.voss , f.wckerle , a.wagner , c.p.ward , d.r.ward , p.m.watkins , a.t.watson , n.k.watson , p.s.wells , n.wermes , j.s.white , g.w.wilson , j.a.wilson , t.r.wyatt , s.yamashita , g.yekutieli , v.zacek , d.zer-zion   school of physics and astronomy , university of birmingham , birmingham b15 2tt , ukdipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italyphysikalisches institut , universitt bonn , d-53115 bonn , germanydepartment of physics , university of california , riverside ca 92521 , usacavendish laboratory , cambridge cb3 0he , ukottawa - carleton institute for physics , department of physics , carleton university , ottawa , ontario k1s 5b6 , canadacentre for research in particle physics , carleton university , ottawa , ontario k1s 5b6 , canadacern , european organisation for particle physics , ch-1211 geneva 23 , switzerlandenrico fermi institute and department of physics , university of chicago , chicago il 60637 , usafakultt fr physik , albert ludwigs universitt , d-79104 freiburg , germanyphysikalisches institut , universitt heidelberg , d-69120 heidelberg , germanyindiana university , department of physics , swain hall west 117 , bloomington in 47405 , usaqueen mary and westfield college , university of london , london e1 4ns , uktechnische hochschule aachen , iii physikalisches institut , sommerfeldstrasse 26 - 28 , d-52056 aachen , germanyuniversity college london , london wc1e 6bt , ukdepartment of physics , schuster laboratory , the university , manchester m13 9pl , ukdepartment of physics , university of maryland , college park , md 20742 , usalaboratoire de physique nuclaire , universit de montral , montral , quebec h3c 3j7 , canadauniversity of oregon , department of physics , eugene or 97403 , usaclrc rutherford appleton laboratory , chilton , didcot , oxfordshire ox11 0qx , ukdepartment of physics , technion - israel institute of technology , haifa 32000 , israeldepartment of physics and astronomy , tel aviv university , tel aviv 69978 , israelinternational centre for elementary particle physics and department of physics , university of tokyo , tokyo 113 - 0033 , and kobe university , kobe 657 - 8501 , japaninstitute of physical and environmental sciences , brunel university , uxbridge , middlesex ub8 3ph , ukparticle physics department , weizmann institute of science , rehovot 76100 , israeluniversitt hamburg / desy , ii institut fr experimental physik , notkestrasse 85 , d-22607 hamburg , germanyuniversity of victoria , department of physics , p o box 3055 , victoria bc v8w 3p6 , canadauniversity of british columbia , department of physics , vancouver bc v6 t 1z1 , canadauniversity of alberta , department of physics , edmonton ab t6 g 2j1 , canadaduke university , dept of physics , durham , nc 27708 - 0305 , usaresearch institute for particle and nuclear physics , h-1525 budapest , p o box 49 , hungaryinstitute of nuclear research , h-4001 debrecen , p o box 51 , hungaryludwigs - maximilians - universitt mnchen , sektion physik , am coulombwall 1 , d-85748 garching , germany and at triumf , vancouver , canada v6 t 2a3 and royal society university research fellow and institute of nuclear research , debrecen , hungary and department of experimental physics , lajos kossuth university , debrecen , hungary on leave of absence from the university of freiburg"}
{"article_id":"hep-ex9810021","section_id":"r","document":"the results of the single - photon and acoplanar - photons selections are given below in sections  [ sec : sp_results ] and  [ sec : g2_results ] . the measured cross - sections for each search topology are given and compared with standard model expectations . as no evidence for new physics processes is seen , the results are presented in terms of upper limits on @xmath152 and . this is done both for the general case of massive @xmath65 and @xmath5 , applicable to conventional supersymmetric models in which @xmath153 and @xmath154 , and also separately for the special case of @xmath69 , which applies both to single and pair production of neutralinos in supersymmetric models in which the lsp is a light gravitino and to single and pair production of excited neutrinos . all efficiencies are evaluated with the decay length of @xmath65 set to zero . for the purposes of new physics searches , only the @xmath79 gev data are considered ; the @xmath155 and 136 gev data do not open any new kinematic regions , nor is the integrated luminosity at these energies sufficient to significantly improve the potential for discovery . for both the xx and xy searches , monte carlo samples were generated for a variety of mass points in the kinematically accessible region of the @xmath156 plane . to set limits for arbitrary @xmath100 and @xmath101 , the efficiency over the entire @xmath156 plane is parametrized using the efficiencies calculated at the generated mass points . in the single - photon search topology , the regions with @xmath157 are kinematically accessible at @xmath158 , and strong limits have already been reported@xcite . in the acoplanar - photons search topology , limits have been reported for masses @xmath159@xcite . in these low mass regions , possible radiative return to the @xmath160 followed by @xmath161 xy or xx would yield very different event kinematics than those produced by the signal monte carlo generator . for these reasons , the search for xy production is restricted to the region with @xmath162 , and the search for xx production is restricted to @xmath100 values larger than about @xmath163/2 . [ sec : sp_results ]    after applying the selection criteria of the single - photon selection to the @xmath164 130 , 136 and 183 gev data samples , a total of 21 , 39 and 191 events are selected . the expected contributions from cosmic ray and beam related backgrounds are 0.02 , 0.02 and 0.4 events , respectively . these backgrounds have been estimated from events having out - of - time tof or te information but passing all other selection criteria and from events selected with looser criteria that have been visually scanned . of the expected physics backgrounds from plausible sources , only @xmath165 , @xmath91 , @xmath166 and @xmath167 have non - negligible contributions . coming primarily from the @xmath91 and @xmath168 final states , the total physics backgrounds contribute 0.07 , 0.09 and 0.4 events , respectively , to the 130 , 136 and 183 gev samples . the background contributions are summarized in table  [ tab : sp_background ] . for each of the three centre - of - mass energies , table  [ tab : sp_results ] shows the number of events observed , the number of events expected from the standard model process @xmath141 evaluated using the koralz generator and the sum of background events expected from other standard model physics processes with those from cosmic ray and beam related processes . the numbers of events observed agree with the numbers expected from @xmath61 plus the background . the estimated efficiencies for selecting @xmath61 events within the kinematic acceptance of the single - photon selection are also given in table  [ tab : sp_results ] , as are the corresponding measured @xmath61 cross - sections within this kinematic acceptance , corrected for detector and selection efficiencies , and subtracting the estimated background . for both the single - photon and acoplanar - photons selections , efficiency losses due to vetoes on random detector occupancy range from about ( 2 - 4)% at the different centre - of - mass energies . quoted efficiencies include these losses .    the total systematic error on the cross - section measurement is estimated to be 3.5% . the contributing uncertainties are from the integrated luminosity ( 0.5% ) , effects due to uncertainties on the electromagnetic calorimeter energy scale and resolution ( 0.7% ) and the detector occupancy estimate ( 1% ) . in addition , the overall selection efficiency uncertainty ( 2% ) is caused mainly by uncertainties in the simulation of the detector material and consequent photon conversion probabilities . an additional error of 2.5% is assigned based on the comparison of the estimated efficiency using two different event generators@xcite . the cross - section as a function of centre - of - mass energy is plotted in figure  [ f : sp_xs130_183 ] . in this plot the measured cross - sections for @xmath169 and 136 gev are 11.1 @xmath170 1.7 and 15.9 @xmath170 1.9 pb , respectively . these are weighted averages of the 1995 data results with the results from this analysis . the results for @xmath171 gev and @xmath172 gev are also plotted . the cross - section results from our earlier publication@xcite have been corrected for the slightly different kinematic acceptance used in the analysis of those data . the corrected cross - sections , obtained for the 1995 and 1996 data at @xmath59 130 , 136 , 161 and 172 gev are 10.6 @xmath170 2.4 , 17.3 @xmath170 3.0 , 5.6 @xmath170 0.8 and 5.8 @xmath170 0.8 pb , respectively . for 1997 data at @xmath59 130 , 136 and 183 gev the measured cross - sections are 11.6 @xmath170 2.5 , 14.9 @xmath170 2.4 and 4.71 @xmath170 0.34 pb , respectively . the curve shows the predicted cross - section from the koralz event generator for the standard model process @xmath61 . the data are in reasonable agreement with the prediction . in figure [ f : sp_xcosth183]a , the scaled energy of the most energetic photon is plotted against the cosine of its polar angle for events in the @xmath2=183 gev sample . the data are distributed as expected from the @xmath61 monte carlo . similar agreement is found for the 130 and 136 gev data . in figure [ f : sp_xcosth183]b the polar angle distribution for the @xmath2=183 gev sample is shown and agrees with the @xmath61 monte carlo expectation . if one calculates the recoil mass @xmath173 , defined as the mass recoiling against the photon ( or against the two - photon system ) , one expects a peak in the @xmath173 distribution at @xmath163 , due to a large contribution from the decay @xmath174 . one clearly sees this feature in the data as shown in figure  [ f : sp_mrec130_183 ] . there is good agreement between data and monte carlo in this distribution for each of the three centre - of - mass energies . the single - photon selection was designed to allow for the presence of a second photon in order to accept events from the @xmath175 process . in the @xmath2 = 130 , 136 and 183  gev data sets , 2 , 4 and 12 observed events are considered to be two - photon events ( i.e. have a second photon with deposited energy exceeding 300  mev in the ecal ) . this is consistent with the expectations of 1.4 , 1.7 and 11.3 events , respectively , from the koralz monte carlo . [ sec : sp_results_allmy ]    the single - photon selection described in section  [ sec : selection ] is designed to maximize acceptance for standard model @xmath61 events . however , when searching for signatures of the process @xmath63 ,  @xmath66 , it is possible to implement further cuts to reduce the contribution from @xmath61 , which is now considered as background . depending on the values of @xmath100 and @xmath101 , various combinations of the following cuts are applied to events in the single - photon sample :    * * kinematic consistency : * the energy of the most energetic photon is required to lie within the range kinematically accessible to a photon from the process @xmath63 , @xmath66 , after accounting for energy resolution effects . * * degraded resolution : * events with @xmath17775  gev are rejected if the most energetic photon lies in the region @xmath178 or @xmath179 . energy resolution in these angular regions is known to be degraded . * * low recoil mass : * require @xmath17775  gev . * * z@xmath76 radiative return : * the event is rejected if @xmath180  gev .    the kinematic consistency cut and the degraded resolution cut are applied to all @xmath156 values . the low recoil mass cut is applied if @xmath181 ( gev ) , in which case a significant portion of the expected photon energy distribution is consistent with low recoil masses for new physics contributions be minimized , where the expected upper limit is defined as the average limit one would expect to set in the absence of new physics contributions . this definition has the advantage that it does not require one to specify the cross - section of possible new physics . ] . the radiative return cut is applied if the low recoil mass cut is not applied , and if @xmath100 and @xmath101 are such that the difference between the maximum and minimum kinematically allowed photon energies ( before energy resolution effects are considered ) is greater than @xmath182 . the selection efficiencies including the above cuts as a function of @xmath156 are given in figure  [ f : sp_xyeff ] . also illustrated is the region in which the radiative return cut is applied . in the region where @xmath183 is small , photon energies are correspondingly small and efficiencies become low . since uncertainties due to energy scale and resolution effects become significant in this region , we do not consider values of @xmath100 and @xmath101 that lead to efficiencies of less than 40% in the absence of the recoil mass or radiative return cuts . the number of selected events in the data consistent with each @xmath156 value is shown in figure  [ f : sp_evsxy_data ] and can be compared with the number expected from standard model @xmath61 events as shown in figure  [ f : sp_evsxy_mc ] . in general there is good agreement , and we proceed to set upper limits at 95% confidence level ( cl ) on the cross - section times branching ratio , @xmath3 , which are shown in figure  [ f : sp_xylim_all ] . the upper limits are calculated taking into account the expected number of standard model @xmath61 background events estimated from koralz using the method described in @xcite . background from sources other than @xmath61 , including the estimated cosmic ray and beam related background , is intentionally not taken into account in the limit calculations . the resulting upper limits range from 0.075 pb to 0.80 pb . the systematic error on the efficiency for selecting events from potential new physics sources is due to the effects already discussed in section 4.1 , as well as the uncertainty on the efficiency parametrization across the ( @xmath184 ) plane . the parametrization was compared to efficiencies obtained from the fully simulated monte carlo samples at 40 selected @xmath185 points , and a resulting systematic error of 1% ( absolute ) was assigned across the plane . the total relative systematic error varies from 2 to 6% depending on @xmath184 ; its effect on the upper limits is small , and is calculated according to @xcite . uncertainties in the @xmath186 background estimate are also taken into account . unlike the systematic error on the efficiency , a relatively small uncertainty in the background estimate can have a significant impact on the resulting 95% cl limit , especially when the number of expected events is large . to account for this uncertainty , a convolution is performed within the upper limit calculations . contributing sources to the background uncertainty are : the factors considered in the cross - section measurement ( 3.5% ) , the estimated theoretical uncertainty in the @xmath186 cross - section ( 2% ) based in part on a comparison between the koralz and nunugpv98@xcite event generators , and a contribution due to uncertainties in the energy scale . this last contribution is dependent on the values of @xmath100 and @xmath101 ; it is calculated separately at each @xmath185 point , and ranges from negligible to 5% . [ sec : sp_results_my0 ]    the case @xmath69 is applicable to excited neutrino models and to some supersymmetric models mentioned earlier . the results presented above include this case and no separate analysis is performed , but the results are highlighted here . as described earlier , the 75 gev recoil mass cut is applied for all @xmath100 hypotheses , so that the expected number of events is small . for example , in the range @xmath187  gev , the expected contribution from @xmath186 is @xmath188 events and there is one event observed . although the numbers of expected and observed events are constant in this range , the efficiency of the recoil mass cut increases with increasing values of @xmath100 , leading to decreasing values for the resulting upper limits on @xmath3 . for @xmath189  gev , the kinematic consistency requirements become more restrictive than the recoil mass cut . there are no longer any events kinematically consistent with hypotheses of @xmath190  gev ; the background expectation in this region varies from @xmath191 events at 173 gev to @xmath192 events at the kinematic limit . the resulting upper limits on @xmath3 for @xmath69 as a function of @xmath100 range from 0.46  pb to 0.075  pb , as shown in figure  [ f : sp_xylim_massless ] . [ sec : g2_results ]    the acoplanar - photons selection applied to the 130 , 136 and 183 gev data samples yields 2 , 2 and 10 events , respectively , in good agreement with the koralz predictions of @xmath193 , @xmath194 and @xmath195 events for the standard model @xmath62 contribution . the expected contributions from other standard model processes and from cosmic ray and beam related backgrounds are small : less than 0.05 , 0.05 and 0.1 events , respectively . the numbers of events expected and observed at the three centre - of - mass energies are summarized in table  [ tab : g2_nevt ] . also shown are the selection efficiencies for @xmath62 events , within the kinematic acceptance of the selection , and the corresponding cross - section measurements at each centre - of - mass energy . the opal measurements of the cross - sections at @xmath164 130 , 136 , 161 , 172 and 183 gev are summarized in table  [ tab : g2_xsec ] . the measurements at 130 and 136 gev are weighted averages of the results obtained from the 1997 and 1995 data samples . the latter results , as well as the results at @xmath164 161 and 172 gev , have been taken from our previous publication@xcite and are corrected for the different definition of the kinematic acceptance . systematic errors arising from uncertainties on the electromagnetic calorimeter energy scale and resolution , the simulation of the detector material and consequent photon conversion probabilities , the integrated luminosity measurement and the detector occupancy estimate have been considered , and a relative systematic error of 8% is assigned to the cross - section measurements . this comes dominantly from uncertainty on the energy scale for low - energy photons and from comparison of different event generators@xcite . the kinematic properties of the selected events in the combined 1997 data sample are displayed in figures  [ f : g2_kin133 ] and [ f : g2_kin183 ] . they are compared with the predicted distributions for @xmath62 obtained using the koralz generator normalized to the integrated luminosity of the data . in each case plot ( a ) shows the recoil mass distribution of the selected acoplanar - photon pairs . these are peaked near the mass of the @xmath160 as expected for contributions from @xmath62 . the resolution of the recoil mass is typically 2 - 4 gev for @xmath196 . plot ( b ) shows the distribution of the scaled energy of the least - energetic photon . plot ( c ) shows the @xmath197 invariant mass distribution for which the mass resolution is typically 0.6 - 1.4 gev . plot ( d ) shows the distribution in scaled transverse momentum of the selected two - photon system . the measured kinematic properties of the events are given in table  [ tab : g2_prop ] . there were no selected events with three photons , compared to an expectation from koralz of @xmath198 events .    in data taken in 1995 at @xmath164 130 and 136 gev , we observed 8 events compared to @xmath199 expected from koralz@xcite . however , the kinematic properties of these events , in particular the recoil mass distribution , agreed reasonably well with expectations . it was demonstrated that plausible detector or beam related backgrounds do not contribute to this excess . analysis of the 1996 opal data samples taken at @xmath164 161 and 172 gev selected a number of events which was consistent with the expected standard model background contributions . in the data taken in 1997 at @xmath164 130 and 136 gev , we select a total of 4 events where @xmath200 are expected . the 1997 data are therefore consistent with the koralz expectation . however , the opal data samples at @xmath155 and 136 gev continue to favour an excess of events over the expectation from koralz . results on this topology have also been reported by the aleph collaboration based on the analysis of 5.8 pb@xmath58 of data taken at @xmath155 and 136 gev in 1995 . that analysis has a kinematic acceptance similar to the one used by opal . no events were observed compared to a monte carlo expectation of two events  @xcite .    as discussed in our previous publication , the status of event generators and analytical calculations of the standard model process @xmath62 is not yet satisfactory . we anticipate that on - going theoretical work by several authors will result in increased understanding of the actual precision of current approaches , and lead to improved approaches . in particular , a new and more complete calculation has recently appeared@xcite . for now , however , with contributions from higher order processes not demonstrably under control , we do not know what theoretical uncertainty to assign to the koralz prediction .    in conclusion , the observed data excess over the koralz prediction at @xmath155 and 136 gev has not been resolved satisfactorily . analysis of all data collected at these centre - of - mass energies by the other lep experiments could help to resolve whether the observed effect is real , rather than simply a statistical fluctuation or a deficiency in the calculation of the standard model prediction .    in the data taken at @xmath79 gev , the agreement with expectations from koralz is rather good . the only point of note is the selection of two events with a rather high invariant mass for the @xmath197 pair . as seen in figure  [ f : g2_kin183]c these events populate the high - mass tail of the distribution expected from @xmath62 . these events are both characterized by almost back - to - back photons in the polar angle region above @xmath201 . [ sec : g2_results_allmy ]    selected events are classified as consistent with a given value of @xmath100 and @xmath101 if the energy of each of the photons falls within the region kinematically accessible to photons from the process @xmath64 , @xmath66 , including resolution effects . the selection efficiencies at each generated grid point for the @xmath64 , @xmath66 monte carlo events at @xmath79 gev are shown in table  [ tab : g2_eff183 ] . these values include the efficiency of the kinematic consistency requirement which is higher than 95% at each generated point in the @xmath156 plane . figure  [ f : g2_mxmy ] shows the 95% cl exclusion regions for @xmath4 . the limits vary from 0.08 pb to 0.37 pb for @xmath202 gev and @xmath203 gev . in the region 2.5 gev @xmath204 gev , the efficiency falls off rapidly ( see table  [ tab : g2_eff183 ] ) . however , even accounting for increased uncertainty on the efficiency , the limits in that region are better than about 1 pb for all ( @xmath100,@xmath101 ) . because of the uncertainties in the modelling of the standard model background , as discussed earlier and in @xcite , these limits and the limits presented below for this topology have been calculated without taking into account the background estimate . events from @xmath62 are typically characterized by a high - energy photon from the radiative return to the @xmath80 and a second lower energy photon . the kinematic consistency requirement is such that the two photons must have energies within the same ( kinematically accessible ) region . as @xmath100 and @xmath101 increase , the allowed range of energy for the photons narrows and fewer @xmath205 events will be accepted . for the 10 selected events at @xmath79 gev , the distribution of the number of events consistent with a given mass point ( @xmath100,@xmath101 ) is consistent with the expectation from @xmath62 monte carlo . systematic errors are due primarily to limited monte carlo statistics at the generated ( @xmath184 ) points and the uncertainty on the efficiency parametrization across the ( @xmath184 ) plane . the combined relative uncertainty on the efficiency varies from about ( 3 - 6)% across the plane ( for @xmath206 gev ) . all systematic uncertainties are accounted for in the manner advocated in reference@xcite . this also applies to the limits for the @xmath69 case , presented in the next section . [ sec : g2_results_my0 ]    for the special case of @xmath69 the kinematic consistency requirements differ from those used for the general case . one can calculate@xcite the maximum mass , @xmath207 , which is consistent with the measured three - momenta of the two photons , assuming a massless @xmath5 . a cut on @xmath207 provides further suppression of the @xmath205 background while retaining high efficiency for the signal hypothesis . this is discussed in more detail in reference@xcite . we require that the maximum kinematically allowed mass be greater than @xmath208 gev , which retains @xmath209% relative efficiency for signal at all values of @xmath100 while suppressing much of the remaining @xmath205 background . figure  [ f : g2_mxmax_mrec]a shows the expected @xmath207 distribution for signal monte carlo events with @xmath210 gev and for @xmath62 monte carlo events . also shown is the distribution of the selected data events . in addition , we require that the recoil mass be less than 80 gev , which approximately maximizes the expected sensitivity of the analysis for all @xmath100 . this cut retains more than 50% of the signal efficiency , for all values of @xmath100 , and dramatically reduces the residual @xmath205 background . this is most true in the region of low @xmath100 and remains valid up to the kinematic limit . a recoil mass cut is not applied in the massive y case since this would lead to a large loss of efficiency in certain regions of the @xmath156 plane . for the @xmath69 case , the efficiencies calculated from monte carlo events generated at 183 gev are shown in table  [ tab : g2_eff183_my0 ] after application of the event selection criteria and the cut on @xmath207 , and then after the additional requirement of @xmath211 gev . also shown in figure  [ f : g2_mxmax_mrec ] are the @xmath173 distributions for selected events with ( b ) no cut on @xmath207 and ( c ) @xmath212 gev ( for consistency with @xmath210 gev ) . no event survives the recoil mass cut ; the expected number of standard model events is @xmath213 . the expected number consistent with @xmath214 gev is @xmath215 decreasing to @xmath216 expected events consistent with @xmath217 gev as shown in table  [ tab : g2_eff183_my0 ] . based on the efficiencies and the number of selected events , we calculate a 95% cl upper limit on @xmath4 for @xmath69 as a function of @xmath100 . this is shown as the solid line in figure  [ f : g2_limit_my0 ] . the limit ranges from 0.094 to 0.14 pb for all @xmath100 from 45 gev to the kinematic limit . also shown as a dashed line is the expected limit , defined in section  [ sec : sp_results_allmy ] . these limits can be used to set model - dependent limits on the mass of the lightest neutralino in supersymmetric models in which the nlsp is the lightest neutralino and the lsp is a light gravitino ( @xmath72 ) . shown in figure [ f : g2_limit_my0 ] as a dotted line is the ( born - level ) cross - section prediction from a specific light gravitino lsp model@xcite in which @xmath218 , @xmath219 and the neutralino composition is purely gaugino ( bino ) . within the framework of this model , @xmath71 masses between 45 and 83 gev are excluded at 95% cl . the expected number of @xmath205 background events consistent with @xmath220 gev is @xmath221 . as described in section 2 , the efficiencies over the full angular range have been calculated using isotropic angular distributions for production and decay of @xmath65 . the validity of this model has been examined based on the angular distributions calculated for photino pair production in @xcite . for models proposed in @xcite , the production angular distributions are more central and so this procedure is conservative . for a @xmath222 production angular distribution expected for t - channel exchange of a very heavy particle according to @xcite , the relative efficiency reduction would be less than 2% at all points in the ( @xmath184 ) plane .","summary":"cross - section measurements are performed within the kinematic acceptance of each selection . no evidence is observed for new physics contributions to these final states . using the data at = 183 gev , upper limits on and","abstract":"photonic events with large missing energy have been observed in collisions at centre - of - mass energies of 130 , 136 and 183  gev collected in 1997 using the opal detector at lep . results are presented for event topologies with a single photon and missing transverse energy or with an acoplanar photon pair . cross - section measurements are performed within the kinematic acceptance of each selection . these results are compared with the expectations from the standard model process + photon(s ) . no evidence is observed for new physics contributions to these final states . using the data at = 183 gev , upper limits on and are derived for the case of stable and invisible . these limits apply to single and pair production of excited neutrinos ( ) , to neutralino production ( ) and to supersymmetric models in which and is a light gravitino .    plus 1pt minus 1pt plus 1pt    plus 1pt minus 1pt plus 1pt    european laboratory for particle physics    cern - ep/98 - 143 + 08 september 1998    * search for anomalous photonic + events with missing energy in collisions + at = 130 , 136 and 183  *    the opal collaboration    ( submitted to eur . phys . j. * c*. )    the opal collaboration     g.abbiendi , k.ackerstaff , g.alexander , j.allison , n.altekamp , k.j.anderson , s.anderson , s.arcelli , s.asai , s.f.ashby , d.axen , g.azuelos , a.h.ball , e.barberio , r.j.barlow , r.bartoldus , j.r.batley , s.baumann , j.bechtluft , t.behnke , k.w.bell , g.bella , a.bellerive , s.bentvelsen , s.bethke , s.betts , o.biebel , a.biguzzi , s.d.bird , v.blobel , i.j.bloodworth , m.bobinski , p.bock , j.bhme , d.bonacorsi , m.boutemeur , s.braibant , p.bright-thomas , l.brigliadori , r.m.brown , h.j.burckhart , c.burgard , r.brgin , p.capiluppi , r.k.carnegie , a.a.carter , j.r.carter , c.y.chang , d.g.charlton , d.chrisman , c.ciocca , p.e.l.clarke , e.clay , i.cohen , j.e.conboy , o.c.cooke , c.couyoumtzelis , r.l.coxe , m.cuffiani , s.dado , g.m.dallavalle , r.davis , s.de jong , l.a.del pozo , a.de roeck , k.desch , b.dienes , m.s.dixit , j.dubbert , e.duchovni , g.duckeck , i.p.duerdoth , d.eatough , p.g.estabrooks , e.etzion , h.g.evans , f.fabbri , m.fanti , a.a.faust , f.fiedler , m.fierro , i.fleck , r.folman , a.frtjes , d.i.futyan , p.gagnon , j.w.gary , j.gascon , s.m.gascon-shotkin , g.gaycken , c.geich-gimbel , g.giacomelli , p.giacomelli , v.gibson , w.r.gibson , d.m.gingrich , d.glenzinski , j.goldberg , w.gorn , c.grandi , e.gross , j.grunhaus , m.gruw , g.g.hanson , m.hansroul , m.hapke , k.harder , c.k.hargrove , c.hartmann , m.hauschild , c.m.hawkes , r.hawkings , r.j.hemingway , m.herndon , g.herten , r.d.heuer , m.d.hildreth , j.c.hill , s.j.hillier , p.r.hobson , a.hocker , r.j.homer , a.k.honma , d.horvth , k.r.hossain , r.howard , p.hntemeyer , p.igo-kemenes , d.c.imrie , k.ishii , f.r.jacob , a.jawahery , h.jeremie , m.jimack , c.r.jones , p.jovanovic , t.r.junk , d.karlen , v.kartvelishvili , k.kawagoe , t.kawamoto , p.i.kayal , r.k.keeler , r.g.kellogg , b.w.kennedy , a.klier , s.kluth , t.kobayashi , m.kobel , d.s.koetke , t.p.kokott , m.kolrep , s.komamiya , r.v.kowalewski , t.kress , p.krieger , j.von krogh , t.kuhl , p.kyberd , g.d.lafferty , d.lanske , j.lauber , s.r.lautenschlager , i.lawson , j.g.layter , d.lazic , a.m.lee , d.lellouch , j.letts , l.levinson , r.liebisch , b.list , c.littlewood , a.w.lloyd , s.l.lloyd , f.k.loebinger , g.d.long , m.j.losty , j.ludwig , d.liu , a.macchiolo , a.macpherson , w.mader , m.mannelli , s.marcellini , c.markopoulos , a.j.martin , j.p.martin , g.martinez , t.mashimo , p.mttig , w.j.mcdonald , j.mckenna , e.a.mckigney , t.j.mcmahon , r.a.mcpherson , f.meijers , s.menke , f.s.merritt , h.mes , j.meyer , a.michelini , s.mihara , g.mikenberg , d.j.miller , r.mir , w.mohr , a.montanari , t.mori , k.nagai , i.nakamura , h.a.neal , b.nellen , r.nisius , s.w.oneale , f.g.oakham , f.odorici , h.o.ogren , m.j.oreglia , s.orito , j.plinks , g.psztor , j.r.pater , g.n.patrick , j.patt , r.perez-ochoa , s.petzold , p.pfeifenschneider , j.e.pilcher , j.pinfold , d.e.plane , p.poffenberger , j.polok , m.przybycie , c.rembser , h.rick , s.robertson , s.a.robins , n.rodning , j.m.roney , k.roscoe , a.m.rossi , y.rozen , k.runge , o.runolfsson , d.r.rust , k.sachs , t.saeki , o.sahr , w.m.sang , e.k.g.sarkisyan , c.sbarra , a.d.schaile , o.schaile , f.scharf , p.scharff-hansen , j.schieck , b.schmitt , s.schmitt , a.schning , m.schrder , m.schumacher , c.schwick , w.g.scott , r.seuster , t.g.shears , b.c.shen , c.h.shepherd-themistocleous , p.sherwood , g.p.siroli , a.sittler , a.skuja , a.m.smith , g.a.snow , r.sobie , s.sldner-rembold , m.sproston , a.stahl , k.stephens , j.steuerer , k.stoll , d.strom , r.strhmer , b.surrow , s.d.talbot , s.tanaka , p.taras , s.tarem , r.teuscher , m.thiergen , m.a.thomson , e.von trne , e.torrence , s.towers , i.trigger , z.trcsnyi , e.tsur , a.s.turcot , m.f.turner-watson , r.van  kooten , p.vannerem , m.verzocchi , h.voss , f.wckerle , a.wagner , c.p.ward , d.r.ward , p.m.watkins , a.t.watson , n.k.watson , p.s.wells , n.wermes , j.s.white , g.w.wilson , j.a.wilson , t.r.wyatt , s.yamashita , g.yekutieli , v.zacek , d.zer-zion   school of physics and astronomy , university of birmingham , birmingham b15 2tt , ukdipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italyphysikalisches institut , universitt bonn , d-53115 bonn , germanydepartment of physics , university of california , riverside ca 92521 , usacavendish laboratory , cambridge cb3 0he , ukottawa - carleton institute for physics , department of physics , carleton university , ottawa , ontario k1s 5b6 , canadacentre for research in particle physics , carleton university , ottawa , ontario k1s 5b6 , canadacern , european organisation for particle physics , ch-1211 geneva 23 , switzerlandenrico fermi institute and department of physics , university of chicago , chicago il 60637 , usafakultt fr physik , albert ludwigs universitt , d-79104 freiburg , germanyphysikalisches institut , universitt heidelberg , d-69120 heidelberg , germanyindiana university , department of physics , swain hall west 117 , bloomington in 47405 , usaqueen mary and westfield college , university of london , london e1 4ns , uktechnische hochschule aachen , iii physikalisches institut , sommerfeldstrasse 26 - 28 , d-52056 aachen , germanyuniversity college london , london wc1e 6bt , ukdepartment of physics , schuster laboratory , the university , manchester m13 9pl , ukdepartment of physics , university of maryland , college park , md 20742 , usalaboratoire de physique nuclaire , universit de montral , montral , quebec h3c 3j7 , canadauniversity of oregon , department of physics , eugene or 97403 , usaclrc rutherford appleton laboratory , chilton , didcot , oxfordshire ox11 0qx , ukdepartment of physics , technion - israel institute of technology , haifa 32000 , israeldepartment of physics and astronomy , tel aviv university , tel aviv 69978 , israelinternational centre for elementary particle physics and department of physics , university of tokyo , tokyo 113 - 0033 , and kobe university , kobe 657 - 8501 , japaninstitute of physical and environmental sciences , brunel university , uxbridge , middlesex ub8 3ph , ukparticle physics department , weizmann institute of science , rehovot 76100 , israeluniversitt hamburg / desy , ii institut fr experimental physik , notkestrasse 85 , d-22607 hamburg , germanyuniversity of victoria , department of physics , p o box 3055 , victoria bc v8w 3p6 , canadauniversity of british columbia , department of physics , vancouver bc v6 t 1z1 , canadauniversity of alberta , department of physics , edmonton ab t6 g 2j1 , canadaduke university , dept of physics , durham , nc 27708 - 0305 , usaresearch institute for particle and nuclear physics , h-1525 budapest , p o box 49 , hungaryinstitute of nuclear research , h-4001 debrecen , p o box 51 , hungaryludwigs - maximilians - universitt mnchen , sektion physik , am coulombwall 1 , d-85748 garching , germany and at triumf , vancouver , canada v6 t 2a3 and royal society university research fellow and institute of nuclear research , debrecen , hungary and department of experimental physics , lajos kossuth university , debrecen , hungary on leave of absence from the university of freiburg"}
{"article_id":"hep-ex9810021","section_id":"c","document":"we have searched for photonic events with large missing energy in two topologies in data taken with the opal detector at lep , at centre - of - mass energies of 130 , 136 and 183 gev .    in the single - photon selection , which requires at least one photon with @xmath223 in the region @xmath109 ( @xmath110 , a total of 21 , 39 and 191 events are observed in the data for @xmath2  =  130 , 136 and 183 gev , respectively . these numbers are in agreement with the expectations of the koralz monte carlo generator for the standard model process @xmath61 . the expected background is small . we derive upper limits on the cross - section times branching ratio for the process @xmath63 , @xmath66 for the general case of massive @xmath65 and @xmath5 . the limits vary from 0.075 to 0.80 pb in the region of interest in the @xmath156 plane and include the special case of @xmath69 , where the limit varies between 0.075 and 0.46 pb for the @xmath100 mass range from @xmath163 to 183 gev . the acoplanar - photons selection requires at least two photons with scaled energy @xmath224 within the polar angle region @xmath225 or at least two photons with energy @xmath226 gev with one satisfying @xmath113 and the other satisfying @xmath225 . in each case , the requirement @xmath115 is also applied . a total of 2 , 2 and 10 events are selected from the data samples at @xmath2 = 130 , 136 and 183 gev , respectively . the koralz predictions for the contributions from @xmath62 are , respectively , 1.02 , 1.22 and 9.14 events . the number of events observed in the 1997 data samples and their kinematic distributions are consistent with expectations for @xmath62 . we derive 95% cl upper limits on @xmath4 ranging from 0.08 to 0.37 pb for the general case of massive @xmath65 and @xmath5 . for the special case of @xmath69 , the 95% cl upper limits on @xmath4 range from 0.094 to 0.14 pb . due to the uncertainties in the current modelling of the standard model process @xmath62 , all limits from the acoplanar - photons analysis were calculated without taking into account the background estimate .    for the single - photon and acoplanar - photons search topologies , the general case of massive @xmath65 and @xmath5 is relevant to supersymmetric models in which @xmath153 and @xmath154 , with @xmath97 and @xmath71 stable . the special case of @xmath69 is of particular interest for single and pair production of excited neutrinos and for supersymmetric models in which the lsp is a light gravitino and the nlsp is @xmath71 which decays as @xmath227 . for the latter scenario , the results of the acoplanar - photons search are used to place model - dependent lower limits on the @xmath71 mass . a specific light gravitino lsp model@xcite is excluded for the case of promptly decaying neutralinos with masses between 45 and 83 gev .","summary":"photonic events with large missing energy have been observed in collisions at centre - of - mass energies of 130 , 136 and 183  gev collected in 1997 using the opal detector at lep . these results are compared with the expectations from the standard model process + photon(s ) .","abstract":"photonic events with large missing energy have been observed in collisions at centre - of - mass energies of 130 , 136 and 183  gev collected in 1997 using the opal detector at lep . results are presented for event topologies with a single photon and missing transverse energy or with an acoplanar photon pair . cross - section measurements are performed within the kinematic acceptance of each selection . these results are compared with the expectations from the standard model process + photon(s ) . no evidence is observed for new physics contributions to these final states . using the data at = 183 gev , upper limits on and are derived for the case of stable and invisible . these limits apply to single and pair production of excited neutrinos ( ) , to neutralino production ( ) and to supersymmetric models in which and is a light gravitino .    plus 1pt minus 1pt plus 1pt    plus 1pt minus 1pt plus 1pt    european laboratory for particle physics    cern - ep/98 - 143 + 08 september 1998    * search for anomalous photonic + events with missing energy in collisions + at = 130 , 136 and 183  *    the opal collaboration    ( submitted to eur . phys . j. * c*. )    the opal collaboration     g.abbiendi , k.ackerstaff , g.alexander , j.allison , n.altekamp , k.j.anderson , s.anderson , s.arcelli , s.asai , s.f.ashby , d.axen , g.azuelos , a.h.ball , e.barberio , r.j.barlow , r.bartoldus , j.r.batley , s.baumann , j.bechtluft , t.behnke , k.w.bell , g.bella , a.bellerive , s.bentvelsen , s.bethke , s.betts , o.biebel , a.biguzzi , s.d.bird , v.blobel , i.j.bloodworth , m.bobinski , p.bock , j.bhme , d.bonacorsi , m.boutemeur , s.braibant , p.bright-thomas , l.brigliadori , r.m.brown , h.j.burckhart , c.burgard , r.brgin , p.capiluppi , r.k.carnegie , a.a.carter , j.r.carter , c.y.chang , d.g.charlton , d.chrisman , c.ciocca , p.e.l.clarke , e.clay , i.cohen , j.e.conboy , o.c.cooke , c.couyoumtzelis , r.l.coxe , m.cuffiani , s.dado , g.m.dallavalle , r.davis , s.de jong , l.a.del pozo , a.de roeck , k.desch , b.dienes , m.s.dixit , j.dubbert , e.duchovni , g.duckeck , i.p.duerdoth , d.eatough , p.g.estabrooks , e.etzion , h.g.evans , f.fabbri , m.fanti , a.a.faust , f.fiedler , m.fierro , i.fleck , r.folman , a.frtjes , d.i.futyan , p.gagnon , j.w.gary , j.gascon , s.m.gascon-shotkin , g.gaycken , c.geich-gimbel , g.giacomelli , p.giacomelli , v.gibson , w.r.gibson , d.m.gingrich , d.glenzinski , j.goldberg , w.gorn , c.grandi , e.gross , j.grunhaus , m.gruw , g.g.hanson , m.hansroul , m.hapke , k.harder , c.k.hargrove , c.hartmann , m.hauschild , c.m.hawkes , r.hawkings , r.j.hemingway , m.herndon , g.herten , r.d.heuer , m.d.hildreth , j.c.hill , s.j.hillier , p.r.hobson , a.hocker , r.j.homer , a.k.honma , d.horvth , k.r.hossain , r.howard , p.hntemeyer , p.igo-kemenes , d.c.imrie , k.ishii , f.r.jacob , a.jawahery , h.jeremie , m.jimack , c.r.jones , p.jovanovic , t.r.junk , d.karlen , v.kartvelishvili , k.kawagoe , t.kawamoto , p.i.kayal , r.k.keeler , r.g.kellogg , b.w.kennedy , a.klier , s.kluth , t.kobayashi , m.kobel , d.s.koetke , t.p.kokott , m.kolrep , s.komamiya , r.v.kowalewski , t.kress , p.krieger , j.von krogh , t.kuhl , p.kyberd , g.d.lafferty , d.lanske , j.lauber , s.r.lautenschlager , i.lawson , j.g.layter , d.lazic , a.m.lee , d.lellouch , j.letts , l.levinson , r.liebisch , b.list , c.littlewood , a.w.lloyd , s.l.lloyd , f.k.loebinger , g.d.long , m.j.losty , j.ludwig , d.liu , a.macchiolo , a.macpherson , w.mader , m.mannelli , s.marcellini , c.markopoulos , a.j.martin , j.p.martin , g.martinez , t.mashimo , p.mttig , w.j.mcdonald , j.mckenna , e.a.mckigney , t.j.mcmahon , r.a.mcpherson , f.meijers , s.menke , f.s.merritt , h.mes , j.meyer , a.michelini , s.mihara , g.mikenberg , d.j.miller , r.mir , w.mohr , a.montanari , t.mori , k.nagai , i.nakamura , h.a.neal , b.nellen , r.nisius , s.w.oneale , f.g.oakham , f.odorici , h.o.ogren , m.j.oreglia , s.orito , j.plinks , g.psztor , j.r.pater , g.n.patrick , j.patt , r.perez-ochoa , s.petzold , p.pfeifenschneider , j.e.pilcher , j.pinfold , d.e.plane , p.poffenberger , j.polok , m.przybycie , c.rembser , h.rick , s.robertson , s.a.robins , n.rodning , j.m.roney , k.roscoe , a.m.rossi , y.rozen , k.runge , o.runolfsson , d.r.rust , k.sachs , t.saeki , o.sahr , w.m.sang , e.k.g.sarkisyan , c.sbarra , a.d.schaile , o.schaile , f.scharf , p.scharff-hansen , j.schieck , b.schmitt , s.schmitt , a.schning , m.schrder , m.schumacher , c.schwick , w.g.scott , r.seuster , t.g.shears , b.c.shen , c.h.shepherd-themistocleous , p.sherwood , g.p.siroli , a.sittler , a.skuja , a.m.smith , g.a.snow , r.sobie , s.sldner-rembold , m.sproston , a.stahl , k.stephens , j.steuerer , k.stoll , d.strom , r.strhmer , b.surrow , s.d.talbot , s.tanaka , p.taras , s.tarem , r.teuscher , m.thiergen , m.a.thomson , e.von trne , e.torrence , s.towers , i.trigger , z.trcsnyi , e.tsur , a.s.turcot , m.f.turner-watson , r.van  kooten , p.vannerem , m.verzocchi , h.voss , f.wckerle , a.wagner , c.p.ward , d.r.ward , p.m.watkins , a.t.watson , n.k.watson , p.s.wells , n.wermes , j.s.white , g.w.wilson , j.a.wilson , t.r.wyatt , s.yamashita , g.yekutieli , v.zacek , d.zer-zion   school of physics and astronomy , university of birmingham , birmingham b15 2tt , ukdipartimento di fisica dell universit di bologna and infn , i-40126 bologna , italyphysikalisches institut , universitt bonn , d-53115 bonn , germanydepartment of physics , university of california , riverside ca 92521 , usacavendish laboratory , cambridge cb3 0he , ukottawa - carleton institute for physics , department of physics , carleton university , ottawa , ontario k1s 5b6 , canadacentre for research in particle physics , carleton university , ottawa , ontario k1s 5b6 , canadacern , european organisation for particle physics , ch-1211 geneva 23 , switzerlandenrico fermi institute and department of physics , university of chicago , chicago il 60637 , usafakultt fr physik , albert ludwigs universitt , d-79104 freiburg , germanyphysikalisches institut , universitt heidelberg , d-69120 heidelberg , germanyindiana university , department of physics , swain hall west 117 , bloomington in 47405 , usaqueen mary and westfield college , university of london , london e1 4ns , uktechnische hochschule aachen , iii physikalisches institut , sommerfeldstrasse 26 - 28 , d-52056 aachen , germanyuniversity college london , london wc1e 6bt , ukdepartment of physics , schuster laboratory , the university , manchester m13 9pl , ukdepartment of physics , university of maryland , college park , md 20742 , usalaboratoire de physique nuclaire , universit de montral , montral , quebec h3c 3j7 , canadauniversity of oregon , department of physics , eugene or 97403 , usaclrc rutherford appleton laboratory , chilton , didcot , oxfordshire ox11 0qx , ukdepartment of physics , technion - israel institute of technology , haifa 32000 , israeldepartment of physics and astronomy , tel aviv university , tel aviv 69978 , israelinternational centre for elementary particle physics and department of physics , university of tokyo , tokyo 113 - 0033 , and kobe university , kobe 657 - 8501 , japaninstitute of physical and environmental sciences , brunel university , uxbridge , middlesex ub8 3ph , ukparticle physics department , weizmann institute of science , rehovot 76100 , israeluniversitt hamburg / desy , ii institut fr experimental physik , notkestrasse 85 , d-22607 hamburg , germanyuniversity of victoria , department of physics , p o box 3055 , victoria bc v8w 3p6 , canadauniversity of british columbia , department of physics , vancouver bc v6 t 1z1 , canadauniversity of alberta , department of physics , edmonton ab t6 g 2j1 , canadaduke university , dept of physics , durham , nc 27708 - 0305 , usaresearch institute for particle and nuclear physics , h-1525 budapest , p o box 49 , hungaryinstitute of nuclear research , h-4001 debrecen , p o box 51 , hungaryludwigs - maximilians - universitt mnchen , sektion physik , am coulombwall 1 , d-85748 garching , germany and at triumf , vancouver , canada v6 t 2a3 and royal society university research fellow and institute of nuclear research , debrecen , hungary and department of experimental physics , lajos kossuth university , debrecen , hungary on leave of absence from the university of freiburg"}
{"article_id":"1412.4025","section_id":"i","document":"quantum coherence is a phenomenon that could have profound impact on technological development . usually understood to appear in temperature regimes much lower than those encountered in everyday practice , quantum coherence effects are not directly utilized in the operation of most conventional devices . superconducting sensors , magnets and transmission cables are examples where macroscopic quantum coherence is maintained at relatively high temperature . nonetheless , even the highest-@xmath0 materials currently remain in the realm of cryogenic temperatures , thus significantly hampering their potential applicability . consequently , much effort has been expended in the quest for higher temperature materials , as room - temperature superconductivity remains one of the most prominent issues in condensed matter physics . although recent experimental evidence may suggest that superconductivity is possible at room temperature @xcite , what is perhaps even more compelling is the emerging evidence that photosynthetic systems found in nature may have already evolved a means of exploiting quantum coherence effects at physiological temperatures @xcite . due to the broad array of organisms sustained by trapping then converting sunlight into chemical energy , photosynthesis is probably the cleanest , most efficient energy collection mechanism on earth , perhaps making high - temperature quantum coherence far more ubiquitous than previously thought . central to the understanding of temperature - dependent quantum coherence is the decoherence or thermalization of quantum systems with their surrounding environment . in the well - known work of caldeira and leggett @xcite , the feynman - vernon influence functional approach @xcite is used to model a thermalizing environment with the purpose of introducing decoherence into a quantum oscillator . following the same path integral approach , it is demonstrated that a thermalizing environment need not always lead to decoherence in the steady - state . arriving at this result requires the realization that because the reservoir can not excite energies too far in excess of its mean thermal energy , a temperature cutoff must be introduced . as a result , low - temperature environments are found to thermalize the quantum oscillator to the usual boltzmann distribution of energy levels , whereas higher - temperature regimes induce a single , coherent oscillator ground state with an imaginary frequency . since the concomitant imaginary energy eigenvalues correspond to decay rates , all excited states become more unstable with increasing quantum number . in this way , environments in this higher - temperature regime damp out the excitations by extracting energy from the quantum oscillator , forcing the oscillator to remain in the stable , coherent ground state . increasing to very high environmental temperatures once again thermalizes the quantum oscillator in the usual way .    in short , a dissipative environment can cause a suppression or damping of excited modes , thus acting to maintain quantum coherence even at relatively high temperatures . this result may underpin recent observations of room - temperature superconducting effects in water - treated graphite grains @xcite . finally , given their emergence and subsequent disappearance of quantum coherence with increasing temperature , photosynthetic molecules most remarkably follow the qualitative behavior described here @xcite .","summary":"the feynman - vernon path integral formalism is used to derive the density matrix of a quantum oscillator that is linearly coupled to an environmental reservoir . although low - temperature reservoirs thermalize the oscillator to the usual boltzmann distribution , reservoirs at intermediate temperatures reduce this distribution to a single , coherent ground state . qualitatively , this result could account for high - temperature quantum effects including the superconducting properties of graphite grains as well as the quantum coherence observed in photosynthetic systems .    decoherence , thermalization , imaginary eigenvalue , excited state decay , photosynthesis , high - temperature superconductivity","abstract":"the feynman - vernon path integral formalism is used to derive the density matrix of a quantum oscillator that is linearly coupled to an environmental reservoir . although low - temperature reservoirs thermalize the oscillator to the usual boltzmann distribution , reservoirs at intermediate temperatures reduce this distribution to a single , coherent ground state . associated with this state is an imaginary frequency indicating an environment which absorbs energy from the oscillator through the suppression of all excited modes . further increase of the environmental temperature results again in the thermalization of the quantum oscillator to the expected boltzmann distribution . qualitatively , this result could account for high - temperature quantum effects including the superconducting properties of graphite grains as well as the quantum coherence observed in photosynthetic systems .    decoherence , thermalization , imaginary eigenvalue , excited state decay , photosynthesis , high - temperature superconductivity"}
{"article_id":"cond-mat0603121","section_id":"i","document":"the magnetic properties of nanoparticles , thin films and wires have attracted recently a lot of attention due to their potential technological applications . it is thus very important to investigate the influence of dimensionality on these properties . in many experimental systems , some atoms are in a bulk - like environment while some others have a very low coordinence in a strongly asymmetric environment . this is the case of clusters , at the edge of adsorbed islands , supported wires , along step edges or in the nanoconstriction region of a break junction etc .. as a consequence the magnetic properties of such systems need to be treated at an atomic level , by studying their electronic structure in the framework of quantum mechanics .    in principle these properties can be determined from ab - initio calculations . however the computer time and storage increase drastically with the number of inequivalent atoms . thus there is a need for simplified methods still based on quantum mechanics which capture the essential physics . in this context tight - binding ( tb ) methods are ideally suited for these calculations . indeed tb methods can be extended to magnetic systems by introducing hubbard two - body terms treated in the hartree - fock approximation @xcite , and can easily include spin - orbit effects@xcite . moreover they allow the calculation of local physical quantities ( spin or orbital moment etc .. ) in a straightforward manner which gives a physically transparent understanding of the phenomena . the anisotropy of the magneto - crystalline energy ( mae ) , although small in transition metals , is of fundamental importance since it determines the easy magnetization axis . the mae results from the coupling of the spin and orbital moments . in the bulk it is well known that the orbital moment is nearly quenched due to the high symmetry of the potential . when dimensionality or symmetry is reduced the orbital moment is less and less quenched and the mae increases rapidly . the mae is routinely measured by magnetic hysteresis or torque measurements@xcite , for instance . more recently the development of x - ray magnetic circular dichroism techniques has allowed the experimental determination of the orbital moment@xcite . on the theoretical side the calculation of the mae in bulk pure ferromagnetic transition metals is a challenge because of its minuteness ( typically some @xmath5ev ) . the first attempts to determine the mae on surfaces have been performed on free standing mono - layers either using a perturbative treatment of the spin - orbit coupling in a tight - binding model@xcite , or with self - consistent ab - initio technique@xcite . the calculations performed by bruno @xcite on mono - layers have been extended to study slabs with several atomic layers@xcite in a pure @xmath2-band model . more recently the case of layered ordered alloys of the cuau or cscl types containing at least one ferromagnetic element@xcite , deposited ferromagnetic over - layers on non - magnetic substrates@xcite , and multilayers have been investigated@xcite . simultaneously the orbital magnetism driven by the spin - orbit interaction has been computed using the tight - binding model ( perturbatively@xcite or non perturbatively@xcite ) as well as ab - initio codes@xcite .    the aim of this paper is to develop a tb model allowing the determination of the magnetic properties of transition metals in various geometrical configurations , going from highly coordinated and symmetric environments to low coordinated and anisotropic geometries . in a first step we have found useful to check the validity of the model by a detailed comparison with the results provided by ab - initio methods on simple systems . in addition , the use of both methods yields a better physical understanding of these properties , and , moreover , the simplicity of our model allows a more detailed analysis of each system . we use a non - orthogonal basis set of @xmath0 , @xmath1 and @xmath2 valence orbitals . the parametrization of the non - magnetic and non - relativistic hamiltonian was derived by mehl and papaconstantopoulos @xcite . the possibility of spin polarization is then introduced using a stoner like model in which the splitting between the energy levels of up and down spin orbitals is governed by the stoner parameter @xmath6 and is proportional to the magnetic moment carried by @xmath2 electrons . indeed it is well known that @xmath0 and @xmath1 electrons are very weakly polarized . the relativistic effects , limited to spin - orbit coupling between @xmath2 electrons , are taken into account by adding the intra atomic matrix elements of this coupling determined by a parameter @xmath7 . the two parameters @xmath6 and @xmath7 are fixed by comparison with ab - initio calculations . for the stoner parameter the variation of the magnetization as a function of interatomic distance in the bulk phase can be used . the determination of the spin - orbit coupling parameter relies on the study of the degeneracy removal of energy bands at high symmetry points or directions of the brillouin zone . we have applied our model to the study of iron in various atomic arrangements going from the bulk , in the experimentally observed phases bcc and fcc , to simple surfaces and finally to the monoatomic wire , at several interatomic distances . it is found that with a unique value of the stoner parameter we are able to reproduce the variation of the spin magnetic moment in a wide range of lattice spacings in the bcc bulk phase . it is well known that the magnetic properties of bulk fcc iron are rather complex . in spite of this complexity the calculations carried out in this work are in excellent agreement with ab - initio predictions . the spin - orbit coupling parameter is then determined , as explained above , and a single value of this parameter is able to reproduce the ab - initio band structure . furthermore the contribution of the orbital moment to the magnetization in bcc fe is very close to the experimental value . the case of surfaces represents a more stringent check since the dimensionality is reduced and all atoms are not geometrically equivalent . it is in particular interesting to follow the variation of the magnetic properties when going from the outermost to inner ( bulk - like ) layers . the spin - polarized surface projected band structure as well as the variation of the spin magnetic moment as a function of depth derived from ab - initio calculations are perfectly reproduced by our model . in particular the @xmath4 surface atoms have a saturated moment contrary to those of the @xmath3 surface . introducing the spin - orbit coupling in the tb hamiltonian allows the calculation of the mae and of the orbital magnetic moment at each inequivalent site . due to the efficiency of our model it is possible to check rigorously the convergence of these quantities when increasing the number of @xmath8 points . the orbital moment is strongly increased on surface atoms ( about twice the bulk value for the @xmath4 surface ) , and recovers its bulk value on the third and innermost layers . the wire is the most anisotropic atomic arrangement with the lowest coordinence . even though the tb parameters are fitted on bulk ab - initio data only , the non - magnetic band structure calculated with these parameters is in good agreement with ab - initio calculations , proving their good transferability . the two additional parameters @xmath6 and @xmath7 are also perfectly transferable . indeed , without changing the stoner parameter , the variation of the spin magnetic moment with the interatomic distance is satisfactorily reproduced ( in particular the saturated solution appears abruptly at the same interatomic spacing ) and the splitting of bands due to spin - orbit coupling is exactly the same , compared to ab - initio results . the calculation of the mae reveals that at theoretical equilibrium the easy axis is parallel to the wire , but at smaller interatomic distances corresponding to unsaturated magnetic solutions the easy axis is perpendicular to the wire . we have finally checked the validity of bruno formula @xcite relating the mae to the anisotropy of the orbital moment , and found that this relation is almost strictly obeyed around the equilibrium distance . indeed at this interatomic distance the up spin bands are filled and the exchange splitting is large compared to the @xmath2 bandwidth , which was not the case for the @xmath4 surface that , although saturated , has much a wider @xmath2 bandwidth . the paper is organized as follows . in section 2 the formalism of our model is presented in details , in particular the derivation of the @xmath9 , @xmath10 and @xmath11 components of the orbital and spin moment formula in a non - orthogonal basis set . the spin - orbit coupling being small we have recalled the perturbation treatment of the mae and of the orbital moment , from which the analytical expression of the anisotropy laws are directly obtained , and are used to analyze our numerical results . in section 3 the stoner parameter is determined and used to study in detail the magnetic properties of bcc and fcc iron . section 4 is devoted to the study of @xmath4 and @xmath3 surfaces . finally in section 5 we present an exhaustive study of the monoatomic wire . conclusions are drawn in section 6 .","summary":"this model is applied to the study of iron in bulk bcc and fcc phases , and surfaces and to the monatomic wire , at several interatomic distances .","abstract":"the magnetic properties of iron ( spin and orbital magnetic moments , magnetocrystalline anisotropy energy ) in various geometries and dimensionalities are investigated by using a parametrized tight - binding model in an , and atomic orbital basis set including spin polarization and the effect of spin - orbit coupling . the validity of this model is well established by comparing the results with those obtained by using an ab - initio code . this model is applied to the study of iron in bulk bcc and fcc phases , and surfaces and to the monatomic wire , at several interatomic distances . new results are derived . the variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth , revealing a significant enhancement in the first two layers , especially for the surface . it is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several mev . this is also true for the orbital moment , which in addition is highly anisotropic . furthermore it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis . at equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression . the success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries ."}
{"article_id":"cond-mat0603121","section_id":"c","document":"we have shown that starting from the parametrized @xmath209 tb model set up by mehl and papaconstantopoulos @xcite , adding a stoner - like spin polarization term and a spin - orbit coupling term , i.e , introducing only two additional parameters @xmath6 and @xmath7 , we have been able to describe in detail the magnetic properties ( spin moments , orbital moments and magnetocrystalline anisotropy energy ) of iron in systems of various dimensionalities and coordinences . whenever possible the results have been compared with those of the pwscf code or other existing theoretical or experimental data , and the agreement is excellent . our simple tb model allowed us to derive some new results . for example in the case of surfaces we have studied the variation of the component of the orbital magnetic moment on the spin quantization axis @xmath276 as a function of depth , and shown that the enhancement of this quantity is still noticeable on the second layer for the @xmath4 surface but almost cancels on the third and innermost layers . in the wire we have found that the easy axis of magnetization is along the wire at the theoretical equilibrium distance but can switch to the perpendicular direction under compression . moreover @xmath276 is strongly enhanced and highly anisotropic since for @xmath277 along the wire it is about @xmath269 and decreases to half this value for the perpendicular direction . in addition for intermediate orientations the orbital moment has a non - negligible component @xmath278 perpendicular to @xmath277 and in the plane made by the wire and @xmath277 . this component is also anisotropic and proportional to @xmath279 as predicted by perturbation theory . finally we have shown that the law of bruno@xcite relating the mae and the anisotropy of the orbital moment , is perfectly obeyed for the wire at equilibrium distance , which is not the case for the surfaces , even for the @xmath4 orientation at which the magnetic moment is saturated . the success of our model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries . it is our pleasure to thank m. viret for very fruitful discussions and a. dal corso and a. smogunov for precious advice concerning the pwscf code .","summary":"the variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth , revealing a significant enhancement in the first two layers , especially for the surface . it is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several mev . furthermore it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis . at equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression . the success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries .","abstract":"the magnetic properties of iron ( spin and orbital magnetic moments , magnetocrystalline anisotropy energy ) in various geometries and dimensionalities are investigated by using a parametrized tight - binding model in an , and atomic orbital basis set including spin polarization and the effect of spin - orbit coupling . the validity of this model is well established by comparing the results with those obtained by using an ab - initio code . this model is applied to the study of iron in bulk bcc and fcc phases , and surfaces and to the monatomic wire , at several interatomic distances . new results are derived . the variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth , revealing a significant enhancement in the first two layers , especially for the surface . it is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several mev . this is also true for the orbital moment , which in addition is highly anisotropic . furthermore it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis . at equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression . the success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries ."}
{"article_id":"1607.05713","section_id":"i","document":"all - sky mid - infrared surveys have revolutionized the science of planet formation by discovering populations of young stars and main sequence stars with excess infrared radiation indicating the presence of dusty circumstellar disks . these disks , which include gas - rich protoplanetary disks around young stellar objects ( ysos ) and dusty debris disks around main sequence stars , serve as the signposts of planet formation ( e.g. , * ? ? ? they inform us about the timescales and the environment of planet formation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and the present day locations and dynamics of planets ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the iras all sky survey discovered the first extrasolar debris disks @xcite and provided a large sample of debris disks ( e.g. , * ? ? ? after iras , akari surveyed the whole sky at 9 and 18 @xmath0 m with @xmath1 times better sensitivity than iras , finding many more new disks . some disk discoveries have come from pointed studies , like the spitzer formation and evolution of planetary systems ( feps ) survey @xcite . but many of the best - studied , most informative disks ( like tw hydra , fomalhaut , etc . ) are relatively isolated on the sky , requiring an all - sky survey to find them . nasa s wide - field infrared survey explorer ( wise ) is the most recent and sensitive all - sky mid - infrared survey @xcite , with a further factor of @xmath2 gain in sensitivity over akari in the mid - ir . using a 16-inch mirror in a sun - synchronous polar orbit , wise scanned the sky at 3.4 @xmath0 m , 4.6 @xmath0 m , 12 @xmath0 m , and 22 @xmath0 m ( bands w1 , w2 , w3 , and w4 respectively ) . the wise cryogenic mission , launched in 2009 , lasted a little over 10 months and was followed by the first post - cyrogenic mission , neowise . the allwise catalog combines data from both phases , making it the most comprehensive mid - infrared multi - epoch view of the sky available today . previous infrared surveys for debris disks have provided target lists for exoplanet searches via direct imaging @xcite . debris disks found with wise should provide crucial targets for upcoming generations of exoplanet searches . wise could detect debris disks around main sequence a stars to a distance of 300 pc and protoplanetary disks around t tauri stars to 1 kpc . indeed , many teams have used the wise data to find new debris disks , searching a vast catalog of @xmath3 million wise sources . @xcite cross - correlated the wise source list with the hipparcos catalog , finding over 86,000 stars with suspected infrared excesses . @xcite , @xcite and @xcite performed more careful searches for debris disks in the wise source list using the hipparcos catalog and found 6 , 70 and 108 new debris disk candidates , respectively . other specific surveys for debris disks have focused on stars with ages determined from chromospheric activity @xcite , white dwarfs @xcite , m dwarfs , g - k dwarfs @xcite , kepler candidate exoplanet systems and other exoplanet catalogs @xcite .    likewise , the wise data on young clusters and star - forming regions have attracted much attention . @xcite scoured the taurus - auriga region . @xcite searched 11 outer galaxy massive star - forming regions and three open clusters . other studies have examined smaller regions , like the western circinus molecular cloud @xcite , the young open cluster ic 1805 the region s155 @xcite , the sco - cen and @xmath4 cha associations @xcite , nearby moving groups of young stars @xcite and @xmath5 and @xmath6 orionis @xcite . still others have attempted to take in the whole sky , using color cuts or cross correlating with iras @xcite . many of these searches were based on preliminary data releases with less sensitivity than the allwise release , but they have already uncovered thousands of candidate class i , ii and iii ysos and transitional disks , helping fill in our picture of the timing and progression of star formation . unfortunately , because of its limited spatial resolution ( 12 arcsec at 22 @xmath0 m ) contamination and confusion limit every search for disks with wise ( e.g. * ? ? ? contamination sources include unresolved companion stars and other stars nearby on the sky , background galaxies , galactic cirrus , and even asteroids and airplanes . for this reason , most recent searches include visual inspection of the wise images ( see e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? computer cuts alone can provide a first stage of vetting , but they generate catalogs riddled with false positives @xcite ; . color cuts and source quality flags can help , but the color loci of disk candidates overlaps with the color loci of blended background galaxies @xcite and peaks in the galactic dust emission . @xcite used the iras 100 @xmath0 m level to discard many false positive disk candidates contaminated with galactic dust emission , but using this method prohibits searching many interesting star - forming regions . because of these challenges , many disks remain to be found with wise data , even after all the efforts described above . the largest published study of debris disks @xcite and the still larger wise science team disk study ( padgett et al . in prep . ) are based on the hipparcos and tycho catalogs . these catalogs are magnitude limited in v band , so they omit a vast population of redder , late type stars . moreover , a vast solid angle in young clusters and star - forming regions remains to be properly searched with wise  each candidate examined by eye and followed up with spectroscopy and higher resolution imaging . when ran the all - sky data through a novel color filter to search for yso candidates ( without vetting the candidates by eye ) , he found a total of @xmath7 objects of interest ; the wise studies of young clusters and star - forming regions described above ( which mostly included visual vetting ) yielded a total of @xmath8 disk candidates . the difference between these numbers provides a minimal measure of what remains for us to study with wise : @xmath9 objects with colors consistent with ysos that have not yet been visually inspected . here we describe a new project to scour the wise data for new debris disks and ysos . the disk detective citizen science / crowdsourcing project classifies wise sources via a website , diskdetective.org , where volunteers examine images from wise , the two micron all sky survey ( 2mass ) , the digitized sky survey ( dss ) and when available , the sloan digital sky survey ( sdss ) , to check them for false positives . this approach should allow us to unleash the full potential of wise for finding new disks , probing the cooler stars and isolated objects missed by previous debris disk searches , a catalog 8 times the size of the large @xcite survey . we describe the online vetting process in section [ sec : approach ] , our small - telescope follow - up program in section [ sec : followup ] and we present our first list of 37 disk candidates in section [ sec : candidates ] .","summary":"the disk detective citizen science project aims to find new stars with 22 m excess emission from circumstellar dust using data from nasa s wise mission . this approach should allow us to unleash the full potential of wise for finding new debris disks and protoplanetary disks .","abstract":"the disk detective citizen science project aims to find new stars with 22 m excess emission from circumstellar dust using data from nasa s wise mission . initial cuts on the allwise catalog provide an input catalog of 277,686 sources . volunteers then view images of each source online in 10 different bands to identify false - positives ( galaxies , background stars , interstellar matter , image artifacts , etc . ) . sources that survive this online vetting are followed up with spectroscopy on the flwo tillinghast telescope . this approach should allow us to unleash the full potential of wise for finding new debris disks and protoplanetary disks . we announce a first list of 37 new disk candidates discovered by the project , and we describe our vetting and follow - up process . one of these systems appears to contain the first debris disk discovered around a star with a white dwarf companion : hd 74389 . we also report four newly discovered classical be stars ( hd 6612 , hd 7406 , hd 164137 , and hd 218546 ) and a new detection of 22 m excess around a previously known debris disk host star hd 22128 ."}
{"article_id":"1607.05713","section_id":"c","document":"we have outlined and demonstrated a novel process for identifying new candidate circumstellar disks in the wise survey data . this paper reports only results from the first 10% of the search , so it might be premature to try to derive any statistically meaningful inferences about the population of debris disk from this limited sample . but our list of 37 new , well - vetted disk candidates demonstrates the utility of crowdsourcing analysis of wise images . one of our disk candidate systems appears to contain the first debris disk discovered around a star with a white dwarf companion : hd 74389 . we also report four newly discovered classical be stars ( hd 6612 , hd 7406 , hd 164137 , and hd 218546 ) and a new detection of 22 @xmath0 m excess around previously known debris disk host star hd 22128 . we decided to only publish in this paper candidates that are in the hipparcos catalog . since the @xcite cross - correlated the wise archive with the hipparcos catalog , they could conceivably have identified all of the candidates that we are announcing . however , @xcite used a [ 2mass ] - [ w4 ] color criterion , as opposed to our [ w1 ] - [ w4 ] color criterion , and used the wise allsky data rather than the wise allwise data . yet all of the candidates presented in this paper would have also been selected by the @xcite color criterion . more importantly , while we examined candidates by eye to discard objects potentially contaminated by nearby stars and galaxies , @xcite used a statistical likelihood - ratio ( lr ) technique to accomplish this goal . perhaps their statistical technique was more conservative than our more labor intensive approach , leaving these candidates unidentified . we have several further improvements to disk detective project underway , which we will describe in upcoming papers , including :    * new ways to retire the sources after fewer classifications . * spectroscopy of southern hemisphere ddois via the casleo telescope in argentina * imaging follow - up of ddois with the robo - ao @xcite instrument at the palomar observatory 60-inch telescope to check for background contaminants located closer to the star than dss can probe .    with its high sensitivity and angular resolution in the mid - infrared , we expect that the james webb space telescope ( jwst ) will be an important tool for following up disks discovered via disk detective . so we aim to have the project mostly completed by the time jwst launches in the fall of 2018 . we acknowledge support from grant 14-adap14 - 0161 from the nasa astrophysics data analysis program . marc kuchner acknowledges funding from the nasa astrobiology program via the goddard center for astrobiology . development of the disk detectives site was supported by a grant from the alfred p. sloan foundation , and the zooniverse platform is supported by a google global impact award . wise is a joint project of the university of california , los angeles , and the jet propulsion laboratory ( jpl)/california institute of technology ( caltech ) , funded by nasa . 2mass is a joint project of the university of massachusetts and the infrared processing and analysis center ( ipac ) at caltech , funded by nasa and the nsf . this paper uses data products produced by the oir telescope data center , supported by the smithsonian astrophysical observatory . the digitized sky survey was produced at the space telescope science institute under u.s . government grant nag w-2166 . the images of these surveys are based on photographic data obtained using the oschin schmidt telescope on palomar mountain and the uk schmidt telescope . the plates were processed into the present compressed digital form with the permission of these institutions . this work has made use of the bess database , operated at lesia , observatoire de meudon , france : http://basebe.obspm.fr    funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/.    the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , university of cambridge , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington .    the data presented in this paper result from the efforts of the disk detective volunteers , without whom this work would not have been possible . the following volunteers helped classify the stars listed in this paper : _ 13lueangel , a.brodersen , abienvenu , alarmingalarm , albeelou , alinastart , anowi , anoxie , arlon , artman40 , arvintan , atmosferah , bc2callhome , bellapagano , berlherm , biggsjrex , billweiler , bmw.996 , braehlerm , brainell , breckwilhite , bromista , cazze74 , chinabob , chloecollins , christania10110 , clairwallis , clayzer - ev , cosmic jerk , cstickmaker , daisy1000 , deke scott t , dianaz , diplomacy42 , djperkins@xmath285live.co.uk , dniergarth , dooces , ercydive , feder , ferrertiago , fireandice , firewatermoonearth , fletrik , ftpol , gbav8r , geckzilla , gez quiruga , giazira , golfmadman , grubenm , haian , hardan , hearzadrsos , helmutu , i - mac , iponenubs , irvset , ivan3 , j.altman@kpnplanet.n , jacedjohnson , jacobus.valk@xmath285polk.de , janiceashdown , jasonjason , jellybelly123 , jessicaelizabeth , jgreyes , jmeyers314 , jojefree , jorge96 , josa310 , justinsbuzz , kafter , kecsap , keel , ki4fyp , kiarash , kijkuit , killoch , kmk , lambrosliamis , lehensuge , ljhinton21 , mack777 , manemag , marca , marchl , marcin.s , maria mar , mattlou117 , mdlw , michiharu , miertje , miltonbosch , mlavall2@xmath285uwo.ca , mric116 , mylesatkins , n5bz , namorris , nipper10 , nirajsanghvi , norbertf , noreal , nunolanca , ohiopugmom , omhans , onetimegolfer , orionsam1 , pamela foster , paulro , peterw143 , petrusperes , pini2013 , pixelfixx , planetari7 , plutoexpress , ptrip2010 , qgr , raymond hall , refugezero , ridence , robhj , rocketman93 , roleca , rt26556@xmath285wdmtigers.or , russ jones , ryangeho , ryanstone87 , sandrisvi , scottwferg , sheilaandpeter , shigeru , shocko61 , shroomzz , silviug , siver , soloslayer9 , star hunter 1 , starbase3 , steve bourne , sumo2011 , sunjinx , symaski62 , ted91 , tigrincs , timothy fitzgerald , tom.luthe , troomander , trumanator , tsgt , turtle0920 , victory1 , vinokurov , vonkohon , voyager1682002 , vulpi , weric1 , wizardhowl , woomaster , wxdestroyer , xantipa , yiska , zealex _ we also thank christoph baranec and katharina doll for providing useful comments on this paper .","summary":"sources that survive this online vetting are followed up with spectroscopy on the flwo tillinghast telescope . one of these systems appears to contain the first debris disk discovered around a star with a white dwarf companion : hd 74389 . we also report four newly discovered classical be stars ( hd 6612 , hd 7406 , hd 164137 , and hd 218546 ) and a new detection of 22 m excess around a previously known debris disk host star hd 22128 .","abstract":"the disk detective citizen science project aims to find new stars with 22 m excess emission from circumstellar dust using data from nasa s wise mission . initial cuts on the allwise catalog provide an input catalog of 277,686 sources . volunteers then view images of each source online in 10 different bands to identify false - positives ( galaxies , background stars , interstellar matter , image artifacts , etc . ) . sources that survive this online vetting are followed up with spectroscopy on the flwo tillinghast telescope . this approach should allow us to unleash the full potential of wise for finding new debris disks and protoplanetary disks . we announce a first list of 37 new disk candidates discovered by the project , and we describe our vetting and follow - up process . one of these systems appears to contain the first debris disk discovered around a star with a white dwarf companion : hd 74389 . we also report four newly discovered classical be stars ( hd 6612 , hd 7406 , hd 164137 , and hd 218546 ) and a new detection of 22 m excess around a previously known debris disk host star hd 22128 ."}
{"article_id":"1207.7273","section_id":"i","document":"cosmology research has entered a new era since the discovery of the acceleration of the universe ( perlmutter et al . 1999 ; riess et al . 1998 ) .  dark energy \" ( de ) , which has negative pressure and accounts for 73% of the total energy density of the universe , is currently the best candidate to explain the cosmic acceleration , and understanding its nature has become one of the most important problems in modern astronomy and physics . there are several promising methods to explore dark energy with high accuracy via its equation - of - state parameter @xmath7 ( frieman , turner & huterer 2008 ) . as pointed out by hu ( 2005 ) , among all observables for probing de in light of the microwave background radiation ( cmb ) , @xmath7 is most sensitive to variations in @xmath8 . hu ( 2005 ) concluded that the single most important complement to the cmb for measuring @xmath7 at @xmath9@xmath100.5 is a determination of the hubble constant ( at @xmath9@xmath100 ) to better than a few percent . this insight forms the fundamental motivation for the megamaser cosmology project ( mcp ; reid et al . 2009 ( paper i ) ; braatz et al . 2010 ( paper ii ) ; kuo et al . 2011 ( paper iii ) ; and reid et al . 2012 ( paper iv ) ) , which aims to determine @xmath8 to 3% accuracy . the key to a precise and direct determination of the hubble constant is to measure accurate distances to galaxies well into the hubble flow ( i.e. @xmath11 30 mpc ) . the galaxies must be distant to reduce the contribution of the uncertainty coming from peculiar velocities relative to a smooth hubble flow . among all the approaches to measure accurate distances directly , the megamaser method pioneered by the study of ngc 4258 ( herrnstein et al . 1999 ) has proven to yield accurate and direct distance measurements to galaxies beyond our local group . the methodology of the megamaser technique for distance determination can be found in paper i , paper ii , and the modified version of the techinique that directly measure the hubble constant can be found paper iv . the application of the megamaser technique for measuring black hole mass can be found in paper iii .    in the mcp , we aim to measure the hubble constant with @xmath1010% or better accuracy from each of about 10 galaxies , thereby determining @xmath8 to @xmath103% after averaging the results . the first galaxy measured by the mcp was ugc 3789 ( paper i , paper ii & paper iv ) . a preliminary analysis using a simple model of the maser disk in paper ii gave a hubble constant of 69@xmath211 mpc ( 16% accuracy ) , and the overall uncertainty of the hubble constant has recently been further reduced to @xmath1010% when new data and better modeling were included ( paper iv ) . in this paper , we present the direct hubble constant measurement from ngc 6264 , the first galaxy beyond 100 mpc measured with the megamaser method . in section 2 , we present our vlbi and single - dish observations . in section 3 , we show the analysis of the centripetal accelerations of the masers in ngc 6264 . the hubble constant and distance determinations are presented in section 4 . in section 5 , we discuss the challenges of applying the maser technique to distant galaxies . finally , we summarize the results in section 6 .","summary":"the result demonstrates the feasibility of measuring distances to galaxies located well into the hubble flow by using circumnuclear megamaser disks .","abstract":"we present the direct measurement of the hubble constant , yielding the direct measurement of the angular - diameter distance to ngc 6264 using the ho megamaser technique . our measurement is based on sensitive observations of the circumnuclear megamaser disk from four observations with the very long baseline array , the green bank telescope and the effelsberg telescope . we also monitored the maser spectral profile for 2.3 years using the green bank telescope to measure accelerations of maser lines by tracking their line - of - sight velocities as they change with time . the measured accelerations suggest that the systemic maser spots have a significantly wider radial distribution than in the archetypal megamaser in ngc 4258 . we model the maser emission as arising from a circumnuclear disk with orbits dominated by the central black hole . the best fit of the data gives a hubble constant of 68 km  s  mpc , which corresponds to an angular - diameter distance of 144 mpc . in addition , the fit also gives a mass of the central black hole of ( 3.09.42) . the result demonstrates the feasibility of measuring distances to galaxies located well into the hubble flow by using circumnuclear megamaser disks ."}
{"article_id":"1207.7273","section_id":"i","document":"our main conclusions are the following :    * the application of the megamaser technique to galaxies deep in the hubble flow is intrinsically more difficult because of significantly lower flux densities and smaller disk angular size . to image the maser disks in distant galaxies more efficiently , we developed a method to use multiple maser lines at different locations in the maser disk for performing self - calibration on weaker sources . * the systemic masers in ngc 6264 are located at four or more radii from the black hole . 3-dimensional modeling that utilizes all information of maser spots including their positions , velocities , and accelerations is essential to measure the distance to ngc 6264 because of the complexity of its maser disks . * we modeled the h@xmath0o maser disk in ngc 6264 with a bayesian approach and obtained a hubble constant of @xmath1 68 @xmath29 km  s@xmath3  mpc@xmath3 , corresponding to an angular - diameter distance of 144@xmath219 mpc . the hubble constant is consistent with the value obtained from ugc 3789 in paper iv ( @xmath55 ) . this is the first time the megamaser technique has been successfully applied to a galaxy beyond 100 mpc . we expect that including new observations will enable a 10% accurate estimate of the hubble constant from ngc 6264 , as well as constraining the magnitude of orbital eccentricity in the maser disk .","summary":"the best fit of the data gives a hubble constant of 68 km  s  mpc , which corresponds to an angular - diameter distance of 144 mpc .","abstract":"we present the direct measurement of the hubble constant , yielding the direct measurement of the angular - diameter distance to ngc 6264 using the ho megamaser technique . our measurement is based on sensitive observations of the circumnuclear megamaser disk from four observations with the very long baseline array , the green bank telescope and the effelsberg telescope . we also monitored the maser spectral profile for 2.3 years using the green bank telescope to measure accelerations of maser lines by tracking their line - of - sight velocities as they change with time . the measured accelerations suggest that the systemic maser spots have a significantly wider radial distribution than in the archetypal megamaser in ngc 4258 . we model the maser emission as arising from a circumnuclear disk with orbits dominated by the central black hole . the best fit of the data gives a hubble constant of 68 km  s  mpc , which corresponds to an angular - diameter distance of 144 mpc . in addition , the fit also gives a mass of the central black hole of ( 3.09.42) . the result demonstrates the feasibility of measuring distances to galaxies located well into the hubble flow by using circumnuclear megamaser disks ."}
{"article_id":"astro-ph0109150","section_id":"i","document":"most of our knowledge of the global structure of the galaxy relies on the comparison of magnitude and colour star counts in different galactic directions . star counts alone do not allow us to solve the dilemma that a star of a given apparent magnitude can be either intrinsically faint and close by , or bright and distant . this problem may be addressed statistically by using the century - old equation of stellar statistics ( von seeliger 1898 ) :    @xmath1    where @xmath2 is the number of stars which have an apparent magnitude in the range @xmath3 $ ] , @xmath4 is the luminosity function , which depends on the intrinsic magnitude , @xmath5 , and the colour band @xmath6 , while @xmath7 is the density at radius @xmath8 ( within @xmath9 ) along the line of sight in the direction given by the galactic longitudes and latitudes @xmath10 ( within the solid angle @xmath11 ) . this equation can not be solved or inverted ( i.e. by determining both the stellar lf and the density law ) except for a few simplified cases . for instance , with a `` homogeneous '' stellar sample for which the absolute magnitudes of stars or more precisely their luminosity functions are known , the density law along the line of sight can be recovered . a classical numerical technique ( mihalas & binney 1981 ) has been proposed  the bok diagram ( 1937 )  while more rigorous treatments are required for small samples to stabilize the inversion so as to produce smooth solutions ( binney & merrifield 1998 ) . the converse situation is the determination of the luminosity function assuming a known density law ( see , for instance , recent studies of the faint end of the disk or halo main sequence based on deep star counts ( reid et al . 1996 , gould et al . 1998 ) .    a simple approach , developed largely in the eighties , was to integrate assuming some prior information concerning the stellar populations ( see , for instance , pritchet 1983 , bahcall et al . , 1983 , buser 1985 , robin & crz 1986 ) . a frequent assumption is , for instance , to assume that the halo stars have the same luminosity function as some low metallicity globular clusters . another approach consists in building a stellar luminosity function from stellar evolution tracks and isochrones of various ages . this has been used to put constraints on the galactic disk star formation rate ( haywood et al 1997ab ) . stronger a priori constraints may also be derived by requiring dynamical consistency , since the vertical kinematics of stars is related to the flattening of stellar disks or spheroidal components . since star counts alone , @xmath12 , are not sufficient to constrain uniquely galactic stellar population models , it is expected that two ( or more ) distinct models will reproduce the same apparent star counts . however , this is not a real worry , since it is likely that adding some relevant extra a priori information must help to lift partially the degeneracy of the models .    in this paper , it is shown that the degeneracy is lifted altogether when we consider , in addition to the star counts in apparent magnitude , the proper motions , @xmath13 and @xmath14 . for a relatively general dynamically consistent model ( stationary , axisymmetric and fixed kinematic radial gradients ) , the statistical equation counts may be formally inverted , giving access to _ both _ the vertical density law of each stellar population _ and _ their luminosity functions . this is developed in section  [ s : deriv ] where we show how the vertical motions are related to the thickness of stellar components . the remaining degeneracy occurs only for a quadratic vertical potential . otherwise  when the vertical component of the potential is known  the departures from quadratic behaviour define a characteristic scale that allows us to transform statistically the magnitudes into distances and proper motions into velocities . similarly , the asymmetric drift and/or the vertical velocity component of the sun provide a natural scale in energy , leading to the same inversion procedure .    for ideal star counts ( infinitely deep and for an infinite number of stars ) , the inversion gives exactly the proportion of stars in each kinematic component , providing a direct diagnostic to split the thin disk from the thick disk or the halo , and its luminosity function @xmath4 is recovered for each kinematic stellar component . this is a direct consequence of the supplementary constraints introduced by the requirement for dynamical consistency . section  [ s : deriv ] presents the generalized stellar statistic equation which accounts for proper motions , and demonstrates the uniqueness of the inversion for two families of plane parallel distribution functions : the singular velocity ellipsoid ( subsection  [ s : toy ] ) and a constant ratio velocity ellipsoid ( subsection  [ s : sch ] ) while subsection  [ s : epi ] presents a basic description of the epicyclic model . section  [ s : simul ] illustrates the inversion procedure on a fictitious superposition of 4 kinematically decoupled populations with distinct main sequence turn - off magnitudes for the constant ratio velocity ellipsoid and the epicyclic models . the next section discusses the effects of truncation in apparent magnitude ( i.e. completude of the catalog ) in the recovered lf as well as noise in the measurements . finally , the last section discuss the applicability of the method to the tycho-2 catalogue and to external clusters , and concludes .","summary":"the effect of noise and incompleteness in apparent magnitude is investigated . it should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo .   ","abstract":"a method for inverting the statistical star counts equation , including proper motions , is presented ; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency . the inversion gives access to both the kinematics and the luminosity function of each population in three rgimes : the singular ellipsoid , the constant ratio schwarzschild ellipsoid plane parallel models and the epicyclic model . this more realistic model is taylored to account for local neighbourhood density and velocity distribution .    the first model is fully investigated both analytically and via means of a non - parametric inversion technique , while the second model is shown to be formally its equivalent . the effect of noise and incompleteness in apparent magnitude is investigated . the third model is investigated via a 5d+2d non - parametric inversion technique where positivity of the underlying luminosity function is explicitely accounted for .    it is argued that its future application to data such as the tycho catalogue ( and in the upcoming satellite gaia ) could lead  provided the vertical potential , and/or the asymmetric drift or are known  to a non - parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks . it should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo .    [ firstpage ]    methods : data analysis stars : hertzsprung - russell , luminosity function galaxy : kinematics and dynamics , structure , stellar content"}
{"article_id":"astro-ph0109150","section_id":"c","document":"the main result of this paper is a demonstration that the generalized stellar statistic equation including proper motions , , can be inverted , giving access to both the kinematics and the luminosity function . the inversion was carried for two rather specific functional decompositions of the underlying distribution ( namely , constant ratio and possibly singular schwarzschild ellipsoids plane parallel models ) and a more realistic physical model ( the epicyclic shu model ) which accounts for gradients . the inversion assumes that the departure from harmonicity of the vertical potential , and/or the asymmetric drift or the sun s vertical velocity , @xmath0 , are known . indeed the break in the potential yields a scale which reflects the fact that statistically the dynamics ( i.e. the velocities ) gives a precise indication of distances in units of that scale . the asymmetric drift or vertical component of the sun s velocity provide another energy scale ( and therefore a distance scale ) . the existence of more than one distance scale is mathematically redundant , but practically of interest for the purpose of accounting for local and remote stars . + in a nutshell , it was shown in section  [ s : deriv ] that has solutions for families of distribution obeying ( singular ellipsoid ) or ( schwarzschild ellipsoid ) . those solutions are unique and can be made explicit for a number of particular cases : ( pin - like velocity ellipsoid ) , ( constant ratio @xmath245 , @xmath246 ) , ( constant ratio @xmath245 and @xmath247 either with @xmath248,@xmath249 , or @xmath250,@xmath251 & @xmath252 : statistical secular parallaxes ) . in all other instances , the solution can be found via the general non - parametric inversion procedure described in section  [ s : np ] , the only constraint being the computation of the model matrix generalizing ( which might require numerical integration , as shown for instance in section  [ s : epi ] ) ; in this more general framework it remains also to demonstrate that the inversion will converge towards a solution which is _ unique_.    for instance , in the rgime where the epicyclic model has been tested ( subsection  [ s : simshu ] ) a unique solution seems to be well defined . the luminosity function of each kinematical component is well recovered throughout the hr diagram . more tests are required before applying the method to real data , and are postponed to a companion paper ( siebert et al . in preparation ) .    for a given vertical potential , it appears that the modelling of star counts indexed by proper motion @xmath253 has a solution for most model parameters . many different models based on distinct _ priors _ have produced realistic magnitude and colour star counts but failed to predict proper motion measurements accurately ( for instance , note that the besanon model  which relies on a nearly dynamical consistent model  produces a good fit to proper motion surveys ( ojha , 1994 ) , while dynamically inconsistent models are more problematic ( ratnatunga , 1989 ) ) . + it should be emphasized that the inversion method presented in section  [ s : np ] is a true deconvolution and should give access to a kinematically indexed hr diagram . together with some model of the time evolution of the different kinematic components ( via , say , a disk heating mechanism ) , the indexing could be translated into one on cosmological time , hence providing a non - parametric measurement of the local neighbourhood luminosity function which is complementary to that obtained by evolutionary track fitting with an assumed initial mass function and star formation rate ( see , for instance , hernandez , valls - gabaud & gilmore , 1999 ) . note that , conversely , the agreement between the standard direct method to predict the local luminosity function and the method presented here could be used to measure the galactic potential . +   the deepest photometric and proper motion of whole sky survey available is the tycho-2 catalogue ( hg et al . , 2000 ) which is a new reduction of the tycho data ( hg et al . , 1998 ) . many tycho stars are disk giants and subgiants covering a large range of distances ; the method developed here can be applied to these stars and will allow us to recover their luminosity function without any prior information from stellar evolution tracks . we intend in a forthcoming paper to apply the method presented here to the tycho-2 catalogue ( hg et al . , 1998 ) and to other proper motion catalogues in order to determine the luminosity function of stars in the solar neighbourhood . we will investigate the limitations introduced by a magnitude - limited catalogue , by the finite size of catalogues and also by our limited knowledge of the galactic potential . reddening is also bound to be a concern since it will bias apparent luminosities as a function of @xmath146 and @xmath80 . if the reddening is diffuse and the absorbing component law is known , the kernel of _ e.g. _ will simply be modified accordingly . alternatively , multicolour photometry could be sufficient to constrain the spatial extinction law . of course the dimensionality of the problem is increased by the number of different colour bands used , since the analysis must be carried while accounting for all colours simultaneously . the final error on the recovered luminosity functions will depend on the photometric errors of the observational catalogue(@xmath254 0.1 for the tycho-2 catalogue down to 0.013 for @xmath255 , @xmath256 for photographic surveys ) . it will also depend on the relative proper motion accuracy ( @xmath257 , with @xmath258 the typical dispersion for a stellar group at a given distances ) . with the tycho-2 catalogue completed by proper motions ( with an accuracy of 2.5 mas / y ) , and for disk giants with velocity dispersions from 10 to 50 km / s and proper motion dispersions from 2 to 10 mas / y , the accuracy on the recovered luminosity function will be limited to about 0.5 magnitude . closer ( and fainter ) stars with proper motions from photographic catalogues will constrain the lower part of the luminosity function with a higher accuracy .    in a decade , sky surveys by the fame , diva and gaia satellites will probe the galactic structure in superb detail , giving directly access to larger volumes of the 6d stellar phase space of the galaxy . it will remain that farther out , only proper motions and photometry will have sufficient accuracy and generalization of methods such as that derived here will be used to extrapolate our knowledge of the kinematic and luminosity function of the galaxy and its satellites . for instance appendix  [ s : external ] sketches the possible inversion of an external globular cluster luminosity function with gaia quality photometry .","summary":"a method for inverting the statistical star counts equation , including proper motions , is presented ; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency . the inversion gives access to both the kinematics and the luminosity function of each population in three rgimes : the singular ellipsoid , the constant ratio schwarzschild ellipsoid plane parallel models and the epicyclic model . the third model is investigated via a 5d+2d non - parametric inversion technique where positivity of the underlying luminosity function is explicitely accounted for .    it is argued that its future application to data such as the tycho catalogue ( and in the upcoming satellite gaia ) could lead  provided the vertical potential , and/or the asymmetric drift or are known  to a non - parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks . [ firstpage ]    methods : data analysis stars : hertzsprung - russell , luminosity function galaxy : kinematics and dynamics , structure , stellar content","abstract":"a method for inverting the statistical star counts equation , including proper motions , is presented ; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency . the inversion gives access to both the kinematics and the luminosity function of each population in three rgimes : the singular ellipsoid , the constant ratio schwarzschild ellipsoid plane parallel models and the epicyclic model . this more realistic model is taylored to account for local neighbourhood density and velocity distribution .    the first model is fully investigated both analytically and via means of a non - parametric inversion technique , while the second model is shown to be formally its equivalent . the effect of noise and incompleteness in apparent magnitude is investigated . the third model is investigated via a 5d+2d non - parametric inversion technique where positivity of the underlying luminosity function is explicitely accounted for .    it is argued that its future application to data such as the tycho catalogue ( and in the upcoming satellite gaia ) could lead  provided the vertical potential , and/or the asymmetric drift or are known  to a non - parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks . it should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo .    [ firstpage ]    methods : data analysis stars : hertzsprung - russell , luminosity function galaxy : kinematics and dynamics , structure , stellar content"}
{"article_id":"1211.7001","section_id":"i","document":"preservation of memory is an important goal for every kind of coherent quantum process . the type of control that this implies becomes more difficult in cases involving multi - particle cooperation , typically including entanglement in some way . preservation of entanglement is often an important goal itself . since dissipation processes induced by natural environments will eventually or quickly take entanglement all the way to zero , two related criteria emerge for consideration . these are ( a ) the minimum degree of entanglement that is still  useful \" , setting a lower bound for entanglement , a threshold disentanglement ( td ) value that must not be crossed , and ( b ) the length of time during which this useful level must be maintained . for example , in order for a quantum computation task to be successful , the decay time to reach the low entanglement threshold must be longer than the time scale for computation . natural environments induce well - known single - party decoherence times ( @xmath2 , etc . ) , but these are often not helpful or even highly misleading because it is well known that disentanglement can , and often does , proceed by its own distinct evolution channel and is notoriously able , in only a finite time , to reach complete disentanglement ( cd ) , colloquially known as entanglement sudden death @xcite . clearly a cd event may possibly violates the td value at a given time . this has led a number of entanglement restoration methods to be proposed , using schemes of local unitary operations @xcite , quantum error correction @xcite , feedback control @xcite , dynamical decoupling @xcite , and environment assisted error correction @xcite , in order to control and restore entanglement during environmental exposure . the proposals @xcite have shown that while these schemes may delay or even avert the occurrence of cd in some cases , they may also counter - intuitively accelerate or even induce cd . the proposal by zhao , et al . @xcite relies on finding random unitary or non - random unitary kraus decompositions , which are relatively difficult to achieve and are absent for universal decay channels . proposals of entanglement preservation based on dynamical single - qubit population trapping have also been presented via the exploitation of structured quantum environments or suitable classical environments @xcite and experimental confirmation has also been realized @xcite . a second category of strategies is disentanglement prevention , in which specific setups are made before the disentanglement process . one typical approach of this category is to establish a decoherence free subspace @xcite , which requires either increasing the number of non - computing redundant qubits to create certain symmetry , or some engineering of the system or reservoir with serious external contacts . another approach is to control disentanglement through initial conditions , i.e. , during the state preparation process . isolated connections between cd time and initial conditions have been identified extensively ( see for example @xcite and a review @xcite ) . huang and zhu derived the necessary and sufficient conditions for cd for a generic two - qubit state under amplitude damping and phase damping channels through the positivity requirement of seven principal minors of a @xmath3 matrix @xcite . fanchini et al . @xcite have extended the results of huang and zhu to more general dissipative hamiltonians . however , such cd conditions engage almost every matrix element of a given two - qubit initial state through various matrix transformations , and are extremely complex to control in reality . recently , we have shown that the susceptibility to cd can be controlled via initial entanglement and purity for a simple type of two - qubit states that undergo symmetric amplitude damping dissipation @xcite . this opens the possibility of pre - managing disentanglement properties with just a few controllable initial resources . yang et al . @xcite followed this by showing that the cd pre - management procedure is also viable for extended werner - like initial states . however , for practical situations , initial states may be arbitrarily mixed and decay channels can be rather versatile and complex . an open challenge arises : is it still possible to manage cd with only limited controllable initial parameters for practical complex situations . a further question follows naturally : is it also possible to include the threshold disentanglement condition within the control process ? an important complication is that even for the simple case of x - form matrices ( first systematically considered by yu and eberly @xcite ) , the cd time can only be found for specific types of states , such as werner - like states , ansatz states , etc . , or symmetric reservoir interactions ( see for example @xcite ) . the complication is mainly due to the fact that the disentanglement process , as well as measures of entanglement such as schmidt weight @xcite , concurrence @xcite , negativity @xcite , etc . , are usually non - linear functions of time for given initial conditions . this is because these non - linear dependences usually correspond to higher order linear equations that are difficult to solve analytically ( see our detailed analysis in section iii ) . for example , no analytic cd time is obtained for arbitrary x - form states with non - symmetric amplitude damping and depolarization channels . however , here we make use of the fact that such difficulties can be avoided if one considers the inverse of the problem . that is , we will obtain the state s initial conditions for an arbitrarily given cd or td time . this corresponds to practical situations when a particular quantum information task requires cd or td to happen no earlier than a prescribed time @xmath1 . thus , in this paper we extend our previous analysis of cd pre - management @xcite by considering arbitrary two - qubit mixed states , and by treating non - symmetric damping of the two qubits for three different quantum channels , i.e. , amplitude damping , phase damping , and depolarization . at the same time , we show explicitly for the first time the pre - management of threshold disentanglement properties and illustrate their connections with cd . we first analyze the entanglement dynamics of an arbitrary x - form two - qubit mixed state . exact cd - free , cd - no - go , cd - tolerable , td - no - go , and td - tolerable phases are explicitly determined in terms of several initial parameters , i.e. , concurrence and excitation probabilities . two types of intuitive and counter - intuitive situations are discussed . we then extend the static entanglement lower bound relation for x - form matrices , developed recently by ma et al . @xcite and hashemi rafsanjani et al . @xcite , to the dynamical evolution of the state . we show that cd and td phase critical conditions of a generic state are lower bounded by these of its x - form component . therefore the control of different cd and td properties of a general complex mixed state can be realized sufficiently through just a few initial parameters of its x - form component . the paper is organized as follows : in section ii , we demonstrate the time evolution of a generic two qubit state under three quantum channels . the dynamics of x - form mixed states are shown explicitly . section iii gives a detailed demonstration of cd and td phases for x - form states in all three quantum channels . in section iv , the static entanglement lower bound conditions between the x - form and the entire matrix is generalized to the dynamical process , and is then used to determine the lower bounds of cd and td phases for the generic time dependent state . it is then followed by summary and acknowledgement sections .","summary":"an important issue is the possibility of non - smooth , typically non - exponential , decay of entanglement into the state of complete disentanglement ( cd ) . three common relaxation processes - amplitude , phase and depolarization - are considered .","abstract":"we define threshold disentanglement ( td ) as the level above which entanglement must be maintained for later use and calculate the values of quantum system parameters at that will ensure that the threshold is not crossed in a specified time . an important issue is the possibility of non - smooth , typically non - exponential , decay of entanglement into the state of complete disentanglement ( cd ) . given a specified operation time , we determine phase diagrams showing entanglement preservation during the evolution of a generic two - qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities . in other words , disentanglement can be pre - managed through these parameters . three common relaxation processes - amplitude , phase and depolarization - are considered ."}
{"article_id":"1211.7001","section_id":"i","document":"in summary we have investigated a new type of disentanglement prevention method , i.e. , pre - management with limited partial resources of initial conditions , for a generic two - qubit system that undergoes three typical decoherence channels . the process of threshold disentanglement ( td ) is analyzed for the first time , and its intuitive and counter - intuitive connections to initial entanglement and to complete disentanglement ( cd ) phenomenon are analyzed explicitly . our analysis illustrates systematically the fundamental connections between open system initial conditions and its disentanglement properties . at the same time , it may also serve as guidance to experimental preparation of robust entangled states . the disentanglement properties of a general x - form initial state are demonstrated with various exact cd and td phases in terms of just a few initial parameters , i.e. , concurrence and excitation probabilities . these disentanglement phases are shown to have provided lower bounds for the corresponding phases of a generic two - qubit initial state . in this way , the initial parameters of the x - form component amount to a set of management tools that can tune the generic and complex state into particular phases with preferred disentanglement properties . the nature of phase analysis allows a well defined amount of margin for errors in practical imprecise state preparations . our treatment of solving initial conditions for a prescribed time scale @xmath1 has avoided much of the difficulty in determining the timing of cd and td , and thus is capable to deal with many complex situations ( e.g. , generic two - qubit decay under non - symmetric amplitude damping and depolarization channels ) that could nt be solved analytically in previous studies . such analysis is well grounded by practical situations when a desired disentanglement time scale is pre - determined by quantum information tasks .","summary":"given a specified operation time , we determine phase diagrams showing entanglement preservation during the evolution of a generic two - qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities . in other words , disentanglement can be pre - managed through these parameters .","abstract":"we define threshold disentanglement ( td ) as the level above which entanglement must be maintained for later use and calculate the values of quantum system parameters at that will ensure that the threshold is not crossed in a specified time . an important issue is the possibility of non - smooth , typically non - exponential , decay of entanglement into the state of complete disentanglement ( cd ) . given a specified operation time , we determine phase diagrams showing entanglement preservation during the evolution of a generic two - qubit mixed state as a function of selected initial parameters such as concurrence and excitation probabilities . in other words , disentanglement can be pre - managed through these parameters . three common relaxation processes - amplitude , phase and depolarization - are considered ."}
{"article_id":"1009.0267","section_id":"i","document":"in the information age , the internet is becoming a _ de facto _ public good , akin to roads , airports , or any other critical infrastructure  @xcite . more than a billion people are estimated to use the internet every day to communicate , search for information , share data , or do business  @xcite . on - line social networks are becoming an integral part of human social activities , increasingly affecting human psychology  @xcite . underlying all these processes is the internet infrastructure , composed , at the large scale , of connections between autonomous systems ( ass ) . an as is , roughly , a part of the internet owned and administered by the same organisation  @xcite . ass range in size from small companies , or even private users , to huge international corporations . there is no central internet authority dictating to any as what other ass to connect to . connections between ass are results of local independent decisions based on business agreements between as pairs . this lack of centralised engineering control makes the internet a truly self - organised system , and poses many scientific challenges . the one we address here is the sustainability of internet growth . the internet has been growing fast according to all measures  @xcite . for example , the number of ass increases by approximately @xmath0 every year  @xcite . despite its growth , the internet must sustainably perform its primary task  routing information packets between any two computers in the world . but can this function be really sustained ? to route information to a given destination in the internet today , all ass must collectively discover the best path to each possible destination , based on the current state of the global internet topology . as the number of destinations grows quickly , the amount of information each as has to maintain becomes a serious scalability concern , endangering the performance and stability of the internet  @xcite . worse yet , the internet is not static . its topology changes constantly due to failures of existing links and nodes , or appearances of new ones . each time such a change occurs anywhere in the internet , the information about this event must be diffused to all ass , which have to quickly process it to recompute new best routes . the constantly increasing size and dynamics of the internet thus leads to immense and quickly growing routing overheads , causing concerns among internet experts that the existing internet routing architecture may not sustain even another decade  @xcite ; parts of the internet have started sinking into black holes already  @xcite .    the scaling limitations with existing internet routing stem from the requirement to have a current state of the internet topology distributed globally . such global knowledge is unavoidable since routing has no source of information other than the network topology . routing in these conditions is equivalent to routing using a hypothetical road atlas , which has no geographic information , but just lists road network links , which are pairs of connected road intersections , abstractly identified . this analogy with road routing suggests that there are better ways to find paths in networks . suppose we want to travel from one geographic place to another . given the geographic coordinates of our starting point and destination , we can readily tell what direction brings us closer to our destination . we see that a coordinate system in a geometric space , coupled with a representation of the world in this space , simplify drastically our routing task . for simple and efficient network routing we thus need a map . constructing such a map for the internet boils down to assigning to each as its coordinates in some geometric space , and then using this space to forward information packets in the right directions toward their destinations . _ greedy forwarding _ implements this routing in the right direction : upon reading the destination address in the packet , the current packet holder forwards the packet to its neighbour closest to the destination in the space . this greedy strategy to reach a destination is efficient only if the network map is congruent with the network topology . in the analogy with road routing , for example , this congruency condition means that there should exists a road path that stays approximately close to the geographic geodesic between the trip s starting and ending points . if the congruency condition holds , then the advantage of greedy forwarding is twofold . first , the only information that ass must maintain is the coordinates of their neighbours . that is , ass do not have to keep any per - destination information . second , once ass are given their coordinates , these coordinates do not change upon topological changes of the internet . therefore , ass do not have to exchange any information about ever - changing internet topology . taken together , these two improvements essentially eliminate the two scaling limitations mentioned above .    in our recent work @xcite we have shown that greedy forwarding is indeed efficient in internet - like _ synthetic _ networks embedded in geometric spaces , and that this efficiency is maximised if the space is hyperbolic . however , putting these ideas in practice needs a crucial piece of information : a map of the _ real _ internet in a hyperbolic space . here we present a method to find such a map . our method uses statistical inference techniques to find coordinates for each as in the hyperbolic space underlying the internet . guided by the inferred coordinates , greedy forwarding in the internet achieves efficiency and robustness , similar to those in synthetic networks . we also find that the method maps geo - politically close ass close to each other in the hyperbolic space . this finding suggests that our mapping method can be used for soft community detection in real networks , where by _ soft communities _ we mean groups of geometrically close nodes .","summary":"the internet infrastructure is severely stressed . rapidly growing overheads associated with the primary function of the internet  routing information packets between any two computers in the world  cause concerns among internet experts that the existing internet routing architecture may not sustain even another decade . here","abstract":"the internet infrastructure is severely stressed . rapidly growing overheads associated with the primary function of the internet  routing information packets between any two computers in the world  cause concerns among internet experts that the existing internet routing architecture may not sustain even another decade . here we present a method to map the internet to a hyperbolic space . guided with the constructed map , which we release with this paper , internet routing exhibits scaling properties close to theoretically best possible , thus resolving serious scaling limitations that the internet faces today . besides this immediate practical viability , our network mapping method can provide a different perspective on the community structure in complex networks ."}
{"article_id":"1009.0267","section_id":"c","document":"we have constructed a hyperbolic map of the internet , and release this map with this paper  @xcite . the map can be used for essentially infinitely scalable internet routing . the amount of routing information that ass must maintain is proportional to the as degree , which is theoretically best possible since ass must always keep some information about their neighbours . routing communication overheads are also minimised , since ass do not exchange any routing information upon dynamic changes of the as topology . the presented solution thus achieves routing efficiency close to theoretically optimal , and resolves serious scaling limitations that the internet faces today . the mapping method we have employed is generic , and can be applied to other complex networks with underlying metric structures and heterogeneous degree distributions . we showed in  @xcite that a good indicator for the presence of an underlying metric structure is self - similarity of clustering in the network , while in  @xcite we showed that as soon as a metric space is present , and the network has a heterogeneous degree distribution , the metric distances can be rescaled such that the underlying geometry is effectively hyperbolic . roughly , self - similar clustering is responsible for the metric structure along the angular coordinate , while degree heterogeneity adds the radial dimension , and makes the space hyperbolic . applied to other networks , our mapping method can provide a different perspective on the community structure in networks . instead of trying to split nodes into discrete community sets  @xcite , it would naturally yield a continuous measure of similarity between nodes based on hyperbolic distances . more similar nodes would be located closer to each other , and form zones of higher connectivity density . it would be then up to an experimenter to define communities , if needed , as histograms of the node density in the hyperbolic space . the spectrum of potential applications of this network - mapping geometrisation agenda is wide . network mapping can reveal geometric forces effectively driving information signaling in the network ; examples include the brain  @xcite and cell signaling networks  @xcite . one can then potentially predict what network perturbations drive these networks to failures , such as brain disorders or cancer . other applications range from recommender systems  @xcite , where to have the right measure of similarity between consumers is a key , to epidemic spreading  @xcite and information theory of networks  @xcite . we have shown that the internet hyperbolic map is remarkably robust with respect to even substantial perturbations of the internet topology , implying that this map is essentially static . it does not significantly depend on topology dynamics , and can thus be computed only once . this property is desirable in view of long running times intrinsic to likelihood maximisation algorithms . our method improves their running times drastically , and the internet map computations take approximately a day on a modern computer . however , for substantially larger networks the running times may still be prohibitive even for one - time mapping . therefore , alternative methods for network mapping , not relying on likelihood maximisation , are highly desirable , and our work in this direction is underway .","summary":"guided with the constructed map , which we release with this paper , internet routing exhibits scaling properties close to theoretically best possible , thus resolving serious scaling limitations that the internet faces today . besides this immediate practical viability , our network mapping method can provide a different perspective on the community structure in complex networks .","abstract":"the internet infrastructure is severely stressed . rapidly growing overheads associated with the primary function of the internet  routing information packets between any two computers in the world  cause concerns among internet experts that the existing internet routing architecture may not sustain even another decade . here we present a method to map the internet to a hyperbolic space . guided with the constructed map , which we release with this paper , internet routing exhibits scaling properties close to theoretically best possible , thus resolving serious scaling limitations that the internet faces today . besides this immediate practical viability , our network mapping method can provide a different perspective on the community structure in complex networks ."}
{"article_id":"astro-ph0502236","section_id":"i","document":"one of the most debated issue of modern astrophysics is the definition of the local distance scale and of the distance of its first step , the large magellanic cloud ( lmc ) , in particular . indeed , current calibrations of the extragalactic distance scale and consequent evaluations of the hubble constant rely upon the classical cepheid pl relations with the zero point fixed by some assumption on the lmc distance ( see e.g. freedman et al . 2001 , tammann , sandage , & reindl 2003 ) . recent determinations of the lmc distance modulus , either based on population i or ii distance indicators , cover the range 18.3 - 18.7 mag ( see discussions in cacciari 1999 , walker 1999 , carretta et al . 2000 , caputo et al . however , in the last couple of years different distance indicators have followed the trend to converge to a common value of @xmath5=18.52 @xmath3 0.02 mag , on the basis of updated accurate photometric data for both rr lyrae and red clump stars , as well as revised techniques and consistent reddening evaluations ( see discussions in clementini et al . 2003 , hereinafter c03 , walker 2003 , and alves 2004 ) .    among the different methods exploiting the radially pulsating stars as standard candles a quite innovative and promising technique is represented by the fitting of the observed light and radial velocity curves of a pulsating star to those predicted by nonlinear pulsation models ( see e.g. wood , arnold & sebo 1997 , hereinafter was ; keller & wood 2002 ; bono , castellani , & marconi 2000 , 2002 , hereinafter bcm00 and bcm02 , respectively ; di fabrizio et al . this technique is based on the direct comparison between observed and predicted curves , rather than involving related parameters such as pulsation amplitudes and fourier parameters , and performs the theoretical reproduction of both general features ( period , shape , amplitude ) and morphological details such as bumps and humps , of the observed curves . given the sensitivity of the curve detailed morphology to the model input parameters , as well as to the physical and numerical assumptions , the fitting of actual light and radial velocity curves offers a unique opportunity to obtain sound estimates of the intrinsic stellar properties of the variables , providing at the same time a key test of the theoretical predictions . high accuracy observational data , consisting of well sampled multiband light and , possibly , radial velocity curves , knowledge of the related pulsation characteristics , namely period , colors and amplitudes , and of the metallicity of the variable star , are needed for a meaningful application of the method . the output of the procedure is a set of models for fixed period and metal abundance and with varying the mass , the luminosity and the effective temperature , among which the best fitting model is that best reproducing the observed characteristics of the pulsation , within acceptable values of the derived intrinsic parameters .    in the case of variables of rr lyrae type this technique has already provided very good results for galactic field first overtone rr lyrae stars ( see bcm00 , di fabrizio et al . 2002 ) , whereas for the fundamental mode pulsators satisfactory results were obtained except for the long period variables close to the red edge of the rr lyrae instability strip ( see castellani , deglinnocenti , & marconi 2002 , di criscienzo , marconi , & caputo 2004 ) .    as for the classical cepheids a similar technique was early applied by was to the lmc bump cepheid hv905 . more recently , relying on the same theoretical pulsational scenario as in bcm00 , the method was applied to two lmc fundamental mode cepheids showing well - defined bumps along the decreasing ( short - period ) and the rising ( long - period ) branch of the light curve , respectively ( bcm02 ) , based on data from the ogle catalogue ( available at sirius.astrouw.edu.pol/@xmath6ogle/ogle2/dia ) . a good fit was obtained for both variables and for an lmc distance modulus ranging from 18.48 to 18.58 mag ( see bcm02 for details ) , in agreement with results by c03 . an independent application to the macho @xmath7 and @xmath8 light curves of 20 _ bump _ cepheids in the lmc ( including hv905 ) was performed by keller & wood ( 2002 ) , on the basis of the was nonlinear pulsation code . they obtained a mean lmc distance modulus of 18.55 @xmath3 0.02 ( intrinsic error of the average ) . both in the case of rr lyrae stars and classical cepheids the best fit models based on bcm00 theoretical scenario seem to suggest that the standard value of the mixing length parameter ( @xmath9 ) adopted to close the dynamical - convective equation system is suitable to reproduce the light variations of variables in the blue region of the instability strip . a higher value of @xmath10 is needed instead toward the red region of the fundamental mode instability strip ( see e.g. bcm02 ) . this occurrence is confirmed by results based on other independent `` pulsational '' methods to constrain the rr lyrae and globular cluster distance scale , in particular the period - amplitude relations and the comparison in the period - magnitude diagram ( see di criscienzo et al . 2004 ) .    in this paper we present results from the theoretical modelling of the observed @xmath0 light curves of 14 rr lyrae stars in the lmc , based on the detailed photometric study of the lmc rr lyrae stars by c03 and di fabrizio et al . ( 2004 , hereinafter df04 ) . our sample includes 7 fundamental mode ( rrab ) and 7 first overtone ( rrc ) pulsators that , according to gratton et al . ( 2004 , hereinafter g04 ) spectroscopic analysis , cover the metallicity range from @xmath12.12 to @xmath10.79 in [ fe / h ] , with average value of @xmath11.54 dex . the application of the method to a significant number of population ii pulsators in the same stellar system , namely the lmc rr lyrae stars , represents a powerful test of the inner consistency and predictive capability of the adopted theoretical scenario , providing at the same time an independent estimate of the lmc distance modulus , and a direct comparison between population i and ii distance indicators , which contributes to strengthen our knowledge of the local distance scale . the organization of the paper is the following . in sect . 2 we briefly discuss the adopted photometric ( light curves and reddening values ) and spectroscopic ( metallicities ) databases . in sect . 3 we present the pulsation models , whereas the fit of the observed light curves and the derivation of the intrinsic stellar parameters ( masses , luminosities , and effective temperatures ) both for fundamental and first overtone pulsators is described in sect . 4 . in this section we also discuss the comparison with the intrinsic parameters predicted for the program stars by the evolutionary horizontal branch ( hb ) models , and by the fourier decomposition of the visual light curves of the fundamental mode rr lyrae stars . the derived lmc distance modulus and the associated uncertainty are presented in sect . 5 along with a discussion of the resulting rr lyrae luminosity - metallicity relation . a summary of the results and some final remarks in section 6 close the paper .","summary":"we present results from the theoretical modelling of the observed light curves of 14 rr lyrae stars in the large magellanic cloud . the sample includes 7 fundamental and 7 first overtone pulsators covering the metallicity range from.12 to.79 dex in [ fe / h ] , with average value of.54 dex . masses , intrinsic luminosities , effective temperatures , and reddenings were derived by fitting high accuracy multiband light curves available for these rr lyrae stars to nonlinear convective pulsation models .","abstract":"we present results from the theoretical modelling of the observed light curves of 14 rr lyrae stars in the large magellanic cloud . the sample includes 7 fundamental and 7 first overtone pulsators covering the metallicity range from.12 to.79 dex in [ fe / h ] , with average value of.54 dex . masses , intrinsic luminosities , effective temperatures , and reddenings were derived by fitting high accuracy multiband light curves available for these rr lyrae stars to nonlinear convective pulsation models . individual distance moduli were determined for each variable , they lead to an average distance modulus for the large magellanic cloud of= 18.54 0.02 (= 0.09 mag , standard deviation of the average ) , in good agreement with the  long \" astronomical distance scale ."}
{"article_id":"hep-ph0505103","section_id":"i","document":"electroweak baryogenesis @xcite is an effective framework for explaining the baryon asymmetry of the universe ( bau ) . the most appealing feature of this mechanism lies in the fact that the relevant physics will soon be explored by experiments , most notably by lhc at cern and by the new generation of electric dipole measurements . it has been realized that the scenario of electroweak baryogenesis depends on extensions of the standard model ( sm ) , since two mandatory conditions are not met in the sm . the first reason is that cp - violation in the sm is marginal , such that the observed magnitude of baryon asymmetry can not be explained . secondly , the electroweak phase transition in the sm is a crossover  @xcite , leading to a too weak departure from equilibrium to be viable for baryogenesis . the minimal supersymmetric standard model ( mssm ) instead has all the necessary ingredients . cp violation is enhanced by adding phases to the parameters in the soft supersymmetry breaking sector , which contribute to the chargino mass matrix . furthermore , the additional bosonic degrees of freedom can lead to a strong first order phase transition as _ e.g. _ in the light stop scenario  @xcite . these considerations indicate that the mssm has the potential of explaining the observed bau _ via _ electroweak baryogenesis . however , a formalism that determines the baryon asymmetry has to incorporate several features . clearly the formalism has to reflect the quantum nature of the involved particles , for cp violation is a purely quantum effect . in addition , since the sphaleron processes are only operative in the unbroken phase , the cp - violating particle densities have to be transported away from the wall into the unbroken phase to lead to a net baryon density . a formalism that can handle both of these aspects is given by the kadanoff - baym equations , which are in turn derived from the out - of - equilibrium schwinger - dyson equations . early approaches that aimed to determine cp - violating densities and have not attempted to derive transport equations from first principles have been based on the dispersion relation of the quasi - particles @xcite deduced with the wkb method . for a recent resurrection of the method see  @xcite .    in @xcite it was suggested that an important contribution is given by mixing effects of the quasi particles in the wall rather than from the dispersion relations in the case of a nearly degenerate mass matrix . however , in the work @xcite transport equations are not derived in a first principle approach either , but the current continuity equation is used to determine cp - violating contributions to the green functions in a perturbative approach , which are subsequently inserted as sources into classical diffusion equations derived in @xcite . these classical diffusion equations neglect oscillations of the off - diagonal elements of the green function that are important for a proper treatment of cp violation .    starting from the kadanoff - baym equations , the authors of  @xcite have derived the cp - violating semiclassical force in kinetic transport equations , which appears in fermionic kinetic equation at second order in derivatives . initially , this was done for the one fermion flavour case  @xcite and then subsequently generalized to the diagonal part of the multiflavour case  @xcite . recently this formalism was advanced to include mixing fermions  @xcite . the formalism provides an accurate description of the dynamics in the thick wall regime , which applies to particles , whose de broglie wave length is much shorter than the thickness of the phase boundary ( bubble wall ) , formally @xmath0 . one conclusion of the work @xcite is that two features of the transport equations are not captured by the procedure used in @xcite . firstly , the densities that are off - diagonal in the mass eigenbasis of the system will perform oscillations analogously to neutrino oscillations . this effect suppresses the transport of the cp - violating sources , especially if the mass spectrum in the chargino sector is far from degeneracy . secondly , while refs . @xcite used a phenomenological prescription ( fick s law ) to introduce the cp - violating sources into the diffusion transport equations , no such prescription is required in our formalism . the sources enter the diffusion transport equations with an unambiguously defined amplitude .    a first goal of this publication is to study the simpler bosonic case , and thus to rectify the conclusions of  @xcite . as a second and principal goal , we consider the chargino mediated baryogenesis in the mssm , in order to study the effects of flavour oscillations and source amplitude ambiguity on the baryon asymmetry within the framework of the reduced set of diffusion equations for charginos and quarks used in  @xcite . we also make a comparison of baryogenesis from the semiclassical force mechanism . the principal difference with respect to the previous work , is that our treatment is basis independent , while the calculations presented in ref . @xcite were performed in the mass eigenbasis . this article is organized as follows . in section [ sec_bos ] we derive transport equations for mixing bosons . this is done mainly to clarify the conclusions from @xcite that are present in the bosonic case , too . in the subsequent section we discuss , how the introduction of phenomenological damping terms can lead to additional unphysical cp - violating sources . the sections [ sec_ferm ] and [ sec_diff ] state the fermionic transport equations derived in @xcite and the system of diffusion equations that is used to determine the baryon asymmetry . numerical results are presented in section [ sec_num ] , and we conclude in section [ sec_conc ] .","summary":" , and calculate the chargino mediated baryogenesis in the minimal supersymmetric standard model . we first discuss the semiclassical transport equations for mixing bosons in a space - time dependent higgs background . to calculate the baryon asymmetry , we solve a standard set of diffusion equations ,","abstract":"we make use of the formalism developed in ref .   , and calculate the chargino mediated baryogenesis in the minimal supersymmetric standard model . the formalism makes use of a gradient expansion of the kadanoff - baym equations for mixing fermions . for illustrative purposes , we first discuss the semiclassical transport equations for mixing bosons in a space - time dependent higgs background . to calculate the baryon asymmetry , we solve a standard set of diffusion equations , according to which the chargino asymmetry is transported to the top sector , where it biases sphaleron transitions . at the end we make a qualitative and quantitative comparison of our results with the existing work . we find that the production of the baryon asymmetry of the universe by cp - violating currents in the chargino sector is strongly constrained by measurements of electric dipole moments ."}
{"article_id":"hep-ph0505103","section_id":"r","document":"-0.2 in [ plot_br ]    in this section we will present numerical results of the transport and diffusion equations . the higgs _ vevs _ and the @xmath107 angle are parametrized by h_1(z ) = h(z ) ( ( z ) ) , h_2(z ) = h(z ) ( ( z ) ) and h(z ) = v(t ) 1- 1- , [ h ] + ( z ) = _ - 1 + 1- . [ beta ] the parameters used are @xmath108 and the complex phase is chosen maximally @xmath109 we have checked , with the help of a program developed by the authors of refs . @xcite , that the values for @xmath110 compatible with present higgs bounds typically lie in the range 165 - 185  gev . the exact value depends on parameters of the higgs and squark sectors which affect our results only through this expectation value . we therefore have fixed the value of @xmath110 to its zero temperature result . the uncertainty arising from our choice is below ten percent . the values of @xmath111 are deduced from @xcite for the different values of @xmath112 . the wall velocity is taken to be @xmath113 and the transport equations are evaluated using the fluid _ ansatz _ for the first six momenta . the parameters of the diffusion equations are given in the last section . the plot fig . [ plot_br ] supports the claim that , within our approximations and for our choice of parameters , the back - reaction of left - handed quarks and squarks , @xmath91 , @xmath90 , on the charginos can be neglected . the amplitude of the higgsino densities coming from the back - reaction is always smaller than @xmath114 and never leads to corrections of the baryon - to - entropy ratio larger than @xmath103 . -0.2 in [ plot_source ]    in fig . [ plot_source ] we plot the first order sources @xmath115 , @xmath116 , @xmath117 and the second order source ( semiclassical force ) @xmath118 , as defined in eqs . ( [ sources_abc][source d ] ) . the first order sources are roughly of the same magnitude , and they peak when @xmath119 , where they also switch the sign . the second order source varies slowly with @xmath120 and tends to dominates when the difference @xmath121 becomes large . note that when the damping is small , the first order sources become more peaked around @xmath122 , but the amplitude of the baryon asymmetry does not significantly change . on the other hand , the second order source is about an order of magnitude larger in the right plot , implying that in the limit of a small damping the second order source ( semiclassical force ) may result in a viable baryogenesis . since our damping term is phenomenological and flavor blind , it would be premature to conclude that the second order source can not lead to a viable baryogenesis , until a more quantitative analysis of the damping term is performed . -0.2 in [ plot_ma_2 ]    the parameters chosen in figs . [ plot_ma_2 ] and  [ plot_ma_1 ] are similar to the ones chosen in @xcite , in order to facilitate comparison . in plot fig . [ plot_ma_2 ] the parameters @xmath112 and @xmath75 are fixed while @xmath74 is varied . the maximum is not exactly at @xmath123 as in @xcite , but rather close to @xmath124  gev . the reason for this difference is that in our case all sources ( [ sources_abc ] ) are of similar order , while in @xcite , the baryon asymmetry is completely dominated by a source term of form @xmath125 in ( [ sources_abc ] ) that is proportional to @xmath111 in the parametrization ( [ beta ] ) and hence suppressed for large values of @xmath112 as shown in  @xcite . another difference is that our plot shows the suppression for @xmath126 what is expected since in this case the quasi - particles have highly separated on - shell conditions and mixing should be suppressed . we would like to emphasize that the peak around @xmath124 gev is due to this suppression and not due to a resonance in the sources as it was in the publications  @xcite and more recently in  @xcite . in the present work , the sources show a resonance but the cp - violating densities do not since they are generated by the oscillations ( see eq . ( [ calc_equ ] ) ) and contain near the degeneracy an additional proportionality to the mass splitting @xmath127 . in fig . [ plot_ma_1 ] the baryon asymmetry is plotted near the maximal value @xmath128 gev . the maximum is reached near @xmath129 gev in contrast to @xcite where the maximum was @xmath130 gev . -0.2 in [ plot_ma_1 ]    finally in fig . [ contour ] two contour plots are shown with regions in the @xmath131 parameter space for the baryon asymmetry expressed in terms of @xmath132 . in these units the observed value is close to unity , @xmath133 . if @xmath134 , the observed value can be attained simply by adjusting the complex phase , which is in our calculation chosen to be maximal . the two plots correspond to the choices @xmath135 gev and @xmath136 gev . -0.2 in [ contour ]    in the following we will comment on differences between the formalism used in this paper and the work  @xcite that lead to the discrepancy in the numerical results  . in the present paper we have found that this effect is strongly suppressed by the oscillations induced by the off diagonal terms . ] . as already mentioned in a previous section the authors in  @xcite work in the flavour basis and write classical boltzmann equations using cp - violating sources whereas in this work the sources appear genuinely in a basis independent set of quantum transport equations . in this work the damping @xmath137 is primarily introduced to obtain consistent boundary conditions and it corresponds to the helicity flip rate @xmath137 in the diffusion equations of  @xcite . we have excluded @xmath137 dependent terms that violate cp and the limit @xmath138 is straightforward . in addition to the damping @xmath137 a breit - wigner width @xmath139 was introduced in the chargino spectrum in  @xcite . we have checked in the simpler bosonic case that , for @xmath140 , the present sources and those in  @xcite are related in a simple way . a detailed discussion is presented in the appendix . of course , the ambiguity related to the magnitude of the source in the chargino diffusion equations remains in the formalism used in refs . @xcite , where a phenomenological thermalization time @xmath141 or the classical fick s law had to be used to incorporate the sources into the diffusion equations . in our formalism the magnitude of the source is completely specified . furthermore , we have checked that the effect of the breit - wigner broadening on our sources is small . this effect can be modeled by replacing the @xmath33-function in ( [ g0_eq ] ) by the corresponding breit - wigner form . to account for the finite @xmath139 in the transport and not just in the sources is on the same level as a treatment of the collision terms in refs . @xcite and it is outside the scope of this paper . in principle , the collision term could as well yield additional cp - violating sources , but a one - loop calculation  @xcite in a model theory of chiral fermions yukawa - coupled to scalars , indicates that the collisional sources are phase space suppressed with respect to our tree level sources .","summary":"we find that the production of the baryon asymmetry of the universe by cp - violating currents in the chargino sector is strongly constrained by measurements of electric dipole moments .","abstract":"we make use of the formalism developed in ref .   , and calculate the chargino mediated baryogenesis in the minimal supersymmetric standard model . the formalism makes use of a gradient expansion of the kadanoff - baym equations for mixing fermions . for illustrative purposes , we first discuss the semiclassical transport equations for mixing bosons in a space - time dependent higgs background . to calculate the baryon asymmetry , we solve a standard set of diffusion equations , according to which the chargino asymmetry is transported to the top sector , where it biases sphaleron transitions . at the end we make a qualitative and quantitative comparison of our results with the existing work . we find that the production of the baryon asymmetry of the universe by cp - violating currents in the chargino sector is strongly constrained by measurements of electric dipole moments ."}
{"article_id":"0903.4882","section_id":"i","document":"heteroepitaxy is the process of slow deposition of a film of one or more crystalline materials on a crystalline substrate of a different material . the classical examples of film / substrate combinations include , for example ge / si , inas / gaas , and inp / gaas . the natural lattice spacing between the film and the substrate differ by a few percent resulting in elastic stress . consequently , as the film grows the elastic energy builds up . the formation of 3d islands reduces the elastic energy by relieving stress at the cost of increased surface energy . in many cases these islands are on the order of tens of nanometers and are referred to as quantum dots . these quantum dot materials are of importance in construction of some optoelectronic devices .    the theory of island formation is well understood in the context of asaro - tiller - grinfeld instability @xcite . this explains the instability of a single component stressed film to perturbations of the flat surface . the flat surface is unstable under sufficiently long wavelength perturbations . these perturbations grow through mass transport on the surface , along the free energy gradients , leading to formation of surface ripples that later grow into large islands with stress concentration in the valleys . the theory however fails to explain an experimental observation , namely in many cases the film first grows in a layer - by - layer fashion until it reaches a certain critical thickness . then islands form on top of this layer ( known as the wetting layer ) . this mode of growth is known as the stranski krastonov ( sk ) growth mode@xcite . it was demonstrated experimentally by cullis and co workers @xcite , that the intermixing between the film and substrate is of importance . the presence of compositional non - uniformity and the dilution of the film by substrate material can have a stabilizing effects . moreover the presence of vertical and lateral segregation in the case of alloy films @xcite , can further change the nature of the instability . subsequently , tu and tersoff@xcite , using a continuum model developed by spencer et al@xcite , argued that stranski krastonov growth is a kinetic effect and the wetting layer is not stable . a crucial aspect of their proposal is the intermixing that occurs between the film and the substrate . another important example in which intermixing occurs on very large length scales is the self assembly of stacked quantum dots . here the dominant mechanism of intermixing results from the deposition process in which several layers of one material deposited which are followed by several layers of another material and so on . since the materials are not lattice matched elastic strain develops and it is observed that the film forms quantum dots . the quantum dots in different layers align themselves to self assemble into stacked quantum dots . intermixing of the film material and the capping layer needs to be addressed in this situation . some related work , both experimental and computational , can be found in refs . @xcite . it is clear that the simulation of strained heteroepitaxial growth with intermixing has important applications . one reasonably popular approach is based on numerical solution of continuum equations . indeed recent work in this direction @xcite has been able to capture many aspects of the film growth . another approach is based on kinetic monte carlo ( kmc ) . since kmc is based on an atomistic scale it is typically slower than a continuum formulation . on the other hand , kmc not only captures all the physical effects modeled by continuum approach but can naturally include discrete and stochastic effects such as nucleation , surface roughness , and intermixing . the purpose of this paper is to present a kmc model of strained heteroepitaxial growth with intermixing and an algorithm for its efficient simulation . we extended the model proposed by orr et al @xcite and lam , lee , & sander @xcite to include intermixing . this model is a solid - on - solid bond counting scheme@xcite in which elastic interaction are included using a ball and spring model . the efficient simulation of this model represents the major contribution of this paper . one computational bottle neck for the simulation of strained film growth is the repeated calculation of elastic field . in this paper we address this by the inclusion of intermixing into the multigrid - fourier method developed by russo & smereka@xcite . in addition we present a cleaner way to incorporate the substrate into the multigrid method and simplify the coarse - graining and prolongation operators . as it turns out , for the kmc model used here , the change in total elastic energy , when a surface atom is removed , is needed . it was established by schulze & smereka@xcite that despite the long range nature of elastic interactions one can accurately compute this energy change by local calculations . in this work , we have verified that this approach also works in case of intermixing . in addition we have presented numerical evidence that the asymptotic expressions presented in ref . @xcite remain valid in the case of intermixing . another computational bottleneck is the computation of the rates . in order to implement rejection - free kmc one must know the hopping rates for all the atoms . to accomplish this one would have to compute the change in elastic energy that occurs when each and every atom is removed . this would be prohibitively expensive . fortunately , it was argued in ref . @xcite that the current elastic energy density can be used to provide fairly sharp upper bounds on the change in elastic energy . these can be used to provide a rejection - reduced kmc algorithm . here we demonstrate that this approach works well for the intermixing case . in our simulations the rejection rate is approximately between .5 and 5 percent .    in the following sections we explain the kmc model and present our algorithm to calculate the elastic displacement field and elastic energy in the case of a multicomponent film . some results are presented that illustrate the effectiveness of the algorithm ; namely , the effects of intermixing on the morphology of a growing strained film and a simulation illustrating the self - assembly of stacked quantum dots . to the best of our knowledge these results are the first kinetic monte carlo simulations of strained heteroepitaxial growth with intermixing .","summary":"an efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic monte carlo is presented . the simulations show the importance of intermixing on the growth of a strained film . further the method is used to simulate the growth of self - assembled stacked quantum dots .","abstract":"an efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic monte carlo is presented . the model used is based on a solid - on - solid bond counting formulation in which elastic effects are incorporated using a ball and spring model . while idealized , this model nevertheless captures many aspects of heteroepitaxial growth , including nucleation , surface diffusion , and long range effects due elastic interaction . the algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection - reduced kinetic monte carlo based on using upper bounds for the rates . the former is achieved by using a multigrid method for global updates of the displacement field and an expanding box method for local updates . the simulations show the importance of intermixing on the growth of a strained film . further the method is used to simulate the growth of self - assembled stacked quantum dots ."}
{"article_id":"0903.4882","section_id":"i","document":"in this work , we have presented a kinetic monte carlo model for strained heteroepitaxial growth with intermixing . the model is based on a solid - on - solid , bond counting formulation @xcite in which elastic interactions are accounted for with balls and springs on cubic lattice @xcite . we have also introduced an algorithm for the efficient simulation of this model . this algorithm is based on the work in @xcite but was extended to include intermixing and other improvements . in particular , the fourier - multigrid method developed in this work has much neater way of coupling the film and the substrate as compared to that in @xcite . in addition , the course - graining and prolongation operators have been simplified . we have presented numerical evidence that the principle of energy localization is valid in the case of intermixing and that the asymptotic results presented in @xcite also remain true . our results also indicate that the expanding box method works well in the case of intermixing . we have also demonstrated that the formula for the upper bounds on the rates proposed by schulze & smereka@xcite appears to work well even for mixtures . a preliminary study on the growth of strained films with intermixing is presented . the study indicates the presence of an asaro - tiller - grinfeld type instability of the flat strained film leading to the formation of quantum dots . the intermixing is found to considerably lower the strain in the film resulting in a stabilizing effect that delays the onset of islands . this gives rise to what tu & tersoff@xcite call an apparent critical thickness . eventually this critical layer disappears as the valleys form . a detailed study of the effects of intermixing on the critical thickness is currently under way . the model also successfully predicts self assembly of stacked arrays of quantum dots .","summary":"the model used is based on a solid - on - solid bond counting formulation in which elastic effects are incorporated using a ball and spring model . while idealized , this model nevertheless captures many aspects of heteroepitaxial growth , including nucleation , surface diffusion , and long range effects due elastic interaction .","abstract":"an efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic monte carlo is presented . the model used is based on a solid - on - solid bond counting formulation in which elastic effects are incorporated using a ball and spring model . while idealized , this model nevertheless captures many aspects of heteroepitaxial growth , including nucleation , surface diffusion , and long range effects due elastic interaction . the algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection - reduced kinetic monte carlo based on using upper bounds for the rates . the former is achieved by using a multigrid method for global updates of the displacement field and an expanding box method for local updates . the simulations show the importance of intermixing on the growth of a strained film . further the method is used to simulate the growth of self - assembled stacked quantum dots ."}
{"article_id":"0710.4328","section_id":"i","document":"we conducted three radiation hydrodynamical , adaptive mesh refinement simulations that supplement our previous cosmological simulations that focused on the hydrodynamics and cooling during early galaxy formation . these new simulations concentrated on the formation and feedback of massive , metal - free stars . we used adaptive ray tracing to accurately track the resulting regions and followed the evolution of the photo - ionized and photo - heated igm . we also explored on the details of early star formation in these simulations . theories of early galaxy formation and reionization and large scale reionization simulations can benefit from the useful quantities and characteristics of the high redshift universe , such as sfr and igm temperatures and ionization states , calculated in our simulations . the key results from this work are listed below . sfrs increase from @xmath20 at redshift 30 to @xmath157 m@xmath49 yr@xmath50 mpc@xmath46  at redshift 20 in our simulations . afterwards the sfr begins to have a bursting nature in halos more massive than @xmath2 and fluctuates around @xmath53 m@xmath49 yr@xmath50 mpc@xmath46 . these rates are larger than the ones calculated in @xcite because our simulation volume samples a highly biased region that contains a 2.5-@xmath48 density fluctuation . the associated emissivity from these stars increase from 1 to @xmath0100 ionizing photons per baryon per hubble time between redshifts 15 and 30 in order to provide a comparison to semi - analytic models , we calculate the star formation efficiency to be @xmath0@xmath148 averaged over all redshifts and the simulation volume . for pop iii star formation , this is a factor of two lower than stars that are not affected by feedback @xcite . shock waves created by d - type i - fronts expel most of the gas in the host halos below @xmath0@xmath59 . above this mass , significant outflows that are still bound to the halo are generated . this feedback creates a dynamical picture of early structure formation , where star formation is suppressed in halos because of this baryon depletion , which is more effective than uv heating or the radiative dissociation of h@xmath10 . we see three instances of induced star formation in halos with masses @xmath158 . here a star forms as a sn blast wave overtakes an overdensity created by an ionization front instability . formation is catalyzed by additional free electrons in the relic region and in the sn blast wave @xcite .    \\5 . as star formation occurs regularly in the simulation after redshift 25 , four ( six ) ionizing photons are needed per sustained hydrogen ionization . as the most massive halo becomes larger than @xmath0@xmath159 in the simulations without sne , regions become trapped and ionizing radiation only escapes into the igm in small solid angles . hence the number of photons per effective ionization increases to 15 ( 50 ) . in simb - sn , stellar radiation from induced star formation have an escape fraction of nearly unity , which occur four times in the calculation . this allows the igm to remain ionized at a volume fraction 3 times higher than without sne . similarly , the ionizing photon to ionization ratio also stays elevated at 10:1 instead of decreasing in the calculations with star formation only . our simulations that include star formation and h@xmath10  formation capture the entire evolution of the clumping factor that is used in semi - analytic models to calculate the effective enhancement of recombinations in the igm . we showed that clumping factors in the ionized medium fluctuate around the 75% of the values found in adiabatic simulations . they evolve from unity at high redshifts and steadily increase to @xmath04 and 3.5 with and without sne at @xmath90 , respectively . photo - evaporation from stellar feedback causes the decrease of the clumping factor . we calculated the jeans filtering mass with the volume - averaged temperature only in fully and partially ionized regions , which yields a better estimate than the temperature averaged over both ionized and neutral regions . the filtering mass depends on the thermal history of the igm , which mainly cools through compton cooling . it increases by two orders of magnitude to @xmath0@xmath160 at @xmath161 . it describes the minimum mass a halo requires to collapse after hosting a pop iii star . for halos forming their first star , the minimum halo mass is regulated by the lw background @xcite and photo - evaporation ( e.g. * ? ? ? pop iii stellar feedback plays a key role in early star formation and the beginning of cosmological reionization . the shallow potential wells of their host halos only amplify their radiative feedback . our understanding of the formation of the oldest galaxies and the characteristics of isolated dwarf galaxies may benefit from including the earliest stars and their feedback in galaxy formation models . although these massive stars only partially reionized the universe , their feedback on the igm and galaxies is crucial to include since it affects the characteristics of low - mass galaxies that are thought to be primarily responsible for cosmological reionization . harnessing observational clues about reionization , observations of local dwarf spheroidal galaxies , and numerical simulations that accurately handle star formation and feedback may provide great insight on the formation of the first galaxies , their properties , and how they completed cosmological reionization . the quality and robustness of this paper was improved through the feedback of an anonymous referee . this work was supported by nsf career award ast-0239709 from the national science foundation and partially supported in part by the national science foundation under grant no . phy05 - 51164 . j. h.  w. thanks renyue cen for helpful discussions . we benefited from fruitful conversations with marcelo alvarez . we are grateful for the continuous support from the computational team at slac . we benefited the hospitality of kitp at uc santa barbara , where this work was completed . we performed these calculations on 16 processors of a sgi altix 3700 bx2 at kipac at stanford university .","summary":"sn blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities .","abstract":"the initial conditions and relevant physics for the formation of the earliest galaxies are well specified in the concordance cosmology . using ab initio cosmological eulerian adaptive mesh refinement radiation hydrodynamical calculations , we discuss how very massive stars start the process of cosmological reionization . the models include non - equilibrium primordial gas chemistry and cooling processes and accurate radiation transport in the case b approximation using adaptively ray traced photon packages , retaining the time derivative in the transport equation . supernova feedback is modeled by thermal explosions triggered at parsec scales . all calculations resolve the local jeans length by at least 16 grid cells at all times and as such cover a spatial dynamic range of . these first sources of reionization are highly intermittent and anisotropic and first photoionize the small scales voids surrounding the halos they form in , rather than the dense filaments they are embedded in . as the merging objects form larger , dwarf sized galaxies , the escape fraction of uv radiation decreases and the regions only break out on some sides of the galaxies making them even more anisotropic . in three cases , sn blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities . these stars form tens of parsecs away from the center of their parent dm halo . approximately 5 ionizing photons are needed per sustained ionization when star formation in 10  halos are dominant in the calculation . as the halos become larger than , the ionizing photon escape fraction decreases , which in turn increases the number of photons per ionization to 1550 , in calculations with stellar feedback only . radiative feedback decreases clumping factors by 25 per cent when compared to simulations without star formation and increases the average temperature of ionized gas to values between 3,000 and 10,000 k."}
{"article_id":"1310.2300","section_id":"i","document":"the problem with interpreters for dynamically typed programming languages is that they are slow . the fundamental lack of performance is due to following reasons . first , their implementation is simple and does not perform known interpreter optimizations , such as threaded code  @xcite or superinstructions  @xcite . second , even if the interpreters apply these known techniques , their performance potential is severely constrained by expensive interpreter instruction implementations  @xcite .    unfortunately , performance - conscious implementers suffer from having only a limited set of options at their disposal to solve this problem . for peak performance , the current best - practice is to leverage results from dynamic compilation . but , implementing a just - in - time , or jit , compiler is riddled with many problems , e.g. , a lot of tricky details , hard to debug , and substantial implementation effort . an alternative route is to explore the area of purely interpretative optimization instead . these are optimizations that preserve innate interpreter characteristics , such as ease - of - implementation and portability , while offering important speedups . prior work in this area already reports the potential of doubling the execution performance  @xcite . as a result , investigating a general and principled strategy for optimizing high abstraction - level interpreters is particularly warranted . interpreting a dynamically typed programming language , such as javascript , python , or ruby , has its own challenges . frequently , these interpreters use one or a combination of the following features :    * dynamic typing to select type - specific operations , * reference counting for memory management , and * modifying boxed data object representations .    to cope with these features , interpreter instructions naturally become expensive in terms of assembly instructions required to implement their semantics . looking at successful research in just - in - time compilation , we know that in order to achieve substantial performance improvements , we need to reduce the complexity of the interpreter instructions implementation . put differently , we need to remove the overhead introduced by dynamic typing , reference counting , and operating on boxed data objects .    in this paper we combine ideas from staged compilation with partial evaluation and interpreter optimization to devise a general framework for interpreter optimization . from staged compilation , we take the idea that optimizations can spread out across several stages . from partial evaluation , we take inspiration from the futamura projections to optimize programs . from interpreter optimization , we model a general theory of continuous optimization based on rewriting instructions . these ideas form the core of our framework , which is purely interpretative , i.e. , it offers ease - of - implementation and portability while avoiding dynamic code generation , and delivers high performance . as a result , close to three decades after deutsch and schiffman  @xcite described the ideas of what would eventually become the major field of just - in - time compilation , our framework presents itself as an alternative to implementing jit compilers .    summing up , this paper makes the following contributions . * we introduce a general theory for optimizing interpreter instructions that relies on speculatively staging of optimized interpreter instructions at interpreter compile - time and subsequent concerting at run - time ( see  ) . * we present a principled procedure to derive optimized interpreter instructions via partial evaluation . here , speculation allows us to remove previous approaches requirement to specialize towards a specific program ( see  ) . * we apply the general theory to the python interpreter and describe the relevant implementation details ( see  ) . * we provide results of a careful and detailed evaluation of our python based implementation ( see  ) , and report substantial speedups of up to more than four times faster than the cpython implementation for the benchmark . for this benchmark our technique outperforms the current state - of - the - art jit compiler , pypy 1.9 , by 14% .","summary":"at run - time we use instruction substitution from the interpreter s original and expensive instructions to optimized instruction derivatives to speed up execution .    our technique unites high performance with the simplicity and portability of interpreters  we report that our optimization makes the cpython interpreter up to more than four times faster , where our interpreter closes the gap between and sometimes even outperforms pypy s just - in - time compiler .","abstract":"interpreters have a bad reputation for having lower performance than just - in - time compilers . we present a new way of building high performance interpreters that is particularly effective for executing dynamically typed programming languages . the key idea is to combine speculative staging of optimized interpreter instructions with a novel technique of incrementally and iteratively concerting them at run - time .    this paper introduces the concepts behind deriving optimized instructions from existing interpreter instructions  incrementally peeling off layers of complexity . when compiling the interpreter , these optimized derivatives will be compiled along with the original interpreter instructions . therefore , our technique is portable by construction since it leverages the existing compiler s backend . at run - time we use instruction substitution from the interpreter s original and expensive instructions to optimized instruction derivatives to speed up execution .    our technique unites high performance with the simplicity and portability of interpreters  we report that our optimization makes the cpython interpreter up to more than four times faster , where our interpreter closes the gap between and sometimes even outperforms pypy s just - in - time compiler ."}
{"article_id":"1310.2300","section_id":"l","document":"[ [ partial - evaluation ] ] partial evaluation + + + + + + + + + + + + + + + + + +    in 1996 , leone and lee  @xcite present their implementation of an optimizing ml compiler that relies on run - time feedback . interestingly , they mention the basic idea for our system :    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ it is possible to pre - compile several alternative templates for the same code sequence and choose between them at run time , but to our knowledge this has never been attempted in practice . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _    substituting `` interpreter instructions''or derivatives , as we frequently refer to them  for the term `` templates '' in the quote , reveals the striking similarity . in addition , both approaches leverage the compiler back - end of the ahead - of - time compiler assembling the run - time system  in our case the interpreter . this approach therefore automatically supports all target architectures of the base - compiler and hence there is no need for building a custom back - end .    in similar vein to leone and lee , other researchers addressed the prohibitive latency requirements of dynamic compilation  @xcite by leveraging ideas from partial evaluation . while we take inspiration from these prior results , we address the latency problem superimposed by dynamic code generation by _ avoiding _ it altogether . instead , we speculate on the likelihood of the interpreter using certain kinds of types and derive optimized instructions for them . at run - time , we rely on our novel procedure of concerting these optimized derivatives via abstract interpretation driven multi - level quickening . that being said , since these approaches are orthogonal , we believe that there are further advancements to be had by combining these approaches . for example  c , or the recently introduced terra / lua  @xcite , could be used to either stage the optimized derivatives inside of the interpreter source code , or generate the necessary derivatives at run - time , thereby eliminating the speculation part . the initial optimization potential of partial evaluation applied to interpreters goes back to futamura in 1971  @xcite . but , prior work has repeatedly revisited this specific problem . in particular , thibault et al . @xcite analyze the performance potential of partially evaluated interpreters and report a speedup of up to four times for bytecode interpreters . this result is intimately related to our work , in particular since they note that partial evaluation primarily targets instruction dispatch when optimizing interpreters  similar to the first futamura projection . in 2009 , brunthaler established that instruction dispatch is not a major performance bottleneck for our class of interpreters  @xcite . instead , our approach targets known bottlenecks in instruction implementation : dynamic typing , reference counting operations , and modifying boxed value representations . glck and jrgensen also connect interpreters with partial evaluation  @xcite , but as a means to optimize results obtained by applying partial evaluation . our technique should achieve similar results , but since it is speculative in nature , it does not need information of the actual program p that is interpreted , which is also a difference between our work and thibault et al . @xcite . [ [ interpreter - optimization ] ] interpreter optimization + + + + + + + + + + + + + + + + + + + + + + + +    the most closely related work in optimizing high - level interpreters is due to brunthaler  @xcite . in fact , the first - level quickening step to capture type feedback goes back to the discovery by brunthaler , and we have compared his publicly available system against our new technique . in addition to the second - level quickening that targets the overheads incurred by using boxed object representations , we also describe a principled approach to using partial evaluation for deriving instructions . [ [ just - in - time - compilers ] ] just - in - time compilers + + + + + + + + + + + + + + + + + + + + + +    type feedback has a long and successful history in just - in - time compilation . in 1994 , hlzle and ungar  @xcite discuss how the compiler uses type feedback to inline frequently dispatched calls in a subsequent compilation run . this reduces function call overhead and leads to a speedup by up to a factor of 1.7 . in general , subsequent research gave rise to adaptive optimization in just - in - time compilers  @xcite . our approach is similar , except that we use type feedback for optimizing the interpreter .    in 2012 , there has been work on `` repurposed jit compilers , '' or rjits , which take an existing just - in - time compiler for a statically typed programming language and add support for a dynamically typed programming language on top  @xcite . this approach is interesting , because it tries to leverage an existing just - in - time compilation infrastructure to enable efficient execution of higher abstraction - level programming languages  similar to what has been described earlier in 2009 by bolz et al . @xcite and yermolovich et al . @xcite , but more invasive . unfortunately , the rjit work is unaware of recent advances in optimizing interpreters , and therefore misses some important optimization opportunities available to a repurposed just - in - time compiler . wrthinger et al . @xcite found that obtaining information from the interpreter has substantial potential to optimize jit compilation , and we anticipate that this is going to have major impact on the future of dynamic language implementation . regarding traditional just - in - time compilers , python nowadays only has one mature project : pypy  @xcite . pypy follows a trace - based jit compilation strategy and achieves substantial speedups over standard cpython . however , pypy has downsides , too : because its internals differ from cpython , it is not compatible with many third party modules written in c. our comparison to pypy finds that it is a much more sophisticated system offering class - leading performance on some of our benchmarks . surprisingly , we find that our technique outperforms pypy by up to 14% on the benchmark , and requires substantially less implementation effort .    [ [ miscellaneous ] ] miscellaneous + + + + + + + + + + + + +    prior research addressed the importance of directly operating on unboxed data  @xcite . there are certain similarities , e.g. , leroy s use of the ` wrap ` and ` unwrap ` operators are related to our ( un-)boxing functions , and there exist similar concerns in how to represent bits in a uniform fashion . the primary difference to the present work is that we apply this to a different language , python , which has a different sets of constraints and is dynamically typed .    in 1998 , shields et al . @xcite address overhead in dynamic typing via staged type inference . this is an interesting approach , but it is unclear if or how efficient this technique scales to python - like languages . our technique is much simpler , but we believe it could very well benefit of a staged inference step .","summary":"interpreters have a bad reputation for having lower performance than just - in - time compilers .","abstract":"interpreters have a bad reputation for having lower performance than just - in - time compilers . we present a new way of building high performance interpreters that is particularly effective for executing dynamically typed programming languages . the key idea is to combine speculative staging of optimized interpreter instructions with a novel technique of incrementally and iteratively concerting them at run - time .    this paper introduces the concepts behind deriving optimized instructions from existing interpreter instructions  incrementally peeling off layers of complexity . when compiling the interpreter , these optimized derivatives will be compiled along with the original interpreter instructions . therefore , our technique is portable by construction since it leverages the existing compiler s backend . at run - time we use instruction substitution from the interpreter s original and expensive instructions to optimized instruction derivatives to speed up execution .    our technique unites high performance with the simplicity and portability of interpreters  we report that our optimization makes the cpython interpreter up to more than four times faster , where our interpreter closes the gap between and sometimes even outperforms pypy s just - in - time compiler ."}
{"article_id":"1310.2300","section_id":"c","document":"we present a general theory and framework to optimize interpreters for high - level languages such as javascript , python , and ruby . traditional optimization techniques such as ahead - of - time compilation and partial evaluation only have limited success in optimizing the performance of these languages . this is why implementers usually resort to the expensive implementation of dynamic compilers  evidenced by the substantial industry efforts on optimizing javascript . our technique preserves interpreter characteristics , such as portability and ease of implementation , while at the same time enabling substantial performance speedups . this important speedup is enabled by peeling off layers of redundant complexity that interpreters conservatively re - execute instead of capitalizing on the `` dynamic locality of type usage''almost three decades after deutsch and schiffman described how to leverage this locality for great benefit . we capitalize on the observed locality by speculatively staging optimized interpreter instruction derivatives and concerting them at run - time . first , we describe how speculation allows us to decouple the partial evaluation from any concrete program . this enables a principled approach to deriving the implementation of optimized interpreter instruction derivatives by speculating on types the interpreter will encounter with a high likelihood . second , we present a new technique of concerting optimized interpreter instructions at run - time . at the core , we use a multi - level quickening technique that enables us to optimize untyped instructions operating on boxed objects down to typed instructions operating on native machine data .    from a practical perspective , our implementation and evaluation of the python interpreter confirms that there is a huge untapped performance potential waiting to be set free . regarding the implementation , we were surprised how easy it was to provide optimized instruction derivatives even without automated support by partial evaluation . the evaluation indicates that our technique is competitive with a dynamic compiler w.r.t . performance _ and _ implementation effort : besides the speedups by a factor of up to 4.222 , we report a reduction in implementation effort by about  17@xmath74 . m.  berndl , b.  vitale , m.  zaleski , and a.  d. brown . context threading : a flexible and efficient dispatch technique for virtual machine interpreters . in _ proceedings of the 3rd ieee / acm international symposium on code generation and optimization , san jose , ca , usa , march 20 - 23 , 2005 ( cgo  05 ) _ , pages 1526 , 2005 .    c.  f. bolz , a.  cuni , m.  fijakowski , and a.  rigo . tracing the meta - level : pypy s tracing jit compiler . in _ proceedings of the 4th workshop on the implementation , compilation , optimization of object - oriented languages and programming systems ( icooolps  09 ) _ , lecture notes in computer science , pages 1825 . springer , 2009 . isbn 978 - 3 - 642 - 03012 - 3 . doi : http://doi.acm.org/10.1145/1565824.1565827 . s.  brunthaler . virtual - machine abstraction and optimization techniques . in _ proceedings of the 4th international workshop on bytecode semantics , verification , analysis and transformation , york , united kingdom , march 29 , 2009 ( bytecode  09 ) _ , volume 253(5 ) of _ electronic notes in theoretical computer science _ , pages 314 , amsterdam , the netherlands , december 2009 . doi : http://dx.doi.org/10.1016/j.entcs.2009.11.011 . s.  brunthaler . inline caching meets quickening . in _ proceedings of the 24th european conference on object - oriented programming , maribor , slovenia , june 21 - 25 , 2010 ( ecoop  10 ) _ , volume 6183/2010 of _ lecture notes in computer science _ , pages 429451 . springer , 2010 . isbn 978 - 3 - 642 - 03012 - 3 . doi : http://dx.doi.org/10.1007/978-3-642-03013-0 . s.  brunthaler . efficient interpretation using quickening . in _ proceedings of the 6th symposium on dynamic languages , reno , nv , usa , october 18 , 2010 ( dls  10 ) _ , pages 114 , new york , ny , usa , 2010 . acm press . isbn 978 - 3 - 642 - 03012 - 3 . doi : http://dx.doi.org/10.1007/978-3-642-03013-0 . k.  casey , d.  gregg , and m.  a. ertl . tiger  an interpreter generation tool . in _ proceedings of the 14th international conference on compiler construction , edinburgh , united kingdom , april 4 - 8 , 2005 ( cc  05 ) _ , volume 3443/2005 of _ lecture notes in computer science _ , pages 246249 . springer , 2005 . isbn 3 - 540 - 25411 - 0 . doi : http://dx.doi.org/10.1007/978-3-540-31985-6_18 . j.  g. castanos , d.  edelsohn , k.  ishizaki , p.  nagpurkar , t.  nakatani , t.  ogasawara , and p.  wu . on the benefits and pitfalls of extending a statically typed language jit compiler for dynamic scripting languages . in _ proceedings of the 27th acm sigplan conference on object oriented programming : systems , languages , and applications , tucson , az , usa , october 21 - 25 , 2012 ( oopsla  12 ) _ , pages 195212 , 2012 . doi : http://doi.acm.org/10.1145/2384616.2384631 .    c.  chambers . staged compilation . in _ proceedings of the acm sigplan workshop on partial evaluation and semantics - based program manipulation , portland , or , usa , january 14 - 15 , 2002 ( pepm  02 ) _ , pages 18 , 2002 . doi : http://doi.acm.org/10.1145/503032.503045 . l.  p. deutsch and d.  g. bobrow . an efficient , incremental , automatic garbage collector . _ communications of the acm _ , 190 ( 9):0 522526 , 1976 . issn 0001 - 0782 . doi : http://doi.acm.org/10.1145/360336.360345 . l.  p. deutsch and a.  m. schiffman . efficient implementation of the smalltalk-80 system . in _ proceedings of the sigplan 84 symposium on principles of programming languages ( popl  84 ) _ , pages 297302 , new york , ny , usa , 1984 . isbn 0 - 89791 - 125 - 3 . doi : http://doi.acm.org/10.1145/800017.800542 . z.  devito , j.  hegarty , a.  aiken , p.  hanrahan , and j.  vitek . terra : a multi - stage language for high - performance computing . in _ proceedings of the acm sigplan conference on programming language design and implementation , seattle , wa , usa , june 16 - 22 , 2013 ( pldi  13 ) _ , pages 105116 , 2013 . doi : http://doi.acm.org/10.1145/2462156.2462166 . m.  a. ertl and d.  gregg . combining stack caching with dynamic superinstructions . in _ proceedings of the 2004 workshop on interpreters , virtual machines and emulators ( ivme  04 ) _ , pages 714 , new york , ny , usa , 2004 . isbn 1 - 58113 - 909 - 8 . doi : http://doi.acm.org/10.1145/1059579.1059583 . m.  a. ertl , d.  gregg , a.  krall , and b.  paysan . vmgen : a generator of efficient virtual machine interpreters . _ software practice & experience _ , 32:0 265294 , march 2002 . issn 0038 - 0644 . doi : 10.1002/spe.434 . url http://portal.acm.org/citation.cfm?id=776235.776238 . b.  grant , m.  mock , m.  philipose , c.  chambers , and s.  j. eggers . . in _ proceedings of the acm sigplan workshop on partial evaluation and semantics - based program manipulation , amsterdam , the netherlands , june 12 - 13 , 1997 ( pepm  97 ) _ , pages 163178 , 1997 . doi : http://doi.acm.org/10.1145/258993.259016 . u.  hlzle and d.  ungar . optimizing dynamically - dispatched calls with run - time type feedback . in _ proceedings of the acm sigplan conference on programming language design and implementation , orlando , fl , usa , june 20 - 24 , 1994 ( pldi  94 ) _ , pages 326336 , 1994 . isbn 0 - 89791 - 662-x . doi : http://doi.acm.org/10.1145/178243.178478 . intel turbo boost technology  on - demand processor performance , 2012 . url http://www.intel.com / content / www / us / en / architecture - and - technology / turb% o - boost / turbo - boost - technology.html[http://www.intel.com / content / www / us / en / architecture - and - technology / turb% o - boost / turbo - boost - technology.html ] . k.  ishizaki , t.  ogasawara , j.  g. castanos , p.  nagpurkar , d.  edelsohn , and t.  nakatani . adding dynamically - typed language support to a statically - typed language compiler : performance evaluation , analysis , and tradeoffs . in _ proceedings of the 8th acm sigplan international conference on virtual execution environments , london , united kingdom , march 3 - 4 , 2012 ( vee  12 ) _ , pages 169180 , 2012 . doi : http://doi.acm.org/10.1145/2151024.2151047 . lee and m.  leone . optimizing ml with run - time code generation . in _ proceedings of the acm sigplan conference on programming language design and implementation , philadephia , pa , usa , may 21 - 24 , 1996 ( pldi  96 ) _ , pages 540553 , 1996 . doi : http://doi.acm.org/10.1145/989393.989448 . x.  leroy . . in _ proceedings of the 196h acm sigplan - sigact symposium on principles of programming languages , albuquerque , nm , usa , january 19 - 22 , 1992 ( popl  92 ) _ , pages 177188 , 1992 . doi : http://doi.acm.org/10.1145/143165.143205 . s.  l. peyton  jones and j.  launchbury . . in _ proceedings of the 5th acm conference on functional programming languages and computer architecture , in cambridge , uk , september 1991 _ , pages 636666 , 1991 . isbn 3 - 540 - 54396 - 1 . doi : http://dl.acm.org/citation.cfm?id=645420.652528 . m.  philipose , c.  chambers , and s.  j. eggers . . in _ proceedings of the 29th acm sigplan - sigact symposium on principles of programming languages , portland , or , usa , january 16 - 18 , 2002 ( popl  02 ) _ , pages 113125 , 2002 . doi : http://doi.acm.org/10.1145/503272.503284 . i.  piumarta and f.  riccardi . optimizing direct threaded code by selective inlining . in _ proceedings of the acm sigplan conference on programming language design and implementation , montral , qc , canada , june 17 - 19 , 1998 ( pldi  98 ) _ , pages 291300 , new york , ny , usa , 1998 . isbn 0 - 89791 - 987 - 4 . doi : http://doi.acm.org/10.1145/277650.277743 . t.  a. proebsting . optimizing an ansi c interpreter with superoperators . in _ proceedings of the 22nd acm sigplan - sigact symposium on principles of programming languages , san francisco , ca , usa , january 23 - 25 , 1995 ( popl  95 ) _ , pages 322332 , 1995 . doi : http://doi.acm.org/10.1145/199448.199526 . a.  rigo and s.  pedroni . s approach to virtual machine construction . in _ proceedings of the 21st acm sigplan conference on object oriented programming : systems , languages , and applications , portland , or , usa , october 22 - 26 , 2006 ( oopsla  06 ) _ , pages 944953 , 2006 . doi : http://doi.acm.org/10.1145/1176617.1176753 . oopsla companion . m.  shields , t.  sheard , and s.  l. peyton  jones . . in _ proceedings of the 25th acm sigplan - sigact symposium on principles of programming languages , san diego , ca , usa , january 19 - 21 , 1998 ( popl  98 ) _ , pages 289302 , 1998 . doi : http://doi.acm.org/10.1145/268946.268970 . t.  wrthinger , a.  w , l.  stadler , g.  duboscq , d.  simon , and c.  wimmer . self - optimizing ast interpreters . in _ proceedings of the 8th symposium on dynamic languages , tucson , az , usa , october 22 , 2012 ( dls  12 ) _ , pages 7382 , 2012 . doi : http://doi.acm.org/10.1145/2384577.2384587 . a.  yermolovich , c.  wimmer , and m.  franz . optimization of dynamic languages using hierarchical layering of virtual machines . in _ proceedings of the 5th symposium on dynamic languages , orlando , fl , usa , october 26 , 2009 ( dls  09 ) _ , pages 7988 , new york , ny , usa , 2009 . isbn 978 - 1 - 60558 - 769 - 1 . doi : http://doi.acm.org/10.1145/1640134.1640147 .","summary":"the key idea is to combine speculative staging of optimized interpreter instructions with a novel technique of incrementally and iteratively concerting them at run - time .   ","abstract":"interpreters have a bad reputation for having lower performance than just - in - time compilers . we present a new way of building high performance interpreters that is particularly effective for executing dynamically typed programming languages . the key idea is to combine speculative staging of optimized interpreter instructions with a novel technique of incrementally and iteratively concerting them at run - time .    this paper introduces the concepts behind deriving optimized instructions from existing interpreter instructions  incrementally peeling off layers of complexity . when compiling the interpreter , these optimized derivatives will be compiled along with the original interpreter instructions . therefore , our technique is portable by construction since it leverages the existing compiler s backend . at run - time we use instruction substitution from the interpreter s original and expensive instructions to optimized instruction derivatives to speed up execution .    our technique unites high performance with the simplicity and portability of interpreters  we report that our optimization makes the cpython interpreter up to more than four times faster , where our interpreter closes the gap between and sometimes even outperforms pypy s just - in - time compiler ."}
{"article_id":"1002.3162","section_id":"i","document":"dark matter is supposed to be the principal driver of structure formation in the universe , and a whole industry has developed over the last few decades searching for the still elusive dark matter particle . particle physics has provided some well - motivated candidates . among them , the neutralino , a weakly interacting massive particle ( wimp ) associated with a supersymmetric extension of the standard model of particle physics , is currently favoured ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * for reviews ) . although this particle interacts with standard model particles only weakly , it may nevertheless be detectable . recently the dark matter community has been stimulated by a variety of observed `` anomalies '' in cosmic - ray signals . among these are : ( i ) an excess in the positron fraction recently ( re)measured by the pamela experiment @xcite ; ( ii ) an excess in the total flux of electrons and positrons measured by the fermi satellite @xcite ; ( iii ) an excess in diffuse microwave radiation in the general direction of the galactic centre ( the  wmap haze  although these results may well find their explanation in ordinary astrophysical processes ( see , for example , @xcite for a pulsar explanation of the pamela results ) , it is alluring to relate them all to dark matter annihilation in the galactic halo . in addition to these indirect signals , the dama / libra dark matter detection experiment has , for about a decade @xcite seen a significant amplitude modulation in its detector count rate . although apparently incompatible with results from other experiments ( see e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , the dama / libra collaboration interprets this as an annual modulation of the flux of dark matter particles through their detectors . the small - scale structure of cold dark matter ( cdm ) haloes can , in principle , substantially influence the signal both in indirect and in direct dark matter detection experiments . annihilation rates and detector count rates depend strongly on the density and energy distributions of particles local to other particles and to detector nuclei , respectively , and so are sensitive to small - scale fluctuations in these distributions . for example , for cross - sections consistent with relic abundance constraints , the pamela data can be explained through annihilation only if rates are 100 to 1000 times those predicted for a locally smooth dark matter distribution , thus requiring substantial `` boost factors '' ( e.g. * ? ? ? such boosts could come from non - standard particle physics , or they might reflect substantial inhomogeneities in the dark matter distribution on small scale . a population of abundant , self - bound subhaloes of very low mass but very high internal density has often been invoked in this context @xcite , but recent high - resolution simulations suggest that such subhaloes are neither dense enough nor abundant enough in the inner regions of @xmath0cdm haloes to have more than a minor effect on the observable signatures of annihilation @xcite .    another possible boost mechanism is related to the fine - grained structure of dark matter haloes . before the onset of nonlinear structure formation , dark matter was almost uniformly distributed , with weak density and velocity perturbations and with very small thermal motions . the particles thus occupied a thin , space - filling and almost three - dimensional sheet in the full six - dimensional phase - space . subsequent collisionless evolution under gravity stretched and folded this sheet , but did not tear it . thus , the dark matter distribution at a typical point in a present - day halo is predicted to be a superposition of many fine - grained streams , each of which has a very small velocity dispersion , has a density and mean velocity which vary smoothly with position , and corresponds to material from the vicinity of a different point in the linear initial conditions . folds in the fine - grained phase - sheet give rise to projective catastrophes known as caustics where the spatial density and hence the annihilation rate is locally very high , limited only by the small but nonzero thickness of the phase - sheet ( e.g. * ? ? ? * ; * ? ? ? although the extraordinary improvement of n - body simulations in recent years has allowed many aspects of the dark matter distribution at the solar position to be predicted in considerable detail ( see , for example , * ? ? * ; * ? ? ? * ; * ? ? ? * ) , such simulations are still very far from resolving the fine - grained phase - space structure which gives rise to caustics . they are thus unable to provide a realistic estimate of how much caustics boost annihilation in the inner galactic halo . fine - grained structure might also play a crucial role in the interpretation and modelling of dark matter signals in laboratory detectors like dama / libra . it is unclear , for example , whether the maxwellian usually assumed describes the dark matter velocity distribution at the solar position accurately . indeed , recent simulation work has shown that a multivariate gaussian is likely a better description , and that the assembly history of the milky way may be reflected in broad features in the particle energy distribution @xcite . one may also wonder whether individual fine - grained streams might eventually be visible in detector signals as spikes at specific velocities . axion detectors like admx , in particular , have very high energy resolution , and could in principle disentangle hundreds of thousands of streams . again this is far beyond the resolution limit of current analysis techniques applied to even the highest resolution n - body simulations of halo formation .    in recent work we have developed an entirely new approach capable of following the evolution of fine - grained streams and their associated caustics in fully general simulations of halo formation . this approach is based on integrating the geodesic deviation equation ( gde ) in tandem with the n - body equations of motion . for every simulation particle and at every timestep it returns the spatial density and the velocity dispersion tensor of the fine - grained stream in which the particle is embedded . this in turn allows all passages of the particle through a caustic to be identified and recorded . in @xcite we presented this gde scheme and tested it on orbits in fixed potentials and on n - body simulations of static equilibrium haloes . in @xcite we then applied the scheme to a simplified model of cdm halo formation : collapse from spherically symmetric , self - similar and linear initial conditions . this showed that earlier work based on spherically symmetric similarity solutions ( e.g. * ? ? ? * ; * ? ? ? * ) was unrealistic because these solutions are violently unstable to nonradial perturbations . these substantially alter the stream and caustic structure . finally in @xcite we showed how the gde scheme allows the annihilation enhancement due to caustics and other fine - grained structure to be calculated explicitly by time - integration along particle orbits rather than by spatial integration over the particle distribution . the current paper is the culmination of this programme and analyses for the first time the fine - grained structure of haloes forming from fully general @xmath0cdm initial conditions . we resimulate haloes from the aquarius project , which studied six milky way mass objects at various numerical resolutions . the coarse - grained structure of these haloes has already been studied in considerable detail in previous papers , e.g. the subhalo population in @xcite and @xcite , the dark matter distribution in the inner regions in @xcite and various radial profiles in @xcite . the plan of our paper is as follows . in section 2 we briefly describe the initial conditions and the numerical approach we use to resolve the fine - grained phase - space structure . section 3 begins by presenting results on one of the aquarius haloes at a variety of resolutions . we demonstrate that , for fixed gravitational softening , convergent results can be obtained , free of significant discreteness or two - body relaxation effects . we then analyse the implications for dark matter detection of the structure predicted for fine - grained streams and caustics . finally , we use our full halo sample to tackle the question of how much scatter in fine - grained properties is expected . we make some concluding remarks in section 4 . an appendix shows that although discreteness effects are negligible in our high resolution simulations , their predictions for fine - grained stream densities ( but not for caustic structure ) are influenced by gravitational softening because this affects the tidal forces on particles passing close to halo centre .","summary":"we present the first and so far the only simulations to follow the fine - grained phase - space structure of galaxy haloes formed from genericcdm initial conditions . we integrate the geodesic deviation equation in tandem with the n - body equations of motion , demonstrating that this can produce numerically converged results for the properties of fine - grained phase - space streams and their associated caustics , even in the inner regions of haloes . our effective resolution for such structures is many orders of magnitude better than achieved by conventional techniques on even the largest simulations . dark matter particles at this radius have typically passed 200 caustics since the big bang , with a 5 to 95% range of 50 to 500 . such caustic counts are a measure of the total amount of dynamical mixing and are very robustly determined by our technique . the peak densities on present - day caustics in the inner halo almost all lie well below the mean local dark matter density . as a result caustics provide a negligible boost ( ) to the predicted local dark matter annihilation rate . the effective boost is larger in the outer halo but never exceeds about . cosmology : dark matter  methods : numerical","abstract":"we present the first and so far the only simulations to follow the fine - grained phase - space structure of galaxy haloes formed from genericcdm initial conditions . we integrate the geodesic deviation equation in tandem with the n - body equations of motion , demonstrating that this can produce numerically converged results for the properties of fine - grained phase - space streams and their associated caustics , even in the inner regions of haloes . our effective resolution for such structures is many orders of magnitude better than achieved by conventional techniques on even the largest simulations . we apply these methods to the six milky way - mass haloes of the aquarius project . at 8 kpc from halo centre a typical point intersects about streams with a very broad range of individual densities ; the most massive streams contribute about half of the local dark matter density . as a result , the velocity distribution of dark matter particles should be very smooth with the most massive fine - grained stream contributing about 0.1% of the total signal . dark matter particles at this radius have typically passed 200 caustics since the big bang , with a 5 to 95% range of 50 to 500 . such caustic counts are a measure of the total amount of dynamical mixing and are very robustly determined by our technique . the peak densities on present - day caustics in the inner halo almost all lie well below the mean local dark matter density . as a result caustics provide a negligible boost ( ) to the predicted local dark matter annihilation rate . the effective boost is larger in the outer halo but never exceeds about . thus fine - grained streams and their associated caustics have no effect on the detectability of dark matter , either directly in earth - bound laboratories , or indirectly through annihilation radiation , with the exception that resonant cavity experiments searching for axions may see the most massive local fine - grained streams because of their extreme localisation in energy / momentum space .    [ firstpage ]    cosmology : dark matter  methods : numerical"}
{"article_id":"1002.3162","section_id":"m","document":"we resimulate the six milky way - mass haloes of the aquarius project @xcite using our gde technique to follow the fine - grained phase - space evolution in detail . the cosmological parameters assumed for these @xmath0cdm simulations are @xmath5 and @xmath6 , where all quantities have their standard definitions . the haloes were selected at @xmath7 based on their mass , and were required to have no close massive companion at that time ; they are named aq - a to aq - f . each halo was resimulated at a variety of numerical resolutions , indicated by a number @xmath8 in its full name , e.g. aq - a-3 . the resolution levels differ in the particle mass and softening length employed , with 1 designating the highest resolution and 5 the lowest . in the following we will use the same naming convention and mass resolution as in the original papers but different softening lengths . this is because accurate integration of the geodesic deviation equation ( gde ) requires a larger softening length to achieve stable results than does integration of the particle trajectories themselves . unless otherwise stated , we use a constant comoving plummer - equivalent softening of @xmath9  kpc in all our simulations . the appendix examines the effect of softening on our results in some detail . all other simulation parameters are the same as in @xcite , to which we refer the reader for further technical information .    our experiments are carried out with the p - gadget-3 code @xcite with the gde modifications described in @xcite and @xcite , where we focused on a description of the relevant equations in physical coordinates and applied them to static potentials , to isolated equilibrium haloes and to halo formation from self - similar , spherically symmetric initial conditions . the simulations of this paper take into account the full @xmath0cdm framework , using the cosmological parameters given above , and are carried out in comoving coordinates . we therefore begin by describing how the gde and the associated tensors can be transformed from physical to comoving coordinates , and how this is implemented in our simulation code . for completeness , we also describe how the physical stream density is calculated and how caustic passages can be identified . the time - dependent transformation to the comoving frame used by our simulation code is given by vector and two of them denote a @xmath10 matrix . an overline denotes a @xmath11 vector and two of them denote a @xmath12 matrix . see also @xcite and @xcite . ] @xmath13 where @xmath14 denotes the hubble parameter , @xmath15 the scale factor , and comoving coordinates are primed . in physical coordinates the distortion tensor is defined as @xmath16 where @xmath17 and @xmath18 denote the initial position and velocity ( in physical coordinates ) , respectively . it describes how a local phase - space element in physical coordinates is deformed along the trajectory of the particle while conserving its volume in order to obey liouville s theorem . in comoving coordinates the distortion tensor is accordingly defined as @xmath19 where all phase - space coordinates are now expressed in comoving coordinates . the relation between physical and comoving distortion tensors can be derived from the differential relations , yielding @xmath20 where we have defined the two transformation tensors @xmath21 and @xmath22 we note that one of these transformation tensors is evaluated at @xmath23 whereas the other is evaluated at the initial time @xmath24 . the reason for this is the time - dependence of the coordinate transformation in eq . 1 , where both the scale factor and the hubble parameter change with time . liouville s theorem guarantees that @xmath25 , so the comoving distortion tensor has the same conserved determinant as the physical one . this means that local phase - space elements in the comoving frame conserve both volume and orientation as the system evolves .    to integrate the comoving distortion tensor , we need to derive its equations of motion . we start with the physical gde equation @xmath26 and introduce the peculiar potential field @xmath27 which is related to the density field via poisson s equation @xmath28 where @xmath29 denotes the comoving mean background density and the laplacian is taken in comoving space . we note that the force field driving the motion of simulation particles is also derived from this peculiar potential . since the gde is directly related to the equations of motion of the particles themselves , it is natural to introduce a peculiar configuration - space tidal tensor @xmath30 with components @xmath31 @xmath32 we can use this tidal tensor to write the equations of motion for the comoving distortion tensor in the following form @xmath33 thus , the equations of motion for the comoving distortion tensor have exactly the same form as those for the physical one . the only difference is the appearance of the scale factor @xmath15 in the comoving equations . the initial conditions for these equations follow from those for the physical distortion tensor , taking into account @xmath34 @xmath35 based on these equations we can construct kick- and drift - operators for the leapfrog time integrator , similar to those for the position and velocity in the comoving frame .    let us now discuss how to derive stream densities from these comoving quantities . each stream density is associated with a particular simulation particle , and describes the local density of the fine - grained stream it is embedded in . our goal is to derive an equation that yields the physical stream density from the comoving distortion tensor discussed above . to begin , we note that the configuration - space distortion tensor can be derived from the phase - space distortion tensor by applying two projection operators as follows @xmath36 where @xmath37 is the spatial gradient of @xmath38 , the mean initial sheet velocity as a function of initial position ( see * ? ? ? * for a more formal definition ) . caustic passages can be identified by sign changes in the determinant of this tensor . we note that this is true both in physical and in comoving space . the physical stream density can be calculated from the volume stretch factor implied by this linear transformation in physical configuration - space @xmath39 as we described in @xcite . using @xmath40 and defining the peculiar velocity gradient @xmath41 we can write the physical stream density as : @xmath42\\right|}.\\ ] ] at early times when the dark matter is nearly uniform , all velocities and thus all velocity gradients are small and the second term in the determinant in this equation is small compared to the first . thus we may approximate @xmath43    this equation is sufficiently accurate for our purposes and we will use it below to calculate the stream densities associated with each particle in our simulations . for consistency we will also neglect the ( small ) initial variations in density and will assume the cosmological mean value everywhere , i.e. @xmath44","summary":"we apply these methods to the six milky way - mass haloes of the aquarius project . at 8 kpc from halo centre a typical point intersects about streams with a very broad range of individual densities ; the most massive streams contribute about half of the local dark matter density . as a result thus fine - grained streams and their associated caustics have no effect on the detectability of dark matter , either directly in earth - bound laboratories , or indirectly through annihilation radiation , with the exception that resonant cavity experiments searching for axions may see the most massive local fine - grained streams because of their extreme localisation in energy / momentum space .    [ firstpage ]   ","abstract":"we present the first and so far the only simulations to follow the fine - grained phase - space structure of galaxy haloes formed from genericcdm initial conditions . we integrate the geodesic deviation equation in tandem with the n - body equations of motion , demonstrating that this can produce numerically converged results for the properties of fine - grained phase - space streams and their associated caustics , even in the inner regions of haloes . our effective resolution for such structures is many orders of magnitude better than achieved by conventional techniques on even the largest simulations . we apply these methods to the six milky way - mass haloes of the aquarius project . at 8 kpc from halo centre a typical point intersects about streams with a very broad range of individual densities ; the most massive streams contribute about half of the local dark matter density . as a result , the velocity distribution of dark matter particles should be very smooth with the most massive fine - grained stream contributing about 0.1% of the total signal . dark matter particles at this radius have typically passed 200 caustics since the big bang , with a 5 to 95% range of 50 to 500 . such caustic counts are a measure of the total amount of dynamical mixing and are very robustly determined by our technique . the peak densities on present - day caustics in the inner halo almost all lie well below the mean local dark matter density . as a result caustics provide a negligible boost ( ) to the predicted local dark matter annihilation rate . the effective boost is larger in the outer halo but never exceeds about . thus fine - grained streams and their associated caustics have no effect on the detectability of dark matter , either directly in earth - bound laboratories , or indirectly through annihilation radiation , with the exception that resonant cavity experiments searching for axions may see the most massive local fine - grained streams because of their extreme localisation in energy / momentum space .    [ firstpage ]    cosmology : dark matter  methods : numerical"}
{"article_id":"1209.0012","section_id":"i","document":"consider the linear model @xmath4 where @xmath5 and @xmath6 are observed outcomes and @xmath1-dimensional predictors , respectively , @xmath7 are unobserved iid errors with @xmath8 and @xmath9 , and @xmath10 is an unknown @xmath1-dimensional parameter . to simplify notation , let @xmath11 denote the @xmath2-dimensional vector of outcomes and @xmath12 denote the @xmath13 matrix of predictors . also let @xmath14 . then ( [ lm ] ) may be re - expressed as @xmath15 in this paper , we focus on the case where the predictors @xmath16 are random . more specifically , we assume that @xmath17 are iid random vectors with mean 0 and @xmath18 positive definite covariance matrix @xmath19 ( many of the results in this paper are applicable if @xmath20 upon centering the data ; however , this is not pursued further here ) . let @xmath21 , where @xmath22 denotes the @xmath0-norm . then @xmath23 is a measure of the overall ( @xmath0- ) signal strength . the residual variance @xmath24 and the signal strength @xmath23 are important quantities in many problems in statistics . for example , in estimation and prediction problems , @xmath25 typically determines the scale of an estimator s risk under quadratic loss . more broadly , @xmath25 , @xmath23 , and associated quantities , such as the signal - to - noise ratio @xmath26 , all play a key role in regression diagnostics . thus , reliable estimators of @xmath25 and @xmath23 are desirable .    for invertible @xmath27 , let @xmath28 be the ordinary least squares estimator for @xmath29 . if @xmath30 , then @xmath31 is a consistent estimator for @xmath25 and , under fairly mild additional conditions , is asymptotically normal . consistent estimators for @xmath23 can also be constructed . for instance , if @xmath32 , it is easily seen that @xmath33 is a consistent estimator for @xmath23 under mild conditions . it is more challenging to construct reliable estimators for @xmath25 and @xmath23 in high - dimensional linear models , where @xmath34 . indeed , if @xmath34 , then the estimator @xmath35 breaks down ; however , estimating @xmath25 and @xmath23 remains important . in high - dimensional linear models with @xmath34 , @xmath25 plays an important role in selecting effective shrinkage parameters for many popular regularized regression methods @xcite . the signal - to - noise ratio @xmath26 is also important for shrinkage parameter selection , and it determines performance limits in certain high - dimensional regression problems @xcite .    in this paper , we propose new estimators for @xmath25 and @xmath23 that are consistent and asymptotically normal , with rate @xmath36 , in an asymptotic regime where @xmath37 ( whenever we write @xmath38 , it is implicit that @xmath39 as well ) . we also show that these estimators may be used to derive consistent and asymptotically normal estimators for function sof @xmath25 and @xmath23 , like the signal - to - noise ratio . previous work on estimating @xmath25 in high - dimensional linear models where @xmath34 has been conducted by @xcite and @xcite . these authors assume that @xmath29 is sparse ( e.g. the @xmath40-norm or @xmath41-norm of @xmath29 is small ) and their results for estimating @xmath25 are related to the fact that @xmath29 itself is estimable under the specified sparsity assumptions . though sun and zhang s ( 2011 ) and fan et al.s ( 2012 ) results even apply in settings where @xmath42 , their sparsity assumptions may be untenable in certain instances and this can dramatically affect the performance of their estimators . in this paper , we make no sparsity assumptions ( however , @xmath25 and @xmath23 are required to be bounded ) and we show that the proposed estimators for @xmath25 and @xmath23 perform well in situations where @xmath34 and @xmath29 is provably non - estimable . this is one of the main messages of the paper : though some type of sparsity is required to consistently estimate @xmath29 in high - dimensional linear models , sparsity in @xmath29 is _ not _ required to estimate @xmath25 and @xmath23 . though sparsity is not required in this paper , we do make strong distributional assumptions about the data . in particular , we henceforth assume that @xmath43 while normality is used heavily throughout our analysis , we expect that key aspects of many of the results in this paper remain valid under weaker distributional assumptions . this is explored via simulation in section 4 . not surprisingly , the analysis in this paper is simplified by the normality assumption ( [ normality ] ) . to explain the relevance of ( [ normality ] ) in more detail , we first point out that our primary consistency results for the proposed estimators of @xmath25 and @xmath23 ( theorem 1 below ) follow from exact calculations of the estimators mean and variance . if the normality assumption ( [ normality ] ) is violated , then these calculations are generally invalid ; similar techniques may be applicable , if other conditions hold , but exact finite sample calculations are not likely to be possible and any corresponding approximation may be more involved . the normality assumption ( [ normality ] ) also facilitates the use of a collection of `` soft - tools '' for random matrices developed by @xcite to prove that the estimators proposed in this paper are asymptotically normal . these tools are related to second order poincar inequalities and stein s method @xcite . asymptotic normality for the proposed estimators follows by bounding the total variation distance to a normal random variable . these bounds contain information about how the variability of the proposed estimators may depend @xmath1 , @xmath2 , @xmath44 , @xmath25 , and @xmath23 . this is easily leveraged to obtain consistent and asymptotically normal estimators for functions of @xmath25 and @xmath23 ( such as the signal - to - noise ratio , @xmath26 ; see corollary 2 below ) , which is an important practical objective . thus , one of the appealing aspects of the `` soft tools '' used in this paper is their flexibility . on the other hand , paraphrasing @xcite , other existing methods for asymptotic analysis in random matrix theory rely heavily on the exact calculation of limits @xcite ; we suggest that this may be a more delicate endeavor in some instances . if the normality assumption ( [ normality ] ) does not hold , then it is unclear if the soft tools used in this paper are still applicable and , consequently , other techniques may be required . existing work in random matrix theory suggests that this may be possible ( see , for example , @xcite ) ; however , the computations are likely more involved and the breadth of applicability of alternative techniques seems unclear .      another challenging issue for estimating @xmath25 and @xmath23 when @xmath45 involves the covariance matrix @xmath46 . our initial estimators for @xmath25 and @xmath23 are devised under the assumption that @xmath44 is known ( equivalently , @xmath47 ; see section 2 ) . these estimators are unbiased , consistent , and asymptotically normal . we subsequently propose modified estimators for @xmath25 and @xmath23 in cases where @xmath44 is unknown , but ( i ) a norm - consistent estimator for @xmath44 is available , or ( ii ) @xmath44 and @xmath29 satisfy certain conditions described in section 3.2 . if a norm - consistent estimator for @xmath44 is available , then the proposed estimators for @xmath25 and @xmath23 are consistent ; if , furthermore , @xmath44 is estimated at rate @xmath48 , then the estimators are asymptotically normal . on the other hand , if @xmath49 , then norm - consistent estimators for @xmath44 are not generally available ( though there are important examples where norm - consistent estimators for @xmath44 can be found  this is discussed in more detail in section 3.1 ) . thus , it is important to construct estimators for @xmath25 and @xmath23 that perform reliably when @xmath44 is completely unknown . while it remains an open problem to find estimators for @xmath25 and @xmath23 that are consistent for completely general @xmath44 , in section 3.2 we propose estimators that are consistent and asymptotically normal , provided @xmath44 and @xmath29 satisfy conditions that are closely related to other conditions that have appeared in the random matrix theory literature @xcite . these conditions basically require that @xmath29 and @xmath44 are _ asymptotically free _ in the sense of free probability ( see , for example , @xcite for a brief overview of free probability and random matrix theory ) . the problems considered in this paper have at least a passing resemblance to the neyman - scott problem @xcite . in a simplified version of this problem , observations @xmath50 , @xmath51 , @xmath52 are available , and the goal is to estimate @xmath25 . the means @xmath53 are nuisance parameters and , without additional specification , none of the @xmath53 are estimable , as @xmath39 . furthermore , the profile maximum likelihood estimator for @xmath54 , which is given by @xmath55 is inconsistent ; indeed , @xmath56 . on the other hand , the simple method of moments estimator @xmath57 is consistent for @xmath54 and asymptotically normal .    in linear models ( [ lm ] ) with @xmath34 , which are the main focus of this paper , the parameter @xmath29 is typically non - estimable . however , we show below that @xmath25 may still be consistently estimated in a variety of circumstances . moreover , as in the neyman - scott problem , it is unclear how to proceed with likelihood inference . indeed , the mle @xmath58 is degenerate when @xmath34 and it can even be troublesome when @xmath59 : if @xmath60 , then @xmath61 . furthermore , similar to the neyman - scott problem described in the previous paragraph , the basic estimator for @xmath25 derived in section 2.1 is a method of moments estimators .    in our view , the major implication of the preceding discussion is that the ambiguities of likelihood inference which arise in this problem contribute to difficulties in devising a systematic approach to estimation and efficiency when studying @xmath25 , @xmath23 , and related quantities in high - dimensional linear models . while the estimators proposed in this paper are shown to have reasonable properties , further research into these broader issues may be warranted . section 2 is primarily devoted to the case where @xmath62 . a motivating discussion and the definition of the basic estimators for @xmath25 and @xmath23 may be found in section 2.1 . section 2.2 and section 2.3 address consistency and asymptotic normality for the basic estimators , respectively . the case where @xmath63 is unknown is addressed in section 3 . section 3.1 is concerned with the case where a norm - consistent estimator for @xmath44 is available ; section 3.2 covers the case where no such estimator may be found , but @xmath29 and @xmath44 satisfy certain additional conditions . the results of three simulation studies are reported in section 4 . two of these studies illustrate basic properties of the estimators proposed in this paper . in the third study , we compare the performance of our estimators for @xmath25 to the performance of estimators for @xmath25 proposed by @xcite . section 5 contains a concluding discussion , where we briefly mention some potential alternatives to the estimators proposed in this paper and issues related to efficiency . proofs may be found in the appendix ; some of the more extended calculations required for these proofs are contained in the supplemental text ( which may be found after the bibliography below ) .","summary":"residual variance and the signal - to - noise ratio are important quantities in many statistical models and model fitting procedures . they play an important role in regression diagnostics , in determining the performance limits in estimation and prediction problems , and in shrinkage parameter selection in many popular regularized regression methods for high - dimensional data analysis . we propose new estimators for the residual variance , the-signal strength , and the signal - to - noise ratio that are consistent and asymptotically normal in high - dimensional linear models with gaussian predictors and errors , where the number of predictors is proportional to the number of observations . existing results on residual variance estimation in high - dimensional linear models depend on sparsity in the underlying signal . our results require no sparsity assumptions and imply that the residual variance may be consistently estimated even when and the underlying signal itself is non - estimable . basic numerical work suggests that some of the distributional assumptions made for our theoretical results may be relaxed .","abstract":"residual variance and the signal - to - noise ratio are important quantities in many statistical models and model fitting procedures . they play an important role in regression diagnostics , in determining the performance limits in estimation and prediction problems , and in shrinkage parameter selection in many popular regularized regression methods for high - dimensional data analysis . we propose new estimators for the residual variance , the-signal strength , and the signal - to - noise ratio that are consistent and asymptotically normal in high - dimensional linear models with gaussian predictors and errors , where the number of predictors is proportional to the number of observations . existing results on residual variance estimation in high - dimensional linear models depend on sparsity in the underlying signal . our results require no sparsity assumptions and imply that the residual variance may be consistently estimated even when and the underlying signal itself is non - estimable . basic numerical work suggests that some of the distributional assumptions made for our theoretical results may be relaxed ."}
{"article_id":"math0601041","section_id":"i","document":"from a geometric point of view tropical geometry describes worst possible degenerations of the complex structure on an @xmath0-fold @xmath1 . such degenerations cause @xmath1 to collapse onto an @xmath0-dimensional ( over @xmath2 , i.e. @xmath3-dimensional ) base @xmath4 which is a piecewise - linear polyhedral complex , see e.g @xcite for a conjectural picture in the special case of calabi - yau @xmath0-folds .    according to an idea of kontsevich such degenerations can be useful , in particular , for computations of the gromov - witten invariants of @xmath1 as holomorphic curves degenerate to graphs @xmath5 . a similar picture appeared in the work of fukaya ( see e.g. @xcite ) where graphs come as degenerations of holomorphic membranes . tropical geometry formalizes the base @xmath4 as an ambient variety so that the graphs @xmath6 become curves in @xmath4 . some problems in complex and real geometry then may be reduced to problems of tropical geometry which are often much easier to solve , thanks to the piecewise - linear nature of the subject . local considerations in tropical geometry correspond to some standard models in classical geometry while the combinatorial tropical structure encodes the way to glue these models together . in this sense it may be viewed an extension of the viro patchworking @xcite . this talk takes a geometric point of view on tropical geometry and surveys its basic notions as well as some of its applications for classical algebro - geometrical problems . the author is indebted to ya . eliashberg , m. kontsevich , a. losev , b. sturmfels and o. viro for many useful conversations on tropical geometry .","summary":"this talk outlines some basic notions of this area and surveys some of its applications for the problems in classical ( real and complex ) geometry .","abstract":"from a formal perspective tropical geometry can be viewed as a branch of geometry manipulating with certain piecewise - linear objects that take over the rle of classical algebraic varieties . this talk outlines some basic notions of this area and surveys some of its applications for the problems in classical ( real and complex ) geometry ."}
{"article_id":"1509.04854","section_id":"i","document":"studies of nuclear energy levels over long isotopic chains reveal structural changes as a function of n and provide important test of nuclear models . spontaneous fission ( sf ) has provided a good approach to study nuclei over long isotopic chains @xcite . in sf , the new transitions in a certain isotope are generally identified by gating on the known transitions in the particular isotope observed in @xmath24-decay or by gating on known transitions in the complementary fission fragment , which are usually less neutron - rich and well studied in most of the cases . usually , this procedure gives reliable identifications . however , in some cases , when the @xmath3-spectrum is complex , the overlapping of transition energies in different isotopes could lead to a wrong mass identification of the bands . recently prompt @xmath3 ray spectroscopy of fully identified ( a ,  z ) fission fragments produced in fusion - fission and transfer - fission reactions around the coulomb barrier @xcite have been reported where due to the advantage of unambiguously identifying the fragments , the assignments of @xmath3-rays to a particular a and z are directly obtained . the combination of the traditional high fold gamma - coincidence method @xcite and this method @xcite is expected to strengthen explorations and understanding of the evolution of nuclear structure as a function of both isospin and spin .    historically , levels of several pr isotopes have been identified from @xmath4cf and @xmath25 cm sf @xcite . only @xmath17pr were reported to have possible octupole correlations between parity - doublet bands @xcite . as mentioned in ref . @xcite the octupole correlations in this region are associated with @xmath26n  =  1 , @xmath26j  =  3 and @xmath27  =  3 orbital pairs such as @xmath28 near z = 56 and @xmath29 near n = 88 . the mass assignments of the previously reported levels assigned to @xmath1pr @xcite have recently been called into question @xcite . the @xmath3-ray transitions and levels in @xmath17pr reported in the previous work @xcite were assigned to @xmath30pr respectively in ref . the two bands proposed to be in @xmath18pr in ref . @xcite were assigned to @xmath17pr separately @xcite . the assignment of gamma transitions to their corresponding nuclei is challenging due to the closely spaced transitions and the complexity of the spectra . in order to have an unambiguous identification of the nuclei in the a @xmath31 150 mass region , two different techniques have been combined in the present work to investigate the high spin states and the possible octupole correlations for neutron rich pr isotopes . in this paper , we provide new analysis of both @xmath4cf sf and @xmath9u+@xmath10be induced fission data @xcite with direct identification of fission fragment mass and z to give reliable assignments of the levels and transitions in these pr isotopes . new level schemes of @xmath23pr and new transitions in @xmath21pr are reported in the present work . the possibility of the occurrence of octupole correlations in the band structures of @xmath32pr are indicated .","summary":" the previously reported levels assigned topr have recently been called into question regarding their mass assignment . the latter were produced usingu beams on abe target at energies around the coulomb barrier .","abstract":" the previously reported levels assigned topr have recently been called into question regarding their mass assignment . + clarify the above questioned level assignments by measuring-transitions tagged with a and z in an in - beam experiment in addition to the measurements fromcf spontaneous fission ( sf ) and establish new spectroscopic information from to in the pr isotopic chain . + the isotopic chainpr has been studied from the spontaneous fission ofcf by using gammasphere and also from the measurement of the prompt-rays in coincidence with isotopically - identified fission fragments using vamos++ and exogam at ganil . the latter were produced usingu beams on abe target at energies around the coulomb barrier . the--- data fromcf ( sf ) and those from the ganil in - beam a- and z - gated spectra were combined to unambiguously assign the various transitions and levels inpr and other isotopes . + a band of 3 new transitions added to the known level inpr , 9 new transitions in two new bands inpr , 6 new transitions in a new level scheme forpr , two new bands with 17 new transitions inpr and 2 new bands with 11 new transitions inpr were identified by using-- and--- coincidences and a and z gated- spectra . the transitions and levels previously assigned topr have been confirmed by the ( a , z ) gated spectra . small changes have been made to their original level schemes . the transitions previously assigned topr are now assigned topr on the basis of the ( a , z ) gated spectra . two new bands with 20 new transitions inpr and one new band with 7 new transitions inpr are identified from the--- coincidence spectra and the ( a , z ) gated spectrum . in addition , new-rays are also reported inpr . + new levels ofpr have been established , reliable mass assignments of the levels inpr have been given in the present work and new transitions have been identified inpr showing the new avenues that are opened by combining the two experimental approaches ."}
{"article_id":"1509.04854","section_id":"r","document":"two complementary methods have been used to investigate the level structure of pr isotopes , which include both the unambiguous identification of the mass ( a ) and the proton number ( z ) of the emitting fission fragment using a large acceptance spectrometer for in - beam measurements and the high fold data from spontaneous fission of a @xmath4cf source . these complementary methods have allowed us to identify new transitions and extend the level schemes to higher spins . in the present work the new transitions identified using ( a ,  z ) gated singles prompt @xmath3-ray spectroscopy did not require knowledge of the spectroscopic information of the complementary fragment . this allowed the study of very neutron rich nuclei , combining the unique in - beam identification with the high fold @xmath33 coincidences from sf . in the following , double gated coincidence spectra have a variable energy binning ranging from 0.7  kev / channel at 100  kev to 1  kev / channel at 1  mev . the triple gated coincidence spectra have a fixed binning of 1.3  kev / channel . the measurements of transfer and fusion induced fission were performed at ganil using a @xmath9u beam at 6.2 mev / u , with a typical intensity of 0.2 pna , impinging on a 10-@xmath34 m thick @xmath10be target . the advantage of the inverse kinematics used in this work is that fission fragments are forward focussed and have a large velocity , resulting in both an efficient detection and isotopic identification in the spectrometer . a single magnetic field setting of the large - acceptance spectrometer vamos++ @xcite , possessing a momentum acceptance of around @xmath35 20% , placed at 20@xmath36 with respect to the beam axis , was used to identify uniquely the fission fragments . the detection system ( 1@xmath370.15 m@xmath38 ) at the focal plane of the spectrometer was composed of ( i ) a multi - wire parallel plate avalanche counter ( mwppac ) , ( ii ) two drift chambers ( x , y ) , ( iii ) a segmented ionization chamber ( @xmath26e ) , and ( iv ) 40 silicon detectors arranged in a wall structure ( e@xmath39 ) . the time of flight ( tof ) was obtained using the signals from the two mwppacs , one located after the target and the other at the focal plane ( flight path @xmath317.5 m ) . the parameters measured at the focal plane [ ( x , y ) , @xmath26e , e@xmath39 , tof ] along with the known magnetic field were used to determine , on an event - by - event basis , the mass number ( a ) , charge state ( q ) , atomic number ( z ) , and velocity vector after the reaction for the detected fragment . isotopic identifications of elements were made up to @xmath40 with a mass resolution of @xmath41% @xcite . the prompt @xmath3 rays were measured in coincidence with the isotopically - identified fragments , using the exogam array @xcite consisting of 11 compton - suppressed segmented clover hpge detectors ( 15 cm from the target ) . the velocity of the fragment along with the angle of the segment of the relevant clover detector were used to obtain the @xmath3-ray energy in the rest frame of the emitting fragment . error on the @xmath3-ray energies of the strong transitions is 0.5  kev , while for the weak transitions it could be as much as 1  kev . as compared to the results presented in ref . @xcite for the zr isotopes the present work is the result of further improvements in the analysis especially improving the z identification and also involves a larger data set . figure  [ fig : fig2d ] shows a two dimensional spectra of a vs singles e@xmath42 for the pr isotopes using such a data set which also allows one to view directly the evolution of the various transitions as a function of mass number . ( color online ) doppler - corrected @xmath3-ray energy as a function of the mass number ( a ) of the pr ( z=59 ) fragment identified in vamos@xmath43 . ] ( color online ) relative yield curves of yttrium by gating on transitions in @xmath19pr ( black square symbol ) , @xmath18pr ( red circular symbol ) and @xmath20pr ( blue triangular symbol ) from @xmath4cf sf data . each pr gate yield set are normalized to the highest y yield for comparison . fission partners of 3n channels for @xmath19pr , @xmath18pr and @xmath20pr are @xmath44y , @xmath45y and @xmath46y respectively . the gaussian fittings for pr gate yields are also shown as lines in the same colors . ] partial @xmath47pr a- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . ]    the experiment with @xmath4cf was carried out at the lawrence berkeley national laboratory(lbnl ) . a 62 @xmath34ci @xmath4cf source was sandwiched between two fe foils of thickness 10mg / cm@xmath38 . by using 101 ge detectors of gammasphere , the data were sorted into 5.7@xmath3710@xmath49 @xmath3-@xmath3-@xmath3 and higher fold @xmath3 events and 1.9@xmath3710@xmath49 @xmath3-@xmath3-@xmath3-@xmath3 and higher fold @xmath3 coincident events . these @xmath3 coincident data were analyzed by the radware software package @xcite . gamma - ray energies of the strong transitions have errors of 0.1  kev while the errors on the weak transitions could be as much as 0.5  kev . another similar experiment was performed earlier at lbnl by using 72 ge detectors of gammasphere with a 28 @xmath34ci @xmath4cf source . less @xmath3-@xmath3-@xmath3 and higher fold coincidence events were collected in this experiment but the data were built according to several discrete coincidence time windows ranging from 4ns to 500ns of the @xmath3-rays @xcite .    to independently confirm the mass assignments obtained above ( fig . [ fig : fig2d ] ) , the relative yield curves of the yttrium partner isotopes coincident with @xmath1pr were measured . [ yield ] is a set of y yield curves measured by double or triple gating on transitions in @xmath50pr . the intensity summations of all the observable transitions which directly feed the ground state were used as a representative of the respective y yields . the @xmath45y isotope has an isomeric state at a level energy of 667.5  kev  ( 1.17s ) . therefore , the intensity summation of two transitions ( 668.6 and 989.9  kev ) , which feed the 667.5  kev state , was used instead . in the @xmath4cf binary spontaneous fission , a pair of correlated partners is produced and followed by neutron emission after fission . the yield is generally maximized at the 3n or 4n channel @xcite in fig . [ yield ] , the highest yields were populated at around @xmath51y for @xmath52pr respectively , which are all 3n reaction channels for these pr isotopes . further gaussian fitting analysis for the curves indicates that the fitting peaks for @xmath1pr are located at the respective 3.4 , 3.3 and 2.8n channels . these yield distribution curves of the y partner isotopes are consistent with the mass assignments of levels in @xmath1pr .","summary":"+ the isotopic chainpr has been studied from the spontaneous fission ofcf by using gammasphere and also from the measurement of the prompt-rays in coincidence with isotopically - identified fission fragments using vamos++ and exogam at ganil . small changes have been made to their original level schemes .","abstract":" the previously reported levels assigned topr have recently been called into question regarding their mass assignment . + clarify the above questioned level assignments by measuring-transitions tagged with a and z in an in - beam experiment in addition to the measurements fromcf spontaneous fission ( sf ) and establish new spectroscopic information from to in the pr isotopic chain . + the isotopic chainpr has been studied from the spontaneous fission ofcf by using gammasphere and also from the measurement of the prompt-rays in coincidence with isotopically - identified fission fragments using vamos++ and exogam at ganil . the latter were produced usingu beams on abe target at energies around the coulomb barrier . the--- data fromcf ( sf ) and those from the ganil in - beam a- and z - gated spectra were combined to unambiguously assign the various transitions and levels inpr and other isotopes . + a band of 3 new transitions added to the known level inpr , 9 new transitions in two new bands inpr , 6 new transitions in a new level scheme forpr , two new bands with 17 new transitions inpr and 2 new bands with 11 new transitions inpr were identified by using-- and--- coincidences and a and z gated- spectra . the transitions and levels previously assigned topr have been confirmed by the ( a , z ) gated spectra . small changes have been made to their original level schemes . the transitions previously assigned topr are now assigned topr on the basis of the ( a , z ) gated spectra . two new bands with 20 new transitions inpr and one new band with 7 new transitions inpr are identified from the--- coincidence spectra and the ( a , z ) gated spectrum . in addition , new-rays are also reported inpr . + new levels ofpr have been established , reliable mass assignments of the levels inpr have been given in the present work and new transitions have been identified inpr showing the new avenues that are opened by combining the two experimental approaches ."}
{"article_id":"1509.04854","section_id":"r","document":"in this section new transitions for @xmath53pr are reported using in - beam fission whereas the new level schemes of @xmath23pr were obtained by combining both the data sets . the a- and z- gated @xmath3-ray spectrum on @xmath47pr is shown in fig .  [ 143mass ] . three new transitions 251(1),445(1 ) and 554(1 ) kev were identified . other transitions are not labelled . the a- and z- gated @xmath3-ray spectrum on @xmath54pr is shown in fig .  [ 144mass ] . the 133(1 )  kev peak could be the 133.5  kev transition identified in @xmath54ce @xmath24-decay @xcite . it should be pointed out that the unbiased singles nature of the data allows the identification of low multiplicity transitions seen in beta decay . in addition two new transitions 155(1 ) and 177(1 )  kev were also identified . due to the complexity of the spectrum and lack of @xmath55 coincidences in this odd - odd nucleus , other transitions above 200  kev are not labelled and no level scheme is presented . partial @xmath54pr mass- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . ] partial @xmath12pr mass- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . part ( a ) is single @xmath3-ray spectrum . part ( b ) is a gated spectrum on the 211.6  kev transition and part ( c ) gated on the 546  kev transition , respectively.,title=\"fig : \" ] partial @xmath12pr mass- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . part ( a ) is single @xmath3-ray spectrum . part ( b ) is a gated spectrum on the 211.6  kev transition and part ( c ) gated on the 546  kev transition , respectively.,title=\"fig : \" ]    ( color online ) the new level scheme of @xmath12pr in the present work . transitions and levels previously reported in @xmath24 decay work are labeled in blue . new ones in the current work are labeled in red and with an asterisk . the width of the transitions in the level scheme in the current work does not indicate the relative intensity . ] partial @xmath56pr a- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . part ( a ) is single @xmath3-ray spectrum . part ( b ) is a spectrum gated on 188.9  kev transition . ] partial @xmath56pr a- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . part ( a ) is single @xmath3-ray spectrum . part ( b ) is a spectrum gated on 188.9  kev transition . ] the a- and z- gated @xmath3-ray spectrum on @xmath12pr is shown in fig .  [ 145mass](a ) . the 207.6 , 211.6 , 284.5 and 492.2  kev peaks were previously identified in @xmath12ce @xmath24-decay @xcite . the 350.9  kev peak could be an overlap of a 350.9  kev transition ( decay from 350.9  kev level to the ground state seen in @xmath24-decay ) and another 350.9  kev transition ( decay from 540.1  kev level to a 188.8  kev level in @xmath24-decay ) identified in @xmath24-decay @xcite . [ 145mass](b ) and ( c ) shows @xmath3-ray spectra gated on the 211.6  kev and 546  kev transitions respectively . in these spectra , the coincident 204.0 , 207.6 , 368.8 , 492.2 , 546.3 and 672.3  kev transitions can be seen . from the energy spacing of the 211.6 , 368.8 , 546.3 and 672.3 kev transitions and the intensities shown in fig . [ 145mass](a ) , these @xmath3-rays are possibly e2 transitions in a rotational band . thus , spins and parities of levels in this band are tentatively assigned . the level scheme for @xmath12pr is shown in fig . [ 145level ] . it should be pointed out that in the beta decay measurements the 211.6 is weak whereas in the present work it is very intense , showing the complementarity of the in - beam and decay work . there is coincidence evidence in the ( a ,  z ) gated data for a 350 - 415 kev cascade feeding a 168  kev transition . it is not definitive that this cascade feeds into the 207 - 212  cascades , so it is not placed in the level scheme . the ( a ,  z ) gated @xmath3 coincidence data ( fig . [ 145mass ] ) indicate the 176.7  kev transition is in coincidence with the 207 - 212 - 284 - 368 - 546  kev cascade , but it is not clear where to place it . the observed 190.0 , 230.1 , 518.0 , 579.8 , 616.7 kev transitions are also new but we have no coincidence data to place them . the a- and z- gated @xmath3-ray spectrum on @xmath56pr is shown in fig .  [ 146mass](a ) . the 87.2  kev transition can be identified with that previously known in @xmath56ce @xmath24-decay @xcite . [ 146mass](b ) is a spectrum gated on the 188.9 kev transition . in this spectrum , the coincident 87.2 , 173.9 and 484.6 kev transitions can be seen . with only these data it was not possible to build a level scheme . ( color online ) the new level scheme of @xmath13pr in the present work . transitions and levels previously reported in @xmath24 decay work are labeled in blue . new ones in the current work are labeled in red and with an asterisk . it is possible there is a low energy transition between the 256.6 and 138.7 kev transitions as discussed in the text . ]     ( a ) partial @xmath13pr a- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . ( b ) is a spectrum gated on the 256.6  kev transition and ( c ) is a spectrum gated on the 374.6  kev transition . the * indicates new transitions.,title=\"fig : \" ]   ( a ) partial @xmath13pr a- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . ( b ) is a spectrum gated on the 256.6  kev transition and ( c ) is a spectrum gated on the 374.6  kev transition . the * indicates new transitions.,title=\"fig : \" ]    partial @xmath3-ray coincidence spectrum by gating on 138.7 and 256.6  kev transitions in @xmath13pr from @xmath4cf sf data . in the spectrum , transitions belonging to y fission partners are indicated with neutron evaporation numbers . the * indicates new transitions . ]    the new level scheme for @xmath13pr is shown in fig . [ 147level ] . in this case , the known transitions were previously observed in the @xmath24-decay of @xmath13ce @xcite . the ground state , 2.7 , 27.9 , 93.2 and 246.4  kev levels were tentatively proposed to have positive parity @xcite . the 363.3  kev level was proposed to have a negative parity @xcite . the ( a ,  z ) gated @xmath3 spectrum is shown in fig . [ 147mass ] , where evidence for a high spin band is seen . a new band is assigned to @xmath13pr by observing the @xmath3-rays in coincidence with the 138.7 , 218.5 and 243.7  kev transitions . a partial coincident @xmath3-ray spectrum obtained with @xmath4cf sf data is shown in fig . [ 147gate ] . in this spectrum with gate on a previously known transition and the strongest transition in fig . [ 147mass ] , one can clearly see the known 218.5 and 243.7  kev transitions , new 423.9 , 536.1 , 607.9 and 660.5  kev transitions and the y partner transitions . note the 179.2  kev transition labeled in the spectrum is a new transition in @xmath57y . the work including the new level scheme of @xmath57y will be published later . these new transitions in @xmath13pr are confirmed in the ( a ,  z ) gated spectrum on @xmath13pr ( fig .  [ 147mass ] ) . the 2.7 and 25.2  kev transitions are not observed in the current work because the @xmath58 and @xmath59 cube data cut off the energy from 33.3  kev . the 66 and 72  kev transitions in this double gate come from the coincidence of the 138 kev transition in @xmath60tc . the 103  kev transition in this gate in fig . [ 147gate ] is caused by the 138 and 255  kev transitions in @xmath61mo . these three contamination transitions are not seen in the 256.6 - 423.9  kev gated spectrum , so are not in @xmath13pr . the time gated data from @xmath4cf sf indicate a short lifetime ( @xmath6220ns ) of the 385.7 kev level . however , since no lifetime of this level was reported by mantica _ _ in @xmath24-decay work @xcite , there might be a very low energy transition between the 138.7 and 256.6  kev transitions . this possible short lifetime would also explain the rather low intensity of the 138.7  kev transition in the prompt ( a ,  z ) gated spectrum . such a loss of intensity has already been found in the case of the neutron rich zr isotopes @xcite . the gated spectrum on the 374  kev transition of ( a ,  z ) gated data shows evidence for a 253 - 374 - 495 - 542 cascade as seen in fig . [ 147mass ]  ( c ) . this cascade is also confirmed by the @xmath4cf sf data , but not in coincidence with any other transitions reported in @xmath13ce @xmath24-decay in ref . thus , level energy of this cascade is not placed in the level scheme . other unlabeled transitions identified in fig .  [ 147mass ] ( 155 , 290 , 343 , 360 , 435 , and 443 kev ) could not be placed in the level scheme for lack of coincidence data . previously , internal conversion coefficient of the 138.7  kev transition was not measured in @xmath24-decay @xcite . in the current work , @xmath63@xmath64 of the 138.7  kev transition can be measured from the intensities of the 138.7 , 218.5 and 243.7  kev transitions in the 256/424 double gate with the internal conversion of the relevant transitions included . the @xmath63@xmath64 value obtained is 0.15(3 ) , which is consistent with a theoretical e1 transition ( 0.10 ) but not m1(0.51 ) or e2(0.67 ) . thus , band ( 1 ) is proposed to have a negative parity and the band - head could be either the 362.3 or 385.1  kev level . from the comparison with the negative parity bands in @xmath12la @xcite and @xmath15pm @xcite , the 256.6  kev @xmath3 ray is more likely to be a transition decaying from 15/2@xmath65 to 11/2@xmath65 . previously , the ground state , 2.7 , 27.9 , 93.2 kev levels were tentatively assigned to 3/2@xmath66 , 5/2@xmath66 , 7/2@xmath66 and 5/2@xmath66 , respectively , in @xmath24-decay work @xcite according to the decay pattern . the 218.5 and 269.1  kev transitions were assigned as m1 and e1 , respectively , according to internal conversion measurement @xcite . assigning 11/2@xmath65 to 385.1 kev level , the 246.4  kev level is proposed to be 9/2@xmath66 . the 362.3  kev level is then 7/2@xmath65 because the 11/2@xmath65 level decays to this state . note that 11/2@xmath65 and 7/2@xmath65 are the lowest two negative levels ( < 250  kev ) in the particle - plus - triaxial rotor model ( ptrm ) calculation in ref . in contrast , the adopted levels in ref . @xcite tentatively assigned the ground state , 2.7 , 27.9 , 93.2 and 362.3  kev states to 5/2@xmath66 , 3/2@xmath66 , 5/2@xmath66 , 7/2@xmath66 and 5/2@xmath65 , respectively , based on the ptrm positive parity calculation in ref . however , this 5/2@xmath65 assignment does not agree with the lowest negative parity levels as the already noted . thus considering both the negative and positive parity calculations , we agree with the spins and parities assigned in ref . @xcite and not with ref . @xcite for the lowest states . ( color online)the new level scheme of @xmath14pr in the present work . relative intensities could not be extracted because of the very strong 219.8 kev transition in @xmath15pr . ] partial @xmath14pr mass- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . the * indicates new transitions . ]    partial @xmath3-ray coincidence spectrum by gating on 132.1 and 290.5  kev transitions in @xmath14pr from @xmath4cf sf data . in the spectrum , transitions belonging to y fission partners are indicated with the corresponding number of evaporated neutrons . the * indicates new transitions . ]    the new level scheme for @xmath14pr is shown in fig . [ 148level ] . in this case , all transitions are newly identified . the new transitions are seen in the mass - z gated spectrum of @xmath14pr ( fig . [ 148mass ] ) . none of transitions from the @xmath24-decay of @xmath14ce @xcite are observed in this work . a partial coincident @xmath3-ray spectrum from the @xmath4cf data is shown in fig .  [ 148gate ] . in this spectrum with gates on 132.1 and 290.5  kev transitions , one can clearly see the 137.6 , 219.9 , 435.2 and 546.4  kev new transitions and the y partner transitions . the order of these new transitions are placed based on the intensities and the similarity to @xmath16pr . in @xmath4cf sf data , the intensity ratios of 137.6/132.1 and 219.9/132.1 decrease about 80@xmath67 as the time coincidence window decreases from 500ns to 8ns . in the contrast , the ratio of the 132.1 , 290.5 , 435.2 and 546.4  kev transition intensities remain almost the same . thus , the 219.9 and 137.6  kev transitions are placed at the bottom and a lifetime of the order of a hundred ns is proposed for the level which the 132.1  kev transition feeds . this is consistent with the non observation of the 219.9  kev transition in coincidence with 290.5  kev in the prompt @xmath3 ray spectrum obtained using the ( a ,  z ) gate where the prompt gamma rays are sensitive only to states with lifetimes shorter than @xmath312 ns .. in addition spectra obtained in a / z coincidence with 219.9  kev suggest the existence of another band consisting of 219.9 and 329  kev transitions . but we can not confirm this cascade in sf data . triple gates ( 137.6 - 132.1 - 290.5 and 219.5 - 132.1 - 290.5 kev ) show no evidence for the strong 105 , 121 , 195 or 289 kev transitions seen in @xmath24-decay . thus we conclude none of the low spins ( 1,2 ) states seen in @xmath24-decay are feed by the cascade seen in fig . [ 148mass ] . this cascade could feed the 2 mins 4@xmath65 isomer at 77 kev @xcite . ( color online)the new level scheme of @xmath15pr in the present work . the 86.5 and 58.5 kev transitions and levels previously reported in @xmath24 decay work are labeled in blue . those reported by hwang _ @xcite are labeled in green , the 103.2 to 520.3 kev transitions in band ( 1 ) . new transitions and levels are labeled in red and with an asterisk . the intensities in black to the right of the @xmath3 ray energies are relative to 100 for the 219.8 kev transition . ]    partial @xmath15pr a- and z- gated @xmath3-ray spectrum obtained from @xmath9u + @xmath10be induced fission data . the * indicates new transitions . ]        the new level scheme of @xmath16pr in the present work . transitions and levels previously reported by hwang@xcite are labeled in green . new ones are labeled in red and with an asterisk . ] partial @xmath16pr mass- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . the * indicates new transitions . ]        the new level scheme for @xmath15pr is shown in fig . [ 149level ] . in this case , the 58.5 and 86.5  kev transitions were previously observed in the @xmath24-decay of @xmath15ce @xcite . the band ( 1 ) in fig .  [ 149level ] was previously reported in ref . @xcite . in fig . [ 149mass ] , previously reported band ( 1 ) transitions and new transitions in band ( 2 ) and ( 3 ) are seen in the ( a ,  z ) gated spectra . these spectra were important in guiding sf @xmath3 ray coincidence spectra analysis to identify the new band ( 3 ) . these two new bands ( 2 ) and ( 3 ) are established in the present work by observing the coincidence between the @xmath3-rays in these bands and the 86.5 or 58.5  kev transition in @xmath4cf sf data . a partial coincident @xmath3-ray spectrum is shown in fig .  [ 149gate](a ) . in this spectrum with a gate on two new transitions in band ( 3 ) , one can clearly see the 86.5  kev transition , three other new transitions and y partner transitions . another partial coincident @xmath3-ray spectrum is shown in fig .  [ 149gate](b ) . in this spectrum with gate on two new transitions in band ( 2 ) one can clearly see the 58.5 , 103.2  kev transitions , six other new transitions and y partner transitions . by gating on these new transitions and analyzing the relative @xmath3-transition intensities , these two new bands are proposed for @xmath15pr . the @xmath4cf data also shows some weak evidence for the coincidences between the 103.2 and 232.4 , 219.8 and 344.7  kev transitions , respectively . the possible low energy 13.2 ( 174.9 to 161.7 ) and 25.8 ( 407.3 to 381.5 )  kev transitions are not indicated in the level scheme in fig . [ 149level ] . spins and parities of levels in band ( 1 ) were tentatively assigned in ref . @xcite by an internal conversion coefficient measurement and theoretical calculations . those results are adopted in this paper . based on the regular energy spacings and @xmath3-ray intensities , the new level at 3724.8  kev is assigned as 43/2@xmath65 . the total internal conversion coefficient of the 86.5  kev transition in @xmath15pr was measured from the intensity ratio between 86.5 and 278.5  kev transition in the coincident spectrum gated on 371.6 and 437.4  kev transitions above them . the value was obtained to be 1.63(22 ) , and is in agreement with the theoretical calculated value @xcite of 1.96 for a m1 transition but not with 3.58 for an e2 transition .    quasiparticle - rotor model ( qprm ) calculations @xcite suggest a @xmath685/2[413 ] configuration for the @xmath15pr ground state level . the lowest three exited level energies at 86.5 , 365.0 , 736.6  kev of band ( 3 ) in @xmath15pr are also reasonably consistent with the qrpm calculations of 7/2@xmath66 , 11/2@xmath66 and 15/2@xmath66 for the states at 87 , 342 and 708  kev , respectively in ref .  @xcite . therefore , the spins and parities of exited states in band ( 2 ) are tentatively assigned as 7/2@xmath66 , 11/2@xmath66 , 15/2@xmath66 , 19/2@xmath66 , 23/2@xmath66 and 27/2@xmath66 in the present work . spins and parities of the levels in band ( 2 ) are tentatively assigned in fig . [ 149level ] based on the structure similarity to the @xmath69 signature s=+i octupole bands ( 1 ) and ( 2 ) in ref . when octupole deformation or octupole correlations are strong , one expects a symplectic quantum number s = i , two bands of opposite parity with the spin show in fig . [ 149level ] and strong e1 transitions between the two bands as found @xcite . note that qprm calculation in ref . @xcite indicates that this band is unlikely to be another signature of band ( 1 ) . further analysis is included in the discussion part .      the new level scheme for @xmath16pr is shown in fig . [ 150level ] . bands ( 1 ) and ( 4 ) were previously assigned to @xmath16pr in ref . @xcite from the sf of @xmath4cf . in this earlier work , the relative yield ratios of partner y isotopes were measured @xcite . the transitions previously assigned to @xmath16pr along with several new ones are shown in the ( a ,  z ) gated spectrum ( fig . [ 150mass ] ) . [ 150gate](a ) shows a coincidence spectrum double - gated on the new 190.2 and 254.6  kev transitions . [ 150gate](b ) shows a coincidence spectrum double gated on the new 244.7 and 340.0  kev transitions.the previously known @xmath3-transitions of 96 , 82.2 and 104.0  kev of @xmath16pr and the @xmath3-transitions in the partner y isotopes can be seen in these spectra . therefore , these new transitions are assigned to @xmath16pr in the present work . the newly observed 334.3 , 419.8 and 503.0  kev transitions are coincident with the new 190.2 and 254.6  kev transitions in fig .  [ 150gate](a ) . also , the new 438.4 and 532.6  kev transitions are coincident with the new 340.7 and 244.7  kev transitions in fig .  [ 150gate](b ) . by using these coincidence relationships in multiple gates , bands ( 2 ) and ( 3 ) were found as shown in fig . [ 150level ] . the 143.7  kev transition is dashed because the intensity is weaker than that of the 190.2  kev transition .       the new level scheme of @xmath19pr in the present work . transitions and levels previously reported by hwang _ et al._@xcite are labeled in green . new levels and transitions are labeled in red and with an asterisk . the 221.9 + 221.3  kev transitions , superscript a , have the normalized intensity of 100 . band ( 3 ) and ( 4 ) are shown in red with other new transitions since both band now feed a single 142.3  kev transition . band ( 3 ) was assigned to @xmath19pr and band ( 4 ) to @xmath20pr in ref . the @xmath3-ray intensities are relative to 100 for the 162.3 kev transition . ] partial @xmath19pr mass- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . part ( a ) is single @xmath3-ray spectrum . part ( b ) is a gated spectrum on the 222  kev transition . ] the new level scheme for @xmath19pr is shown in fig . [ 151level ] . the @xmath19pr a and z gated spectra obtained from @xmath9u + @xmath10be induced fission are shown in figs .  [ 151mass](a ) and ( b ) . bands ( 1 ) and ( 2 ) in fig . [ 151level ] were assigned previously to @xmath19pr in ref . @xcite . in this earlier work , the relative yield ratios of partner y isotopes were measured . however , bands ( 1 ) and ( 2 ) were assigned to @xmath18pr , by malkiewicz _ the previously reported @xcite @xmath3-transitions in bands ( 1 ) and ( 2 ) are confirmed from the mass and z gated spectrum in fig .  [ 151mass](a ) . in the present work , the 204.2 and 41.9  kev transitions in ref . @xcite are replaced with the new 214.6 and 52.3  kev transitions in bands ( 1 ) and ( 2 ) of fig . [ 151level ] . also , a possible new 143.1  kev transition is added . previously , bands ( 3 ) and ( 4 ) were assigned to @xmath18pr in ref . .    then band ( 3 ) was assigned to @xmath19pr and band ( 4 ) to @xmath20pr from the sf work of @xmath25 cm and @xmath4cf @xcite . now band ( 3 ) and band ( 4 ) in fig . [ 151level ] are assigned to @xmath19pr in the present work because the 142.3 , 221.3 + 221.9 , 296.4 , 291.9 , 365.2 and 358.4  kev transitions are seen in the @xmath19pr mass and z gated spectra in figs . [ 151mass](a ) and [ 151mass](b ) . the 221.3 and 221.9  kev transitions were reported earlier as one 221.9  kev transition @xcite . later , the 142.3  kev transition in ref . @xcite was separated into 142.1 and 141.6  kev transitions in ref . the 221.9  kev transition in ref . @xcite was separated into 221.8 and 221.0  kev transitions in ref . @xcite . in this paper , a shift of about 0.6  kev of the 221.9  kev peak has been confirmed by comparing the gates between bands ( 3 ) and ( 4 ) , for example , double gates on 296.4 and 356.2  kev in band ( 3 ) , 291.9 and 358.4  kev in band ( 4 ) , triple gates on 296.4,356.2 and 428.7  kev in band ( 3 ) , 291.9 , 358.4 and 420.8  kev in band ( 4 ) . but no visible energy difference of the 142.3  kev transition is seen when comparisons are set between any of the gates in bands ( 3 ) and ( 4 ) . thus , two different 221.9 and 221.3  kev transitions are proposed but there is only one 142.3  kev transition in the level scheme . in the present work all of bands ( 1 ) , ( 2 ) , ( 3 ) and ( 4 ) are definitely assigned to @xmath19pr , as shown fig . [ 151level ] . further analysis about the mass assignment will be presented in the @xmath70pr and discussion sections . [ 151gate](a ) is a coincidence spectrum from @xmath4cf sf data by gating on 216.3 and 292.0  kev transitions showing the new 52.3 and 143.1  kev transitions . the peak around 40  kev is an overlap of a 39.4  kev @xmath3 transition and 41.0  kev pr x - ray . therefore , the energy of the 39.4  kev transition has a relative large uncertainty and might range from 39 to 42  kev . if the 39.4  kev transition is the same as the 38.9  kev one reported in @xmath24-decay work @xcite , bands ( 1 ) and ( 2 ) would decay to the ground state . however , since the energy of this transition has a large uncertainty , an x  kev level is used in fig . [ 151level ] . the 143.1  kev transition is much weaker than the 90.8  kev one and is bracketed in the level scheme . [ 151gate](b ) is a coincidence spectrum from @xmath4cf sf data triple gated on 298.8 , 377.2 and 445.0  kev transitions . the 204.2  kev transition is not seen compared to 214.6  kev in this gate , which suggest some contamination at 204.2  kev in the spectrum of the previous work ( ref . thus , the 204.2  kev transition is replaced by the 214.6 one in the present work .    fig . [ 151gate2](a ) is a coincidence spectrum from @xmath4cf sf data by gating on 221.9 , 296.4 and 365.2  kev transitions . the 428.7 , 487.3 , 540.5 and 584.4  kev transitions in band ( 3 ) can be seen . [ 151gate2](b ) is a coincidence spectrum from @xmath4cf sf data by gating on 221.3 , 291.9 and 358.4  kev transitions . the 420.8 , 479.1 and 534.6  kev transitions in band ( 4 ) can be seen . the @xmath4cf sf data also show coincidence of the 296.4 and 358.4  kev transitions , as well as the 365.2 and 420.8  kev transitions , but interband transitions linking bands ( 3 ) and ( 4 ) are not observed in the current work . these coincidences indicate the existence of a very low energy transition to lift up band ( 4 ) in @xmath19pr . the analysis result for @xmath3 transition intensities are also labeled in the level scheme . the intensities have been separated into two parts . the intensities of transitions in band ( 1 ) and band ( 2 ) are normalized to that of the 162.3  kev transition and those in band ( 3 ) and band ( 4 ) are normalized to the summation of the 221.9 and 221.3 kev transition intensities . previously , internal conversion measurements established the 47.2 and 54.0  kev transitions as e1 and 90.8  kev one as m1 @xcite . the value of the 90.8  kev transition was obtained from the 90.8 and 292.0 kev transition intensities in the coincidence spectrum gated on 216.3 and 363.3  kev in ref . this measurement did not include the contribution of the 47.2  kev transition . if this contribution is taken into account , the internal conversion value will increase by a factor of @xmath3120% , which will make it closer to the theoretical m1 value . those corrections can be seen in the erratum ref . the branching of the 143.1  kev transition is very small ( see fig .  [ 151gate](a ) ) and does not change the result much . the @xmath63@xmath64 value of the 54.0  kev was obtained from the 54.0 , 162.0 and 204.0  kev transition intensities in the 292.0 and 363.3  kev double gate in ref . this measurement is also questionable because the 204.0  kev transition is not confirmed in the current work . the peak around 54.0  kev in the 292.0 and 363.3  kev double gate is a overlap of the 52.3 and 54.0  kev transitions . thus , the intensity as well as the @xmath63@xmath64 value of the 54.0  kev transition can not be accurately obtained in the present work . the @xmath63@xmath64 value of the 52.3  kev can be obtained from the 52.3 and 90.8  kev transition intensities in the 216.3 and 292.0  kev double gate . the value is 3.5(9 ) , which lies between the theoretical value of e1(1.4 ) and m1(8.3 ) . however , the 216/292 gate might be interfered by the 214.6  kev transition so that the error of the @xmath63@xmath64 value of the 52.3  kev would be much higher . the level scheme of @xmath18pr in the present work . the 114.8 and 98.1 kev transitions and levels previously reported in @xmath24 decay work are labeled in blue . all others are new ones labeled in red . * this level is an isomer with a lifetime of 4.1@xmath34s according to the measurement in ref . @xcite the @xmath3 ray intensities are relative to 100 for the 200.3 kev transition . ] partial @xmath18pr mass- and z- gated @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . the position of the 162.3 kev transition from @xmath19pr is also indicated to illustrate its non - observation ( see text for details ) . note the absence of the 114.8  kev isomeric transition . the * indicates new transitions . ]          the new level scheme for @xmath18pr is shown in fig . [ 152level ] . all levels and transitions are newly established in the present work except for the 114.8 and 98.1  kev transitions , which were identified in @xmath18ce @xmath24- decay @xcite . [ 152mass ] shows the @xmath18pr a- and z- gated single @xmath3 spectrum from @xmath9u + @xmath10be induced fission data , illustrating the evidence for the mass assignment for these three new bands . all the strong transitions in these three bands can be seen . as can be seen from the figure the 221.3 , 221.9 , 358.4 and 365.3  kev transitions are not seen in a = 152 spectrum ( fig . [ 152mass ] ) as compared to a = 151 gated spectra ( figs . [ 151mass](a),(b ) ) . this confirms that 142.3 - 221.9 - 296.4 ( @xmath19pr ) and 142.3 - 221.3 - 292.0  kev cascades do not belong to @xmath18pr as previously reported in ref . @xcite but in @xmath19pr and the latter does not belong to @xmath20pr as recently reported@xcite . the position of the 162.3  kev transition in @xmath19pr ( 100 relative intensity ) is labeled in fig . [ 152mass ] . the absence of the 162.3  kev peak ( the weak peak seen in the valley is at 160.5 kev ) indicates that bands ( 1 ) and ( 2 ) assigned to @xmath19pr belong there and not to @xmath18pr as recently reported in ref . these facts give further evidence for the mass assignment for the four bands in @xmath19pr in the present work . further analysis of the mass assignments will be reported in the @xmath20pr . the relatively strong 90 and 188 kev peaks in fig . [ 152mass ] are not seen in any of the sf coincidence data connected to bands ( 1 ) and ( 2 ) in fig . [ 152level ] . the sf coincidence data do indicate a 188 - 279 - 322 - 385 kev cascade which could form another band in @xmath18pr . [ 152gate](a ) shows a coincidence spectrum from the @xmath4cf sf data by double gating on 264.5 and 327.3  kev transitions . the 136.0 , 200.4 , 386.1 , 440.1 , 488.7 and 534.0  kev transitions in band ( 1 ) and 60.0 , 76.0 , 92.0 , 108.4  kev linking transitions between band ( 1 ) and band ( 2 ) can be seen . [ 152gate](b ) shows a coincidence spectrum from the @xmath4cf sf data by triple gating on 232.6 , 295.3 and 353.4  kev transitions , where 168.0 , 405.4 , 452.4 , 496.2 and 539.5  kev transitions in band ( 2 ) and 60.0 , 76.0 , and 92.0 linking transitions between band ( 1 ) and band ( 2 ) can be seen . [ 152gate](c ) shows a coincidence spectrum from @xmath4cf sf data by triple gating on 219.6 , 274.1 and 306.9  kev transitions , where 98.1 and 155.5  kev transitions in band ( 3 ) can be seen . the 114.8  kev transition is not observed in the current work since the electronic coincidence time window for the @xmath4cf fission experiment is about 1 @xmath34s , which is relatively smaller than the 4.1 @xmath34s life time ( @xcite ) of the 114.8  kev level . for prompt-@xmath3-ray data , the present ganil experimental setup is sensitive only to states with lifetimes shorter than @xmath71  ns . the result for @xmath3 transition intensities are also given in the level scheme . the new level scheme for @xmath20pr is shown in fig . [ 153level ] . band ( 1 ) in fig . [ 153level ] was assigned previously to @xmath20pr in ref . @xcite , but was assigned , recently , to @xmath72pr from the sf work of @xmath25 cm and @xmath4cf @xcite . in the earlier work , the relative yield ratios of partner y isotopes were measured  @xcite . the @xmath20pr mass and z gated spectra obtained from @xmath9u + @xmath10be induced fission are shown in fig . [ 153mass ] . the previously reported @xmath3-transitions of 88.0 , 156.7 , 206.6 , 279.5 , 351.1 , 417.8 and 477.9  kev transitions in @xmath20pr @xcite are confirmed from the mass and z gated spectrum shown in fig . [ 153mass ] . the 142.3 , 221.3 and 292.2  kev cascade previously assigned to @xmath20pr by malkiewicz _ et al . _ @xcite is not confirmed by the mass and z gated spectrum in fig . [ 153mass ] . the position of the 292.2  kev transition is shown in fig . [ 153mass ] to illustrate its non - observation . instead , a new cascade with 143.1 , 221.9 and 297.7  kev transition can be seen in the spectrum . further analysis about the mass assignment will be reported in the discussion part . the level scheme of @xmath20pr in the present work . transitions and levels previously reported by hwang _ et al._@xcite are labeled in green , bands ( 1 ) and ( 2 ) . new ones in band ( 3 ) are labeled in red . a : the 206.6 + 207.1  kev transitions have the relative intensity of 100 . b : the 49.9 + 50.4  kev transition have the relative intensity of @xmath62127 . the new transitions in red were too close in energy to transitions in @xmath19pr to measure intensities . ] partial @xmath20pr mass- and z- gated single @xmath3-ray spectra obtained from @xmath9u + @xmath10be induced fission data . the position of the 291.9 kev transition from @xmath19pr is also indicated to illustrate its non - observation ( see text for details ) . the * indicates new transitions . ]    partial @xmath3-ray coincidence spectrum by triple gating on 221.9 , 297.7 and 368.9  kev transitions in @xmath20pr from @xmath4cf sf data . in the spectrum , transitions belonging to the y fission partner are indicated with neutron evaporation numbers , specifically , 3n correspond to @xmath46y . the * indicates new transitions . ]    the previously assigned 51.7 , 227.8 and 277.7  kev transitions are not placed in fig . [ 153level ] because these transitions are not clearly seen in the @xmath4cf sf data . furthermore , the 227.8  kev transition is not observed in the 206.6 and 969.1  kev ( a fission partner @xmath73y transition@xcite ) double gate and the 206.6 and 417.8  kev double gate . thus , the previously reported 13/2 level and its three transitions are tentatively removed from the level scheme . the results for @xmath3 transition intensities are shown in the level scheme . previous internal conversion measurements established the 50.4  kev transition as e1 and the 88.0  kev one as m1@xcite . the value of the 50.4  kev transition is questionable because the 206.6/351.1  kev gate used in ref . @xcite might be interfered by the 207.1  kev transition . if one approximately assumes the 49.9 and 50.4  kev transitions have the same @xmath63@xmath64 value , the 2.3(7 ) value in ref . @xcite should be used , not 3.2(9 ) in the erratum ref . @xcite because the 227.8  kev transition is not confirmed in the current work . [ 153gate ] shows a coincidence spectrum from @xmath4cf sf data by gating on the 221.9 , 297.7 and 368.9  kev transitions . in this gate , four other @xmath3-ray transitions in band ( 3 ) can be seen . the ( a ,  z ) gated spectra were important in guiding the @xmath3 ray coincidence spectra analysis to identify new band ( 3 ) .","summary":"+ clarify the above questioned level assignments by measuring-transitions tagged with a and z in an in - beam experiment in addition to the measurements fromcf spontaneous fission ( sf ) and establish new spectroscopic information from to in the pr isotopic chain . the transitions previously assigned topr are now assigned topr on the basis of the ( a , z ) gated spectra . two new bands with 20 new transitions inpr and one new band with 7 new transitions inpr are identified from the--- coincidence spectra and the ( a , z ) gated spectrum . in addition , new-rays are also reported inpr .","abstract":" the previously reported levels assigned topr have recently been called into question regarding their mass assignment . + clarify the above questioned level assignments by measuring-transitions tagged with a and z in an in - beam experiment in addition to the measurements fromcf spontaneous fission ( sf ) and establish new spectroscopic information from to in the pr isotopic chain . + the isotopic chainpr has been studied from the spontaneous fission ofcf by using gammasphere and also from the measurement of the prompt-rays in coincidence with isotopically - identified fission fragments using vamos++ and exogam at ganil . the latter were produced usingu beams on abe target at energies around the coulomb barrier . the--- data fromcf ( sf ) and those from the ganil in - beam a- and z - gated spectra were combined to unambiguously assign the various transitions and levels inpr and other isotopes . + a band of 3 new transitions added to the known level inpr , 9 new transitions in two new bands inpr , 6 new transitions in a new level scheme forpr , two new bands with 17 new transitions inpr and 2 new bands with 11 new transitions inpr were identified by using-- and--- coincidences and a and z gated- spectra . the transitions and levels previously assigned topr have been confirmed by the ( a , z ) gated spectra . small changes have been made to their original level schemes . the transitions previously assigned topr are now assigned topr on the basis of the ( a , z ) gated spectra . two new bands with 20 new transitions inpr and one new band with 7 new transitions inpr are identified from the--- coincidence spectra and the ( a , z ) gated spectrum . in addition , new-rays are also reported inpr . + new levels ofpr have been established , reliable mass assignments of the levels inpr have been given in the present work and new transitions have been identified inpr showing the new avenues that are opened by combining the two experimental approaches ."}
{"article_id":"1509.04854","section_id":"c","document":"in conclusion , new bands in @xmath92pr have been reported ; the previous questionable assignments of transitions and levels in @xmath17pr were clarified by a- and z- gated spectra and yield curves ; a new high spin level scheme for @xmath18pr has been established and confirmed by mass - z gated spectra . spins and parities of the levels in the new band in @xmath15pr have been tentatively assigned . new transitions have been identified in @xmath21pr . more work on both experiment and theory is needed to understand the nuclear structure of @xmath93pr well . the levels in @xmath32pr are similar to octupole structures . the bands in @xmath17pr are very similar in transition energies and @xmath26e2 , which indicates they are relatively rigid rotors . the long multiple high spin bands with increasing neutron number in the pr isotopes provide interesting tests for nuclear model calculations . the unique combination of ( a ,  z ) identified in - beam @xmath3-rays and high fold data from a cf source has opened new vista to study the evolution of nuclear structure as functions of spin and isospin . further improvements in the sensitivity for fission fragment spectroscopy are planned using the next generation tracking detector agata combined with an improved vamos++ spectrometer at ganil . the work at vanderbilt university and lawrence berkeley national laboratory are supported by the us department of energy under grant no . de - fg05 - 88er40407 and contract no . de - ac03 - 76sf00098 . the work at tsinghua university was supported by the national natural science foundation of china under grant no . the work at jinr was supported by the russian foundation for basic research grant no . 08 - 02 - 00089 and by the intas grant no . 03 - 51 - 4496 . one of us ( s.b . ) acknowledges partial financial support through the lia france - india agreement . we would like to thank j.  goupil , g.  fremont , l.  mnager , j.  ropert , c.  spitaels , and the ganil accelerator staff for their technical contributions .","summary":"the--- data fromcf ( sf ) and those from the ganil in - beam a- and z - gated spectra were combined to unambiguously assign the various transitions and levels inpr and other isotopes . + a band of 3 new transitions added to the known level inpr , 9 new transitions in two new bands inpr , 6 new transitions in a new level scheme forpr , two new bands with 17 new transitions inpr and 2 new bands with 11 new transitions inpr were identified by using-- and--- coincidences and a and z gated- spectra . the transitions and levels previously assigned topr have been confirmed by the ( a , z ) gated spectra . + new levels ofpr have been established , reliable mass assignments of the levels inpr have been given in the present work and new transitions have been identified inpr showing the new avenues that are opened by combining the two experimental approaches .","abstract":" the previously reported levels assigned topr have recently been called into question regarding their mass assignment . + clarify the above questioned level assignments by measuring-transitions tagged with a and z in an in - beam experiment in addition to the measurements fromcf spontaneous fission ( sf ) and establish new spectroscopic information from to in the pr isotopic chain . + the isotopic chainpr has been studied from the spontaneous fission ofcf by using gammasphere and also from the measurement of the prompt-rays in coincidence with isotopically - identified fission fragments using vamos++ and exogam at ganil . the latter were produced usingu beams on abe target at energies around the coulomb barrier . the--- data fromcf ( sf ) and those from the ganil in - beam a- and z - gated spectra were combined to unambiguously assign the various transitions and levels inpr and other isotopes . + a band of 3 new transitions added to the known level inpr , 9 new transitions in two new bands inpr , 6 new transitions in a new level scheme forpr , two new bands with 17 new transitions inpr and 2 new bands with 11 new transitions inpr were identified by using-- and--- coincidences and a and z gated- spectra . the transitions and levels previously assigned topr have been confirmed by the ( a , z ) gated spectra . small changes have been made to their original level schemes . the transitions previously assigned topr are now assigned topr on the basis of the ( a , z ) gated spectra . two new bands with 20 new transitions inpr and one new band with 7 new transitions inpr are identified from the--- coincidence spectra and the ( a , z ) gated spectrum . in addition , new-rays are also reported inpr . + new levels ofpr have been established , reliable mass assignments of the levels inpr have been given in the present work and new transitions have been identified inpr showing the new avenues that are opened by combining the two experimental approaches ."}
{"article_id":"astro-ph0007421","section_id":"i","document":"a great deal of effort and observing time has been expended in the past decade or so in a systematic effort to  map \" the central regions of active galactic nuclei ( hereafter agn ) . because the relevant sizes are too small to image with current technology , the attempted  mapping \" has been effected through the time reverberation technique , i.e. , the monitoring of the system in response to fluctuations in luminosity across the electromagnetic spectrum and the comparison of the relative amplitudes and lags between different wavelengths to models . while the original reverberation effort was aimed at estimating the size of the broad line region ( blr ) by measuring the lags between variations in the ionizing continuum and the broad emission lines ( see netzer & peterson 1997 for a review ) , it was quickly realized that the same data could also be used to test models of the continuum emission itself by measuring the lags between variations in the uv and optical flux . the agn optical  uv ( hereafter o  uv ) continuum is generally dominated by a broad quasi - thermal component , the so - called big blue bump ( hereafter bbb ) , thought to be due to  and modeled as  the emission of a geometrically thin , optically thick accretion disk radiating in black body form the locally dissipated accretion kinetic energy ( malkan & sargent 1983 ; malkan 1984 ; laor & netzer 1989 ; sun & malkan 1989 ) . thus , monitoring the o  uv continuum variability and the corresponding interband lags , places constraints on the models of such accretion disks . it became apparent early on in this extensive mapping effort that the interband lags between optical and uv wavelengths were far shorter than those expected by most modes of information propagation in a thin accretion disk ( the lags of the earlier campaigns were generally shorter than the sampling rates ) . this situation prompted the suggestion that the correlated o  uv continuum variability is due entirely to reprocessing of the more variable x - ray component by the geometrically thin accretion disk responsible for the emission associated with the bbb feature ( krolik et al 1991 ) . this suggestion appeared to also fit nicely with the evidence of x - ray reflection by cold matter in agn ( pounds et al . 1990 ) and the presence of relativistically broadened lines ( e.g. , tanaka et al . 1995 ; see also a recent review by fabian et al . 2000 ) . thus , a  picture \" of the innermost regions of accreting black holes began to emerge , consisting of a geometrically thin , optically thick accretion disk radiating away the dissipated kinetic energy in black body form , supplemented by an x - ray source located at a height @xmath0 of a few radii above the disk ( or modeled as a spherical source occupying the inner part of the disk ) . the disk s soft photons were then thought to be the seed photons that in interactions with the electrons of the hot corona produce the observed x - rays , which are in turn reprocessed by the disk to provide the x - ray reflection feature , the line , as well as the observed rapid , inter band variability between the optical and uv wavelengths . while fits to the observed x - ray spectra within the general framework of this arrangement seem to be in good agreement with observations , as well known , spectra generally provide information about column densities and optical depths rather than about densities and actual lengths , which are the quantities needed to confirm the actual geometry of the x - ray  uv  o emission . verification of the precise geometrical arrangement requires a  mapping \" of this geometry through timing observations . such a ( so - called ) reverberation mapping requires sufficiently high data sampling rate , set by the light crossing time from the x - ray source to the reprocessing disk . for a source size @xmath7 a few radii of a @xmath10 m@xmath5 black hole , this time scale ( assuming that the source is located several radii above the disk ) is of order of @xmath11 sec . at the same time , the monitoring campaign has to be of sufficiently long duration to sample a large number of peaks and troughs to produce a reliable interband cross correlation . there have been to date two monitoring campaigns specifically planned to comply with these criteria , namely those of ngc  7469 ( nandra et al . 1998 , 2000 ) and of ngc  3516 ( edelson et al . 2000 ) . earlier coordinated multiwavelength observations , while forming a rather extended data base ( see nandra et al . 1998 for a summary ) , were deemed of inadequate sampling rate to provide conclusive results . the results of the ngc 7469 campaign ( nandra et al . 1998 ) were puzzling in that they indicated no clear correlation between the x - ray variations and that of uv emission , while the flux in both bands exhibited 50% variations in amplitude . at the same time there were clearly detected lags between the uv ( 1315  ) and the optical ( 6962  ) emission or order of 12 days ( collier et al . revisiting these observations , nandra et al . ( 2000 ) have indicated that the softening of the x - ray spectrum with increasing uv flux underestimated the soft x - ray emission . taking this fact into consideration , they showed that the long term ( @xmath12 day ) variations in the uv and x - ray bands were in fact  in synch \" with each other . however , the x - rays exhibited in addition strong variations on time scales of @xmath13 sec which had absolutely no counterpart in the uv or optical light curves . motivated by these results , berkley , kazanas & ozik ( 2000 ; hereafter bko ) , examined in detail these observations in the framework of the  disk reprocessing model \" : they produced simulated uv  o light curves using the observed x - ray light curves as input in a geometric arrangement of a point x - ray source at a given distance above the plane of a disk , as thought to be the situation in agn . their conclusions were that for any reasonable estimate of the black hole mass ( @xmath14 m@xmath5 ) , both the uv ( 1315  ) and the optical ( 6962  ) emission should follow closely that of the x - rays . the short time @xmath15 sec ) x - ray variability was always present in the model reprocessed emission , with almost undetectable ( @xmath16 day ) lags in the cross correlation function of the simulated uv  o light curves , in disagreement with the results of collier et al . however , they also found that if the reprocessing was driven by a component with light curve similar to that of the uv rather than the x - ray emission ( i.e. it contained _ no _ high frequency variations ) , then the reprocessed emission could indeed produce a ccf with uv  o lags of order of a day , in rough agreement with collier et al . ( 1998 ) , provided that the x - ray source was located at a height of @xmath17 cm above the disk plane .    in the present paper we present an analysis of the campaign results of ngc 3516 ( edelson et al . 2000 ) similar to that of ngc 7469 given in bko . however , the present analysis is more complete in several respects : ( a ) the albedo of the illuminated disk is computed ( rather than assumed to be small ) using the analysis of nayakshin , kazanas & kallman ( 2000 ; hereafter nkk ) which takes into account the effects of an ionized  skin \" on the surface of the disk induced by the action of x - rays . ( b ) the effect of the presence of the black hole , more precisely the absence of reprocessing in a region of size @xmath18 underneath the x - ray source is taken into account . ( c ) the calculation of the simulated light curves includes a constant component , associated with the intrinsic emission by the geometrically thin accretion disk , of flux consistent with observations . the main effect of this component is to reduce the variability amplitude . ( d ) we compute  standard \" accretion disk o  uv continuum spectra for the values of the mass and accretion rate obtained from the best fits of the model light curves which we then compare to observations . ( e ) we also compute the full x - ray reflection spectra which , by comparison to those observed by nandra et al . ( 1999 ) , yield additional constraints to the value of the black hole mass and the disk inclination . the combination of timing and spectral fits yields constraints which are generally not commensurate with each other , thereby excluding , as it will be discussed below , the simplest form of this specific model . our paper is structured as follows :  2 contains a description of the physics involved in the reprocessing of x - rays by a thin disk in hydrostatic equilibrium and also the method for the approximate computation of the x - ray albedo for different x - ray energies under these circumstances . using the results of the albedo computation ,  3 presents the response functions of the _ reflected _ x - rays at two different energies , in order to exhibit the x - ray energy dependence of this effect . in  4 simulated light curves , due to reprocessing of the x - rays observed in ngc 3516 , are produced for the wavelengths used in the monitoring campaign ; their cross correlation functions as well as those with the x - rays are computed and compared to those observed . in  5 we exhibit model o  uv continuum spectra for different values of our system parameters , which we compare to those observed . we also compute the associated x - ray reflection spectra , with particular emphasis in the x - ray reflection and line features , which are compared to those observed . finally in  6 the results are summarized and conclusions are drawn .","summary":"= cmr10    submitted to astrophys . j.","abstract":"we test the  reprocessing paradigm \" of the optical  uv agn variability , according to which the variations in this wavelength range are driven by a variable x - ray component , by detailed modeling of the correlated x - ray  optical ( 3590 and 5510  ) variability of the recent multiwavelength campaign of ngc 3516 . to this end we produce model optical light curves by convolving the observed x - ray flux with the response function of an infinite , thin accretion disk , illuminated by a point - like x - ray source at a given height above the compact object ( the lamp - post model ) and compare their properties ( amplitude , morphology , lags ) to those observed . special attention is given to the correct computation of the x - ray albedo of the disk , by including an x - ray heated ionized layer in hydrostatic equilibrium on its surface . we further compute the x - ray reflection response at two energies ( kev ) and argue for the possibility of hard lags in their cross spectra . we also compute the continuum optical  uv and the x - ray reflection spectra as well as the fluorescent line profiles which we also compare to observations . despite the large ( ) amplitude excursions of the x - ray flux , the model optical light curves exhibit variability amplitudes of 3  4 % , not unlike those observed . the model light curves exhibit clearly a feature associated with a large x - ray flux excursion not seen in the data , arguing for a reprocessing region of size cm , even though no lags are discernible in the cross correlation functions ( ccf ) of the 3590 and 5510    model light curves . however , the ( ccf ) between the x - ray and the model optical variations show clear lags of 0.1 and 0.25 days for black hole masses m respectively , not apparent in the data . the synchrony of x - ray - optical variations points toward the smaller mass values ( m ) , which however are inconsistent with the model x - ray reflection spectra which exhibit several features below 4 kev and above kev not observed in the data . in fact , the model x - ray reflection spectra are roughly consistent with observations only for m . the observed line profiles are too broad to be consistent with our models . lowering the distance of the x - ray source from the disk , , helps a little in this respect , but only at the expense of reducing unrealistically the amplitude of optical  uv variations . our conclusion is that the combination of the observed optical / uv / x - ray spectral and timing observations are inconsistent with the lamp - post model geometry for ngc  3516 .    = cmr10    submitted to astrophys . j."}
{"article_id":"astro-ph0007421","section_id":"i","document":"we have examined in detail the spectro - temporal properties of the  standard \" model of the central regions in agn , which consists of a geometrically thin , optically thick accretion disk along with an overlying illuminating x - ray source at a height @xmath0 , in view of the observations of the recent monitoring campaign of ngc 3516 ( edelson et al . 2000 ) . to this end we have produced model light curves at the observed wavelengths 1360 , 3590 and 5510  , assuming that they result from the reprocessing of the observed x - ray flux by the geometrically thin , optically thick accretion disk . comparison of the timing characteristics ( amplitudes , lags between the various wavelengths ) of our model light curves to those observed set the range of acceptable values for the parameters which characterize geometry of the model , namely @xmath192 . using values of these parameters derived from the timing considerations , we produced the o  uv continuum , as well as the detailed x - ray reflection spectra expected from the x - ray illumination of the accretion disk , taking into detailed account the ionization , radiative transfer , hydrostatic balance and kinematic and gravitational effects . the model light curves also include ( in addition to the variable x - ray reprocessed flux ) a constant contribution due to the energy liberation in the thin disk itself as inferred from observations of ngc  3516 . the variability amplitudes of the reprocessed emission at 3590 , 5510    are in reasonable agreement with those observed , given the inferred ratio @xmath193 of the x - ray - to - disk luminosities and assuming @xmath194 . the reprocessed light curves in these two wavelengths appear to vary in synchrony for the smaller of the values of the black hole mass examined ( @xmath172 ) , with only a small lag ( @xmath195 days ) between the x - rays and the reprocessed radiation , which could be accommodated by the data . however , the data exhibit a noticeable absence of direct correspondence between the x - ray and the optical emission , not observed in the model light curves . in particular , the x - rays exhibit , at day 916.8 , a specific large amplitude ( @xmath196 )  flare \" , of 0.7 day duration not observed at 3590 , 5510  , while it is very clearly present in the model light curves of the same wavelengths . this suggests that the size of the reprocessing region should be larger than 0.7 light days . indeed , increasing the black hole mass results in model light curves which progressively suppress this feature but which , at the same time , destroy the overall synchrony of variation between the x - rays and the flux at 3590 and 5510 . already for a mass @xmath153 the lags between the x - rays and the model light curves are inconsistent with observation , while this feature is still clearly present in the model light curve . a mass of @xmath197 suppresses this feature to the extent that it is consistent with observations , but only for 5510  , thereby not resolving the inconsistency ( for brevity we do not exhibit these results in a figure ) . interestingly , however , the synchrony in the variation between 3590 and 5510    is not destroyed ; their ccf still peaks close to zero lag but it becomes progressively asymmetric with the increase in @xmath83 , more than allowed by the data . we have not explored the effects of any larger values for the mass as they appear unreasonable and inconsistent with the o  uv continuum data ( see next point ) . one could decrease the x - ray - o  uv lags by increasing the disk inclination angle , @xmath198 , but this is not allowed by the line profile data ( see last point ) . we can conclude , therefore , that the timing observations alone are not consistent with range of the model parameters explored herein , and likely with any set of values of these parameters . the observed o  uv spectral distribution of ngc 3516 is generally narrower than that of the  standard \" accretion disks . hence , a reasonable fit of the uv flux ( @xmath199 ) overproduces the optical emission , while producing a good fit to the optical flux ( @xmath200 ) places the peak emission at wavelengths far shorter of the observed 12001500  , underproducing the observed flux at this range . interestingly , each mass range is consistent with only one specific aspect of the timing data : the smaller mass with the x - ray - optical variation synchrony and the larger one with the suppression of the x - ray flux feature near day 916.8 , in the model light curves . the model x - ray reflection spectra are clearly inconsistent with those observed for the `` small '' values of the black hole mass ( @xmath200 ) , due to the high thomson thickness of the non fully ionized skin , which produces atomic transition features not observed in the data . increasing the mass to @xmath201 leads to a much smaller thomson depth of the skin , and hence x - ray reflection spectra resembling those observed ( but see the last point ) . note , however , that high black hole masses are strongly ruled out by the timing data ( first point ) . significantly , our models predict specific correlations ( hard lags ) between photons at @xmath202 kev and at @xmath203 kev , of order @xmath204 sec ( for @xmath205 , as assumed in our models ) in the cross spectra of these energies , even without any lag present in their ccf . the x - ray sampling rate of the source is sufficiently high that a search for these lags may be reasonable and possible . \\4 . the fe line ( more accurately the fe line complex ) observations , in conjunction with our models , serve mainly to constrain the inclination angle of the disk to @xmath206 . while our models produce reasonable equivalent widths for this line , they are unable to match , even approximately , the best fit of the observed profile . the main reason is the large red wing of the line extending to @xmath207 kev , which requires that most of this emission , and therefore the associated x - ray illumination , be confined to a region very close to the black hole horizon . our models , with the source located at any source height , fall far short from achieving this . an extreme kerr hole would help in this respect , however , quantitative models do not exist for this case ; furthermore , it is not apparent how such models would provide a resolution of the issues raised in point 1 above . finally , concentrating too much of the x - ray luminosity in the @xmath208 few @xmath53 region will leave too little of this luminosity to illuminate the region @xmath209 tens of @xmath53 ( that emits the o  uv part of the spectra ) so that it will underproduce the amount of the o  uv variations compared to those observed .    where do all these leave us ? it is apparent that one can not fulfill all the observational constraints within this picture of the central engine of agn . the alternatives are few : ( a ) ignore some of the constraints as less important and attempt concordance within this less restricted constraint list ( b ) abandoned this model in favor of a different one .    of the present constraints , those set by timing seem to be the more significant ones , in that by themselves point to a possible internal inconsistency of the model . as argued elsewhere ( e.g. kazanas , hua & titarchuk 1996 ) , spectral fits and observations can , generally , yield information only about optical depths and column densities and that timing information is necessary to convert these to the length and densities necessary to determine the geometry of the source . the problem with the timing observations is that it is not known , in the absence of repeated observations , whether they reveal a typical or a transient property of the object under consideration . clearly  more observations are needed \" , with as broad wavelength coverage as possible , given that it is the interband variability which provides the most stringent constraints on the models .    of our model spectra and their fits to the data , those of the o  uv continuum maybe thought as the more suspect given the simplicity of their assumptions and the possibility of their contamination by the host galaxy . however , since that such a contamination would more likely contribute to the optical rather than the uv flux , its removal it would only increase the discrepancy between model and observation . the x - ray reflection spectra , on the other hand , are very robust within the specific model examined and seem to argue for the larger values of the mass considered . the energy dependent albedo and the related timing analysis within the x - ray band itself , if feasible , should clearly set additional , independent limits on size of the system . we hope that such analysis in this and other objects be carried out and set as one of the observing goals .","summary":"we test the  reprocessing paradigm \" of the optical  uv agn variability , according to which the variations in this wavelength range are driven by a variable x - ray component , by detailed modeling of the correlated x - ray  optical ( 3590 and 5510  ) variability of the recent multiwavelength campaign of ngc 3516 . to this end we also compute the continuum optical  uv and the x - ray reflection spectra as well as the fluorescent line profiles which we also compare to observations . despite the large ( ) amplitude excursions of the x - ray flux , the model optical light curves exhibit variability amplitudes of 3  4 % , not unlike those observed . the model light curves exhibit clearly a feature associated with a large x - ray flux excursion not seen in the data , arguing for a reprocessing region of size cm , even though no lags are discernible in the cross correlation functions ( ccf ) of the 3590 and 5510    model light curves . however , the ( ccf ) between the x - ray and the model optical variations show clear lags of 0.1 and 0.25 days for black hole masses m respectively , not apparent in the data . the synchrony of x - ray - optical variations points toward the smaller mass values ( m ) , which however are inconsistent with the model x - ray reflection spectra which exhibit several features below 4 kev and above kev not observed in the data . in fact , the model x - ray reflection spectra are roughly consistent with observations only for m .","abstract":"we test the  reprocessing paradigm \" of the optical  uv agn variability , according to which the variations in this wavelength range are driven by a variable x - ray component , by detailed modeling of the correlated x - ray  optical ( 3590 and 5510  ) variability of the recent multiwavelength campaign of ngc 3516 . to this end we produce model optical light curves by convolving the observed x - ray flux with the response function of an infinite , thin accretion disk , illuminated by a point - like x - ray source at a given height above the compact object ( the lamp - post model ) and compare their properties ( amplitude , morphology , lags ) to those observed . special attention is given to the correct computation of the x - ray albedo of the disk , by including an x - ray heated ionized layer in hydrostatic equilibrium on its surface . we further compute the x - ray reflection response at two energies ( kev ) and argue for the possibility of hard lags in their cross spectra . we also compute the continuum optical  uv and the x - ray reflection spectra as well as the fluorescent line profiles which we also compare to observations . despite the large ( ) amplitude excursions of the x - ray flux , the model optical light curves exhibit variability amplitudes of 3  4 % , not unlike those observed . the model light curves exhibit clearly a feature associated with a large x - ray flux excursion not seen in the data , arguing for a reprocessing region of size cm , even though no lags are discernible in the cross correlation functions ( ccf ) of the 3590 and 5510    model light curves . however , the ( ccf ) between the x - ray and the model optical variations show clear lags of 0.1 and 0.25 days for black hole masses m respectively , not apparent in the data . the synchrony of x - ray - optical variations points toward the smaller mass values ( m ) , which however are inconsistent with the model x - ray reflection spectra which exhibit several features below 4 kev and above kev not observed in the data . in fact , the model x - ray reflection spectra are roughly consistent with observations only for m . the observed line profiles are too broad to be consistent with our models . lowering the distance of the x - ray source from the disk , , helps a little in this respect , but only at the expense of reducing unrealistically the amplitude of optical  uv variations . our conclusion is that the combination of the observed optical / uv / x - ray spectral and timing observations are inconsistent with the lamp - post model geometry for ngc  3516 .    = cmr10    submitted to astrophys . j."}
{"article_id":"astro-ph0402238","section_id":"i","document":"classical t tauri stars ( cttss ) are roughly solar - mass pre - main sequence ( pms ) stars that are accreting gas from their circumstellar disks . the extent and mass of dust in disks have been determined from ir spectral energy distributions ( seds ) and imaging ( see review by * ? ? ? cold gas at large radii is traced by observations of molecules such as co and hcn ( e.g. , * ? ? ? * ) . warmer neutral and ionized gases are used as diagnostics of accretion ( e.g. , * ? ? ? * ; * ? ? ? however , observing the gas in the disk close to the star , which is important for the formation and evolution of planets , has been difficult . gas at these radii can induce planet migration @xcite , dampen the eccentricity of terrestrial planets @xcite , and is neccessary for accretion onto giant planets @xcite .    in search of gas at planet - forming radii , @xcite investigated the formation of co overtone lines at 2.3 @xmath8 m in disks around cttss . these models predict that cttss as a group should show both co emission and absorption , while herbig ae / be stars should show co in emission . using high spectral resolution observations , @xcite showed that the co overtone emission from the probable herbig ae / be star wl 16 arises in the inner disk , confirming the prediction of @xcite . @xcite find the same result for the herbig ae / be star 1548c27 . however , broader searches at high spectral resolution for co overtone emission or absorption from cttss generally find no evidence for contributions to these lines from the disks around these stars @xcite . on the other hand , @xcite find that co fundamental emission near 4.6 - 4.9 @xmath8 m is common among cttss . they suggest that overtone emission has not been detected at the observed co temperatures ( 1100  1300 k ) , mainly because the overtone bands have much lower transition rates . however , co is not expected to be the dominant gas constituent in the disks around cttss , and it is the major component of the gas , h@xmath0 , that we seek to probe here . previous observations of h@xmath0 have not provided a clear picture of the gas in the disk . @xcite detected cold h@xmath0 emission in the pure rotational s(0 ) and s(1 ) lines from iso observations of a large sample of cttss , herbig ae / be stars , and debris - disk stars . however , in ground - based observations of the s(1 ) and s(2 ) lines , using much smaller apertures than iso , @xcite and @xcite did not detect any h@xmath0 emission from some of the same sources , indicating that the emission is probably extended . on the other hand , the emission in the h@xmath0 1 - 0 s(1 ) transition detected by @xcite in phoenix spectra of 4 t tauri stars is narrow and centered at the radial velocity of the stars , presumably formed in low - velocity circumstellar gas .    while h@xmath0 lines in the ir are typically weak and are observed against a strong dust continuum , fluorescent h@xmath0 lines dominate the far - ultraviolet ( fuv ) spectrum of cttss at wavelengths longward of . @xcite found that narrow h@xmath0 lines can be blueshifted by up to 20  in _ hst_/ghrs spectra of cttss , observed with a @xmath9 aperture . high - resolution echelle and long - slit spectroscopy with _ hst_/stis is providing the critical data needed to identify the source of the h@xmath0 emission . observations of t tau reveal two components of h@xmath0 emission . @xcite and @xcite detect off - source uv h@xmath0 emission , that is pumped near line - center of , and most likely produced where stellar outflows shock the surrounding ambient molecular material . the same set of fluorescent h@xmath0 lines are detected in low - excitation hh objects such as hh43 and hh47 @xcite , suggestive of a similar excitation mechanism . @xcite find that the on - source h@xmath0 emission is photoexcited by a much broader  emission line , likely produced by the accretion shock at the surface of t tau .    in ( * ? * hereafter paper i ) , we presented observations of h@xmath0 fluorescence in the uv spectrum of tw hya obtained with _ hst_/stis and _ fuse_. several lines of evidence suggested a disk origin for the h@xmath0 emission : ( i ) the h@xmath0 emission is not spatially extended beyond a point source in the cross - dispersion direction , ( ii ) the h@xmath0 lines are emitted interior to tw hya s wind because emission in one h@xmath0 line is supressed by wind absorption , ( iii ) the h@xmath0 line centroids have the same radial velocity as the photospheric lines of tw hya , ( iv ) no h@xmath0 absorption is detected against the  emission , and ( v ) the tw hya association is isolated from large reservoirs of interstellar molecular material , making a circumstellar origin for the h@xmath0 emission unlikely . because the h@xmath0 emission is not extended beyond a point source , the spatial resolution of _ hst_/stis restricts the emitting region to be within 2 au of the star . analysis of on - source ir h@xmath0 emission lines to date has been limited because typically only one or two lines are observed . the ir lines could be excited by shocks , uv fluorescence , x - rays , or thermal heating . in contrast , over 140 h@xmath0 lines from 19 different upper levels are detected in the fuv spectrum of tw hya . the excitation of h@xmath0 can be determined from relative line strengths in this rich spectrum either by measuring self - absorption in low excitation members of individual fluorescent progressions or by using an assumed ly@xmath10 profile to reconstruct initial level populations in various pumping transitions .    in this paper , we calculate the temperature of warm gas at planet - forming distances by modelling warm h@xmath0 in a disk around tw hya . we use the h@xmath0 emission to reconstruct the ly@xmath10 profile incident on the fluoresced h@xmath0 . the observed ly@xmath10 profile differs from the incident profile because of interstellar absorption along our line of sight to tw hya . we discuss the strength of ly@xmath10 emission and its affect on the circumstellar disk .","summary":"we measure the temperature of warm gas at planet - forming radii in the disk around the classical t tauri star ( ctts ) tw hya by modelling the h fluorescence observed in _ hst_/stis and _ fuse _ spectra . we simulate a 1d plane - parallel atmosphere to estimate fluxes for the 140 observed h emission lines and to reconstruct the  emission profile incident upon the warm h . the excitation of h can be determined from relative line strengths by measuring self - absorption in lines with low - energy lower levels , or by reconstructing the  profile incident upon the warm h using the total flux from a single upper level and the opacity in the pumping transition . tw hya produces approximately in the fuv , about 85% of which is in the  emission line . from the absorption observed in the  emission","abstract":"we measure the temperature of warm gas at planet - forming radii in the disk around the classical t tauri star ( ctts ) tw hya by modelling the h fluorescence observed in _ hst_/stis and _ fuse _ spectra . strong  emission irradiates a warm disk surface within 2 au of the central star and pumps certain excited levels of h . we simulate a 1d plane - parallel atmosphere to estimate fluxes for the 140 observed h emission lines and to reconstruct the  emission profile incident upon the warm h . the excitation of h can be determined from relative line strengths by measuring self - absorption in lines with low - energy lower levels , or by reconstructing the  profile incident upon the warm h using the total flux from a single upper level and the opacity in the pumping transition . based on those diagnostics , we estimate that the warm disk surface has a column density ofh , a temperature k , and a filling factor of h , as seen by the source of  emission , of ( all 2 error bars ) . tw hya produces approximately in the fuv , about 85% of which is in the  emission line . from the absorption observed in the  emission , we infer that dust extinction in our line of sight to tw hya is negligible ."}
{"article_id":"astro-ph0402238","section_id":"c","document":"figures 11 and 13 , and table 5 , compare results from our analysis of individual h@xmath0 line fluxes with our results from the  profile reconstruction . based on the overlap region of acceptable models for both the individual h@xmath0 line fluxes and the reconstructed  profile , we conclude that a column density of @xmath48h@xmath2 is heated to a temperature of @xmath126  k , with a filling factor of @xmath127 around tw hya ( @xmath128 error bars ) . table 2 lists the percentage @xmath96 of h@xmath0 that dissociates from the upper level , the h@xmath0 dissociation rate in terms of mass ( @xmath129 ) , and the total flux for each progression ( @xmath130 ) for our best - fit model of @xmath48h@xmath81 and @xmath79  k. the notion of a single temperature is a simplistic assumption , but it is sufficient to reproduce our data . the temperature derived here is warmer than the @xmath131 k temperatures seen in the fundamental co emission by @xcite .    the mass column corresponding to @xmath48h@xmath0)=18.5 is @xmath132 g @xmath35 , which is about @xmath133 times smaller than the mass column predicted to be within 1 au by @xcite this suggests that h@xmath0 fluorescence probably occurs in a very shallow surface layer of the disk , which could be a warm , extended disk atmosphere . the  fluorescence process can not be used to detect cold h@xmath0 , which most likely represents the bulk of the mass in the disk .    in our models , we assume that h@xmath0 gas is thermalized , so that relative level populations depend only on temperature . this is reasonable because the gas density at the disk surface should be between @xmath134  @xmath29 @xcite , which is far larger than the critical density of @xmath135=@xmath136  @xmath29 at which collisions typically dominate over quadrupole radiative de - excitation . below the critical density , collisions can not repopulate excited h@xmath0 levels as fast as they radiatively deexcite . fluorescent progressions pumped out of higher energy states would be weaker than expected from our thermal models , generating scatter that we do not see in our reconstructed  profile . this conclusion confirms the assumption of thermally excited h@xmath0 gas used by @xcite and @xcite to model h@xmath0 fluorescence . figure 13 shows that the filling factor of the h@xmath0 around the  emitting region is @xmath127 . this factor represents the solid angle of the sky subtended by h@xmath0 as seen from the source of  photons near tw hya , although other geometrical effects may contribute . neutral hydrogen mixed with the warm h@xmath0 could scatter  photons , increasing the effective path length of the  photons and thereby reducing the calculated filling factor . any directional dependence of the  emission , and the percentage of  emission visible to us versus the percentage visible to the warm h@xmath0 , will also affect the calculated filling factor . a total of 1 - 2% of the intrinsic  emission is reprocessed into h@xmath0 emission ( see table 6 and  4 ) , which places a lower limit of 0.01 on the filling factor .    for any flared disk geometry , the filling factor can be converted into a disk height by comparing the surface areas of a cylinder and a sphere . for @xmath103 , the implied geometrical disk height from the midplane to the surface at distance @xmath137 from the center of the star is h=@xmath138 au , compared with predicted disk heights from @xcite of about 0.15  au at a distance of 1  au from the star . emission in the 1 - 0  s(1 ) rovibrational transition at 2.1218 @xmath8 m has been detected from 4 t tauri stars @xcite . the narrow width and absence of any velocity shift with respect to the stars suggests a disk origin of this emission . the flux in this line from an optically thin emission region @xmath139 where @xmath140 is the h@xmath0 column density of the disk in the @xmath141 level , @xmath142 is the projected surface area of the emission region , and @xmath143 s@xmath12 . if the 1 - 0 s(1 ) line flux of @xmath144 erg @xmath35 s@xmath12 measured by weintraub et al . ( 2000 ) comes from a heated disk surface layer with n(h2)=18.5 and t=2500 k , then the 1 - 0 s(1 ) emission must extend out to at least 5 au for a face - on disk . this corresponds to an angular extent of @xmath145 , which could have been resolved in our hst observations , but was not . thus , it seems likely that at least some of the 1 - 0 s(1 ) emission comes from h@xmath0 gas that is not fluoresced by . some of the emission in the 1 - 0 s(1 ) line may be produced deeper in the disk or farther from the star , as a result of x - ray ionization and subsequent collisional excitation of h@xmath0 by non - thermal electrons @xcite .      from the flux in observed transitions , we calculate a dissociation rate of @xmath146 @xmath14  yr@xmath12 for h@xmath0 in the disk . forward modelling of undetected lyman and werner - band transitions excited by  photons increases the calculated dissociation rate to @xmath147 @xmath14 yr@xmath12 . depending on the timescale for collisional de - excitation of h@xmath0 , the actual dissociation rate could be much higher due to multiple pumping [ pumping from lower rovibrational levels of h@xmath0 that are populated by the initial pump and subsequent fluorescence  see @xcite for details ] , which can populate highly excited rovibrational levels in the b electronic state that have dissociation probabilities as high as 50% . the h@xmath0 dissociation rate we estimate is within a factor of 10 of tw hya s mass accretion rate ( see  2.1 ) , meaning that the dissociation provided by  fluorescence may be an important process in the accretion of hydrogen onto the star . the neutral h released by dissociation will cause the incident  to scatter , increasing the probability of absorption in the pumping transitions and therefore decreasing the required filling factor . the neutral h could also be sufficiently optically thick to produce the self - reversal of the  profile that irradiates the disk ( see fig . 14 ) . the fuv radiation field incident on the accretion disk can significantly affect the chemistry and temperature structure of the disk . in table 6 we list the flux for spectral features in the fuv spectrum of tw hya . the observed  line contributes 67% of the observed fuv flux of @xmath148  ergs  @xmath35  s@xmath12 between 11701700  . from the reconstructed  profile , we infer an intrinsic flux of @xmath149  ergs  @xmath35  s@xmath12 , depending on the correction for the central absorption . with this correction , emission contributes 8090% of the fuv flux of tw hya , of which 1 - 2% is reprocessed into h@xmath0 emission . the continuum accounts for about @xmath150  ergs  @xmath35  s@xmath12 , or about 4% of the total emission , including the estimated intrinsic  flux . the remaining flux occurs in other emission lines such as the 1550    doublet . the uv flux below 1170  measured by _ fuse _  adds at most 2% additional flux to the strength of the radiation field . the uv radiation between 17002000    may add to the radiation field , primarily due to emission in lines such as ]  @xmath941817 and ]  @xmath941909 , but will have little effect on the excitation of molecules and atoms in the disk . the estimated total emission after including flux that is not observable is approximately @xmath6 @xmath7 , assuming isotropic emission and a distance of 56 pc . the properties of the disk , both in the pdr - like disk atmosphere and in the cooler outer regions , will be partially controlled by the  emission , as evidenced by the fluorescent h@xmath0 emission . not only does  dominate the fuv flux of tw hya , but it can also scatter off neutral h towards the interior of the disk , allowing it to penetrate the disk further than continuum uv radiation .  can dissociate molecules such as h@xmath0 and h@xmath0o , and can ionize si and c. @xcite explain that the enhancement of cn relative to hcn occurs in disks because ly@xmath10 radiation can photodissociate hcn , whereas cn can be dissociated only by radiation with @xmath151  .      we have found evidence for a warm surface layer of h@xmath0 on the disk around tw hya . from the lack of spatial extent in the stis  echelle cross - dispersion direction , the heated surface is located within 2 au of the star . models of dust in disks of cttss typically predict @xmath152 k only within 0.1 au of the star @xcite . the fuv radiation field at 1 au from the star is approximately @xmath153 @xmath154 , where the habing field @xmath155 erg @xmath35 s@xmath12 ( the local interstellar field is 1.7 @xmath154 ) , which is stronger than the fuv radiation field incident upon most pdrs ( @xmath156 @xmath154 ) . @xcite predicted from models of photo - dissociation regions that a warm atmosphere - like structure , heated by uv radiation , should surround the inner regions of a disk , with a temperature between 500 and 3000 k.    because of the absence of micron - sized dust grains within 5 au of tw hya @xcite , a large percentage of the fuv radiation may be deposited into the gas . in their analysis of the h@xmath0 fluorescence from mira b , @xcite found that the temperature increases sharply with radius from the uv source , and that the  fluorescence process is a significant heating source for the gas . the energy deposited into the warm gas near tw hya due to ly@xmath10 photoexcitation and subsequent fluorescence is @xmath157 erg s@xmath12 , which corresponds to roughly 0.01 ev s@xmath12 per molecule of h@xmath0 . the strong x - ray luminosity of tw hya , @xmath158 between 0.456.0  kev @xcite , could heat the disk surfaces by an additional 500 k @xcite by ionizing atoms to produce a large reservoir of energetic non - thermal electrons ( e.g. , * ? ? ? * ; * ? ? ? x - rays can also penetrate deeper into the gas than uv radiation and , consequently , may heat gas deeper in the disk than the uv radiation . certain observed fluorescence progressions are pumped from lower rovibrational levels with large energies , such as @xmath159 ( @xmath160 ev ) and @xmath161 ( @xmath162 ev ) . the measured flux in these progressions , comibed with the observed flux at the pumping wavelengths , requires that of order 1% of the h@xmath0 resides in these levels . this population is too large to be thermally populated at any reasonable temperature for the h@xmath0 gas . therefore , non - thermal processes must be populating these levels . although the fluorescence process can populate high vibrational levels in the ground electronic state , fluorescence can not directly populate high rotational levels , and no direct paths exist to the levels @xmath159 and @xmath161 . h@xmath0 can form in highly excited states @xcite via dissociative recombination of h@xmath163 . given a dense medium and a large ionizing flux , then h@xmath164 may be present in large enough quantities to react with h@xmath0 to produce h@xmath163 in highly excited states . more attempts to detect h@xmath163 would be useful .","summary":"strong  emission irradiates a warm disk surface within 2 au of the central star and pumps certain excited levels of h . based on those diagnostics , we estimate that the warm disk surface has a column density ofh , a temperature k , and a filling factor of h , as seen by the source of  emission , of ( all 2 error bars ) .","abstract":"we measure the temperature of warm gas at planet - forming radii in the disk around the classical t tauri star ( ctts ) tw hya by modelling the h fluorescence observed in _ hst_/stis and _ fuse _ spectra . strong  emission irradiates a warm disk surface within 2 au of the central star and pumps certain excited levels of h . we simulate a 1d plane - parallel atmosphere to estimate fluxes for the 140 observed h emission lines and to reconstruct the  emission profile incident upon the warm h . the excitation of h can be determined from relative line strengths by measuring self - absorption in lines with low - energy lower levels , or by reconstructing the  profile incident upon the warm h using the total flux from a single upper level and the opacity in the pumping transition . based on those diagnostics , we estimate that the warm disk surface has a column density ofh , a temperature k , and a filling factor of h , as seen by the source of  emission , of ( all 2 error bars ) . tw hya produces approximately in the fuv , about 85% of which is in the  emission line . from the absorption observed in the  emission , we infer that dust extinction in our line of sight to tw hya is negligible ."}
{"article_id":"cond-mat0609103","section_id":"i","document":"photoluminescence ( pl ) is a powerful method in the experimental studies of two - dimensional ( 2d ) electron systems in high magnetic fields.@xcite in a typical experiment , an additional electron  hole ( @xmath0@xmath1 ) pair is introduced into the electron system through absorption of a photon . this causes energy relaxation via coulomb scattering , followed by optical recombination of the well - defined , quantized eigenstates involving an @xmath0@xmath1 pair coupled in different ways to the surrounding electrons . this coupling is a response of the 2d electron system to the perturbation associated with the photo - injection of a hole ( particle of the opposite charge ) . depending on the nature of this response and on the number of electrons involved , the pl spectrum either reveals information about dynamics of an illuminated system @xcite or `` merely '' probes the few - body excitonic complexes which form under given conditions ( quantum well geometry , magnetic field , etc . ) but are weakly affected by the surrounding electrons . the latter scenario occurs at sufficiently high magnetic fields @xmath2 and low electron concentrations @xmath3 , corresponding to small landau level ( ll ) filling factors @xmath4 ( with @xmath5 being the magnetic length ) . the pl spectra at @xmath6 are usually dominated by recombination of three - body states called trions ( x@xmath7 ) , consisting of an exciton ( @xmath8 ) bound to an additional electron.@xcite the trion binding energy is @xmath9 where @xmath10 is the x / x@xmath11 ground state energy . the lowest ll energy @xmath12 is set to zero for each particle . the exhaustive reviews of experimental and theoretical work on trions have been written by peeters _ et al._,@xcite bar - joseph,@xcite and also by us.@xcite let us hence only summarize here that despite involving only three particles , quantum dynamics of a trion in the presence of confinement and magnetic field is neither trivial nor completely understood . the complications include the competition of several ( cyclotron , coulomb , subband , and zeeman ) energy scales , complex structure of the valence band , spin - orbit effects ( and their effect on relaxation ) , and coupling to free carriers , lattice defects , and phonons .    however , it is established that , depending on the parameters ( composition and width @xmath13 of the quantum well , electron concentration @xmath3 , magnetic field @xmath2 , etc . ) , the trion energy spectrum contains one or more bound states , distinguished by the total spin of the pair of electrons @xmath14 and the relative angular momentum @xmath15 . ( i ) at small @xmath2 , the only bound trion is the `` singlet '' x@xmath16 with @xmath17 and @xmath18 , a 2d analog of the hydrogen ion.@xcite it was first observed in cdte by kheng _ et al._@xcite and then also in gaas and znse@xcite ( with considerably different effective rydbergs @xmath19 and bohr radii @xmath20 ) . positive singlet trions x@xmath21 ( with the opposite effective - mass ratio ) were also observed@xcite in acceptor - doped samples . ( ii ) in the ( unrealistic ) limit of very high @xmath2 and vanishing @xmath13 , the singlet trion unbinds as predicted from the `` hidden symmetry '' @xcite ( particle  hole symmetry between conduction electrons and valence holes in the lowest ll ) . however , it is replaced by a different bound state : the `` dark triplet '' x@xmath22 with @xmath23 and @xmath24,@xcite and with an infinite optical lifetime.@xcite despite initial difficulties@xcite it was also eventually detected in pl,@xcite and its vanishing oscillator strength was confirmed directly in optical absorption . @xcite the singlet  triplet crossover occurs in rather high magnetic fields,@xcite and it is fairly sensitive to the parameters.@xcite ( iii ) additional , less strongly bound trions occur at intermediate fields , including the `` bright triplet '' x@xmath25 with @xmath23 and @xmath18.@xcite all three trions were later confirmed by several independent calculations@xcite and experiments . @xcite    trions were also identified beyond the `` dilute regime , '' in pl spectra of the fractional quantum hall states . it was found@xcite that a trion immersed in a laughlin @xmath26 liquid may survive in form of a fractionally charged `` quasiexciton '' state which retains the characteristic internal @xmath0@xmath1 correlations of its trion parent . this extends the variety of systems in which trions occur and also allows to use their recombination spectrum as an indirect probe of incompressible electron fluids . @xcite this possibility seems especially attractive for systems in which these fluids may form but can not be studied by transport . @xcite remarkably , the recombination spectra of the quasiexcitons formed from different trions and interacting with fractionally charged quasiparticles of the laughlin liquid behave differently when the filling factor passes through @xmath26 : they show a discontinuity for the x@xmath22 but no anomaly for the x@xmath16 . therefore , the quantum wells for studying incompressible fluids by pl need be designed so as to yield the x@xmath22 ground state . this could be greatly helped by accurate theoretical predictions .    in this paper we address this problem by extensive realistic numerical calculations of the binding energies of ( negative and positive ) trions in doped gaas quantum wells in high magnetic fields . compared to the earlier studies , asymmetry of the quantum well caused by one - sided doping is fully taken into account by self - consistent calculation of the subband wave functions and by inclusion of up to three subbands along with several landau levels in the hilbert space . especially for the the singlet trion and for doped wells , the results are significantly different from the previous , less accurate models . another goal of this paper is to explain and justify the configuration - interaction exact numerical diagonalization in haldane spherical geometry for the realistic calculations of the few - body excitonic complexes . the method was recently used in several related studies without giving a detailed description,@xcite leaving the questions of its validity and accuracy largely unanswered . the detailed secs . [ secmodel ] and [ seccaa ] fill this gap , and with the future studies in perspective , point out the advantages over the ( complementary ) variational approch .","summary":"binding energies of negative and positive trions in doped gaas quantum wells in high magnetic fields are studied by exact numerical diagonalization in spherical geometry . compared to earlier calculations , finite width of the quantum well and its asymmetry caused by one - sided doping are both fully taken into account by using self - consistent subband wave functions in the integration of coulomb matrix elements , and by inclusion of higher subbands along with several landau levels in the hilbert space . detailed analysis of the accuracy and convergence of the exact diagonalization scheme is presented , including dependence on landau level and subband mixing , sensitivity to the ( not well known ) single - particle spectrum in the valence band , and the estimate of finite - size errors .","abstract":"binding energies of negative and positive trions in doped gaas quantum wells in high magnetic fields are studied by exact numerical diagonalization in spherical geometry . compared to earlier calculations , finite width of the quantum well and its asymmetry caused by one - sided doping are both fully taken into account by using self - consistent subband wave functions in the integration of coulomb matrix elements , and by inclusion of higher subbands along with several landau levels in the hilbert space . detailed analysis of the accuracy and convergence of the exact diagonalization scheme is presented , including dependence on landau level and subband mixing , sensitivity to the ( not well known ) single - particle spectrum in the valence band , and the estimate of finite - size errors . the main results are the exciton dispersion and trion binding energy spectrum calculated as a function of the magnetic field , quantum well width , electron concentration , and the presence of an ionized impurity . as a complementary approach , a combination of the exact diagonalization in the quantum well plane and the variational calculation in the normal direction is used as well ."}
{"article_id":"math0504103","section_id":"i","document":"the simplicial volume is a topological invariant of oriented closed connected manifolds , measuring the complexity of the fundamental class . despite its topological nature , the simplicial volume is linked to riemannian geometry in various ways  @xcite .    originally , gromov defined the simplicial volume to be the @xmath0-seminorm of the fundamental class ( with real coefficients)@xcite . in his famous lecture notes ( * chapter  6 ) , thurston suggested an alternative description of the simplicial volume for smooth manifolds : he replaced singular homology and the @xmath0-seminorm by a new homology theory , called smooth measure homology , and a corresponding seminorm . however , except for the case of hyperbolic manifolds ( * ? ? ? * remark  0.1 ) , there is no published proof that these two constructions result in the same simplicial volume . it is the purpose of the present article to close this gap . more generally , we prove the following :    [ isomisomthm ] for all connected -complexes  @xmath1 , the inclusion @xmath2 of the singular chain complex into the measure chain complex induces a natural isomorphism @xmath3 this isomorphism is isometric with respect to the @xmath0-seminorm on singular homology and the seminorm on measure homology induced by the total variation . [ smisomisomthm ] for all connected smooth manifolds  @xmath4 the canonical inclusions @xmath5 ( of the smooth singular chain complex into the smooth measure chain complex ) and @xmath6 induce a natural isomorphism @xmath7 this isomorphism is isometric with respect to the @xmath0-seminorm on singular homology and the seminorm on smooth measure homology induced by the total variation . we will now explain the occurring terminology in more detail . the @xmath0-seminorm on singular homology with real coefficients is the seminorm induced by the @xmath0-norm on the singular chain complex :    let @xmath1 be a topological space and let @xmath8 . we define a norm  @xmath9 on the singular @xmath10-chains  @xmath11 with real coefficients by @xmath12{\\ssim k } x } |a_\\sigma|\\ ] ] for all @xmath13{\\ssim k}x } a_\\sigma \\cdot \\sigma     \\in \\csing k x.$ ] this norm induces a seminorm on the @xmath10-th singular homology  @xmath14 with real coefficients by @xmath15 = \\alpha                            \\bigr\\}\\ ] ] for all @xmath16 . one of the most important properties of  @xmath9 is `` functoriality , '' i.e. , for all continuous maps  @xmath17 the induced homomorphism  @xmath18 does not increase the seminorm . ( based on this property , gromov introduced a more general framework of functorial seminorms @xcite . ) measure homology is a curious generalisation of singular homology : let @xmath1 be a topological space , let @xmath8 and let @xmath19{\\ssim k}{x}$ ] be some set of singular simplices . the idea of measure homology is to think of a singular chain @xmath20 with real coefficients as a signed measure on  @xmath21 having the mass  @xmath22 on the set  @xmath23 the measure chain complex consists of all signed measures on  @xmath21 satisfying some finiteness condition .    thus the measure chain complex is larger than the singular chain complex and hence provides more room for constructions such as `` smearing '' ( * ? ? ? * ; * ? ? ? * , page  547ff ) . the other side of the coin is that it is quite hard to gain a geometric intuition of more complicated measure chains . depending on the choice of the mapping spaces  @xmath21 and their topology , there are two main flavours of measure homology :    * one for general topological spaces using the compact - open topology on the set of all singular simplices  the corresponding chain complexes and homology groups are denoted by  @xmath24 and  @xmath25 . * one for smooth manifolds using the -topology on the set of smooth singular simplices  the corresponding chain complexes and homology groups are denoted by  @xmath26 and  @xmath27 .    in both cases , measure homology is equipped with the seminorm induced by the total variation on the chain level . measure homology of the second kind ( so - called smooth measure homology ) was introduced by thurston  @xcite . some basic properties of smooth measure homology are also listed in ratcliffe s book  @xcite . a thorough treatment of measure homology for general spaces is given in the papers of zastrow and hansen @xcite . in both papers it is shown that measure homology for -complexes coincides _ algebraically _ with singular homology with real coefficients . the general idea of the proof of theorem  [ isomisomthm ] and  [ smisomisomthm ] is to take a dual point of view : singular homology and the @xmath0-seminorm admit a dual concept , called bounded cohomology . the key property is that the canonical seminorm on bounded cohomology and the @xmath0-seminorm are intertwined by a duality principle ( theorem  [ duality ] ) .    unlike the @xmath0-seminorm , bounded cohomology and its seminorm are rather well understood by ivanov s homological algebraic approach @xcite . in our proof of theorem  [ isomisomthm ] and  [ smisomisomthm ] , we take advantage of a special cochain complex  @xmath28 computing bounded cohomology . more precisely , we construct a dual  @xmath29 of the measure chain complex ( together with a corresponding duality principle ) fitting into a commutative diagram @xmath30 \\ar[d ] & \\\\ \\bmcch * x \\ar[r ]          & \\bchn * x ,    } \\end{aligned}\\ ] ] where @xmath31 is the cochain complex defining bounded cohomology . the crux of this diagram is that the vertical arrow induces an isometric isomorphism on the level of cohomology and that the arrows on the left do not increase the seminorm . then the duality principles allow us to deduce that the algebraic isomorphism  @xmath32 must be isometric .    for simplicity , we only prove theorem  [ isomisomthm ] in detail . the smooth case , requiring a small detour to smooth singular homology , is considered briefly in section  [ smoothsec ] ( and is also explained in the author s diploma thesis @xcite ) this paper is organised as follows : measure homology ( the non - smooth version ) is defined in section  [ mhsec ] . section  [ dualsec ] is concerned with the dual point of view , i.e. , the construction of a dual for measure homology and the derivation of a corresponding duality principle . a proof of theorem  [ isomisomthm ] is presented in section  [ proofsec ] . in section  [ smoothsec ] , we have a glimpse at the smooth universe , that is at smooth measure homology and at a proof of theorem  [ smisomisomthm ] . finally , in section  [ applications ] , we list some applications to the simplicial volume , including gromov s proportionality principle and some of its consequences .","summary":"measure homology is a variation of singular homology designed by thurston in his discussion of simplicial volume . zastrow and hansen showed independently that singular homology ( with real coefficients ) and measure homology coincide algebraically on the category of cw - complexes . it is the aim of this paper to prove that this isomorphism is _ isometric _ with respect to the-seminorm on singular homology and the seminorm on measure homology induced by the total variation . for example , measure homology can be used to prove gromov s proportionality principle of simplicial volume .","abstract":"measure homology is a variation of singular homology designed by thurston in his discussion of simplicial volume . zastrow and hansen showed independently that singular homology ( with real coefficients ) and measure homology coincide algebraically on the category of cw - complexes . it is the aim of this paper to prove that this isomorphism is _ isometric _ with respect to the-seminorm on singular homology and the seminorm on measure homology induced by the total variation . this , in particular , implies that one can calculate the simplicial volume via measure homology  as already claimed by thurston . for example , measure homology can be used to prove gromov s proportionality principle of simplicial volume ."}
{"article_id":"astro-ph9906499","section_id":"i","document":"in the past decade , globular cluster systems were established as powerful probes for the formation and evolution of galaxies ( e.g.  harris 1991 and ashman & zepf 1998 for reviews ) . with very few exceptions , globular clusters exist in large numbers around all galaxies . they are not only easy to detect ; their properties are readily influenced by the formation and evolution of their host galaxies and , in a larger sense , their environment . globular cluster formation is also closely related to the star  formation history of the galaxies ( e.g.  kissler - patig  1998a ) . the study of globular cluster systems , combined with the predictions of their properties from various galaxy formation scenarios , can therefore be used to constrain galaxy formation and evolution .    in recent years , tens of galaxies have been studied for their globular cluster population ( e.g.  compilation in ashman & zepf 1998 ) . however , no systematic study of the properties of globular cluster systems , including more than a dozen hosts , has been carried out . motivated by the need for a homogeneous study of a large number of systems , we have exploited the archive of the hubble space telescope as an ideal starting point for such a study , since it includes a large number of images centered on galaxies in different filters and taken in nearly identical conditions , leading to homogeneous photometry . we begin by studying the properties of globular cluster systems around a large number of _ early  type _ galaxies , then describe the resulting sample in sect .  2 and the pipeline reduction in sect .  3 . we study the color distributions of the systems ( presented in sect .  4 and 5 ) , followed by a discussion of the properties of the color distributions , correlations among these properties , and their relation to the properties of the host galaxies ( sect .  6 and 7 ) . because color denotes a mix of age and metallicity of the systems , globular cluster systems have gained considerable interest after the discovery of multi  modal distributions in some systems ( zepf & ashman 1993 ) . such a system implies that at least in some galaxies , globular clusters formed from several different mechanisms and possibly at several epochs . color distributions alone are thus already a strong diagnostic for the history of the globular clusters systems and , by implication , for the history of the host galaxies . we discuss the properties of the color distributions of our sample for various formation scenarios in sect . 8 . in a companion paper , we use these data to constrain the models of  ( 1998 ) .","summary":"we have compiled data for the globular cluster systems of 50 galaxies from the hst wfpc2 archive , of which 43 are type s0 or earlier . in this paper , we present the data set and derive the color distributions . overall , roughly half of all the systems in our sample show hints of a bimodal color distribution . in general , the distributions of the faint galaxies are consistent with unimodality , whereas those of the brighter galaxies are not . we discuss their possible origins .    in comparing the moments of the distributions with various galaxy properties for the early - type galaxies","abstract":"we have compiled data for the globular cluster systems of 50 galaxies from the hst wfpc2 archive , of which 43 are type s0 or earlier . in this paper , we present the data set and derive the color distributions . we derive the first four moments of the color distributions , as well as a measure for their non  unimodality . the number of globular clusters in each galaxy ranges from 18 ( in ngc  2778 ) to 781 ( ngc  5846 ) . for those systems having more than 100 clusters , seven of sixteen ( 44% ) show significant bimodality . overall , roughly half of all the systems in our sample show hints of a bimodal color distribution . in general , the distributions of the faint galaxies are consistent with unimodality , whereas those of the brighter galaxies are not . we also find a number of systems with narrow color distributions  with both mean red and blue colors  suggesting that systems exist with only metal  rich or only metal  poor globular clusters . we discuss their possible origins .    in comparing the moments of the distributions with various galaxy properties for the early - type galaxies , we find the following difference in the correlations between the field and cluster galaxy populations : the peak color of the globular cluster distribution correlates well with the central velocity dispersion  and hence the mg2 index and total luminosity  for galaxies in cluster environments ; there exists no such correlation for field galaxies . this difference between cluster and field galaxies possibly reflects different formation scenarios for their globular cluster systems . among the explanations for such a correlation , we consider either a larger age spread in the field populations or the possibility that cluster galaxies are always affected by significant accretion whereas some field galaxies could host pure `` in situ '' formed populations ."}
{"article_id":"astro-ph9906499","section_id":"c","document":"an important discovery in the study of globular clusters systems in the last decade is the fact that the globular clusters color distribution of many ellipticals show several peaks ( zepf & ashman 1993 ) . this property has been interpreted as the presence of several distinct populations of globular clusters around the host galaxy . the origin of these different populations is still under debate and might well have several causes . the original explanation argues that spiral  spiral mergers provide old globular clusters from the progenitors as well as produce a new population during the merger ( ashman & zepf 1992 , see also schweizer 1987 ) . however , the accretion of enough dwarf galaxies with metal poor clusters will also obviously build up a distinct metal  poor population . ct  ( 1998 ) , and hilker ( 1999 ) investigated this idea . yet another process involves the pre  galactic formation of metal  poor clusters as the building blocks of galaxies , followed by the formation of more metal  rich globular clusters during the collapse of the galaxy ( see kissler - patig 1997 , and kissler - patig  1998a ) . only slightly different is the theory that galaxies formed all their globular clusters _ in situ _ and had two main phases of star formation ( e.g.  forbes  1997 , harris  1998 , harris  1999 ) . today s challenge is to discriminate between the various scenarios with detailed comparison to the present data . the diversity of the color distributions present in our sample indicates that indeed the scenario is complex . we discuss in turn some of the groups :    @xmath29 galaxies that host `` only red clusters''  those having a red peak and a small scale value . the existence of a blue population in these galaxies is not excluded but is unlikely to be significant . the favored scenario for these galaxies is that a single dominant collapse created a bulge and a red population of clusters . we can not rule the accretion scenario out if these galaxies were formed in an environment poor in material suitable for accretion ( e.g.  dwarf galaxies , cf . chapelon 1999 ) . these galaxies would then be in low density environments or in the outskirts of clusters ; neither is confirmed nor ruled out by our present statistics . finally , the merger scenario could also work for these galaxies if the progenitors were poor in blue clusters . if the merger happened at early times , the progenitors could be still in a gaseous form , or , alternatively , could be low  surface  brightness galaxies for late mergers in the field that host a large amount of gas but apparently few clusters . however , a scenario with gaseous mergers at early times is hard to distinguish from the two - stage _ in situ _ scenario . @xmath29 galaxies that host `` only blue clusters''  that have a blue peak and a small scale value . these galaxies do not seem to host a significant population of red ( presumably metal  rich ) clusters . in this case , none of the above scenarios would easily be able to explain such systems ; one would have to advocate the formation of bulge stars without the formation of clusters . more likely is a `` blue '' red peak , either because the red clusters formed with a low metallicity or because they have a significant younger age ( about half as old as the true blue clusters , cf . kissler - patig  1998a ) that make them appear blue . in these last two cases , all scenarios work , with some preference to the merger scenario in the frame of hierarchical clustering models that predict late mergers in the field . @xmath29 galaxies with broad or bimodal color distributions  that which presumably host a comparable amount ( say within a factor of about 3 ) of blue and red clusters . these are the cases for which the scenarios described above were designed , and we refer to the respective papers for the pros and cons .    finally , we note that as long as some information is missing ( merger epoch , globular clusters formation mechanisms , faint end of the luminosity function in different environments , etc ... ) , and given the diversity of scenarios , it seems that not always the same mechanism is the dominant one . although based on small number statistics , field and cluster early  type galaxies seem to differ in the properties of their globular cluster systems . whereas cluster galaxies show a correlation between peak value and the galaxy size ( as measured by the velocity dispersion ) , such a relation must be ruled out for field galaxies .    for cluster ellipticals , the recent spectroscopic studies ( cohen  1998 , kissler - patig  1998b ) show that all globular clusters are old ( around 10 gyr or older ) . at these ages , the clusters can be considered coeval with respect to the influence of their ages on color . color differences can therefore be interpreted as almost pure metallicity differences , and the relation between peak color and galaxy luminosity might reflect the equivalent of the mg2@xmath3 relation for galaxies . forbes  ( 1997 ) suggest that in systems with two distinct globular cluster populations , the mean metallicity of the red clusters correlates with the luminosity of the host galaxy ; the blue peak does not . their conclusion implies that the correlation of the total sample s mean color with galaxy size is driven by the metal  rich globular clusters only . consequently , this would support scenarios in which the metal  poor globular clusters formed in events uncorrelated with their future host galaxy  e.g . ,  in systems that are separate entities from their future hosts . on the other hand , the same research suggests that the metal  rich globular clusters formed in events correlated with the future host galaxy  e.g . ,  the formation of a bulge in a collapse or merger event . in addition , this correlation suggests that the blue sub  populations have roughly a constant color , while for the red population both the peak shifts and the scale increase as a function of color .    perhaps surprisingly , the peak color of globular clusters in field galaxies does not correlate with the velocity dispersion ( @xmath30 size ) of their host galaxy . this result appears to be in contrast with the observation that field and cluster galaxies do exhibit the same mg2@xmath3 relations ( bernardi  1998 ) . we see several possible explanations . a first alternative might be that the correlation for cluster galaxies is artificial . we verified that it is not caused by sampling different regions in the different galaxies . indeed , the ratio of blue to red galaxies does vary with radius ( geisler  1997 , kissler - patig  1997b , puzia  1999 ) . furthermore , the wfpc2 field samples the outer parts less in larger galaxies than in small ones , so that the relative ratio of blue to red galaxies is systematically smaller in large galaxies at fixed field of view . puzia  ( 1999 ) tested the importance of this effect on ngc 4472 , which has exposures centered on the galaxy as well as several arcminute offsets north and south . the respective peaks of the blue and red populations do not change with radius within the errors ; however , the varying ratio of blue to red causes the overall peak to shift by 0.02 mag from the inner to the outer field . the effect is too small , though , to explain any systematic correlation . moreover , in our sample , field and cluster galaxies span different values of galaxy @xmath3 . where cluster galaxies are of intermediate to giant size , the field galaxies span the low to intermediate size range . if indeed intermediate and giant early  type galaxies differ ( see above , cf . kissler - patig 1997 ) , the presence / absence of a correlation would be due not to environment , but rather to a function of the galaxy size . for example , one could speculate that small galaxies are not surrounded by a `` halo '' of blue clusters , thus showing a small trend of system peak with size . intermediate size or larger galaxies might or might not have such a halo of blue clusters , complicating the interpretation of the peak color and introducing a scatter due to the possible existence of blue clusters . giant ellipticals would always have blue clusters , and a significant redder population that correlates with galaxy size , leading to an overall trend of peak color with galaxy size again . in other words , the correlation would be an artifact of the mix of populations which show a correlation with environment , rather than a physical difference in the enrichment histories . a second alternative would be a physical interpretation of the result . thus , the presence of a mg2@xmath3 relations in field and cluster galaxies , but absence / presence respectively of a peak@xmath3 relation , would indicate that stars and globular clusters are coupled in cluster galaxies but not in field galaxies . we regard this alternative as unlikely , however , since cluster formation and star formation appear to go together . finally , mg2 and @xmath0 color could vary differently with age and metallicity . the variations of mg2 with age and metallicity are still uncertain and if , for example , the metal  rich population in field ellipticals show a large spread in age from galaxy to galaxy , a trend could mimic an mg2@xmath3 relation in the field but not a peak@xmath3 relation . in contrast , since all globular clusters in cluster galaxies are old , such a trend would not be present , and both mg2 and peak would trace metallicity only . clearly such speculations require a much better understanding of the influence of age and metallicity on the properties of composite stellar populations . detailed studies of the ages and metallicities of the systems are needed .","summary":", we find the following difference in the correlations between the field and cluster galaxy populations : the peak color of the globular cluster distribution correlates well with the central velocity dispersion  and hence the mg2 index and total luminosity  for galaxies in cluster environments ; there exists no such correlation for field galaxies . this difference between cluster and field galaxies possibly reflects different formation scenarios for their globular cluster systems . among the explanations for such a correlation","abstract":"we have compiled data for the globular cluster systems of 50 galaxies from the hst wfpc2 archive , of which 43 are type s0 or earlier . in this paper , we present the data set and derive the color distributions . we derive the first four moments of the color distributions , as well as a measure for their non  unimodality . the number of globular clusters in each galaxy ranges from 18 ( in ngc  2778 ) to 781 ( ngc  5846 ) . for those systems having more than 100 clusters , seven of sixteen ( 44% ) show significant bimodality . overall , roughly half of all the systems in our sample show hints of a bimodal color distribution . in general , the distributions of the faint galaxies are consistent with unimodality , whereas those of the brighter galaxies are not . we also find a number of systems with narrow color distributions  with both mean red and blue colors  suggesting that systems exist with only metal  rich or only metal  poor globular clusters . we discuss their possible origins .    in comparing the moments of the distributions with various galaxy properties for the early - type galaxies , we find the following difference in the correlations between the field and cluster galaxy populations : the peak color of the globular cluster distribution correlates well with the central velocity dispersion  and hence the mg2 index and total luminosity  for galaxies in cluster environments ; there exists no such correlation for field galaxies . this difference between cluster and field galaxies possibly reflects different formation scenarios for their globular cluster systems . among the explanations for such a correlation , we consider either a larger age spread in the field populations or the possibility that cluster galaxies are always affected by significant accretion whereas some field galaxies could host pure `` in situ '' formed populations ."}
{"article_id":"astro-ph9906499","section_id":"i","document":"the results presented in this paper suggest that we can use globular cluster systems to study the merger / formation history of both itself and its host galaxy . the differences we see between the field and cluster systems suggest that the cluster galaxies are more influenced by accretion , whereas the field systems may be the result of `` in situ '' globular cluster formation . combining this result with the strong signature of multi - modality seen in many of the systems provides an observational comparison to the various formation scenarios . in a companion paper (  2000 ) , we will compare these results to the theoretical predictions of  ( 1998 ) . more detailed studies of the systems that are candidates for bimodal distributions are underway , including follow  up near  infrared photometry and multi  object spectroscopy . we are indebted to pat  for his help and advises in some of the early  stages of this study . thanks to thomas puzia for his help with the ngc 4472 data and extra  tests . we thank alvio renzini for enlightening discussions , as well as the enear team for providing galaxy data prior to publication , especially mariangela bernardi for her help in digging these latter out . kg is supported by nasa through hubble fellowship grant hf-01090.01 - 97a awarded by the space telescope science institute , which is operated by the association of the universities for research in astronomy , inc . , for nasa under contract nas 5 - 26555 . mkp was partly supported by a feodor lynen fellowship of the alexander von humboldt foundation . lccrl n0584 & f555w & 1520 & 5 & faber ( 6099 ) & f814w & 1450 & 7 & faber ( 6099 ) n0596 & f555w & 1600 & 4 & richstone ( 6587 ) & f814w & 1800 & 3 & richstone ( 6587 ) n0821 & f555w & 1520 & 5 & faber ( 6099 ) & f814w & 1450 & 7 & faber ( 6099 ) n1023@xmath31 & f555w & 2920 & 11 & faber , richstone ( 6099,6587 ) & f814w & 3780 & 10 & faber , richstone ( 6099,6587 ) n1316 & f450w & 5000 & 5 & grillmair ( 5990 ) & f814w & 1860 & 3 & grillmair ( 5990 ) n1399 & f450w & 5200 & 4 & grillmair ( 5990 ) & f814w & 1800 & 3 & grillmair ( 5990 ) n1404 & f450w & 5000 & 5 & grillmair ( 5990 ) & f814w & 1860 & 3 & grillmair ( 5990 ) n1426 & f555w & 1600 & 4 & richstone ( 6587 ) & f814w & 1800 & 3 & richstone ( 6587 ) n1700 & f555w & 1600 & 4 & richstone ( 6587 ) & f814w & 1800 & 3 & richstone ( 6587 ) n2300 & f555w & 1520 & 5 & faber ( 6099 ) & f814w & 1450 & 7 & faber ( 6099 ) n2434 & f555w & 1300 & 2 & carollo ( 5943 ) & f814w & 1000 & 2 & carollo ( 5943 ) n2778 & f555w & 1520 & 5 & faber ( 6099 ) & f814w & 1450 & 7 & faber ( 6099 ) n3115 & f555w & 1015 & 6 & faber ( 5512 ) & f814w & 1236 & 6 & faber ( 5512 ) n3377 & f555w & 1330 & 6 & faber ( 5512 ) & f814w & 1236 & 6 & faber ( 5512 ) n3379 & f555w & 1660 & 4 & faber ( 5512 ) & f814w & 1340 & 4 & faber ( 5512 ) n3384 & f555w & 1430 & 6 & faber ( 5512 ) & f814w & 1290 & 6 & faber ( 5512 ) n3585 & f555w & 1200 & 6 & richstone ( 6587 ) & f814w & 1900 & 3 & richstone ( 6587 ) n3610 & f555w & 1400 & 6 & richstone ( 6587 ) & f814w & 2100 & 3 & richstone ( 6587 ) n3640 & f555w & 1200 & 6 & richstone ( 6587 ) & f814w & 2100 & 3 & richstone ( 6587 ) n4125 & f555w & 1400 & 6 & faber ( 6587 ) & f814w & 2100 & 3 & faber ( 6587 ) n4192 & f555w & 660 & 3 & rubin ( 5375 ) & f814w & 660 & 3 & rubin ( 5375 ) n4291 & f555w & 1520 & 5 & faber ( 6099 ) & f814w & 1450 & 7 & faber ( 6099 ) n4343 & f555w & 660 & 3 & rubin ( 5375 ) & f814w & 660 & 3 & rubin ( 5375 ) n4365 & f555w & 2200 & 2 & brodie ( 5920 ) & f814w & 2300 & 2 & brodie ( 5920 ) n4374 & f547 m & 1200 & 2 & bower ( 6094 ) & f814w & 520 & 2 & bower ( 6094 ) n4406 & f555w & 1500 & 3 & faber ( 5512 ) & f814w & 1500 & 3 & faber ( 5512 ) n4450 & f555w & 520 & 3 & rubin ( 5375 ) & f814w & 520 & 3 & rubin ( 5375 ) n4458 & f555w & 1340 & 4 & faber ( 5512 ) & f814w & 1120 & 5 & faber ( 5512 ) n4472@xmath31 & f555w & 4400 & 4 & brodie ( 5920 ) & f814w & 4600 & 4 & brodie ( 5920 ) n4473 & f555w & 1800 & 3 & faber ( 6099 ) & f814w & 2000 & 4 & faber ( 6099 ) n4478 & f555w & 1600 & 4 & richstone ( 6587 ) & f814w & 1800 & 3 & richstone ( 6587 ) n4486 & f555w & 2810 & 6 & macchetto ( 5477 ) & f814w & 2430 & 5 & macchetto ( 5477 ) n4486b & f555w & 1800 & 3 & faber ( 6099 ) & f814w & 2000 & 4 & faber ( 6099 ) n4526 & f555w & 520 & 3 & rubin ( 5375 ) & f814w & 520 & 3 & rubin ( 5375 ) n4536 & f555w & 660 & 3 & rubin ( 5375 ) & f814w & 660 & 3 & rubin ( 5375 ) n4550 & f555w & 1200 & 3 & rubin ( 5375 ) & f814w & 1200 & 3 & rubin ( 5375 ) n4552 & f555w & 2400 & 4 & faber ( 6099 ) & f814w & 1500 & 3 & faber ( 6099 ) n4569 & f555w & 520 & 3 & rubin ( 5375 ) & f814w & 520 & 3 & rubin ( 5375 ) n4594 & f547 m & 1340 & 4 & faber ( 5512 ) & f814w & 1470 & 6 & faber ( 5512 ) n4621 & f555w & 1380 & 6 & faber ( 5512 ) & f814w & 1280 & 6 & faber ( 5512 ) n4649 & f555w & 2100 & 2 & westphal ( 6286 ) & f814w & 2500 & 2 & westphal ( 6286 ) n4660 & f555w & 1000 & 5 & faber ( 5512 ) & f814w & 850 & 5 & faber ( 5512 ) n4881 & f555w & 7200 & 8 & westphal ( 5233 ) & f814w & 7200 & 8 & westphal ( 5233 ) n5018 & f555w & 1200 & 6 & richstone ( 6587 ) & f814w & 1900 & 3 & richstone ( 6587 ) n5061 & f555w & 1200 & 6 & richstone ( 6587 ) & f814w & 1900 & 3 & richstone ( 6587 ) n5845 & f555w & 2140 & 5 & faber ( 6099 ) & f814w & 1120 & 5 & faber ( 6099 ) n5846@xmath31 & f555w & 6600 & 6 & brodie ( 5920 ) & f814w & 6900 & 6 & brodie ( 5920 ) n7192 & f555w & 1300 & 2 & carollo ( 5943 ) & f814w & 1000 & 2 & carollo ( 5943 ) n7457 & f555w & 1380 & 6 & faber ( 5512 ) & f814w & 1280 & 6 & faber ( 5512 ) ic4889 & f555w & 600 & 1 & carollo ( 5943 ) & f814w & 600 & 1 & carollo ( 5943 )    llccccrc n584 & e4 & 21.16 & 2.34 & 0.29 & 0.42 & 1.50 & 3.51 n596 & epec & 20.93 & 2.22 & 0.25 & 0.40 & 1.30 & n821 & e6 & 20.84 & 2.32 & 0.32 & 0.08 & 2.50 & 3.45 n1023 & sb0 & 20.61 & 2.34 & 0.34 & 0.57 & & 3.26 n1399 & e1pec & 21.97 & 2.52 & 0.37 & 1.59 & 0.00 & n1404 & e1 & 21.56 & 2.38 & 0.34 & 1.59 & 0.50 & n1426 & e4 & 20.42 & 2.18 & 0.28 & 0.66 & & 3.44 n1700 & e4 & 21.90 & 2.36 & 0.28 & & 0.90 & n2300 & sa0 & 20.76 & 2.42 & 0.33 & 0.14 & 0.60 & 3.58 n2434 & e0 & 20.60 & 2.31 & 0.27 & 0.19 & & 3.49 n2778 & e & 19.43 & 2.26 & 0.34 & 0.28 & & n3115 & s0 & 20.82 & 2.45 & 0.34 & 0.08 & 8.00 & 3.17 n3377 & e5 & 19.96 & 2.18 & 0.29 & 0.49 & 1.20 & 3.21 n3379 & e1 & 20.83 & 2.35 & 0.34 & 0.52 & 0.10 & 3.23 n3384 & sb0 & 19.89 & 2.21 & 0.29 & 0.54 & & n3585 & e7 & 21.75 & 2.34 & 0.32 & 0.12 & 4.50 & 3.50 n3610 & e5 & 20.92 & 2.21 & 0.27 & 0.30 & 2.50 & n3640 & e3 & 21.75 & 2.24 & 0.27 & 0.18 & 0.20 & n4125 & e6pec & 22.09 & 2.25 & 0.32 & 0.34 & 1.00 & 3.43 n4291 & e & 20.69 & 2.43 & 0.32 & 0.36 & 0.40 & 3.64 n4365 & e3 & 22.12 & 2.42 & 0.35 & 2.93 & 1.10 & 3.79 n4374 & e1 & 22.21 & 2.44 & 0.32 & 3.99 & 0.40 & n4406 & s0 & 22.41 & 2.40 & 0.33 & 1.41 & 0.70 & n4458 & e0 & 19.06 & 2.02 & 0.25 & 3.21 & & n4472 & e2 & 22.59 & 2.48 & 0.34 & 3.31 & 0.30 & 3.89 n4473 & e5 & 20.80 & 2.26 & 0.33 & 2.17 & 0.90 & 3.60 n4478 & e2 & 19.94 & 2.13 & 0.27 & 3.92 & 0.80 & n4486 & e0 & 22.48 & 2.56 & 0.30 & 4.17 & 0.00 & 3.89 n4486b & ce0 & 17.75 & 2.30 & 0.30 & 4.17 & & 3.51 n4526 & sab0 & 20.89 & 2.47 & 0.30 & 2.45 & & 3.57 n4550 & sb0 & 18.81 & 2.01 & 0.17 & 2.97 & 0.70 & n4552 & e & 21.26 & 2.42 & 0.35 & 2.97 & & 3.35 n4621 & e5 & 21.63 & 2.40 & 0.35 & 2.60 & 1.50 & 3.54 n4649 & e2 & 22.31 & 2.56 & 0.37 & 3.49 & 0.50 & 3.74 n4660 & e & 19.26 & 2.29 & 0.33 & 3.37 & 2.70 & 3.56 n4881 & e & 21.60 & 2.33 & 0.29 & & & n5018 & e3 & 22.31 & 2.32 & 0.21 & 0.29 & 2.00 & n5061 & e0 & 21.62 & 2.30 & 0.27 & 0.31 & 1.80 & 3.90 n5845 & e & 19.63 & 2.42 & 0.32 & 0.84 & 0.80 & n5846 & e0 & 22.23 & 2.40 & 0.34 & 0.84 & 0.00 & 3.37 n7192 & sa0 & 21.49 & 2.27 & 0.26 & 0.28 & & 3.71 n7457 & sa0 & 18.25 & 1.76 & 0.19 & 0.13 & & ic4889 & e5 & 21.26 & 2.22 & 0.26 & 0.13 & 1.00 &    lcccccc n584 & 67 & @xmath32 & @xmath33 & @xmath34 & @xmath35 & @xmath36 n596 & 31 & @xmath37 & @xmath38 & @xmath39 & @xmath40 & @xmath41 n821 & 55 & @xmath42 & @xmath43 & @xmath44 & @xmath45 & @xmath46 n1023 & 149 & @xmath47 & @xmath48 & @xmath49 & @xmath50 & @xmath51 & 186 & @xmath52 & @xmath53 & @xmath54 & @xmath55 & @xmath56 n1399 & 410 & @xmath57 & @xmath58 & @xmath59 & @xmath60 & @xmath61 n1404 & 138 & @xmath62 & @xmath63 & @xmath64 & @xmath65 & @xmath66 n1426 & 74 & @xmath67 & @xmath68 & @xmath69 & @xmath70 & @xmath71 n1700 & 27 & @xmath72 & @xmath73 & @xmath74 & @xmath75 & @xmath76 n2300 & 82 & @xmath77 & @xmath78 & @xmath79 & @xmath80 & @xmath81 n2434 & 143 & @xmath82 & @xmath83 & @xmath84 & @xmath85 & @xmath86 n2778 & 18 & @xmath87 & @xmath88 & @xmath89 & @xmath90 & @xmath91 n3115 & 94 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 n3377 & 86 & @xmath97 & @xmath98 & @xmath99 & @xmath100 & @xmath101 n3379 & 52 & @xmath102 & @xmath103 & @xmath104 & @xmath105 & @xmath106 n3384 & 39 & @xmath107 & @xmath108 & @xmath109 & @xmath110 & @xmath111 n3585 & 70 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 n3610 & 29 & @xmath117 & @xmath118 & @xmath119 & @xmath120 & @xmath121 n3640 & 48 & @xmath122 & @xmath123 & @xmath124 & @xmath125 & @xmath126 n4125 & 68 & @xmath127 & @xmath128 & @xmath129 & @xmath130 & @xmath131 & 49 & @xmath132 & @xmath133 & @xmath134 & @xmath135 & @xmath136 n4291 & 71 & @xmath137 & @xmath138 & @xmath139 & @xmath140 & @xmath141 & 25 & @xmath142 & @xmath143 & @xmath144 & @xmath145 & @xmath146 n4365 & 409 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & @xmath151 n4374 & 123 & @xmath152 & @xmath153 & @xmath154 & @xmath155 & @xmath156 n4406 & 131 & @xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & 29 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath116 n4458 & 33 & @xmath166 & @xmath167 & @xmath168 & @xmath169 & @xmath170 n4472 & 486 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 n4473 & 112 & @xmath176 & @xmath177 & @xmath178 & @xmath179 & @xmath180 n4478 & 50 & @xmath181 & @xmath182 & @xmath183 & @xmath184 & @xmath185 n4486 & 655 & @xmath186 & @xmath187 & @xmath188 & @xmath189 & @xmath190 n4486b & 87 & @xmath191 & @xmath192 & @xmath193 & @xmath194 & @xmath195 n4526 & 75 & @xmath196 & @xmath197 & @xmath198 & @xmath199 & @xmath200 & 87 & @xmath201 & @xmath202 & @xmath203 & @xmath204 & @xmath205 n4550 & 37 & @xmath206 & @xmath207 & @xmath208 & @xmath209 & @xmath210 n4552 & 171 & @xmath211 & @xmath212 & @xmath213 & @xmath214 & @xmath215 & 67 & @xmath216 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & 122 & @xmath221 & @xmath222 & @xmath223 & @xmath224 & @xmath225 n4621 & 126 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 n4649 & 378 & @xmath231 & @xmath232 & @xmath233 & @xmath234 & @xmath235 n4660 & 74 & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath195 n4881 & 84 & @xmath240 & @xmath241 & @xmath242 & @xmath243 & @xmath244 n5018 & 10 & @xmath245 & @xmath246 & @xmath247 & @xmath248 & @xmath249 n5061 & 84 & @xmath250 & @xmath251 & @xmath252 & @xmath253 & @xmath254 n5845 & 28 & @xmath255 & @xmath256 & @xmath257 & @xmath258 & @xmath259 n5846 & 781 & @xmath260 & @xmath261 & @xmath262 & @xmath263 & @xmath264 n7192 & 95 & @xmath265 & @xmath266 & @xmath267 & @xmath268 & @xmath269 n7457 & 48 & @xmath270 & @xmath271 & @xmath272 & @xmath273 & @xmath106 ic4889 & 48 & @xmath274 & @xmath275 & @xmath276 & @xmath277 & @xmath254    llcrlcrcc faint & m@xmath278 & 15 & 803 & @xmath279 & @xmath280 & @xmath281 & @xmath282 & @xmath283 bright & m@xmath284 & 13 & 2737 & @xmath285 & @xmath286 & @xmath287 & @xmath288 & @xmath289 & & & & & & & & low @xmath3 & log@xmath290 & 16 & 872 & @xmath291 & @xmath292 & @xmath293 & @xmath294 & @xmath295 high @xmath3 & log@xmath296 & 12 & 2992 & @xmath297 & @xmath298 & @xmath299 & @xmath300 & @xmath301 & & & & & & & & low mg2 & mg2 @xmath302 & 18 & 1496 & @xmath303 & @xmath304 & @xmath305 & @xmath306 & @xmath307 high mg2 & mg2 @xmath308 & 15 & 2597 & @xmath309 & @xmath310 & @xmath311 & @xmath312 & @xmath313 & & & & & & & & low @xmath314 & log@xmath315 & 24 & 2202 & @xmath316 & @xmath317 & @xmath318 & @xmath319 & @xmath320 high @xmath314 & log@xmath321 & 17 & 3441 & @xmath322 & @xmath323 & @xmath324 & @xmath325 & @xmath326    ashman , k.m . , & zepf , s.e . 1992 , , 384 , 50 ashman , k.m . , & zepf , s.e . 1998 , `` globular cluster systems '' , cambridge university press ( cambridge astrophysics series , 30 ) baugh , c.m . , cole , s. , frenk , c.s . 1996 , , 283 , 1361 beers , t. , flynn , k. , & gebhardt , k. 1991 , , 100 , 32 bernardi , m. , renzini , a. , da costa , l. , wegner , g. , alonso , m. , pellegrini , p. , rit , c. , & willmer , c. 1998 , , 508 , 143 bertin , e. , & arnouts , s. 1996 , , 117 , 393 bird , t. , & beers , t. 1993 , , 105 , 1596 bruzual , a. , & charlot , s. 1993 , , 405 , 538 chapelon , s. 1999 , in press cohen , j. , blakeslee , j. , & ryzhov , a. 1998 , , 496 , 808 , p. , marzke , r. , & west , m. 1998 , , 501 , 554 , p. ,  2000 , in preparation elson , r. , & santiago , b. 1996 , , 280 , 971 forbes , d. , brodie , j. , & huchra , j. 1997 , , 113 , 887 forbes , d. , grillmair , c. , williger , g. , elson , r. , & brodie , j. 1998 , , 293 , 325 geisler , d. , lee , m. , & kim , e. 1996 , , 111 , 1529 harris , g.l.h . , harris , w.e . , & poole , g.b . 1999 , , 117 , 855 harris , w.e . 1991 , , 29 , 543 harris , w.e . , harris , g.l.h . , & mclaughlin , d.e . 1998 , , 115 , 1801 hartigan , j.a . , & hartigan , p.m. 1985 , ann . statist.,13 , 70 hilker , m. , infante , l. , & richtler , t. 1999 , astro - ph/9905112 holtzman , j. , burrows , c. , casertano , s. , hester , j. , trauger , j. , watson , a. , & worthey , g. 1995 , , 107 , 1065 kauffmann , g. 1996 , , 281 , 487 kissler - patig , m. 1997 , , 319 , 83 kissler - patig , m. , kohle , s. , hilker , m. , richtler , t. , infante , l. , & quintana , h. 1997a , , 319 , 470 kissler - patig , m. , richtler , t. , storm , j. , & della valle , m. 1997b , , 327 , 503 kissler - patig , m. , forbes , d. , & minniti , d. 1998a , , 298 , 1123 kissler - patig , m. , brodie , j. , schroder , l. , forbes , d. , grillmair , c. , & huchra , j. 1998b , , 115 , 105 kissler - patig , m. , brodie , j.p . , & minniti , d. 1999 , in preparation kundu , a. , & whitmore , b. 1998 , , 116 , 2841 neilsen , e. , & tsvetanov , z. 1999 , astro - ph 9902164 ostrov , p. , forte , j. , & geisler , d. 1998 , , 116 , 2854 puzia , t. , kissler - patig , m. , & brodie , j. 1999 , submitted schindler , s. , binggeli , b. , & bhringer , h. 1999 , , 343 , 420 schlegel , d. , finkbeiner , d. , & davis , m. 1998 , , 500 , 525 silverman , b.w . , 1986 , density estimation for statistics and data analysis ( new york : chapman and hall ) whitmore , b. , sparks , w. , lucas , r. , macchetto , r. , & biretta , j. 1995 , , 454 , l73 whitmore , b.c . , miller , b.w . , schweizer , f. , & fall , s.m . 1997 , , 114 , 1797 williams , r.e . , 1996 , , 112 , 1335 worthey , g. 1994 , , 95 , 107 zepf , s.e . , & ashman , k.m . 1993 , , 264 , 611","summary":", we consider either a larger age spread in the field populations or the possibility that cluster galaxies are always affected by significant accretion whereas some field galaxies could host pure `` in situ '' formed populations .","abstract":"we have compiled data for the globular cluster systems of 50 galaxies from the hst wfpc2 archive , of which 43 are type s0 or earlier . in this paper , we present the data set and derive the color distributions . we derive the first four moments of the color distributions , as well as a measure for their non  unimodality . the number of globular clusters in each galaxy ranges from 18 ( in ngc  2778 ) to 781 ( ngc  5846 ) . for those systems having more than 100 clusters , seven of sixteen ( 44% ) show significant bimodality . overall , roughly half of all the systems in our sample show hints of a bimodal color distribution . in general , the distributions of the faint galaxies are consistent with unimodality , whereas those of the brighter galaxies are not . we also find a number of systems with narrow color distributions  with both mean red and blue colors  suggesting that systems exist with only metal  rich or only metal  poor globular clusters . we discuss their possible origins .    in comparing the moments of the distributions with various galaxy properties for the early - type galaxies , we find the following difference in the correlations between the field and cluster galaxy populations : the peak color of the globular cluster distribution correlates well with the central velocity dispersion  and hence the mg2 index and total luminosity  for galaxies in cluster environments ; there exists no such correlation for field galaxies . this difference between cluster and field galaxies possibly reflects different formation scenarios for their globular cluster systems . among the explanations for such a correlation , we consider either a larger age spread in the field populations or the possibility that cluster galaxies are always affected by significant accretion whereas some field galaxies could host pure `` in situ '' formed populations ."}
{"article_id":"gr-qc0702100","section_id":"i","document":"the problem of generating gravitational radiation in the laboratory has historically been an exceedingly difficult one because of the extreme smallness of newton s constant @xmath0 and the extreme largeness of the speed of light @xmath1 . this paper explores situations in which the introduction of yet another physical constant , namely planck s constant @xmath2 , due to its extreme smallness , can under certain circumstances lead to the efficient generation , as well as detection , of gravity waves . under these circumstances , the reciprocity principle ( i.e. , time - reversal symmetry ) demands the existence of nonnegligible back - actions of a quantum measuring device upon incident gravitational radiation fields . this leads to the possibility of generating , as well as detecting , gravity waves in a symmetric manner . the quantum approach being suggested here is in stark contrast to the classical , test - particle approaches being taken in contemporary , large - scale gravity - wave experiments , which are based solely on classical physics . the back - actions of classical measuring devices such as weber bars and large laser interferometers upon the incident gravitational fields that are being measured , are completely negligible . hence they can only detect gravity waves from powerful astronomical sources such as supernovae @xcite , but they certainly can not generate these waves .    specifically , the quantum physics of planck - mass - scale millikan oil drops  consisting of electron - coated superfluid helium drops at milli - kelvin - scale temperatures in the presence of tesla - scale magnetic fields , will be explored to see if radiative couplings mediated by such drops are large enough to be experimentally interesting . we shall see that numerical estimates based on quantum mechanics lead to the conclusion that efficient quantum transducers between electromagnetic and gravitational waves consisting of pairs of such drops should indeed be possible to implement in table - top - scale experiments . such experiments , some of which will be described below , have become practical to perform because of advances in dilution refrigerator technology , and i am planning to perform them with my colleagues at the new 10th campus of the university of california at merced . these experiments will explore some interesting new physics lying at the interface of quantum mechanics and general relativity , in which gravitational radiative effects on macroscopically coherent , charged quantum systems , and their reciprocal effects back on gravitational radiation fields , should become observable .    the paper is organized as follows : sections 2 and 3 introduce the ratio of coupling constants of gravity to electricity for two electrons in the vacuum , which ratio also applies to the radiative powers emitted by these electrons when they are set into motion . section 4 introduces the planck mass scale in the context of the low temperature physics of macroscopically coherent , charged quantum matter . maxwell - like equations for weak gravitational radiation fields that result from linearizing einstein s equations are introduced in section 5 , and the boundary conditions and the solutions of these equations for the reflections of gravity waves from superconductors and quantum hall fluids are discussed . in sections 7 and 8 , millikan oil drops  are described in more detail , and their role as quantum transducers in a hertz - like experiment to generate and detect gravitational radiation is discussed.section 9 examines the quantum conditions for these drops to exhibit a mssbauer - like response to radiation fields . in section 10 , time - reversal symmetry is applied to the differential scattering cross - section , and an estimation of the total cross - section based on the maxwell - like equations introduced in section 5 is made for a pair of mie - resonant drops . a common misconception that the drops are too heavy to move appreciably , which ignores the role of the equivalence principle , is corrected in section 11 . the final three sections present numerical considerations to show the feasibility of the hertz - like experiment , and discuss its possible applications .","summary":"should be practical to perform .","abstract":"pairs of planck - mass - scale drops of superfluid helium coated by electrons ( i.e. , millikan oil drops ) , when levitated in the presence of strong magnetic fields and at low temperatures , can be efficient quantum transducers between electromagnetic ( em ) and gravitational ( gr ) radiation . a hertz - like experiment , in which em waves are converted at the source into gr waves , and then back - converted at the receiver from gr waves back into em waves , should be practical to perform . this would open up observations of the gravity - wave analog of the cosmic microwave background from the extremely early big bang , and also communications directly through the interior of the earth ."}
{"article_id":"1509.05604","section_id":"i","document":"the origin of neutrino masses is one of the great open puzzles in particle physics . one of the best motivated mechanisms for generating the observed masses is the type i seesaw mechanism @xcite , where @xmath0 right - handed neutrinos are added to the particle content of the standard model ( sm ) . when the masses of the right - handed neutrinos are much larger than the electroweak scale ( ew ) , this can explain the smallness of the masses of the light neutrinos ( after ew symmetry breaking ) . the type i seesaw mechanism can also be embedded in extensions of the sm such as e.g.  in two - higgs - doublet models or in the minimal supersymmetric standard model ( mssm ) .    in order to compare the prediction of neutrino models , which are defined at high energy , with the experimental data obtained at low energies , one has to calculate the renormalization group ( rg ) running of the relevant quantities . above the mass threshold of the heaviest of the right - handed neutrinos , these include in particular the neutrino yukawa couplings and the mass matrix of the right - handed neutrinos . below the mass threshold of the lightest of the right - handed neutrinos , the heavy particles are integrated out of the theory generating the effective dimension five neutrino mass operator , and its running has to be computed . between the mass thresholds , one has to deal with the effective theories where the neutrino yukawa matrix , the right - handed neutrino mass matrix as well as the neutrino mass operator are present . at the thresholds , the effective theories are matched . the renormalization group equations ( rges ) for the running of the neutrino mass operator have been calculated at one - loop in the sm @xcite , in two - higgs - doublet models @xcite and in the mssm @xcite . for one - loop running tree - level matching is sufficient , and the formalism and rges for the intermediate effective theories have been described in @xcite . in the mssm extended by @xmath0 right - handed neutrinos , the rge for the running of the neutrino mass operator has been calculated at the two - loop level in @xcite . however , for consistent two - loop running one also needs to compute the matching of the effective theories at one - loop level , also referred to as the one - loop threshold corrections .    in this work , we calculate the one - loop matching formulae in the mssm extended by @xmath0 right - handed neutrinos using supergraph techniques . moreover we present a general formula for one - loop matching of superpotential operators which can be applied to any supersymmetric theory where chiral superfields are integrated and the effective theories are matched at the mass thresholds . we also comment on other choices of the matching scale , which may simplify the matching procedure in some cases . the paper is organized as follows : in section 2 we review neutrino mass generation in the mssm extended by @xmath0 right - handed neutrinos , and the effective theories which arise from integrating out the heavy particles at their mass thresholds . section 3 contains a brief review of the method for calculating rges using supergraph techniques ( following @xcite ) . the general formula for one - loop matching of superpotential operators in supersymmetric theories , when integrating out chiral superfields , is derived in section 4 and applied to the mssm extended by @xmath0 right - handed neutrinos in section 5 . section 6 contains a summary and our conclusions .","summary":"the renormalization group ( rg ) running of the neutrino mass operator is required for comparing the predictions of neutrino models at high energies with the experimental data at low energies . in the type i seesaw scenario with right - handed neutrinos , the effective theories are matched . when calculating the two - loop rg running , the matching has to be performed at the one - loop level . in this work , we calculate the one - loop matching formulae in the mssm extended by right - handed neutrinos using supergraph techniques . moreover we present a general formula for one - loop matching of superpotential operators which can readily be applied to any supersymmetric theory where chiral superfields are integrated out .     +    stefan antusch and eros cazzato    _ department of physics , university of basel , _    _ klingelbergstr .  82 , ch-4056 basel , switzerland _   ","abstract":"the renormalization group ( rg ) running of the neutrino mass operator is required for comparing the predictions of neutrino models at high energies with the experimental data at low energies . in the type i seesaw scenario with right - handed neutrinos , the rg running is also performed in the effective theories above and between the thresholds given by the masses of the right - handed neutrinos . at these thresholds , the effective theories are matched . when calculating the two - loop rg running , the matching has to be performed at the one - loop level . in this work , we calculate the one - loop matching formulae in the mssm extended by right - handed neutrinos using supergraph techniques . moreover we present a general formula for one - loop matching of superpotential operators which can readily be applied to any supersymmetric theory where chiral superfields are integrated out .     +    stefan antusch and eros cazzato    _ department of physics , university of basel , _    _ klingelbergstr .  82 , ch-4056 basel , switzerland _     _ max - planck - institut fr physik ( werner - heisenberg - institut ) , _    _ fhringer ring 6 , d-80805 mnchen , germany _"}
{"article_id":"1407.7525","section_id":"c","document":"both spatially resolved line ratios and x - ray data ( detections and stacked non - detections ) indicate that there is little or no difference in agn fraction between clumpy galaxies and those with smoother morphologies . while integrated line ratios in the mex method suggest a slightly higher agn fraction among clumpy galaxies , the lack of a nuclear agn signature suggests that this is due to extended phenomena like dense star - forming clumps rather than black hole growth . galaxies at @xmath0 in each morphology category have similar agn fractions of @xmath52530% , depending on whether x - ray data or spatially resolved line ratios are used for agn selection . we discuss several implications of these results below . in section 3.2 we argued that the high @xmath44}}/{\\hbox{{\\rm h}$\\beta$}}$ ] ratio in the extended regions of clumpy galaxies indicates shocks or high - ionization  regions rather than agn activity ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , it is instead possible that some clumpy galaxies host off - nuclear agn ( e.g. * ? ? ? * ; * ? ? ? we test for the presence of off - nuclear agn by creating a 2d stack of clumpy galaxies classified as mex - agns , centering on the @xmath44}}$ ] emission lines rather than the continuum trace . the brightest knot of @xmath44}}$ ] emission would be most likely to correspond to any off - nuclear agn}}$ ] knot corresponds to an agn is inaccurate if there is large - scale dust asymmetrically obscuring an agn narrow - line region . ] . the `` nuclear '' region of the @xmath44}}$]-centered stack corresponds to the brightest @xmath44}}$ ] knots rather than the galaxy center , and should therefore be where off - nuclear agns are most likely to reside . figure [ fig : bpt_linectr ] compares the nuclear and extended @xmath44}}/{\\hbox{{\\rm h}$\\beta$}}$ ] ratios for the continuum - centered stack with the @xmath44}}$]-centered stack of clumpy galaxies . the right panel suggests that the brightest @xmath44}}$ ] knots are somewhat _ _ l__ess likely to host agns than the galaxy centers . the lack of widespread off - nuclear agns is also supported by the x - ray data , which indicate that clumpy galaxies do not host a greater number of x - ray agns ( whether nuclear or off - nuclear ) than smoother mass - matched galaxies . we conclude that there is unlikely to be a large population of off - nuclear agns in clumpy galaxies misclassified by the spatially resolved line ratio method .      at first glance , our @xmath3 result is in apparent contrast to the preference for agn in clumpy galaxies at @xmath8 observed by @xcite . our clumpy galaxy sample has very similar images and morphologies to theirs , as seen in a comparison of figure [ fig : images ] with figure 4 of @xcite . and although we study a much larger sample ( three times more clumpy galaxies ) , @xcite performed a comprehensive bootstrap analysis which indicates that sample size is very unlikely to lead to the difference . our studies differ greatly , however , in the comparison samples of smooth galaxies . @xcite required that both their clumpy and smooth galaxy samples be extended disks . meanwhile we impose no requirements on morphology beyond the clumpiness classification , and figure [ fig : sersic ] demonstrates that our @xmath2 clumpy and smooth galaxies are quite different in size and @xcite index . these quantities were measured using galfit @xcite and presented by @xcite . clumpy galaxies are much more likely to be extended disks , with a median semi - major axis of @xmath173 and 41/44 galaxies having disk - dominated srsic indices ( @xmath174 ) . the smooth galaxies are still mostly disk - dominated , as 30/41 have @xmath174 , but they are significantly smaller ( with a median semi - major axis of @xmath175 ) and have higher srsic indices . it is interesting that so few smooth extended disks are observed in candels and 3d - hst . the data are sensitive to the @xmath2 star - forming main sequence at @xmath176 ( figure [ fig : sfrmass ] ) , and so if smooth extended disks exist they must be low - mass and/or weakly star - forming . @xcite and @xcite argue that ordered disks are rare in @xmath9 galaxies of any mass , suggesting that the lack of smooth extended disks at @xmath2 is a consequence of galaxy evolution rather than selection effects . regardless , the lack of smooth extended disks at @xmath2 means we can not perform the same comparison between clumpy and smooth extended disks as @xcite at @xmath8 . instead we conclude that clumpy extended galaxies have the same agn fraction as more compact and higher - sersic smooth galaxies matched in stellar mass . our results demonstrate that clumpy galaxies at @xmath2 are no more likely to host agns than are smooth galaxies of the same stellar mass and similar star formation rate . what does this indicate about agn fueling modes at @xmath2 ? @xcite argue that compact star - forming galaxies ( also called blue nuggets ) might actually be constructed by a history of violent disk instabilities . our smooth galaxies , which tend to be more compact and bulgy than the clumpy extended disks , have sizes and sersic indices consistent with this category ( see also * ? ? ? the observed similarity in agn fraction between @xmath10 clumpy and smooth galaxies would then indicate that nuclear inflow onto the agn must persist until after the galaxy becomes stable and the star - forming clumps are no longer visible . in this scenario the violent disk instabilities are responsible for building a gas reservoir in the galaxy s center . since the actual nuclear inflow onto the agn persists into the smooth compact galaxy phase , it must not depend on violent instabilities in the larger disk . so while the gas reservoir is deposited by violent disk instabilities , the agn fueling within @xmath521  kpc must instead be driven by secular processes .    on the other hand , the disk - dominated nature of the smooth galaxies might imply that they are unlikely to have experienced violent mixing in the past from extreme disk instabilities ( or major mergers ) . it is also not clear that the smooth galaxies are older than the clumpy galaxies , given their similar position in the sfr - m * plane ( excepting the most massive galaxies : see figure [ fig : sfrmass ] ) . this might imply that even the large - scale fueling occurs via secular processes , perhaps due to stochastic turbulence from the high gas fractions which are common in @xmath2 galaxies @xcite . indeed , @xcite predict that this turbulence - driven stochastic fueling is the dominant mode of smbh growth for @xmath2 galaxies with @xmath177 ( or @xmath178 ) : the same mass range occupied by much of our sample . assuming that the smooth and clumpy morphologies in our sample trace different fueling modes , then our data best support the scenario of @xcite , where agn growth depends not on fueling mode , but on gas fraction .","summary":"the lack of smooth extended disks is probably a general feature of the galaxy population , and means we can not directly compare with the clumpy and smooth extended disks observed at lower redshift .","abstract":"we use candels imaging , 3d - hst spectroscopy , and chandra x - ray data to investigate if active galactic nuclei ( agns ) are preferentially fueled by violent disk instabilities funneling gas into galaxy centers at . we select galaxies undergoing gravitational instabilities using the number of clumps and degree of patchiness as proxies . the candels visual classification system is used to identify 44 clumpy disk galaxies , along with mass - matched comparison samples of smooth and intermediate morphology galaxies . we note that , despite being being mass - matched and having similar star formation rates , the smoother galaxies tend to be smaller disks with more prominent bulges compared to the clumpy galaxies . the lack of smooth extended disks is probably a general feature of the galaxy population , and means we can not directly compare with the clumpy and smooth extended disks observed at lower redshift . we find that clumpy galaxies have slightly enhanced agn fractions selected by integrated line ratios ( in the mass - excitation method ) , but the spatially resolved line ratios indicate this is likely due to extended phenomena rather than nuclear agns . meanwhile the x - ray data show that clumpy , smooth , and intermediate galaxies have nearly indistinguishable agn fractions derived from both individual detections and stacked non - detections . the data demonstrate that agn fueling modes at - whether violent disk instabilities or secular processes - are as efficient in smooth galaxies as they are in clumpy galaxies ."}
{"article_id":"1407.7525","section_id":"i","document":"we use spatially resolved line ratios and x - ray data to demonstrate that @xmath3 clumpy galaxies are no more likely to host agns than are smoother galaxies at the same redshift . while integrated line ratios indicate a higher agn fraction in clumpy galaxies , the spatially resolved emission lines show that this is likely due to extended phenomena ( like shocks or high - ionization @xmath91 regions ) rather than nuclear ( or off - nuclear ) agns . while the smooth galaxies have the same masses and nearly the same star formation rates , they are somewhat smaller and not quite as disk - dominated as the clumpy galaxies . whatever process drives agn fueling in the smooth galaxies is just as efficient as are violent disk instabilities in clumpy galaxies at @xmath2 . we thank frederic bournaud for valuable discussion which significantly improved this work . support was provided by nasa through hubble fellowship grant # 51330 awarded by 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scoville ( arxiv:1112.3970 )    trump , j. r. , konidaris , n. p. , koo , d. c.  2013a , apj , 763 , 6    trump , j. r. , hsu , a. d. , fang , j. j.  2013b , apj , 763 , 133    van der laan , t. p. r. , schinnerer , e. , boeker , t. & armus , l. 2013 , a&a , 560 , 99    van der wel , a. , bell , e. f. , hussler , b. 2012 , apjs , 203 , 24    veilleux , s. & osterbrock , d. e.  1987 , apjs , 63 , 295    wright , s. a. , larkin , j. e. , graham , j. r. & ma , c .- p . 2010 , apj , 711 , 1291    wuyts , s. , frster schreiber , n. m. , van der wel , a. 2011 , apj , 742 , 96    wuyts , s. , frster schreiber , n. m. , genzel , r. 2012 , apj , 753 , 114    xue , y. q. , luo , b. , brandt , w. n.  2011 , apjs , 195 , 10    xue , y. q. , wang , s. x. , brandt , w. n.  2012 , apj , 758 , 129    yan , r. & blanton , m. r.  2012 , apj , 747 , 61    york , d.  g.  2000 , aj , 120 , 1579","summary":"we use candels imaging , 3d - hst spectroscopy , and chandra x - ray data to investigate if active galactic nuclei ( agns ) are preferentially fueled by violent disk instabilities funneling gas into galaxy centers at . we note that , despite being being mass - matched and having similar star formation rates , the smoother galaxies tend to be smaller disks with more prominent bulges compared to the clumpy galaxies . we find that clumpy galaxies have slightly enhanced agn fractions selected by integrated line ratios ( in the mass - excitation method ) , but the spatially resolved line ratios indicate this is likely due to extended phenomena rather than nuclear agns . the data demonstrate that agn fueling modes at - whether violent disk instabilities or secular processes - are as efficient in smooth galaxies as they are in clumpy galaxies .","abstract":"we use candels imaging , 3d - hst spectroscopy , and chandra x - ray data to investigate if active galactic nuclei ( agns ) are preferentially fueled by violent disk instabilities funneling gas into galaxy centers at . we select galaxies undergoing gravitational instabilities using the number of clumps and degree of patchiness as proxies . the candels visual classification system is used to identify 44 clumpy disk galaxies , along with mass - matched comparison samples of smooth and intermediate morphology galaxies . we note that , despite being being mass - matched and having similar star formation rates , the smoother galaxies tend to be smaller disks with more prominent bulges compared to the clumpy galaxies . the lack of smooth extended disks is probably a general feature of the galaxy population , and means we can not directly compare with the clumpy and smooth extended disks observed at lower redshift . we find that clumpy galaxies have slightly enhanced agn fractions selected by integrated line ratios ( in the mass - excitation method ) , but the spatially resolved line ratios indicate this is likely due to extended phenomena rather than nuclear agns . meanwhile the x - ray data show that clumpy , smooth , and intermediate galaxies have nearly indistinguishable agn fractions derived from both individual detections and stacked non - detections . the data demonstrate that agn fueling modes at - whether violent disk instabilities or secular processes - are as efficient in smooth galaxies as they are in clumpy galaxies ."}
{"article_id":"1309.5301","section_id":"i","document":"futures  @xcite are an attractive way to structure many parallel programs because they are easy to reason about ( especially if the futures have no side - effects ) and they lend themselves well to sophisticated dynamic scheduling algorithms , such as work - stealing  @xcite and its variations , that ensure high processor utilization . at the same time , however , modern multicore architectures employ complex multi - level memory hierarchies , and technology trends are increasing the relative performance differences among the various levels of memory . as a result , processor utilization can no longer be the sole figure of merit for schedulers . instead , the _ cache locality _ of the parallel execution will become increasingly critical to overall performance . as a result , cache locality will increasingly join processor utilization as a criterion for evaluating dynamic scheduling algorithms . several researchers  @xcite have shown , however , that introducing parallelism through the use of futures can sometimes substantially reduce cache locality . in the worst case , if we add futures to a sequential program , a parallel execution managed by a work - stealing scheduler can incur @xmath0 deviations , which , as we show , implies @xmath1 more cache misses than the sequential execution . here , @xmath2 is the number of cache lines , @xmath3 is the number of processors , @xmath4 is the number of touches , and @xmath5 is the computation s _ span _ ( or _ critical path _ ) . as technology trends cause the cost of cache misses to increase , this additional cost is troubling . this paper makes the following three contributions . first , we show that if futures are used in a simple , disciplined way , then the situation with respect to cache locality is much better : if each future is touched only once , either by the thread that created it , or by a later descendant of that thread , then parallel executions with work stealing can incur at most @xmath6 additional cache misses , a substantial improvement over the unstructured case . this result provides a simple way to identify computations for which introducing futures will not incur a high cost in cache locality , as well as providing guidelines for the design of future parallel computations . ( informally , we think these guidelines are natural , and correspond to structures programmers are likely to use anyway . ) our second contribution is to observe that when the scheduler has a choice between running the thread that created a future , and the thread that implements the future , running the future thread first provides better cache locality . finally , we show that certain variations of structured computation also have good cache locality .    the paper is organized as follows . section  [ section : model ] describes the model for future - parallel computations . in section  [ section : work - stealing and cache locality ] , we describe parsimonious work - stealing schedulers , and briefly discuss their cache performance measures . in section [ section_structured ] , we define some restricted forms of structured future - parallel computations . among them , we highlight structured single - touch computations , which , we believe , are likely to arise naturally in many programs . in section  [ section_futurethreadfirst ] , we prove that work - stealing schedulers on structured single - touch computations incur only @xmath6 additional cache misses , if a processor always chooses the future to execute first when it creates that future . we also prove this bound is tight within a factor of @xmath2 . in section  [ section : parent thread first at each fork ] , we show that if a processor chooses the current thread over the future thread when it creates that future , then the cache locality of a structured single - touch computation can be much worse . in section  [ section : other kinds of structured computations ] , we show that some other kinds of structured future - parallel computations also achieve relatively good cache locality . finally , we present conclusions in section  [ section : conclusions ] .","summary":"a thread creates a future to hold the results of a computation , which may or may not be executed in parallel . recent research has shown that while futures can , of course , enhance parallelism in a structured way , they can have a deleterious effect on cache locality . in the worst case , futures can incur deviations , which implies additional cache misses , where is the number of cache lines , is the number of processors , is the number of touches , and is the _ computation span_. since cache locality has a large impact on software performance on modern multicores , this result is troubling .    in this paper , however , we show that if futures are used in a simple , disciplined way , then the situation is much better : if each future is touched only once , either by the thread that created it , or by a later descendant of the thread that created it , then parallel executions with work stealing can incur at most additional cache misses , a substantial improvement . = 10000 = 10000    scheduling ; work stealing ; futures ; parallel programming ; cache locality ; performance bounds","abstract":"in _ fork - join parallelism _ , a sequential program is split into a directed acyclic graph of tasks linked by directed dependency edges , and the tasks are executed , possibly in parallel , in an order consistent with their dependencies . a popular and effective way to extend fork - join parallelism is to allow threads to create _ a thread creates a future to hold the results of a computation , which may or may not be executed in parallel . that result is returned when some thread _ touches _ that future , blocking if necessary until the result is ready .    recent research has shown that while futures can , of course , enhance parallelism in a structured way , they can have a deleterious effect on cache locality . in the worst case , futures can incur deviations , which implies additional cache misses , where is the number of cache lines , is the number of processors , is the number of touches , and is the _ computation span_. since cache locality has a large impact on software performance on modern multicores , this result is troubling .    in this paper , however , we show that if futures are used in a simple , disciplined way , then the situation is much better : if each future is touched only once , either by the thread that created it , or by a later descendant of the thread that created it , then parallel executions with work stealing can incur at most additional cache misses , a substantial improvement . this structured use of futures is characteristic of many ( but not all ) parallel applications .    = 10000 = 10000    scheduling ; work stealing ; futures ; parallel programming ; cache locality ; performance bounds"}
{"article_id":"nlin0012055","section_id":"i","document":"the two - centre coulomb problem , that is , the problem of solving the schrdinger equation for the motion of an electron with the charge @xmath8 @xmath9 in the field of two fixed coulomb centres with charges @xmath10 and @xmath11 at the distance @xmath12 from each other , plays an important role in several fields of theoretical physics , for example in the theory of diatomic molecules , in scattering theory , and in the three - body problem . the two - centre coulomb problem has therefore been the subject of extensive studies both by numerical and by approximate analytical methods , and hence the literature on this problem is very comprehensive . in spite of this fact it is still of interest to continue the treatment of this problem for arbitrary values of @xmath13 and @xmath12 . one reason for this is that the numerically exact solution of the problem meets with difficulties when @xmath14 increases . there appear also numerical difficulties for large values of @xmath12 . for a general review of the problem we refer to eyring _ @xcite , herzberg @xcite , slater @xcite and rosen @xcite .    ignoring the finiteness of the mass of the protons , bates _ et al._@xcite obtained important numerical results for the hydrogen molecule ion . corresponding numerical results were obtained by wallis and hulburt @xcite for the homonuclear one - electron two - centre problem , by bates and carson @xcite for the ion @xmath15 , by wind @xcite for the ground state of the hydrogen molecule ion , by peek @xcite for the states @xmath16 and @xmath17 of the hydrogen molecule ion , and by ponomarev and puzynina @xcite for several states of the coulomb two - centre system with @xmath18 and @xmath19 . hunter and pritchard@xcite used a numerical procedure to compute nonadiabatic energies for the first few rotation - vibration levels of @xmath20 , @xmath21 and @xmath22 . for the hydrogen molecule ion rosenthal and e. bright wilson , jr . , @xcite calculated an accurate value of the ground state energy which is in agreement with the values obtained by wind @xcite and peek@xcite . for different internuclear distances bates and reid @xcite , murai @xcite and murai and takatsu @xcite calculated electronic energies for various states of the hydrogen molecule ion under the assumption of infinite proton mass . for a large range of internuclear distances winter _ et al._@xcite made very accurate calculations for the lowest 20 states of the molecule ion @xmath23 . klaus@xcite studied the electronic energy of the ground state of the hydrogen molecule ion for small internuclear separation @xmath12 and confirmed the remarkable discovery by byers brown and steiner @xcite that the electronic energy can not be expanded in powers of @xmath12 alone , but that powers of ln@xmath12 must also be included . klaus @xcite also obtained for the hydrogen molecule ion further terms in the series given by byers brown and steiner @xcite for the general two - centre coulomb problem . there exist also various approximate analytical methods for solving the quantal two - centre coulomb problem . in one of them one uses the quasiclassical approximation , that is , the first order of the phase - integral approximation . in using this method , one encountered in the early papers difficulties associated with the divergence of the phase - integral due to an inappropriate choice of the phase - integrand ( also called the quasimomentum ) , which is not determined quite uniquely . different authors have mastered these difficulties in different ways , but no single unifying method has until now been proposed for the two - centre coulomb problem . an essential feature in our method is the use of the phase - integral approximation generated from an unspecified base function ; see the appendix . the semiclassical quantization of the low - lying electronic states of the hydrogen molecule ion was treated by strand and reinhardt @xcite . pajunen @xcite calculated the energy levels of the hydrogen molecule ion ( under the assumption of infinitely heavy nuclei ) in the first and the third order of the phase - integral approximation . although he refers to one of the papers ( his reference 10 ) in which the phase - integral approximation generated from an unspecified base function was introduced , he does not use the freedom to choose optimal expressions for the functions that he denotes by @xmath24 and @xmath25 , and that in the present paper correspond to the more general base functions @xmath26 and @xmath27 , respectively . in the present paper we shall make full use of the possibility to choose @xmath26 and @xmath27 most conveniently .    the phase - integral method , in which one uses the phase - integral approximation generated from an unspecified base function @xcite , offers a method for mastering the previously mentioned difficulties in a unified way for an arbitrary order of the phase - integral approximation . in the present paper we shall apply this method to the quantal two - centre coulomb problem with fixed coulomb centres .    for the convenience of the reader a short review of the phase - integral method and formulas to be used are given in the appendix . the present paper will be the basis for further work , in which convenient transformations to complete elliptic integrals will be used , analogously as in papers by lakshmanan and kaliappan@xcite and lakshmanan _ et al._@xcite . thereby the contour integrals , occurring in the quantization conditions , will be expressed in terms of complete elliptic integrals .","summary":"self - contained , a short review of the phase - integral method is given in the appendix .","abstract":"the present paper concerns the derivation of phase - integral quantization conditions for the two - centre coulomb problem under the assumption that the two coulomb centres are fixed . with this restriction we treat the general two - centre coulomb problem according to the phase - integral method , in which one uses an _ a priori _ unspecified _ base function_. we consider base functions containing three unspecified parameters and . when the absolute value of the magnetic quantum number is not too small , it is most appropriate to choose . when , on the other hand , is sufficiently small , it is most appropriate to choose . arbitrary - order phase - integral quantization conditions are obtained for these choices of . the parameters and are determined from the requirement that the results of the first and the third order of the phase - integral approximation coincide , which makes the first - order approximation as good as possible .    in order to make the paper to some extent self - contained , a short review of the phase - integral method is given in the appendix ."}
{"article_id":"nlin0012055","section_id":"m","document":"the essential features of the phase - integral method are briefly sketched in the appendix . the phase - integral solutions of the differential equations ( 2.8a ) and ( 2.8b ) , respectively , are linear combinations of the phase - integral functions    @xmath57    and @xmath58    respectively , where @xmath59 and @xmath60 , respectively , are generated according to ( a5a , b ) , ( a6a , b , c ) , ( a3 ) and ( a2 ) in the appendix , with @xmath61 replaced by the appropriate functions @xmath62 and @xmath63 , respectively , the quantities pertaining to the @xmath64-equation being characterized by a tilde .      as is seen from ( 2.9a , b ) , the functions @xmath65 and @xmath66 have poles at @xmath67 and @xmath68 , respectively ; these poles are of the second order if @xmath69 , but of the first order if @xmath70 . furthermore , we note that when @xmath71 the coefficients of the second - order poles differ from @xmath72 , while for @xmath73 they are equal to @xmath72 . there are two main alternatives , discussed in the appendix for the case of the radial schrdinger equation , for choosing the base functions generating the phase - integral functions ( 3.1a ) and ( 3.1b ) . unifying these two alternatives , we choose the squares of the base functions to be    @xmath74    @xmath75    where @xmath0 and @xmath1 are parameters , the choice of which we shall discuss below . the introduction of these parameters increases essentially the flexibility of the phase - integral formulas to be obtained .    by choosing @xmath76 one obtains in the limit when @xmath77 the energy e and the reduced separation constant @xmath78 correctly from the first - order phase - integral quantization conditions ( to be derived in section 3.2 ) . for arbitrary values of @xmath12 it is most appropriate to determine @xmath6 and @xmath7 as functions of @xmath12 such that one obtains the same value of @xmath79 ( i.e. , of the energy ) and also of @xmath78 in the first and in the third order of the phase - integral approximation . one thereby achieves the optimal accuracy obtainable from the first - order quantization conditions . we emphasize that this can be achieved by the use of the phase - integral approximation generated from an unspecified base function ( described in the appendix ) , but can not be achieved by means of the jwkb approximation . the decisive properties of the phase - integral approximation in question versus the jwkb approximation have been explained in some detail by dammert and p.o . frman @xcite and by frman and frman @xcite . when @xmath4 is not too small , we choose @xmath80 , but when @xmath4 is sufficiently small we choose @xmath81 . for @xmath82 one should always choose @xmath83 . the two alternatives @xmath80 and @xmath81 yield solutions with different properties . when @xmath80 the phase integral solutions of the differential equations ( 2.8a ) and ( 2.8b ) remain valid as @xmath84 and @xmath85 , respectively . when @xmath81 the phase - integral solutions of the differential equations in question break down as @xmath86 and @xmath87 , respectively , but the regular solutions of the @xmath64- and @xmath56-equations can be obtained at some distances from those points by the use of the connection formula described in subsection a.2.b of the appendix , when one there replaces @xmath88 by @xmath89 ; cf . ( 2.9a , b ) . the wave functions obtained in that way are expected to be the more accurate the stronger the coulomb singularities of @xmath65 and @xmath66 at @xmath90 and @xmath91 are . however , even if the coulomb singularities are strong , these wave functions are not expected to be good if @xmath4 is too large , in which case one should use @xmath92 , as mentioned in the beginning of this paragraph .    using the terminology classically allowed region and classically forbidden region in a generalized sense , _ viz . _ to characterize regions where @xmath93 or @xmath94 is larger than zero and less than zero , respectively , we shall now discuss the wave functions pertaining to the @xmath64-equation and the @xmath56-equation .      according to ( 3.2a ) the function @xmath95 , where @xmath96 , always corresponds to a single - well potential .    for @xmath3 there are four zeros of @xmath93 , which we denote by @xmath97 and @xmath98 ; see fig . 1(a ) . the zeros @xmath99 and @xmath100 may be real and both less than 1 , or they may be complex conjugate . the zeros @xmath101 and @xmath102 are real . there is thus a classically allowed region between @xmath103 and @xmath98 , but classically forbidden regions for @xmath104 and @xmath105 . the phase - integral wave functions generated from @xmath106 are good at @xmath107 , and we can use the arbitrary - order connection formula , given by ( a13 ) and ( a14 ) in the appendix , for tracing the physically acceptable wave function from the classically forbidden region between @xmath108 and @xmath103 to the classically allowed region , that is , the region between @xmath103 and @xmath102 where @xmath109 ; see fig . 1(a ) .    for @xmath83 there are two zeros of @xmath93 , which we denote by @xmath110 and @xmath111 . the classically allowed region lies between @xmath103 and @xmath98 when @xmath112 , but between 1 and @xmath98 when @xmath113 ; see fig . the phase - integral wave function is not good at @xmath114 , but for the physically acceptable wave function one can obtain a phase - integral expression in the interior of the classically allowed region , when @xmath112 and the classically forbidden region between @xmath108 and @xmath103 is sufficiently large , by means of the arbitrary - order connection formula given by ( a13 ) and ( a14 ) in the appendix , and when @xmath113 by means of the connection formula presented in subsection a.2.b of the appendix .    both when @xmath115 and when @xmath83 the wave function , obtained in the classically allowed region to the left of @xmath98 as described above , can be joined to the physically acceptable wave function traced from the classically forbidden region to the right of @xmath98 into the classically allowed region to the left of @xmath98 with the aid of the arbitrary - order connection formula given by ( a13 ) and ( a14 ) in the appendix . in this way alternative quantization conditions , corresponding to @xmath80 and @xmath81 , can be obtained . they can be combined into one quantization condition . 1 illustrates the two possible situations that the classically allowed region is delimited either by @xmath103 and @xmath98 [ fig . 1(a ) ] or by the pole at @xmath116 and the turning point at @xmath117 [ fig . 1(b ) ] . the function @xmath118 may correspond either to a single - well potential or to a double - well potential . for @xmath3 the phase - integral solution is valid at the poles @xmath91 ( which delimit classically forbidden regions ) and can be traced into the classically allowed region closest to the pole in question with the aid of the connection formula given by ( a13 ) and ( a14 ) in the appendix . when there is only one classically allowed region , one obtains the quantization condition by identifying the two expressions for the wave function in that region . this case applies when @xmath118 is a single - well potential ( fig . 2 ) , or when the energy lies so far above the top of an underdense barrier [ fig . 4(b ) ] that it is appropriate to disregard the presence of the complex conjugate zeros @xmath119 and @xmath120 of @xmath94 . when @xmath118 corresponds to a double - well potential , the wave function can be traced from the region on one side of the barrier to the region on the other side with the aid of the arbitrary - order connection formula for a barrier described in section a.3 of the appendix ; see fig . 3 and fig . 4 . joining the two expressions for the wave function thus obtained to each other , one obtains the quantization condition . when @xmath81 [ fig . 2 or fig . 4(b ) ] the phase - integral wave function is not good at @xmath121 , but at some distance from these points physically acceptable solutions can be obtained in the same classically allowed region by the use of the connection formulas presented in sections a.2 and a.3 of the appendix . thus one obtains two expressions for the wave function , and by identifying these expressions one obtains a quantization condition .        for the differential equation ( 2.8a ) the physically relevant interval is @xmath122 . the phase - integral quantization condition for the situation in fig . 1(a ) involves a contour integral in the complex @xmath64-plane encircling @xmath103 and @xmath98 , while the phase - integral quantization condition for the situation in fig . 1(b ) involves a contour integral encircling the simple pole at @xmath114 and the generalized classical turning point @xmath98 . the quantization condition ( a31 ) in the appendix applies to the first situation , and the quantization condition ( a32 ) in the appendix applies to the second situation . introducing the notations    @xmath123    @xmath124    @xmath125    @xmath126    where @xmath59 is obtained according to ( a5a , b ) , ( a6a , b , c ) , ( a3 ) and ( a2 ) in the appendix , and @xmath127 and @xmath128 are the appropriate contours of integration pertaining to @xmath112 and @xmath113 , respectively , and shown in fig . 1(a ) and fig . 1(b ) , respectively , we can write the two quantization conditions corresponding to @xmath112 and @xmath113 as follows    @xmath129    @xmath130    where @xmath131 is an integer . if , when @xmath3 and hence @xmath112 , we enlarge the contour of integration @xmath127 in fig . 1(a ) , so that the new contour @xmath132 encloses the turning points @xmath103 and @xmath98 as well as the pole at @xmath114 , and if we compensate in ( 3.5a ) along with ( 3.3a , b ) for this change by taking the residue of the integrand at @xmath107 into account , we obtain a general quantization condition , valid for both cases @xmath112 and @xmath113 , i.e. , for both situations depicted in fig . 1 , @xmath133 . @xmath134 besides condensing the two alternative quantization conditions ( 3.5a ) and ( 3.5b ) nicely into one formula , the quantization condition ( 3.6 ) has the further merit that , if the integration along the contour is made numerically ( in cases where expressions in terms of complete elliptic integrals are not available ) , it may be advantageous to use the contour @xmath132 instead of @xmath127 when @xmath112 . the quantization condition ( 3.6 ) yields the value of the reduced separation constant @xmath78 as a function of @xmath79 and @xmath7 ; see ( 3.2a ) .      in the physically relevant interval @xmath135 the function @xmath118 may correspond to a single - well potential ( fig . 2 ) or to a double - well potential with a superdense ( fig . 3 ) or underdense ( fig . 4 ) barrier . when , in the case of an underdense barrier , the energy lies sufficiently far above the top of the barrier , it may be preferable to disregard the barrier and to treat the double - well potential problem as a single - well potential problem . when @xmath3 or @xmath81 , and @xmath118 is or can be considered as a single - well potential , and the classically allowed region is delimited by two simple zeros of @xmath94 , as shown in fig . 2 and in fig . 4(a ) , we obtain from ( a31 ) the single - well quantization condition    @xmath136    where by definition @xmath137 @xmath138 being a closed contour encircling the generalized classical turning points . note that in the derivation of ( 3.7 ) we have considered the classically forbidden regions to be thick also when @xmath81 ( fig . when @xmath3 we can with the aid of residue calculus write ( [ l1 ] ) along with ( [ l2 ] ) as    @xmath139    where @xmath140 is defined by @xmath141 @xmath142 being a closed contour encircling @xmath143 and @xmath144 ; see fig . 2 and fig . 4(a ) .    when @xmath81 , and the classically allowed region is delimited by two first - order poles of @xmath94 , as shown in fig . 4(b ) , and the energy lies far above the top of the barrier , one can consider @xmath118 as a single - well potential . from ( a33 ) one then obtains the quantization condition ( 3.9 ) with @xmath140 defined by ( 3.10 ) , where @xmath142 is now the contour in fig . we disregard the possibility that @xmath83 and the residues of @xmath94 at @xmath145 and @xmath146 have different signs , since this case has so far not appeared in the applications .    when @xmath118 corresponds to a double - well potential ( fig . 3 and fig 4 ) , which is usually the case , the quantization condition ( a39 ) gives @xmath147^\\frac{1}{2}}},\\ ] ] where    @xmath148    @xmath149    @xmath150    @xmath151    @xmath152    @xmath153    @xmath154    @xmath155    for the super - barrier case ( fig . 4 ) we can instead of ( 3.15b ) use the alternative formula @xmath156 which is useful in connection with the transformation to complete elliptic integrals . with the use of ( 3.13a , b ) , ( 3.14a , b ) and ( 3.15a,@xmath157 ) each one of the quantities @xmath158 and @xmath159 is then obtained as the real or imaginary part of an integral over the contour @xmath160 or @xmath161 . the contours of integration @xmath162 and @xmath163 for sub - barrier and super - barrier energies are shown in fig . 3 and fig . the analytic expressions for the quantity @xmath164 are given in terms of @xmath165 and @xmath166 by ( a28 ) and ( a29a , b , c ) in the appendix . the quantity @xmath164 is of decisive importance for energies in the neighbourhood of the top of the barrier . the quantities @xmath167 and @xmath168 are positive . the quantity @xmath169 is positive when @xmath119 and @xmath120 are real , it is equal to zero when @xmath119 and @xmath120 coincide , and it is negative when @xmath119 and @xmath120 are complex conjugate . the quantity @xmath170 may be positive or negative irrespectively of whether @xmath119 and @xmath120 are real or complex conjugate . analogously as we changed the original contour @xmath171 into @xmath132 , when dealing with the quantization condition ( 3.5a ) , we can , when @xmath3 , change the contours @xmath160 and @xmath161 depicted in fig . 3(a ) and fig . 4(a ) , so that , instead of letting them enclose only @xmath172 and @xmath173 , respectively , we make each one of them enclose also a pole , @xmath174 or @xmath175 , respectively . calling the new contours @xmath176 and @xmath177 [ see fig . 3(a ) and fig . 4(a ) ] and defining    @xmath178    @xmath179    @xmath180    @xmath181    and recalling that the functions @xmath182 are regular analytic at @xmath183 when @xmath184 , we find with the use of residue calculus that for @xmath184    @xmath185    @xmath186    with the aid of ( 3.18a , b ) we obtain from ( 3.11 ) along with ( 3.12a ) for @xmath3 the following quantization condition @xmath187 = { { \\mbox{cos}[b\\pi/(2p)]}\\over { [ 1+\\mbox{exp}(-2\\pi\\bar k)]^\\frac{1}{2}}},\\ ] ] which has the same merits , relative to the original form of the quantization condition , i.e. , ( 3.11 ) with ( 3.12a ) , as were mentioned in connection with the quantization condition ( 3.6 ) , pertaining to the @xmath64-equation . when @xmath83 we define    @xmath188    @xmath189    @xmath190    @xmath191    and note that ( 3.18a ) is obviously valid also for @xmath83 . with the use of the theory of complex integration one finds that also ( 3.18b ) is valid for @xmath83 . then it follows from ( 3.11 ) , ( 3.12b ) and ( 3.18a , b ) that the quantization condition ( 3.19 ) is valid also when @xmath83 . the quantization condition ( 3.19 ) thus covers in a unified and convenient form both cases @xmath115 and @xmath83 . the quantization condition ( 3.19 ) can be rewritten as @xmath192}\\over   { [ 1+\\mbox{exp}(-2\\pi\\bar k)]^\\frac{1}{2}}}+2s'\\pi,\\end{aligned}\\ ] ] where @xmath193 is an integer . as already mentioned , ( 3.18b ) is valid for @xmath115 as well as for @xmath83 . when the plus sign in ( 3.22 ) applies , we use ( 3.18b ) to express @xmath194 in terms of @xmath195 , and when the minus sign in ( 3.22 ) applies , we use ( 3.18b ) to express @xmath195 in terms of @xmath196 . replacing @xmath193 by @xmath197 or @xmath198 , we thus obtain from ( 3.22 ) and ( 3.18b ) the two quantization conditions    @xmath199^\\frac{1}{2}}},\\end{aligned}\\ ] ]    @xmath200^\\frac{1}{2}}},\\end{aligned}\\ ] ]    where we choose the branch of such that the last two terms on the right - hand side of ( 3.23a , b ) cancel in the limit @xmath201 , that is , when the barrier becomes infinitely thick . in this limit , the formulas ( 3.23a , b ) simplify to    @xmath202    @xmath203    for the particular case that we have a symmetric two - centre coulomb problem , i.e. , that @xmath54 , as is the case for the ion @xmath204 , the double - well potential pertaining to the @xmath56-equation becomes symmetric ( @xmath205 ) , and the quantization conditions ( 3.23a , b ) can be simplified :    @xmath206    @xmath207    the reduced separation constant @xmath78 , obtained from ( 3.23a , b ) in the general case and from ( 3.25a , b ) in the symmetric case , is a function of @xmath79 and @xmath6 .      in the existing semi - classical treatments , the quantization conditions derived on assumptions valid for @xmath71 are in general extrapolated to @xmath82 ( corresponding to a particularization of our case @xmath83 ) without any motivation . it is , however , not allowed to obtain a quantization condition corresponding to @xmath82 from a quantization condition corresponding to @xmath71 by letting @xmath2 take continuous values and tend to zero by a limiting procedure . that the formulas obtained by such an extrapolation are valid is an _ a posteriori _ conclusion . the correct justification of the quantization conditions for @xmath5 rests on the use of the connection formula in subsection a.2.b of the appendix .    for given values of @xmath208 and @xmath209 one can , as already mentioned , obtain the possible values of the reduced separation constant @xmath78 in the differential equation ( 2.8a ) with ( 2.9a ) by applying phase - integral quantization conditions for a single - well potential , while to obtain the possible values of the reduced separation constant @xmath78 in the differential equation ( 2.8b ) with ( 2.9b ) one has to use quantization conditions either for a single - well potential or for a double - well potential . the appropriate quantization condition for the @xmath64-equation determines @xmath78 as a function of @xmath79 and @xmath7 . the appropriate quantization condition for the @xmath56-equation determines @xmath78 as a function of @xmath79 and @xmath6 . the eigenvalues of @xmath79 , and hence the energy eigenvalues @xmath209 , are obtained from the requirement that these two expressions for @xmath78 must be equal to each other . one then obtains @xmath78 from the quantization condition for the @xmath64-equation or the @xmath56-equation . the value thus obtained for @xmath78 depends obviously on the choice of @xmath6 and @xmath7 . one should choose these parameters as funcitons of @xmath12 in such a way that very accurate values of @xmath79 and @xmath78 are obtained already in the first order of the phase - integral approximation . a practically useful criterion for this can be formulated as follows . for every value of @xmath12 one determines @xmath6 and @xmath7 such that the first - order approximation gives the same value as the third - order approximation for @xmath79(and hence for the energy ) as well as for @xmath78 . in this way one can make all calculations within the framework of the phase - integral method . the work of m.l . forms part of a department of science and technology , government of india , research project . support from the swedish natural science research council for m. lakshmanan s visits to uppsala is gratefully acknowledged .","summary":"arbitrary - order phase - integral quantization conditions are obtained for these choices of .","abstract":"the present paper concerns the derivation of phase - integral quantization conditions for the two - centre coulomb problem under the assumption that the two coulomb centres are fixed . with this restriction we treat the general two - centre coulomb problem according to the phase - integral method , in which one uses an _ a priori _ unspecified _ base function_. we consider base functions containing three unspecified parameters and . when the absolute value of the magnetic quantum number is not too small , it is most appropriate to choose . when , on the other hand , is sufficiently small , it is most appropriate to choose . arbitrary - order phase - integral quantization conditions are obtained for these choices of . the parameters and are determined from the requirement that the results of the first and the third order of the phase - integral approximation coincide , which makes the first - order approximation as good as possible .    in order to make the paper to some extent self - contained , a short review of the phase - integral method is given in the appendix ."}
{"article_id":"nlin0012055","section_id":"m","document":"since the present paper is based on phase - integral formulas that are scattered in different publications , we collect in this appendix the background material that is necessary for reading the paper .          1 .   arbitrary - order phase - integral approximation generated from an unspecified base function @xmath211 , as described in chapter 1 of @xcite ; see also dammert and p.o . frman @xcite . the method for solving connection problems developed by frman and frman @xcite , generalized to apply to the phase - integral approximation referred to in the above item . supplementary quantities , expressed analytically in terms of phase - integrals . an example is the quantity @xmath164 , which is a new notation for the quantity @xmath212 in frman _ et al._@xcite , and which is of decisive importance , when two transition zeros lie close to each other . we shall first briefly describe the phase - integral approximation referred to in item 1 . then we collect connection formulas pertaining to a single transition point [ first - order zero or first - order pole of @xmath213 and to a real potential barrier , which can be derived by means of the method mentioned in item 2 combined with comparision equation technique for obtaining the supplementary quantity @xmath164 mentioned in item 3 and appearing in the connection formula for a real barrier . finally we present quantization conditions for single - well and double - well potentials , which can be derived by means of the connection formulas just mentioned . these quantization conditions are used in our treatment of the two - centre coulomb problem . [ [ phase - integral - approximation - generated - from - an - unspecified - base - function ] ] phase - integral approximation generated from an unspecified base function ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~      in the arbitrary - order phase - integral approximation in question there appears an unspecified function @xmath211 called the _ base function_. this function is often chosen to be equal to @xmath214 , but in many physical problems it is important to use the possibility of choosing @xmath211 differently when there exist certain exceptional points , for example the origin in connection with the radial schrdinger equation , and , correspondingly , the poles of @xmath93 and @xmath94 at @xmath107 and @xmath121 in the two - centre coulomb problem . in the present paper we introduce in the base functions a parameter @xmath1 , chosen such that either @xmath3 or @xmath81 , and two parameters @xmath6 and @xmath7 to be determined such that the first- and third - order results coincide , in order that the first - order approximation be as good as possible .    to be able to write the phase - integral approximation generated from an unspecified base function in condensed form one introduces the new independent variable @xmath215 and the function @xmath216 it can be shown that in a local region of the complex @xmath217-plane , where the absolute value of @xmath218 is small , the differential equation ( a1 ) has the approximate solutions                      the choice of the function @xmath211 does not affect the expressions for @xmath182 in terms of @xmath218 and @xmath229 ; only the expressions for @xmath218 and @xmath229 as functions of @xmath217 are affected . it is an essential advantage of the phase - integral approximation described above versus the carlini@xcite ( jwkb ) approximation in higher order that the former approximation contains the unspecified base function @xmath211 , which one can take advantage of in several ways . a criterion for the determination of the base function is that the function @xmath218 be in some sense small in the region of the complex @xmath217-plane that is relevant for the problem under consideration . however , this criterion does not determine the base function @xmath211 uniquely ; it turns out that , within certain limits , the results are not very sensitive to the choice of @xmath211 , when the approximation is used in higher orders . with a convenient choice of @xmath211 already the first - order approximation can be very good . on the other hand an inconvenient , but possible , choice of @xmath211 introduces in the first - order approximation an unnecessarily large error that , however , in general becomes corrected already in the third - order approximation . however , the replacement of ( a7a ) by @xmath232 where the coefficient of @xmath233 should be comparatively small , does not destroy the great accuracy of the results usually obtained with the phase - integral approximation in higher orders . there is thus a whole set of base functions that may be used , and there are various ways in which one can take advantage of this nonuniqueness to make the choice of the base function well adapted to the particular problem under consideration . for instance , by adapting the choice of @xmath230 to the analytical form of @xmath234 one can sometimes achieve the result that the integrals occurring in the phase - integral approximation can be evaluated analytically . to give an example we assume that @xmath234 contains only @xmath235 but not @xmath217 itself . in this case it is convenient to replace the choice ( a7b ) by the choice @xmath236 by a convenient choice , for instance of the unspecified coefficient in ( a7b ) or ( a7c ) , one can sometimes attain the result that , for example , eigenvalues or phase - shifts are obtained exactly for some particular parameter value in every order of the phase - integral approximation . by making this exactness fulfilled in the limit of a parameter value , for which the phase - integral result without this adaptation would not be good , one can actually extend the region of validity of the phase - integral treatment ; see p. 12 in @xcite . when the differential equation contains one or more parameters , the accurate calculation of the wave function may require different choices of the base function @xmath211 for different ranges of the parameter values . to illustrate this fact we consider the radial schrdinger equation . for sufficiently large values of the angular momentum quantum number @xmath88 we obtain an accurate phase - integral approximation ( valid also close to @xmath237 ) if we choose @xmath230 according to ( a7a ) or ( a7b ) . if the value of @xmath88 is too small , this phase - integral approximation is not good . it can be considerably improved ( except close to @xmath237 ) , when the absolute value of the coefficient of @xmath233 in @xmath234 is sufficiently large , if one chooses instead @xmath238    the corresponding phase - integral approximation is not valid close to @xmath237 , but the wave function that is regular and tends to @xmath239 as @xmath240 can be obtained sufficiently far away from @xmath237 by means of the connection formula that will be presented in subsection a.2.b of this appendix . the appearance of the unspecified base function @xmath211 in the phase - integral approximation is thus very important from several points of view . in our treatment of the two - centre coulomb problem we use two essentially different kinds of base function [ corresponding to @xmath115 and @xmath241 in ( 3.2a , b ) ] , which yield approximate solutions with different regions of validity . when the first - order approximation is used , it is often convenient to choose the constant lower limit of integration @xmath221 in ( a4b ) to be a zero or a first - order pole of @xmath230 . this is , however , in general not possible when a higher - order approximation is used , since the integral in ( a4b ) would then in general be divergent . if @xmath221 is an odd - order zero or an odd - order pole of @xmath230 , it is therefore convenient to replace the definition ( a4b ) of @xmath242 by the definition      where @xmath244 is a path of integration that starts at the point corresponding to @xmath217 on a riemann sheet adjacent to the complex @xmath217-plane under consideration , encircles @xmath221 in the positive or in the negative sense , and ends at @xmath217 . it is immaterial for the value of the integral in ( a8 ) if the path of integration encircles @xmath221 in the positive or in the negative sense , but the endpoint must be @xmath217 . for the first - order approximation the definitions ( a4b ) and ( a8 ) are identical . it is useful to introduce a short - hand notation for the integral in the right - hand member of ( a8 ) by the definition @xmath245 for the first order of the phase - integral approximation one can replace @xmath246 by @xmath221 in the left - hand member of ( a9 ) and thus get an ordinary integral from @xmath221 to @xmath217 instead of half of the integral along the contour @xmath244 . in analogy to ( a9 ) one defines a short - hand notation for an integral in which the upper limit of integration is an odd - order zero or an odd - order pole of @xmath230 . when one has two transition points of that kind as limits of integration , the definition of the short - hand notation with both limits within parentheses implies that the integral is equal to half of the integral along a closed loop enclosing both transition points . the simplified notation in the left - hand member of ( a9 ) for the integral in the right - hand member of ( a9 ) was introduced by frman _ @xcite , pp 160 - 161 . it makes it possible to use , for an arbitrary order of the phase - integral approximation , a similar simple notation and almost the same simple language ( although in a generalized sense ) as for the first order of the phase - integral approximation . one thus achieves a great formal and practical simplification in the treatment of concrete problems , when an arbitrary order of the phase - integral approximation is used . we remark that the notations used above differ from the notations in the original papers published up to the beginning of the eighties in the respect that @xmath230 and @xmath247 in those papers correspond in the present paper to @xmath234 and @xmath230 , respectively .      [ [ connection - formulas - pertaining - to - a - first - order - real - transition - zero ] ] connection formulas pertaining to a first - order , real transition zero ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^    before the phase - integral approximation generated from an unspecified base function had been introduced , n. frman @xcite derived arbitrary - order connection formulas associated with a turning point for the particular phase - integral approximation of arbitrary order corresponding to @xmath248 . after the phase - integral approximation generated from an unspecified base function had been introduced , it turned out that these connection formulas remain valid also when @xmath249 . below we shall present the general connection formulas .    the functions @xmath234 and @xmath230 are assumed to be real on the real @xmath217-axis ( the @xmath250-axis ) . on this axis there is a generalized classical turning point @xmath251 , i.e. , a simple zero of @xmath230 , and there is , in a generalized sense , a classically allowed region on one side of @xmath251 , i.e. , a region where @xmath252 , and a classically forbidden region on the other side of @xmath251 , i.e. , a region where @xmath253 . defining @xmath254 we can write the connection formula for tracing a phase - integral solution of ( a1 ) from the classically allowed to the classically forbidden region as @xmath255 are constants , which are arbitrary except for the requirement that @xmath256 must not be too close to zero . as a consequence of ( a11 ) we have the connection formula @xmath257 \\lesssim\\mbox{exp } \\left[-\\left|w(x)\\right|\\right],\\ ] ] is fulfilled . for a numerical study of the accuracy and the properties of the connection formula ( a13 ) with @xmath258 we refer to n. frman and mrazek@xcite . we emphasize the one - directional character of the connection formulas ( a11 ) , ( a12 ) and ( a13 ) , which means that the tracing of a solution must always be made in the direction of the arrow . this property of the connection formulas has been thoroughly investigated and even illustrated numerically by n. frman @xcite for the first order of the carlini @xcite ( jwkb ) approximation . the whole discussion in @xcite applies in principle to the connection formulas for the higher orders of the phase - integral approximation as well . the above connection formulas for the phase - integral approximation of any order may in many cases be used for obtaining very accurate solutions of physical problems , when the classical turning points are well separated , and when there are no other transition points near the real axis in the region of the complex @xmath217-plane of interest . within their range of applicability the connection formulas are very useful because of their simplicity and the great ease with which they can be used . now we assume that in a certain region of the complex @xmath217-plane around a first - order transition pole @xmath251 , i.e. , a first - order pole of @xmath230 , we have @xmath259 @xmath260 where @xmath261 is a non - negative integer . we assume that the absolute values of @xmath262 and @xmath263 are sufficiently large , while the absolute value of @xmath264 and the absolute value of the difference between the two regular functions in ( a15 ) and ( a16 ) are sufficiently small . there is one particular curve on which @xmath242 , defined as @xmath265 is real . for the first order of the phase - integral approximation this is the anti - stokes line that emerges from @xmath251 . therefore we use , also when a higher order of the phase - integral approximation is used , the terminology an _ anti - stokes line that emerges from @xmath251 _ in a generalized sense to denote the anti - stokes line on which @xmath242 , defined in ( a17 ) , is real . for the first - order approximation ( and under certain unnecessarily restrictive assumptions ) frman and frman @xcite obtained a phase - integral formula [ their eq.(7.28 ) ] , valid sufficiently far away from @xmath251 on the anti - stokes line that emerges from @xmath251 , for the particular solution @xmath266 of ( a1 ) that fulfils the condition @xmath267 this formula can be generalized to be valid for an arbitrary order of the phase - integral approximation generated from an unspecified base function and can then be formulated as follows . on the lip of the anti - stokes line emerging from @xmath251 , where _ arg _ @xmath242 is smallest , the solution of ( a1 ) that fulfils the condition ( a18 ) is , sufficiently far away from @xmath251 , given by the phase - integral formula @xmath268,\\ ] ] where @xmath269 is the residue of [ @xmath270^{-2}$ ] at @xmath271 and is thus determined by the expansion of @xmath266 in powers of @xmath272 , and the sign of @xmath273^{-\\frac{1}{2}}$ ] has to be chosen conveniently . for the special case that @xmath274 one finds that @xmath275 . formula ( a19 ) can easily be particularized to the case that @xmath234 and @xmath230 are real on the real @xmath217-axis ( the @xmath250-axis ) and @xmath251 lies on that axis . [ [ connection - formula - for - a - real - smooth - single - hump - potential - barrier ] ] connection formula for a real , smooth , single - hump potential barrier ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~    our starting point is a paper by frman and frman @xcite . although it was assumed in the treatment there that @xmath248 with the notations in the present paper , the results obtained are valid also when @xmath249 . in the present paper it is convenient to introduce partly other notations than in @xcite . thus we now denote by @xmath276 and @xmath277 the two relevant zeros of @xmath230 , i.e. , the two generalized classical turning points in the sub - barrier case @xmath278 and the two complex conjugate transition zeros in the super - barrier case ( i m @xmath279 ) . let @xmath280 , called @xmath281 in @xcite , be a point in the classically allowed region of the real @xmath217-axis to the left of the barrier , and let @xmath282 , called @xmath283 in @xcite , be a point in the classically allowed region of the real @xmath217-axis to the right of the barrier . we introduce the notations          where @xmath287 and @xmath288 are defined in @xcite , and @xmath289 is defined by eq.(12 ) in @xcite . in the definitions ( a20a , b , c ) it is assumed that the phase of @xmath290 is chosen as shown in fig.1 in @xcite . we shall , however , in the following write the formulas in such a way that they remain unchanged if one changes the phase of @xmath291 and hence the phase of @xmath290 ; see ( a5a , b ) . the quantity @xmath289 in ( a20a ) is then given by @xmath292 where @xmath1 [ not to be confused with the parameter @xmath1 in the base function @xmath27 ] is a closed contour of integration encircling both @xmath276 and @xmath277 , but no other transition point , and the integration is performed in the direction that in the _ first - order approximation _ yields @xmath294 for energies below the top of the barrier and @xmath295 for energies above the top of the barrier . if higher - order approximations are used , the quantity @xmath289 may become negative also for energies below ( but not too far from ) the top of the barrier ; see table i in @xcite . we have replaced @xmath296 , defined by eq . ( 28 ) in @xcite , by @xmath297 [ cf . ( a20c ) ] in order to get better agreement with a notation used by other authors ; see for instance child @xcite . now we define        where the notations in the right - hand members are those used in @xcite . using the short - hand notation defined in ( a9 ) , we obtain from eqs . ( 25a ) and ( 9a ) , with @xmath281 replaced by @xmath280 , in @xcite and ( a22a , b ) in the present paper              it is seen from ( a23a , b ) that the coefficients @xmath78 and @xmath305 are associated with waves travelling away from the barrier , while the coefficients @xmath306 and @xmath307 are associated with waves incoming towards the barrier . from ( a25a , b ) we obtain @xmath308 & ( \\theta^2 + 1)^{\\frac{1}{2}}\\mbox{exp}(+i\\tilde\\phi)\\cr ( \\theta^2 + 1)^{\\frac{1}{2}}\\mbox{exp}(-i\\tilde\\phi ) & \\theta\\mbox{exp}\\left [ + i(\\frac{\\pi}{2}-\\vartheta)\\right ] \\end{pmatrix}.\\ ] ] one thus obtains @xmath309 from @xmath310 by replacing @xmath311 by @xmath312 . we emphasize that the above formulas are in principle exact , provided that one knows the quantities @xmath313 and @xmath314 , which depend slightly on @xmath280 and @xmath282 . furthermore , the two transition zeros associated with the potential barrier need not lie far away from other possibly existing transition points ; see @xcite . however , when one introduces for @xmath313 and @xmath314 the approximate values that will be given below , the barrier is assumed to be well separated ( in the sense just described ) from all transition points that are not associated with the barrier .    when @xmath78 and @xmath306 are given constants , associated with a wave function that is given at the point @xmath280 , the coefficients @xmath305 and @xmath307 , which are obtained from ( a24 ) along with ( a25a ) , depend slightly on @xmath280 and @xmath282 via the quantities @xmath315 and @xmath314 . one obtains the derivatives of @xmath316 and @xmath317 from ( a23a , b ) by considering @xmath318 and @xmath307 @xmath319 as constants . the quantity @xmath164 is particularly important when the energy is close to the top of the barrier , but it is important also for energies well below the top , if one with the use of higher orders of the phase - integral approximation wants to obtain very accurate results . in practice one can not obtain useful expressions for @xmath314 from the exact formula ( a20c ) . under the assumption that @xmath323 is not too close to zero at the top of the barrier , frman _ @xcite derived by means of comparision equation technique , adapted to yield formulas for supplementary quantities in the phase - integral method , an approximate , but very accurate , formula in the @xmath324th order of the phase - integral approximation [ their eqs . ( 5.5.30 ) , ( 5.5.25a - g ) , ( 5.4.23 ) and ( 5.4.21 ) ] , from which we can obtain the formula @xmath325 where                @xmath1 being the previously described contour of integration encircling @xmath276 and @xmath277 but no other transition point , with the integration performed in the direction that makes @xmath169 positive when @xmath276 and @xmath277 are real , i.e. , when the barrier is superdense , but negative when @xmath276 and @xmath277 are complex conjugate , i.e. , when the barrier is underdense . ( note that we perform the integrations in ( a21 ) and ( a30a ) in opposite directions in order to make these formulas to agree with eq . ( 12 ) in @xcite and eq . ( 5.4.21 ) in @xcite , respectively . ) the result given by ( a28 ) , ( a29a , b , c ) and ( a30a , b ) can also be obtained from @xcite , where @xmath212 is the same as our @xmath164 . we emphasize again that for the validity of ( a28 ) with the expressions ( a29a - c ) for @xmath331 the essential restriction is that @xmath332 must not be too small at the top of the barrier , which means that close to its top the barrier is approximately parabolic . however , when the energy is close to the top of the barrier , it is the slight deviation from parabolic shape close to the top of the barrier that determines the values of the quantities @xmath333 , and one needs accurate values of these quantities for obtaining accurate values of @xmath164 in higher orders of the phase - integral approximation . the barrier connection formula presented in this section is valid uniformly for all energies , below and above the top of the barrier . we would also like to emphasize that while the connection formulas pertaining to an isolated turning point ( n. frman @xcite ) are one - directional , the barrier connection formula ( a23a , b ) with ( a24 ) and ( a25a ) , which is valid when the barrier is well isolated and has an approximately parabolic top , is bi - directional . however , the neighbourhood of an energy that corresponds to a resonance requires a careful discussion . [ [ quantization - conditions - for - single - well - and - double - well - potentials ] ] quantization conditions for single - well and double - well potentials ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~    in this section we shall present quantization conditions for general single - well potentials @xcite and double - well potentials @xcite , valid for any conveniently chosen order of the phase - integral approximation , in forms especially adapted to the two - centre coulomb problem . in the quantization conditions pertaining to the double - well potential there appears the supplementary quantity @xmath164 , which was discussed in section a.3 , and which is of particular importance for energy eigenvalues in the neighbourhood of the top of the barrier ; cf . numerical results in @xcite , where @xmath334 and @xmath296 correspond to @xmath335 and @xmath336 , respectively , in the present paper . comparision with numerical results @xcite shows that all energy eigenvalues , also the low - lying ones and those in the neighbourhood of the top of the barrier , are obtained very accurately from the phase - integral quantization conditions when the third- or fifth - order approximation is used .    since arbitrary - order phase - integral quantization conditions for the single - well and for the double - well potential problem have been given in previous work , we restrict ourselves to quoting those results and taking into account the fact that we are dealing with the special potentials pertaining to the two - centre coulomb problem . we assume that @xmath234 and @xmath230 are real on the real @xmath217-axis ( the @xmath250-axis ) and that there are two transition points @xmath276 and @xmath277 @xmath337 on this axis , each one of which may be either a first - order transition zero , i.e. , a first - order zero of @xmath230 , or a first - order transition pole , i.e. , a first - order pole of @xmath230 . these transition points are assumed to lie far away from all other transition points . on the real axis between @xmath276 and @xmath277 it is assumed that @xmath338 is positive . with the aid of the connection formulas in section a.2 we can derive the quantization conditions that will be presented below . when one of the transition points @xmath276 and @xmath277 is a first - order transition zero , and the other is a first - order transition pole in the neighbourhood of which @xmath234 and @xmath230 can be expanded according to ( a15 ) and ( a16 ) with @xmath340 , i.e. , @xmath341 , we obtain under the assumptions introduced below those expansions the quantization condition @xcite @xmath342 where @xmath2 is an integer ( positive , negative or zero ) , and @xmath343 is also an integer . when both transition points @xmath276 and @xmath277 are first - order transition poles , in the neighbourhood of which @xmath234 and @xmath230 can be expanded according to ( a15 ) and ( a16 ) with @xmath340 , i.e. , @xmath341 for both transition poles but possibly with different coefficients @xmath262 and @xmath263 for the two transition poles , we obtain under the assumptions introduced below ( a15 ) and ( a16 ) the quantization condition @xcite @xmath344 where @xmath2 is an integer ( positive , negative or zero ) , and @xmath343 is also an integer . we assume that @xmath234 and @xmath230 are real on the real @xmath217-axis ( the @xmath250-axis ) and that there are either two generalized classical turning points @xmath276 and @xmath345 [ real , simple zeros of @xmath213 associated with a superdense potential barrier or two complex conjugate simple transition zeros @xmath276 and @xmath277 [ simple zeros of @xmath230 ; i m @xmath346 , i m @xmath347 associated with an underdense potential barrier . the classically allowed region to the left of the barrier is to the left delimited by a transition point @xmath348 ( on the real axis ) , and the classically allowed region to the right of the barrier is to the right delimited by a transition point @xmath349 ( on the real axis ) , where @xmath348 and @xmath349 are both either generalized classical turning points , i.e. , simple zeros of @xmath230 , or first - order transition poles , i.e. , first - order poles of @xmath230 . the points @xmath350 and @xmath351 , as well as other possibly existing transition points that are not associated with the barrier , are assumed to lie far away from @xmath276 and @xmath277 . when @xmath348 and @xmath349 are simple transition poles we assume that in the neighbourhood of @xmath352 we have @xmath353 @xmath354 where @xmath2 is an integer ( positive , negative or zero ) , @xmath355 and @xmath356 are sufficiently large to their absolute values , while the absolute values of @xmath357 , as well as the difference between the regular functions in ( a34 ) and ( a35 ) , is not too large . under the above assumptions we obtain with the aid of connection formulas in section a.2 and section a.3 the quantization condition @xmath358^{\\frac{1}{2}}-1}{[1+\\mbox{exp}(-2k)]^{\\frac { 1}{2}}+1},\\end{aligned}\\ ] ] where @xmath359 @xmath1 being a closed contour , enclosing @xmath276 and @xmath277 , along which the integration is performed in the direction that makes the first - order contribution to @xmath289 positive when the barrier is super - dense but negative when the barrier is under - dense , and @xmath360 the quantization condition ( [ a36 ] ) can be rewritten into the form @xmath361^\\frac{1}{2}}}. \\end{aligned}\\ ] ]    10 h. eyring , j. walter , and g. e. kimball , _ quantum chemistry _ ( john wiley & sons and chapman & hall , new york and london , 1944 ) . g. herzberg , _ molecular spectra and molecular structure _ , volume i. _ spectra of diatomic molecules _ ( van nostrand reinhold company , new york , cincinnati , toronto , london , and melbourne , 1950 ) . j. c. slater , _ quantum theory of molecules and solids _ , volume i. _ electronic structure of molecules _ ( mcgraw - hill , new york , 1963 ) . b. rosen , _ spectroscopie lectronique molculaire_. encyclopedia of physics volume * xxvii * , edited by s. flgge ( springer - verlag , berlin , gttingen , and heidelberg , 1964 ) . d. r. bates , k. ledsham , and a. l. stewart , phil . trans . london * a246 * , 215 ( 1953 ) . r. f. wallis and h. m. hulburt , j. chem . * 22 * , 774 ( 1954 ) . d. r. bates and t. r. carson , proc . a234 * , 207 ( 1956 ) . h. wind , j. chem . phys . * 42 * , 2371 ( 1965 ) . j. m. peek , j. chem . phys . * 43 * , 3004 ( 1965 ) . l. i. ponomarev and t.p . puzynina , j. exp . 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{"article_id":"1507.01927","section_id":"c","document":"we provide mean 3d model spectra for wds with @xmath106 , extending the previously published 3d model grid to very low - mass wds . our 3d models now cover the entire temperature and surface gravity range for the observed population of convective da wds . we list 1d to 3d correction factors , which can be as large as 0.35 dex in surface gravity . these corrections largely resolve the discrepancies seen in the @xmath71 and radius estimates for relatively cool elm wds that are observed in double wd or wd + milli - second pulsar systems . we also update the boundaries of the zz ceti instability strip for wds , including the elm pulsators as well as the normal ( @xmath107 ) wds . support for this work was provided by nasa through hubble fellowship grant # hf-51329.01 awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . mk and ag gratefully acknowledge the support of the nsf and nasa under grants ast-1312678 and nnx14af65 g . ag acknowledges support provided by nasa through grant number hst - go-13319.01 from the space telescope science institute , which is operated by aura , inc . , under nasa contract nas  5 - 26555 . the computing for this project was performed at the ou supercomputing center for education & research ( oscer ) at the university of oklahoma ( ou ) . acknowledges financial support by the sonderforschungsbereich sfb 881 `` the milky way system '' ( subproject a4 ) of the german research foundation ( dfg ) . j.j.h . acknowledges funding from the european research council under the european union s seventh framework programme ( fp/2007 - 2013 ) / erc grant agreement n. 320964 ( wd - tracer ) . allard , n.  f. , kielkopf , j.  f. , & loeillet , b.  2004 , , 424 , 347 althaus , l.  g. , miller bertolami , m.  m. , & crsico , a.  h.  2013 , , 557 , aa19 antoniadis , j. , van kerkwijk , m.  h. , koester , d. , et al . 2012 , , 423 , 3316 asplund , m.  2005 , , 43 , 481 asplund , m. , grevesse , n. , sauval , a.  j. , & scott , p.  2009 , , 47 , 481 bassa , c.  g. , van kerkwijk , m.  h. , & kulkarni , s.  r.  2003 , , 403 , 1067 bassa , c.  g. , van kerkwijk , m.  h. , koester , d. , & verbunt , f.  2006 , , 456 , 295 bergeron , p. , wesemael , f. , fontaine , g. , & liebert , j.  1990 , , 351 , l21 bhm - vitense , e.  1958 , , 46 , 108 brown , w.  r. , kilic , m. , allende prieto , c. , & kenyon , s.  j.  2010 , , 723 , 1072 brown , w.  r. , kilic , m. , hermes , j.  j. , et al . 2011 , , 737 , ll23 caffau , e. , ludwig , h .- g . , steffen , m. , freytag , b. , & bonifacio , p.  2011 , , 268 , 255 callanan , p.  j. , garnavich , p.  m. , & koester , d.  1998 , , 298 , 207 eisenstein , d.  j. , liebert , j. , harris , h.  c. , et al . 2006 , , 167 , 40 freytag , b. , steffen , m. , ludwig , h .- , et al . 2012 , journal of computation al physics , 231 , 919 genest - beaulieu , c. , & bergeron , p.  2014 , , 796 , 128 gianninas , a. , bergeron , p. , & ruiz , m.  t.  2011 , , 743 , 138 gianninas , a. , dufour , p. , kilic , m. , et al .  2014a , , 794 , 35 gianninas , a. , hermes , j.  j. , brown , w.  r. , et al . 2014b , , 781 , 104 grevesse , n. , & sauval , a.  j.  1998 , , 85 , 161 hermes , j.  j. , montgomery , m.  h. , winget , d.  e. , et al . 2013 , , 765 , 102 hermes , j.  j. , brown , w.  r. , kilic , m. , et al . 2014 , , 792 , 39 hummer , d.  g. , & mihalas , d.  1988 , , 331 , 794 jacoby , b.  a. , hotan , a. , bailes , m. , ord , s. , & kulkarni , s.  r.  2005 , , 629 , l113 kaplan , d.  l. , marsh , t.  r. , walker , a.  n. , et al . 2014 , , 780 , 167 kepler , s.  o. , kleinman , s.  j. , nitta , a. , et al . 2007 , , 375 , 1315 kilic , m. , brown , w.  r. , allende prieto , c. , kenyon , s.  j. , & panei , j.  a.  2010a , , 716 , 122 kilic , m. , allende prieto , c. , brown , w.  r. , et al .  2010b , , 721 , l158 kilic , m. , gianninas , a. , brown , w.  r. , et al . 2013 , , 434 , 3582 kilic , m. , brown , w.  r. , gianninas , a. , et al . 2014 , , 444 , l1 kilic , m. , hermes , j.  j. , gianninas , a. , & brown , w.  r.  2015 , , 446 , l26 kleinman , s.  j. , kepler , s.  o. , koester , d. , et al . 2013 , , 204 , 5 ludwig , h .- , & steffen , m.  2008 , in precision spectroscopy in astrophysics , ed . santos , l. pasquini , a.c.m . correia , & m. romanielleo ( berlin : springer ) , 133 ludwig , h .- g . , behara , n.  t. , steffen , m. , & bonifacio , p.  2009a , , 502 , l1 ludwig , h .- , caffau , e. , steffen , m. , et al .  2009b , , 80 , 711 scott , p. , grevesse , n. , asplund , m. , et al . 2015a , , 573 , a25 scott , p. , asplund , m. , grevesse , n. , bergemann , m. , & sauval , a.  j.  2015b , , 573 , a26 spite , m. , andrievsky , s.  m. , spite , f. , et al . 2012 , , 541 , a143 steffen , m. , ludwig , h .- & freytag , b.  1995 , , 300 , 473 tremblay , p .- e . , & bergeron , p.  2009 , , 696 , 1755 tremblay , p .- e . , bergeron , p. , kalirai , j.  s. & gianninas , a.  2010 , , 712 , 1345 tremblay , p .- e . , ludwig , h .- g . , steffen , m. , bergeron , p. , & freytag , b.  2011 , , 531 , l19 tremblay , p .- e . , ludwig , h .- g . , steffen , m. , & freytag , b.  2013a , , 552 , a13 tremblay , p .- e . , ludwig , h .- g . , freytag , b. , steffen , m. , & caffau , e.  2013b , , 557 , a7 tremblay , p .- e . , ludwig , h .- , steffen , m. , & freytag , b.  2013c , , 559 , a104 van kerkwijk , m.  h. , bergeron , p. , & kulkarni , s.  r.  1996 , , 467 , l89","summary":"we present an extended grid of mean three - dimensional ( 3d ) spectra for low - mass , pure - hydrogen atmosphere da white dwarfs ( wds ) . we revisit the spectroscopic analysis of the extremely low - mass ( elm ) wds , and demonstrate that the 3d models largely resolve the discrepancies seen in the radius and mass measurements for relatively cool elm wds in eclipsing double wd and wd + milli - second pulsar binary systems . we also use the 3d corrections to revise the boundaries of the zz ceti instability strip , including the recently found elm pulsators .","abstract":"we present an extended grid of mean three - dimensional ( 3d ) spectra for low - mass , pure - hydrogen atmosphere da white dwarfs ( wds ) . we use co5bold radiation - hydrodynamics 3d simulations covering  =  600011,500  k and  =  56.5 ( in cm s ) to derive analytical functions to convert spectroscopically determined 1d temperatures and surface gravities to 3d atmospheric parameters . along with the previously published 3d models , the 1d to 3d corrections are now available for essentially all known convective da wds ( i.e. ,  =  59 ) . for low - mass wds , the correction in temperature is relatively small ( a few per cent at the most ) , but the surface gravities measured from the 3d models are lower by as much as 0.35  dex . we revisit the spectroscopic analysis of the extremely low - mass ( elm ) wds , and demonstrate that the 3d models largely resolve the discrepancies seen in the radius and mass measurements for relatively cool elm wds in eclipsing double wd and wd + milli - second pulsar binary systems . we also use the 3d corrections to revise the boundaries of the zz ceti instability strip , including the recently found elm pulsators ."}
{"article_id":"astro-ph0402241","section_id":"c","document":"the evidence for self - produced photoevaporative disk winds around low - mass stars is largely circumstantial . the primary reason for this has been the lack of detailed calculations on the outflow properties of these winds to compare with observations . photoevaporative disk wind models have , however , been shown to fit the observational data of externally - heated low - mass stars in the vicinity of massive stars ( e.g. , johnstone et al . 1998 ; bally et al . 1998 ; strzer & hollenbach 1998 ) because the disk wind geometry and flow characteristics are much simpler .    in this paper we use hydrodynamic simulations to compute the properties of the photoevaporative disk wind model and , subsequently , the predicted observational signatures . we show that the hydrodynamic simulations converge to steady - state solutions and that a number of general properties ( e.g. , scale height distribution , integrated disk wind mass - loss rate ) agree well with the earlier analytic results of sjh93 and hjls94 . the outflows become nearly spherically symmetric and match the analytic solution to the parker solar wind problem at large radii , as expected . we further demonstrate that the photoevaporative winds produce blue - shifted ionized forbidden lines with typical offset velocities of @xmath129 km s@xmath5 , widths of @xmath130 km s@xmath5 , and integrated luminosities of @xmath131 . these values compare favorably with the observations of heg95 ( see figs . 9 and 10 ) . the strength of the observed oi emission is difficult to account for with the present model , however . the photoevaporative disk winds examined here are intuitive and physically - simplistic . they rely on the availability of @xmath132 ionizing photons per second to be emitted by the central star disk accretion shock . theoretical arguments support such high levels of ionizing emission ( e.g. , matsuyama et al . observationally , it is extremely difficult to directly pin down the value of @xmath18 for low - mass t tauri stars . heg95 measured the mass accretion rates onto the surface of the t tauri stars , however , and these , in principle , can be used to estimate the value of @xmath18 . given the mass accretion rate and the stellar radius , we calculate the accretion shock luminosity of the gas as it falls onto the star s surface via      where @xmath134 is the mass accretion rate and @xmath135 is the radius of the t tauri star ( see also matsuyama et al . 2003a ) . using the inferred values of @xmath136 and assuming black - body radiation with a characteristic temperature of 10,000 k ( johns - krull et al . 2000 ; gullbring et al . 2000 ) , we indeed estimate @xmath137 s@xmath5 . this lends credence to the photoevaporative wind hypothesis .    utilizing these ultraviolet photons , however , may be difficult . as mentioned above , both the protostellar jet ( shang et al . 2002 ) and the accretion column ( alexander et al . 2004 ) are likely to be optically thick to ionizing radiation , protecting the disk . nevertheless , energy released within the accretion disk , and in the fast - moving jet , may produce significant ionizing radiation . alternatively , the disk may be heated by another source such as fuv photons ( johnstone et al . 1998 , strzer & hollenbach 1998 ) . the calculations presented here reveal that heating the disk surface to @xmath6k will produce a thermal wind with flow characteristics similar to those observed around t tauri stars . additionally , if the mass - loss rate is high enough , comparable to the evaporating disk model , the forbidden line profiles of sii and nii can be explained . curiously , if the @xmath6k wind is not ionized by euv photons the resultant oi forbidden line radiation also would be comparable to that observed . thus , the observations of heg95 seem to require a partially ionized @xmath6k wind . \" alternative models have also been proposed to explain the observed low - velocity component . in fact , the prevailing view is that t tauri winds are magnetically - driven ( e.g. , anderson et al . this is largely because strong magnetic fields seem to be the only way to power the collimated , high velocity jets that are responsible for the high - velocity component observed in t tauri spectra . in addition , magnetic wind models are able to reproduce a number of the observed features of the high - velocity component ( e.g. , shang , shu , & glassgold 1998 ; garcia et al . 2001a , 2001b ) . it is less clear , however , if the magnetic wind models can account for the low - velocity component , which was the subject of investigation in  4 . below , we briefly discuss how the predicted low - velocity components of magnetic wind models compare with their observational counterparts . we argue that the photoevaporative disk wind model proposed in the present study matches the current suite of observations at least as well magnetic wind models .    generally speaking , magnetic wind models may be divided into two classes : ` x - winds ' and ` disk winds ' . the primary difference between these two classes is the physical extent of the magnetic field and , therefore , the location of the outflow launching radius . in x - wind models , the magnetic field is contained entirely within the very inner regions of the disk immediately next to the star . disk wind models , on the other hand , assume that there is a large scale magnetic field present which extends to several au . unfortunately , it is extremely difficult to work out the exact observational predictions of such models in a self - consistent manner ( garcia et al . 2001a , 2001b ) . this is one advantage the physically - simplistic photoevaporative disk wind model has over the magnetic wind models .    while it is difficult to calculate the precise observational characteristics of magnetic wind models , there have been a number of basic predictions made which are testable with current observational data . in terms of the x - wind models , the predicted launching radius for the disk outflow is extremely close to the star . however , recent high resolution observations suggest that the low - velocity component probably originates at ` large ' disk radii ( e.g. , bacciotti et al . 2002 ; anderson et al . 2003 ) , suggesting that some other mechanism is responsible for the observed low - velocity component . in fact , irrespective of the model , one should expect the outflow velocity to be of order the escape velocity at the region where the wind originated . this is a strong argument that the low - velocity component must originate at moderate radii ( @xmath138 au ) . magnetic ` disk wind ' models , on the other hand , are able to produce both high and low - velocity components ( e.g. , cabrit et al . 1999 ; garcia et al . 2001a , 2001b ) , with the low - velocity component being launched from reasonably large disk radii . furthermore , such models predict that the high velocity component is spatially extended while the low - velocity component is confined within the central ( projected ) regions of the system , which is in good agreement with observations . however , the problem with ` disk wind ' models is that the level of ionization at large disk radii ( i.e. , at the launching radius ) is too low to allow for strong magnetic coupling ( e.g. , gammie 1996 ) . hence , such models tend to under - predict the luminosity of the low - velocity component by a substantial margin ( e.g. , garcia et al . as we have shown , however , the pdw model presented here ( which contains no magnetic field ) can naturally produce an outflow that matches a number of observed trends seen in low - mass t tauri stars , so long as the photons can penetrate from the central star out to large radii ( or if an external mechanism for producing euv photons is present ) . it is possible , however , that _ both _ photoevaporation and a large scale magnetic field could be contributing to the low - velocity component , especially since the higher level of ionization due to photoevaporation should increase the effectiveness of the magnetic disk wind . this two component model could possibly explain the relatively large amount of scatter in the forbidden line profiles and luminosities and why some stars apparently show multiple low - velocity components ( e.g. , uy aur , see fig . additionally , it is likely that an interface between the fast jet - like wind arising from the inner disk will modify these results . hjls94 modeled the effect of a strong stellar wind on the ionized atmosphere and concluded that only the inner regions would be affected . this suggests that the results of the calculations in this paper would need to be modified only in the central densest regions , resulting in somewhat lower line fluxes . this would predominantly affect transitions having high critical densities such as the nitrogen line . moreover , matsuyama et al . ( 2003a ) found that gaps could form in the inner part of the disk , near @xmath20 , due to the erosive power of photoevaporation coupled to the viscous evolution of the disk . although the matsuyama models should be recalculated , taking into account the results of this paper , these gaps would remove the inner densest part of the ionized atmosphere produced in this paper . an evolutionary sequence might be visible in the low - velocity spectra from t tauri stars dependent upon the state of the underlying disk . detailed calculations , taking into account each of these factors , should be undertaken . 0.1 in the authors wish to thank the referee , david hollenbach , for suggesting significant improvements to the paper . thanks also to g. mellema for providing his software package for calculating forbidden line emissivities . i.g.m . thanks a. babul for useful discussions . acknowledges financial support from j.f . i.g.m . is supported by a postgraduate scholarship from the natural sciences and engineering research council of canada ( nserc ) . the research of d.j . has been supported by an nserc discovery grant . thanks nserc for financial support . alexander , r. d. , clarke , c. j. , & pringle , j. e. 2004 , mnras , in press ( astro - ph/0311276 ) anders , e. , & grevesse , n. 1989 , geo . et cosmo . acta , 53 , 197 anderson , j. m. , li , z. y. , krasnopolsky , r. , & blandford , r. 2003 , apj , 590 , l107 bacciotti , f. , mundt , r. , ray , t. p. , eislffel , j. , solf , j. , & camezind , m. 2000 , apj , 537 , l49 bacciotti , f. ray , t. p. , mundt , r. , eislffel , j. & solf , j. 2002 , apj , 576 , 222 bally , j. , odell , c.r . , & mccaughrean , m.j . 2000 , aj , 119 , 2919 bally , j. , sutherland , r.s . , devine , d. , & johnstone , d. 1998 , aj , 116 , 293 cabrit , s. , ferreira , j. , & raga , a. c. 1999 , a&a , 343 , l61 clarke , c. j. , gendrin , a. , & sotomayor , m. 2001 , mnras , 328 , 485 gammie , c. f. 1996 , apj , 457 . 355 garcia , p. j. v. , ferreira , j. , cabrit , s. , & binette , l. 2001 , a&a , 377 , 589 garcia , p. j. v. , cabrit , s. , ferreira , j. , & binette , l. 2001 , a&a , 377 , 609 gullbring , e. , calvet , n. , muzerolle , j. , & hartmann , l. 2000 , apj , 544 , 927 haisch , k. e. jr . , lada , e.a . , & lada , c. 2001 , apj , 553 , l153 hartigan , p. , edwards , s. , & ghandour , l. 1995 , apj , 452 , 736 ( heg95 ) hartmann , l. , calvet , n. , gullbring , e. , & dalessio , p. 1998 , apj , 495 , 385 hirth , g. a. , mundt , r. , & solf , j. 1997 , a&as , 126 , 437 hollenbach , d. , johnstone , d. , lizano , s. , & shu , f. 1994 , apj , 428 , 654 ( hjls94 ) hollenbach , d. , yorke , h. w. , & johnstone , d. 2000 , in protostars and planets iv , ed . v. mannings , a. p. boss & s. s. russell ( tucson : univ . arizona press ) , 401 jayawardhana , r. , luhman , k. l. , dalessio , p. , & stauffer , j. r. 2002 , apj , 571 , l51 johns - krull , c. m. , valenti , j. a. , & linsky , j. l. 2000 , apj , 539 , 815 johnstone , d. , hollenbach , d. , & bally , j. 1998 , apj , 539 , 815 kwan , j. , & tademaru , e. 1988 , apj , 332 , l41 kwan , j. , & tademaru , e. 1995 , apj , 454 , 382 lada , c. j. , muench , a. a. , haisch , k. e. jr . , lada , e. a. , alves , j. f. , tollestrup , e. v. , & willner , s. p. 2000 , aj , 120 , 3162 lee , c. f. , stone , j. m. , ostriker , e. c. & mundy , l. g. 2001 , apj , 557 , l429 matsuyama , i. , johnstone , d. , & hartmann , l. 2003a , apj , 582 , 893 matsuyama , i. , johnstone , d. , & murray , n. 2003b , apj , 585 , l143 osterbrock , d.e . 1989 , astrophysics of gaseous nebulae and active galactic nuclei , ( mill valley : university science books ) parker , e. n. 1963 , interplanetary dynamical processes , ( new york : interscience publishers ) shang , h. , glassgold , a. e. , shu , f. h. , & lizano , s. 2002 , apj , 564 , 853 shang , h. , shu , f. h. , & glassgold , a. e. 1998 , apj , 493 , l91 shu , f. , johnstone , d. , & hollenbach , d. 1993 , icarus , 106 , 92 ( sjh93 ) stone , j. m. , & norman , m. l. 1992a , apjs , 80 , 753 stone , j. m. , & norman , m. l. 1992b , apjs , 80 , 791 stone , j. m. , mihalas , d. , & norman , m. l. 1992 , apjs , 80 , 819 strzer , h. & hollenbach , d. 1998 , apj , 502 , l71 strzer , h. & hollenbach , d. 2000 , apj , 539 , 751    ccccccc & [ nii ] & [ nii ] & [ sii ] & [ sii ] & [ sii ] & [ sii ] + & 6583 & 6583 & 6731 & 6731 & 6716 & 6716 +   + & fwhm & shift & fwhm & shift & fwhm & shift + @xmath94 ( deg . ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) +   + 0 & 26.5 & -9.2 & 28.2 & -10.9 & 29.4 & -11.8 + 30 & 28.7 & -8.1 & 29.8 & -9.6 & 31.0 & -10.3 + 60 & 33.2 & -4.9 & 33.2 & -5.6 & 34.2 & -6.0 + 90 & 35.4 & 0.0 & 34.9 & 0.0 & 35.8 & 0.0 +   +   + & fwhm & shift & fwhm & shift & fwhm & shift + region & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) & ( km s@xmath5 ) +   + 0 - 20 @xmath20 & 26.5 & -9.2 & 28.2 & -10.9 & 29.4 & -11.8 + 1 - 20 @xmath20 & 28.0 & -10.3 & 29.2 & -11.4 & 30.4 & -12.3 + 3 - 20 @xmath20 & 31.6 & -11.8 & 31.5 & -11.8 & 32.5 & -12.7 + 5 - 20 @xmath20 & 32.8 & -12.6 & 32.7 & -12.5 & 33.1 & -13.0 +   +","summary":"we examine the ability of photoevaporative disk winds to explain the low - velocity components observed in the forbidden line spectra of low - mass t tauri stars . using the analytic model of shu , johnstone , & hollenbach ( 1993 ) and hollenbach et al . general results from the simulations agree well with the analytic predictions , although some small differences are present .","abstract":"we examine the ability of photoevaporative disk winds to explain the low - velocity components observed in the forbidden line spectra of low - mass t tauri stars . using the analytic model of shu , johnstone , & hollenbach ( 1993 ) and hollenbach et al . ( 1994 ) as a basis , we examine the characteristics of photoevaporative outflows with hydrodynamic simulations . general results from the simulations agree well with the analytic predictions , although some small differences are present . most importantly , the flow of material from the disk surface develops at smaller radii than in the analytic approximations and the flow - velocity from the disk surface is only one - third the sound speed . a detailed presentation of observational consequences of the model is given , including predicted line widths , blue - shifts , and integrated luminosities of observable sulfur and nitrogen emission lines . we demonstrate that these predictions are in agreement with current observational data on the low - velocity forbidden line emission of ionized species from t tauri stars . this is in contrast with magnetic wind models , which systematically under - predict these forbidden line luminosities . however , the present model can not easily account for the luminosities of neutral oxygen lines in t tauri stars ."}
{"article_id":"math0012169","section_id":"i","document":"let @xmath2 be a point configuration in @xmath3 with its convex hull @xmath4 having dimension @xmath0 . a set of @xmath0-simplices with vertices in @xmath2 is a _ dissection _ of @xmath2 if no pair of simplices has an interior point in common and their union equals @xmath4 . a dissection is a _ triangulation _ of @xmath2 if in addition any pair of simplices intersects at a common face ( possibly empty ) . the _ size _ of a dissection is the number of @xmath0-simplices it contains . we say that a dissection is _ mismatching _ when it is not a triangulation ( i.e.  it is not a simplicial complex ) . in this paper we study mismatching dissections of maximal possible size for a convex polytope and compare them with maximal triangulations . this investigation is related to the study of hilbert bases and the hierarchy of covering properties for polyhedral cones which is relevant in algebraic geometry and integer programming ( see @xcite ) . maximal dissections are relevant also in the enumeration of interior lattice points and its applications ( see @xcite and references there ) . it was first shown by lagarias and ziegler that dissections of maximal size turn out to be , in general , larger than maximal triangulations , but their example uses interior points @xcite . similar investigations were undertaken for mismatching minimal dissections and minimal triangulations of convex polytopes @xcite . in this paper we augment previous results by showing that it is possible to have _ simultaneously _ , in the same @xmath1-polytope , that the size of a mismatching minimal ( maximal ) dissection is smaller ( larger ) than any minimal ( maximal ) triangulation . in addition , we show that the gap between the size of a mismatching maximal dissection and a maximal triangulation can grow linearly on the number of vertices and that this occurs already for a family of simplicial convex @xmath1-polytopes . a natural question is how different are the upper and lower bounds for the size of mismatching dissections versus those bounds known for triangulations ( see @xcite ) . we prove lower and upper bounds on their size with respect to the number of vertices for dimension three and exhibit examples showing that our technique of proof fails already in dimension four . here is the first summary of results :    [ main ] [ boundsul ]    1 . there exists an infinite family of convex simplicial @xmath1-polytopes with increasing number of vertices whose mismatching maximal dissections are larger than their maximal triangulations . this gap is linear in the number of vertices @xmath5corollary [ cor.pm]@xmath6 . 2 .   1 .   there exists a lattice @xmath1-polytope with @xmath7 vertices containing no other lattice point other than its vertices whose maximal dissection is larger than its maximal triangulations . 2 .   there exists a @xmath1-polytope with @xmath7 vertices for which , simultaneously , its minimal dissection is smaller than minimal triangulations and maximal dissection is larger than maximal triangulations . + @xmath5proposition [ prop.latticepoly]@xmath6 3 . if @xmath8 is a mismatching dissection of a @xmath1-polytope with @xmath9 vertices , then the size of @xmath8 is at least @xmath10 . in addition , the size of @xmath8 is bounded above by @xmath11 @xmath5proposition [ bounds]@xmath6 . a consequence of our third point is that the result of @xcite , stating a linear gap between the size of minimal dissections and minimal triangulations , is best possible . the results are discussed in sections [ maxdissvsmaxt ] and [ upperlower ] . the last section presents a study of maximal and minimal triangulations for combinatorial @xmath0-cubes , three - dimensional prisms and anti - prisms , as well as other archimedean polytopes . the following theorem and table summarize the main results :    1 .   there is a constant @xmath12 such that for every @xmath13 the maximal triangulation among all possible combinatorial @xmath0-cubes has size at least @xmath14 @xmath5proposition [ combinatorialcube]@xmath6 . 2 .   for a three - dimensional @xmath15-prism , in any of its possible coordinatizations , the size of a minimal triangulation is @xmath16 . for an @xmath15-antiprism , in any of its possible coordinatizations , the size of a minimal triangulation is @xmath17 @xmath5proposition [ prismantip]@xmath6 . the size of a maximal triangulation of an @xmath15-prism depends on the coordinatization , and in certain natural cases it is @xmath18 @xmath5proposition [ maxprism]@xmath6 . 3 .   the following table specifies sizes of the minimal and maximal triangulations for some platonic and archimidean solids . these results were obtained via integer programming calculations using the approach described in @xcite . all computations used the canonical symmetric coordinatizations for these polytopes @xcite . the number of vertices is indicated in parenthesis @xmath5remark [ rem.dhss]@xmath6 : + = cmr8 +    @xmath19 icosahedron ( 12 ) & 15 & 20 dodecahedron ( 20 ) & 23 & 36 cuboctahedron ( 12 ) & 13 & 17 icosidodecahedron ( 30 ) & 45 & ? truncated tetrahedron ( 12 ) & 10 & 13 truncated octahedron ( 24 ) & 27 & ? truncated cube ( 24 ) & 25 & 48 small rhombicuboctahedron ( 24 ) & 35 & ? pentakis dodecahedron ( 32 ) & 54 & ? rhombododecahedron ( 14 ) & 12 & 21","summary":"triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex . the size of a dissection is the number of-simplices it contains . this paper compares triangulations of maximal size with dissections of maximal size . we also exhibit lower and upper bounds for the size of dissections of a-polytope and analyze extremal size triangulations for specific non - simplicial polytopes : prisms , antiprisms , archimedean solids , and combinatorial-cubes .    dissection ; triangulation ; mismatched region ; lattice polytope ; combinatorial-cube ; prism ; antiprism ; archimedean solid    52b45 , 52b05 , 52b70 , 52b55 .","abstract":"a dissection of a convex-polytope is a partition of the polytope into-simplices whose vertices are among the vertices of the polytope . triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex . the size of a dissection is the number of-simplices it contains . this paper compares triangulations of maximal size with dissections of maximal size . we also exhibit lower and upper bounds for the size of dissections of a-polytope and analyze extremal size triangulations for specific non - simplicial polytopes : prisms , antiprisms , archimedean solids , and combinatorial-cubes .    dissection ; triangulation ; mismatched region ; lattice polytope ; combinatorial-cube ; prism ; antiprism ; archimedean solid    52b45 , 52b05 , 52b70 , 52b55 ."}
{"article_id":"1609.00792","section_id":"i","document":"15p / finlay ( hereafter 15p ) was an undistinguished comet discovered by william henry finlay at cape of good hope , south africa , on 1886 september 26 . this comet has a semi - major axis of @xmath9 = 3.488 au , eccentricity of @xmath10 = 0.720 , inclination of @xmath11 = 6.80 , and tisserand parameter with respect to jupiter of @xmath12 = 2.62 , which are typical of jupiter - family comets ( jfcs ) . since the discovery , it showed irregular magnitude light curves at different apparitions @xcite . the effective radius of 15p is estimated to be 0.92 @xmath1 0.05 km @xcite , which is consistent with early results in @xcite and @xcite . it has maintained the perihelion around the earth orbit at 0.981.10 au for about a century and is sometimes linked to a meteor shower @xcite . it is likely that the measured absolute magnitude reduced by a factor of @xmath810 from 7.5 mag in 1886 to 10.1 mag in 1981 @xcite , suggesting that 15p might have lost a fraction of volatile components near the surface while developing a dust mantle layer on the surface similar to other periodic comets ( e.g. , * ? ? ? * ; * ? ? ? the comet exhibited two large - scale outbursts around the perihelion passage in 20142015 , with the first outburst occurring on 2014 december 16 @xcite . the image showed an envelope feature and near  nuclear tail , which is reminiscent of past cometary outbursts at 17p / holmes and 332p/2010 v1 ( ikeya  murakami ) , hereafter referred to as 17p and 332p , respectively @xcite . soon after the report of the first outburst , we conducted an observation from 2014 december 23 to 2015 march 16 for deepening our understanding of cometary outbursts . we used six ground - based telescopes that constitute a portion of the optical and infrared synergetic telescopes for education and research ( oister ) inter - university observation network . as a result of frequent observation several times a week , we witnessed the second outburst on ut 2015 january 15 . such cometary outbursts have drawn the attention of researchers because they offer insight into the physical properties of comet nuclei @xcite . the huge outburst of 17p could be explained by the crystallization of buried amorphous ice @xcite . although similar morphological features were found at 332p @xcite , numerous of fragments were identified at its return in 2016 @xcite . motivated by a series of detections regarding cometary outbursts , we investigated the physical properties of the 15p multiple outbursts and estimated the frequency and mass production rate of outbursts on a scale similar to 15p . we describe our observations and data analysis in section 2 , and the photometric and polarimetric results in section 3 . we then discuss our findings considering the reports of recent outbursts in section 4 .","summary":"multiple outbursts of a jupiter - family comet , 15p / finlay , occurred from late 2014 to early 2015 .","abstract":"multiple outbursts of a jupiter - family comet , 15p / finlay , occurred from late 2014 to early 2015 . we conducted an observation of the comet after the first outburst and subsequently witnessed another outburst on 2015 january 15.615.7 . the gas , consisting mostly of c and cn , and dust particles expanded at speeds of 1,110 180 m s and 570 40 m s at a heliocentric distance of 1.0 au . we estimated the maximum ratio of solar radiation pressure with respect to the solar gravity = 1.6 0.2 , which is consistent with porous dust particles composed of silicates and organics . we found that 10 kg of dust particles ( assumed to be 0.3 1 mm ) were ejected through each outburst . although the total mass is three orders of magnitude smaller than that of the 17p / holmes event observed in 2007 , the kinetic energy per unit mass ( 10 j kg ) is equivalent to the estimated values of 17p / holmes and 332p/2010 v1 ( ikeya  murakami ) , suggesting that the outbursts were caused by a similar physical mechanism . from a survey of cometary outbursts on the basis of voluntary reports , we conjecture that 15p / finlay  class outbursts occur.5 times annually and inject dust particles from jupiter - family comets and encke - type comets into interplanetary space at a rate of kg s or more ."}
{"article_id":"1609.00792","section_id":"r","document":"figure [ fig : timeseries ] shows time - series false - color composite images at the @xmath14band . we chose these images because the @xmath14band is the most sensitive to cometary dust among the available filters . in fact , we examined the contribution of the spherical gas component by using the same technique as that described in section 3.1 of @xcite . we found that gas intensity took up only 10 @xmath1 2% ( within an aperture at @xmath31 km from the nucleus ) of @xmath14band total intensity on ut 2014 december 26 , which supports the weak gas flux contribution shown in figure [ fig : timeseries ] . some images taken in close time intervals are similar and are thus not shown separately . in the first image captured on ut 2014 december 23 ( figure [ fig : timeseries ] ( a ) ) , an envelope structure extends approximately toward the anti - solar direction . it is likely that the envelope is related to the first outburst around ut 2014 december 16 . the surface brightness of the envelope reduced quickly and became undetectable after around ut 2014 december 29 ( figure [ fig : timeseries ] ( c ) ) . after that time , a near nuclear dust coma and dust tail remained . the coma and tail are attributed to steady activity of the comet because both the shape and magnitude were almost constant over several months . a dramatic change was observed in images after ut 2015 january 16 . the inner coma brightened on ut 2015 january 16 ( figure [ fig : timeseries ] ( j ) ) , and dust ejecta appeared soon afterward were stretched toward the anti - solar direction ( figure [ fig : timeseries ] ( k)(n ) ) . the appearance of the dust cloud on ut 2015 january 23 ( figure [ fig : timeseries ] ( n ) ) , is similar to the image taken on ut 2014 december 23 ( figure [ fig : timeseries ] ( a ) ) , in which the comet was enclosed by a widely expanded envelope . the envelope dimmed quickly , leaving behind a near - nuclear dust cloud similar to that from the pre - second outburst . in summary , we observed at least two outburst ejecta superposed on the continuous activity of the comet during its perihelion passage .      to clarify the time variation of the activity in more quantitative manner , we conducted aperture photometry of the dust particles in the inner coma . we set a constant physical aperture distance from the nucleus at @xmath31 km and integrated the signal within @xmath32 by using the iraf / apphot package . the aperture distances correspond to 7.49.9  on the sky plane , which is large enough to enclose the seeing disk sizes of these data ( typically 23 ) but small enough to detect daily changes in dust production ( an ejection speed of @xmath8100 m s@xmath2 was assumed ) . in general , the measured magnitudes are determined not only by the time - variable activity of comets but also by the observing geometry ( i.e. , distances and viewing angles ) . to correct the latter effect , we converted the observed magnitudes into absolute values , which are magnitudes at a unit heliocentric distance @xmath33 = 1 au , observer s distance @xmath34= 1 au , and solar phase angle @xmath35 = 0 . these values were determined by    @xmath36    where @xmath37 and @xmath38 denote the observed and absolute magnitudes in the @xmath14band . the third term in the right - hand side is given to correct the phase darkening , which is given by    @xmath39    where the constant @xmath40 was assumed to a generally quoted value for cometary dust particles , 0.035 mag deg@xmath2 @xcite . over our observation period , the observed magnitudes were subtracted by 2.23.3 mag by eqs . ( [ eq : abs - mag])([eq : phase - func ] ) to convert the absolute magnitudes . figure [ fig : mag ] shows the absolute magnitudes with respect to ( a ) the observed time and ( b ) the true anomaly @xmath41 ; by definition , the perihelion and aphelion occur at @xmath41 = 0  and 180 , respectively . the magnitude was almost constant or slightly decreased by 0.03 mag day@xmath2 until the day of second outburst . a minor eruption appears to have occurred on ut 2015 january 7 with a true anomaly of @xmath41 = 15.1 , brightening the comet by 0.46 @xmath1 0.14 mag . a careful review of the above time - sequence images revealed a sharp tail on ut 2015 january 711 , as shown in figure [ fig : timeseries ] ( f)(h ) . because it extended toward the position angle of 158.4 @xmath1 1.0 , which matches to anti - solar direction on that day ( 158.9 ) , we considered that a sudden ejection of fresh , small grains or ionized particles might have been stretched to the direction soon after the minor eruption on ut 2015 january 7 . a more outstanding brightening was observed on ut 2015 january 16 ( @xmath41 = 26.5 ) . the near - nuclear absolute magnitude was @xmath38 = 6.37 @xmath1 0.10 . after the brightening , the magnitudes remained smaller than the pre - outburst magnitudes over three days and returned to a normal magnitude within about one week . although the image on ut 2015 january 23 ( figure [ fig : timeseries ] ( n ) ) showed the widespread envelope , it is likely that a large part of the dust grains expanded beyond the aperture size of our photometry ( i.e. , @xmath42 km ) and became obscured by a steady stream of ejecta from the nucleus . to eliminate the magnitude excess on ut 2015 january 23 , the outburst ejecta should have an ejection speed able to reach the aperture ( i.e. , @xmath42 km ) . we determined that a large fraction of outburst ejecta should have an effective speed of @xmath4315 m s@xmath2 to reach the aperture radius within one week . polarimetric observation was conducted to find the optical similarities and differences between normal cometary dust and the outburst ejecta . the polarimetric data were acquired about 10 days after the first outburst by using no 1.6 m and hho 1.5 m telescopes . @xmath14band filters were employed for our observations because this band is less contaminated by gaseous components and is sensitive to the solar - like dust spectrum , as we mentioned above ( section [ subsec : results ] ) . we integrated the signals of the observed data within apertures of @xmath32 = 8,000 km and 12,000 km , and derived the polarization degree ( @xmath24 ) and the position angle of the polarization vector ( @xmath21 ) . we obtained @xmath24 = 6.5 @xmath1 0.3% on ut 2014 december 26 and @xmath24 = 7.0 @xmath1 0.5% on ut 2014 december 27 . the position angle was aligned to the normal vector of the scattering plan , that is , @xmath21 = 1 @xmath1 4 . no significant difference was noted within the errors in @xmath24 between measurements with the large and small apertures ( i.e. , @xmath32 = 8,000 km and 12,000 km ) . figure [ fig : pol ] compares the polarimetric results with those of the other comets . the phase angle dependence of the polarization degree is known to be classified into two groups : dust - rich comets with high polarization degrees and gas - rich comets with low polarization degrees @xcite . o1 ( hale  bopp ) did not match these two categories and showed a very high polarization degree @xcite . the polarization degree of 15p fell into common values of comets between gas - rich and dust - rich groups . as described above , the surface brightness of the outburst ejecta faded out within @xmath8seven days from the near - nuclear region in the case of the second outburst , which is likely similar to the case of the first outburst , and was undistinguishable from the background dust particles produced by continuous activity . therefore , the similarity in polarization degree does not mean that the optical properties of outburst ejecta are the same as those in normal comets . as a result of the data analysis , we learned that earlier follow - up observations within @xmath8three days are required to determine the characteristics of such fresh particles during outbursts , such as fluffy or compact optical properties . this topic should be covered in future observation planning .      in this section , we provide an approximate but straightforward estimate of outburst ejecta mass to compare with previous outbursts , and subsequently present a more sophisticated estimate by conducting dynamical analysis of dust particles in section [ subsec : dynamics ] . we measured the total @xmath14band magnitudes with apertures large enough to enclose the entire visible dust cloud for obtaining the total mass of the outburst materials . we set aperture radii of @xmath32 = 4.5  ( ut 2014 december 23 ) and 1  ( ut 2015 january 16 ) , and obtained @xmath37 = 9.44 @xmath1 0.10 ( ut 2014 december 23 ) and @xmath37 = 7.95 @xmath1 0.10 ( ut 2015 january 16 ) . the magnitude was @xmath37 = 11.12 @xmath1 0.12 on ut 2015 january 1113 , which was obtained just prior to the second outburst and well after the first outburst , when little outburst material was present as a result of radiation pressure sweeping . by using eqs . ( [ eq : abs - mag])([eq : phase - func ] ) , we derived the absolute magnitudes of @xmath37(1,1,0 ) = 7.20 @xmath1 0.10 ( ut 2014 december 23 ) , 8.82 @xmath1 0.12 ( ut 2015 january 1113 ) , and 5.61 @xmath1 0.10 ( ut 2015 january 16 ) . with these magnitudes , the optical cross - sections of the dust cloud ( @xmath44 ) were calculated by    @xmath45    where @xmath46 is the geometric albedo ( @xmath46 = 0.04 was assumed ) , and @xmath47 = @xmath48 is the @xmath14band magnitude of the sun at @xmath33 = 1 au @xcite .    by substituting @xmath38 in eq . ( [ eq : crosssection ] ) , we obtained @xmath44 = 3.32 @xmath16 10@xmath49 m@xmath50 ( ut 2014 december 23 ) , 7.47 @xmath16 10@xmath51 m@xmath50 ( ut 2015 january 1113 ) , and 1.44 @xmath16 10@xmath52 m@xmath50 ( ut 2015 january 16 ) . we attributed the cross - section on ut 2015 january 11 - 13 to dust grains ejected via continual activity , which is irrelevant to these outbursts . we subtracted this value from the other two values and obtained the cross - section associated with the first outburst , @xmath44 = 2.56 @xmath16 10@xmath49 m@xmath50 , and the second outburst @xmath44 = 1.36 @xmath16 10@xmath52 m@xmath50 . there is a possibility that we miss some fraction of the cross - section from the first outburst because our data might not cover its entire dust cloud on ut 2014 december 23 . we thus considered the total cross - section of the first outburst ejecta as the lower limit ( i.e. , @xmath44 @xmath53 2.56 @xmath16 10@xmath49 m@xmath50 for the first outburst ejecta ) . the ejecta masses of the outbursts can be given by @xmath54    where @xmath55 and @xmath56 are the effective dust grain radius and mass density , respectively . the effective radius is given by    @xmath57    where @xmath58 denotes the power index of the size distribution in the range of @xmath59 .    with assumptions of @xmath56 = 1000 kg m@xmath60 and @xmath55 = 1 @xmath16 10@xmath61 m ( i.e. , 1 ) , @xmath44 gives @xmath62 @xmath7 3.41 @xmath6310@xmath64 kg for the first outburst and @xmath62 = 1.81 @xmath16 10@xmath4 kg for the second outburst . these values are equivalent to masses of @xmath65 20 m and 35 m bodies . it should be noted , however , that this simple assumption likely underestimated the dust mass . although the small particle ( @xmath55 = 1 ) assumption is occasionally quoted in previous research , abundant evidence exists for large particles from comets , which is subsequently discussed . thus , it is better to consider that the masses should be the lowest limits . @xcite derived @xmath44 = 7 @xmath16 10@xmath5 m@xmath50 for the first outburst and @xmath44 = 2 @xmath16 10@xmath49 m@xmath50 for the second outburst , which are smaller than our estimates . in addition , they reported @xmath62 = ( 23 ) @xmath16 10@xmath66 kg for the first outburst and @xmath62 = ( 45 ) @xmath16 10@xmath66 kg for the second outburst , which are more than two orders of magnitude less than our estimates . although we were unable to verify their results with the information available in their paper , we found that these orders - of - magnitude estimates reveal that the ejecta masses of 15p outbursts are equivalent to that of the 332p event ( 10@xmath410@xmath5 kg ) @xcite . we further investigated the images soon after the second outburst . figure [ fig : col2nd ] shows images taken after ut 2015 january 16.4 on the day in which brightening in figure [ fig : mag ] was detected . we do not show the image taken on ut 2015 january 18 because of its bad quality ( the total exposure time was only 3 min due to unstable weather ) . to clarify the movement of dust grains via solar radiation pressure , we rotated these images to match the sun  comet s direction to the horizontal direction . we produced color images assigning _ g_@xmath13-band images ( the effective wavelength and the full width at half - maximum of @xmath67 = 483 nm and @xmath68 = 134 nm ) to blue ; @xmath14band images ( @xmath67 = 655 nm and @xmath68 = 121 nm ) to green ; and @xmath15band images ( @xmath69 = 799 nm and @xmath68 = 157 nm ) to red colors . in these images , a whitish component expanded in space and simultaneously stretched toward the anti - solar direction . on the contrary hand , a bluish component expanded spherically with respect to the nuclear position . in general , prominent emissions associated with c@xmath70 and cn appear in the _ g_@xmath13 band , weak emissions with nh@xmath70 in the @xmath14band , and negligibly faint signals with nh@xmath70 and cn in the @xmath15band @xcite . in theory , dust particles are accelerated by solar radiation pressure , whereas neutral gas molecules are less sensitive to the radiation pressure and expand almost spherically . thus , it is reasonable to consider that the whitish elongated structure originated from scattered sunlight from dust particles and that the bluish structure originated from cn and c@xmath70 emissions . we attempted to extract the signals from the second outburst and to discriminate the gas flux from the scattered light by dust grains . the observed angles rotated very little over 2015 january 1123 ( that is , 0.4  for the phase angle , 2.4  for the position angles of the anti - solar vector , and 1.4  for the position angle of negative orbital velocity ) . therefore , we subtracted the pre - outburst signals by using images observed on 2015 january 11 ( iao 1.05 m ) and 2015 january 13 ( oao 0.5 m ) from post - outburst images to adjust the apparent sizes of the comet based on the geocentric distances without rotating these images . next , assuming that @xmath15band images have little gas contamination , we subtracted them from _ g_@xmath13-band images by adjusting the @xmath15band intensity scales to minimize the extended dust structure ( i.e. dust tail ) in the residual images to produce gas intensity maps . specifically , we detected a very weak spherical component in the @xmath15band images that likely originated from weak cn emissions at 790820 nm , which were noticeable until ut 2015 january 17 but were unclear after january 19 . we subtracted the faint spherical component in the @xmath15band images by using the above gas intensity maps , scaling the gas intensities to obscure the spherical components in the residuals to produce new dust intensity maps assuming that the intensity distributions of the gas components are the same in _ g_@xmath13 and @xmath15bands . the resultant images are shown in figure [ fig : gasdust ] . as expected , we extracted a spherical structure centered on the nucleus for the gas component associated with the second outburst ( figure [ fig : gasdust ] right ) . the surface brightness reduced rapidly in a few days not only because the gas diffused out in space , but also because the molecules had lifetimes equivalent to the observed period , i.e. , two days for cn and five days for c@xmath70 during the active solar phase ( huebner et al . we then examined the radius of the gas component from the images . figure [ fig : radial ] shows the radial profile of the gaseous coma . considering the sky background noise , we derived the radii of 89@xmath15  on ut 2015 january 16.4 and 182@xmath110  on ut 2015 january 17.4 . assuming that the gas expanded at a constant speed since its ejection , we derived the onset time and expansion speed of the gas component as ut 2015 january 15.5 @xmath1 0.2 and @xmath71 = 1,110 @xmath1 180 m s@xmath2 ( figure [ fig : speed ] ) . we quoted the maximum ranges of these parameters as these errors in consideration of the margin of measurement because we had only two data points , which is insufficient for deriving the errors by using the least squares method . we found that the derived gas speed was slightly faster than the observed values of cn emission at other comets around 1 au probably because we derived the speed at a very large distance from the nucleus ( @xmath72 km ) , where the gas flow velocity continued to increase @xcite .    in the left - hand column of figure [ fig : gasdust ] , we show the dust component images . a short tail was visible on the first night ( a ) , and an irregular cloud appeared on the second night ( b ) that extended toward the anti - solar direction via the radiation pressure . from the apparent cloud size , we derived the ejection onset time . we focused on the widths of the dust cloud perpendicular to the sun  comet direction because dust particles were not accelerated by radiation pressure along that direction . figure [ fig : speed ] shows the time evolution of the dust cloud width . the width increased linearly with the progression of time . by using a linear least squares method , we obtained the onset time on ut 2015 january 15.7 @xmath1 0.1 for dust particles . although this result agrees with the onset time of gas within the accuracy of our measurements , the trivial lag may suggest that the dust required more time to reach terminal velocity , which should be accelerated by the gas outflow . we conclude that the second outburst occurred on ut 2015 january 15.615.7 from gas and dust components . in addition , we derived the dust speed perpendicular to the sun  comet direction as @xmath73 = 280 @xmath1 20 m s@xmath2 . here , we should note that this speed might be misleading . because we measured the speed perpendicular to the sun  comet direction , we must underestimate the ejection speed for dust particles in @xmath73 . to derive the ejection speed , mass , and kinetic energy of the dust cloud in a comprehensive manner , we conducted a model simulation to reproduce the observed morphologies of dust ejecta from the second outburst by following the scheme in @xcite . the morphologies of dust clouds are generally determined by the ejection speeds and the effects of solar radiation pressure , which can be approximately given by a function of grain size . therefore , the sizes and ejection speeds of the dust particles can be determined essentially through an investigation of dust cloud morphologies . for a spherical particle , the ratio of the radiation pressure with respect to the solar gravity ( @xmath74 ) is given as @xmath74 = @xmath75 , where @xmath9 and @xmath76 are dust radius ( m ) and mass density ( kg m@xmath60 ) , and @xmath77 is a radiation pressure coefficient @xcite . here , we assumed @xmath32 = 1@xmath1610@xmath78 kg m@xmath60 and @xmath77 = 1 . for convenience of fitting , we assumed that the dust ejecta consisted of two components , a high  speed envelope and a low  speed tail . we set the ejection epoch of ut 2015 january 15.5 , which gives negligible influence in the result within the error range ( i.e. , 0.1 day ) . for simplicity , we assumed that dust particles were ejected symmetrically with respect to the solar direction within a cone of a half opening angle of @xmath79 . we employed a size  dependent ejection speed of @xmath80 = @xmath81 and power  law size frequency distribution given by @xmath82 = @xmath83 in the range between @xmath84 and @xmath85 . because the ranges of these parameters and fitting scheme are same as those given in @xcite , we do not describe the details here .    through the fitting , we derived the best - fit parameters as shown in table [ tab : parameter ] . because large particles are not sensitive to solar radiation pressure and still resided near the nucleus , we found it impossible to derive the maximum size of particles . we fixed the minimum value for @xmath74 to @xmath86 ( i.e. , @xmath871 mm ) on the ground that large cometary boulders may not be ejected efficiently through outbursts @xcite . figure [ fig : model ] shows a comparison of the observed dust cloud morphology and our best - fit model , which broadly match . however , the entire morphology was not perfectly reconstructed by our model probably because the dust ejection was not symmetric with respect to the solar direction . although we do not intend to upgrade the model fitting by fine tuning the central axis of the dust emission here , we would insist that the outburst location might deviate slightly from the sub - solar point because of this asymmetry . the maximum @xmath74 was determined well to be @xmath3 = 1.6 @xmath1 0.2 because our observation data covered the faint end of the dust cloud , where particles with @xmath3 were dominant . to fit the width and sunward extension of the cloud , we obtained the best fit parameters , @xmath88 = 450 @xmath1 30 m s@xmath2 for the envelope particles and @xmath88 = 330@xmath89 m s@xmath2 for the tail . these parameters resulted in the maximum speed for the smallest particles of @xmath90 = 570 @xmath1 40 m s@xmath2 . for confirmation , we calculated the speed perpendicular to the sun  comet direction with these simulation results , @xmath73 = @xmath91 = 285 @xmath1 40 m s@xmath2 , which is consistent with the value given in section [ subsec : dustgas ] ( i.e. , @xmath73 = 280 @xmath1 20 m s@xmath2 ) . from the model fitting , we determined that @xmath820% of the cross - section originated from the envelop , whereas @xmath880% was from the tail and coma . we calculated the total mass and kinetic energy for the second outburst by using the parameters derived from the simulation ( see table [ tab : parameter ] ) and obtained @xmath62 = 7.0 @xmath16 10@xmath4 kg and @xmath92 = 6.5 @xmath16 10@xmath93 j for the second outburst .","summary":"we estimated the maximum ratio of solar radiation pressure with respect to the solar gravity = 1.6 0.2 , which is consistent with porous dust particles composed of silicates and organics .","abstract":"multiple outbursts of a jupiter - family comet , 15p / finlay , occurred from late 2014 to early 2015 . we conducted an observation of the comet after the first outburst and subsequently witnessed another outburst on 2015 january 15.615.7 . the gas , consisting mostly of c and cn , and dust particles expanded at speeds of 1,110 180 m s and 570 40 m s at a heliocentric distance of 1.0 au . we estimated the maximum ratio of solar radiation pressure with respect to the solar gravity = 1.6 0.2 , which is consistent with porous dust particles composed of silicates and organics . we found that 10 kg of dust particles ( assumed to be 0.3 1 mm ) were ejected through each outburst . although the total mass is three orders of magnitude smaller than that of the 17p / holmes event observed in 2007 , the kinetic energy per unit mass ( 10 j kg ) is equivalent to the estimated values of 17p / holmes and 332p/2010 v1 ( ikeya  murakami ) , suggesting that the outbursts were caused by a similar physical mechanism . from a survey of cometary outbursts on the basis of voluntary reports , we conjecture that 15p / finlay  class outbursts occur.5 times annually and inject dust particles from jupiter - family comets and encke - type comets into interplanetary space at a rate of kg s or more ."}
{"article_id":"1609.00792","section_id":"i","document":"we made an observation of 15p during the perihelion passage in 20152016 , following a report of an outburst in the middle of 2015 december and detected the second outburst on ut 2015 january 15.615.7 , which was equivalent to the first outburst . the results of our analysis are summarized in the following points . 1 .    gas consisting mostly of c@xmath0 and cn expanded at a speed of 1,110 @xmath1 180 km s@xmath2 , which is slightly faster than the speeds for other comets around 1 au . the excess in speed can be explained by the large distance from the nucleus ( @xmath123 km ) , where the gas flow velocity continues to increase . the dust ejecta accelerated up to a speed of 570 @xmath1 40 km s@xmath2 , which is comparable to the ejection speeds of 17p and 332p ejecta . these consistent speeds would have resulted in the similar appearances of these outburst ejecta . we derived the total mass of dust ejecta as 10@xmath410@xmath5 kg ( @xmath9 = 0.3 1 mm was assumed ) . this mass is equivalent to that of the 2010 event at 332p but is three orders of magnitude smaller than the 2007 event at 17p . the polarization degree was measured to 6.8 @xmath1 0.2% at the phase angle @xmath35 = 43 , which fell into the common values of other comets . this similarity does not mean that outburst ejecta have similar polarimetric properties because it was diffused out at the time of our polarimetric measurement . 5 .   based on the immediate observation of dust ejecta for the second outburst , we derived a reliable estimate of @xmath3 = 1.6 @xmath1 0.2 . this value is consistent with the theoretical prediction for porous absorbing particles , suggesting that such porous dust particles could remain inside the cometary nucleus and are released during the outburst . the kinetic energy per unit mass ( 10@xmath6 j kg@xmath2 ) is close to estimated values of 17p and 332p . in addition , the dust mass , speed , and kinetic energy are broadly comparable to the measured values of the 2010 outburst at 332p . this may suggest that these three outbursts occurred by a similar mechanism . 7 .    from a survey of cometary outbursts in publications in the sao / nasa ads , we estimated that 15p / finlay  class outbursts occur annually , injecting cometary materials into interplanetary space at a rate of @xmath4310 kg sec@xmath2 or more .    * acknowledgments * + this research , conducted at seoul national university was supported by the basic science research program through the national research foundation of korea ( nrf ) funded by the ministry of education ( nrf-2015r1d1a1a01060025 , no . 2012r1a4a1028713 ) . the acquisition of observation data was supported by the optical and near - infrared astronomy inter - university cooperation program . we would like to thank seiichi yoshida for useful discussion and s. goda for supporting observation at the nayoro observatory . y. g. kwon is supported by global ph.d fellowship program through the nrf funded by the ministry of education ( nrf-2015h1a2a1034260 ) .","summary":"we conducted an observation of the comet after the first outburst and subsequently witnessed another outburst on 2015 january 15.615.7 . the gas , consisting mostly of c and cn , and dust particles expanded at speeds of 1,110 180 m s and 570 40 m s at a heliocentric distance of 1.0 au . we found that 10 kg of dust particles ( assumed to be 0.3 1 mm ) were ejected through each outburst . although the total mass is three orders of magnitude smaller than that of the 17p / holmes event observed in 2007 , the kinetic energy per unit mass ( 10 j kg ) is equivalent to the estimated values of 17p / holmes and 332p/2010 v1 ( ikeya  murakami ) , suggesting that the outbursts were caused by a similar physical mechanism . from a survey of cometary outbursts on the basis of voluntary reports , we conjecture that 15p / finlay  class outbursts occur.5 times annually and inject dust particles from jupiter - family comets and encke - type comets into interplanetary space at a rate of kg s or more .","abstract":"multiple outbursts of a jupiter - family comet , 15p / finlay , occurred from late 2014 to early 2015 . we conducted an observation of the comet after the first outburst and subsequently witnessed another outburst on 2015 january 15.615.7 . the gas , consisting mostly of c and cn , and dust particles expanded at speeds of 1,110 180 m s and 570 40 m s at a heliocentric distance of 1.0 au . we estimated the maximum ratio of solar radiation pressure with respect to the solar gravity = 1.6 0.2 , which is consistent with porous dust particles composed of silicates and organics . we found that 10 kg of dust particles ( assumed to be 0.3 1 mm ) were ejected through each outburst . although the total mass is three orders of magnitude smaller than that of the 17p / holmes event observed in 2007 , the kinetic energy per unit mass ( 10 j kg ) is equivalent to the estimated values of 17p / holmes and 332p/2010 v1 ( ikeya  murakami ) , suggesting that the outbursts were caused by a similar physical mechanism . from a survey of cometary outbursts on the basis of voluntary reports , we conjecture that 15p / finlay  class outbursts occur.5 times annually and inject dust particles from jupiter - family comets and encke - type comets into interplanetary space at a rate of kg s or more ."}
{"article_id":"astro-ph0203392","section_id":"c","document":"we present first results from our deep , 184.7  ks _ chandra _ map of the lynx field . this is the third - deepest x - ray field observed thus far by _ , exceeded in depth only by the megasecond campaigns in the hdf - n and cdf - s ( hornschemeier et  al . 2001 ; tozzi et  al . 2001 ) . we present a catalog of all 153 unresolved field x - ray sources detected in this survey which will provide essential information on the sources responsible for the soft ( @xmath92  kev ) and hard ( @xmath229  kev ) x - ray backgrounds . we discuss basic results from the x - ray data alone , showing the fainter x - ray sources predominantly have steeper x - ray spectra . we also present multiband optical and near - ir ( @xmath249 ) identifications for the @xmath250%  of lynx _ chandra _ sources which are within the area studied by spices , the @xmath107-selected imaging and redshift survey we are pursuing ( see eisenhardt et  al . we find @xmath251%  of the spectroscopically - studied subsample are identified with galaxies showing obvious agn features ( broad lines and high - ionization emission ) , @xmath17%  are identified with galaxies showing no obvious agn features , and 2 ( @xmath252% ) of the sources are identified with late - type galactic dwarfs . one galactic source , cxo72 , is unusual , having an m7 spectral classification and an unusually hard x - ray spectrum . we discuss this sparse spectroscopic sample in relation to other recently reported deep _ fields and briefly review x - ray emission from sources not showing obvious agn features in their optical spectra . we conclude indirectly that many such sources in our survey must indeed harbor an obscured agn . the catalogs presented here will prove useful for more complete spectroscopic followup allowing direct comparison to models of the x - ray background and studies of the fraction of massive galaxies harboring active , enshrouded nuclei . we are indebted to numerous colleagues for stimulating conversation and insight regarding this work . in particular , we thank john gizis , davy kirkpatrick , john stauffer , jim liebert , and bob rutledge for their input regarding cxo72 , the hard x - ray - emitting , late - type galactic dwarf . we also thank fiona harrison , peter mao , david helfand , and ed moran for contributing discussion regarding the whole breadth of this project . we thank roberto della  ceca for providing us with the hard - band @xmath70 results from _ asca_. the authors wish to extend special thanks to those of hawaiian ancestry on whose sacred mountain we are privileged to be guests . without their generous hospitality , many of the observations presented herein would not have been possible . the work of ds and pe were carried out at the jet propulsion laboratory , california institute of technology , under a contract with nasa . the work of sd was supported by igpp / llnl university collaborative research program grant # 02@xmath3ap@xmath3015 , and was performed under the auspices of the u.s . department of energy by university of california lawrence livermore national laboratory under contract no .  w@xmath37405@xmath3eng@xmath348 . ad s research is supported by noao which is operated by aura under cooperative agreement with the nsf . this work has been supported by the following grants : nsf grant ast  95@xmath328536 ( hs ) and nsf career grant ast  9875448 ( re ) .","summary":"these sources comprise a mix of broad - lined active galaxies / quasars , apparently normal galaxies , and two late - type galactic dwarfs . intriguingly , one galactic source is identified with an m7 dwarf exhibiting non - transient , hard x - ray emission .   ","abstract":"we present our first results on field x - ray sources detected in a deep , 184.7  ks observation with the advanced ccd imaging spectrometer ( acis - i ) on the _ chandra x - ray observatory_. the observations target the lynx field ( + 4454 ) of spices , the spectroscopic photometric infrared - chosen extragalactic survey , which contains three known x - ray - emitting clusters at redshifts of , and 1.27 . not including the known clusters , in the 17  acis - i field we detect 132 sources in the 0.5  kev ( soft ) x - ray band down to a limiting flux of and 111 sources in the 2  kev ( hard ) x - ray band down to a limiting flux of . the combined catalog contains a total of 153 sources , of which 42 are detected only in the soft band and 21 are detected only in the hard band . confirming previous _ chandra _ results , we find that the fainter sources have harder x - ray spectra , providing a consistent solution to the long - standing ` spectral paradox ' .    from deep optical and near - infrared follow - up data , 77% of the x - ray sources have optical counterparts to and 71% of the x - ray sources have near - infrared counterparts to . four of the 24 sources in the near - ir field are associated with extremely red objects ( eros ; ) . we have obtained spectroscopic redshifts with the keck telescopes of 18 of the lynx _ chandra _ sources . these sources comprise a mix of broad - lined active galaxies / quasars , apparently normal galaxies , and two late - type galactic dwarfs . intriguingly , one galactic source is identified with an m7 dwarf exhibiting non - transient , hard x - ray emission .    thirteen of the _ chandra _ sources are located within regions for which we have _ hubble space telescope _ imaging . nine of the sources are detected , showing a range of morphologies : several show compact cores embedded within diffuse emission , while others are spatially extended showing typical galaxy morphologies . two of the _ chandra _ sources in this subsample appear to be associated with mergers .    we briefly review non - agn mechanisms to produce x - ray emission and discuss properties of the lynx _ chandra _ sample in relation to other samples of x - ray and non - x - ray sources .    2 2 2s 2 2hz    # 1to 0pt#1    # 1= # 1#2=.45 = .45 # 1#2#3#4#5#6#7    to#2    ' '' ''"}
{"article_id":"0909.1247","section_id":"i","document":"a long standing question  @xcite asks whether the set of algebraic knots , those that are links of isolated singularities of complex curves , is linearly independent in the knot concordance group . following rudolph s initial work  @xcite , litherland  @xcite used signature functions to prove that the subset consisting of positive torus knots is independent . however , it was then shown in  @xcite by means of an example that invariants of the algebraic concordance group , such as the signature functions , are insufficient to prove the independence of algebraic knots . somewhat later , miyazaki  @xcite showed that the particular example in  @xcite was not _ ribbon _ , and rudolph  @xcite then used this result to conclude that ribbon knots do not behave well with respect to a certain operation called _ plumbing_. here we develop tools based on casson - gordon theory  @xcite to prove the independence of a large family of algebraic knots , a family which includes the particular example first found in  @xcite .    to be more specific , let @xmath0 denote the group of ( topologically locally flat ) concordance classes of knots in @xmath1 , and let @xmath2 denote the algebraic concordance group . in  @xcite , levine constructed a surjection @xmath3 whose counterpart in higher dimensions is an isomorphism . the main result of this article is the following .    * theorem 1 . * _ let @xmath4 denote the subgroup of the knot concordance group @xmath0 generated by algebraic knots : connected links of isolated singularities in @xmath5 . then the intersection of @xmath4 with the kernel of @xmath6 contains an infinitely generated free abelian subgroup . _    we use the following notation : given a knot @xmath7 and a pair of relatively prime integers @xmath8 and @xmath9 , @xmath10 denotes the oriented @xmath11cable of @xmath7 . thus @xmath10 represents @xmath8 times the generator of the first homology of the tubular neighborhood of @xmath7 . in the special case that @xmath7 is the unknot @xmath12 , so that @xmath10 is a torus knot , we use the standard notation of @xmath13 rather than @xmath14 . the notation can be iterated ; for instance , @xmath15 denotes the @xmath16cable of the @xmath11cable of @xmath7 . an _ algebraic knot _ is , by definition , the connected link of an isolated singularity of a polynomial map @xmath17 . a knot is isotopic to an algebraic knot if and only if it is an iterated torus knot @xmath18 with indices satisfying @xmath19 and @xmath20 ( see , for instance ,  @xcite ) . our results concern @xmath21cables of knots . in particular , we resolve an old question of whether a particular linear combination of @xmath21cables is slice ; this combination is the simplest algebraically slice knot in the span of the algebraic knots ,  @xcite :    * theorem 2 . * _ the linear combination of algebraic knots @xmath22 is algebraically slice but has infinite order in @xmath0 . _ theorems 1 and 2 are consequences of the following result , which establishes the linear independence of an infinite collection of algebraic knots . * theorem 3 . * _ for appropriately chosen integers @xmath23 , the set of algebraic knots @xmath24 form a basis of a free abelian subgroup of the concordance group @xmath0 . this subgroup intersects the kernel of @xmath3 in a free abelian subgroup , with basis given by the following set of algebraically slice knots @xmath25 _    our arguments apply more generally , for example to cables of knots other than the trefoil @xmath26 . we refer the reader to the body of the paper for details . the methods we use are those introduced by casson - gordon in  @xcite . a novel feature of our approach is the essential interplay between signature and discriminant invariants on the witt group of hermitian forms over @xmath27 . casson - gordon signature invariants , which are @xmath28valued and hence more effective in identifying elements of infinite order , are often intractable to compute . discriminant invariants are computable algorithmically  @xcite , but because they take values in a group that is @xmath29torsion , they are less effective in determining linear independence . by combining the two types of invariants we are able to apply the power of signatures while bypassing the need to explicitly compute their values ; we can also avoid most of the typically messy work of analyzing metabolizers which plagues many discriminant arguments used to show that certain knots have infinite order in @xmath0 . we finish this introduction by giving some background to place our results in context .    given an oriented knot @xmath7 , let @xmath30 denote the mirror image of @xmath7 with its orientation reversed . two oriented knots , @xmath31 and @xmath32 , are called _ concordant _ if the connected sum @xmath33 bounds a locally flat embedded disk in @xmath1 . the set of concordance classes of knots forms an abelian group @xmath0 with operation induced by connected sum . knots which represent the zero element in @xmath0 are called _ slice_.    from this point forward we do not distinguish in our notation between a knot and its concordance class . in particular , we write @xmath34 for the connected sum @xmath35 . we will also write @xmath36 for @xmath37 , both of which equal @xmath38 . fox and milnor observed  @xcite that if two knots are concordant , then the product of their alexander polynomials is a norm in @xmath39 $ ] : that is , @xmath40 for some polynomial @xmath41 $ ] . ( recall that the alexander polynomial is defined up to multiplication by @xmath42 . ) an early result of seifert  @xcite ( see  ( * ? ? ? * theorem 6.15 ) for a recent reference ) states that the alexander polynomial of a satellite knot is determined by the alexander polynomials of the knots involved in the construction , together with an integer called the winding number . in the case of cables , the formula is given by @xmath43 for a connected sum , the alexander polynomial is simply the product of the alexander polynomials of the constituent knots . a bit of calculation using these facts shows that distinct algebraic knots are not concordant . the levine  tristram signatures of a knot  @xcite , which define integer - valued homomorphisms on @xmath0 , can be used to further show that algebraic knots have infinite order in @xmath0 . these observations might lead one to conjecture that the set of algebraic knots forms a basis for an infinitely generated free abelian subgroup @xmath44 . a first line of attack to this question , as taken in  @xcite and  @xcite , is to consider the _ algebraic concordance group _ @xmath2 and to determine the image of the composite @xmath45 . for the purposes of this article the precise definition of @xmath2 is not needed and it will suffice to say that @xmath2 is the group generated by seifert forms of knots , modulo seifert forms of slice knots . the relevant facts surrounding @xmath2 are :    1 . there is a surjection @xmath3  @xcite . the algebraic concordance class of a knot @xmath7 is determined by its blanchfield ( torsion ) form  @xcite : @xmath46)\\times h_1(s^3-k;\\zz[t^\\pm])\\to\\frac{\\qq(t)}{\\zz[t^\\pm]}.\\ ] ]    with respect to the interplay of cabling and algebraic concordance , the formula  @xcite @xmath47 based on a mayer - vietoris argument , gives a quick method to determine if certain linear combinations of cable knots are _ algebraically slice _ , that is lie in the kernel of @xmath6 .    as observed in  @xcite ( see lemma [ summarylemma ] below ) , this formula implies that the knot in theorem 2 , @xmath48 , is algebraically slice . it represents the simplest example of a knot in the kernel of the composite @xmath45 . showing this knot is not slice has remained open until now , although miyazaki proved it is not ribbon  @xcite . the reader will have noticed that the term `` algebraic '' has two different meanings in this paper ; on the one hand it describes a class of knots defined as links of isolated singularities , and on the other it describes a certain quotient of the knot concordance group . algebraic knots are iterated cables , and we will typically work with general cables , so this should cause no confusion . progress in identifying the structure of algebraic knots in the setting of smooth concordance has been achieved largely through analytic means or the deep combinatorial approach stemming from khovanov homology theory . this is most notable in the solutions to the milnor conjecture and the proof that the smooth 4ball genus of a torus knot is realized by an algebraic curve  @xcite . highlighting the necessity of smooth techniques in studying algebraic knots , rudolph  @xcite observed that the milnor conjecture is false in the topological locally flat category . thus , it comes as a surprise that casson - gordon methods apply so effectively in the present setting , having the further advantage that we can establish the independence of these knots in the topological concordance group . nonetheless , it would be interesting to know the extent to which the array of existing smooth concordance invariants can be used to address the question of independence of algebraic knots . we should point out , however , that the ozsvth - szab  @xcite and rasmussen  @xcite concordance invariants , @xmath49 and @xmath50 , coming from knot floer homology and khovanov homology , respectively , contain no information for the knots at hand . we make this precise in proposition [ prop : stau ] , which shows that both invariants vanish for the family above and its obvious generalization to positively iterated torus knots .    despite the failure of @xmath50 and @xmath49 , it seems likely that grading information from the floer homology of branched covers ( in the form of the fryshov invariant  @xcite , ozsvth - szab correction terms  @xcite , or chern - simons invariant of @xmath51 representations  @xcite ) could be useful in our pursuit . however , extensive computations of such invariants in the first two cases is difficult , and computing chern - simons invariants of covers in the spirit of fintushel - stern  ( * ? ? ? * theorem 5.1 ) and furuta  ( * ? ? * theorem 2.1 ) have failed to determine if any member of the family of knots in the present article are slice . * acknowledgment : * conversations with tom mrowka about the ribbon - slice conjecture led naturally to the investigations of this paper . the relationship between this ribbon - slice problem and the concordance independence of algebraic knots is discussed in the second appendix .","summary":"we show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup .    [ multiblock footnote omitted ]","abstract":"we show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup .    [ multiblock footnote omitted ]"}
{"article_id":"1101.1033","section_id":"i","document":"frobenius splittings of algebraic varieties appear prominently in tight closure theory , have emerged as a fundamental tool in the study of the representation theory of algebraic groups , and have tantalizing links to concepts in the minimal model program . suppose that @xmath6 is a reduced ring of characteristic @xmath7 with normalization in its total ring of fractions @xmath8 . it follows from ( * ? ? ? * exercise 1.2.4(e ) ) that if @xmath9 is frobenius split then so is @xmath10 . the goal of this paper is to study to what extent the converse holds . of course , there are many non - frobenius split affine varieties whose normalizations are regular and thus frobenius split ( for example , the cusp @xmath11 in any characteristic ) and so we focus our attention not just on the ring , but on the ring and a choice of a potential frobenius splitting .    by definition , frobenius splitting _ on a variety @xmath12 is an @xmath13-linear map @xmath14 which sends the section @xmath15 to @xmath15 . when @xmath0 is affine , the existence of a frobenius splitting is equivalent to existence of a map @xmath14 such that @xmath16 for some section @xmath17 ( in other words , to require that @xmath4 is surjective ) .    on a normal @xmath12 , surjective maps @xmath18 are very closely related to boundary divisors @xmath19 such that @xmath20 is log canonical , see @xcite and @xcite . based upon our intuition with non - normal log canonical singularities ( which are usually called _ semi - log canonical _ ) one should be able to detect surjective @xmath18 by studying the normalization of @xmath0 . in fact , this correspondence between log canonical pairs @xmath20 and surjective @xmath4 suggests that the following question should have an affirmative answer . [ quest.motivation ] suppose that @xmath0 is an affine variety in characteristic @xmath7 with normalization @xmath21 , and set @xmath22 to be the @xmath23-iterated frobenius . given a map @xmath24 , it always extends to a unique map @xmath25 . if @xmath26 is surjective , does it follow that @xmath4 is also surjective ? perhaps unfortunately , this question has a negative answer . a counterexample is given by the scheme @xmath27/(x^2y - z^2)$ ] , ( * ? ? ? * example 8.4 ) . however , that counterexample possesses substantial inseparability : if @xmath28 is the non - normal locus of @xmath0 and @xmath29 is its pre - image inside @xmath30 , then the induced map @xmath31 is generically inseparable . we show that if we can avoid this inseparability and also a certain variant of wild ramification , then the question has a positive answer . in particular , we say that a ring possesses _ _ if it avoids these positive characteristic pathologies ( see definition [ def.hst ] for a precise definition ) . our main theorem follows :    [ thm : maintheorem ] [ theorem [ thm : main ] ] suppose that @xmath0 is a reduced @xmath5-finite affine scheme having . further suppose that @xmath24 is an @xmath13-linear map . if the unique extension @xmath25 is surjective , then @xmath4 is also surjective . the main theorem should also be viewed as complementary to ( * ? ? ? * theorem 6.26 ) . in the context of a finite surjective map @xmath32 between _ normal _ varieties , that result answers the same question for @xmath14 and its extension @xmath33 ( if it exists ) . also see @xcite where 1-dimensional non - normal @xmath5-pure rings are studied . we now discuss in more detail the motivation for this theorem . in this context , maps @xmath34 correspond to @xmath35-divisors @xmath19 on @xmath30 such that @xmath36 is @xmath35-cartier , see @xcite and section [ sec : prelim ] . the condition @xmath4 being surjective ( _ i.e. _ the pair @xmath37 being @xmath5-pure ) corresponds to the pair @xmath37 having log canonical singularities @xcite , @xcite . on a characteristic zero variety @xmath0 that is s2 ( _ i.e. _ serre s second condition ) and g1 ( _ i.e. _ gorenstein in codimension @xmath15 ) with normalization @xmath38 and conductor divisor @xmath39 , if there exists a @xmath40-divisor @xmath41 on @xmath0 such that @xmath42 is @xmath35-cartier and furthermore that @xmath43 is log canonical , then @xmath44 is called _ semi - log canonical_. via the map-(@xmath4 ) divisor-(@xmath19 ) correspondence , our main theorem should be interpreted as saying :    ll    as an explicit example of this statement , and of the translation between maps @xmath45 and divisors , we have the following corollary of our main theorem , a criterion for certain non - normal algebraic varieties to be @xmath5-split . * corollary [ cor.hstnormalizationqgorenstein ] . * _ suppose that @xmath12 is an affine @xmath5-finite scheme satisfying and which is also s2 , g1 and @xmath40-gorenstein with index not divisible by the characteristic @xmath46 . set @xmath30 to be the normalization of @xmath0 and set @xmath29 to be the divisor on @xmath30 corresponding to the conductor ideal , _ i.e. _ @xmath47 . then @xmath0 is @xmath5-pure ( equivalently @xmath5-split ) if and only if @xmath48 is @xmath5-pure . _ in the above corollary , if one replaces the two occurrences of the word @xmath5-pure by semi - log canonical and log canonical ( respectively ) , one obtains a well known criterion for a scheme having semi - log canonical singularities , see @xcite .    more generally , the correspondence between log canonical and @xmath5-pure singularities is still conjectural , although an area of active research . [ conj.fpurevslogcanonical ] suppose that @xmath49 is a normal variety of characteristic zero and that @xmath19 is a divisor on @xmath49 such that @xmath50 is @xmath35-cartier . the pair @xmath51 is log canonical if and only if @xmath51 has dense @xmath5-pure type pair @xmath52 has dense @xmath5-pure type if the map corresponding to @xmath19 is surjective after reduction to characteristic @xmath7 for infinitely many @xmath7 . see @xcite for more details . ] . see @xcite and @xcite for connections between this conjecture and open conjectures in arithmetic geometry ( these connections will not be utilized in this paper ) . the setting for our applications will necessarily deal with geometry on non - normal schemes , and as such we will be dealing with an extended notion of divisors , see @xcite . for us , the important divisors are the @xmath35-almost cartier divisor ( or simply _ @xmath35-ac divisors _ ) , and we will review the definitions in detail in section [ sec : divisors ] . our main result implies the following : * corollary [ cor.fpurevsslc ] . * _ assume now that @xmath0 is an s2 , g1 and seminormal variety in characteristic zero . further suppose that @xmath19 is an @xmath35-ac divisor ( _ i.e. _ @xmath35-weil sheaf ) on @xmath53 assuming that conjecture [ conj.fpurevslogcanonical ] holds , @xmath20 has semi - log canonical singularities if and only if it has dense @xmath5-pure type . _ another application of theorem [ thm : maintheorem ] is to give a statement of inversion of adjunction for divisors on characteristic @xmath7 schemes with that closely aligns with the characteristic @xmath54 picture , compare with @xcite . inversion of adjunction for characteristic @xmath7 schemes was studied first in @xcite , see also takagi @xcite and @xcite . however the direct analog of kawakita s result is not possible in characteristic @xmath7 ( * ? ? ? * example 8.4 ) . the culprit is the same conditions of inseparability and wild ramification which obstruct a positive answer to the motivating question . however : * corollary [ cor.invofadj ] . * _ suppose that @xmath0 is a normal scheme of characteristic @xmath7 , @xmath19 is a @xmath35-divisor on @xmath0 and @xmath55 is a reduced integral weil divisor on @xmath0 , with no common components with @xmath19 , such that @xmath56 is @xmath35-cartier with index not divisible by @xmath46 . denote by @xmath57 the normalization of @xmath55 and @xmath58 the natural map . there exists a canonically determined @xmath35-divisor @xmath59 on @xmath57 such that @xmath60 . furthermore , if @xmath61 has , then @xmath62 is @xmath5-pure near @xmath55 if and only if @xmath63 is @xmath5-pure . _ -12pt_acknowledgements : _ the authors would like to thank bryden cais , neil epstein and kevin tucker for inspiring conversations related to this project . the authors would also like to thank the referee , shunsuke takagi and kevin tucker for numerous useful comments on an earlier draft of this manuscript . this work was initiated when the second author was visiting the university of utah during fall 2010 .","summary":"our result has geometric consequences including a connection between-pure singularities and semi - log canonical singularities , and a more familiar version of the (-)inversion of adjunction formula .   ","abstract":"if is frobenius split , then so is its normalization and we explore conditions which imply the converse . to do this , we recall that given an-linear map , it always extends to a map on the normalization of . in this paper , we study when the surjectivity of implies the surjectivity of . while this does nt occur generally , we show it always happens if certain tameness conditions are satisfied for the normalization map . our result has geometric consequences including a connection between-pure singularities and semi - log canonical singularities , and a more familiar version of the (-)inversion of adjunction formula .    frobenius map , frobenius splitting , f - purity , semi - log canonical , log canonical , inversion of adjunction , normalization , seminormal"}
{"article_id":"1602.07593","section_id":"i","document":"the vickrey - clarke - groves ( vcg ) mechanism stands as one of the pillars of mechanism design theory , but in the real world is used with surprising rarity . in past work , this mismatch between theory and practice has been attributed to a number of properties that affect the mechanism in certain settings , like susceptibility to collusion or prohibitive computational costs  @xcite . here we identify another property of the mechanism that may be problematic in practice , a relative lack of robustness to inaccuracies in the choice of its parameters . unlike most of the known deficiencies it applies already in settings with unit demand . we start from the standard position auction model of @xcite and @xcite , where  @xmath0 bidders compete for the assignment of  @xmath1 positions . bidders have unit demand and the value of bidder  @xmath2 for position  @xmath3 is given by @xmath4 , where @xmath5 is a bidder - specific value and a non - increasing vector @xmath6 describes the relative values of the positions . the most prominent application of this model is to sponsored search , which contributed over 90% to google s revenue of $ 66 billion in 2014 . what is rather curious is that all successful sponsored search services have used non - truthful auction mechanisms . overture , the first company to provide such a service , used a generalized first - price ( gfp ) mechanism . google and microsoft use a generalized second - price ( gsp ) mechanism . facebook does use the vcg mechanism to place ads , but not in the context of sponsored search and not in a position auction . it is hard to say in retrospect what led to the choice of non - truthful mechanisms over a truthful one , and changing the mechanism at this point would clearly come with huge financial risks . we will see , however , that under certain assumptions choosing the non - truthful mechanisms may have been wise even if it was not entirely deliberate . a mechanism for the above setting accepts a bid  @xmath7 for each bidder  @xmath2 and from these bids determines a one - to - one assignment of bidders to positions and a monetary payment for each bidder . bidder behavior can then be analyzed using game - theoretic reasoning , where it is commonly assumed that each bidder tries to maximize the value of its assigned position minus its payment . in the vcg mechanism in particular it is an equilibrium for each bidder to bid its true valuation , and we refer to the resulting assignment and payments in a given situation as the truthful vcg outcome . in addition to the standard model of auction theory , where bidders have only probabilistic information about one another s valuations , it has become common to analyze position auctions also in a complete - information model where valuations are common knowledge among the bidders . this is motivated by practical auctions that provide bidders with aggregate statistics of others bids and thus enable best - response bidding , by empirical support that has been given for a family of nash equilibria  @xcite , and by cyclic bidding behavior observed in the absence of pure nash equilibria  @xcite . the bid  @xmath7 can be interpreted alternatively as a vector of bids @xmath8 , one for each position  @xmath3 . here we vary the standard model by assuming that mechanisms instead work with bids @xmath9 , where @xmath10 is another non - increasing vector and generally @xmath11 . we then ask for which values of  @xmath12 and  @xmath13 different mechanisms obtain the truthful vcg outcome in equilibrium . intuitively this question concerns the robustness of mechanisms to uncertainty regarding the true value of  @xmath13 . it draws its motivation from current practice to infer  @xmath13 from data using machine learning techniques , which will hopefully produce a good estimate @xmath14 but will usually mean that @xmath11 . this is , however , not currently being done  ( e.g. , * ? ? ? * ; * ? ? ? indeed there are good reasons why the value of a position may depend on other factors besides the probability of a click . @xcite for example considers a situation with two types of users of a search engine , one of them genuinely interested in the products being advertised and one merely curious . the two types come with different rates at which clicks on an advertisement result in a purchase , but are indistinguishable from the point of view of the search engine . ] the truthful vcg outcome is a natural point of reference for at least two reasons . under complete information it coincides with the bidder - optimal envy - free outcome , which happens to be unique  @xcite . under incomplete information it is the unique outcome compatible with the maximization of social welfare  @xcite . we show that under both complete and incomplete information a non - truthful mechanism obtains the truthful vcg outcome in an equilibrium for a strictly larger set of values of  @xmath12 and  @xmath13 than the vcg mechanism itself . failure of the vcg mechanism to support the truthful vcg outcome in fact occurs already when  @xmath12 is very close to  @xmath13 . the result for complete information concerns the gsp mechanism and is developed in section  [ sec : complete ] in two steps . through direct arguments that combine the equilibrium conditions and the structure of allocation and payments in the truthful vcg outcome we obtain precise characterizations , for both the vcg and the gsp mechanism , of those values of @xmath12 and @xmath13 that enable this outcome in equilibrium . we then exploit the recursive nature of vcg payments to show that any violation of the characterization for the gsp mechanism necessarily leads to a violation of the characterization for the vcg mechanism .    in section  [ sec : incomplete ] the same type of result is shown for incomplete information , but here the vcg mechanism is compared to the gfp mechanism and a more elaborate argument is required to establish superiority of the latter . we begin with a standard technique for characterizing equilibria , by equating the expected payments in a welfare - maximizing equilibrium as given by myerson s lemma with the respective payments in the two mechanisms . this gives us a candidate equilibrium bidding function for each the two mechanisms , and each of these functions constitutes an equilibrium if and only if it is strictly increasing almost everywhere . in the case of the vcg mechanism we encounter an ordinary differential equation , but avoid the use of heavy machinery by appealing to a surprising combinatorial equivalence . even with the bidding functions for the vcg and gfp mechanisms at hand it is not trivial to show that the latter is increasing for a larger set of values of  @xmath12 and  @xmath13 , and we use a surprising connection between the two functions to show that this is indeed the case .    that the vcg mechanism fails already when  @xmath12 is very close to  @xmath13 is shown by means of two examples in sections  [ sec : complete - example ] and  [ sec : incomplete - example ] . in these examples equilibria supporting the truthful vcg outcome cease to exist when mechanisms underestimate the value of less valuable positions . this makes the less valuable positions more attractive by reducing their associated payments , incentivizing bidders to shade their bid and do so more strongly as their value increases . the relatively lower payments in the vcg mechanism only magnify this effect and cause it to fail for smaller discrepancies between  @xmath12 and  @xmath13 . in settings with sufficiently many positions the failure also occurs when mechanisms overestimate the quality of some positions but underestimate the quality of others . more generally , the gsp and gfp mechanisms seem to benefit from the relative simplicity of their payments , which for a given position depend only on one bid . in the vcg mechanism a particular bid may simultaneously affect the payments of many bidders , setting the correct equilibrium payments thus becomes impossible more quickly as  @xmath12 and  @xmath13 move out of alignment . an orthogonal requirement for equilibrium existence that favors different non - truthful mechanisms under complete and incomplete information is that a bidder s ability to control its own payment must match the degree of knowledge it has of other bidders valuations . it is well known , for example , that the gfp mechanism may not possess a pure nash equilibrium under complete information  @xcite and that the gsp mechanisms may not possess a welfare - maximizing bayes - nash equilibrium under incomplete information  @xcite , even when  @xmath15 . the main focus of our analysis is on mechanisms and parameters currently in use . the investigation of additional mechanisms and parameters , and of the interaction between the auction mechanisms and the learning algorithm used to infer  @xmath13 from data , provide ample scope for future work . an increased robustness of non - truthful mechanisms for position auctions in the sense we discuss here was first suggested by @xcite , who compared the gsp and vcg mechanisms in a complete - information setting . this result was then strengthened by @xcite , who identified a single value of  @xmath12 with which the gsp and gfp mechanisms respectively obtain the truthful vcg outcome under complete and incomplete information for all values of  @xmath13  @xcite , as well as a single gfp mechanism with more expressive bids that achieves the same under both complete and incomplete information  @xcite . what distinguishes our results from this past work is that they characterize , for any given value of  @xmath13 , which values of  @xmath12 enable the truthful vcg outcome . they thus apply in particular to mechanisms currently in use .    the performance of the vcg mechanism and that of alternative , non - truthful mechanisms have also been compared in the standard position auction model , where @xmath15 , and a number of authors have noted certain advantages or lack of disadvantages of the alternative mechanisms . under complete information , the gsp mechanism obtains the truthful vcg outcome in a locally envy - free equilibrium , and payments that at least match those of the truthful vcg outcome in any locally envy - free equilibrium  @xcite . under incomplete information the gfp mechanism admits a unique bayes - nash equilibrium , which yields the truthful vcg outcome  @xcite . each of the two mechanisms has severe disadvantages in the respective other setting , such as non - existence of a pure nash equilibrium or of an efficient bayes - nash equilibrium  @xcite . in cases where equilibria exist , however , the worst - case welfare loss is bounded in the sense of a small price of anarchy  @xcite . and @xmath13 for which the price of stability is one . arguments similar to the ones used to establish the price - of - anarchy guarantees for the standard model also apply to the more general setting we study here , providing welfare guarantees that degrade gracefully in  @xmath12 and  @xmath13 . ] in the standard model , and other things being equal , the vcg mechanism of course has the advantage of truthfulness . our results concern a more general and arguably more realistic model and apply in a very similar way to both complete- and incomplete - information environments . a concurrent line of research has sought to emphasize the advantages of non - revelation mechanisms for position auctions under incomplete information  @xcite . in addition to uniqueness of equilibria these include computational tractability , amenability to statistical inference , and the ability to approximately maximize welfare in general one - dimensional environments . our results finally fit more generally into an increasing body of work that emphasizes robustness and simplicity in economic and algorithmic design . relevant examples of this type of work in economics include the literature on robust mechanism design  @xcite and the design of the upcoming fcc incentive auctions  @xcite . the former seeks to obtain mechanisms with more robust common knowledge assumptions and has in fact identified robustness properties that directly lead to simpler mechanisms as an important direction . the latter employs a greedy mechanism to achieve computational and strategic simplicity . additional examples come from algorithmic game theory , where recent work has obtained simple mechanisms with near - optimal revenue  @xcite or welfare  @xcite , but has also pointed out computational barriers to near - optimal equilibria  @xcite .","summary":"we exhibit a property of the vcg mechanism that can help explain the surprising rarity with which it is used even in settings with unit demand : a relative lack of robustness to inaccuracies in the choice of its parameters . for a standard position auction environment in which the auctioneer may not know the precise relative values of the positions , we show that under both complete and incomplete information a non - truthful mechanism supports the truthful outcome of the vcg mechanism for a wider range of these values than the vcg mechanism itself . the result for complete information concerns the generalized second - price mechanism and lends additional theoretical support to the use of this mechanism in practice . particularly interesting from a technical perspective is the case of incomplete information , where a surprising combinatorial equivalence helps us to avoid confrontation with an unwieldy differential equation .","abstract":"we exhibit a property of the vcg mechanism that can help explain the surprising rarity with which it is used even in settings with unit demand : a relative lack of robustness to inaccuracies in the choice of its parameters . for a standard position auction environment in which the auctioneer may not know the precise relative values of the positions , we show that under both complete and incomplete information a non - truthful mechanism supports the truthful outcome of the vcg mechanism for a wider range of these values than the vcg mechanism itself . the result for complete information concerns the generalized second - price mechanism and lends additional theoretical support to the use of this mechanism in practice . particularly interesting from a technical perspective is the case of incomplete information , where a surprising combinatorial equivalence helps us to avoid confrontation with an unwieldy differential equation ."}
{"article_id":"0903.0425","section_id":"i","document":"let @xmath2 be a random force field on @xmath0 defined on a probability space @xmath3 . the motion of a particle is described by the equation @xmath4 where @xmath5 denotes the position of the particle at time @xmath6 . let @xmath7 be the velocity of the particle at time @xmath6 . as initial conditions we take @xmath8 and @xmath9 , where @xmath10 is a non - random vector . the force field is assumed to be stationary and isotropic . the precise form of the force field will be discussed below . we shall be interested in the asymptotic behavior of @xmath5 and @xmath11 as @xmath12 . the process @xmath11 can be written in the integral form as @xmath13 formal arguments , based on the near - independence of contributions to the integral on the right - hand side of ( [ vel ] ) from non - intersecting sub - intervals , suggest that @xmath11 behaves as a diffusion process , if time is re - scaled appropriately . in fact , we shall prove that there is an event @xmath14 in the underlying probability space @xmath15 , such that @xmath16 as @xmath17 , and @xmath18 converges , as @xmath19 , to a diffusion process on @xmath14 ( the probability measure on @xmath14 is defined by conditioning @xmath20 on the event @xmath14 ) . in particular , the kinetic energy of the particle will be shown to tend to infinity as @xmath12 . the precise formulation of these results will be provided in section  [ mr ] . we can not , however , expect that @xmath18 converges to the diffusion process for almost all realizations of the force field , if @xmath10 is fixed . indeed , depending on the assumptions imposed on @xmath2 , the trajectory may remain in a bounded region of space and the velocity may remain bounded with positive probability .    it must be noted that we must exclude the case @xmath21 , where @xmath22 is a stationary field , since in this case @xmath23 is a hamiltonian flow with the hamiltonian @xmath24 ) . earlier papers primarily studied the behavior of @xmath5 and @xmath11 on long time intervals , whose length , however , depended on @xmath25 , where the initial velocity @xmath10 was treated as a large parameter . we shall assume that @xmath10 is fixed and @xmath6 tends to infinity . the trade - off is that we need to exclude an event of small but positive measure from the underlying probability space . let us mention some of the earlier results concerning the long - time behavior of @xmath5 and @xmath11 . in @xcite , kesten and papanicolaou considered the equation @xmath26 with the initial data @xmath27 and @xmath28 . certain mixing assumptions were imposed on the force field @xmath2 . it was shown that if @xmath29 , the process @xmath30 converges weakly to a diffusion process @xmath31 with the initial data @xmath32 . the generator of the limiting process can be written out explicitly . the process @xmath33 converges weakly to @xmath34 . note that equations ( [ large ] ) and ( [ small ] ) are related via the change of variables @xmath35 therefore , the convergence result for @xmath30 can be formulated in terms of @xmath11 as follows : the process @xmath36 converges to a diffusion process when @xmath10 tends to infinity in such a way that @xmath37 remains fixed . similarly , @xmath38 converges weakly to a limiting process .    in @xcite , durr , goldstein , and lebowitz extended the convergence results to the two - dimensional case . the field @xmath2 was assumed to be a gradient of @xmath39 , where @xmath40 is a smooth function with compact support , and the points @xmath41 form a poisson field on the plane . an additional difficulty in the two - dimensional case is that , unlike the case with @xmath29 , typical trajectories of ( [ large ] ) will self - intersect . in @xcite , komorowski and ryzhik proved the two - dimensional result in the case when @xmath22 is sufficiently mixing , but is not necessarily generated by a poisson field .    in @xcite , komorowski and ryzhik considered the process ( [ large ] ) on a longer time scale . namely , they demonstrated that @xmath42 converges to a brownian motion for all sufficiently small @xmath43 . it was assumed that @xmath44 , where @xmath22 is sufficiently mixing .    unlike the above papers , we shall consider the asymptotic behavior of @xmath11 when @xmath10 is fixed and @xmath12 . first , however , assume that @xmath45 , @xmath46 , and let @xmath47 be the limiting process for @xmath48 as @xmath45 . ( it satisfies the stochastic differential equation ( [ diff1 ] ) , below . ) as has been noted by dolgopyat and de la llave in @xcite , the process @xmath47 is self - similar , that is for @xmath49 the process @xmath50 satisfies the same stochastic differential equation with initial condition @xmath51 . therefore , for @xmath52 fixed , @xmath53 tends to the diffusion process ( [ diff1 ] ) starting at @xmath54 . if , instead , we assume that @xmath10 is large but fixed , and take the limit as @xmath55 , we formally obtain that @xmath56 tends to the diffusion process ( [ diff1 ] ) starting at the origin . we remark that the diffusion processes satisfying the self - similarity property described above are well understood ( see e.g. @xcite , section xi ) . in particular the fact that this process is non - recurrent for @xmath57 plays a crucial role in our analysis .","summary":"department of mathematics , university of maryland    college park , md 20742    dmitry@math.umd.edu , koralov@math.umd.edu    _ mathematical subject classification : _ 60k37","abstract":"we consider the motion of a particle in a random isotropic force field . assuming that the force field arises from a poisson field in , , and the initial velocity of the particle is sufficiently large , we describe the asymptotic behavior of the particle .    department of mathematics , university of maryland    college park , md 20742    dmitry@math.umd.edu , koralov@math.umd.edu    _ mathematical subject classification : _ 60k37"}
{"article_id":"1301.6412","section_id":"i","document":"this paper addresses a version of the random access model of luo , epremides @xcite and wang , luo @xcite , which is similar to the model studied for one - way channels by csiszr @xcite . in the terminology of this paper , in @xcite the performance of a codebook library consisting of several constant composition codebooks with pre - determined rates has been analyzed . it has been shown that simultaneously for each codebook the same error exponent can be achieved as the random coding exponent of this codebook alone . this theorem is used in @xcite to give an achievable error exponent for joint source - channel coding ( jscc ) .    here , the mentioned results of @xcite are generalized to ( discrete memoryless ) multiple access channels ( macs ) . a two - senders random access model is introduced , in which the senders have codebook libraries with constant composition codebooks for multiple rate choices . the error exponent of liu and hughes @xcite for an individual codebook pair is shown to be simultaneously achievable for each codebook pair in the codebook libraries , supplemented with collision detection in the sense of @xcite . this is achieved via a universal decoder , hence , a positive answer is given to the question in @xcite whether or not the results there are still valid if the receiver does not know the channel . moreover , achievable jscc error exponents for transmitting independent sources over a mac are given , admitting improvements when special error free @xmath0 rate communication is allowed between the two senders . the most direct extension of the jscc result in @xcite is obtained in the latter case . nazari , anastasopoulos , and pradhan in @xcite derive achievable error exponents for mac s using @xmath1-decoding rules introduced for one - way channels by csiszr and krner in @xcite . in the present paper a particular @xmath1-decoder is used , modified similarly as in @xcite and supplemented by a threshold criterion in order to allow collision detection . as the proofs follow @xcite closely , it can be seen that other @xmath1-decoders could also be appropriate , depending on actual assumptions on the analyzed models . note that another multiterminal generalization of the jscc result in @xcite appears in zhong , alajaji , campbell @xcite . we also mention that this paper , as @xcite , has connections with the topic of unequal protection of messages , see for example borade , nakiboglu , zheng @xcite . finally we list here some connected recent papers . luo in @xcite generalizes the earlier results in @xcite . papers @xcite and @xcite by wang , ingber , kochman and shkel , tan , draper , respectively , analyze the models and the results of @xcite in the finite blocklength regime . campo , vazquez - vilar , fbregas , koch , martinez in @xcite analyze the jscc exponent achieved in @xcite for one - way channels in greater detail .","summary":"the result is used to give an achievable joint source - channel coding error exponent for multiple access channels in the case of independent sources .","abstract":"a new universal coding / decoding scheme for random access with collision detection is given in the case of two senders . the result is used to give an achievable joint source - channel coding error exponent for multiple access channels in the case of independent sources . this exponent is improved in a modified model that admits error free rate communication between the senders .    random access , error exponent , multiple access , source - channel coding , collision detection , rate communication"}
{"article_id":"quant-ph0610016","section_id":"i","document":"the knowledge of the density matrix at finite temperature @xmath0 for few interacting particles , is of paramount importance for studying equilibrium properties of quantum many - body systems . indeed , such density matrices occur in low - fugacity expansions , while they are also key ingredients in quantum monte carlo simulations . in this context , the feynman - kac ( fk ) representation of the density matrix in terms of path integrals  @xcite is particularly useful . on the one hand , it has been used for deriving exact ( analytical ) expressions for simple models  @xcite . on the other hand , beyond the well - known wigner - kirkwood expansion  @xcite around the classical limit , various approximations , non - perturbative in @xmath1 , have been introduced within that framework : for instance , the celebrated semi - classical approximation  @xcite ( widely used in numerous situations ) , the variational approach of feynman and kleinert  @xcite , or the renormalized wigner - kirkwood scheme . the fk representation is described in sec . [ quantumformalism ] . for the sake of simplicity , we consider the simple case of a single particle in one dimension submitted to a stationary confining potential . the mean spatial extension of the brownian paths , which intervene in the fk representation , is controlled by the thermal de broglie wavelength of the quantum particle . at high temperatures , since that extension vanishes , exact asymptotic expansions , as well as direct numerical estimations , become rather straightforward . at the analytical level , wigner - kirkwood @xmath2-expansions around the classical limit , which have been derived long ago in other frameworks , are easily recovered . on the computational side , functional integration over paths can be replaced , within a good accuracy , by ordinary integrals over a discrete set of parameters , _ via _ the use of either free propagators in trotter formula  @xcite or simple modelizations of brownian paths  @xcite . however , at low temperatures , similar calculations loose accuracy , while they also become rather time - consuming . moreover , the corresponding asymptotic structure of the density matrix , provided by the groundstate contribution in its spectral expression , does not clearly emerge from its fk representation . in fact , in that temperature regime , the average extension of paths diverge , whereas the main contribution to the functional integral arises from paths with a finite extension , of the order of the localization length of the ground state : contributions of such minority paths are significantly different from the average contribution . most of our knowledge is negative , i.e. tells us which trajectories are not important  @xcite , so , in some sense , we will try to have a positive attitude  @xcite .    in this paper , we derive a new functional representation of the density matrix , which is more suitable than the genuine fk formula for tackling the low - temperature regime ( see sec .  [ rewritingfeynamankac ] ) . the starting central observations are described in sec . first , in the fk functional integral , only marginal paths with finite extensions ( i.e. large deviations with respect to the average ) contribute when @xmath0 goes to zero . second , many of such paths with quite different jagged shapes , provide similar contributions , mainly determined by the corresponding local occupation times . thus , it is quite natural to collect paths into sets defined by their spatial extension and their local occupation times . that procedure allows us to transform exactly fk representation  ( [ fk ] ) into the so - called box formula  ( [ 2b3 ] ) . that formula is defined _ via _ the introduction of paths constrained to stay in a box with size @xmath3 and characterized by an intermediate flight time @xmath4 ( in @xmath5 units with @xmath6 ) . it involves a double ordinary integral over @xmath3 and @xmath4 , combined to functional integrals over local occupation times associated with the constrained paths . as required , box formula  ( [ 2b3 ] ) provides a better understanding of the low - temperature behaviour of the density matrix than fk representation  ( [ fk ] ) . when @xmath0 vanishes , leading contributions obviously arise from typical sizes @xmath3 much smaller than de broglie wavelength . in a forthcoming paper , we will argue how groundstate quantities emerge from box formula  ( [ 2b3 ] ) , by using scaling properties of the probability distribution function ( pdf ) of occupation times at low temperatures .    beyond its conceptual interest for understanding low - temperature behaviours of path integrals , box formula  ( [ 2b3 ] ) also allows us to derive new approximations . this is illustrated in section  [ constrainedaverages ] , where we present the so - called ergodic approximation . that approximation results from the truncation to first order of cumulant expansions of the functional averages . it amounts to replace each local occupation time associated with a given constrained path , by its average over the pdf of such occupation times . this can be viewed as some kind of ergodic hypothesis , because the ( imaginary ) time average of the potential experienced by the particle along that path , is then replaced by a spatial average with a measure defined by the previous mean occupation - time . ergodic expression  ( [ est1_1b ] ) involves only an ordinary double integral over @xmath3 and @xmath4 . the key ingredient , namely the mean occupation - time ( in units of @xmath7 ) , depends on three dimensionless parameters . using its low and high temperature behaviours ( derived analytically ) , we propose simple tractable expressions for that quantity , which turn out to be quite accurate at any temperature . section  [ applications ] is devoted to the applications of the ergodic approximation to various simple forms of the confining potential . first , we determine the asymptotic analytical forms of the approximate density matrices at both low and high temperatures . when @xmath0 diverges , wigner - kirkwood expansion is partially recovered . when @xmath0 vanishes , the main features of the exact behaviours are well reproduced . the approximate density matrices then do factorize as a product of a boltzmann factor associated with a given energy , times a function of position only : this provides satisfatory approximate expressions for the groundstate energy and wavefunction . second , numerical calculations are performed at finite intermediate temperatures . as expected from the previous analytical results , the ergodic approximation turns out to be quite reasonably accurate over the whole range of considered temperatures , and discrepancies with ( numerically ) exact results ( in part inferred from the spectral representation ) do not exceed a few percent . moreover , it significantly improves over the well - known semi - classical approximation , which completely fails at low temperatures ( except of course for the harmonic potential where semi - classical calculations become exact ) . further applications and extensions of our approach will be presented elsewhere . in particular , the ergodic approximation can be applied to unconfining potentials , and it can be straightforwardly extended to higher dimensions and to systems with several particles . furthermore , other approximations might be easily introduced by starting from box formula as argued at the end of section iii .","summary":"as shown by its applications to different confining potentials , the ergodic approximation turns out to be quite efficient , especially in the low - temperature regime where other usual approximations fail .","abstract":"we study the low temperature behaviour of path integrals for a simple one - dimensional model . starting from the feynman - kac formula , we derive a new functional representation of the density matrix at finite temperature , in terms of the occupation times of brownian motions constrained to stay within boxes with finite sizes . from that representation , we infer a kind of ergodic approximation , which only involves double ordinary integrals . as shown by its applications to different confining potentials , the ergodic approximation turns out to be quite efficient , especially in the low - temperature regime where other usual approximations fail ."}
{"article_id":"1301.4186","section_id":"i","document":"the nature of the dark matter is a challenging problem in the modern science . from astrophysical observations there are gravitational sources which are invisible to us besides the visible stars and galaxies . so far , we know little about the invisible objects and call them to be the dark matter ( dm ) , which could be massive to gravitate and non - baryonic to keep the evidence of big - bang nucleosynthesis ( bbn ) intact . the dm is now believed to be responsible for @xmath3 23% energy density of our universe , where the visible stars , galaxies and dim stellar gas only contribute @xmath3 4% @xcite . from the viewpoint of the particle physics , the dm may be a particle which goes beyond the standard model , and its identity remains elusive . one of the authors ( k.c.y . ) has investigated the possibility that the galactic dark matter exists in an scenario where the phantom field is responsible for the dark energy @xcite . the relic abundance can be used to determine the interaction strength between the thermal dm and the standard model ( sm ) particles . a stronger interaction keeps the dark matter staying in the thermal equilibrium longer , so that the boltzmann factor further suppresses its number density . to reproduce the correct dark matter relic @xcite , the governed boltzmann s equation shows that the annihilation cross - section @xmath4 of the dark matter into sm particles is of order @xmath5@xmath6sec which is about 1 picobarn@xmath7 ( pb@xmath7 ) @xcite . this @xmath8 pb cross - section interacting with sm particles infers that the dark matter could be produced in recent collider experiments . if the mass of the dm is of order several hundred gev , the dm can undergo a typical interaction with the electroweak scale . this is the so - called weakly interacting massive particle ( wimp ) miracle . therefore it was suggested that the dark matter can couple to the higgs boson in the effective theory below tev scale and this kind of model is the so - called higgs portal model @xcite . substituting the annihilation cross - section @xmath9 obtained from the recent wmap data into the formula of the partial wave unitarity given in @xcite , the upper bound on the mass of the thermal dark matter is approximately @xmath10  tev . some efforts are devoted to directly searching for wimps with masses of order @xmath11  gev @xcite .    a number of underground experiments , _ e.g. _ , xenon , cdms and dama / libra , have being performed to detect the dm directly scattered by the nuclei @xcite . although the controversial signals were detected by dama / libra and cogent groups , the null result has been reported by xenon100 and cdms groups , respectively @xcite . the xenon100 data lead not only to the strongest limit so far for constraining the dm - nucleon cross section to below @xmath12 @xmath13 for @xmath14  gev ( and @xmath15 @xmath13 for @xmath16  gev ) , but have also the constraints for cross section to below @xmath17 @xmath13 in the low mass region around 10 gev @xcite . the dm may be produced at the hadronic colliders . since the dm interacts weakly with sm particles , they can escape from the detector . dm signals could be relevant to the processes for jets plus large missing transverse energy ( @xmath18 ) in the final states . the process with monojet + missing transverse energy @xmath18 final states has been reported by cdf @xcite , cms @xcite , and atlas @xcite , and is one of the main channels for the dark matter searches at the hadronic colliders . recently , atlas @xcite has analyzed monojets with varying jet @xmath19 cuts using an integrated luminosity of 1.00 fb@xmath20 . for all of these experiments , no obvious excess has been observed compared with sm backgrounds . on the other hand , if the dark matter interacts with the hadron via a mediator , it is possible to find out this mediator from the dijet mass spectrum at the hadron colliders , for which the searches by the cdf @xcite and d0 @xcite collaborations have used data from @xmath21 collisions at the tevatron , while searches by the atlas @xcite and cms @xcite have used data from @xmath22 collisions at the lhc @xcite . however , all measurements show no evidence for the new narrow resonance .    in this paper , we take into account in a model - independent way that a dirac fermionic dm can couple to the sm quarks via a scalar mediator , where the interaction can be parity conserving or violating . adopting this framework , we will constrain the masses of the dark matter and mediator as well as the couplings from the thermal relic abundance , and the recent results of the xenon100 direct detection and colliders involving the monojet measurements with large missing transverse energy @xcite and dijet resonance searches @xcite . some works for the interaction between the dm and sm particles via a neutral spin-1 mediator can be found in refs . @xcite    in the effective hamiltonian approach with a contact interaction between the dm and sm quarks , which is just suitable for the heavy mediator and has been discussed in the literature @xcite , only an annihilation topology ( usually the @xmath23-channel ) contributes to the processes for the thermal relic abundance . however , for the general case , not only @xmath23-channel , but also the @xmath24- and @xmath25-channels may enter to participate the interactions , where the @xmath24- and @xmath25-channels can be switched off when the dm mass is smaller than the mediator or the @xmath23-channel is predominant if the coupling between the dm and mediator is much smaller than that between the quark and mediator . ( see also fig . [ fig : chichi2yy ] . ) the mass of the mediator for the dm interacting with sm particles could be comparable with the energy scale of the colliders , so that the interactions can be resolved and the mediator is produced on shell . in this condition , the description of the effective contact operator is no longer valid . there are two possible ways to detect the relevant effect at the colliders . one is to measure the monojet plus missing transverse energy in the final state , for which in addition to the sm background it is dominated by @xmath26 @xmath27 , with @xmath28 being the dark matter . the other one is to search for the mediator @xmath29 in the dijet mass spectrum . we will show that the lhc monojet constraints on the dm mass as well as related parameters could be competitive with but not stronger than the dark matter direct detection at the present stage . for the dijet search , interchange with the mediator @xmath29 in the @xmath23-channel interaction is predominant in the bump like component of the resonances , for which the upper limit is set by the collider measurements . this paper is organized as follows . we begin in sec . [ sec : dm - model ] with a generic form of a lagrangian , which describes the dirac fermonic dm interacting with the sm quarks via the scalar mediator . in sec . [ sec : analyses ] , we perform a detailed numerical analysis for the relevant operators , and obtain the constraint on the parameter space of the dm and mediator masses . together with discussions for the constraint from indirect detections and diphoton resonance searches , we conclude in sec . [ sec : conclusions ] .","summary":"we constrain the masses of the dark matter and mediator as well as the couplings from the thermal relic abundance , and the recent results of the xenon100 direct detection and collider experiments involving the two channels : ( i ) monojet plus large missing transverse energy , and ( ii ) dijet . = 1","abstract":"we take into account a generic form of a dirac fermionic dark matter ( dm ) , which communicates with the standard model quarks via a scalar mediator , in a model - independent way . four special interaction scenarios are investigated , where one is parity conserving and the other three are parity violating . three of them result in the suppressed dm - nucleon cross sections , where is the velocity of the dm in the laboratory frame . we constrain the masses of the dark matter and mediator as well as the couplings from the thermal relic abundance , and the recent results of the xenon100 direct detection and collider experiments involving the two channels : ( i ) monojet plus large missing transverse energy , and ( ii ) dijet . the current monojet constraint is not stronger than that from the requirement of the correct relic density and the null result by the xenon100 direct detection . we find that the dijet resonance measurements can exclude a large part of the parameter space , where the couplings for the mediator coupled to the dark matter and to the quarks are small and have roughly the same magnitude . the constraint from indirect detections and diphoton resonance searches is also briefly discussed .    = 1"}
{"article_id":"1301.4186","section_id":"c","document":"before we summarize , let us briefly discuss the constraints from indirect detections and diphoton resonance searches .    for the indirect detections , dark matter annihilation in the galactic halo can generate observable signals . the annihilation cross section @xmath4 , which can also read from eq . ( [ eq : relic ] ) , is proportional to @xmath269 for @xmath69 and @xmath98 scenarios , but is approximately independent of @xmath0 for @xmath99 and @xmath100 scenarios , where @xmath144 is the velocity of the dm in the galactic halo . compared to the dm annihilation cross section at thermal freeze - out , the present @xmath4 in the latter scenarios will be roughly the same as @xmath270 @xmath271 s@xmath20 , while the one in the former scenarios is velocity suppressed since the velocity of the dm is @xmath272 at freeze - out temperature . thus , the fermi - lat measurements from observations of milky way dwarf spheroidal galaxies @xcite and bess - polar ii @xcite data have no constraints on the @xmath69 and @xmath98 scenarios due to their velocity suppression , but disfavor the dark matter mass @xmath273 30 gev for @xmath99 and @xmath100 scenarios . nevertheless , one should note that the recent fermi - lat search for dm in gamma - ray lines and the inclusive photon spectrum @xcite does not constrain all interacting scenarios that we consider in this paper . the results for the diphoton resonance analyses at the collider experiments may be relevant to the exotic @xmath29 production that we consider in the present work . the diphoton channel has been used to search for the higgs @xcite and randall - sundrum graviton @xcite . as for the search for higgs decaying into diphoton at the lhc and tevatron , the three main higgs production channels are the gluon - gluon fusion , vector boson fusion , and vector boson associate production . in our case , the @xmath29 particle is produced mainly from the @xmath219 annihilation . requiring that the couplings for the dm into the quark pair are constrained by the correct relic abundance , we find that the cross section for @xmath274 into @xmath275 via @xmath29 is at least 100 times smaller than that via the higgs . therefore , the contribution to the diphoton production due to the exotic scalar @xmath29 particle can be negligible . in other words , the diphoton resonance experiments can not offer the efficient constraint to the mass of the @xmath29 .    in summary , we have studied the experimental constraints , which are due to measurements from the correct relic abundance , direct / indirect detections , and colliders , on a scenario that a dirac fermionic dm interacts with sm quarks via a scalar mediator in a model - independent way . we respectively consider four special scenarios denoted as @xmath276 and @xmath100 , where the former one is the parity conserving interaction , while the latter three are parity violating . our present study can apply to the case of the pseudoscalar mediator , for which the @xmath100 scenario is the parity conserving interaction . for each interaction , we take three limits for couplings , @xmath277 and @xmath278 , in the analysis . the main results are summarized as follows .    * requiring @xmath279 , so that the resulting width of the scalar mediator @xmath29 is smaller than its mass , the @xmath2 parameter space maintaining the correct relic abundance is very small for the couplings @xmath280 or @xmath278 , as shown in fig . [ fig : result1 ] . for @xmath278 , in addition to a narrow region corresponding to the @xmath23-channel resonance , the allowed region satisfying @xmath281 is dominated by the @xmath24- and @xmath25-channels of the relic annihilation processes . * in the direct detection , the @xmath69 and @xmath99 interactions , where @xmath137 and @xmath138 , are spin - independent on the nucleus side , while the @xmath98 and @xmath100 interactions , where @xmath139 and @xmath140 , are spin - dependent . compared with the direct detection cross sections @xmath182 , @xmath183 and @xmath184 are velocity suppressed by @xmath185 and @xmath186 , respectively , where the dm velocity @xmath282 , while @xmath187 is further suppressed by @xmath188 . as for @xmath189 , we have shown @xmath190 . compared with the results constrained by the correct relic abundance in fig . [ fig : result1 ] , the xenon100 null measurement further excludes most @xmath2 region in the @xmath69 scenario ( except the resonance region ) and in the @xmath98 scenario with @xmath197 . * the current monojet constraint is not stronger than that from the requirement of the correct relic density and the null result by the xenon100 direct detection . only a very small fraction located in the region with @xmath226 can be further excluded in @xmath99 and @xmath100 scenarios . however , although the calculation is perturbatively convergent in that region , the decay width of the @xmath29 particle may be comparable with its mass , so that @xmath29 is no longer a good resonant state . * we have used the results from the dijet resonance search in the cdf and cms experiments to constrain the mass of the scalar mediator @xmath29 with the narrow width @xmath266 . 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","abstract":"we take into account a generic form of a dirac fermionic dark matter ( dm ) , which communicates with the standard model quarks via a scalar mediator , in a model - independent way . four special interaction scenarios are investigated , where one is parity conserving and the other three are parity violating . three of them result in the suppressed dm - nucleon cross sections , where is the velocity of the dm in the laboratory frame . we constrain the masses of the dark matter and mediator as well as the couplings from the thermal relic abundance , and the recent results of the xenon100 direct detection and collider experiments involving the two channels : ( i ) monojet plus large missing transverse energy , and ( ii ) dijet . the current monojet constraint is not stronger than that from the requirement of the correct relic density and the null result by the xenon100 direct detection . we find that the dijet resonance measurements can exclude a large part of the parameter space , where the couplings for the mediator coupled to the dark matter and to the quarks are small and have roughly the same magnitude . the constraint from indirect detections and diphoton resonance searches is also briefly discussed .    = 1"}
{"article_id":"astro-ph0203085","section_id":"i","document":"there is presently a growing body of circumstantial evidence linking some long - duration gamma ray bursts ( grbs ) with afterglows to the explosions of massive stars . supernovae ( sn ) or supernova - like features have been identified in seven afterglows although some of these could be light echoes from dust clouds @xcite . the afterglows of six other grbs have been interpreted in terms of a wind - like ambient medium as expected around a massive star at the end of its life . however these are often equally well explained by a collimated flow in a uniform medium . x - ray lines have been detected with moderate confidence in about half the afterglows for which they were investigated @xcite ; however , the data analysis has been questioned ( see * ? ? ? if real , these are most easily explained by dense material surrounding the burst engine , suggesting a stellar origin ( e.g. , * ? ? ? @xcite have recently derived beaming angles for a number of grbs from observations of their afterglows . these authors derive gamma - ray energies reminiscent of supernovae : roughly @xmath0 erg for the observed lobes of grbs . similar results were reported by @xcite and @xcite . clear evidence that grbs occur very close to massive star formation would be almost as conclusive as a sn signature in an individual grb . several grb afterglows show evidence for high column densities ( 980703 and 980329 ; @xcite ) or high local gas densities ( 000926 and 980519 ; @xcite , @xcite ) , both of which connote star - forming regions . likewise , the intrinsic extinction of grb 000926 is characteristic of a galaxy disk @xcite . @xcite have shown that the observed locations within hosts imply a tight correlation between grbs and stellar populations , considered too tight @xcite to be matched by merging neutron stars . note however that the locations of merging neutron star pairs depends on their uncertain distribution of natal kicks . if grbs are a rare byproduct of star formation , rapidly star - forming galaxies should be over - represented as grb hosts . in optical light host galaxies tend to look ordinary compared to contemporaries in the hubble deep field , but [ ne iii ] and [ o ii ] and infrared observations often indicate elevated star formation rates @xcite . at least eight afterglows have been associated with starburst or interacting galaxies @xcite . although the association between long - duration grbs and sne is tentative ( and applies only to the long - duration bursts for which afterglows are observed ) , the above evidence warrants a careful evaluation . there are two ways a sn can create a grb . @xcite predicted that gamma rays might be produced in the very fastest , outermost ejecta of an ordinary supernova explosion . this proposal was recently revived by @xcite and @xcite . these authors showed that the grb ( 980425 ) most compellingly associated with a sn ( 1998bw ) is likely to be the result of trans - relativistic sn ejecta colliding with a stellar wind ( see also * ? ? ? * ) . in their model , as conjectured by @xcite , sn 1998bw was spherically symmetric or mildly asymmetric , and produced the grb in an external shock . scaled - up versions of this model could produce external shock grbs , at the expense of vast amounts ( @xmath1 erg ) of energy in nonrelativistic ejecta . in contrast , @xcite have argued that most grbs require internal emission ( e.g. , by internal shocks ) within unsteady ultrarelativistic winds or jets , as originally suggested by @xcite . the arguments for internal emission are strongest for rapidly - fluctuating cosmological bursts with hard spectra , those least resembling grb 980425 ; also , see @xcite for arguments in support of external shocks . i shall assume for the purposes of this investigation that cosmological grbs involve internal emission within optically thin , ultrarelativistic outflows . for this to result from a sn , a jet must emanate from a star s core and pierce its envelope  shedding the baryons in its path  prior to producing the gamma rays observed at earth . such a jetlike explosion is the conventional model ( e.g. , * ? ? ? * ) for a supernova origin of cosmological grbs . the goal of this paper will be to develop analytical models for the phase of this latter model in which a jet , already created by the stellar core , must traverse the envelope and shove aside material in its path . these models , which are complementary to numerical simulations @xcite , are meant to elucidate under what conditions the hypothesis of a stellar origin is viable for the observed grbs . in   [ inside star ] and [ envelopeconstraints ] i assume that jets travel ballistically within their stars ; this allows one to place strict constraints on stellar envelopes . in  [ widening ] this assumption is reconsidered . it is shown that a phase in which the jet is hot , pressure confined , and mixing with its environs would have interesting consequences . figure [ fig1 ] sketches the typical masses and radii of the stellar grb progenitor candidates considered in this paper . in general , those that retain an outer envelope ( e.g. , supergiants ) have quite large radii ( @xmath2 ) at the time of core collapse , whereas those depleted in hydrogen due to winds or binary interaction ( e.g. , those that have been through a wolf - rayet phase ) are quite compact ( @xmath3 ) . among post - wolf - rayet stars , those containing helium ( `` he wolf - rayets '' on the plot ) are less compact than their he - depleted peers ( `` c / o wolf - rayets '' ) .    very massive objects ( vmos ) might have formed at high redshift due to the difficulty of cooling in the absence of metals and thus the large jeans mass in primordial gas . vmos may also form today in rare conditions . those initially more massive than @xmath4 die when their cores collapse to black holes , and are candidates for producing grbs ; @xcite discuss their evolution . again , the pre - collapse radii of these stars depend on their mass loss . if present , their h envelope is quite diffuse ( see * ? ? ? otherwise the remaining convective core is very compact at the point of collapse . in addition to winds and binary mass transfer , vmos may shed their envelopes in a super - eddington phase during helium core contraction . lone vmos are thought to retain h envelopes if they are formed from sufficiently low - metallicity gas ( although this is uncertain ; * ? ? ? the `` supranova '' model of @xcite posits that a sn explosion produces a rapidly spinning neutron star massive enough to collapse after shedding its angular momentum @xcite along with @xmath5 erg of rotational energy . the object collapses to a black hole with an accretion torus , firing a jet through the pulsar s wind nebula and its sheath of stellar ejecta . because of the short viscous times of such tori , this model is most appropriate for short grbs rather than the long bursts for which there is evidence of a sn connection . also , we will see in  [ envelopeconstraints ] that the expanding stellar ejecta would prevent the production of a grb entirely , unless it has either become thompson optically thin or has been cleared aside by the breakout of the pulsar wind nebula . the latter is possible in this model , because the pulsar spindown energy exceeds the typical kinetic energy of sn ejecta . @xcite and @xcite discuss a scenario in which the stellar core collapse leading to a grb results from the coalescence of a helium wolf - rayet star with a compact companion . similarly , @xcite argue that binary mergers are likely to dominate the production stars whose cores collapse to black holes accreting through a disk . progenitors created in this fashion will typically be stripped of their outer envelopes , hence compact . however the stripped envelope poses a potential barrier to jet propagation , as in the supranova model , unless it is strictly confined to the equator of the system or has expanded to the point of being optically thin .    in sections [ s : freefalltimes ] and [ s : pressureconf ] i examine the properties of stellar cores at the point of collapse . for this i shall assume that collapse sets in at the oxygen ignition temperature , @xmath6 ( e.g. , * ? ? ?","summary":"the only stellar progenitors that comfortably satisfy these constraints , if one assumes that jets move ballistically within their host stars , are compact carbon - oxygen or helium post - wolf - rayet stars ( type ic or ib supernovae ) ; type ii supernovae are ruled out . if so , jets responsible for observed grbs must either have been launched from a region several hundred kilometers wide , or have mixed with envelope material as they travel . a phase of pressure confinement and mixing would imprint correlations among jets that may explain observed grb variability - luminosity and lag - luminosity correlations .   ","abstract":"i constrain a possible supernova origin for gamma - ray bursts by modeling the dynamical interaction between a relativistic jet and a stellar envelope surrounding it . the delay in observer s time introduced by the jet traversing the envelope should not be long compared to the duration of gamma - ray emission ; also , the jet should not be swallowed by a spherical explosion it powers . the only stellar progenitors that comfortably satisfy these constraints , if one assumes that jets move ballistically within their host stars , are compact carbon - oxygen or helium post - wolf - rayet stars ( type ic or ib supernovae ) ; type ii supernovae are ruled out . notably , very massive stars do not appear capable of producing the observed bursts at any redshift unless the stellar envelope is stripped prior to collapse . the presence of a dense stellar wind places an upper limit on the lorentz factor of the jet in the internal shock model ; however , this constraint may be evaded if the wind is swept forward by a photon precursor . shock breakout and cocoon blowout are considered individually ; neither presents a likely source of precursors for cosmological grbs .    these envelope constraints could conceivably be circumvented if jets are laterally pressure - confined while traversing the outer stellar envelope . if so , jets responsible for observed grbs must either have been launched from a region several hundred kilometers wide , or have mixed with envelope material as they travel . a phase of pressure confinement and mixing would imprint correlations among jets that may explain observed grb variability - luminosity and lag - luminosity correlations .    [ firstpage ]    gamma rays : bursts , supernovae : general , shock waves , relativity"}
{"article_id":"astro-ph0203085","section_id":"c","document":"this paper constrains possible stellar progenitors for grbs by requiring that jets of grb - like luminosities and durations can clear a path for themselves in the star s envelope prior to producing gamma rays . of all the possible progenitors , only the compact carbon - oxygen post - wolf - rayet stars ( sn ic progenitors ) and the bare cores of very massive objects can plausibly collapse in the durations of long grbs at low redshift (  [ s : freefalltimes ] , figures [ fig1 ] and [ fig2 ] ) . in more extended stars , the outer stellar envelope remains to impede the progress of the jet , and it is likely to violate observational constraint . therefore , i conclude that grbs with sn progentiors come primarily from type ic or vmo - core events . type ib is not thoroughly ruled out by this work , but type ii ( supergiant stars ) are . the most stringent constraint on a stellar envelope arises from the requirement that the jet can traverse it in an observed time not much longer than the duration of the grb . under the assumption of a ballistic rather than a pressure - confined jet , this constraint is independent of the inferred opening angle of the burst , and ( given an observed fluence and duration ) depends on its inferred comoving distance rather than its luminosity distance . this makes it insensitive to an uncertainty in redshift . given the luminosities and durations of grbs ( regardless of their redshift ; fig . [ figtiming ] ) , only post - wolf - rayet stars and vmo cores are compact enough to satisfy this criterion . the variability - luminosity correlation discussed by @xcite and @xcite allows this constraint to be applied to a large number of bursts in the batse catalog ( figure [ figtiming ] ) . only a few are compatible with blue supergiant progenitors ; red supergiants and vmos with envelopes are ruled out . also ruled out is the `` supranova '' model of @xcite ( a supernova followed by a grb ) , unless the sn ejecta are optically thin by the time of the grb , or unless the pulsar nebula is energetic enough to clear them aside . post - wolf - rayet stars have been favored among stellar grb progenitors since the work of @xcite , on the basis that their compact envelopes delay the grb jet breakout the least . the above constraint quantifies and strengthens this conclusion , and relates it to the observed properties of grbs rather than those of a specific model for the central engine .    for ballistic jets , an additional constraint arises from the requirement that the grb jet cocoon should not overtake its driving jet and produce a spherical explosion . this is generally not as restrictive as the constraint from burst durations discussed above , but it does become important for jets with opening angles exceeding @xmath320 ( figure [ figcocoon ] ) . vmo cores , being the most compact , are the progenitors most likely to be ruled out this way if they have not collapsed prior to the grb . the requirement of a jet - cocoon structure also gives interesting upper and lower bounds on the energy entrained in the stellar envelope during the phase of jet propagation ( eq . [ [ einconstraint ] ] ) . this energy is stored in the jet cocoon and is available to drive a `` dirty '' fireball @xcite of expanding cocoon material after the jet breaks out . the breakout phenomenon is itself a candidate for producing a transient , as may have happened in sn 1998bw to produce grb 980425 . in section [ breakout ] it is calculated how much kinetic energy is channeled into relativistic envelope ejecta during a jet s breakout , by matching the propagation law for the jet s terminal shock onto the relativistic shock and post - shock acceleration behavior described by @xcite . i find the energy of this ejecta to be small compared to that of the burst . @xcite have recently discussed how the upscattering of photons from the shocked envelope by the jet may produce a precursor of hard gamma rays ; however , note that this is reduced in importance for the compact stellar progenitors favored by the timing constraints . @xcite have suggested breakout ejecta as the origin of short , hard bursts ; however their estimate of the energy is at odds with that calculated here . if the gamma - ray photons are not able to clear away a stellar wind in the region around the star in the manner described by @xcite , @xcite , and @xcite , then the presence of this wind places an upper limit on the jet lorentz factor . this limit arises in the internal shock model for grb emission because the presence of the external shock limits the distance within which internal shocks can form . the equivalent limit has been presented previously for uniform ambient media @xcite ; however , for a sufficiently dense stellar wind it can conflict with the lower limits on jet lorentz factor ( e.g. , * ? ? ? figure [ fig418 ] illustrates the above criteria for the specific case of grb 000418 , assuming a ballistic jet with @xmath321 . its seven - second duration is briefer even than the free - fall times of vmo cores . because of its large opening angle ( @xmath322 ; * ? ? ? * ) , it would not succesfully form a jet - cocoon structure in any uncollapsed portion of the vmo core . in fact , a jet of its inferred luminosity could cross nothing more extended than the most compact of wolf - rayet stars in the grb duration . i conclude from this that it came either from a compact carbon - oxygen wolf - rayet star , or from a vmo core that managed to produce a grb of briefer duration than its free - fall time , or that it did not have a supernova origin . these restrictions change quantitatively , but not qualitatively , if @xmath323 . pressure confinement of jets provides a way for grb hosts to evade the constraints on stellar envelopes listed above for ballistic jets . this occurs because , for a given @xmath113-ray opening angle , confined jets are narrower and more intense than their ballistic counterparts . the computational results of @xcite and @xcite correspond to pressure - confined jets . in  [ adiabatics ] it was shown that jets that do not mix with their environs can not remain pressure - confined ( see also * ? ? ? simulations that do not resolve the jets launching scale may not observe this effect , however . mixing of jet and envelope (  [ ss : mixing ] ) is capable of sustaining a pressure - confined state . intriguingly , mixing of jet and envelope imprints on the jet a tight correlation ( the `` mixing attractor '' of eq . [ [ mixingattractor ] ] and figure [ figmix ] ) between its lorentz factor and energy per unit mass . this leads to a correlation between final opening angle and lorentz factor , which in turn may be related to the lag - luminosity and variability - luminosity correlations observed in burst catalogs . excessive mixing , however , has the effect of filtering rapid fluctuations from jets . this work was stimulated by a visit to uc santa cruz and by interactions with stan woosley , andrew macfadyen , alex heger , and weiqun zhang while i was there . it was further motivated by conversations with and encouragement from roger blandford , reem sari , sterl phinney and josh bloom during a visit to caltech . it is a pleasure to thank woosley , blandford , and phinney for their hospitality during those visits . i am especially grateful to nicole lloyd - ronning for explaining the grb luminosity - variability relation and suggesting clarifications . i also thank andrei beloborodov and chris thompson for discussing jet - envelope interactions and chris fryer for discussing progenitor scenarios . comments from beloborodov , charles dermer , jonathan tan , chris mckee , john monnier , and the referee , ralph wijers , are also appreciated . this work was supported by nserc and by the canada research chairs program . e. , diercks a. , frail d.  a. , kulkarni s.  r. , bloom j.  s. , sari r. , halpern j. , mirabal n. , taylor g.  b. , hurley k. , pooley g. , becker k.  m. , wagner r.  m. , terndrup d.  m. , statler t. , wik d.  r. , mazets e. , cline t. , 2001 , , 556 , 556                                        d.  a. , kulkarni s.  r. , sari r. , djorgovski s.  g. , bloom j.  s. , galama t.  j. , reichart d.  e. , berger e. , harrison f.  a. , price p.  a. , yost s.  a. , diercks a. , goodrich r.  w. , chaffee f. , 2001 , , 562 , l55","summary":"the presence of a dense stellar wind places an upper limit on the lorentz factor of the jet in the internal shock model ; however , this constraint may be evaded if the wind is swept forward by a photon precursor .","abstract":"i constrain a possible supernova origin for gamma - ray bursts by modeling the dynamical interaction between a relativistic jet and a stellar envelope surrounding it . the delay in observer s time introduced by the jet traversing the envelope should not be long compared to the duration of gamma - ray emission ; also , the jet should not be swallowed by a spherical explosion it powers . the only stellar progenitors that comfortably satisfy these constraints , if one assumes that jets move ballistically within their host stars , are compact carbon - oxygen or helium post - wolf - rayet stars ( type ic or ib supernovae ) ; type ii supernovae are ruled out . notably , very massive stars do not appear capable of producing the observed bursts at any redshift unless the stellar envelope is stripped prior to collapse . the presence of a dense stellar wind places an upper limit on the lorentz factor of the jet in the internal shock model ; however , this constraint may be evaded if the wind is swept forward by a photon precursor . shock breakout and cocoon blowout are considered individually ; neither presents a likely source of precursors for cosmological grbs .    these envelope constraints could conceivably be circumvented if jets are laterally pressure - confined while traversing the outer stellar envelope . if so , jets responsible for observed grbs must either have been launched from a region several hundred kilometers wide , or have mixed with envelope material as they travel . a phase of pressure confinement and mixing would imprint correlations among jets that may explain observed grb variability - luminosity and lag - luminosity correlations .    [ firstpage ]    gamma rays : bursts , supernovae : general , shock waves , relativity"}
{"article_id":"astro-ph9812317","section_id":"i","document":"galaxies that emit the bulk of their luminosity in the far - infrared ( hereafter far - ir galaxies ) are an energetically significant component of the local universe ( e.g soifer et al 1987 ; sanders & mirabel 1997 ) . they are also the only local systems ( apart from qsos ) that have bolometric luminosities similar to typical high - redshift galaxies selected by uv ( steidel et al 1996 ; meurer , heckman , & calzetti 1998 ) or sub - millimeter ( e.g. hughes et al 1998 ; blain et al 1998 ) techniques . as such , they offer unique laboratories to study the physical processes that were important in the formation and early evolution of galaxies ( heckman 1998 ) . one of their most interesting attributes are their galactic - scale and highly luminous gaseous emission - line nebulae ( cf . armus , heckman , & miley 1990 ; veilleux et al . in several well - known cases like m 82 and ngc 253 , hot x - ray emitting gas has also been discovered , and this gas shows a clear morphological relationship to the optical emission - line nebula ( cf . dahlem , weaver , & heckman 1998 and references therein ) . it seems clear in these cases that the x - ray nebulae are energized by the mechanical energy of an outflow driven by the multiple supernovae in the starburst ( a ` superwind '  cf . heckman , lehnert , & armus 1993 ; bland - hawthorn 1995 ) . it would be important to establish the ubiquity of the superwind phenomenon in far - ir galaxies , since such outflows could play an important role in heating and chemically - enriching galactic halos and the inter - galactic medium ( cf . heckman , armus , & miley 1990 ; gibson , loewensten , & mushotzky 1997 ) . the x - ray nebulae studied in detail and at high spatial resolution to date have been mostly associated with far - ir galaxies of modest luminosity ( @xmath15 few @xmath16 ) . the situation may be different and more complex for more powerful far - ir galaxies . these systems are also primarily powered by intense starbursts ( genzel et al 1998 ) although deeply - buried agn are energetically significant in some cases and may dominate the systems with the highest bolometric luminosities ( cf . sanders & mirabel 1997 and references therein ) . they are created in the aftermath of a galactic collision or merger ( cf . mihos & hernquist 1994 ) , so that the dissipation of the kinetic energy of the colliding interstellar media may be energetically significant ( harwit et al . it is also particularly interesting to study the effects of possible superwinds on the interstellar media of merging disk galaxies in general , since such hydrodynamical processes may be important in the subsequent transformation of the merger product into an elliptical galaxy ( e.g. schweizer 1992 ) . we have therefore undertaken an analysis of x - ray and optical data for a small sample of some of the nearest and brightest powerful infrared galaxies ( l@xmath17 @xmath18 10@xmath19 erg s@xmath2 ) in order to determine the characteristics of their nebulae and thereby determine the nature of their energy sources . heckman et al .  ( 1996 ) presented x - ray and optical data on the prototypical ` ultraluminous ' far - ir galaxy arp 220 , and showed that this galaxy appears to have an outflow that is qualitatively similar to ( but more powerful than ) the outflows seen in m 82 and ngc 253 . in wang et al . ( 1997 ) , we reported the results for the case of mrk 266 , and here we discuss a third example . iwasawa & comastri ( 1998 ) have recently reported on the x - ray properties of the ir - bright merger system ngc 6240 . our approach is complementary to the recent work by read & ponman ( 1998 ) , who have systematically studied the x - ray properties of an optically- selected sample of merging galaxies using _ rosat _  data . the members of their sample are not in general powerful starbursts , and only arp 220 meets the above far - ir luminosity criterion . the powerful far - ir system arp 299 ( also known as ngc 3690 and mrk 171 ) consists of two overlapping galaxies that appear to be in the late stages of a merger . to the northwest of the merging galaxy pair , while ngc 3690 properly refers to the merging pair . to avoid further confusion , we will adopt the name arp 299 to refer to the system rather than ngc 3690 . ] = 75 km s@xmath2 mpc@xmath2 . this implies a scale of 1= 0.21 kpc and 1= 13 kpc . ] it has one of the brightest , most luminous , and largest emission - line nebulae in the extensive h@xmath10 imaging survey of far - ir galaxies by ahm90 . as we will describe in this paper , this material is immersed in and surrounded by a large and bright region of soft x - ray emission . arp 299 is therefore a prime target for a detailed examination of the relationship between the warm and hot gaseous components in powerful far infrared galaxies . arp 299 has been extensively studied following the landmark paper of gerhz , sramek , & weedman ( 1983 ) : in the x - ray ( zezas , georgantopoulos , & ward 1998 - hereafter zgw ) , uv ( meurer et al 1995 ) , optical ( friedman et al 1987 ) , ir ( fischer et al 1983 ; telesco , decher , & gatley 1985 ; beck et al 1986 ; nakagawa et al 1989 ; joy et al 1989 ; wynn - williams et al 1991 ) , and radio ( condon 1991 ; lonsdale , lonsdale , & smith 1992 ; smith , lonsdale , & lonsdale 1998 ) wavebands , and in hi ( stanford & wood 1989 ; hibbard 1997 ) , oh ( baan & haschick 1990 ) , co ( aalto et al 1997 ; sargent & scoville 1991 ) , and hcn ( aalto et al 1997 ) . it has been the site of several recent supernovae ( sn1992bu - iau circular 5960 ; sn1993 g - iau circular 5718 ; sn1998 t - iau circular 6859 ; and a possible radio supernova described in iau circular 4988 ) . arp 299 has a bolometric luminosity of approximately 6 @xmath11 10@xmath20 l@xmath21 , which is dominated by far - ir emission . @xmath22 spectroscopy ( genzel et al . 1998 ) shows that even in the mid / far - ir there is no sign of a substantial contribution to the energetics of arp 299 by a dust - buried agn . as we will report below , this is also true in the hard x - ray band probed by @xmath23 . thus , arp 299 s impressive luminosity seems to be provided largely or entirely by stars . the centers of the two merging galaxies in arp 299 are separated by only about 22(4.5 kpc in projection ) , with a clear overlap in the disks . following the nomenclature of gerhz , sramek , & weedman ( 1983 ) , the compact site of activity in the central region of the eastern galaxy is denoted ` a ' , while the activity in the western galaxy breaks up into a complex of sources ( a double source  b1 \" , and  b2 \" the first of which is evidently associated with the nucleus of the galaxy , and a third source  c \" roughly 8or 1.6 kpc nnw of b1 ) .    in the present paper we present an analysis of both x - ray and optical imaging and spectroscopy of arp 299 . our approach complements that of zgw , who analyzed the pspc spectrum , but not the morphological structure of the _ rosat _  data . our data analysis is described in  2 and the results for x - ray and optical data are presented in  3 and  4 respectively . we will discuss and interpret these results in  5 in an attempt to determine how the bright optical / x - ray nebula is heated and how arp 299 and its nebula may fit in to the general class of powerful far - ir galaxies . in  6 we will summarize our conclusions .","summary":"= 0em    \\1 . = 2em","abstract":"we present a detailed investigation of the x - ray and optical properties of the starburst - merger system arp299 ( ngc 3690 , mrk 171 ) , with an emphasis on its spectacular gaseous nebula . we analyse _ rosat _  and _ asca _  x - ray data and optical spectra and narrow - band images . the x - ray nebula in arp 299 has a diameter of kpc , is elongated roughly along the hi minor axis of the merging system , has an outer ( inner ) temperature of 2.3 ( 9 ) million k , a luminosity of erg s , a gas mass of 7 m , and a thermal energy content of ergs . an additional hard x - ray component is present with a luminosity in the 0.1 to 10 kev band of erg s most likely due to x - ray binaries or possibly inverse compton scattering . the overall x - ray spectrum is consistent with that of other starbursts ( dahlem , weaver & heckman ) . compared to the x - ray nebula , the optical emission - line nebula is smaller ( 20 kpc ) but much more luminous ( erg s 4% l for arp 299 ) . the kinematics of the emission - line nebula are complex , with the line - widths increasing systematically with decreasing h surface - brightness to values of 500 to 700 km s in the faint outer filaments . the relative strengths of the low - ionization forbidden lines ( [ sii],[nii ] , and [ oi ] ) also increase systematically as the gas surface - brightness decreases and as the line widths increase . we measure high gas pressures in the inner emission - line nebula ( p / k few 10 k ) that decline systematically with increasing radius .    we suggest that the on - going galaxy collision has tidally - redistributed the ism of the merging galaxies . the optical emission - line nebula results as this gas is photoionized by radiation that escapes from the starburst , and is shock - heated , accelerated , and pressurized by a ` superwind ' driven by the collective effect of the starburst supernovae and stellar winds . since empirically only those galaxy mergers that that contain luminous starbursts have bright x - ray nebulae , this implies that the luminous x - ray nebula in arp 299 is also powered by the starburst outflow ( rather than by the collisions of gas clouds during the merger ) . this outflow can be most directly traced by its x - ray emission , which is plausibly a mass - loaded flow ( m yr ) of adiabatically - cooling gas that carries out a substantial fraction of the energy and metals injected by the starburst at a speed close to the escape velocity from arp 299 . the mass outflow rate exceeds the star - formation rate in this system . we conclude that powerful starbursts are able to heat ( and possibly eject ) a significant fraction of the interstellar medium in galaxies that are the products of mergers .    = 0em    \\1 . visiting astronomers , kitt peak national observatory , noao , operated by aura , inc . under cooperative agreement with the national science foundation .    = 2em"}
{"article_id":"astro-ph9812317","section_id":"r","document":"the background - subtracted @xmath43 kev pspc image of arp 299 is shown superimposed on the palomar sky survey image in figure 1 . accurate astrometry is not possible for the pspc because no independent x - ray point sources are present in the field of view , and so the image is aligned with the optical centroid of the arp 299 system to within the accuracy of the _ rosat _  pointing uncertainties ( @xmath44 ) .    in order to investigate the morphology of the x - ray image as a function of energy , we constructed `` soft '' band ( @xmath45 kev ) and `` hard '' band ( @xmath46 kev ) images . photons were selected from the appropriate pulse invariant ( pi ) channels and the central @xmath47 by @xmath47 regions were extracted from the original unbinned x - ray map ( @xmath48 pixels ) . these images were then smoothed with a gaussian function with @xmath49 pixels ( @xmath50 fwhm ) . after smoothing , the images were shifted slightly to align the center of the hard _ rosat _   image ( which represents the core of x - ray emission from the galaxy ) with the center of emission mapped with the hri ( see below ) . the pspc images , shown in figure 2 , reveal that the hard and soft x - ray isophotes are elongated in nearly orthogonal directions . the hard x - ray image is more compact , possibly oriented in the east - west direction ( no doubt resulting from the complex of point sources seen in the hri data ) . the soft x - ray isophotes on the other hand , are clearly oriented in the nne / ssw direction , and are extended on a scale of @xmath51 , or 45 kpc . the size of the soft x - ray emission is similar to that of the hi mapped by stanford & wood ( 1989 ) , but the x - ray emission is roughly perpendicular to the nw / se orientation of the hi . the shapes of the soft - band and hard - band images imply at least two distinct emission regions .      the hri image ( fig . 3 ) has a total background - subtracted count rate of 0.0426 cnts s@xmath2 , and shows a complex , clearly resolved structure extended over more than an arcminute in a predominantly east - west direction . this is the direction of the two galaxies in the interacting system . there are numerous local maxima in the x - ray image , but the brightest source to the east is only @xmath52 north of the non - thermal radio and near - infrared nucleus of the eastern galaxy ( gehrz , sramek & weedman 1983 ; condon 1991 ; wynn - williams , et al . this is nucleus `` a '' in the nomenclature of gehrz , sramek & weedman ( 1983 ) . given the pointing accuracy of the _ rosat _ and the fact that nucleus a is the single primary peak in both the radio and near infrared data , we hereafter identify the eastern x - ray peak with nucleus a. the western x - ray peak is extended in a `` ridge '' of emission with two prominent knots separated by 4 to 5 @xmath40 . when the eastern peak is aligned with nucleus  a \" , the southeast knot in the ridge is coincident with component  b1 \" and the northwest knot appears to be associated with a bright knot of h@xmath10 emission a few @xmath40 to the west of component  b2 \" . note that while b1 is the peak in the 2.2 micron , 10 micron , and radio emission in the western galaxy ,  b2 \" is the optical continuum peak . finally , the infrared and radio peak known as component  c \" is not located at the position of a relative peak in the _ rosat _  hri image ( a weak x - ray source tabulated by zgw is located about 5@xmath40 to the nw of c ) . thus , although component  c \" is a source of optical , near - infrared and radio emission , it does not appear to be a strong source of x - rays . we can estimate the contribution of point sources to the total number of counts in the hri image by summing the flux from the three strongest point sources within 5@xmath40 square apertures ( a `` detection cell '' that includes 50% of the total flux expected from a point source ) . these three x - ray sources are equally bright ( to within @xmath5310% ) and together account for approximately 21% of the total counts in the hri image , after correction for the 50% of the flux beyond the 5@xmath40 detection cells ( 0.0087 counts s@xmath2 ) . although the hri data do not provide much spectral information , we can estimate their fluxes and luminosities over @xmath43 kev range by assuming a simple spectral model ( david et al 1997 ) . if the point sources are modelled as a mekal plasma with kt @xmath54 0.8 kev ( see  3.2.2 ) and line of sight neutral hi column of n@xmath55 @xmath56 ( n@xmath57 @xmath56 ) , they have a combined unabsorbed x - ray luminosity of about @xmath58 erg s@xmath2 ( @xmath59 erg s@xmath2 ) from @xmath43 kev . alternatively , if the point sources are modelled as having power law spectral shapes with a photon index of 1.6 ( the index of the hard x - ray component - see  3.2.3 ) they have a combined x - ray luminosity of @xmath60 erg s@xmath2 ( 3.1@xmath61 erg s@xmath2 ) from @xmath43 kev . each of the three sources thus has a luminosity in the 0.1 to 2.4 kev band of @xmath5 few @xmath62 to 10@xmath63 erg s@xmath2 . this can be compared to the most powerful individual x - ray sources known in nearby galaxies , which have peak x - ray luminosities of @xmath5 10@xmath64 erg s@xmath2 : sn1978c in ngc 1313 ( ryder et al 1993 ) , sn1986j in ngc 891 ( bregman & pildis 1992 ) , sn 1993j in m 81 ( zimmermann et al 1994 ; kohmura et al 1994 ) , and the highly variable sources in the nuclei of m 82 ( collura et al 1994 ) and ngc 3628 ( dahlem , heckman , & fabbiano 1995 ) . it is worth emphasizing that at the distance of arp 299 , 5@xmath40 corresponds to roughly 1 kpc , and that the sources are coincident with the sites of the most intense star - formation in arp 299 . higher resolution x - ray imaging with axaf may well resolve these sources into multiple sub - components . the different morphologies of the hard and soft - band pspc images suggest that there are at least two sources of x - rays in the arp 299 system with different spectral shapes and possibly different emission mechanisms . to uncover these emission mechanisms we extract spatially - resolved spectra from the central and outer regions . the central or `` core '' region is defined with a circle of diameter = 1.3@xmath65 centered on the x - ray peak of fig . 2a . the outer or `` halo '' region is defined with an ellipse having a major axis = 2.78@xmath65 , minor axis = 2.22@xmath65 , and p.a . @xmath66 centered on the x - ray peak of figure 2a . background is taken from source - free regions near the galaxy . the extraction regions , source counts and count rates are listed in table 1 and the spatially - resolved halo and core spectra are shown in figure 4 . there are 328 counts from within the halo region , 119 of which are source counts and 209 ( almost 2/3 ) of which are background counts . we estimate the contribution of background counts to the total spectrum by calculating the areas of the halo and background regions and then using the ratio of areas to predict the contribution of background in the halo region . we then determine an empirical spectral model for the background and include this model ( properly normalized ) in our spectral fits to `` subtract '' the background contribution . our empirical background model consists of a power law with @xmath67 = 2.3 @xmath530.2 and an unresolved gaussian - shaped emission line at 0.53 kev . the line represents oxygen fluorescence from earth s atmosphere and the power law approximates contributions from the particle background and diffuse x - ray background , as well as long - term and short - term enhancements in the background rate . the statistics are too poor to distinguish between different physical models for the halo emission . in particular , the data can not distinguish between the two most natural choices , which are a power - law spectrum ( where the x - rays are produced by inverse - compton scattering of lower energy photons ) and a thermal spectrum ( where the x - rays are produced in a plasma that has been heated by shocks ) . a power - law spectrum is expected if the soft x - rays result from emission associated with an extended synchrotron - emitting radio halo , such as that found around m82 ( seaquist & odegard 1991 ) . however , the radio emission in arp 299 is not extended on the same scale as the soft x - rays ( condon et al . in fact , the soft x - ray emission is extended in a direction ( north - south ) that is roughly perdendicular to the radio source major axis . this implies that the x - ray emission is not related to the emission at radio wavelengths in arp 299 , and hence a power - law description of the halo is unlikely . recent studies of extended emission in starburst galaxies indicate that the soft emission is primarily thermal ( see dahlem , weaver & heckman 1998 ) and so we choose a model that consists of an emission spectrum from hot , diffuse gas based on calculations by mewe and kaastra with fe l calculations by liedahl ( mewe , gronenschild & van den oord 1985 ; mewe , lemen & van den oord 1986 ; kaastra 1992 - hereafter referred to as the mekal model ) .    when the data are fitted with a single temperature mekal model and solar abundances are assumed , we find no evidence for absorption in excess of the galactic column density ( 0.9@xmath1110@xmath68 @xmath56 ; burstein & heiles 1982 ) , and the spectrum is well described with a plasma having kt@xmath69 kev ( table 2 ) . the @xmath43 kev unabsorbed flux for this model is @xmath70 ergs @xmath56 s@xmath2 , corresponding to a halo luminosity of @xmath71 erg s@xmath2 . for the core spectrum , a single - component power - law model yields a poor fit ( table 2 ; model a ) and results in positive residuals near 0.9 kev that resemble a blend of primarily fe l and ne line emission ( figure 5a ) . mekal plasma models with solar abundances also yield poor fits ( table 2 ; models b1 and b2 ) , even when the absorbing column density is a free parameter in the fit . this can be seen in figure 5b , which shows evidence for excess flux toward higher energies . if the abundance is allowed to vary , the fit improves ( table 2 ; model b3 ) implying an abundance of 0.12(+0.10 -0.06)@xmath72 . such a low abundance seems highly unusual , especially in light of the intense starburst in arp 299 , but since abundance calculations are derived from line equivalent widths , the possibility exists that a second thermal or hard x - ray component ( not uniquely detectable with the pspc ) may contribute continuum flux at low energies . such a component would dilute the line emission from the plasma and cause the abundance of the hot gas to be underestimated . this behavior is typical of starburst spectra that intrinsically contain multiple emission components but are fitted with single - component plasma models ( dahlem , weaver , & heckman 1998 ; weaver , heckman , & dahlem 1998 ) . for the remainder of this paper we therefore assume that the x - ray emitting gas has solar abundance .    for the case of solar abundances , the pspc data require at least two spectral components . models that consists of a medium - temperature mekal plasma and a thermal bremsstrahlung with kt = 7.0 kev ( table 2 ; model c ) or a medium - temperature mekal plasma and a power law with @xmath67=1.7 ( not shown ) provide excellent fits as long as the column density is allowed to be about 2 to 3 times larger than the galactic value . in this case , kt@xmath73 kev for the medium - temperature plasma . the ratio of the core spectrum to the two - component mekal plus bremsstrahlung model is shown in figure 5c . the @xmath43 kev unabsorbed flux for this model is @xmath74 ergs @xmath56 s@xmath2 , corresponding to a core luminosity of @xmath75 erg s@xmath2 . _ asca _  can not spatially resolve the x - ray emission and so we use the integral pspc spectrum for joint fits . the spectral coverage to @xmath77 kev provided by _ asca _  allows us to detect a distinct hard x - ray component . single power - law or mekal plasma models provide extremely poor fits to the _ asca _  plus pspc spectrum ( table 3 ; models a and b ) . note that this is true even if the abundance is a free parameter in the fits . the ratio of the joint data to the mekal model ( figure 6 ) clearly illustrates both excess line emission near 0.9 kev and a high energy excess beyond about 5 kev . a two - component mekal plus power - law model provides the best fit ( model c ) but the mekal temperature is higher than that found for the halo (  3.2.1 ) and the derived abundances are sub - solar . the abundances can be reconciled with solar if we add to the model the 0.2 kev mekal plasma component found in the halo ( model d ) . in this case , the hard x - ray component requires absorption in excess of the galactic value . we note that our approach and results differ somewhat from zgw who also fit the joint _ asca _  plus pspc spectrum . they did not require our soft ( 0.2 kev ) component , nor did they find evidence for intrinsic absorption . the inclusion of the soft component in our model fits is dictated primarily by our spatial analysis of the pspc image as a function of energy ( which zgw did not undertake ) . our analysis demonstrates that the soft 0.2 kev component is definitely present in the halo ( and hence must be incorporated in the global fit to the _ asca _  plus pspc spectrum ) . as described in the previous paragraph , inclusion of the 0.2 kev component then leads to higher values of n@xmath78 for the hard component . this nicely illustrates the power of combining all the available information provided by the x - ray images and spectra when interpreting the complex x - ray emission from starbursts . the data and best - fitting three component model ( model d ) are shown together in figure 7 and the deconvolved model is shown at full resolution in figure 8 . the goodness of the fit is illustrated by the ratio of the data to the best - fitting model ( model d ) in figure 9 . in addition to the 0.2 kev halo component , the second thermal component has a temperature of 0.77 kev , and the hard component is well represented as either a power - law with photon index 1.6 or thermal bremsstrahlung emission with kt @xmath5 11 kev . the intrinsic column of hi in model d ( of - order @xmath79 @xmath56 ) is similar to that inferred from the dust extinction measured in our optical spectra ( see section 4.2 below ) . the unabsorbed fluxes for the @xmath43 kev and @xmath80 kev bands are @xmath81 erg @xmath56 s@xmath2 and @xmath82 erg @xmath56 s@xmath2 , respectively ( table 4 ) . the corresponding x - ray luminosities are 3.3@xmath61 erg s@xmath2 and 2.5@xmath61 erg s@xmath2 .      we will discuss the nature of the two mekal plasma components extensively in sections 3.3 and 5.2 below . here we remark that the hard ( powerlaw or bremsstrahlung ) component is most likely due to a combination of inverse compton scattering of soft starburst photons by the relativistic electrons responsible for the radio synchrotron emission ( see moran & lehnert 1997 ) and a population of x - ray binaries . comparing the flux of this hard component in the energy band of the _ rosat _  hri to that of the ensemble of bright point sources seen in the hri image we find that they are similar . the absorption - corrected @xmath43 kev flux of the hard x - ray component is @xmath83 ergs @xmath56 s@xmath2 ( table 4 ) . the hri flux from the three brightest point sources ( having a combined count rate of 0.009 counts s@xmath2 ) is @xmath84 ergs @xmath56 s@xmath2 for @xmath85 @xmath56 ( table 3 ) . the hard component seen with @xmath23 could thus account for most of the flux from the bright point sources in the hri image . an identification of the hard component with the three bright point - like sources seen in the hri bandpass ( @xmath5 1 kev ) then argues strongly against the hardest ( @xmath86 kev ) x - rays being dominated by emission from a heavily absorbed agn ( both on morphological grounds , and because a heavily absorbed source would produce too few counts in the hri band ) . the point - like nature of the hri sources also argues against inverse compton scattering from a diffuse population of radio - synchrotron - emitting electrons . instead , emission from a population of high - mass x - ray binaries is most likely ( as zgw conclude on independent grounds ) .      the joint _ rosat _  plus _ asca _  x - ray spectrum of arp 299 requires a multi - component fit , as outlined in section 3.2 . in addition , the different morphologies of the hard and soft pspc images suggest that these spectral components are dominant over different spatial regions in arp 299 . the soft , cooler x - ray gas appears to be more extended than the hard , hotter x - ray gas ( see fig . 2 ) . in order to derive the physical parameters of the x - ray gas and compare them with those predicted from models of a superwind , we must estimate the appropriate volumes for the soft and hard spectral components . in the calculations that follow , we assume the hard , 0.77 kev thermal plasma occupies a region of @xmath87 radius ( our extraction region for the core spectrum ) , corresponding to a volume of @xmath88 @xmath89 . the soft , 0.20 kev plasma is assumed to occupy a volume of @xmath90 @xmath89 , equivalent to the volume enclosed by the  total \" spectrum described in section 3.2.3 . we have divided this volume into core and halo components , as in section 3.2 , in order to derive gas parameters for the soft thermal component . the emission integral ( the volume integral of the density squared ) for the soft component is @xmath91 @xmath13 , 60% of which is contained within a radius of @xmath87 , the boundary of the extracted core spectrum . if the volume filling factor of the x - ray gas is @xmath92 , where @xmath93 , the physical parameters of the soft thermal component can be estimated :    \\1 . the mean core gas density is @xmath94 @xmath13 . the mean halo gas density is @xmath95 @xmath13 . \\2 . for t@xmath96k , the corresponding presssures are @xmath97 dyne @xmath56 for the core gas and @xmath98 dyne @xmath56 for the halo gas . the mass of the gas at t@xmath96k in the core is @xmath99 m@xmath4 . the mass of gas at this temperature in the halo is @xmath100 m@xmath4 . the thermal energy contents of the core and halo components are @xmath101 erg and @xmath102 erg , respectively . the radiative cooling times are @xmath103 yrs and @xmath104 yrs , for the core and halo gas , respectively . here , we have used t@xmath105 , where @xmath106 erg @xmath107 s@xmath2 ( sutherland & dopita 1993 ) for gas at solar abundances at these temperatures . we can similarly calculate the the physical parameters for the second mekal thermal plasma identified in the spectrum of arp 299 by our joint _ rosat _  plus _ asca _  spectral fits . for a volume integral of the density squared of this second , hard thermal plasma at kt=0.77 kev of @xmath108 @xmath13 , the physical parameters of this hot gas are :    \\1 . the mean gas density is @xmath109 @xmath13 . the corresponding pressure is @xmath110 dyne @xmath56 . the mass of gas at t@xmath111k is @xmath112 m@xmath113 . the thermal energy content of the gas is @xmath114 erg . the radiative cooling time of the gas is @xmath115 yrs for solar metallicity ( sutherland & dopita 1993 ) .","summary":"we analyse _ rosat _  and _ asca _  x - ray data and optical spectra and narrow - band images . the x - ray nebula in arp 299 has a diameter of kpc , is elongated roughly along the hi minor axis of the merging system , has an outer ( inner ) temperature of 2.3 ( 9 ) million k , a luminosity of erg s , a gas mass of 7 m , and a thermal energy content of ergs . an additional hard x - ray component is present with a luminosity in the 0.1 to 10 kev band of erg s most likely due to x - ray binaries or possibly inverse compton scattering . , this implies that the luminous x - ray nebula in arp 299 is also powered by the starburst outflow ( rather than by the collisions of gas clouds during the merger )","abstract":"we present a detailed investigation of the x - ray and optical properties of the starburst - merger system arp299 ( ngc 3690 , mrk 171 ) , with an emphasis on its spectacular gaseous nebula . we analyse _ rosat _  and _ asca _  x - ray data and optical spectra and narrow - band images . the x - ray nebula in arp 299 has a diameter of kpc , is elongated roughly along the hi minor axis of the merging system , has an outer ( inner ) temperature of 2.3 ( 9 ) million k , a luminosity of erg s , a gas mass of 7 m , and a thermal energy content of ergs . an additional hard x - ray component is present with a luminosity in the 0.1 to 10 kev band of erg s most likely due to x - ray binaries or possibly inverse compton scattering . the overall x - ray spectrum is consistent with that of other starbursts ( dahlem , weaver & heckman ) . compared to the x - ray nebula , the optical emission - line nebula is smaller ( 20 kpc ) but much more luminous ( erg s 4% l for arp 299 ) . the kinematics of the emission - line nebula are complex , with the line - widths increasing systematically with decreasing h surface - brightness to values of 500 to 700 km s in the faint outer filaments . the relative strengths of the low - ionization forbidden lines ( [ sii],[nii ] , and [ oi ] ) also increase systematically as the gas surface - brightness decreases and as the line widths increase . we measure high gas pressures in the inner emission - line nebula ( p / k few 10 k ) that decline systematically with increasing radius .    we suggest that the on - going galaxy collision has tidally - redistributed the ism of the merging galaxies . the optical emission - line nebula results as this gas is photoionized by radiation that escapes from the starburst , and is shock - heated , accelerated , and pressurized by a ` superwind ' driven by the collective effect of the starburst supernovae and stellar winds . since empirically only those galaxy mergers that that contain luminous starbursts have bright x - ray nebulae , this implies that the luminous x - ray nebula in arp 299 is also powered by the starburst outflow ( rather than by the collisions of gas clouds during the merger ) . this outflow can be most directly traced by its x - ray emission , which is plausibly a mass - loaded flow ( m yr ) of adiabatically - cooling gas that carries out a substantial fraction of the energy and metals injected by the starburst at a speed close to the escape velocity from arp 299 . the mass outflow rate exceeds the star - formation rate in this system . we conclude that powerful starbursts are able to heat ( and possibly eject ) a significant fraction of the interstellar medium in galaxies that are the products of mergers .    = 0em    \\1 . visiting astronomers , kitt peak national observatory , noao , operated by aura , inc . under cooperative agreement with the national science foundation .    = 2em"}
{"article_id":"astro-ph9812317","section_id":"c","document":"from the extinction - corrected h@xmath10+[nii ] luminosity we estimated in  4.2 above , we deduce that the the total luminosity of the optical emission  line nebula ( summing over all emission lines ) is @xmath145 erg s@xmath2 . this represents about 4% of the bolometric luminosity of arp 299 and several hundred times the x - ray luminosity of the nebula . the luminosity of the nebula is so large that we can exclude the possibility that it is heated _ primarily _ by mechanical energy supplied either by the starburst or the galaxy collision itself . the rate at which a starburst produces mechanical energy ( in the form of supernovae and stellar winds ) is only about 1% of the starburst s bolometric luminosity ( leitherer & heckman 1995 ) . even if all this mechanical energy is used to heat the emission - line nebula , the resulting luminosity will only be 25% of the observed value . similarly , the kinetic energy of 10@xmath146 m@xmath21 of interstellar gas moving at 300 km s@xmath2 is @xmath147 ergs . if this energy is entirely dissipated and radiated away by the emission - line nebula during one dynamical crossing - time ( @xmath5 10@xmath148 years ) , the resulting heating rate is only 3@xmath1110@xmath149 erg s@xmath2 or 3% of the observed value . we conclude that the _ primary _ source of energy input to the optical emission - line nebula is most likely to be the ionizing radiation that escapes from the starburst complexes and propogates into the nebula . the leitherer & heckman ( 1995 ) models predict a luminosity in ionizing radiation that is roughly 10% of the bolometric luminosity of the starburst , so that only about 40% of the available radiation is required to power the nebula . this picture provides a simple and natural explanation for the inverse correlation between the relative strength of the low - ionization lines and the gas surface brightness discussed above ( fig . 13 ) . for individual gas clouds of a given density , the higher the value of the local intensity of the ionizing radiation field , the higher the resulting value of the ionization parameter @xmath150 ( defined to be the ratio of the densities of ionizing photons and electrons within a photoionized gas cloud ) . simple ionization equilibrium arguments show that @xmath150 determines the ionization state of the gas , and the h@xmath10 surface brightness will be proportional , through recombination , to the intensity of the ionizing radiation field . thus , the proportionality between @xmath150 and the h@xmath10 surface brightness will naturally produce enhanced relative intensities of low - ionization lines in the faint gas ( see wang , heckman , & lehnert 1998 ) . we can examine this more quantitatively . the h@xmath10 luminosity of the nebula ( 3.3@xmath1110@xmath149 implies an ionization rate of @xmath151 . if we assume that this arises equally in nuclei  a \" and  b1 \" , then the radial electron density profile discussed above ( figure 12 ) , leads to a predicted ionization parameter @xmath152 for the gas located at radii of one to a few kpc from the nuclei . j. sokolowski ( private communication ) has kindly run @xmath153 models of gas that is photoionized by a starburst population of hot stars using the evolutionary synthesis code discussed by leitherer & heckman ( 1995 ) . we use the models in which the cosmically - abundant , refractory elements ( e.g. fe and si ) are locked - up in dust grains ( as in the case of diffuse clouds in our own galaxy ) . this depletion of gas - phase coolants has the effect of increasing the equilibrium temperature in the photoionized gas and thereby increasing the emissivity in the collisonally - excited forbidden lines with respect to the balmer recombination lines ( shields & kennicutt 1995 ) . for the above value of @xmath150 , the predicted line - ratios are [ sii]@xmath42 6716,6730/h@xmath10 = 0.4 , [ nii]@xmath1346583/h@xmath10 = 0.6 , [ oi]@xmath1346300/h@xmath10 = 0.03 , and [ oiii]@xmath1345007/h@xmath126 = 1.6 , in reasonable agreement with the typical observed values in the _ high_-surface - brightness part of the nebula ( figures 11 , 13 , and 14 ; table 5 ) . while photoionization clearly dominates the total energy input into the nebula and the excitation near the nuclei , mechanical heating also plays an important role , especially in the diffuse low - surface - brightness gas . firstly , recall that the estimated mechanical luminosity of the starburst is 25% of the nebula s emission - line luminosity . secondly , the good correlation we find between the widths of the emission - lines and the line - ratios ( figure 14 ) suggests that there is a connection between the dynamics of the gas and its physical state ( as expected for shock heating ) . finally , shock - heating may be required to explain the extreme line - ratios present in the very faint outer regions where [ oi]/h@xmath10 = 10 to 20% and [ oiii]/h@xmath154 ( see table 5 ) . most likely , both photoionization and shocks play a role , with the former being more globally significant , and the latter being important in the most kinematically - disturbed ( faint , outer ) regions . one property of the emission - line nebula that can be most clearly ascribed to the mechanical energy supplied by the starburst is the gas density / pressure profile ( figure 12 ) . in the starburst  driven wind models of chevalier & clegg ( 1985 ) , there is a region of radius r@xmath155 ( the starburst ) inside which mass and kinetic energy are injected at a constant rate per unit volume , resulting in a region of hot gas which slowly expands through a sonic radius ( located approximately at the radius of the starburst ) and is then transformed into a supersonic outflow . the gas pressure inside the starburst is just the static , thermal pressure of the hot fluid that has been produced by thermalization ( shock - heating ) in high - speed collisions between material ejected by supernovae and the ambient interstellar medium . this pressure is essentially determined by the size of the starburst and the rate at which mass and kinetic energy is injected . since the sound - crossing time inside the starburst is much shorter than the outflow time ( e.g. since the flow is subsonic inside the starburst itself ) , the pressure is roughly constant throughout this central region .    using the starburst models of leitherer & heckman ( 1995 ) to relate the rate at which the starburst injects mass and thermal / mechanical energy to its bolometric luminosity , we expect the central pressure to be given approximately by :    @xmath156^{-2}\\ k\\,cm^{-3}\\ ] ]    at radii much larger than the starburst radius , the pressure of the outflow is dominated by the wind s ram pressure . this will essentially be set by the rate at which the starburst injects mass and energy into the outflow , and will drop like the inverse square of distance from the starburst :    @xmath157^{-2}\\ k\\,cm^{-3}\\ ] ]    where @xmath158 is the distance from the starburst ( assuming @xmath159 ) . these predictions agree reasonably well with the observations of arp 299 . taking l@xmath9 = 3@xmath1110@xmath20l@xmath21 as a rough estimate of bolometric luminosity for each of the two starbursts and r@xmath155 = 1.3 kpc as their estimated radii , the predicted value p / k = 5 @xmath11 10@xmath12 k @xmath13 is the same as that derived from the temperatures and densities given in  4.1 . similarly , the predicted value for p / k at a radius of 3 kpc is @xmath160 k @xmath13 ( n@xmath161 = 50 @xmath13 ) , consistent with figure 12 .      in principle , the x - ray nebula could arise as a significant fraction of the gas initially in the disks of two spiral galaxies is heated collisionally during the galaxies on - going merger . as discussed in  5.1 above , the maximum rate of collisional heating in a merger will be of - order 3@xmath162 erg s@xmath2 , which is about an order - of - magnitude larger than the observed x - ray luminosity . the mass of hot gas ( 7@xmath1110@xmath163 m@xmath4 ) is also consistent with this picture . there are however at least two problems with this model . first , the observed gas temperatures are much too high in the inner region . that is , cloud collision speeds appropriate to a galactic merger ( 300 to 500 km s@xmath2 ) correspond to postshock temperatures of 1.3 to 3.5 million k , while the observed temperature is 9 million k in the inner region . second , if x - ray nebulae in colliding / merging galaxies are directly produced by the galactic collision , then we would expect that bright x - ray nebulae would be a common feature of mergers of disk galaxies ( regardless of whether these mergers are undergoing a starburst ) . wang et al ( 1997 ) and read & ponman ( 1998 ) have shown that this is _ not _ the case . in the wang et al sample of 12 merging / colliding galaxies ( including arp 299 ) , the only strong soft x - ray emitters are also strong h@xmath10+[nii ] and far - ir emitters . put another way , strong soft x - ray emission is not a ubiquitous feature of galaxy mergers ( read & ponman 1998 ) , but instead appears to share a a common power source with the optical line and far - ir emission ( a starburst ) . we therefore regard the most likely origin of the x - ray nebula in arp 299 to be a superwind . evidence for outflowing gas in arp 299 comes from the optical spectroscopic data on the kinematically - disturbed faint emission - line filaments and loops ( see  4.4 ) . the presence of diffuse x - ray - emitting gas extending well outside the optical boundaries of the galaxy and oriented roughly perpendicular to the system s hi major axis is also highly suggestive of an outflow . in order to quantitatively assess whether the soft x - ray emission can indeed be produced by gas heated by supernovae and stellar winds in the central star - bursting complexes , we will adopt a simple model that assumes that mechanical energy is being continuously injected inside the starburst and used to heat the surrounding gas . this gas then flows out of the starburst and emits x - rays ( cf . wang 1995 ) . in such a model we need to specify the heating rate and the mass - injection rate into the outflow . as noted earlier , the ir luminosity of arp 299 , when used in conjunction with the starburst models of leitherer & heckman ( 1995 ) , corresponds to a total mechanical heating rate of about @xmath164 erg s@xmath2 . we will assume that the gas in the starburst is initially heated to a temperature of about @xmath165 k ( the temperature of the hottest diffuse gas that we detect in our x - ray data ) . for the heating rate given above , conservation of energy then implies that gas is heated at a rate of @xmath166 m@xmath4 per year ( chevalier & clegg 1985 ) . this is about an order of magnitude greater than the predicted rate at which supernovae and stellar winds return mass to the interstellar medium in this system . this implies that the outflow is strongly `` mass - loaded '' : most of the outflowing material is ambient interstellar gas in and around the starburst that has been heated by the supernovae and stellar winds ( see suchkov et al 1996 ) . in effect , each supernova heats up , on average , about 200 m@xmath4 of interstellar gas . in this case , we would expect the average metallicity of the x - ray emitting gas to be similar to that in the interstellar medium of arp 299 . since the predicted mechanical heating rate is about @xmath167 times the total luminosity of the two mekal thermal components , we will ignore the dynamical effect of radiative cooling in our simple model . this neglect is further justified since the estimated radiative cooling time of the x - ray gas ( approximately a gyr - see  3.3 above ) is much longer than the adiabatic expansion timescale ( @xmath168 years ) . following chevalier & clegg ( 1985 ) and wang ( 1995 ) we therefore consider a spherically - symmetric wind with a mass outflow rate of 100 m@xmath4 per year which is `` fed '' by hot gas that is injected at a uniform temperature of @xmath165 k. we will take the overall size of the energy injection region ( encompassing both the eastern and western starbursts ) to be similar to that of the bright x - ray emission in the hri data ( radius @xmath5 4 kpc ) . this is obviously an oversimplication , but might roughly represent the effect of the collision between the two outflows produced by the eastern and western starbursts , and the subsequent shocks and rethermalization of the gas on these size - scales . in the absence of gravitational decelleration , the wind would reach a terminal velocity of v@xmath169 = 800 km s@xmath2 ( chevalier & clegg 1985 ) . we assume the wind cools through adiabatic expansion while also emitting soft x - rays . the emissivity of gas in the 0.1 to 2.4 kev energy band is constant to within about a factor of @xmath170 as a function of temperature over the range between @xmath171 k to @xmath172 k ( @xmath173 erg @xmath89 s@xmath2 for solar metallicity ) . this then allows us to predict an x - ray luminosity from the outflow of @xmath174 erg s@xmath2 from within a region equal in size to the x - ray halo ( radius of @xmath5 20 kpc ) . this rough estimate compares reasonably well with the measured luminosity of the two mekal x - ray components of @xmath175 erg s@xmath2 . the total predicted mass of the hot gas will be about @xmath176 m@xmath4 and the predicted thermal plus kinetic energy in the outflow will be @xmath177 ergs . again , these predicted values agree reasonably well with the derived values for the sum of the hot ( 0.77 kev ) and warm ( 0.2 kev ) components : m @xmath178 m@xmath4 and e@xmath179 ergs . note that a radius of 20 kpc and a wind terminal velocity of 800 km s@xmath2 corresponds to a rough dynamical age of 25 myr ( reasonable for a starburst ) . if the outflow has lasted much longer than this , the total mass and energy in the flow will rise accordingly , but this will comprise material at larger radii ( @xmath180 20 kpc ) . such material will have a low density and ( due to adiabatic cooling ) a low temperature , and would therefore not produce significant x - ray emission ( cf . wang 1995 ) . in fact , our simple model predicts a temperature range in the hot gas ranging from @xmath165 k in the energy injection region to @xmath181 k at a radius of 4 kpc to @xmath182 k at a radius of 20 kpc . these temperatures then span the observed / inferred range , and the temperatures reach the lower limit where the rosat pspc sensitivity plummets ( @xmath183 k ) at roughly the same radius as where the observed emission ends .    having demonstrated that this simple model can very roughly reproduce the gross properties of the x - ray emission , we next consider the fate of this outflowing gas . following wang ( 1995 ) , the `` escape temperature '' for hot gas in a galaxy potential with an escape velocity v@xmath184 is given by :    t@xmath184 @xmath185 @xmath186 ( v@xmath184/300 km s@xmath2)@xmath187 @xmath188k    the hi rotation curve of arp 299 has an amplitude of 240 km s@xmath2 out to the edge of the hi distribution at a radius of 22 kpc ( stanford & wood 1989 ) . assuming that arp 299 has an isothermal dark matter halo extending to a radius of 300 kpc , the escape velocity ( see equation 13 in heckman et al . ( 1995 ) ) at r = 4 ( 22 ) kpc is about 780 ( 650 ) km s@xmath2 and t@xmath184 = 6.7 ( 4.6 ) @xmath189 k. these temperatures are similar to the range of temperatures we measure for the hot gas ( @xmath190 k for the cooler component and @xmath191 k for the hotter component ) . the escape velocity is also similar to the estimated terminal velocity for the wind ( see above ) . these rough arguments suggest that the outflowing gas _ may _ be able to escape the gravitational potential of arp 299 .","summary":"the kinematics of the emission - line nebula are complex , with the line - widths increasing systematically with decreasing h surface - brightness to values of 500 to 700 km s in the faint outer filaments . . the optical emission - line nebula results as this gas is photoionized by radiation that escapes from the starburst , and is shock - heated , accelerated , and pressurized by a ` superwind ' driven by the collective effect of the starburst supernovae and stellar winds . since empirically only those galaxy mergers that that contain luminous starbursts have bright x - ray nebulae . this outflow can be most directly traced by its x - ray emission , which is plausibly a mass - loaded flow ( m yr ) of adiabatically - cooling gas that carries out a substantial fraction of the energy and metals injected by the starburst at a speed close to the escape velocity from arp 299 .","abstract":"we present a detailed investigation of the x - ray and optical properties of the starburst - merger system arp299 ( ngc 3690 , mrk 171 ) , with an emphasis on its spectacular gaseous nebula . we analyse _ rosat _  and _ asca _  x - ray data and optical spectra and narrow - band images . the x - ray nebula in arp 299 has a diameter of kpc , is elongated roughly along the hi minor axis of the merging system , has an outer ( inner ) temperature of 2.3 ( 9 ) million k , a luminosity of erg s , a gas mass of 7 m , and a thermal energy content of ergs . an additional hard x - ray component is present with a luminosity in the 0.1 to 10 kev band of erg s most likely due to x - ray binaries or possibly inverse compton scattering . the overall x - ray spectrum is consistent with that of other starbursts ( dahlem , weaver & heckman ) . compared to the x - ray nebula , the optical emission - line nebula is smaller ( 20 kpc ) but much more luminous ( erg s 4% l for arp 299 ) . the kinematics of the emission - line nebula are complex , with the line - widths increasing systematically with decreasing h surface - brightness to values of 500 to 700 km s in the faint outer filaments . the relative strengths of the low - ionization forbidden lines ( [ sii],[nii ] , and [ oi ] ) also increase systematically as the gas surface - brightness decreases and as the line widths increase . we measure high gas pressures in the inner emission - line nebula ( p / k few 10 k ) that decline systematically with increasing radius .    we suggest that the on - going galaxy collision has tidally - redistributed the ism of the merging galaxies . the optical emission - line nebula results as this gas is photoionized by radiation that escapes from the starburst , and is shock - heated , accelerated , and pressurized by a ` superwind ' driven by the collective effect of the starburst supernovae and stellar winds . since empirically only those galaxy mergers that that contain luminous starbursts have bright x - ray nebulae , this implies that the luminous x - ray nebula in arp 299 is also powered by the starburst outflow ( rather than by the collisions of gas clouds during the merger ) . this outflow can be most directly traced by its x - ray emission , which is plausibly a mass - loaded flow ( m yr ) of adiabatically - cooling gas that carries out a substantial fraction of the energy and metals injected by the starburst at a speed close to the escape velocity from arp 299 . the mass outflow rate exceeds the star - formation rate in this system . we conclude that powerful starbursts are able to heat ( and possibly eject ) a significant fraction of the interstellar medium in galaxies that are the products of mergers .    = 0em    \\1 . visiting astronomers , kitt peak national observatory , noao , operated by aura , inc . under cooperative agreement with the national science foundation .    = 2em"}
{"article_id":"astro-ph9812317","section_id":"c","document":"we have discussed optical and x - ray data on the spectacular gaseous nebula surrounding the infrared - luminous merger / starburst system arp 299 (= ngc 3690 or mrk 171 ) . we suggest that the on  going galaxy collision has tidally redistributed the cold interstellar media of the merging galaxies . the total luminosity of the optical emission - line nebula ( 10@xmath192 erg s@xmath2 @xmath5 4% l@xmath9 ) is too high to be powered primarily by either the collision of two galaxies directly , or by a starburst - driven superwind . instead , the gas is mostly photoionized by radiation from the ongoing starburst . we find strong trends in which the relative strengths of low - ionization lines ( [ sii ] , [ nii ] , and [ oi ] ) increase systematically with both decreasing nebular surface brightness and with increasing velocity dispersion . these trends can be understood if both hot stars and large  scale shocks play a role in energizing the gas . the shocks become increasingly important in the faint , outer regions of the nebula , and they provide for the coupling between the dynamical and physical state of the gas . we also find that the gas pressures are high in the inner optical emission - line nebula ( p / k @xmath5 5@xmath1110@xmath12 k @xmath13 within a radius of a kpc , and fall systematically with radius ( dropping below p / k @xmath5 10@xmath12 k @xmath13 at a radius of @xmath5 3 kpc ) . the shape and amplitude of the radial pressure profile agrees with the pressures predicted for starburst - driven outflows . while the luminosity ( @xmath193 erg s@xmath2 ) and mass ( @xmath194 m@xmath4 ) of the x - ray nebula can be explained by the collision of the interstellar media of two galaxies , we believe a more plausible heating source is the superwind . the thermal energy content ( @xmath147 ergs ) and dynamical age ( @xmath195 years ) of the x - ray nebula agree with a superwind model , but its high gas mass and x - ray luminosity , and it relatively low temperature ( 9 million k in the inner region and 2.3 million k in the outer ) imply that the outflow must be strongly ` mass - loaded ' ( most of the x - ray emitting gas is ambient interstellar material that has been mixed into the outflow ) . the implied outflow rate of @xmath196 per year can be compared to the estimated star - formation rate in the starburst of 40 ( 100 ) @xmath197 per year for a salpeter imf extending down to 1 ( 0.1 ) @xmath197 . the inner gas temperature of 9 million k implies a terminal velocity for such a flow of about 800 km s@xmath2 . these respective values are similar to the estimated escape temperature and escape velocity from the system . thus , perhaps the most striking result of this investigation is that in arp 299 a powerful starburst has apparently been able to heat up a significant fraction of the interstellar medium of the merger product ( nearly 10@xmath146 m@xmath21 ) to a temperature and outflow speed that may allow this gas ultimately to escape the system . this has implications for understanding how disk - disk galaxy mergers may produce ( at least some ) elliptical galaxies ( mihos & hernquist 1994 ; schweizer 1992 ) and how the intergalactic medium could have been polluted by metal - enriched material ( see gibson , loewenstein , & mushotzky 1997 ) .      this research was primarily supported by nasa ltsa grants nagw-3138 to th and nagw-4025 to kw . the research by la described in this paper was carried out by the california institute of technology , under a contract with nasa . this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , caltech , under contract with the national aeronautics and space administration . hughes , d. , serjeant , s. , dunlop , j. , rowan - robinson , m. , blain , a. , mann , r. , ivison , r. , peacock , j. , efstathiou , a. , gear , w. , oliver , s. , lawrence , a. , longair , m. , goldschmidt , & jenness , t. 1998 , nature , in press","summary":"we present a detailed investigation of the x - ray and optical properties of the starburst - merger system arp299 ( ngc 3690 , mrk 171 ) , with an emphasis on its spectacular gaseous nebula . the overall x - ray spectrum is consistent with that of other starbursts ( dahlem , weaver & heckman ) . compared to the x - ray nebula , the optical emission - line nebula is smaller ( 20 kpc ) but much more luminous ( erg s 4% l for arp 299 ) . the relative strengths of the low - ionization forbidden lines ( [ sii],[nii ] , and [ oi ] ) also increase systematically as the gas surface - brightness decreases and as the line widths increase . we measure high gas pressures in the inner emission - line nebula ( p / k few 10 k ) that decline systematically with increasing radius .    we suggest that the on - going galaxy collision has tidally - redistributed the ism of the merging galaxies the mass outflow rate exceeds the star - formation rate in this system . we conclude that powerful starbursts are able to heat ( and possibly eject ) a significant fraction of the interstellar medium in galaxies that are the products of mergers .    visiting astronomers , kitt peak national observatory , noao , operated by aura , inc . under cooperative agreement with the national science foundation .   ","abstract":"we present a detailed investigation of the x - ray and optical properties of the starburst - merger system arp299 ( ngc 3690 , mrk 171 ) , with an emphasis on its spectacular gaseous nebula . we analyse _ rosat _  and _ asca _  x - ray data and optical spectra and narrow - band images . the x - ray nebula in arp 299 has a diameter of kpc , is elongated roughly along the hi minor axis of the merging system , has an outer ( inner ) temperature of 2.3 ( 9 ) million k , a luminosity of erg s , a gas mass of 7 m , and a thermal energy content of ergs . an additional hard x - ray component is present with a luminosity in the 0.1 to 10 kev band of erg s most likely due to x - ray binaries or possibly inverse compton scattering . the overall x - ray spectrum is consistent with that of other starbursts ( dahlem , weaver & heckman ) . compared to the x - ray nebula , the optical emission - line nebula is smaller ( 20 kpc ) but much more luminous ( erg s 4% l for arp 299 ) . the kinematics of the emission - line nebula are complex , with the line - widths increasing systematically with decreasing h surface - brightness to values of 500 to 700 km s in the faint outer filaments . the relative strengths of the low - ionization forbidden lines ( [ sii],[nii ] , and [ oi ] ) also increase systematically as the gas surface - brightness decreases and as the line widths increase . we measure high gas pressures in the inner emission - line nebula ( p / k few 10 k ) that decline systematically with increasing radius .    we suggest that the on - going galaxy collision has tidally - redistributed the ism of the merging galaxies . the optical emission - line nebula results as this gas is photoionized by radiation that escapes from the starburst , and is shock - heated , accelerated , and pressurized by a ` superwind ' driven by the collective effect of the starburst supernovae and stellar winds . since empirically only those galaxy mergers that that contain luminous starbursts have bright x - ray nebulae , this implies that the luminous x - ray nebula in arp 299 is also powered by the starburst outflow ( rather than by the collisions of gas clouds during the merger ) . this outflow can be most directly traced by its x - ray emission , which is plausibly a mass - loaded flow ( m yr ) of adiabatically - cooling gas that carries out a substantial fraction of the energy and metals injected by the starburst at a speed close to the escape velocity from arp 299 . the mass outflow rate exceeds the star - formation rate in this system . we conclude that powerful starbursts are able to heat ( and possibly eject ) a significant fraction of the interstellar medium in galaxies that are the products of mergers .    = 0em    \\1 . visiting astronomers , kitt peak national observatory , noao , operated by aura , inc . under cooperative agreement with the national science foundation .    = 2em"}
{"article_id":"1105.4849","section_id":"i","document":"the existence of a charged elementary scalar particle implies necessarily an extended higgs sector beyond the standard model ( sm ) and , thus , an imprint for new physics . signals of charged elementary scalars production and effects related with such particles are an important part of the research at the colliders . this is well justified because searching for experimental proof of fundamental scalars is a necessary step to establish which of the many new proposed theories will be able to explain the experimental facts . charged scalars are part of spectrum of several models for physics beyond the sm . but the investigations realized until now have mainly been concentrated in the two - higgs doublet model ( 2hdm ) and the minimal supersymmetric standard model ( mssm ) . at present , the most stringent experimental constraints for the mass of a charged scalar , which we denote generically as the @xmath5 , comes from lep - ii and from tevatron direct searches . considering 2hdm the experiments yielded the mass constraint @xmath6 gev for the charged higgs boson , considering decays only into the channels @xmath7 and @xmath8 , @xcite . for the mssm , we have the result from the cdf collaboration stating that no signal was found in the mass region @xmath9 gev @xmath10 @xmath11 gev for the charged higgs boson @xcite . the atlas and the cms collaborations have made studies about the production and detection of charged higgs considering the pair production , and the associated production with the quark top or with the charged gauge boson @xcite , @xcite . these studies have shown that for the lhc energy and luminosities , the charged higgses could have a significant potential for discovery . it gives additional motivation to perform analyses , in the lhc context , of charged scalars predicted by models different from the 2hdm and the mssm . interesting extensions of the sm are the class of models based on @xmath0 group , known as 3 - 3 - 1 models @xcite,@xcite,@xcite,@xcite . these models have a symmetry breakdown pattern @xmath0/@xmath12 which can be connected to a scalar field condensation at the tev scale . the first proposals of these models were constructed considering three triplets of scalar fields , but a construction with two triplets of scalar fields is possible as well @xcite . taking into account the symmetry breakdown , 8 degrees of freedom from the scalars fields are incorporated as longitudinal components of the massive gauge bosons . therefore , there are more than one physical scalar left in the particle spectrum of these models , with at least one charged state . the characteristics of the charged scalars , like electric charge and couplings , depend on the specific model version . detailed analysis of the interactions and production are then crucial in order to validated or rule out some of these models . besides coinciding with the sm at low energies , these models have several attractive features . some of them are the following : the anomalies cancellation occur only when the number of generations are a multiple of three , and assuming asymptotic freedom in qcd it is concluded that there must be three generations ; the @xmath1 symmetry restricts the electroweak mixing angle @xmath13 , furnishing a hint for an explanation of its value , since @xmath14 in the models of refs . @xcite , and @xmath15 in the models of refs . @xcite ; also , quantization of the electric charge can be explained in the context of these models @xcite .    these and other features have motivated many studies concerning the 3 - 3 - 1 models . for example , new gauge bosons are predicted by these models and production analysis of such particles has been investigated in several aspects in refs . @xcite showing , in general , a great potential for discovering at the lhc and linear colliders . for other phenomenological issues involving the 3 - 3 - 1 models see @xcite .    the version in focus here is known as 3 - 3 - 1 model with right - handed neutrinos ( 3 - 3 - 1rhn ) . it has a new neutral fermionic field , with the usual charged and neutral fields , for completing each leptonic triplet representation @xcite , @xcite . in order to break the symmetry three scalar triplets are taken into account . in principle , those triplets may form several invariant operators through multiplication resulting in a great set of free parameters . in face of it we , additionally , impose a sort of global custodial symmetry which reduces the number of free parameters in the scalar potential @xcite . our main goal was to investigate in the 3 - 3 - 1rhn the lightest charged higgs boson production at hadron colliders . we analyzed several production channels of phenomenological interest including higgs pairs , associated production to @xmath16 bosons , associated production to top quarks , and from top quark decay . as a result we find that the cross sections for all these processes are at least as high as the mssm analogues . the presence of the new gauge boson @xmath2 of the model affects some of the production processes that we have studied endowing the model some distinguishing features compared to other standard model extensions . in particular , we found that the process @xmath17+@xmath18 at the 14 tev lhc allows , through a reconstruction analysis , a clear identification of the charged higgs boson decaying to a top and a bottom quark . this paper is organized as follows : in sec . ii , we present briefly the 3 - 3 - 1rhn version and discuss the reduced potential and the scalar spectrum . the decay channels and the production of the charged higgs at the lhc are shown in the sec . iii . in the sec . iv , we comment our results involving the decay of the charged scalar and the gauge boson . finally , we present our conclusions in sec . v.","summary":"one of the new neutral gauge bosons , , affects some production cross sections distinguishing the model from other standard model extensions like , for example , the minimal supersymmetric standard model and general two - higgs doublets models .","abstract":"we perform a study of the charged higgs production from an model with right - handed neutrinos , postulating a custodial symmetry which reduces the number of free parameters in the scalar potential . we compute the cross sections for charged scalars for typical and new production modes . one of the new neutral gauge bosons , , affects some production cross sections distinguishing the model from other standard model extensions like , for example , the minimal supersymmetric standard model and general two - higgs doublets models . the interplay between the higgs sector of the model and that gauge boson enhances substantially all the production rates of the lightest charged higgs boson , , at hadron colliders compared to the mssm . we found that a large portion of the parameters space can be probed at the lhc running at 14 tev center - of - mass energy in the associated production channel in the low luminosity run stage of the experiment ."}
{"article_id":"1105.4849","section_id":"c","document":"if the lhc collaborations could find experimental evidence for an scalar charged particle this will be an undisputed evidence of new physics beyond the sm . moreover , it will shed light on the mechanism of electroweak symmetry breaking . in this work , we analyzed the scalar spectrum of the 3 - 3 - 1 model with right - handed neutrinos but with a custodial symmetry that reduces the number of parameters in the scalar potential . there are two charged and five neutral scalar states in the particle spectrum . the lightest charged higgs bosons , @xmath3 , can be as light as 100 gev . the model presents several distinguishing features associated to the new gauge bosons and scalars . in special , there is an important interplay between one of the new neutral gauge bosons , @xmath2 , and the charged scalars of the model that enhances the production cross sections as compared to the mssm or 2hdm . yukawa interactions between the charged higgses and heavy quarks are strong , which results in large cross sections for the typical production modes as the associated top - charged higgs and charged higgses from top quark decays . the charged higgs pair production is also expected to be larger than its mssm and 2hdm analogues as a consequence of the enhanced yukawa interactions and the contribution from the new @xmath2 gauge boson .    as an example of the role played by this new @xmath1 neutral gauge boson , the light charged higgs bosons @xmath3 can be produced in association to a sm @xmath16 boson through the @xmath2 decay . the charged higgses decay into top and bottom quarks for @xmath166 , which lead to a @xmath224 final state at hadron colliders as the lhc and the tevatron . the top quark , the @xmath16 boson , and the charged higgs resonances make the task to separate the signal from backgrounds relatively simple , and as a consequence a large portion of the parameters space of the model will be accessible to the 14 tev lhc collaborations with up to @xmath225 , and even a @xmath219 integrated luminosity would be just enough to discover a charged higgs boson . we found that the same conclusion can not be claimed for the 7 tev lhc and the tevatron because of the reduced amount of data designed for these experiments . nevertheless the lighter charged higgs , @xmath121 , decays predominantly to tau leptons and if the @xmath2 is not too heavy this channel might be a good search channel for the tevatron or even a 7 tev lhc in a longer run . we did not try to optimize our analyses for very specific points of the parameters space , instead we focused on a more or less blind set of cuts taking into account only acceptance , trigger and tagging techniques . the robustness of the analyses shows up as signal to background ratio greater than 1 for a large portion of the parameters space under study in this work . detailed studies can be made though in order to take advantage of the hard jets and leptons expected for even heavier @xmath2 and charged higgses . [ [ acknowledgments ] ] acknowledgments : + + + + + + + + + + + + + + + + +    e. r. b. thanks pnpd - capes and fapesp for the financial support . a.g.d . also thanks fapesp and cnpq for the financial support .","summary":"we perform a study of the charged higgs production from an model with right - handed neutrinos , postulating a custodial symmetry which reduces the number of free parameters in the scalar potential . the interplay between the higgs sector of the model and that gauge boson enhances substantially all the production rates of the lightest charged higgs boson , , at hadron colliders compared to the mssm .","abstract":"we perform a study of the charged higgs production from an model with right - handed neutrinos , postulating a custodial symmetry which reduces the number of free parameters in the scalar potential . we compute the cross sections for charged scalars for typical and new production modes . one of the new neutral gauge bosons , , affects some production cross sections distinguishing the model from other standard model extensions like , for example , the minimal supersymmetric standard model and general two - higgs doublets models . the interplay between the higgs sector of the model and that gauge boson enhances substantially all the production rates of the lightest charged higgs boson , , at hadron colliders compared to the mssm . we found that a large portion of the parameters space can be probed at the lhc running at 14 tev center - of - mass energy in the associated production channel in the low luminosity run stage of the experiment ."}
{"article_id":"0811.4140","section_id":"i","document":"ckm phases explain all observed cp violations . however , baryogenesis apparently requires more cp - violation than is provided for by the standard model ( sm ) . thus physics beyond sm should contain new source of cp violation that is somehow small enough not to be in conflict with experiment . cp violation from new physics can manifest itself in several ways . one way is by measuring an electric dipole moment ( edm ) of a fermion . no edm has been found to date . the current experimental electron edm ( eedm ) bound is @xmath4 at @xmath5 cl @xcite , which already puts a strong constraint on physics beyond the sm . in supersymmetric theories  @xcite , the eedm induced at one - loop is usually larger than this bound so we need several assumptions @xcite or cancellation mechanisms @xcite to avoid this limit for a wide range of parameter space . cp violation can also be seen in cp asymmetries of particle energy - momentum distributions at colliders . one such cp asymmetric collider observable was proposed recently using the interference effect between cp conserving and violating @xmath6 interactions in the diboson production processes at lhc  @xcite . this observable may be able to improve collider sensitivities on cp violating couplings such as triple boson vertices ( tbv ) by up to two orders of magnitude from the most recent lep results . since we expect that abundant diboson production will occur at lhc , and they have clean tri - lepton decay signals , this observable is useful to probe new physics at the lhc . this improvement raises the hope of discovery , and it is worthwhile studying the possible reach of both the collider observable and edm measurements in more detail . intuition holds in the physics community that edms are the most powerful probes of new physics contributions to flavor - preserving cp violation . that intuition is largely based on the varieties of supersymmetric theories that have dipole moments induced at the one - loop level however , given the possibility of the lhc increasing the probing sensitivity by a few orders of magnitude , we investigate how solid that intuition is within the context of theories that have suppressed one - loop contributions to edms . our primary example is supersymmetry with heavy sfermion masses . ultimately , we shall not disagree that edms are unlikely to be supplanted by the lhc in the search for new sources of cp violation . we detail the path to that strengthened conclusion below .","summary":"cp violation from physics beyond the standard model may reside in triple boson vertices of the electroweak theory . to give example to these general considerations we perform the comparison between edms and collider observables within supersymmetric theories that have heavy sfermions , such that substantive edms at the one - loop level are disallowed .","abstract":"cp violation from physics beyond the standard model may reside in triple boson vertices of the electroweak theory . we review the effective theory description and discuss how cp violating contributions to these vertices might be discerned by electric dipole moments ( edm ) or diboson production at the large hadron collider ( lhc ) . despite triple boson cp violating interactions entering edms only at the two - loop level , we find that edm experiments are generally more powerful than the diboson processes . to give example to these general considerations we perform the comparison between edms and collider observables within supersymmetric theories that have heavy sfermions , such that substantive edms at the one - loop level are disallowed . edms generally remain more powerful probes , and next - generation edm experiments may surpass even the most optimistic assumptions for lhc sensitivities .    mctp-08 - 65 + cern - ph - th-2008 - 229 +    comparison of electric dipole moments and + the large hadron collider for probing + cp violation in triple boson vertices    sunghoon jung , james d. wells +   michigan center for theoretical physics ( mctp ) +  university of michigan , ann arbor , mi 48109 - 1120 , usa +cern , theory division , ch-1211 geneva 23 , switzerland    november 2008"}
{"article_id":"0811.4140","section_id":"c","document":"our basic conclusion , which is supported by detailed investigations of various candidate theories that had a chance to contravene it , is this : whatever the origin may be of cp violating triple boson vertices , they induce edms , and although the physics that induces edms is  one loop down \" compared to collider cp asymmetries , the edm experiments are sufficiently precise that they overcome the loop factor and are generally more powerful probes . we expect this conclusion to strengthen into the foreseeable future as edm experiments become more sensitive .","summary":"mctp-08 - 65 + cern - ph - th-2008 - 229 +    comparison of electric dipole moments and + the large hadron collider for probing + cp violation in triple boson vertices    sunghoon jung , james d. wells +   michigan center for theoretical physics ( mctp ) +  university of michigan , ann arbor , mi 48109 - 1120 , usa +cern , theory division , ch-1211 geneva 23 , switzerland    november 2008","abstract":"cp violation from physics beyond the standard model may reside in triple boson vertices of the electroweak theory . we review the effective theory description and discuss how cp violating contributions to these vertices might be discerned by electric dipole moments ( edm ) or diboson production at the large hadron collider ( lhc ) . despite triple boson cp violating interactions entering edms only at the two - loop level , we find that edm experiments are generally more powerful than the diboson processes . to give example to these general considerations we perform the comparison between edms and collider observables within supersymmetric theories that have heavy sfermions , such that substantive edms at the one - loop level are disallowed . edms generally remain more powerful probes , and next - generation edm experiments may surpass even the most optimistic assumptions for lhc sensitivities .    mctp-08 - 65 + cern - ph - th-2008 - 229 +    comparison of electric dipole moments and + the large hadron collider for probing + cp violation in triple boson vertices    sunghoon jung , james d. wells +   michigan center for theoretical physics ( mctp ) +  university of michigan , ann arbor , mi 48109 - 1120 , usa +cern , theory division , ch-1211 geneva 23 , switzerland    november 2008"}
{"article_id":"0907.1903","section_id":"i","document":"groups of galaxies represent a more common , more typical environment than their well - studied cousins massive clusters . most galaxies in the local universe lie in groups ( e.g.  turner & gott 1976 ) and groups lie at a transition between the densest environments in the universe , cluster cores , and the field , making them important environments in the study of galaxy evolution ( e.g.  zabludoff & mulchaey 1998 ) . groups are also important environments for diagnosing the origin of the non - gravitational heating of the intracluster medium ( icm ) . from low - redshift studies , non - gravitational heating of the icm appears to be proportionally more important in groups than in clusters , leading to a steepening of the @xmath2 relation for group mass systems ( e.g.  helsdon & ponman 2000 ) and excess group entropy compared to the self - similar expectations based on massive clusters ( e.g.  ponman et al . 2003 ; sun et al . 2009 ) . in fact , the evolution of the group x - ray scaling relations with redshift can help to constrain models of non - gravitational heating ( balogh et al . 2006 ) , distinguishing , for example , between excess entropy that is constant with redshift ( i.e.  preheating ) versus entropy that is tied to halo cooling time ( i.e.  increasing with time ) . groups of galaxies , and in particular their evolution with redshift , have been relatively poorly studied compared to massive clusters . their faint x - ray luminosities and low galaxy densities make groups difficult to detect outside of the local universe , and we have only recently begun to study the evolution of this important environment with redshift ( e.g.  mulchaey et al . 2006 ; jeltema et al . 2006 , 2007 , 2008a ; willis et al . 2005 ; pacaud et al . 2007 ; wilman et al . 2005a , b ; gerke et al . 2007 ) . for example , only a handful of groups / poor clusters at moderate redshifts ( @xmath8 ) have both deep enough x - ray data and optical spectroscopy to be able to look at the relationships between group x - ray temperature , luminosity and group velocity dispersion ( jeltema et al . 2006 , 2007 , 2008a ; mulchaey et al .  2006 ; willis et al . 2005 ; gastaldello et al . 2008 ) .    in this paper , we seek to extend studies of the x - ray emission from groups to higher redshifts using the deep _ chandra _ data in the extended groth strip ( egs ) . these data cover a @xmath9 deg@xmath10 field with a nominal exposure time of 200 ksec . the area covered represents an increase by a factor of eight over a previous search for groups in a single egs chandra pointing @xcite which yielded no detections . the depth of the _ chandra _ data allows us to both detect and to determine average temperatures for groups at high redshifts ( @xmath11 ) . specifically , we conduct an x - ray search for groups through their extended x - ray emission . in addition to the _ chandra _ coverage , the egs field was one of four fields targeted by the deep2 spectroscopic survey ( davis et al . 2003 ) , giving the added benefit of deep optical spectroscopic coverage . in particular , the deep2 spectroscopy in the egs is magnitude limited , but not colour - selected , giving a large galaxy sample at all redshifts and allowing us to optically identify and determine velocity dispersions for x - ray - detected group candidates ( davis et al . these data allow us to take a first look at the @xmath2 , @xmath3 , and @xmath4 scaling relations for high - redshift groups and poor clusters , and in future work we will investigate the properties of galaxies in these systems . while previous x - ray surveys have found a few high - redshift groups , these currently lack this depth of optical spectroscopy @xcite . our data reduction , group selection and optical identification procedures are presented in  2 and  3 . in  4 we present our main results including the discovery of a `` supergroup '' at @xmath5 (  4.1 ) , three high - redshift groups (  4.2 ) at @xmath0 , and several group agn (  4.3 ) . the high - redshift systems represent the first x - ray detections of deep2 spectroscopically selected groups @xcite , and we present a first look at the scaling relations of systems of this mass at high redshifts . our results are summarised in  5 , and in the appendix we discuss the one x - ray - selected group for which no optical identification was possible . throughout the paper , we assume a cosmology of @xmath12 km s@xmath13 mpc@xmath13 , @xmath14 , @xmath15 and @xmath16 .","summary":"in addition , we report on agn activity associated to these systems . for the six extended sources which lie within the deep2 galaxy redshift survey coverage , we identify optical counterparts and determine velocity dispersions . we also present a first look at the the , , and scaling relations for high - redshift massive groups .","abstract":"we present the discovery of seven x - ray emitting groups of galaxies selected as extended x - ray sources in the 200 ksec _ chandra _ coverage of the all - wavelength extended groth strip international survey ( aegis ) . in addition , we report on agn activity associated to these systems . for the six extended sources which lie within the deep2 galaxy redshift survey coverage , we identify optical counterparts and determine velocity dispersions . in particular , we find three massive high - redshift groups at , one of which is at , the first x - ray detections of spectroscopically selected deep2 groups . we also present a first look at the the , , and scaling relations for high - redshift massive groups . we find that the properties of these x - ray selected systems agree well with the scaling relations of similar systems at low redshift , although there are x - ray undetected groups in the deep2 catalogue with similar velocity dispersions . the other three x - ray groups with identified redshifts are associated with lower mass groups at and together form part of a large structure or `` supergroup '' in the southern portion of the aegis field . similar to other x - ray - luminous groups , all of the low - redshift systems are centred on massive elliptical galaxies , and all of the high - redshift groups have likely central galaxies or galaxy pairs . interestingly , the central galaxies in the highest redshift system show indications of ongoing star formation . all of the central group galaxies host x - ray point sources , radio sources , and/or show optical agn emission . particularly interesting examples of central agn activity include a bent - double radio source plus x - ray point source at the center of a group at , extended radio and double x - ray point sources associated to the central galaxy in the lowest - redshift group at , and a bright green valley galaxy ( part of a pair ) in the group which shows optical agn emission lines .    galaxies : clusters : general  x - rays : galaxies : clusters  galaxies : active"}
{"article_id":"0907.1903","section_id":"r","document":"the three extended x - ray sources associated with low - redshift groups are shown in figure 1 . these three systems lie in the southern portion of the aegis _ chandra _ coverage , and they all appear to lie in a superstructure at @xmath28 . the galaxy distribution in this superstructure is shown in the right panel of figure 1 . two of the groups lie close together in both position and velocity space , while the northern most group lies in the foreground at @xmath7 . a couple of other associations of @xmath49 group - scale systems , or supergroups , have been found previously ( gonzalez et al . 2005 ; brough et al . 2006 ) , and these systems may be the precursors of massive clusters formed through multiple mergers . however , despite the obvious large - scale structure in the egs seen in figure 1 , we find that even the closer two groups ( 1 and 2 ) are unlikely to be bound given their projected distance ( @xmath50 mpc ) and relative velocity ( @xmath51 km s@xmath13 ) ( beers , geller , & huchra 1982 ) . notable from figure 1 ( left ) is the fact that all three groups have luminous elliptical galaxies at their x - ray centres , similar to other x - ray - bright , low - redshift groups @xcite . these groups are fairly x - ray faint having measured bolometric x - ray luminosities of @xmath52 @xmath53 ergs s@xmath13 and luminosities within @xmath34 of @xmath54 @xmath53 ergs s@xmath13 . the detected x - ray emission in all cases appears to extend beyond the optical extent of the central galaxy , consistent with group - scale emission . for all three groups the detected emission extends beyond 60 kpc , the criterion used to by osmond & ponman ( 2004 ) to separate galactic halos from group - scale halos , as shown by the surface brightness profiles in figure 4 . and @xmath42 @xmath39 kpc convolved with the psf at the group location . at a redshift of @xmath55 , 10 pixels is 6.6 @xmath39 kpc . , title=\"fig:\",width=264 ]   and @xmath42 @xmath39 kpc convolved with the psf at the group location . at a redshift of @xmath55 , 10 pixels is 6.6 @xmath39 kpc . , title=\"fig:\",width=264 ]   and @xmath42 @xmath39 kpc convolved with the psf at the group location . at a redshift of @xmath55 , 10 pixels is 6.6 @xmath39 kpc . , title=\"fig:\",width=264 ]    for the two low - redshift groups for which we can measure temperatures , group 1 and group 4 , we find @xmath56 and @xmath57 , respectively . the third group , group 2 , is the lowest velocity dispersion system in our sample and was previously identified in the sdss c4 dr3 cluster catalogue ( miller et al . 2005 ; von der linden et al .  2007 ) . , @xmath3 , and @xmath4 scaling relations for low - redshift groups in aegis ( red squares ) compared to x - ray luminous , low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ] , @xmath3 , and @xmath4 scaling relations for low - redshift groups in aegis ( red squares ) compared to x - ray luminous , low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ] , @xmath3 , and @xmath4 scaling relations for low - redshift groups in aegis ( red squares ) compared to x - ray luminous , low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ]    in figure 5 , we plot the @xmath2 , @xmath3 , and @xmath4 scaling relations for the low - redshift aegis groups ( red squares ) compared to the relations observed for other low - redshift groups and clusters with extended x - ray emission @xcite . within the uncertainties on the individual group properties and the scatter observed in these scaling relations , the aegis groups are consistent with other low - redshift groups . however , group 4 appears to have a temperature which is high compared to its x - ray luminosity . as discussed in  4.3 , this group has a central agn which could contribute to heating the gas . as noted above , the x - ray emission for all three low - redshift groups is centred on a luminous elliptical galaxy , and despite the extended nature of the emission the observed x - ray luminosities are not significantly different from those found for isolated , massive elliptical galaxies . as an indication of how much of the detected x - ray emission might be due to the central group galaxy , in figure 6 , we compare the detected x - ray luminosities to those of nearby elliptical galaxies . the x - ray luminosity of galaxies is known to correlate with optical / near - ir luminosity , although with large scatter , indicating a correlation between x - ray emission and galaxy stellar mass . here we consider the correlation between @xmath58 and @xmath59 , because @xmath60 band luminosity is more tightly correlated with stellar mass than bluer bands . @xmath61 band luminosities for the central galaxies are taken from 2mass . to compare to galaxy samples from the literature , here we use the x - ray luminosity in the @xmath62 kev band , and we do not assume that the x - ray emission extends beyond the detection radius ( i.e.  we use the luminosity measured within @xmath33 rather than projecting to @xmath34 ) .    in figure 6 , we compare the @xmath63 relation for the aegis systems ( red squares ) to a sample of satellite early - type galaxies ( central galaxies are excluded ) in low - redshift clusters and groups @xcite observed with _ chandra _ and to a sample of field early - types observed with _ rosat _ @xcite . as noted in @xcite , there appears to be an offset between satellite galaxies in groups and clusters and more isolated ellipticals in this relation with satellite galaxies having lower average x - ray luminosities for their k - band luminosities . this offset may indicate that some of the hot gas has been stripped from galaxies in groups and clusters , but higher resolution x - ray observations of a field sample are needed to check this result . we might expect central galaxies to have similar or brighter x - ray emission to field galaxies . we find , however , that the aegis systems span the full range of @xmath63 shown by field , group , and cluster galaxies . two of the three low - redshift aegis groups have x - ray luminosities which are completely consistent with the k - band luminosities of their central galaxy without the need for group x - ray emission . one group , group 1 , with the faintest central galaxy may have excess x - ray emission but is also consistent within the observed scatter with the @xmath63 relation of field galaxies . for this group in particular , we see from figure 1 that the detected x - ray emission extends beyond the central galaxy and includes other group members . however , it is clear that the detected x - ray emission for all of the low - redshift aegis groups likely has a significant contribution from , or is dominated by , the central galaxy . relation for the aegis systems ( red squares ) is compared to non - central early - type galaxies in groups and clusters ( diamonds ; jeltema et al . 2008b , sun et al .  2007 ) and to early - type galaxies in the field ( stars ; ellis & osullivan 2006 ) . the best - fitting relations are shown for the group and cluster galaxies ( solid line ) and the field galaxies ( dashed line ) . here the x - ray luminosities are in the 0.5 - 2 kev band and are not extrapolated . , width=302 ]      the three high - redshift groups with extended x - ray emission are shown in figure 2 . these groups are all at redshifts above @xmath64 . they represent the first x - ray confirmation of spectroscopically selected deep2 groups and have velocity dispersions at the high end of those found for groups in the deep2 survey @xcite . a previous search for x - ray emission from deep2 groups based the single _ chandra _ pointing in the aegis region taken in a03 yielded no detections and concluded that the deep2 groups appear to be underluminous in x - rays compared to low - redshift groups with similar velocity dispersions @xcite . however , this one pointing contained relatively few groups ( 7 ) , all of which had only 3 - 6 member galaxies making their velocity dispersions uncertain . in fact , we do not detect any groups in this pointing . the high - redshift systems detected here have bolometric x - ray luminosities of a few times @xmath65 @xmath53 ergs s@xmath13 and temperatures of @xmath66 kev , placing them in the massive group to poor cluster regime of galaxy associations . in particular , the highest redshift system in our sample has a velocity dispersion of @xmath67 km s@xmath13 and @xmath68 kev ; at a redshift of @xmath1 , it is one of only a few such low - mass systems at @xmath69 observed in x - rays @xcite .    , @xmath3 , and @xmath4 scaling relations for high - redshift groups in aegis ( @xmath0 ; red squares ) compared to x - ray luminous intermediate - redshift groups ( @xmath8 ) from the rdcs and xmm - lss samples ( blue circles ; jeltema et al .  2008a , 2007 ; pacaud et al . 2007 ; willis et al . 2005 ) and low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the intermediate - redshift groups ( blue solid line ) , the low - redshift gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ] , @xmath3 , and @xmath4 scaling relations for high - redshift groups in aegis ( @xmath0 ; red squares ) compared to x - ray luminous intermediate - redshift groups ( @xmath8 ) from the rdcs and xmm - lss samples ( blue circles ; jeltema et al .  2008a , 2007 ; pacaud et al . 2007 ; willis et al . 2005 ) and low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the intermediate - redshift groups ( blue solid line ) , the low - redshift gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ] , @xmath3 , and @xmath4 scaling relations for high - redshift groups in aegis ( @xmath0 ; red squares ) compared to x - ray luminous intermediate - redshift groups ( @xmath8 ) from the rdcs and xmm - lss samples ( blue circles ; jeltema et al .  2008a , 2007 ; pacaud et al . 2007 ; willis et al . 2005 ) and low - redshift groups from the gems sample ( open stars ; osmond & ponman 2004 ) . fits show the best - fitting relations for the intermediate - redshift groups ( blue solid line ) , the low - redshift gems groups ( dashed line ; helsdon & ponman , in preparation ) and low - redshift clusters ( dotted line ; markevitch 1998 ) . luminosities for all systems are bolometric ( 0.01 - 100 kev ) and calculated within @xmath34 . , title=\"fig:\",width=302 ]    figure 7 shows the @xmath2 , @xmath3 , and @xmath4 scaling relations for the high - redshift aegis groups . as in figure 5 , we compare the aegis systems to the scaling relations observed for low - redshift groups and clusters . here we also show the relations for x - ray luminous , intermediate - redshift groups / poor clusters at @xmath8 derived primarily from two samples : dedicated optical and x - ray follow - up of groups discovered in the _ rosat _ deep cluster survey ( rdcs ; jeltema et al .  2008a , 2007,2006 ; mulchaey et al . 2006 ) and the xmm - lss ( pacaud et al . 2007 ; willis et al . the best - fitting scaling relations for the intermediate - redshift systems are taken from @xcite . the intermediate - redshift group sample shows a similar range in x - ray luminosity and temperature to the higher - redshift aegis groups . an @xmath70 correction is applied to the @xmath2 and @xmath3 relations to account for the expected self - similar evolution with redshift of the scaling relations as calculated within a spherical overdensity radius ( e.g.  bryan & norman 1998 ) . the high - redshift aegis groups agree quite well with the scaling relations found for lower - redshift systems , with no indications of significant evolution . they are particularly well - matched to the intermediate - redshift groups , showing a similar flatter relationship in @xmath3 and steeper relationship in @xmath4 compared to local groups and clusters . from these three x - ray selected systems , there is no indication that deep2 groups are underluminous in x - rays for their velocity dispersions ; however , there are other deep2 groups with similar velocity dispersions and redshifts within the _ chandra _ coverage that are not found by our x - ray selection . the x - ray detected group at @xmath1 is a more massive system , but taking the two x - ray groups at @xmath71 with @xmath72 km s@xmath13 as a model , there are five groups not detected in x - rays with @xmath73 km s@xmath13 , @xmath74 , and at least five member galaxies in the deep2 catalogue within the aegis region @xcite . here we limit the sample to groups with at least five members to reduce the uncertainty in the velocity dispersions . for five members and @xmath75 km s@xmath13 , the 1@xmath17 error range is @xmath76 km s@xmath13 . the x - ray properties of optical spectroscopically selected groups , including upper limits and average luminosities through stacking , will be considered in detail in a future paper after the completion of a new aegis group catalogue taking advantage of newer spectroscopy and optimised for the aegis spectroscopic selection ( gerke et al . 2009 , in preparation ) . as mentioned in  3.2 , the deep2 group selection in the aegis region may have a higher false positive rate due to the denser galaxy sampling compared to the rest of the deep2 survey . in addition , deeper x - ray data with a total exposure time of 800 ksecs is currently being taken for @xmath77% of the field and will be used in future studies . as stated above , at low redshifts x - ray luminous groups are typically found to have bright elliptical galaxies near the x - ray peak . the same is true of the low - redshift aegis groups presented here . at intermediate - redshifts ( @xmath8 ) , follow - up of x - ray - selected groups from the rdcs , found a range of central galaxy properties for systems of similar x - ray luminosity to the high - redshift aegis groups @xcite . more specifically , only a couple of the rdcs groups have single , dominant central galaxies . in some groups the central galaxy has multiple luminous nuclei , while other groups have no clear brightest cluster galaxy ( bcg ) , containing instead groups of bright galaxies and/or a brightest galaxy that is significantly offset from the x - ray centre . kpc on a side and centred on the approximate x - ray centre . group member galaxies are marked with black circles . all of the groups have plausible central galaxies or galaxy pairs . , title=\"fig:\",width=226 ]   kpc on a side and centred on the approximate x - ray centre . group member galaxies are marked with black circles . all of the groups have plausible central galaxies or galaxy pairs . , title=\"fig:\",width=226 ]   kpc on a side and centred on the approximate x - ray centre . group member galaxies are marked with black circles . all of the groups have plausible central galaxies or galaxy pairs . , title=\"fig:\",width=226 ]    unfortunately , the peak of the x - ray emission is not well - determined for the faint , high - redshift aegis groups , but here we consider whether there are group members which might be central galaxies . in figure 8 , we show optical images of the group galaxies within 100 @xmath39 kpc of the x - ray centre as determined by vtpdetect . all three high - redshift groups contain potential central galaxies ( i.e.  consistent with the x - ray peak ) . for group 5 , in particular , acs imaging is available and shows a bright elliptical group member near the x - ray centre whose colours place it on the red sequence . the lack of acs imaging for the other two groups makes the assessment of galaxy morphology more challenging . group 6 also appears to have a bright , red sequence , likely early - type galaxy near the x - ray centre ; this galaxy has a smaller companion nearby in both position and velocity space . the highest - redshift system , group 7 , contains a group of similar magnitude galaxies near the centre . closest to the centre of this group is a galaxy pair . both galaxies in the pair fall at the bright end of the green valley in colour - magnitude space , unlike the other central galaxies , and at least one appears asymmetric / disky at the resolution of the cfht image . we may , therefore , be observing an earlier stage of bcg evolution in the highest redshift group . figure 9 shows the position of the likely central group galaxies on the colour - magnitude diagram ( left ) as well as their spectra ( right ) . while the centrals of groups 5 and 6 show strong stellar absorption features , typical of passive galaxies , both galaxies in the central pair of group 7 show strong [ oii ] emission , indicative of ongoing star - formation or agn activity . in particular , the spectrum of galaxy 7b also shows weak [ neiii ] and [ nev ] emission indicating the presence of an agn in this green valley central galaxy . the right panel of figure 2 shows that for all three groups , the galaxies near the x - ray peak also lie near the centre of the group velocity distribution , as one would expect . in summary , all of the x - ray detected aegis groups have likely central galaxies or galaxy associations . in two groups , the central galaxy may have one or more companions . in the highest redshift group at @xmath1 , the central galaxy pair appears to have younger stellar populations than are typically seen for centrals in x - ray luminous groups at lower redshifts , and one member of this pair hosts an agn seen through its optical emission lines .    . groups 5 and 6 lie on the bright end of the red sequence , suggesting that these are red - and - dead objects , as typical of local groups . the central pair of group 7 , by contrast , lies at the bright end of the `` green valley '' between the red and blue populations , suggesting that these galaxies may not have fully ceased star - formation . right : optical spectra for each of the central galaxies . centrals 6 and 7b were observed with the deimos spectrograph on the keck ii telescope , as part of the deep2 galaxy redshift survey ; centrals 5 and 7a were observed with the mmt . each spectrum has been shifted to its rest frame , and prominent spectral features are labelled . while the centrals of groups 5 and 6 show strong stellar absorption features , typical of passive galaxies , both galaxies in the central pair of group 7 show strong [ oii ] emission , indicative of ongoing star - formation or agn activity . the presence of both [ neiii ] and [ nev ] emission in the spectrum of 7b indicate that this galaxy does in fact host an agn.,width=680 ]      as is evident from figures 1 and 2 , in addition to diffuse x - ray emission , we detect x - ray point sources associated with several group member galaxies . in particular , for all three low - redshift groups we detect point sources associated with the central elliptical galaxy . these central x - ray sources have relatively low luminosities of @xmath78 @xmath53 ergs s@xmath13 . the central location of these sources within their respective elliptical galaxies and their relatively high x - ray luminosities compared to low mass x - ray binaries ( lmxbs ) , however , make them likely low - luminosity agn . the central galaxy in group 4 shows a pair of x - ray point sources with broad band ( 0.5 - 10 kev ) luminosities of @xmath79 and @xmath80 @xmath53 ergs s@xmath13 , with the latter slightly offset from the centre of the galaxy . in addition , the 1.4 ghz vla data shows extended , bright radio emission associated to the central galaxy , so this group almost certainly hosts a central agn or dual agn , given the pair of x - ray point sources . figure 10 shows the central galaxy overlaid with contours of radio ( red ) , diffuse x - ray ( black ) , and x - ray point source ( green ) emission . the radio emission is extended but not aligned with the optical axis , and a large , faint , asymmetric radio structure appears to the southeast along the jet axis . from the aegis20 radio catalogue , the central radio emission has a luminosity of @xmath81 w hz@xmath13 @xcite . the mmt spectrum of this galaxy does not show significant [ oiii ] emission , but does show weak h@xmath82 emission offset by @xmath83 km s@xmath13 from the galaxy . interestingly , this group has a relatively high x - ray temperature compared to the @xmath2 relation . kpc on a side . as in figure 1 , contours of diffuse x - ray emission are shown in black , and x - ray point sources are shown in green . all contours are linearly spaced . bottom : same for the high - redshift group group 5 . here the hst - acs i - band image is shown and the scale is 400 @xmath39 kpc on a side.,title=\"fig:\",width=302 ]   kpc on a side . as in figure 1 , contours of diffuse x - ray emission are shown in black , and x - ray point sources are shown in green . all contours are linearly spaced . bottom : same for the high - redshift group group 5 . here the hst - acs i - band image is shown and the scale is 400 @xmath39 kpc on a side.,title=\"fig:\",width=302 ]    the central source in group 2 has a luminosity of @xmath84 @xmath53 ergs s@xmath13 , while the central source in group 1 has a somewhat lower luminosity of @xmath85 @xmath53 ergs s@xmath13 . unfortunately , radio data are not available for groups 1 and 2 . spitzer data for the bcg in group 1 show a potential , though not conclusive , excess at 8 @xmath86 m and 24 @xmath86 m . in addition to the central sources in the low - redshift groups , we detect three x - ray point sources with lower luminosities of @xmath87 @xmath53 ergs s@xmath13 associated with spiral galaxies showing spectral signatures of ongoing star formation .    in the high - redshift groups , we detect two x - ray point sources associated with group member galaxies in the @xmath71 groups and one additional x - ray source within the redshift range of group 5 but outside the group radius . the two group sources have broad band x - ray luminosities greater than @xmath65 @xmath53 ergs s@xmath13 and the neighbouring source has @xmath88 @xmath53 ergs s@xmath13 , making them difficult to explain as anything other than agn . overall , we find an x - ray agn fraction in @xmath71 groups of @xmath89% for galaxies brighter than @xmath90 with @xmath91 @xmath53 ergs s@xmath13 ( 2 out of 27 ) , consistent within the sizeable errors with the cluster fractions of @xmath92% ( @xmath93 and @xmath94 ergs s@xmath13 ) found at @xmath95 by eastman et al . ( 2007 ) and @xmath96% ( @xmath93 and @xmath91 ergs s@xmath13 ) found by kocevski et al .  ( 2008 ) at @xmath97 . our agn fraction is marginally higher than the cluster fraction of @xmath98% at low redshift ( sivakoff et al . 2008 ) . a previous study in the aegis field of x - ray agn associated with high - redshift , optically selected deep2 groups found an excess of agn in groups , but once the host galaxy properties were accounted for , the x - ray agn fraction in groups was consistent with the field ( georgakakis et al . 2008 ) . one of the high - redshift x - ray point sources is associated with the likely central elliptical galaxy in group 5 . this galaxy also hosts a bright , bent double radio source with @xmath99 w hz@xmath13 shown in figure 10 . the bent nature of this source may indicate that it is moving with respect to the icm ( e.g.  owen & rudnick 1976 ) ; however its line - of - sight velocity relative to the group is small . alternatively , it has been suggested that bent radio sources may indicate a recent group / cluster merger ( e.g.  burns et al . in fact , the galaxy distribution surrounding group 5 shows that it may be part of a larger - scale / filamentary structure , and there is a potential second peak in the velocity distribution at slightly higher redshift , supporting the possibility of a merger . fainter radio sources ( @xmath100 between @xmath101 w hz@xmath13 and @xmath102 w hz@xmath13 ) are also found in the other two high - redshift groups associated to the central galaxy in group 6 , the x - ray agn in group 6 , and both the central pair and the galaxy south of this pair in group 7 . as noted above , one the the central galaxies in group 7 , 7b , also shows optical emission lines indicating an agn .    in summary , all of the central group galaxies , and several other groups members , show signs of activity in x - ray , radio , and/or optical emission . in particular , the central galaxies in groups 4 and 5 host both x - ray and radio jet sources .","summary":"interestingly , the central galaxies in the highest redshift system show indications of ongoing star formation . all of the central group galaxies host x - ray point sources , radio sources , and/or show optical agn emission . galaxies : clusters : general  x - rays : galaxies : clusters  galaxies : active","abstract":"we present the discovery of seven x - ray emitting groups of galaxies selected as extended x - ray sources in the 200 ksec _ chandra _ coverage of the all - wavelength extended groth strip international survey ( aegis ) . in addition , we report on agn activity associated to these systems . for the six extended sources which lie within the deep2 galaxy redshift survey coverage , we identify optical counterparts and determine velocity dispersions . in particular , we find three massive high - redshift groups at , one of which is at , the first x - ray detections of spectroscopically selected deep2 groups . we also present a first look at the the , , and scaling relations for high - redshift massive groups . we find that the properties of these x - ray selected systems agree well with the scaling relations of similar systems at low redshift , although there are x - ray undetected groups in the deep2 catalogue with similar velocity dispersions . the other three x - ray groups with identified redshifts are associated with lower mass groups at and together form part of a large structure or `` supergroup '' in the southern portion of the aegis field . similar to other x - ray - luminous groups , all of the low - redshift systems are centred on massive elliptical galaxies , and all of the high - redshift groups have likely central galaxies or galaxy pairs . interestingly , the central galaxies in the highest redshift system show indications of ongoing star formation . all of the central group galaxies host x - ray point sources , radio sources , and/or show optical agn emission . particularly interesting examples of central agn activity include a bent - double radio source plus x - ray point source at the center of a group at , extended radio and double x - ray point sources associated to the central galaxy in the lowest - redshift group at , and a bright green valley galaxy ( part of a pair ) in the group which shows optical agn emission lines .    galaxies : clusters : general  x - rays : galaxies : clusters  galaxies : active"}
{"article_id":"0907.1903","section_id":"i","document":"we have conducted an x - ray search for groups of galaxies in the extended groth strip utilising the chandra coverage of @xmath9 deg@xmath10 , part of the aegis survey . groups of galaxies are selected based on the presence of extended x - ray emission and then matched against optically selected groups from the deep2 spectroscopy in the field . in total , we find seven extended x - ray sources , and we identify optical counterparts for six . three of these groups lie at @xmath0 and represent the first x - ray detections of high - redshift deep2 groups . the other three groups are low - luminosity , low - redshift groups which form part of a larger structure or `` supergroup '' at @xmath28 in the southern portion of the aegis field . the seventh group candidate unfortunately lies outside of the current spectroscopy , but as discussed in the appendix , it is also a high - redshift group candidate . our main results are summarised below .    _ low - redshift groups : _ the three low - redshift extended x - ray sources are all centred on luminous elliptical galaxies in groups at @xmath28 , one of which was previously identified in the sdss c4 cluster catalogue . together the deep2 , mmt , and sdss spectroscopy reveal a large - scale structure in the southern portion of the aegis field dominated by these three groups . the groups are relatively low - mass systems with @xmath103 kev and @xmath104 km s@xmath13 . when projected to @xmath34 , their x - ray luminosities are consistent with the total group velocity dispersion ; however , their detected x - ray luminosities are similar to those found for individual massive elliptical galaxies .    _ high - redshift groups : _ for the high - redshift systems , we find x - ray temperatures in the range of @xmath66 kev and bolometric x - ray luminosities of a few times @xmath65 @xmath53 ergs s@xmath13 , placing them in the massive group to poor cluster regime of galaxy associations . the hottest system with @xmath105 kev lies at a redshift of 1.13 , making it one of only a few systems of its mass known at @xmath106 . the extensive deep2 spectroscopy supplemented by additional redshifts from mmt allow us to identify @xmath107 members for each group and to determine group velocity dispersions . these data allow us the first look at the @xmath2 , @xmath3 , and @xmath4 scaling relations for systems in this mass range at high redshifts . we find no evidence for evolution in these scaling relations when comparing the x - ray - selected deep2 groups to x - ray luminous groups at lower redshifts . however , there are x - ray undetected deep2 groups in the field with similar velocity dispersions , which will be studied in detail in a future paper . similar to x - ray luminous , low - redshift groups , all of the detected systems have potential central galaxies , though two of the central galaxies appear to have close companions . the likely central galaxies in the two groups at @xmath108 are bright , red galaxies with strong stellar absorption features typical of passive bcgs . the central galaxy pair in the highest redshift system at @xmath1 , however , both show [ oii ] emission and lie at the bright end of the green valley in colour - magnitude space . here we may be witnessing an early stage of bcg formation . _ group agn : _ we find x - ray point sources associated to all of the central galaxies in the low - redshift groups and one of the centrals in the high - redshift groups . we also detect radio sources near the centres of all of the groups with radio observations ( all three high - redshift and one low - redshift group ) . particularly convincing and intriguing examples of central agn activity include the bright bent - double radio source and x - ray point source at the center of group 5 at @xmath6 , the extended radio and double x - ray point sources associated to the central galaxy in the lowest - redshift group , group 4 , and the bright green valley pair of galaxies in group 7 at @xmath1 , one of which shows optical agn emission lines . considering all group galaxies , we find an x - ray - selected agn fraction in @xmath71 groups of @xmath89% for galaxies brighter than @xmath90 with @xmath91 @xmath53 ergs s@xmath13 , consistent with previous studies of high - redshift clusters @xcite . + we would like to sincerely thank the anonymous referee for their comments which led to several improvements in the paper . we would also like to thank members of the aegis team , particularly d.  rosario and rob ivison , for their advice and support with the multiwavelength data . support for this work was provided by the national aeronautics and space administration through _ chandra _ award number ar9 - 0017x issued by the _ chandra _ x - ray observatory centre , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics space administration under contract nas8 - 03060 . t.e.j . is grateful for support from the alexander f. morrison fellowship , administered through the university of california observatories and the regents of the university of california . b.f.g . was supported by the u.s . department of energy under contract number de - ac3 - 76sf00515 . support for m.c.c . was provided by nasa through the _ spitzer space telescope _ fellowship program . e.s.l . acknowledges financial support from the uk science and technology facilities council . this study makes use of data from aegis , a multiwavelength sky survey conducted with the chandra , galex , hubble , keck , cfht , mmt , subaru , palomar , spitzer , vla , and other telescopes and supported in part by the nsf , nasa , and the stfc .","summary":"we present the discovery of seven x - ray emitting groups of galaxies selected as extended x - ray sources in the 200 ksec _ in particular , we find three massive high - redshift groups at , one of which is at , the first x - ray detections of spectroscopically selected deep2 groups . we find that the properties of these x - ray selected systems agree well with the scaling relations of similar systems at low redshift , although there are x - ray undetected groups in the deep2 catalogue with similar velocity dispersions . the other three x - ray groups with identified redshifts are associated with lower mass groups at and together form part of a large structure or `` supergroup '' in the southern portion of the aegis field . similar to other x - ray - luminous groups , all of the low - redshift systems are centred on massive elliptical galaxies , and all of the high - redshift groups have likely central galaxies or galaxy pairs . particularly interesting examples of central agn activity include a bent - double radio source plus x - ray point source at the center of a group at , extended radio and double x - ray point sources associated to the central galaxy in the lowest - redshift group at , and a bright green valley galaxy ( part of a pair ) in the group which shows optical agn emission lines .   ","abstract":"we present the discovery of seven x - ray emitting groups of galaxies selected as extended x - ray sources in the 200 ksec _ chandra _ coverage of the all - wavelength extended groth strip international survey ( aegis ) . in addition , we report on agn activity associated to these systems . for the six extended sources which lie within the deep2 galaxy redshift survey coverage , we identify optical counterparts and determine velocity dispersions . in particular , we find three massive high - redshift groups at , one of which is at , the first x - ray detections of spectroscopically selected deep2 groups . we also present a first look at the the , , and scaling relations for high - redshift massive groups . we find that the properties of these x - ray selected systems agree well with the scaling relations of similar systems at low redshift , although there are x - ray undetected groups in the deep2 catalogue with similar velocity dispersions . the other three x - ray groups with identified redshifts are associated with lower mass groups at and together form part of a large structure or `` supergroup '' in the southern portion of the aegis field . similar to other x - ray - luminous groups , all of the low - redshift systems are centred on massive elliptical galaxies , and all of the high - redshift groups have likely central galaxies or galaxy pairs . interestingly , the central galaxies in the highest redshift system show indications of ongoing star formation . all of the central group galaxies host x - ray point sources , radio sources , and/or show optical agn emission . particularly interesting examples of central agn activity include a bent - double radio source plus x - ray point source at the center of a group at , extended radio and double x - ray point sources associated to the central galaxy in the lowest - redshift group at , and a bright green valley galaxy ( part of a pair ) in the group which shows optical agn emission lines .    galaxies : clusters : general  x - rays : galaxies : clusters  galaxies : active"}
{"article_id":"1209.1747","section_id":"i","document":"the correlation femtoscopy , or intensity interferometry method , is the direct tool to measure the spatial and temporal scales of extremely small and short - lived systems created in particle and nuclear collisions with accuracy of @xmath2 m and @xmath3 sec , respectively . the method @xcite , is grounded on the bose - einstein ( be ) or fermi - dirac ( fd ) symmetric properties of the quantum states . it has a deep analogy with the intensity interferometry telescope that was proposed by hanbury brown and twiss for measurements of angular sizes of remote stars @xcite . in distinction on standard telescopic and microscopic techniques based on the registration of intensities of light or particles , e.g. , electrons , coming from ( or through ) the object , this method deals with the correlation between intensities of the source radiation registered by two ( many ) spatially separated parts of devices , such as telescopes , reflectors , particle detectors , etc . in fact , it measures the correlations between numbers of emitted identical particles detected in separated parts of the detector . the femtoscopic space - time structure of the systems is typically represented in terms of the interferometry radii . they are result of the gaussian fit of the correlation function defined as a ratio of the two- ( identical ) particle spectra to the product of the single - particle ones . in the pioneer papers @xcite the measured interferometry radii were interpreted as the geometrical sizes of the systems . later on it was found @xcite that for typical systems formed in experiments with heavy ions , the above geometrical interpretation needs to be generalized . the treatment of the interferometry radii as the homogeneity lengths @xcite in the systems and the crucial suggestion for femtoscopy scanning of the source radiation in different momentum bins bring the possibility to analyze different parts of the source and explain the behavior of the interferometry radii . in addition , the practical method how to use the final state interactions ( fsi ) and effects of long - lived resonances to extract the be correlations in relatively large systems created in heavy ion collisions has been proposed @xcite .    the other challenge , which is still actual , concerns the femtoscopy analysis of relatively small systems created in particle interactions such as @xmath0 and @xmath1 , where the observed femtoscopic scales are approximately 1 fm or smaller @xcite . typically , the suppression of the correlation function is fairly large in these processes . here we will analyze the femtoscopy of such small systems accounting for the uncertainty principle , coherence of the radiation from spatially very closely set emitters and non - femtoscopic ( non be , fd and fsi ) correlations . the latter appear due to the energy - momentum conservation law and incoherent contributions to the two- and single - particle spectra induced by particle clusterization in momentum space and fluctuations of initial conditions of the collision processes . the detailed analysis of these theoretical problems can help to provide the correct femtoscopy study of the small systems .","summary":"e - mail : sinyukov@bitp.kiev.ua_","abstract":"the basic principles of the correlation femtoscopy , including its correspondence to the hanbury brown and twiss intensity interferometry , are re - examined . the main subject of the paper is an analysis of the correlation femtoscopy when the source size is as small as the order of the uncertainty limit . it is about 1 fm for the current high energy experiments . then the standard femtoscopy model of random sources is inapplicable . the uncertainty principle leads to the partial indistinguishability and coherence of closely located emitters that affect the observed femtoscopy scales . in thermal systems the role of corresponding coherent length is taken by the thermal de broglie wavelength that also defines the size of a single emitter . the formalism of partially coherent phases in the amplitudes of closely located individual emitters is used for the quantitative analysis . the general approach is illustrated analytically for the case of the gaussian approximation for emitting sources . a reduction of the interferometry radii and a suppression of the bose - einstein correlation functions for small sources due to the uncertainty principle are found . there is a positive correlation between the source size and the intercept of the correlation function . the peculiarities of the non - femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in and collisions are also analyzed . the factorization property for the contributions of femtoscopic and non - femtoscopic correlations into complete correlation function is observed in numerical calculations in a wide range of the model parameters .    keywords : _ correlation femtoscopy , hanbury brown - twiss intensity interferometry , proton - proton collisions , uncertainty principle , coherence , hbt correlations . _    corresponding author : _ yu.m . sinyukov , bogolyubov institute for theoretical physics , kiev 03680 , metrolohichna 14b , ukraine . e - mail : sinyukov@bitp.kiev.ua_"}
{"article_id":"1209.1747","section_id":"c","document":"we discussed the principal problems of the correlation interferometry of small sources , in particular , the similarity and the principal difference between hanbury brown & twiss intensity interferometry and pion correlation interferometry methods . the main subject of the paper is to build the correlation femtoscopy method that is going beyond the standard approach of independent / random particle emission . it is found that the uncertainty principle leads to ( partial ) indistinguishability of closely located emitters , which fundamentally impedes their full independence and incoherence . the partial coherence of emitted particles is because of the quantum nature of particle emission and happens even if there is no specific mechanism to produce a coherent component of the source radiation . the measure of distinguishability / indistinguishability and mutual coherence of the two emitted wave packets is associated with their overlap integral . in thermal systems the role of corresponding coherent length is played by the thermal de broglie wavelength . the formalism of partially coherent phases in the amplitudes of located close individual emitters is developed for the quantitative analysis . the specific treatment is required for elimination of the double accounting to the correlation function from the configurations in the four - point phase correlator when all individual emission centers are close . it is shown that the effects are significant for the systems with the sizes and emission duration times about 1 fm , and they are expressed in the reduction of the interferometry radii and suppression of the bose - einstein correlation functions . there is the positive correlation between the source size and the intercept of the correlation function . at the typical slopes of the momentum spectra in @xmath170 and @xmath169 collisions these effects are negligible for fairly large sources with radii about or more than 23 fm . the peculiarities of the non - femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in @xmath0 and @xmath1 collisions are analyzed also . the factorization property for the contributions of femtoscopic and non - femtoscopic correlations into the complete correlation function is demonstrated in a wide range of parameter values in the simple analytic models . the application of the theoretical results to @xmath0 and @xmath1 collisions will be done in separate works .","summary":"the basic principles of the correlation femtoscopy , including its correspondence to the hanbury brown and twiss intensity interferometry , are re - examined . the main subject of the paper is an analysis of the correlation femtoscopy when the source size is as small as the order of the uncertainty limit . it is about 1 fm for the current high energy experiments . the uncertainty principle leads to the partial indistinguishability and coherence of closely located emitters that affect the observed femtoscopy scales . in thermal systems the role of corresponding coherent length is taken by the thermal de broglie wavelength that also defines the size of a single emitter . the formalism of partially coherent phases in the amplitudes of closely located individual emitters is used for the quantitative analysis . a reduction of the interferometry radii and a suppression of the bose - einstein correlation functions for small sources due to the uncertainty principle are found . there is a positive correlation between the source size and the intercept of the correlation function . the peculiarities of the non - femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in and collisions are also analyzed . the factorization property for the contributions of femtoscopic and non - femtoscopic correlations into complete correlation function is observed in numerical calculations in a wide range of the model parameters .    keywords : _ correlation femtoscopy , hanbury brown - twiss intensity interferometry , proton - proton collisions , uncertainty principle , coherence , hbt correlations .","abstract":"the basic principles of the correlation femtoscopy , including its correspondence to the hanbury brown and twiss intensity interferometry , are re - examined . the main subject of the paper is an analysis of the correlation femtoscopy when the source size is as small as the order of the uncertainty limit . it is about 1 fm for the current high energy experiments . then the standard femtoscopy model of random sources is inapplicable . the uncertainty principle leads to the partial indistinguishability and coherence of closely located emitters that affect the observed femtoscopy scales . in thermal systems the role of corresponding coherent length is taken by the thermal de broglie wavelength that also defines the size of a single emitter . the formalism of partially coherent phases in the amplitudes of closely located individual emitters is used for the quantitative analysis . the general approach is illustrated analytically for the case of the gaussian approximation for emitting sources . a reduction of the interferometry radii and a suppression of the bose - einstein correlation functions for small sources due to the uncertainty principle are found . there is a positive correlation between the source size and the intercept of the correlation function . the peculiarities of the non - femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in and collisions are also analyzed . the factorization property for the contributions of femtoscopic and non - femtoscopic correlations into complete correlation function is observed in numerical calculations in a wide range of the model parameters .    keywords : _ correlation femtoscopy , hanbury brown - twiss intensity interferometry , proton - proton collisions , uncertainty principle , coherence , hbt correlations . _    corresponding author : _ yu.m . sinyukov , bogolyubov institute for theoretical physics , kiev 03680 , metrolohichna 14b , ukraine . e - mail : sinyukov@bitp.kiev.ua_"}
{"article_id":"1408.6837","section_id":"i","document":"the concept of typicality @xcite states that a single pure state can have the same properties as the full statistical ensemble . this concept is not restricted to specific states and applies to the overwhelming majority of all possible states , drawn at random from a high - dimensional hilbert space . in the cleanest realization , even a single eigenstate of the hamiltonian may feature the properties of the full equilibrium density matrix , assumed in the well - known eigenstate thermalization hypothesis @xcite . the notion of property is manifold in this context and also refers to the expectation values of observables . remarkably , typicality is not only a static concept and includes the dynamics of expectation values @xcite . recently , it has become clear that typicality even provides the basis for powerful numerical approaches to the dynamics of quantum many - particle systems at nonzero temperatures @xcite . these approaches are in the center of this paper . understanding relaxation and transport dynamics in quantum many - body systems is certainly one of the most desired and ambitious aims of condensed - matter physics and experiencing an upsurge of interest in recent years , both experimentally and theoretically . on the one hand , the advent of ultracold atomic gases raises challenging questions about the equilibration and thermalization in isolated many - particle systems @xcite , including the existence , origin , or speed of relaxation processes in the absence of any external bath . on the other hand , future information technologies such as spintronics call for a deeper insight into transport dynamics of quantum degrees of freedom such as spin excitations . spin transport in conventional nano - systems @xcite is inevitably linked to the dynamics of itinerant charge carriers . in contrast , mott - insulating quantum magnets allow for pure spin currents and thus open new perspectives in quantum transport . in the past decade , magnetic transport in one - dimensional quantum magnets has attracted considerable attention because of the discovery of very large magnetic heat - conduction @xcite and long nuclear magnetic relaxation times @xcite . genuine spin transport , however , still remains to be observed in experiments and particularly its classification in terms of ballistic or diffusive propagation is an issue of ongoing experimental research @xcite . the theoretical study of transport in low - dimensional quantum magnets has a long and fertile history . amongst all questions , the dissipation of currents is a key issue and has been investigated extensively at zero momentum and frequency in connection with the linear - response drude weight @xcite . the drude weight is the nondissipating part of the current autocorrelation function and , if existent , indicates a ballistic channel close to equilibrium . while in generic nonintegrable systems it is commonly expected that drude weights do not exist in the thermodynamic limit @xcite , the picture is different and more complicated in integrable systems : since an overlap of currents with the macroscopic number of conserved quantities is probable , drude weights are expected to exist . but this overlap is not necessarily finite for all model parameters and drude weights can vanish in the thermodynamic limit . in this context , an important example is the antiferromagnetic and anisotropic heisenberg ( xxz ) spin-@xmath0 chain . this chain is studied in the present paper . it is a fundamental model for the magnetic properties of interacting electrons in low dimensions . it is not only relevant to the physics of one - dimensional quantum magnets @xcite but also to physical questions in a much broader context @xcite .    in the xxz spin-@xmath0 chain , the heat current is strictly conserved for all values of the exchange anisotropy @xmath2 @xcite and energy flows through a ballistic channel only . this type of flow is at the heart of the colossal heat conduction observed experimentally in almost ideal material realizations of the model @xcite . in contrast , the spin current is not strictly conserved and the existence of a spin drude weight is a demanding problem , resolved only partially despite much effort . at zero temperature , @xmath3 , early work @xcite showed that the spin drude weight is nonzero in the gapless regime @xmath4 ( metal ) but zero in the gapped regime @xmath5 ( insulator ) . bethe - ansatz solutions @xcite support a qualitatively similar picture at nonzero temperatures , @xmath6 , but with a disagreement at the isotropic point @xmath7 . recent progress in combining quasi - local conservation laws and mazur s inequality has lead to a rigorous lower bound to the spin drude weight in the limit of high temperatures @xcite . this bound is very close to the bethe - ansatz solution but still allows for a vanishing drude weight at @xmath7 . numerically , a large variety of sophisticated methods has been applied to transport and relaxation dynamics in the anisotropic heisenberg spin-@xmath0 chain , including full exact diagonalization ( ed ) @xcite , @xmath6 lanczos methods @xcite , quantum monte - carlo techniques @xcite , as well as time - dependent density matrix renormalization group ( tdmrg ) approaches to the real - time dynamics of wave packets or correlators @xcite and to the solution of the lindblad quantum master equation @xcite . the overwhelming majority of results for the spin drude weight , however , is only available from ed and tdmrg . since ed is at present restricted to chains of length @xmath8 , the long - time / low - frequency limit is still governed by finite - size effects and intricate extrapolation schemes to the thermodynamic limit have been invoked , with different results depending on details . such details are using even or odd @xmath9 @xcite and choosing grand - canonical and canonical ensembles @xcite . clearly , these details should be irrelevant in the thermodynamic limit . alternatively , tdmrg is exceedingly more powerful w.r.t . system size and chains of length @xmath10 are accessible . but still the method is confined to a maximum time scale depending on the exchange anisotropy @xmath2 @xcite . even though there is an ongoing progress to increase this time scale , it is at present too short for a reliable extraction of the spin drude weight at the isotropic point @xmath7 @xcite , which is both , experimentally relevant and theoretically most challenging . in this situation , typicality can provide a fresh numerical perspective @xcite . much less is known on transport dynamics apart from the mere existence of drude weights . for spin transport at @xmath7 , steady - state bath scenarios @xcite and classical simulations @xcite suggest super - diffusive dynamics in the limit of high temperatures , while bosonization predicts diffusion at low but nonzero temperatures @xcite . at @xmath5 , signatures of diffusion have been observed also at high temperatures in different approaches @xcite ( see ref .   for a discussion of the limit @xmath11 ) . diffusion of heat , however , necessarily requires integrability - breaking perturbations . for nonintegrable problems , perturbation theory is the only analytical technique available but hard to perform in the thermodynamic limit @xcite . the perturbative regime of small integrability - breaking is further challenging for numerical methods since dynamics is slow and physically relevant time scales are long . these long time scales are a challenge for tdmrg and , due to finite - size effects , also for ed . thus , typicality may complement both numerical methods in this demanding regime .    in this paper , we use the concept of typicality to study the real - time dynamics of spin and energy currents in integrable and nonintegrable spin-@xmath0 chains at nonzero temperatures . in this way , we extend our previous work in ref . to energy transport and nonintegrable systems as well . within the framework of linear response theory , we numerically obtain autocorrelation functions from the propagation of a single pure state , drawn at random as a typical representative of the full statistical ensemble . by comparing to small - system data from ed and existing short - time data from tdmrg , we show that typicality is satisfied in finite systems down to low temperatures and holds in both , integrable and nonintegrable systems . in particular , we demonstrate two numerical advantages of typicality : first , for integrable systems , we can calculate the long - time dynamics and extract the drude weight for large systems outside the range of ed . thus , typicality improves the reliability of finite - size scaling . second , for nonintegrable systems , we can obtain the full relaxation curve for large systems with little finite - size effects on the physically relevant time scale . hence , typicality provides also the basis for determining the dc conductivity in the regime of small integrability - breaking model parameters without using any fits / extrapolations . both advantages yield significant progress in the numerical investigation of spin and energy dynamics in particular and of other observables in a much broader context . this paper is structured as follows : in sec . [ models ] we first introduce the two models studied , namely , the integrable xxz spin-@xmath0 chain and a nonintegrable version due to the presence of a staggered magnetic field oriented in @xmath1 direction . in this sec . we also define the spin and energy currents , as well as their time - dependent autocorrelation functions , and we discuss symmetries . the next sec . [ typicality ] is devoted to the concept of dynamical typicality and the closely related numerical technique used throughout this paper . then we turn to our results : in sec.[integrable ] we focus on spin - current dynamics in the integrable model and study the spin drude weight as a function of anisotropy and temperature . in the following sec . [ nonintegrable ] we extend our study in two directions : the nonintegrable model and the dynamics of the energy current . in this sec . we analyze the dependence of the dc conductivity on magnetic field , anisotropy , and temperature . the last sec . [ summary ] closes with a summary and draws conclusions .","summary":"we use the concept of typicality to study the real - time dynamics of spin and energy currents in spin- models in one dimension and at nonzero temperatures . , we numerically calculate autocorrelation functions by propagating a single pure state , drawn at random as a typical representative of the full statistical ensemble . by comparing to small - system data from exact diagonalization ( ed ) and existing short - time data from time - dependent density matrix renormalization group ( tdmrg ) ,","abstract":"we use the concept of typicality to study the real - time dynamics of spin and energy currents in spin- models in one dimension and at nonzero temperatures . these chains are the integrable xxz chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in direction . in the framework of linear response theory , we numerically calculate autocorrelation functions by propagating a single pure state , drawn at random as a typical representative of the full statistical ensemble . by comparing to small - system data from exact diagonalization ( ed ) and existing short - time data from time - dependent density matrix renormalization group ( tdmrg ) , we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both , integrable and nonintegrable systems . for the integrable case , we calculate the long - time dynamics of the spin current and extract the spin drude weight for large systems outside the range of ed . we particularly provide strong evidence that the high - temperature drude weight vanishes at the isotropic point . for the nonintegrable case , we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field , exchange anisotropy , and temperature ."}
{"article_id":"1408.6837","section_id":"i","document":"in summary , we used the concept of typicality to study the real - time relaxation of spin and energy currents in spin-@xmath0 chains at finite temperatures . these chains were the integrable xxz chain and a nonintegrable version due to the presence of a staggered magnetic field oriented in @xmath1 direction . in the framework of linear response theory , we numerically calculated autocorrelation functions by propagating a single pure state , drawn at random as a typical representative of the full statistical ensemble . by comparing to data from exact diagonalization for small system sizes and existing data from tdmrg for short times , we showed that typicality holds in finite systems over a wide range of temperature and is fulfilled in both , integrable and nonintegrable systems . for the integrable model , we calculated the dynamics of the spin current for long times and extracted the spin drude weight for large system sizes outside the range of state - of - the - art exact diagonalization . employing proper finite - size scaling , we provided strong evidence that , at high temperatures above the exchange coupling constant @xmath300 , the drude weight vanishes at the isotropic point . this finding , and also our results for other values of the exchange anisotropy , were in good agreement with existing bethe - ansatz and mazur - inequality results . for lower temperatures on the order of @xmath300 , we found at least indications that the drude weight is nonzero at the isotropic point . for the nonintegrable model , we calculated the decay of the energy current for large system sizes and did not observe significant finite - size effects . therefore , we were able to obtain the full decay curve in the thermodynamic limit and to extract the dc conductivity without invoking difficult fits / extrapolations . analyzing the dependence of the dc conductivity on the parameters of the model , we found a quadratic scaling with the inverse magnetic field and exchange anisotropy , in agreement with conventional perturbation theory . moreover , we detailed the temperature dependence of the dc conductivity , including low- and high - temperature power laws with an intermediate maximum . our numerical results seem to provide a lower bound on the dc conductivity .    from a merely numerical point of view , we profit from two central advantages of the typicality - based technique used in this paper . first , the numerical technique allows us to perform finite - size scaling . this is certainly similar to exact diagonalization . however , system sizes are much larger and extrapolations are more reliable . second , the numerical technique also yields exact information on an extended time window in the thermodynamic limit . this is certainly similar to tdmrg . however , time windows accessible seem to be much longer for generic nonintegrable systems , as evident for the example studied in this paper . because of these two advantages , our numerical method may complement other numerical approaches in a much broader context , including problems with few symmetries and/or in two dimensions . moreover , our numerical method may be applied to other observables @xcite and not only to current operators .","summary":"these chains are the integrable xxz chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in direction . in the framework of linear response theory we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both , integrable and nonintegrable systems . for the integrable case , we calculate the long - time dynamics of the spin current and extract the spin drude weight for large systems outside the range of ed . we particularly provide strong evidence that the high - temperature drude weight vanishes at the isotropic point . for the nonintegrable case , we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field , exchange anisotropy , and temperature .","abstract":"we use the concept of typicality to study the real - time dynamics of spin and energy currents in spin- models in one dimension and at nonzero temperatures . these chains are the integrable xxz chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in direction . in the framework of linear response theory , we numerically calculate autocorrelation functions by propagating a single pure state , drawn at random as a typical representative of the full statistical ensemble . by comparing to small - system data from exact diagonalization ( ed ) and existing short - time data from time - dependent density matrix renormalization group ( tdmrg ) , we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both , integrable and nonintegrable systems . for the integrable case , we calculate the long - time dynamics of the spin current and extract the spin drude weight for large systems outside the range of ed . we particularly provide strong evidence that the high - temperature drude weight vanishes at the isotropic point . for the nonintegrable case , we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field , exchange anisotropy , and temperature ."}
{"article_id":"0908.3500","section_id":"i","document":"dwarf galaxies are the most common galaxies in the local group ( lg ) , and probably in the entire universe . as the closest late - type star - forming dwarf , the smc is an ideal laboratory for a detailed study of these very common objects : its low dust and high gas content , as well as its low present - day metallicity ( z=0.004 ) , make it an excellent local analog to the majority of dwarf irregulars and blue compact galaxies , whose metallicity distribution is peaked at this mean value . as a member of a triple system , the smc is also a natural benchmark to study interaction - driven modulations of the sf activity . furthermore its proximity ( 60.6 kpc , corresponding to a distance modulus @xmath4 , * ? ? ? * ) allows us to resolve into single stars its stellar populations well below its oldest main sequence turn off ( msto ) , and thus to study in detail its star formation history ( sfh ) over a hubble time by exploring ages , metallicities , and spatial distribution of its stellar content . the properties of old ( age@xmath5 gyr ) and intermediate ( 2@xmath6 age@xmath5 gyr ) stellar populations can help us understand the formation and evolution of the lg . deep photometric studies of a number of dwarf galaxies have demonstrated that some of them started to form stars at the same epoch : the oldest globular clusters in the milky way ( mw ) , the large magellanic cloud ( lmc ) , sagittarius , and fornax are coeval , and similar results have been obtained for the oldest stars in the fields of the milky way , fornax , draco , ursa minor , sculptor , carina and leoii @xcite . by contrast , the oldest ( and only ) globular cluster in the smc is @xmath1 gyr younger than the oldest globulars in the milky way @xcite .    while it is clear that the oldest surviving smc cluster is younger than the oldest clusters in other lg galaxies ( e.g. * ? ? ? * ) , we still do not know whether the onset of sf in the smc , and possibly in other galaxies , was also delayed compared to the mw . to answer this question we need to analyze the smc field - star population . however , thus far only a few authors have investigated the sf history ( sfh ) of field stars in the smc . a first evidence of a stellar population older than 9 - 10 gyr comes from the detection of rr - lyrae stars @xcite . however the overall small number ( @xmath7 arcsec@xmath8 ) of rr - lyrae found in the smc bar @xcite suggests that in the first 2 - 3 gyr the star formation rate in the smc was low . @xcite have performed the most extensive study of the sfh of the smc , covering @xmath9 to a depth of @xmath10 . they found that the smc formed approximately 50% of all its stars more than 8.4 gyr ago , and only a few stars between 3 and 8.4 gyr ago . in the last 3 gyr , the smc formed stars at a constant rate , with two bursts occurred approximately 2.5 and 0.4 gyr ago . @xcite suggested that these two events may have been triggered by the perigalactic passages of the smc with the milky way . other authors have focused on smaller regions , but with deeper and better photometry . the wide field planetary camera 2 ( wfpc2 ) on board of the hubble space telescope ( hst ) was used to analyzed the stellar content of the smc wing @xcite , and in the vicinity of some smc star clusters ( e.g. * ? ? ? * ) . according to @xcite wing stars formed during a long episode of formation between 3.5 and 12 gyr ago , followed by a period of quiescence with a very recent ( @xmath3 myr ago ) pick up in sf activity . @xcite found periods of enhanced sf 0.3 - 0.4 , 3 - 4 and 6 gyr ago , and that sf in the smc was likely quiescent at earlier epochs . @xcite presented the first analysis of the stellar content in the outskirts of the smc using ground - based data . they found that stars in the outskirts of the smc formed during a prolonged episode of sf between 2.5 and 15 gyr ago , with a progressive chemical enrichment from [ fe / h]@xmath111.4 up to [ fe / h]@xmath110.7 . @xcite presented a deep ground - based study of 12 fields of the smc . due to the high crowding conditions , they avoided the densest regions , such as the bar . in all their fields the intermediate - age ( @xmath12 gyr ) population is the dominant component , while the younger stars have a more asymmetric distribution , peaked in the wing . none of their fields showed a clear extended horizontal branch ( hb ) , which would indicate a very old stellar population . from this they concluded that the smc formed only a few stars at the beginning , and experienced an intense and prolonged period of sf between 1 and 6 gyr ago . finally , @xcite derived the sfh of the hst field around the young star - forming cluster ngc  602 in the smc wing , where many pre - main sequence stars are also present , finding that the current sf activity is similar to that of galactic ob associations , that the bulk of the old stars are 6 - 8 gyr old , and with only few stars older than @xmath138 gyr .    in order to get a more accurate and complete evaluation of the sfh of the smc from the earliest epochs up to the present day , and also to extend the analysis to the densest regions , we have started a long - term project ( the small magellanic cloud in space and time ) aimed at getting deep and tight color magnitude diagrams ( cmds ) of several selected smc fields with hst , and in addition covering the whole galaxy down to several magnitudes below the oldest msto using the vlt survey telescope ( vst ; * ? ? ? the primary goals of this project are to combine deep and accurate photometry with high and intermediate - resolution spectra in order to map the sfh and abundance variations across the whole galaxy . these data will allow us to determine the age - metallicity relation ( if there is one ) of stars in different regions of the galaxy and to better constrain numerical models for the chemical evolution of the various smc regions as well as for the galaxy as a whole . we will study the spatial distribution of the various types of variables and this will provide unique information on the space and time confinement of the formation of their parent stellar populations and on the 3d structure of the galaxy . finally the sfh will be derived from the color - magnitude diagrams using the synthetic cmd technique to study how , when and where the sf occurred in the smc . by combining the age - metallicity relation with the sfh through the galaxy we will be able to model the chemical evolution of the smc with unprecedented accuracy for an external galaxy , reaching the same level of reliability that has been attained only for the solar neighborhood .    in this paper we present the stellar content of six fields observed with hst in the smc bar ( sfh1 , sfh4 , and sfh5 ) , wing ( sfh9 and sfh10 ) and the smc outskirts ( sfh8 ) . all the regions have been observed with the wide field channel ( wfc ) of the advanced camera for surveys ( acs ) . to our knowledge this study represents the deepest and highest - resolution survey ever published for smc fields . the sfh , as derived from the synthetic cmd technique , will be presented in a forthcoming paper ( cignoni et al . , in preparation ) . the paper is organized as follows : in section  [ obs ] we present the data sets and discuss their reduction . section  [ at ] presents artificial - star tests and photometric completeness . the fields are discussed in   [ 6fields ] , while a more detailed characterization of the stellar content of the various smc regions ( bar , wing and outskirts ) is given in   [ stellar content ] . section   [ conclusions ] summarizes our conclusions .","summary":"we observed six fields of the small magellanic cloud ( smc ) with the advanced camera for survey on board the hubble space telescope in the f555w and f814w filters . star formation increased again in the recent past , especially in the bar and the wing of the smc , where we see an enhancement in the star - formation activity starting from myr ago .","abstract":"we observed six fields of the small magellanic cloud ( smc ) with the advanced camera for survey on board the hubble space telescope in the f555w and f814w filters . these fields sample regions characterized by very different star and gas densities , and , possibly , by different evolutionary histories . we find that the smc was already forming stars gyr ago , even if the lack of a clear horizontal branch suggests that in the first few billion years the star formation activity was low . within the uncertainties of our two - band photometry , we find evidence of a radial variation in chemical enrichment , with the smc outskirts characterized by lower metallicity than the central zones . from our cmds we also infer that the smc formed stars over a long interval of time until gyr ago . after a period of modest activity , star formation increased again in the recent past , especially in the bar and the wing of the smc , where we see an enhancement in the star - formation activity starting from myr ago . the inhomogeneous distribution of stars younger than myr indicates that recent star formation has mainly developed locally ."}
{"article_id":"0908.3500","section_id":"c","document":"the smc is the closest dwarf galaxy with ongoing star formation , but until recently it has received less attention than the lmc . as mentioned in the introduction , only a few groups have studied the sfh of its field stars , @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite . our survey is designed to help fill this gap . the six fields we observed with the hst / acs sample smc regions characterized by very different star and gas densities , and , possibly , by different evolutionary histories . in all the six regions our photometry goes @xmath156 magnitudes below the oldest msto , allowing us to investigate in detail the properties of stars formed over the entire hubble time . our survey is currently the deepest and has the highest spatial resolution ever performed for the smc fields , and allows us to investigate even its densest regions , such as the bar . our data show that the smc was already forming stars @xmath0 gyr ago , yet we did not find a well - defined hb , i.e. the signature of an old and metal - poor stellar population , in any of our fields . on the other hand , a comparison with the ridgeline of smc star clusters shows that old ( @xmath0 gyr ) and metal - poor ( z@xmath153 ) stars are likely present in every field . these circumstances suggest that in the first few billion years the sf activity in the smc was low . this is also confirmed by the overall small number ( @xmath7 arcsec@xmath8 ) of rr - lyrae found in the smc bar @xcite . if fields and star clusters in the smc have similar sfhs , this can also explain why ngc  121 , the only globular cluster in the smc , is a couple of billion years younger than the globulars in the mw and lmc @xcite . the hypothesis of a slow start of the sf activity is at odds with the conclusion by @xcite that the smc formed approximately 50% of all the stars more than 8.4 gyr ago , and only few stars between 3 and 8.4 gyr ago . on the other hand , our result is consistent with that of @xcite , who did not find the hb in any of their 12 fields , and concluded that the smc formed very few stars at the beginning , experiencing an intense and prolonged sf activity between 1 and 6 gyr ago . @xcite also found that the sf activity in the field population presents periods of enhancement 0.3 - 0.4 , 3 - 4 and 6 gyr ago , and a likely quiescence at earlier epochs , as if early on , the tidal interactions between the clouds were not able to trigger any significant sf . a negligible sf activity at the earliest epochs was also found by @xcite in the ngc  602 region in the wing . future surveys devoted to identify all the variable stars in the smc ( i.e. with the eso survey telescopes vista , in the ir , and vst , in the optical bands ; see * ? ? ? * respectively ) will provide a complete census of the rr - lyrae in the whole smc , thus allowing to fully trace the spatial distribution of oldest populations . this will also allow us to establish whether any of the stars in our fields is an rr - lyrae , and therefore belongs to the hb .    from our cmds we infer that the smc formed stars over a long interval of time until @xmath1 gyr ago . with the exception of the external field sfh8 , intermediate - age stars show rather uniform characteristics , and a possible increase in the star forming activity approximately between 4 and 6 gyr ago , in agreement with @xcite and @xcite . also sfh8 shows evidence of prolonged star formation in the past , but the lower metallicity of this region suggests that sf might have occurred at a lower rate .    according to cold dark matter simulations hierarchical structures should form at all scales @xcite , therefore if the mcs formed outside the mw halo @xcite and now are at their first passage near the sun @xcite , they should be still surrounded by their own stellar halo . an extended dynamically hot stellar - like halo has been indeed found around the lmc @xcite , and stars that belong to the smc have been found up to @xmath27 kpc away from this galaxy . is this extended component part of a mc halo ? a systematic spectro - photometric analysis of the surroundings of the smc is needed not only to verify the existence of an extended halo , and characterize its properties , but also to provide new insights in the formation and evolution of the entire lg . we find that stars younger than 800 myr are concentrated in the bar and the wing of the smc . in the inner fields ( sfh1 , sfh4 , sfh5 and sfh10 ) , we see an enhancement in the sf activity starting from approximately 500 myr ago , again in agreement with @xcite . stars younger than @xmath3 myr have a very inhomogeneous distribution , indicating that recent sf has locally developed .    within the uncertainties of our two - band photometry , we found evidence of radial chemical enrichment , with the most external regions ( the outskirts and the external wing ) characterized by lower metallicity than the central zones . this result is in agreement with that by @xcite and suggests that the sf activity was significantly lower in the periphery of the smc than in the center . a weak gradient of decreasing metallicities at larger distance has been also found in old and intermediate  age clusters @xcite . stellar fields and clusters seems to have had a similar history of formation in the smc , opposite to what we observe in the lmc , where clusters formed in two main episodes ( occurred @xmath155and @xmath0 gyr ago * ? ? ? * ; * ? ? ? * ) , while the sfh in the field was fairly continuous @xcite    the qualitative analysis of the cmds presented here has already led to some interesting insights into the sfh of the smc . in a future paper we will perform a more quantitative analysis of the sfh in the six regions , fully exploiting all the photometric information , by applying the synthetic cmd method , which takes into account photometric errors , incompleteness and crowding effects as estimated with the artificial star tests . for a better assessment of the uncertainties involved in the sfh derivation , we will apply three different and independent approaches of the synthetic cmd method : ( see e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? we thank gisella clementini and luigi ( rolly ) bedin for their useful suggestions , and livia origlia for providing unpublished photometric conversion tables . support for program go-10396 was provided by nasa through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . jsg thanks nasa / stsci for their support of this research , which also benefited from funding supplied by prin - inaf-2005 , asi - inaf i/016/07/0 and swiss national science foundation grant 200020 - 113697 . majewski , s.r , nidever , d.l . , munoz , r.r . , patterson , r.j . , kunkel , w.e . , & carlin , j.l . 2009 , iau symposium 256 , `` discovery of an extended , halo - like stellar population around the large magellanic cloud '' , eds . van loon j.t . and oliveira j.m . tosi , m. annibali , f , & greggio , l. 2002 , in `` observed hr diagrams and stellar evolution '' , asp conference proceedings , vol . 274 . edited by thibault lejeune and joo fernandes . isbn : 1 - 58381 - 116 - 8 . asp , 2002 , 529              sfh1 & j96110010 & 00@xmath15851@xmath15939.31@xmath160 & -73@xmath16107@xmath16200.9@xmath163 & 2006 jan 17 & @xmath164 & f814w + bar ( sw ) & j96110020 & 00@xmath15851@xmath15939.36@xmath160 & -73@xmath16107@xmath16202.8@xmath163 & 2006 jan 17 & @xmath165 & f814w + & j96110030 & 00@xmath15851@xmath15939.31@xmath160 & -73@xmath16107@xmath16200.9@xmath163 & 2006 jan 17 & @xmath164 & f555w + & j96110040 & 00@xmath15851@xmath15939.36@xmath160 & -73@xmath16107@xmath16202.8@xmath163 & 2006 jan 17 & @xmath166.0 & f555w + & j96110dtq & 00@xmath15851@xmath15940.00@xmath160 & -73@xmath16107@xmath16201.0@xmath163 & 2006 jan 17 & @xmath167 & f814w + & j96110e5q & 00@xmath15851@xmath15940.00@xmath160 & -73@xmath16107@xmath16201.0@xmath163 & 2006 jan 17 & @xmath168 & f555w + sfh10 & j96112010 & 01@xmath15808@xmath15939.00@xmath160 & -72@xmath16158@xmath16245.0@xmath163 & 2006 jan 17 & @xmath164 & f814w + wing ( se ) & j96112020 & 01@xmath15808@xmath15939.18@xmath160 & -72@xmath16158@xmath16246.9@xmath163 & 2006 jan 17 & @xmath165 & f814w + & j96112030 & 01@xmath15808@xmath15939.12@xmath160 & -72@xmath16158@xmath16245.0@xmath163 & 2006 jan 17 & @xmath164 & f555w + & j96112040 & 01@xmath15808@xmath15939.18@xmath160 & -72@xmath16158@xmath16246.9@xmath163 & 2006 jan 17 & @xmath169 & f555w + & j96112fjq & 01@xmath15808@xmath15939.80@xmath160 & -72@xmath16158@xmath16245.0@xmath163 & 2006 jan 17 & @xmath167 & f814w + & j96112fvq & 01@xmath15808@xmath15939.80@xmath160 & -27@xmath16158@xmath16245.0@xmath163 & 2006 jan 17 & @xmath168 & f555w + sfh4 & j96111010 & 01@xmath15800@xmath15902.63@xmath160 & -72@xmath16132@xmath16206.5@xmath163 & 2005 nov 23 & @xmath164 & f814w + bar ( center ) & j96111020 & 01@xmath15800@xmath15903.01@xmath160 & -72@xmath16132@xmath16207.3@xmath163 & 2005 nov 23 & @xmath165 & f814w + & j96111030 & 01@xmath15800@xmath15902.63@xmath160 & -72@xmath16132@xmath16206.5@xmath163 & 2005 nov 23 & @xmath164 & f555w + & j96111040 & 01@xmath15800@xmath15903.01@xmath160 & -72@xmath16132@xmath16207.3@xmath163 & 2005 nov 23 & @xmath169 & f555w + & j96111loq & 01@xmath15800@xmath15903.00@xmath160 & -72@xmath16132@xmath16204.0@xmath163 & 2005 nov 23 & @xmath167 & f814w + & j96111m0q & 01@xmath15800@xmath15903.00@xmath160 & -72@xmath16132@xmath16204.0@xmath163 & 2005 nov 23 & @xmath168 & f555w + sfh5 & j96116010 & 01@xmath15800@xmath15924.31@xmath160 & -73@xmath16111@xmath16209.9@xmath163 & 2006 jan 18 & @xmath170 & f814w + bar & j96116020 & 01@xmath15800@xmath15924.54@xmath160 & -73@xmath16111@xmath16207.8@xmath163 & 2006 jan 18 & @xmath171 & f814w + & j96116030 & 01@xmath15800@xmath15924.31@xmath160 & -73@xmath16111@xmath16209.9@xmath163 & 2006 jan 18 & @xmath172 & f555w + & j96116040 & 01@xmath15800@xmath15924.54@xmath160 & -73@xmath16111@xmath16207.8@xmath163 & 2006 jan 18 & @xmath173 & f555w + sfh8 & j96114010 & 00@xmath15841@xmath15947.58@xmath160 & -71@xmath16103@xmath16247.2@xmath163 & 2005 nov 29 & @xmath170 & f814w + halo ( n ) & j96114020 & 00@xmath15841@xmath15947.38@xmath160 & -71@xmath16103@xmath16245.0@xmath163 & 2005 nov 29 & @xmath171 & f814w + & j96114030 & 00@xmath15841@xmath15947.58@xmath160 & -71@xmath16103@xmath16247.2@xmath163 & 2005 nov 29 & @xmath172 & f555w + & j96114040 & 00@xmath15841@xmath15947.38@xmath160 & -71@xmath16103@xmath16245.0@xmath163 & 2005 nov 29 & @xmath173 & f555w + sfh9 & j96115010 & 01@xmath15821@xmath15952.68@xmath160 & -73@xmath16118@xmath16248.7@xmath163 & 2005 nov 21 & @xmath170 & f814w + wing / bridge & j96115020 & 01@xmath15821@xmath15952.33@xmath160 & -73@xmath16118@xmath16246.8@xmath163 & 2005 nov 21 & @xmath171 & f814w + & j96115030 & 01@xmath15821@xmath15952.68@xmath160 & -73@xmath16118@xmath16248.7@xmath163 & 2005 nov 21 & @xmath172 & f555w + & j96115040 & 01@xmath15821@xmath15952.33@xmath160 & -73@xmath16118@xmath16246.8@xmath163 & 2005 nov 21 & @xmath173 & f555w +      sfh1 & 0.08 & 18.45@xmath1740.45 & 18.89 & 1.00@xmath1740.06 + sfh4 & 0.07 & 18.55@xmath1740.27 & 18.97 & 1.03@xmath1740.05 + sfh5 & 0.06 & 18.56@xmath1740.28 & 18.96 & 0.99@xmath1740.04 + sfh10 & 0.06 & 18.49@xmath1740.31 & 18.89 & 1.00@xmath1740.04 + sfh9 & 0.07 & 18.48@xmath1740.28 & 18.90 & @xmath175 + sfh8 & 0.07 & 18.56@xmath1740.27 & 18.95 & @xmath176 +","summary":"these fields sample regions characterized by very different star and gas densities , and , possibly , by different evolutionary histories . we find that the smc was already forming stars gyr ago , even if the lack of a clear horizontal branch suggests that in the first few billion years the star formation activity was low . within the uncertainties of our two - band photometry , we find evidence of a radial variation in chemical enrichment , with the smc outskirts characterized by lower metallicity than the central zones . from our cmds we also infer that the smc formed stars over a long interval of time until gyr ago . after a period of modest activity , the inhomogeneous distribution of stars younger than myr indicates that recent star formation has mainly developed locally .","abstract":"we observed six fields of the small magellanic cloud ( smc ) with the advanced camera for survey on board the hubble space telescope in the f555w and f814w filters . these fields sample regions characterized by very different star and gas densities , and , possibly , by different evolutionary histories . we find that the smc was already forming stars gyr ago , even if the lack of a clear horizontal branch suggests that in the first few billion years the star formation activity was low . within the uncertainties of our two - band photometry , we find evidence of a radial variation in chemical enrichment , with the smc outskirts characterized by lower metallicity than the central zones . from our cmds we also infer that the smc formed stars over a long interval of time until gyr ago . after a period of modest activity , star formation increased again in the recent past , especially in the bar and the wing of the smc , where we see an enhancement in the star - formation activity starting from myr ago . the inhomogeneous distribution of stars younger than myr indicates that recent star formation has mainly developed locally ."}
{"article_id":"0812.3606","section_id":"i","document":"in this paper , we study the nonlinear and nonlocal hartree initial - boundary value problem for the ( wave ) function @xmath0 being defined by stands for the derivative of @xmath1 w.r.t . the time variable @xmath2 . ] @xmath3 where @xmath4 is some domain in @xmath5 with boundary @xmath6 , and @xmath7 is some upper limit of the time interval on which we want to study the time evolution of @xmath1 . moreover , @xmath8 stands for an external potential , @xmath9 denotes the coupling strength , and @xmath10 is the interaction potential responsible for the nonlinear and nonlocal interaction generated by the convolution . the system has many physical applications , in particular for the case @xmath11 . as a first application , we mention the appearance of within the context of the quantum mechanical description of large systems of nonrelativistic bosons in their so - called mean field limit . for the case of a local nonlinearity , i.e. @xmath12 , an important application of equation lies in the domain of bose - einstein condensation for repulsive interatomic forces where it governs the condensate wave function and is called the gross - pitaevskii equation . this dynamical equation , and its corresponding energy functional in the stationary case , have been derived rigorously ( see for example @xcite and @xcite , respectively . ) . in @xcite , minimizers of this nonlocal hartree functional have been studied in the attractive case , and symmetry breaking has been established for sufficiently large coupling . a large coupling phase segregation phenomenon has also been rigorously derived for a system of two coupled hartree equations which are used to describe interacting bose - einstein condensates ( see @xcite and references therein ) . such coupled systems also appear in the description of crossing sea states of weakly nonlinear dispersive surface water waves in hydrodynamics ( see for example @xcite ) , of electromagnetic waves in a kerr medium in nonlinear optics , and in nonlinear plasma physics . furthermore , we would like to mention that equation with attractive interaction potential possesses a so - called point particle limit . consider the situation where the initial condition is composed of several interacting hartree minimizers sitting in an external potential which varies slowly on the length scale defined by the extension of the minimizers . it turns out that , in a time regime inversely related to this scale , the center of mass of each minimizer follows a trajectory which is governed , up to a small friction term , by newton s equation of motion for interacting point particles in the slowly varying external potential . hence , in this limit , the system can be interpreted as the motion of interacting extended particles in a shallow external potential and weakly coupled to a dispersive environment with which mass and energy can be exchanged through the friction term . this allows to describe , and hence to numerically compute , some type of structure formation in newtonian gravity ( see @xcite ) . the main content of the present paper consists in setting up the framework for the numerical analysis on bounded @xmath4 which will be used in @xcite for the study through numerical computation of such phenomena , like , for example , the dissipation through radiation for a hartree minimizer oscillating in an external confining potential ( see also @xcite ) .    in section [ sec : cp ] , we start off with a brief study of the hartree initial - value boundary problem in the continuum setting and we discuss its existence - uniqueness and regularity properties . in section [ sec : semidiscrete ] , the system is discretized in space with the help of galerkin theory . we derive existence - uniqueness and a bound on the @xmath13-approximation error . in the main section [ sec : fd ] , we proceed to the full discretization of , more precisely , we discretize the foregoing semidiscrete problem in time focusing on two time discretization schemes of crank - nicholson type . the first is the so - called one - step one - stage gauss - legendre runge - kutta method which conserves the mass of the discretized wave function under the discrete time evolution . the second one is the so - called delfour - fortin - payre scheme which , besides the mass , also conserves the energy of the system . we prove existence - uniqueness using contraction methods suitable for implementation in @xcite . moreover , we derive a time quadratic accuracy estimate on the @xmath13-error of these approximation schemes . in the proofs of these assertions , we write down rather explicit expressions for the bounds in order to have some qualitative idea how to achieve a good numerical control of the fully discrete approximations of the hartree initial - value boundary problem for the computation of delicate nonlinear and nonlocal features of the various physical scenarios discussed above .","summary":"we study the time dependent hartree equation in the continuum , the semidiscrete , and the fully discrete setting . we prove existence - uniqueness , regularity , and approximation properties for the respective schemes , and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the hartree dynamics in various physical applications .    _ 2000 mathematics subject classification . _ 35q40 , 35q35 , 35j60 , 65m60 , 65n30    _ key words . _ hartree equation , quantum many - body system , weakly nonlinear dispersive waves , newtonian gravity , galerkin theory , finite element methods , discretization accuracy","abstract":"we study the time dependent hartree equation in the continuum , the semidiscrete , and the fully discrete setting . we prove existence - uniqueness , regularity , and approximation properties for the respective schemes , and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the hartree dynamics in various physical applications .    _ 2000 mathematics subject classification . _ 35q40 , 35q35 , 35j60 , 65m60 , 65n30    _ key words . _ hartree equation , quantum many - body system , weakly nonlinear dispersive waves , newtonian gravity , galerkin theory , finite element methods , discretization accuracy"}
{"article_id":"1309.3722","section_id":"i","document":"the su uma stars are one of the sub - classes of dwarf novae characterized by the so - called `` superoutburst '' and `` superhumps '' . it is now well established that the outbursts of dwarf novae are produced by a sudden brightening of the accretion disk around the central white dwarf in the semi - detached close binary systems in which the red - dwarf secondary star supplies mass to the accretion disk . in addition to the ordinary normal outbursts observed in the u gem type dwarf novae , the su uma stars show a longer and brighter outburst called the superoutburst . during a superoutburst , a periodic photometric hump with amplitude 0.20.3 mag appears and it is called the superhump whose period is very near to the orbital period of the system but it is longer than that by a few percent . the ordinary superhump mentioned above is also called the  positive \" superhump ( abbreviated as psh ) because another periodic hump with a period shorter than the orbital period appears in some su uma and nova - like variable stars and the latter is called the `` negative '' superhump ( nsh ) . the origin of the positive superhump is now understood as due to a deformation of accretion disk into eccentric form and a slow apsidal precession of the eccentric disk is responsible for the basic clock of the positive superhump . on the other hand the negative superhump is now thought to be produced by a tilted accretion disk whose nodal line precesses retrograde , giving rise to the underlying clock of the negative superhump . the general reviews on these subjects are found in @xcite and @xcite .    in a series of papers we have studied the superoutbursts and superhumps in su uma stars by using the kepler light curves of su uma stars . in the first paper @xcite ( hereafter referred to paper i ) we have studied the kepler light curve of an su uma star , v1504 cyg , and we have demonstrated that various observational lines of evidence in v1504 cyg support the thermal - tidal instability ( tti ) model for the superoutburst of su uma stars proposed by @xcite ( for a review on the tti model , see , @xcite ) . in particular , we have shown that the frequency of the negative superhump varies systematically during a supercycle ( a cycle from one superoutburst to the next ) and by interpreting those variations basically as the result of variations in the disk radius , we have demonstrated that observed disk radius variation fits very well with a prediction of the thermal - tidal instability model . in the second paper @xcite ( paper ii ) , we have examined the kepler short - cadence light curves of two su uma stars , v344 lyr and v1504 cyg . we have analyzed the simultaneous frequency variations of the positive and negative superhumps . we have demonstrated that these two signals vary in unison , if appropriately converted , indicating the disk radius variation . the kepler public data are released every three - months and the new data continue to arrive . as shown below , the newly released data of v1504 cyg and v344 lyr have basically supported our main conclusions reached in our paper i and paper ii . however , the new data also give us some surprise and in section [ sec : analysisnewdata ] we made a supplemental study to our paper i and paper ii on the superoutbursts and superhumps of v1504 cyg and v344 lyr by using newly released public kepler data . @xcite has recently criticized our paper i by arguing that our interpretation and our main conclusion about the nature of superoutbursts were incorrect . as his preprint already appeared in astro - ph ( arxiv:1301.0187 ) on 2013 january 2 , we examined in our paper ii his criticism about our interpretation on variation of the negative superhump periods . since his paper has finally appeared in a published form in acta astronomica , here we present our own accounts once again to almost of all his criticisms in section [ sec : replytosmak ] . this paper consists of two parts : the first part concerns a supplemental study of newly released kepler data of v1504 cyg and v344 lyr in section [ sec : analysisnewdata ] , and the second part our reply to smak s criticisms in section [ sec : replytosmak ] . a summary is given in section [ sec : summary ] .","summary":"we made a supplemental study of the superoutbursts and superhumps in su uma stars by using the recently released kepler public data of v1504 cyg and v344 lyr . smak ( 2013 , acta astron . , 63 , 109 ) criticized our previous paper ( osaki and kato , 2013 , pasj , 65 , 50 ) and challenged our main conclusion that various observational lines of evidence of v1504 cyg support the thermal - tidal instability model for the superoutbursts of su uma stars .","abstract":"we made a supplemental study of the superoutbursts and superhumps in su uma stars by using the recently released kepler public data of v1504 cyg and v344 lyr . one of the superoutbursts in v1504 cyg was preceded by a precursor normal outburst which was well separated from the main superoutburst . the superhump first appeared during the descending branch of the precursor normal outburst and it continued into quiescence ( the deep dip between the precursor and the main superoutburst ) , and it began to grow in amplitude with the growth of the main superoutburst after quiescence ended . a similar phenomenon was also observed in v344 lyr . this observation demonstrates very clearly that the superoutburst was triggered by the superhump ( i.e. , by the tidal instability ) , supporting the thermal - tidal instability model . smak ( 2013 , acta astron . , 63 , 109 ) criticized our previous paper ( osaki and kato , 2013 , pasj , 65 , 50 ) and challenged our main conclusion that various observational lines of evidence of v1504 cyg support the thermal - tidal instability model for the superoutbursts of su uma stars . we present our detailed accounts to all of his criticisms by offering clear explanations . we conclude that the thermal - tidal instability model is after all only the viable model for the superoutbursts and superhumps in su uma stars ."}
{"article_id":"1309.3722","section_id":"i","document":"\\(1 ) we made a supplemental study of the superoutbursts and superhumps of v1504 cyg and v344 lyr by using the recently released kepler data . we have basically confirmed the results given in paper i and paper ii . in addition to them , we have found that the supercycle lengths of the type l supercycles are shorter than those of the type s supercycles in v1504 cyg . \\(2 ) the superoutburst no . 8 of v1504 cyg was preceded by a precursor normal outburst which was well separated from the main superoutburst . the ordinary superhump first appeared during the descending branch of the normal outburst and it continued to quiescence and it began to grow in amplitude with the growth of the system brightness and these two reached simultaneously their maxima ( the main superoutburst maximum ) . this superoutburst is understood as an extreme case of the precursor - main type in which the precursor and the main were separated by the quiescence . this demonstrates that the superoutburst is triggered by the superhump ( i.e. , the tidal instability ) , supporting the thermal - tidal instability model . a similar phenomenon was observed in v344 lyr . \\(3 ) in one of the normal outbursts just prior to the next superoutburst of v1504 cyg , a signal of `` ordinary superhump '' nature appeared in its descending branch but it disappeared before quiescence and thus failed to trigger a superoutburst . this phenomenon called the failed superhump is exactly the same as that of `` aborted superhump '' discussed by @xcite . in v344 lyr , on the other hand , superoutbursts were found to be preceded always by one to three normal outbursts in which impulsive negative superhumps appeared during the descending branch but they disappeared before quiescence . \\(4 ) we discussed mini - outbursts which occurred exclusively in the later half of the type s supercycles of v1504 cyg . we proposed a possible scenario wherein the outburst intervals and the outburst amplitudes decrease in the later half of the type s supercycles in v1504 cyg . \\(5 ) @xcite criticized our paper i @xcite in which he argued that our conclusions of paper i were incorrect . we presented our replies to almost of all his criticisms by offering clear explanations to his criticisms . in particular , we presented more evidence for the frequency variation in the negative superhump in other su uma stars . \\(6 ) the study of kepler light curves of two su uma stars , v1504 cyg and v344 lyr presented in this paper and our papers i & ii demonstrates that almost all of the observational evidence supports the tti model but it seems against the emt model . we conclude that the tti model is the only viable model for the superoutbursts and superhumps in su uma stars , in particular in v1504 cyg and v344 lyr . the kepler data for q13 of v1504 cyg and v344 lyr were released to public on october 22 , 2013 . by taking into account these new kepler data , we replaced the original figures 14 and tables 12 to new ones . we thank the kepler mission team and the data calibration engineers for making kepler data available to the public . we are grateful to enrique de miguel for providing bk lyn data . this work was supported by the grant - in - aid `` initiative for high - dimensional data - driven science through deepening of sparse modeling '' from the ministry of education , culture , sports , science and technology ( mext ) of japan . we are grateful to the referee , dr . john cannizzo , for his critical reading and constructive comments .","summary":"the superhump first appeared during the descending branch of the precursor normal outburst and it continued into quiescence ( the deep dip between the precursor and the main superoutburst ) , and it began to grow in amplitude with the growth of the main superoutburst after quiescence ended . a similar phenomenon was also observed in v344 lyr . we conclude that the thermal - tidal instability model is after all only the viable model for the superoutbursts and superhumps in su uma stars .","abstract":"we made a supplemental study of the superoutbursts and superhumps in su uma stars by using the recently released kepler public data of v1504 cyg and v344 lyr . one of the superoutbursts in v1504 cyg was preceded by a precursor normal outburst which was well separated from the main superoutburst . the superhump first appeared during the descending branch of the precursor normal outburst and it continued into quiescence ( the deep dip between the precursor and the main superoutburst ) , and it began to grow in amplitude with the growth of the main superoutburst after quiescence ended . a similar phenomenon was also observed in v344 lyr . this observation demonstrates very clearly that the superoutburst was triggered by the superhump ( i.e. , by the tidal instability ) , supporting the thermal - tidal instability model . smak ( 2013 , acta astron . , 63 , 109 ) criticized our previous paper ( osaki and kato , 2013 , pasj , 65 , 50 ) and challenged our main conclusion that various observational lines of evidence of v1504 cyg support the thermal - tidal instability model for the superoutbursts of su uma stars . we present our detailed accounts to all of his criticisms by offering clear explanations . we conclude that the thermal - tidal instability model is after all only the viable model for the superoutbursts and superhumps in su uma stars ."}
{"article_id":"0912.4137","section_id":"i","document":"in recent years , many theoretical as well as experimental investigations in condensed matter physics have been devoted to the study of low - dimensional strongly correlated electron systems where long - range coulomb interactions play an important role . a crucial problem is to understand the effects of competing interactions and the corresponding phase transitions . one of the seminal models adopted to take into account long - range coulomb interactions is the so - called extended hubbard model ( ehm ) , which , beside the on - site interaction @xmath1 , contains also a nearest - neighbor interaction @xmath2 . although the ehm looks deceptively simple and in spite of a very intensive study , both analytical and numerical , there is no complete exact solution even in @xmath5 . these difficulties have led to the investigation of the so - called atomic limit of the extended hubbard model ( al - ehm ) . according to the conventional definition used in the literature , the atomic limit stands for the classical limit of the model , where the hopping matrix elements @xmath6 are set to zero from the very beginning . the al - ehm is exactly solvable in one dimension ( see ref . @xcite and references therein ) , as well as when it is defined on the bethe lattice @xcite . here we consider the bethe lattice as the infinite version of a cayley tree ; thus we are not concerned with surface effects . the bethe lattice , beside being an useful framework for studying the electronic structure of amorphous and glassy solids , has a relevant role in condensed matter physics and statistical mechanics . due to its peculiar structure , on the bethe lattice it is possible to exactly solve several interesting physical problems involving interactions @xcite . there are two special properties that make bethe lattices particularly suited for theoretical investigations : the self - similar structure which may lead to recursive solutions and the absence of closed loops which restricts interference effects of quantum - mechanical particles in the case of nearest - neighbor coupling . furthermore , bethe and bethe - like lattices have attracted a lot of interest because they usually reflect essential features of systems even when conventional mean - field theories fail @xcite . the reason is that such lattices are capable to take into account correlations which are usually lost in conventional mean - field calculations . very recently , the bethe lattice has been considered as the underlying lattice to study the suppression of the paramagnetic metal - insulator transition in the hubbard model at half - filling in the presence of nearest - neighbor and next - nearest - neighbor hoppings when the latter is increased with respect to the former @xcite . furthermore , there exist in nature hyperbranched polymers with distinct regular molecular architecture ( so - called dendrimers ) which can be conveniently modelized by a bethe - like hamiltonian @xcite .    in this article , we study the al - ehm on the bethe lattice by means of the equations of motion approach @xcite . for one - dimensional lattices , or more generally for lattices with no closed loops , classical fermionic and spin systems can be easily solved by means of the transfer matrix method @xcite . however , this method is hardy implementable when more complex lattices are considered . the onsager solution for the two - dimensional ising model is an emblematic example @xcite . we feel that there is the necessity to foster alternative methods which can be used for a large class of lattices . in ref . @xcite we have shown that the equations of motion method provides an answer to this exigency . by using this method , localized fermionic systems and ising - like models can be in principle solved for any underlying lattice . indeed , one can find a set of eigenenergies and eigenoperators of the hamiltonian which closes the hierarchy of the equations of motion . as a result , one can derive exact analytical expressions for the relevant green s functions and correlation functions , which turn out to depend on a finite set of parameters . the knowledge of these parameters is essential to obtain a solution of these models . in a series of articles @xcite , we have analyzed several fermionic and spin systems and we have developed a self - consistent method which allows us to determine these parameters for the case of one - dimensional and bethe lattices . some preliminary results for the al - ehm on the bethe lattice were presented in refs . @xcite , where we considered only the case of attractive intersite interactions ( @xmath4 ) . upon varying the temperature , we found a region of negative compressibility , hinting at a transition from a thermodynamically stable to an unstable phase , characterized by phase separation . in this paper , we provide a comprehensive and systematic exact analysis of the al - ehm on the bethe lattice with coordination number @xmath0 by considering relevant response and correlation functions as well as thermodynamic quantities . we consider both the cases @xmath4 and @xmath3 and cover a wide range of values of the parameters @xmath7 , @xmath8 and @xmath1 ( @xmath7 is the particle density and @xmath8 the temperature ) . the possibility for the parameters @xmath1 and @xmath2 to take positive as well as negative values - representing effective interaction couplings taking into account also other interactions ( for instance with phonons ) - gives rise to a rich phenomenology and a variety of phases . in particular , the ratio of the two competing terms in the model hamiltonian , i.e. , the on - site and the intersite interactions , determines the different distributions of the electrons and the accessible phases , which we identified as charge ordered ( co ) or phase separated ( ps ) . indeed , several studies of the ehm on regular lattices have pointed at the presence of states with phase separation @xcite and of charge - ordered phases @xcite . furthermore , the introduction of an intersite interaction can mimic longer - ranged coulomb interactions needed to describe effects observed in conducting polymers @xcite . in this article , we report the phase diagram in the space ( @xmath9 ) showing the existence of critical regions where charge ordering ( @xmath3 ) and phase separation ( @xmath4 ) are observed . these studies have not been reported in the literature and bring some more information on the properties of the hubbard model . the plan of the paper is as follows . in sec . [ sec_ii ] , we review and extend the analysis of the al - ehm defined on a bethe lattice with coordination number @xmath0 leading to the computation of the green s and correlation functions @xcite . in sec . [ sec_iii ] , the attractive @xmath2 case is reviewed in detail and the phase diagram is reported for a wide range of values of the external parameters @xmath7 , @xmath10 , @xmath11 . in sec . [ sec_iv ] , we investigate the case of repulsive intersite interactions . the phase diagram in the space @xmath7 , @xmath12 , @xmath13 is derived and a long - range co state is observed . the lattice is characterized by a inhomogeneous distribution of the particles in alternating shells . relevant thermodynamic quantities - such as the specific heat , susceptibility , entropy - are also investigated as functions of the temperature , on - site potential and particle density . finally , sec . [ sec_v ] is devoted to our concluding remarks while the appendix reports some relevant computational details .","summary":"we find the existence of critical regions where charge ordering ( ) and phase separation ( ) are observed .","abstract":"we present the exact solution of a system of fermi particles living on the sites of a bethe lattice with coordination number and interacting through on - site and nearest - neighbor interactions . this is a physical realization of the extended hubbard model in the atomic limit . within the green s function and equations of motion formalism , we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model s parameter space , allowing for the on - site and nearest - neighbor interactions to be either repulsive or attractive . we find the existence of critical regions where charge ordering ( ) and phase separation ( ) are observed . this scenario is endorsed by the study of several thermodynamic quantities ."}
{"article_id":"0912.4137","section_id":"c","document":"statistical models on the bethe lattice are of considerable interest since they admit a direct analytical approach for a number of problems that may be otherwise intractable on euclidean lattices . in this paper , we have evidenced how the use of the green s function and equations of motion formalism leads to the exact solution of the extended hubbard model on the bethe lattice in the narrow - band limit . we provided a comprehensive and systematic analysis of the model by considering relevant thermodynamic quantities in the whole space of the parameters @xmath7 , @xmath8 , @xmath1 and @xmath2 and we obtained the finite temperature phase diagram , for both attractive and repulsive on - site and intersite interactions . the phase diagram dramatically depends on the sign of the nearest - neighbor interaction . in the attractive case , there is a critical temperature @xmath163 , located by the divergence of the charge susceptibility , at which there is a transition from a thermodynamically stable to an unstable phase ; the latter is characterized by phase separation . the surface separating the two phases has a rounded vault in the 3d ( @xmath7 , @xmath1 , @xmath8 ) space , which splits in two for @xmath375 . below @xmath163 , the same critical value of the on - site potential separates the two possible configurations of phase separated states , namely clusters of singly or doubly occupied sites . for repulsive nearest - neighbor interactions , the phase diagram has a richer structure : we found a transition temperature below which translational invariance is broken . the bethe lattice effectively splits in two sublattices with different thermodynamic properties . as a result , a charge ordered phase , characterized by a different distribution of the electrons in alternating shells , is established for @xmath376 . the co phase is energetically favored as demonstrated by the study of the helmholtz free energy . by investigating the behavior of several thermodynamic quantities , we attained a full comprehension of the phase diagram . the study of the particle density and of the double occupancy is particularly enlightening to unveil the distribution of the particles on the sites of the bethe lattice . the specific heat exhibits not only high and low temperature peaks due to charge excitations induced by the hubbard operators @xmath308 and @xmath309 , but also peaks due to the phase transition from the homogeneous phase to the co state ( or viceversa ) . by studying separately the contribution to the charge and spin susceptibilities coming from the two sublattices , the onset of a co phase is also signalled by the separation of the values of the sublattices quantities @xmath377 and @xmath378 . the different population of the two sublattices in the co phase is reflected by the divergence or the vanishing , in the limit @xmath379 , of the spin susceptibilities @xmath357 and @xmath358 . if the electrons are paired , no alignment of the spin is possible ( @xmath380 ) , whereas single occupation of the sites leads to an alignment ( @xmath381 ) even when the magnetic field is turned off .","summary":"this is a physical realization of the extended hubbard model in the atomic limit . within the green s function and equations of motion formalism , we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model s parameter space , allowing for the on - site and nearest - neighbor interactions to be either repulsive or attractive . this scenario is endorsed by the study of several thermodynamic quantities .","abstract":"we present the exact solution of a system of fermi particles living on the sites of a bethe lattice with coordination number and interacting through on - site and nearest - neighbor interactions . this is a physical realization of the extended hubbard model in the atomic limit . within the green s function and equations of motion formalism , we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model s parameter space , allowing for the on - site and nearest - neighbor interactions to be either repulsive or attractive . we find the existence of critical regions where charge ordering ( ) and phase separation ( ) are observed . this scenario is endorsed by the study of several thermodynamic quantities ."}
{"article_id":"cond-mat0105588","section_id":"i","document":"as has been known since bohr , van leeuwen and landau @xcite , edge effects play an important role in the physics of magnetized charged - particle systems in equilibrium . in particular , the diamagnetic response of these systems in the quantum regime is determined by electric currents flowing near the walls . the profiles of these currents , and of the closely related particle density , for a non - interacting magnetized electron gas near a hard wall parallel to the magnetic field have been investigated in detail @xcite , @xcite  @xcite . much less is known about the profiles in an interacting magnetized electron gas .    equally important for a physical understanding of the properties of an equilibrium quantum system are the correlation functions . for positions in the bulk of the system these have been studied extensively , both for a non - interacting magnetized electron gas and for its interacting counterpart . for the non - interacting gas the bulk pair correlation function can be determined analytically both for dilute systems at high temperatures and for dense low - temperature systems , in which quantum degeneracy effects are important @xcite . for the interacting electron gas information on the behaviour of the bulk correlation functions is more difficult to obtain . even for the non - magnetized case these functions have surprising properties . in fact , it has been demonstrated that the bulk correlation functions of the interacting electron gas possess slowly decaying tails with an algebraic dependence on the position difference @xcite . for the magnetized interacting gas similar methods have been employed to prove the existence of analogous algebraic tails , albeit with a different exponent @xcite . the correlation functions are expected to change near a hard wall . for a non - magnetized free - particle system these changes are easily determined by using a reflection principle @xcite . the problem becomes a lot more complicated when either interactions between the particles or a magnetic field or both are incorporated . in a recent paper @xcite the interactions between the charged particles have been taken into account in a model system consisting of two quantum charges immersed in a classical plasma confined by a wall . an algebraic tail in the pair correlation function of the quantum particles near the wall was found . however , the exponent governing the algebraic tail turned out to be different from that of the bulk correlation functions discussed above . the result corroborates earlier findings based on linear response arguments @xcite . the influence of a magnetic field on the surface correlation functions in the adopted model system remains to be studied . as the influence of a wall on the correlations in magnetized quantum systems is not yet fully understood , it appears to be useful to try and investigate the correlation functions for the relatively simple case of a non - interacting magnetized electron gas in the presence of a hard wall . in the following we present some new results for this system . in particular , we will analyze the correlations for the strongly degenerate case of high density and low temperature , where the influence of fermi statistics is important . both strong and weak fields will be considered , so that the number of filled landau levels can vary considerably . the paper is organized as follows . we start with two sections that serve to prepare the ground . in section 2 we define the relevant correlation functions for a system of independent particles and discuss their relation to the one - particle green functions . the pair correlation function in the bulk is considered in section 3 , where the influence of the magnetic field on the correlations is determined both analytically and numerically . after these preparatory sections we start considering the influence of the wall in section 4 . in that section we use the so - called ` path - decomposition expansion ' , which follows from a path - integral formulation , to determine the lowest - order corrections in the correlation functions at positions in the transition region , where the presence of the wall starts to be felt . an alternative way to determine these corrections is based on an eigenfunction expansion of the green function , which is the subject of section 5 . the asymptotic form of the correlation functions for large position differences is established in section 6 , separately for directions parallel with and transverse to the magnetic field . in section 7 the correlation functions for positions close to the wall are studied , again for both directions . in the final section 8 some conclusions will be drawn .","summary":"equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free - electron gas in the presence of a hard wall that is parallel to the field . with the help of a path - integral technique and a green function representation","abstract":"equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free - electron gas in the presence of a hard wall that is parallel to the field . with the help of a path - integral technique and a green function representation the modifications in the correlation function caused by the wall are determined both for a non - degenerate and for a completely degenerate gas . in the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field , is found to change from gaussian in the bulk to algebraic near the wall ."}
{"article_id":"cond-mat0105588","section_id":"c","document":"our results show that the presence of a magnetic field and of a wall leads to remarkable changes in the pair correlation function of a completely degenerate non - interacting electron gas . in the bulk the correlation function follows from ( [ 2.7 ] ) , with the @xmath6-dependent green functions ( [ 3.6 ] ) and ( [ 3.14 ] ) for the cases with and without field . whereas the correlation function is isotropic and decays algebraically ( @xmath309 ) in the field - free case , it becomes anisotropic with a gaussian dependence in the transverse direction and an algebraic one ( @xmath310 ) in the parallel direction .    in the neighborhood of a plane hard wall the pair correlation function becomes anisotropic even for the field - free case . its form , which follows directly from a reflection principle , is given by ( [ 2.7 ] ) with ( [ 4.2 ] ) . for two positions far apart , but at equal distance from the wall , the ensuing correlation function decays algebraically , as in the bulk . however , the decay is proportional to @xmath311 , as follows from ( [ 7.7 ] ) .    if in addition to the wall a magnetic field is present , the pair correlation function in the vicinity of the wall becomes anisotropic for two reasons , as both the field and the wall break the symmetry . the general expression for the correlation function , for arbitrary field strengths and arbitrary distances from the wall , follows by substitution of ( [ 5.7 ] ) in ( [ 2.7 ] ) . relatively far from the wall the corrections to the bulk correlation function are still small . the first - order correction terms were given in ( [ 4.14 ] ) and ( [ 4.19 ] ) , and checked numerically in figures [ fig3 ] and [ fig5 ] . near the wall the correlation function  and in particular its tail for large separations  is modified considerably as compared to its form in the bulk . in fact , the qualitative difference between the behaviour in the directions parallel and transverse to the field , which is a prominent feature of the bulk correlation function , is lost in the vicinity of the wall . in both directions the tails become algebraic , albeit with a different exponent . this is seen by inspecting ( [ 6.5 ] ) ( or ( [ 7.6 ] ) ) for the transverse direction and ( [ 6.20 ] ) ( or ( [ 7.16 ] ) ) for the parallel direction . in the former case the decay is proportional to @xmath312 , whereas in the latter it is @xmath309 . qualitatively , the change in the decay of the transverse correlation function from gaussian in the bulk to algebraic near the wall can be understood in a semiclassical picture . in the bulk the cyclotron motion of the particles leads to a strong localization of the correlations , which is associated with a gaussian decay . on approaching the wall the so - called ` skipping orbits ' along the wall become important . they lead to a delocalization effect in the particle motion , which manifests itself as an increase in the range of the correlations . in this way , the cross - over to an algebraic decay of the correlation function finds an explanation .    in conclusion , we have shown that for a non - interacting electron gas the influence of a wall on the correlations is quite considerable , especially in the presence of a magnetic field . it would be interesting to determine the edge effects in the correlations for an interacting electron gas in a magnetic field .","summary":"is found to change from gaussian in the bulk to algebraic near the wall .","abstract":"equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free - electron gas in the presence of a hard wall that is parallel to the field . with the help of a path - integral technique and a green function representation the modifications in the correlation function caused by the wall are determined both for a non - degenerate and for a completely degenerate gas . in the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field , is found to change from gaussian in the bulk to algebraic near the wall ."}
{"article_id":"1502.05982","section_id":"i","document":"is a high - energy transient in a low - mass x - ray binary ( lmxb ) system , and only the second source , besides the rapid burster @xcite , observed to emit multiple type ii x - ray bursts , i.e. , due to spasmodic accretion rather than thermonuclear burning . the source was discovered in 1996 with the burst and transient source experiment ( batse ) on board the _ compton gamma ray observatory ( cgro ) _ , when it emitted a series of hard x - ray bursts during a period lasting @xmath6 days @xcite . soon after its discovery , @xcite reported that the timing properties of the persistent x - ray emission pointed towards a magnetized neutron star pulsating at 2.14  hz , accreting material from a low - mass companion in a nearly circular orbit with an orbital period of 11.8  days . at that time was the first source to show bursts and pulsations , hence the source was nicknamed `` the bursting pulsar '' ( hereafter bp ) . the bp emerged from quiescence again almost exactly one year after its first outburst , in december 1996 @xcite . this second outburst was very similar to the first including both burst and persistent x - ray emission characteristics @xcite . the bp and its two outbursts were studied extensively during the first few years after its discovery . the x - ray bursts from the source were classified as type ii bursts , based on their spectra , energetics @xcite , and their resemblance to the bursts observed from the rapid burster @xcite . type ii bursts are most likely the result of some sort of instability ( whose origin is still unknown ) in the accretion disk resulting in the onset of mass inflow onto the neutron star which is responsible for the bursting activity . the bp average burst duration was 10  s and each burst was followed by a dip in flux below that of the pre - burst persistent emission . the flux recovered exponentially back to the pre - burst persistent emission level on time - scales of a few hundred seconds @xcite . pulsations at the spin frequency of the source were also detected during bursts , albeit with an average time lag of about 50 ms compared to the pre - burst pulses @xcite . the pre - burst pulse profile was subsequently recovered on timescales of a few hundred seconds @xcite . @xcite attributed these lags to the accretion column geometry at the pole . there is no direct estimate as yet of the magnetic field of the bp . * see also @xcite ) placed an upper limit on the dipole magnetic field of @xmath7  g based on the spin - up rate of the source and the persistent pulsed luminosity . @xcite deduced from binary evolution calculations that the dipole magnetic field of  lies in the range of @xmath8  g , with a most probable value of @xmath9  g. finally , @xcite derived a surface magnetic field of @xmath10  g , assuming that the propeller effect is the reason for the non - detection of x - ray pulsations when the source persistent flux dropped below a certain level . it is , therefore , likely that the surface magnetic field of the bp lies between classical x - ray accreting pulsars ( @xmath11  g ) and lmxbs ( @xmath12  g ) . this intermediate strength surface field could be an important parameter defining the unusual properties of this source ; hence , the determination of its exact value is of crucial importance . @xcite studied the @xmath13kev spectrum of  during outbursts using _ asca_. they found a spectrum well described by an absorbed power - law ( pl ) and line - like emission between 6 and 7  kev , most likely from fe reprocessed in the accretion disk . the heavy absorption towards the source ( @xmath14  @xmath15 ) places the bp at the galactic center , likely at 8  kpc . the quiescent x - ray counterpart of the bp was discovered with _ chandra _ @xcite and was confirmed one month later with _ xmm - newton _ the spectrum in quiescence is soft and could be fit with either a pl model with @xmath16 or a blackbody with @xmath17  kev , implying a quiescent @xmath13  kev x - ray luminosity of @xmath18  erg  s@xmath19 at 8  kpc . using the _ chandra _  position , ( * ? ? ? * see also @xcite ) found two potential infrared counterparts within the bp error circle , with the most likely candidate being a giant star of type g4  iii .    on 2014 january 18 , the _ monitor of all - sky x - ray image ( maxi _ ) gas slit camera detected enhanced hard x - ray emission from the galactic center region @xcite . following the detection , they examined archival data from the _ swift _ burst alert telescope ( bat ) , and found that the x - ray emission from the bp had increased compared to its quiescent level . soon after , the source triggered bat on 2014 january 18 @xcite . @xcite detected pulsations from the direction of  at the 2.14  hz spin period of the source during january @xmath20 using the _ fermi _ gamma - ray burst monitor . finally , the _ swift _ x - ray telescope ( xrt ) observed the bp on 2014 february 2 @xcite , detecting a bright source at the _ chandra _  location , confirming that the source entered a new outburst after about 18  years of quiescence ( see also * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite discovered infrared brightening of the g4 iii candidate counterpart contemporary with the x - ray outburst , confirming its identification as the bp companion . here we report our results of the analysis of a 10  ks simultaneous _ chandra _  and _ nustar _ observation of the bp taken on 2014 march 3 . section  [ obs ] describes the observations and data reduction techniques . our results are presented in section  [ res ] , and discussed in section  [ discuss ] .","summary":"we report on a 10  ks simultaneous _ chandra_/hetg_nustar chandra _ , three of which are also detected with _","abstract":"we report on a 10  ks simultaneous _ chandra_/hetg_nustar _  observation of the bursting pulsar , , during its third detected outburst since discovery and after nearly 18 years of quiescence . the source is detected up to 60  kev with an eddington persistent flux level . seven bursts , followed by dips , are seen with _ chandra _ , three of which are also detected with _ nustar_. timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy ( from% to% ) up to 10  kev , above which it remains constant . the  kev spectra of the persistent and dip emission are the same within errors , and well described by a blackbody ( bb ) , a power - law with an exponential rolloff , a 10  kev feature , and a 6.7  kev emission feature , all modified by neutral absorption . assuming that the bb emission originates in an accretion disc , we estimate its inner ( magnetospheric ) radius to be about  cm , which translates to a surface dipole field  g. the _ chandra_/hetg spectrum resolves the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi emission lines . xstar modeling shows these lines to also emanate from a truncated accretion disk . the burst spectra , with a peak flux more than an order of magnitude higher than eddington , are well fit with a power - law with an exponential rolloff and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectra lack a thermal component and any fe features . anisotropic ( beamed ) burst emission would explain both the lack of the bb and any fe components ."}
{"article_id":"1502.05982","section_id":"r","document":"we show in figure  [ channuslc ] the @xmath37 kev _ chandra _  heg 1st order light curve ( top panel ) of the entire 10  ks observation , with 10  s time bins . seven bursts are detected from the source during this observation . following each burst , a dip in the count rate is observed , which recovers exponentially back to the persistent level . the fpma light curve of the simultaneous _ nustar _ observation is shown in the second panel in figure  [ channuslc ] , in the energy range of @xmath35  kev and also at 10  s resolution . only three bursts are detected simultaneously by both _ chandra _  and _ nustar_. figure  [ channuslcbursts ] is a zoom in on these three bursts plotted with a 0.5  s resolution . kev light curves of bp bursts with 0.5  s resolution ( left panels ) , along with their bayesian blocks representation ( right panels ) . times are from the start of the _ chandra _ observation.,title=\"fig:\",scaledwidth=43.0% ] +  kev light curves of bp bursts with 0.5  s resolution ( left panels ) , along with their bayesian blocks representation ( right panels ) . times are from the start of the _ chandra _ observation.,title=\"fig:\",scaledwidth=43.0% ]    we use a bayesian blocks algorithm @xcite to identify the beginning and end times of the 7 bursts detected with _ chandra _ , and to search for weaker bursts in the _ chandra _  light curve binned with 0.5  s resolution . we chose this temporal resolution as a trade - off between speed and accuracy , considering that the source has a comparable pulse period . bayesian blocks have been frequently used for the temporal analysis of gamma - ray bursts , magnetars , and even flares from sgr  a@xmath38 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we find that only the 7 bursts clearly visible in figure  [ channuslc ] show significant deviations ( @xmath39 ) from the persistent level of the source . we do not find any weaker ( mini@xmath0 ) bursts similar to the ones seen during the first two outbursts , e.g. , @xcite . the start and end times of the 7 _ chandra _  bursts are recorded from the bayesian blocks analysis ( figure  [ burstsbayes ] ) . table  [ burstprop ] shows these start times in mjd , and durations in seconds . the uncertainty on these durations is dominated by the temporal resolution we used , and it is @xmath40  s ( @xmath41  s error at the beginning and end of each burst ) . all durations , except the last , are narrowly distributed with a mean and 1@xmath42 standard deviation of @xmath43  s. the last burst consists of two pulses with a total duration of @xmath44  s ( figure  [ burstsbayes ] ) . the rise and decay times of all bursts have a mean and 1@xmath42 standard deviation of @xmath45  s , and @xmath46  s , respectively ( excluding the decay time of the last burst ) .    kev light curve with 10  s resolution . the black solid line is the mean rate of a pre - defined persistent emission interval far away from bursts and dips . the grey areas are the persistent emission intervals used in our spectral analysis . the red solid curves are exponential fits to the dip intervals . _ bottom panel . _ hardness ratio , @xmath47 , evolution during the entire _ chandra _  observation ( @xmath48 is computed in the @xmath49 and @xmath50 kev range , and @xmath51 in the @xmath52  kev range).,title=\"fig:\",scaledwidth=45.0% ] +    we identify the dip durations using the following method on the 2@xmath010  kev _ chandra _  light curve binned at 10  s. we search for the time - bin with the minimum count rate immediately after the end of a burst and up to the start of the following burst ( the end of the observation after the last burst ) . we then fit the light curve of each of these time intervals with an exponential function of the form ,    @xmath53 absorbed pl with @xmath54  @xmath15 , and @xmath55 . @xmath56 assuming a distance of 8  kpc . @xmath57 combined _ chandra _  and _ nustar _  data fit with an absorbed _ cutoffpl _ with @xmath58  @xmath15 , @xmath59 , and @xmath60  kev . @xmath61 derived in the energy range @xmath13  kev . @xmath53 dip times at minimum count rate after burst . @xmath56 dip characteristic time - scale for recovery . @xmath57 duration of interval from end of burst to @xmath62 . @xmath61 calculated in an 80  s interval centered on @xmath62 . @xmath63 calculated at @xmath62 over 10  s by converting count rates to fluxes with pimms . errors reflect the count rate errors only . @xmath64 fluence deficiency in the dip . @xmath65 combined _ chandra _  and _ nustar _  data .    @xmath66    where @xmath67 is the minimum count rate at time @xmath62 , @xmath68 is the persistent count rate level , and @xmath69 is the characteristic time - scale representing 63.2% recovery of the count rate to @xmath68 . we first performed fits keeping both @xmath68 and @xmath69 as free parameters . we find that @xmath68 is similar in all cases with good enough coverage after the recovery , hence we keep @xmath68 constant at the mean count rate value calculated from time intervals far away from bursts and dips ( black solid line in figure  [ fitdips ] ) . figure  [ fitdips ] shows in red our exponential fits to the dips , and table  [ dipprop ] lists the dip temporal properties . we find that @xmath69 ranges between @xmath70 and @xmath71  s , with a mean and 1@xmath42 standard deviation of @xmath72  s , whereas the average time from the end of a burst to the minimum count rate of the dip , @xmath73 , is @xmath74  s. we note that no bursts are seen during the dipping intervals , i.e. , all bursts are emitted after the dip recovered to at least the @xmath75 level of the persistent emission . the grey areas in figure  [ fitdips ] represent the persistent emission time intervals excluding bursts and dip intervals .    finally , we searched for any strong spectral variations in the _ chandra _  observation , especially during bursts , by looking at the evolution of the source flux hardness ratio , @xmath47 , where @xmath48 includes the energy ranges @xmath49 and @xmath50  kev ( to avoid contamination from the fe line complex , see section  [ specana ] ) , and @xmath51 includes the @xmath52  kev range . the bottom panel of figure  [ fitdips ] shows the @xmath47 derived from light curves with a 0.5  s resolution during bursts and with 10  s bins elsewhere . we do not find any spectral variations during bursts in the _ chandra _  observation compared to the non - burst emission , at the above temporal resolution . for each of the intervals defined in the previous section , we first apply a barycenter correction for the _ chandra _  and _ nustar_time - tagged events ( see also section  [ chanobs ] for a description of the _ chandra _  grating time correction ) . we then correct these times for the binary motion of the system , using the orbital parameters provided by the gbm pulsar team . we estimate the spin frequency of the pulsar from the persistent data by locating the peak rayleigh power , @xmath76 , in a frequency range expected to contain the spin frequency . the rayleigh power is given by    @xmath77    @xcite , where @xmath78 is the number of events , @xmath79 a trial frequency , and @xmath80 a barycenter and binary corrected event time . the peak power of 891 occurs at frequency 2.1411203(16 )  hz . the one sigma error is determined by the change in frequency required for the rayleigh power to drop by 0.5 . finally , we epoch - fold the data at the spin frequency derived above to compute a pulse profile ( pp ) . for the persistent and dip intervals , we extract _ chandra _  and _ nustar _  pulse profiles in different energy bands , chosen to have comparable number of events ( figure  [ pp_persisnu ] ) . we fit the different pps with a sine plus cosine function of the form @xcite ,    @xmath81\\ ] ]    where @xmath82 is the count rate at phase bin @xmath83 , @xmath84 is the average count rate throughout the pp , and @xmath85 , @xmath86 are the coefficients of the different harmonics @xmath87 of the sine and cosine functions . the pp is nearly sinusoidal . the second harmonic contribution is highest in between 8 and 10  kev ( @xmath88 ) for _ chandra _ , and between 6 and 8  kev ( @xmath89 ) for _ nustar_.    the rms pulsed fraction ( pf ) is defined as @xcite ,    @xmath90^{0.5}/c_{\\rm mean}\\ ] ]    where @xmath91 and @xmath92 are the 1 sigma standard deviations on the model coefficients . we calculate the pf of the persistent emission pps in different energy bands and find a slight energy dependence in both _ chandra _  and _  data . at the lowest energies , @xmath93  kev , the pf is about @xmath25 . it increases to @xmath94 in the @xmath95  kev energy range , and remains constant at higher energies ( figure  [ rmsvsene ] ) . we find the same dependence and pf values during the dip intervals in both _ chandra _  and _ nustar_.    we do not perform timing analysis on the burst intervals . both _ chandra _  and _ nustar _ suffer high instrumental dead - time during bursts , and _ chandra _ data suffer a small pile - up percentage at the peak of the bursts ( @xmath25 ) , all of which distorts the burst pp . we perform our spectral analysis using xspec @xcite version 12.8.1 . the photo - electric cross - sections of @xcite and the abundances of @xcite are used throughout to account for absorption by neutral gas . all quoted uncertainties are at the @xmath96 level , unless otherwise noted . we extract the heg  m1 spectrum of the persistent emission intervals as defined in section  [ timeana ] and fit it ( binned to a s / n ratio of 10 ) with an absorbed pl . residuals in the form of narrow emission lines are present in the spectra in the energy range @xmath97  kev ( figure  [ specpersisaio ] ) .    to properly model the continuum we ignore data in the energy range @xmath98  kev . the absorbed pl provides a good fit to the data with a reduced @xmath99 of 0.7 for 247 degrees of freedom ( d.o.f . ) . we also fit the continuum with a black - body function ( bbody in xspec , bb hereafter ) , and although we find a statistically acceptable fit with a reduced @xmath99 of 0.9 , significant fit residuals at low and high energies ( @xmath100 and @xmath101  kev ) are present . a diskbb model gives as good a fit as the pl with a reduced @xmath99 of 0.76 ; however , the temperature @xmath102  kev of the inner disk , is too high for an accreting pulsar . we conclude that a simple pl is sufficient to explain the _ chandra _  data alone . we add the 6.0 to 8.0  kev data , including three gaussian lines at 6.4 , 6.65 , and 7.0 kev to account for the residuals , and re - fit . we find a reduced @xmath99 of 0.7 for 291 d.o.f ( figure  [ specpersisaio ] ) . table  [ persisprop ] lists the best fit parameters to the persistent emission continuum and features , along with their @xmath96 uncertainties . the addition of the 6.4 , 6.65 , and 7.0  kev gaussian components ( one at a time ) improve the fit by a @xmath103 of 24 , 31 , and 10 , respectively . we find that all three lines are narrow with comparable fluxes and equivalent widths ( ew ) within uncertainties . most likely the lines are due to neutral or near - neutral fe , and highly ionized fe xxv ( he - like ) and fe xxvi ( h - like ) . we note here that there is a ccd gap in the heg  m1 at 6.3  kev , right below the energy of the 6.4  kev fe feature , resulting in loss of counts at that energy , which renders the fit parameters of this line uncertain . @xmath53 in units of photons  kev@xmath19 @xmath15  s@xmath19 . @xmath56 in units of erg  @xmath15  s@xmath19 . @xmath57 total unabsorbed flux . @xmath104 and @xmath105 are caclualted in the 0.5 - 70  kev energy range . fluxes of the gaussian components are in the 6 - 8  kev range . +    next , we extract the _ nustar _  fpma and fpmb spectra , in the 3@xmath070 kev range for the persistent intervals simultaneous with _ chandra _ , and group them to have a s / n ratio of 25 . we fit the _ nustar _  spectra and the heg  m1 spectrum simultaneously , including a normalization factor to all model fits to take into account any cross - calibration uncertainties between the three instruments . we link all fit parameters between the three spectra except for the normalization factor . both _ spectra show a broad emission line centered at around 6.65  kev , most likely corresponding to the fe line complex detected with _ chandra_. hence , for our initial fits , we exclude from both _ chandra _  and _ nustar _ the @xmath98  kev energy range . a single component model , i.e. , pl or bb , does not give a satisfactory fit with a reduced @xmath106 . an absorbed _ cutoffpl _ ( a pl with an exponential rolloff ) model gives a better fit , but it is also statistically unacceptable ( reduced @xmath107 ) . the addition of a bb model improves the fit dramatically with a reduced @xmath108 ( figure  [ nuschanfit ] , panel  e ) . however , this model results in an absorption hydrogen column density three times lower than what we get from _ chandra _  alone , resulting in large residuals at the lower end of the spectrum , along with residuals at 10  kev . hence , we fix @xmath109 to the _ chandra _  value of @xmath110  @xmath15 . this gives a similar fit quality compared to the above , but emphasizes the residuals around 10  kev in the form of a broad trough ( figure  [ nuschanfit ] , panel  d ) . adding a negative broad feature ( _ cyclabs _ for the same number of d.o.f . hence , we use _ cyclabs _ in the rest of the analysis . ] in xspec ) to the model and thawing @xmath109 results in the best fit to the continuum with a reduced @xmath99 of 0.95 ( for 767 d.o.f . ) . we also investigate the effect of other model continua on the presence and shape of the 10  kev feature . first , instead of a _ cutoffpl _ model , we fit the spectrum using ( 1 ) a fermi - dirac form of cutoff ( _ fdcut _ , * ? ? ? * ) , and ( 2 ) a negative@xmath0positive pl exponential ( _ npex _ , * ? ? ? * ) , both used for fitting accreting x - ray pulsar spectra . neither model , modified by absorption , gives a good fit to the data ( reduced @xmath111 ) . adding a bb results in a reduced @xmath99 of 1.3 . we then remove the bb component and add a negative broad feature to the models . both _ fdcut _ and _ npex _ give a reduced @xmath99 of 1.1 but fail to reproduce the soft part of the spectrum . adding both a bb component and a negative feature gives a good fit to the data in both cases ( reduced @xmath99 of 0.94 and 0.95 for 765 and 766 d.o.f for _ npex _ and _ fdcut _ , respectively ) . we conclude that the 10  kev feature and the bb component are present in the data regardless of the shape of the continuum used . we , therefore , adopt the simplest empirical model , i.e. , _ cutoffpl _ , for the rest of our analysis since it has less free parameters than the above two for comparable fit results . moreover , the parameters of the bb component and the 10 kev feature are consistent within 1@xmath42 in all three models . +    finally , using the _ cutoffpl _ continuum model , we add the 6.0@xmath08.0  kev data . we include three gaussian lines with centroid energies and widths fixed to the values derived from the _ chandra_data ( reduced @xmath99 of 0.91 for 919 d.o.f . ) . we also fit one gaussian line to the data , with all parameters left free to vary . we find a line centroid energy @xmath112  kev and a width @xmath113  kev ( reduced @xmath99 of 0.92 for 919 d.o.f . ) . we conclude that our best fit model for the _ nustar _  and heg  m1 persistent emission spectra consists of a bb , a _ cutoffpl _ , a @xmath1  kev feature , three gaussian lines with centroid energies and widths fixed to the _ chandra_-alone values ( or 1 gaussian component with all parameters left free to vary ) , all affected by neutral absorption ( _ tbabs _ in xspec ) , and a constant normalization . table  [ nuschanpersisprop ] gives the best fit parameters . @xmath53 in units of photons  kev@xmath19 @xmath15  s@xmath19 . @xmath56 in units of erg  @xmath15  s@xmath19 . @xmath114 fitting one gaussian line to the fe line complex . @xmath115 fixed to the _ chandra _  best fit results . @xmath63 total unabsorbed flux . @xmath116 , @xmath104 , and @xmath105 are caclualted in the 0.5 - 70  kev energy range . fluxes of the gaussian components are in the 6 - 8  kev range . we extract the _ chandra _  heg  m1 spectra for each of the dip intervals separately ( here we define the duration of a dip interval as starting from the end of a burst until the time it recovers to 95% of the persistent level ) . we fit all 7 intervals simultaneously with an absorbed pl model . the hydrogen column density is linked for all spectra to ensure that they are all equally absorbed . first , we allow the pl indices and normalizations to vary and we find that the pl index is consistent across all spectra . therefore , we also keep the indices linked . we do not find any flux variability between the different dips , and estimate an average flux and 1@xmath42 standard deviation of @xmath117  erg  s@xmath19  @xmath15 . we also find no variability in the fluence deficiency during the different dips ( the actual deficit of fluence from the persistent emission during a dip ) with an average of @xmath118  erg  @xmath15 . table  [ dipprop ] gives the spectral results for the individual dip intervals . motivated by the differences in the count rates at the dip minima ( figure  [ fitdips ] ) , we extract the heg  m1 spectra of all seven dips in an 80  s interval centered at @xmath62 and fit them simultaneously with an absorbed pl model , keeping only the normalizations free . we do not find any flux variability ( at the @xmath119 level ) in the minimum level the dips reach after each burst ( table  [ dipprop ] ) . we repeat the analysis for a 40  s interval centered at @xmath62 , and reach the same conclusions . next , we extract the heg  m1 spectrum for dip intervals _ collectively _ , and group them so that each bin has a s / n ratio of 10 . we fit the spectrum with an absorbed pl and find an absorption hydrogen column density and a pl index consistent within errors with the results we find for the persistent emission intervals ( table  [ persisprop ] ) . we find an unabsorbed average flux @xmath120  erg  s@xmath19  @xmath15 . the ratio of the average flux ( over the entire dip intervals ) to the persistent emission flux is @xmath121 , or a @xmath122% drop in the persistent emission flux . finally , we find that some residuals are present in the heg  m1 at high energies ( @xmath123  kev ) , in the form of excess emission , similar to what is seen in the persistent emission spectrum . hence , we add three gaussian lines at 6.4 , 6.65 , and 7.0 kev . table  [ persisprop ] lists the best fit parameters to the dip intervals . unfortunately , due to the low number of counts in the dip spectra , we are not able to adequately constrain the parameters of the gaussian components , except for their energies . nonetheless , comparing the dip and persistent emission fit parameters , we do not find dramatic changes in the line properties . these results are discussed in section  [ discuss ] . we then apply the same model we used to fit the persistent interval _ chandra_+_nustar _  broadband spectrum to the dip broadband spectrum . we find very similar values between persistent and dip intervals , except for the flux of the _ cutoffpl _ component , which decreased by 10% during dips . the fluxes of the bb and the fe line component ( considering one gaussian line fit to the 6.7  kev excess ) did not change within their @xmath96 error . these results are shown in table  [ nuschanpersisprop ] .      to achieve better s / n ratio for the spectral fitting of the lines , we extract the heg  m1 spectrum of the persistent and dip intervals together . we fit the spectrum with an absorbed pl model and three gaussian emission lines ( figure  [ specpersisaio ] ) . table  [ persisprop ] lists the best fit parameters along with their @xmath96 uncertainties .    according to the persistent+dip spectrum , which has better statistics than the persistent or dip spectra alone , the highly ionized lines are narrow with widths of about 30  ev . they also contribute similarly to the total flux . the neutral fe , on the other hand , has a larger width and flux compared to the other two . the broadband model used to fit the persistent and dip spectra alone is also successfully fit to the dips+persistent _ nustar _  and _ chandra _  spectra ( table  [ nuschanpersisprop ] ) . all the parameters of the best - fit model were compatible with the persistent and dip fits . a one gaussian emission line fit to the 6.7  kev excess results in a width @xmath124  kev and an ew=129  ev . finally , we also fit the 6.7  kev excess using a diskline model and find @xmath125  kev , @xmath126  gm / c@xmath127 ( @xmath128  cm ) , and @xmath129@xmath130  ( all quoted uncertainties are at the @xmath131 level ) . we extract the heg  1 spectrum for each of the seven bursts seen with _ chandra _ , and fit them simultaneously with an absorbed pl . we link the hydrogen column density in the fit . we find a consistent pl index for all spectra and , therefore , we also link the index thereafter . the pl normalizations are left free to vary , to account for any flux variability between the bursts . we find @xmath132  @xmath15 , and a pl index of @xmath133 . we report in table  [ burstprop ] all burst spectral parameters . we find very similar energetics between the different bursts ; flux and luminosity variability ( at the @xmath131 level ) is observed only between bursts # 4 and # 7 ( these are the shortest and the longest burst , respectively , table  [ burstprop ] ) . in terms of fluence , all bursts emitted comparable ( at the @xmath134 level ) amounts of energy . the mean and 1@xmath42 standard deviation of the fluxes and fluences are @xmath135  erg  @xmath15  s@xmath19 , and @xmath136  erg  @xmath15 , respectively . we also convert the 1  s peak count rates of the seven bursts to fluxes using pimms ( due to the low count statistics ) . we find an average peak flux of @xmath137  erg  s@xmath19  @xmath15 , equivalent to a luminosity of @xmath138  erg  s@xmath19 at 8  kpc . this value should be regarded as a lower limit due to a @xmath25 pile - up , and the narrow energy band for which it was derived ( @xmath13  kev ; _ nustar _ data were excluded from this analysis due to severe dead - time effects ) . we extract the heg  1 spectrum of all seven bursts collectively , grouped to a s / n of 7 , to search for any features present in their added spectrum . we fit the spectrum with an absorbed pl , and find a hydrogen column density @xmath139  @xmath15 , and a pl index @xmath140 . no prominent absorption and/or emission features are seen in the spectrum . we then extract the @xmath141  kev _ nustar _ spectrum of the three bursts seen simultaneously with _ chandra _ , binned to a s / n ratio of 15 . we fit the spectrum with an absorbed _ cutoffpl _ resulting in a reduced @xmath99 of 0.89 for 637 d.o.f .. some residuals around 10  kev can be seen , similar to what we find in the persistent and dip spectra . including a _ cyclabs _ feature to the model improved the fit slightly , resulting in a reduced @xmath99 of 0.86 for 634 d.o.f . , which is a @xmath103 of 17 for 3 additional parameters . figure  [ specburstaio ] shows the data and best fit model , while the parameter values are listed in table  [ persisprop ] . we see no excess emission between 6 and 8  kev . we derive a 3@xmath42 upper limit of 119  ev on the ew of a line with centroid energy at 6.7  kev . we also derive a 3@xmath42 upper limit on the flux of a line at the same energy and a width of 0.4  kev of @xmath142  erg  s@xmath19  @xmath15 . using the co - added _ chandra _  burst spectra , we derive a 30  ev @xmath131 upper limit on the ew of the neutral fe , and @xmath143  ev on the highly ionized species . assuming a width of 0.05  kev for the fe  k and the highly ionized species , we find a @xmath131 flux upper limits of the order of @xmath144  erg  s@xmath19  @xmath15 for all three lines . these upper limits indicate that if any of the lines we detect in the dip and persistent spectra brightened proportionally to the burst flux ( on the average by a factor of 5 ) , we should have been able to detect them . however , if the line fluxes remained constant during the bursts , their presence could be masked by the much brighter burst continuum . finally , we note that the bb component is not required by the fit to the bursts spectrum at a high significance . however , the hydrogen column density is lower at the @xmath131 level than the value derived for the dips and persistent intervals ( table  [ nuschanpersisprop ] ) . hence , fixing the column density at @xmath145  @xmath15 , we find residuals at the lower end of the spectrum , which are well fit with a bb component with @xmath146  kev and a @xmath3  kev flux of @xmath147  erg  s@xmath19  @xmath15 , consistent with the bb temperatures and fluxes during the persistent and dip intervals . these results are discussed in section  [ discussbbs ] . +      we divide the broadband persistent emission spectrum into five pulse phase bins , which we fit simultaneously with our best fit model described above . we fit the @xmath148  kev excess energy with one gaussian line . we first leave all model parameters free to vary . we link one model parameter after another ( starting from the least variable according to a @xmath99 test ) , and record the f - test significance at each step to assess the significance of leaving the parameter free in the fit . we find that the fit parameters of the 6.7 and 10  kev features do not show significant changes with pulse phase . on the other hand , the bb and _ cutoffpl _ fit parameters tightly follow the pp shape ( figure  [ phaseresspec ] ) . we find a decrease in the photon index @xmath149 and an increase in the bb temperature indicating that the x - ray spectrum hardens at pulse maximum . the rolloff energy is also anti - correlated with the pulse shape .","summary":"nustar_. timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy ( from% to% ) up to 10  kev , above which it remains constant .","abstract":"we report on a 10  ks simultaneous _ chandra_/hetg_nustar _  observation of the bursting pulsar , , during its third detected outburst since discovery and after nearly 18 years of quiescence . the source is detected up to 60  kev with an eddington persistent flux level . seven bursts , followed by dips , are seen with _ chandra _ , three of which are also detected with _ nustar_. timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy ( from% to% ) up to 10  kev , above which it remains constant . the  kev spectra of the persistent and dip emission are the same within errors , and well described by a blackbody ( bb ) , a power - law with an exponential rolloff , a 10  kev feature , and a 6.7  kev emission feature , all modified by neutral absorption . assuming that the bb emission originates in an accretion disc , we estimate its inner ( magnetospheric ) radius to be about  cm , which translates to a surface dipole field  g. the _ chandra_/hetg spectrum resolves the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi emission lines . xstar modeling shows these lines to also emanate from a truncated accretion disk . the burst spectra , with a peak flux more than an order of magnitude higher than eddington , are well fit with a power - law with an exponential rolloff and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectra lack a thermal component and any fe features . anisotropic ( beamed ) burst emission would explain both the lack of the bb and any fe components ."}
{"article_id":"1502.05982","section_id":"c","document":"our temporal analysis shows that six out of the seven detected bursts have comparable durations with an average of about @xmath150  s. these consist of a single pulse with a faster rise than decay time . the seventh burst detected by _ chandra _  is the only outlier with a duration of about 25  s , consisting of two pulses . these temporal properties are similar to the properties of hundreds of bursts recorded during the first two outbursts from the bp ( e.g. , * ? ? ? * ) .    from the _ chandra _  data , we can derive the @xmath151 parameter , the ratio of the fluence in the persistent emission to the fluence in the bursts . we find @xmath152 for all bursts ( except for the sixth one where @xmath153 ) , with an average value of 10 . the same value was also derived during the first two outbursts from the source @xcite . as pointed out by @xcite , this small value of @xmath151 is inconsistent with thermonuclear burning as the origin for the bp bursts . this value is consistent with the observed bursts being type  ii bursts , similar to what is seen in the rapid burster , caused by some sort of instability associated with the accretion disk @xcite . unlike the rapid burster , however , the bp does not display any correlation between the fluence in a burst and the time to the following burst ( e.g. , * ? ? ? this is also evidenced by our data , where the fluence emitted during all seven bursts is constant while the intervals between bursts changed by up to a factor of 4 . similar to the previous two outbursts , the bursts we detect in _ chandra _  and _ nustar _ are followed by a dip , where the x - ray emission decreases by 10% on average , and 40% at dip minimum . the emission exponentially recovers back to the pre - burst persistent level , on time - scales of a few hundred seconds . we find that the fluence in a burst and the integrated flux deficiency of the following dip are consistent within @xmath96 ( tables  [ burstprop ] and [ dipprop ] ) . we estimate an average burst fluence ( @xmath37  kev ) of @xmath154 erg @xmath15 , and an average _ missing _ dip fluence of @xmath155  erg  @xmath15 . such a correlation was also seen during the previous two outbursts ( e.g. , * ? ? ? these authors suggested that the energy emitted during a burst could be compensated by the deficit in energy during the following dip . a very simple picture would be that accretion - disk instabilities would allow for a sudden and rapid increase of the mass - inflow rate onto the polar cap of the neutron star from a reservoir ( e.g. , the accretion disk ) . the dips , then , would be the result of a small fraction of the continuously accreted matter disappearing to replenish this reservoir . the broadband spectrum of the bp is the typical spectrum of an accreting x - ray pulsar at high accretion rates ( see e.g. , * ? ? ? * for a review ) . it is well fit with a hard component , modeled as a pl with an exponential rolloff , an fe line complex , a soft component modeled with a bb , and a 10  kev feature , all modified by absorption . in the following , we will discuss these different components and their interplay between persistent , dip , and burst emission , except for the fe line complex which is discussed in section  [ disfe ] . the high persistent x - ray luminosity of  during the present observation ( @xmath156  erg  s@xmath19 ) implies that the emission is coming from an accretion column , where the kinetic energy of the infalling gas onto the polar cap is converted to radiation via a radiative shock above the thermal mound @xcite . thermal photons from the mound , as well as cyclotron and bremsstrahlung radiation , are converted to high - energy photons via inverse compton scattering . hence , the resulting x - ray spectrum will depend on several parameters such as the geometry of the system and the properties of the compact source @xmath0 mainly its dipole magnetic field @xmath0 among others @xcite . even with the small dipole magnetic field of , and its complicated accretion geometry @xcite , the parameters we derive from our phenomenological fit compare reasonably well to other accreting x - ray pulsars ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the photon index of the _ cutoffpl _ is slightly lower than in most cases implying a harder spectrum , which could be the result of the higher luminosity of the source . simply put , a higher accretion rate onto the poles , would lead to a higher electron density in the accretion column and to higher compton @xmath157parameter causing a harder spectrum . the  spectrum also shows a lower energy rolloff compared to other sources , which could be due to the relatively low magnetic field of the source @xcite . the 10  kev feature is not unique to , and has previously been reported in other accreting x - ray pulsars , e.g. , vela  x-1 ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * see also @xcite for a review ) . this feature is not always necessarily observed as an absorption trough and sometimes manifests itself as a broad emission feature or a wiggle . it is believed to be the result of modeling accreting x - ray pulsar spectra with simple empirical functions , when the true physics giving rise to their x - ray spectra is far more complicated , especially when they are emitting near the eddington limit ( see * ? ? ? * for a discussion ) . in a few cases , however , such as in the case of the be / x - ray binary swift  j1626.6@xmath05156 @xcite , an absorption line at 10  kev was interpreted as a cyclotron resonance scattering feature ( crsf ) , evidenced by the presence of a weak second harmonic and the fact that the b field strength , derived from the line energy , was consistent to the value derived from the spin - up rate of the source @xcite . in the 10  ks of _ nustar _ data that we consider here , we find no evidence of a second harmonic at about twice the energy of the 10  kev feature ( i.e. , @xmath158  kev ) , and the @xmath159field strength corresponding to the line energy ( @xmath160  g for a 10  kev line energy ) is significantly larger than the estimates we derive in section 4.4 . moreover , crsfs usually show strong dependence with pulse phase ( e.g. , * ? ? ? * ) , which we do not observe in our phase - resolved spectroscopy . hence , we consider the 10  kev feature in  spectrum to be a defect of our continuum modeling . we note , however , that unlike the bp , other x - ray pulsars showing 10  kev features invariably show crsfs .    soft excess emission is often modeled with a bb component in accreting x - ray pulsars . * see also @xcite ) showed that in luminous sources such as , the most likely source for this bb - like emission is the inner region of the accretion disk , from where the reprocessed hard x - ray emission of the accretion column is emitted . such reprocessed emission also pulsates at the pulse period of the hard x - ray component , most likely with a lower pulsed fraction due to the large area where the reprocessing is taking place . this is in agreement with both the change of the bb temperature and flux with pulse phase ( figure  [ phaseresspec ] ) , and the slight decrease of the pf at low energies compared to the high energies ( figure  [ rmsvsene ] ) . under this assumption and for isotropic emission , the inner radius of the disk is , @xmath161 @xcite , where @xmath42 is the stefan - boltzmann constant , @xmath162 is the non - thermal x - ray luminosity , and @xmath163 is the bb temperature in k. the temperature we calculate , however , is the apparent temperature of the plasma and is related to the effective temperature through a color - correction ( or hardness ) factor , @xmath164 @xcite , which is usually taken to be between 1.5 and 2 . hence , the true inner radius of the bb emission area is @xmath165 @xcite . we find @xmath166  cm ( 3@xmath42 confidence ) , for @xmath167 . this is consistent with the expected small accretion disk radius considering the low b field of the source and its high luminosity . the burst broadband spectrum requires only emission from the non - thermal component , with fit parameters similar to the ones we derive for the persistent emission . this reinforces our above picture where we envisioned the burst emission to be the result of a sudden increase of the mass accretion rate onto the neutron - star pole . the non - detection of the bb component implies that the reprocessing of the non - thermal emission may not have taken place during bursts . this is possible , for instance , if the burst emission is anisotropic away from the reprocessing material , i.e. , the inner accretion disk . such anisotropy for the bp has already been discussed by @xcite and @xcite to explain the extremely high luminosities of the bursts during the previous two outbursts , which reached luminosities two orders of magnitude above eddington . this conclusion is also supported by the timing properties of the source , for which the hard x - ray pf has been seen to increase prominently during the bursts @xcite . finally , the broadband spectrum of the dip intervals is similar to the persistent emission spectrum . the flux deficiency during dips is primarily seen in the non - thermal component , where the _ cutoffpl _ flux decreased by @xmath25 compared to the persistent emission flux . this is again in agreement with the accretion picture where the dips are essentially the result of a fraction of the long - term accreted matter not reaching the neutron star pole , instead replacing the matter that produced the preceding burst . the _ asca _ observations during the first outburst of  revealed a feature between 6 and 8  kev in its persistent emission spectrum . @xcite modeled the spectrum with a gaussian line with a centroid energy of @xmath148 kev and an ew of about 300  ev . the line was not resolved by the spectral resolution of _ asca _ , but its energy is indicative of a blend of emission lines from different species . the _ nustar _ persistent and dip spectra show a similar emission excess at the same centroid energy and a somewhat smaller ew ( although consistent at the 3@xmath42 level ) .    using the _ chandra _ hetgs we are able to resolve the broad feature into three emission lines , which we identify as fe  k from neutral and/or lowly ionized species at @xmath168  kev , and highly ionized fe  xxv and fe  xxvi at @xmath169 and @xmath170  kev ( these are the best estimates of the line energies from the dip@xmath171persistent emission spectrum , see also @xcite ) . we discuss first the fe emission lines from highly ionized species in the x - ray spectrum of . the gas producing the lines is most likely photo - ionized by the x - ray emission of the neutron star . in photo - ionized gas , he - like fe emission lines are produced by recombination and resonant scattering @xcite , and include four different transitions at slightly different energies , the resonant line @xmath172 , the two inter - combination lines @xmath173 and @xmath174 , and the forbidden line @xmath175 ( see e.g. , * ? ? ? * ; * ? ? ? , we could not resolve the different resonances , however , from the centroid energy of the fe  xxv line , @xmath169  kev , we can safely conclude that the resonant line @xmath172 ( with mean energy at 6.700  kev ) contributed minimally to the line strength , hence the emission is dominated by recombination @xcite .    to investigate the origin of the highly ionized species , we simulate xstar grids @xcite based on the broadband x - ray spectrum of the source . we choose a covering fraction of 0.2 ( assuming an accretion disk ) , and solar abundances as in @xcite . due to the high accretion rate of the source , one would expect the photo - ionized gas to have a very large density ; hence , we examined different values of the gas density @xmath78 from @xmath176 to @xmath177  @xmath178 , each time multiplying by 10 , to test the effects of density on reproducing the line shapes . we find that the best densities to reproduce the lines , resulting in reasonable values of the ionization parameter ( @xmath179 ) , are 10@xmath180 and 10@xmath181  @xmath178 . here we consider a density of @xmath182  @xmath178 . finally , we assumed no turbulence in the gas . fitting this xstar simulated grid to the persistent+dip spectrum , we find a best fit value for the column density in the gas of @xmath183  @xmath15 ( @xmath184  @xmath15 ) , and for the ionization parameter @xmath185 . the @xmath186 parameter is related to the total x - ray luminosity of the source , @xmath187 , the density of the ionized gas , @xmath78 , and its distance from the ionizing source , @xmath188 , by @xmath189 . solving for @xmath188 , we find @xmath190  cm ( 3@xmath42 confidence ) . this distance is similar to the estimates of the ionized gas location in other sources ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and points towards reprocessing in an accretion disk corona .    the other interesting feature in our spectra is the ( quasi@xmath0 ) neutral fe at 6.4  kev . there are three possibilities for the formation site of the fluorescence fe  k line in x - ray binaries : ( i ) a wind from the companion seems to be unlikely in the case of , since the companion is a low - mass star and accretion is most likely occurring through roche - lobe overflow @xcite ; ( ii ) the companion surface via reflection , which is also hard to achieve , because of the very low inclination of the system @xcite would result in a very low ew for any fe features @xcite ; or ( iii ) the outer regions of the accretion disk , by means of irradiation from the central source . to test this third possibility , we fit a second xstar grid , similar to the one above , to the dips+persistent spectrum . we find that the ( quasi@xmath0 ) neutral fe line is well reproduced with an ionization parameter @xmath191 ( @xmath192 at 3@xmath42 confidence ) , much lower than the value required to model the highly ionized lines . this ionization parameter corresponds to a distance from the neutron star of @xmath193  cm ( @xmath194  cm at 3@xmath42 confidence ) . this seems to point to the outer regions of the accretion disk as the likely origin of the fe  k. other x - ray binary sources showed , similar to , fe  k@xmath151 lines most likely from the outer region of an irradiated disk ( e.g. , * ? ? ? the 6.7  kev excess in the simultaneous _ nustar _  and _ chandra _  data is also consistent with a broad line which we fit using a diskline model ( see also @xcite ) . the inner - disk radius that we find ( @xmath195  cm ) is consistent with the results of @xcite and in agreement with a magnetically truncated accretion disk . this radius , however , is more than an order of magnitude smaller than the result we get from the xstar fits to the highly ionized lines ( assuming that the broad line is consistent with fe  xxv , @xcite ) . this could either be due to the uncertainties in the density of the ionizing gas and/or in the distance to the source , or the fact that other broadening mechanisms , e.g. , compton scattering , are contributing to the line profile .    due to the low statistics of the present observation , we could not constrain any variations in the separate _ chandra _  lines during dips ( table  [ persisprop ] ) . the _ nustar _ gaussian line fit to the @xmath148  kev excess has energy , width , ew , and flux consistent within @xmath96 between persistent and dip emission ( table  [ persisprop ] ) . the excess emission is not detected during bursts , which means that either the super - eddington burst x - ray luminosity fully ionized the line - emitting region , including the fe  k region , or that the line strength remained more or less constant during bursts , but was masked by the very bright continuum . to explore the first possibility , we simulated the same xstar grid as above , but instead of the persistent x - ray luminosity , we used the x - ray luminosity as derived from the bursts . we fit this xstar table to the burst spectrum and derived a 3@xmath42 lower limit on the ionization parameter @xmath196 . this limit represents the lowest ionization state that would result in the featureless spectrum that we see during bursts . this lower limit translates into an upper - limit on the radius of the ionized material of @xmath197  cm . hence , the burst luminosity is capable of fully ionizing the region of the disk where the highly ionized lines are thought to originate ( @xmath198  cm ) . at the @xmath131 upper limit , it is capable of fully ionizing the region of the neutral fe ( @xmath199  cm ) . this result does not exclude the second possibility . similar to the previous two outbursts from , the increase in the x - ray luminosity of the source is accompanied by an increase in the spin period of the neutron star ( gbm pulsar team , see footnote 2 ) . this spin - up factor and persistent pulsed emission indicate that the accretion onto the neutron star is not quenched at the disk - magnetosphere boundary , i.e. , the propeller effect is not acting . for spin - up to occur during accretion , the inner disk rotational frequency at the magnetospheric radius has to be greater than the neutron star spin frequency , which results in an upper limit on the magnetic dipole field of ,    @xmath200    where @xmath187 is the total x - ray luminosity assuming a distance of 8  kpc , @xmath201 is the gravitational constant , @xmath202 and @xmath188 are the mass and radius of the neutron star , taken to be 1.4  @xmath203 and 10  km , @xmath79 is the neutron star spin frequency , and @xmath204 is a dimensionless parameter between 0.5 and 1 @xcite . we find @xmath205  g. this value is consistent with the estimates of the previous two outbursts ( e.g. , * ? ? ? * ; * ? ? ? we note that the true upper - limit is lower than the above derived value since the source started spinning - up at earlier stages in the outburst when the source luminosity was lower .    assuming that the bb component is the result of reprocessing in the inner regions of the accretion disk , we could also use the bb radius estimate ( section  [ discussbbs ] ) to derive the strength of the dipole field of the source . the inner accretion disk radius can be written as    @xmath206    with @xmath207 . we find    @xmath208    which is consistent with the above upper - limit and the expected low dipole field of the source .","summary":"xstar modeling shows these lines to also emanate from a truncated accretion disk .","abstract":"we report on a 10  ks simultaneous _ chandra_/hetg_nustar _  observation of the bursting pulsar , , during its third detected outburst since discovery and after nearly 18 years of quiescence . the source is detected up to 60  kev with an eddington persistent flux level . seven bursts , followed by dips , are seen with _ chandra _ , three of which are also detected with _ nustar_. timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy ( from% to% ) up to 10  kev , above which it remains constant . the  kev spectra of the persistent and dip emission are the same within errors , and well described by a blackbody ( bb ) , a power - law with an exponential rolloff , a 10  kev feature , and a 6.7  kev emission feature , all modified by neutral absorption . assuming that the bb emission originates in an accretion disc , we estimate its inner ( magnetospheric ) radius to be about  cm , which translates to a surface dipole field  g. the _ chandra_/hetg spectrum resolves the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi emission lines . xstar modeling shows these lines to also emanate from a truncated accretion disk . the burst spectra , with a peak flux more than an order of magnitude higher than eddington , are well fit with a power - law with an exponential rolloff and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectra lack a thermal component and any fe features . anisotropic ( beamed ) burst emission would explain both the lack of the bb and any fe components ."}
{"article_id":"1502.05982","section_id":"c","document":"we studied the broad - band x - ray emission ( @xmath3  kev ) of the bp from a @xmath209  h simultaneous _ nustar_-_chandra _  observation during its third detected outburst since discovery and after nearly 18 years of quiescence . these data were taken a few days before the outburst reached its peak . a total of seven bursts are detected during our observation . temporal analysis revealed that the first six bursts have comparable shapes , consisting of a single pulse with duration of @xmath150  s , and a faster rise than decay time . the last burst has a double - peaked morphology with a duration of about 25  s. all seven bursts , however , have equal fluences with an average of about @xmath210  erg  @xmath15 . similar to previous results , we find an average ratio of the burst to the persistent emission fluence @xmath211 ( with the exception of one burst where @xmath153 ) , pointing to the type  ii origin for the bursts . each of the seven bursts is followed by a dip in the persistent emission flux , which recovers exponentially with a characteristic time - scale @xmath212  s. we find an average missing fluence in the dip of about @xmath210  erg  @xmath15 , consistent with the fluence emitted in the bursts . this indicates that the energy emitted during the burst is compensated for in the dip , and that the long - term accretion rate is constant . the pulse - profiles of the persistent and the dip intervals are nearly sinusoidal with only weak contribution from the second harmonic . the pf increases from about 10% at 4  kev to 15% at 13  kev , and remains constant thereafter . the bp persistent and dip broadband spectra are identical and well fit with a bb with @xmath213  kev , a _ cutoffpl _ with an index @xmath214 and an energy rolloff @xmath215  kev , a 10  kev feature assumed to be the result of inadequate modeling of the _ cutoffpl _ , and a 6.7  kev emission feature , all modified by neutral absorption . phase - resolved spectroscopy shows that the bb and the _ cutoffpl _ components show variations at the pulse period of the source , both getting harder at pulse maximum , whereas no significant changes are seen in the 10  kev and the 6.7  kev feature .    assuming that the bb is reprocessing of the non - thermal emission in the inner regions of the accretion disk , we derive an inner disk radius @xmath216  cm . this radius translates into a dipole magnetic field of @xmath5  g.    the _ chandra_/hetg spectrum resolved the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi narrow emission lines . modeling the highly ionized lines with xstar places the emitting region at a distance of about @xmath217  cm from the neutron star , consistent with an accretion disk corona origin . using a similar xstar grid to model the ( quasi- ) neutral fe , we find that it originates from a distance @xmath218  cm , most likely the outer regions of an accretion disk .    the broadband burst spectrum , with a peak flux more than an order of magnitude higher than eddington , is well fit with a _ cutoffpl _ and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectrum , however , lacks a thermal component ( bb ) and fe features . if the burst emission were anisotropic ( beamed ) , the lack of the bb component is expected since no reflection of the burst photons on the inner disk would take place . similarly the fe xxv , fexxvi , and the neutral fe lines would remain at the flux levels detected in the persistent and dip emission and , therefore , are too weak to be detected above the strong burst continuum . if , on the other hand , the burst emission is isotropic , we show that the disk region where the fe xxv and fexxvi lines would be produced is now fully ionized ; the neutral iron line could still be at very low levels and masked by the continuum . in that case , however , we would expect a strong bb component , which is not detected . we conclude that , as suggested by @xcite and @xcite , the burst emission is highly beamed .","summary":"_  observation of the bursting pulsar , , during its third detected outburst since discovery and after nearly 18 years of quiescence . the source is detected up to 60  kev with an eddington persistent flux level . seven bursts , followed by dips , are seen with _ the  kev spectra of the persistent and dip emission are the same within errors , and well described by a blackbody ( bb ) , a power - law with an exponential rolloff , a 10  kev feature , and a 6.7  kev emission feature , all modified by neutral absorption . assuming that the bb emission originates in an accretion disc , we estimate its inner ( magnetospheric ) radius to be about  cm , which translates to a surface dipole field  g. the _ chandra_/hetg spectrum resolves the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi emission lines . the burst spectra , with a peak flux more than an order of magnitude higher than eddington , are well fit with a power - law with an exponential rolloff and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectra lack a thermal component and any fe features . anisotropic ( beamed ) burst emission would explain both the lack of the bb and any fe components .","abstract":"we report on a 10  ks simultaneous _ chandra_/hetg_nustar _  observation of the bursting pulsar , , during its third detected outburst since discovery and after nearly 18 years of quiescence . the source is detected up to 60  kev with an eddington persistent flux level . seven bursts , followed by dips , are seen with _ chandra _ , three of which are also detected with _ nustar_. timing analysis reveals a slight increase in the persistent emission pulsed fraction with energy ( from% to% ) up to 10  kev , above which it remains constant . the  kev spectra of the persistent and dip emission are the same within errors , and well described by a blackbody ( bb ) , a power - law with an exponential rolloff , a 10  kev feature , and a 6.7  kev emission feature , all modified by neutral absorption . assuming that the bb emission originates in an accretion disc , we estimate its inner ( magnetospheric ) radius to be about  cm , which translates to a surface dipole field  g. the _ chandra_/hetg spectrum resolves the 6.7  kev feature into ( quasi-)neutral and highly ionized fe  xxv and fe  xxvi emission lines . xstar modeling shows these lines to also emanate from a truncated accretion disk . the burst spectra , with a peak flux more than an order of magnitude higher than eddington , are well fit with a power - law with an exponential rolloff and a 10  kev feature , with similar fit values compared to the persistent and dip spectra . the burst spectra lack a thermal component and any fe features . anisotropic ( beamed ) burst emission would explain both the lack of the bb and any fe components ."}
{"article_id":"hep-ph0501194","section_id":"i","document":"quark - hadron duality is a fascinating phenomenon that was first observed by bloom and gilman @xcite more than 30 years ago . it is receiving plenty of attention today from both the experimentalist @xcite and theorist @xcite communities , due to an interest in duality itself , and due to the huge field of experimental applications of duality in kinematic regions that are very difficult to access without it . the most straightforward definition of quark - hadron duality says that any hadronic process can be described in terms of either a quark and gluon picture , or in terms of a purely hadronic picture , provided either calculation contains all fock states . however , in the former case , a full numerical solution of qcd is prohibitive in most situations , despite the impressive progress of lattice qcd , and in the latter case , a full hadronic solution , e.g. employing an effective field theory , also is not feasible unless the kinematic region is restricted to low energies and momenta . thus , this most general version of duality is not very useful , as many interesting processes take place in a region that is neither perturbative nor very low energy . there is a much more practical version of duality : in certain kinematic regimes , properly averaged hadronic observables can be described by a perturbative qcd ( pqcd ) calculation . this version of duality is highly relevant as perturbative qcd calculations can be performed . using duality , these pqcd calculations can then be related to averaged data taken in the resonance region . quark - hadron duality has been observed experimentally in many processes : it was discovered by bloom and gilman in inclusive , inelastic electron scattering , it made its way into the textbooks in @xmath1 , was studied in the semileptonic decays of heavy mesons @xcite , is considered in the analysis of heavy ion reactions @xcite , and forms the basis for using qcd sum rules @xcite . in addition to the `` classical '' examples and applications of duality , duality ideas are applied in new areas , too . for neutrino scattering , the beam energies are not well known , and an averaging will thus take place almost automatically . the application of duality is discussed for several planned neutrino experiments , see e.g. @xcite , and duality ideas have been applied in @xcite to nucleon / nuclear duality in neutrino scattering . there is also interest in duality in parity violation experiments @xcite , and with regard to generalized parton distributions @xcite . a very local version of duality - assuming that it holds for just one resonance - has been used in @xcite to extract information on structure functions at @xmath0 in the scaling limit from form factor data . these ideas were also applied to neutrino - nucleon scattering @xcite . duality ideas might also be useful for pion photoproduction @xcite . duality is a major point in the 12 gev upgrade of cebaf at jefferson lab @xcite .    in this paper , we investigate duality in inclusive , inelastic electron scattering . new experimental data from jefferson lab and desy have impressively confirmed that quark - hadron duality is valid down to rather low four - momentum transfers , and for many observables : duality in @xmath2 was confirmed to hold down to @xmath3 @xcite , and very recently , the longitudinal structure function @xmath4 and the purely transverse @xmath5 were separated , and found to exhibit duality for @xmath6 @xcite . experimental evidence for duality in spin observables has been reported for @xmath7 from hermes @xcite and from jefferson lab @xcite for the first moment of @xmath8 . while this is exciting all by itself , these data have inspired experimentalists to apply duality to the extraction of information on the deep inelastic region in kinematics that are not readily accessible . duality allows us to connect the perturbative regime of quarks and gluons with the strongly non - perturbative resonance regime . the earliest example discussed was the extraction of the elastic nucleon form factor from the deep inelastic scaling curve @xcite . in @xcite , higher twist contributions were inferred from the resonance data . these two kinematical regions have traditionally been separated , as it was believed that the physics of quarks and gluons had little connection to the collective phenomena of resonances . at low invariant masses @xmath9 of the final state in an @xmath10 reaction on the nucleon , one observes many resonance bumps in the cross section , and @xmath11 is traditionally referred to as the resonance region . for higher invariant masses , @xmath12 , the cross section becomes smooth and exhibits bjorken scaling , and this region is referred to as the deep inelastic region . note that this strict division of kinematics was introduced historically , even though non - resonant processes are present for low @xmath9 , and resonances with larger mass may contribute for high @xmath9 . the demarcation line of @xmath13 is plotted in the @xmath14 - @xmath15 plane in fig . [ kinplot ] .     and @xmath15 kinematic plane . this kinematic plot shows the deep inelastic regime and the resonance regime . the solid line corresponds to an invariant mass of the final state of @xmath13 . every point above the line lies in the resonance region , @xmath16 , and every point below the line lies in the deep inelastic region @xmath12 . the invariant mass of the final state , @xmath9 , is related to the four momentum transfer @xmath15 and bjorken @xmath14 by @xmath17 , where @xmath18 is the nucleon mass . ] one consequence of this traditional subdivision is that large amounts of data with @xmath11 were cut from deep inelastic analyses of data , leading to a paucity of data at very high bjorken @xmath14 . the region of large @xmath14 , @xmath0 , is referred to as the ( deep ) valence region , and is the subject of much interest . in particular , one would like to study the valence quark spin distribution of the nucleon . this can be achieved by measuring the polarization asymmetry @xmath19 of the proton and neutron . for @xmath0 , many , and widely different predictions , exist for the polarization asymmetry of the neutron , running the gamut from @xmath20 , predicted in unbroken su(6 ) , to @xmath21 , predicted in pqcd , and everything in between , see @xcite for good reviews of the situation . in the chiral soliton model , there are even predictions of negative values @xcite .    the experimental data available for @xmath22 at high @xmath14 was rather scarce and afflicted with very large error bars for @xmath23 before the advent of the recent jefferson lab data @xcite . they also extended only up to @xmath24 @xcite . this is due not only to the fact that polarization experiments are always more difficult to perform than unpolarized measurements , but mainly due to the fact that in order to achieve @xmath0 for the deep inelastic regime , one has to use very high four - momentum transfers @xmath15 , see fig . [ kinplot ] . this drastically reduces the cross section , as the cross section is proportional to the mott cross section , which in turn is proportional to @xmath25 . thus , accessing one and the same @xmath14 in the resonance region and in the deep inelastic regime leads to much lower count rates in the deep inelastic regime . for example , a measurement at @xmath26 can be performed at @xmath27 in the resonance region , or at @xmath28 in the deep inelastic region . the count rate in the deep inelastic region will be lowered by more than a factor of 50 compared to the resonance region measurement . this makes taking data in the deep inelastic regime for large @xmath14 extremely difficult . a recent jefferson lab experiment improved the situation by measuring in the deep inelastic regime , up to @xmath29 with very reasonable error bars , thus decreasing the uncertainty by an order of magnitude compared to older data @xcite . still , the experimental exploration of @xmath22 at really large @xmath0 has not been feasible yet , thus making it the prime application for duality . even with the planned 12 gev upgrade of jefferson lab , data in the deep inelastic regime will be accessible only up to @xmath30 @xcite . as the kinematics plot shows , large values of @xmath14 can be accessed at low @xmath15 in the resonance regime . a measurement of @xmath22 - or any other observable of interest - in the resonance region can then be averaged , and will yield the same information as a direct measurement in the deep inelastic region , provided that duality holds . using this approach , @xmath22 could be measured up to @xmath31 , by taking data in the delta resonance region @xcite . another interesting application of duality that was recently discussed is the application of duality to the emc effect @xcite . even though the emc effect has been mapped out for a large kinematic region , data at very high @xmath14 and for lighter nuclei are scarce . the data base could be significantly expanded by the application of duality to lepton scattering from nuclei . before we can embark on this new experimental approach , we need a good , solid understanding of how well duality holds , and where it holds . ideally , one would come up with a certain accuracy of the duality procedure , which then could be quoted as a systematic error for the extraction of @xmath22 or other observables in the relevant region . here , we need more theoretical input and guidance . as we currently do not understand quark - hadron duality from first principles , modeling is our best tool to obtain the answers necessary for applying duality to extract @xmath22 . currently , theorists tackle this problem by modeling duality in two different ways : one branch starts out from the non - relativistic constituent quark model , with some relativistic corrections , to describe duality @xcite , the other branch starts the modeling with a relativistic one - body equation @xcite . the former branch makes contact with the phenomenology . it was started by the pioneering work of close and isgur @xcite , where the authors investigated how a summation over the appropriate sets of nucleon resonances leads to parton model results for the structure function ratios in the su(6 ) symmetric quark model . this work was recently expanded @xcite to include the effects of su(6 ) spin - flavor symmetry breaking . in @xcite , the authors considered the first five low - lying resonances , and performed a careful analysis of the onset of duality for @xmath2 and @xmath32 . our results belong to the latter branch . the goal of these modeling efforts is obvious : to gain an understanding of quark - hadron duality and the conditions under which it holds , by capturing just the essential physical conditions of this rather complex phenomenon . we imposed these basic requirements for a model : we require a relativistic description of confined valence quarks , and we treat the hadrons in the infinitely narrow resonance approximation . this paper is the fourth in a series of papers , in which we have modeled duality with increasing complexity . all models that we have presented so far have reproduced the features of duality in a qualitative manner . we started out with an all scalar model @xcite , and gradually improved the model until all the particles had proper spin @xcite . in @xcite , we focused on the model results for the unpolarized responses . for the first time , we investigated the dependence of our results on the type of potential we employed . in the present paper , we focus on the spin observables : the responses @xmath33 and @xmath34 that are accessible only with spin , the spin structure functions @xmath32 and @xmath35 , and the polarization asymmetries @xmath19 and @xmath36 . this paper is organized as follows : in section [ secmodel ] , we briefly state the properties of the model , then , in section [ secformalism ] , we discuss some of the formalism for polarized inclusive electron scattering . in section [ secresults ] we discuss our numerical results for the various spin observables for the bound - free and the bound - bound transitions . we end with a brief summary of our results and an outlook .","summary":"we apply a model for the study of quark - hadron duality in inclusive electron scattering to the calculation of spin observables . the model is based on solving the dirac equation numerically for a scalar confining linear potential and a vector color coulomb potential . duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering , namely for , and we discuss which observables are most suitable for this application of duality .    = 10000 = 10000","abstract":"we apply a model for the study of quark - hadron duality in inclusive electron scattering to the calculation of spin observables . the model is based on solving the dirac equation numerically for a scalar confining linear potential and a vector color coulomb potential . we qualitatively reproduce the features of quark - hadron duality for all potentials considered , and discuss the onset of scaling and duality for the responses , spin structure functions , and polarization asymmetries . duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering , namely for , and we discuss which observables are most suitable for this application of duality .    = 10000 = 10000"}
{"article_id":"hep-ph0501194","section_id":"r","document":"now , we turn to the numerical results of our model calculations . within our model , we calculate two different processes : the bound - bound transition and the bound - free transition of the light quark . the bound - free transition ( referred to as pwia in @xcite ) , is the analog to perturbative qcd . the bound quark is knocked into the continuum by the absorption of the virtual photon . we discuss the bound - free transition first , employing just the linear confining potential . we investigate the scaling results and the onset of scaling for the bound - free transition . next , in section [ secbb ] , we show our results for the bound - bound transition and the linear confining potential . there , we focus on the onset of scaling and the low-@xmath110 duality . then , we take a look at the role of the ground state p - wave contribution in section [ secpwave ] . finally , we investigate the effect of employing a static coulomb and a running coulomb potential in section [ secpotmodels ] .      for the bound - free transition , we can reach arbitrarily high energy transfers without any numerical complications , as we do not have to solve for any high energy bound states in the final state . moreover , we can determine the analytic expressions for the responses , and thus for all other observables , for @xmath113 at fixed @xmath93 . as the responses @xmath114 and @xmath115 , which can be accessed in unpolarized scattering , enter some spin observables , we quote all four responses for the reader s convenience @xcite :    @xmath116    @xmath117    @xmath118 \\left ( \\frac{(y^2 + 2 y q - p^2}{2 p q } \\right)^2 \\nonumber\\\\ % & & \\left . % + \\sqrt{(y+q)^2+m^2 } \\ , n_s(p ) - m \\ , n^0_v(p ) - \\frac{y^2 + 2 y q -p^2}{2p } \\ , n^s_v(p)\\right\\}\\,,\\end{aligned}\\ ] ]    and @xmath119 n_-(p ) + q \\ , n_s(p ) \\nonumber\\\\ & & \\left.- \\frac{y^2 + 2 y q - p^2}{2 p q } \\big ( m \\ , n^s_v(p ) - p \\ , n_s(p ) \\big ) \\right\\}\\,.\\end{aligned}\\ ] ]    in the limit of large @xmath110 , the bound - free response functions become @xmath120 @xmath121 @xmath122 and @xmath123    these response functions therefore scale in @xmath93 .    the vector and scalar momentum density distributions @xmath124 and @xmath125 are defined in terms of the ground state wave function @xmath126 as @xmath127 with @xmath128 and @xmath129 and @xmath130 moreover , @xmath131    the asymptotic responses for the bound - free transition are shown in fig . [ figbfasymresp ] . the two purely transverse responses , @xmath115 and @xmath33 , have opposite signs but similar peak positions at slightly negative @xmath93 values and peak heights . the longitudinal response @xmath114 is the smallest of the four responses , and the only one to peak at a slightly positive @xmath93 . the transverse - longitudinal interference response is the largest response , and peaks at @xmath132 . this response is symmetric around @xmath132 as it contains only terms proportional to @xmath133 and @xmath134 , but no contributions linear in @xmath93 .     and fixed @xmath93 of the responses for the bound - free transition . we show @xmath114 ( solid line ) , @xmath115 ( dotted line ) , @xmath33 ( dashed line ) , and @xmath34 ( dash - dotted line ) . ] the similar size and shape of @xmath115 and @xmath33 , together with their opposite signs , leads to a value of the polarization asymmetry @xmath135 close to 1 , see fig . [ figbfasymssf ] . we show @xmath19 only for @xmath93 values for which the responses have appreciable values , i.e. for @xmath136 . while we could calculate @xmath19 in a region where the responses are tiny , the results would be meaningless . our result is close to the pqcd prediction of 1 for @xmath19 in the limit of @xmath137 . for large @xmath15 , large negative values of @xmath93 - much bigger than @xmath138 - correspond to @xmath139 .     and fixed @xmath93 of the spin structure functions @xmath32 and @xmath35 and the polarization asymmetry @xmath19 for the bound - free transition . we show @xmath32 ( solid line ) , @xmath35 ( dotted line ) , and @xmath19 ( dashed line ) . note that @xmath36 vanishes in this limit . ] the asymptotic values of the spin structure functions @xmath32 and @xmath35 are also shown in fig . [ figbfasymssf ] . the spin structure functions have peaks at small , negative @xmath93 values . they have opposite signs . of the two functions , @xmath35 has the slightly larger peak value . note that the asymptotic value of @xmath36 is zero . now , after showing the asymptotic values , we will consider the approach to scaling in the bound - free transition . previously , we have studied the approach to scaling of the unpolarized longitudinal and transverse response functions @xcite . there , we found that the onset of scaling is not influenced very much by the spin of the target particle . the two response functions @xmath33 and @xmath34 are accessible only with polarized beams and targets . it is interesting to check if they scale just like their unpolarized counterparts .     is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]   is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]    the scaling behavior of the transverse - primed response @xmath33 for the bound - free transition is shown in fig .  [ figbfrtp ] . the lower panel shows the response for several @xmath110 values up to @xmath140  gev . with increasing momentum transfer , the peak of the response moves to more negative values of @xmath93 , and increases in height . the width of the response also increases . the change in the response when going from @xmath141 to @xmath142 is significant , and the difference between the @xmath142 and @xmath143 results is noticeable . increasing @xmath110 leads to very small changes , visible mainly at the peak and the large , negative @xmath93 flank . the top panel , displaying the response for various higher values of @xmath110 and the asymptotic value discussed above , shows that the response has converged to the asymptotic value roughly at @xmath144 . is plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential . ] the transverse - longitudinal primed response @xmath34 for the bound - free transition is shown in fig . [ figbfrtlp ] . the figure shows the response for lower values of the three - momentum transfer @xmath110 . while there are small changes , amounting to a small shift of the entire response towards the negative @xmath93 values , one can see that this response scales much faster than @xmath33 . we do not include another panel with @xmath34 calculated for higher @xmath110 values , as the curves all coincide . is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]   is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]    from this , we can see that the transverse - primed response @xmath33 shows a scaling behavior very similar to @xmath115 ( as discussed in @xcite ) , and that the only interference response that is accessible in inclusive electron scattering , @xmath34 , exhibits the earliest onset of scaling . now , we will consider the @xmath93-scaling behavior of the spin structure functions . the spin structure functions are simply combinations of the spin - dependent responses multiplied with some kinematic factors , see section [ secformalism ] . we have already seen how the relevant responses , @xmath33 and @xmath34 , scale . taking a look at the kinematic coefficients shows us that the onset of @xmath93-scaling will be determined by the @xmath110 values at which the kinematic factors reach their asymptotic values . for the convenience of the reader , we recall eq . ( [ defpolobs ] ) here :    @xmath145    @xmath146    the asymptotic values of the kinematic factors multiplying the responses are , for fixed @xmath93 and large @xmath110 ,    @xmath147    leading to the asymptotic values of the spin structure functions :    @xmath148    from eq . ( [ ssfkinfac ] ) , one can see that the relevant scale for the onset of scaling is given by the ground state energy @xmath149 . all responses peak roughly in the region @xmath150 , so that the three - momenta @xmath110 necessary to reach the asymptotic values are determined by @xmath149 alone . the spin structure function @xmath32 for the bound - free transition is shown in fig . [ figbfg1 ] . the lower panel shows the spin structure function for several @xmath110 values up to @xmath140  gev . one can see clearly that @xmath32 changes significantly for each increase in @xmath110 , and that convergence has not set in at @xmath151 . this behavior is due to the slow approach of the kinematic factors in @xmath32 to their asymptotic values . the responses themselves scale much faster , and are very close to their asymptotic values at @xmath152 , whereas the spin structure function @xmath32 is off its asymptotic value by almost @xmath153 . results for @xmath35 at lower ( bottom panel ) and higher ( top panel ) three - momentum transfers are shown in fig . [ figbfg2 ] . just like @xmath35 , it approaches its scaling limits only at high momentum transfers . is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]   is plotted versus @xmath93 for several low ( bottom panel ) and high ( top panel ) values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]    the polarization asymmetries @xmath19 and @xmath36 are ratios of response functions , and may therefore show a different scaling behavior than the responses themselves . as we have seen that the two purely transverse responses , @xmath115 and @xmath33 , have a very similar approach to scaling , one may expect to see an even more rapid scaling of @xmath19 , the ratio of the two transverse responses . the results for @xmath19 are shown in the top panel of fig . [ figbfa1a2 ] . as @xmath19 is a pure ratio of two responses that scale at reasonable values of @xmath110 , without any kinematic factors , we can expect @xmath19 to scale fast . indeed , one clearly sees that in the region of @xmath154 , where the responses are largest , @xmath19 scales almost immediately . only the @xmath155 curve differs very slightly from all the other curves , including the asymptotic value , in this @xmath93 interval . outside of that region , where the responses have less strength , the scaling takes a bit longer . in all cases , @xmath151 is very close to the asymptotic value . ( top panel ) and @xmath36 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 , as well as their asymptotic value for @xmath156 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]    ( top panel ) and @xmath36 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 , as well as their asymptotic value for @xmath156 . the results shown have been calculated for the bound - free transition , using the linear potential.,title=\"fig : \" ]    the approach to scaling of the polarization asymmetry @xmath36 is shown in the bottom panel of fig . [ figbfa1a2 ] . note that @xmath157 for @xmath113 and fixed @xmath93 , because the kinematic factor @xmath158 goes to zero in this limit and the responses scale in @xmath93 . thus , the approach to scaling of @xmath36 will mainly be determined by the kinematic factor @xmath158 . so , even though both @xmath34 and @xmath115 scale at reasonable values of @xmath110 , the scaling of @xmath36 is delayed . the differences between the curves for increasing @xmath110 values decrease , but the result for @xmath159 is still far away from the asymptotic value of @xmath20 . just as for the spin structure functions , the kinematic factor that is present determines the very slow onset of scaling .    in summary , we observe that the response functions reach values very close to their asymptotic values around @xmath160 , and scale at the latest at @xmath161 . the response @xmath34 is the fastest scaling response , and the response @xmath33 is the response that scales most slowly . the spin structure functions and the polarization asymmetry @xmath36 scale only for much higher momentum transfers , due to the kinematic factors in their definitions . the polarization asymmetry @xmath19 , on the other hand , is the observable for which we observe scaling at the lowest momentum transfers . note that the scaling behavior of the discussed observables does not change when we use an `` x - type '' scaling variable , as in our previous papers @xcite . this is demonstrated in fig . [ figuqsqg1 ] , where we show @xmath32 as a function of @xmath162 , for fixed @xmath15 . note that @xmath163 goes to @xmath164 for large @xmath15 , its properties have been discussed previously @xcite . this is the appropriate scaling variable for use with fixed @xmath15 even at low @xmath15 . we have generated the plot by starting out with our results as functions of @xmath110 and @xmath93 , then calculated the corresponding values of the four - momentum transfer @xmath15 and the scaling variable @xmath163 . the results were then sorted into @xmath15 bins . this is why there are no continuous lines in the figure , just single data points . one can see clearly that the scaling behavior of @xmath32 is independent of the variables chosen : just as seen in fig . [ figbfg1 ] for fixed @xmath110 and the variable @xmath93 , at low @xmath15 , @xmath32 starts out negative , then changes sign , and takes a very long time to scale . even between the points for @xmath165 and @xmath166 , there is a significant difference . thus , we see that u - scaling is just as slow for @xmath32 ( and @xmath35 and @xmath36 ) as @xmath93-scaling . the scaling behavior does not change at all with the use of different scaling variables . is plotted versus @xmath163 for several values of the four - momentum transfer squared @xmath15 . the results shown have been calculated for the bound - free transition , using the linear potential . ] now we proceed to discuss the behavior of the responses , spin structure functions , and polarization asymmetries for final states consisting solely of resonances . we refer to this case as the `` bound - bound '' transition . the wave functions for the excited states have to be obtained by solving the dirac equation numerically . due to the involved nature of the numerics , the highest accessible momentum transfer is @xmath160 . work on extending our calculations up to @xmath167 using a wkb approximation will be reported elsewhere . here , we focus on the approach to scaling and on duality at low @xmath110 . we start again by considering the two polarized responses . we show @xmath33 in the top panel of fig . [ figbbresp ] . the resonance bumps at lower @xmath110 values give way to smooth curves formed by many , closely spaced resonances . the graph shows that there is still a small difference between the results for @xmath168 and @xmath160 , we have not yet reached the scaling value . this is to be expected , as the bound - free transition scales only at higher @xmath110 values for this response . in general , the more complicated interplay of the various final state resonances leads to slower scaling for the bound - bound transition . the resonances oscillate around the smooth curves for higher momenta @xmath110 on the positive @xmath93 flank , but are a bit below the smooth curves at the negative @xmath93 flank . we see a very similar behavior for @xmath34 , in the bottom panel of fig . [ figbbresp ] . ( top panel ) and the transverse - longitudinal primed response function @xmath34 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential.,title=\"fig : \" ]   ( top panel ) and the transverse - longitudinal primed response function @xmath34 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential.,title=\"fig : \" ]    for @xmath19 , the bound - bound transition results scale very quickly in the region of the response peaks , @xmath169 . this is consistent with the scaling behavior of @xmath19 as observed in the bound - free transition , and stems from the definition of @xmath19 as ratio of two fast - scaling responses . it is interesting to note that the resonance bumps that are visible at @xmath170 have vanished almost completely at @xmath171 , even though they are clearly present at @xmath171 for the transverse and transverse - primed responses , whose ratio forms @xmath19 . this exemplifies the very quick onset of scaling for this observable , which we can observe even in the region of low momentum transfer @xmath110 . our current model gives at best a very qualitative insight on the workings of duality for proton targets , as it is most closely related to electron scattering off a heavy - light meson , i.e. a b - meson . nevertheless , our results seem to be very encouraging as far as the prospects of applying quark - hadron duality to extracting deep inelastic information on @xmath19 from data in the resonance region are concerned . is plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential . ] the polarization asymmetry @xmath36 , which contains a kinematic factor multiplying the ratio of two responses , is shown in fig . [ figbba2 ] . in contrast to @xmath19 , @xmath36 changes significantly with changing momentum transfer , and approaches its scaling value of zero only slowly . as mentioned when discussing the bound - free transition results for @xmath36 in the previous section , the behavior of this polarization asymmetry is mainly determined by the kinematic factor , not by the ratio of the responses . the same scenario - large variation for changes in momentum transfer @xmath110 and slow approach to the scaling values - is repeated for the spin structure functions @xmath32 and @xmath35 . as for @xmath36 , their behavior is determined by the slowly - scaling kinematic factors , not by the fast - scaling responses . for the lowest considered momentum transfer , @xmath32 even has a different sign , compared to the higher momentum transfer results . our results suggest that the application of duality to resonance region data for @xmath19 should be quite safe , while @xmath36 , @xmath32 , and @xmath35 seem to be observables that are not amenable to such an extraction procedure .    as far as duality in the spin structure function @xmath32 is concerned , the available data @xcite are not yet conclusive , and may imply a different onset of duality for @xmath172 and @xmath8 . the hermes data @xcite for @xmath172 indicate that the onset of duality takes place at @xmath173 . a recent analysis @xcite of jefferson lab data @xcite for the first moment of @xmath8 indicates that duality could hold at @xmath15 as low as @xmath174 . a dedicated jefferson lab experiment to study duality in neutron spin structure functions in the resonance region is currently being analyzed @xcite . dong et al . @xcite recently used a constituent quark model for the five lowest - lying resonances and various parametrizations of scaling data for a careful theoretical analysis of duality in @xmath2 and @xmath32 for the proton target . they included target mass corrections and find that duality in @xmath32 is not seen below @xmath175 . close and isgur @xcite , using an @xmath176-symmetric , constituent quark model , also predicted a slower onset of duality for @xmath32 , and pointed out that duality sets in faster in this model for @xmath8 than for @xmath172 . dominant magnetic interactions are necessary for the symmetric quark model , and for the neutron target , this is realized . our simple model is , of course , far from describing actual electron scattering measurements . it is not intended to provide a quantitative description of data , but to provide qualitative insights into nature . however , our findings on the scaling behavior of the polarization asymmetries and spin structure function might provide more general guidance : what we see is that the onset of scaling is driven mainly by the kinematic factors multiplying the reasonably fast - scaling response functions in the definitions eq . ( [ defpolobs ] ) of the spin structure functions and polarization asymmetries . where the factors are missing , i.e. for @xmath19 , convergence is rapid and the prospects for a successful application of duality are very good . where the factors are present , and take a very high momentum to reach their asymptotic value , e.g. in @xmath32 , scaling is very slow and duality does not hold . this suggests that the validity of quark - hadron duality in spin observables may be strongly related to kinematic factors , and less to dynamics . the faster scaling for @xmath8 might be explained due to a smaller longitudinal - transverse interference response @xmath34 , see eqs . ( [ ssfkinfac],[ssfasym ] ) . however , one has to be cautious as certain features of nature are not included in our model : it is well - known that the @xmath177 resonance has an unnaturally small coefficient multiplying the leading term and therefore gives rise to peculiarities in the scaling and duality behavior , see @xcite . is plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential . ] ( top panel ) and @xmath35 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential.,title=\"fig : \" ]   ( top panel ) and @xmath35 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the linear potential.,title=\"fig : \" ]      one interesting question is which role the p - wave in the ground state plays . we will discuss the role of the ground state p - wave contribution for the onset of scaling for the observables , and for the scaling results themselves .      for the bound - free transition , we can read off from the momentum distributions in section [ secpwiayscal ] that , without the ground state p - wave ,    @xmath178    thus , in the scaling limit , we can introduce the response @xmath179 and then write all the bound - free responses in the scaling limit as @xmath180 from these equations , one sees that in the scaling limit , the peak position is now identical for all four responses , and that the responses differ only by a simple numerical factor . this leads automatically to @xmath181 for all values of @xmath110 and @xmath93 . just like the responses , the spin structure functions @xmath32 and @xmath35 also peak at @xmath182 without the p - wave in the ground state . apart from slight shifts in the peak position , there are no major changes in the asymptotic forms of the observables , see fig . [ figbfasymnop ] . for @xmath114 , omission of the p - wave leads to a slight reduction in peak height . @xmath115 also has a reduced peak height ( a reduction of about 10% ) . in contrast , @xmath33 maintains its peak height . the only response not to experience any noticeable change is @xmath34 , which was centered around @xmath183 to start with , and does not change its peak height , either .     and fixed @xmath93 of the responses for the bound - free transition , without the ground - state p - wave ( top panel ) . we show @xmath114 ( solid line ) , @xmath115 ( dotted line ) , @xmath33 ( dashed line ) , and @xmath34 ( dash - dotted line ) . the asymptotic behavior for @xmath113 and fixed @xmath93 of the spin structure functions @xmath32 and @xmath35 for the bound - free transition , without the ground - state p - wave ( bottom panel ) . we show @xmath32 ( solid line ) and @xmath35 ( dotted line ) . note that @xmath36 vanishes in this limit , and that @xmath181 . , title=\"fig : \" ]   and fixed @xmath93 of the responses for the bound - free transition , without the ground - state p - wave ( top panel ) . we show @xmath114 ( solid line ) , @xmath115 ( dotted line ) , @xmath33 ( dashed line ) , and @xmath34 ( dash - dotted line ) . the asymptotic behavior for @xmath113 and fixed @xmath93 of the spin structure functions @xmath32 and @xmath35 for the bound - free transition , without the ground - state p - wave ( bottom panel ) . we show @xmath32 ( solid line ) and @xmath35 ( dotted line ) . note that @xmath36 vanishes in this limit , and that @xmath181 . , title=\"fig : \" ]    the omission of the p - wave in the ground state simplifies the analytic expressions obtained for the responses , and one expects that scaling should set in more quickly . this is observed at low @xmath110 values for @xmath114 and @xmath115 . for @xmath33 and @xmath34 , the presence of the p - wave contribution plays a negligible role in the scaling behavior . this behavior is consistent with the fact that the asymptotic forms of @xmath114 and @xmath115 are more strongly affected by the omission of the p - wave .    for @xmath32 , the results change significantly for low @xmath110 , see the top panel of fig . [ figbfg1a2nop ] . at @xmath184 , the spin structure function is changing sign at @xmath185 and becomes positive . for higher @xmath110 values , @xmath32 peaks at slightly higher @xmath93 values without p - wave , and the peak height is somewhat higher , too . the onset of scaling is very slow , independent of the p - wave contribution . ( top panel ) and the polarization asymmetry @xmath36 ( bottom panel ) are shown without the ground - state p - wave for several values of the three - momentum transfer @xmath110 at fixed @xmath93.,title=\"fig : \" ]   ( top panel ) and the polarization asymmetry @xmath36 ( bottom panel ) are shown without the ground - state p - wave for several values of the three - momentum transfer @xmath110 at fixed @xmath93.,title=\"fig : \" ]    the onset of scaling is dramatically accelerated for @xmath19 by dropping the p - wave , as @xmath115 and @xmath186 coincide apart from an overall sign , and @xmath19 is the ratio of these two responses . therefore , @xmath19 scales directly to @xmath21 for even the lowest value of @xmath110 , if there is no p - wave present . while @xmath36 is still scaling slowly , it has quite a different shape now , see the bottom panel of fig . [ figbfg1a2nop ] . instead of starting at its maximum value at large negative @xmath93 , and decreasing to a minimum around @xmath187 , without the p - wave , it starts out at its minimum value at large negative @xmath93 and steadily increases . the situation for the bound - bound transition is similar : for the longitudinal response , we observe small changes in peak position and peak height due to the omission of the p - wave , just like for the bound - free transition . for the transverse response , we see a more pronounced reduction in peak height , as well as the already familiar shift in the peak position . the transverse - longitudinal primed response remains largely unaffected by the omission of the p - wave , while the transverse primed response has a shifted peak position , and no reduction in peak height . these observations are very similar to the observations made above concerning the effects of the p - wave on the asymptotic shapes of the responses for the bound - free transition . the polarization asymmetry @xmath19 again takes the value of @xmath21 immediately , as @xmath115 and @xmath33 only differ by a sign . @xmath36 without the ground state p - wave has the same shape for bound - bound and bound - free transitions , markedly different from the shape including the p - wave . the spin structure function @xmath32 behaves similarly for bound - bound and bound - free transitions , too . we do not present any figures for the bound - bound results , as they are so similar to the bound - free transition results shown above . strictly speaking , one would have to renormalize the remaining wave function when switching off the p - wave . however , the effect of this rescaling will be small , and we omit it here . the goal of this discussion was to learn where the p - wave is important , and where not . summarizing , the p - wave has the biggest impact on the polarization asymmetries , where switching off the p - wave leads to immediate scaling for @xmath19 and a different shape for @xmath36 , before @xmath36 reaches its asymptotic value of zero . the spin structure function @xmath32 also shows sensitivity to the p - wave contribution at low @xmath110 .    our results for the role of the p - wave in @xmath19 confirm the results in @xcite . there , the authors noted a distinct suppression of @xmath19 at low nachtmann @xmath188 due to the p - waves . the region of large positive @xmath93 , where we observe a fall - off of @xmath19 when it is calculated with the complete wave function , and find a value of @xmath21 when @xmath19 is calculated without the p - wave contribution , corresponds to the low @xmath188 region .      in this section , we discuss the influence of the chosen potential on the results for the observables . for brevity , we restrict ourselves to the bound - bound transition . previously @xcite , we found that there is no qualitative difference between the linear , static coulomb , and running coulomb potential results in the longitudinal and transverse responses . peak height and position are different , but the approach to scaling and the low @xmath110 oscillatory behavior are qualitatively the same . first , we discuss the results for the coulomb potential in the bound - bound transition . the responses agree qualitatively with the results for the linear potential , with similar shapes , peak heights , peak locations , and scaling behavior . the same holds for the spin structure functions @xmath32 and @xmath35 . for the polarization asymmetry @xmath19 , the decrease from values close to @xmath21 is slightly more pronounced for positive @xmath93 values , but the differences are still small . ( top panel ) and @xmath36 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the running coulomb potential . the results for @xmath160 for the linear potential and the static coulomb potential are also shown for comparison.,title=\"fig : \" ]   ( top panel ) and @xmath36 ( bottom panel ) are plotted versus @xmath93 for several values of the three - momentum transfer @xmath110 . the results shown have been calculated for the bound - bound transition , using the running coulomb potential . the results for @xmath160 for the linear potential and the static coulomb potential are also shown for comparison.,title=\"fig : \" ]    this somewhat faster fall - off of @xmath19 is seen more distinctly for the running potential , see fig . [ figa1run ] . however , the responses and spin structure functions look very similar for the running coulomb potential and the static coulomb potential . @xmath36 has a slightly different shape for the running coulomb potential , it starts out more flatly at negative @xmath93 values than for the linear potential and the static coulomb potential . the onset of convergence , however , does not seem to be affected noticeably by the potential in the low @xmath110 region . these results for the dependence of the spin observables on the employed model potential are consistent with the results found for the behavior of the longitudinal and transverse response functions : while the results differ quantitatively , there is no qualitative difference due to the different potentials , neither in the results for the highest @xmath110 valuable attainable for bound - bound transitions in our model , nor in the convergence of the results .    the polarization asymmetries , as ratios of responses , are naturally more sensitive than the other observables , but even they only show a minor influence of the potential .","summary":"we qualitatively reproduce the features of quark - hadron duality for all potentials considered , and discuss the onset of scaling and duality for the responses , spin structure functions , and polarization asymmetries .","abstract":"we apply a model for the study of quark - hadron duality in inclusive electron scattering to the calculation of spin observables . the model is based on solving the dirac equation numerically for a scalar confining linear potential and a vector color coulomb potential . we qualitatively reproduce the features of quark - hadron duality for all potentials considered , and discuss the onset of scaling and duality for the responses , spin structure functions , and polarization asymmetries . duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering , namely for , and we discuss which observables are most suitable for this application of duality .    = 10000 = 10000"}
{"article_id":"astro-ph0405122","section_id":"i","document":"the fast winds from massive stars and their subsequent supernovae ( sne ) ejecta dominate the mass and energy input to the interstellar medium ( ism ; e.g. , abbott 1982 ) and so may regulate star formation and galaxy evolution . most massive stars form in ob associations , and the concentrated energy input from massive stars in ob associations sweeps up the ambient ism to form expanding shells called superbubbles ( e.g. , mccray & snow 1979 ) . the physical structure of a superbubble is very similar to that of a bubble blown by the stellar wind of an isolated massive star @xcite . however , theories of such bubbles are still very uncertain and have not had much serious appraisal with observations of high quality . studies of galactic superbubbles are difficult because of their large angular sizes and the confusion of objects in the line of sight . the large magellanic cloud ( lmc ) , in contrast , provides an excellent laboratory to study superbubbles since it is nearby ( at a distance of @xmath20  kpc , as adopted here , @xmath21 pc ; eastman & kirshner 1989 ) and almost face - on ( inclined by @xmath22 to the line of sight ; van der marel & cioni 2001 ) . it also has little foreground ( @xmath23 ; xu et al . 1992 ) or internal extinction ( @xmath24 in the range from @xmath25 to @xmath26 ; bessel 1991 ) . the superbubble 30 dor c (= dem l 263 ; davies , elliott , & meaburn 1976 ) is southwest of the main 30 doradus complex in the lmc , and is coincident with the large ob association lh 90 (= ngc 2044 ; lucke & hodge 1970 ) . this ob association consists of a number of stellar clusters and is particularly rich in wolf - rayet ( w - r ) stars @xcite . the most massive stars appear to have ages in the range from @xmath27 to @xmath28  myr ( testor , schild , & lortet 1993 ) . in x - ray imaging observations , 30 dor c appears almost as a complete shell with a diameter of @xmath29 ( wang & helfand 1991 ; dennerl et al . 2001 ; dunne , points , & chu 2001 ) . the x - ray shell is confined within the h@xmath17-emitting filaments ( see fig . 1__l _ _ of dunne et al . 2001 ) , as expected from the evaporation of cool gas into the hot interior of a superbubble . there is also an indication for a substantial nonthermal contribution in addition to an assumed one - temperature thermal component , particularly in the western part of shell @xcite . the radio emission from 30 dor c may be due to a combination of synchrotron - emitting relativistic electrons produced by shocks within the superbubble and thermal emission from the h@xmath17-emitting shell @xcite .    in this paper , we report on a spatially resolved spectroscopic analysis with _ xmm - newton _ of the diffuse x - ray emission emanating from 30 dor c. we specifically use the wind - blown bubble model of weaver et al . ( 1977 ; see also mac low & mccray 1988 ) to infer the temperature and density structure of the x - ray emitting gas , which in turn are used to estimate both the density of the ambient medium and the rate at which energy is injected into the ism by the stellar winds .","summary":"we present an analysis of _ xmm - newton _ observations of the superbubble 30 dor c and compare the results with the predictions from the standard wind - blown bubble model .","abstract":"we present an analysis of _ xmm - newton _ observations of the superbubble 30 dor c and compare the results with the predictions from the standard wind - blown bubble model . we find that the observed x - ray spectra can not be fitted satisfactorily with the model alone and that there is evidence for nonthermal x - ray emission , which is particularly important at  kev . the combination of the bubble model and a power - law gives a reasonable fit to the observed spectra . the thermal pressure and central temperature of the bubble are dyne and  k , respectively , and we infer that , for a bubble age of years , the ambient density is , the mechanical luminosity is erg s , and the coefficient of thermal conductivity is of the spitzer value . the total unabsorbed  kev luminosities of the eastern and western parts of the bubble are erg s and erg s , respectively . the unabsorbed  kev luminosity of the bubble model is erg s and so the power - law component contributes between and to the total unabsorbed luminosity in this energy band . the nature of the hard nonthermal emission is not clear , although recent supernovae in the bubble may be responsible . we expect that about one or two core - collapse supernovae could have occured and are required to explain the enrichment of the hot gas , as evidenced by the overabundance of-elements by a factor of , compared to the mean value of solar for the interstellar medium in the large magellanic cloud . as in previous studies of various superbubbles , the amount of energy currently present in 30 dor c is significantly less than the expected energy input from the enclosed massive stars over their lifetime . we speculate that a substantial fraction of the input energy may be radiated in far - infrared by dust grains , which are mixed with the hot gas because of the thermal conduction and/or dynamic mixing ."}
{"article_id":"astro-ph0405122","section_id":"r","document":"figure  1 shows the _ xmm - newton _ image of the @xmath72 ( @xmath73 ) region centered on 30 dor c in the @xmath56@xmath48  kev band . in this image , 30 dor c is a roughly elliptical feature with major axis @xmath74 ( @xmath75  pc ) . this feature appears to be the observational manifestation of a bubble blown in the ism by the winds from massive stars in the bubble s interior @xcite . other sources of x - ray emission in figure  [ fig1 ] include sn 1987a , which is located @xmath76 southwest of the bubble center and close to a region of diffuse x - ray emission associated with the honeycomb nebula @xcite . there is also a compact x - ray source , j0536.9 - 6913 , to the east of 30 dor c , which has a radio counterpart and is probably a background agn @xcite . the bright source at the left of the image is the crab - like supernova remnant n157b @xcite .    in figure [ fig2 ] , we compare an h@xmath17 emission - line image from university of michigan / ctio magellanic cloud emission - line survey ( mcels ; smith et al . 1998 ) to an adaptively smoothed image of the inner @xmath77 region of the 30 dor c field in the @xmath56@xmath48  kev band . the edge - brightened x - ray emission is presumably due to an increase in gas density around the edge of the bubble , and is spatially enclosed by the h@xmath17-emitting filaments . it is conceivable that the increase in gas density is due to the evaporation of cool ( @xmath78  k ) gas into the hot interior from the surrounding h@xmath17-emitting shell @xcite . we also show adaptively smoothed images of the central @xmath79 region of the 30 dor c field in the soft ( @xmath56@xmath80  kev ) , medium ( @xmath80@xmath47  kev ) , and hard ( @xmath47@xmath48  kev ) bands ( fig . [ fig3 ] ) . in these images , there is evidence for spectral variations in the x - ray emission across the face of the bubble . while the western part of the bubble is easily seen in the medium and hard band images , it is almost invisible in the soft band image , clearly due to the x - ray absorption by foreground cool gas ( see also dennerl et al . 2001 and dunne et al . there is a region of localized co emission projected onto the western part of 30 dor c @xcite . assuming a @xmath81co(1 - 0 ) intensity of @xmath82 k km s@xmath8 for the cloud ( see table  3 of johansson et al . 1998 ) and a co to @xmath83 conversion factor of @xmath84 for the lmc @xcite , we estimate an @xmath83 column density of @xmath85 towards the western part of 30 dor c. this absorption column density is sufficient to absorb the soft x - ray emission from the western part of bubble . intriguingly , in the hard band image , the western part of the bubble appears much brighter than the eastern part , and is presumably more luminous . finally , we note that j0536.9 - 6913 is almost invisible in the soft band image , due to either absorption by gas in the lmc or absorption intrinsic to the source . this source also went undetected in the pspc observations reported by @xcite , which would require either an increase in the absorption column density towards the source or a decrease in the intensity of the source .      in earlier studies of 30 dor c with _ einstein _ and _ rosat _ , the x - ray luminosity expected from the stellar wind - blown bubble model of @xcite was often compared with that derived from spectral fits to the data using a single temperature thermal plasma model ( e.g. , dunne et al . the main disadvantage of this approach is that the data are not directly compared to the model and so any test of the model will depend on the measurements used to derive the expected x - ray luminosity of the bubble ( e.g. , the number density and expansion velocity of the h ii region ) . also , the wide range of gas temperatures inside the bubble gives rise to soft x - ray emission in excess of that expected from a single temperature plasma model and emission lines from a wider range of ionization states than those expected from a single temperature thermal plasma model , which will naturally result in an underestimate of the heavy element abundances . the shortfall in the soft x - ray emission below @xmath86  kev from the single temperature thermal plasma model can also lead to an underestimate of the absorption column density , and hence the soft x - ray luminosity . in a more sophisticated analysis of 30 dor c with the _ einstein _ data , @xcite compared the ipc spectrum with that expected from integrating the model over the bubble interior and folding the result through the ipc response . however , with the limited quality of the ipc data , they were unable to constrain tightly the basic spectral parameters such as temperature and absorption column density , let alone to test other interesting parameters such as the efficiency of thermal conduction and metal abundance of the x - ray emitting gas . in a more recent analysis of the _ chandra _ and _ xmm - newton _ data , @xcite discovered nonthermal x - ray emission from 30 dor c , although the discovery was made using a single temperature , non - equilibrium , ionized plasma model to describe the thermal emission from the bubble . here we have compared the x - ray spectra of 30 dor c directly with the stellar wind - blown bubble model of weaver et al . ( 1977 ; see also mac low & mccray 1988 ) by implementing it into the spectral analysis package xspec . the x - ray emission in their model arises primarily from a region of thermally evaporated material ( see fig .  3 of weaver et al . the temperature and density of the hot gas as a function of radius @xmath87 within this region can be approximated as @xmath88 and @xmath89 , respectively , where @xmath90 and @xmath91 are the corresponding central values , and @xmath92 is the outer radius of the bubble . the x - ray flux , @xmath93 , expected from the bubble is @xmath94 \\ , n(r)^{2 } \\ , 4\\pi r^{2 } dr \\label{eqn - dem}\\end{aligned}\\ ] ] where @xmath95 is the mean emissivity of the hot gas in the x - rays and @xmath96 is the distance to the source . we have calculated the x - ray spectrum with a multi - temperature , variable heavy element abundance mekal ( mewe , kaastra , & liedahl 1995 ) model , as implemented in xspec , using @xmath97 \\ , { \\rm d}t / t_{\\rm c}\\end{aligned}\\ ] ] for the differential emission measure @xmath98 , which is a function of temperature . $ ] is the normalization of the spectrum in xspec . in this form , the model spectrum can be applied approximately to a slightly aspherical bubble of an equivalent volume @xmath100 . the mos1 and mos2 spectra of the diffuse emission in the eastern and western parts of 30 dor c ( a total of 8 spectra ) were simultaneously fitted to the above wind - blown bubble model and a foreground absorption of a column density of @xmath101 . the absorption cross - sections and atomic abundances were taken from @xcite and @xcite , respectively . while the foreground absorption was allowed to be different between the eastern and western parts of 30 dor c , we constrained the bubble model to have the same temperature , metal abundance , and intensity in the eastern and western parts of 30 dor c. this model , which has 5 free parameters , gives a poor , simultaneous fit to the mos1 and mos2 data with @xmath102 ( 349 dof ) . we also did not obtain a significant improvement in the fit when we allowed the normalization of the bubble model to be different between the mos1 and mos2 datasets . an inspection of the spectra indicates that much of the deviation from the best - fit bubble model is due to an excess of hard x - rays in the spectra of the diffuse emission , particularly in the western part of 30 dor c. such an hard x - ray excess can naturally be explained as nonthermal x - ray emission , which can typically be described by a power - law . we therefore added a power - law component of photon index @xmath103 to our model fits . the normalization of the power - law continuum was allowed to vary between the eastern and western parts of 30 dor c , to account for the spatial variation in the hard x - ray emission ( fig  [ fig3 ] ) . in our initial modeling of the data , the metal abundance was poorly constrained , with a lower limit of @xmath104 solar and an upper limit of several times solar . we therefore fixed the metal abundance at the known mean value of @xmath105 solar for the ism in the lmc @xcite . in comparison to the bubble model , this model ( model b+p ) gives a much improved , although still statistically unacceptable , simultaneous fit to the mos1 and mos2 data with @xmath106 ( @xmath107 dof ; table  [ tbl-1 ] , column 2 ) . the absorbed @xmath105@xmath11  kev flux in the western and eastern parts of 30 dor c are @xmath108 and @xmath109 erg s@xmath8 @xmath2 , respectively . these fluxes are slightly larger than the fluxes reported in @xcite for their regions 14 , due to the differences in the sizes of the regions used for extracting spectra between the present work and @xcite . we note that a marginal ( at greater than @xmath110% confidence  a @xmath111 result ) improvement in the fit is obtained when we allowed the normalization of the bubble model to be different between the eastern and western parts of 30 dor c.    the spectra of the diffuse x - ray emission in wind - blown bubbles have often been fitted to single temperature plasma models in collisional ionization equilibrium ( e.g. , dunne et al . 2001 ) , although with little physical justification . in order to compare with these earlier observations and analyses , we have replaced the bubble model with a single temperature mekal model . we have also fixed the metal abundance of the mekal at @xmath105 solar , since it is poorly constrained by the data . this model ( model m+p ) gives a similar quality fit to the data as the b+p model , with @xmath112 ( @xmath107 dof ; table  [ tbl-1 ] , column 3 ) . the best - fit equivalent hydrogen column densities and normalizations of the power - law continua are comparable to the values obtained from the fitting the data to the b+p model , and the best - fit temperature of the mekal is consistent with the value reported in @xcite for the thermal emission in their region 1 . we have also considered the possibility that the hard x - ray excess in 30 dor c is attributable to a second thermal component that might be caused by a recent supernova explosion , for example . we replaced the power - law component in the above m+p model with a second mekal model , with the metal abundances of the two mekals fixed at the same value of @xmath105 solar and the normalization of the high - temperature mekal allowed to vary between the eastern and western parts of 30 dor c. we find that this model provides a much worse fit to the data than do either the b+p or m+p models , with @xmath113 ( @xmath107 dof ) . this is due to the data at high energies being much too flat compared to the model . although a significant ( at greater than @xmath114% confidence ) improvement in the fit is obtained when we allowed the metal abundances of the two mekals to vary together , this model , with one extra free parameter , still provides a worse fit to the data than do either the b+p or m+p models , with @xmath115 ( @xmath116 dof ) . moreover , the metal abundance of @xmath117 solar is uncomfortably small for the ism in the lmc . more sophisticated models , such as the non - equilibrium , ionized ( nei ) plasma codes as implemented in xspec ( see e.g. , borkowski , lyerly , & reynolds 2001 for a detailed critique of these models ) , also gave poorer fits to the data than do either the b+p or m+p models . we therefore conclude that the hard x - ray excess in 30 dor c is best described by a nonthermal emission component . because 30 dor c is a massive star forming region with possible recent core - collapse supernovae occurring inside the bubble , we have further examined the data for an over - abundance of the @xmath17-process elements compared to fe - like elements . we did this by dividing the elements into two groups : the @xmath17-process elements o , ne , mg , si , s , ar , and ca ; and the remaining fe - like elements c , n , na , al , fe , and ni . elements in each group were constrained to have the same abundance relative to solar . the abundances of he and the fe - like elements were fixed at the solar and @xmath105 solar values , respectively , which are appropriate for the ism in the lmc @xcite . this model ( model vb+p ) further improves the fit to the mos1 and mos2 data with @xmath118 ( @xmath116 dof ; table  [ tbl-1 ] , column 3 ) . for clarity , we show the co - added mos spectra from the eastern and western parts of the bubble , together with the residuals to this model fit ( fig . [ fig4 ] ) . there are some large residuals around the energies of the al k@xmath17 fluorescence line that arises from the detector housing and the au m - edge that arises from x - ray absorption in the telescope mirror surface . with the possible exception of si , the @xmath17-process elemental abundance of @xmath119 solar ( errors here and elsewhere in this paper are 90% confidence for one interesting parameter , @xmath120 ) is higher than that of the ism in the lmc @xcite . there is no improvement ( at greater than 90% confidence ) in the fit when we allow the abundance of the fe - like elements to vary . although the model spectrum can still be rejected statistically at @xmath121% confidence , we consider the fit to be reasonably good . the model is certainly still an over - simplification . for example , we have assumed that the normalization of the soft bubble component is the same for both the eastern and western parts of 30 dor c. this assumption is problematic , however , since the power - law components of the two parts are very different . because of the heavy absorption , the data below @xmath80  kev does not allow us to independently constrain the bubble component in the western part of 30 dor c. dividing the data into the two parts ( east and west ) is an oversimplification ; in general , the transition from east to west must be gradual and so the parameters inferred from our model should be considered as averaged values within the divided regions . we have also not included any systematic error in the data due to uncertainties in the calibration , background subtraction , and modeling , which are difficult to quantify at present . we therefore decided not to add more complications ( such as varying abundances of individual elements ) into the model .","summary":"we find that the observed x - ray spectra can not be fitted satisfactorily with the model alone and that there is evidence for nonthermal x - ray emission , which is particularly important at  kev . the combination of the bubble model and a power - law gives a reasonable fit to the observed spectra . the unabsorbed  kev luminosity of the bubble model is erg s and so the power - law component contributes between and to the total unabsorbed luminosity in this energy band .","abstract":"we present an analysis of _ xmm - newton _ observations of the superbubble 30 dor c and compare the results with the predictions from the standard wind - blown bubble model . we find that the observed x - ray spectra can not be fitted satisfactorily with the model alone and that there is evidence for nonthermal x - ray emission , which is particularly important at  kev . the combination of the bubble model and a power - law gives a reasonable fit to the observed spectra . the thermal pressure and central temperature of the bubble are dyne and  k , respectively , and we infer that , for a bubble age of years , the ambient density is , the mechanical luminosity is erg s , and the coefficient of thermal conductivity is of the spitzer value . the total unabsorbed  kev luminosities of the eastern and western parts of the bubble are erg s and erg s , respectively . the unabsorbed  kev luminosity of the bubble model is erg s and so the power - law component contributes between and to the total unabsorbed luminosity in this energy band . the nature of the hard nonthermal emission is not clear , although recent supernovae in the bubble may be responsible . we expect that about one or two core - collapse supernovae could have occured and are required to explain the enrichment of the hot gas , as evidenced by the overabundance of-elements by a factor of , compared to the mean value of solar for the interstellar medium in the large magellanic cloud . as in previous studies of various superbubbles , the amount of energy currently present in 30 dor c is significantly less than the expected energy input from the enclosed massive stars over their lifetime . we speculate that a substantial fraction of the input energy may be radiated in far - infrared by dust grains , which are mixed with the hot gas because of the thermal conduction and/or dynamic mixing ."}
{"article_id":"astro-ph0405122","section_id":"c","document":"in summary , the nature of the apparent nonthermal hard x - ray component is still uncertain . the expansion of the bubble is much too slow in order to produce the energetic particles necessary for nonthermal x - ray synchrotron emission . although such energetic particles can be produced at the inner reverse shock , they can not cross the bubble within their synchrotron half - lives . nonthermal bremsstrahlung is an inefficient process , requiring at least three orders of magnitude more energy than can be supplied by the o - type stars in lh  90 . a recent supernova could supply the necessary energy , but this would mean that we are seeing the event by chance ( a probability of @xmath277 percent ) . the ic scattering of cmb and infrared photons can not account for all of the nonthermal x - ray emission unless the radio flux is purely synchrotron radiation , which seems unlikely . while the x - ray emission from ic - scattered optical photons should be much higher than that from ic - scattered cmb and infrared photons , it should be concentrated in the central region of 30 dor c , where the optical photon density is greatest , in sharp contrast to the data . the nonthermal x - ray emission could instead be due to the ic scattering of cmb and infrared photons by relativistic particles originating in young pulsar wind material with energies peaking between @xmath263@xmath216 . high spatial resolution x - ray imaging , which can be afforded by an on - axis _ chandra _ observation , will be particularly useful to further the understanding of the component . such an observation will allow for an accurate determination of the size and geometry of the x - ray - emitting region and for a detailed comparison with images in other wavelength bands . a substantial fraction of the expected energy input from stellar winds and supernovae may be radiated in the infrared by dust grains entrained in the hot gas . we thank r. chris smith for providing his optical image of 30 dor c in computer - readable format , glenn allen for discussions on the nonthermal emission , and the referee for insightful comments on an earlier draft of the paper . this research is supported by the nasa ltsa grant nag5 - 8935 . abbott , d. c. 1982 , , 263 , 723 anders , e. , & grevesse , n. 1989 , geochimica et cosmochimica acta , 53 , 197 arnaud , k. a. 1996 , in asp conf . proc . 101 , astronomical data analysis software and systems v , ed . g. jacoby & j. barnes ( san francisco : asp ) , 17 arons , j. & tavani , m. 1994 , , 90 , 797 atoyan 1999 ,  , 346 , l49 bamba , a. , ueno , m. , koyama , k. , & itoh , m. 2003 , in the proceedings of the 8th iau asian - pacific regional meeting , volume ii , ed . , s. ikeuchi , j. hearnshaw , and t. hanawa ( san francisco : asp ) , 129 bamba , a. , ueno , m. , nakajima , h. , & koyama , k. 2004 , , 602 , 257 bessel , m. s. 1991 , , 242 , l17 blandford , r. d. , & eichler , d. 1987 , phys . , 154 , 1 blumenthal , g. r. , & gould , r. j. 1970 , rev . phys . , 42 , 237 bohlin , r. c. , savage , b. d. , & drake , j. f. 1978 , , 224 , 132 borkowski , k. j. , lyerly , w. j. , & reynolds , s. p. 2001 , , 548 , 820 cass , m. , & paul , j. a. 1980 , , 237 , 236 chandran , b. d. g. , & cowley , s. c. 1998 , phys . lett . , 80 , 3077 cherepashchuk a. m. , 1991 , in proc . 143 , wolf - 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blown bubble ( model valid for gas temperatures in the range from 8  ev to 80  kev ) ; vb @xmath322 wind - blown bubble with variable abundances ( model valid for gas temperatures in the range from 8  ev to 80  kev ) ; m @xmath322 mekal ( model valid for gas temperatures in the range from 8  ev to 80  kev ) ; p @xmath322 power - law . + @xmath323measured column density towards the eastern part of the bubble . + @xmath324measured column density towards the western part of the bubble . + @xmath325the gas temperature at the center of the bubble . + @xmath326c , n , na , al , fe , and ni abundance relative to solar of the bubble . + @xmath327fixed at the known value of @xmath247% solar for the ism in the lmc . + @xmath328o , ne , mg , si , s , ar , and ca abundance relative to solar of the bubble . + @xmath329the normalization of the bubble model . the units are cgs . + @xmath330photon spectral index . + @xmath331normalization for the power - law model in the eastern part of the bubble . + @xmath332normalization for the power - law model in the western part of the bubble . + @xmath333probability that the model describes the data and that @xmath314 exceeds the observed value by chance .","summary":"we speculate that a substantial fraction of the input energy may be radiated in far - infrared by dust grains , which are mixed with the hot gas because of the thermal conduction and/or dynamic mixing .","abstract":"we present an analysis of _ xmm - newton _ observations of the superbubble 30 dor c and compare the results with the predictions from the standard wind - blown bubble model . we find that the observed x - ray spectra can not be fitted satisfactorily with the model alone and that there is evidence for nonthermal x - ray emission , which is particularly important at  kev . the combination of the bubble model and a power - law gives a reasonable fit to the observed spectra . the thermal pressure and central temperature of the bubble are dyne and  k , respectively , and we infer that , for a bubble age of years , the ambient density is , the mechanical luminosity is erg s , and the coefficient of thermal conductivity is of the spitzer value . the total unabsorbed  kev luminosities of the eastern and western parts of the bubble are erg s and erg s , respectively . the unabsorbed  kev luminosity of the bubble model is erg s and so the power - law component contributes between and to the total unabsorbed luminosity in this energy band . the nature of the hard nonthermal emission is not clear , although recent supernovae in the bubble may be responsible . we expect that about one or two core - collapse supernovae could have occured and are required to explain the enrichment of the hot gas , as evidenced by the overabundance of-elements by a factor of , compared to the mean value of solar for the interstellar medium in the large magellanic cloud . as in previous studies of various superbubbles , the amount of energy currently present in 30 dor c is significantly less than the expected energy input from the enclosed massive stars over their lifetime . we speculate that a substantial fraction of the input energy may be radiated in far - infrared by dust grains , which are mixed with the hot gas because of the thermal conduction and/or dynamic mixing ."}
{"article_id":"hep-ph9611433","section_id":"i","document":"in two recent papers @xcite it was shown how the cross section for diffractive electroproduction of vector mesons can be predicted in perturbative qcd . production , i.e. , that the vector meson is composed of a heavy quark and antiquark . this work used a charmonium model for the meson , rather than treating the meson more generally in terms of the light - cone wave function that the factorization theorem requires . ] this process provides a novel probe of the dynamics of diffractive scattering in qcd . one notable prediction is that the cross section is proportional to the square of the gluon density in the hadron . experimental data @xcite appear to be in accord with the predictions , including an enhancement due to the rapid rise of the gluon density at small @xmath1 .    in this paper we extend the factorization theorem to the general case of electroproduction of any meson , and we provide a general proof of the theorem . the theorem expresses the amplitude for the process in terms of off - diagonal generalizations of the usual parton densities . our demonstration is valid for the whole leading power for the process , in contrast with the calculations in ref .  , which were in a leading - logarithm approximation . production . in this paper we treat very generally corrections to all orders . ] our results will enable the process to be treated with the inclusion of non - leading logarithms . apart from establishing the factorization theorem for the process , one aim of this paper is to attempt a pedagogical exposition of the methods by which the theorem is derived , since many of the concepts are unfamiliar . most importantly , the process of constructing a proof led us to new results . first , the theorem applies to the general case of two - body final states at low transverse momentum in electroproduction at large @xmath0 . the diffractive case simply corresponds to the small-@xmath1 region , with vacuum quantum number exchange . so we have extended the theorem to the full range of @xmath1 and to all mesons , pions in particular , not just vector mesons . in addition we find that we need not only the usual unpolarized parton densities ( generalized to be off - diagonal ) , but also the helicity densities ( @xmath2 or @xmath3 ) and the transversity densities ( @xmath4 or @xmath5 ) . since the cross section is proportional to the square of the densities , it is sensitive to the polarized parton densities without needing a polarized proton beam and without needing a measurement of the polarization of the final - state proton . indeed we can choose which kind of density is probed merely by choosing the final state meson . the amplitude for longitudinally polarized vector mesons depends only on the unpolarized parton densities . the amplitude for transversely polarized vector mesons depends only on the transversity densities ( @xmath4 ) . the amplitude for pseudoscalar mesons depends only on the helicity densities . this result clearly adds to the meager list of processes where the transversity of valence quarks can be probed without the need of some other unknown quantity ( such as an antiquark density or a polarized fragmentation function ) . all the above statements apply when the incoming virtual photon is longitudinally polarized . we also prove that the cross section is suppressed by a power of @xmath0 when the photon is transversely polarized . we give a fairly detailed account of the proof of the factorization theorem . the style of proof is based on that of refs .  , which treat inclusive hard scattering . there are some differences . first , our derivation of the power - counting formula shows some useful improvements . secondly , and rather importantly , we have to examine more closely exchanges of relatively soft quarks , since , in contrast to the case of inclusive scattering , there can be leading contributions from soft quark exchange ( otherwise known as the endpoint contributions ) . thus we have to examine the power - counting arguments in more detail . after this work was substantially complete , radyushkin @xcite published a preprint treating some of the same processes that we consider . his work appears to be completely compatible with ours ; he takes the same point of view as we do concerning a generalized operator product expansion , although the details of his notation are a little different . however , he considered only the diffractive limit of small @xmath1 for vector meson production , and hence , just as in ref . , he did not include the quark contribution . ( the quark operator is presumably unimportant at small @xmath1 . ) he does not present a complete proof of factorization . ji @xcite and radyushkin @xcite also showed how the same operators appear in an expansion for deeply virtual compton scattering .    in a future paper we hope to explore further consequences of our results , including detailed calculations .","summary":"the proof is valid for the leading power in and all logarithms . this generalizes previous work on vector meson production in the diffractive region of small . the amplitude is expressed in terms of off - diagonal generalizations of the usual parton densities . the parton densities used include not only the ordinary parton density , but also the helicity density ( or ) and the transversity density ( or ) , and these can be probed by measuring the polarization of the produced mesons with unpolarized protons .","abstract":"we formulate and prove a qcd factorization theorem for hard exclusive electroproduction of mesons in qcd . the proof is valid for the leading power in and all logarithms . this generalizes previous work on vector meson production in the diffractive region of small . the amplitude is expressed in terms of off - diagonal generalizations of the usual parton densities . the full theorem applies to all kinds of meson and not just to vector mesons . the parton densities used include not only the ordinary parton density , but also the helicity density ( or ) and the transversity density ( or ) , and these can be probed by measuring the polarization of the produced mesons with unpolarized protons ."}
{"article_id":"hep-ph9611433","section_id":"c","document":"we have proved a factorization theorem for exclusive meson production in high @xmath0 electroproduction . the level of the proof is comparable to that for the classic inclusive hard scattering processes , like drell - yan . an important consequence is that higher - order corrections can be systematically calculated in powers of @xmath237 . we have derived new results that the theorem applies to large @xmath1 as well as to small @xmath1 , and that it applies to the production of all mesons , and not just vector mesons . thus we are able to treat the process @xmath238 for example . in addition , we have shown that the theorem applies separately to the case of production of transversely polarized vector mesons . in that case we probe the @xmath4 or transversity distribution . although we expect this case to be suppressed at small @xmath1 , we see no reason for a suppression at large @xmath1 . this process then provides an interesting new method to measure @xmath4 , admittedly the off - diagonal version . an important consideration is that it is not necessary to have any polarization information about the proton , unlike the situation when one measures @xmath4 in inclusive scattering . the proof applies only to the case of that the virtual photon that induces the scattering has longitudinal polarization . the treatment of the same process with transversely polarized photons appears to be a much harder problem in qcd , with a definite power suppression . an important question that needs further study is to understand how much predictive power there is in the theorem . as always with perturbative qcd , the problem is that physical quantities are represented in terms of parton densities etc which we are unable to calculated perturbatively . if we had predictions for the non - perturbative quantities , we would have complete predictions for the cross - sections . but at the present state of the art , we only have models for the non - perturbative quantities , and very little that can be regarded as qcd predictions from first principles . only for the perturbative quantities , the hard scattering and the evolution kernels , do we possess a systematic method of calculation within qcd . now , for ordinary inclusive processes , we able to measure the parton densities from a limited set of processes at one energy and then predict many other processes at all energies that allow the hard scattering to be perturbative . the reason that this is straightforward is that the parton densities are functions of just one longitudinal variable , and that the deep - inelastic structure functions depend on a corresponding variable , @xmath1 . indeed , with the lowest order hard scattering , the structure functions are just simple linear combinations of parton densities . obvious generalizations of these remarks apply to other processes , in hadron - hadron scattering , for example . an immediate consequence is that it is possible to make many real predictions from qcd for inclusive hard scattering . ( of course , practical limitations arise from uncalculated higher order corrections and from substantial experimental errors . ) but the situation is totally different for our process of elastic meson production . the cross section is function of one momentum - fraction variable , but we have total of three such variables in the factorization formula . it is not so obvious that we can measure the non - perturbative quantities , even in principle .    at small @xmath1 , the situation is better , since the parton densities are dominated by exchange of vacuum quantum numbers : we have a normal regge limit . to the extent that there are universal regge trajectories , we get a relation between the power laws for the @xmath1 dependence in our process and in ordinary deep - inelastic scattering . since there is an integral over a longitudinal momentum fraction there need not be an exact relation between the off - diagonal parton densities and the diagonal ones probed in ordinary deep - inelastic scattering . thus we may not be able to get precise quantitative information on the diagonal gluon density , particularly as regards the normalization . our hope is that by some kind of regge factorization we could say that the two parton densities differ by some kind of regge vertex , and that since this regge vertex would be probed at large virtuality , we might be able to calculate it .    in the leading @xmath239 approximation , the leading non - diagonal terms are in fact computable in terms of the diagonal parton densities ( in the limit @xmath240 ) . similarly , after evolution in @xmath209 , the non - diagonal terms come dominantly from the calculated evolution kernel , rather than from the non - diagonal terms in the initial distribution . our proof of the theorem also applies to charge exchange scattering . then the generalized parton densities are off - diagonal in flavor . they are related by an isospin transformation to non - singlet parton densities ( at non - zero momentum transfer ) . there should therefore be some possibilities to improve the phenomenology of the ordinary non - singlet quark densities from an analysis of processes like @xmath241    our analysis also has direct implications for scattering off nuclei implying that color transparency phenomena should be present for exclusive production of leading mesons . we leave the discussion of this subject to a separate paper . _ note added in proof : _ in fact , the `` off - diagonal parton distributions '' that we use were actually introduced long ago in ref . @xcite , where the diffractive production of the z boson in dis was considered . subsequently there is a long history @xcite , including the previously cited paper by balitsky and braun @xcite .","summary":"we formulate and prove a qcd factorization theorem for hard exclusive electroproduction of mesons in qcd . the full theorem applies to all kinds of meson and not just to vector mesons .","abstract":"we formulate and prove a qcd factorization theorem for hard exclusive electroproduction of mesons in qcd . the proof is valid for the leading power in and all logarithms . this generalizes previous work on vector meson production in the diffractive region of small . the amplitude is expressed in terms of off - diagonal generalizations of the usual parton densities . the full theorem applies to all kinds of meson and not just to vector mesons . the parton densities used include not only the ordinary parton density , but also the helicity density ( or ) and the transversity density ( or ) , and these can be probed by measuring the polarization of the produced mesons with unpolarized protons ."}
{"article_id":"1603.07010","section_id":"i","document":"@xcite suggests and investigates coding without restriction for infinite arrays such as lattices on the additive white gaussian noise ( awgn ) channel . that is a communication without power constraints . in such a communication system , instead of the coding rate and capacity , two new concepts are defined : normalized logarithmic density ( nld ) and generalized capacity @xmath3 . forney et al . @xcite proved theoretically , the existence of sphere - bound - achieving and capacity - achieving lattices via construction d. they also established the concept of volume - to - noise ( vnr ) ratio as a parameter for measuring the efficiency of lattices . therefore , generalized capacity for lattices means the existence of a lattice with high enough dimension @xmath4 that enables transmission with arbitrary small error probability whenever vnr approaches  @xmath5 . in addition , it can be shown  @xcite that this error probability is bounded away from zero when @xmath6 . a capacity - achieving lattice can raise to a capacity - achieving lattice code by selecting a proper shaping region  @xcite . the search for sphere - bound - achieving and capacity - achieving lattices and lattice codes has begun with  @xcite . low density parity check ( ldpc ) lattices are those that have sparse parity check matrices . these lattices were introduced first by sadeghi _ _  @xcite . in this class of lattices , a set of nested binary ldpc codes along with construction d are used to generate lattices with sparse parity check matrices . another class of lattices , so - called low density lattice codes ( ldlc ) introduced and investigated in  @xcite and @xcite . turbo lattices employed construction d along with turbo codes to achieve capacity gains  @xcite . integer low - density lattices based on construction a which are known as lda lattices @xcite and polar lattices  @xcite , are another families of lattices with practical decoding methods . by applying non - binary ldpc codes and construction a , lda lattice of dimension @xmath7 have obtained an error performance within @xmath8db of poltyrev s limit @xcite . these lattices are shown to be capacity - achieving even without using dithering technique @xcite . all the above mentioned high - dimensional lattices share many common properties . for example , they all ( except turbo lattices ) exploit the parity check matrix of the lattice and employ a relevant message - passing decoding algorithm . however , they are different in some aspects especially when it comes to practical implementations . in fact , owning a simple and low complexity encoding method is an advantage in the implementation considerations for a family of lattices . in order to design a simple low complexity lattice encoder with low - storage requirement , the first prerequisite is obtaining a generator matrix of the lattice in a special form like circular or quasi - cyclic structure with small integer components . hence , the main contributions of this work are as follows . * we introduce and investigate quasi cyclic ( qc ) ldpc lattices which are special case of ldpc lattices @xcite . this family of lattices are supported with both a practical decoder as well as an efficient lattice encoder . different encoding approaches based on parallel , serial and two - stage shift - register - adder - accumulator ( sraa ) circuits can be adapted . furthermore , the computational complexity of these algorithms with respect to clock - cycles and flip - flops are determined . * we establish qc - ldpc lattice codes to be used in power constraint gaussian channels . in order to obtain finite constellations from these lattices , we employ voronoi shaping method . we compute the shaping gain of these lattice codes at low dimensions . finally , we conduct simulations providing numerical results to reveal the effectiveness of qc - ldpc lattices in terms of fundamental coding gain and symbol error probability . this paper is organized as follows . in section  [ preliminaries ] , we provide some preliminaries about lattices . the definition of qc - ldpc lattices is also presented in this section . in section [ encoding ] , the generator matrix of qc - ldpc lattices in different cases is obtained . in section  [ decod ] , we propose a practical method for encoding of qc - ldpc lattices . we also present two decoding methods for qc - ldpc lattices based on sum - product decoding algorithm of ldpc codes . in section  [ shaping_sec ] , voronoi shaping method is applied to qc - ldpc lattices and shaping gain / loss of these lattices at low dimensions are computed approximately . in section  [ simulations ] , we present the simulation results of the error decoding performance . section  [ conclusionandsuggestionforlaterresearch ] contains the concluding remarks . * notation * : matrices and vectors are denoted by bold upper and lower case letters . the @xmath9 element of a vector @xmath10 is denoted by @xmath11 and the @xmath12 entry of a matrix @xmath13 is denoted by @xmath14 unless otherwise stated . @xmath15^t$ ] denotes the transposition for vectors and matrices .","summary":"we provide a low - complexity decoding algorithm of qc - ldpc lattices based on sum product algorithm . to design lattice codes , qc - ldpc lattices are combined with nested lattice shaping that uses the voronoi region of a sublattice for code shaping . the shaping gain and shaping loss of our lattice codes with dimensions , and using an optimal quantizer , are presented . ldpc lattice , qc - ldpc codes , shaping .","abstract":"ldpc lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions . in this paper , we introduce quasi cyclic low density parity check ( qc - ldpc ) lattices as a special case of ldpc lattices with one binary qc - ldpc code as their underlying code . these lattices are obtained from construction a of lattices providing us to encode them efficiently using shift registers . to benefit from an encoder with linear complexity in dimension of the lattice , we obtain the generator matrix of these lattices in _ quasi cyclic _ form . we provide a low - complexity decoding algorithm of qc - ldpc lattices based on sum product algorithm . to design lattice codes , qc - ldpc lattices are combined with nested lattice shaping that uses the voronoi region of a sublattice for code shaping . the shaping gain and shaping loss of our lattice codes with dimensions , and using an optimal quantizer , are presented . consequently , we establish a family of lattice codes that perform practically close to the sphere bound .    ldpc lattice , qc - ldpc codes , shaping ."}
{"article_id":"0903.4238","section_id":"i","document":"let @xmath5 be the quantum enveloping algebra associated to an affine algebra @xmath6 without derivation . let @xmath7 be finite - dimensional @xmath5-modules . suppose @xmath8 is irreducible and @xmath7 have crystal bases @xmath9 . then it is known @xcite that there exists a unique map @xmath0 from @xmath10 to @xmath11 commuting with any crystal operators @xmath12 and @xmath13 . there also exists an integer - valued function @xmath14 on @xmath10 , called energy function , satisfying a certain recurrence relation under the action of @xmath12 ( see ) . combinatorial @xmath0-matrices or energy functions play an important role in the affine crystal theory . in the kyoto path model @xcite , that realizes the affine highest weight crystal in terms of a semi - infinite tensor product of perfect crystals , the energy function is an essential ingredient for the computation of the affine weight . in the box - ball system @xcite or its generalizations @xcite in the formulation of crystal bases , the time evolution of the system is defined by using the combinatorial @xmath0-matrix . energy functions are also crucial in the calculation of conserved quantities . in @xcite a new connection was revealed between the energy function and the kkr or kss bijection @xcite that gives a one - to - one correspondence between highest weight paths and rigged configurations . recently , for all nonexceptional affine types , all kr crystals , crystal bases of kirillov  reshetikhin ( kr ) modules ( if they exist ) , were shown to exist and their combinatorial structures were clarified @xcite . hence , it is natural to consider the problem of obtaining a rule to calculate the combinatorial @xmath0-matrix and energy function .    in this paper , for type @xmath2 we calculate the image of the combinatorial @xmath0-matrix for any classical highest weight element in the tensor product of kr crystals @xmath1 ( theorem [ th : main ] ) . ( note that the first upper index of the second component is 1 . ) we also obtain the value of the energy function for such elements . although we get the rule only for highest weight elements , there is an advantage from the computational point of view , since it is always easy to calculate the action of crystal operators @xmath15 for @xmath16 not only by hand but also by computer . to identify highest weight elements in the image @xmath4 the notion of @xmath3-diagrams , introduced in @xcite , is used effectively . the paper is organized as follows . in section 2 we briefly review crystals and @xmath3-diagrams . in section 3 we recall the kr crystal @xmath17 for type @xmath18 and @xmath19 , and the notion of combinatorial @xmath0-matrix and energy function . the condition for an element of @xmath1 or @xmath4 to be classically highest is also presented . the main theorem is given in section 4 . in section 5 we prove a special case of the theorem , and reduction to this case is discussed in section 6 according to whether @xmath20 is odd or even . mo was supported by grant jsps 20540016 . the work of rs is supported by the core research for evolutional science and technology of japan science and technology agency .","summary":"we calculate the image of the combinatorial-matrix for any classical highest weight element in the tensor product of kirillov  reshetikhin crystals of type . the notion of-diagrams is effectively used for the identification of classical highest weight elements in .","abstract":"we calculate the image of the combinatorial-matrix for any classical highest weight element in the tensor product of kirillov  reshetikhin crystals of type . the notion of-diagrams is effectively used for the identification of classical highest weight elements in ."}
{"article_id":"1101.4927","section_id":"i","document":"consider a finite set @xmath1 of cardinality at least @xmath2 . we denote by @xmath4 the complement @xmath5 for any subset @xmath6 of @xmath1 . and we call a bipartition @xmath7 into a proper non - empty subset @xmath6 of @xmath1 and its complement @xmath8 a _ split _ or , more specifically , an @xmath1-_split_. for any non - empty collection @xmath9 of @xmath1-splits , we define the _ buneman graph _ @xmath10 to be the graph whose vertex set @xmath11 consists of all maps @xmath12 from @xmath9 into the power set @xmath13 of @xmath1 that satisfy , for all @xmath14 , the following two conditions    x    @xmath15 , i.e. , if @xmath7 , then @xmath16 or @xmath17 , and    @xmath18 . and we define its edge set @xmath19 to consist of all those subsets @xmath20 of @xmath11 for which the _ difference set _ @xmath21 , defined by @xmath22 has cardinality @xmath23 . we also denote by @xmath24 the superset of @xmath11 consisting of _ all _ maps @xmath25 that just satisfy ( bg1 ) ( but not necessarily ( bg2 ) ) . and we define the _ extended buneman graph _ @xmath26 to be the ( necessarily connected ) graph with vertex set @xmath27 and edge set @xmath28 defined exactly as @xmath19 above , yet with @xmath29 replaced by @xmath27 in its definition . note that @xmath30 is clearly isomorphic to an @xmath31-dimensional hypercube . an example of a buneman graph is pictured in figure  [ example ] . note that some of the vertices of the graph are labelled by elements in @xmath1 . this arises from a canonical labelling map @xmath32 mapping @xmath1 into the vertex set of @xmath33 , where , for each @xmath34 , @xmath35 denotes the map in @xmath11 that associates , to any @xmath36 , that subset @xmath37 of @xmath1 in @xmath38 that contains @xmath39 . clearly , this map is necessarily contained in @xmath11 . in particular , the cardinality of @xmath11 must be at least @xmath2 for any non - empty collection @xmath9 of @xmath1-splits . , the buneman graph @xmath40 for the collection @xmath41 of @xmath1-splits given by @xmath42 ( where , for example , @xmath43 denotes the @xmath1-split @xmath44 ) . the vertex @xmath12 is a cut - vertex of @xmath40 . , width=264,height=132 ]    the buneman graph has appeared in the literature in various guises : as a co - pair hypergraph in @xcite , as a special type of median graph in e.g.@xcite ( see also @xcite for a review of median graphs ) , and in the above form in @xcite . in addition , buneman graphs and median networks are regularly used to help analyze viral or mitochondrial sequence data gathered from populations ( see e.g. @xcite ) .    it is a well - known basic fact essentially established by peter buneman in 1971 ( cf . @xcite ) that @xmath33 is a tree if and only if any two splits @xmath45 in @xmath0 are _ compatible _ , i.e. , if and only if , for any two splits @xmath46 in @xmath0 , one of the four intersections @xmath47 is empty .    here , we will generalize this fact in a rather natural way as follows : given _ any _ split system @xmath0 , let @xmath48 denote the set of connected components of the so - called _ incompatibility graph _ @xmath49 of @xmath0 , i.e. , the graph with vertex set @xmath9 whose edge set consists of all pairs of splits contained in @xmath9 that are _ not _ compatible . for example , for @xmath50 the collection of splits in figure  [ example ] , @xmath51 consists of five cliques , _ viz _ @xmath52 , @xmath53 , @xmath54 , @xmath55 and @xmath56 . further , let @xmath57 denote the ( by construction necessarily bipartite ) graph with vertex set @xmath58 the disjoint union of @xmath59 and @xmath48 and edge set @xmath60 the set of all pairs @xmath61 with @xmath62 , and @xmath63 for all @xmath64 and all @xmath65 for some  or , equivalently , every  split @xmath66 . then , this graph @xmath67 is always a tree ( theorem  [ xtree ] ) . for example , the tree @xmath68 for the split system @xmath50 referred to in figure  [ example ] is presented in figure  [ construction ] ( a ) in the last section .    to establish this fact , we will first introduce appropriate notations and discuss some generalities in section  [ preliminaries ] . then , in the next section , we will study the _ cut vertices _ of @xmath33 , that is , the vertices @xmath69 of @xmath33 for which the induced subgraph @xmath70 of @xmath33 with vertex set @xmath71 is disconnected ( see e.g. figure  [ example ] ) . remarkably , these vertices can be characterized in quite a few equivalent ways ( cf . theorem [ cut - vertex ] ) . in particular , given any map @xmath72 , one can define as many as at least eight significantly distinct graphs all of which have the property that there is a canonical one - to - one correspondence between their connected components and the connected components of @xmath70 . so , a map @xmath72 is a cut vertex if and only if any of these graphs is disconnected .    in section [ blocks ] , we shall use the cut vertices to provide an explicit description of the _ blocks _ ( or _ two - connected components _ ) of @xmath33 @xcite , that is , the maximal subsets @xmath73 of @xmath11 for which the graph induced on @xmath73 is connected and does not contain a cut vertex . more specifically , we will show that there is a canonical one - to - one correspondence between @xmath48 and the set @xmath74 of blocks of @xmath33 given by associating , to each connected component @xmath75 of @xmath49 , the set @xmath76 consisting of all maps @xmath72 with @xmath77 , see theorem  [ blockbijection ] for details . thus , for example , we see that in figure  [ example ] the buneman graph has 5 blocks that correspond to the 5 cliques in the associated incompatibility graph .    and finally , in the last section , we will establish the above - mentioned generalization of peter buneman s result from 1971 . in addition , we will establish some refinements that will allow us to associate , to any split system @xmath0 , a  proper \" @xmath1-tree @xmath78 , i.e. , a triple @xmath79 consisting of a tree with vertex set @xmath80 and edge set @xmath81 , and a labelling map @xmath82 such that the degree of any vertex in @xmath80 that is not contained in the image of @xmath83 is at least @xmath84 . for example , the tree @xmath85 for the split system @xmath50 in figure  [ example ] is presented in figure  [ construction ] ( b ) . note that besides providing important structural information concerning the buneman graph ( and median networks  see e.g. @xcite ) , cut vertices have been used to help in the computation of most parsimonious trees for dna - sequence data ( see e.g. @xcite ) . and the blocks of @xmath3 determined by them are also closely related to the `` blobs '' defined in terms of directed graphs described by d. gusfield et al .  in @xcite ( see also e.g. @xcite ) .    in @xcite , we will use the results described above to show that @xmath3 can be described as a push - out in terms of the data involved in the construction of @xmath57 , and discuss further potential applications .","summary":"this graph has several interesting mathematical properties  for example , it is a median network and therefore an isometric subgraph of a hypercube . it is commonly used as a tool in studies of dna sequences gathered from populations . in this paper split , split system , buneman graph , median graph , cut vertex , block , compatible partitions ,-tree , phylogenetics + classification numbers : 05c05 , 05c40 , 05c90 , 92b10 , 92d15","abstract":"given a set of bipartitions of some finite set of cardinality at least , one can associate to a canonical-labeled graph , called the buneman graph . this graph has several interesting mathematical properties  for example , it is a median network and therefore an isometric subgraph of a hypercube . it is commonly used as a tool in studies of dna sequences gathered from populations . in this paper , we present some results concerning the _ cut vertices _ of , i.e. , vertices whose removal disconnect the graph , as well as its _ blocks _ or-_connected components _  results that yield , in particular , an intriguing generalization of the well - known fact that is a tree if and only if any two splits in are compatible .    split , split system , buneman graph , median graph , cut vertex , block , compatible partitions ,-tree , phylogenetics + classification numbers : 05c05 , 05c40 , 05c90 , 92b10 , 92d15"}
{"article_id":"0710.5479","section_id":"i","document":"in quantum phase space methods , operators in a hilbert space are mapped to functions in a `` mock '' phase space  @xcite . one example is the wigner representation which is particularly useful for establishing quantum - classical correspondence . in the wigner representation , the wigner function represents a density matrix operator @xmath1 with a quasi - probability distribution in classical phase space . the wigner functions are conveniently applied in semiclassical methods  @xcite , to visualize or characterize quantum states , and experimentally allows one to recover information of quantum systems through tomographic measurements of their phase - space distributions  @xcite .    in the related weyl function representation @xcite , the hilbert space operators are mapped to functions in a `` reciprocal phase space '' where each function is simply a fourier transform of those in the wigner representation . in particular , weyl function @xmath2 is the fourier transform of the wigner function @xmath3 over the phase space coordinates  @xmath4  @xcite . the weyl function can also be expressed as : @xmath5 here @xmath6 and @xmath7 are the position and momentum operators , and @xmath8 is the displacement operator  @xcite , that shifts the density matrix by @xmath9 in momentum and @xmath10 in position . thus the weyl function @xmath2 is a phase - space correlation function that measures the coherence of matter - waves . though both weyl and wigner functions completely specify any density matrix operators , application of weyl function , or the fourier transform of the wigner function , has been much less discussed before  @xcite .    in this work , we demonstrate the power of the weyl function technique by applying it to an important class of wave interference phenomena , the talbot - lau effects associated with matter - waves in quadratic or periodic potentials . various examples of talbot - lau type interference , including those closely related to recent experiments  @xcite , are discussed . to our knowledge , this work gives the first vectorial and diagrammatic formula of talbot - lau effects . apart from the expected application in matter - wave optics , the formula may also provide a convenient framework for the design of various lens - less imagine systems  @xcite . periodic light wavefronts can repeatedly reconstruct themselves during free propagation . the phenomena is known as the talbot effect that was discovered by henry f. talbot  @xcite in 1836 . a demonstration of the talbot effect usually starts with a collimated monochromatic light with wavelength @xmath11 . the light passes through a transmission grating with a grating constant @xmath12 to generate a periodic wavefront . full or partial re - constructions of the transmission wavefront at integer or fractional multiples of the talbot distance @xmath13 are observed downstream . many intricate and elegant features of the talbot phenomena have been discussed in the literature  @xcite . instead of using a collimated or spatially coherent input , in 1948 ernst lau  @xcite found that spatially incoherent light , propagating through two gratings with same grating constant @xmath12 separated by a distance @xmath14 , can generate an interference pattern at the focal plane of a lens ( fraunhofer diffraction ) placed downstream from the second grating . the contrast of the interference is maximized if @xmath14 takes integer multiples of @xmath15 . more general than fraunhofer diffraction , in the lau effect the interference pattern appears at a distance @xmath16 downstream from the second grating where @xmath17 are two integers . lau s original discovery corresponds to @xmath18  @xcite .    instead of using light waves , both the talbot  @xcite and the lau effects @xcite have been demonstrated using matter - waves and in particular using neutral atoms . interferometry with multiple gratings using the lau effect is referred to as talbot - lau or talbot - vonlau interferometry ( tli ) . the lau effect is of particular interest for observing matter - wave interference in the circumstances where a bright and collimated matter - wave input is not available . talbot - lau interferometers are used to demonstrate wave properties of atoms and molecules  @xcite , to study decoherence  @xcite and to measure the polarizability of large molecules  @xcite . talbot - lau interferometers have also been explored to sense inertial forces with matter - waves  @xcite .    based on fresnel diffraction , matter - wave talbot and lau effects can also happen in the time domain instead of in the spatial domain , due to the equivalence of schdinger s equation and the paraxial wave equations . matter - wave talbot  @xcite and lau  @xcite effects in the time domain have been observed with atoms cooled down to a thermal velocity of centimeters per second or lower . in the time domain , spatially separated gratings are replaced by successive pulses of optical standing waves acting as either phase or amplitude gratings for the matter - waves . time - domain interferometry using optical standing wave pulses with laser - cooled atoms were pioneered by the authors of ref . @xcite . in that experiment , off - resonant standing wave pulses act as thin phase gratings to an atomic cloud . after each standing wave pulse the atoms bunch to the potential minima of the standing wave to form a density grating . the density grating washes out due to velocity spreading of atoms . however , with two successive standing wave pulses separated by time @xmath19 applied to atoms , the atomic density grating revives around time @xmath20 if @xmath21 and more generally if @xmath22 , where @xmath23 is an integer . the contrast of the revived density grating is a periodic function of @xmath19 , similar to the spatial lau effect . the revived atomic density grating is probed using a bragg - scattering of a probe light to induce a grating echo  @xcite , and the interferometry based on this setup is referred as a time - domain grating echo interferometer  @xcite . experiments and the theory of the interferometry were further developed in ref . @xcite that generalizes the technique to include multiple standing wave pulses . recently a direct spatial image of sub - wavelength spatial interference pattern due to the lau effect after two standing wave pulses ( act as either amplitude or phase gratings ) is achieved using an on - resonant standing wave mask  @xcite . developed theories of matter - wave talbot - lau effect ( tle ) usually simplify the analysis by making particular assumptions on the coherence properties of input matter - waves . closely related to the spatial ( beam ) talbot - lau setup with amplitude transmission gratings , in the first approach  @xcite the atom flux through each opening of the first grating are treated essentially as individual point sources , from which the fresnel diffraction on the image plane is calculated . an incoherent sum of the contribution from all the openings at the @xmath24 grating gives the final interference pattern . instead of incoherent summation of point sources , the second approach  @xcite assumes the input atoms as an incoherent sum of plane waves . however , a general theory of talbot - lau interferometry applicable to matter - waves with arbitrary initial spatial coherence hasnt been presented in the literature .    the approach to tle in this work is motivated by an obvious link between the weyl function [ eq . ( [ weyldefine ] ) ] and the time - domain matter - wave tle due to a sequence of standing wave pulses . in the following we consider a single atom picture with atomic motion characterized by a density matrix operator @xmath25 . tle corresponds to a revival of atomic density grating at a certain time t. since the revived density grating is spatially periodic , we shall consider its particular @xmath26 component given by : @xmath27 where @xmath28 is the weyl function defined in eq . ( [ weyldefine ] ) .    to express eq . ( [ rhoqdefine ] ) in terms of an arbitrary initial condition described by @xmath29 , one can propagate @xmath30 forward in time by considering the interaction of atoms with a sequence of standing wave pulses . alternatively , we shall define the time - dependent displacement operator @xmath31 in the heisenberg picture and propagate the displacement operator @xmath32 backward in time . here we take the latter approach which is advantageous for two reasons : 1 ) it applies to general initial conditions . 2 ) as we will see , the equation of motion for @xmath33 due to pulsed periodic potentials , during free - propagations and due to a quadratic potential can be integrated easily . since our analysis is generally applied to different types of interferometers using tle , we shall generally consider an interferometry configuration using tle as a talbot - lau interferometer , that will be referred to with the abbreviation tli in this work .      in what follows the paper is organized into three sections . in the first section we introduce a diagrammatic technique to calculate the grating echo of an n - pulse tli in free - space . in the second part we discuss the application of the theory to matter - waves in a quadratic potential . in the discussion section we extend the formula to include arbitrary grating transmission functions , discuss the weyl function representation of matter - wave coherence , and compare the approach here with other diagrammatic techniques  @xcite .","summary":"we conclude the paper with a general discussion on the weyl function representations of matter - wave coherence , and relate the conservation of matter - wave coherence with the conservation of purity that distinguishes decoherence effects from dephasing effects .","abstract":"weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials . in this work we use weyl functions to study the `` talbot - lau effect '' in a time - domain matter - wave interferometer . a `` displacement diagram '' is introduced to analyze and calculate the matter - wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo . unlike previous treatments , this new approach allows the atomic ensemble to have an arbitrary initial phase - space distribution , and the standing wave grating vectors to span three dimensions . several examples are discussed to illustrate the convenience of the diagrammatic technique including the following : a two - dimensional talbot - lau effect , the shift in the echo time and the recoil phase for the interferometer perturbed by a quadratic potential ; and the realization of a time - domain `` lau effect '' using a pulsed harmonic potential . the diagrammatic technique is applicable to diffraction gratings with arbitrary grating transmission functions . we conclude the paper with a general discussion on the weyl function representations of matter - wave coherence , and relate the conservation of matter - wave coherence with the conservation of purity that distinguishes decoherence effects from dephasing effects ."}
{"article_id":"0710.5479","section_id":"c","document":"the discussion so far has been restricted to grating potentials using sinusoidal light shifts . in the following we shall discuss the generalization of the formula to include arbitrary grating transmission functions . we shall first modify the light shift in eq . ( [ waveequ ] ) to include an imaginary part , e.g. , @xmath328 , with @xmath329 . the imaginary part of the light shift potential could be due to the optical pumping effect of the light pulses  @xcite that act as an amplitude mask for atoms . more generally , the imaginary potential could also describe a particular harmonic component of an absorptive material grating  @xcite . following the principle of analytical continuation , equation  ( [ wignerrule2 ] ) and the scattering diagram in fig . [ proprulefig](b ) can be modified to include this imaginary part as ( appendix a ) : @xmath330 where @xmath331    for a general amplitude / phase grating that has more than one spatial fourier component in its transmission function , in eq . ( [ wignerrule2b ] ) @xmath332 has to sum over contribution from all the fourier components for the @xmath333 grating , e.g. , @xmath334 where @xmath335 give the effective pulse area due to the @xmath336 order harmonic of the grating potential , @xmath337 and @xmath338 . notice here in eqs . ( [ wignerrule2b ] ) ,  ( [ wignerrule2c ] ) ,  ( [ sumharmonic ] ) and also in eq . ( [ wignerrule2 ] ) the subindex @xmath36 is used to refer to the @xmath333 pulse in a tli in fig . [ npulserulefig ] , and can in fact be ignored for convenient reading .    to detect the resulting atomic density grating as the output of tli , in this paper we have considered the method of a grating echo using bragg scattering of a probe light , that is formulated in eq . ( [ backamp ] ) . another detection method frequently used for matter gratings and for resonant standing wave masks is instead to monitor the overall transmission after an amplitude grating  @xcite . the formula developed in this work , e.g. , eq . ( [ backamp ] ) and fig .  [ proprulefig](c ) can be modified accordingly to ( coherently ) sum over the interaction with all the spatial harmonics of the transmission grating . we end up with the transmission signal @xmath339 given by [ compare with eq . ( [ backamp ] ) ] : @xmath340 where @xmath341 is the coefficient of the @xmath336 order spatial harmonic of the @xmath133 grating transmission function .      in this work we discussed using weyl functions to study the talbot - lau effect ( in three dimensions ) in free space and in a quadratic potential . we now come back to eq . ( [ weyldefine ] ) to discuss the weyl function as a measure of matter - wave coherence , and compare the `` displacement diagram '' technique here with the `` recoil diagram '' introduced by the authors of ref . @xcite that has been widely used in the atom interferometry community  @xcite . we come back to eq . ( [ weyldefine ] ) . as mentioned in the introduction , @xmath28 measures the overlap , or the second order field - correlation of matter - waves displaced in phase space by @xmath342 . as a particular example , @xmath343 measure the spatial coherence of a wavepacket before and after a particular displacement @xmath84 , which is also called the longitudinal coherence in matter - wave interferometry  @xcite . in  @xcite it was pointed out that longitudinal coherence is conserved during free evolution , which is a fairly counterintuitive observation since wavepackets of atoms may expand a lot and one may suspect the coherence length of the wavepackets increases accordingly . the conservation of @xmath344 during free evolution is only a particular example of eq . ( [ wignerrule1 ] ) , which more generally describes the conservation of matter - wave coherence that propagates in reciprocal phase space @xmath82 . in particular , momentum coherence of matter - waves given by @xmath345 is a fourier component of atomic density grating ( fringes ) , that propagates according to @xmath346 but with conserved magnitude . these propagating coherences reflect the correlation of matter - waves at different locations with different velocities , though they can not be measured directly with any _ local measurement _ , except those on the axis @xmath347 . equation  ( [ wignerrule2 ] ) or  ( [ wignerrule2b ] ) show how these phase space coherence can be manipulated with periodic potentials to create a revived momentum coherence @xmath348 for a local measurement .    even more generally , it is easy to see from eq . ( [ weyldefine ] ) the identity  @xcite @xmath349 which is equal to @xmath350 , the purity or linear entropy of matter - waves  @xcite . matter - wave entropy is conserved in a non - dissipative / isolated potential , which may also be interpreted as a conservation of matter - wave coherence through the weyl function , given by : @xmath351      ) . b ) recoil diagram of a 3-pulse grating echo interferometer ( the correspondent displacement diagram is given by fig . [ 1dexpfig1 ] ) . standing wave is pulsed at time @xmath235 , @xmath232 . at around time @xmath159 the billiard balls along each line cross each other to create interference . the circles of `` billiard balls '' are not shown . , title=\"fig:\",width=192 ] +    the recoil diagram was introduced by the authors of ref . @xcite together with a `` billiard ball model '' of atom wavepackets to explain the photon echo phenomena , and also the ramsey interference and two - photon echo in matter - wave interferometry  @xcite . in a ( x - t ) recoil diagram such as fig . [ recoildiagramfig](a ) , lines represent the trajectories of centers of wavepackets diffracted by optical pulses . the wavepackets are represented with `` billiard balls '' with a fixed radius equal to the coherence length of the wavepackets . matter - wave interferes whenever two billiard balls cross each other . the visibility of the interfering fringe relies on the overlap of the billiard balls , while the fringe position is determined by the relative phase between the two wavepackets . a rigorous justification of using the `` billiard ball model '' is presented in  @xcite , which is related to the conclusion in ref . @xcite and also our previous discussion . examples of recoil diagrams due to a standing wave pulse ( displacement diagram in fig . [ iniconditionfig ] ) , and for an `` equal time 3-pulse '' ( displacement diagram in fig . [ 1dexpfig1 ] ) grating echo interferometer is shown in fig . [ recoildiagramfig ] ( a ) , ( b ) respectively . in contrast to the recoil diagram that concerns the coherence between individual pairs of wavepackets [ such as the green path in fig . [ recoildiagramfig](b ) ] , the displacement diagram describes the overall coherence of the atomic sample , which is a sum of the coherence amplitudes between all pairs of the wavepackets with a same relative phase - space displacement . the displacement diagram is particularly convenient to describe the overall coherence of multiple diffraction orders , particularly when a sequence of multiple diffractions is considered ( such as an n - pulse sequence given by fig . [ npulserulefig ] ) . the overall coherence of an atomic sample is directly related to interference readouts in most interferometry setups where the interference fringes are retrieved across the whole atomic sample . finally , it is instructive to consider the dephasing effect in both the recoil diagram picture and in the displacement diagram picture . for a matter - wave interferometer perturbed by an external potential , the phase of wavepackets may be in - homogeneously broadened that reduce the overall coherences of matter - waves and thus the fringe contrast . this is referred to as a dephasing effect . dephasing effects can be described by a recoil diagram , by assigning each  billiard ball with a different phase and by varying the `` radius of the billiard ball '' to account for wavepacket distortions .    in the displacement diagram picture , the dephasing effect broadens and shifts the weyl function distribution in the reciprocal phase space , for example , the dephasing effect due to a quadratic potential corresponds to a shift of weyl function described by eq . ( [ harmonicexten ] ) . however , any broadenings or shifts of weyl function distribution need to obey the conservation law given by eq . ( [ eqwconserv ] ) . in contrast , the reduction of interferometer fringe visibility accompanied by a violation of eq . ( [ eqwconserv ] ) is due to a loss of information or an increase of entropy in the matter - wave system , and should be referred to as decoherence effects  @xcite . we have generally discussed a vector theory of talbot - lau effects due to n standing wave pulses by considering an n - pulse grating echo interferometry configuration ( fig . [ gratingechotlifigure ] ) . a displacement diagram ( figs . [ proprulefig ] and  [ harmonicfig ] ) is introduced to calculate the grating echo diagrammatically . to illustrate the convenience of the diagrammatic technique , we discuss examples of tli that are related to recent experiments  @xcite , in particular , we discuss an example tli with standing wave k - vector span two dimensions . we study the dephasing of these tli schemes due to harmonic confinements ( table  [ tabletliexamples0 ] ) , and predict the echo shift [ eq . ( [ echoshift0 ] ) ] and the recoil phase shift [ eq . ( [ recoilshift0 ] ) ] that have been observed experimentally  @xcite . these effects should be useful to measure the curvature of an atomic potential . the displacement diagram method is further extended to include a pulsed harmonic trap [ eq .  ( [ wignerrule1d ] ) ] and we discuss a time - domain version of the original lau effect [ eq . ( [ equlau ] ) ] . using the displacement diagram in a tightly confined trap , we give the expression of the atomic density grating revivals [ eq .  ( [ harmonicrevival ] ) ] . the formula introduced in this work can be extended to describe tle due to diffraction gratings with general grating transmission functions . application of weyl functions in this work has been restricted to talbot - lau effects involving multiple diffraction orders from diffractive gratings . but the method is generalizable to other interferometry configurations with fewer interfering paths . coherences , or `` off - diagonal terms of a density matrix ''  @xcite , have a clear definition in discrete systems but not so clear for matter - waves that have a continuous spectrum  @xcite . in the last part of this work we have briefly discussed weyl function as a convenient measure of matter - wave coherence . weyl function as a phase - space correlation function measures the overlap of matter - waves before and after a phase - space displacement . similar to the definition of the wigner function , equation  ( [ weyldefine ] ) involves _ a fourier transform of off - diagonal part of a density matrix_. the fourier transform removes the ambiguity due to the ill - defined off - diagonal terms , while keeping all the physical information of matter - wave coherences  @xcite . we thus suggest using weyl function to define matter - wave coherence and more generally to define coherences in system with a continuous spectrum . we suggest that according to this definition , a conservation law of matter - wave coherence [ eq . ( [ eqwconserv ] ) ] that directly link to the matte - wave entropy can unambiguously distinguishes decoherence and dephasing effects . practically , it seems that to consider the weyl function or the displacement operator , instead of considering the evolution of particular matter - wave states , is more convenient for elucidating the dynamics of matter - wave coherences during a particular interferometric observation . we thank dr . a. tonyushkin for careful reading and helpful suggestions to the manuscript of this paper .","summary":"weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials . in this work we use weyl functions to study the `` talbot - lau effect '' in a time - domain matter - wave interferometer . a `` displacement diagram '' is introduced to analyze and calculate the matter - wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo . unlike previous treatments , this new approach allows the atomic ensemble to have an arbitrary initial phase - space distribution , and the standing wave grating vectors to span three dimensions . several examples are discussed to illustrate the convenience of the diagrammatic technique including the following : a two - dimensional talbot - lau effect , the shift in the echo time and the recoil phase for the interferometer perturbed by a quadratic potential ; and the realization of a time - domain `` lau effect '' using a pulsed harmonic potential . the diagrammatic technique is applicable to diffraction gratings with arbitrary grating transmission functions .","abstract":"weyl functions conveniently describe the evolution of wave coherences in periodic or quadratic potentials . in this work we use weyl functions to study the `` talbot - lau effect '' in a time - domain matter - wave interferometer . a `` displacement diagram '' is introduced to analyze and calculate the matter - wave interference for an atomic cloud in a quadratic potential that interacts with a sequence of short optical standing wave pulses producing an atomic grating echo . unlike previous treatments , this new approach allows the atomic ensemble to have an arbitrary initial phase - space distribution , and the standing wave grating vectors to span three dimensions . several examples are discussed to illustrate the convenience of the diagrammatic technique including the following : a two - dimensional talbot - lau effect , the shift in the echo time and the recoil phase for the interferometer perturbed by a quadratic potential ; and the realization of a time - domain `` lau effect '' using a pulsed harmonic potential . the diagrammatic technique is applicable to diffraction gratings with arbitrary grating transmission functions . we conclude the paper with a general discussion on the weyl function representations of matter - wave coherence , and relate the conservation of matter - wave coherence with the conservation of purity that distinguishes decoherence effects from dephasing effects ."}
{"article_id":"1309.2209","section_id":"i","document":"the large @xmath0 asymptotics of the hankel functions @xmath1 , @xmath2 , and the bessel functions @xmath3 , @xmath4 , beside theoretical and practical importance , have historical significance . in 1909 , debye @xcite developed the method of steepest descents to deduce asymptotic expansions for these functions with fixed @xmath5 as @xmath6 . since then , these expansions become standard textbook examples to illustrate various techniques , such as the method of steepest descents itself or the method of stationary phase ( see , for example , copson ( * ? ? ? * and pp . 7582 ) ; olver @xcite ; wong @xcite ) . meijer @xcite and olver @xcite were able to derive error bounds for debye s expansions when @xmath7 . meijer s approach was based on the lagrange inversion theorem while olver used differential equation methods . gatteschi @xcite estimated the remainder of debye s series when @xmath8 . dingle @xcite investigated the resurgence properties of debye s expansions and obtained asymptotic approximations for their late terms . nevertheless , the derivation of his results is based on interpretive , rather than rigorous , methods . the drawback of debye s expansions is their non - uniformity in @xmath9 . each expansion has different form according to whether @xmath10 , @xmath8 or @xmath7 . in the first and the third cases , it is also required that @xmath11 . in 1952 , olver @xcite modified the expansions corresponding to @xmath8 , obtaining asymptotic series in the so - called transition regions , i.e. , when @xmath12 is bounded ( see also schbe @xcite ) . two years later , he published new asymptotic expansions for the hankel and bessel functions that are uniformly valid for all @xmath5 @xcite . it might be supposed therefore that there is no need for the non - uniform expansions of debye and that little could be added to their well - established theory . the uniformity of the expansion is an important property , however , in general , uniform asymptotic expansions have much more complicated forms than non - uniform expansions . olver s uniform asymptotic expansions involve the airy functions , whereas debye s ones build from elementary functions . in addition , we have simple recurrence formulas for the coefficients in the latter ones . the coefficients in olver s uniform expansions are slightly more complicated , and their computation requires the ones in debye s series . for the asymptotic properties of these coefficients , see howls and olde daalhuis @xcite . the aim of this paper is to establish new resurgence - type integral representations for the functions @xmath1 , @xmath2 , @xmath3 and @xmath4 when @xmath13 . our derivation is based on the reformulation of the method of steepest descents by berry and howls @xcite ( see also boyd @xcite and paris @xcite ) . here resurgence has to be understood in the sense of berry and howls , meaning that the function reappears in the remainder of its own asymptotic series . using these representations , we obtain several new properties of debye s classical expansions , including explicit and numerically computable error bounds , asymptotics for the late coefficients , exponentially improved asymptotic expansions , and the smooth transition of the stokes discontinuities . our analysis also provides a rigorous treatment of dingle s formal results . our first theorem describes the resurgence properties of the asymptotic expansions of @xmath1 , @xmath2 , @xmath3 and @xmath4 for @xmath14 . we employ the usual substitution @xmath15 with an appropriate @xmath16 . the notations follow the ones given in @xcite . throughout this paper , empty sums are taken to be zero . [ thm1 ] let @xmath16 be a fixed acute angle , and let @xmath17 be a non - negative integer . we have @xmath18 for @xmath19 ; @xmath20 for @xmath21 ; @xmath22 @xmath23 for @xmath24 with @xmath25 . the coefficients @xmath26 are given by @xmath27_{t = 0}\\\\ & = \\frac{i^n}{2\\left ( { 2\\pi \\cot \\beta } \\right)^{\\frac{1}{2}}}\\int_0^ { + \\infty } { t^{n - \\frac{1}{2 } } e^ { -t \\left ( { \\tan \\beta   - \\beta } \\right ) } \\left ( { 1 + e^ { - 2\\pi t } } \\right)i h_{it}^{\\left ( 1 \\right ) } \\left ( { it\\sec \\beta } \\right)dt } . \\end{split}\\end{gathered}\\ ] ] the remainder terms can be expressed as @xmath28 @xmath29 @xmath30 the square roots are defined to be positive on the positive real line and are defined by analytic continuation elsewhere .    using the continuation formulas ( see , e.g. , @xcite ) @xmath31 @xmath32 and the resurgence formulas , and , we can derive analogous representations in sectors of the form @xmath33 respectively . the lines @xmath34 are the stokes lines for the function @xmath35 , and the lines @xmath36 are the stokes lines for the function @xmath37 .    similarly , applying the continuation formulas @xmath38 @xmath39 and the representations  , we can obtain analogous formulas in any sector of the form @xmath40 finally , from @xmath41 @xmath42 and the resurgence formulas  , we can derive the corresponding representations in sectors of the form @xmath43 the lines @xmath44 are the stokes lines for the functions @xmath45 and @xmath46 .    when @xmath0 is an integer , the limiting values have to be taken in these continuation formulas . the second theorem provides resurgence formulas for @xmath47 , @xmath48 , @xmath49 and @xmath50 . the notations follow the ones used by wong @xcite . [ thm2 ] for any non - negative integer @xmath17 , we have @xmath51 for @xmath19 ; @xmath52 for @xmath21 ; @xmath53 @xmath54 for @xmath24 . the coefficients @xmath55 are given by @xmath56_{t = 0 }   = \\frac{{\\left ( { - 1 } \\right)^n } } { { \\gamma \\left ( { \\frac{{2n + 1}}{3 } } \\right)}}\\int_0^ { + \\infty } { t^{\\frac{{2n - 2}}{3 } } e^ { - 2\\pi t } i h_{it}^{\\left ( 1 \\right ) } \\left ( { it } \\right)dt } .\\ ] ] the remainder terms can be expressed as @xmath57 @xmath58 @xmath59 the cube roots are defined to be positive on the positive real line and are defined by analytic continuation elsewhere . again , these formulas can be extended to other sectors of the complex plane like the ones in theorem [ thm1 ] . ( one has to replace the factor @xmath60 by @xmath61 in the continuation formulas given above . )    in section [ section3 ] , we will show how to obtain numerically computable bounds for the remainder terms using their explicit form given in theorems [ thm1 ] and [ thm2 ] . if we neglect these remainder terms and extend the sums to @xmath62 in theorems [ thm1 ] and [ thm2 ] , we recover debye s asymptotic series . some other formulas for the coefficients @xmath63 and @xmath55 can be found in appendix [ appendixa ] .    in the following two theorems , we give exponentially improved asymptotic expansions for the function @xmath64 when @xmath7 and @xmath8 , respectively . the related expansions for the functions @xmath2 , @xmath3 and @xmath4 may be derived from the corresponding connection formulas . the resulting expansions for @xmath3 and @xmath4 can be viewed as the mathematically rigorous forms of the terminated expansions of dingle @xcite . in these theorems we truncate the asymptotic series of @xmath64 at about the least term and re - expand the remainders into new asymptotic expansions . the resulting exponentially improved asymptotic series are valid in larger regions than the original debye expansions . the terms in these new series involve the terminant function @xmath65 , which allows the smooth transition through the stokes line @xmath66 . for the definition and basic properties of the terminant function , see section [ section5 ] . it is interesting to note that for the case @xmath7 , an additional sum is needed for the re - expansion beside the truncated debye series . the appearance of this second sum is due to the presence of the exponential quantity @xmath67 in .    for exponentially improved expansions using hadamard series , see paris @xcite , @xcite . [ thm3 ] let @xmath68 be a fixed acute angle . define @xmath69 by @xmath70 where @xmath71 @xmath72 @xmath73 being large , @xmath74 and @xmath75 being bounded quantities such that @xmath76 . then @xmath77 where @xmath78 and @xmath79 are arbitrary fixed non - negative integers , and @xmath80 for @xmath81 , @xmath82 for @xmath83 . [ thm4 ] define @xmath84 by @xmath85 where @xmath86 @xmath73 being large , @xmath74 and @xmath75 being bounded quantities such that @xmath87 . then @xmath88 where @xmath78 and @xmath79 are arbitrary fixed non - negative integers satisfying @xmath89 , and @xmath90 for @xmath91 , @xmath92 for @xmath93 . moreover , if @xmath94 then the bound remains valid in the larger sector @xmath95 . the assumption that @xmath89 is only for simplicity . estimations for @xmath96 when @xmath78 or @xmath79 may not be divisible by @xmath97 can be obtained similarly . the rest of the paper is organised as follows . in section [ section2 ] , we prove the resurgence formulas stated in theorems [ thm1 ] and [ thm2 ] . in section [ section3 ] , we give explicit and numerically computable error bounds for debye s expansions when @xmath13 using the results of section [ section2 ] . in section [ section4 ] , asymptotic approximations for the late terms in debye s expansions are given . in section [ section5 ] , we prove the exponentially improved expansions presented in theorems [ thm3 ] and [ thm4 ] , and provide a detailed discussion of the stokes phenomenon related to the expansions of @xmath64 . the paper concludes with a discussion in section [ section6 ] .","summary":"the aim of this paper is to derive new representations for the hankel and bessel functions , exploiting the reformulation of the method of steepest descents by m. v. berry and c. j. howls ( berry and howls , proc . lond . a * 434 * ( 1991 ) 657675 ) . using these representations , we obtain a number of properties of the large order asymptotic expansions of the hankel and bessel functions due to debye , including explicit and numerically computable error bounds , asymptotics for the late coefficients , exponentially improved asymptotic expansions , and the smooth transition of the stokes discontinuities .","abstract":"the aim of this paper is to derive new representations for the hankel and bessel functions , exploiting the reformulation of the method of steepest descents by m. v. berry and c. j. howls ( berry and howls , proc . r. soc . lond . a * 434 * ( 1991 ) 657675 ) . using these representations , we obtain a number of properties of the large order asymptotic expansions of the hankel and bessel functions due to debye , including explicit and numerically computable error bounds , asymptotics for the late coefficients , exponentially improved asymptotic expansions , and the smooth transition of the stokes discontinuities ."}
{"article_id":"0904.2301","section_id":"i","document":"one of the outstanding problems for high - energy physics remains the understanding of the dynamics of flavor . existing experimental results on kaon , @xmath1-meson , @xmath0-meson , and hyperon decays , as well as neutral - meson mixing , are all consistent with the loop - induced nature of flavor - changing neutral currents ( fcnc s ) in the standard model  ( sm ) and also with the unitarity of the cabibbo - kobayashi - maskawa ( ckm ) matrix with three generations . the continuing study of these processes with increased precision will play a crucial role in the search for physics beyond the  sm .    in many types of new physics , the new particles are heavier than their sm counterparts and their effects can be described by an effective low - energy theory . a complete set of operators of dimension six describing deviations from the sm has been presented in ref . a less ambitious program is to study only those operators that appear when the new physics effectively modifies the sm couplings between gauge bosons and certain fermions  @xcite . the case of anomalous top - quark couplings has been treated before in the literature  @xcite , and it was found that they are most tightly constrained by the @xmath3 decay . interestingly , this mode does not place severe constraints on anomalous charm - quark couplings due to the relative smallness of the charm mass .    in this paper we focus on new physics affecting primarily the charged weak currents involving the charm quark . including the sm term , the effective lagrangian in the unitary gauge for a  general parametrization of anomalous interactions of the @xmath2 boson with an up - type quark @xmath4 and a  down - type quark @xmath5 can be written as @xmath6 d_l^{}\\ , w_\\mu^+ \\,\\,+\\,\\ , { \\rm h.c . } \\,\\,,\\end{aligned}\\ ] ] where @xmath7 is the weak coupling constant , we have normalized the anomalous couplings @xmath8 relative to the usual ckm - matrix elements @xmath9 , and @xmath10 . in general , @xmath8 are complex and , as such , provide new sources of @xmath11 violation . in appendix  [ keff ] we discuss the general parametrization of the quark - mixing matrix underlying eq . ( [ ludw ] ) , paying particular attention to the number of independent parameters that are allowed . in addition to affecting weak decays though tree - level interactions , the new couplings in eq . ( [ ludw ] ) modify effective flavor - changing and -conserving couplings at one loop . in this work , we evaluate several one - loop transitions induced by the new couplings via magnetic - dipole , penguin , and box diagrams . we include the operators generated this way in our phenomenological analysis . we present a comprehensive picture of existing constraints which shows that deviations from sm couplings at the percent level are still possible , particularly for right - handed interactions . our study will also serve as a guide as to which future measurements provide the most sensitive tests for new physics that can be parametrized with anomalous @xmath2-boson couplings to the charm quark . for the @xmath11-violating ( imaginary ) parts of the couplings , the electric dipole moment of the neutron and the hyperon asymmetry @xmath12 are the most promising channels to probe for right - handed couplings , whereas more precise measurements of @xmath13 and @xmath14 are the most promising probes for left - handed couplings . constraints on the real parts of the right - handed couplings can be further improved with better measurements of semileptonic @xmath0 and @xmath1 decays .","summary":"low - energy experiments involving kaon ,-meson ,-meson , and hyperon flavor - changing neutral transitions have confirmed the loop - induced flavor - changing neutral current ( fcnc ) picture of the standard model  ( sm ) . the continuing study of these processes is essential to further refine this picture and ultimately understand the flavor dynamics . in this paper specifically , we parametrize new physics in terms of left- and right - handed anomalous couplings of the boson to the charm quark . we present a comprehensive study of existing constraints and point out those measurements that are most sensitive to new physics of this  type .","abstract":"low - energy experiments involving kaon ,-meson ,-meson , and hyperon flavor - changing neutral transitions have confirmed the loop - induced flavor - changing neutral current ( fcnc ) picture of the standard model  ( sm ) . the continuing study of these processes is essential to further refine this picture and ultimately understand the flavor dynamics . in this paper we consider deviations from the sm in the charm sector and their effect on fcnc processes . specifically , we parametrize new physics in terms of left- and right - handed anomalous couplings of the boson to the charm quark . we present a comprehensive study of existing constraints and point out those measurements that are most sensitive to new physics of this  type ."}
{"article_id":"1409.0673","section_id":"c","document":"in this paper , we have demonstrated a general method to construct local , canonical coordinates in the vicinity of a fixed point of a noncanonical hamiltonian system via normal form expansions . the method allows for the general and systematic investigation of noncanonical hamiltonian systems in the vicinity of fixed points . furthermore , it is applicable for systems with arbitrary degrees of freedom , in arbitrary orders of the local expansion , and it is independent of the precise form of the hamiltonian . as a possible field of application , we have discussed a variational approach to quantum systems which defines a noncanonical hamiltonian system for the variational parameters . a further generalization of the method presented here can be achieved by dropping the assumption of rational independence of the eigenvalues . this step will allow to construct the system s canonical normal form also in situations with strong mode coupling of the different degrees of freedom . the general procedure presented in this paper also works in this case , however , additional terms in the normal form hamiltonian will occur . this generalization is currently in progress . due to the additional terms in the normal form and with the above made definition of action variables , one then expects the local canonical hamiltonian to depend on both its action and angle variables , @xmath263 , to which e.g.  classical perturbation theory can be applied in a subsequent step .","summary":"we demonstrate a general method to construct such darboux coordinates in the vicinity of a fixed point of a noncanonical hamiltonian system via normal form expansions . the method is general in the sense that it is applicable for arbitrary degrees of freedom , in arbitrary orders of the local expansion , and it is independent of the precise form of the hamiltonian . the method presented allows for the general and systematic investigation of noncanonical hamiltonian systems in the vicinity of fixed points , which e.g.   correspond to ground , excited or transition states . as an exemplary field of application , we discuss a variational approach to quantum systems which defines a noncanonical hamiltonian system for the variational parameters and which directly allows to apply transition state theory to quantum mechanical wave packets .","abstract":"darboux s theorem guarantees the existence of local canonical coordinates on symplectic manifolds under certain conditions . we demonstrate a general method to construct such darboux coordinates in the vicinity of a fixed point of a noncanonical hamiltonian system via normal form expansions . the procedure serves as a tool to naturally extract canonical coordinates and at the same time to transform the hamiltonian into its poincar - birkhoff normal form . the method is general in the sense that it is applicable for arbitrary degrees of freedom , in arbitrary orders of the local expansion , and it is independent of the precise form of the hamiltonian . the method presented allows for the general and systematic investigation of noncanonical hamiltonian systems in the vicinity of fixed points , which e.g.   correspond to ground , excited or transition states . as an exemplary field of application , we discuss a variational approach to quantum systems which defines a noncanonical hamiltonian system for the variational parameters and which directly allows to apply transition state theory to quantum mechanical wave packets ."}
{"article_id":"astro-ph0404260","section_id":"i","document":"the lynds 1630 ( l1630 ) dark cloud is part of the orion b molecular cloud . at a distance of approximately 450 pc , it is one of the nearest giant molecular clouds . its mass is estimated to be more than @xmath7 m@xmath8   ( maddalena et al . 1986 ) . l1630 shows many signs of on - going star formation : ( _ a _ ) dense cores of molecular gas and high velocity outflows ( snell & edwards 1982 ; gibb & heaton 1993 ; gibb et al . 1995 ) ; ( _ b _ ) bright reflection nebulae ( e.g. , ngc 2068 and ngc 2071 ) ; ( _ c _ ) t tauri stars ( herbig & kuhi 1963 ; wiramihardja et al . 1989 ) ; ( _ d _ ) herbig - haro ( hh ) objects , including the morphologically complex hh2426 ( herbig 1974 ; solf 1987 ; mundt , ray , & raga 1991 ; eislffel & mundt 1997 ) ; ( _ e _ ) luminous far - infrared and submillimeter sources ( cohen et al . 1984 ; cohen & schwartz 1987 ; gibb & heaton 1993 ; schwartz , burton , & herrmann 1997 ; mitchell et al . 2001 ) ; ( _ f _ ) radio continuum sources ( bontemps , andr , & ward - thompson 1995 ; verdes - montenegro & ho 1996 ; reipurth et al . 2002 ) ; and ( _ g _ ) dense clusters of optically obscured near - infrared sources ( strom et al . 1975 ; strom , strom , & vrba 1976 ) . the number density of young stars in l1630 , 450 pc@xmath9 , is comparable with that of the @xmath10  ophiuchus star - forming region ( lada et al . 1991 ) . starting with the work of the stroms , l1630 has been studied in ever increasing detail at infrared wavelengths . particular attention has been focused recently on its many outflows and hh features . evidence for emission in the 2@xmath6 near - infrared lines of h@xmath11 from parsec - scale hh flows and jets has been presented by zealey et al . ( 1992 ) , and more extensively by davis et al . ( 1997 ) and chrysostomou et al . images of hh24 in narrow emission lines at optical and infrared wavelengths trace out at least three intersecting , collimated , bipolar flows ( e.g. , mundt et al . 1991 : fig . 1719 ; davis et al . 1997 : fig . the flows emanate from the vicinity of hh24b , at the location of the bright near - infrared sources ssv63e and ssv63w . both objects are presumed from their steep spectral energy distributions to be class i protostars ( cohen et al . 1984 ) , that is , they are in a very early stage of evolution preceding the t tauri star ( tts ) or so - called class ii phase , and in the process of actively accreting material from their protostellar disks . the dynamical age of hh24 is of the order of @xmath12  yr ( eislffel & mundt 1997 ; snell & edwards 1982 ) , which implies that the class i objects powering those flows must be very young , and also in a very short - lived phase of evolution .    in the past , the bright hh24a knot was interpreted as the `` working surface '' or bow shock for one of those outflows ( mundt et al . 1991 ; solf 1987 ) , but it is now recognized ( e.g. , eislffel & mundt 1997 ) to be the terminus of an independent outflow , which originates in a region immediately to the southwest , at the location of a deeply embedded class  0 protostar , hh24-mms . class  0 objects like hh24-mms represent the main accretion phase for protostars and are extremely rare because their lifetimes are so short . hh24-mms is observed directly at near - infrared wavelengths only in shocked h@xmath11 ( bontemps , ward - thompson , & andr 1996 ; davis et al . it was discovered as a bright source at submillimeter and radio wavelengths ( chini et al . 1993 ; ward - thompson et al . 1995 ; bontemps et al . 1995 ) . greybody fits suggest a color temperature of 20  k and a total luminosity of @xmath13520 l@xmath8 , of which @xmath14 l@xmath8  originates from an unresolved and possibly disk - like central source ( ward - thompson et al . the compact source is surrounded by a much more extended envelope , from which it is most likely accreting material at a very high rate ( chandler et al . 1995b ) . the detection of an h@xmath11 jet , blue - shifted co emission ( bontemps et al . 1996 ) , and indications of disk structure suggest that hh24-mms , even at its remarkably young age , has already begun to drive a powerful collimated outflow into the surrounding molecular cloud . various theories and mechanisms have been advanced in the past to explain such highly focused ( and frequently bipolar ) jets . in the class of magnetic models , for example , it has been proposed that the outflow is confined and driven by interactions between the magnetosphere of the protostar and the primordial field that threads its accretion disk ( e.g. , shu et al . 1994 ) .    south of hh24 , high resolution radio , millimeter , and submillimeter maps have revealed a number of strong molecular peaks and bipolar outflows in the proximity of hh25 and hh26 ( gibb & heaton 1993 ; gibb et al . 1995 ; gibb & davis 1998 ) . the surrounding areas have been extensively mapped in the @xmath15(1 ) line of h@xmath11 at 2@xmath6 ( davis et al . 1997 ; chrysostomou et al . 2000 ; davis et al . a class  0 object , hh25-mms , was discovered @xmath16 south of the optically - visible knot hh25a as both a 1.3-mm and a 3.6-cm source ( bontemps et al . strong 450 and 850@xmath6 continuum emission has been observed from the same location ( mitchell et al . 2001 ; phillips , gibb , & little 2000 ) . the brightest near - infrared objects in the vicinity of hh2526 are ssv59 , ssv60 , and hh26-ir ( strom et al . 1976 ; davis et al . none of the three has been shown conclusively to be the origin of a large - scale flow , although the weight of the evidence for hh26 ( in particular , the discovery of a compact h@xmath11 jet : davis et al . 2002 ) now points most convincingly to hh26-ir . the latter , as well as ssv59 , is generally regarded as a class  i protostar ( e.g. , bontemps et al . 1995 , davis et al . 2002 ) . the status of ssv60 is unknown ; unlike the other two sources , it is associated with neither a submillimeter peak ( lis , menten , & zylka 1999 ; mitchell et al . 2001 ; phillips et al . 2001 ) nor a molecular core ( e.g. , torrelles et al . 1989 ; gibb & heaton 1993 ) .    the same process that drives the outflows and jets of young stellar objects ( ysos ) is expected to result in the repeated shearing and reconnection of the magnetic field lines that attach such a star to its circumstellar disk , and thereby to generate a substantial amount of x - ray emission ( hayashi , shibata , & matsumoto 1996 ; shu et al . 1997 ; goodson , winglee , & bhm 1997 ) . the numerical simulations of hayashi et al . and goodson et al . in particular demonstrated that as a consequence of reconnection events some of the magnetically entrapped gas that is close to an accreting yso ( not necessarily its outflowing jet ) will reach temperatures as high as 100 mk and will be flung outwards , away from the star . such high temperatures should give rise to hard x - ray spectra . x - ray emission at equally high temperatures can also be produced in an accretion shock at the footpoints of the magnetic field , where infalling material from the disk streams down onto the surface of the forming star ( uchida & shibata 1984 ) . the hh2426 region was observed in x - rays with asca for a net exposure time of 30 kiloseconds ( ks ) by ozawa et al . the strongest source in the soft x - ray band ( 0.72.0 kev ) in that observation was ssv61 , a t  tauri star ( tts ) which is embedded in an unusual patch of nebulosity situated mid - way on the sky between hh24 and hh2526 ( e.g. , scarott , gledhill , & warren - smith 1987 ) . strom et al . ( 1975 ) classified the star as an m2m4 giant from image - tube spectra . a ccd spectrum of ssv61 , kindly made available to us by g. herbig , exhibits h@xmath0 emission and @xmath17 absorption equivalent widths that are typical of the class of weak - lined t tauri stars ( wtts ) , ew(h@xmath0 ) = @xmath18   and ew ( ) = 480 m  ( cf . walter 1986 ; martn et al . the brightest emission in the hard asca band ( 2.08.0 kev ) is located north of ssv61 , in the vicinity of hh24 . the high - energy peak lies nearest ssv63 , but can not be identified unambiguously with either of its infrared components due to the low spatial resolution of asca . ozawa et al . noted the great difficulty of separating the x - ray flux of ssv63 from that of ssv61 , given their offset of just @xmath19 , at roughly the half - power radius of asca . the quiescent luminosity @xmath20 ergs  s@xmath3  they derive for ssv63 places it above the top end of the range thus far observed for all but a few class i objects , by factors of 50100 ( carkner , kozak , & feigelson 1998 ; preibisch , neuhuser , & stanke 1998 ) . whether ssv63 is truly one of the most x - ray luminous ysos in the sky , however , has awaited confirmation from high resolution imaging that resolves not only ssv61 from ssv63 , but also the individual infrared components of ssv63 itself . that task , including the requisite high precision astrometry , has now been accomplished by the _ chandra _ observations reported here . as for the class  0 sources in l1630 , ozawa et al . found no sign of x - ray emission at the position of hh24-mms , located in the saddle between the soft and hard x - ray peaks in their image , nor any emission at the position of hh25-mms , which was also in the asca field of view . their @xmath21 upper limit of @xmath22 ergs  s@xmath3  is not a stringent limit on the emission , however , since ysos elsewhere in orion and in other star forming regions have been detected at much fainter levels , @xmath23 ergs  s@xmath3  ( e.g. , feigelson et al . 2002 ; imanishi , koyama , & tsuboi 2001 ) . using the _ chandra observatory _ , we have undertaken a far more sensitive search for the onset of x - ray emission in the class 0 objects within the l1630 cloud . our objective was to establish an evolutionary progression in x - ray properties within a single cloud , and to examine the possible relationship between protostellar x rays , accretion disks , magnetically confined jets , and large - scale molecular outflows . taking advantage of the lower background , greater sensitivity , and unsurpassed spatial resolution of _ chandra _ , we are now able to set a 10 times smaller bound on possible x - ray emission from the three established class 0 protostars in the l1630 cloud , hh24-mms , hh25-mms , and lbs17-h .","summary":"the hh24 - 26 star forming region within the lynds 1630 ( l1630 ) dark cloud in orion contains a remarkable collection of rare class  0 and class  i protostars , collimated molecular and ionized jets , and a luminous but spatially unresolved asca x - ray source . to study the x - ray properties of the embedded protostar population of that region two class  i protostars aligned with optical jets in hh24 , ssv63e and ssv63w , were also detected , as was the continuum radio source ssv63ne , which is very likely an extreme class  i or class  0 object . we observed no x rays from the class  0 protostars hh24-mms and hh25-mms , nor any from regions of the cloud bounded by hh25 and hh26 , at a upper limit of ergs  s . hh26-ir , the class  i object thought to be the origin of the hh26 flow , was not detected .","abstract":"the hh24 - 26 star forming region within the lynds 1630 ( l1630 ) dark cloud in orion contains a remarkable collection of rare class  0 and class  i protostars , collimated molecular and ionized jets , and a luminous but spatially unresolved asca x - ray source . to study the x - ray properties of the embedded protostar population of that region , we have obtained a deep x - ray image with the acis - s camera on board the _ chandra x - ray observatory_. a number of h emission - line objects were detected in the areas surrounding hh2426 , of which the weak - line t  tauri star ssv61 was the brightest source , at a steady luminosity of(0.310 kev) ergs  s . two class  i protostars aligned with optical jets in hh24 , ssv63e and ssv63w , were also detected , as was the continuum radio source ssv63ne , which is very likely an extreme class  i or class  0 object . we observed no x rays from the class  0 protostars hh24-mms and hh25-mms , nor any from regions of the cloud bounded by hh25 and hh26 , at a upper limit of ergs  s . hh26-ir , the class  i object thought to be the origin of the hh26 flow , was not detected . near - infrared spectroscopy obtained at the nasa irtf reveals 3 ice bands in the spectra of ssv59 , 63e , 63w , and hh26-ir , and 2.3 co overtone absorption bands for ssv61 . ssv60 , which lies astride one end of the great arc of nebulosity forming hh25 , exhibits a deep infrared ice band and co absorption , but is not an x - ray source , and is most likely a distant background giant of late spectral type ."}
{"article_id":"astro-ph0404260","section_id":"r","document":"l1630 was observed with the advanced ccd imaging spectrometer array ( acis : garmire et al . 2002 ) on the _ chandra x - ray observatory _ for a net exposure time ( livetime ) of 62.8 ks . the date of observation was 1415 november 2002 . all six detector chips of the acis - s camera , s0s5 , were activated during the observation . the aim point of the observation was chosen to place ssv61 close to the center of the back - illuminated s3 chip and to put hh24 and hh2526 on the same device within a few arcminutes of the optical axis of the telescope , thereby ensuring the best optical performance for our highest priority targets within the acis field of view . the roll angle of the observation , @xmath24 , was selected to position the ngc 2068 reflection nebula , located to the northeast of hh2426 , on the back - illuminated s1 chip of the detector array and the class 0 object , ngc 2068/lbs17-h ( gibb & little 2000 ) , on the adjacent , front - illuminated s2 chip . the majority of the field of view is shown in fig . 1 , superposed on the red image of the digitized sky survey of the space telescope science institute  ( dss ) . the approximate locations of hh objects in the neighboring areas are marked , as are the positions of the two dozen x - ray sources we have detected in our _ chandra _ observation . to analyze the _ image , we initially filtered the level-2 x - ray event file provided by the pipeline data processing system , retaining only the photon events that were assigned asca grades 0 , 2 , 3 , 4 , and 6 and that were within the broad ( 0.510 ) kev energy band in which the acis detector has its highest response and the background radiation is at its lowest levels . subsequent steps in the analysis , including photometry and astrometry , were carried out following various data analysis threads within ciao , the interactive _ chandra _ data analysis package . for source detection , we applied the celldetect sliding - cell detection algorithm . twenty - five sources , all of them point - like , were found on the six chips . to extract x - ray counts for each source , we used the dmextract tool . we employed a circular extraction region with a radius of 10 pixels ( @xmath25 ) to measure the brightness of sources located within 7  of the optical axis of the telescope , a radius twice as large for sources more than 7  off - axis , and an annulus at least 10 times as large to evaluate the background emission . the results of the photometry are given in table 1 . listed there are the right ascension and declination ( j2000 ) of each source , its off - axis angle , the net source counts extracted within the 0.510 kev band , and the statistical errors in the source counts . in the final column we tabulate the count rate for the effective exposure time of each source , which takes account of the variations in the sensitivity of the camera across the field of view , as indicated by our exposure map calculations . the adjustments are negligible for the nearly on - axis sources on the s3 chip that are the main interest of the present study , but may be as great as 50% for the few objects that are located either near the edge of a detector chip or else far away from the optical axis of the telescope . we also list possible optical and infrared counterparts , which were found by cross - matching the x - ray coordinates with entries in the simbad database and by visual comparison with red images from the dss as well as infrared images from the 2mass sky survey . the identifications include several h@xmath0 emitters ( herbig & kuhi 1963 ) , named infrared sources ( strom et al . 1976 ) , anonymous near - infrared objects from the 2mass survey , and entries in the _ hubble space telescope _ guide star catalog - ii ( identified here with the prefix of s ) . the correspondence of each x - ray and optical / infrared position is within 1  (= 2 acis pixels ) or less . the position of x - ray source no . 4 coincides with the location of a previously known non - thermal , extragalactic radio source ( bontemps et al . 1995 ; anglada et al . a search of the nasa / ipac extragalactic database ( ned ) turned up no other background objects in the acis field of view . ssv63 is resolved into three separate x - ray components , which correspond to the vla 3.6-cm radio positions of ssv63e , 63w , and 63ne ( reipurth et al . an overlay of the radio source positions on the 28 kev hard - band x - ray image from _ chandra _ is shown in fig . 2 . within the uncertainties in the absolute coordinates of the radio and infrared sources ( see table 1 of bontemps et al . 1995 ) , and the astrometric error in _ observations ( nominally 1 pixel , or @xmath26 , for positions close to the optical axis of the telescope ) , the x - ray centroids coincide with the infrared counterpart of ssv63e and the brighter , southern , infrared component of ssv63w . the fainter infrared component of ssv63w , located 2  farther north ( see fig . 2 of davis et al . 2002 ) , appears dark in x rays . ssv63ne is a source of both radio emission and x - ray emission , but has no near - infrared counterpart ( as we will show below in  2.2 ) . if not a distant background object , it may qualify on that basis as an extreme class i or possible class  0 yso . all three components of ssv63 have hard x - ray spectral indices : 96% of the x - ray photons detected from ssv63w have pulse - height energies greater than 2 kev , while all of those detected for ssv63e and ne have energies of 2 kev or more . we performed individual @xmath27 timing analyses for the three x - ray components , using the xronos software package from the high energy astrophysics science archive research center ( heasarc ) of the nasa / goddard space flight center . we found no indication of variability on timescales of 6 ks or longer , certainly nothing comparable in amplitude or duration to the order - of - magnitude outburst in x - ray flux recorded by asca ( ozawa et al . the x - ray count rates listed in table 1 therefore likely correspond to the quiescent activity levels of those sources . changes on timescales shorter than 6 ks were not investigated owing to the faintness of the sources . the strongest x - ray source in the _ chandra _ field of view was the wtts , ssv61 , for which we accumulated very nearly 13,000 counts in the 0.510 kev bandpass . the x - ray light curve of ssv61 was stable throughout the entire observation ; various @xmath27 tests performed with xronos found no evidence of variability on timescales greater than 300 s. to analyze the x - ray spectrum of ssv61 , we used the heasarc xspec spectral analysis package in order to fit simple multi - temperature thermal plasma models to the pulse height distribution of the extracted photons . the quality of the fit was determined by @xmath27 minimization . in the calculations , we removed a small ( @xmath28 ) contribution of emission from the background and also updated the instrumental response function to compensate for the on - orbit decline in the low - energy sensitivity of the acis detectors .    in terms of the reduced @xmath27 value of the fit , no satisfactory model was found . typical of the results we obtained are the following parameters for a two - temperature , reduced - metal mekal fit ( mewe , kaastra , & liedahl 1995 ) , which we matched to the observed counts in the 0.57.0 kev pulse - height energy channels : reduced @xmath29 ; @xmath30 kev , @xmath31 kev ; one - third solar elemental abundance , z = @xmath32 ; hydrogen column density , n@xmath33 @xmath34 ; volume emission measure , @xmath35 , three - quarters of which are due to the high - temperature component ; broadband flux at earth , @xmath36(0.310 kev ) = @xmath37 ergs  @xmath34  s@xmath3 ; and intrinsic ( absorption - corrected ) x - ray luminosity for an assumed distance of 450 pc , @xmath1(0.310 kev ) = @xmath38 ergs  s@xmath3 . here , @xmath39(=254 ) is the number of degrees of freedom in the model . closely similar fits were obtained with both the xspec pileup model ( see davis 2001 ) , which we used to account for the @xmath40% pileup fraction in our spectrum of ssv61 , and also the apec plasma emission code described by smith et al . an example of an apec model fit is shown in fig . 3 . except for a few possible camera artifacts , the largest residuals in all the model fits are attributable to excess emission in the observed spectrum near photon energies of 1 kev . the apparent excess may be due to lines of ne ix and x or to inner shell transitions of high ionization stages of fe . a similar excess has also been observed in the acis spectra of pre - main sequence stars in other star - forming regions , e.g. , orion and @xmath10 ophiuchus ( feigelson et al . 2002 ; imanishi , tsujimoto , & koyama 2002 ) . an evaluation of the intrinsic 0.310 kev brightness of ssv61 for a variety of xspec models produced very nearly the same results for the x - ray flux and for the luminosity . the various models also yielded closely similar amounts for the hydrogen column density . from the models and the empirical relation of bohlin , savage , & drake ( 1978 ) , we infer a visual extinction of @xmath41 mag . our estimate , drawn from the _ chandra _ spectrum of ssv61 , is a factor of four less than the extinction ozawa et al . ( 1999 ) derived from their asca observation , but is consistent with the conclusion reached by strom et al . ( 1975 ) on the basis of infrared colors that the foreground reddening to this star is relatively small . infrared spectroscopy ( discussed below ) further confirms the low extinction for this star . the three x - ray sources identified with ssv63 were too faint for detailed spectral model fitting , and so we limited ourselves to a few simple models of the strongest component , ssv63w . for that source we chose an isothermal , one temperature ( 1-t ) mekal model , constrained it to a sub - solar abundance of z = 0.5 , and allowed xspec to search for values of n@xmath42 and @xmath43 that minimized the @xmath27 of the fit . the best - fit values derived by xspec were n@xmath44 @xmath34 ( equivalent to 48 mag of visible extinction ) and @xmath45 kev . the resulting hydrogen column density is at the low end of the range of values deduced by ozawa et al . ( 1999 ) , while our temperature is a factor of 3 lower than their best - fit value for a quiescent interlude in the asca observation . a reddened bremsstrahlung model , which we chose as an alternative fit , produced a similar @xmath27 , temperature , and n@xmath42 as the mekal model . both models , the mekal and the bremsstrahlung , yielded a comparable 0.310 kev flux and absorption - corrected luminosity for ssv63w : @xmath46 ergs  @xmath34  s@xmath3  and @xmath47 ergs  s@xmath3 . raising the temperature to a fixed value of @xmath48 kev for consistency with the asca result reduced the column density to @xmath49 @xmath34 , corresponding to an extinction of @xmath50 mag , but yielded a much poorer fit to the _ chandra _ pulse - height spectrum in terms of its @xmath27 value . no model analysis was possible for the two remaining components of ssv63 , given the small numbers of counts recorded for them during our _ chandra _ observation . to estimate x - ray luminosities for those sources , we scaled from ssv63w in proportion to the background - adjusted number of counts detected for each source . in doing so , we implicitly assumed that the optimal xspec models of ssv63e and ssv63ne would yield the same parameters as the best - fitting model for ssv63w . our normalization procedure is equivalent to using a counts - to - energy conversion factor ( ecf ) of @xmath51 ergs  @xmath34  s@xmath3  per count s@xmath3 for the x - ray flux observed at earth , and @xmath52 ergs  s@xmath3  per count s@xmath3 for the extinction - corrected broadband luminosity . anticipating the results of  3.2 , we note that sub - millimeter observations of l1630 corroborate the high extinction value provided by our x - ray analysis of ssv63w . on the other hand , spectroscopy of the infrared ice band in the direction of ssv63e and w ( discussed in  2.3 ) suggests that the foreground extinction towards both sources may be only half as large , @xmath53 mags . the apparent discrepancy raises the possibility that the x - ray sources may be more deeply obscured than are the near - infrared sources , reflecting , perhaps , an anomalous gas - to - dust ratio along the line of sight . the x - ray luminosities for ssv61 and ssv63 are summarized in table 2 . our @xmath1 value for ssv61 is 15% higher than the asca result of ozawa et al . ( 1999 ) but lies substantially above the high end of the range found in an extensive survey of wtts in taurus by rosat ( neuhuser 1997 ) and is well above the range of x - ray luminosities measured by _ chandra _ for low - mass stars in both ophiuchus ( imanishi et al . 2001 ) and the orion nebula cluster ( feigelson et al . 2003 ) . our @xmath1 value for ssv63w falls near the top end of those three luminosity distributions , while the values for the two other detected class i ysos , ssv63e and 63ne , are in the top quartile of each range . also listed in the table are upper limits on the x - ray emission of the near - infrared objects ssv60 and 59 , the former lying between hh25c and 25d along the curving ribbon of emission knots that define hh25 ( being closer to d ) , the latter lying just north of hh26a . the upper limits on the count rates given in the table are three times the poisson uncertainties in the total counts ( uncorrected for background emission ) measured through a 10  diameter circular detection cell , which we centered on the respective 2mass positions listed in the second and third columns of the table . based on eqn . 10 in gehrels ( 1986 ) , the significance level of these upper limits corresponds to @xmath4 , i.e. , to a confidence level of 0.95 . the upper limits obtained for a smaller 5   diameter detection cell , which still encircles more than 95% of the energy in the _ chandra _ point spread function , are @xmath54 dex lower at a confidence level of 0.95 , in accordance with either gehrels ( 1986 ) or the bayesian approach of kraft , burrows , & nousek ( 1991 ) , but may be subject to a somewhat greater uncertainty due to the imprecision of the infrared coordinates of both objects . for lack of a more compelling choice , the conversion from count rate to luminosity in table 2 is based on the ecf derived from our xspec modelling of ssv63w . the upper limits cited on the luminosity assume both objects lie at a distance of 450 pc within the l1630 cloud , which may not be true for ssv60 , as we discuss further in  2.3 .    in similar fashion , we derived @xmath4 upper limits on the possible x - ray emission from the three class 0 objects in the l1630 cloud , hh24-mms , hh25-mms , and lbs 17-h . those results are also given in table 2 . in each case , the detection cell was centered at the known long - wavelength or radio position of the object . the j2000 coordinates of hh24-mms and hh25-mms were precessed from the b1950 vla positions of bontemps et al . ( 1995 ) and gibb ( 1999 ) ; those of lbs 17-h were precessed from the b1950 location of the peak in the 450@xmath6 dust continuum map of phillips et al . ( 2001 ) . finally , we list an upper limit for our x - ray non - detection of hh26-ir , the possible driving source for the hh26 outflow ( schwartz et al . 1997 , wherein the object is known as irs 4 ) . the b1950 location for that source was taken from the discovery paper of davis et al . ( 1997 ) and precessed to an equinox of j2000 . two sets of _ jhk _ near - infrared images were obtained of the hh2426 region on 18 november 2002 , using the university of hawaii quirc hgcdte camera array ( hodapp et al . the instrument was mounted at the f/10 cassegrain focus of the 2.2-m telescope on mauna kea . the image scale was 019 pixel@xmath3 , the field of view was 32 . one set of images was centered on ssv63 and hh24 , the other mid - way between ssv59 and 60 in the vicinity of hh2526 . at both locations , a sequence of @xmath55 s exposures was obtained at each of 20 separate positions , offset by 10  in right ascension and declination , to produce a heavily sampled dither - pattern . the same cycle was repeated in each of the three filter bands . we alternated the observations of both hh fields with similar integrations on a pair of flanking fields 150  e and w , from which the bright stars were subsequently removed in order to create suitable sky frames . flat - field frames were created by median - averaging observations of the 2.2-m dome under illumination by incandescent lamps . in the reductions , the dithered hh frames were flat - fielded and sky - subtracted , then aligned by cross - matching the positions of bright stars to form an enlarged median - averaged mosaic . the cumulative exposure time in the center of the final co - added image in each filter is @xmath56 s. taking into account the intermittent , non - photometric observing conditions , we estimate brightness limits of 20.9 mags , 20.1 mags , and 18.5 mags in @xmath57 , @xmath58 , and @xmath59 , respectively . the typical seeing in the course of the observations was 05 in @xmath59 ( fwhm ) . however , the psf of stellar images in the co - added data proved to be somewhat broader than this , and also slightly distorted , as a result of a misalignment of the primary mirror of the 2.2-m telescope . our images of hh24 in the three colors are shown in fig . the positions of the individual components of ssv63 , as listed in table 2 , are marked on the @xmath57-band image . we have also identified the expected locations of the two most prominent hh emission knots , 24a and 24b . the position from table 2 of the class 0 object , hh24-mms , is also noted . that source is faintly visible in the @xmath59 image , the bandpass of which includes a number of h@xmath11 lines , and is also very weakly present in the @xmath58 image , whose bandpass includes [ ] @xmath60 , a low - excitation emission line that is observed in the jets of some hh objects ( e.g. , reipurth et al . as noted earlier , the elongated jet associated with hh24-mms is very prominent in the continuum - subtracted , narrow - band h@xmath11 images of bontemps et al . ( 1996 , their fig . 1a ) and davis et al . ( 1997 , their fig . 2 ) , and also in the fabry - perot image of davis et al . ( 2002 , their fig . the n  s components of ssv63w are cleanly separated in our @xmath57-band image , but are heavily exposed in the longer - wavelength images , as is true of ssv63e . an extended halo around the latter component , pointing westward , becomes increasingly evident with increasing wavelength . contrary to previous reports ( moneti & reipurth 1995 ; terquem et al . 1999 ) , we see no evidence to suggest this star is double or that the emission peak in @xmath58 lies 1  west of the peak in @xmath59 . in our images , there is no shift in the position of the peak with color to a limit of 1 pixel or 02 . the coordinates of the radio and x - ray source ssv63ne place it adjacent to two very red patches of nebulosity known from earlier work ( e.g. , zealey et al . 1992 ) . a false - color image that combines the three separate panels of fig . 4 exhibits a noticeable gradient in color from w to e , possibly originating at ssv63e . the variation in color suggests that both patches of infrared nebulosity may be illuminated by an embedded source to the west , either the class i source , ssv63e , which scarott et al . ( 1987 ) proposed as the illuminating source for the diffuse optical nebulosity of hh24 , or else a much more deeply embedded infrared object at the location of 63ne . the radio and x - ray coordinates of ssv63ne coincide to within 33 with the position for the predicted but unobserved `` jet g star '' of jones et al . ( 1987 ) , which those authors proposed to be the driving source of the hh24 g outflow ( see also mundt et al . 1991 , in particular the highly detailed [ ] image in their fig . the absence in fig . 4 of any obvious point source at the same location to a limit of @xmath61 mag implies that this star , presuming it does exist , lies exceedingly deep within the molecular cloud . given our detection of x - ray emission at the radio position , there can be no doubt that ssv63ne , if it is a protostar of class 0 , has already evolved past the stage of isothermal collapse . submillimeter maps of the region obtained with the scuba bolometer array on the jcmt ( phillips et al . 2001 ; mitchell et al . 2001 ) show extended emission at the position of ssv63 but are unable to resolve 63ne from the two other radio components , 63e and 63w . consequently , although it seems quite likely that ssv63ne is a bona fide yso , its exact status is not yet entirely settled . our infrared images of the southern region containing hh25 and 26 are presented in fig . 5 . again , for orientation , the positions of the notable objects in the field of view are marked . the class 0 protostar , hh25-mms , is invisible in both the @xmath57 and @xmath58 images , although a hint of emission ( presumably from ro - vibrational lines of h@xmath11 ) can be seen at the radio position of this object in the @xmath59-band image . hh25a and ssv59 are both immersed in nebulosity . nebulae of similar appearance have been seen in high resolution images of other embedded protostars , e.g. , hl tau ( close et al . 1997 , especially their figs . 2 and 4 ) and interpreted as the outline of bipolar cavities . ssv59 has been classified as a class i object . no star has been observed before at the location of hh25a at optical wavelengths . however , this hh knot is uncommonly bright in the @xmath57 and @xmath58 frames in fig . 5 to be merely the `` working surface '' of a high - velocity outflow from hh25-mms , located immediately to the south . our underexposed 1.92.5@xmath6 infrared spectrum of hh25a displays an array of very strong emission lines of h@xmath11 , which likely arise from shock - heated gas , but no spectral signatures of an underlying star . a very red , compact emission knot is observed at the location of hh25c , in approximate alignment with hh25a , ssv60 , and hh25d . as mentioned earlier , we believe ssv60 is a heavily reddened background giant , not a member of l1630 . no other plausible candidate for the exciting source of hh25 is revealed by our images . infrared spectra of ssv59 , 60 , 61 , 63e , 63w ( both the north and south components combined ) , and hh26-ir were acquired with the spex cross - dispersed , medium - resolution spectrograph ( rayner et al . 2003 ) at the 3.0-m nasa irtf telescope on mauna kea on 3 january and 13 february 2003 . spex covers the full wavelength range from 0.8 to 5.5@xmath6 in two grating settings . we observed each source in the 1.94.2@xmath6 wavelength region , using the lxd setting ; the two brightest objects , ssv60 and 61 , were also observed in the 0.82.4@xmath6 region with the sxd setting . observing conditions were photometric and dry throughout , with t ypical seeing values near 05 fwhm ( measured in @xmath59-band ) . slit widths of 03 and 05 at the short- and long - wavelength settings provided a nominal spectral resolving power , @xmath62 , of 2000 and 1500 , respectively . our on - source integration times ranged from 300 to 1200s and resulted in signal - to - noise ratios of 2050 in both the @xmath59 and @xmath63 bands . each observing sequence began with a nearby ( less than 0.05 difference in airmass ) a0v standard star , moved to the target object , and finished with a set of internal calibration spectra . to cancel the sky background , we observed in the conventional way by nodding along the 15-long slit . the data were reduced with the spextool software package ( see cushing et al . 2003 for details ) . spectra were extracted using a 12 aperture along the slit , corrected for telluric features , and calibrated in flux by means of the standard star spectra according to the techniques that have been described by vacca , cushing , & rayner ( 2003 ) . the processed spectra are shown in fig . 6 , where they are plotted on a logarithmic flux scale . the infrared continua of ssv60 and 61 come to a peak blueward of the @xmath59-band , near 1.9 and 1.5@xmath6 , respectively . absorption lines from a variety of neutral and ionized metals , including , , , , , and , can be seen in the spectra of both stars . no emission lines are observed in the spectrum of ssv60 . the br@xmath0 line of at 4.05@xmath6 appears in emission in the spectrum of ssv61 ; its equivalent width is entirely consistent with the observed strength of h@xmath0 , case b recombination , and very little foreground reddening . both spectra exhibit deep absorption bands from the first overtone ro - vibrational transitions of co near 2.32.5@xmath6 . assuming the observed atomic and molecular features are photospheric in origin , we have used their relative strengths to estimate the spectral type and luminosity class of the underlying stars in the manner described by kleinmann & hall ( 1986 ) , hodapp & deane ( 1993 ) , and greene & meyer ( 1995 ) . here we have adopted aspin s ( 2003 ) formulation , in which an atomic index formed by the sum of the equivalent widths of the doublet at 2.21@xmath6 and the triplet at 2.26@xmath6 is compared to a molecular index represented by the equivalent width of the @xmath64=20 co bandhead at 2.29@xmath6 ( see fig . according to their atomic and molecular index values , ssv60 ( 4.2 , 10.0 ) is definitely a giant , whereas ssv61 ( 5.9 , 9.4 ) is intermediate to a dwarf and giant ( a not uncommon finding for a tts ) . we have combined the spectral indices , the strengths of the various photospheric absorption lines of the metals , the deep co bandheads , and the general continuum shapes to estimate spectral classifications of k5m0iii for ssv60 and m0m2iii / v for ssv61 . those spectral types , resting solely on the infrared spectra , are consistent with the locations of both stars in a ( @xmath65 , @xmath66 ) color - color plot based on their 2mass photometry , and also with the effective temperatures we have derived following the procedure of greene & meyer ( 1995 ) , which makes use not only of the absorption line strengths but the broadband colors as well . the latter technique provides , among other things , an estimate of the fraction of excess light from veiling continuum emission , which we find to be constrained to low values for both stars ( @xmath67 , @xmath68 at @xmath58 and @xmath59 ) . the association of ssv61 with the l1630 molecular cloud is hardly in question , but the same can not be said for ssv60 . with its bright , attendant nebula , ssv61 would be a rare star indeed to be in the far foreground of this region , while the absence of any ice absorption at 3.08@xmath6 in its infrared spectrum ( fig . 6 ) argues against the likelihood it lies far behind the molecular cloud at a very considerable distance from earth . for an early m giant , ssv60 is clearly much more heavily absorbed than ssv61 , as is apparent from its spectral energy distribution shortward of 2@xmath6 and its strong ice absorption band . the broad ice feature is common to the spectra of other sources which are either background to or deeply embedded within molecular clouds , where the ice has condensed onto dust grains but not undergone significant processing at high temperature ( smith , sellgren , & tokunaga 1989 ) . for ssv60 , the optical depth at band center , @xmath69 = 0.96 , leads ( according to the results of whittet et al . 1988 ) to an optical extinction of roughly @xmath70 mag . such heavy extinction is not to be found in the foreground to l1630 . on the other hand , ssv60 shows none of the signposts of youth or activity that are expected for an embedded class i protostar  no x - ray emission , no high velocity outflow or jet in co or h@xmath11 , no far infrared or sub - mm emission . we conclude , therefore , that ssv60 is a background giant star that is unconnected either with l1630 or with hh25 , on which it is apparently coincidentally projected . the strong red continua and deep ice bands of hh26-ir , ssv59 , 63e , and 63w , on the other hand , suggest that each of those objects is deeply embedded within the l1630 cloud . their observed ice - band optical depths range from @xmath71 ( for hh26-ir ) to @xmath72 ( for ssv63e and w ) , corresponding to approximate @xmath73 values of 10 to 20 mags . at close inspection , the ice band spectra of ssv59 and 63e also show a broad , shallow depression near 3.45@xmath6 . that feature , according to smith et al . ( 1989 ) , can be identified with the c  h stretching modes of hydrocarbons ( in the ch@xmath11 and ch@xmath74 subgroups ) . emission lines of are visible in the spectra of all four objects , including br@xmath0 4.05@xmath6 , br@xmath75 2.17@xmath6 , and ( in the case of ssv63e ) @xmath76=85 pf@xmath75 3.74@xmath6 . the emission is a clear indication of ionized gas in the close vicinity of each star , but whether the warm gas is inflowing or outflowing is a matter of continuing debate ( e.g. , najita , carr , & tokunaga 1996 ; folha & emerson 2001 ) . there are no signs in our spectra of any photospheric absorption lines , which we suspect may be hidden beneath a large continuum veiling flux . emission lines from ro - vibrational transitions of h@xmath11 are present throughout the @xmath59-band spectra of ssv63w and hh26-ir , the 2.12@xmath6 @xmath77(1 ) line being the strongest ( fig . the same lines are often observed in the spectra of class i objects ( greene & lada 1996 ) . they are also commonly observed in the spectra of high velocity outflows ( e.g. , gredel 1994 , 1996 ) and have been attributed to excited h@xmath11 molecules that form behind shocks which arise as jet material collides with the ambient gas in a cloud ( garden , russell , & burton 1990 ) . the h@xmath11 emission in our spectral images does not appear to be spatially extended in a n  s direction along the slit . however , it has already been shown by davis et al . ( 2002 ) that the h@xmath11 emission of hh26-ir has a modest extension along its jet in the ne  sw direction . the @xmath59-band spectra of ssv59 , 63e , and hh26-ir ( fig . 8) display the first overtone ro - vibrational co bands in emission . various explanations have been offered for the co lines : they may be formed in the innermost portion of a keplerian disk or in the neutral component of a stellar wind or outflow ( carr 1989 ; chandler , carlstrom , & scoville 1995a ; najita et al . alternatively , the emission may be produced by accretion of disk material onto the central star via a magnetic `` funnel flow '' ( martin 1997 ; see , however , najita et al . 2003 ) . in any case , biscaya et al . ( 1997 ) have demonstrated that in some cases the co bands can be highly variable , perhaps even exhibiting periodic behavior . carr ( 1989 ) , in fact , observed the co bands of ssv59 in absorption , whereas they are definitely in emission in our spex spectra , as can be readily seen from fig .","summary":"near - infrared spectroscopy obtained at the nasa irtf reveals 3 ice bands in the spectra of ssv59 , 63e , 63w , and hh26-ir , and 2.3 co overtone absorption bands for ssv61 . ssv60 , which lies astride one end of the great arc of nebulosity forming hh25 , exhibits a deep infrared ice band and co absorption , but is not an x - ray source , and is most likely a distant background giant of late spectral type .","abstract":"the hh24 - 26 star forming region within the lynds 1630 ( l1630 ) dark cloud in orion contains a remarkable collection of rare class  0 and class  i protostars , collimated molecular and ionized jets , and a luminous but spatially unresolved asca x - ray source . to study the x - ray properties of the embedded protostar population of that region , we have obtained a deep x - ray image with the acis - s camera on board the _ chandra x - ray observatory_. a number of h emission - line objects were detected in the areas surrounding hh2426 , of which the weak - line t  tauri star ssv61 was the brightest source , at a steady luminosity of(0.310 kev) ergs  s . two class  i protostars aligned with optical jets in hh24 , ssv63e and ssv63w , were also detected , as was the continuum radio source ssv63ne , which is very likely an extreme class  i or class  0 object . we observed no x rays from the class  0 protostars hh24-mms and hh25-mms , nor any from regions of the cloud bounded by hh25 and hh26 , at a upper limit of ergs  s . hh26-ir , the class  i object thought to be the origin of the hh26 flow , was not detected . near - infrared spectroscopy obtained at the nasa irtf reveals 3 ice bands in the spectra of ssv59 , 63e , 63w , and hh26-ir , and 2.3 co overtone absorption bands for ssv61 . ssv60 , which lies astride one end of the great arc of nebulosity forming hh25 , exhibits a deep infrared ice band and co absorption , but is not an x - ray source , and is most likely a distant background giant of late spectral type ."}
{"article_id":"astro-ph0404260","section_id":"c","document":"we have acquired a deep x - ray image of the hh2426 region in the l1630 cloud with the acis - s camera on _ chandra _ , which has resulted in the detection of a number of anonymous 2mass infrared sources and optically visible h@xmath0 emission - line stars , including the x - ray luminous coronal source , the wtts ssv61 . also detected at what appear to be their quiescent levels of activity are two deeply embedded class  i protostars ( ssv63e and w ) , which have been identified in earlier work as the source of energetic molecular and ionized flows in the region . the two were blended together in an earlier detection by asca , but are well separated at the much higher spatial resolution of _ chandra_. two other hh - associated class  i objects ( ssv59 and hh26-ir ) as well as three class  0 ysos in the same cloud ( hh24-mms , hh25-mms , and lbs 17-h ) were not detected . although x - ray observations of several different star forming regions thus far reveal a striking lack of class  0 detections , no firm conclusions can be drawn from our small sample of ysos regarding a possible evolutionary trend in the intrinsic x - ray luminosities of the class  0 and class  i protostars . x - ray emission was detected from a deeply embedded continuum radio source ( hh24ne ) , whose location within hh24 suggests that it may be the highly obscured driving source for one of the long hh filaments in this area . the object has no visible or near - infrared counterpart , and therefore is potentially a class  0 or extreme class  i object . + this research has made use of the simbad database , operated at _ cds _ , strasbourg , france , and is based in part on observations made with the _ chandra x - ray observatory_. support for this work was provided by the national aeronautics and space administration  through chandra award number go2 - 3007x issued by the _ chandra x - ray observatory _  center , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics and space administration  under contract nas8 - 39073 . the digitized sky surveys ( dss ) were produced at the space telescope science institute under nasa grant nag w-2166 and are based on photographic data obtained using the oschin schmidt telescope on palomar mountain and the uk schmidt telescope with the permission of those institutions . the guide star catalogue - ii is a joint project of the space telescope science institute and the osservatorio astronomico di torino . space telescope science institute is operated by the association of universities for research in astronomy , for the national aeronautics and space administration under contract nas5 - 26555 . the participation of the osservatorio astronomico di torino is supported by the italian council for research in astronomy . additional support is provided by european southern observatory , space telescope european coordinating facility , the international gemini project and the european space agency astrophysics division . the two micron all sky survey ( 2mass ) is a joint project of the university of massachusetts and the infrared processing and analysis center ( ipac)/california institute of technology , funded by the national aeronautics and space administration and the national science foundation . lccrlrr 1 ...... & 05 45 46.3 & @xmath98 15 15 & 8.5 & & @xmath99 & @xmath100 + 2 ...... & 05 45 51.7 & @xmath98 16 33 & 8.5 & & @xmath101 & @xmath102 + 3 ...... & 05 45 53.1 & @xmath98 13 26 & 6.1 & gsc2 s02000123390 ( = kh@xmath0174 ) & @xmath103 & @xmath104 + 4 ...... & 05 45 57.8 & @xmath98 09 29 & 3.8 & & @xmath105 & @xmath106 + 5 ...... & 05 46 00.3 & @xmath98 08 26 & 3.5 & ssv65 & @xmath107 & @xmath108 + 6 ...... & 05 46 04.2 & @xmath98 05 59 & 4.5 & 2mass j05460427 - 0005591 & @xmath109 & @xmath110 + 7 ...... & 05 46 07.8 & @xmath98 10 01 & 1.3 & ssv63w & @xmath111 & @xmath112 + 8 ...... & 05 46 07.8 & @xmath98 11 57 & 2.4 & ssv61 & @xmath113 & @xmath114 + 9 ...... & 05 46 08.1 & @xmath98 05 32 & 4.6 & & @xmath115 & @xmath116 + 10 .... & 05 46 08.5 & @xmath98 10 03 & 1.2 & ssv63e & @xmath117 & @xmath118 + 11 .... & 05 46 08.9 & @xmath98 09 56 & 1.0 & ssv63ne & @xmath119 & @xmath120 + 12 .... & 05 46 09.5 & @xmath98 03 31 & 6.5 & 2mass j05460960 - 0003312 & @xmath121 & @xmath122 + 13 .... & 05 46 09.8 & @xmath98 05 59 & 4.0 & 2mass j05460984 - 0005591 & @xmath123 & @xmath124 + 14 .... & 05 46 11.6 & @xmath98 02 20 & 7.6 & gsc2 s02000125079 & @xmath125 & @xmath126 + 15 .... & 05 46 11.6 & @xmath98 06 28 & 3.5 & 2mass j05461162 - 0006279 & @xmath127 & @xmath128 + 16 .... & 05 46 12.3 & @xmath98 08 08 & 1.8 & 2mass j05461226 - 0008078 & @xmath129 & @xmath130 + 17 .... & 05 46 13.0 & @xmath98 18 27 & 8.5 & & @xmath131 & @xmath132 + 18 .... & 05 46 16.3 & @xmath98 01 19 & 8.7 & & @xmath133 & @xmath134 + 19 .... & 05 46 17.7 & @xmath98 16 12 & 6.4 & & @xmath135 & @xmath136 + 20 .... & 05 46 18.9 & @xmath98 05 38 & 4.6 & gsc2 s020001258 & @xmath137 & @xmath138 + 21 .... & 05 46 19.5 & @xmath98 05 20 & 4.9 & ssv64 ( = lkh@xmath0301 ) & @xmath139 & @xmath140 + 22 .... & 05 46 20.2 & @xmath98 10 20 & 1.8 & 2mass j05462018 - 0010197 & @xmath141 & @xmath142 + 23 .... & 05 46 22.4 & @xmath98 08 53 & 2.6 & ssv68 ( = lkh@xmath0302 ) & @xmath143 & @xmath144 + 24 .... & 05 46 25.9 & @xmath98 10 15 & 3.2 & & @xmath145 & @xmath146 + 25 .... & 05 46 33.3 & @xmath147 02 54 & 13.8 & ssv13 & @xmath148 & @xmath149    lcccccc ssv59 ........... & i & 05 46 04.8 & @xmath98 14 17 & @xmath150 & @xmath151 & @xmath152 + ssv60 ........... & gk / m & 05 46 08.4 & @xmath98 14 25 & @xmath153 & @xmath154 & @xmath155 + ssv61 ........... & wtts & 05 46 07.8 & @xmath98 11 57 & @xmath156 & @xmath157 & @xmath158 + ssv63w ....... & i & 05 46 07.8 & @xmath98 10 01 & @xmath112 & @xmath159 & @xmath160 + ssv63e ......... & i & 05 46 08.5 & @xmath98 10 03 & @xmath118 & @xmath161 & @xmath162 + ssv63ne ...... & i/0 & 05 46 08.9 & @xmath98 09 56 & @xmath120 & @xmath163 & @xmath164 + hh24-mms ... & 0 & 05 46 08.3 & @xmath98 10 43 & @xmath153 & @xmath154 & @xmath155 + hh25-mms ... & 0 & 05 46 07.3 & @xmath98 13 30 & @xmath165 & @xmath166 & @xmath167 + hh26-ir ........ & i & 05 46 03.9 & @xmath98 14 53 & @xmath165 & @xmath166 & @xmath167 + lbs17-h ........ & 0 & 05 46 30.8 & @xmath98 02 40 & @xmath168 & @xmath169 & @xmath170","summary":", we have obtained a deep x - ray image with the acis - s camera on board the _ chandra x - ray observatory_. a number of h emission - line objects were detected in the areas surrounding hh2426 , of which the weak - line t  tauri star ssv61 was the brightest source , at a steady luminosity of(0.310 kev) ergs  s .","abstract":"the hh24 - 26 star forming region within the lynds 1630 ( l1630 ) dark cloud in orion contains a remarkable collection of rare class  0 and class  i protostars , collimated molecular and ionized jets , and a luminous but spatially unresolved asca x - ray source . to study the x - ray properties of the embedded protostar population of that region , we have obtained a deep x - ray image with the acis - s camera on board the _ chandra x - ray observatory_. a number of h emission - line objects were detected in the areas surrounding hh2426 , of which the weak - line t  tauri star ssv61 was the brightest source , at a steady luminosity of(0.310 kev) ergs  s . two class  i protostars aligned with optical jets in hh24 , ssv63e and ssv63w , were also detected , as was the continuum radio source ssv63ne , which is very likely an extreme class  i or class  0 object . we observed no x rays from the class  0 protostars hh24-mms and hh25-mms , nor any from regions of the cloud bounded by hh25 and hh26 , at a upper limit of ergs  s . hh26-ir , the class  i object thought to be the origin of the hh26 flow , was not detected . near - infrared spectroscopy obtained at the nasa irtf reveals 3 ice bands in the spectra of ssv59 , 63e , 63w , and hh26-ir , and 2.3 co overtone absorption bands for ssv61 . ssv60 , which lies astride one end of the great arc of nebulosity forming hh25 , exhibits a deep infrared ice band and co absorption , but is not an x - ray source , and is most likely a distant background giant of late spectral type ."}
{"article_id":"1605.01523","section_id":"i","document":"the extra - galactic background light , or ebl ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; and @xcite ) , represents the flux received today from a steradian of extragalactic sky . it includes all far - uv to far - ir sources of photon production since the era of recombination , and thereby encodes a record of the entire energy production history of the universe from @xmath7380,000yrs after the big bang to the present day  see @xcite and @xcite for an interesting digression regarding the ebl s relation to olber s paradox . by convention , the ebl is defined as the radiation received between 0.1@xmath0 m to 1000@xmath0 m ( e.g. , @xcite , @xcite ; @xcite ; @xcite ) . this arises predominantly from star - light , agn - light , and dust reprocessed light  with some minimal ( @xmath8 ) contribution from direct dust heating due to accretion ( @xcite ; @xcite ) . photon production occurs not only at far - uv to far - ir wavelengths , but across the entire electro - magnetic spectrum ( e.g. , the cosmic x - ray background , see @xcite ; and the cosmic radio background , see @xcite ) . however , based on integrated energy considerations ( i.e. , @xmath9 ) , the cosmic emission is dominated , in terms of newly minted photons , by the far - uv to far - ir range . compared to the cosmic microwave background ( cmb ) the integrated - ebl is smaller by a factor of @xmath10 , despite the @xmath11 diminution of the cmb photon energies , but more than a factor of @xmath12 brighter than the other backgrounds . putting aside the cmb and the pre - recombination universe , the ebl is a product of the dominant astrophysical processes which have taken place over the past 13  billion years , in terms of energy redistribution ( baryonic mass @xmath13 photons ) . in particular , because of the expansion , the precise shape of the spectral energy distribution of the ebl depends on the cosmic star - formation history , agn activity history , and the evolution of dust properties over cosmic time . it therefore represents rich territory for comparison to galaxy formation and evolution models ( e.g. , @xcite ; @xcite ; @xcite ) . the ebl can be broken down into two roughly equal contributions from the uv - optical - near - ir and the mid- to far- ir wavelength ranges : the cosmic optical background ( cob ; 0.1@xmath0 m  8@xmath0 m ) and the cosmic infrared background ( cib @xmath14 m  1000@xmath0 m ; @xcite ) . despite the different wavelength ranges , the cob and cib ultimately derive from the same origin : star - formation and gravitational accretion onto super - massive black holes . the cob represents the star- and agn- light which directly escapes the host system , and obsequiously pervades into the inter - galactic medium . the cib represents that component which is first attenuated by dust near the radiation sources , and subsequently re - radiated in the mid- and far - ir . the near equal balance between the energy of the integrated cob and cib is very much a testimony to the severe impact of dust attenuating predominantly uv and optical photons , particularly given the very modest amount of baryonic mass in the form of dust ( @xmath15% relative to stellar mass , see for example @xcite ; @xcite ) . previous measurements of the ebl have come two flavours : direct measurements ( e.g. , @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) and integrated galaxy - counts ( e.g. , @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . these two methods should converge if the ebl is predominantly derived from galaxies ( including any agn component ) , and if the photometric data used to detect these galaxies are sufficiently deep .    until fairly recently , insufficient deep data existed to completely resolve the ebl using galaxy number - counts , and direct measurements appeared the more compelling constraint . however , with the advent of space - based facilities ( _ galex _ , _ hst _ , _ spitzer _ and _ herschel _ ) , and large ground - based facilities ( vlt , subaru ) , deep field data have now been obtained across the entire far - uv to far - ir range . the comparison of the direct estimates and integrated number - counts are proving fertile ground for debate . in the cib , the direct estimates agree reasonably well with the integrated source counts , which account for over 75% of the directly measured cib ( see @xcite and @xcite ) . the remaining discrepancy can be readily reconciled from extrapolations of the source counts , plus some additional contribution from lensed systems ( @xcite ) . in the optical and near - ir the situation is less clear , with many direct estimates being a factor of five or more greater than the integrated galaxy counts ( see for example the discussion on the near - ir background excess in @xcite or @xcite ) , despite the advent of very wide and deep data . either the integrated source counts are missing a significant quantity of the ebl in a diffuse component , or the direct measures are over - estimated ( i.e. , the backgrounds are under - estimated ) . recently a third pathway to the ebl has opened up , via the indirect attenuation of tev photons emanating from blazars , as observed with very high energy ( vhe ) experiments ( e.g. , the high energy stereoscopic system , h.e.s.s . , and the major atmospheric gamma imaging cherenkov telescope , magic ) . here the tev flux from a distant blazar , believed to extrude a well behaved power - law spectrum , interacts with the intervening ebl photon - field . preferential interactions between tev and micron photons create electron - positron pairs , thereby removing power from the received tev spectrum over a characteristic wavelength range . the proof of concept was demonstrated by @xcite and comprehensive measurements have recently been made by both the h.e.s.s . consortium ( @xcite ) and the magic team ( @xcite ) . these two independent measurements very much favour the low - ebl values . however , uncertainty remains as to the strength , and hence , impact of the inter - galactic magnetic field , the intrinsic blazar spectrum shape , and the role of secondary pev cascades . moreover , the two vhe studies mentioned above require a pre - defined ebl model , and use the shape of the received tev signal compared to the assumed intrinsic spectrum , to provide a normalisation point . hence spectral information is essentially lost . trickier to determine but more powerful is the potential for the vhe data to constrain both the normalisation _ and _ the shape of the ebl spectrum . a first effort was recently made by @xcite who again found results consistent with the low - ebl value , but perhaps more crucially provided independent confirmation of the overall shape across the far - uv to far - ir wavelength range . nevertheless , caveats remain as to the true intrinsic blazar spectral slope in the tev range , contaminating cascades from pev photons , the strength of any intervening magnetic fields , and in some cases the actual redshift of the blazars studied .    here we aim to provide the first complete set of integrated - galaxy light measurements based on a combination of panchromatic wide and deep number / source - count data from a variety of surveys which collectively span the entire ebl wavelength range ( 0.1@xmath0 m  1000@xmath0 m ) . our approach varies from previous studies , in that we abandon the concept of modeling the data with a galaxy - count ( backward propagation ) model . instead , as the number - count data is bounded in all bands  in terms of the contribution to the integrated luminosity density  we elect to fit a simple spline to the luminosity density data . in section  2 , we present the adopted number - count data , the trimming required before fitting , and estimates of the cosmic ( sample ) variance associated with each dataset . in section  3 , we describe our fitting process and the associated error analysis . we compare our measurements to previous estimates in section 4 , including direct and vhe constraints , before exploring possible sources of missing light . we finish by using the ebl model of driver & andrews ( see @xcite and @xcite ) as an appropriate fitting function to derive the total integrated energy of the cob and cib . all magnitudes are reported in the ab system , and where relevant we have used a cosmology with @xmath16 , and , @xmath17km / s / mpc .","summary":", we derive the igl and the extrapolated - igl in all bands . close agreement between our results and recent very high - energy experiments ( h.e.s.s . and magic ) , suggest that there may be an additional foreground affecting the direct estimates","abstract":"we combine wide and deep galaxy number - count data from gama , cosmos / g10 , _ hst _ ers , _ hst _ uvudf and various near- , mid- and far- ir datasets from eso , _ spitzer _ and _ herschel_. the combined data range from the far - uv ( 0.15 m ) to far - ir ( m ) , and in all cases the contribution to the integrated galaxy light ( igl ) of successively fainter galaxies converges . using a simple spline fit , we derive the igl and the extrapolated - igl in all bands . we argue undetected low surface brightness galaxies and intra - cluster / group light is modest , and that our extrapolated - igl measurements are an accurate representation of the extra - galactic background light . our data agree with most earlier igl estimates and with direct measurements in the far - ir , but disagree strongly with direct estimates in the optical . close agreement between our results and recent very high - energy experiments ( h.e.s.s . and magic ) , suggest that there may be an additional foreground affecting the direct estimates . the most likely culprit could be the adopted zodiacal light model . finally we use a modified version of the two - component model to integrate the ebl and obtain measurements of the cosmic optical background ( cob ) and cosmic infrared background ( cib ) of : nw m sr and nw m sr respectively ( 48:52% ) . over the next decade , upcoming space missions such as _ euclid _ and _ wfirst _ , have the capacity to reduce the cob error to , at which point comparisons to the very high energy data could have the potential to provide a direct detection and measurement of the reionisation field ."}
{"article_id":"1605.01523","section_id":"i","document":"we have brought together a number of panchromatic datasets ( gama , cosmos / g10 , _ hst _ ers , uvudf and other mid and far - ir data ) to produce galaxy number counts which typically span over 10 magnitudes and from the far - uv to the far - ir . having homogenized the data , we apply a consistent methodology to derive an integrated galaxy light and an extrapolated galaxy - count light ( eigl ) measurement . the method avoids traditional galaxy number - count models and , as all datasets are bounded in terms of the contribution to the igl , are simply fit with a 10-point spline . integrating the spline with or without extrapolation then leads to a complete set of igl measurements from the far - uv to far - ir . our error analysis includes four key components : a systematic photometry and/or zero - point offset of @xmath35 mag in all datasets , a re - fit based on 8 or 12 point splines , 10,001 monte - carlo realizations of the random errors , and 10,001 monte - carlo realizations of the cosmic variance estimates . we combine the errors linearly to produce our final eigl measurements , which are accurate to 2 - 30% depending on bandpass .    in comparison to previous data we generally agree with previous igl measurements , agree with direct measurements in the far - ir , but disagree with direct measurements in the optical ( see fig . [ fig : eblall ] , blue data points ) . we question whether the milky way or zodiacal light model requires revisiting for the direct optical and near - ir measurements . in particular we note ( see fig . [ fig : eblplot2 ] ) that the direct estimates from _ pioneer _ agree well with our eigl estimates as do the constraints from very high energy experiments , suggesting a possible issue with the inner solar system dust model . we briefly acknowledge that the eigl measurements could potentially miss light from low surface brightness systems ( 0 - 20% ) and intra cluster / group light ( 0 - 35% ) . insofar as studies exists evidence suggests such emissions are likely small ( @xmath80% ) and within our quoted errors . however studies to further constrain both the space - density of low surface brightness galaxies and the intra - halo light would clearly be pertinent . finally we overlay the two - component model of @xcite , which now includes agn @xcite and find that we can explain the eigl distribution rather trivially in terms of a spheroid / agn formation phase ( @xmath81 ) , followed by disc formation ( @xmath82 ) . using a slightly modified version of the model as a fitting function we find that the cob and cib contain @xmath2 nw m@xmath3 sr@xmath4 and @xmath5 nw m@xmath3 sr@xmath4 respectively , essentially a 48:52% split .    over the coming years with the advent of wide - field space - based imaging , and in particular _ euclid _ and _ wfirst _ , we note the great potential to constraint the uv , optical and near - ir optical backgrounds to below 1% . we thank the anonymous referee for comments which led to improvements in the paper , in particular the inclusion of cosmic variance errors . we thank adriano fontana for providing the hugs @xmath83 band number - count data . spd acknowledges support from the australian research council via discovery project dp130103505 . raw acknowledges support from nasa jwst interdisciplinary scientist grant nag5 - 12460 from gsfc . ld acknowledges support from the european research council in the form of advanced investigator grant , cosmicism and consolidated grant cosmicdust . ska and ahw are supported by the australian governments department of industry australian postgraduate award . gama is a joint european - australasian project based around a spectroscopic campaign using the anglo - australian telescope . the gama input catalogue is based on data taken from the sloan digital sky survey and the ukirt infrared deep sky survey . complementary imaging of the gama regions is being obtained by a number of independent survey programmes including galex mis , vst kids , vista viking , wise , herschel - atlas , gmrt and askap providing uv to radio coverage . gama is funded by the stfc ( uk ) , the arc ( australia ) , the aao , and the participating institutions . the gama website is http://www.gama - survey.org/. based on observations made with eso telescopes at the la silla paranal observatory under programme i d 179.a-2004 . the cosmos / g10 data is based on the spectroscopic catalogue of @xcite , containing a reanalysis of the zcosmos @xcite data obtained from observations made with eso telescopes at the la silla or paranal observatories under programme i d 175.a-0839 . photometric measurements are outlined in @xcite and use data acquired as part of the cosmic evolution survey ( cosmos ) project , derived using the lambdar software @xcite . all data and derived products are available via the cosmos / g10 web portal : http://ict.icrar.org / cutout / g10/. this web portal is hosted and maintained by funding from the international centre for radio astronomy research ( icrar ) at the university of western australia . data from a wide - 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count data from gama , cosmos / g10 , _ hst _ ers , _ hst _ uvudf and various near- , mid- and far- ir datasets from eso , _ spitzer _ and _ herschel_. the combined data range from the far - uv ( 0.15 m ) to far - ir ( m ) , and in all cases the contribution to the integrated galaxy light ( igl ) of successively fainter galaxies converges . using a simple spline fit our data agree with most earlier igl estimates and with direct measurements in the far - ir , but disagree strongly with direct estimates in the optical . finally we use a modified version of the two - component model to integrate the ebl and obtain measurements of the cosmic optical background ( cob ) and cosmic infrared background ( cib ) of : nw m sr and nw m sr respectively ( 48:52% ) . over the next decade , upcoming space missions such as _ euclid _ and _ wfirst _ , have the capacity to reduce the cob error to , at which point comparisons to the very high energy data could have the potential to provide a direct detection and measurement of the reionisation field .","abstract":"we combine wide and deep galaxy number - count data from gama , cosmos / g10 , _ hst _ ers , _ hst _ uvudf and various near- , mid- and far- ir datasets from eso , _ spitzer _ and _ herschel_. the combined data range from the far - uv ( 0.15 m ) to far - ir ( m ) , and in all cases the contribution to the integrated galaxy light ( igl ) of successively fainter galaxies converges . using a simple spline fit , we derive the igl and the extrapolated - igl in all bands . we argue undetected low surface brightness galaxies and intra - cluster / group light is modest , and that our extrapolated - igl measurements are an accurate representation of the extra - galactic background light . our data agree with most earlier igl estimates and with direct measurements in the far - ir , but disagree strongly with direct estimates in the optical . close agreement between our results and recent very high - energy experiments ( h.e.s.s . and magic ) , suggest that there may be an additional foreground affecting the direct estimates . the most likely culprit could be the adopted zodiacal light model . finally we use a modified version of the two - component model to integrate the ebl and obtain measurements of the cosmic optical background ( cob ) and cosmic infrared background ( cib ) of : nw m sr and nw m sr respectively ( 48:52% ) . over the next decade , upcoming space missions such as _ euclid _ and _ wfirst _ , have the capacity to reduce the cob error to , at which point comparisons to the very high energy data could have the potential to provide a direct detection and measurement of the reionisation field ."}
{"article_id":"astro-ph9801167","section_id":"i","document":"understanding the origins of the chemical elements is a fundamental goal of contemporary astrophysics . as this understanding has advanced in recent years , a few elements have been rather neglected . boron is one such element . a primary reason for its neglect has been that stellar absorption lines of the boron atom and ions are not detectable in spectra obtainable from the ground ; the low abundance of boron means that this element is detectable only through its strong resonance lines which are in the ultraviolet . the advance in ultraviolet stellar spectroscopy made possible by the _ hubble space telescope _ ( hst ) and its goddard high resolution spectrograph ( ghrs ) has led to new data on the boron abundance of cool and hot stars .    pioneering work on stellar boron abundances was presented by boesgaard & heacox ( 1978 ) who analyzed the @xmath0 1362   resonance line in spectra of early - type stars observed with the _ copernicus _ satellite . to map the evolution of boron with metallicity it is necessary to observe unevolved metal - poor stars . since these are cool , boron detection has to be made using the atomic resonance lines . no advance in our knowledge of the boron abundance came with the _ international ultraviolet explorer _ ( iue ) satellite ( an attempt to detect the resonance lines near @xmath0 2497   in a metal - poor star was made by molaro 1987 ) . duncan , lambert , & lemke s ( 1992 ) detection and analysis of the @xmath0 2497 lines in three metal - poor stars observed with the ghrs has been followed by other studies of these lines  see edvardsson et al . ( 1994 ) , rebull et al . ( 1996 ) , and duncan et al . ( 1997a , 1998 ) . kiselman ( 1994 ) and kiselman & carlsson ( 1996 ) showed that non - local thermodynamic equilibrium ( nlte ) effects have to be considered in analyses of the 2497   lines . standard big bang nucleosynthesis calculations do not predict a significant production of @xmath13li , @xmath14be , @xmath15b , and @xmath16b , which are thought to be produced by spallation reactions between cosmic rays and cno nuclei ( see ramaty , kozlovsky , & lingenfelter 1996 and ramaty et al . 1997 for recent discussions on the theoretical yields ) . models of inhomogeneous big bang nucleosynthesis suggest that observable amounts of be and b could be produced ( e.g. malaney & fowler 1989 ; kajino & boyd 1990 ; jedamzik et al . 1994 ) , but this possibility has been questioned on the theoretical grounds ( e.g. terasawa & sato 1990 ; reeves et al . 1990 ) .    in this paper , we derive the boron abundances of two metal - poor stars observed by us to fill in specific places of the study of the evolution of boron . bd @xmath173130 is a cool very metal - poor star ( [ fe / h]@xmath5 ) selected to extend b abundance determinations to a star of a factor of two more deficient than hd 140283 ( [ fe / h]@xmath18 ; previously studied by duncan et al . 1992 and edvardsson et al . 1994 ) , and is probably the most metal - poor slightly evolved star for which boron can be measured with hst . duncan et al . ( 1997a ) has also observed two stars ( bd @xmath193442 and bd @xmath13740 ) with metallicities [ fe / h]@xmath20 ; however , they are much warmer and , hence , boron is mainly ionized making more difficult to obtain a precise measurement of its abundance from the lines . our second star , hd 84937 , is of special interest because @xmath13li ( another expected product of spallation and fusion reactions driven by cosmic rays ) has been traced in its atmosphere ( smith , lambert , & nissen 1993 ; hobbs & thorburn 1994 , 1997 ) . both stars also have previous measurements of @xmath21li in the literature , and have been included in the samples for deriving beryllium and oxygen ( from uv oh lines ) abundances in metal - poor stars by garca lpez et al . ( 1998 ) and israelian , garca lpez , & rebolo ( 1998 ) , respectively , using the same stellar parameters .    to better study the dependence of the derived abundances on the tools usually employed in the analyses , we present here the first detailed comparison of boron abundances derived using the two sets of model photospheres widely employed in the analyses of stellar spectra : those calculated with the atlas program , constructed by r. l. kurucz , and those from the marcs program , developed at uppsala astronomical observatory . in both cases there have been considerable recent developments in these codes and their underlying input data . this careful analysis of boron abundances in very metal - poor stars , in which we also re - assess published abundances of old disk and halo unevolved stars , is aimed at better constraining observationally the nucleosynthetic origins of boron .","summary":"we have observed the 2497   line to derive the boron abundances of two very metal - poor stars selected to help in tracing the origin and evolution of this element in the early galaxy : bd and hd 84937 . the observations were conducted using the goddard high resolution spectrograph on board the _ hubble space telescope_. a very detailed abundance analysis via spectral synthesis has been carried out for these two stars , as well as for two other metal - poor objects with published spectra , using both kurucz and osmarcs model photospheres , and taking into account consistently the nlte effects on the line formation . we have also re - assessed all published boron abundances of old disk and halo unevolved stars . the evolution of the boron abundance with metallicity that emerges from the seven remaining stars with k and [ fe / h ] , for which beryllium abundances were derived using the same stellar parameters , shows a linear increase with a slope .","abstract":"we have observed the 2497   line to derive the boron abundances of two very metal - poor stars selected to help in tracing the origin and evolution of this element in the early galaxy : bd and hd 84937 . the observations were conducted using the goddard high resolution spectrograph on board the _ hubble space telescope_. a very detailed abundance analysis via spectral synthesis has been carried out for these two stars , as well as for two other metal - poor objects with published spectra , using both kurucz and osmarcs model photospheres , and taking into account consistently the nlte effects on the line formation . we have also re - assessed all published boron abundances of old disk and halo unevolved stars . our analysis shows that the combination of high effective temperature ( k , for which boron is mainly ionized ) and low metallicity ( [ fe / h ] ) makes it difficult to obtain accurate estimates of boron abundances from the 2497   line . this is the case of hd 84937 and three other published objects ( including two stars with [ fe / h ] ) , for which only upper limits can be established . bd , with [ fe / h ] and log n(b) , appears then as the most metal - poor star for which a firm measurement of the boron abundance presently exists . the evolution of the boron abundance with metallicity that emerges from the seven remaining stars with k and [ fe / h ] , for which beryllium abundances were derived using the same stellar parameters , shows a linear increase with a slope . furthermore , the b / be ratio found is constant at a value for stars in the range<-1 $ ] . these results point to spallation reactions of ambient protons and particles with energetic particles enriched in cno as the origin of boron and beryllium in halo stars ."}
{"article_id":"astro-ph9801167","section_id":"c","document":"hd 84937 was selected as a key target for this work because it is the only star for which there exist previous measurements of @xmath113li and @xmath14be . however , due to its high @xmath30 , our observations failed to provide a convincing detection of the @xmath0 2496.772   line and consequently we were forced to set an upper limit to the boron abundance . this disappointment led us to reexamine published spectra of similarly warm extremely metal - poor stars and to conclude that upper limits to rather than certain determinations of the boron abundance may be reached . this result has some influence on determinations of the evolution of the boron abundance with metallicity .    in the case of bd @xmath173130 , a cool giant , a concern may be that boron has been depleted below its initial abundance . to investigate this concern , we compare its li and be abundances with those of some other stars in our sample . equivalent widths of the @xmath0 6708   line were taken from thorburn ( 1994 ) and ryan et al . ( 1996 ) , and the abundances were derived using the stellar parameters adopted in table 1 and nlte curves of growth provided by ya . v. pavlenko ( obtained as described in pavlenko et al . 1995 and pavlenko & magazz 1996 ) . beryllium abundances were derived by garca lpez et al . li and be abundances are listed in table 2 , where the latter include an upwards correction of 0.1 dex to consider the mean difference with the gravities derived by nissen et al . ( 1997 ) from _ hipparcos _ parallaxes ( which does not affect either boron or lithium abundances ) .    evidently but not surprisingly li is depleted in bd @xmath173130 by more than 0.7 dex . a part of the observed depletion may have occurred as a dilution when the star evolved to the giant phase . boron and beryllium are less fragile elements than lithium , and it is unlikely that their abundances have been reduced by nuclear reactions . it can not be completely ruled out that these abundances have been slightly reduced by dilution . it will be shown below that the be and b abundances of the star fit the trends with metallicity defined by the other stars , and a small increment of the observed abundances of bd @xmath173130 would not change the general conclusions about the synthesis of boron . initial results on the evolution of the b abundance with metallicity ( [ fe / h ] ) were provided by duncan et al . ( 1992 ) from just three lte b abundances of halo stars . the linear trend between log n(b ) and [ fe / h ] was confirmed in essence by kiselman & carlsson ( 1996 ) who included non - lte effects for boron , and by duncan et al . ( 1997a ) who analyzed additional stars . our rediscussion adds two stars and recognizes that only upper limits to the b abundance are presently obtainable for the warmest stars . in addition , we give b and be abundances for stellar parameters derived in a uniform way for the entire sample . figure 9 shows the lte and nlte boron abundances of those stars listed in table 1 against [ fe / h ] . in the upper panel the symbols are also labeled with the adopted effective temperatures . as explained in section 4 , we are only considering as real measurements those made in metal - poor stars with @xmath114 k. nlte corrections also affect more strongly to the hotter stars , inducing a larger scatter in the boron - metallicity plot when including the abundances associated with the upper limits . for comparison , we have also included in figure 9 the boron abundances of two solar - metallicity stars : @xmath115 peg and @xmath116 uma , taken directly from lemke et al . nlte effects on the b abundances were taken into account for these stars following kiselman & carlsson ( 1996 ) . two sets of fits are shown in figure 9 . dashed lines represent linear regressions performed using all metal - poor stars with @xmath117 k , and solid lines restrict the fits to cool stars with [ fe / h]@xmath118 . this distinction is done to compare with the behavior of beryllium abundances , for which a change of slope at [ fe / h]@xmath119 is apparent from the observations ( garca lpez et al . 1998 ) . all regression analyses were carried out taking into account the error bars in boron abundances and metallicities , using the routine _ fitexy _ of press et al . ( 1992 ) available in the idl astronomy user s library . these are the results :    * lte , @xmath117 k : + @xmath120 } ,   \\ , n=9 , \\ , \\chi^2_\\nu=0.86 , \\ , q=0.54 $ ] , + where @xmath121 is the number of stars included in the fit , @xmath122 is @xmath123 divided by the number of degrees of freedom @xmath124 ( also called _ reduced _ @xmath123 ; @xmath125 in this case ) , and @xmath126 is the probability that a correct model would give a value equal or larger than the observed chi squared ( a small value of @xmath126 indicates a poor fit ; @xmath127 provides an acceptable fit ) . * lte , @xmath117 k and [ fe / h]@xmath118 : + @xmath128 } ,   \\ , n=7 , \\ , \\chi^2_\\nu=0.42 , \\ , q=0.84 $ ] . * nlte , @xmath117 k : + @xmath129 } ,   \\ , n=9 , \\ , \\chi^2_\\nu=0.86 , \\ , q=0.54 $ ] . * nlte , @xmath117 k and [ fe / h]@xmath118 : + @xmath130 } ,   \\ , n=7 , \\ , \\chi^2_\\nu=0.34 , \\ , q=0.89 $ ] . the plots make evident that a linear increase of the boron abundance with increasing metallicity describes very well the trend observed in the data , and a change of slope may occur at the halo - disk transition at [ fe / h ] @xmath131 . duncan et al . ( 1997a ) found slopes of @xmath132 and @xmath133 for their linear fits to 11 stars in lte and nlte , respectively . our corresponding slopes of @xmath134 and @xmath135 , obtained using 9 stars ( without upper limits ) are consistent with those of duncan et al . within the error bars . if we include the data associated with the metal - rich stars @xmath115 peg and @xmath116 uma , which have not been adjusted to our @xmath30 scale , the lte and nlte slopes do not change appreciably ( @xmath136 and @xmath137 , respectively ) . the slopes are slightly steeper and outside the error bars when compared with the results of duncan et al . , if we consider only those 7 stars with [ fe / h ] @xmath118 . we will consider our nlte abundances and the fit for stars with @xmath117 k and [ fe / h]@xmath118 as the actual values to be used in the discussion performed below this point .    in studies of boron evolution , oxygen abundances may be a preferable alternative to the iron abundances for astrophysical reasons . in particular , oxygen is synthesized primarily by the most massive supernovae whose ejecta ( see below ) may be the source of the energetic particles responsible for boron production by spallation . unfortunately , observational determinations of oxygen abundances in metal - poor stars have been a matter of controversy during the last years ( e.g. abia & rebolo 1989 ; bessell , sutherland , & ruan 1991 ; nissen et al . 1994 ; cavallo , pilachowski , & rebolo 1997 ) . we examined the boron - oxygen trend using the oxygen abundances found by cavallo et al . ( 1997 ) from high - resolution spectra of the ir triplet in a sample of 24 stars with @xmath138\\leq -0.48 $ ] . these results were employed to define the relation between [ o / h ] and [ fe / h ] which was then used to establish the b versus o trend . we find :    @xmath139}$ ] . this slope is steeper than the comparable trend found by duncan et al . ( 1997a ) , with a slope of 0.82@xmath140 when using a mean [ o / h ] versus [ fe / h ] relation established using abundances extracted from the literature for the stars in their sample . almost in parallel with our analysis of boron , israelian et al . ( 1998 ) are deriving oxygen abundances in a wide sample of metal - poor stars , including those considered here , using oh lines in the 30853256   region and the same stellar parameters employed in this paper . until controversy about oxygen in metal - poor stars is clearly resolved , it must suffice to note that the boron and oxygen abundances are approximately linearly related . two modes of nucleosynthesis of boron compete ( in theory ) for primacy : spallation reactions driven by energetic ( cosmic rays ) particles in extra - stellar environments , and neutrino - induced spallation of @xmath141c occurring in type ii supernovae . a measure of the relative contributions of the two modes is offered by the b / be ratio ( at a given [ fe / h ] ) because beryllium is synthesized ( in theory ) only by spallation reactions with high energy particles . moreover , in these spallation reactions , the b / be production ratio is essentially independent of the composition and the energy spectrum of the high energy particles . thus , the observed b / be ratio reveals the relative roles of the two modes of boron nucleosynthesis . figure 10 shows the comparison between boron ( nlte ) and beryllium abundances against metallicity . beryllium data were taken from garca lpez et al . ( 1998 ) , who carried out a detailed spectral synthesis of the @xmath0 3131   region for 28 stars with @xmath142\\leq -3 $ ] , using high - resolution observed spectra . these authors also included all metal - poor stars with accurate be abundance available , and repeated measurements on the same star were averaged both in be and in [ fe / h ] . also shown for comparison are the be abundances given by lemke et al . ( 1993 ) for the metal - rich stars @xmath115 peg and @xmath116 uma , estimated from boesgaard s ( 1976 ) equivalent widths measured on photographic spectra . a linear regression analysis for stars with [ fe / h ] @xmath118 , without considering the upper limits ( not shown in fig . 10 ) , provides :    @xmath143 } ,   \\ , n=29 , \\ , \\chi^2_\\nu=0.81 , \\ , q=0.75 $ ] . these values of @xmath122 and @xmath126 indicate an excellent fit over a significant sample of metal - poor stars . these are lte abundances but corrections for non - lte effects are small ( @xmath144 dex in general see garca lpez et al . 1995 and kiselman & carlsson 1995 ) . the slopes of the observed trends against metallicity are very similar for be and b for stars with [ fe / h ] @xmath118 . indeed , the slopes are identical within the error bars . duncan et al . ( 1997a ) found a similar behavior when comparing their nlte b abundances and published be abundances for their sample of stars . using the be abundances given by garca lpez et al . ( 1998 ) , derived with the stellar parameters listed in table 1 and shown in table 2 , the average b / be ratio for the seven stars with @xmath117 k and [ fe / h ] @xmath118 is b@xmath145/be @xmath146 ( 1 @xmath147 ) . for all of these stars , with the exception of bd @xmath173130 , independent beryllium measurements are available in the literature based on high - resolution ccd spectra , slightly different stellar parameters , and employing spectral synthesis or curves of growth . garca lpez et al . ( 1995 ) showed that these independent lte analyses provide very similar be abundances when adjusted for differences in the stellar parameters ( especially the surface gravity ) . the average be abundances for these seven stars differ by @xmath148 dex from the individual values listed in table 2 . using the average be values we obtain a mean ratio b@xmath145/be @xmath149 . figure 11 shows the behavior of log ( b@xmath145/be ) against metallicity . the solid line represents the mean value and dotted lines show the @xmath150 uncertainties : @xmath151 . all ratios are compatible with this mean value and its uncertainty within the error bars . a linear regression fit taking into account the errors in both coordinates provides :    @xmath152 } ,   \\ , n=7 , \\ , \\chi^2_\\nu=0.32 , \\ , q=0.90 $ ] ,    which is fully consistent with the mean value and is shown as a dashed line in figure 11 . duncan et al . ( 1997a ) obtained a mean value b@xmath153/be @xmath154 using 9 stars . be abundances adopted by duncan et al . ( 1997a ) are , in general , larger than those adopted here and that is the main reason why they obtain a smaller b / be ratio . it is worthwhile to consider the trends given by the regression analyses of boron and beryllium against metallicity , which better represent their overall behavior . molaro et al . ( 1997 ) derived beryllium abundances for a sample of metal - poor stars and , combining them with measurements available in the literature , obtained a linear fit of be abundance against metallicity with a slope of @xmath155 for 19 stars in the interval @xmath156 < -0.8 $ ] . this value is compatible with the slope @xmath157 found by garca lpez et al . ( 1998 ) for 29 stars in the interval @xmath158 < -1 $ ] . using this relation and the fit obtained in this work between log n(b)@xmath153 and [ fe / h ] for stars with @xmath117 k and [ fe / h ] @xmath118 , we find a mean ratio of b@xmath145/be @xmath159 . using our boron relation and the beryllium fit provided by molaro et al . ( 1997 ) , this ratio is just 17 .      two observational facts about the b and be abundances stand out : ( i ) metal - poor ( [ fe / h]@xmath160 ) stars have a constant boron - to - beryllium ratio @xmath10 , and ( ii ) the relation between boron ( or beryllium ) and metallicity has a slope of @xmath9 . the linear dependence , first seen for be vs fe by gilmore et al . ( 1992 ) and then by duncan et al . ( 1992 ) for b vs fe , was a surprise . simple models of spallation of ambient cno nuclei in the interstellar medium by cosmic ray protons and @xmath12s had predicted a quadratic dependence ( b @xmath161 fe@xmath162 ) . several explanations for the observed linear dependence have been advanced . in essence , most explanations invoke spallation of cno nuclei in energetic collisions with ambient protons and @xmath12s . if the composition of the energetic particles is greatly enriched in cno , as could be assumed for supernovae ejecta or winds from wolf - rayet stars , a quasi - linear relation between b ( and be ) and metallicity would result ( duncan et al . 1992 ; vangioni- flam et al . other possibilities , such as local spallation by high - energy protons and @xmath12s in enriched regions around supernovae , seem less probable ( feltzing & gustafsson 1994 ) . at any rate , fact ( ii ) is to be explained largely by astrophysical issues . the simplest interpretation of fact ( i ) is that b and be are made by the same nucleosynthetic process . this process is spallation of cno nuclei by collisions with protons and @xmath12s . early calculations of yields from spallation gave a b / be ratio near 20 : reeves ( 1994 ) gives the ratio as 17 for production by high energy ( @xmath163 100 mev nucleon@xmath29 ) cosmic rays . the primary factors setting the ratio are the cross - sections for the spallation reactions , i.e. , nuclear physics rather than astrophysics . theoretical yields are thoroughly discussed by ramaty et al . ( 1996 ) who investigate their dependence on the energy spectrum and composition of the energetic particles ( cosmic rays ) , and on the composition of the ambient medium . this investigation shows that a ratio of b / be @xmath10 from spallation does not constrain the composition of either the energetic particles or the ambient medium , and , provided the energy spectrum of the particles is not biased to threshold energies for the proton and @xmath12 on cno nuclei spallation reactions , the ratio does not constrain the energy spectrum . ramaty et al . stress that the various combinations of energy and composition of energetic particles and composition of the ambient medium call for different amounts of energy to be put into energetic particles : certain combinations are very inefficient . if the particles have the predicted composition of the ( most massive ) supernovae ejecta or wolf - rayet winds , ramaty et al.s condition on the energy available for high energy particles is met . the condition is very difficult to impossible to meet if the high energy particles have the composition of the sun , the galactic cosmic rays or of the ejecta of low mass type ii supernovae . it is intriguing that this argument about the composition of the high energy particles is consistent with that adduced from the linear relation between b ( and be ) and fe . this constancy of be / fe and b / fe for metal - poor stars led ramaty et al . ( 1997 ) to relate the production rates of be and b to the fe production rate by type ii supernovae via cosmic - ray acceleration . considering that the @xmath16b/@xmath15b value in metal - poor stars is probably not lower than the solar system ratio of @xmath164 ( chaussidon & robert 1995 ) , a b / be @xmath10 would imply an initial acceleration energy of about 60 mev nucleon@xmath29 ( see fig . 13@xmath165 of ramaty et al . 1997 ) , and a rapid increase in the initial energy needed ( @xmath166 mev nucleon@xmath29 ) for slightly lower values ( 1718 ) of b / be . beryllium is thought to be synthesized only by spallation reactions but boron synthesis by spallation may be supplemented by type ii supernovae in which boron is made by neutrino - induced spallation of carbon ( the @xmath124-process ) . timmes , woosley , & weaver ( 1996 ) in a detailed study of galactic chemical evolution suggest that predicted yields of boron by supernovae reproduce well the b versus fe trend of the halo and disk _ without _ the introduction of spallation processes . this is incompatible with the attribution of be synthesis to spallation processes and the observed ratio b / be @xmath10 which implies that boron synthesis is also by spallation processes . we conclude that yields of boron from the @xmath124-process have been overestimated . vangioni - flam et al . ( 1996 ) , on the basis of few published b abundances , concluded that the @xmath124-process is at least a factor of 5 less efficient than supposed by timmes et al . ( 1995 ) . alternative models of chemical evolution of the galactic halo ( e.g. , casuso & beckman 1997 ) also give consistent results with the observed linear trends of b and be vs. fe at very low metallicity . these authors consider an exponentially increasing flow of gas from the halo to form the bulge . the strong be and b enrichment in the halo is attributed to the presence of more star - forming gas at very low metallicity , and to increased yields of carbon in intermediate and low - mass metal - poor stars . the be / b ratios that they predict are also similar to the observed ones . it seems that under certain hypothesis for the evolution of the gas and for the initial mass function , conventional cosmic ray spallation processes may then provide an explanation to the observations .    in short , the ratio b / be @xmath10 is strong evidence that b and be are products of spallation reactions between protons and/or @xmath12s and cno nuclei .    the beryllium abundances ( figure 10 ) indicate that there is a change of slope in the run of be with fe at about [ fe / h ] @xmath119 , the canonical transition between halo and disk ( a more detailed discussion based on the be data is presented in garca lpez et al . the very limited data on the boron abundance in disk stars suggests that the b versus fe trend follows the be versus fe trend such that b / be remains constant at @xmath10 . additional data for boron at these metallicities is crucial to confirm this and for a better understanding of the halo - disk transition . the meteoritic abundances ( grevesse , noels , & sauval 1996 ) give b / be @xmath167 in agreement with our result from metal - poor stars .","summary":"these results point to spallation reactions of ambient protons and particles with energetic particles enriched in cno as the origin of boron and beryllium in halo stars .","abstract":"we have observed the 2497   line to derive the boron abundances of two very metal - poor stars selected to help in tracing the origin and evolution of this element in the early galaxy : bd and hd 84937 . the observations were conducted using the goddard high resolution spectrograph on board the _ hubble space telescope_. a very detailed abundance analysis via spectral synthesis has been carried out for these two stars , as well as for two other metal - poor objects with published spectra , using both kurucz and osmarcs model photospheres , and taking into account consistently the nlte effects on the line formation . we have also re - assessed all published boron abundances of old disk and halo unevolved stars . our analysis shows that the combination of high effective temperature ( k , for which boron is mainly ionized ) and low metallicity ( [ fe / h ] ) makes it difficult to obtain accurate estimates of boron abundances from the 2497   line . this is the case of hd 84937 and three other published objects ( including two stars with [ fe / h ] ) , for which only upper limits can be established . bd , with [ fe / h ] and log n(b) , appears then as the most metal - poor star for which a firm measurement of the boron abundance presently exists . the evolution of the boron abundance with metallicity that emerges from the seven remaining stars with k and [ fe / h ] , for which beryllium abundances were derived using the same stellar parameters , shows a linear increase with a slope . furthermore , the b / be ratio found is constant at a value for stars in the range<-1 $ ] . these results point to spallation reactions of ambient protons and particles with energetic particles enriched in cno as the origin of boron and beryllium in halo stars ."}
{"article_id":"astro-ph9801167","section_id":"c","document":"bd @xmath168 3130 observed and analyzed here is the most metal - poor star for which a firm measurement of the boron abundance presently exists ( two slightly more metal - poor stars  bd @xmath169 and bd @xmath170 740  have been analyzed but we consider that the @xmath0 2497   line has not been positively identified in published spectra . ) our result and slightly revised results from other metal - poor stars establish the run of boron with iron for halo stars : the boron abundance increases linearly , with a slope @xmath171 , with the iron abundance . with beryllium abundances consistently derived for the same stars using the same atmosphere parameters , the b / be ratio is found to be @xmath10 . a direct interpretation of these results is that b and be in the halo were synthesized by spallation reactions between ambient protons and @xmath12s and high energy particles with a composition enriched in cno . the b / be ratio is in fine agreement with the predictions ( vangioni - flam et al . 1996 ; ramaty et al . 1996 , 1997 ) . this is a significant result because the predicted b / be ratio is largely independent of the details of the modeling of the spallation process being largely determined by laboratory measurements of spallation cross - sections . the linear trend of b ( and be ) with fe is dependent on the astrophysics of spallation in the halo but can be reproduced with plausible assumptions ( vangioni - flam et al . 1996 ) . a consistent picture of boron synthesis has emerged for the halo of our galaxy . stars more metal - poor than bd @xmath168 3130 are now known but it will not be easy to extend measurements of boron abundance to these stars . the @xmath0 2497   line will be too weak in the warmest of these stars , as we have found for less extreme stars . some extension to lower metallicity will be possible for cool stars but for the fact that the candidate stars are faint requiring prohibitively long exposures with hst . almost certainly , the boron plateau signifying detection of primordial boron will elude us ; boron ( and beryllium ) from homogeneous and inhomogeneous big bangs is predicted to have an abundance 7 or 8 dex below the abundance found here for bd @xmath168 3130 ( thomas et al . 1993 , 1994 ) . it is a pleasure to acknowledge the following people for their help with the analyses described in this work : martin asplund for computing several osmarcs models and their corresponding fluxes , ya . v. pavlenko for providing nlte li curves of growth , and the staff at stsci and ecf for their support during all phases of these hst observations . the comments of an anonymous referee have been of value in improving the content of this article . this work was partially supported by the space telescope science institute ( grant go-05862 ) , and the spanish dges under projects pb92 - 0434-c02 - 01 and pb95 - 1132-c02 - 01 . be and bg acknowledge support from the swedish natural science research council ( nfr ) and the swedish space board . lccccccc bd @xmath173130 & 5170@xmath172150 & 2.50@xmath1720.30 & @xmath173 & @xmath174 & @xmath175 & 0.05 & 1,a hd 84937 & 6210@xmath172120 & 4.00@xmath1720.10 & @xmath176 & @xmath79 & @xmath79 & @xmath177 & 1,a bd @xmath193442 & 6200@xmath172150 & 3.50@xmath1720.20 & @xmath178 & @xmath96 & @xmath96 & @xmath179 & 2,a bd @xmath973578 & 6080@xmath172120 & 3.85@xmath1720.10 & @xmath180 & @xmath103 & @xmath103 & @xmath181 & 3,a hd 142373 & 5795@xmath172100 & 4.30@xmath1720.10 & @xmath182 & @xmath183 & 1.96 & 2.03 & 3,b hd 184499 & 5810@xmath172100 & 4.00@xmath1720.10 & @xmath184 & @xmath185 & 1.71 & 1.83 & 3,b hd 76932 & 5800@xmath172100 & 3.85@xmath1720.10 & @xmath186 & @xmath187 & 1.68 & 1.85 & 3,b hd 201891 & 5870@xmath172100 & 4.00@xmath1720.10 & @xmath188 & @xmath189 & 1.52 & 1.75 & 4,b hd 194598 & 5960@xmath172120 & 4.15@xmath1720.10 & @xmath190 & @xmath191 & 1.38 & 1.67 & 3,b hd 64090 & 5385@xmath172100 & 4.45@xmath1720.10 & @xmath192 & @xmath193 & 1.02 & 1.21 & 3,b hd 19445 & 5810@xmath172150 & 4.30@xmath1720.10 & @xmath194 & @xmath195 & 0.18 & 0.53 & 4,b hd 140283 & 5550@xmath172100 & 3.35@xmath1720.10 & @xmath196 & @xmath197 & @xmath198 & 0.23 & 4,b bd @xmath105740 & 6295@xmath172120 & 4.00@xmath1720.10 & @xmath199 & @xmath200 & 0.42 & 1.31 & 3,b    lccc hd 76932 & @xmath186 & @xmath201 & @xmath202 hd 201891 & @xmath188 & @xmath203 & @xmath204 hd 194598 & @xmath190 & @xmath205 & @xmath206 hd 64090 & @xmath192 & @xmath207 & @xmath208 hd 19445 & @xmath194 & @xmath209 & @xmath210 hd 140283 & @xmath196 & @xmath211 & @xmath206 bd @xmath173130 & @xmath173 & @xmath212 & @xmath213","summary":"bd , with [ fe / h ] and log n(b) , appears then as the most metal - poor star for which a firm measurement of the boron abundance presently exists .","abstract":"we have observed the 2497   line to derive the boron abundances of two very metal - poor stars selected to help in tracing the origin and evolution of this element in the early galaxy : bd and hd 84937 . the observations were conducted using the goddard high resolution spectrograph on board the _ hubble space telescope_. a very detailed abundance analysis via spectral synthesis has been carried out for these two stars , as well as for two other metal - poor objects with published spectra , using both kurucz and osmarcs model photospheres , and taking into account consistently the nlte effects on the line formation . we have also re - assessed all published boron abundances of old disk and halo unevolved stars . our analysis shows that the combination of high effective temperature ( k , for which boron is mainly ionized ) and low metallicity ( [ fe / h ] ) makes it difficult to obtain accurate estimates of boron abundances from the 2497   line . this is the case of hd 84937 and three other published objects ( including two stars with [ fe / h ] ) , for which only upper limits can be established . bd , with [ fe / h ] and log n(b) , appears then as the most metal - poor star for which a firm measurement of the boron abundance presently exists . the evolution of the boron abundance with metallicity that emerges from the seven remaining stars with k and [ fe / h ] , for which beryllium abundances were derived using the same stellar parameters , shows a linear increase with a slope . furthermore , the b / be ratio found is constant at a value for stars in the range<-1 $ ] . these results point to spallation reactions of ambient protons and particles with energetic particles enriched in cno as the origin of boron and beryllium in halo stars ."}
{"article_id":"1209.4654","section_id":"i","document":"long - duration gamma - ray bursts ( grbs ) have been linked to the deaths of massive stars , and hence to star formation activity , through their association with star forming galaxies ( e.g. , @xcite ) and with type ic supernova explosions ( e.g. , @xcite ) . across a wide range of cosmic history a substantial fraction of the star formation activity ( @xmath15 at the peak of the star formation history , @xmath16 ) is obscured by dust , with about 15% of the total star formation rate density occurring in ultra - luminous infrared galaxies ( e.g. , @xcite ) . as a result , we expect some grbs to occur in dusty environments that will diminish or completely extinguish their optical ( and perhaps even near - ir ) afterglow emission . such events can be used as signposts for the locations and relative fraction of obscured star formation across a wide redshift range . in addition , they can provide insight into the role of metallicity in grb progenitors since dusty environments generally require substantial metallicity . these so - called optically - dark grbs are indeed known to exist ( e.g. , @xcite ) , but the lack of an optical detection does not necessarily point to dust obscuration . most prosaically , the lack of detected optical emission may be due to inefficient follow - up observations , or to intrinsically dim events ( e.g. , @xcite ) . another potential origin of dark bursts is a high redshift , with the optical emission suppressed by ly@xmath17 absorption at @xmath18@xmath19 @xcite . such events are clearly of great interest since a dropout above @xmath20 @xmath21 m points to @xmath22 , while events which are also dark in the near - ir can potentially arise at @xmath23 ( @xmath24-band dropout ) . naturally , high redshift bursts will also lack host galaxy detections in the optical band . on the other hand , their afterglow emission redward of the ly@xmath17 break will follow the expected synchrotron spectrum ( @xmath25 ) with @xmath26 @xcite .    to determine whether a burst is genuinely dark , due to extinction or to a high redshift rather than to an inefficient search , it is common to compare the observed limits with the expected optical / near - ir brightness based on the x - ray afterglow . this approach relies on the simple power law shape of the afterglow synchrotron emission . one definition of dark bursts uses an optical to x - ray spectral index of @xmath27 ( @xmath28 is the slope of the synchrotron spectrum in log space ; see @xcite for details ) , since this is the shallowest expected slope in the standard afterglow model . a variant of this condition uses knowledge of the x - ray spectral index ( @xmath29 ) , and defines bursts as dark if @xmath30 @xcite , since this is the shallowest expected relative slope . these definitions can reveal evidence for dust extinction even if an optical afterglow is detected . this approach has been used by several groups to identify and study dark bursts . in the pre-  sample @xcite found that about 10% of the bursts are dark , while @xcite found a mean extinction of @xmath31 mag , indicating that most events are not dark . @xcite studied several bursts with  x - ray and uv / optical detections and found a mean extinction level of @xmath32 mag , and that bursts which are dark blueward of @xmath33-band are likely to have rest - frame extinction about an order of magnitude larger . @xcite used rapid optical observations of 63  bursts and found that about 50% showed evidence of mild extinction . a similar conclusion was reached by @xcite based on rapid optical observations of 29  bursts , with an 80% detection fraction , but with roughly half exhibiting suppression with respect to the x - ray emission . a follow - up study of the latter sample by @xcite aimed at identifying host galaxies in the optical ( thereby ruling out a high redshift origin ) and found that @xmath34 of  bursts are located at @xmath22 . the majority of the dark bursts in their sample instead require @xmath35 mag , with a few cases reaching @xmath36 mag . @xcite studied a complete sample of 58 bright  bursts , of which 52 have known redshifts and found that the fraction of dark bursts is about 30% , mainly due to extinction ( nearly all the dark bursts in their sample have @xmath0 ) . thus , the afterglow emission of @xmath37 of all grbs are affected by dust , although in most cases the required extinction is modest , @xmath32 mag @xcite . there are only a few known cases with large extinction of @xmath38 mag . concurrent studies of the neutral hydrogen column density distribution , inferred from the x - ray afterglow spectra , suggest that dark bursts exhibit systematically larger values of @xmath39 @xmath6 compared to bursts with little or no extinction , which have a median of @xmath40 @xmath6 @xcite . on the other hand , the measured extinction for grbs is generally lower than expected based on the values of @xmath41 and the galactic @xmath7 relation , previously attributed to dust destruction by the bright x - ray / uv emission ( e.g. , @xcite ) .    finally , the host galaxies of at least some dark bursts appear to be redder , more luminous , more massive , and more metal rich than the hosts of optically - bright grbs @xcite , potentially indicating that the extinction is interstellar in origin rather than directly associated with the burst environment . one specific example is grb030115 , not only one of the first examples of a heavily extinguished grb afterglow , but residing in a host classified as an extremely red object ( ero ; @xcite ) . some host galaxies of optically - bright bursts have been detected in the radio and ( sub)millimeter ranges ( e.g. , @xcite , indicating obscured star formation rates of @xmath42 m@xmath10 yr@xmath11 @xcite . this suggests that the dust distribution within the host galaxies is patchy and that not all grbs in dusty host galaxies are necessarily dust - obscured @xcite . further work by @xcite indicates that dark grb host galaxies may be systematically redder and more massive than optically bright grb host galaxies and have lower metallicity than sub - millimeter galaxies , leading to prior biases in grb host galaxy population studies . here we present multi - wavelength observations that reveal two of the darkest known bursts to date , grbs 110709b and 111215a . these events have such large rest - frame extinction that they lack any afterglow detection in the optical and near - ir bands ( to @xmath43 @xmath21 m ) despite rapid follow - up . however , both events are detected in the radio , providing sub - arcsecond positions and secure associations with host galaxies detected in the optical . this allows us to rule out a high redshift origin , while the combination of radio and x - ray data place robust lower limits on the rest - frame extinction , with @xmath2 and @xmath44 mag ( for @xmath4 ) , respectively . the radio and x - ray data also allow us to determine the explosion properties and the circumburst densities . this study demonstrates that radio detections with the jvla , and soon the atacama large millimeter / submillimeter array ( alma ) , provide a promising path to accurate localization of dark grbs , robust estimates of the extinction in the absence of any optical / near - ir detections , and a comparative study of their explosion properties and parsec - scale environments . the plan of the paper is as follows . we describe the multi - wavelength observations of grbs 110709b and 111215a and their host galaxies in  [ sec : obs ] . these observations establish that both events are dark due to extinction . we model the radio and x - ray data to extract the minimum required extinction , as well as the explosion and circumburst properties in  [ sec : model ] . in  [ sec : disc ] we place the large inferred extinction values and the inferred burst properties within the framework of existing samples of optically - bright and dark bursts . we summarize the results and note key future directions in  [ sec : conc ] . throughout the paper we report magnitudes in the ab system ( unless otherwise noted ) and use galactic extinction values of @xmath45 mag for grb110709b and @xmath46 mag for grb111215a @xcite . we use the standard cosmological parameters : @xmath47 km s@xmath11 mpc@xmath11 , @xmath48 , and @xmath49 .","summary":"sub - arcsecond positions enabled by radio detections lead to robust host galaxy associations , with optical detections that indicate ( 110709b ) and ( 111215a ) . these are among the largest extinction values inferred for dark bursts to date . this study establishes the critical role of radio observations in demonstrating the origin and properties of dark grbs .","abstract":"we present x - ray , optical , near - infrared ( ir ) , and radio observations of grbs 110709b and 111215a , as well as optical and near - ir observations of their host galaxies . the combination of x - ray detections and deep optical / near - ir limits establish both bursts as `` dark '' . sub - arcsecond positions enabled by radio detections lead to robust host galaxy associations , with optical detections that indicate ( 110709b ) and ( 111215a ) . we therefore conclude that both bursts are dark due to substantial rest - frame extinction . using the radio and x - ray data for each burst we find that grb110709b requires mag and grb111215a requires mag ( ) . these are among the largest extinction values inferred for dark bursts to date . the two bursts also exhibit large neutral hydrogen column densities of ( ) as inferred from their x - ray spectra , in agreement with the trend for dark grbs . moreover , the inferred values are in agreement with the galactic relation , unlike the bulk of the grb population . finally , we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming - corrected energy of erg ( ) expanding into a wind medium with a high density , m yr ( at cm ) . while the energy release is typical of long grbs , the inferred density may be indicative of larger mass loss rates for grb progenitors in dusty ( and hence metal rich ) environments . this study establishes the critical role of radio observations in demonstrating the origin and properties of dark grbs . observations with the jvla and alma will provide a sample with sub - arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in grb progenitors ."}
{"article_id":"1209.4654","section_id":"c","document":"the large rest - frame extinction that is required to explain the lack of optical and near - ir emission from grbs 110709b and 111215a is uncommon amongst known grbs . in figure [ fig : avz ] we plot the minimum values of @xmath240 for the two bursts as a function of redshift , along with several comparison samples from the literature of optically - bright bursts and previous dark bursts . in general , optically - bright grbs have inferred extinction values of @xmath241 mag , with a mean of @xmath242 mag @xcite . dark grbs span @xmath243 mag @xcite , with the largest extinction values of @xmath244 mag inferred for grbs 061222 , 070306 , and 070521 @xcite . in this context , the extinction values measured here are at the top of the distribution , @xmath2 mag ( 110709b ) and @xmath245 mag ( 111215a ) at @xmath4 .    in figure [ fig : nhz ] we plot the intrinsic neutral hydrogen column densities , @xmath41 , from our x - ray analysis as a function of redshift , in comparison with the population of all  long grbs with known redshifts ( up to december 2010 ; @xcite ) . we find that grbs 110709b and 111215a lie at the upper end of the distribution for long grbs . in particular , at a fiducial redshift of @xmath4 they have @xmath246 and @xmath247 , respectively , in comparison to the median value of all detections and upper limits of @xmath248 . this result confirms recent suggestions that dark grbs have systematically larger neutral hydrogen columns , generally with @xmath249 @xcite ; see figure  [ fig : nhz ] . indeed , only a handful of events in the sample have values of @xmath41 that are comparable to that of grb111215a . the same conclusion is true for grb110709b if it resides at the upper end of the allowed redshift distribution ( @xmath250 ) , although at @xmath251 its neutral hydrogen column is typical of the overall long grb population . a correlation between extinction and @xmath252 is known to exist in the milky way and the magellanic clouds , with @xmath253 @xmath6 @xcite . as shown in figure  [ fig : avnh ] , optically - bright grbs generally have lower values of @xmath240 than would be inferred from this relation ( e.g. , @xcite ) , with mean values of @xmath254 @xmath6 and @xmath255 mag ; the expected extinction based on the galactic relation is @xmath256 mag . dark grbs also generally have lower extinction than expected , with @xmath257 @xmath6 and @xmath258 mag , whereas extinctions of @xmath259 mag would be expected .    for the bursts presented here we find potentially different results . grb111215a agrees with the galactic relation if it resides at the lower redshift bound ( @xmath260 ) , in which case @xmath261 @xmath6 and @xmath262 mag . at the higher redshift bound ( @xmath263 ) we find @xmath264 @xmath6 and @xmath265 mag ( with an expected @xmath266 mag ) . this is still consistent with the galactic relation since we only place a lower bound on @xmath240 . similarly , grb110709b crosses the galactic relation at @xmath267 , with @xmath268 @xmath6 and @xmath2 mag . however , at @xmath269 it has larger extinction than expected ; for example , at @xmath223 we measure @xmath270 mag compared to the expected value of @xmath271 mag . at @xmath272 the situation is similar to grb111215a , namely the minimum value of @xmath240 is below the expected galactic relation , but this is only a lower limit . we therefore conclude that the dark bursts with the largest known extinction values are potentially in line with the galactic @xmath273 relation , although they may also reside below the expected correlation in line with the bulk of the grb population .      a few previous dark grbs have been localized to sub - arcsecond precision in the radio . grb970828 was detected in a single radio observation with @xmath274 @xmath21jy ( @xmath275 ) , but was not detected in observations only 1 d earlier and 2 d later @xcite . this single marginal detection was used to refine the position from the x - ray region of @xmath276 radius , and to claim an association with a galaxy at @xmath277 . the inferred extinction at this redshift is @xmath278 mag . grb000210 was localized to sub - arcsecond precision with , and was also marginally detected in the single epoch in the radio with @xmath279 @xmath21jy ( @xmath280 ; @xcite ) . the associated host galaxy has @xmath281 , and the inferred extinction is @xmath282 mag . grb020819 was detected at high significance in several epochs of radio observations , leading to an association with a face - on spiral galaxy at @xmath283 @xcite . the required extinction was a mild @xmath284 mag . finally , grb051022 was localized using radio and millimeter observations to a host galaxy at @xmath285 , requiring an extinction of @xmath286 mag @xcite . broad - band modeling indicates a beaming - corrected energy of @xmath287 erg , and a circumburst density characterized by @xmath288 m@xmath10 yr@xmath11 @xcite . the beaming - corrected energy inferred for grbs 110709b and 111215a , @xmath8 erg , is not unusual for long grbs , although it is somewhat higher than the median value of @xmath289 erg ( e.g. , @xcite ) . on the other hand , the inferred densities are substantial , with inferred mass loss rates of about @xmath290 m@xmath10 yr@xmath11 ( 110709b ) and @xmath291 m@xmath10 yr@xmath11 ( 111215a ) . at the radii appropriate for the jet break times of the two bursts , @xmath292 cm @xcite , these mass loss rates correspond to particle densities of about 100 and 350 @xmath13 , respectively , higher than typical values for long grbs , which are @xmath293 @xmath13 ( e.g. , @xcite ) . if confirmed with future detailed observations of dark bursts , the high densities may be indicative of larger mass loss rates for long grbs in dusty , and hence metal rich environments . such a trend may be expected if the mass loss is driven by radiation pressure mediated by metal lines @xcite . the durations of grb110709b ( @xmath294 s ) and grb111215a ( @xmath295 s ) are extremely long . to assess whether this type of unusually long duration correlates with optical / near - ir darkness , we collect all  bursts with durations of @xmath296  s , excluding nearby sub - energetic grbs ( e.g. , xrf060218 , grb100316d ) . the sample includes 9 events of which three bursts are dark ( 060929 , 110709b , 111215a ) , five have optical and/or near - ir detections with no clear evidence for extinction , and one event lacks rapid follow - up observations . thus , at least @xmath297 of these events are dark , similar to the fraction of dark bursts in the overall long grb population . we therefore conclude that there is no obvious correlation between unusually long duration and darkness , with the caveat that the current sample size is small .","summary":"moreover , the inferred values are in agreement with the galactic relation , unlike the bulk of the grb population . finally , we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming - corrected energy of erg ( ) expanding into a wind medium with a high density , m yr ( at cm ) . while the energy release is typical of long grbs , the inferred density may be indicative of larger mass loss rates for grb progenitors in dusty ( and hence metal rich ) environments .","abstract":"we present x - ray , optical , near - infrared ( ir ) , and radio observations of grbs 110709b and 111215a , as well as optical and near - ir observations of their host galaxies . the combination of x - ray detections and deep optical / near - ir limits establish both bursts as `` dark '' . sub - arcsecond positions enabled by radio detections lead to robust host galaxy associations , with optical detections that indicate ( 110709b ) and ( 111215a ) . we therefore conclude that both bursts are dark due to substantial rest - frame extinction . using the radio and x - ray data for each burst we find that grb110709b requires mag and grb111215a requires mag ( ) . these are among the largest extinction values inferred for dark bursts to date . the two bursts also exhibit large neutral hydrogen column densities of ( ) as inferred from their x - ray spectra , in agreement with the trend for dark grbs . moreover , the inferred values are in agreement with the galactic relation , unlike the bulk of the grb population . finally , we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming - corrected energy of erg ( ) expanding into a wind medium with a high density , m yr ( at cm ) . while the energy release is typical of long grbs , the inferred density may be indicative of larger mass loss rates for grb progenitors in dusty ( and hence metal rich ) environments . this study establishes the critical role of radio observations in demonstrating the origin and properties of dark grbs . observations with the jvla and alma will provide a sample with sub - arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in grb progenitors ."}
{"article_id":"1209.4654","section_id":"c","document":"using x - ray , optical / near - ir , and radio observations we have demonstrated that : ( i ) grbs 110709b and 111215a are dark bursts ; ( ii ) they are robustly associated with galaxies at @xmath0 ( 110709b ) and @xmath1 ( 111215a ) ; ( iii ) they require unusually large rest - frame extinction of @xmath2 mag ( 110709b ) and @xmath245 mag ( 111215a ) at @xmath4 ; ( iv ) they exhibit commensurately large neutral hydrogen column densities in their x - ray spectra , @xmath298 @xmath6 , which at @xmath299 are consistent with the galactic @xmath273 relation , unlike the overall long grb population ; and ( v ) their circumburst environments on a sub - parsec scale are shaped by large progenitor mass loss rates of @xmath300 m@xmath10 yr@xmath11 .    radio observations played a critical role in this study for three reasons . first , they provided sub - arcsecond positions , which led to a secure identification of the host galaxies . this allowed us to distinguish the extinction scenario from a high - redshift origin . second , the combination of radio and x - ray data allowed us to robustly determine the required extinction , instead of simply assuming an optical to x - ray spectral index . indeed , in cases with only x - ray data the unknown location of the synchrotron cooling frequency prevents a unique determination of the extinction . finally , the radio and x - ray data allowed us to determine the burst parameters , including the geometry , beaming - corrected energy , and the circumburst density . we find that the energy scale for grbs 110709b and 111215a is similar to the overall population of optically - bright grbs . however , the inferred mass loss rates are larger by about an order magnitude compared to optically - bright bursts , potentially indicating that grb progenitors in dusty environments have stronger metal line driven winds . the increased sensitivity of the jvla played an important role in the study and utilization of the radio afterglow . alma will provide similar capabilities , with an expected spatial resolution of about @xmath301 at 100 ghz ( depending on configuration ) , and hence an assured sub - arcsecond centroiding accuracy for signal - to - noise ratios of @xmath302 even in the most compact configuration . as demonstrated here ,  observations can also provide sub - arcsecond positions , but such observations may not be available for all dark grb candidates ( e.g. , grb111215a ) . in addition ,  data will not enhance the ability to determine the required extinction through broad - band modeling . the jvla and alma will also allow us to study the host galaxies of grbs 110709b and 111215a ( as well as those of past and future dark bursts ) in greater detail than optical / near - ir studies alone . in particular , they will address the question of highly - obscured star formation in these galaxies , and may even lead to redshift determinations through the detection of molecular lines . existing observations with the vla and the mambo and scuba bolometers ( in the small samples published to - date ) have led to only a few detections of grb hosts @xcite , with no obvious preference for dark burst hosts @xcite . however , the enhanced sensitivity of alma will allow for detections even with star formation rates of tens of m@xmath10 yr@xmath11 at @xmath179 . the combination of detailed host galaxy properties from rest - frame radio to uv , coupled with measurements of the local environments of dark bursts through broad - band afterglow modeling will shed light on the location of the obscuring dust ( interstellar vs.  circumstellar ) and the impact of metallicity on grb progenitor formation . we thank r.  chary for helpful discussions regarding obscured star formation in distant galaxies and y.  cao for his assistance in attaining the optical spectrum of grb111215a while observing at keck . the berger grb group at harvard is supported by the national science foundation under grant ast-1107973 , and by nasa / swift ao7 grant nnx12ad69 g . b.a.z . , w.f . , and a.s .  acknowledge partial support of this research while in residence at the kavli institute for theoretical physics under national science foundation grant phy11 - 25915 . e.n . acknowledges partial support by an erc starting grant . f.o .  acknowledges funding of his ph.d . through the _ deutscher akademischer austausch - dienst _ ( daad ) . funding for grond was generously granted from the leibniz prize to g.  hasinger ( dfg grant ha 1850/28 - 1 ) . d.  p.  is supported by grant hst - hf-51296.01-a , provided by nasa through a hubble fellowship grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . support for this work was provided by the national aeronautics and space administration ( nasa ) through chandra award number 09900712 issued by the chandra x - ray observatory center , which is operated by the sao for and on behalf of nasa under contract nas8 - 03060 . the jvla is operated by the national radio astronomy observatory , a facility of the nsf operated under cooperative agreement by associated universities , inc . jvla observations were undertaken as part of project numbers 10c-145 and 11b-242 . support for carma construction was derived from the gordon and betty moore foundation , the kenneth t. and eileen l. norris foundation , the james s. mcdonnell foundation , the associates of the california institute of technology , the university of chicago , the states of california , illinois , and maryland , and the nsf . ongoing carma development and operations are supported by the nsf under a cooperative agreement , and by the carma partner universities . carma observations were undertaken as part of projects c0773 and cx334 . the submillimeter array is a joint project between the smithsonian astrophysical observatory ( sao ) and the academia sinica institute of astronomy and astrophysics and is funded by the smithsonian institution and the academia sinica . sma observations were undertaken as part of project 2011b - s003 . some observations were obtained at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the nsf ( united states ) , the science and technology facilities council ( united kingdom ) , the national research council ( canada ) , conicyt ( chile ) , the australian research council ( australia ) , ministrio da cincia , tecnologia e inovao ( brazil ) and ministerio de ciencia , tecnologa e innovacin productiva ( argentina ) . gemini observations were undertaken as part of programs gs-2011a - q-25 and gn-2011b - q-10 . some observations were made with the nasa / esa hubble space telescope , obtained at the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 . _ hst _ observations were undertaken as part of program 12378 . this research has made use of  data obtained from the high energy astrophysics science archive research center ( heasarc ) , provided by nasa s goddard space flight center . this research has made use of the xrt data analysis software ( xrtdas ) developed under the responsibility of the asi science data center ( asdc ) , italy . , r.  j. , teuben , p.  j. , & wright , m.  c.  h. 1995 , in astronomical society of the pacific conference series , vol . 77 , astronomical data analysis software and systems iv , ed . r.  a. shaw , h.  e. payne , & j.  j.  e. hayes , 433                                                                                                  , r.  a. , mackenty , j.  w. , oconnell , r.  w. , & townsend , j.  a. 2008 , in society of photo - optical instrumentation engineers ( spie ) conference series , vol . 7010 , society of photo - optical instrumentation engineers ( spie ) conference series    , a.  m. , fruchter , a.  s. , hook , r.  n. , hack , w. , & hanley , c. 2006 , in the 2005 hst calibration workshop : hubble after the transition to two - gyro mode , ed . a.  m. koekemoer , p.  goudfrooij , & l.  l. dressel , 423                                                          , r.  j. , teuben , p.  j. , & wright , m.  c.  h. 1995 , in astronomical society of the pacific conference series , vol . 77 , astronomical data analysis software and systems iv , ed . r.  a. shaw , h.  e. payne , & j.  j.  e. hayes , 433                                    lcccccc|cccc 0.03 in & & & @xmath303 & @xmath304 & @xmath305 & @xmath306 & & @xmath307 & @xmath308 & @xmath113 + 2011 jul 9.949 & 0.051 & 585 & 20.76 & 20.53 & 20.32 & 20.49 & 621 & 20.03 & 19.02 & 18.79 + 2011 jul 10.009 & 0.111 & 2311 & 24.26 & 24.57 & 23.83 & 23.61 & 2335 & 20.83 & 20.00 & 19.27 + 2011 jul 10.045 & 0.147 & 1633 & 22.61 & 22.80 & 22.39 & 21.12 & 1640 & 19.83 & 18.83 & 18.66 + 2011 jul 10.003@xmath309 & 0.105 & 5275 & 23.63 & 23.89 & 23.28 & 23.09 & 5282 & 21.16 & 19.83 & 19.40    lccl 2011 jul 11.97 & 2.07 & 5.8 & @xmath310 + 2011 jul 12.92 & 3.02 & 5.8 & @xmath311 + 2011 jul 16.88 & 6.98 & 5.8 & @xmath312 + 2011 jul 21.97 & 12.07 & 5.8 & @xmath313 + 2011 jul 29.96 & 20.06 & 5.8 & @xmath314 + 2011 aug 19.85 & 40.59 & 5.8 & @xmath315 + 2011 sep 17.70 & 69.72 & 5.8 & @xmath316 + 2011 jul 22.01 & 12.11 & 21.8 & @xmath317    lllcl jvla & 2011 dec 17.00 & 1.41 & 4.9 & @xmath318 + & & & 6.7 & @xmath319 + & 2011 dec 23.05 & 7.46 & 4.9 & @xmath320 + & & & 6.7 & @xmath321 + & 2011 dec 29.03 & 13.44 & 4.9 & @xmath322 + & & & 6.7 & @xmath323 + & 2011 dec 31.00 & 15.41 & 4.9 & @xmath324 + & & & 6.7 & @xmath325 + & 2012 jan 10.99 & 26.40 & 4.9 & @xmath326 + & & & 6.7 & @xmath327 + & 2012 jan 29.84 & 45.25 & 4.9 & @xmath328 + & & & 6.7 & @xmath329 + & 2012 mar 12.82 & 88.23 & 4.9 & @xmath330 + & & & 6.7 & @xmath331 + & 2011 dec 31.00 & 15.41 & 8.4 & @xmath332 + & 2012 jan 10.99 & 26.40 & 8.4 & @xmath333 + & 2012 jan 29.84 & 45.25 & 8.4 & @xmath334 + & 2012 mar 12.82 & 88.23 & 8.4 & @xmath335 + & 2011 dec 18.93 & 3.35 & 19.1 & @xmath336 + & & & 24.4 & @xmath337 + & 2011 dec 27.08 & 11.49 & 19.1 & @xmath338 + & & & 24.4 & @xmath339 + & 2011 dec 31.00 & 15.41 & 19.1 & @xmath340 + & & & 24.4 & @xmath341 + & 2012 jan 10.99 & 26.40 & 19.1 & @xmath342 + & & & 24.4 & @xmath343 + & 2012 jan 29.84 & 45.25 & 19.1 & @xmath344 + & & & 24.4 & @xmath345 + & 2012 mar 12.82 & 88.23 & 19.1 & @xmath346 + & & & 24.4 & @xmath347 + carma & 2011 dec 17.05 & 1.46 & 93 & @xmath348 + & 2011 dec 20.02 & 4.43 & 93 & @xmath349 + & 2011 dec 22.04 & 6.45 & 93 & @xmath350 + & 2011 dec 24.10 & 8.51 & 93 & @xmath351 + & 2011 dec 26.01 & 10.42 & 93 & @xmath351 + & 2012 jan 1.14 & 16.55 & 93 & @xmath352 + sma & 2011 dec 18.30 & 2.71 & 230 & @xmath353    lcccc 0.1 in @xmath354 ( erg ) & 0.5 & 2.8 & 7.1 & 13.2 + @xmath355 ( @xmath356 g cm@xmath11 ) & 4.0 & 5.7 & 7.2 & 8.5 + @xmath358 & 0.18 & 0.11 & 0.08 & 0.07 + @xmath213 & 0.002 & 0.002 & 0.002 & 0.002 + @xmath359 & 2.07 & 2.06 & 2.05 & 2.05 + @xmath218 ( d ) & 3.65 & 3.45 & 3.27 & 3.11 + @xmath360 & 0.40 & 0.25 & 0.19 & 0.16 + @xmath361 ( erg ) & 0.4 & 0.9 & 1.3 & 1.7 + @xmath362 ( erg ) & 7.0 & 26 & 52 & 83 + @xmath363 ( erg ) & 5.4 & 8.0 & 9.4 & 10.6 + @xmath364 ( mag ) & @xmath365 & @xmath366 & @xmath367 & @xmath368    lcc 0.1 in @xmath354 ( erg ) & 4.3 & 10.6 + @xmath355 ( @xmath356 g cm@xmath11 ) & 19 & 26 + @xmath358 & 0.22 & 0.18 + @xmath213 & @xmath369 & @xmath370 + @xmath359 & 2.35 & 2.35 + @xmath218 ( d ) & 12 & 12 + @xmath219 ( rad ) & 0.42 & 0.33 + @xmath361 ( erg ) & 3.7 & 5.7 + @xmath362 ( erg ) & 4.5 & 9.0 + @xmath363 ( erg ) & 3.9 & 4.9 + @xmath364 ( mag ) & @xmath245 & @xmath371     d and by multiple orbits thereafter . the  @xmath54 upper limit at @xmath372 d is indicated with a black arrow . afterglow model fits in each band are shown with solid lines . to satisfy the near - ir upper limits we require @xmath373 mag ( for @xmath224 to @xmath374 ; dashed red line ) . the derived afterglow parameters for grb110709b are listed in table  [ tab:110709model ] . [ fig:110709lc ] ]         radius ; 90% containment ) is indicated with the black circle . the jvla afterglow position is shown with a blue circle ( @xmath168 radius ; @xmath137 systematic ) , while the  position is shown with a red circle ( @xmath169 ; @xmath137 ) . the jvla and  positions coincide with a galaxy that we consider to be the host of grb110709b . [ fig:110709host],title=\"fig : \" ] radius ; 90% containment ) is indicated with the black circle . the jvla afterglow position is shown with a blue circle ( @xmath168 radius ; @xmath137 systematic ) , while the  position is shown with a red circle ( @xmath169 ; @xmath137 ) . the jvla and  positions coincide with a galaxy that we consider to be the host of grb110709b . [ fig:110709host],title=\"fig : \" ]    -band image of the host galaxy of grb111215a . the xrt error circle ( @xmath52 radius ; @xmath375 containment ) is indicated with the black circle . the jvla and carma afterglow positions are shown with a blue circle ( @xmath376 ; @xmath137 systematic ) coinciding with a galaxy that we consider to be the host of grb111215a . [ fig:111215host ] ]    ) versus redshift for grbs 110709b ( blue triangles ) and 111215a ( red triangle ) ; for both bursts these are lower limits . previous dark bursts are marked with solid symbols . triangles indicate limits on @xmath240 and/or redshift . allowed values for grbs without firm redshifts are indicated by black lines @xcite . optically - bright grbs are marked with open symbols ; these bursts generally have @xmath377 mag . grbs 110709b and 111215a exhibit some of the highest extinction values to date . [ fig : avz ] ]    ) inferred from x - ray observations versus redshift for grbs 110709b and 111215a ( contours ) . the allowed redshift ranges for each burst are marked by the gray shaded regions . for comparison , we overlay data for long grbs in the  sample up to december 2010 @xcite ; dark bursts are marked by blue / black circles , while optically - bright events are marked by gray circles . grbs 110709b and 111215a clearly lie in the upper portion of the @xmath378 distribution of long grbs , as expected for dark bursts . [ fig : nhz ] ]    ) versus intrinsic neutral hydrogen column density ( @xmath41 ) inferred from x - ray observations for grbs 110709b ( blue triangles ) and 111215a ( red triangle ) . for comparison , we plot the same sample of bursts shown in figure  [ fig : avz ] . the diagonal lines indicate the empirical @xmath7 relations for the milky way and magellanic clouds . most grbs exhibit lower values of @xmath240 than expected from the local relations , but grbs 110709b and 111215a may be consistent with these relations . [ fig : avnh ] ]","summary":"the two bursts also exhibit large neutral hydrogen column densities of ( ) as inferred from their x - ray spectra , in agreement with the trend for dark grbs . observations with the jvla and alma will provide a sample with sub - arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in grb progenitors .","abstract":"we present x - ray , optical , near - infrared ( ir ) , and radio observations of grbs 110709b and 111215a , as well as optical and near - ir observations of their host galaxies . the combination of x - ray detections and deep optical / near - ir limits establish both bursts as `` dark '' . sub - arcsecond positions enabled by radio detections lead to robust host galaxy associations , with optical detections that indicate ( 110709b ) and ( 111215a ) . we therefore conclude that both bursts are dark due to substantial rest - frame extinction . using the radio and x - ray data for each burst we find that grb110709b requires mag and grb111215a requires mag ( ) . these are among the largest extinction values inferred for dark bursts to date . the two bursts also exhibit large neutral hydrogen column densities of ( ) as inferred from their x - ray spectra , in agreement with the trend for dark grbs . moreover , the inferred values are in agreement with the galactic relation , unlike the bulk of the grb population . finally , we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming - corrected energy of erg ( ) expanding into a wind medium with a high density , m yr ( at cm ) . while the energy release is typical of long grbs , the inferred density may be indicative of larger mass loss rates for grb progenitors in dusty ( and hence metal rich ) environments . this study establishes the critical role of radio observations in demonstrating the origin and properties of dark grbs . observations with the jvla and alma will provide a sample with sub - arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in grb progenitors ."}
{"article_id":"1601.03106","section_id":"i","document":"general relativity is one of the most accurate and mathematically elegant theories of modern physics . quite appropriately , in his classification of physical theories as 1 . superb , 2 . useful , or 3 . tentative , roger penrose @xcite clearly places it in the first category . in the context of cosmology , it was the investigation of solutions to einstein s field equations and their comparison with observations that led to the detailed picture of our universe and its evolution that we currently have . astonishing implications like the existence of dark energy and dark matter , the accelerated expansion and the indication that everything arose out of a big bang are all part of general relativistic cosmological models . moreover , no alternative theory of gravity ( like string theory , loop quantum gravity , brans - dicke theory , etc . ) has yet provided a model of the large - scale universe that makes experimentally testable predictions that are beyond those of general relativity .    on the other hand , it is also well - known that not _ all _ mathematical solutions to the einstein equations are physically acceptable . some cosmological models violate reasonable assumptions that are widely believed to hold in the real universe , like causality and determinism . a famous example of a solution with such an interesting pathological behaviour is the taub solution @xcite , a 2-parameter family of spatially homogeneous cosmological models . these maximal globally hyperbolic spacetimes @xcite are perfectly well - behaved in the time interval in which they are initially defined . however , they can be extended into the future and past to obtain the taub - nut solutions @xcite . interestingly , there are several non - equivalent extensions @xcite , so that information about the solutions in the original domain does not uniquely determine which of these extensions is realised  determinism breaks down . moreover , beyond the cauchy horizons ( the hypersurfaces that separate the maximal globally hyperbolic region from the extended regions ) there exist closed causal curves , which would allow observers or photons to travel back in time  clearly a violation of causality . these unusual properties of the taub - nut solution have led to the question as to whether such a pathological behaviour is a typical feature of solutions to einstein s field equations , or whether it can only occur under very special circumstances , such as for spacetimes with a high degree of symmetry or very restricted types of matter . according to the famous strong cosmic censorship conjecture @xcite ( see also @xcite for more details and further references ) , the maximal globally hyperbolic development of generic data on some cauchy surface is _ inextendible_. if this hypothesis were true , it would imply that solutions which , like the taub solution , can be extended into acausal regions are rare exceptions . they could only occur for a ( in some sense ) negligibly small set of `` non - generic '' initial data . unfortunately , in the current state of the art , it seems unrealistic to prove or disprove the strong cosmic censorship conjecture in full generality . instead , a practicable and promising approach is to start from suitable small classes of symmetric models and investigate their properties . then one can try to gradually increase the complexity of the models and explore their behaviour . for each class of models , one can attempt to prove existence of solutions with cauchy horizons and acausal regions , and study properties like the presence of curvature singularities .    along those lines , the existence of a class of vacuum solutions with cauchy horizons  the _ generalised taub - nut spacetimes _  was shown by moncrief @xcite . more recently , a different class of cosmological models with cauchy horizons has been introduced : the _ smooth gowdy - symmetric generalised taub - nut ( sggtn ) solutions_. existence of these inhomogeneous cosmological vacuum models was shown in @xcite . compared to moncrief s class of solutions , the sggtn models require less regularity ( smoothness instead of analyticity ) but more symmetry ( gowdy symmetry with two spacelike killing vectors instead of just one ) . a number of properties of these solutions can be studied with abstract methods , but in order to get a more complete picture of the behaviour of some of these models , it is desirable to obtain families of exact solutions . recently , two families of exact sggtn solutions were constructed with methods from soliton theory @xcite . both families contain cauchy horizons and acausal regions , but their causal and singularity structure is quite different , as will be summarised below . the goal of the present paper is to construct more general families of exact solutions , again using methods from soliton theory . the nature of the desired generalizations is twofold : ( i ) we want to embed the two above - mentioned exact solution families into a larger family that contains both as special cases , a family which combines all of the interesting properties that these two families have , and ( ii ) to extend the considerations from vacuum to electrovacuum , in order to include a non - trivial additional field , and to construct an exact solution family for that case too .    to this end , we will start by summarizing the definition and important properties of the class of sggtn solutions in sec . [ sec : sggtn ] . in the same section , we also give an overview of the two exact solution families that we intend to generalize . in sec . [ sec : vacuum ] we present a new family of vacuum solutions and discuss their properties . afterwards , in sec . [ sec : newelectrovac ] , we work out the generalization of the underlying equations to electrovacuum and derive a corresponding family of exact solutions . finally , in sec . [ sec : discussion ] , we discuss our results .","summary":"the corresponding exact vacuum solution to einstein s field equations is obtained with methods from soliton theory . we also study properties of these models and find that they combine all interesting features of both earlier solution families : general regularity within the maximal globally hyperbolic region , particular singular cases in which a curvature singularity with a directional behaviour forms , a highly non - trivial causal structure , and cauchy horizons whose null generators can have both closed or non - closed orbits . in the second part of the paper , we discuss the generalisation from vacuum to electrovacuum . moreover , we also present a family of exact solutions for that case and study its properties .","abstract":"we construct a 4-parameter family of inhomogeneous cosmological models , which contains two recently derived 3-parameter families as special cases . the corresponding exact vacuum solution to einstein s field equations is obtained with methods from soliton theory . we also study properties of these models and find that they combine all interesting features of both earlier solution families : general regularity within the maximal globally hyperbolic region , particular singular cases in which a curvature singularity with a directional behaviour forms , a highly non - trivial causal structure , and cauchy horizons whose null generators can have both closed or non - closed orbits . in the second part of the paper , we discuss the generalisation from vacuum to electrovacuum . moreover , we also present a family of exact solutions for that case and study its properties ."}
{"article_id":"0705.3977","section_id":"i","document":"it is still not clear how ultraluminous x - ray sources ( ulxs ) relate to the class of stellar - mass black holes ( bhs ) first identified and extensively studied in the galaxy and large magellanic cloud ; in particular , whether and how they differ from high - mass x - ray binaries ( systems where the donor is an ob star ) . they could represent the upper end of the bh mass distribution , perhaps up to @xmath14 . alternatively , the emission could be mildly beamed in our direction , enhancing the apparent luminosity perhaps by a factor of a few . finally , the emission could be super - eddington by a factor of a few . one of the reasons the ulx classification remains controversial is that very little is known about their spectral state transitions . the identification and interpretation of state transitions over characteristic timescales of a few months / years has provided a powerful tool to understand the accretion processes ( for example the disk / corona / jet interplay as a function of a variable mass accretion rate ) in galactic bhs over the last two decades ( remillard & mcclintock 2006 ) .    because of their distance , ulxs are too faint to be regularly observed by the current generation of x - ray all - sky monitors , and require targeted observations . few ulxs have been observed regularly enough to determine their long - term x - ray behaviour ; most of them may vary by a factor of a few ( compare for example the catalogues of swartz et al . 2004 and liu & bregman 2005 ) but tend to be persistently in a bright state . from this point of view , they are more similar to the ( few ) galactic bhs in high - mass binary systems ( i.e. , accreting from an ob donor star ) than to the more numerous ones in low - mass systems ( accreting from a low - mass star ) . significant variability or on / off transitions have been monitored in some of the fainter ulxs ( @xmath15 a few @xmath16 erg s@xmath1 ) , for example in the antennae ( fabbiano et al . 2003 ) . however , spectral state transition or flux variations by more than one order of magnitude are rarer among the brightest systems ( @xmath17 erg s@xmath1 ) . among the few notable exceptions ( apart from ngc1365 x1 , object of this paper ) are the two brightest ulxs in m82 ( kaaret , simet & lang 2006 ) , the brightest ulx in the cartwheel ( wolter , trinchieri & colpi  2006 ) , a source in ngc3628 ( strickland et al . 2001 ) , and a peculiar super - soft source that underwent an outburst in m101 ( kong & di stefano 2005 ) . the last source may or ( more likely ) may not belong to the same physical class as most other ulxs .    in the few ulxs where the flux and/or spectral variations are significant enough to be considered a state transition , the pattern does not appear to correspond to the `` canonical '' sequence of physical states displayed by stellar - mass bhs : quiescence ; low / hard state ( hard power - law ) ; thermal - dominant state ( disk - blackbody with @xmath18 kev ) ; very high state state ( softer power - law plus disk - blackbody component ) ( remillard & mcclintock 2006 ; fender , belloni & gallo  2004 ) . instead , ulx spectra in the @xmath2@xmath3 kev band seem to show three phenomenological features ( stobbart , roberts & wilms  2006 ) , which may or may not correspond to truly different physical components : a ) a broad , power - law - like component with photon index @xmath11@xmath19 ; b ) a curvature or break above @xmath20 kev ; c ) an additional soft component ( @xmath21@xmath22 kev ) . strong flux changes generally correspond to one or two of those features becoming more prominent or disappearing . for example , at higher luminosities , the power - law component appears to increase more than the soft thermal component ; the high - energy steepening is also more noticeable at higher luminosities ( e.g. , roberts 2007 ; dewangan et al .  2004 ; kubota et al . it is difficult to classify this behaviour in terms of state transitions , because there is still no consensus on the physical origin of those three basic features . in the standard scenario , the soft component is emitted by a cool disk , the power - law component is the result of comptonization , and its curvature / break is due to an increased optical depth of the comptonizing region . alternatively , it was suggested that the curved emission component may come from a hot accretion disk ( e.g. , kubota et al . 2001 ; roberts et al .  2005 ; stobbart et al .  2006 ; tsunoda et al . 2006 ) .    for our study , we have targeted the brightest ulx in ngc1365 ( henceforth , x1 , following the _ rosat _ identification ; komossa & schulz 1998 ) which was already known to be highly variable ( a factor @xmath23 ) over a few months timescale , from _ rosat _ and _ asca _ studies ( komossa & schulz 1998 ; iyomoto et al . the source is located in the most luminous spiral galaxy of the fornax cluster , a supergiant barred spiral ( type sbb(s)i : sandage & tammann 1981 ) with a total gas mass @xmath24 , a kinematic mass @xmath25 , and a star formation rate @xmath26 yr@xmath1 ( roussel et al . 2001 ; lindblad 1999 ) . the cepheid distance to ngc1365 is @xmath27 mpc ( ferrarese et al . 2000 ) ; at that distance , @xmath28 pc . in this paper , we will show that this source varies dramatically in luminosity over short timescales , and that such changes are associated to spectral changes , including the signature of an ionized outflow . we will then discuss whether and how those changes may be consistent with a standard disk plus corona scenario , and what constraints we can obtain on the bh mass and accretion rate .","summary":"we have studied a highly variable ultraluminous x - ray source ( ulx ) in the fornax galaxy ngc1365 , with a series of 12 _ chandra _ and _ xmm - newton _ observations between 2002 and 2006 . in 2006 april ,","abstract":"we have studied a highly variable ultraluminous x - ray source ( ulx ) in the fornax galaxy ngc1365 , with a series of 12 _ chandra _ and _ xmm - newton _ observations between 2002 and 2006 . in 2006 april , the source peaked at a luminosity erg s in the kev band ( similar to the maximum luminosity found by _ asca _ in 1995 ) , and declined on an-folding timescale days . the x - ray spectrum is always dominated by a broad power - law - like component . when the source is seen at x - ray luminosities erg s , an additional soft thermal component ( which we interpret as emission from the accretion disk ) contributes of the x - ray flux ; when the luminosity is higher , erg s , the thermal component is not detected and must contribute of the flux . at the beginning of the decline , ionized absorption is detected around kev ; it is a possible signature of a massive outflow . the power - law is always hard , with a photon index ( and even flatter at times ) , as is generally the case with bright ulxs . we speculate that this source and perhaps most other bright ulxs are in a high / hard state : as the accretion rate increases well above the eddington limit , more and more power is extracted from the inner region of the inflow through non - radiative channels , and is used to power a comptonizing corona , jet or wind . the observed thermal component comes from the standard outer disk ; the transition radius between outer standard disk and comptonizing inner region moves further out and to lower disk temperatures as the accretion rate increases . this produces the observed appearance of a large , cool disk . based on x - ray luminosity and spectral arguments , we suggest that this accreting black hole has a likely mass ( even without accounting for possible beaming ) .    [ firstpage ]    x - rays : binaries  x - rays : individual ( ngc1365 x1 )  black hole physics  accretion , accretion disks"}
{"article_id":"0705.3977","section_id":"r","document":"we found three ulxs within a projected distance @xmath41 kpc from the active nucleus ( figures 1 , 2 , 3 ) . we unofficially designate them , for simplicity , x1 , x2 and x3 , in order of average x - ray brightness over the whole series of our observations . x1 is the ulx previously found by _ rosat _ and _ asca_. a more accurate source position for x1 , from the _ chandra _ image , is ra = @xmath42 , dec @xmath43 . all three ulxs ( but most remarkably , x1 and x3 ) vary significantly between different observations . in this paper , we discuss the main properties of x1 , and leave a study of the other ulxs and non - nuclear x - ray sources in ngc1365 to a follow - up paper . the long - term variability of x1 was already known from _ asca _ and _ rosat _ observations ( figure 4 ) . as a first step , we fitted all the _ chandra _ and _ xmm - newton _ spectra with absorbed power - law models ( table 2 ) , confirming that its x - ray luminosity fluctuated by a factor of 10 over the few years of our observations . our sequence of six _ chandra _ observations between 2006 april 1023 caught the rise , peak and decline of an outburst , in which the source reached unabsorbed x - ray luminosities of @xmath44 erg s@xmath1 in the @xmath2@xmath3 kev band . this luminosity is similar to the peak observed by asca in 1995 january , which we have re - estimated from the original _ asca_/sis data as @xmath45 erg s@xmath1 in the same band erg s@xmath1 in the @xmath2@xmath3 kev band , less than half of what is reported in section 2.2.1 of that paper . as a further check , we have re - extracted and re - analysed the _ asca _ data , confirming the lower value for the unabsorbed luminosity . ] . it was considered remarkable at that time that the source must have risen and declined by more that an order of magnitude in less than a few weeks . in fact , the 2006 outburst shows that the characteristic timescale for the rise and decline is only a few days ( tables 1 , 2 ) . the peak of the outburst lasted for about a week , corresponding to the observations a3 , a4 and a5 ( 2006 april 1217 ) . such long - term changes in the x - ray luminosity do not seem to correspond to significant variations in the slope of the continuum . when the spectra are fitted with an absorbed power - law model , the photon index remains @xmath46@xmath47 over all our _ xmm - newton _ and _ chandra _ observations , consistent the value @xmath11 that was estimated from the _ asca _ data during the 2005 january outburst ( iyomoto et al . such slopes are similar to what is often found in other bright ulxs , but are flatter than the power - law slope in most galactic bhs when they are in a high or very high state ( remillard & mcclintock 2006 ) . in fact , a more detailed spectral analysis based on two - component models ( power - law plus disk - blackbody ) reveals that the true slope of the power - law is in some cases even flatter , with a photon index @xmath48 ( section 3.2 ) .    only two of our observations ( e4 and e5 ) are long enough to enable an analyis of short - term variability . we find that the count rate during e5 is consistent with being constant , while some flickering ( quite common in accreting sources ) is marginally detected in e4 ( kolmogorov - smirnoff probability of constancy @xmath49 ) . the total , soft - band and hard - band lightcurves for the epic - pn observation e4 are shown in figure 4 . we do not find any evidence of x - ray hardness changes during that observation , nor any significant features in its power density spectrum . lcccccc label & date & mjd ( start ) & mission & obs i d & good time interval ( ks ) & optical monitor + a1 & 2002 dec 24 & 52632.62 & _ chandra _ acis - s & 3554 & 13.8 & + e1 & 2003 jan 16 & 52655.98 & _ xmm - newton _ epic & 0151370101 & 19.0 ( mos ) , 15.3 ( pn ) & @xmath37 ( 3.5 ks ) + e2 & 2003 feb 09 & 52679.86 & _ xmm - newton _ epic & 0151370201 & 4.4 ( mos ) , 2.5 ( pn ) & + e3 & 2003 aug 13 & 52864.01 & _ xmm - newton _ epic & 0151370701 & 8.0 ( mos ) , 6.4 ( pn ) & @xmath37 ( 1.9 ks ) + e4 & 2004 jan 17 & 53021.13 & _ xmm - newton _ epic & 0205590301 & 57.1 ( mos ) , 49.7 ( pn ) & @xmath34 ( 3.4 ks ) , @xmath35 ( 3.4 ks ) , + & & & & & & @xmath36 ( 3.4 ks ) + e5 & 2004 jul 24 & 53210.27 & _ xmm - newton _ epic & 0205590401 & 64.3 ( mos ) , 55.6 ( pn ) & @xmath34 ( 3.8 ks ) , @xmath35 ( 3.8 ks ) , + & & & & & & @xmath36 ( 4.5 ks ) + a2 & 2006 apr 10 & 53835.29 & _ chandra _ acis - s & 6871 & 13.4 & + a3 & 2006 apr 12 & 53837.52 & _ chandra _ acis - s & 6872 & 14.6 & + a4 & 2006 apr 15 & 53839.98 & _ chandra _ acis - s & 6873 & 14.6 & + a5 & 2006 apr 17 & 53842.79 & _ chandra _ acis - s & 6868 & 14.6 & + a6 & 2006 apr 20 & 53845.42 & _ chandra _ acis - s & 6869 & 15.5 & + a7 & 2006 apr 23 & 53848.42 & _ chandra _ acis - s & 6870 & 14.6 & +    [ t : allsources ]    lcccccc label & & + & @xmath50 acis - s cts s@xmath1 & @xmath50 epic cts s@xmath1 & @xmath51 ( @xmath52 @xmath53 ) & photon index & @xmath54 & @xmath55 ( @xmath16 erg s@xmath1 ) + a1 & @xmath56 & & @xmath57 & @xmath58 & @xmath59 & @xmath60 + e1 & & @xmath61 & @xmath62 & @xmath63 & @xmath64 & @xmath65 + e2 & & @xmath66 & @xmath67 & @xmath68 & @xmath69 & @xmath70 + e3 & & @xmath71 & @xmath72 & @xmath73 & @xmath74 & @xmath75 + e4 & & @xmath76 & @xmath77 & @xmath78 & @xmath79 & @xmath80 + e5 & & @xmath81 & @xmath82 & @xmath83 & @xmath84 & @xmath85 + a2 & @xmath86 & & @xmath87 & @xmath88 & @xmath89 & @xmath90 + a3 & @xmath91 & & @xmath92 & @xmath93 & @xmath94 & @xmath95 + a4 & @xmath96 & & @xmath97 & @xmath98 & @xmath99 & @xmath100 + a5 & @xmath101 & & @xmath102 & @xmath103 & @xmath104 & @xmath105 + a6 & @xmath106 & & @xmath107 & @xmath108 & @xmath109 & @xmath110 + a7 & @xmath111 & & @xmath112 & @xmath113 & @xmath114 & @xmath115 +    [ t : allsources ]    lccccc observation & parameter & & more complex models + & & diskbb & power - law & power - law + diskbb & + a1 & @xmath116 & 1.06 ( 20.1/19 ) & 0.80 ( 15.3/19 ) & 0.66 ( 11.3/17 ) & see table 4 + & @xmath117 & 4.3 & 7.4 & 18.0 & + e1 & @xmath116 & 1.71 ( 37.7/22 ) & 0.92 ( 20.1/22 ) & no improv & + & @xmath117 & 2.2 & 3.3 &  & + e2 & @xmath116 & 2.22 ( 6.7/3 ) & 2.17 ( 6.5/3 ) & no improv & + & @xmath117 & 1.7 & 2.2 &  & + e3 & @xmath116 & 1.14 ( 13.6/12 ) & 0.64 ( 7.71/12 ) & no improv & + & @xmath117 & 1.7 & 2.9 &  & + e4 & @xmath116 & no fit & 1.15 ( 158.2/138 ) & 0.95 ( 129.1/136 ) & see table 5 + & @xmath117 & no fit & 8.5 & 10.5 & + e5 & @xmath116 & no fit & 1.33 ( 155.9/117 ) & 1.02 ( 117.7/115 ) & see table 6 + & @xmath117 & no fit & 8.3 & 9.2 & + a2 & @xmath116 & 1.15 ( 39.4/34 ) & 0.99 ( 33.7/34 ) & no improv & + & @xmath117 & 11.7 & 18.4 &  & + a3 & @xmath116 & 0.82 ( 39.5/48 ) & 0.64 ( 30.6/48 ) & no improv & see table 7 + & @xmath117 & 18.9 & 29.6 &  & + a4 & @xmath116 & 0.80 ( 39.1/49 ) & 0.81 ( 39.5/49 ) & no improv & see table 7 + & @xmath117 & 20.1 & 29.3 &  & + a5 & @xmath116 & 0.71 ( 31.2/44 ) & 0.75 ( 32.9/44 ) & no improv & see table 7 + & @xmath117 & 17.4 & 24.8 &  & + a6 & @xmath116 & 0.50 ( 15.5/31 ) & 0.38 ( 11.7/31 ) & no improv & + & @xmath117 & 10.6 & 15.8 &  & + a7 & @xmath116 & 1.28 ( 14.1/11 ) & 0.90 ( 9.88/11 ) & no improv & + & @xmath117 & 2.8 & 4.8 &  & +    [ t : allsources ]     +    lr parameter & value + @xmath118 & @xmath119 + @xmath120  ( kev ) & @xmath121 + @xmath122 & @xmath123 + @xmath124 & @xmath125 + @xmath126 & @xmath127 + @xmath128 & @xmath129 + @xmath130 & @xmath131 + @xmath132 & @xmath133 +    lcc parameter & model 1 value & model 2 value + @xmath118 & @xmath87 & @xmath134 + @xmath120  ( kev ) & @xmath135 & @xmath136 + @xmath122 & @xmath137 & @xmath138 + @xmath139 & @xmath140 & @xmath141 + @xmath142 &  & @xmath143 + @xmath144 &  & @xmath145 + @xmath126 & @xmath146 & @xmath147 + @xmath128 & @xmath148 & @xmath149 + @xmath130 & @xmath150 & @xmath151 + @xmath132 & @xmath152 & @xmath153 +    lr parameter & value + @xmath118 & @xmath154 + @xmath120  ( kev ) & @xmath155 + @xmath122 & @xmath156 + @xmath124 & @xmath157 + @xmath126 & @xmath158 + @xmath128 & @xmath159 + @xmath130 & @xmath75 + @xmath132 & @xmath160 +     +     +   +      in all the observations with a sufficient number of counts , the x - ray spectrum appears dominated by a broad power - law - like component . in particular , the wider spectral coverage of _ xmm - newton _ clearly rules out the possibility that the source is in a thermal dominant state , when most of the emission comes from a standard multicolour disk . most ulxs ( especially those with x - ray luminosities @xmath161 erg s@xmath1 ) seem to share this phenomenological property , indicating perhaps that most of the disk photons are compton - upscattered . the two longest _ xmm - newton _ observations ( e4 and e5 ) have a sufficiently high signal - to - noise ratio , allowing a more detailed spectral analysis . firstly , in both datasets , significant systematic residuals at low energies are found when the source spectra are fitted with a simple power - law model : an additional soft component is required and @xmath162 for e4 and e5 respectively ( table 3 ) , as opposed to @xmath163 and @xmath164 for disk - blackbody plus power - law fits . to verify that this is a statistically significant improvement , we have simulated pure power - law spectra using _ fakeit _ in xspec , and fitted them both with power - law and disk - blackbody plus power - law models ; we have then compared the decrease in @xmath128 with what we obtain from the real datasets . this method is essentially equivalent to an f - test ( protassov et al . 2002 ) . ] . the soft excess contributes @xmath7 of the emitted luminosity times the respective fluxes , assuming isotropic emission for both the power - law and the disk - blackbody components . more rigorously , disk - blackbody luminosities should be calculated as @xmath165 times the flux , where @xmath166 is the ( unknown ) viewing angle to the disk . the difference between the two estimates is less than a factor of 2 for @xmath167 . ] in the @xmath2@xmath3 kev band , but dominates below @xmath168 kev ( figure 6 and tables 5 , 6 ) . this emission is well fitted by a standard disk - blackbody model , with colour temperatures @xmath169@xmath170 kev . such temperatures are intermediate between those generally found in `` typical '' ulxs ( miller , fabian & miller  2004 ; stobbart et al . 2006 ) and those observed from the disks of galactic stellar - mass bhs ( e.g. , remillard & mcclintock 2006 ) . a possible soft excess is marginally found also for the _ chandra _ observation a1 ( table 4 ) , but there are not enough counts to significantly constrain its flux and temperature .    secondly , we find that in e4 there is a significant steepening of the continuum slope above @xmath171 kev ( figure 6 ) . similar breaks are also found in various other bright ulxs : they have been interpreted as the effect of comptonization in a warm ( @xmath172 kev ) , moderately optically - thick ( @xmath173@xmath174 ) corona ( stobbart et al .  2006 ; goad et al . 2006 ; dewangan , griffiths & rao 2006 ) . the alternative interpretation for the spectral steepening is that the harder emission above @xmath168 kev is in fact from a hot ( @xmath175 kev ) accretion disk , so that the steeper continuum above @xmath176 kev would represent the wien part of the thermal disk component , somewhat modified ( broadened ) by comptonization . physically , this may be consistent with a `` slim disk '' model , also sometimes used to explain some ulx spectra ( e.g. , ebisawa et al . 2003 ; mizuno et al . although such model provides an equally good fit for the e4 spectrum , it is not acceptable for e5 nor for the brightest _ chandra _ spectra ; therefore we do not consider it as a viable physical scenario for this particular source . thirdly , we find that the true value of the power - law photon index may be lower ( harder spectrum ) when the thermal component is also taken into account . simple power - law fits to the e4 and e5 spectra give @xmath177@xmath178 ( table 2 ) . but when the same e4 spectrum is fitted with a broken power - law plus disk - blackbody , the photon index is @xmath179 below the break , steepening to @xmath180 at higher energies ( table 5 ) . for e5 , the photon index is @xmath181 ( table 6 ) , at least up to energies @xmath182 kev ; we can not determine where the expected spectral break occurred on that occasion . we tried to find evidence of high - energy spectral breaks also in our series of _ chandra _ spectra . however , the acis sensitivity drops rapidly above @xmath183 kev , making this task impossible for such short observations . +      the most important result from the sequence of _ chandra _ observations in 2006 april is that we caught the rise , peak and decline of an outburst , in which the source reached unabsorbed x - ray luminosities @xmath0 erg s@xmath1 , similar to the values observed by _ asca _ in the 1995 january outburst . it was considered remarkable at that time that the source must have risen and declined by more that an order of magnitude in less than a few weeks . in fact , the 2006 outburst shows that the characteristic timescale for the rise and decline is only a few days ( figure 4 and tables 1 , 2 ) . the full sequence of spectra , fitted with absorbed power - law models , is shown in figures 710 . the outburst peaked between observations a3 ( 2006 april 12 ) and a4 ( 2006 april 15 ) . the best - fitting models are consistent with being the same for both spectra , within the errors : a simple power - law component ( @xmath184 for a3 , @xmath185 for a4 ) with neutral absorption , and essentially identical flux . in fact , the a5 spectrum is also essentially identical to a3 and a4 below @xmath186 kev and above @xmath187 kev . the difference , however , is that the a5 spectrum has a statistically significant `` soft deficit '' at energies @xmath186@xmath10 kev ( figures 8 , 9 ) , that can not be modelled with additional cold absorption or with any kind of thermal emission . this feature suggests the presence of additional ionized absorption in the a5 spectrum .    to test this hypothesis , we fitted those three outburst spectra simultaneously , assuming the same primary spectrum ( same power - law slope and normalization ) and the same amount of neutral absorption , leaving only the amount of ionized absorption ( absori model in xspec ) free to vary between them . as expected , the ionized column densities in a3 and a4 is consistent with @xmath188 ; we then fixed both of them at @xmath188 to obtain a better constraint on the error range for the other parameters ; we also fixed the metal abundance to the solar value . the ionized column density of the a5 spectrum is @xmath189 @xmath53 , with a corresponding ionization parameter @xmath190 , or @xmath191@xmath192 , if we adopt the definition of ionization parameter used for example by murray et al . we also note that the neutral absorbing column density around the peak of the outburst ( a3 , a4 , a5 ) appears to be higher ( @xmath193@xmath194 @xmath53 ) than the value found at other epochs , when it is typically @xmath195 @xmath53 . the a6 spectrum , taken three days after a5 , already shows the beginning of the decline , with a reduction of the emitted luminosity by a factor @xmath187 ( figure 10 , top panel ) . the spectrum is well fitted with a simple power law absorbed by neutral gas . after three more days ( observation a7 : figure 10 , bottom panel ) the luminosity had declined by another factor of @xmath196 . in summary , the x - ray luminosity has an @xmath4-folding timescale @xmath5 days in the decline . we could compare this timescale with typical decline timescales observed at the end of galactic stellar - mass bh outbursts . for example , the @xmath4-folding timescale for xte j1550@xmath197564 at the end of the 1998 outburst was 11 days ( wu et al . 2002 ) ; and it was @xmath187 weeks for gro j1655@xmath19740 at the end of the 19961997 outburst ( sobczak et al . those decline timescales very likely correspond to the viscous timescale on which the disk is emptied after the mass inflow rate from the donor star is strongly reduced ; they depend on the size of the roche lobe and on the effective viscosity . as the disk is emptied , a spectral state transition occurs from the high / soft to the low / hard state . however , the situation for ngc1365 x1 is entirely different . in our interpretation , the x - ray spectrum is power - law dominated during the outburst ; this is consistent with the suggestion that ulxs are in a state similar to the very high state of stellar - mass bhs ( roberts et al . hence , we argue that the flare observed in the _ chandra _ observations is probably comparable to the hard flares seen in the very high state ( often at the very beginning of an outburst ) of stellar - mass bhs ( for example , xte j1550@xmath197564 : sobczak et al .  2000 ; gro j1655@xmath19740 : sobczak et al .  1999 ; xte j1859@xmath198226 : brocksopp et al . 2002 ; 4u 1630@xmath19747 : trudolyubov , borozdin & priedhorsky 2001 ) . typical amplitudes of those x - ray flares are a factor of @xmath187@xmath199 ; typical decline timescales are @xmath187@xmath174 days . physically , such flares may correspond to the formation and ejection of a comptonizing region in the inner part of the accretion flow . this is consistent with the decline being associated with an outflow . finally , we checked whether there is any evidence of a soft excess in the 2006 outburst spectra , that can be attributed to disk emission . none of the individual spectra are improved by adding a disk - blackbody component . we find the tightest constraint by modelling the coadded spectrum of the observations a3 and a4 . any disk - blackbody component with inner - disk colour temperature @xmath200 kev must have an emitted luminosity @xmath201 erg s@xmath1 ( @xmath202 confidence level ) in the @xmath2@xmath3 kev band . if the inner - disk colour temperature @xmath203 kev , the upper limit to the emitted luminosity is @xmath204 erg s@xmath1 in the same band . those apper limits are comparable to the inferred disk fluxes from e4 and e5 . we can not tell whether the disk has significantly decreased in flux during the outburst , but clearly it did not become more luminous . we argue that the disk emission represented @xmath205 of the x - ray emission when the total @xmath2@xmath3 kev luminosity was @xmath206 erg s@xmath1 ; and it represented @xmath8 of the x - ray emission when the source had brightened to @xmath0 erg s@xmath1 . thus , the brightening is entirely characterized by the enhancement of the power - law - like component . we further examined the behaviour at the peak of the 2006 outburst , when spectral fitting suggested the onset of an outflow . we directly compared the observed spectra a3 and a5 , after rebinning them to increase the signal - to - noise . the ratio of the two spectra confirms in a model - independent way that a portion of the soft x - ray spectrum is absorbed in a5 , consistent with an ionized column density @xmath207 @xmath53 , and an ionization parameter @xmath208 ( figure 9 , bottom panel ) . those two characteristic values , similar to those often found in seyfert galaxies ( e.g. , crenshaw , kraemer & george 2003 ) , are clearly inconsistent with a simple uniform shell of absorbing material around the x - ray source . the ionizing luminosity ( above @xmath209 ev ) emitted by the ulx is @xmath210 erg s@xmath1 . this would imply a characteristic size @xmath211 cm for the absorbing gas , much larger than the characteristic size of the binary system . considering that the increase in the absorption column density has occurred over only few days , and that typical maximum radial velocities of radiatively - driven outflows are @xmath212 cm s@xmath1 , we can not expect the outflow to have reached distances larger than a few @xmath213 cm .    for a more accurate study , we tried using a radiatively - driven disk - wind model ( murray & chiang 1995 ; murray et al . we assume that @xmath214 , in which case we expect a mass loss rate in the wind @xmath215 g s@xmath1 . if the wind is launched from the inner disk , the initial ( thermal ) velocity @xmath216@xmath217 cm s@xmath1 and the mass loss rate @xmath218 g s@xmath1 . the column density , integrated along a streamline , is @xmath219 ( murray & chiang 1995 ) . for typical @xmath220 cm s@xmath1 and a column density @xmath189 @xmath53 as inferred from our spectral modelling , the wind would have to be launched from radii @xmath221 cm @xmath222 gravitational radii for a @xmath223 bh . this is two orders of magnitude larger than expected , by comparison with disk winds in agn .    in summary , the problem we face is that if we were looking into a disk wind launched from @xmath224 cm we would see a column density @xmath225 @xmath53 and , for @xmath226 erg s@xmath1 , an ionization parameter a few orders of magnitude higher than inferred from the soft x - ray absorption , and also too high for the wind to be radiatively accelerated . increasing the mass outflow rate would decrease the ionization state of the gas but increase the column density . an analogous problem was discussed by schurch & done ( 2006 ) . a possible way to keep the ionization parameter in the wind sufficiently low is to assume ( following murray et al . 1995 , proga , stone & kallman 2000 , proga & kallman 2004 ) that the outflowing gas does not see most of the soft x - ray photons : it is shielded by `` hitchhiking gas '' at the inner face of the wind , or by the disk atmosphere at the base of the wind . in particular , this is expected to occur when the mass outflow rate is @xmath227 eddington accretion rate , because the outflow is compton thick ( pounds et al . 2003 ) and the gas in the outer wind does not directly see the soft x - ray irradiation . however , we do see most of the x - ray flux from x1 : the ionized absorber is only removing @xmath182% of the @xmath2@xmath10 kev flux from _ our _ line of sight ( figure 11 ) . qualitatively , we can explain this by assuming a low filling factor for the absorber ( @xmath228% ) . alternatively , we can speculate that the observed soft x - ray flux has a direct ( unabsorbed ) component and an additional ( @xmath182% ) component scattered into our line of sight by the outflowing gas ; it is only the latter that bears the imprint of ionized absorption . lr parameter & value + @xmath118 & @xmath229 + @xmath124 & @xmath230 + @xmath126 & @xmath231 + @xmath232  ( k ) & @xmath233 ( fixed ) + @xmath234  ( @xmath235 ) & @xmath192 ( fixed ) + @xmath236  ( cgs ) & @xmath237 + @xmath238 & for a3 : @xmath188 + & for a4 : @xmath239 + & for a5 : @xmath240 + @xmath128 & @xmath241 + @xmath242 @xmath243 & for a3 : @xmath244 + & for a4 @xmath245 + & for a5 : @xmath246 + @xmath247 @xmath243 & for a3 : @xmath248 + & for a4 @xmath249 + & for a5 : @xmath250 + @xmath132 & @xmath251 +","summary":"the x - ray spectrum is always dominated by a broad power - law - like component . the power - law is always hard , with a photon index ( and even flatter at times ) , as is generally the case with bright ulxs .","abstract":"we have studied a highly variable ultraluminous x - ray source ( ulx ) in the fornax galaxy ngc1365 , with a series of 12 _ chandra _ and _ xmm - newton _ observations between 2002 and 2006 . in 2006 april , the source peaked at a luminosity erg s in the kev band ( similar to the maximum luminosity found by _ asca _ in 1995 ) , and declined on an-folding timescale days . the x - ray spectrum is always dominated by a broad power - law - like component . when the source is seen at x - ray luminosities erg s , an additional soft thermal component ( which we interpret as emission from the accretion disk ) contributes of the x - ray flux ; when the luminosity is higher , erg s , the thermal component is not detected and must contribute of the flux . at the beginning of the decline , ionized absorption is detected around kev ; it is a possible signature of a massive outflow . the power - law is always hard , with a photon index ( and even flatter at times ) , as is generally the case with bright ulxs . we speculate that this source and perhaps most other bright ulxs are in a high / hard state : as the accretion rate increases well above the eddington limit , more and more power is extracted from the inner region of the inflow through non - radiative channels , and is used to power a comptonizing corona , jet or wind . the observed thermal component comes from the standard outer disk ; the transition radius between outer standard disk and comptonizing inner region moves further out and to lower disk temperatures as the accretion rate increases . this produces the observed appearance of a large , cool disk . based on x - ray luminosity and spectral arguments , we suggest that this accreting black hole has a likely mass ( even without accounting for possible beaming ) .    [ firstpage ]    x - rays : binaries  x - rays : individual ( ngc1365 x1 )  black hole physics  accretion , accretion disks"}
{"article_id":"0705.3977","section_id":"c","document":"we have investigated the intriguing behaviour of a ulx in the spiral galaxy ngc1365 ( in the fornax cluster ) , characterized by high x - ray luminosity ( peaking at @xmath0 erg s@xmath1 ) and order - of - magnitude variability over timescales of weeks and months . we studied the system with _ xmm - newton _ and _ chandra _ , at different luminosities between 2002 and 2006 . the x - ray spectrum of ngc1365 x1 is always dominated by a broad component well modelled as a power - law . the power - law photon index is @xmath177@xmath47 , consistent with the 1995 _ asca _ observations . in fact , when an additional thermal component is also taken into account , the slope may be even higher , @xmath287 , at least in the @xmath192@xmath199 kev range , with a possible break at higher energies . a soft excess consistent with disk - blackbody emission is significantly detected in the _ xmm - newton _ spectra with higher signal - to - noise ratio . it contributes @xmath7 of the observed x - ray flux when the ulx has a @xmath2@xmath3 kev luminosity @xmath6 erg s@xmath1 , but it is not detected , and must contribute @xmath8 of the flux , when the ulx is near the outburst peak , at luminosities three times higher . this  and similar findings for other bright ulxs  suggests that one of the fundamental physical properties of this class of systems is that a large fraction of accretion power is extracted via non - thermal processes ( for example , magnetic torques ) rather than being directly radiated by an accretion disk , and that such fraction increases at higher accretion rates . a likely consequence is that the temperature profile of the inner accretion disk may be flatter than that of a standard disk ; alternatively , the inner disk may be entirely replaced or covered by a comptonizing region . in all cases , the direct disk emission component would appear cooler and truncated at larger radii . this may lead to an overestimate of the central bh mass from simple spectral fitting ( intermediate - mass bh scenario ) . a similar phenomenon has been seen in at least one galactic bh , xte j1550@xmath197564 ( done & kubota 2006 ) , and may be triggered when @xmath288 . it is sometimes noted that the spectral state behaviour of ulxs does not appear to follow the same pattern of canonical state transitions extensively studied in stellar - mass bhs ( section 1 ) . we suggest that we can now start to outline a general sequence of spectral states applicable to both stellar - mass bhs and ulxs . accreting bhs of any mass are in a low / hard state at low accretion rates ( @xmath289 ) , when the inner disk is truncated at large radii because not enough mass is flowing inwards . they are found in a soft ( thermal - dominant ) state at intermediate accretion rates ( @xmath290 ) , when the disk reaches the innermost stable orbit and radiates all the accretion power . they might switch to a high / hard state at higher accretion rates ( @xmath291 ) when most of the power begins to be extracted from the inner disk via non - radiative mechanisms ( poynting flux or mechanical power ) , and most of the emerging photons are coming from the comptonizing medium . for @xmath288 the comptonizing corona may become optically thick or replace the disk altogether . the open question is why ulxs seem to spend most of their active time in the high / hard state , rather than in the thermal dominant state . the reason may be related either to their higher bh mass or , more likely , to a consistently higher mass transfer rate from their massive donor stars . an exceptional , serendipitous result of our _ chandra _ sequence of observations in 2006 april is that we caught the rise , peak and decline of a strong but short - lived outburst ( @xmath4-folding timescale @xmath5 d ) . this flare may be similar to those observed in the power - law - dominated very high state of galactic bhs . there is evidence of increased absorption from ionized gas ( column density @xmath253 @xmath53 , ionization parameter @xmath254 ) as the flux starts to decline . this might be due to the onset of an outflow as the source exceeded its eddington limit . we speculate that the relatively low ionization parameter of the absorber is due to partial shielding of the wind from direct x - ray irradiation .    finally , we discussed two possible arguments , based on the x - ray luminosity and spectral features , to constrain the mass of the accreting bh . we argue that the most likely range ( consistent with both arguments ) is @xmath292@xmath13 even without taking into account the possibility of mild geometrical beaming or super - eddington emission ( which would further reduce the required bh mass ) .","summary":"when the source is seen at x - ray luminosities erg s , an additional soft thermal component ( which we interpret as emission from the accretion disk ) contributes of the x - ray flux ; when the luminosity is higher , erg s , the thermal component is not detected and must contribute of the flux . at the beginning of the decline , ionized absorption is detected around kev ; it is a possible signature of a massive outflow . we speculate that this source and perhaps most other bright ulxs are in a high / hard state : as the accretion rate increases well above the eddington limit , more and more power is extracted from the inner region of the inflow through non - radiative channels , and is used to power a comptonizing corona , jet or wind . this produces the observed appearance of a large , cool disk . based on x - ray luminosity and spectral arguments , we suggest that this accreting black hole has a likely mass ( even without accounting for possible beaming ) .   ","abstract":"we have studied a highly variable ultraluminous x - ray source ( ulx ) in the fornax galaxy ngc1365 , with a series of 12 _ chandra _ and _ xmm - newton _ observations between 2002 and 2006 . in 2006 april , the source peaked at a luminosity erg s in the kev band ( similar to the maximum luminosity found by _ asca _ in 1995 ) , and declined on an-folding timescale days . the x - ray spectrum is always dominated by a broad power - law - like component . when the source is seen at x - ray luminosities erg s , an additional soft thermal component ( which we interpret as emission from the accretion disk ) contributes of the x - ray flux ; when the luminosity is higher , erg s , the thermal component is not detected and must contribute of the flux . at the beginning of the decline , ionized absorption is detected around kev ; it is a possible signature of a massive outflow . the power - law is always hard , with a photon index ( and even flatter at times ) , as is generally the case with bright ulxs . we speculate that this source and perhaps most other bright ulxs are in a high / hard state : as the accretion rate increases well above the eddington limit , more and more power is extracted from the inner region of the inflow through non - radiative channels , and is used to power a comptonizing corona , jet or wind . the observed thermal component comes from the standard outer disk ; the transition radius between outer standard disk and comptonizing inner region moves further out and to lower disk temperatures as the accretion rate increases . this produces the observed appearance of a large , cool disk . based on x - ray luminosity and spectral arguments , we suggest that this accreting black hole has a likely mass ( even without accounting for possible beaming ) .    [ firstpage ]    x - rays : binaries  x - rays : individual ( ngc1365 x1 )  black hole physics  accretion , accretion disks"}
{"article_id":"1608.04280","section_id":"i","document":"the role active galactic nuclei ( agn ) play in the evolution of their host galaxy remains an outstanding problem in theoretical astrophysics @xcite . the discrepancy between the number of luminous galaxies predicted in a @xmath4cdm universe and observed by astronomers persists and is mainly explained by negative feedback through agn quenching @xcite . in many of today s cosmological simulations , this feedback is treated through the injection of thermal energy into the galaxy ( e.g. * ? ? ? * ; * ? ? ? * ) , others actually include jets and outflows @xcite , and both contribute to achieve the necessary quenching to match with the observed luminosity functions .    observers still investigate the different impacts of jets and outflows on the host galaxy . recent observational evidence shows greater star formation rates ( sfr ) in radio - loud quasars than in radio - quiet quasars . @xcite analyze approximately 20,000 quasars from the sloan digital sky survey ( sdss ) , and employ the [ oii ] emission line to calculate sfrs . they find higher sfrs in the radio - loud agn , indicating agn jet triggered star formation . @xcite utilize _ herschel_-atlas @xcite and find that the far - infrared ( fir ) data are critical to calculating sfrs in agn , particularly in quasars where radiation from the accretion disk can contaminate calculations of the sfrs calculated from optical and ultraviolet ( uv ) data . once the fir data is incorporated into the sfr calculations , the group finds both that high redshift radio loud agn can have high star formation rates and that these bursts of star formation happen simultaneously with the growth of super massive black holes ( smbh ) . these results are in tension with the idea of universal agn quenching . similarly , @xcite study several hundred agn from the chandra deep field south and compare the sfrs , as determined from archived infrared data , finding higher sfrs in the radio - loud agn , concluding agn jets trigger star formation . the differences in sfrs between radio - loud and radio - quiet quasars underscore the importance of understanding the feedback mechanisms on a smaller scale .    however , with all the restrictions inherent to cosmological simulations on large physical scales , many of the critical physical processes in agn feedback can not be resolved due to density , velocity , and related time scales and dynamic ranges . @xcite simulate agn jet feedback on a smaller , single - galaxy scale and show that mildly relativistic jets may induce star formation in their host galaxies . the discrepancy between the two approaches requires a closer look on smaller time and physical scales to treat the problem . @xcite also explore both positive and negative agn feedback from a theoretical perspective and identify the challenges of simulations . one such problem is the huge range of physical scales important to agn feedback , scaling from the pc size of the accretion disc , out to tens of kpc to the edges of the host galaxies , extending even further to mpc scales and interaction with the inter - galactic medium . covering these spatial scales with good resolution while simultaneously capturing the extreme velocities close to the speed of light is virtually impossible . additionally including self - gravity and detailed radiative processes would make this computationally prohibitive . it is important then to focus on specific aspects of agn feedback with a given suite of simulations . as an example , @xcite examine the feedback effect from the pressure confinement of a jet driven bubble on a disk radio galaxy , avoiding the computational costs of an actual jet by artificially introducing overpressure . this frees up computational power to include self gravity . they find the pressure causes an increased fragmentation of dense clouds in the host galaxy and subsequent increase in star formation ( positive feedback ) . another specific aspect of agn feedback that is not well understood is the impact of winds from expanding jet cocoons or outflow bubbles on dense clouds of gas on small scales ( i.e. cloud scales ) , though there is some observational evidence of this . @xcite analyze observations from alma and find that agn jets can blow giant molecular clouds away from the galactic nucleus with jet - driven bubbles before gravity draws them back , similar to mechanical pumps . these observations reveal star formation along the outer edges of the clouds that is potentially triggered by the expansion of the jet bubble . employing observations from the measuring active galactic nuclei under muse microscope ( magnum ) survey on ngc 5643 , a radio - quiet agn with outflows , @xcite find positive feedback . the observations show star formation in clumps within the double sided ionization cones with high - velocity gas , likely caused by the compression of the clouds from the outflow . they also find a ring of star formation at 2.3 kpc , possibly triggered by the agn outflow , a phenomenon also seen in @xcite and @xcite .    simulations of agn feedback on smaller scales provide a complementary view to observations as well as to large scale simulations . the fate of the clouds and hence potential star formation is eventually decided on small scales . @xcite , @xcite and @xcite have performed important studies to this end . understanding the relationship between these winds and the clouds of gas available to form stars in a galaxy is critical to understanding the role agn feedback has in galaxy evolution .    in this paper , we seek to build on past research of agn feedback on clouds of gas by focusing on realistic agn winds and gravitational collapse on the scale of a single cloud . we simulate high velocity winds characteristic of agn jet cocoons and outflow bubbles striking bonnor  ebert spheres @xcite . we have better resolution than in the past , and we include gravity , heating and cooling for the entire temperature range ( including very low temperatures ) . we organize this paper as follows : in section 2 , we discuss some previous literature , in section 3 we describe our simulation setup , and in section 4 our results . in section 5 , we include our findings and conclude in section 6 .","summary":"feedback from active galactic nuclei ( agn ) and subsequent jet cocoons and outflow bubbles can have a significant impact on star formation in the host galaxy . to investigate feedback physics on small scales , we perform hydrodynamic simulations of realistically fast agn winds striking bonnor - ebert ( be ) spheres and examine gravitational collapse and ablation .","abstract":"feedback from active galactic nuclei ( agn ) and subsequent jet cocoons and outflow bubbles can have a significant impact on star formation in the host galaxy . to investigate feedback physics on small scales , we perform hydrodynamic simulations of realistically fast agn winds striking bonnor - ebert ( be ) spheres and examine gravitational collapse and ablation . we test agn wind velocities ranging from 3003,000 km s and wind densities ranging from 0.510 . we include heating and cooling of low- and high - temperature gas , self - gravity , and spatially correlated perturbations in the shock , with a maximum resolution of 0.01 pc . we find that the ram pressure is the most important factor that determines the fate of the cloud . high ram pressure winds increase fragmentation and decrease the star formation rate , but also cause star formation to occur on a much shorter time scale and with increased velocities of the newly formed stars . we find a threshold ram pressure of dyne above which stars are not formed because the resulting clumps have internal velocities large enough to prevent collapse . our results indicate that simultaneous positive and negative feedback will be possible in a single galaxy as agn wind parameters will vary with location within a galaxy ."}
{"article_id":"1608.04280","section_id":"c","document":"these simulations cover the broad range of physical parameters for the winds caused by agn feedback from jets or radio quiet quasars . these winds can drive the peak densities of the cloud by up to five orders in magnitude through the formation of dense filaments and clumps , subsequently resulting in a drastic shortening of the free fall time . we find threshold values for the ram pressure and momentum of the incoming wind below which the resulting clumps binding energy overcomes internal kinetic energy and pressure , resulting in gravitational collapse and star formation ( shown in table [ tab : table_2 ] ) . increased ram pressure and momentum of the incoming wind decrease the total mass of resulting stars but increase the velocities of formed stars , some achieving velocities of up to 35 km s@xmath0 . the results require some interpretation to be applicable to the debate between positive and negative feedback . we have taken a dense cloud of gas , that by itself would not collapse , and then applied realistic physical circumstances expected for agn feedback that induce star formation in half of the simulations . in this sense , our results are complementary to previous studies that shock uniform spheres , that would collapse on their own , preventing the spheres from collapsing and showing negative feedback . however , nearly all of those do not include gravity and shock uniform spheres . in our suite of simulations , we include gravity and simulate be spheres , and find that the distribution of gas within the sphere can make a considerable difference to the results . our simulations show the formation of dense filaments reported in @xcite , @xcite , @xcite , @xcite , and @xcite . our results are in agreement with the latter three studies in that the geometry of the cloud impacts the results . only @xcite includes gravity , and we both report star formation . however , we build on their results by identifying the velocity , density , and ram pressure range in which star formation is possible . we also include substantially higher velocities , characteristic of agn jet cocoons and outflow bubbles . with respect to the three phases of uniform cloud shocking introduced by @xcite and identified in @xcite , among others , @xcite includes a fourth phase in which the cloud is ablated and destroyed . we find another possible phase in which gravitational collapse outpaces ablation . comparisons between cloud collapse time and ablation time have been made previously . @xcite argued that for clouds less than 50 pc in size the collapse time would be longer , resulting in negative feedback . however , @xcite and @xcite speculated that only the outer , more diffuse envelopes of these clouds might be ablated , leaving behind the dense inner core to continue collapsing . our results corroborate this idea . we find that a stratified density distribution of the sphere may change the manner in which the cloud is stripped , the mass that is lost , and how the remaining core is shielded and collapses , as in @xcite . with a uniform sphere , shielding from the sphere s dense edge prevents the wind from injecting kinetic energy into the sphere , which leaves the thermal pressure as the main mechanism of support . this is considerably different from the other simulations , in which the internal velocity dispersions are crucial to the clump s support . it is also worth noting that the extreme ram pressures resulting from agn feedback quickly change the nature of the cloud being shocked , increasing the density and ablation time , decreasing the free fall time , and causing star formation . in the longer term , however , after the outer envelopes have been stripped and the cores have collapsed to form stars , the remaining gas budget for continued star formation may be depleted , causing long term negative feedback after a burst of positive feedback . strong fragmentation of the cloud may result in cloudlets too small too collapse or too small to form stellar objects .    within an entire galaxy , as a jet cocoon or outflow bubble expands through the galaxy , some clouds will be struck with velocities of 3,000 km s@xmath0 while others , shielded by other clouds , will be struck with slower velocities of 1,000 km s@xmath0 or even 300 km s@xmath0 depending on the location . @xcite discusses the idea that positive and negative feedback can occur simultaneously within the same galaxy , depending on the size of the clouds being struck with shocks , that the larger clouds will collapse under the pressure and form stars while the smaller clumps will be blown away . since we did not change the cloud properties systematically in our study , we can not assess the impact of variations in the typical sizes clouds or cloud complexes , e.g. with redshift @xcite . we only vary the the winds striking the clouds , but we too find that simultaneous positive and negative feedback is possible in the same galaxy provided that the winds will depend on time and location within the galaxy . we also include gravity and have spatial resolutions that are much better than those achievable in galaxy wide simulations . we see that the star formation efficiency decreases with ram pressure . this is an interesting result that fits as a data point on the spectrum between negative and positive feedback , that agn feedback can trigger star formation , but at a possibly lower efficiency than would otherwise occur , depending on the parameters of the feedback . there is , however , another intricacy that might be relevant : if star formation is not entirely prevented by high ram pressures , the time scale for collapse and the formation of stars within a cloud should be much shorter and happen more synchronously rather than be spread over the ( long ) free - fall time of the uncompressed cloud or cloud complex . correspongingly , the impact of ( negative ) stellar feedback within the cloud by other young stars should be considerably smaller and thereby increase the efficiency of star formation .    among other interesting conclusions , @xcite found that that the wind destroyed regions of lower density faster than those of higher density . combined with our results in which the density of the core clumps can climb up to five orders of magnitude in @xmath11750 kyr , this would indicate that the clumps would survive for long periods of time . @xcite also found that radiative cooling increases the survival time of the clouds . the clouds in @xcite survive up to 1 myr , achieving velocities of 150400 km s@xmath0 , and it is reasonable to believe that our dense clumps could survive that long if they were not already collapsing . those velocities are higher than our clump velocities at the simulation s end , but that is to be expected because our simulations have maximum times of 250 kyr and because our clumps are much denser . the results from our simulations are similar to our previous studies , @xcite and @xcite , which show both that feedback in radio - loud galaxies may be positive and that stars formed during this period of feedback will have a positive velocity bias . specifically , these stars are typically formed with greater radial and vertical ( off the disk ) velocity distributions . while we found velocities of up to 35 km s@xmath0 within the simulated time span for our small cloud , we note that larger clouds might survive longer , would be accelerated to higher velocities due to the larger effective cross section and thus form stars with higher peculiar velocities .    in turn , this also provides further computational support to previously existing theory linking agn feedback with hypervelocity stars @xcite . in this scenario , the cocoon or bow shock of a jet accelerates a pocket of gas to high velocities while compressing it to form stars . @xcite makes analytical arguments based on energy and momentum , but here we provide computational evidence to the same end . again , because our simulations are limited in the size of the cloud and the time with which we have to accelerate the cloud , we do not achieve stellar velocities as high as some of those observed in the milky way . however , what we show here is that the phenomenon is possible on smaller scales .    it would be interesting in the future to extend the simulations to larger gas complexes such as giant molecular clouds ( gmc ) . for these , the assumption of having be spheres is no longer suitable and a turbulent gmc would need to be included . this may address the idea that the larger the cloud is , the more positive the feedback could be .","summary":"high ram pressure winds increase fragmentation and decrease the star formation rate , but also cause star formation to occur on a much shorter time scale and with increased velocities of the newly formed stars .","abstract":"feedback from active galactic nuclei ( agn ) and subsequent jet cocoons and outflow bubbles can have a significant impact on star formation in the host galaxy . to investigate feedback physics on small scales , we perform hydrodynamic simulations of realistically fast agn winds striking bonnor - ebert ( be ) spheres and examine gravitational collapse and ablation . we test agn wind velocities ranging from 3003,000 km s and wind densities ranging from 0.510 . we include heating and cooling of low- and high - temperature gas , self - gravity , and spatially correlated perturbations in the shock , with a maximum resolution of 0.01 pc . we find that the ram pressure is the most important factor that determines the fate of the cloud . high ram pressure winds increase fragmentation and decrease the star formation rate , but also cause star formation to occur on a much shorter time scale and with increased velocities of the newly formed stars . we find a threshold ram pressure of dyne above which stars are not formed because the resulting clumps have internal velocities large enough to prevent collapse . our results indicate that simultaneous positive and negative feedback will be possible in a single galaxy as agn wind parameters will vary with location within a galaxy ."}
{"article_id":"1608.04280","section_id":"c","document":"our simulations show that the unique combination and range of ram pressure and thermal pressure agn feedback provides can either trigger or prevent star formation in dense clumps within the ism , depending mostly on the ram pressure . our setup includes a broad range of parameters expected for winds originating from agn jet cocoons or quasar winds . in the simulations that form stars , the wind compresses the cloud in the high - pressure post - shock region , then followed by the simultaneous stripping and collapse of the sphere . the initial compression from the shock and not gravity causes the peak density in the sphere to climb by as much as 5 orders of magnitude in as little as 50 kyr , reaching regimes where gravitational collapse overcomes internal pressure and kinetic energy . during this phase , the free fall time of the cloud drops from 3 myr initially , to as low as 10 kyr in subsequent clumps . we analyze these clumps resulting from this collapse , and subsequent star formation within the clumps , finding indications of both positive and negative feedback , depending on the parameters of the wind . we find that the stratified density profile of bonnor  ebert spheres can have a considerable impact on gravitational collapse and star formation . we find that increased ram pressure , momentum , and mach number of the incoming wind decreases the total mass of stars formed , but increases the velocities of these stars . furthermore , star formation would happen on a much shorter time scale and more synchronously . we identify threshold values for ram pressure and momentum of @xmath2 dyn @xmath3 above which star formation is not expected to occur because high internal velocities generated within the clumps support them against gravitational collapse long enough for the cloud to be destroyed . our results indicate that simultaneous positive and negative feedback will be possible in a single galaxy as agn wind parameters will vary with location within a galaxy . similar phenomena are observed in agn @xcite . zd was supported by a centre for cosmological studies balzan fellowship . vg was supported by the sonderforschungsbereich sfb 881 `` the milky way system '' ( subproject b4 ) of the german research foundation ( dfg ) . the research of js has been supported at iap by the erc project 267117 ( dark ) hosted by universit pierre et marie curie - paris 6 and at jhu by nsf grant oia-1124403 . we would like to thank alex wagner for his input .","summary":"we find a threshold ram pressure of dyne above which stars are not formed because the resulting clumps have internal velocities large enough to prevent collapse . our results indicate that simultaneous positive and negative feedback will be possible in a single galaxy as agn wind parameters will vary with location within a galaxy .","abstract":"feedback from active galactic nuclei ( agn ) and subsequent jet cocoons and outflow bubbles can have a significant impact on star formation in the host galaxy . to investigate feedback physics on small scales , we perform hydrodynamic simulations of realistically fast agn winds striking bonnor - ebert ( be ) spheres and examine gravitational collapse and ablation . we test agn wind velocities ranging from 3003,000 km s and wind densities ranging from 0.510 . we include heating and cooling of low- and high - temperature gas , self - gravity , and spatially correlated perturbations in the shock , with a maximum resolution of 0.01 pc . we find that the ram pressure is the most important factor that determines the fate of the cloud . high ram pressure winds increase fragmentation and decrease the star formation rate , but also cause star formation to occur on a much shorter time scale and with increased velocities of the newly formed stars . we find a threshold ram pressure of dyne above which stars are not formed because the resulting clumps have internal velocities large enough to prevent collapse . our results indicate that simultaneous positive and negative feedback will be possible in a single galaxy as agn wind parameters will vary with location within a galaxy ."}
{"article_id":"1002.4292","section_id":"i","document":"in this paper we use the definition of a generic subset of a countable set , introduced in definition 4.1 of @xcite ( see also subsection [ subsec_genericity ] below ) , to investigate whether for each fixed genus @xmath1 the set of high distance heegaard splittings is generic in the set of all irreducible heegaard splittings . for this purpose , we consider irreducible heegaard diagrams composed of two _ complete decomposing systems _ @xmath3 on a closed surface @xmath0 , i.e. two curve systems which both decompose @xmath0 into pair - of - pants . we define the set @xmath4 of such pairs @xmath5 , by requiring the pairs to have the additional property that they do not have _ waves _ ( see definition [ smallwave ] ) with respect to each other . a pair of such curve systems , which determine a heegaard splitting that is of distance greater or equal to some @xmath6 , will be said to belong to @xmath7 . for precise definitions see sections [ prelims ] and [ tt ] below . our main result is :    * theorem [ large_distance_snows_are_generic ] . * _ let @xmath0 be a closed surface of genus @xmath1 . then for any integer @xmath8 the set @xmath9 is generic in the set @xmath4 . _ the fact that a heegaard splitting is high distance has important consequences for the geometry of the @xmath10-manifold determined by it . hence the question , raised in the title of this paper , is natural and relevant . indeed , since the distance is measured in the _ curve complex _ @xmath11 , which is not locally finite , it is a priory not clear , despite of the fact that @xmath11 has infinite diameter , whether one should expect random points in @xmath11 to be close or far away from each other . the question becomes even less evident if asked for subsets of @xmath11 with infinite diameter , such as the handlebody sets @xmath12 and @xmath13 , which are used to determine the distance of a heegaard splitting @xmath14 , see section [ prelims ] . there are several ways to attack this question , and this paper presents one which is described in detail in subsection [ mando ] . j. maher @xcite has provided another such approach , based on random walks in the mapping class group and the issuing notion of a `` random 3-manifold '' , which was introduced and investigated by n. dunfield and w. thurston in @xcite . it is well known that making mathematical sense of the term `` generic '' is particularly problematic when considering subsets of countable sets @xmath15 . in the `` classic '' setting a set @xmath16 would be called _ generic _ if and only if the complement @xmath17 is finite . this definition is very restrictive and , in practice , there are many cases where intuitively one would like to call a set generic , yet it does not satisfy this criterium . a common method to deal with this situation is the following : one considers a family of finite subsets @xmath18 that exhaust @xmath15 ( typically given by enumerating @xmath19 , and by defining @xmath20 ) . one then computes the the ratio @xmath21 , and defines @xmath22 to be generic if @xmath23 tends to 1 . of course , the obtained limit ratio depends heavily on the particular chosen enumeration of @xmath15 . another difficulty with statements about `` genericity '' is that of _ double counting_. a typical example here is to count group presentations instead of groups , so that the same group may well be counted several times , or even infinitely often . the problem arises when in the given mathematical context it is impossible to count the objects in question directly , so that double counting becomes unavoidable .    in this paper we do indeed consider a countable set @xmath15 as base set , but we use the fact that our set @xmath15 is given as subset of a space @xmath24 that is already equipped with a natural measure , or rather , measure class . this enables us to use the following definition , which was introduced in a previous paper @xcite . it is motivated by the observation that a `` generic '' point with rational coordinates in the unit square @xmath25 \\times [ 0 , 1]$ ] should rightfully be expected to lie in the interior rather than on the boundary of @xmath25 \\times [ 0 , 1]$ ] .    [ generic ] let @xmath24 be a topological space , provided with a borel measure @xmath26 . let @xmath27 be a ( possibly countable ) subset , which is a disjoint union @xmath28 . the set @xmath22 is called _ generic in @xmath15 _ ( or simply _ generic _ , if @xmath29 ) if the closure @xmath30 of @xmath22 has measure @xmath31 , and the closure @xmath32 of @xmath33 has measure @xmath34 . ( here `` closure '' always means `` closure in @xmath24 '' . ) notice that in this definition the sets @xmath35 and @xmath32 may well not be disjoint , although @xmath22 and @xmath33 are assumed to be disjoint . note also , that this definition of genericity extends to sets @xmath15 that are not embedded but are just mapped to @xmath24 , by a properly chosen `` natural '' map . furthermore , note that this definition does not depend on the actual measure @xmath26 but rather only on its measure class . the following is an immediate consequence of the above definition :    [ lemma 4.3 ( 1 ) of @xcite ] [ equivalentgeneric ] given sets @xmath36 and @xmath22 as in definition [ generic ] . then @xmath22 is generic in @xmath15 if and only if the closure @xmath30 contains a set @xmath37 which is open in @xmath38 and of full measure @xmath39 , and which is disjoint from @xmath40 . we will specify precisely in the next subsection the sets @xmath41 and the measure @xmath26 that are used in this paper . the borel measure space @xmath24 , as in the last subsection , that is used in this paper is the space @xmath42 , where @xmath43 is the space of projective measured laminations on a `` model surface '' @xmath0 of genus @xmath1 . as shown by thurston , the space @xmath43 is a @xmath44-dimensional sphere , equipped with a canonical p.l .- structure , and thus with a canonical lebesgue measure class . the countable subset @xmath27 , required by this definition of the term `` generic '' in the statement of theorem [ large_distance_snows_are_generic ] , is a set of pairs @xmath45 , called @xmath4 , where @xmath46 and @xmath47 are curve systems on @xmath0 that satisfy a certain combinatorial condition , see definition [ snow ] . however , in order to focus on the objects of our primary interest , namely heegaard splittings , we have to be more careful , in order to avoid a potential double - counting problem as evoked in the previous subsection :    a _ marked heegaard surface of genus @xmath2 _ is a surface @xmath48 of genus @xmath2 embedded in a 3-manifold @xmath49 , with handlebody complementary components @xmath50 and @xmath51 , which is equipped with a _ marking homeomorphism _ @xmath52 . two such marked heegaard surfaces , with markings @xmath53 and @xmath54 , are _ equal _ if there exists a homeomorphism @xmath55 which is isotopic to the identity , such that @xmath56 . let @xmath57 denote the set of marked heegaard surfaces of genus @xmath1 , and let @xmath58 be the subset of those heegaard surfaces of distance @xmath59 . here the _ distance _ of a marked heegaard surface @xmath48 is measured in the curve complex of the model surface @xmath0 : more precisely , one measures the distance between the two handlebody sets @xmath60 and @xmath61 that are given by the @xmath62-images of all meridian curves in @xmath48 , for each of the two complementary handlebodies @xmath50 and @xmath51 respectively . now choose a map @xmath63 , where @xmath64 and @xmath65 are systems of meridian curves on @xmath50 and @xmath51 respectively . there are infinitely many such maps , and none seems to be prefered in any obvious way . in section [ generic - h - splittings ] we prove for any such map @xmath66 :    [ large_distance_hss_are_generic_intro ] for any integers @xmath1 and @xmath67 the set @xmath68 is generic in the set @xmath69 .    * acknowledgments . * we would like to thank the high council for scientific and technological cooperation between france and israel for supporting this project , the department of mathematics at the technion haifa israel and latp at the universit p. czanne - aix - marseille iii in marseilles france for their hospitality .","summary":"in a previous paper we introduced a notion of  genericity \" for countable sets of curves in the curve complex of a surface , based on the lebesgue measure on the space of projective measured laminations in . with this definition we prove that for each fixed the set of irreducible genus heegaard splittings of high distance is generic , in the set of all irreducible heegaard splittings . our definition of  genericity \" is different and more intrinsic then the one given via random walks .    = 1     this research is supported by a grant from the high council for scientific and technological cooperation between france and israel ]","abstract":"in a previous paper we introduced a notion of  genericity \" for countable sets of curves in the curve complex of a surface , based on the lebesgue measure on the space of projective measured laminations in . with this definition we prove that for each fixed the set of irreducible genus heegaard splittings of high distance is generic , in the set of all irreducible heegaard splittings . our definition of  genericity \" is different and more intrinsic then the one given via random walks .    = 1     this research is supported by a grant from the high council for scientific and technological cooperation between france and israel ]"}
{"article_id":"0902.3901","section_id":"i","document":"the prediction of a possible existence of the quark - gluon plasma ( qgp ) created in the relativistic heavy ion collisions is one of the most interesting theoretical achievements of quantum chromodynamics ( qcd ) at non - zero temperatures and densities . a fairly full list of the relevant pioneering papers is given in @xcite ) and the present status of the investigations of the properties of qcd matter is described in @xcite .    the equation of state ( eos ) for the qgp has been derived analytically up to the order @xmath3 by using the perturbation theory ( pt ) expansion for the evaluation of the corresponding thermodynamic potential term by term ( @xcite and references therein ) . however , the most characteristic feature of the thermal pt expansion is its non - analytical dependence on the coupling constant @xmath4 , which means that pt qcd is not applicable at finite temperatures . the problem is not the poor convergence of this series @xcite but rather the fact that a radius of convergence can not even be defined ; any next calculated term can be bigger than the previous one . this is an in - principle problem which can not be overcome . from the strictly mathematical point of view , four - dimensional qcd at non - zero temperatures effectively becomes a three - dimensional theory . at the same time , three - dimensional qcd has more severe infrared singularities @xcite and its coupling constant becomes dimensional . it is as a consequence of this that the dependence becomes non - analytical when using the dimensionless coupling constant @xmath4 . one also needs to introduce three different scales , @xmath5 , @xmath6 and @xmath7 , where @xmath5 is the temperature , in order to try somehow to understand the dynamics of the qgp within the thermal pt qcd approach .    at present , the only practical method to investigate the problem is lattice qcd at finite temperature and baryon density , which has recently shown rapid progress ( @xcite and references therein ) . however , lattice qcd , being a very specific regularization scheme , is primary aimed at obtaining well - defined corresponding expressions in order to get realistic numbers for physical quantities . one may therefore get numbers and curves without understanding what the physics is behind them . such understanding can only come from the dynamical theory , which is continuous qcd . for example , any description of the qgp has to be formulated within the framework of a dynamical theory . the need for an analytical eos remains , but , of course , it should be essentially non - perturbative ( np ) , approaching the so - called stefan - boltzmann ( sb ) limit only at very hight temperatures . thus the approaches of analytic np qcd and lattice qcd to finite - temperature qcd do not exclude each other , but , on the contrary , should be complementary . this is especially true at low temperatures where the thermal qcd lattice calculations suffer from big uncertainties @xcite . on the other hand , any analytic np approach has to correctly reproduce thermal lattice qcd results at high temperatures ( see papers cited above ) . there already exist interesting analytical approaches based on quasi - particle picture @xcite ( and references therein ) to analyze results of @xmath0 lattice qcd calculations for the qgp eos . the main purpose of this paper is to derive the np analytical eos for the gluon matter ( gm ) , i.e. , a system consisting purely of yang - mills ( ym ) fields without quark degrees of freedom . the formalism we use to generalize it to non - zero temperatures is the effective potential approach for composite operators @xcite . in the absence of external sources it is nothing but the vacuum energy density ( ved ) . the approach is np from the very beginning , since it deals with the expansion of the corresponding skeleton vacuum loop diagrams . the key element is the extension of our initial work @xcite to non - zero temperatures . this makes it possible to introduce the temperature - dependent bag constant ( pressure ) as a function of the mass gap . it is this which is responsible for the large - scale structure of the qcd ground state . the confining dynamics in the gm will therefore be nontrivially taken into account directly through the mass gap and via the temperature - dependent bag constant itself , but other np effects will be also present . let us note that the temperature - dependent bag constant within the thermal pt qcd has been introduced into the gibbs equilibrium criteria for a phase transition @xcite ( see also @xcite ) . the effective potential approach has been already used in order to study the structure of qcd at very large baryon density for an arbitrary number of flavors @xcite . the present paper is organized as follows . in section 2 the effective potential approach for composite operators is discussed in general terms . an explicit expression is obtained for the ved for pure ym fields . in section 3 the expression for the gluon pressure is derived taking into account the expression for the bag constant at zero temperature as a function of the mass gap @xcite . taken together this makes it possible to derive a formula for the pressure that is suitable for the generalization to non - zero temperatures . this consists of the two independent parts , describing the np and pt contributions to the gluon pressure . in section 4 the generalization to non - zero temperatures is performed using the imaginary - time formalism . all the analytic results for the gluon pressure as a function of temperature are collected together in section 5 . in section 6 the expressions are given for the main thermodynamic quantities , such as the entropy and energy densities , the heat capacity , etc . , as functions of the pressure . in section 7 we discuss all the numerical results for the np part of the gluon pressure . section 8 concludes our discussion . some explicit expressions for the summation of the thermal logarithms over the matsubara frequencies are present in appendix a , while in appendix b a scale - setting scheme of our calculations is formulated .","summary":"this is nothing but the vacuum energy density . this is responsible for the large - scale structure of the qcd ground state . the important thermodynamic quantities , such as the pressure , energy and entropy densities , etc . , have been calculated . the proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures , below . an analytic calculation of the gluon condensate is obtained as a function of temperature .","abstract":"the effective potential approach for composite operators is generalized to non - zero temperatures in order to derive the equation of state for pure yang - mills fields . in the absence of external sources , this is nothing but the vacuum energy density . the key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant . the non - perturbative analytical equation of state for gluon matter does not depend on the coupling constant , but instead introduces a dependence on the mass gap . this is responsible for the large - scale structure of the qcd ground state . the important thermodynamic quantities , such as the pressure , energy and entropy densities , etc . , have been calculated . we show explicitly that the pressure may vary continuously around , whereas all other thermodynamic quantities undergo drastic changes at this point . the proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures , below . we reproduce the properties of the so - called `` fuzzy bag''-type models through the presence of the mass gap in our equation of state . an analytic calculation of the gluon condensate is obtained as a function of temperature ."}
{"article_id":"0902.3901","section_id":"r","document":"all our numerical results obtained for the thermodynamical quantities discussed in the previous section and calculated with the help of the np pressure ( 30 ) are shown in figs . 3 , 4 and 5 . the np gluon pressure has a maximum at some finite ( `` characteristic '' ) temperature , @xmath134 . this means that it may change continuously its regime in the near neighborhood of this point in order for its full counterpart to achieve the thermodynamic sb limit ( 40 ) at high temperatures . however , this is not possible for the other np thermodynamic quantities , as is seen from the curves shown in fig . 3 ( none of the power - type fall off around @xmath2 can be continuously transformed into the almost constant behavior at high temperatures ) . in order to achieve the corresponding thermodynamic sb limits at high temperatures their full counterparts would have to undergo drastic changes around this point . as we already know from the thermodynamics of @xmath0 lattice qcd @xcite ( see @xcite ) the energy and entropy densities have discontinuities ( jump or , equivalently , step discontinuities ) at a temperature of about @xmath135 . our characteristic temperature @xmath129 is surprisingly very close to this value . if we were not aware of the thermal lattice qcd results then we would be able to predict them . since we are aware of them , these lattice results confirm our expectation of a sharp changes in the behavior of the entropy and energy densities in the region where the pressure is continuous . one of the interesting features of our calculations is seen in fig . 3 . at the characteristic temperature @xmath2 the np pressure , the entropy and energy densities satisfy a sb - type relations , namely    @xmath136    where , obviously , the right - hand - side is half of the general sb number ( 40 ) . in turn this yields    @xmath137    so that the np trace anomaly relation approaches zero from below in the @xmath138 ) limit ( see fig . 4 ) , i.e , satisfying the sb relation ( 42 ) in this limit as well . since the np entropy and energy densities satisfy the sb - type relations ( 43 ) , we expect for their full counterparts to have step discontinuities at @xmath2 , as discussed above . the np heat capacity and the velocity of sound squared do not satisfy the sb - type relations ( 43 ) , as can be seen in figs . 3 and 4 . we expect , therefore , for the full heat capacity to have an essential discontinuity at @xmath2 , since , in general , @xmath139^{-1 } = 0 $ ] , and hence @xmath140 due to the relation ( 36 ) . they are defined through derivatives of the entropy and energy densities in eqs . ( 35)-(36 ) , i.e. , they involve the second derivatives of the pressure . that is a reason why these thermodynamic quantities are too sensitive to the dynamical structure of the gm in the near neighborhood of @xmath2 . moreover , due to the sb - type relations ( 43)-(44 ) , and on account of the sb relations ( 40 ) , for example it follows that    @xmath141_{t = t_c } = 0 , \\ \\bigl \\ { { \\partial \\over \\partial t } \\bigl [ p_{sb}(t ) - 2p_{np}(t ) \\bigr ] \\bigr\\}_{t = t_c } = 0.\\ ] ]    combining these relations again with the sb - type relations ( 43)-(44 ) it is possible to derive some other exact relations between different thermodynamic quantities at @xmath2 . their importance will be explicitly shown in part ii of our investigation , where they will be extensively exploited .    from fig . 3 it clearly follows that the temperature range for the np thermodynamic quantities can be divided into the three different intervals :    _ ( i ) . the low - temperatures interval up to its upper bound of about @xmath130_. it is defined by the first maximum of the heat capacity which appears in this region before temperature reaches @xmath2 . this region is obviously dominated by the np contributions ( 30 ) to the gluon pressure ( 29 ) . the behavior of all the np thermodynamic quantities are shown in figs . 5 , 6 and 7 . we do not expect any serious changes in the behavior of their full counterparts in this region . however , whatever changes may occur they will be under our control , since the np part ( 30 ) is exactly calculated . the important observation is that all the np thermodynamic quantities which have been properly scaled go down exponentially as temperature approaches zero . this is a general feature of the behavior of all the full thermodynamic quantities far below @xmath2 ; otherwise their zero temperature limit would not be realized . the almost constant behavior of the np velocity of sound squared and conformity seen in fig . 7 is due to the fact that they are the ratios of the corresponding thermodynamic quantities , see eqs . ( 36)-(37 ) . it seems that for the first time it is possible to predict the behavior of all the important thermodynamic quantities in this interval . we shall refer to the gm in this region as a `` confining phase '' ( there are no lattice data for this region at all ) .    _ the transition interval @xmath131_. in this region all the thermodynamic quantities should undergo sharp changes in their regimes , so that their full counterparts will be able to achieve their corresponding sb limits at high temperatures . the full gm pressure remains continuous in this region . however , the existence of maxima in the behavior of the np thermodynamic quantities is expected in this interval , since they should `` die '' at high temperatures . the np pressure is a part of the full gm pressure , which should be a continuously growing function of @xmath5 throughout the whole temperature range . all other full thermodynamic quantities are continuous functions of @xmath5 only below and above @xmath2 . within our approach they are expected to have discontinuities of different character at @xmath2 , as mentioned above ( apart from the gluon condensate ) . following the authors of @xcite , we shall refer to the gm in the transition region as a `` mixed phase '' . the changes in the dynamical structure of the gm just in this region will determine the nature of the phase transition at @xmath2 .    _ the temperatures interval starting at @xmath2_. this interval itself can be clearly subdivided into two intervals , since in the integrals ( 31)-(32 ) @xmath142 : _ ( a ) the moderate - temperatures @xmath143 _ , when the np effects are still significant and _ ( b ) the high - temperatures starting at @xmath144 _ , when the np effects become small .    therefore , even above @xmath2 , the gm can be understood as being in the two different forms . the first one can be considered as strongly coupled gm , where the np effects are still important . the second one can be considered as weakly coupled gm , where the np effects become already negligible . the typical temperature which is of about @xmath145 for the gm , is too high to be reached even at lhc . for qcd matter this temperature should be substantially decreased , and therefore be accessible at rhic , and especially at lhc . the general feature for the behavior of all the properly scaled np thermodynamic quantities above @xmath2 is their power - type fall off , while their full counterparts should show a power - type rise at high temperatures . apparently , we may refer to the gm in the moderate temperature region as an `` extended mixed phase '' . the behavior of all the full thermodynamic quantities in both mixed phases is governed by the np pressure ( 30 ) and by the first term in the pt pressure ( 33 ) . we shall refer to the gm in the high temperatures region as an `` af phase '' , since the behavior of all the full thermodynamic quantities will be determined by the second term in the pt pressure ( 33 ) and the free gluons contribution . a few remarks in advance are here in order . from our discussion it clearly follows that the approximation of the gluon pressure ( 29 ) by its np part ( 30 ) only ( though exactly calculated in the present investigation ) breaks down at @xmath2 , when the np pressure achieves its maximum . for the derivatives of the pressure , this approximation breaks down even earlier , starting from about @xmath130 , as discussed above . this explains the sign change in the interaction measure and the supersonic value of the speed of sound squared both at @xmath2 as seen in fig . 4 . the rapid rise of conformity and the speed of sound squared above @xmath2 in fig . 4 is also unphysical . this also explains why the gluon condensate in fig . 5 increases drastically above @xmath2 . taking into account the np ( 30 ) , pt ( 33 ) , and free gluons contributions to the full gm pressure , all these unphysical effects will disappear in the full thermodynamic quantities , thus allowing them to achieve their corresponding sb limits . this will allow one to compare with lattice data above @xmath2 @xcite as well .     in the low - temperatures region shown up to @xmath130.,width=377 ]    . they are shown in the low - temperatures region up to @xmath130.,width=377 ]     in @xmath146 units ( see eq . ( 48 ) ) as a function of @xmath132 . it clearly approaches a finite constant in the high temperature limit ( compare with fig . 4).,width=377 ]     and shown as functions of @xmath132.,width=377 ]     as a function of @xmath132 . the zero temperature gluon condensate scaled by @xmath147 is also shown . at temperatures above @xmath148 they go down as explicitly shown by eq . , width=377 ]      on account of the first of eqs . ( 28 ) and eq . ( 31 ) , it is instructive to re - write the np gluon pressure ( 30 ) equivalently as follows :    @xmath149,\\ ] ]    where    @xmath150    it scales as @xmath151 in the @xmath152 limit , while the integrals @xmath153 , @xmath154 and @xmath155 remain unchanged , see eqs . let us emphasize the explicit presence of the np mass gap term in eq . ( 46 ) , namely @xmath156 . it will be present in the full eos as well , since in the pt part of the gluon pressure the mass gap contribution is logarithmical suppressed ( see eq . ( 33 ) ) , and hence its contribution can not be canceled . this is in full agreement with the so - called `` fuzzy bag '' model @xcite and with the massless boltzmann stringy model @xcite . the presence of the mass gap @xmath43 in our approach from the very beginning naturally explains the properties of such models .    the np trace anomaly relation scaled by @xmath157 , t.e . ,    @xmath158    is shown in fig . it clearly goes to a finite constant ( having the dimensions of @xmath43 ) in the high temperature limit , as it should in accordance with the previous discussion and the thermal lattice qcd results @xcite . this effect immediately shows up in the np gluon condensate ( 39 ) . scaled by @xmath147 , analytically it becomes    @xmath159 \\over t^2 } \\times { 1 \\over t^2 } \\sim   { const . \\over t^2 } , \\ t \\rightarrow \\infty.\\ ] ]    the difference in the fall off at high temperatures between the zero temperature gluon condensate and minus trace anomaly relation ( as it enters eq . ( 49 ) ) , both scaled by @xmath147 , is clearly seen in fig . 9 . evidently , this difference is due to the asymptotic behavior of eq . ( 48 ) . at temperatures below @xmath2 there is no difference between @xmath160 and @xmath161 , which is as it should be ( see , for example again fig . 5 ) . at temperatures above @xmath2 the difference between these two quantities is explicitly determined by eq . ( 49 ) and is clearly shown in fig . 10 . the presence of the mass gap contribution in eq . ( 46 ) , and hence in the trace anomaly relation ( 38 ) scaled by @xmath147 , explains that the way it goes down is not @xmath162 @xcite but , as follows from our consideration , it decreases as @xmath163 . the inclusion of the pt contribution @xmath164 / t^4 $ ] in eq . ( 49 ) will produce a rather small numerical correction at high temperatures due to the sb limit ( 42 ) for the trace anomaly . the numerical results presented in table 1 confirm this statement . it shows rather good numerical agreement between our np analytical trace anomaly , as it enters eq . ( 49 ) , and its lattice counterpart at hight temperatures starting already from @xmath165 @xcite .    in conclusion , let us note that in lattice qcd at non - zero temperatures there is a possibility to distinguish between the magnetic ( m ) and electric ( e ) parts of the gluon condensate ( see , for example @xcite and references therein ) . in @xcite and @xcite , such a gauge - invariant field - strength correlators in pure ym theory have been calculated at finite temperatures around @xmath2 and above @xmath2 , respectively . following @xcite , we can formally write @xmath166 , but at this stage we do not know how to calculate these two parts separately within our approach . there is therefore as yet no possibility to compare with lattice data . in any case , such an analytical investigation at zero and non - zero temperatures is beyond the scope of the present investigation . .the np analytical and lattice trace anomalies at high temperatures . [ cols=\"^,^,^ \" , ]      the np dynamical structure of the gm within our approach is highly non - trivial . in the whole temperature range we have the two different massive gluonic excitations @xmath94 and @xmath104 with the effective masses @xmath167 and @xmath168 , respectively . both effective masses are due to the mass gap @xmath43 , which is responsible for the large - scale structure of the qcd ground state . it is dynamically generated by the nonlinear interaction of massless gluon modes @xcite . the first massive excitations can be interpreted as the glueballs , since @xmath169 is comparable to the masses of scalar glueballs ( though it is lighter than the pseudoscalar ones ) @xcite . the second one @xmath170 might be identified with an effective gluon mass of about @xmath171 , which arises in different approaches ( see again the above - mentioned review @xcite and references therein ) . we also have the two different massless gluonic excitations @xmath172 : the np massless gluons , propagating according to the integral @xmath173 in eq . ( 31 ) , and almost sb massless gluons , propagating according to the integral @xmath153 in eqs . we stress that the integral ( 31 ) should be multiplied by @xmath174 , and all other integrals ( 32 ) are to be multiplied by @xmath175 , when one speaks about different np contributions to the np pressure ( 30 ) . it is worth emphasizing once more that all these np gluonic excitations are of dynamical origin , and only such can be accounted for within our approach . whether the pt part ( 33 ) of the gluon pressure ( 29 ) will introduce a new massless or even massive gluonic excitations ( or , equivalently , an effective gluonic degrees of freedom @xcite ) is an open question at this stage . in our opinion , however , they may be really present in the full gm eos . in addition to the mass gap the pt part ( 33 ) depends on the asymptotic scale parameter of qcd . the combination of these two fundamental scale parameters may lead to the creation of new massive gluonic excitations around @xmath2 , for example , pseudoscalar glueballs @xcite . in any case , we should definitely have the sb free massless gluons far away from @xmath2 . however , one thing should be made perfectly clear . because of these and a possible new massive excitations in the gm , the behavior of all the thermodynamic variables in the moderate temperatures region @xmath143 will be substantially different from the behavior of a gas of free massless gluons . this our qualitative yet conclusion is in agreement with recent lattice data and quasi - particle approaches both cited above . the recent lattice data will be reproduced quantitatively after the evaluation of the np ( 30 ) , pt ( 33 ) , and free gluon contributions to the full gm pressure . the existence of the sb - type relations ( 43)-(44 ) indicates that in the transition region near @xmath2 a dramatic increase in the number of effective gluonic degrees of freedom will appear ( for example , the glueballs will begin rapidly to dissolve ) . this effect will be reflected in the strong increase of the thermodynamic variables near @xmath2 , in agreement with recent lattice results @xcite . this will lead to drastic changes in the structure of the gm . a change in this number is enough to generate pressure gradients , but not enough to affect the pressure itself . it varies slowly and therefore remains continuous in this region . at the same time , the pressure gradients , such as the energy and entropy densities , etc . , should undergo sharp changes in their behavior . the penetration of the pt part ( 33 ) of the gluon pressure below @xmath2 should not go deeply into the transition region @xmath176 , since the inp effective charge is logarithmical suppressed . however , it should go sufficiently deep in order to eliminate `` non - physical '' maxima and other effects , created by the derivatives of @xmath177 in the transition region . instead of `` non - physical '' maxima , the full thermodynamic quantities ( apart from the pressure ) should have discontinuities at @xmath2 , as follows from our approach . this has also been established by the thermal qcd lattice cited above .    of course , not all the glueballs will be dissolved in the transition region . some of them will remain above @xmath2 , along with other massive and massless gluonic excitations , forming thus a possible mixed and extended mixed phases around @xmath2 @xcite . after the evaluation of the pt part ( 33 ) , which is also `` contaminated '' by the np contributions , we hope that the np physics of the mixed phases will be well understood in the gm . at very high temperatures , starting at @xmath144 the np effects become very small , and the structure of the gm will be mainly determined by the sb relations ( 40)-(42 ) between all the important thermodynamic quantities .","summary":"we show explicitly that the pressure may vary continuously around , whereas all other thermodynamic quantities undergo drastic changes at this point .","abstract":"the effective potential approach for composite operators is generalized to non - zero temperatures in order to derive the equation of state for pure yang - mills fields . in the absence of external sources , this is nothing but the vacuum energy density . the key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant . the non - perturbative analytical equation of state for gluon matter does not depend on the coupling constant , but instead introduces a dependence on the mass gap . this is responsible for the large - scale structure of the qcd ground state . the important thermodynamic quantities , such as the pressure , energy and entropy densities , etc . , have been calculated . we show explicitly that the pressure may vary continuously around , whereas all other thermodynamic quantities undergo drastic changes at this point . the proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures , below . we reproduce the properties of the so - called `` fuzzy bag''-type models through the presence of the mass gap in our equation of state . an analytic calculation of the gluon condensate is obtained as a function of temperature ."}
{"article_id":"0902.3901","section_id":"c","document":"the effective potential approach for composite operators @xcite has been generalized to non - zero temperatures in order to derive analytical eos for pure @xmath0 ym fields , shown in eqs . ( 29)-(33 ) . in its np part ( 30 ) there is no dependence on the coupling constant , only the dependence on the mass gap , which is responsible for the large - scale structure of the qcd ground state . a key element of this work is the generalization of the expression for the bag constant at zero temperature @xcite to non - zero temperatures . the np part ( 30 ) of the gluon pressure ( 29 ) has been exactly evaluated , while its pt part ( 33 ) has been left undetermined at this stage , since it requires a separate investigation . our main quantitative and qualitative results in this investigation , which will not be changed ( or only slightly changed ) after the inclusion of the pt part ( 33 ) , are :    * ( i)*. in eq . ( 29 ) the confining dynamics at non - zero temperatures ( 15 ) is taken into account through the @xmath5-dependent bag constant ( 22 ) and the mass gap @xmath43 .    * ( ii)*. other np effects are also taken into account via the ym part ( 27 ) .    * ( iii)*. the mass gap @xmath43 or , equivalently , @xmath83 is the only one independent input scale parameter needed to calculate the np thermodynamic quantities .    * ( iv)*. the presence of the four different types of massive and massless gluonic excitations of the np origin .    * ( v)*. the characteristic temperature @xmath1 is a temperature at which the maximum of the np part of the gluon pressure is achieved .    * ( vi)*. the low - temperatures region up to @xmath178 is under control . the exponential fall off in the @xmath179 limit of all the main np thermodynamic quantities ( see fig . 6 ) is expected to be preserved for their full counterparts as well .    * ( vii)*. the behavior of all the thermodynamic quantities in the transition region @xmath176 depends on how deeply the pt part ( 33 ) penetrates this region .    * ( viii)*. the existence of the sb - type relations ( 43)-(44 ) at @xmath2 shows that the structure of the gm below and above @xmath2 may be really rather different .    * ( ix)*. since the np entropy and energy densities satisfy them , we expect for their full counterparts to have jump discontinuities at @xmath2 , while the full pressure remains continuous . * ( x)*. since the np heat capacity does not satisfy them , we expect for its full counterpart to have an essential discontinuity at @xmath2 , while the full speed of sound squared is to be zero at @xmath2 .    * ( xi)*. in the moderate temperatures region @xmath143 the np vacuum effects are still significant .    * ( xii)*. because of this , our qualitative prediction is that in this region the behavior of all the thermodynamic variables will be substantially different from the behavior of a gas of free massless gluons .    * ( xiii)*. all the full thermodynamic quantities , therefore , approach their sb limits rather slowly .    * ( xiv)*. a possible understanding of new forms of the gm below and above @xmath144 as strong and weak coupling gm , respectively , has to be pointed out .    * ( xv)*. the existence of the mass gap term @xmath156 in the np pressure ( 46 ) , which remains in the gluon pressure ( 29 ) as well . * ( xvi)*. because of the mass gap term @xmath156 the full trace anomaly and the gluon condensate will go down as @xmath163 at high temperatures , and not as @xmath162 .    in the subsequent paper ( part ii ) we shall evaluate the pt part ( 33 ) of the gluon pressure ( 29 ) , as well as include the free gluons contribution . it will make it possible to establish the order of the phase transition at @xmath2 . we will be able to compare our numerical results with thermal qcd lattice calculations @xcite at high temperatures above @xmath2 and in the transition region @xcite as well . only after completion of this programme , we will include the quark degrees of freedom in order to derive the np qgp eos within our formalism . for example , this will allow one to confirm a possible existence of quarkyonic matter ( qm ) @xcite and of a triple point in the qcd phase diagram ( see @xcite and references therein ) . finally , let us note that recently @xcite the pressure and the trace anomaly relation both scaled by @xmath147 have been calculated in 3d `` electrostatic qcd '' in apparent contradiction with the 4d lattice data @xcite . it is worth noting once more that our calculations are in a good agreement with them ( see table 1 and discussion above ) .","summary":"the effective potential approach for composite operators is generalized to non - zero temperatures in order to derive the equation of state for pure yang - mills fields . in the absence of external sources , the key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant .","abstract":"the effective potential approach for composite operators is generalized to non - zero temperatures in order to derive the equation of state for pure yang - mills fields . in the absence of external sources , this is nothing but the vacuum energy density . the key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant . the non - perturbative analytical equation of state for gluon matter does not depend on the coupling constant , but instead introduces a dependence on the mass gap . this is responsible for the large - scale structure of the qcd ground state . the important thermodynamic quantities , such as the pressure , energy and entropy densities , etc . , have been calculated . we show explicitly that the pressure may vary continuously around , whereas all other thermodynamic quantities undergo drastic changes at this point . the proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures , below . we reproduce the properties of the so - called `` fuzzy bag''-type models through the presence of the mass gap in our equation of state . an analytic calculation of the gluon condensate is obtained as a function of temperature ."}
{"article_id":"1204.5250","section_id":"c","document":"in this paper , motivated by the very recent measurements performed at the lhcb and the tevatron of the mass difference @xmath4 , the decay width difference @xmath12 , the cp - violating phase @xmath5 , as well as the like - sign dimuon charge asymmetry in semi - leptonic b - hadron decays , we have revisited the @xmath0 mixing in a family non - universal @xmath1 model , to check if the specific model could simultaneously explain the present measured values of these observables . our main conclusions are summarized as follows :    1 .   in both data sets d1 and d2 , the combination of measured mass difference @xmath4 and cp - violating phase @xmath5 could give a strong constraint on the flavour - changing @xmath2 couplings @xmath179 , especially in the case where both the left- and right - handed currents are present at the same time . 2 .   in the first scenario where the @xmath2 boson contributes only to the off - diagonal element @xmath3 , we find that , once constraints from @xmath4 , @xmath5 and @xmath6 are taken into account , the specific model could not reproduce the present measured value of the flavour - specific cp asymmetry @xmath7 within its @xmath8 ranges . 3 .   motivated by the failure of the first scenario , we have then considered the second scenario where the @xmath2 boson contributes both to @xmath3 and to @xmath9 . for simplicity , we have assumed that the np contribution to @xmath9 comes only from tree - level @xmath2-induced @xmath10 operators , with only the presence of left - handed flavour - changing coupling @xmath116 . 4 .   in the second scenario , due to the presence of flavour - diagonal couplings @xmath165 , we have considered the constraint from the indirect cp asymmetry in @xmath11 , in addition to the ones from @xmath4 and @xmath5 . with these constraints imposed , we find that a large correction to @xmath9 is already excluded . while the predicted value of @xmath6 is roughly compatible with the experimental data , the measured @xmath8 experimental ranges of @xmath7 still could not be reproduced in such a np model . 5 .   for completeness , we have also presented the @xmath2 effects on the mixing observables @xmath166 and @xmath167 , assuming that the np contribution comes only from the flavour - changing couplings @xmath168 . it is interesting to note that , similar to the hierarchy of the ckm matrix elements , @xmath176 , the allowed magnitudes @xmath142 and @xmath177 satisfy roughly the same hierarchy , @xmath178 . this may imply that the flavour - changing @xmath2 couplings are also linked to the known structure of the sm yukawa couplings  @xcite .    in conclusion , the specific @xmath2 model we are considering could not simultaneously explain the measured @xmath0 mixing observables , especially the like - sign dimuon charge asymmetry observed by the d0 collaboration . future improved measurements from the lhcb and the proposed superb experiments , especially of the flavour - specific cp asymmetries , are expected to shed light on the issue .","summary":"motivated by the very recent measurements performed at the lhcb and the tevatron of the mixing , in this paper we revisit it in a family non - universal model , to check if a simultaneous explanation for all the mixing observables , especially for the like - sign dimuon charge asymmetry observed by the d0 collaboration , could be made in such a specific model . in the first scenario where the boson contributes only to the off - diagonal element , it is found that , once the combined constraints from , and are imposed , the model could not explain the measured flavour - specific cp asymmetry , at least within its ranges . in the second scenario where the np contributes also to the absorptive part via tree - level-induced operators , we find that , with the constraints from , and the indirect cp asymmetry in taken into account , the present measured experimental ranges for could not be reproduced too . thus , such a specific model with our specific assumptions could not simultaneously reconcile all the present data on mixing . future improved measurements from the lhcb and the proposed superb experiments , especially of the flavour - specific cp asymmetries , are expected to shed light on the issue .","abstract":"motivated by the very recent measurements performed at the lhcb and the tevatron of the mixing , in this paper we revisit it in a family non - universal model , to check if a simultaneous explanation for all the mixing observables , especially for the like - sign dimuon charge asymmetry observed by the d0 collaboration , could be made in such a specific model . in the first scenario where the boson contributes only to the off - diagonal element , it is found that , once the combined constraints from , and are imposed , the model could not explain the measured flavour - specific cp asymmetry , at least within its ranges . in the second scenario where the np contributes also to the absorptive part via tree - level-induced operators , we find that , with the constraints from , and the indirect cp asymmetry in taken into account , the present measured experimental ranges for could not be reproduced too . thus , such a specific model with our specific assumptions could not simultaneously reconcile all the present data on mixing . future improved measurements from the lhcb and the proposed superb experiments , especially of the flavour - specific cp asymmetries , are expected to shed light on the issue ."}
{"article_id":"1412.0736","section_id":"i","document":"the motivation of this paper is to study a convergence of continuous stochastic processes on varying compact metric spaces . if state spaces are fixed , we have the weak convergence as a standard notion of convergences of stochastic processes . when state spaces are not fixed , but embedded into one common space , it is possible to consider the weak convergence . there have been many studies in such embedded situations : for example , approximations of diffusion processes on @xmath6 by discrete markov chains on @xmath7 in @xcite , @xcite and @xcite ; approximations of jump processes on proper metric spaces by markov chains on discrete graphs in @xcite and @xcite , and on ultra - metric spaces in @xcite ; diffusion processes on thin tubes shrinking to graphs in @xmath6 in @xcite and references therein ; many studies about scaling limits of random processes on random environments ( see , e.g. , @xcite and references therein ) .    in this paper , we consider a convergence of continuous stochastic processes on compact metric spaces converging _ in the lipschitz distance . _ in this setting , state spaces are not necessarily embedded initially into one common space . by the aid of the lipschitz convergence , however , we can choose a family of bi - lipschitz embeddings , which enables us to embed varying state spaces into one common space . after embedding , we can consider the weak convergence of stochastic processes on such the common space . with such ideas , we will first introduce a new distance on the set of pairs of compact metric spaces and continuous stochastic processes , and show the completeness of this distance . we will second study several topological properties induced by this new distance .    to be more precise , the main object of this paper is a pair @xmath8 where @xmath3 is a compact metric space and @xmath4 is the law of a continuous stochastic process on @xmath3 . let @xmath1 be the set of all pairs @xmath8 modulo by an isomorphism relation ( defined in section [ sec : lp ] ) . we will define ( in section [ sec : lp ] ) a new distance on @xmath1 , which we will call _ the lipschitz  prokhorov distance _ @xmath0 , as a kind of mixture of the lipschitz distance and the prokhorov distance . the lipschitz distance is a distance on the set of isometry classes of metric spaces , which was first introduced by gromov ( see e.g. , @xcite ) . we summarize our results as follows :    ( a ) : :    @xmath5 is a complete metric space    ( theorem [ thm : lpd ] and theorem [ thm : polish ] ) ; ( b ) : :    relative compactness in @xmath5 follows    from bounds for sectional curvatures , diameters and volumes of    riemannian manifolds and uniform heat kernel estimates of markov    processes ( theorem [ thm : rrc ] ) ; ( c ) : :    sequences in a relatively compact set are convergent if the    corresponding dirichlet forms of markov processes are mosco - convergent    in the sense of kuwae  shioya @xcite ( theorem [ thm : scf ] ) ; ( d ) : :    examples for    +    * brownian motions on riemannian manifolds ( section [ subsec : bm ] ) ;    * uniformly elliptic diffusions on riemannian manifolds ( section    [ subsec : ue ] ) . let us explain ( a ) . let @xmath9 be the set of continuous paths from @xmath10 $ ] to @xmath3 equipped with the uniform metric where @xmath11 is a fixed positive real number . a map @xmath12 is called _ an @xmath13-isomorphism _ if    * @xmath14 is an @xmath15-isometry ( see section [ sec : lp ] ) ; * the following inequalities hold : @xmath16 for any borel sets @xmath17 and @xmath18 and we mean that @xmath19 is defined by @xmath20 . we define @xmath0 as @xmath21    the inequalities indicate how to measure the distance between @xmath4 and @xmath22 , which live on different path spaces @xmath9 and @xmath23 : first we push - forward @xmath4 by @xmath24 , and then @xmath25 and @xmath22 live on the same path space @xmath23 . second we measure @xmath25 and @xmath22 by a kind of a modified prokhorov metric , which involves a space error @xmath26 due to an @xmath15-isometry . note that , if we replace @xmath26 to @xmath27 in , then the triangle inequality for the lipschitz  prokhorov distance @xmath0 fails . we explain ( b ) . after we have the complete metric space @xmath5 , one of the important questions is :    ( q1 ) : :    which subsets in @xmath5 are compact ? we restrict our interest to paris of riemannian manifolds and markov processes . we introduce a certain subset @xmath28 consisting of pairs @xmath29 where @xmath30 is a riemannian manifold with bounds for the sectional curvature , diameter and volume , and @xmath31 be the law of a markov process with an initial distribution @xmath32 associated with a dirichlet form whose heat kernel has a uniform bound by a given function @xmath33 ( see details in section [ sec : rc ] ) . in theorem [ thm : rrc ] , we will show that @xmath34 is relatively compact in @xmath5 . we explain ( c ) . let @xmath35 be a sequence in the relatively compact subset @xmath34 . by the relative compactness , we can take a converging subsequence from a sequence @xmath36 . then a question is :    ( q2 ) : :    when does @xmath37 converge in @xmath0    without taking subsequences ?    in theorem [ thm : scf ] , we will give a sufficient condition for such convergence in terms of the mosco - convergence of the corresponding dirichlet forms in the sense of kuwae - shioya @xcite . the mosco - convergence was first introduced by mosco @xcite ( see also @xcite ) . in @xcite , they generalized the mosco - convergence to the case of varying state spaces .    here we refer to some related topics . there have been many studies of convergences of analytical objects related to markov processes , such as eigenvalues of laplacians , heat kernels , dirichlet forms , tensor fields , differentials of lipschitz functions , on state spaces converging in the ( measured ) gromov  hausdorff sense in @xcite . in ogura @xcite , the author dealt with a convergence of stochastic processes on varying state spaces adopting rather a different approach from ours . he considered a convergence of brownian motions on riemannian manifolds under the gromov  hausdorff convergence . since approximation maps are not necessarily continuous in the case of the gromov  hausdorff convergence , the push - forward measures of the laws of continuous stochastic processes do not necessarily live on the continuous path space ( but live on the borel measurable path space ) . this constitutes a great difficulty because there is no standard notion of convergence for probability measures on the borel measurable path space . in @xcite , the author overcame this difficulty by discretizing the time parameters of processes , which makes the push - forward measures live on the space of right - continuous paths with left - hand limits . the present paper is organized as follows . in section [ sec : lp ] , we introduce the lipschitz  prokhorov distance @xmath0 and show that @xmath0 is complete . in section [ sec : rc ] , we give a sufficient condition for relative compactness and also give a sufficient condition for sequences in relatively compact sets to be convergent without taking subsequences . in section [ sec : ex ] , we give several examples . in section [ subsec : bm ] , we consider the case of brownian motion on riemannian manifolds . in section [ subsec : ue ] , we consider the case of diffusions associated with the uniformly elliptic second - order differential operators .","summary":" , on the set of isomorphism classes of pairs where is a compact metric space and is the law of a continuous stochastic process on . for markov processes on riemannian manifolds , we study relative compactness and convergence .","abstract":"we introduce a new distance , _ a lipschitz  prokhorov distance _  , on the set of isomorphism classes of pairs where is a compact metric space and is the law of a continuous stochastic process on . we show that is a complete metric space . for markov processes on riemannian manifolds , we study relative compactness and convergence ."}
{"article_id":"1504.03672","section_id":"i","document":"among possible interacting superconformal field theories ( scfts ) in diverse dimensions , the six - dimensional ( 6d ) theories are less well understood . it is expected that 6d @xmath6 scfts involve tensionless strings and show very non - trivial physics . this non - trivial nature of the 6d scfts is deeply related to the strong coupling physics of superstring theory , but its detailed features have yet to be discovered . the e - string theory is a typical 6d @xmath6 scft . originally , the e - string theory was found in the heterotic strings for the small @xmath7 instanton @xcite . there are also several other realizations of the theory . for instance , by considering m5-brane probing the end of the world m9 boundary @xcite , we can find the e - string theory on the m5 world - volume . m - theory or a topological string , on the local @xmath0k3 surface , which describes a calabi  yau 3-fold in the vicinity of the @xmath0k3 4-cycle , is dual to the e - string theory @xcite . shrinking a @xmath0k3 4-cycle in calabi  yau compactification of f - theory also leads to the e - string theory @xcite . the seiberg  witten curve , the prepotential , and the partition function of the e - string theory have been studied in @xcite . moreover , quite recently there was an attempt at classifying all 6d @xmath6 scfts @xcite . the anomaly polynomials of these 6d theories were also determined in @xcite . recently there has been significant progress on the localization computation in 5d gauge theories . in @xcite , the localization calculation was formulated for the superconformal index of 5d @xmath8 @xmath9 gauge theories with @xmath10 flavors , and it was found that this index shows the enhancement of global symmetry @xmath11 as was expected from seiberg s argument @xcite . the same index was also derived from the topological string theory in @xcite , and the enhancement was studied in more detail in @xcite from the perspective of topological strings on local calabi  yau 3-folds . in @xcite , it was found that nekrasov partition functions also show the enhancement . these developments led to exact computation on the partition function and superconformal index of a 5d theory starting directly from the ir lagrangian or from the corresponding brane web configuration / calabi  yau geometry . this technology is the main ingredient of our approach to the e - string theory . thanks to the developments in localization , quantitative study on 6d @xmath6 scfts is getting more manageable . in @xcite , based on the elliptic genus computation , the e - string partition function up to four e - strings was computed . see also @xcite .    in this paper we propose a different description of the e - string theory based on the familiar type iib 5-brane setup . in the case of 5d @xmath8 gauge theories , the world - volume theory of the corresponding @xmath12 5-brane web configuration leads to the desired gauge theory @xcite . the same web diagram specifies the toric calabi  yau 3-fold of the compactified m - theory dual to the 5-brane web , and then we calculate the 5d nekrasov partition function @xcite using the topological string method @xcite known as the topological vertex @xcite through geometric engineering @xcite . if these techniques are also applicable to the 6d e - string theory , they will be a very powerful method conceptually and computationally to investigate 6d dynamics . to this end , we utilize the key fact : the e - string theory of interest , which is a 6d @xmath6 scft , appears as the uv fixed point of _ 5d _ @xmath8 @xmath13 gauge theory with eight flavors . indeed , the agreement of the corresponding partition functions is checked in @xcite . this means that once one finds a 5-brane web for @xmath13 gauge theory with eight flavors , one can apply all the established techniques to study the e - strings . in this paper , we discuss such @xmath12 5-brane web description of the e - string theory . the @xmath12 5-brane web that we found is of a spiral shape with a cyclic structure associated with the spiral direction , which is the source of the hidden 6d direction accounting for the kaluza  klein ( kk ) direction . by implementing the topological vertex to this spiral web , we can write down a combinatorial expression of the full - order partition function , which is the generating function of the elliptic genera of the e - strings . this generating function is precisely the full partition function of topological strings on the local @xmath0k3 surface . our analysis may provide a stepping stone allowing one to look for a similar description for other 6d theories as well as a new class of 5-brane web . the paper is organized as follows . in sect . [ sec : tao 5 and 7branes ] , we review type iib @xmath12 5-brane web construction for @xmath13 gauge theory with eight flavors based on 7-brane monodromies , and find a spiral structure of the web diagram , which we call the `` tao diagram . '' in sects . [ sec : taopara ] and [ sec : e - stringviatopver ] , applying the topological vertex method to this tao diagram , we compute the partition function and compare the obtained result to the elliptic genera computed in @xcite . we discuss various tao diagrams as well as other future work in sect . [ sec : discussion ] .","summary":"we introduce a new type iib 5-brane description for the e - string theory which is the world - volume theory on the m5-brane probing the end of the world m9-brane . kias - p15010 ` + ` riken - stamp-3 ` +    * tao probing the end of the world *   +sung - soo kim ,","abstract":"we introduce a new type iib 5-brane description for the e - string theory which is the world - volume theory on the m5-brane probing the end of the world m9-brane . the e - string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions . utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the e - string elliptic genera , namely the full partition function of topological strings on the localk3 surface .    ` kias - p15010 ` + ` riken - stamp-3 ` +    * tao probing the end of the world *   +sung - soo kim ,  masato taki , and futoshi yagi + _ korea institute for advanced study ( kias ) + 85 hoegiro dongdaemun - gu , 130 - 722 , seoul , korea + _ ithes research group , riken , saitama 351 - 0198 , japan + _ _    1.0 cm"}
{"article_id":"hep-ph9905376","section_id":"i","document":"applications of perturbative qcd to deeply virtual compton scattering ( dvcs ) and hard exclusive electroproduction processes @xcite involve nonforward matrix elements @xmath14 of quark and gluon light - cone operators . they can be parametrized by two basic types of nonperturbative functions . the double distributions ( dds ) @xmath15 @xcite specify the sudakov light - cone `` plus '' fractions @xmath16 and @xmath17 of the initial hadron momentum @xmath18 and the momentum transfer @xmath19 carried by the initial parton . treating the proportionality coefficient @xmath20 as an independent parameter one can introduce an alternative description in terms of the nonforward parton distributions ( nfpds ) @xmath21 with @xmath22 being the total fraction of the initial hadron momentum taken by the initial parton . the shape of nfpds explicitly depends on the parameter @xmath20 characterizing the _ skewedness _ of the relevant nonforward matrix element . this parametrization of nonforward matrix elements by @xmath21 is similar to that proposed by x. ji @xcite who introduced off - forward parton distributions ( ofpds ) @xmath23 in which the parton momenta and the skewedness parameter @xmath24 are measured in units of the average hadron momentum @xmath25 . ofpds and nfpds @xcite can be treated as particular forms of _ skewed _ parton distributions ( spds ) . one can also introduce the version of dds ( `` @xmath8-dds '' @xcite ) in which the active parton momentum is written in terms of symmetric variables @xmath26 .    in our approach , dds are primary objects producing spds after an appropriate integration . in refs . @xcite it was shown that using the the support and symmetry properties of dds , one can easily establish important features of spds such as nonanalyticity at border points @xmath27 [ or @xmath28 , polynomiality of their @xmath29 and @xmath30 moments in skewedness parameters @xmath20 and @xmath10 , etc . the physical interpretation of dds @xmath31 [ or @xmath32 ] and their relation to the usual parton densities @xmath33 suggests that the @xmath4-profile of dds @xmath34 is driven by the shape of @xmath33 while their @xmath35 or @xmath8-profile is analogous to the shape of two - body distribution amplitudes like @xmath36^n$ ] , fixing the profile parameter @xmath37 gives simple models @xcite for dds which can be converted into models for spds . in the present paper , our main goal is to study the self - consistency of these models with respect to the pqcd evolution . in section ii , we briefly review the basic elements of the formalism of double distributions , discuss their support and symmetry properties and relation to usual parton densities . in section iii , we describe factorized profile models for double distributions and give explicit model expressions for skewed distributions . in section iv we consider a practically important case when skewedness parameters @xmath20 or @xmath10 are small . the factorized models for dds in this case can be taken in a very simple form @xmath38 , where @xmath39 is a normalized profile function . as a result , spds @xmath40 ( or @xmath41 ) in this model are obtained by averaging the relevant forward distribution @xmath42 over the interval @xmath43 [ or @xmath44 with the weight @xmath3 ( we use the convention @xcite that `` tilded '' parton distributions are those defined on the @xmath45 interval ) . in section v , we study the impact of the pqcd evolution on the profile function @xmath3 . since the @xmath8-dds are hybrids which look like usual parton densities wrt @xmath4 and like distribution amplitudes wrt @xmath8 , the simplest renormalization properties at one loop have the combined @xmath46 moments of @xmath9 . as a result , independently of the initial condition , the @xmath8-profile of the @xmath5 moment @xmath6 of the @xmath8-dd @xmath9 under the pqcd evolution asymptotically tends to @xmath7 . we investigate the `` asymptotic profile model '' in which @xmath47 are given by their asymptotic form and show that it imposes a remarkable correlation @xmath48 between the @xmath4-dependence of the @xmath8-dds and their @xmath8-profile . to study the impact of pqcd evolution on the dd based models of spds , we perform an explicit numerical evolution of spds . in section vi , we describe a simple algorithm for the leading - log evolution of spds based on direct iterative convolutions of evolution kernels @xmath49 with spds @xmath50 . in section vii , we discuss the results of our numerical calculations . in appendix a , we show that the approximation ( used in ref . @xcite ) in which the gegenbauer moments of spds do not depend on skewedness , is equivalent to the asymptotic profile model for dds . in appendix b , we present explicit form of evolution equations for spds used in our numerical calculations .","summary":"we demonstrate that , for small , the model with asymptotic profiles for is equivalent to that proposed recently by shuvaev et al . , in which the gegenbauer moments of spds do not depend on . -48pt -0.5 cm -0.5 cm    jlab - thy-99 - 12 +    * evolution and models for skewed parton distributions *    i.v . musatov and a.v . radyushkin   + _physics department , old dominion university , norfolk , va 23529 , usa _ + _jefferson lab , newport news , va 23606 , usa _","abstract":"we discuss the structure of the `` forward visible '' ( fw ) parts of double and skewed distributions related to usual distributions through reduction relations . we use factorized models for double distributions ( dds ) in which one factor coincides with the usual ( forward ) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer . the model dds are used to construct skewed parton distributions ( spds ) . for small skewedness , the fw parts of spds can be obtained by averaging forward parton densities with the weight coinciding with the profile function of the double distribution at small . we show that if the moments of dds have the asymptotic profile , then the-profile of for small is completely determined by small- behavior of the usual parton distribution . we demonstrate that , for small , the model with asymptotic profiles for is equivalent to that proposed recently by shuvaev et al . , in which the gegenbauer moments of spds do not depend on . we perform a numerical investigation of the evolution patterns of spds and gave interpretation of the results of these studies within the formalism of double distributions .    -48pt -0.5 cm -0.5 cm    jlab - thy-99 - 12 +    * evolution and models for skewed parton distributions *    i.v . musatov and a.v . radyushkin   + _physics department , old dominion university , norfolk , va 23529 , usa _ + _jefferson lab , newport news , va 23606 , usa _"}
{"article_id":"hep-ph9905376","section_id":"c","document":"in this paper , we discussed the structure of double and skewed distributions and their relation to the usual ( forward ) parton distributions . we emphasized that there are meson - exchange type terms in dds and spds which are invisible in the forward limit . theoretically , they can be modeled within approaches involving the mesons as elementary fields , e.g. , this has been done in ref.@xcite within the chiral soliton model framework . there are also terms in spds and dds which are related to usual distributions through reduction relations and which are , in this sense , visible from the forward limit . it is just these `` forward visible '' parts of dds and spds which are the subject of our studies in the present paper . we proposed factorized models for double distributions in which one factor coincides with the usual ( forward ) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer . by construction , these models satisfy reduction formulas . then we used the factorized model dds to construct skewed parton distributions and studied the skewedness dependence of spds . we established that , for small skewedness , the relevant parts of spds @xmath411 can be obtained by averaging the usual parton densities @xmath2 with the weight @xmath3 coinciding with the profile function of the double distribution @xmath0 at small @xmath4 . this result allows one to get estimates for the ratio of spds taken at the border point @xmath412 ( or @xmath160 ) and usual parton densities taken at @xmath413 . this ratio is larger than 1 in all cases which we have considered , i.e. , spds in this sense are enhanced compared to the forward densities . we found that , for small @xmath414 , the enhancement factor is directly related to the parameter @xmath75 characterizing the effective power behavior @xmath221 of the usual parton densities . we gave an explicit expression for the enhancement factor which involves @xmath75 and the parameter @xmath138 characterizing the effective power profile @xmath415 of the relevant dd . furthermore , we demonstrated that if the @xmath5 moments @xmath6 of the @xmath8-dds have the asymptotic @xmath7 profile , then the parameters @xmath75 and @xmath138 are correlated : @xmath416 , i.e. , the @xmath8-profile of @xmath9 for small @xmath4 is completely determined in this case by the small-@xmath4 behavior of the usual parton distribution . we also demonstrated that in the case of small skewedness @xmath10 , the deviation of @xmath6 from its asymptotic form leads to very small @xmath220 corrections only . this means that the `` forward visible '' parts of spds can be rather accurately deduced from the purely forward usual parton densities . the absence of higher harmonics in @xmath6 is equivalent to the absence of @xmath10-dependence in the gegenbauer moments of spds , which is the starting point of the model for spds constructed in the recent paper by shuvaev et al . for this reason , the results based on the asymptotic profile model ( apm ) developed in the present paper coincide with those of ref . @xcite , though its authors refrained from using dds in their approach . finally , we performed a numerical investigation of the evolution patterns of spds and gave interpretation of the results of these studies within the dd framework . in particular , if the initial profile of dds is too wide , the pqcd evolution makes it more narrow and the profile widens if initially it was too narrow . our numerical results also support the expectation that if one takes spd derived from the forward distribution by apm prescription and evolves it using nonforward evolution kernels , the result coincides with spd which is apm - derived from evolved forward distribution . summarizing , our results based on numerical evolution of spds are in full accord with theoretical expectations based on dd formalism . the next step in this investigation should be a direct numerical evolution of double distributions . we thank i. balitsky , a. belitsky , v. braun , c. coriano , l. frankfurt , a. freund , k. golec - biernat , l. gordon , i. grigentch , v. guzey , x. ji , g. korchemsky , a. martin , l. mankiewicz , d. mller , g. piller , m. polyakov , m. ryskin , a. schfer , a. shuvaev , m. strikman and c. weiss for stimulating discussions and correspondence . this work was supported by the us department of energy under contract de - ac05 - 84er40150 .","summary":"we discuss the structure of the `` forward visible '' ( fw ) parts of double and skewed distributions related to usual distributions through reduction relations . we use factorized models for double distributions ( dds ) in which one factor coincides with the usual ( forward ) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer . the model dds are used to construct skewed parton distributions ( spds ) . for small skewedness , the fw parts of spds can be obtained by averaging forward parton densities with the weight coinciding with the profile function of the double distribution at small . we show that if the moments of dds have the asymptotic profile , then the-profile of for small is completely determined by small- behavior of the usual parton distribution . we perform a numerical investigation of the evolution patterns of spds and gave interpretation of the results of these studies within the formalism of double distributions .   ","abstract":"we discuss the structure of the `` forward visible '' ( fw ) parts of double and skewed distributions related to usual distributions through reduction relations . we use factorized models for double distributions ( dds ) in which one factor coincides with the usual ( forward ) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer . the model dds are used to construct skewed parton distributions ( spds ) . for small skewedness , the fw parts of spds can be obtained by averaging forward parton densities with the weight coinciding with the profile function of the double distribution at small . we show that if the moments of dds have the asymptotic profile , then the-profile of for small is completely determined by small- behavior of the usual parton distribution . we demonstrate that , for small , the model with asymptotic profiles for is equivalent to that proposed recently by shuvaev et al . , in which the gegenbauer moments of spds do not depend on . we perform a numerical investigation of the evolution patterns of spds and gave interpretation of the results of these studies within the formalism of double distributions .    -48pt -0.5 cm -0.5 cm    jlab - thy-99 - 12 +    * evolution and models for skewed parton distributions *    i.v . musatov and a.v . radyushkin   + _physics department , old dominion university , norfolk , va 23529 , usa _ + _jefferson lab , newport news , va 23606 , usa _"}
{"article_id":"1702.06759","section_id":"i","document":"let @xmath6 be a bounded domain with a @xmath7-boundary @xmath8 . in this paper we study the following semilinear parametric robin problem with an indefinite and unbounded potential @xmath9 : @xmath10 \\displaystyle\\frac{\\partial u}{\\partial n}+\\beta(z)u=0\\ \\ \\mbox{on}\\ \\partial\\omega,\\ u\\geq0 . \\end{array}\\right\\ } \\hspace{2 cm } ( p_{\\lambda})\\ ] ]    in this problem @xmath11 is a parameter and @xmath12 is a potential function which is indefinite ( that is , @xmath12 is sign changing ) and unbounded from below . we can think of ( @xmath13 ) as a perturbation of the standard eigenvalue problem for the differential operator @xmath14 with robin boundary condition . we look for positive solutions and consider two cases : a sublinear perturbation @xmath15 and a superlinear perturbation @xmath15 . for both cases we determine the dependence of the set of positive solutions as the parameter @xmath11 varies . we mention that the standard eigenvalue problems for the robin laplacian have recently been studied by dagui , marano & papageorgiou @xcite and by papageorgiou & rdulescu @xcite . additional existence and multiplicity results for parametric robin and neumann problems can be found in the works of papageorgiou & rdulescu @xcite . let @xmath16 be the principal eigenvalue of the operator @xmath17 with robin boundary condition . in the _ sublinear _ case ( that is , when @xmath15 is sublinear near @xmath18 ) we show that for @xmath2 problem ( @xmath13 ) has no positive solution , whereas for @xmath0 problem ( @xmath13 ) has at least one positive solution . in fact , we show that under an additional monotonicity condition on the quotient @xmath19 on @xmath20 , this positive solution is unique . in the _ superlinear _ case ( that is , when @xmath15 is superlinear near @xmath18 ) the situation changes and uniqueness of the solution fails . in fact , we show that the equation exhibits a kind of bifurcation phenomenon . namely , for @xmath2 problem ( @xmath13 ) has no positive solution , whereas for @xmath0 it has at least two positive solutions . for both cases , we show that the problem has a minimal ( that is , smallest ) positive solution @xmath3 and we determine the monotonicity and continuity properties of the map @xmath4 . our approach is variational , based on the critical point theory , together with suitable truncation and perturbation techniques . in the next section , for the convenience of the reader , we recall the main mathematical tools which will be used in the sequel","summary":"we study perturbations of the eigenvalue problem for the negative laplacian plus an indefinite and unbounded potential and robin boundary condition . first we consider the case of a sublinear perturbation and then of a superlinear perturbation . there are no positive solutions . in the superlinear case , for we establish the existence of a minimal positive solution and we investigate the properties of the map","abstract":"we study perturbations of the eigenvalue problem for the negative laplacian plus an indefinite and unbounded potential and robin boundary condition . first we consider the case of a sublinear perturbation and then of a superlinear perturbation . for the first case we show that for ( being the principal eigenvalue ) there is one positive solution which is unique under additional conditions on the perturbation term . for there are no positive solutions . in the superlinear case , for we have at least two positive solutions and for there are no positive solutions . for both cases we establish the existence of a minimal positive solution and we investigate the properties of the map .    nikolaos s. papageorgiou    viceniu d. rdulescu    duan d. repov    ( communicated by manuel del pino )"}
{"article_id":"1702.06759","section_id":"i","document":"in this section we examine problem ( @xmath13 ) under the hypothesis that the perturbation term @xmath15 is sublinear near @xmath18 . more precisely , our conditions on the nonlinearity @xmath160 are the following : + @xmath161 :  @xmath162 is a carathodory function such that for a.a . @xmath64 , @xmath163 , @xmath164 for all @xmath165 and    1 .   for every @xmath166 , there exists @xmath167 such that @xmath168 for a.a . @xmath64 , all @xmath169 ; + 2 .   @xmath170 uniformly for a.a . @xmath64 ; + 3 . there exist @xmath171 and @xmath172 such that @xmath173 . * remarks . * since we are looking for positive solutions and all the above hypotheses concern the positive semiaxis @xmath174 , we may assume without any loss of generality that @xmath175 for a.a . @xmath64 , all @xmath176 . hypothesis @xmath161(ii ) implies that @xmath15 is sublinear near @xmath18 . hypothesis @xmath161(iii ) says that there is a concave term near the origin . * examples . * the following functions satisfy hypotheses @xmath161 . for the sake of simplicity we drop the @xmath177-dependence @xmath178 @xmath179\\\\ [ 0.3 cm ] x^{s-1}-x^{p-1 } & \\mbox{if}\\ 1<x \\end{array}\\right . \\mbox{with}\\ 1<p < s<2,\\ ; 1<q<2.\\ ] ]    we can improve the properties of the positive solutions of ( @xmath13 ) , provided we strengthen hypothesis @xmath79 . + @xmath180 :  @xmath80 with @xmath81 if @xmath57 , @xmath82 if @xmath59 and @xmath113 . we introduce the following two sets : @xmath181 @xmath182    we start with a simple but useful observation concerning the solution set @xmath183 . for this result the precise behavior of @xmath15 near @xmath18 and near @xmath184 are irrelevant . we only need nonnegativity of @xmath160 and subcritical growth in @xmath62 . under these very general conditions , the result is also applicable in the superlinear case ( see section [ sec4 ] ) . the new hypotheses on the perturbation term @xmath160 are the following :    1 . @xmath162 is a carathodory function such that for a.a . @xmath64 , @xmath163 , @xmath185 for all @xmath186 and @xmath187 with @xmath188 , @xmath189 . [ proposition 4 ] if hypotheses @xmath79 ( resp . @xmath180 ) , @xmath83 , @xmath190 hold , then for all @xmath11 , @xmath191 ( resp . @xmath192 ) ( possibly empty ) .    let @xmath193 . then we have @xmath194 ( see papageorgiou & rdulescu @xcite ) . we introduce the functions @xmath195 and @xmath196    evidently , @xmath197 ( see hypotheses @xmath79 and @xmath190 ) . also @xmath198 note that if @xmath57 ( the cases @xmath59 are straightforward ) , then @xmath199 since @xmath53 , by the sobolev embedding theorem , we have @xmath200 we rewrite as follows @xmath201 by lemma 5.1 of wang @xcite we have that @xmath202 . using the calderon - zygmund estimates ( see lemma 5.2 of wang @xcite ) , we obtain @xmath203 . then the sobolev embedding theorem implies @xmath204 with @xmath205 . therefore we have @xmath206 . suppose that @xmath180 holds . from we obtain @xmath207{6}}).\\end{aligned}\\ ] ]    thus , we have proved that when @xmath180 holds , then @xmath208 for all @xmath11 . next , we show that for every @xmath2 problem ( @xmath13 ) has no positive solutions ( that is , @xmath209 for all @xmath2 ) . [ proposition 5 ] if hypotheses @xmath180 , @xmath83 , @xmath161 hold and @xmath2 , then @xmath209 . let @xmath2 and suppose that @xmath210 . let @xmath193 . due to proposition [ 4 ] , we know that @xmath211 . let @xmath212 and consider the function @xmath213 from picone s identity ( see , for example , motreanu , motreanu & papageorgiou @xcite ) , we derive @xmath214{6}})\\vspace{0.3cm}\\\\ & { } \\hspace{0.2cm}=\\|dv\\|_{2}^{2}-\\int_{\\omega}(\\lambda-\\xi(z))u\\left(\\frac{v^2}{u}\\right)dz-\\int_{\\omega}f(z , u)\\frac{v^2}{u}\\,dz + \\int_{\\partial\\omega}\\beta(z)v^2\\,d\\sigma\\vspace{0.3cm}\\\\ & { } \\hspace{0.2cm}<\\gamma(v)-\\lambda\\|v\\|_2 ^ 2\\ \\ \\left(\\mbox{since}\\ f(z , u)\\frac{v^{2}}{u}>0\\ \\mbox{a.a.}\\ z\\in\\omega\\right).\\end{aligned}\\ ] ] let @xmath215 . then @xmath216 ( recall @xmath217 ) , a contradiction . therefore for all @xmath218 , we have @xmath209 . next , we show that for @xmath219 there exist positive solutions . [ proposition 6 ] if hypotheses @xmath180 , @xmath83 , @xmath161 hold and @xmath219 , then @xmath210 . let @xmath136 be as in and consider the carathodory function @xmath220 defined by @xmath221 we set @xmath222 and consider the @xmath70-functional @xmath223 defined by @xmath224 hypotheses @xmath161(i),(ii ) imply that given @xmath225 , we can find @xmath226 such that @xmath227 using , we obtain @xmath228 choosing @xmath229 ( recall @xmath230 ) and using lemma [ lemma 3 ] , from we obtain @xmath231    also , invoking the sobolev embedding theorem and the compactness of the trace map , we see that @xmath232 is sequentially weakly lower semicontinuous . therefore by the weierstrass theorem , we can find @xmath233 such that @xmath234.\\end{aligned}\\ ] ] let @xmath235 be so small that @xmath236 $ ] for all @xmath237 ( recall that @xmath238 and note that @xmath171 is as in hypothesis @xmath239(iii ) ) . then @xmath240 since @xmath241 , choosing @xmath235 even smaller if necessary , from we obtain @xmath242 by we have @xmath243 @xmath244 in we choose @xmath245 . then @xmath246 thus , equation becomes @xmath247    in fact , we can show that for every @xmath219 problem ( @xmath248 ) has a smallest positive solution . to this end note that given @xmath249 , because of hypotheses @xmath161(i),(iii ) , we can find @xmath250 with @xmath251 bounded on bounded subsets of @xmath252 such that @xmath253 this unilateral growth restriction on the reaction term of problem ( @xmath248 ) leads to the following auxiliary robin problem : @xmath254 \\displaystyle\\frac{\\partial u}{\\partial n}+\\beta(z)u=0\\ \\ \\mbox{on}\\ \\partial\\omega,\\ u\\geq0 . \\end{array}\\right\\ } \\hspace{2 cm } ( a u_{\\lambda})\\ ] ]    [ proposition 7 ] if hypotheses @xmath180 , @xmath83 hold and @xmath11 , then problem ( @xmath255 ) admits a unique positive solution @xmath256 . first , we establish the existence of a positive solution for problem ( @xmath257 ) . so , we introduce the @xmath258-functional @xmath259 defined by @xmath260 by lemma [ lemma 3 ] , we have @xmath261 since for @xmath57 , @xmath81 , by the sobolev embedding theorem , we have @xmath262 and so due to hlder s inequality , @xmath263 note that @xmath264 ( recall that for @xmath265 , @xmath266 $ ] and @xmath267 ) , hence @xmath268 . therefore @xmath269 thus we have @xmath270\\|u^+\\|_{\\tau}^2-c_7.\\end{aligned}\\ ] ]    we return to , use and recall that @xmath271^{1/2}$ ] is an equivalent norm on the sobolev space @xmath272 ( see , for example , gasinski & papageorgiou @xcite ) . so , from we infer that @xmath273 is coercive . the cases @xmath59 are straightforward because    * if @xmath274 , then @xmath275 ( compactly ) ; * if @xmath276 , then @xmath277 for all @xmath58 ( compactly ) .    the sobolev embedding theorem and the compactness of the trace map , imply that @xmath278 is sequentially weakly lower semicontinuous . so , we can find @xmath279 such that @xmath280.\\end{aligned}\\ ] ] as before ( see the proof of proposition [ proposition 6 ] ) , exploiting the fact that @xmath281 , we obtain @xmath282 by we have @xmath283 in we choose @xmath284 . then @xmath285    next , we infer from that @xmath286 is a positive solution of ( @xmath257 ) . again , using lemmata 5.1 and 5.2 of wang @xcite , we infer that @xmath287 . moreover , we have @xmath288u_{*}^\\lambda(z)\\ \\ \\mbox{for a.a.}\\ z\\in\\omega\\\\ \\vspace{0.3 cm } & \\hspace{5 cm } ( \\mbox{see hypothesis}\\ h(\\xi)'),\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & u_{*}^\\lambda\\in\\textrm{int}\\ , c_{+}\\ ( \\mbox{by the strong maximum principle}).\\end{aligned}\\ ] ]    next , we prove the uniqueness of this positive solution . so let @xmath289 be another positive solution for ( @xmath257 ) . as above , we show that @xmath290 . let @xmath291 be the biggest real number such that @xmath292 ( see marano & papageorgiou ( * ? ? ? * proposition 2.1 ) ) . suppose that @xmath293 . let @xmath294 and let @xmath295 be such that @xmath296 is nondecreasing on @xmath297 $ ] . we have @xmath298\\\\ \\vspace{0.3 cm } = & t\\left[c_1(v_{*}^\\lambda)^{q-1}-c_{4}(\\lambda)(v_{*}^\\lambda)^{\\tau-1}+\\hat\\xi_{\\rho}v_{*}^\\lambda\\right]\\\\ \\vspace{0.3 cm } < & c_1(t v_{*}^\\lambda)^{q-1}-c_4(\\lambda)(t v_{*}^\\lambda)^{\\tau-1}+\\hat\\xi_\\rho(t v_{*}^\\lambda)\\\\ \\vspace{0.3 cm } & { } \\hspace{2cm}(\\mbox{since}\\ t\\in(0,1)\\ \\mbox{and}\\ q<2<\\tau)\\\\ \\vspace{0.3 cm } \\leq & c_1(u_{*}^\\lambda)^{q-1}-c_{4}(u_{*}^\\lambda)^{\\tau-1}+\\hat\\xi_\\rho u_{*}^\\lambda\\\\ \\vspace{0.3 cm } & { } \\hspace{2cm}(\\mbox{since}\\ t v_{*}^\\lambda\\leq u_{*}^\\lambda)\\\\ \\vspace{0.3 cm } = & -\\delta u_{*}^\\lambda+(\\xi(z)+\\hat{\\xi}_{\\rho})u_{*}^\\lambda,\\end{aligned}\\ ] ] @xmath299 however , this contradicts the maximality of @xmath235 . hence @xmath300 and so we have @xmath301 .    if in the above argument we reverse the roles of @xmath302 and @xmath303 , we obtain @xmath304 and this proves the uniqueness of the positive solution of problem ( @xmath257 ) .    * remark . * we can have an alternative proof of the uniqueness based on the picone identity . the argument goes as follows . suppose again that @xmath305 is another positive solution of ( @xmath257 ) . we have @xmath306 . therefore @xmath307{6}})\\nonumber\\]]@xmath308 interchanging the roles of @xmath286 and @xmath309 in the above argument , we obtain @xmath310 we add and and use picone s identity . we obtain @xmath311dz\\nonumber \\\\ \\vspace{0.3 cm } & = \\int_\\omega\\left[c_1\\left(\\frac{1}{(u_{*}^\\lambda)^{2-q}}-\\frac{1}{(v_{*}^\\lambda)^{2-q}}\\right ) -c_4(\\lambda)\\left((u_{*}^\\lambda)^{\\tau-2}-(v_{*}^\\lambda)^{\\tau-2}\\right)\\right]\\left((u_{*}^\\lambda)^{2}-(v_{*}^\\lambda)^{2}\\right)dz.\\end{aligned}\\ ] ] since the function @xmath312 is strictly decreasing on @xmath20 ( recall @xmath281 ) , it follows from that @xmath313 so , we again get the uniqueness of the positive solution of @xmath314 .    note also that since @xmath251 is bounded on bounded sets of @xmath252 , if @xmath315 is bounded and @xmath316 for all @xmath317 , then the unique solution @xmath318 of @xmath319 \\displaystyle\\frac{\\partial u}{\\partial n}+\\beta(z)u=0\\ \\ \\mbox{on}\\ \\partial\\omega , \\end{array}\\right\\}\\ ] ] satisfies @xmath320 for all @xmath321 .    using proposition [ proposition 7 ] , we can produce a lower bound for the solution set @xmath183 . [ proposition 8 ] if hypotheses @xmath180 , @xmath83 , @xmath239 hold and @xmath322 , then @xmath323 for all @xmath193 . let @xmath193 and consider the following carathodory function @xmath324 c_1 x^{q-1}-c_4(\\lambda)x^{\\tau-1}+\\mu x & \\mbox{if}\\ 0\\leq x\\leq u(z)\\\\ [ 0.3 cm ] c_1u(z)^{q-1}-c_4(\\lambda)u(z)^{\\tau-1}+\\mu u(z ) & \\mbox{if}\\ u(z)<x . \\end{array}\\right.\\end{aligned}\\ ] ] here @xmath136 is as in . we set @xmath325 and consider the @xmath258-functional @xmath326 defined by @xmath327    invoking and , we see that @xmath328 is coercive . it is also sequentially weakly lower semicontinuous . therefore we can find @xmath329 such that @xmath330.\\end{aligned}\\ ] ]    as before ( see the proof of proposition [ proposition 6 ] ) , exploiting the fact that @xmath281 , we can show that @xmath331 by we have @xmath332 in we choose @xmath333 and obtain @xmath334 next , in we choose @xmath335 . then @xmath336 @xmath337 therefore we have proved that @xmath338=\\{v\\in h^1(\\omega):\\ , 0\\leq v(z)\\leq u(z)\\ , \\mbox{for a.a}\\ z\\in \\omega\\},\\ ; \\tilde u_{*}^\\lambda\\neq0.\\end{aligned}\\ ] ] by and , we see that equation becomes @xmath339dz \\\\ \\vspace{0.3 cm } & \\hspace{8 cm } \\mbox{for all}\\ h\\in h^1(\\omega ) , \\\\ \\vspace{0.3 cm } & \\rightarrow\\ , \\tilde u_{*}^\\lambda\\ \\mbox{is a positive solution of}\\ ( au_\\lambda ) , \\\\ \\vspace{0.3 cm } & \\rightarrow\\ , \\tilde u_{*}^\\lambda = u_{*}^\\lambda\\in\\textrm{int}\\ , c_{+}\\ ( \\mbox{see proposition \\ref{proposition 7}}).\\end{aligned}\\ ] ] therefore @xmath340 for all @xmath193 . this lower bound leads to the existence of a smallest positive solution for problem ( @xmath248 ) , @xmath341 .    [ proposition 9 ] if hypotheses @xmath180 , @xmath83 , @xmath161 hold and @xmath322 , then problem @xmath342 admits a smallest positive solution @xmath343 .    as in filippakis & papageorgiou @xcite , we can show that @xmath183 is downward directed , that is , if @xmath344 , then we can find @xmath193 such that @xmath345 , @xmath346 . for completeness we sketch a proof . so , given @xmath225 consider the function @xmath347\\\\ \\varepsilon\\quad&\\mbox{if}\\ s>\\varepsilon\\ , . \\end{array}\\right.\\ ] ] evidently , @xmath348 is lipschitz and so @xmath349 . moreover , the chain rule for sobolev functions implies that @xmath350 let @xmath351 . then we introduce the test functions @xmath352 which belong to @xmath353 . we have @xmath354 @xmath355 we add these two equalities and divide by @xmath225 . taking into account that @xmath356 and @xmath357 we obtain @xmath358    so , if @xmath359 , then @xmath360 is an upper solution of ( @xmath248 ) and so by standard truncation techniques we can find @xmath193 such that @xmath361 . then lemma 3.10 of hu & papageorgiou @xcite , implies that there exist @xmath362 , @xmath132 , @xmath363 decreasing such that @xmath364 for every @xmath132 , we have @xmath365h\\,dz \\\\ \\vspace{0.3 cm } & \\hspace{8cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega).\\nonumber\\end{aligned}\\ ] ] evidently , @xmath366 is bounded and so we may assume that @xmath367 in we pass to the limit as @xmath30 and use . then @xmath368h\\ , dz \\\\ \\vspace{0.3 cm } & \\hspace{8cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega ) , \\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\bar u_\\lambda\\ \\mbox{is a solution of}\\ ( p_\\lambda).\\end{aligned}\\ ] ] due to proposition [ proposition 8 ] we know that @xmath369    we examine the monotonicity and continuity properties of the map @xmath370 from @xmath371 into @xmath372 . [ proposition 10 ] if hypotheses @xmath180 , @xmath83 , @xmath239 hold , then the map @xmath373 is nondecreasing and left continuous from @xmath374 into @xmath372 .    first , we establish the monotonicity of the map @xmath375 . so let @xmath376 and consider @xmath377 the minimal positive solution of problem ( @xmath378 ) . we introduce the following carathodory function @xmath379 ( \\lambda+\\mu)x+f(z , x ) & \\mbox{if}\\ 0\\leq x\\leq u_\\eta(z)\\\\ [ 0.3 cm ] ( \\lambda+\\mu)u_\\eta(z)+f(z , u_\\eta(z ) ) & \\mbox{if}\\ u_\\eta(z)<x . \\end{array}\\right.\\end{aligned}\\ ] ] as always , @xmath136 is as in . we set @xmath380 and consider the @xmath258-functional @xmath381 defined by @xmath382    it follows from and that @xmath383 is coercive . it is also sequentially weakly lower semicontinuous . so , we can find @xmath384 such that @xmath385<0=w_\\lambda(0)\\\\ \\vspace{0.3 cm } & \\hspace{4cm}(\\mbox{as before since}\\ q<2).\\nonumber\\end{aligned}\\ ] ] by we have @xmath386 and @xmath387 as in the proof of proposition [ proposition 8 ] , choosing in , first @xmath388 and then @xmath389 , we can show that @xmath390=\\left\\{v\\in h^1(\\omega):\\ , 0\\leq v(z)\\leq\\bar u_\\eta(z)\\ \\mbox{for a.a.}\\ z\\in\\omega\\right\\},\\ \\tilde u_\\lambda\\neq0.\\end{aligned}\\ ] ] then we can infer from , , that @xmath391    next , we establish the left continuity of this map . to this end , let @xmath392 with @xmath341 . evidently , @xmath393 is bounded and increasing . therefore we may assume that @xmath394 we have @xmath395h\\ , dz \\\\ \\vspace{0.3 cm } & \\hspace{8cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega),\\ \\mbox{all}\\ n\\in{\\mathbb n}.\\nonumber\\end{aligned}\\ ] ] in we pass to the limit as @xmath30 and use . we obtain @xmath396h\\ , dz \\\\ \\vspace{0.3 cm } & \\hspace{9cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega).\\nonumber\\end{aligned}\\ ] ]    set @xmath397 and let @xmath316 for all @xmath317 ( recall that @xmath398 is bounded on bounded sets of @xmath252 ) . let @xmath399 be the unique positive solution of the following semilinear robin problem @xmath400 \\displaystyle\\frac{\\partial u}{\\partial n}+\\beta(z)u=0\\ \\ \\mbox{on}\\ \\partial\\omega . \\end{array}\\right\\}\\\\ & \\hspace{6cm}(\\mbox{see proposition \\ref{proposition 7}}).\\end{aligned}\\ ] ] we know that @xmath401 ( see the remark following proposition [ proposition 7 ] ) . hence @xmath402 we claim that @xmath403 . if this is not true , then we can find @xmath404 such that @xmath405 from wang @xcite , we know that we can find @xmath406 and @xmath94 such that @xmath407 exploiting the compact embedding of @xmath408 into @xmath372 and using , we obtain @xmath409 a contradiction to the monotonicity of @xmath370 ( recall that @xmath410 for all @xmath132 ) . so @xmath411 and this proves the left continuity of @xmath373 from @xmath371 into @xmath372 ( see ) . we can improve the monotonicity of the map @xmath370 provided that we strengthen the conditions on @xmath15 .    1 . @xmath162 is a carathodory function such that @xmath163 for a.a . @xmath64 , hypotheses @xmath412(i ) , ( ii ) , ( iii ) are the same as hypotheses @xmath239(i ) , ( ii ) , ( iii ) and 1 .   for every @xmath166 , there exists @xmath413 such that for a.a . @xmath64 , the function @xmath414 is nondecreasing on @xmath297 $ ] .    * remark . * the new condition on @xmath15 is satisfied , if for a.a . @xmath64 , @xmath15 is differentiable and @xmath415 is locally @xmath416-bounded ( just use the mean value theorem ) . * examples . * the following functions satisfy hypotheses @xmath412 . as before , for the sake of simplicity , we drop the @xmath177-dependence @xmath417 @xmath418\\\\ [ 0.3 cm ] 2x^{\\tau-1}-x^{s-1 } & \\mbox{if}\\ 1<x \\end{array}\\right . \\mbox{with}\\ 1<q,\\tau , s<2,\\ ; s<\\tau,\\ ] ] @xmath419\\\\ [ 0.3 cm ] x^{\\tau-1}\\ln x & \\mbox{if}\\ 1<x \\end{array}\\right . \\mbox{with}\\ 1<q , s,\\tau<2,\\ ; q < s,\\ ] ] @xmath420\\\\ [ 0.3 cm ] x^{\\tau-1}-x^{s-1}+c & \\mbox{if}\\ 1<x \\end{array}\\right . \\mbox{with}\\ 1<q,\\tau , s<2,\\ ; s<\\tau,\\ ; c=\\ln2.\\ ] ]    [ proposition 11 ] if hypotheses @xmath180 , @xmath83 , @xmath412 hold , then the map @xmath370 from @xmath371 into @xmath372 is strictly increasing ( that is , if @xmath421 , then @xmath422 ) . let @xmath421 and let @xmath423 , @xmath377 be the corresponding minimal positive solutions of problems ( @xmath248 ) and ( @xmath424 ) , respectively . by proposition [ proposition 10 ] we know that @xmath425 let @xmath426 and let @xmath413 be as postulated by hypothesis @xmath412(iv ) . we have @xmath427{6}}).\\end{aligned}\\ ] ] this proves the strict monotonicity of @xmath370 . in fact , under a monotonicity restriction on the quotient @xmath428 , we can conclude that for all @xmath341 problem ( @xmath248 ) admits a unique positive solution .    hence the new conditions on the perturbation @xmath160 are the following :    1 . @xmath162 is a carathodory function such that @xmath163 for a.a . @xmath64 , hypotheses @xmath429(i ) , ( ii ) , ( iii ) are the same as hypotheses @xmath239(i ) , ( ii ) , ( iii ) and 1 .   for a.a . @xmath64 , @xmath19 is strictly decreasing on @xmath20 .    * examples . * the following functions satisfy the new conditions . again , for the sake of simplicity we drop the @xmath177-dependence : @xmath417 @xmath418\\\\ [ 0.3 cm ] x^{\\tau-1 } & \\mbox{if}\\ 1<x \\end{array}\\right . \\mbox{with}\\ 1<q,\\ , \\tau < q.\\ ] ]    [ proposition 12 ] if hypotheses @xmath180 , @xmath83 , @xmath429 hold and @xmath341 , then @xmath183 is a singleton , that is , @xmath430 and @xmath370 is nondecreasing and continuous from @xmath431 into @xmath44 . the nonemptiness of @xmath183 follows from proposition [ proposition 6 ] . suppose that @xmath432 . we have @xmath433 @xmath434 we multiply with @xmath435 and with @xmath436 , then integrate both equations over @xmath437 and use green s identity . we obtain @xmath438 @xmath439 we subtract from and obtain @xmath440dz=0,\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\int_{\\omega}\\left[\\frac{f(z,\\bar u_\\lambda)}{\\bar u_\\lambda}-\\frac{f(z,\\bar v_\\lambda)}{\\bar v_\\lambda}\\right]\\bar u_\\lambda\\bar v_\\lambda dz=0\\ ( \\mbox{recall}\\ \\bar u_\\lambda,\\bar v_\\lambda\\in\\textrm{int}\\ , c_{+})\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\bar u_\\lambda=\\bar v_\\lambda\\ ( \\mbox{see hypothesis}\\ h_3\\mbox{(iv)}).\\end{aligned}\\ ] ] this proves the uniqueness of the positive solution of problem ( @xmath248 ) . the uniqueness of this positive solution , together with proposition [ proposition 10 ] , imply that the map @xmath370 from @xmath371 into @xmath372 is nondecreasing and continuous .    as before , by strengthening the conditions on the perturbation @xmath15 we can improve the monotonicity of the map @xmath375 . the new condition on @xmath160 are the following :    1 .   @xmath162 is a carathodory function such that @xmath163 for a.a . @xmath64 , hypotheses @xmath441(i ) , ( ii ) , ( iii ) , ( iv ) are the same as the corresponding hypotheses @xmath429(i ) , ( ii ) , ( iii ) , ( iv ) and 1 .   for every @xmath166 , there exists @xmath413 such that for a.a . @xmath64 the function @xmath442 is nondecreasing on @xmath297 $ ] . * the examples after hypotheses @xmath429 , also satisfy hypotheses @xmath441 . then propositions [ proposition 11 ] and [ proposition 12 ] imply the following result .    [ proposition 13 ] if hypotheses @xmath180 , @xmath83 , @xmath441 hold and @xmath341 , then the set @xmath183 is a singleton @xmath443 and the map @xmath444 from @xmath445 into @xmath372 is strictly increasing ( that is , if @xmath421 , then @xmath422 ) . summarizing the situation for problem ( @xmath248 ) when the perturbation term @xmath15 is sublinear , we can state the following theorem .    [ theorem 14 ]    1 . if hypotheses @xmath180 , @xmath83 , @xmath239 hold , then for every @xmath218 we have @xmath209 , while for every @xmath219 , @xmath210 , @xmath446 , problem ( @xmath248 ) admits a smallest positive solution @xmath447 and the map @xmath370 from @xmath371 into @xmath372 is nondecreasing ( that is , @xmath448 implies @xmath449 ) and left continuous . 2 .   if hypotheses @xmath180 , @xmath83 , @xmath412 hold , then the map @xmath370 from @xmath371 into @xmath372 is strictly increasing ( that is , @xmath421 implies @xmath450 ) . if hypotheses @xmath180 , @xmath83 , @xmath429 hold and @xmath341 , then @xmath183 is a singleton @xmath443 ( @xmath447 ) and the map @xmath370 from @xmath371 into @xmath372 is nondecreasing and continuous . if hypotheses @xmath180 , @xmath83 , @xmath441 hold , then the map @xmath370 is strictly increasing from @xmath371 into @xmath372 .","summary":"for the first case we show that for ( being the principal eigenvalue ) there is one positive solution which is unique under additional conditions on the perturbation term . for .    nikolaos s. papageorgiou    viceniu d. rdulescu    duan d. repov    ( communicated by manuel del pino )","abstract":"we study perturbations of the eigenvalue problem for the negative laplacian plus an indefinite and unbounded potential and robin boundary condition . first we consider the case of a sublinear perturbation and then of a superlinear perturbation . for the first case we show that for ( being the principal eigenvalue ) there is one positive solution which is unique under additional conditions on the perturbation term . for there are no positive solutions . in the superlinear case , for we have at least two positive solutions and for there are no positive solutions . for both cases we establish the existence of a minimal positive solution and we investigate the properties of the map .    nikolaos s. papageorgiou    viceniu d. rdulescu    duan d. repov    ( communicated by manuel del pino )"}
{"article_id":"1702.06759","section_id":"i","document":"in this section , we investigate the case of a superlinear perturbation @xmath15 . now we can not have uniqueness of the positive solution and in fact we show that the problem exhibits a kind of bifurcation phenomenon , that is , for @xmath219 , problem ( @xmath248 ) has at least two positive solutions , while for @xmath218 , @xmath209 . we stress that for the superlinearity of @xmath15 we do not use the ambrosetti - rabinowitz condition ( ar - condition for short ) . the hypotheses on the perturbation @xmath160 are the following :    1 .   @xmath162 is a carathodory function such that for a.a . @xmath64 , @xmath163 , @xmath185 for all @xmath186 , @xmath164 for a.a . @xmath451 with @xmath452 , all @xmath165 and 1 . @xmath453 for a.a . @xmath64 , all @xmath186 , with @xmath188 and @xmath454 ; 2 .   if @xmath455 , then @xmath456 and there exists @xmath457 such that @xmath458 3 . @xmath459 uniformly for a.a . @xmath64 . * remarks . * as in the _ sublinear _ case , since we are looking for positive solutions and the above hypotheses concern the positive semiaxis @xmath460 , we may assume without any loss of generality that @xmath175 for a.a . @xmath64 , all @xmath176 . hypothesis @xmath461(ii ) implies that for a.a . @xmath64 , @xmath15 is superlinear near @xmath18 . however , we do not assume the usual for superlinear problems ar - condition . recall that the ar - condition ( unilateral version since it is imposed only on the positive semiaxis ) , says that there exist @xmath462 and @xmath463 such that @xmath464 @xmath465 ( see ambrosetti & rabinowitz @xcite and mugnai @xcite ) . integrating and using , we obtain @xmath466 from and it follows that for a.a . @xmath64 , @xmath15 has at least @xmath467-polynomial growth near @xmath18 . our hypothesis is implied by the ar - condition . we may assume that @xmath468 . we have @xmath469 thus , hypothesis @xmath470(ii ) is satisfied ( recall that @xmath462 ) . this more general superlinearity condition , incorporates in our framework superlinear nonlinearities with _ slower _ growth near @xmath18 , which fail to satisfy the ar - condition ( unilateral version ) . * examples . * the following functions satisfy hypotheses @xmath470 . as in the previous examples , for the sake of simplicity we drop the @xmath177-dependence . @xmath471 @xmath472 note that @xmath473 satisfies the unilateral ar - condition , but @xmath474 does not . using proposition [ proposition 4 ] and reasoning exactly as in the proof of proposition [ proposition 5 ] , we obtain the following result .    [ proposition 15 ] if hypotheses @xmath180 , @xmath83 , @xmath461 hold and @xmath475 , then @xmath209 .    so according to this proposition , we have @xmath476 . in fact we will show that equality holds . [ proposition 16 ] if hypotheses @xmath180 , @xmath83 , @xmath461 hold , then @xmath371 . we fix @xmath477 and consider the carathodory function @xmath478 \\lambda x+f(z , x ) & \\mbox{if}\\ 0<x . \\end{array}\\right.\\end{aligned}\\ ] ] we set @xmath479 and consider the @xmath258-functional @xmath480 defined by @xmath481 here , @xmath136 is as in . hypotheses @xmath470(i ) , ( iii ) imply that given @xmath225 , we can find @xmath482 such that @xmath483 choosing @xmath484 ( recall @xmath219 ) , for all @xmath485 we obtain @xmath486 since @xmath487 , from we infer that @xmath129 is a strict local minimizer of @xmath232 . it is easy to see that @xmath488 ( see ) . thus , we may assume that @xmath129 is an isolated critical point of @xmath232 or otherwise we already have a whole sequence of distinct positive solutions of ( @xmath248 ) which converge to zero in @xmath272 . therefore we can find @xmath489 small such that @xmath490=m_\\rho^\\lambda\\\\ & ( \\mbox{see aizicovici , papageorgiou \\ & staicu \\cite{1 } , proof of proposition 29}).\\nonumber\\end{aligned}\\ ] ] hypothesis @xmath470(ii ) implies that given any @xmath211 , we have @xmath491 * claim . * _ @xmath232 satisfies the c - condition . _    let @xmath366 such that @xmath492 by we have @xmath493 in we choose @xmath494 . using , we obtain @xmath495 it follows from and that @xmath496dz\\leq m_4\\\\ \\vspace{0.3 cm } & \\hspace{3 cm } \\mbox{for some}\\ m_4>0,\\ \\mbox{all}\\ n\\in{\\mathbb n}. \\nonumber\\end{aligned}\\ ] ] on the other hand , if in we choose @xmath497 , then @xmath498dz\\leq\\varepsilon_n\\ \\mbox{for all}\\ n\\in{\\mathbb n}\\\\ \\vspace{0.3 cm } & \\hspace{7 cm } ( \\mbox{see \\eqref{46}}).\\nonumber\\end{aligned}\\ ] ] adding and , we obtain @xmath499dz\\leq m_5\\ \\mbox{for some}\\ m_5>0,\\ \\mbox{all}\\ n\\in{\\mathbb n}.\\end{aligned}\\ ] ] hypotheses @xmath470(i ) , ( ii ) imply that we can find @xmath500 and @xmath501 such that @xmath502    we use in and infer that @xmath503 first , suppose that @xmath504 . by hypothesis @xmath470(ii ) , we see that we may assume without loss of generality that @xmath505 . so , we can find @xmath235 such that @xmath506 invoking the interpolation inequality ( see , for example , gasinski & papageorgiou @xcite ) , we have @xmath507 in we choose @xmath497 . then @xmath508dz\\ \\mbox{for all}\\ n\\in{\\mathbb n}\\ ( \\mbox{see \\eqref{46}}),\\nonumber \\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\gamma(u_n^+)\\leq c_{13}(1+\\|u_n^+\\|_r^r)\\ \\mbox{for some}\\ c_{13}>0,\\ \\mbox{all}\\ n\\in{\\mathbb n}\\nonumber \\\\ \\vspace{0.3 cm } & \\hspace{2cm}(\\mbox{see hypothesis}\\ h_5\\mbox{(i ) and recall that}\\ 2<r ) \\nonumber \\\\ \\vspace{0.3 cm } & \\hspace{1cm}\\leq c_{14}(1+\\|u_n^+\\|^{tr})\\ \\mbox{for some}\\ c_{14}>0 , \\mbox{all}\\ n\\in{\\mathbb n}\\\\ \\vspace{0.3 cm } & \\hspace{2cm}(\\mbox{see \\eqref{61}}).\\nonumber\\end{aligned}\\ ] ] by hypothesis @xmath470(i ) , we see that we can always assume that @xmath509 is close to @xmath510 , hence @xmath511 ( see hypothesis @xmath470(ii ) ) . then implies that @xmath512 is bounded and so by we have @xmath513 due to and hypothesis @xmath470(ii ) , we see that @xmath514 if @xmath276 , then @xmath515 and the sobolev embedding theorem says that @xmath516 for all @xmath517 . let @xmath518 and @xmath235 such that @xmath519 note that @xmath520 therefore the previous argument works if instead of @xmath510 we use @xmath521 big such that @xmath522 . we again obtain . it follows from and that @xmath523 thus , we may assume that @xmath524 in we choose @xmath525 , pass to the limit as @xmath30 and use . then @xmath526@xmath527 therefore @xmath232 satisfies the c - condition and this proves the claim . then , and the claim , permit the use of theorem [ theorem 1 ] ( the mountain pass theorem ) and so we can find @xmath528 such that @xmath529    next , we show that for every @xmath477 , problem ( @xmath248 ) has a smallest positive solution . first , let us recall the following lemma from hu and papageorgiou @xcite . * lemma a. * _ if @xmath530 is a finite measure space and @xmath531 is a family of @xmath532-valued measurable functions which is downward directed , then there exists a unique ( modulo equality @xmath533-a.e . ) function @xmath534 such that + ( a ) @xmath535 @xmath533-a.e . in @xmath437 for all @xmath536 ; + ( b ) if @xmath537 is a measurable function such that @xmath538 then @xmath539 @xmath533-a.e . , that is , @xmath540 . moreover , there is a decreasing sequence @xmath541 such that @xmath542 . _    [ proposition 17 ] if hypotheses @xmath180 , @xmath83 , @xmath470 hold and @xmath341 , then problem ( @xmath248 ) admits a smallest positive solution @xmath543 . we again have that @xmath183 is downward directed ( that is , if @xmath344 , then we can find @xmath193 such that @xmath345 , @xmath346 ; see filippakis & papageorgiou @xcite ) . therefore lemma a above implies that we can find a decreasing sequence @xmath544 such that @xmath364 we have @xmath545hdz\\\\ \\vspace{0.3 cm } & \\hspace{7cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega),\\ \\mbox{all}\\ n\\in{\\mathbb n}.\\nonumber\\end{aligned}\\ ] ] choosing @xmath546  , we obtain @xmath547 since @xmath548 for all @xmath132 ( recall that @xmath366 is decreasing ) and by , and hypotheses @xmath549 , @xmath83 , @xmath470(i ) , we can conclude that @xmath523 hence , we may assume that @xmath550    returning to , passing to the limit as @xmath30 and using , we obtain @xmath551h\\ , dz\\\\ \\vspace{0.3 cm } & \\hspace{8cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega),\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\bar u_\\lambda\\geq0\\ \\mbox{is a solution of}\\ ( p_\\lambda).\\end{aligned}\\ ] ]    we will show that @xmath552 . arguing by contradiction , suppose that @xmath553 . let @xmath554 , @xmath132 . then @xmath141 , @xmath555 for all @xmath132 . so we may assume that @xmath556 by we have @xmath557h\\ , dz\\\\ \\vspace{0.3 cm } & \\hspace{8cm}\\ \\mbox{for all}\\ h\\in h^1(\\omega),\\ \\mbox{all}\\ n\\in{\\mathbb n}.\\nonumber\\end{aligned}\\ ] ] let @xmath558 . hypotheses @xmath470(i ) , ( iii ) imply that @xmath559,\\ \\mbox{some}\\ c_{16}>0,\\nonumber\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\frac{f(z , u_n(z))}{\\|u_n\\|}\\leq c_{18}\\ , y_n(z)\\ \\mbox{for a.a.}\\ z\\in\\omega,\\ \\mbox{all}\\ n\\in{\\mathbb n},\\nonumber\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & \\left\\{\\frac{n_f(u_n)}{\\|u_n\\|}\\right\\}_{n\\geq1}\\subseteq l^2(\\omega)\\ \\mbox{is bounded ( see \\eqref{69})}.\\end{aligned}\\ ] ] by passing to a subsequence if necessary and using hypothesis @xmath470(iii ) we infer that @xmath560 ( see aizicovici , papageorgiou & staicu @xcite , proof of proposition 14 ) . in , we first choose @xmath561 , pass to the limit as @xmath30 and use and . then @xmath562    next in we choose @xmath563 and pass to the limit as @xmath30 . using and we obtain @xmath564 a contradiction to . hence , @xmath552 and therefore @xmath565    reasoning as in the proof of proposition [ proposition 10 ] , we can establish the monotonicity and continuity properties of the map @xmath370 . [ proposition 18 ] if hypotheses @xmath180 , @xmath83 , @xmath470 hold , then the map @xmath370 from @xmath371 into @xmath372 is nondecreasing and continuous .    as before ( see proposition [ proposition 11 ] and hypotheses @xmath412 ) , by strengthening the conditions on @xmath15 , we can improve the monotonicity of @xmath370 . the new conditions on @xmath160 are the following :    1 .   @xmath162 is a carathodory function such that @xmath163 for a.a . @xmath64 , hypotheses @xmath566(i ) , ( ii ) , ( iii ) are the same as the corresponding hypotheses @xmath470(i ) , ( ii ) , ( iii ) and 1 .   for every @xmath166 , there exists @xmath413 such that for a.a . @xmath64 , the function @xmath414 is nondecreasing on @xmath297 $ ] . reasoning as in the proof of proposition [ proposition 9 ] , we obtain . [ proposition 19 ] if hypotheses @xmath180 , @xmath83 , @xmath566 hold , then the map @xmath370 from @xmath371 into @xmath372 is strictly increasing ( that is , if @xmath421 , then @xmath422 ) .    next , we show that for all admissible @xmath341 , problem ( @xmath248 ) has at least two positive solutions , which are ordered . [ proposition 20 ] if hypotheses @xmath180 , @xmath83 , @xmath566 hold and @xmath341 , then problem ( @xmath248 ) admits at least two positive solutions @xmath567    by proposition [ proposition 16 ] we already have one positive solution @xmath568 . we may assume that @xmath569 is the minimal positive solution ( that is , @xmath570 , see proposition [ proposition 17 ] ) . we consider the following carathodory function @xmath571 ( \\lambda+\\mu)x+f(z , x ) & \\mbox{if}\\ u_\\lambda(z)<x . \\end{array}\\right.\\end{aligned}\\ ] ] we set @xmath572 and consider the @xmath258-functional @xmath573 defined by @xmath574 from , we see that on @xmath575 we have @xmath576    * claim . * _ we may assume that @xmath568 is a local minimizer of the functional @xmath577 . _    let @xmath421 and let @xmath578 . from proposition [ proposition 19 ] , we obtain @xmath579 . we introduce the following truncation of @xmath580 : @xmath581 \\widetilde g_{\\lambda}(z , u_\\eta(z ) ) & \\mbox{if}\\ u_\\eta(z)<x . \\end{array}\\right.\\end{aligned}\\ ] ] evidently , this is a carathodory function . we set @xmath582 and consider the @xmath258-functional @xmath583 defined by @xmath584 as before ( see the proof of proposition [ proposition 10 ] ) , we can show that @xmath585=\\left\\{u\\in h^1(\\omega):\\ , u_\\lambda(z)\\leq u(z)\\leq u_\\eta(z)\\ \\mbox{for a.a.}\\ z\\in\\omega\\right\\}.\\end{aligned}\\ ] ] moreover , by and , we see that @xmath586 is coercive . it is also sequentially weakly lower semicontinuous . so we can find @xmath587 such that @xmath588,\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & u_\\lambda^{*}\\in k_{\\psi_\\lambda^{*}}\\subseteq[u_\\lambda , u_\\eta]\\ ( \\mbox{see \\eqref{78}}),\\\\ \\vspace{0.3 cm } \\rightarrow\\ , & u_\\lambda^{*}\\in s(\\lambda)\\subseteq\\textrm{int}\\ , c_{+}\\ ( \\mbox{see \\eqref{77}}).\\end{aligned}\\ ] ]    if @xmath589 , then this is the second positive solution of problem ( @xmath248 ) and , as we will see in the last part of the proof , we have @xmath590 , so we are done . so , suppose @xmath591 . we have @xmath592}=\\widetilde\\psi_\\lambda|_{[0,u_\\eta]}\\ ( \\mbox{see \\eqref{75 } and \\eqref{77}}).\\ ] ] since @xmath593 and @xmath579 ( see proposition [ proposition 19 ] ) , it follows that @xmath594 this proves the claim . we assume that @xmath595 is finite or otherwise we already have a sequence of distinct positive solutions , all strictly bigger than @xmath569 ( note that @xmath596 for a.a . @xmath597 ) and so we are done . using the claim , we can find @xmath489 small such that @xmath598=\\widetilde m_\\rho^{\\lambda}.\\end{aligned}\\ ] ] hypothesis @xmath566(ii ) implies that @xmath599 then , , permit the use of theorem [ theorem 1 ] ( the mountain pass theorem ) . therefore we can find @xmath600 such that @xmath601 moreover , if @xmath602 and @xmath413 is as postulated by hypothesis @xmath566(iv ) , then @xmath603@xmath604    summarizing the situation for problem ( @xmath248 ) when the perturbation @xmath15 is superlinear , we can state the following theorem .    [ theorem 21 ] if hypotheses @xmath180 , @xmath83 , @xmath605 hold , then    1 .   for all @xmath218 problem ( @xmath248 ) has no positive solution ( that is , @xmath209 ) ; 2 .   for every @xmath341 problem ( @xmath248 ) has at least two positive solutions @xmath569 , @xmath606 , @xmath607 ; 3 .   for every @xmath341 problem ( @xmath248 ) has a smallest positive solution @xmath608 and the map @xmath370 from @xmath371 is strictly increasing and left continuous .","summary":"we have at least two positive solutions and for there are no positive solutions . for both cases","abstract":"we study perturbations of the eigenvalue problem for the negative laplacian plus an indefinite and unbounded potential and robin boundary condition . first we consider the case of a sublinear perturbation and then of a superlinear perturbation . for the first case we show that for ( being the principal eigenvalue ) there is one positive solution which is unique under additional conditions on the perturbation term . for there are no positive solutions . in the superlinear case , for we have at least two positive solutions and for there are no positive solutions . for both cases we establish the existence of a minimal positive solution and we investigate the properties of the map .    nikolaos s. papageorgiou    viceniu d. rdulescu    duan d. repov    ( communicated by manuel del pino )"}
{"article_id":"0903.1771","section_id":"i","document":"even after more than a decade of very intense research efforts,@xcite the unique electronic and mechanical properties of carbon nanotubes ( cnts ) continue to attract considerable interest . a major driving force for this interest comes from the prominent role played by phonons in cnts . phonons are crucial when interpreting experimental data for resonant raman or photoluminescence excitation spectra,@xcite and for the understanding of electrical@xcite and thermal@xcite transport in cnts . moreover , phonons are responsible for interesting nanoelectromechanical effects in suspended cnts,@xcite and they lead to quantum size effects in the specific heat.@xcite the real - time nonlinear dynamics of a cnt phonon mode has also been monitored experimentally by femtosecond pump - probe techniques ( coherent phonon spectroscopy).@xcite    recent experiments have shown that mechanical oscillations of suspended carbon nanotubes can be excited by a cantilever and detected by scanning force microscopy.@xcite such experiments yield both the frequency @xmath0 and the quality factor @xmath1 ( with decay rate @xmath2 ) of the respective phonon mode . the so far observed@xcite values , @xmath3 , imply significant decay rates even at rather low temperatures , and require to identify the relevant decay channels for phonons in individual cnts . our paper is primarily devoted to understanding the importance of phonon - phonon interactions in such decay processes . the quality factor can also be extracted from raman spectroscopy@xcite and from nanoelectromechanical measurements , using phonon - assisted coulomb blockade spectroscopy@xcite or capacitive detection of mechanical oscillations.@xcite in principle , coherent phonon spectroscopy also allows to access damping rates of phonon modes , and hence their quality factors . very recently , the possibility of cooling a vibrating carbon nanotube to its phononic ground state has also been discussed.@xcite    the recent experimental progress described above highlights the need for a reliable theory of phonon - phonon ( ph - ph ) interactions in cnts . on the theoretical side , many authors have analyzed the noninteracting problem , i.e. the harmonic ( or linear ) theory , which allows to derive explicit theoretical results for the thermal conductance@xcite and for the specific heat.@xcite motivated by the observation that molecular dynamics calculations seem to be in good agreement with thin - shell model predictions,@xcite several theoretical works@xcite have adapted thin - shell hollow cylinder models@xcite to the calculation of phonon spectra . however , the thin - shell approach leaves open the question of how to actually choose the width of the carbon sheet . a popular and more microscopic approach is to instead start from force - constant models,@xcite taking into account up to fourth - nearest - neighbor couplings in the most advanced formulations.@xcite these calculations predict four acoustic phonon branches ( with @xmath4 ) , namely a longitudinal stretch mode , a twist mode , and two degenerate flexural modes ( see sec .  [ seciic ] for details ) . the resulting phonon spectra are in very good agreement with a much simpler calculation based on continuum elasticity theory,@xcite building on the known elastic isotropy of the honeycomb lattice.@xcite the elastic approach will be employed in our study as well . provides a general discussion of the accuracy of elastic continuum theories for phonons in cnts . for very small cnt radius @xmath5 , however , hybridization effects involving carbon @xmath6 orbitals lead to qualitative changes , elastic continuum theories ( at least in the form below ) may break down , and first - principle calculations become necessary.@xcite    in contrast , the problem of ph - ph interactions in cnts is much more difficult and has been treated in only a few works , although phonon anharmonicities are important for several physical observables,@xcite e.g. for thermal expansion ( which is a controversial issue in cnt theory@xcite ) , to explain the stability of low - dimensional materials ( which would be unstable in harmonic approximation due to the mermin - wagner theorem ) , in order to establish a finite thermal conductivity , or to provide a finite lifetime for phonons . the latter issue is particularly relevant in our context , but aside from a numerical high - temperature study@xcite which ignored the ( lowest - lying ) flexural phonons , to the best of our knowledge ph - ph interactions in cnts have only been studied by mingo and broido.@xcite their work considered three - phonon processes and their effects within a boltzmann transport equation . the main conclusion of refs . , was that anharmonic effects are generally weak but important in establishing upper bounds for the thermal conductance . in addition , they computed the lengthscale up to which phonons show ballistic motion . where applicable , our results below are in accordance with theirs , but four - phonon processes ( which govern the decay of flexural phonons ) have not been studied so far . we shall consider two important mechanisms for the decay of long - wavelength acoustic phonons in single - wall cnts , namely electron - phonon ( e - ph ) and ph - ph scattering . we show that the dominant e - ph coupling terms ( resulting from the deformation potential contribution ) do not allow for phonon decay due to kinematic restrictions , and thus an intrinsic upper bound for the temperature - dependent quality factor of the various modes can be derived from ph - ph interactions alone . these upper bounds are given below . the problem of phonon decay has in fact a rather long history . early work on the decay of an optical phonon into two acoustic phonons via anharmonicities@xcite proposed a scheme for nonlinear phonon generation . phonon decay via ph - ph interaction is also important for the understanding of neutron scattering data@xcite and for the collective excitations in liquid helium.@xcite such effects have even been considered in a proposal for a phonon - based detector of dark matter.@xcite general kinematic restrictions often prevent the decay of phonon modes . have shown@xcite that a given acoustic phonon can not decay into other modes with higher velocity at any order in the anharmonicity . for the lowest - lying acoustic phonon mode , one then expects _ anomalously long lifetimes _ , while the higher acoustic modes typically decay  in three - dimensional ( 3d ) isotropic media with rate @xmath7 for phonon momentum @xmath8.@xcite such questions are particularly interesting in the cnt context , where a degenerate pair of flexural modes has the lowest energy , and the low dimensionality and the quadratic dispersion relation of the flexural mode may give rise to unconventional behavior .    before describing the organization of the paper , we pause for some guidance for focused readers . experimentally minded readers can find our central predictions for the decay rate ( and hence the quality factor ) of the low - energy phonon modes in eqs . ( [ gamml ] ) , ( [ gammt ] ) and ( [ finalrate ] ) . the dependence of the resulting @xmath9 factors on the cnt radius @xmath5 is shown in fig . those interested in the main new theoretical results will find them in eqs . ( [ 3phonon ] ) and ( [ 4phonon ] ) , where the complete low - energy hamiltonian for interacting acoustic phonons in single - wall cnts is given , with the modified flexural dispersion relation ( [ flexnew ] ) . this modification takes into account the instability of a harmonic theory implied by the mermin - wagner theorem , and includes interaction effects in a nonperturbative manner . the calculation of the decay rates is then possible in a perturbative manner , and leads to the results quoted above . let us conclude this introduction with the organization of the paper . in this work , based on the elastic continuum description , we formulate a complete and analytical theory of interacting long - wavelength acoustic phonons in single - wall cnts . in section [ sec2 ] we show that the simplicity of the elastic approach allows us to go beyond the harmonic approximation ( which is briefly reviewed in sec . [ seciic ] ) , and thereby provides a complete theory of all possible three- and four - phonon scattering processes , described in detail in sec .  [ sec3 ] . the theory is then applied in sec . [ sec4 ] to the calculation of phonon decay rates . we thereby infer intrinsic upper bounds for the quality factor of the relevant acoustic modes . we comment on effects of e - ph interactions on the quality factor in sec . [ sec5 ] , and end the paper with a discussion and an outlook in sec . calculational details have been relegated to two appendices . finally , we note that while some of our results are also relevant to 2d graphene monolayers,@xcite for the sake of clarity , we restrict ourselves to the cnt case throughout the paper . we sometimes set @xmath10 in intermediate steps .","summary":"a general and analytical derivation of all three- and four - phonon processes is provided , and the relevant coupling constants are determined in terms of few elastic coefficients . due to the low dimensionality and the parabolic dispersion , the finite - temperature density of noninteracting flexural phonons diverges , and a nonperturbative approach to their interactions is necessary . within a mean - field description , we find that a dynamical gap opens . in practice , this gap is thermally smeared , but still has important consequences . using our theory , we compute the decay rates of acoustic phonons due to phonon - phonon and electron - phonon interactions , implying upper bounds for their quality factor .","abstract":"we formulate and study the effective low - energy quantum theory of interacting long - wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory . a general and analytical derivation of all three- and four - phonon processes is provided , and the relevant coupling constants are determined in terms of few elastic coefficients . due to the low dimensionality and the parabolic dispersion , the finite - temperature density of noninteracting flexural phonons diverges , and a nonperturbative approach to their interactions is necessary . within a mean - field description , we find that a dynamical gap opens . in practice , this gap is thermally smeared , but still has important consequences . using our theory , we compute the decay rates of acoustic phonons due to phonon - phonon and electron - phonon interactions , implying upper bounds for their quality factor ."}
{"article_id":"0903.1771","section_id":"c","document":"in this paper , we have formulated and studied a general analytical theory of phonon - phonon interactions for low - energy long - wavelength acoustic phonons in carbon nanotubes . the continuum elasticity approach employed here reproduces the known dispersion relations of all gapless modes , including the flexural mode , @xmath187 with `` effective mass '' @xmath166 . we have then included the most general cubic and quartic elastic nonlinearities allowed by symmetry . remarkably , the relevant phonon - phonon scattering processes giving the dominant contributions to the decay rates are already found from the geometric nonlinearities ( i.e. using the nonlinear strain tensor in a lowest - order expansion of the elastic energy density ) , and for a quantitative discussion of the decay rates , only the knowledge of the well - known lam coefficients ( or equivalently of the sound velocities ) is necessary . we have provided a complete classification of all possible three - phonon processes involving gapless modes , along with the respective coupling constants . at the level of four - phonon processes we have focussed on the flexural modes , where a peculiarity is encountered , since the four - phonon processes lead to a singular behavior of the finite - temperature decay rate . the physical reason for this singularity is the proliferation of phonons at finite temperature , implying a divergent 1d density of flexural modes . interactions effectively regularize this divergence and lead to a finite density . we have employed mean - field theory to quantitatively describe this mechanism , and found a dynamical temperature - dependent gap @xmath359 for flexural phonons . while this gap is in practice always below the thermal scale @xmath273 , it nevertheless leads to important consequences and allows to compute a well - defined decay rate for flexural phonons in low - order perturbation theory .    using this approach , we have determined the decay rate and the quality factor for all long - wavelength gapless phonons in carbon nanotubes . we have also shown that electron - phonon interactions are ineffective in relaxing those modes due to a mismatch in energy scales . the reported quality factors ( @xmath9 ) are remarkably small , especially for thin cnts , pointing to important phonon damping effects . phonon - phonon interactions in cnts are therefore significant and quite strong . moreover , the values we have found are rather close to the typical @xmath9 reported in recent experiments.@xcite our predictions represent intrinsic upper bounds for @xmath9 . such upper bounds can be valuable in assessing the predictions of approximate theories , or when interpreting experimental data in terms of phonon damping . we hope that our work will motivate further experimental and theoretical studies along this line . we thank i. affleck for useful discussions . this work was supported by the dfg sfb transregio 12 , by the esf network instans , and by the humboldt foundation .","summary":"we formulate and study the effective low - energy quantum theory of interacting long - wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory .","abstract":"we formulate and study the effective low - energy quantum theory of interacting long - wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory . a general and analytical derivation of all three- and four - phonon processes is provided , and the relevant coupling constants are determined in terms of few elastic coefficients . due to the low dimensionality and the parabolic dispersion , the finite - temperature density of noninteracting flexural phonons diverges , and a nonperturbative approach to their interactions is necessary . within a mean - field description , we find that a dynamical gap opens . in practice , this gap is thermally smeared , but still has important consequences . using our theory , we compute the decay rates of acoustic phonons due to phonon - phonon and electron - phonon interactions , implying upper bounds for their quality factor ."}
{"article_id":"0806.3599","section_id":"i","document":"the quantum bit ( qubit ) is a new concept for the basic unit of information . it is an extension of the classical bit and it enables us to develop much more powerful methods for achieving secure communication and information processing . to implement a qubit , the information of a qubit ( quantum information ) is encoded in the quantum state of a microscopic physical system that is surrounded by a macroscopic system ( the environment ) . since the quantum state of the microscopic system is sensitive to the environment in general , it is not easy to maintain quantum coherence of the system during the time taken to perform operations on qubits . thus , quantum information media has to be appropriately chosen in order to maintain quantum coherence during operations on qubits . photons and atoms are promising candidates for quantum information media , since their internal states have a high resistance to decoherence due to interaction with the environment . photons are suited to the transmission and processing of quantum information , and atoms are suited to the storing of that information . photons and atoms should thus assume complementary roles in quantum information technology . in addition , an efficient interface for transferring quantum information between photons and atoms is required . if quantum information is encoded in the polarization of a photon and in the ground and excited states of an atom , it will be important to generate an atom - photon entangled state . this is because the quantum information encoded in the polarization of a signal photon can be transferred to the internal state of the atom by performing a bell measurement between a signal photon and a photon entangled with an atom . this information transfer corresponds to one - qubit quantum teleportation by a two - qubit entangled state @xcite . a controlled - not ( c - not ) operation between two qubits is required to implement atom - photon entanglement . this operation changes the bit value of the target qubit to its opposite value only when the bit value of the control qubit is 1 . recently , the implementation and application of the c - not operation for photons and atoms have been studied extensively in the field of cavity quantum electrodynamics @xcite , since strong coherent interactions between a single atom and a few photons can be investigated using a small - volume optical cavity @xcite .    in order to efficiently generate atom - photon entangled states , the c - not operation needs to be implemented such that the input photon state must be a single - photon state and the input photon must interact with an atom within a time limited by the decoherence time of the internal state of the atom . for this purpose , it will be useful to confirm the arrival times and the number of the input photons at the input port of the c - not gate before commencing the c - not operation . since current single - photon sources @xcite are not perfect on - demand sources ( i.e. , the light that they emit is described as a mixed state of zero- and single - photon ) the above - mentioned confirmation will be especially important for efficiently generating atom - photon entangled states .    in this paper , we propose a photon - arrival detector ( pad ) , which detects the arrival of signal photon and simultaneously projects the signal input state to a single photon state , with an atom - cavity system . the performance of the proposed pad is quantitatively evaluated by calculating the detection probability of a signal photon . the proposed pad enables us to repeatedly detect the arrival of the input photons . the detection probability of the proposed pad will exceed the quantum efficiency of conventional photodetectors for a small number ( i.e. , less than ten ) attempts , when the linear transmittance per attempt exceeds the quantum efficiency . the key element of the proposed pad is the implementation of a controlled - phase - flip ( cpf ) operation by an atom - cavity system . this operation changes the phase of the target qubit by @xmath0 only when the bit values of the control and the target qubits are 1 with each other . duan and kimble have proposed a scheme for carrying out cpf @xcite . a schematic setup to implement cpf between an atom and a photon is shown in fig .  [ fig : cpf ] . a polarization beam splitter ( pbs ) transmits the x - polarized component of the signal photon coming from the signal input port @xmath1 and reflects the y - polarized component of that photon , where x and y represent any two mutually orthogonal axes . the cavity is a one - sided cavity and the intracavity atomic system consists of one excited state @xmath2 and two ground states @xmath3 and @xmath4 , making it a @xmath5-type system . the transition between the ground state @xmath4 and the excited state @xmath2 is resonant with the x - polarized cavity mode . the x - polarized component of the signal photon excites that cavity mode . we evaluated the fidelity of the proposed scheme using the cpf operation described by the unitary operation @xmath6 by numerically calculating the shape mismatch between the input and the output photon pulses . the resultant gate fidelity was more than 99.9 % in the strong - coupling regime described by @xmath7 , where @xmath8 is the coupling strength between the cavity mode and the intracavity atomic system and @xmath9 is the cavity decay rate . schematic of the setup to implement cpf between an atom and a photon . with a polarization beam splitter ( pbs ) , the x - polarized component of the single - photon signal pulse is reflected by the cavity , while the y - polarized component is reflected by the mirror m. the optical paths from the pbs to the cavity and to the mirror m are assumed to be equal . x and y are any two mutually orthogonal axes.,width=170 ]    when processing many photonic or atomic qubits on an individual basis in a laboratory , it is important to miniaturize and integrate devices used to process qubits , and not just to increase the repetition rate of individual devices . in order to miniaturize and integrate cpf implementation in an atom - cavity system and to obtain stable optical responses of an atom - cavity system to single photons , it is important to realize solid - state atom - cavity systems . solid - state three - level systems have been extensively studied in experiments involving v - type systems , which consist of a single ground state and two excited states @xcite . it is thus interesting to discuss quantitatively cpf in a v - type system together with its potential applications . the remainder of this paper is organized as follows . in sec . ii , the scheme for the proposed pad is explained . in sec . iii , the hamiltonian is presented for an atom in a one - sided cavity coupled with input and output radiative fields . the temporal evolution of the intracavity atomic system is then derived for a coherent pulse input ( sec . the fidelity of the signal output from the atom - cavity system for an ideal output after applying the unitary operation @xmath10 is estimated by analyzing the responses of the atom - cavity for single - photon input in sec .  v. the performance of the pad is then estimated in sec . vi , based on the results of sec . iv and v. in sec . vii , experimental realization of an atom - cavity for the pad is discussed . in sec . viii , our scheme for cpf is compared with that of duan and kimble .","summary":"we propose a photon - arrival detector ( pad ) , which detects the arrival of a signal photon and simultaneously projects the signal input state to a single photon state , with an atom - cavity system . in this proposal , use of a v - type system as the intracavity atom is discussed for implementing the pad , since v - type systems have been widely studied in the field of solid state , enabling us to miniaturize and integrate that implementation .","abstract":"we propose a photon - arrival detector ( pad ) , which detects the arrival of a signal photon and simultaneously projects the signal input state to a single photon state , with an atom - cavity system . in this proposal , use of a v - type system as the intracavity atom is discussed for implementing the pad , since v - type systems have been widely studied in the field of solid state , enabling us to miniaturize and integrate that implementation . the performance of the proposed pad is evaluated for a specific method of the detection process . the proposed pad is capable of repeating the procedure for detecting the arrival of input photons and it has improves the detection probability so that it has a higher quantum efficiency than those of conventional photodetectors ."}
{"article_id":"0806.3599","section_id":"c","document":"detection of photon arrival based on a cpf using a v - type system was discussed . the gate fidelity for the cpf was calculated by analyzing the responses of the atom - cavity system to single photon input . a maximum gate fidelity of more than 0.99 in the strong coupling regime @xmath373 was achieved . the efficiency of the proposed pad was estimated by analyzing the responses of an atom in a one - sided cavity for laser pulse input and calculating the accuracy and the average total number of counts . an efficiency of up to @xmath374 was found to be possible by increasing the transmittance per round trip of a signal photon . there are two drawbacks in the present scheme of the pad . one is that it takes a long time ( @xmath375 ) to initialize the intracavity atomic system to the ground state @xmath12 before starting the pad procedure . a long initialization time decreases the repetition rate of the pad procedure . the other drawback is that the accuracy @xmath329 is smaller than 0.989 due to the linear transmittance @xmath321 being smaller than 1 . these problems may be solved by direct detection of the excited state @xmath14 in a quantum dot molecule with a quantum point contact . nevertheless , the proposed pad procedure enables us to apply the pad procedure many times to detect the arrival of input photons and the average number of counts @xmath376 exceeds the quantum efficiency of photodetectors in a small number ( less than ten ) of applications , when the linear transmittance is larger than the quantum efficiency . furthermore , by minimizing the cavity size our scheme for atom - photon cpf may be capable of achieving a higher repetition rate than the duan - kimble scheme @xcite .","summary":"the proposed pad is capable of repeating the procedure for detecting the arrival of input photons and it has improves the detection probability so that it has a higher quantum efficiency than those of conventional photodetectors .","abstract":"we propose a photon - arrival detector ( pad ) , which detects the arrival of a signal photon and simultaneously projects the signal input state to a single photon state , with an atom - cavity system . in this proposal , use of a v - type system as the intracavity atom is discussed for implementing the pad , since v - type systems have been widely studied in the field of solid state , enabling us to miniaturize and integrate that implementation . the performance of the proposed pad is evaluated for a specific method of the detection process . the proposed pad is capable of repeating the procedure for detecting the arrival of input photons and it has improves the detection probability so that it has a higher quantum efficiency than those of conventional photodetectors ."}
{"article_id":"0803.4177","section_id":"i","document":"modern particle physics has reached a level of experimental accuracy in the percent range , and some present and future precision experiments require theoretical uncertainties to be at the permille level . this need for precise theory predictions has pushed forward the frontier for calculations of higher orders in perturbation theory considerably in recent years . the calculation of higher order corrections relies to a large extent on tree or loop level feynman diagrams , where the unobserved degrees of freedom , respectively the loop momenta , have to be integrated out . it is well known that these integrations become increasingly difficult at higher orders , as the dimensionality of the integration parameter space and/or the number of scales involved is growing . the intricacy is closely related to the fact that these integrals in general contain ultraviolet ( uv ) or infrared ( ir ) divergences which need to be renormalised respectively factorised , because they hinder an immediate numerical evaluation of complicated expressions . the subtraction of these singularities becomes more and more cumbersome at higher orders , due to the fact that the divergences will be entangled in an increasingly complicated way .    for ultraviolet divergences , bogoliubov , parasiuk , hepp and zimmermann  @xcite , established a subtraction scheme valid to all orders in perturbation theory . in fact , the original idea of sector decomposition goes back to the proof of the bphz theorem by hepp  @xcite , who used a decomposition of integration parameter space into certain sectors in order to disentangle overlapping ultraviolet singularities .    concerning infrared divergences , the finiteness of sufficiently inclusive observables is guaranteed by the kinoshita - lee - nauenberg theorem  @xcite , but in most practical applications , more exclusive information about the final state is required , such that a subtraction scheme for ir divergences has to be established . a constructive scheme to do so to all orders in perturbation theory has not been formulated in full generality yet , at least in what concerns soft _ and collinear _ divergences . however , the sector decomposition algorithm as outlined below offers a constructive method to isolate these divergences from feynman parameter integrals , which in principle is valid to all orders in perturbation theory .    for the subtraction of ( soft ) ir divergences , several approaches have been suggested . early ones , which are based already on the subdivision of the integration parameter space into different sectors where the parameters go to zero in an ordered way , can be found e.g. in @xcite . these sectors , associated with certain sets of one - particle irreducible subgraphs , are more advanced than the sectors needed in the uv case , and provide a resolution of the singularities without the need for an iterative procedure for diagrams with off - shell external momenta . further , the so - called @xmath0-operation  @xcite has been developed , which removes not only uv - divergences but also soft ir divergences by a procedure similar to the @xmath1-operation  @xcite in the uv case . for a review of these methods , see e.g. @xcite . later , the decomposition into sectors has been employed to extract logarithmic mass singularities from massive multi - scale integrals in the high energy limit at two loops  @xcite . in  @xcite , the concept of sector decomposition has been elaborated to a general algorithm in the context of dimensional regularisation , allowing to isolate ultraviolet as well as infrared singularities from parameter integrals in an automated way  @xcite . the algorithm also has been implemented in a public code available from  @xcite .    at next - to - leading order ( nlo ) in perturbation theory , the use of dimensional regularisation  @xcite and the universal infrared structure of gauge theories involving massless particles , like qed and qcd , allowed to establish a framework to isolate ir singularities analytically , leading to a multitude of phenomenological predictions . more recently , an increasing number of results at next - to - next - to - leading order ( nnlo ) has also become available , and quite a number of them made use of the sector decomposition technique to isolate infrared singularities or to check analytical results  @xcite .    as most problems encountered in the calculation of perturbative higher order corrections can be reduced to the evaluation of multi - dimensional parameter integrals , the applicability of sector decomposition is quite universal . the first application of the algorithm presented in @xcite was the numerical evaluation of massless two - loop box diagrams at certain euclidean points . pioneering the analytic calculation of two - loop box diagrams , the planar topology with light - like external legs has been calculated by v.a . smirnov  @xcite , the non - planar one by j.b.tausk  @xcite , where the numerical results obtained by sector decomposition served as an important check of the analytical calculation . for massless two - loop box diagrams with one off - shell leg , the numerical results of ref . @xcite were predictions which played a major role to validate the subsequent analytical calculations  @xcite , finally allowing the calculation of the full two - loop qcd matrix element for @xmath2 jets  @xcite . subsequently , sector decomposition was used to check a considerable number of analytical results for two - loop  @xcite , three - loop  @xcite and four - loop  @xcite diagrams . sector decomposition also has been combined with other methods for an efficient numerical calculation of one - loop multi - leg amplitudes , first on a diagrammatic level in refs . @xcite , later for whole amplitudes in refs . the latter approach contains a combination of sector decomposition and contour deformation  @xcite , which allows to integrate the feynman parameter representation of an amplitude numerically in the physical region . it also contains the application of sector decomposition to phase space integrals , which will be discussed below . similar ideas , i.e. the combination of sector decomposition and contour deformation , are employed in refs . @xcite for the numerical evaluation of multi - loop feynman diagrams with infrared and threshold singularities . @xcite describes the implementation of an algorithm based on sector decomposition to extract the @xmath3 poles as well as the large logarithms of type @xmath4 in the high - energy limit , allowing to obtain the next - to - leading logarithmic electroweak corrections of multi - loop diagrams .    despite its success in practical applications , until very recently there was no formal proof that a strategy for the iterated sector decomposition can always be found such that the iteration is guaranteed to stop . this gap has been filled in ref . @xcite , by mapping the problem to hironaka s polyhedra game  @xcite . the findings of ref . @xcite subsequently have been used to prove that the coefficients of the laurent series representing feynman integrals in the euclidean region with rational values for all invariants are a special class of numbers known by mathematicians as periods  @xcite .    also on a more formal level , it is outlined in @xcite that sector decomposition can be used to automate the renormalisation of quantum field theories , by mapping to the so - called henge decomposition  @xcite , which served to provide a simple proof of the bphz theorem  @xcite . this mapping also allowed to establish a direct correspondence between overlapping divergences in feynman parameter space and in momentum space  @xcite . in this context , one should also mention the formulation of renormalisation using hopf algebras  @xcite , which provide a framework to describe the disentanglement of divergent subgraphs of feynman diagrams . after the results for various two - loop box diagrams had become available , the bottleneck to make progress in the calculation of differential nnlo cross sections for @xmath5 or @xmath6 processes was the complicated infrared singularity structure of phase space integrals over matrix elements for the real radiation of ( doubly ) unresolved massless particles . as these phase space integrals can be written as dimensionally regularised parameter integrals , sector decomposition can serve to factorise entangled singularity structures in the case of real radiation as well . this idea has first been presented in  @xcite and subsequently has been applied to calculate all master four - particle phase space integrals where up to two particles in the final state can become soft and/or collinear  @xcite . shortly after , this approach has been extended to be applicable to exclusive final states as well by expressing the functions produced by sector decomposition in terms of distributions  @xcite . a rapid development  @xcite lead to the calculation of @xmath7jets at @xmath8  @xcite . further elaboration on this approach resulted in the first fully differential program to calculate an nnlo cross section  @xcite and has lead to differential nnlo results for a number of processes meanwhile  @xcite .","summary":"sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory . we explain the general algorithm in detail and review its application to multi - loop feynman parameter integrals as well as infrared divergent phase - space integrals over real radiation matrix elements .    ippp/08/16 + dcpt/08/32 +    3.5 cm    * sector decomposition *    1.cm    gudrun heinrich    0.7 cm    _ ippp , department of physics , university of durham , + south road , durham dh1 3le , uk + gudrun.heinrich@durham.ac.uk_","abstract":"sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory . we explain the general algorithm in detail and review its application to multi - loop feynman parameter integrals as well as infrared divergent phase - space integrals over real radiation matrix elements .    ippp/08/16 + dcpt/08/32 +    3.5 cm    * sector decomposition *    1.cm    gudrun heinrich    0.7 cm    _ ippp , department of physics , university of durham , + south road , durham dh1 3le , uk + gudrun.heinrich@durham.ac.uk_"}
{"article_id":"astro-ph0606242","section_id":"i","document":"from the emergence of a hydrostatic core , the collapse of a protostellar core is accompanied by winds and mass loss @xcite probably driven by magnetospheric accretion ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? integrated over time , the effect of a wind from a young star is to blow away the material that shrouds it during its earliest evolution . the discovery of bipolar molecular outflows has been a key to the understanding of this process ( e.g. * ? ? ? * slp hereafter ) . these molecular outflows have dimensions of up to several parsecs , masses one or two orders of magnitude larger than their driving sources , and tremendous kinetic energies @xcite . such massive flows must represent swept - up material as the winds , emerging from the star and/or its circumstellar disk , interact with their ambient medium . one of the important unanswered questions in outflow studies is the mechanism by which the jets / winds emerging from the embedded star / disk entrain and accelerate the surrounding molecular material . currently there are three scenarios : the `` wide - angle wind '' model in which a wide - angled magnetized wind expands like a bubble and sweeps up the ambient medium in a momentum conserving manner into the shell at the wind - bubble ambient medium interface @xcite . then there are two types of `` jet '' entrainment models , the  turbulent  jet entrainment model , in which ambient material is accelerated through a turbulent viscous mixing layer that surrounds the jet formed by kelvin - helmholtz instabilities @xcite ; and the  prompt  entrainment model in which bow shock formed in the jet head drives material ahead and laterally to the axis of the flow @xcite . it is essential to distinguish between these models to not only understand the processes that govern the formation of molecular outflows , but also the nature of the jet / wind launching mechanism and the underlying accretion disk processes . since it is difficult to observe the jet / wind launching regions directly , the properties of large scale bipolar outflows can shed some light on the nature of their initial conditions . in addition , the energy and momentum deposited by molecular outflows within the molecular cloud can be large enough to power turbulence in the cloud or even disrupt the parts of the cloud . understanding outflow properties over the entire outflow history is critical in determine their impact on the cloud .    within the last decade , with the advent of ccd cameras with 20fields - of - view , more than two dozen giant herbig - haro ( hh ) flows with dimensions ranging from 1 to 7 pc have been discovered @xcite . hh flows are chains of optically visible shock - excited nebulae which , demonstrate the existence , at least during certain evolutionary phases , of exceedingly well collimated and highly supersonic wind components ( e.g. * ? ? ? the tremendous size of parsec - scale outflows implies that molecular material is being entrained at parsec - scale distances from the driving source , and thus it may have a significant impact on the kinematics and energy density of a substantial volume of the parent molecular cloud . our current estimates of the  typical  outflow properties may be far from accurate , since there is no large homogeneous sample of molecular outflows which have been mapped with good resolution and sensitivity @xcite . consequently , our current understanding of the processes might be heavily subjective , and biased by a few frequently studied examples . we have been involved in a multi - wavelength study of a dozen or so parsec - scale outflows , complementing narrow - band optical observations with wide - field , sensitive , multi - transitional co   and co  observations ( stojimirovi et al . 2006 in prep . ) here , we present the detailed results of our multi - wavelength study on the l1551 molecular outflow . the bipolar molecular outflow associated with the l1551 small dark cloud in the taurus molecular cloud complex , was the first recognized bipolar outflow from a young stellar object ( slp ) and is considered one of the best examples of its kind . at a distance of 140 pc @xcite , the l1551 dark cloud has been the site of many multi - wavelength studies that reveal the dynamical complexity of this low mass star formation region . optical images of the l1551 outflow region , show new distant hh object , hh 286 @xcite , making the whole extent of the optical emission in the l1551 flow 1.3 pc . we made sensitive , large spatial extent , high spatial and velocity resolution maps at millimeter and submillimeter wavelengths . large - spatial extent mapping performed on parsec - scale outflows , allows us to study in detail the entrainment mechanisms by which jets / winds drive the observed molecular flows . with the availability of both co  and co  data over the full spatial extent of the flow , we are able to take a _ full _ and proper accounting of the mass and hence energetics of the outflows in the l1551 system . comparing optical and millimeter data , we are able to discriminate among entrainment models based on morphological grounds .","summary":"we present high sensitivity co  and co  j=1molecular line maps covering the full extent of the parsec scale l1551 molecular outflow , including the redshifted east - west ( ew ) flow . , the redshifted molecular gas terminates within the cloud , short of the most distant hh object , hh 286 , which lies well beyond the cloud boundary . we use velocity dependent opacity correction to estimate the mass and the energy of the outflow .","abstract":"we present high sensitivity co  and co  j=1molecular line maps covering the full extent of the parsec scale l1551 molecular outflow , including the redshifted east - west ( ew ) flow . we also present co  j=3  data that extends over a good fraction of the area mapped in the j=1  transition . we compare the molecular data to widefield , narrow - band optical emission in h . while there are multiple outflows in the l1551 cloud , the main outflow is oriented at 50  position angle and appears to be driven by embedded source(s ) in the central irs  5 region . the blueshifted outflowing molecular gas extends to the edge of the molecular cloud and beyond the last hh object , hh 256 . on the contrary , the redshifted molecular gas terminates within the cloud , short of the most distant hh object , hh 286 , which lies well beyond the cloud boundary . the j=3  data indicate that there may be molecular emission associated with the l1551 ne jet , within the redshifted lobe of main outflow . we have also better defined the previously known ew flow and believe we have identified its blueshifted counterpart . we further speculate that the origin of the ew outflow lies near hh 102 . we use velocity dependent opacity correction to estimate the mass and the energy of the outflow . the resulting mass spectral indices from our analysis , are systematically lower ( less steep ) than the power law indices obtained towards other outflows in several recent studies that use a similar opacity correction method . we show that systematic errors and biases in the analysis procedures for deriving mass spectra could result in errors in the determination of the power - law indices . the mass spectral indices , the morphological appearance of the position - velocity plots and integrated intensity emission maps of the molecular data , compared with the optical , suggest that jet - driven bow - shock entrainment is the best explanation for the driving mechanism of outflows in l1551 . the kinetic energy of the outflows is found to be comparable to the binding energy of the cloud and sufficient to maintain the turbulence in the l1551 cloud ."}
{"article_id":"astro-ph0606242","section_id":"c","document":"the combination of optical h@xmath1 , millimeter and submillimeter co data provides a more complete picture of the structure and kinematics of the molecular outflows in the l1551 region , allowing us to better investigate the driving mechanism of molecular outflows . currently the two most promising models of entrainment of outflows are the jet - driven bow - shock model and the wind - driven shell model . numerous hydrodynamic and analytical models have treated both types of entrainment mechanisms and predict distinct morphologies for the appearance of the integrated intensity maps , position - velocity maps , and the mass - velocity power law indices ( for examples see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? one of the most distinctive observational characteristics of molecular outflows is the power - law dependence of flow mass with velocity , @xmath57 . usually , log(dm / dv ) versus log(v ) has a linear dependence , with a single power law index @xmath62 ranging from about 0.5 to 3.5 , with the majority of observations indicating @xmath732 @xcite . at velocities larger than 10  kms@xmath3from the ambient cloud velocity , many outflows show a break in the power - law with higher velocities showing a steeper slope . the break at higher velocities might indicate that there are two distinct outflow components , perhaps corresponding to a recently accelerated component , and a slower - moving swept - up component . it also appears that the low - velocity power - law index of @xmath74 is the same for low - mass as well as high - mass objects , indicating that some common acceleration mechanism operates over several decades of stellar luminosity @xcite . there is also some indication , especially for high - mass objects that the slope , @xmath62 steepens with age @xcite . thus , observations of @xmath62 and the occurrence of breaks in the power law could thus be used to constrain the driving mechanism in a given outflow . in turn , the trends seen in the mass versus velocity ( @xmath65 ) power laws of observed outflows can be used to refine the theoretical models of outflow entrainment . accurate determination of the value of @xmath62 is thus quite important . numerical simulation of both jet- and wind - driven models @xcite show that the power law index in @xmath65  plots for jet - driven bow - shock systems ranges from 1.5 to 3.5 , while the wind models yield smaller value of @xmath62 in the range of 1.3 to 1.8 . in the jet - driven models , @xmath62 is a strong function of inclination , with lower values of @xmath62 obtained when the outflow has larger angles of inclination to the plane of the sky . @xcite show that power - law with break is produced for the jet - driven entrained gas . jet - driven bow - shock models show hubble - law like features in the position - velocity plots with the highest velocities at the  hot spots  ( head of the jet ) and decreasing velocity trend toward the source ( wings of the bow shock ) . the p - v structure is associated with the broad range of velocity near the bow tip while there is a small and almost constant velocity in the bow wings , often producing a convex spur structure along the jet axis at the highest velocities @xcite . figure 20 in @xcite shows a strong dependence on inclination angle for the p - v diagram structure in bow shock model . in the case where several bow shocks are driven because of the presence of a pulsed jet , several spur structures can be seen in the p - v diagram . ( see fig . 7 , * ? ? ? * hh 212 ) . on the other hand , wind - driven entrainment mechanism do not show any evidence for spur features in the p - v plots ; the p - v plots are typically parabolic in shape with the vertex of the parabola coincident with the location of the source . the morphology of the shape is somewhat inclination dependent , but the p - v plots are quite distinctive in appearance from that produced by jet - driven models .    in  [ sec : mvresults ] , we report our results for the mass - velocity power laws . our main result is that when there is a break in the power law , the power law slope for low velocities is shallow , @xmath75 . the power law index for high velocities is @xmath76 ( see figure  [ fig : mv ] ) . the main co outflow oriented at 50  from irs  5 shows mostly jet - driven bow - shock features , but also shows some morphological features seen in wind - driven flows . the @xmath65  plots for the blue and redshifted lobes ( regions a1 and a2 ) of the main irs 5 outflow show a power - law break as predicted by a jet - driven flow ( see figure  [ fig : mv ] ) . the millimeter and submillimeter p - v plots for irs 5 ( figures [ fig : pv_irs5 ] and [ fig : pv_submm ] ) show multiple hubble - law wedges , with spur - like features at the highest velocities ( see especially the submillimeter data in figure  [ fig : pv_submm ] ) . the blueshifted side of the co j=1@xmath00   p - v plot ( figure  [ fig : pv_irs5 ] ) might be interpreted as a parabolic feature , or it may be two hubble like wedges adjacent to each other . but the redshifted side shows no evidence for any parabolic structure . a single convex spur - like feature is seen in the p - v plot on the redshifted side . the channel maps in figures [ fig : mosaic_blue ] through [ fig : mosaic_red_submm ] show a morphology where the highest velocity emission is the most collimated , and is along the projected jet axis , and is often seen in the vicinity of hh objects , probably highlighting the interaction regions of shocks at the heads of the bow - shock interfaces of the underlying jet with the swept - up molecular material . the overall spatial morphology of the low - velocity gas in blue and redshifted lobes is roughly parabolic ( see figures [ fig : mosaic_blue ] through [ fig : mosaic_red_submm ] ) , with the slower swept - up gas manifesting itself as limb - brightened shell - like features . it has been proposed that the entrainment mechanism itself may evolve in outflows , with the early stages being a collimated jet - driven flow , which in later stages evolves into very wide - angle wind @xcite . if so , the characteristics of both jet - like and wind - driven entrainment for the irs 5 flow might be indicative of its relatively evolved stage as an outflow . the ew flow on the other hand shows only jet - like features . the flow is highly collimated ( see figure  [ fig : ew ] ) , the @xmath65  plots for both the redshifted western component and the possible blueshifted component ( in the redshifted lobe of irs  5 flow ) show single sloped power law with steep power - law indices ( @xmath77 and @xmath78 respectively ) indicative of jet - driven bow - shock entrainment . the p - v diagram for the ew flow ( figure  [ fig : pv_ew ] ) shows no parabolic features , but a low - intensity hubble - like wedge ending in a broad spur at the tip . it is noteworthy that the @xmath65  plot ( see figure  [ fig : mv ] ) for the ew flow is quite distinct from that of the irs 5 flow . as suggested earlier , it is possible that the ew flow is dynamically younger flow , driven from an hitherto undetected source close to the location of hh 102 at about the location of the 850  @xmath13 m peak emission seen by @xcite . unlike the irs 5 flow , no optical counterpart hh objects have yet been detected along the ew jet axis . the power law indices at both low and high velocities that we derive for l1551 are not as steep as some recent determinations of @xmath62 in other outflows . for example , other groups have found @xmath79 ( single power - law ) for circinus @xcite and barnard 5 @xcite , broken power - law with @xmath80 ( low velocities ) and @xmath81 ( high velocities ) in omc-2/3 @xcite , broken - power law with @xmath82 ( low velocities ) and @xmath83 ( high velocities ) for hh 300 @xcite , broken power - law with @xmath84 ( low velocities ) and @xmath85 ( high velocities ) for pv cep @xcite . these recent studies have reported systematically steeper power law indices than reported before , and when accompanied with a break in the power law , much steeper slopes at higher velocities . one common feature of these recent results with larger values of @xmath62 was that they employed a velocity - dependent opacity correction . in this work , we have employed a similar velocity - dependent opacity correction approach , but we derive smaller values of @xmath62 . our results here seem to counter this trend towards larger values of @xmath62 . does this indicate that l1551 is a different kind of outflow system than these other outflows ? there are several systematic effects in the derivation of mass - velocity spectra that if not properly accounted for , can result in errors in the determination of @xmath62 . below we consider these systematic effects to explain the difference in @xmath62 derived in this paper compared to some recent determinations of this quantity . \\(1 ) the overall mass estimate at all velocities can be affected by the size of the outflow mapped . if high velocity portions of the outflow are missed in the mapping , the derived @xmath62 would be an over - estimate . our study as well as the studies of @xcite have mapped a larger area of the outflow lobes than most previous studies ( primarily due to the higher sensitivities of receivers and the advent of otf mapping ) . the size of the mapped region is probably not the cause of difference in derived value of @xmath62 . \\(2 ) the exact form for the functional fit to the velocity dependent opacity correction can affect the slopes of the mass spectra . in the studies of @xcite , parabolic fits were used to extrapolate the value of the ratio ( @xmath86co/@xmath87co ) beyond values where the ratio is well determined . we use a logarithmic function ( see figure  [ fig : averaged ] ) instead . the logarithmic function is a better fit to the variation of the ratio seen in our data , but it tends to be a more slowly varying function with velocity than the parabolic fits . this makes for larger corrections ( more mass ) for the higher velocity points , which in turn makes the mass spectral slopes shallower . it should be noted that , compared to earlier studies , our data have higher sensitivity even at higher velocities from the systemic velocity , and this leads to a better constraint of the @xmath86co/@xmath87co ratio to much higher velocities . the variation of optical depth of co in molecular outflows with velocity has not been well determined to high velocities . however , when high signal - to - noise ratio spectral data have been obtained towards high velocity molecular outflows , the ratio of @xmath86co/@xmath87co seems to be slowly varying with velocity @xcite , as is seen in our study . as another example , in figures 7(c ) and 7(d ) of @xcite , it is seen that the ratio of @xmath86co/@xmath87co seems to be actually flat , however , the authors use a parabolic fit . a parabolic fit is a much faster extrapolation function in velocity and predicts that the gas gets to the optically thin limit at lower velocity offsets from the systemic velocity . \\(3 ) previous studies of mass spectra apply a method of only using data which exceeds a specified threshold in rms value of @xmath88 . for example , @xcite used a 2@xmath32 threshold , while @xcite used a 1@xmath32 threshold . figure  [ fig : rms_vs_norms ] shows the effect of using a rms threshold in the determination of the mass spectra . the rms thresholding method preferentially rejects points at higher velocity channels , since those points have the lowest signal to noise , and hence do not meet the rms threshold . because of this , mass is under - estimated preferentially at higher velocities , thereby artificially steepening the mass - spectral slopes .    the velocity - dependent optical depth correction used in @xcite as also in this work does result in more accurate mass determinations . in particular , not using the correction results in an under - estimation of the mass at especially lower velocities , artificially giving low mass - spectra slopes . on the other hand , care must be taken with the functional form of the fit of optical depth with velocity . figure  [ fig : rms_vs_norms ] shows the importance of using all the data or at least being aware of the effect that posing a specified threshold in rms value will have on mass spectrum . the mass for the l1551 cloud estimated from the fully sample co  map at line core velocities of 5 to 8  kms@xmath3  is @xmath89  m@xmath69 . outside of the line core velocities , the total mass estimated in the outflow is @xmath90  m@xmath69 for @xmath50  k or @xmath91  m@xmath69 for @xmath51  k. therefore the mass in the outflow is approximately 5 - 6.5@xmath92 of the mass of surrounding cloud , depending on the adopted value for the @xmath93 . the total momentum and energy carried by the outflow , estimated from only the line of sight ( radial ) velocity , is 20  @xmath94kms@xmath3and 1.5@xmath95 ergs , respectively . it it usually assumed that the l1551 outflows have small inclination angles relatively to the plane of the sky , so there is a large inclination correction to the momentum and energy determinations . however , since the inclination angle is extremely uncertain , we will use the values quoted above as lower limits to the true values . many authors suggest that outflows provide a mechanism to regulate star formation by removal of the gas from star - forming regions , especially in the regions that lack massive stars ( eg . @xcite , and references therein ) . for the outflow entrained gas , to escape from the cloud , it must be moving at least at the escape velocity . using a mass of 110 m@xmath69 and @xmath96  pc radius for the cloud , the escape velocity is calculated to be @xmath97  kms@xmath3 . if all of the momentum of the outflowing molecular gas was transferred to the cloud uniformly , then the gas would not escape . however , since outflows are highly collimated , momentum is transferred non - uniformly and much of the present outflowing molecular gas is likely to escape , unless it is slowed down by encounters with ambient gas . our observations suggest that in fact the main blue lobe has broken out of the cloud near hh 256 , and that their is insufficient column density of gas to slow the gas as it escapes . however , in the main red lobe , the molecular outflow is still well within the boundaries of the cloud and it remains to be determined if there is sufficient column density of gas to halt the outflow . thus , the outflows are unlikely to disperse the entire cloud , but in local regions will be a major agent for disruption . the total binding energy of the cloud is given by @xmath98 . using a cloud mass of 110 m@xmath69 and @xmath99  pc for the cloud radius , we find the binding energy to be 2@xmath100  ergs . thus , the energy of the outflow 1.5 - 2@xmath100  ergs , is comparable to the binding energy of the cloud , even if no correction for the inclination angle is made . it has been suggested that parsec - scale outflows can be a source of energy to replace the energy dissipated in turbulence and thus provide the power to maintain the magnetohydrodynamic ( mhd ) turbulence @xcite . the rate of turbulent energy dissipation can be estimated from equation ( 7 ) in @xcite . assuming a cloud mass of 110  m@xmath69 and a mean turbulent velocity dispersion of 0.45  kms@xmath3  ( estimated from the co   line width ) , we find that the energy dissipation rate of turbulence in l1551 cloud is 0.003  l@xmath101 . thus , if even a small fraction of the outflow energy could be coupled into cloud turbulence , the outflow could sustain the turbulence for over a million years , much greater than the lifetimes of molecular outflows . we have shown that the molecular outflows contain substantial kinetic energy . however , the effect outflows have on their parent clouds depends on the efficiency in which momentum and energy can be transferred from the outflowing molecular gas to the surrounding cloud material . currently , the observations are insufficient to answer this question , and there are no good theoretical models that address the effect outflows have on disruption of the cloud or on their role in replenishing the reservoir of turbulence energy in clouds . however , our work and several recent studies of parsec scale outflows , suggest that young stars , through the combined effect of their outflows , may have an important impact on the dispersal of their parent molecular cloud and to power turbulent motions . the l1551 molecular core is an active star - forming region which harbors at least 2 small clusters of protostars , one centered in the irs  5 and l1551 ne region , and another in the hl  tau region . these two mini - clusters are clearly undergoing active star - formation characterized by hh objects , optical and near - infrared jets . in addition , multi - wavelength surveys in mid infrared @xcite , x - ray @xcite , optical and near - ir @xcite , optical spectra @xcite , and in h@xmath1 @xcite have shown that the whole l1551 molecular core is surrounded by a halo of young stars in the class ii stage or older , indicating that star - formation activity has been ongoing in this region for at least a few million years . here , we explore the possibility that the current epoch of star - formation activity in l1551 may be the result of sequential star - formation induced by the effects of the multiple outflows in the system . the protobinary system in irs 5 has two active jets . the current direction of either of these jets is not aligned with the @xmath102  oriented main co outflow in this region , the latter being driven by the source(s ) at irs 5 . at least at some point in the past , the predominant direction of the jets from the irs  5 system was probably aligned with the bulk molecular outflow direction in l1551 . it has been suggested that l1551 ne was formed in the swept - up shell of gas produced by the irs 5 outflow @xcite . l1551 ne is itself a multiple stellar system , and possesses optical jets , and is thought to power a large - scale hh flow including hh 454 , hh 28 and hh 29 @xcite . the evidence for a co outflow from l1551 ne is not as clear - cut despite many observational attempts to delineate the outflow , mostly because of its similar alignment and close proximity to the main flow from irs 5 . the high angular resolution interferometric observations of @xcite and @xcite show two symmetric cs structures , one eastward from irs  5 near l1551 ne , and thought to be responsible for the formation of l1551 ne , and another near hh 102 . as discussed before , with the presence of a 850 @xmath13 m dust - continuum clump near hh 102 @xcite , it is tempting to suggest that a similar triggering mechanism can be attributed to the ew outflow . it is possible that the same bipolar jet streaming eastward started the star - formation process in l1551 ne , and streaming westward , started the star - formation process in the clump near hh 102 . this new driving source near hh 102 is maybe responsible for the ew flow . this new protostar is obscured in the hh 102 region , and the highly collimated co outflow , and the jet - like characteristics of the ew flow are indeed consistent with a relatively young protostellar system . follow - up high angular resolution observations of the hh 102 region would allow us to probe the possibility that there is a new embedded source near hh 102 . the evidence for sequential star - formation activity is further strengthened by some recent observations of the l1551 region . a new pre - protostellar clump , dubbed l1551-mc has been discovered near hh 265 @xcite using nh@xmath103 observations , and later confirmed @xcite by 850 @xmath13 m continuum observations . l1551-mc is located at the edge of hh 265 , which may be a hh object at the end of a jet arising from a driving source within the hl tau complex ( see figure 17 of @xcite ) . it is possible that the next generation of star - formation in the l1551 molecular cloud could occur at the l1551-mc region .","summary":"we show that systematic errors and biases in the analysis procedures for deriving mass spectra could result in errors in the determination of the power - law indices .","abstract":"we present high sensitivity co  and co  j=1molecular line maps covering the full extent of the parsec scale l1551 molecular outflow , including the redshifted east - west ( ew ) flow . we also present co  j=3  data that extends over a good fraction of the area mapped in the j=1  transition . we compare the molecular data to widefield , narrow - band optical emission in h . while there are multiple outflows in the l1551 cloud , the main outflow is oriented at 50  position angle and appears to be driven by embedded source(s ) in the central irs  5 region . the blueshifted outflowing molecular gas extends to the edge of the molecular cloud and beyond the last hh object , hh 256 . on the contrary , the redshifted molecular gas terminates within the cloud , short of the most distant hh object , hh 286 , which lies well beyond the cloud boundary . the j=3  data indicate that there may be molecular emission associated with the l1551 ne jet , within the redshifted lobe of main outflow . we have also better defined the previously known ew flow and believe we have identified its blueshifted counterpart . we further speculate that the origin of the ew outflow lies near hh 102 . we use velocity dependent opacity correction to estimate the mass and the energy of the outflow . the resulting mass spectral indices from our analysis , are systematically lower ( less steep ) than the power law indices obtained towards other outflows in several recent studies that use a similar opacity correction method . we show that systematic errors and biases in the analysis procedures for deriving mass spectra could result in errors in the determination of the power - law indices . the mass spectral indices , the morphological appearance of the position - velocity plots and integrated intensity emission maps of the molecular data , compared with the optical , suggest that jet - driven bow - shock entrainment is the best explanation for the driving mechanism of outflows in l1551 . the kinetic energy of the outflows is found to be comparable to the binding energy of the cloud and sufficient to maintain the turbulence in the l1551 cloud ."}
{"article_id":"astro-ph0606242","section_id":"i","document":"all l1551 molecular outflows have been mapped at high sensitivities in the co  and co  j=1@xmath00  transitions . follow - up submillimeter observations in co  j=3@xmath02  emission towards a good fraction of the l1551 outflow system were carried out as well . the millimeter and submillimeter data are combined with large - scale , narrow band , optical h@xmath1 images in order to perform a detailed study of the outflows in l1551 . the main conclusions of the paper are summarized below .    1 . the full extent of the main co outflow is 32  ( 1.3 pc ) , and is oriented at @xmath104  position angle . the molecular outflow extent is similar to the optical extent of the flow seen by @xcite . outflowing molecular material extends well beyond the last known hh object , hh 256 in the south - west , but stops short of hh 286 in the north - east . our molecular line maps indicate that hh 286 has completely exited the l1551 cloud most of the co molecular outflow appears to be driven by source(s ) in the irs 5 region . some features , especially in the redshifted lobe of the outflow may be attributed to outflows originating in l1551 ne and the hl tau region . 3 .   our maps cover a much larger extent of the collimated redshifted ew flow . the ew flow is @xmath105 pc in length , and is @xmath106 pc in width . in contrast to earlier studies , the sensitivity in our data reveals that the ew flow extends to high velocities ( 6.5  kms@xmath3  to 20  kms@xmath3 ) . it is suggested that a smaller extent blueshifted component seen in the main northwestern redshifted lobe is the blueshifted counterpart of the ew flow , and that the driving source for the ew flow is close to the location of hh 102 . we refine the procedure of velocity - dependent opacity correction adopted by recent authors to obtain a more accurate determination of outflow mass with velocity . the resultant mass - spectral power law indices are lower ( less steep ) than recently obtained indices towards other outflows . we attribute this systematic difference in power - law index to the better quality of our data , and the more careful approach we use in calculating mass . the resulting mass of the l1551 molecular cloud core is @xmath89  m@xmath101 and the combined mass of the outflows in l1551 is @xmath107  m@xmath101 . 5 .   even for no inclination angle correction , and lower @xmath93 assumption , the kinetic energy of the outflow is comparable to the binding energy of the cloud and there seems to be enough outflow energy to maintain turbulence in the cloud . therefore the parsec scale outflow in l1551 has a potential of making a strong impact on the cloud s evolution and fate . multiple lines of evidence from @xmath65  spectral indices , position velocity plots , and morphological appearance of our multi - wavelength data indicate that the ew molecular outflow is a good example of jet - driven bow shock entrainment . the main molecular outflow in l1551 shows evidence for entrainment from both jet - driven and wind - driven mechanisms . we suggest that new stars are being triggered to form in the l1551 system as a result of the effects of the multiple outflows in the region . we gratefully acknowledge the staff of the hht for their excellent support during observations . dan logan , abby hedden , naomi ridge , and john howe are thanked for helping with part of the hht observations . this work was supported by nsf grant ast 02 - 28993 to the five college radio astronomy observatory . arce , h.  g.  & goodman , a.  a.  2002 , , 575 , 928 arce , h.  g.  & goodman , a.  a.  2001a , , 554 , 132 arce , h.  g.  & goodman , a.  a.  2001b , , 551 , l171 bally , j. , reipurth , b. , lada , c.  j. , & billawala , y.  1999 , , 117 , 410                                                                                                reipurth , b. , yu , k. , heathcote , s. , bally , j. , & rodrguez , l.  f.  2000 , , 120 , 1449 reipurth , b. , rodrguez , l.  f. , anglada , g. , & bally , j.  2002 , , 124 , 1045 reipurth , b. , bally , j. , & devine , d.  1997 , , 114 , 2708                                                        ccccccc a1 b & 4.25 & 15.65 & 111.5 & 3.28 & 12.09 & 88.33 + a2 r & 1.40 & 7.46 & 60.7 & 1.08 & 5.76 & 46.80 + a2 b & 0.53 & 1.52 & 6.2 & 0.41 & 1.17 & 4.75 + a3 r & 0.34 & 1.46 & 8.6 & 0.26 & 1.13 & 6.63 + a3 b & 0.23 & 1.06 & 15.6 & 0.18 & 0.82 & 12.02 + a4 r & 0.59 & 1.92 & 9.82 & 0.46 & 1.48 & 7.57 + bt&4.54 & 15.66 & 116.7 & 3.50 & 12.08 & 90.01 + rt & 2.33 & 10.84 & 79.12 & 1.80 & 8.37 & 61.00 + total & 6.87 & 26.50 & 195.19 & 5.30 & 20.45 & 151.01 + ac & 110 & & 85 & & & +","summary":"we compare the molecular data to widefield , narrow - band optical emission in h . while there are multiple outflows in the l1551 cloud , the main outflow is oriented at 50  position angle and appears to be driven by embedded source(s ) in the central irs  5 region . the blueshifted outflowing molecular gas extends to the edge of the molecular cloud and beyond the last hh object , hh 256 . on the contrary the resulting mass spectral indices from our analysis , are systematically lower ( less steep ) than the power law indices obtained towards other outflows in several recent studies that use a similar opacity correction method . the mass spectral indices , the morphological appearance of the position - velocity plots and integrated intensity emission maps of the molecular data , compared with the optical , suggest that jet - driven bow - shock entrainment is the best explanation for the driving mechanism of outflows in l1551 . the kinetic energy of the outflows is found to be comparable to the binding energy of the cloud and sufficient to maintain the turbulence in the l1551 cloud .","abstract":"we present high sensitivity co  and co  j=1molecular line maps covering the full extent of the parsec scale l1551 molecular outflow , including the redshifted east - west ( ew ) flow . we also present co  j=3  data that extends over a good fraction of the area mapped in the j=1  transition . we compare the molecular data to widefield , narrow - band optical emission in h . while there are multiple outflows in the l1551 cloud , the main outflow is oriented at 50  position angle and appears to be driven by embedded source(s ) in the central irs  5 region . the blueshifted outflowing molecular gas extends to the edge of the molecular cloud and beyond the last hh object , hh 256 . on the contrary , the redshifted molecular gas terminates within the cloud , short of the most distant hh object , hh 286 , which lies well beyond the cloud boundary . the j=3  data indicate that there may be molecular emission associated with the l1551 ne jet , within the redshifted lobe of main outflow . we have also better defined the previously known ew flow and believe we have identified its blueshifted counterpart . we further speculate that the origin of the ew outflow lies near hh 102 . we use velocity dependent opacity correction to estimate the mass and the energy of the outflow . the resulting mass spectral indices from our analysis , are systematically lower ( less steep ) than the power law indices obtained towards other outflows in several recent studies that use a similar opacity correction method . we show that systematic errors and biases in the analysis procedures for deriving mass spectra could result in errors in the determination of the power - law indices . the mass spectral indices , the morphological appearance of the position - velocity plots and integrated intensity emission maps of the molecular data , compared with the optical , suggest that jet - driven bow - shock entrainment is the best explanation for the driving mechanism of outflows in l1551 . the kinetic energy of the outflows is found to be comparable to the binding energy of the cloud and sufficient to maintain the turbulence in the l1551 cloud ."}
{"article_id":"0907.4417","section_id":"i","document":"magnetic nanoparticles ( mnps ) are minute parts of magnetic materials with typical size well below @xmath0 . they are present in different materials found in nature such as rocks , living organisms , ceramics and corrosion products , but they are also artificially made and used as the active component of ferrofluids , permanent magnets , soft magnetic materials , biomedical materials and catalysts . their diverse applications in geology , physics chemistry , biology and medicine renders the study of their properties of great importance both to science and technology .    in geology , the nature and origin of magnetic phenomena related to the presence of magnetite nanoparticles in rocks is of great interest to the palaeomagnetist who searches for the geomagnetic record of rocks . the presence of magnetite particles associated with the trigeminal nerve in pigeons offers a reliable explanation to the earth s magnetic field detection and the consequent navigation capability . in fine arts , magnetic analysis of ancient paintings facilitates the reconstruction of the production techniques of ancient ceramics . in living organisms , the role of ferritin , a magnetic nanoparticle per se , is important among the iron storage proteins . mnps are also used as contrast agents in magnetic resonance imaging . recent work has involved the development of bioconjugated mnps , which facilitated specific targeting of these mri probes to brain tumors . mnps are also used as highly active catalysts which has long been demonstrated by the the use of finely divided metals in several reactions . owing to their high surface - to - volume ratio mnps of iron are more efficient at waste remediation than bulk iron . high density magnetic data storage media provide a major technological driving force for further exploration of mnps . it is expected that if mnps with diameter @xmath1 can be used as individually addressed magnetic bits , magnetic data storage densities of @xmath2 would be achieved , namely an order of magnitude higher than the present record ( moser 2002 ) . mnps have also been demonstrated to be functional elements in magneto - optical switches , sensors based on giant magneto - resistance and magnetically controllable single electron transistor devices .    the most common preparation methods for mnps produce assemblies with different structural and compositional characteristics that depend on the particular method adopted . granular films , ferrofluids and cluster - assembled films are characterized as assemblies with random order in mnp locations , while ordered arrays are found in patterned media ( known also as magnetic dots ) and self - assembled films . the mnp preparation methods are divided to top - down and bottom - up . in top - down methods , the nps are formed from a larger system by appropriate physical processing , such as thermal treatment , etching , etc . in bottom - up methods , the nps are formed by an atomic nucleation process that takes place either in ultrahigh vacuum or in a liquid environment . the latter method relies on colloidal chemistry techniques and presently appears to be the most promising method for production of nanoparticles with extremely narrow size distribution . colloidal synthesis methods combined with self - assembly methods produce mnp samples with both size uniformity and long range structural order . it is worth noticing that structural order in a mnp assembly is a decisive property for production of ultrahigh density storage media . owing to their attractive features and their low cost , colloidal synthesis methods and self - assembly attract presently intense research activity in the field of mnp preparation ( petit 1998 , murray 2001 , willard 2004 , farrell 2005 , darling 2005 ) . the magnetic properties of mnps and their assemblies provide a fascinating field for basic research , which is done on two different scales , the atomic and the mesoscopic . in the atomic scale , the properties of individual mnps are examined and they are revealed in samples with low particle concentration . in the mesoscopic scale , dense samples are examined which exhibit collective magnetic behavior arising from interparticle interactions . the study of the magnetic properties can be naturally divided in the investigation of the ground state configuration ( long range order , disorder , etc ) and the excitations from it . excitations can be either weak , as for example at low temperature and weak external magnetic field , or strong , as for example , close to a thermal phase transition or under a reversing magnetic field . for individual mnps the ground state configuration can differ remarkably from the parent bulk material in various ways . for example , owing to energy balance reasons , the abundance of magnetic domains that form in a bulk magnet can be replaced by a single domain in a mnp , which then becomes magnetically saturated even in the absence of an external magnetic field ( nel 1949 ) . the application of an external field forces the atomic magnetic moments of a single - domain mnp to rotate coherently ( stoner 1948 ) . also , for temperature above a threshold , the direction of particle s magnetization fluctuates at random , making the particle bahave as a molecule with a giant magnetic moment . the applications of this effect , known as superparamagnetism ( bean 1959 ) , are presently a lot , ranging from geology to medicine . finally , we should remark that the above described simplified picture of a single - domain mnp becomes invalid if one considers the crucial effect of the mnp surface . reduced crystal symmetry and chemical disorder close to the surface can produce variations between the surface and interior magnetic structure and modify the overall response of the mnp to an applied field ( kodama 1999 ) .    when mnps form dense assemblies , interparticle interactions produce a collective behavior , by coupling the magnetic moments of individual mnps this fact renders in most cases even the determination of the ground state configuration an intricate physical problem . the collective behavior of dense ( interacting ) assemblies is reflected also on the modified magnetic response of the assembly , compared to isolated mnps . the most complex behavior occurs in samples with random morphology and long - range magnetostatic interactions . various experimental measurements have been proposed to reveal the nature of the interparticle interactions , and various measuring protocols probe different aspects of the collective behavior . on the other hand , analytical models have difficulties in predicting or explaining the magnetic behavior of these interacting mnp assemblies , and most of the curret research relies on numerical simulations .    in this chapter we provide an introduction to the fundamental ideas and concepts pertaining to the magnetic properties of mnp assemblies . emphasis is given to the response of mnp assemblies to an applied magnetic field and the related issue of magnetization reversal . the chapter is organized as follows : in section [ sec_back ] we discuss the magnetic properties of individual ( isolated ) mnps . fist , the condition under which a single - domain mnp is formed is derived , and then the magnetic response under an applied field is examined . the presentation is based on a simple theoretical model ( nel 1949 , stoner 1948 ) . in section [ sec_exp_methods ] we give a brief overview of the most common magnetic characterization techniques and explain the information extracted from each one . in section [ sec_state ] we discuss the response of a dense mnp assembly to a magnetic field , when the interparticle interactions are important and lead to a collective behavior of the mnps . mean - field models are presented and an introduction to modern numerical techniques ( monte carlo , magnetization dynamics ) to tackle this problem are presented . the chapter is summarized in section [ sec_sum ] and the perspectives in this field are presented in sections [ sec_persp ] .","summary":"this chapter provides an introduction to the fundamental physical ideas and models relevant to the phenomenon of magnetic hysteresis in nanoparticle assemblies . modern numerical techniques ( monte carlo simulations , magnetization dynamics ) used to study dense nanoparticle assemblies are presented .","abstract":"this chapter provides an introduction to the fundamental physical ideas and models relevant to the phenomenon of magnetic hysteresis in nanoparticle assemblies . the concepts of single - domain particles and superparamagnetism are discussed . the mechanisms of magnetization by coherent rotation and the role of temperature in the gradual decay of magnetization are analyzed in the framework of simple analytical models . modern numerical techniques ( monte carlo simulations , magnetization dynamics ) used to study dense nanoparticle assemblies are presented . an overview of the most common experimental techniques used to measure the magnetic hysteresis effect in nanoparticle assemblies are presented and the underlying principles are exposed .    department of sciences , school of pedagogical and technological education ( aspete ) , athens 14121 , greece    _ keywords _ : magnetic nanoparticles ; magnetic anisotropy ; dipolar interactions ; magnetic hysteresis ; superparamagnetism ; mean field theory ; monte carlo ; magnetization dynamics"}
{"article_id":"0907.4417","section_id":"i","document":"we have discussed the main theoretical concepts that pertain to the magnetization properties of isolated ( non - interacting ) nanoparticles and their assemblies . we estimated the critical radius for formation of single domain particles and studied the zero - temperature magnetization reversal mechanism of coherent rotation ( stoner - wohlfarth model ) , the thermally activated reversal ( nel - brown model ) and the related phenomenon of superparamagnetism occurring above the blocking temperature . complications arising from size polydispersity , distribution of easy axes directions , and applied field on the relaxation time for magnetization reversal were discussed . two standard experimental techniques for ( static ) magnetic measurements , namely the field and temperature dependence of magnetization were outlined . finally , the subject of interparticle dipolar interactions was introduced along with the most common theoretical techniques used to analyze interacting systems . examples from monte carlo studies of mnp assemblies were given .","summary":"the concepts of single - domain particles and superparamagnetism are discussed .","abstract":"this chapter provides an introduction to the fundamental physical ideas and models relevant to the phenomenon of magnetic hysteresis in nanoparticle assemblies . the concepts of single - domain particles and superparamagnetism are discussed . the mechanisms of magnetization by coherent rotation and the role of temperature in the gradual decay of magnetization are analyzed in the framework of simple analytical models . modern numerical techniques ( monte carlo simulations , magnetization dynamics ) used to study dense nanoparticle assemblies are presented . an overview of the most common experimental techniques used to measure the magnetic hysteresis effect in nanoparticle assemblies are presented and the underlying principles are exposed .    department of sciences , school of pedagogical and technological education ( aspete ) , athens 14121 , greece    _ keywords _ : magnetic nanoparticles ; magnetic anisotropy ; dipolar interactions ; magnetic hysteresis ; superparamagnetism ; mean field theory ; monte carlo ; magnetization dynamics"}
{"article_id":"1402.6136","section_id":"i","document":"_ pursuit / evasion _ ( pe ) and related problems ( search , tracking , surveillance ) have been the subject of extensive research in the last fifty years and much of this research is connected to mobile robotics @xcite . when the environment is represented by a graph , the original pe  problem is reduced to a _ graph game _ played between the pursuers and the evader .    in the current paper , inspired by isler and karnad s recent work @xcite , we study the role of _ information _ in _ cops - and - robber _ ( cr )  games , an important version of graph - based pe . by information we mean specifically the players _ location_. for example , we expect that when the cops know the robber s location they can do better than when the robber is invisible . our goal is to make  precise the term better . reviews of  the graph theoretic cr  literature appear in @xcite . in the classical  cr  variant @xcite it is assumed that the cops always know the robber s location and vice versa . the invisible  variant , in which the cops can not see the robber ( but the robber always sees the cops ) has received less attention in the graph theoretic literature ; among the few papers which treat this case we mention @xcite and also @xcite in which _ both _ cops and robber are invisible . both the visible and invisible cr  variants are natural models for discretized robotic pe  problems ; the connection has been noted and exploited relatively recently @xcite . if it is further assumed that the robber is not actively trying to avoid capture ( the case of _ drunk _ robber ) we obtain a _ one - player _ graph game ; this model has been used quite often in mobile robotics @xcite and especially ( when assuming random robber movement ) in publications such as @xcite , which utilize _ partially observable markov decision processes _ ( pomdp , @xcite ) . for a more general overview of pursuit / evasion and search problems in robotics , the reader is referred to @xcite ; some of the works cited in this paper provide a useful background to the current paper . this paper is structured as follows . in section [ sec02 ] we present preliminary material , notation and the definition of the classical  cr game ; we also introduce several node and edge cr _ variants_. in section [ sec03 ] we define rigorously the _ cop number _ and _ capture time _ for the classical cr game and the previously introduced cr  variants . in section [ sec04 ] we study the _ cost of visibility _ ( _ cov _ ) . in section [ sec05 ] we present algorithms which compute capture time and optimal strategies for several cr  variants . in section [ sec06 ] we further study cov using computational experiments . finally , in section [ sec07 ] we summarize and present our conclusions .","summary":"several of these variants are relevant as models or robotic pursuit / evasion . in this paper","abstract":"the _ cops - and - robber _ ( cr )  game has been used in mobile robotics as a discretized model ( played on a graph ) of _ pursuit / evasion _ problems . the classic  cr version is a _ perfect information game _ : the cops ( pursuer s ) location is always known to the robber ( evader ) and vice versa . many variants of the classic game can be defined : the robber can be _ invisible _ and also the robber can be either _ adversarial _ ( tries to avoid capture ) or _ drunk _ ( performs a random walk ) . furthermore , the cops and robber can reside in either nodes or edges of . several of these variants are relevant as models or robotic pursuit / evasion . in this paper , we first define carefully several of the variants mentioned above and related quantities such as the _ cop number _ and the _ capture time_. then we introduce and study the _ cost of visibility _ ( _ cov _ ) , a quantitative measure of the increase in difficulty ( from the cops point of view ) when the robber is invisible . in addition to our theoretical results , we present algorithms which can be used to compute capture times and cov of graphs which are analytically intractable . finally , we present the results of applying these algorithms to the numerical computation of cov ."}
{"article_id":"1402.6136","section_id":"c","document":"in this paper we have studied two versions of the cops and robber game : the one is played on the nodes of a graph and the other played on the edges . for each version , we studied four variants , obtained by changing the visibility and adversariality assumptions regarding the robber ; hence we have a total of eight cr games . for each of these we have defined _ rigorously _ the corresponding optimal capture time , using game theoretic and probabilistic tools .    then , for the node games we have introduced the adversarial cost of visibility @xmath500 and the drunk cost of visibility @xmath501 . these ratios quantify the increase in difficulty of the cr  game when the cop is no longer aware of the robber s position ( this situation occurs often in mobile robotics ) . we have studied analytically @xmath504 and @xmath505 and have established that both can get arbitrarily large . we have established similar results for @xmath506 and @xmath507 . in addition , we have studied @xmath234 and @xmath507 by numerical experiments which support both the game theoretic results of the current paper and the analytical computations of capture times presented in @xcite . dariusz dereniowski , danny dyer , ryan  m tifenbach , and boting yang , _ zero - visibility cops and robber game on a graph _ , frontiers in algorithmics and algorithmic aspects in information and management , springer , 2013 , pp . 175186 . h.  lau , s.  huang , and g.  dissanayake , _ probabilistic search for a moving target in an indoor environment _ , intelligent robots and systems , 2006 ieee / rsj international conference on , ieee , 2006 , pp . 33933398 . littman , a.r . cassandra , and l.p . kaelbling , _ efficient dynamic - programming updates in partially observable markov decision processes _ , tech . report cs-95 - 19 , comp . science dep . , brown university , 1996 . a.  sarmiento , r.  murrieta , and s.a . hutchinson , _ an efficient strategy for rapidly finding an object in a polygonal world _ , intelligent robots and systems , 2003.(iros 2003 ) . proceedings . 2003 ieee / rsj international conference on , vol .  2 , ieee , 2003 , pp .","summary":"the _ cops - and - robber _ ( cr )  game has been used in mobile robotics as a discretized model ( played on a graph ) of _ pursuit / evasion _ problems . , we first define carefully several of the variants mentioned above and related quantities such as the _ cop number _ and the _ capture time_. then we introduce and study the _ cost of visibility _","abstract":"the _ cops - and - robber _ ( cr )  game has been used in mobile robotics as a discretized model ( played on a graph ) of _ pursuit / evasion _ problems . the classic  cr version is a _ perfect information game _ : the cops ( pursuer s ) location is always known to the robber ( evader ) and vice versa . many variants of the classic game can be defined : the robber can be _ invisible _ and also the robber can be either _ adversarial _ ( tries to avoid capture ) or _ drunk _ ( performs a random walk ) . furthermore , the cops and robber can reside in either nodes or edges of . several of these variants are relevant as models or robotic pursuit / evasion . in this paper , we first define carefully several of the variants mentioned above and related quantities such as the _ cop number _ and the _ capture time_. then we introduce and study the _ cost of visibility _ ( _ cov _ ) , a quantitative measure of the increase in difficulty ( from the cops point of view ) when the robber is invisible . in addition to our theoretical results , we present algorithms which can be used to compute capture times and cov of graphs which are analytically intractable . finally , we present the results of applying these algorithms to the numerical computation of cov ."}
{"article_id":"hep-th0205232","section_id":"c","document":"our aim in this paper has been not only to analyze and solve a fascinating problem in supersymmetric classical mechanics but also to stress the relations between supersymmetric mechanical models in one and more than one dimensions . an example is that the fermionic variables should really be thought of as components of a @xmath276-dimensional vector @xmath277 which moves on a @xmath278-sphere . in the one - dimensional case this means that all fermionic vectors move on circles  which is consistent with our findings in @xcite . furthermore , the motion is coupled to the motion of a purely bosonic vector , made of the dynamical variables @xmath279 and @xmath14 , by the supercharges . while these completely determine the fermionic motion in one dimension we have seen that the situation in higher dimensions is more complicated and the supercharges only prescribe a geometric subspace for the true solution . motion on this subspace is then no longer characterized by the rigid connection of bosonic and fermionic motion found in the one - dimensional case but exhibits a rather interesting time - dependent phase . we have shown that for rotationally invariant scalar potentials there will always be a conserved angular momentum so that to lowest order bosonic motion takes place in a plane . it is not unreasonable to conjecture that for every direction orthogonal to that plane we will have to solve a one - dimensional problem for the fermionic quantities corresponding to that direction  as was the case for the coulomb problem . this leads us to another generalization from the one - dimensional case , namely that trivial solutions to the bosonic equations of motion do not imply that the corresponding fermionic equations can only be solved trivially . in fact , for our particular problem we found that the third components of the fermionic quantities still `` felt '' the presence of the bosonic motion in the plane orthogonal to them . one of the most fruitful ideas for the higher bosonic layers which can be applied in any dimension turned out to be that solutions for these layers are variations of the solutions of the classical problem . while in one dimension every solution can be conveniently described by the energy and some choice for the initial time , in higher dimensions more of these parameters are needed  in case of the coulomb problem we have conveniently related them to the elements describing the classical orbit . so the view taken in @xcite for the one - dimensional case , namely that supersymmetric dynamics captures information over a whole range of _ energies _ of the system , can be confirmed in a more general sense for our higher dimensional model : the bosonic ( but grassmann - valued ) part of the solution describes not only one particular classical solution ( by its component of order zero ) but also includes all possible variations of it with all possible free parameters or , in other words , a bosonic solution corresponds not just to a point in the real parameter space but to something like a fuzzy subset .    for reasons of simplicity we have described in this paper solutions for a grassmann algebra with two generators . from our experience with the one - dimensional model and the clear links that it exhibits to the three - dimensional system we have studied in this paper , we conjecture that the picture for a larger number of generators is similar to that in the one - dimensional case . there we were able to show that solutions to the fermionic equations corresponding to three generators consist of two parts : one that looks like the first order solutions themselves ( i.e. movement on a circle in one dimension ) and one that consists of the _ variations _ of these solutions with energy and initial time . similarly , the bosonic equations for four generators are solved by the first and second variations of the lowest order bosonic solutions _ and _ first variations of the interaction term . it is therefore not unreasonable to assume that the general picture in three dimensions is not much different and that the higher order equations of motion can be solved by a suitable combination of ( first and higher order ) variation terms with respect to the free parameters of the physical model in question .","summary":"after setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their poisson algebra .","abstract":"after setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their poisson algebra . we then apply this information to the investigation and solution of the supersymmetric coulomb problem , specified by an repulsive bosonic potential .    pacs : 45.50.-j ; 11.30.pb    25 pages , 2 figures"}
{"article_id":"astro-ph0211436","section_id":"i","document":"the detection of linear polarization in the radio emission from the galaxy confirmed the synchrotron origin of the emission @xcite . while theory suggested that the polarized fraction at the point of emission could reach @xmath870% , the detected fraction was far lower , and both discovery papers discussed the role of faraday rotation in the interstellar magneto - ionic medium ( mim ) in altering the polarization angle as well as its possible role in reducing the fractional polarization of the received emission . at the point of origin the electric vector is perpendicular to the local magnetic field , but the polarization angle changes as the radiation crosses regions where free electrons and magnetic fields are both present . the extent of this faraday rotation is @xmath17 where @xmath18 ( @xmath19 ) is the electron density , @xmath20 ( @xmath21 g ) is the component of the magnetic field parallel to the line of sight , @xmath22 ( pc ) is the path length , @xmath23 ( m ) is the wavelength , and the quantity rm ( radm@xmath10 ) is denoted the rotation measure . faraday rotation can lead to depolarization , a reduction in the apparent fractional polarization arising from vector averaging within the telescope beam of emission from different regions , or from superposition of emission which has suffered different faraday rotation in separate regions , or a combination of both . there has been a revival of interest in the polarized signals from the galactic `` background '' , based on new observations of high angular resolution made with large single antennas @xcite and with aperture - synthesis telescopes @xcite . a striking property of the polarization images from these observations is the almost complete absence of correlation between regions of polarized emission and features in total intensity . the accepted interpretation of this result states that the appearance of the sky is dominated by faraday rotation in the intervening medium , outweighing the effects of structure in the synchrotron emission regions . the structure in total intensity ( stokes parameter @xmath24 ) is generally smooth , while faraday rotation in the intervening medium imposes structure with fine scale on the linearly polarized emission ( stokes parameters @xmath25 and @xmath26 ) . aperture - synthesis telescopes preferentially detect small - scale structure , and are quite insensitive to the smooth @xmath24 component , leading to apparent fractional polarization in excess of 100% . the structure imposed by faraday rotation is the product of tangled magnetic fields and irregular electron - density distributions that arise from turbulence in the ism . furthermore , most modern radio telescopes are more sensitive to rotation measure than they are to emission measure : an ionized region well below the threshold of detectability in the total - power channel can cause a significant and measurable faraday rotation . polarimetry is consequently a useful new tool for probing the magneto - ionic component of the ism .    in this paper we present polarization images at a frequency of 1420mhz of a region of area 117 deg@xmath1 in the galactic plane ( @xmath2 , @xmath27 ) made as part of the canadian galactic plane survey ( cgps ) . angular resolution is about @xmath28 , an order of magnitude improvement over any existing polarization data for this region . the cygnus region covered by our observations is a very complex one , since the line of sight is nearly along the local arm . in section 2 we describe the processing of the data and the construction of wide - field images . section 3 presents the results and describes some general properties of the polarized emission . in section 4 we develop a general framework for the interpretation of these results . section  5 discusses our rotation measure results , and we proceed in section  6 to a discussion of individual polarization features .","summary":"we develop a conceptual framework for interpretation of the observations . we can detect only that polarized emission which has its origin closer than the _ polarization horizon _ , at a distance ; more distant polarized emission is undetectable because of depth depolarization ( differential faraday rotation ) and/or beam depolarization ( due to internal and external faraday dispersion ) .  depends on the instrument used ( frequency and beamwidth ) as well as the direction being studied . in our data","abstract":"we present 1420mhz ( cm ) observations of polarized emission from an area of 117  deg in the galactic plane in cygnus , covering , , a complex region where the line of sight is directed nearly along the local spiral arm . the angular resolution is , and structures as large as are fully represented in the images . polarization features bear little resemblance to features detected in total power : while the polarized signal arises in diffuse galactic synchrotron emission regions , the appearance of the polarized sky is dominated by faraday rotation occurring in small - scale structure in the intervening warm ionized medium . there is no concentration of polarization structure towards the galactic plane , indicating that both the emission and faraday rotation occur nearby . we develop a conceptual framework for interpretation of the observations . we can detect only that polarized emission which has its origin closer than the _ polarization horizon _ , at a distance ; more distant polarized emission is undetectable because of depth depolarization ( differential faraday rotation ) and/or beam depolarization ( due to internal and external faraday dispersion ) .  depends on the instrument used ( frequency and beamwidth ) as well as the direction being studied . in our data we find thatkpc , consistent with the polarization features originating in the local arm . the filling factor of the warm ionized medium is constrained by our data to be considerably less than unity : polarized signals that pass through multiple regions of faraday rotation experience severe depolarization , but polarized fractions up to% are seen , implying that there are lines of sight that intersect only one faraday rotation region within the polarization horizon . the rotation measure ( rm ) of the extended polarized emission has a distribution which peaks atradm and has a width to half - maximum ofradm . the peak and half - width of the distribution of rms of extragalactic sources in the region areradm andradm respectively . this suggests that rm increases monotonically with length of propagation path through the interstellar medium in this direction .    among localized polarization features that we discuss , g83.2 + 1.8 and g91.8.5 , stand out for their circular or quasi - circular form and extent of more than ; both are probably related to the impact of stellar activity on the surrounding medium , although the stars responsible can not be identified . another polarization feature , g91.5 + 4.5 , extends , and coincides with a molecular cloud ; it plausibly arises in an ionized skin on the outside of the cloud . polarized emission seen across the face of the large , dense region , w80 , must be generated in the 500pc between the sun and w80 , since w80 must depolarize all extended non - thermal emission generated behind it . of the supernova remnants g84.2.8 , g89.0 + 4.7 ( hb21 ) , g93.7.2 ( ctb104a ) , and g94.0 + 1.0 ( 3c434.1 ) , only hb21 and ctb104a show polarized emission ; the other two lie beyond the polarization horizon and their emission suffers beam depolarization . emission from the surrounding medium is depolarized on passage through hb21 ."}
{"article_id":"astro-ph0211436","section_id":"r","document":"before discussing individual polarized regions or `` objects '' , we need to consider the general characteristics of the polarized emission in this part of the sky and establish a conceptual framework within which our results can be understood . we know that synchrotron emission is strongly polarized at its point of origin , but only about half of the area portrayed in figures  [ fig1 ] to [ fig4 ] shows detectable polarization . any interpretation of the polarization phenomena in this direction must explain both regions of high _ and _ low polarized intensity . interpretation of our data thus requires a full consideration of the mechanisms that create small - scale polarization structure and the mechanisms that remove it ( i.e.  depolarization ) . a central issue in interpretation is establishing the distance to the polarization features as this is the key to using the data to examine the physical properties of the mim . the ultimate source of the polarized emission is galactic synchrotron radiation . observations of the synchrotron emission from external galaxies ( e.g. * ? ? ? * ) show a high level of order in magnetic fields in galactic halos and thick disks . based on 408 mhz observations , @xcite have established that the synchrotron emission in the milky way is generated within a thin disk of scale height 180pc , accounting for 10% of the emission , and within a thick disk of scale height 1kpc which provides 90% of the emission ( these heights apply near the solar circle ) . the thin synchrotron disk more or less coincides with the gas disk . observations of external galaxies show magnetic structure usually aligned with the spiral arms , and the fractional polarization is sometimes stronger in inter - arm regions than in the arms themselves @xcite , implying that the irregular component of the field is stronger in the spiral arms , where it is generated by the turbulent motions associated with star formation .    we know from our @xmath24 images that the intensity structure of the synchrotron emission that we are detecting is smooth , but we have no information on the variability of polarization angle at the point of origin because we do not know how smooth the magnetic field is there . however , we can say that the magnetic field can not be completely irregular , or we would not detect any polarized emission at all . we note that we have detected fractional polarization up to about 10% ( calculated as the measured _ pi _ as a fraction of the @xmath24 data with single - antenna data incorporated ) . in the absence of small - scale structure in @xmath24 , we proceed on the assumption that the intrinsic polarization ( i.e.  @xmath25 and @xmath26 ) is smooth or slowly varying . simple considerations give information on the physical location of the polarized emitting regions relevant to our data . we can easily find the galactic plane by inspecting the @xmath24 image , but there is no concentration of polarized structure towards the plane . this suggests that the polarized emission detected in this field must be nearby . ( this is related to longitude : in the cgps data there are regions near @xmath69 where polarized emission appears strongly concentrated near the galactic plane , and so must be more distant ) . if the polarized emission is intrinsically smooth , the small - scale structure observed in @xmath25 and @xmath26 must then be produced by faraday rotation along the propagation path ( the exception is snr emission , where there definitely is fine structure in @xmath24 ) . the faraday rotation occurs in regions of the warm ionized medium ( wim ) , loosely referred to as `` faraday screens '' . the word `` screen '' suggests a thin foreground , distinct from the emitting region , but we consider the term to include deep regions . since synchrotron emission is generated everywhere in the galaxy , the screen will always be an emission region as well . the wim is confined to the galactic thick disk , of height @xmath701kpc @xcite . the filling factor is unknown , but is significantly lower than unity . the uneven distribution of ionized gas is related to star formation in the thin disk , and the effects of stars also create a high degree of disorder in magnetic field structure . we can anticipate that any line of sight will pass through one or more `` cells '' of wim . this is certainly the case for lines - of - sight that traverse the entire galactic disk  nearly all polarized extragalactic sources show significant rm @xcite . faraday rotation alone can not alter the amplitude of the polarized signal , but a number of physical and instrumental effects can reduce the fractional polarization of the recorded signal ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) :    * bandwidth depolarization occurs when the rm is so high that the polarization angle changes significantly across the received bandwidth , and the resulting non - parallel vectors are averaged . * depth depolarization ( also known as differential faraday rotation ) occurs when synchrotron emission and faraday rotation co - exist within the same volume of space . emission generated at different depths along the line of sight suffers different rotation , and vector averaging then reduces the observable polarized intensity . * beam depolarization occurs when many turbulent cells of the ism ( due to internal or external faraday dispersion ) and/or large rm gradients exist within the beam of the telescope , again leading to vector averaging . we need to evaluate each of these mechanisms for the drao synthesis telescope at 1420mhz , and for the region studied here . bandwidth depolarization is not a significant factor in the interpretation of the present data . in band - averaged data a rotation measure of @xmath71radm@xmath10 is required to produce 50% depolarization , with total depolarization occuring when @xmath72radm@xmath10 . the equivalent values in single - band data are @xmath73radm@xmath10 and 6600radm@xmath10 , respectively . for the general ism , @xmath74radm@xmath10 usually holds ( see figure  7 , in which 93% of points lie in that range ) , producing a depolarization of @xmath75% in band - averaged data , and @xmath76% in a single band . an indication of which areas in our data are most affected by bandwidth depolarization can be obtained by comparing the rm image of figure  6 with the band - averaged images in figures  25 . depth depolarization is without doubt a major factor in these data . in a volume of ism with uniform synchrotron emissivity , electron density and magnetic field , the integrated emission is totally depolarized for a path length @xmath77 in this direction the line of sight is very close to the direction of the uniform component of the field ( determined to be @xmath78@xcite ) . we therefore take @xmath79 g , the full value of the uniform component @xcite . we take the mean value of the electron density to be @xmath80@xmath19 , the electron density near the sun from the model of @xcite . then total depth depolarization at 1420mhz occurs over a path length @xmath81kpc . however , we should be careful not to apply this result too literally , since the uniformity assumed in the calculation is very far from the truth . significant though it may be , depth depolarization requires integration along a path of at least 100pc to produce a 10% change in polarized intensity , and therefore can not create arcminute structure on the sky . the presence of widespread small - scale polarization structure requires small - scale structure in faraday rotation _ transverse _ to the line of sight , and under these circumstances beam depolarization becomes significant , and is likely responsible for the smallest - scale structure that we see . the combined effects of depth depolarization and beam depolarization do not allow us to detect polarized emission features that originate beyond a certain distance . this applies equally to supernova remnant emission and to general galactic emission . in particular , beam depolarization will act in the same way on snr emission and on small - scale features generated in a localized faraday screen . we capture these ideas in the concept of the _ polarization horizon _ , and will attempt to establish its distance , @xmath6 . we emphasize that @xmath6 is wavelength dependent , beamwidth dependent , and direction dependent . in particular , a telescope of higher angular resolution will experience less beam depolarization and will `` see through '' to a larger distance and in general , at a fixed angular resolution , an observation at higher frequency will `` see '' to a larger distance . snrs provide a means of estimating the distance to the polarization horizon in our data . all snrs generate polarized emission at source , and are typically bright objects that subtend many beamwidths , but not all snrs in our data have detectable polarized emission . those that are not detected must either be intrinsically faint , or lie beyond the polarization horizon . table  [ tbl-2 ] lists snrs in the range @xmath82 , including some at latitudes beyond the boundaries of the present dataset . data are taken from the catalog of @xcite or from the references given in the table . the most straightforward conclusion from the data of table  [ tbl-2 ] is that the emission from snrs more distant than about 2  kpc is not detected . the weakness of this argument is that a very dense region , w80 , lies in front of three of the snrs in table  [ tbl-2 ] ( g84.2@xmath140.8 , g84.9 + 0.5 , and g85.9@xmath140.6 ) , and it is hardly surprising that beam depolarization occurs on passage of the emission through such a region ( see more detailed discussion in section  6 ) . furthermore , g85.4 + 0.7 and g85.9@xmath140.6 are snrs of very low surface brightness , among the faintest known , and our observations simply do not have the sensitivity to detect polarization from these snrs . this leaves only g94.0 + 1.0 as a reasonably bright snr that lacks detected polarization and is not seen through an region ; its distance is 5.6kpc @xcite , placing it in the perseus arm . ( some polarized emission is seen coincident with both g84.2@xmath140.8 and g94.0 + 1.0 , but is not believed to be associated with the snrs ; see section  6 ) . a safe conclusion is that beam depolarization will eliminate polarization from snrs beyond the local arm in the region we are examining ; i.e.  the polarization horizon is at a few kpc distance , and is likely within the local arm . regions can also be of use in determining @xmath6 . electron densities in regions are much higher than in the surrounding ism , and motions are turbulent , resulting in very tangled magnetic fields . since magnetic fields are frozen into the ionized gas , and move with it , quite high field strengths can result from compression . the resulting high faraday rotation with variations on small spatial scales causes strong beam depolarization , making polarized emission from behind the region undetectable , and creating an area of very low _ pi _ whose outline matches that of the region . this signature effect has been used by @xcite , @xcite , and by @xcite to establish distances to faraday screens , and places a lower limit on @xmath6 . examination of the present data shows that , while there are many bright regions in the field ( see table  [ tbl-1 ] ) , they are _ not _ seen as depolarization features . this implies that the faraday screens which define the polarization structure in this region are significantly _ closer _ to us than the regions , which are mostly at distances of 2 to 3 kpc ( see section  6 for a detailed discussion of w80 , which shows strong coincident polarization ) . thus the regions do not allow us to place a strong limit on @xmath6 . weighing the evidence , we conclude that , for lines - of - sight in the galactic plane in this region , the polarization horizon is probably about 2kpc distant , and all the polarization features seen in figures  [ fig2 ] and [ fig3 ] are generated within the local arm . we note that our coverage in galactic latitude of @xmath27 implies that our lines - of - sight are within the thin disk out to distances of about 2kpc . we are therefore seeing synchrotron radiation that arises predominantly in the thin disk . the drao synthesis telescope at 1420mhz has a much greater sensitivity to rm than to emission measure : it can detect ionized material in its polarization channels which it can not detect in total power . for example , at 1420mhz an ionized region of extent 10pc with @xmath83@xmath19 and @xmath20 = 2@xmath21 g will produce a faraday rotation of @xmath84 , which is easily detectable . this same region produces an emission measure of 2.5@xmath85pc , which is only one tenth of the rms thermal noise in the @xmath24 image . this great sensitivity to faraday rotation , along with the fact that faraday screens do not affect total intensity , leads to the effect remarked on earlier , that the polarized sky has a completely different appearance from the total - intensity sky . while this great sensitivity facilitates study of the mim , it is often impossible to isolate a single region or object causing the faraday rotation along the line of sight . the following conditions are required to generate a polarization feature that is detectable with the synthesis telescope : ( a ) the presence of a faraday screen within the polarization horizon , ( b ) structure within that faraday screen on size scales between @xmath28 and about @xmath5 , and ( c ) the absence of confusing faraday screens along the line of sight . the third point merits some elaboration . faraday screens are transparent structures , and one faraday screen can strongly modify the appearance of another on the same line of sight . for example , the smooth appearance of g91.8@xmath142.5 must be produced by a faraday screen whose structure is extremely smooth . that smooth structure could easily be altered , if not completely obscured , by the presence of another screen anywhere along the line of sight within the polarization horizon , either closer or more distant than g91.8@xmath142.5 , with fine structure . we take the absence of confusing faraday rotation along the line of sight as evidence that the filling factor of ionized gas is quite low . in the same vein , the short path to w80 favours the detection of polarized emission from the foreground mim : along a longer path , the superposition of the effects of several faraday screens could cause partial or total depolarization . this leads us to a conjecture about the regions where we detect only very low levels of polarized emission , the `` empty '' regions . faraday rotation is not absent from these regions , as witnessed by the rms of extragalactic sources seen through them @xcite . small - scale angular structure in faraday rotation exists in many directions , detected through an analysis of the variation of rms between the individual components of extragalactic sources @xcite . small - scale variations are also reported by @xcite . since faraday rotation is present in the `` empty '' regions , and probably has small - scale structure , we interpret the absence of detectable polarization as an indication that a number of patches of wim exist along the line of sight , to the point where the emission is almost totally depolarized . this is still consistent with a low filling - factor for the wim , as there may in fact be no faraday screens within the polarization horizon . that is , we are `` seeing '' the depolarization at the polarization horizon , and any polarized emission arising closer to us is too smooth to be detected by the interferometer .        there have been six discussions of the distance to polarized galactic emission ( including the present work ) on the basis of data obtained with antenna beams smaller than @xmath86 . these results are summarized in table  [ tbl-3 ] . among these results , the present work stands out as showing very nearby emission regions . can this be understood in terms of the conceptual framework that we have outlined above ? the only work that has examined part of the galaxy beyond the solar circle is that of @xcite , also based on cgps data . these authors describe polarized features related to the region w4 ( near @xmath87 ) which is definitely a perseus arm object . w4 is seen as a depolarizing feature , so the polarized emission must arise behind it . in this direction the telescope evidently `` sees through '' the local - arm faraday rotation . there are several reasons to expect the polarization horizon to be closer at @xmath88 to @xmath89 than at @xmath87 . first , the local magnetic field is directed towards @xmath90 @xcite , so that , in the region we are considering , the line of sight is nearly parallel to the uniform component of the field , and faraday rotation will be higher . second , in these directions , the line of sight passes for a considerable distance through the local spiral arm ( or spur ) , which is directed towards @xmath91 . on the other hand , along sight lines toward @xmath92 the path through the local arm is fairly short . furthermore , the line of sight is at an angle of about @xmath93 to the direction of the uniform component of the magnetic field and we expect that rms will be lower ; this is confirmed by @xcite on the basis of analysis of rms of extragalactic sources . inter - arm fields are probably quite smooth , and little depolarization will occur there . in these directions , the polarization horizon at 1420mhz must lie in the perseus arm , or even beyond it . the other work at a wavelength very similar to ours is that of @xcite who looked towards the inner galaxy ( at @xmath94 , almost directly opposite the region consdered by * ? ? ? they estimate that most of the polarized emission is in the crux arm ; surprisingly , they `` see through '' the closer carina arm , although again the large angle to the field direction helps . @xcite used absorption to establish a minimum distance to the polarized emission in one direction in the same field ; absorption by gas in the carina arm was detected , placing the emission regions in or beyond that arm . the extensive surveys of @xcite used shorter wavelengths . because of dependence of faraday rotation on @xmath95 we expect the polarimeter to `` see '' more distant emission . because of the use of single - antenna telescopes , we might expect greater sensitivity to large - scale emission , and @xcite detected an apparently isotropic , and so nearby , component . the emission in the first quadrant mapped by @xcite is associated with the sagittarius arm by the correlation of depolarization with emission . this locates it at distances between 2.5 and 8 kpc . comparing our results with the others listed in table  [ tbl-3 ] , we reach the conclusion that the local arm has a substantial magneto - ionic component , and is a strong faraday rotator . this is contrary to some other ideas of galactic structure around the sun : for example , the electron density model of @xcite shows no enhancement of electron density corresponding to the local arm . there is some low - resolution polarization data for the region discussed here , and we now consider its relevance to the above discussion . @xcite present single - antenna polarization data for most of the northern sky at several frequencies from 408 to 1411mhz ( hereafter the dwingeloo data ) . at the highest frequency the angular resolution is @xmath96 . sampling is irregular , with a minimum interval between points of @xmath66 . in the @xmath97 region considered here there are only 14 data points ; sampling at half - power beamwidth would have given data at about 1300 points . the extreme under - sampling makes a meaningful comparison with our data quite difficult . in a slightly larger area ( @xmath98 ) there are 24 data points at 1411mhz in the dwingeloo data . in that area the average _ pi _ is 0.143k , and the average polarization angle is @xmath99 ( angle increases east of galactic north ) with a scatter of @xmath100 rms . the average angle weighted by _ pi _ is @xmath101 . within the uncertainties , these results are consistent with an electric vector perpendicular to the galactic plane , that is with a magnetic field aligned parallel to the plane . there is reason to believe that the low - resolution data sample very nearby regions ( see section 5 ) .","summary":"there is no concentration of polarization structure towards the galactic plane , indicating that both the emission and faraday rotation occur nearby . we find thatkpc , consistent with the polarization features originating in the local arm . polarized emission seen across the face of the large , dense region , w80 , must be generated in the 500pc between the sun and w80 , since w80 must depolarize all extended non - thermal emission generated behind it . emission from the surrounding medium is depolarized on passage through hb21 .","abstract":"we present 1420mhz ( cm ) observations of polarized emission from an area of 117  deg in the galactic plane in cygnus , covering , , a complex region where the line of sight is directed nearly along the local spiral arm . the angular resolution is , and structures as large as are fully represented in the images . polarization features bear little resemblance to features detected in total power : while the polarized signal arises in diffuse galactic synchrotron emission regions , the appearance of the polarized sky is dominated by faraday rotation occurring in small - scale structure in the intervening warm ionized medium . there is no concentration of polarization structure towards the galactic plane , indicating that both the emission and faraday rotation occur nearby . we develop a conceptual framework for interpretation of the observations . we can detect only that polarized emission which has its origin closer than the _ polarization horizon _ , at a distance ; more distant polarized emission is undetectable because of depth depolarization ( differential faraday rotation ) and/or beam depolarization ( due to internal and external faraday dispersion ) .  depends on the instrument used ( frequency and beamwidth ) as well as the direction being studied . in our data we find thatkpc , consistent with the polarization features originating in the local arm . the filling factor of the warm ionized medium is constrained by our data to be considerably less than unity : polarized signals that pass through multiple regions of faraday rotation experience severe depolarization , but polarized fractions up to% are seen , implying that there are lines of sight that intersect only one faraday rotation region within the polarization horizon . the rotation measure ( rm ) of the extended polarized emission has a distribution which peaks atradm and has a width to half - maximum ofradm . the peak and half - width of the distribution of rms of extragalactic sources in the region areradm andradm respectively . this suggests that rm increases monotonically with length of propagation path through the interstellar medium in this direction .    among localized polarization features that we discuss , g83.2 + 1.8 and g91.8.5 , stand out for their circular or quasi - circular form and extent of more than ; both are probably related to the impact of stellar activity on the surrounding medium , although the stars responsible can not be identified . another polarization feature , g91.5 + 4.5 , extends , and coincides with a molecular cloud ; it plausibly arises in an ionized skin on the outside of the cloud . polarized emission seen across the face of the large , dense region , w80 , must be generated in the 500pc between the sun and w80 , since w80 must depolarize all extended non - thermal emission generated behind it . of the supernova remnants g84.2.8 , g89.0 + 4.7 ( hb21 ) , g93.7.2 ( ctb104a ) , and g94.0 + 1.0 ( 3c434.1 ) , only hb21 and ctb104a show polarized emission ; the other two lie beyond the polarization horizon and their emission suffers beam depolarization . emission from the surrounding medium is depolarized on passage through hb21 ."}
{"article_id":"astro-ph0211436","section_id":"c","document":"we have described the polarization properties at 1420mhz of emission from the galactic plane in a complex region in cygnus , a direction where the line of sight is directed along the local spiral arm . the drao synthesis telescope is extremely sensitive to faraday rotation , allowing the detection of ionized regions which can not be detected by their total - power emission . consequently , the appearance of the polarized sky is dominated by faraday rotation in the warm ionized medium , rather than by structure in the synchrotron emitting regions which are the ultimate source of the radiation . by considering the effects of faraday rotation , we have developed a general framework for understanding our results . a key concept is the _ polarization horizon _  polarization features generated beyond that point can not be detected . the distance to the polarization horizon depends on the wavelength and the telescope beamwidth , and on direction . we have shown that snrs and regions whose distances are known can be used to constrain the distance to the polarization horizon . in this direction , this distance is about 2kpc , and the observed polarization features lie within the local arm . the detectability of polarization features requires the presence of a faraday rotation `` screen '' along the line of sight with structure on a scale that the telescope can detect . if many such screens lie along the line of sight , the detected polarization will be very low . the detection of regions of substantial polarized intensity ( as high as 10% of the smooth galactic synchrotron background ) then implies that the filling factor of faraday screens , and so of the warm ionized medium , is low . the distribution of rm of the extended emission peaks at negative values , but the rms of compact sources in the field tend to be more negative . this implies that , in this direction , rm increases as the propagation path through the ism increases , and is consistent with the absence of a field reversal between the local and perseus arms . rms from single - antenna data are much lower , implying that these observations , with beamwidths of @xmath107 to @xmath66 have detected emission arising at very near distances .    localized features in this region exhibit a surprising variety of attributes , some not seen before . polarized emission is associated with a molecular cloud . a feature larger than @xmath15 displays a sharp circular transition of polarization angle . a feature whose size is nearly @xmath66 has exceptionally smooth polarization structure . we have offered interpretations for some , but not all , of these within the conceptual framework that we have established . while many of the observed phenomena have extents of several degrees , arcminute angular resolution is essential in detecting and understanding them . the two nearby snrs in this direction whose polarized emission can be detected reveal small - scale structure which differs from the polarized emission from their surroundings . nevertheless , it can be difficult to separate polarized emission from snrs from their polarized surroundings , and polarization observations of snrs at frequencies as low as 1420mhz must employ high angular resolution and cover substantial areas of sky to identify clearly any polarization arising in the snr . polarization phenomena which are contained in a more or less circular region on the sky , or have a radial structure , strongly suggest that a star has influenced the surrounding environment . g83.2 + 1.8 and g91.8@xmath142.5 are examples , although in neither case can a central star be found . many more such objects should be investigated closely , with the aim of elucidating the role that stars play in shaping polarization features . the novelty of the polarized sky still presents challenges , and we regard our interpretations of the observed features as provisional . much more work must be done , through the observation of a wider area of the galactic plane , complemented by modelling of the emission and faraday rotation regions . while this one field can not provide a sufficient number of examples to lead to representative astrophysical data , we believe that our approach has laid the foundation for future work . the canadian galactic plane survey is a canadian project with international partners and is supported by the natural sciences and engineering research council of canada . the dominion radio astrophysical observatory is operated as a national facility by the national research council of canada . we have gained insight from discussions with many colleagues , particularly rainer beck , david green , marijke haverkorn , and wolfgang reich . cazzolato , f. , landecker , t.l . , gray , a.d . , and veidt b.g . , in _ galactic radio polarization : a new window on the interstellar medium _ , edited by t.l . landecker , dominion radio astrophysical observatory , penticton , b.c . , canada , 69 , april 2001                        green , d.a . , _ a catalogue of galactic supernova remnants ( 2001 december version ) _ , mullard radio astronomy observatory , cavendish laboratory , cambridge , u.k . , available at http://www.mrao.cam.uk/surveys/snrs/              landecker , t.l . , dewdney , p.e . , burgess , t.a . , gray , a.d . , higgs , l.a . , hoffmann , a.p . , hovey , g.j . , karpa , d.r . , lacey , j.d . , prowse , n. , purton , c.r . , roger , r.s . , willis , a.g . , wyslouzil , w. , routledge , d. , and vaneldik , j.f . 2000 , , 145 , 509        peracaula , m. , taylor , a.r . , bellchamber , t.l . , gray , a.d . , and landecker , t.l . , 1999 , in _ new perspectives on the interstellar medium _ , eds . taylor , t.l . landecker , g. joncas , asp conf . series , 168 , 86                    taylor , a.r . , dougherty , s.m . , gibson , s.j . , peracaula , m. , landecker , t.l . , brunt , c.m . , dewdney , p.e . , gray , a.d . , higgs , l.a . , , kerton , c.r . , knee , l.b.g . , kothes , r. , purton , c.r . , uyaniker , b. , wallace , b.j . , willis , a.g . , martin , p.g . , and durand , d. 2002 ,  submitted                                      lccclc  object & @xmath150 & size & distance &  notes & reference + & & arcmin & kpc & & for distance + cyg - x & 80@xmath119 , 0@xmath119 & 360 @xmath151 360 & 1 to 4 & /snr complex & 1 + w63 & 82.2@xmath119 , 5.3@xmath119 & 95 @xmath151 65 & @xmath82 & snr & 2 + s112 & 83.8@xmath119 , 3.3@xmath119 & 15 & 2.1 & region & 3 + s115 & 84.8@xmath119 , 3.9@xmath119 & 50 @xmath151 25 & 3.0 & region & 3 + w80 & 85@xmath119 , @xmath141@xmath119 & 140 @xmath151 140 & 0.5 & region & 4 + hb21 & 89.0@xmath119 , 4.7@xmath119 & 120 @xmath151 90 & 0.8 & snr & 5 + bg2107 + 49 & 91@xmath119 , 1.7@xmath119 & 40 & 10 & stellar - wind bubble & 6 + ctb102 & 92.9@xmath119 , 2.7@xmath119 & 60 & 5 & region & 7 + nrao655 & 93.4@xmath119 , 1.8@xmath119 & 35 @xmath151 25 & 5.3 & region & 8 + ctb104a & 93.7@xmath119 , @xmath140.2@xmath119 & 80 & 1.4 & snr & 9 + 3c434.1 & 94.0@xmath119 , 1.0@xmath119 & 30 @xmath151 25 & 5.6 & snr & 8 + s124 & 94.6@xmath119 , @xmath141.5@xmath119 & 50 @xmath151 40 & 2.6 & region & 3 +    lccclc  snr & size & distance & 1420mhz polarization &  notes & reference + & ( arcmin ) & ( kpc ) & detected ? & & + g82.2 + 5.3 ( w63 ) & 95 @xmath151 65 & @xmath82 & yes & & 1 + g84.2@xmath140.8 & 20 @xmath151 16 & 4 & no & behind w80 & 2 + g84.9 + 0.5 & 6 & & no & behind w80 & 3 + g85.4 + 0.7 & 40 & 3.8 & no & very faint & 4 + g85.9@xmath140.6 & 25 & @xmath85 & no & very faint & 4 + g89.0 + 4.7 ( hb21 ) & 120 @xmath151 90 & 0.8 & yes & &  5 , 6 + g93.3 + 6.9 ( da530 ) & 27 @xmath151 20 & 3.5 & yes & & 7 + g93.7@xmath140.2 ( ctb104a ) & 80 & 1.4 & yes & & 8 + g94.0 + 1.0 ( 3c434.1 ) & 30 @xmath151 25 & 5.6 & no & & 9 +    ccccllc frequency & beam & @xmath152 & distance & spiral & method & ref + ( mhz ) & ( arcmin ) & ( @xmath119 ) & ( kpc ) &  arm & & + 1420 & 1 & 135 & 2 & perseus & regions & 1 + 1420 & 1 & 82  95 & up to 2 & local & snrs , regions & 2 + 1420 & 6 & 329.5 & @xmath153 & carina & absorption & 3 + 1384 & 1.3 & 325.5  332.5 & 3.5 & crux & pulsar rms , reg . & 4 + 2400 & 10.4 & 238  5 & up to 5 & carina & regions & 5 + & & & & crux & & + 2695 & 4.3 & 5  74 & 2.5 to 8 & sagittarius & depolarization & 6 + & & & & & assoc .","summary":"we present 1420mhz ( cm ) observations of polarized emission from an area of 117  deg in the galactic plane in cygnus , covering , , a complex region where the line of sight is directed nearly along the local spiral arm . polarization features bear little resemblance to features detected in total power : while the polarized signal arises in diffuse galactic synchrotron emission regions , the appearance of the polarized sky is dominated by faraday rotation occurring in small - scale structure in the intervening warm ionized medium . localized polarization features that we discuss , g83.2 + 1.8 and g91.8.5 , stand out for their circular or quasi - circular form and extent of more than ; both are probably related to the impact of stellar activity on the surrounding medium , although the stars responsible can not be identified . of the supernova remnants g84.2.8 , g89.0 + 4.7 ( hb21 ) , g93.7.2 ( ctb104a ) , and g94.0 + 1.0 ( 3c434.1 ) , only hb21 and ctb104a show polarized emission ; the other two lie beyond the polarization horizon and their emission suffers beam depolarization .","abstract":"we present 1420mhz ( cm ) observations of polarized emission from an area of 117  deg in the galactic plane in cygnus , covering , , a complex region where the line of sight is directed nearly along the local spiral arm . the angular resolution is , and structures as large as are fully represented in the images . polarization features bear little resemblance to features detected in total power : while the polarized signal arises in diffuse galactic synchrotron emission regions , the appearance of the polarized sky is dominated by faraday rotation occurring in small - scale structure in the intervening warm ionized medium . there is no concentration of polarization structure towards the galactic plane , indicating that both the emission and faraday rotation occur nearby . we develop a conceptual framework for interpretation of the observations . we can detect only that polarized emission which has its origin closer than the _ polarization horizon _ , at a distance ; more distant polarized emission is undetectable because of depth depolarization ( differential faraday rotation ) and/or beam depolarization ( due to internal and external faraday dispersion ) .  depends on the instrument used ( frequency and beamwidth ) as well as the direction being studied . in our data we find thatkpc , consistent with the polarization features originating in the local arm . the filling factor of the warm ionized medium is constrained by our data to be considerably less than unity : polarized signals that pass through multiple regions of faraday rotation experience severe depolarization , but polarized fractions up to% are seen , implying that there are lines of sight that intersect only one faraday rotation region within the polarization horizon . the rotation measure ( rm ) of the extended polarized emission has a distribution which peaks atradm and has a width to half - maximum ofradm . the peak and half - width of the distribution of rms of extragalactic sources in the region areradm andradm respectively . this suggests that rm increases monotonically with length of propagation path through the interstellar medium in this direction .    among localized polarization features that we discuss , g83.2 + 1.8 and g91.8.5 , stand out for their circular or quasi - circular form and extent of more than ; both are probably related to the impact of stellar activity on the surrounding medium , although the stars responsible can not be identified . another polarization feature , g91.5 + 4.5 , extends , and coincides with a molecular cloud ; it plausibly arises in an ionized skin on the outside of the cloud . polarized emission seen across the face of the large , dense region , w80 , must be generated in the 500pc between the sun and w80 , since w80 must depolarize all extended non - thermal emission generated behind it . of the supernova remnants g84.2.8 , g89.0 + 4.7 ( hb21 ) , g93.7.2 ( ctb104a ) , and g94.0 + 1.0 ( 3c434.1 ) , only hb21 and ctb104a show polarized emission ; the other two lie beyond the polarization horizon and their emission suffers beam depolarization . emission from the surrounding medium is depolarized on passage through hb21 ."}
{"article_id":"gr-qc9905039","section_id":"i","document":"not very much is known about the collision and merger of black holes in general relativity . previous results mainly concern the axisymmetric head - on collision , in which numerical evolution has successfully produced computational space - times @xcite . in recent work @xcite , the geometric details of the event horizon in such a collision , first obtained by locating the horizon in numerical space - times @xcite , has been described in terms of a simple analytic model .    however , the axisymmetry of the head - on collision is a non - generic feature . here we analyze the event horizon for a class of generic examples of black hole collisions and obtain features of the coalescence which differ substantially from the axisymmetric case . the event horizon @xmath0 of a black hole space - time is the boundary of the space - time region visible to observers at future null infinity @xmath1 . assuming that there are no singularities lying on @xmath0 , general theorems @xcite imply that @xmath0 is a null hypersurface whose light rays extend into the past until they either caustic with neighboring rays at a set of points @xmath2 or intersect a non - neighboring ray at a crossover set @xmath3 . together @xmath3 and @xmath2 form the set of points where light rays from outside the black hole join the horizon . catastrophe theory @xcite shows that a caustic set consisting of a single point is structurally unstable , i.e. a small perturbation can produce qualitative changes in the features . this applies to the point caustic associated with black hole formation in the oppenheimer - snyder model of spherically symmetric collapse . the simplest structurally stable caustics are folds and cusps , which are the only stable caustics which can occur in the axially symmetric case . these caustics were found in the numerical studies of the head - on collision of axisymmetric black holes @xcite and in gravitational collapse of an axisymmetric rotating cluster @xcite . an analytic solution of the curved space horizon geometry which reproduces these numerical results has been obtained by a conformal transformation of the intrinsic geometry of the flat space null hypersurface produced by the wavefront emanating from a convex , topologically spherical surface @xmath4 , which is embedded in a euclidean time slice @xmath5 of minkowski space @xcite . the boundary of the past of @xmath6 is generated by null geodesics normal to @xmath4 . the black hole event horizon is modeled conformally on the flat space null hypersurface @xmath7 consisting of the outgoing portion of this causal boundary and its extension to @xmath8 .    followed into the future , @xmath9 expands to asymptotically approach an infinite surface with conformally spherical geometry . the conformal transformation to the curved space horizon @xmath0 is tailored to stop this expansion in accord with the final equilibrium of a black hole . followed into the past , the generators of @xmath7 trace out a smooth null hypersurface with a non - smooth boundary consisting of caustics @xmath2 and crossover points @xmath3 . again followed into the past , the @xmath10 slices @xmath11 of @xmath9 shrink to zero as they pinch off at @xmath2 and @xmath3 . provided the conformal transformation is non - singular and single - valued on @xmath3 , the curved space horizon can be consistently constructed to pinch off at the same caustic and crossover points so that @xmath0 and @xmath9 can be identified . this will be the case considered here , although more general constructions are possible .    as a result of the conformal transformation , the affine parameter @xmath12 along the flat space wavefront has to be replaced by a new affine parameter @xmath13 for the curved space horizon . this new affine parameter @xmath13 is chosen such that the new geometry satisfies the single einstein equation ( the focusing equation ) constraining the intrinsic geometry of the horizon . this equation takes the form of one ordinary differential equation ( ode ) along each ray . the values of the parameter @xmath13 along each ray are uniquely fixed by the conditions that @xmath14 on @xmath4 and @xmath15 as @xmath16 .    because the topology of a spatial slice of a null hypersurface depends on the particular time - slicing , the 2-dimensional leaves of the @xmath17 and @xmath12 foliations have the same topology at late times , but they differ qualitatively at early times where they intersect @xmath2 and @xmath3 . for the head - on collision of axisymmetric black holes , @xmath4 is chosen to be a prolate spheroid and it is the foliation @xmath18 in terms of the curved space affine parameter that gives rise to the pair - of - pants structure of the event horizon @xcite . although the cusps and folds formed in the axisymmetric head - on collision are structurally stable , there is a non - generic line on the symmetry axis whose points are both caustics and crossover points . the horizon pinches off along this line to give rise to the separate black holes . in the absence of axisymmetry this crossover line would be expected to broaden into a 2-surface . generically , the intersection of two 2-surfaces is a curve and it is the history of this curve , as different portions of the wavefront cross , that corresponds to the entire 2-dimensional set of crossover points that initiate a black hole horizon . note that the intersection of two null surfaces , and thus in particular the crossover surface , is generically spacelike . in the axisymmetric head - on collision , this curve degenerates to a point and its history to the line that forms the trouser seam in the pair - of - pants picture .    in the absence of axisymmetry , it has been argued @xcite that in the formation of a generic event horizon toroidal black holes are more probable than spherical black holes and should be observed more frequently in an appropriate time - slicing . this leaves some vagueness as to how toroidal topology fits in with the formation of individual black hole and their coalescence . the main purpose of this paper is to describe and clarify such features of binary black hole formation and coalescence in the generic case where @xmath4 is chosen to be a triaxial ellipsoid . we show that the individual black holes can form with spherical topology but that there is typically an intermediate toroidal epoch as they merge into a final spherical black hole . ( see the discussion in sec . [ sec : discussion ] for the relevance to topological censorship . )    in section [ sec : flat ] we present the essential geometry of the flat space wavefront . in geometric optics , the chief consideration in the study of wavefronts is the 2-dimensional caustic surface where classically the intensity of a beam would be infinite . in contrast , the dominant structure in horizon formation is the crossover set . we first describe some elementary generic properties of this set . then we consider as a particular model the class of wave fronts that emanate from an ellipsoid .    in section [ sec : hor ] we describe the construction of the conformally related horizon and its properties . since the event horizon of a _ black hole _ is defined as the boundary of the past of @xmath8 and naturally calculated in a backwards - in - time fashion , it is conceptually simpler to describe the horizon structure from the time reversed point of view of a _ white hole _ horizon ( the boundary of the future of @xmath19 ) . in this description , the conformally related flat space null hypersurface lies on the ingoing ( future directed ) wavefront from the convex surface @xmath4 . the white hole horizon @xmath20 is a null hypersurface with the property that its surface area decreases into the future and has a a finite asymptotic limit in the past . the generating null rays leave @xmath20 at future endpoints consisting of caustics and crossover points . all our results are easily restated in a time reversed sense to the black hole case . as in section [ sec : flat ] , we first discuss general properties and then specialize to the conformally ellipsoidal case . the phenomenology found for conformally ellipsoidal horizons is presented in section [ sec : results ] , and we conclude with a discussion of our results in sec . [ sec : discussion ] .","summary":"we study event horizons of non - axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non - generic and how new features emerge . most of the details of black hole formation and black hole merger are known only in the axisymmetric case , in which numerical evolution has successfully produced dynamical space - times . , our method produces the familiar pair - of - pants structure found in previous numerical simulations of black hole mergers , as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter . the main purpose of this paper is to show how new  substantially different  features emerge in the non - axisymmetric case . in particular , we show how black holes generically go through a toroidal phase before they become spherical , and how this fits together with the merger of black holes .","abstract":"we study event horizons of non - axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non - generic and how new features emerge . most of the details of black hole formation and black hole merger are known only in the axisymmetric case , in which numerical evolution has successfully produced dynamical space - times . the work that is presented here uses a new approach to construct the geometry of the event horizon , not by locating it in a given spacetime , but by direct construction . in the axisymmetric case , our method produces the familiar pair - of - pants structure found in previous numerical simulations of black hole mergers , as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter . the main purpose of this paper is to show how new  substantially different  features emerge in the non - axisymmetric case . in particular , we show how black holes generically go through a toroidal phase before they become spherical , and how this fits together with the merger of black holes ."}
{"article_id":"astro-ph0607393","section_id":"c","document":"during stellar evolution along the red giant branch the abundance of carbon and nitrogen change due to the extensive convective envelope of the giant dredging material exposed to the cn - cycle to the spectroscopically observable surface . the main nuclei involved in the cn - cycle transmutations are @xmath3c , @xmath18n , and @xmath21c ( with @xmath22n being a very minor constituent ) . this phase of stellar evolution has been labelled first dredge - up , and extensively studied both observationally and theoretically . a simple sketch of first dredge - up would highlight the expectation that @xmath3c nuclei are converted to mostly @xmath18n , with some gain in the @xmath21c abundance , and the @xmath3c/@xmath21c ratio declines . if only the cn - cycle has operated significantly in the stellar matter the total number of c+n nuclei will be conserved , thus , as @xmath3c is converted to @xmath18n the @xmath3c/@xmath18n will be lowered along a nearly predictable relation . the target red giants are all evolved enough that they should have undergone some amount of first dredge - up . the combination of @xmath3c and @xmath18n abundances derived here can be used to quatify the consequence of first dredge - up . conservation of c+n nuclei allows a check on the metallicity , i.e. fe abundance , dependence of [ c+n / fe ] . ignoring @xmath21c , a minor constituent , as we have no @xmath21c information from the observed spectra , calculation of [ @xmath3c+@xmath18n / fe ] reveals no upward or downward trend : @xmath3c+@xmath18n scales as solar with fe . the average [ @xmath3c+@xmath18n / fe]=0.00 @xmath9 0.18 with the scatter of 0.18 dex being consistent within the uncertainties of combining three individual elemental abundances into one ratio . evidence of the first dredge - up in the bulge red - giants is shown in figure 4 ; the top panel plots a(@xmath18n ) versus a(@xmath3c ) . the wavelength intervals observed in this study did not include measurable features with @xmath21c , so the @xmath3c/@xmath21c is not known . the solar point is plotted here with the solid straight line delineating [ @xmath3c / fe ] and [ @xmath18n / fe ] equal to 0.0 . all of the studied bulge red giants fall above the scaled solar line , i.e. , to the @xmath18n - rich zone . the solid curves show lines of constant @xmath3c+@xmath18n , or the so - called cn - mixing lines. although the @xmath21c is not known , its maximum abundance due to h - burning will be only @xmath01/3.5 that of @xmath3c , which is itself depleted in mixed giants . the result of accounting for @xmath21c in figure 4 would flatten slightly the mixing curves as some @xmath3c goes into @xmath21c instead of @xmath18n . nevertheless , the mixing curves provide good approximations to what is observed in the bulge giants . each of the three curves at the lower @xmath3c abundances ( for iv-003 , iv329 , and i-322 ) begin with initial @xmath3c and @xmath18n scaled by the respective fe abundances . the most @xmath3c- and @xmath18n - rich mixing line begins an average fe - abundance representative of the most metal - rich stars . the position of the bulge red giants is similar to what has been found for galactic disk k and m giants ( smith & lambert 1990 ) or even field m - giants in the lmc ( see figure 8 in smith et al . 2002 ) . the @xmath3c - depletion and @xmath18n - enhancements are indicative of cn - cycle material . the conclusion of this investigation of the @xmath3c and @xmath18n abundances is that the @xmath4o abundances in these bulge red giants are not measurably altered from their primordial values , as the mixing is not nearly extensive enough to have altered the initial @xmath4o measurably . the bottom panel of figure 4 shows another view of cn - cycle mixing with all of the bulge giants scaled to a single mixing line . here a solar @xmath3c/@xmath18n=3.16 is taken as the initial value and this ratio declines as @xmath3c is converted to @xmath18n ( or , as [ @xmath3c / fe ] declines ) . the mixing curve is a reasonable approximation to the observed giants . alpha boo is also plotted with its @xmath3c , @xmath18n , and fe abundances derived from the same lines as used for the bulge giants . this comparison bolsters confidence in the analysis and the interpretation that this sample of bulge stars are first dredge - up red giants .      in red giants the c and n abundances are excellent monitors of dredge - up on the red giant branch . in old , low - mass red giants , such as the ones studied here , only the surface abundances of the isotopes of c and n , along with the minor oxygen isotopes @xmath23o and @xmath24o will be altered measurably by internal mixing . when studying low - mass giants it must be noted , however , that significant fractions of globular cluster giants do show @xmath4o depletions that result from destruction by the higher temperature on parts of the cno cycles . the oxygen abundance variations are also observed in globular cluster turn - off and main - sequence stars ( e.g. gratton et al . 2001 ) , thus the globular cluster o - variations arise from chemical evolution seemingly peculiar to them ( smith et al . 2005 ; ventura & dantona 2005 ) . the agreement in the bulge giants with the simple cn - mixing picture , as discussed in the previous section , demonstrates that the @xmath4o abundances have not been altered measurably due to red giant dredge - up .    with confidence that the bulge red giant oxygen abundances represent the original values with which the star was born , they provide one of the key monitors of bulge chemical evolution . oxygen has basically a single nucleosynthetic origin from massive stars and is produced over short timescales . as the iron yields from sn ii are much less than oxygen , with fe being synthesized most effectively in sn ia over a significantly longer timescale , the ratio of o / fe is the best indicator of sn ii to sn ia activity . the galactic disk and halo populations have had numerous published studies with [ o / fe ] versus [ fe / h ] and its overall behavior is fairly well - defined . this is illustrated in the top panel of figure 5 , with [ o / fe ] taken from a number of studies ( edvardsson et al . 1993 ; cunha , smith & lambert 1998 ; melendez , barbuy & spite 2001 ; smith , cunha & king 2001 ; melendez & barbuy 2002 ; fulbright & johnson 2003 ) . the asterisks in this figure are specific stars identified as thick disk stars from bensby , feltzing , & lundstrom ( 2004 ) . the decreasing values of [ o / fe ] as [ fe / h ] increase , for [ fe / h]@xmath25 - 1 , is due to the increased fe production from the onset of sn ia . below [ fe / h ] of @xmath0 -1.0 all galactic stars exhibit an elevated value of [ o / fe ] . the simple exercise of combining oxygen and iron yields ( with the caveat that the fe yields are uncertain in the models ) from the grid of models by woosley & weaver ( 1995 ) , convolved with a standard imf results in a value of [ o / fe]@xmath0 + 0.5 : not very different from the observed halo values .    the beginning of the decrease in [ o / fe ] in the galactic halo occurs at roughly [ fe / h]=-1 . the overall metallicity a population reaches ( caused by sn ii ) when sn ia s begin to contribute to the chemical evolution is sensitive to the efficiency at which gas has been turned into stars . in this simple picture , the offset between the thin and thick disks in the [ o / fe][fe / h ] plane is caused by early , higher star formation rate in the thick disk , relative to the thin disk , with the result that the thick disk was more metal - rich by the time sn ia s began to explode . the solid curve in the top panel of figure 5 is a simple numerical model of chemical evolution assuming no outflows or infalls and instantaneous recycling . the model has been adjusted to approximately follow the evolution from halo to thin disk . the thick disk stars from bensby et al . ( 2004 ) are offset from this curve , with the dashed line a linear fit to the thick disk points . bulge values of [ o / fe ] versus [ fe / h ] are plotted in the bottom panel of figure 5 and can be compared to the halo and disk populations . red giants from this study are the large filled pentagon while the open squares are the recent rich & origlia ( 2005 ) m - giant abundances . the advantage of this study is the wider range in metallicity of targets , while the strong point of rich & origlia is the fairly large number of stars in a limited metallicity range ( providing some limits on the intrinsic scatter in [ o / fe ] in the bulge ) . at [ fe / h]@xmath0 -0.2 to 0.0 , the [ o / fe ] trend indicated by the abundances obtained here seems to be slightly lower ( on average by 0.18 dex ) than the results by rich & origlia ( 2005 ) ; within the uncertainties , however , the abundances in the two studies roughly overlap . the halo and thin disk model curve and the thick disk line are also plotted as references . the lowest - metallicity giant , iv-003 at [ fe / h]=-1.1 , has a [ o / fe ] value that is consistent with the galactic halo . among the more metal - rich bulge giants , there is a significant decline in [ o / fe ] relative to star iv-003 ; the bulge population has undergone evolution in its o / fe ratios . the decline in [ o / fe ] in the bulge is not as large as for the thin disk , but is reminiscent of the thick disk trend . the most straightforward explanation of this trend is that the bulge underwent more rapid metal enrichment than the halo , but that star formation did continue over timescales that may include the onset of sn ia . the chemical evolution of oxygen , the subject of the previous section , is dominated by sn ii and its production is dependent on the mass function of its high - mass parent stars . one strong point of using oxygen to track the formation history of massive stars , with the subsequent dispersal of heavy elements and enrichment of the ism , is that o - yields from sn ii are not very sensitive to the progenitor - star metallicities . the integrated yields of oxygen are determined mostly by the shape of the stellar mass function : the ratios of very massive to less massive sn ii .    moving up the periodic table to study sodium provides different , and in some ways complementary insights into the details of chemical evolution . in most stellar populations studied to date na is , like o , primarily a product of sn ii ( clayton 2003 ) . in globular clusters this may not be the case , but we will discuss the globulars later in this section . the key to sodium s complementarity to an @xmath14-element such as oxygen is that the yields of na from sn ii are quite sensitive to the inital sn ii metallicities . the main source of na is carbon - burning , but at the same time it can be destroyed at these temperatures by proton captures . the final yield from sn ii thus depends on the p / n ratio , which is itself a function of metallicity , decreasing as the overall metallicity increases . figure 6 illustrates the behavior of na and o in various stellar populations and betrays their origins by plotting [ na / o ] versus [ o / h ] . the top panel shows results for field stars of the milky way halo , thick disk , and thin disk as small open circles , with these abundances from reddy et al . ( 2003 ) ; fulbright ( 2000 ) ; fulbright & johnson ( 2003 ) ; nissen & schuster ( 1997 ) ; bensby , feltzing & lundstrom ( 2003 ) ; prochaska et al . the small filled symbols show [ na / o ] and [ o / h ] for the dwarf galaxies sculptor ( circles ; shetrone et al . 2003 ; geisler et al . 2005 ) , carina ( triangles ; shetrone et al . 2003 ) , fornax and leo ( pentagons ; shetrone et al . 2003 ) , and the lmc ( squares ; smith et al . there are two key points to the top panel : 1 ) all of the various populations overlap within the estimated errors of the many analyses ( with the errors shown as representative errorbars ) , and 2 ) these diverse populations define a sequence of increasing na / o with increasing metallicity ( o / h ) . the scatter in [ na / o ] at a given metallicity is not much larger , if at all , than the expected abundance uncertainties . the nearly unique relation of na / o with o / h is dominated by sn ii nucleosynthesis driving their evolution . the large filled pentagons in the top panel of figure 6 are the abundance results for the bulge stars . this sample includes a few quite metal - rich giants and provides values of [ na / o ] at large [ o / h ] , plus sample stars overlap with the less o - rich populations . in the overlap region of [ o / h ] the bulge stars agree well in [ na / o ] versus [ o / h ] with the other populations . near solar metallicity ( [ o / h ] @xmath0 0.0 ) , the bulge stars overlap with the field - star sample but the lowest metallicity bulge star in our sample ( iv-003 ) falls well below the trend . the na i line in this star is very weak and the low na abundance does not result from incorrect stellar parameters . ( see the na i synthesis in figure 2 . ) since the na / o yields from sn ii are metallicity sensitive , the low value of na / o for iv-003 may indicate that the initial enrichment of the bulge to [ o / h ] @xmath0 -1 ( or , [ fe / h ] @xmath0 -1.3 ) was very rapid and dominated by very metal - poor massive stars ( with [ m / h ] less than -2 ) . this would be an example in which a metallicity - dependant ratio ( na / o ) retained the metallicity signature of its parent sn ii , regardless of how polluted the primordial cloud had become from the sn ii ( as measured by [ o / h ] ) . the field star trend , as defined by both the milky way halo and the dwarf galaxies , suggests a less efficient cycling of gas into stars when compared to the metal - poor tail of the bulge population . the trend defined by the highest metallicity bulge stars appears to be a smooth continuation from the lower metallicities . the overall behavior of na / o is suggestive of sn ii dominating the nucleosynthesis of na in the bulge population .    in less massive stars than those that become sn ii , na production is possible via h - burning on the nena - cycle . this can occur at temperatures of a few to several times 10@xmath26k and one byproduct of this process can be @xmath4o depletion due to the on parts of the cno - cycles . in the presence of significant contributions from nena- and cno - cycles ( as an explantion for the large na abundances in the bulge ) would be an expected anticorrelation of o and na . the bottom panel of figure 6 illustrates just such an effect where the same galactic and dwarf galaxy field stars are plotted , as well as the bulge stars , with the addition of stars from two galactic globular clusters ( m13 and m4 as the 4-sided and 3-sided crosses , respectively ) . here the h - burning signature is clear with the expected striking na - o anticorrelations . no such trend is hinted at in this ( admittedly small ) bulge sample , indicating that chemical evolution in na and o for the bulge has been driven largely by sn ii .    in addition , in the bottom panel of figure 6 we also show na and o results for the metal - rich old open clusters ngc 6791 ( peterson & green 1998 ) which agrees with the high sodium found here for the bulge targets . the solid curve plotted in this panel represents the na and o yields from the sn ii models of woosley & weaver ( 1995 ) convolved with a standard , i.e. , salpeter , mass function . the model curve is suggestive of the trend observed in the field stars , open clusters , and bulge stars and , within modest differences , points to sn ii enrichment . it should be mentioned , however , that until more metal - rich sn ii model yields are added to this plot , it may be that the most metal - rich bulge stars could show some contamination in na and o from h - burning in a generation of intermediate mass stars . in addition , because the bulge exhibits an abundance range in fe , as well as a large variation in its na / o values , it may show some similarities in the behavior of these 3 elements to that of the peculiar globular cluster @xmath27 centauri ( norris & da costa 1995 ; smith et al . 2000 ) .      in the majority of stars studied in the milky way field halo and disk populations titanium behaves as an @xmath14-element with respect to iron ( e.g. see review by mcwilliam 1997 ) . this statement can be illustrated in figure 7 ( top panel ) with [ ti / fe ] plotted versus [ fe / h ] and the galactic field stars shown as the small symbols . the galactic results are taken from gratton & sneden ( 1988 ) ; edvardsson et al . ( 1993 ) ; mcwilliam et al . ( 1995 ) ; prochaska et al . ( 2000 ) ; carretta et al . ( 2002 ) ; fulbright ( 2002 ) ; johnson ( 2002 ) ; bensby et al . ( 2003 ) ; reddy et al . ( 2003 ) . at metallicities with [ fe / h]@xmath28 - 0.6 to -0.8 , [ ti / fe ] is elevated at a nearly constant plateau of @xmath0 + 0.3 dex . at increasing fe abundances there is a rapid , perhaps even abrupt decline in [ ti / fe ] to near - solar ratios , with a roughly constant [ ti / fe]@xmath00.0 over [ fe / h]= -0.5 to + 0.4 . other populations are also illustrated in the top panel of figure 7 with the large filled circles being sculptor ( shetrone et al . 2003 ; geisler et al . 2005 ) and the large filled squares the lmc ( smith et al . these two dwarf galaxies do not track the galactic trend , with both smaller galaxies exhibiting the decline in [ ti / fe ] at lower values of [ fe / h ] when compared to the milky way disk and halo fields . the bulge stars in figure 7 are the large filled pentagons ( plotted with error bars ) and they define a somewhat different trend than any of the other populations . there is a tendancy of the bulge red giants to continue with elevated [ ti / fe ] values past the downturn shown by the halo - disk field stars ( but the results presented here are based on a small number of 7 stars ) . the behavior of [ ti / fe ] as a function of [ fe / h ] in the bulge is reminiscent of that of [ o / fe ] . the suggestion would be that the bulge underwent a more rapid metallicity enrichment from sn ii than the halo , but in the most metal - rich bulge stars there is a decline in [ @xmath14/fe ] ( found in our sample for both o and ti ) . the bottom panel of figure 7 shows the same stars as in the top panel but now plotted as [ ti / o ] versus [ o / h ] . as in figure 6 , replacing fe with o in the comparisons removes to some approximation the role of sn ia and focusses on the role of sn ii . as in the comparison of [ na / o ] versus [ o / h ] , the various stellar populations now fall along a similar trend , in this case one of an increase of [ ti / o ] as metallicity , i.e. [ o / h ] , increases . this behavior was not expected based on the sn ii model yields , which are plotted in this panel as the solid curve . this curve is defined by the woosley & weaver ( 1995 ) yields convolved with a salpeter mass function at each metallicity . given the large number , and varied natures of the studies plotted here , the scatter in [ ti / o ] at a given [ o / h ] is not large ( @xmath0@xmath90.25 dex ) . the lower - metallicity bulge stars studied here fall right in the trend defined by the galactic halo - disk field stars . the metal - rich bulge stars continue as an extension of this trend . the small cluster of metal - rich disk stars ( with [ o / h]@xmath250.0 ) are from bensby et al . ( 2003 ) and agree well with the metal - rich bulge stars . titanium is a product of explosive si - burning , probably as a result largely of sn ii , with the dominant @xmath29ti isotope derived from the production and subsequent decay of @xmath29cr . the smooth trend defined by the populations of sculptor , the lmc , the galactic field stars , and the bulge all point to one source and would suggest sn ii . we offer no explanation for the trend in [ ti / o ] but point out the significant trend in [ ti / si ] as a function of galactocentric distance in galactic globular clusters noted by lee and carney ( 2002 ) .","summary":"the evolution of c and n abundances in the studied red - giants show that their oxygen abundances represent the original values with which the stars were born . oxygen is a superior element for probing the timescale of bulge chemical enrichment via [ o / fe ] versus [ fe / h ] . the [ o / fe]-[fe / h ] relation in the bulge does not follow the disk relation , with [ o / fe ] values falling above those of the disk . titanium also behaves similarly to oxygen with respect to iron . based on these elevated values of [ o / fe ] and [ ti / fe ] extending to large fe abundances , it is suggested that the bulge underwent a more rapid chemical enrichment than the halo . in addition , there are declines in both [ o / fe ] and [ ti / fe ] in those bulge targets with the largest fe abundances , signifying another source affecting chemical evolution : perhaps supernovae of type ia . sodium abundances increase dramatically in the bulge with increasing metallicity , possibly reflecting the metallicity dependant yields from supernovae of type ii , although na contamination from h - burning in intermediate mass stars can not be ruled out .","abstract":"we present chemical abundances in k and m red - giant members of the galactic bulge derived from high - resolution infrared spectra obtained with the phoenix spectrograph on gemini - south . the elements studied are carbon , nitrogen , oxygen , sodium , titanium , and iron . the evolution of c and n abundances in the studied red - giants show that their oxygen abundances represent the original values with which the stars were born . oxygen is a superior element for probing the timescale of bulge chemical enrichment via [ o / fe ] versus [ fe / h ] . the [ o / fe]-[fe / h ] relation in the bulge does not follow the disk relation , with [ o / fe ] values falling above those of the disk . titanium also behaves similarly to oxygen with respect to iron . based on these elevated values of [ o / fe ] and [ ti / fe ] extending to large fe abundances , it is suggested that the bulge underwent a more rapid chemical enrichment than the halo . in addition , there are declines in both [ o / fe ] and [ ti / fe ] in those bulge targets with the largest fe abundances , signifying another source affecting chemical evolution : perhaps supernovae of type ia . sodium abundances increase dramatically in the bulge with increasing metallicity , possibly reflecting the metallicity dependant yields from supernovae of type ii , although na contamination from h - burning in intermediate mass stars can not be ruled out ."}
{"article_id":"math0607289","section_id":"i","document":"all algebras and operads in this paper are defined over the field of rational numbers @xmath0 .      the following series of quadratic algebras are well known .    the _ orlik  solomon algebra _ @xmath1 is a super - commutative associative algebra with odd generators @xmath2 , @xmath3 , and relations @xmath4 the _ even orlik  solomon algebra _ @xmath5 is a super - commutative associative algebra with even generators @xmath2 , @xmath3 , and relations @xmath6    these algebras are closely related to the type @xmath7 hyperplane arrangements . the orlik  solomon algebra @xmath1 is isomorphic to the cohomology algebra of the complement of the arrangement @xmath8 over the complex numbers ( see @xcite , @xcite ) , while the even orlik  solomon algebra @xmath5 gives a graded version of the algebra of locally constant functions on the complement of the arrangement @xmath8 over the real numbers ( see @xcite ) . [ os ] @xmath9    another interpretation of the orlik  solomon algebras was found in @xcite . one of the central results in @xcite is the computation of the homology for the ( topological ) operad of little discs . this homology ( being an operad itself ) turns out to be isomorphic to the gerstenhaber operad ( which is a graded version of the poisson operad ) . since components of the operad of little discs are homotopically equivalent to the complements of complex hyperplane arrangements , cohomology algebras of these components are isomorphic to orlik  solomon algebras . thus there exists a cooperadic structure on the collection of orlik  solomon algebras . the even orlik  solomon algebras are also equipped with a cooperadic structure ( and the dual operad is the poisson operad ) . we show how these structures themselves can be used to compute the dimensions and monomial bases for these algebras . the main results of our paper deal with the following generalisations of these algebras suggested by b.l.feigin . these algebras are related to some other quadratic algebras introduced by a.n.kirillov @xcite . both our algebras and the `` diagonal coinvariants '' of haiman @xcite coincide with certain quotients of kirillov s algebras , and this could possibly lead to some new interpretation of diagonal coinvariants .    the _ double orlik  solomon algebra _ @xmath10 is an associative super - commutative algebra with odd generators @xmath2 , @xmath11 , @xmath3 , and relations @xmath12 the _ double even orlik  solomon algebra _ @xmath13 is an associative super - commutative algebra with even generators @xmath2 , @xmath11 , @xmath3 , and relations @xmath14    the main result of this paper is    [ os2 ] @xmath15    there exists a neater way to describe the relations for @xmath13 . let @xmath16 . then the relations mean that for each choice of coefficients @xmath17 and @xmath18 the elements @xmath19 satisfy the relations of  @xmath5 . the analogous description for @xmath10 fails : due to skew - commutativity , the relations @xmath20 do not follow . remarkably , the algebra obtained from the algebra @xmath1 in a similar way seems to be very interesting as well . for example , its dimension is conjectured to be @xmath21 ( a.n.kirillov ) , which is also the conjectured dimension of the space of `` three - diagonal harmonics '' @xcite .    unfortunately , we do not know of any relationship between these algebras and hyperplane arrangements . nevertheless , collections of these algebras form cooperads , and we can use operadic formalism to prove our theorem . it turns out that there exists a natural pairing between even orlik  solomon algebras and components of the bi - hamiltonian operad . this operad ( introduced in @xcite ) corresponds to algebraic structures arising on the ring of functions on a manifold equipped with two compatible poisson brackets . thus we also obtain additional structures on the bi - hamiltonian operad . our results provide another interpretation of the hopf operad structure on this operad analogous to a well known hopf operad structure on the poisson operad . ( existence of a hopf structure means that the tensor product of two bi - hamiltonian algebras naturally possesses a structure of a bi - hamiltonian algebra . )    all known proofs for ordinary orlik  solomon algebras do not work in our case . the problem is that our algebras are not of pbw type ( @xcite ) : in fact , they are not koszul ; the algebra @xmath22 has betti number @xmath23 , and the algebra @xmath24 has betti number @xmath25 ( both were computed by a.n.kirillov @xcite using the ` bergman ` computer algebra system ) . thus there is no straightforward reduction of the problem to a combinatorial problem on monomial algebras . the paper is organised as follows . in section [ operad ] we recall the necessary definitions . the details can be found in @xcite . in section [ graph ] we fix some notation for the various types of graphs used in our proofs . to make the proof more transparent , we include a new proof of theorem [ os ] ( where we make use of known facts about the poisson operad ) in section 4 . in section [ bihamiltonian ] we prove theorem [ os2 ] . in fact , in both cases we prove only the part concerning the even orlik  solomon algebras ; the other case is similar , and proofs are omitted . first of all , we prove upper bounds on the dimensions of our algebras . to do this , we take a basis of the bi - hamiltonian operad and introduce a bijection between this basis and a certain set of monomials in our algebras , and then show that these monomials form a spanning set for our algebras . ( these monomials are indexed by some special kind of graphs . ) we then prove a lower bound . we define a pairing between our algebras and components of the bi - hamiltonian operad . it remains to prove that this pairing is non - degenerate . to do this , we introduce a linear ordering of our basis in the bi - hamiltonian operad and the constructed spanning set of our algebras and then show that the corresponding pairing matrix is non - degenerate . [ the proof for the double orlik  solomon algebras is essentially the same , but one has to replace the bi - hamiltonian operad by the bi - gerstenhaber operad . ]      we are grateful to b.feigin and a.n.kirillov for numerous useful discussions . the second author is thankful to a.szenes and m.vergne for their interest in his work . we would like to thank the referees for several helpful remarks . we are also thankful to alexander frolkin for improving the language of our original text and for several typesetting hints . the work of the second author is partially supported by intas grant no.03 - 3350 and a liegrits fellowship ( contract no.mrtn-ct-2003-505078 ) . the work of the third author is partially supported by intas grant no.03 - 3350 and rfbr grant 04 - 02 - 16538 .","summary":"we prove the conjectures on dimensions and characters of some quadratic algebras stated by b.l.feigin . it turns out that these algebras are naturally isomorphic to the duals of the components of the bi - hamiltonian operad .","abstract":"we prove the conjectures on dimensions and characters of some quadratic algebras stated by b.l.feigin . it turns out that these algebras are naturally isomorphic to the duals of the components of the bi - hamiltonian operad ."}
{"article_id":"astro-ph0502268","section_id":"i","document":"supernova 1987a , the first naked - eye supernova ( sn ) in four centuries , was first discovered on 1987 feb . 24.23 at the las campanas observatory ( shelton 1987 ) , and was later identified with the large magellanic cloud ( lmc ) progenitor , sk @xmath8202 @xcite , a b3 i supergiant @xcite . from its spectral type and distance , we infer a luminosity of @xmath9 , a surface temperature 1500018000  k , and a radius @xmath10 , which imply that the star exploded as a blue supergiant ( or bsg ; * ? ? ? spectra taken shortly after the explosion was discovered revealed balmer lines , indicating a type ii sn , but expanding at nearly @xmath11 . a number of anomalies , such as this high expansion velocity , a weak initial outburst , a very hot uv spectrum at early times , and subsequent rapid color evolution , indicated a compact progenitor envelope , typical of a bsg , rather than the expected red supergiant ( rsg ) progenitor . heavy mass loss could have driven sk @xmath8202 to the bsg stage ( mass loss being reasonable given the large number of wolf - rayet stars in the lmc ) , although evidence for a substantial envelope ( the long slow rise of the optical light source , the late appearance of near - ir h lines and a lack of early escape x and @xmath12-rays ) also exists . for a complete accounting , see the review by @xcite . @xcite reported narrow uv emission lines in _ international ultraviolet explorer _ spectra taken on day 80 , which they interpreted as arising from pre - existing cs material . an analysis of these spectra by @xcite revealed a large overabundance of nitrogen , suggesting both significant cno processing by the progenitor , and that a reasonable fraction of the progenitor s hydrogen envelope had to have been ejected to reveal such material . this argues that the star first evolved into a rsg before returning to the blue in a so - called `` blue loop '' @xcite . both rsg @xcite and bsg @xcite stars are known within the lmc , thus this evolutionary sequence is consistent with known populations . the first resolved images of this cs material were taken on days 750 @xcite and 1027 @xcite , showing a central , elliptical structure , surrounded by two outer loops @xcite . the geometry of this material was the subject of some debate , remaining poorly understood until _ hubble space telescope _ ( _ hst _ ) imaging ( * ? ? ? * and references therein ) clearly revealed a dense circumstellar equatorial ring ( er ) flanked by two larger outer rings ( ors ) , as shown in figure [ pcmap ] . to explain how a mass - losing supergiant produced this nebula , most authors invoke the interacting stellar winds scenario @xcite , in which colliding winds from the bsg and rsg mass - loss stages conspire to create three ring - like overdensities within the cs environment ( cse ) . these were ionized by the sn light pulse and are observed today through recombination cooling . field surrounding sn  1987a , taken in f656n ( h@xmath13 and ) . north is up , east is left . the er ( central ring ) surrounds the ejecta from the sn ( center ) , and is flanked by the north and south ors ( nor and sor , respectively ) . the companion stars 2 and 3 @xcite are positionally coincident along the line of sight . to increase the display range , the er has a separate color stretch . [ pcmap ] ]    since the sn lightcurve was strongly peaked for a finite duration , and the progenitor is surrounded by a structured cse , we expect that the light pulse will scatter off of surrounding reflective material ( e.g.,dust ) , producing `` light echoes '' that are observable long after the sn has faded @xcite . @xcite , @xcite , and @xcite discovered a light echo at @xmath14 whose position agrees well with the predicted location of a contact discontinuity ( cd ) between the rsg outflows and the interstellar bubble formed by the early - type blue ms progenitor s winds @xcite . crotts et al . ( e.g. , * ? ? ? * ; * ? ? ? * hereafter ckh95 ) have continued to search for light echoes in a regular campaign using emission - suppressed continuum imaging . they have found echoes indicative of the structure of the three - ring nebulosity , forming an equatorial waist and sides of an hourglass , yet ending abruptly near the ors with no capping surface . outside this inner nebula , they found four additional features : ( 1 ) a reconfirmation of the cd light echo of @xcite at @xmath15 ; ( 2 ) a sheet along the equatorial plane of the er , bisecting the nebula ; ( 3 ) diffuse flux from the hourglass nebula to the cd ; and ( 4 ) a discontinuity in this nebula , called `` napolean s hat '' @xcite . observation and modeling of this circumstellar environment provide a unique opportunity to reconstruct the mass - loss history of the progenitor . the sn  1987a nebula is one example of a much larger class of bipolar outflows , which occur in nearly all evolved stars ( e.g.,luminous blue variables , b[e ] stars , agb mass loss , bipolar and asymmetric planetary nebulae ) . this `` stellar paleontology '' is of immense importance for understanding bipolar - outflow and bipolar - nebula formation mechanisms , not just of this object or in intermediate - to - high mass stars , but in stars of all masses . we summarize in this paper an observational effort , at the highest sensitivity and resolution to date , to understand more fully the entire circumstellar environment of sn  1987a , and to recreate a more complete history of the progenitor s mass - loss , as revealed by light echoes in 16 years of optical imaging . after introducing echoes in  [ sec - le ] , we summarize the data and reduction in  [ sec - echodata ] . these data are used to build a complete model of all material within @xmath1630 ly of the sn , the 3-d analyses of which are summarized in  [ sec - cse ] , followed by the dust properties in  [ sec - density ] . full details of these sections are presented in ( * ? ? ? * hereafter paper ii ) .    with a much greater volume of the progenitor s cse revealed , we find that no extant model adequately explains how that environment was formed . in  [ sec - echointerp ] , we review and critique formation scenarios for this system , including the progenitor s ms wind , interacting supergiant winds , wind - compressed disks , and the influence of a binary companion . we use the light - echo data to constrain the parameter space of these models , and we qualitatively sketch a hybrid formation sequence for the entire cse in  [ sec - evol ] . it is our hope that the results presented here will serve as a significantly - improved set of constraints for hydrodynamic models of the cse formation , for stellar - evolution models of the progenitor , and for addressing the general question of asymmetric and bipolar stellar outflows .","summary":"we summarize the analysis of a uniform set of both previously - known and newly - discovered scattered - light echoes , detected within 30of sn  1987a in ten years of optical imaging , and with which we have constructed the most complete three - dimensional model of the progenitor s circumstellar environment . surrounding the sn is a richly - structured bipolar nebula . an outer , double - lobed `` peanut , '' which we believe is the contact discontinuity between the red supergiant and main sequence winds , is a prolate shell extending 28 ly along the poles and 11 ly near the equator . the 3-d geometry of the three circumstellar rings is studied , suggesting the northern and southern rings are located 1.3 and 1.0 ly from the sn , while the equatorial ring is elliptical ( ) , and spatially offset in the same direction as the hourglass .","abstract":"we summarize the analysis of a uniform set of both previously - known and newly - discovered scattered - light echoes , detected within 30of sn  1987a in ten years of optical imaging , and with which we have constructed the most complete three - dimensional model of the progenitor s circumstellar environment . surrounding the sn is a richly - structured bipolar nebula . an outer , double - lobed `` peanut , '' which we believe is the contact discontinuity between the red supergiant and main sequence winds , is a prolate shell extending 28 ly along the poles and 11 ly near the equator . napoleon s hat , previously believed to be an independent structure , is the waist of this peanut , which is pinched to a radius of 6 ly . interior , the innermost circumstellar material lies along a cylindrical hourglass , 1 ly in radius and 4 ly long , which connects to the peanut by a thick equatorial disk . the nebulae are inclined 41south and 8east of the line of sight , slightly elliptical in cross section , and marginally offset west of the sn . the 3-d geometry of the three circumstellar rings is studied , suggesting the northern and southern rings are located 1.3 and 1.0 ly from the sn , while the equatorial ring is elliptical ( ) , and spatially offset in the same direction as the hourglass . dust - scattering models of the observed echo fluxes suggest that between the hourglass and bipolar lobes : the gas density drops from 13 to ; the maximum dust - grain size increases fromto 2 ; and the silicate : carbonaceous dust ratio decreases . the nebulae have a total mass of , yielding a red - supergiant mass loss around  yr . we compare these results to current formation models , and find that no model has successfully reproduced this system . however , our results suggest a heuristic evolutionary sequence in which the progenitor evolves through two `` blue - loops , '' perhaps accompanied by a close binary companion ."}
{"article_id":"0804.3966","section_id":"i","document":"the detailed distribution of stars in galaxies gives vital information regarding their formation and subsequent evolution . of particular interest are the oldest stellar populations , which in the milky way are the thick disk and halo . these old components provide the best record of early galaxy assembly . originally detected in edge - on s0 galaxies @xcite , thick stellar disks have now been found in a wide variety of galaxies  s0 s @xcite , sb s @xcite , and later type galaxies @xcite . observations with hst have allowed thick disks in other galaxies to be studied as resolved population @xcite , while observations at high redshift show potential thick disks in the process of forming @xcite . the most detailed studies of thick disks come from observations within the milky way . since its discovery @xcite , the mw thick disk has been found to be structurally , chemically , and kinematically distinct from the thin disk . structurally , star counts with large surveys such as sdss and 2mass reveal the galaxy is best fit with two disk components ( e.g. , * ? ? ? * ; * ? ? ? chemically , thick disk stars are more metal - poor and older than stars in the thin disk ( e.g. , * ? ? ? * ; * ? ? ? they are also significantly enhanced in @xmath0-elements , compared to thin disk stars of comparable iron abundance @xcite . kinematically , thick disk stars have both a larger velocity dispersion and slower net rotation than stars in the thin disk @xcite . all of these facts lead to the conclusion that the thick disk is a relic of the young galaxy . as such , it provides an excellent probe of models of disk galaxy formation ( see reviews by @xcite ) . given these systematic differences between their properties , thick and thin disks are likely to have distinct formation mechanisms . the structure , dynamics , and chemical abundance of the thin disk strongly suggest that the majority of its stars formed gradually from a thin rotating disk of high angular momentum gas @xcite . in contrast , the formation of the thick disk is still poorly constrained and is likely to be more complex . thick disk formation models can be grouped into three broad categories . in the first , a previously thin disk is kinematic heated . in this scenario , stars form in a thin disk and increase their velocity dispersion with time . this vertical heating can be rapid , due to interactions and mergers @xcite or gradual , due to scattering off giant molecular clouds , spiral arms , and/or dark matter substructure @xcite . in the second formation scenario , stars `` form thick '' with star formation occurring above the midplane of the galaxy @xcite or form with large initial velocity dispersions in large stellar clusters @xcite . in the final class of models , thick disk stars are directly accreted from satellite galaxies . numerical simulations have shown that stars in disrupted satellite galaxies can be deposited onto thick disk like orbits @xcite , producing extended stellar debris such as seen around m31 @xcite . while these models were originally developed to explain the origin of the mw thick disk , they should work equally well for thick disks in other galaxies . measuring the kinematics of thick disk stars is one of the best discriminators between the formation models . if the thick disk forms from a heated thin disk , we expect the kinematics of the two components to be closely related . on the other hand , if the thick disk stars form outside the galaxy and are later accreted , we could find systems where the thick disk kinematics are completely decoupled from the thin disk .    in this paper , we present observations of stellar and gas kinematics in nine edge - on systems as part of our continuing analysis of thick disks in a large sample of edge - on galaxies @xcite . compared to @xcite , which presented the first two galaxies in this study , we have improved the analysis techniques and significantly expanded our sample size .","summary":"we present kinematic measurements of thin and thick disk components in a sample of nine edge - on galaxies .","abstract":"we present kinematic measurements of thin and thick disk components in a sample of nine edge - on galaxies . we extract stellar and ionized gas rotation curves at and above the galaxies midplanes using the ca ii triplet absorption features and h emission lines measured with the gmos spectrographs on gemini north and south . for the higher mass galaxies in the sample , we fail to detect differences between the thin and thick disk kinematics . in the lower mass galaxies , there is a wide range of thick disk behavior including thick disks with substantial lag and one counter - rotating thick disk . we compare our rotation curves with expectations from thick disk formation models and conclude that the wide variety of thick disk kinematics favors a formation scenario where thick disk stars are accreted or formed during merger events as opposed to models that form thick disks through gradual thin disk heating ."}
{"article_id":"1408.6196","section_id":"i","document":"let @xmath0 be a simple undirected graph . an edge @xmath8 _ dominates _ itself and all edges sharing a common endpoint with it . a subset @xmath9 of edges is called an _ edge domination _ if each edge in the graph is dominated by at least one edge in @xmath4 . an edge domination @xmath4 is called _ efficient _ if each edge in the graph is dominated by exactly one edge in @xmath4 . a graph has many edge dominations but may not have an efficient edge domination . to find an optimal edge domination or an efficient edge domination in a graph is a hard problem and this problem finds applications in the fields of design and analysis of communication networks , network routing and coding theory  @xcite . note that an efficient edge domination is an induced matching in the graph such that each edge is dominated by exactly one edge in it . so an efficient edge domination is also called a _ dominating induced matching_. the dominating induced matching problem ( dominating induced matching ) , also called efficient edge domination in the literature , is to check whether a graph admits a dominating induced matching or not . this problem has been extensively studied , especially in terms of the computational complexity of it in different graph classes  @xcite . grinstead et al . @xcite first established the np - hardness of this problem . later it is was further shown to be np - hard even in planar bipartite graphs of maximum degree 3  @xcite and @xmath10-regular graphs for @xmath11  @xcite . on the other hand , this problem is polynomial - time solvable in many graph classes such as at - free graphs  @xcite , hole - free graphs  @xcite , @xmath12-free graphs  @xcite , and claw - free graphs  @xcite .    in terms of exact algorithms , the edge domination problem , a problem of finding an edge domination of minimum size , has been extensively studied  @xcite . most exact algorithms for the edge domination problem are analyzed by using the measure - and - conquer method . however , none of them can be easily modified for dominating induced matching . some exact algorithms for dominating induced matching were also introduced recently  @xcite . lin et al . @xcite obtained a @xmath13-time algorithm . their algorithm branches on a vertex by including it to the vertex set of the dominating induced matching or not . in this paper , we also use this idea to design a branch - and - reduce algorithm . however , our improvement is not obtained by carefully checking the worst cases of previous algorithms . we derive several graph properties of the problem , which will reduce some bad cases and allow us to design an improved algorithm . our paper is organized as follows . the notation system and our algorithm type are introduced in section  [ sec_pre ] . some conditions for feasibility and several rules to simplify problem instances are given in section  [ sec_rules ] . the full algorithm is described in section  [ sec_alg ] and the detailed analysis is given in section  [ sec_analy ] . finally , some concluding remarks are put in section  [ sec_con ] .","summary":"a _ dominating induced matching _ , also called an _ efficient edge domination _ , of a graph with vertices and edges is a subset of edges in the graph such that no two edges in share a common endpoint and each edge in is incident with exactly one edge in . it is np - hard to decide whether a graph admits a dominating induced matching or not . in this paper , we design a-time exact algorithm for this problem , improving all previous results . combinatorial optimization , graph algorithms , graph partition , exact algorithms , dominating induced matching","abstract":"a _ dominating induced matching _ , also called an _ efficient edge domination _ , of a graph with vertices and edges is a subset of edges in the graph such that no two edges in share a common endpoint and each edge in is incident with exactly one edge in . it is np - hard to decide whether a graph admits a dominating induced matching or not . in this paper , we design a-time exact algorithm for this problem , improving all previous results . this problem can be redefined as a partition problem that is to partition the vertex set of a graph into two parts and , where induces an independent set ( a 0-regular graph ) and induces a perfect matching ( a 1-regular graph ) . after giving several structural properties of the problem , we show that the problem always contains some `` good vertices , '' branching on which by including them to either or we can effectively reduce the graph . this leads to a fast exact algorithm to this problem .    combinatorial optimization , graph algorithms , graph partition , exact algorithms , dominating induced matching"}
{"article_id":"astro-ph9604073","section_id":"i","document":"a neutron star crust extends from the stellar surface to the internal core , up to densities of about @xmath3 g  @xmath4 . the properties of crustal matter are most important for studying neutron star physics and observational data ( surface thermal x - ray emission , x - ray burst phenomena , evolution of magnetic fields , etc . ) . this article has two goals . first , we analyze nuclear composition of matter in neutron star crusts . second , we reconsider the neutrino - pair bremsstrahlung ( npb ) in liquid phase of the matter due to scattering of electrons on atomic nuclei , @xmath5 npb is known to be one of the most powerful mechanisms of neutrino emission in matter with density lower than the nuclear density , @xmath6 g @xmath4 . npb was considered in a number of works ( see itoh et al . 1989 , and references therein ) . let us mention detailed studies of festa & ruderman ( 1969 ) , flowers ( 1973 ) , dicus et al . ( 1976 ) , soyeur & brown ( 1979 ) , itoh & kohyama ( 1983 ) , and itoh et al . ( 1984a ) who analyzed npb due to electron scattering in liquid and crystalline dense matter . pethick & thorsson ( 1994 ) have shown that the band structure effects of electrons in solid matter drastically suppress the static lattice contribution to npb . finally , the reconsideration of the neutrino energy loss rate due to the electron - phonon scattering in the crystal phase was recently performed by two of us ( see yakovlev & kaminker 1996 ) . in the present paper , we will reconsider the problem of the calculation of the neutrino losses from npb in the hot neutron star crusts . we will restrict ourselves to the case of a liquid phase of the crust ( temperature above melting temperature at given density ) . the actual nuclear composition of the crust depends on the formation scenario . in contrast to previous studies , our calculations will be performed for realistic models of nuclear composition , which are based on specific assumptions about the formation of the neutron star envelope . the paper is organized as follows . in sect . 2 we analyze physical conditions and nuclear composition of neutron star crusts . we discuss those differences between various neutron star crusts , which are important for the npb emissivities . in sect . 3 we recalculate the npb energy generation rate for degenerate relativistic electrons and coulomb liquid of atomic nuclei . contrary to the previous works , we include the non - born corrections and the effects associated with thermal width of the electron fermi sphere . we express our results in a simple form  through a coulomb logarithm , which is a slowly varying function of density , temperature , and nuclear composition of matter . in sect . 4 we discuss npb for various models of matter in neutron star crusts , and indicate possible implications of our results . general formalism of npb is presented in appendix  a , mathematical aspects of the thermal broadening of electron fermi sphere are considered in appendix  b. dynamic screening of the electron - nucleus interaction is outlined in appendix  c.","summary":"neutrino emissivity from the electron bremsstrahlung in the liquid layers of the neutron star crusts is studied . nuclear composition of matter in neutron star crusts neutrino - pair bremsstrahlung , due to collisions of relativistic degenerate electrons in a coulomb liquid of atomic nuclei , is considered . the neutrino energy loss rate is expressed in a simple form through a coulomb logarithm  a slowly varying function of density , temperature , and nuclear composition . non - born corrections , thermal width of electron fermi sphere , and finite sizes of nuclei are taken into account . implications for cooling of neutron stars are discussed .    [ sampout ]","abstract":"neutrino emissivity from the electron bremsstrahlung in the liquid layers of the neutron star crusts is studied . nuclear composition of matter in neutron star crusts is considered for various scenarios of neutron star evolution . for the deep layers of the crust , the compositions of cold catalyzed matter , accreted matter and hot matter (  k ) are shown to be very different , and this implies differences in the neutrino emissivity at given density and temperature . neutrino - pair bremsstrahlung , due to collisions of relativistic degenerate electrons in a coulomb liquid of atomic nuclei , is considered . the neutrino energy loss rate is expressed in a simple form through a coulomb logarithm  a slowly varying function of density , temperature , and nuclear composition . non - born corrections , thermal width of electron fermi sphere , and finite sizes of nuclei are taken into account . implications for cooling of neutron stars are discussed .    [ sampout ]"}
{"article_id":"astro-ph9604073","section_id":"c","document":"we have analyzed nuclear composition of neutron star crusts ( sect . 2 ) for three models of dense matter : cold catalyzed matter , accreted matter , and hot matter in thermodynamic equilibrium . the first and second models are valid for @xmath37  k , while the third one is appropriate for higher temperatures . nuclear composition ( @xmath56 ) , melting temperature and other properties of dense matter are different for these models .    in sect . 3 we have reconsidered the neutrino - pair bremsstrahlung ( [ eq : reaction ] ) of relativistic degenerate electrons due to scattering on atomic nuclei at @xmath40 . we have shown that the neutrino energy generation rate can be expressed ( eq .  ( [ eq : qthroughl ] ) ) through a coulomb logarithm @xmath2 , which varies slowly in stellar matter . we have obtained a general expression ( [ eq : l ] ) for @xmath2 , which takes into account two effects neglected in previous works . first , it includes the non - born corrections , and , second , it describes the thermal effects associated with the finite width of the shell around the electron fermi surface . the thermal effects are shown to be quite important at moderate electron degeneracy , and they lead to the appearance of the new ` moderate temperature regime ' ( sect . 3.4 ) overlooked in previous studies of npb from relativistic degenerate electrons . we have calculated the coulomb logarithm numerically for possible parameters of dense matter in neutron star crusts , and found a simple analytic fit ( [ eq : fit ] ) . note that npb of electrons in a coulomb liquid of atomic nuclei is similar to npb at @xmath264 produced due to coulomb scattering of electrons on ` charged impurities '  nuclei ( @xmath265 ) immersed accidentally in a lattice of bulk nuclei ( @xmath56 ) . when the nuclei crystallize ( @xmath41 ) but temperature does not drop much below @xmath69 , the most important is the neutrino pair generation due to electron phonon scattering in solid matter ( this follows from the recent results of pethick & thorsson 1994 ) . the neutrino energy generation rate drops rapidly with decreasing @xmath28 at @xmath266 ( e.g. , itoh et al . 1984b , yakovlev & kaminker 1996 ) , and the coulomb impurity scattering can be dominant even for not very low @xmath28 . the energy generation rate @xmath267 is obviously given by the expression similar to ( [ eq : qthroughl ] ) but with @xmath67 replaced by the impurity number density @xmath268 , and with @xmath269 replaced by @xmath270 . the expression for @xmath267 contains a coulomb logarithm @xmath271 which should be quite similar to the coulomb logarithm ( [ eq : llowt ] ) in liquid matter ( although the thermal effects become unimportant ) . the major difference is in the coulomb screening . in solid matter , the screening is described by the impurity structure factor @xmath272 which takes into account impurity distribution over lattice sites . if the impurity correlation length is large , the main contribution into the screening comes from the electrons . the results of the present article can be useful for numerical modeling various phenomena related to the thermal evolution of neutron stars . first of all , we should mention cooling of young neutron stars ( of age @xmath273 ( 1  10@xmath274 ) yrs ) where internal thermal relaxation is not achieved ( lattimer et al . 1994 ) . the thermal relaxation is accompanied by the propagation of the cooling wave from the interior to the surface . the associated variations of surface temperature are , in principle , observable . the dynamics of thermal relaxation is sensitive to the properties of matter in the neutron star crust , particularly to nuclear composition and neutrino generation mechanisms . in addition , the above results are useful for studying thermal evolution of accreting neutron stars ( see , e.g. , miralda - escud@xmath246 et al . 1990 , and references therein ) . this work was supported partly by intas , grant no . 94 - 3834 , the russian basic research foundation , grant no . 96 - 02 - 16870a , and by the eso c&ee programme , grant no . a-01 - 068 . we acknowledge also the support of the polish state committee for scientific research ( kbn ) , grant no . 2 p304 014 07 .","summary":"the compositions of cold catalyzed matter , accreted matter and hot matter (  k ) are shown to be very different , and this implies differences in the neutrino emissivity at given density and temperature .","abstract":"neutrino emissivity from the electron bremsstrahlung in the liquid layers of the neutron star crusts is studied . nuclear composition of matter in neutron star crusts is considered for various scenarios of neutron star evolution . for the deep layers of the crust , the compositions of cold catalyzed matter , accreted matter and hot matter (  k ) are shown to be very different , and this implies differences in the neutrino emissivity at given density and temperature . neutrino - pair bremsstrahlung , due to collisions of relativistic degenerate electrons in a coulomb liquid of atomic nuclei , is considered . the neutrino energy loss rate is expressed in a simple form through a coulomb logarithm  a slowly varying function of density , temperature , and nuclear composition . non - born corrections , thermal width of electron fermi sphere , and finite sizes of nuclei are taken into account . implications for cooling of neutron stars are discussed .    [ sampout ]"}
{"article_id":"1310.5716","section_id":"i","document":"baados , silk and west pointed out that a rapidly rotating black hole may act as a particle accelerator to arbitrarily high energy  @xcite . we call this acceleration mechanism the baados - silk - west  ( bsw ) mechanism or bsw process . there are several discussions on the bsw process  @xcite . from a purely relativistic point of view , it is suggested in  @xcite that an arbitrarily high energy collision induced by the bsw process implies that an extremal kerr black hole is linearly unstable . if we consider the free - fall test particles with an arbitrarily small mass from the far region , we expect that the gravity induced by those test particles will be well described by a linear perturbation around the background spacetime . if one of the test particles has the fine - tuned angular momentum for given energy such that the bsw process works well , an arbitrarily high energy particle collision can occur near the horizon . in principle , the center of mass  ( cm ) energy can be as large as the mass energy of the background black hole , where such intense gravity can not be described by a linear perturbation around the background black hole . thus , it seems that we can construct a perturbation which can be described by a linear perturbation around an extremal kerr black hole initially , but it can not be after time evolution , so that an extremal kerr black hole is linearly unstable . recently , it is shown that the second - order derivative of a test field on the horizon of an extremal black hole blows up in late times if the test field has a nonzero value on the horizon as an initial condition  @xcite . unlike in the case of a nonextremal black hole , the test field can stay on the horizon for a long time and grow up . in this sense , an extremal black hole has an instability on the horizon . we would like to point out that there are some analogies between these two instabilities , both of which imply that the extremal black hole horizon is linearly unstable . first , it seems that both phenomena come from the vanishing surface gravity of the extremal horizon . in this case , an observer on the horizon does not feel gravitational force , and hence a particle or a field can stay in the vicinity of the horizon . note that it is essential for the bsw process that there exists a geodesic particle which stays in the vicinity of the horizon . next , a wave with sufficiently short wavelength behaves like a test particle . so , there should be a natural analogy between the dynamics of test particles and test fields . therefore , we suggest that there is a close relationship between the bsw process and the instability of fields on extremal black holes . according to the previous works  @xcite , for an arbitrarily high energy particle collision to occur by the bsw process , we need to impose at least two conditions : ( i ) the black hole horizon is extremal and ( ii ) the parameters of either of the two colliding particles are fine - tuned . we can derive these two conditions by imposing that a particle can asymptote to the event horizon in infinite proper time . the condition ( ii ) is known as the critical particle condition which is a relation among energy , angular momentum and electric charge of the particle  @xcite . since both the radial velocity and the acceleration of such a particle asymptote to zero as it approaches the horizon , i.e. , @xmath0 where @xmath1 is the proper time of the particle and @xmath2 is the radius of the horizon , we might regard this condition as `` force balance '' conditions in an approach to the horizon . it is proposed that the critical particle condition can be naturally realized if we consider an innermost stable circular orbit  ( isco ) particle . in the case of a near extremal kerr black hole , the radius of the isco is close to the horizon and such a particle satisfies @xmath3 and @xmath4 in the vicinity of the horizon which is similar to the conditions  ( [ eq : forcebalance1 ] )  and  ( [ eq : forcebalance2 ] ) . if we consider a collision between an isco particle and another free - fall particle around an extremal kerr black hole , an arbitrarily high energy particle collision can also occur in the extremal limit as shown in  @xcite . we can expect that there is a relation between the approach of the isco to the horizon and the bsw process .    in this paper , to understand the nature of the bsw process deeper , we study high energy particle collision around higher dimensional extremal black holes . the effective potential for the radial coordinate @xmath5 roughly has the form of @xmath6 , where @xmath7 is the mass of the black hole and @xmath8 is the conserved angular momentum for a particle in a @xmath9-dimensional spacetime . the first term is the gravitational potential and the second term is the potential of centrifugal force . in higher dimensions @xmath10 , the power of gravitational force @xmath11 is not greater than that of centrifugal force @xmath12 . in that case , the effective potential does not have a local minimum ; namely , there is no stable circular orbit in contrast with four dimensions . if the existence of isco is important for the bsw process , we can expect that high energy particle collision can not occur around higher dimensional extremal black holes . on the other hand , recently , it was shown that there are linear instabilities of test fields on the horizon of higher dimensional extremal black holes  @xcite . if there exists an analogy between instabilities of the test field and the bsw process , we can expect that a high energy particle collision can also occur in higher dimensions . there is also a discussion for the case of charged particles around an extremal reissner - nordstrm black hole , which can be considered as a similar system for a free - fall test particle around an extremal kerr black hole  @xcite . in this case , we can understand the critical particle condition for a radially moving charged particle as the force balance between gravitational force and coulomb force . in the case of higher dimensions , we can expect high energy collision between two charged particles can also occur around an extremal charged black hole . this is because gravitational force and coulomb force have the same power law of radial distance in higher dimensional spacetimes , and the situation is the same as the four - dimensional case . this paper is organized as follows . in sec . [ secii ] , we review the motion of a test particle around myers - perry black hole spacetimes and investigate a cm energy for the colliding two particles . we show that the collision with an arbitrarily high cm energy can occur in the case of higher dimensions . in secs . [ seciii ] and [ seciv ] , we discuss whether critical particles can reach the event horizon by investigating effective potentials of test particles . as a typical case , we also investigate the cases of five and six dimensions in detail . in sec . [ secv ] , we study the case of @xmath9-dimensional charged black holes . section  [ secvi ] is devoted to the summary and discussion . in this paper we use the units in which the light speed @xmath13 .","summary":"we study high energy particle collisions around higher dimensional black holes .","abstract":"we study high energy particle collisions around higher dimensional black holes . it is shown that the center of mass energy can be arbitrarily large in the vicinity of the event horizon like the baados , silk and west  ( bsw ) process in four dimensions if the following two conditions are satisfied : ( i ) the horizon is extremal and ( ii ) the parameters of either of the two colliding particles are fine - tuned , which is called a critical particle condition . we also show that a test particle which satisfies the critical particle condition can reach the event horizon from a distant region for a simple case . finally , we discuss the relation between the bsw process and the linear instability of test fields around extremal black holes , the latter of which has been recently found by aretakis  ."}
{"article_id":"1310.5716","section_id":"i","document":"in this paper , we have investigated the collision of two particles around higher dimensional black holes . we have assumed that the spin parameters of the myers - perry black hole take only two different values at most and test particles with one conserved angular momentum for simplicity . we have shown that the collision with an arbitrarily high center of mass energy can occur in the vicinity of the event horizon if either of the two colliding particles satisfies the critical particle condition . if we consider a massless particle or a highly relativistic particle with @xmath347 as a simple case , we can see that the critical particle can reach the event horizon from a distant region as shown in appendixes  [ vnegativeodd ] and [ vnegativeeven ] . in the cases of five and six dimensions , the motion of particles has been investigated in detail for general parameters .    as expected in the discussion of analogies between the bsw process and the test - field instability of the extremal black hole in sec . [ intro ] , an arbitrarily high energy particle collision can occur in the vicinity of the horizon in higher dimensional extremal black hole spacetimes . by considering a critical particle with an arbitrarily small rest mass and the other noncritical particle around an extremal myers - perry black hole , we can construct a perturbation induced by gravity of these two particles which is expected to be well described by linear perturbation around the background spacetime before the collision . however , if the collision occurs in the vicinity of the event horizon , the center of mass energy can be arbitrarily large , and such intense gravity can not be described in the linear level . since a field with a short wavelength behaves like a test particle , there holds analogies between the phenomena of test particles and fields . for example , it is well known that there exists an analogy between the penrose process and the superradiance around rotating black holes . similarly , we conjecture that the bsw process around an extremal black hole suggests the existence of the linear instability of test fields on the extremal black hole .    on the other hand , our results suggest that the existence of isco is not essential for the bsw process . this is because the bsw process works well in higher dimensions as shown in this paper , though it is known that isco does not exist around the higher dimensional black holes .    for the rest of this section , we discuss gravitational backreaction . recently , murata _ et al . _  studied the test - field instabilities of an extremal reissner - nordstrom black hole , taking gravitational backreaction into account  @xcite . they found that the linearly developed perturbation does not decay even with backreaction but the spacetime evolves to a time - dependent extremal black hole if the initial perturbation is fine - tuned , while the final state is a nonextremal reissner - nordstrom black hole if the initial perturbation is generic . one can expect that the analogy between the bsw process and the test - field instability may hold even if the gravitational backreaction is taken into account . it is left as a future work to check this analogy because we currently have a quite limited knowledge about the fate of the bsw process in the presence of the gravitational backreaction  @xcite .    while this paper was being prepared for submission , an interesting paper  @xcite by abdujabbarov  _ et al . _ appeared , where the case of five - dimensional myers - perry black holes was discussed . here we briefly comment on their claims . they deal with the center of mass energy of colliding particles around five - dimensional myers - perry black holes not only with equal angular momenta but also with unequal ones . in particular , in the case of @xmath348 and @xmath116 , they showed that the center of mass energy diverges at @xmath349 without the fine - tuned angular momenta of particles . we point out , however , that as is noted in  @xcite , @xmath350 and @xmath351 in the case of @xmath348 and @xmath116 do not correspond to a regular horizon but to a naked conical singularity . there also exists a naked curvature singularity at @xmath350 and @xmath352 in the case of @xmath348 and @xmath116  @xcite . hence , this diverging energy should be interpreted in a different context . abdujabbarov  _ et al . _ @xcite also claimed that the center of mass energy of particles which do not have the fine - tuned angular momenta may diverge near the extremal five - dimensional black holes with or without equal angular momenta based on numerical results . however , eq . ( [ eq : cme ] ) in the current paper clearly disproves this claim .","summary":"it is shown that the center of mass energy can be arbitrarily large in the vicinity of the event horizon like the baados , silk and west  ( bsw ) process in four dimensions if the following two conditions are satisfied : ( i ) the horizon is extremal and ( ii ) the parameters of either of the two colliding particles are fine - tuned , which is called a critical particle condition . we also show that a test particle which satisfies the critical particle condition can reach the event horizon from a distant region for a simple case . finally , we discuss the relation between the bsw process and the linear instability of test fields around extremal black holes , the latter of which has been recently found by aretakis  .","abstract":"we study high energy particle collisions around higher dimensional black holes . it is shown that the center of mass energy can be arbitrarily large in the vicinity of the event horizon like the baados , silk and west  ( bsw ) process in four dimensions if the following two conditions are satisfied : ( i ) the horizon is extremal and ( ii ) the parameters of either of the two colliding particles are fine - tuned , which is called a critical particle condition . we also show that a test particle which satisfies the critical particle condition can reach the event horizon from a distant region for a simple case . finally , we discuss the relation between the bsw process and the linear instability of test fields around extremal black holes , the latter of which has been recently found by aretakis  ."}
{"article_id":"cond-mat0308247","section_id":"i","document":"the nature of a reentrant spin glass ( rsg ) phase and a ferromagnetic ( fm ) phase in reentrant ferromagnets has been a topic of much controversy . @xcite spin frustration effects occur as a result of a competition between ferromagnetic interactions as a majority and antiferromagnetic interactions as a minority . as the temperature is lowered , the reentrant ferromagnet exhibits first a transition from a paramagnetic ( pm ) phase to a fm phase with decreasing temperature and then a second transition from the fm phase to a rsg phase . such a reentry behavior of the reentrant ferromagnets has been extensively studied experimentally in the last two decades . @xcite there are four types of reentrant ferromagnets : ( i ) metallic spin glasses such as fe@xmath21al@xmath22,@xcite ( fe@xmath23ni@xmath24)@xmath25p@xmath26b@xmath27al@xmath3 , @xcite ( fe@xmath28mn@xmath29)@xmath25p@xmath26b@xmath27al@xmath3 ( @xmath30),@xcite and n@xmath31mn@xmath32@xcite having ruderman - kittel - kasuya - yosida ( rkky)-type interactions between distant spins , ( ii ) insulating spin glasses such as cdcr@xmath33in@xmath34s@xmath35 ( @xmath36),@xcite ( iii ) dilute magnetic semiconductors such as eu@xmath29sr@xmath28s ( @xmath37),@xcite and ( iv ) colossal magnetoresistance materials such as y@xmath21ca@xmath22mno@xmath3.@xcite in the case of ( ii ) and ( iii ) , ferromagnetic nearest neighbor interactions compete with antiferromagnetic next nearest neighbor interactions .    the nature of the rsg and fm phases in reentrant ferromagnets is basically understood in terms of a mean - field picture . the phase diagram ( @xmath38 vs @xmath39 ) of the sherrington - kirkpatrick ( sk ) model with ising spins,@xcite consists of the pm phase , fm phase , and the spin glass ( sg ) phase , where an infinite - ranged gaussian distribution of exchange interactions with variance @xmath40 and mean @xmath41 is assumed.@xcite for @xmath42 , as @xmath17 is lowered , the system undergoes a transition from the pm phase to the sg phase . for @xmath43 , as @xmath17 is lowered , the system undergoes a pm - fm transition followed by a fm - sg transition . this sg phase for @xmath43 is called a rsg phase . however , the nature of the rsg phase is essentially the same as that of the normal sg phase for @xmath42 . when the parisi s solution for the sk model@xcite is discovered , the vertical phase boundary at @xmath39 = 1 is added to the sk phase diagram . for @xmath43 , consequently the whole rsg phase and a part of the fm phase in the sk model are newly replaced by a rsg phase with replica symmetry breaking ( rsb ) . this rsg phase is very different from the normal sg phase for @xmath42 . it is a mixed phase of the sg phase and the fm phase .    in the mean - field picture , a true reentrance from the fm phase to the normal sg phase is not predicted . there is a normal fm long - range order in the fm phase . this picture , which assumes infinite - range interactions , is not always appropriate for real reentrant magnets where the short - range interactions are large and random in sign and the spin symmetry is rather heisenberg - like than ising - like . neutron scattering studies on ( fe@xmath28mn@xmath29)@xmath25p@xmath26b@xmath27al@xmath3@xcite have questioned the existence of a true long - range order even in the fm phase . aeppli et al.@xcite have proposed a phenomenological random - field picture to explain their result . in this picture , the system in the fm phase consists of regions which would order ferromgnetically and other regions forming pm clusters . the frustrated spins in the pm clusters can generate random molecular fields , which act on the unfrustrated spins in the infinite fm network . in the fm phase well above @xmath6 , the fluctuations of the spins in the pm clusters are so rapid that the fm network is less influenced by them and their effect is only to reduce the net fm moment . on decreasing the temperature toward @xmath6 , the thermal fluctuations of the spins in the pm clusters become slower . the coupling between the pm clusters and the fm network becomes important and the molecular field from the slow pm spins acts as a random magnetic field . this causes breakups of the fm network into finite - sized clusters . below @xmath6 , the ferromagnetism completely disappears , leading to a sg phase . this picture is very different from the mean - field picture . the rsg phase is not a mixed phase but a normal sg phase . jonason et al.@xcite have shown from a dynamic scaling analysis of low - field dynamic susceptibility of ( fe@xmath23ni@xmath24)@xmath25p@xmath26b@xmath27al@xmath3 that there is a spin - glass relaxation time which diverges at a finite temperature with a dynamic critical exponent similar to that observed for an ordinary pm - sg transition . this suggests that the rsg phase is a normal sg phase . the fm phase just above @xmath6 shows a dynamic behavior characterized by an aging effect and chaotic nature similar to that of sg phase . dupuis et al.@xcite have shown that the aging behavior of the low frequency ac susceptibility is observed both in the fm phase and rsg phase of cdcr@xmath33in@xmath34s@xmath35 with @xmath9 = 0.90 , 0.95 , and 1.00 , with the same qualitative features as in normal spin glasses . it seems that these results are explained in terms of the random - field picture .    in this paper we report our experimental study on the magnetic properties of the rsg phase and the fm phase of a reentrant ferromagnet cu@xmath0co@xmath1cl@xmath2-fecl@xmath3 graphite bi - intercalation compound ( gbic ) . this compound undergoes three phase transitions at @xmath4 (= 16 k ) , @xmath5 (= 9.7 k ) , and @xmath6 (= 3.5 k ) . there are the helical spin ordered phase between @xmath4 and @xmath5 , the fm phase between @xmath5 and @xmath6 , and the rsg phase below @xmath6.@xcite the static and dynamic natures of the fm and rsg phases are examined from the linear and nonlinear ac magnetic susceptibility , the magnetizations in the zero - field cooled ( zfc ) , field - cooled ( fc ) , isothermal remnant ( ir ) , and thermoremnant ( tr ) states . the time dependence of the ac susceptibility and the zfc magnetization , showing the aging phenomena , is also studied . cu@xmath0co@xmath1cl@xmath2-fecl@xmath3 gbic has a unique layered structure where the cu@xmath0co@xmath1cl@xmath2 intercalate layer (= @xmath44 ) and fecl@xmath3 intercalate layers (= @xmath45 ) alternate with a single graphite layer ( @xmath46 ) , forming a stacking sequence ( -@xmath46-@xmath44-@xmath46-@xmath45-@xmath46-@xmath44-@xmath46-@xmath45-@xmath46-@xmath47 ) along the @xmath48 axis . in the cu@xmath0co@xmath1cl@xmath2 intercalate layer two kinds of magnetic ions ( cu@xmath49 and co@xmath49 ) are randomly distributed on the triangular lattice . the spin order in the cu@xmath0co@xmath1cl@xmath2 layers is coupled with that in the fecl@xmath3 intercalate layer (= @xmath45 ) through an interplanar exchange interaction , leading to the spin frustration effect .","summary":"linear and nonlinear dynamic properties of a reentrant ferromagnet cucocl-fecl graphite bi - intercalation compound are studied using ac and dc magnetic susceptibility . this compound undergoes successive phase transitions at the transition temperatures (= 16 k ) , (= 9.7 k ) , and (= 3.5 k ) . a prominent nonlinear susceptibility is observed between and and around , suggesting a chaotic nature of the ferromagnetic phase ( ) and the helical spin ordered phase ( ) . the aging phenomena are observed both in the rsg and fm phases , with the same qualitative features as in normal spin glasses . the aging of zero - field cooled magnetization indicates a drastic change of relaxation mechanism below and above .","abstract":"linear and nonlinear dynamic properties of a reentrant ferromagnet cucocl-fecl graphite bi - intercalation compound are studied using ac and dc magnetic susceptibility . this compound undergoes successive phase transitions at the transition temperatures (= 16 k ) , (= 9.7 k ) , and (= 3.5 k ) . the static and dynamic behaviors of the reentrant spin glass phase below are characterized by those of normal spin glass phase with critical exponent = 0.57 0.10 , a dynamic critical exponent = 8.5 1.8 , and an exponent (= 1.55 0.13 ) for the de almeida -thouless line . a prominent nonlinear susceptibility is observed between and and around , suggesting a chaotic nature of the ferromagnetic phase ( ) and the helical spin ordered phase ( ) . the aging phenomena are observed both in the rsg and fm phases , with the same qualitative features as in normal spin glasses . the aging of zero - field cooled magnetization indicates a drastic change of relaxation mechanism below and above . the time dependence of the absorption is described by a power law form ( ) in the ferromagnetic phase , where at = 0.05 hz and = 7 k. no-scaling law for [ is observed ."}
{"article_id":"cond-mat0308247","section_id":"r","document":"@xmath17 dependence of ( a ) @xmath63 and ( b ) @xmath64 at various @xmath65 for cu@xmath0co@xmath1cl@xmath2-fecl@xmath3 gbic . @xmath16 = 1 hz . @xmath61 = 0.,width=283 ]    we have measured the dispersion @xmath63 and absorption @xmath64 at fixed @xmath17 as a function of @xmath65 , where 1 moe @xmath67 4.2 oe and @xmath16 = 1 hz . both @xmath63 and @xmath64 are strongly dependent on @xmath65 , suggesting the existence of nonlinear magnetic susceptibility . we determine the @xmath17 dependence of nonlinear ac magnetic susceptibilities ( @xmath68 , @xmath69 , @xmath70 , @xmath71 ) from the least squares fits of the data to the power law forms:@xcite @xmath72 and @xmath73 note that for convenience we use the linear ac susceptibility @xmath74 and @xmath13 instead of @xmath75 and @xmath76 . in figs . [ fig : one](a ) and ( b ) we show the @xmath17 dependence of the dispersion @xmath63 and the absorption @xmath64 at @xmath16 = 1 hz . the different curves correspond to different amplitudes of the ac field , where @xmath65 is varied between 1 moe and 4.2 oe . the susceptibility @xmath63 and @xmath64 are independent of @xmath65 for @xmath77 within experimental error , where @xmath78 0.1 oe , implying that @xmath63 and @xmath79 coincide with the linear susceptibilities @xmath74 and @xmath13 , respectively . note that @xmath79 shows a sharp peak at 4 k , which is almost independent of @xmath65 . this sharp peak is associated with the transition between the fm and rsg phases : @xmath6 = 3.5 k.    @xmath17 dependence of ( a ) @xmath80 and ( b ) @xmath81 at various @xmath65 . @xmath16 = 1 hz . @xmath61 = 0 . @xmath80 is defined by the difference between @xmath63 at @xmath65 ( @xmath82 30 moe ) and @xmath63 at @xmath65 = 30 moe . @xmath83 is defined by the difference between @xmath64 at @xmath65 ( @xmath82 30 moe ) and @xmath64 at @xmath65 = 30 moe.,width=283 ]    in figs . [ fig : two](a ) and ( b ) we show the @xmath17 dependence of @xmath80 and @xmath83 at various @xmath65 , where @xmath80 and @xmath83 are defined as the differences between @xmath63 and @xmath64 at @xmath65 ( @xmath82 30 moe ) and those at @xmath65 = 30 moe , respectively : @xmath84 and @xmath85 . the differences @xmath80 and @xmath83 are strongly dependent on @xmath65 . the difference @xmath83 has two local maxima at 16.2 k ( 15.8 k ) and 8.6 k ( 7.8 k ) , and a local minimum at 10.3 k ( 10.1 k ) at @xmath65 = 1 oe ( @xmath65 = 4 oe ) . in contrast , @xmath80 has two local maxima at 15.8 k ( 15.6 k ) and 8.3 k ( 7.8 k ) , and two local minima at 9.9 k ( 9.5 k ) and 16.6 k ( 16.5 k ) at @xmath65 = 1 oe ( @xmath65 = 4 oe ) . in summary , the positions of the local maxima and minima shift to low-@xmath17 side as @xmath65 increases . ( a ) and ( b ) @xmath86 dependence of @xmath83 at various @xmath17 . @xmath16 = 1 hz . the inset of ( a ) shows the @xmath17 dependence of the peak field @xmath87 for @xmath80 and @xmath88 for @xmath83.,width=283 ]    ( a ) and ( b ) @xmath86 dependence of @xmath80 at various @xmath17 . @xmath16 = 1 hz.,width=283 ]    in figs . [ fig : three ] and [ fig : four ] we show the plot of @xmath83 and @xmath80 as a function of @xmath86 near @xmath5 (= 9.7 k ) and @xmath4 (= 16 k ) , respectively . both @xmath83 and @xmath80 are strongly dependent on @xmath86 in these limited temperature regions . a linear increase of @xmath80 and @xmath89 with @xmath86 at low @xmath65 indicates a positive sign of @xmath68 and @xmath70 . we find a peak in @xmath80 [ @xmath83 ] at a peak field @xmath87 [ @xmath88 ] , which shifts to the low-@xmath65 side with increasing @xmath17 . the fields @xmath87 and @xmath88 are defined as d(@xmath92d@xmath65 = 0 and d(@xmath93/d@xmath65 = 0 , respectively : @xmath94 and @xmath95 . the existence of @xmath87 and @xmath88 indicates a negative sign of @xmath69 and @xmath96 . in the inset of fig . [ fig : three](a ) , we show the @xmath17 dependence of @xmath87 and @xmath88 . the peak fields @xmath87 and @xmath88 , which decrease with increasing @xmath17 , tend to reduce to zero around 9.8 and 10.4 k , respectively . ( a ) @xmath17 dependence of @xmath68 and @xmath69 , where the units of @xmath97 are emu/(av mol oe@xmath98 ) . @xmath16 = 1 hz . ( b ) @xmath17 dependence of @xmath99 , @xmath100 , and @xmath101 , where the units of @xmath102 are emu/(av mol oe@xmath98).,width=283 ]    the least squares fits of the data ( @xmath63 vs @xmath86 and @xmath103 vs @xmath86 ) at each @xmath17 for 30 moe @xmath104 0.7 oe to eqs.([eq : one ] ) and ( [ eq : two ] ) yield the values of @xmath75 , @xmath68 , @xmath69,@xmath47 , and @xmath99 , @xmath100 , @xmath101,@xmath47 . figure [ fig : five ] shows the @xmath17 dependence of @xmath68 , @xmath69 , @xmath100 , and @xmath101 thus obtained . the nonlinear susceptibility @xmath68 at @xmath16 = 1 hz shows a positive peak at 16.0 k , a negative local minimum at 10.2 k , and two positive peaks at 8.8 and 8.3 k. the sign of @xmath68 changes from negative to positive at 9.65 k and from positive to negative at 4.0 k with decreasing @xmath17 . no anomaly is observed below 4 k. in contrast , @xmath69 at @xmath16 = 1 hz exhibits a negative local minimum at 16.0 k , a positive peak at 10.2 k , and two negative peaks at 9.0 k and 8.3 k. the sign of @xmath69 changes from positive to negative at 4.0 k with decreasing @xmath17 . we note that the @xmath17 dependence of @xmath68 around 10 k in our system is similar to that in stage-2 cocl@xmath2 gic which magnetically behave like a quasi 2d ferromagnet with an extremely weak antiferromagnetic interplanar exchange interaction.@xcite in stage-2 cocl@xmath2 gic , @xmath68 exhibits a negative local minimum at 10.5 k , becomes positive below 10.2 k , and shows a positive peak below the upper critical temperature @xmath105 . the nonlinear susceptibility @xmath100 shows a positive peak at 16.2 k , a negative local minimum at 11.0 k , and a positive peak at 8.7 k. the sign of @xmath100 changes from negative to positive at 9.9 k and from positive to negative at 5.7 k with decreasing @xmath17 . in contrast , @xmath101 shows a negative local minimum at 16.4 k , a positive peak at 11.0 k , and a negative peak at 9.0 k. the sign of @xmath101 changes from negative to positive at 6.5 k with decreasing @xmath17 . here we discuss the @xmath17 dependence of @xmath68 . basically the singularity of @xmath68 could reflect the breaking of spatial magnetic symmetry . the sign of @xmath68 is negative for the pm phase and the sg phase and positive for the fm phase . thus the critical temperatures @xmath5 for the pm - fm transition and @xmath6 for the fm - rsg transition could be defined as temperatures at which the sign of @xmath68 changes . using this definition , in fact we find 9.65 k as @xmath5 and 4.0 k as @xmath6 at @xmath16 = 1 hz for our system . similar behaviors have been reported in other reentrant ferromagnets . sato and miyako@xcite have reported that the sign of @xmath68 in ( pd@xmath106fe@xmath107)@xmath108mn@xmath109 changes from negative to positive at @xmath5 . sato et al.@xcite have shown that the sign of @xmath68 in ni@xmath31@xmath110fe@xmath111mn@xmath32 changes from positive to negative at @xmath6 : @xmath68 has a small negative local minimum near @xmath6 . figures [ fig : six](a ) and ( b ) show the @xmath17 dependence of the linear ac susceptibility @xmath74 and @xmath112 below 12 k at @xmath65 = 50 moe , where @xmath113 and @xmath114 . the absorption @xmath112 at @xmath16 = 0.01 hz shows a relatively sharp peak at 3.69 k. this peak shifts to the high-@xmath17 side with increasing @xmath16 : 5.10 k at @xmath16 = 1 khz . in contrast , the derivative d@xmath112/d@xmath17 at @xmath16 = 0.01 hz shows two negative local minima at 4.0 k corresponding to @xmath6 and 10.0 k corresponding to @xmath5 . the local minimum d@xmath112/d@xmath17 vs @xmath17 at 4.0 k shifts to the high-@xmath17 side with increasing @xmath16 , while the local minimum at 10.0 k does not shift with increasing @xmath16 . figures [ fig : six](c ) and ( d ) show the @xmath17 dependence of @xmath74 and @xmath112 around @xmath4 at @xmath65 = 500 moe , where @xmath115 and @xmath116 . the dispersion @xmath74 at @xmath16 = 0.01 hz shows peaks at 16.2 k and 8.35 k. the peak at 16.2 k slightly shift to the high-@xmath17 side with increasing @xmath16 : 16.4 k at @xmath16 = 1 khz . another peak at 8.35 k does not shift with increasing @xmath16 . the dispersion @xmath74 at @xmath16 = 0.01 hz has an inflection point at 3.5 k corresponding to the positive peak of d@xmath74/d@xmath17 , and another inflection point at 9.7 k corresponding to the negative local minimum of d@xmath74/d@xmath17 . the inflection point at 3.5 k shift to the high-@xmath17 side with increasing @xmath16 . @xmath17 dependence of the relaxation time @xmath117 which is determined from the @xmath16 dependence of peak temperature of @xmath13 vs @xmath17 , @xmath118 vs @xmath17 , and d@xmath13/d@xmath17 vs @xmath17 . the solid lines denote the least - squares fit of the data to eq.([eq : three]).,width=283 ]    here we assume that the singular behavior of @xmath112 around 4 k is due to the critical slowing down associated with the fm - rsg transition . either the peak temperatures of @xmath112 vs @xmath17 and @xmath119 vs @xmath17 or the local - minimum temperature of d@xmath112/d@xmath17 vs @xmath17 around 4 k coincide with a spin freezing temperature @xmath120 , at a relaxation time @xmath117 ( @xmath121 ) . the relaxation time @xmath117 can be described by@xcite @xmath122 where @xmath123 , @xmath124 is the dynamic critical exponent , @xmath125 is the critical exponent of the spin correlation length @xmath126 , and @xmath127 is the characteristic time . in fig .  [ fig : seven ] we show the @xmath17 dependence of @xmath117 thus obtained for d@xmath112/d@xmath17 , @xmath119 ( figure of @xmath119 vs @xmath17 is not shown ) , and @xmath112 . the least squares fits of the data of @xmath117 vs @xmath17 yield @xmath9 = 8.5 @xmath8 1.8 , @xmath6 = 3.45 @xmath8 0.31 k , and @xmath127 = ( 4.77 @xmath8 0.10 ) @xmath128 10@xmath129 sec for the local minimum temperature of d@xmath112/d@xmath17 vs @xmath17 , @xmath9 = 12.3 @xmath8 1.7 , @xmath6 = 2.90 @xmath8 0.26 k , and @xmath127 = ( 1.49 @xmath8 0.05 ) @xmath128 10@xmath130 sec for the peak temperature of @xmath119 vs @xmath17 , and @xmath9 = 16.6 @xmath8 1.8 , @xmath6 = 2.27 @xmath8 0.25 k , and @xmath127 = ( 4.67 @xmath8 0.10 ) @xmath128 10@xmath131 sec for the peak temperature of @xmath112 vs @xmath17 . the value of @xmath9 for @xmath112 vs @xmath17 and @xmath119 vs @xmath17 is unphysically large . in contrast , the value of @xmath9 for d@xmath112/d@xmath17 vs @xmath17 is on the same order as that ( @xmath9 = 7.9 ) rep orted by jonason et al.@xcite for the fm - rsg transition of ( fe@xmath23ni@xmath24)@xmath25p@xmath26b@xmath27al@xmath3 . a relatively good agreement between the value of @xmath9 for cu@xmath0co@xmath1cl@xmath2-fecl@xmath3 gbic and the value predicted by ogielski@xcite for the 3d @xmath132 ising sg ( @xmath9 = 7.9 @xmath8 1.0 ) , suggests that the fm - rsg transition in our system is dynamically similar to an ordinary pm - sg transition . note that the value of @xmath127 for d@xmath112/d@xmath17 vs @xmath17 is much larger than a typical value of microscopic relaxation time @xmath133 ( typically 10@xmath134 - 10@xmath135 sec ) . such a large value of @xmath127 has been also reported by kleemann et al.@xcite for co@xmath136fe@xmath137/al@xmath2o@xmath3 multilayers : @xmath127 = ( 6.7 @xmath8 0.4 ) @xmath128 10@xmath138 sec and @xmath9 = 10.0 @xmath8 3.6 . the large @xmath127 suggests that the pm clusters play a significant role in the fm - rsg transition . in the random - field picture,@xcite the fm phase consists of the fm region with a longer relaxation time and the pm clusters with a shorter relaxation time . on decreasing @xmath17 toward @xmath6 , the thermal fluctuations of the spins in the pm clusters become slower . the molecular field of the slow pm spins acting as random magnetic field causes breakups of the fm network into finite - sized clusters . it is predicted that the following dynamic scaling equation is valid for the normal sg phase:@xcite @xmath139 , where @xmath140 is a scaling function of @xmath141 and is assume to take a maximum at @xmath141 = constant . the value @xmath142 (= @xmath143 ) is a critical exponent , where @xmath7 is a critical exponent of the order parameter . the curve of @xmath119 vs @xmath17 exhibits a peak , which shifts to the high-@xmath17 side as @xmath16 increases . the peak height of @xmath119 increases with increasing @xmath16 . the least squares fit of the data for the peak height of @xmath119 vs @xmath16 ( for 0.01 @xmath144 1000 hz ) to the form of ( @xmath145 ) yields @xmath142 = 0.066 @xmath8 0.001 . then the value of @xmath7 (= @xmath146 ) is estimated as @xmath7 = 0.57 @xmath8 0.10 , where @xmath9 = 8.5 @xmath8 1.8 . this value of @xmath7 is similar to that ( @xmath7 = 0.54 ) for fe@xmath147mn@xmath147tio@xmath3.@xcite in summary , the nature of the fm - rsg transition is similar to that of the normal pm - sg transition . the pm clusters for the fm - rsg transition play the same role as individual spins for the pm - sg transition . @xmath16 dependence of ( a ) @xmath74 and ( b ) @xmath112 at various @xmath17 . @xmath65 = 50 moe.,width=283 ]    figures [ fig : eight](a ) and ( b ) show the @xmath16 dependence of @xmath148 and @xmath149 at various @xmath17 in the vicinity of @xmath6 , respectively . the absorption @xmath149 curves exhibit different characteristics depending on @xmath17 . above @xmath6 , @xmath149 shows a peak at a characteristic frequency , shifting to the low @xmath16-side as @xmath17 decreases . below @xmath6 , @xmath149 shows no peak for @xmath150 0.01 hz . it decreases with increasing @xmath16 , following a power law form ( @xmath151 ) . this is in contrast to the @xmath16 dependence of @xmath112 for conventional spin glass systems such as fe@xmath147mn@xmath147tio@xmath3 : @xmath112 increases with increasing @xmath16.@xcite the exponent @xmath152 is weakly dependent on @xmath17 : @xmath152 = 0.083 @xmath8 0.004 at 2.5 k and @xmath152 = 0.079 @xmath8 0.002 at 3 k. according to the fluctuation - dissipation theorem , the magnetic fluctuation spectrum @xmath153 is related to @xmath149 by @xmath154 . then @xmath155 is proportional to @xmath156 , which is similar to 1/@xmath157 character of typical spin glass . in contrast , @xmath158 decreases with increasing @xmath16 above and below @xmath6 : @xmath74 exhibits a power law form ( @xmath159 ) . the exponent @xmath160 is weakly dependent on @xmath17 : @xmath160 = 0.079 @xmath8 0.001 at @xmath17 = 2.5 k and @xmath160 = 0.094 @xmath8 0.001 at @xmath17 = 3.0 k. the value of @xmath160 agrees well with that of @xmath152 . note that @xmath112 is related to @xmath74 through a so called `` @xmath161/2 rule '' : @xmath162d@xmath74/d@xmath163 ( kramers - kronig relation ) , leading to the relation @xmath164 .    here we note the @xmath16 dependence of @xmath112 above 5 k ( which is not shown in fig . [ fig : eight](b ) ) . the absorption @xmath112 increases with increasing @xmath16 for 5 @xmath165 7.2 k. a newly small peak is added around @xmath16 = 2 hz for 7.3 @xmath165 9.2 k. the absorption @xmath112 decreases with increasing @xmath16 for @xmath166 70 hz and increases with further increasing @xmath16 for 9.3 @xmath167 9.8 k. above 9.9 k it decreases with increasing @xmath16 . we find that @xmath112 for 6.1 @xmath165 7.3 k can be described by a power law form ( @xmath168 ) in the limited frequency range ( 0.01 @xmath169 10 hz ) . the exponent @xmath170 increases with increasing @xmath17 : @xmath170 = 0.04 @xmath8 0.01 at 6.1 k , 0.081 @xmath8 0.02 at 6.7 k , and 0.12 @xmath8 0.01 at 7.2 k.      ( a)-(c ) @xmath17 dependence of @xmath59 and @xmath60 at various @xmath61 . @xmath173.,width=264 ]    figures [ fig : nine ] shows the @xmath17 dependence of @xmath60 and @xmath59 at various @xmath61 , where @xmath61 is applied along the @xmath48 plane which is perpendicular to the @xmath48 axis . it is strongly dependent on @xmath61 . the susceptibility @xmath60 at @xmath61 = 0.5 oe decreases with increasing @xmath17 . it has inflection points at @xmath17 = 16.4 , 9.70 , and 4.0 k where d@xmath60/d@xmath17 exhibits negative local minima . these temperatures correspond to the transition temperatures @xmath4 , @xmath5 , and @xmath6 . in contrast , @xmath59 at @xmath61 = 0.5 oe exhibits two peaks at 16.2 and 8.2 k , and an inflection point at 3.2 k where d@xmath59/d@xmath17 shows a positive local maximum . the peaks of @xmath59 at 8.2 and 16.2 k shifts to the low-@xmath17 side with increasing @xmath61 . the deviation of @xmath59 at @xmath61 = 0.5 oe from @xmath60 starts to occur at temperatures above 18 k. the peak of @xmath59 at @xmath4 is very sensitive to the application of @xmath61 . it shifts to the low-@xmath17 side with increasing @xmath61 and disappears above 50 oe . @xmath17 dependence of @xmath171 (= @xmath172 ) at various @xmath61 . the value of @xmath171 is derived from fig . [ fig : nine].,width=283 ]    figure [ fig : eleven ] shows the @xmath17 dependence of the difference @xmath174 (= @xmath172 ) at various @xmath61 . the difference @xmath174 has three inflection points at @xmath4 , @xmath5 , and @xmath6 , where d(@xmath171)/d@xmath17 exhibits negative local minima : 16.2 k ( @xmath175 ) , 9.60 k ( @xmath176 ) , and 3.40 k ( @xmath177 ) . the @xmath17 dependence of @xmath171 shown in fig . [ fig : eleven ] is very different from standard one observed in many reentrant ferromagnets , where @xmath171 reduces to zero at @xmath6 . typical examples of @xmath59 vs @xmath17 and @xmath60 vs @xmath17 have been reported for cdcr@xmath33in@xmath34s@xmath35,@xcite au@xmath178fe@xmath179,@xcite ni@xmath31mn@xmath180,@xcite and ( fe@xmath181cr@xmath109ni@xmath109)@xmath2p.@xcite both inflection points of @xmath171 at @xmath182 and @xmath183 become less pronounced with increasing @xmath61 . only an inflection point at @xmath184 survives for @xmath185 100 oe . note that the inflection point at @xmath184 shifts to the low-@xmath17 side with increasing @xmath61 : 2.8 k at @xmath61 = 100 oe . the @xmath61 dependence of @xmath184 will be discussed in sec . [ resulte ] . we have measured the magnetization @xmath188 in the zfc , fc , ir ( isothermal remnant ) , and tr ( thermoremnant ) states in the case of @xmath61 = 5 and 15 oe , as a function of @xmath17 . this magnetization @xmath188 is slightly different from usual @xmath189 , because of different methods of measurements . the measurements of @xmath188 were carried out as follows . first the sample was quenched from 298 to 1.9 k at @xmath61 = 0 . then @xmath61 (= 5 or 15 oe ) was applied . the measurements of @xmath190 and @xmath186 were done with increasing @xmath17 from 1.9 to 20 k. at each @xmath17 , @xmath190 was measured at the same @xmath61 and then @xmath186 was measured 100 sec later after the field was changed from @xmath61 to 0 oe . second , the sample was annealed at 100 k for 1200 sec at @xmath61 . the measurements of @xmath191 and @xmath187 were done with decreasing @xmath17 from 20 to 1.9 k. at each @xmath17 , @xmath191 was measured at @xmath61 and then @xmath187 was measured 100 sec later after the field was changed from @xmath61 to 0 oe . figure [ fig : twelve ] shows the @xmath17 dependence of @xmath190 , @xmath186 , @xmath191 , and @xmath187 , @xmath192 (= @xmath193 ) , @xmath194 (= @xmath195 ) in the case of @xmath61 = 5 and 15 oe . note that the @xmath17 dependence of @xmath191 is not exactly the same as that of @xmath60 , because of the difference in the method of field cooling . while @xmath60 shown in fig . [ fig : nine](a ) increases with decreasing @xmath17 , @xmath191 shows a peak at 7.5 k between @xmath5 and @xmath6 and an inflection point at @xmath6 where d@xmath191/d@xmath17 exhibits a positive local maximum . this result is indicative of a non - uniformity in the fm phase : frustrated spins coexists with ferromagnetically aligned spins . the @xmath17 dependence of @xmath187 is exactly the same as that of @xmath196 . the magnetization @xmath187 ( measured at @xmath61 = 0 ) in the case of @xmath61 = 5 oe shows a broad peak around 10.6 k just above @xmath5 , and reduces to zero at @xmath4 . in contrast , @xmath186 is much smaller than @xmath187 . the difference @xmath192 is different from @xmath197 between @xmath6 and @xmath5 . in fact , the difference ( @xmath198 ) is larger than zero only between @xmath6 and @xmath5 and near @xmath4 .    as far as we know , there has been only one report on @xmath199 ( measured by a conventional method ) in a reentrant ferromagnet ( fe@xmath181cr@xmath109ni@xmath109)@xmath2p.@xcite @xmath199 was measured as @xmath17 increases after cooling down the system to the lowest @xmath17 in the presence of @xmath61 ( fc cooling ) , annealing at @xmath17 at a waiting time @xmath200 , and then reducing @xmath61 to zero . the magnetization @xmath199 shows a local minimum at @xmath6 and a broad peak between @xmath6 and @xmath5 . it reduces to zero at @xmath5 with increasing @xmath17 . ( a ) @xmath61-@xmath17 phase diagram near @xmath6 : for each @xmath61 the local - minimum temperatures of d@xmath112/d@xmath17 vs @xmath17 at _ f _ = 0.1 hz ( @xmath201 ) and at 100 hz ( @xmath202 ) , and d@xmath171/d@xmath17 vs @xmath17 ( @xmath203 ) , and the peak temperatures of @xmath112 vs @xmath17 at 0.1 hz ( @xmath204 ) and 100 hz ( @xmath205 ) . the solid line denotes the least squares fitting curve ( see the text for detail ) . ( b ) @xmath61-@xmath17 phase diagram near @xmath4 : for each @xmath61 the local - minimum temperature of d@xmath171/d@xmath17 vs @xmath17 ( @xmath205 ) , and the peak temperatures of @xmath59 vs @xmath17 ( @xmath201 ) and @xmath112 vs @xmath17 at 100 hz ( @xmath204).,width=283 ]    we have measured the @xmath17 dependence of @xmath74 and @xmath112 at various @xmath61 for @xmath206 hz and 0.1 hz , where @xmath61 ( @xmath207 koe ) is applied along the @xmath48 plane perpendicular to the @xmath48-axis . figures [ fig : thirteen ] shows the @xmath17 dependence of @xmath74 and @xmath112 at various @xmath61 for @xmath16 = 100 hz . the ac field @xmath65 (= 50 moe ) was used for 1.9 @xmath165 12 k and a larger @xmath65 (= 500 moe ) was used for 14 @xmath165 19 k. the peak of @xmath74 and the shoulder of @xmath112 around @xmath5 disappears for @xmath185 50 oe , and the peaks of @xmath74 and @xmath112 around @xmath4 disappears for @xmath185 7 oe . the peak of @xmath112 around @xmath6 shifts to the low @xmath17-side with increasing @xmath61 for 0 @xmath208 1 koe . the peak of @xmath112 around @xmath4 also shifts to the low @xmath17-side with increasing @xmath61 for 0 @xmath62 7 oe . in figs . [ fig : fifteen](a ) and ( b ) we show the @xmath61-@xmath17 diagrams around @xmath6 and @xmath4 , respectively . here the temperature ( denoted as @xmath209 ) of negative local minimum of d@xmath112/d@xmath17 vs @xmath17 at 0.1 hz ( data are not shown ) is plotted as a function of @xmath61 . for comparison , we also show the @xmath61 dependence of the negative local minimum temperatures of d@xmath171/d@xmath17 vs @xmath17 and the peak temperatures of @xmath112 vs @xmath17 at @xmath16 = 0.1 and 100 hz . these lines are away from the line @xmath209 . the least squares fit of the data of the line @xmath209 for 0 @xmath62 600 oe to @xmath210^{p } ,   \\label{eq : four}\\ ] ] yields parameters @xmath10 = 1.55 @xmath8 0.13 , @xmath211 = 4.26 @xmath8 0.11 k , and @xmath212 = ( 2.6 @xmath8 0.3 ) koe . note that the value of @xmath211 (= 4.26 k ) is larger than that of @xmath6 (= 3.45 @xmath8 0.31 k ) . the value of exponent @xmath10 is close to that ( @xmath10 = 1.50 ) for the de almeida - thouless ( at ) line.@xcite in the mean field picture , the at line separates the replica - symmetry ( fm ) phase from the replica - symmetry - breaking ( rsb ) phase in the ( @xmath61,@xmath17 ) line . @xmath216 dependence of @xmath217 at @xmath17 = 3 and 7 k. @xmath200 = 2.0 @xmath128 10@xmath218 sec . @xmath61 = 10 oe . @xmath173 . see the detail of the measurement and the definition of @xmath216 = 0 in the text.,width=283 ]    @xmath216 dependence of @xmath219 [ @xmath220 at various @xmath17 . @xmath221 sec.,width=283 ]    in order to reveal a possible aging phenomenon in the rsg phase and fm phase , we have studied time ( @xmath216 ) dependence of the zero - field cooled magnetization @xmath217 . first the system was cooled from 100 k to @xmath17 in the absence of @xmath61 , where the remnant magnetic field is less than 3 moe . the system was kept at @xmath17 for a wait time @xmath200 (= 2.0 @xmath128 10@xmath218 sec ) . a dc magnetic field ( @xmath61 = 10 oe ) was applied at @xmath216 = 0 . the magnetization ( @xmath217 ) was measured as a function of @xmath216 elapsed after the field application . figure [ fig : sixteen ] shows the @xmath216 dependence of @xmath222 at @xmath17 = 3 and 7 k. the corresponding relaxation rate @xmath219 [ @xmath223 is shown in fig . [ fig : seventeen ] as a function of @xmath216 for each @xmath17 . the relaxation rate @xmath219 at @xmath17 = 3 k has a peak around @xmath224 = 4 @xmath128 10@xmath218 sec which is larger than @xmath200 . note that the inflection point of @xmath217 corresponds to the peak of @xmath219 . at @xmath17 = 4 k , @xmath219 shows a very flat plateau between 3.2 @xmath128 10@xmath218 and 10@xmath225 sec , in addition to a small peak at @xmath224 = 1.1 @xmath128 10@xmath225 sec . such an aging behavior does not end at @xmath6 , but sustains into the fm phase . the relaxation rate @xmath219 has a peak at a time shorter than @xmath200 for 5 @xmath165 7 k : @xmath224 = 1.6 @xmath128 10@xmath218 sec at @xmath17 = 5 k , 1 @xmath128 10@xmath218 sec at 6 k , and 1.3 @xmath128 10@xmath218 sec at 7 k. the peak time @xmath224 is equal to is 2.1 @xmath128 10@xmath218 sec at 8 k and 1.8 @xmath128 10@xmath218 sec at 9 k , which are close to @xmath200 . similar behavior is observed in the fm phase of ( fe@xmath23ni@xmath24)@xmath25p@xmath26b@xmath27al@xmath3 by jonason et al.@xcite : @xmath219 has a peak around @xmath200 (= 100 - 10@xmath225 sec ) . .[table : one]least squares fitting parameters of @xmath222 to the power law form given by eq.([eq : six ] ) . @xmath61 = 10 oe . @xmath200 = 2.0 @xmath128 10@xmath218 sec . the values of @xmath226 and @xmath217 are obtained from fig . [ fig : nine](b ) at @xmath61 = 10 oe . @xmath227 , @xmath228 , @xmath226 and @xmath217 are in the units of emu / av mol . [ cols= \" < , < , < , < , < , < \" , ]     we have measured the @xmath216 dependence of @xmath112 at @xmath17 = 7 and 8.5 k , where @xmath61 = 0 . the system was quenched from 100 k to @xmath17 at time ( age ) zero . both @xmath74 and @xmath112 were measured simultaneously as a function of time @xmath216 at constant @xmath17 . each point consists in the successive measurements at various frequencies ( @xmath229 hz ) . figure [ fig : eighteen ] shows the @xmath216 dependence of @xmath112 and @xmath74 at @xmath17 = 7 k for @xmath16 = 0.05 and 1 hz , respectively . the absorption @xmath112 decreases with increasing @xmath216 and is well described by a power - law decay @xmath230 where @xmath231 is an exponent , and @xmath232 and @xmath233 are @xmath216-independent constants . in the limit of @xmath234 , @xmath214 tends to @xmath232 . the least squares fit of the data of @xmath214 at @xmath17 = 7 k to eq.([eq : seven ] ) yields parameters listed in table [ table : two ] . the exponent @xmath231 , which is dependent on @xmath16 , is smaller than that of the fm phase of reentrant ferromagnet cdcr@xmath235in@xmath0s@xmath35 ( @xmath236 0.2)@xcite and the sg phase of pure spin glass fe@xmath147mn@xmath147tio@xmath3 ( @xmath236 0.14 @xmath8 0.03).@xcite the value of @xmath237 tends to decrease with increasing @xmath16 . in contrast , the value of @xmath238 tends to increase with increasing @xmath16 . it follows that the second term of eq.([eq : seven ] ) can not be described by a power form @xmath239 , suggesting no @xmath18-scaling law in the form of @xmath240 . this is in contrast to the @xmath18-scaling of @xmath112 in the fm phase of reentrant ferromagnet cdcr@xmath235in@xmath0s@xmath35.@xcite the @xmath216 dependence of @xmath74 can be also described by the power law form ( @xmath241 ) which is similar to eq.([eq : seven ] ) . the value of @xmath242 at @xmath17 = 7 and 8.5 k which is listed in table [ table : two ] , is on the same order as that of @xmath231 . note that similar aging behavior is also observed both in @xmath112 and @xmath74 below @xmath6 . the change of @xmath112 and @xmath74 with @xmath216 below @xmath6 is not so prominent compared to that above @xmath6 , partly because of relatively small magnitude of @xmath112 and @xmath74 below @xmath6 .","summary":"the time dependence of the absorption is described by a power law form ( ) in the ferromagnetic phase , where at = 0.05 hz and = 7 k. no-scaling law for [ is observed .","abstract":"linear and nonlinear dynamic properties of a reentrant ferromagnet cucocl-fecl graphite bi - intercalation compound are studied using ac and dc magnetic susceptibility . this compound undergoes successive phase transitions at the transition temperatures (= 16 k ) , (= 9.7 k ) , and (= 3.5 k ) . the static and dynamic behaviors of the reentrant spin glass phase below are characterized by those of normal spin glass phase with critical exponent = 0.57 0.10 , a dynamic critical exponent = 8.5 1.8 , and an exponent (= 1.55 0.13 ) for the de almeida -thouless line . a prominent nonlinear susceptibility is observed between and and around , suggesting a chaotic nature of the ferromagnetic phase ( ) and the helical spin ordered phase ( ) . the aging phenomena are observed both in the rsg and fm phases , with the same qualitative features as in normal spin glasses . the aging of zero - field cooled magnetization indicates a drastic change of relaxation mechanism below and above . the time dependence of the absorption is described by a power law form ( ) in the ferromagnetic phase , where at = 0.05 hz and = 7 k. no-scaling law for [ is observed ."}
{"article_id":"cond-mat0308247","section_id":"c","document":"the rsg phase below @xmath6 is not a mixed phase but a normal sg phase . the static and dynamic behaviors of the rsg phase are characterized by that of the normal sg phase : a critical exponent @xmath7 = 0.57 @xmath8 0.10 , a dynamic critical exponent @xmath9 = 8.5 @xmath8 1.8 , and an exponent @xmath10 (= 1.55 @xmath8 0.13 ) for the at line.@xcite the aging phenomena are observed . the relaxation of @xmath222 obeys a stretched exponential law , which is usually used in analysis of the dynamics of the normal sg phase . no appreciable nonlinear magnetic susceptibility is observed below @xmath6 . these results suggest that the long - range ferromagnetic correlation completely disappears in the rsg phase . in contrast , the fm phase of our system is very different from that of regular fm phase . the chaotic behavior observed in the fm phase is rather similar to that in the rsg phase . the prominent nonlinear susceptibility of the fm phase arises mainly from the unfrustrated ferromagnetically ordered spins ( the fm network ) . the aging phenomena are also observed in the fm phase . a dynamic crossover of the relaxation of@xmath222 is observed around @xmath6 . above @xmath6 the relaxation of @xmath222 obeys a weak power law . these results can be well explained in terms of the phenomenological random - field picture proposed by aeppli et al.@xcite ( see sec . [ intro ] ) . the fm phase consists of the fm network ( with slow dynamics ) surrounded by frustrated spins ( the pm clusters with fast dynamics ) . such a nonuniformity gives rise to the chaotic nature of the fm phase . on approaching @xmath6 from the high-@xmath17 side , the thermal fluctuations of the spins in the pm clusters become so slow that the slow dynamics of the fm network is significantly influenced by the dynamics of the pm clusters . the coupling between the fm network and the pm clusters becomes important . the molecular fields from the slow pm spins act a random magnetic field . this causes breakups of the fm network in to finite - sized clusters . below @xmath6 , the system becomes into the rsg phase . next we discuss the nature of the aging phenomena in the fm phase . the features of the aging phenomena are summarized as follows . ( i ) @xmath222 has a power law form ( @xmath243 ) for 5 @xmath244 9 k. the value of @xmath245 is listed in table [ table : one ] . ( ii ) both @xmath214 and @xmath215 at @xmath17 = 7 and 8.5 k have power law forms ( @xmath246 and @xmath247 ) at fixed @xmath16 ( = @xmath248 ) . the values of @xmath242 and @xmath231 are listed in table [ table : two ] . ( iii ) @xmath249 for 6.1 @xmath165 7.3 k has a power law form ( @xmath250 ) , where @xmath170 = 0.04 @xmath8 0.01 at 6.1 k and 0.12 @xmath8 0.01 at 7.2 k. the increase of @xmath249 with increasing @xmath157 is similar to that reported in conventional sg s such as fe@xmath147mn@xmath147tio@xmath3.@xcite    as is listed in table [ table : one ] , the exponent @xmath251 increases exponentially with increasing @xmath17 and is described by @xmath252 $ ] with @xmath5 = 9.7 k. similar result on @xmath251 has been reported by ito et al.@xcite for the sg phase of fe@xmath147mn@xmath147tio@xmath3 : @xmath253/0.17\\}$ ] with @xmath254 = 17.6 k at @xmath61 = 3.2 koe . from monte - carlo simulations on the 3d @xmath132 ising spin glass model , ogielski@xcite has discussed the @xmath216 dependence of the order parameter @xmath255 below the spin freezing temperature @xmath256 . the order parameter @xmath255 is described by a power law form [ @xmath257 , where @xmath251 is well fitted by @xmath258$]:@xcite @xmath245 = 0.07 at @xmath17 = @xmath256 . the similarity between our result and the computer simulation is remarkable . this implies that the growth of @xmath217 in the fm phase ( but not in the rsg phase ) is essentially the same as that in the sg phase of spin glass systems . what is the relation between the exponent @xmath245 for @xmath222 and the exponent ( @xmath242 , @xmath231 , @xmath170 ) for @xmath74 and @xmath112 ? according to lundgren et al.,@xcite @xmath222 is related to the linear ac susceptibility @xmath249 and @xmath259 through the following relations @xmath260 and @xmath261 when @xmath222 is described by a power law form given by eq.([eq : six ] ) , @xmath249 and @xmath259 can be estimated as @xmath262 ( or @xmath263 ) and @xmath264 ( or @xmath263 ) , respectively , leading to a prediction that the exponents @xmath170 , @xmath242 , and @xmath231 are essentially the same as the exponent @xmath245 . experimentally we find @xmath245 = 0.059 @xmath8 0.001 ( @xmath17 = 8 k ) , @xmath231 = 0.074 @xmath8 0.016 ( @xmath17 = 7 k and @xmath16 = 0.05 hz ) , and @xmath242 = 0.046 @xmath8 0.006 ( @xmath17 = 7 k , @xmath16 = 1 hz ) , and @xmath170 = 0.081 @xmath8 0.02 ( @xmath17 = 6.7 k ) . there are relatively large differences among @xmath170 , @xmath242 , @xmath231 , and @xmath245 , depending on the conditions . nevertheless , we can say that these exponents are roughly the same and are on the order of 0.05 - 0.08 around 7 k. the value of these exponents is nearly equal to that of the exponent @xmath142 ( = 0.066 @xmath8 0.001 ) derived from the scaling analysis in sec . [ resultb ] . note that our result of @xmath245 is in good agreement with @xmath245 = 0.060 - 0.088 for the fm phase of the reentrant ferromagnet ( fe@xmath265ni@xmath266)@xmath267mn@xmath268.@xcite    finally we estimate the value of @xmath142 . the exponent @xmath142 is given by @xmath269 , where @xmath123 . when we use the scaling relation , @xmath270 , which is derived in our previous paper,@xcite @xmath142 is given by @xmath271 , where @xmath272 is the energy exponent and @xmath124 is the dynamic critical exponent . the values of @xmath272 and @xmath124 are theoretically predicted : @xmath124 = 6.0 @xmath8 0.5 for the 3d @xmath132 ising spin glass model ( ogielski@xcite ) and @xmath272 = 0.19 @xmath8 0.01 ( bray and moore@xcite ) . using these values , @xmath142 is estimated as @xmath142 = 0.063 @xmath8 0.017 , which is in good agreement with our result ( @xmath142 = 0.066 @xmath8 0.001 ) .","summary":"the static and dynamic behaviors of the reentrant spin glass phase below are characterized by those of normal spin glass phase with critical exponent = 0.57 0.10 , a dynamic critical exponent = 8.5 1.8 , and an exponent (= 1.55 0.13 ) for the de almeida -thouless line .","abstract":"linear and nonlinear dynamic properties of a reentrant ferromagnet cucocl-fecl graphite bi - intercalation compound are studied using ac and dc magnetic susceptibility . this compound undergoes successive phase transitions at the transition temperatures (= 16 k ) , (= 9.7 k ) , and (= 3.5 k ) . the static and dynamic behaviors of the reentrant spin glass phase below are characterized by those of normal spin glass phase with critical exponent = 0.57 0.10 , a dynamic critical exponent = 8.5 1.8 , and an exponent (= 1.55 0.13 ) for the de almeida -thouless line . a prominent nonlinear susceptibility is observed between and and around , suggesting a chaotic nature of the ferromagnetic phase ( ) and the helical spin ordered phase ( ) . the aging phenomena are observed both in the rsg and fm phases , with the same qualitative features as in normal spin glasses . the aging of zero - field cooled magnetization indicates a drastic change of relaxation mechanism below and above . the time dependence of the absorption is described by a power law form ( ) in the ferromagnetic phase , where at = 0.05 hz and = 7 k. no-scaling law for [ is observed ."}
{"article_id":"hep-ph0409115","section_id":"c","document":"with the development of soft - collinear effective theory ( scet ) , theoretical predictions for inclusive @xmath0-meson decay distributions have recently received renewed attention . while these processes had been studied extensively during the past decade , the ever increasing precision of the measurements at the @xmath0 factories requires a new level of accuracy . this is an area where scet is not only a useful conceptual tool , but where it provides concrete means of pushing the limits of theoretical calculations . earlier this year , two groups have performed systematic analyses of short - distance corrections in the semileptonic decay @xmath314 @xcite and radiative decay @xmath5 @xcite , including a complete scale separation and resummation of sudakov logarithms . as a result , the behavior of the leading shape function under renormalization is now well understood . this leaves power corrections to the heavy - quark limit as the principal source of theoretical uncertainties .    in the present work , we have used the formalism of scet to perform a systematic study of such power - suppressed effects . at tree level , the results can be expressed in terms of a set of subleading shape functions defined via the fourier transforms of forward matrix elements of bi - local light - cone operators in heavy - quark effective theory . we have identified a new contribution arising from four - quark operators , which was not considered previously . we have shown that , when shape functions appearing in process - independent combinations are combined into single functions , then a total of three subleading shape functions are required to describe arbitrary current - induced decay distributions of @xmath0 mesons into light final - state particles . while subleading shape - function effects had been studied in the past , our results do not agree with those found in the original papers @xcite .    in the last part of this work , we have presented analytical expressions for a variety of distributions in @xmath2 decay , which can be used directly for the analysis of experimental data . we have also given a formula for the triple differential rate , which allows for arbitrary cuts on kinematic variables . while this concludes the problem of tree - level power corrections in semileptonic decay , we have stressed that no complete ( tree - level ) analysis of power - suppressed corrections to the @xmath5 decay exists to date . the formalism developed in this work can , however , readily be extended to this case . we are grateful to martin beneke , masahiro morii , and ben pecjak for useful comments . s.w.b .  would like to thank daniel wyler at the university of zurich for hospitality during the final stage of this work . this research was supported by the national science foundation under grant phy-0355005 . the research of m.n . is also supported in part by the department of energy under grant de - fg02 - 90er40542 . m. neubert , phys .  rev . d * 49 * , 3392 ( 1994 ) [ hep - ph/9311325 ] ; 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c.  w.  bauer , d.  pirjol and i.  w.  stewart , phys . d * 65 * , 054022 ( 2002 ) [ hep - ph/0109045 ] . m.  beneke , a.  p.  chapovsky , m.  diehl and t.  feldmann , nucl . b * 643 * , 431 ( 2002 ) [ hep - ph/0206152 ] ; m.  beneke and t.  feldmann , phys . b * 553 * , 267 ( 2003 ) [ hep - ph/0211358 ] . m.  neubert , phys . rept .   * 245 * , 259 ( 1994 ) [ hep - ph/9306320 ] . t.  becher , r.  j.  hill and m.  neubert , phys . d * 69 * , 054017 ( 2004 ) [ hep - ph/0308122 ] . r.  j.  hill and m.  neubert , nucl . b * 657 * , 229 ( 2003 ) [ hep - ph/0211018 ] . r.  j.  hill , t.  becher , s.  j.  lee and m.  neubert , jhep * 0407 * , 081 ( 2004 ) [ hep - ph/0404217 ] . d.  pirjol and i.  w.  stewart , phys .  rev . d * 67 * , 094005 ( 2003 ) [ erratum - ibid . d * 69 * , 019903 ( 2004 ) ] [ hep - ph/0211251 ] . b.  o.  lange and m.  neubert , nucl .  phys . b * 690 * , 249 ( 2004 ) [ hep - ph/0311345 ] . m.  e.  luke , phys . b * 252 * , 447 ( 1990 ) . a.  f.  falk and m.  neubert , phys . d * 47 * , 2965 ( 1993 ) [ hep - ph/9209268 ] . a.  v.  manohar and m.  b.  wise , phys . d * 49 * , 1310 ( 1994 ) [ hep - ph/9308246 ] . m.  neubert and c.  t.  sachrajda , nucl . b * 483 * , 339 ( 1997 ) [ hep - ph/9603202 ] . i.  i.  y.  bigi , b.  blok , m.  a.  shifman , n.  uraltsev and a.  i.  vainshtein , hep - ph/9401298 ; i.  i.  y.  bigi , hep - ph/9508408 . m.  di pierro and c.  t.  sachrajda , nucl . b * 534 * , 373 ( 1998 ) [ hep - lat/9805028 ] . d.  becirevic , hep - ph/0110124 . m.  s.  baek , j.  lee , c.  liu and h.  s.  song , phys . d * 57 * , 4091 ( 1998 ) [ hep - ph/9709386 ] . m.  b.  voloshin , phys . b * 515 * , 74 ( 2001 ) [ hep - ph/0106040 ] . f.  de fazio and m.  neubert , jhep * 9906 * , 017 ( 1999 ) [ hep - ph/9905351 ] .","summary":"the contributions of subleading shape functions to inclusive decay distributions of mesons are derived from a systematic two - step matching of qcd current correlators onto soft - collinear and heavy - quark effective theory . at tree - level , the results can be expressed in terms of forward matrix elements of bi - local light - cone operators . clns  04/1890 + hep - ph/0409115 +","abstract":"the contributions of subleading shape functions to inclusive decay distributions of mesons are derived from a systematic two - step matching of qcd current correlators onto soft - collinear and heavy - quark effective theory . at tree - level , the results can be expressed in terms of forward matrix elements of bi - local light - cone operators . four - quark operators , which arise at , are included . our results are in disagreement with some previous studies of subleading shape - function effects . a numerical analysis of decay distributions suggests that power corrections are small , with the possible exception of the endpoint region of the charged - lepton energy spectrum .    clns  04/1890 + hep - ph/0409115 + september 9 , 2004    * subleading shape functions in inclusive b decays *    stefan w. bosch , matthias neubert , and gil paz +"}
{"article_id":"0711.4201","section_id":"c","document":"as illustrated throughout this review , various progresses have been reported during the last years concerning the description of the ferroelectric properties in oxide ultrathin films and superlattices . in this context , first - principles theory and modeling constituted an efficient guide and provided a significant support to experimental works . on the one hand , proper understanding of the crucial role played by the electrical and mechanical allowed to realize significant advances as discussed above . on the other hand , however , many issues still remain unclear so that this field of research is still at an exciting and incipient stage .    in ferroelectric thin films , despite recent achievements , some important questions remain without clear answer and interesting perspectives ask for further confirmations . only recently addressed from first - principles,@xcite the mechanism and the quality of the screening at free surfaces with air remains unclear . also the reason why some ferroelectric films on metallic electrodes stay monodomain with a reduced polarization while others break into domains is particularly intriguing.@xcite the roles of defects , such as oxygen vacancies , and of leakage currents on the amplitude of the depolarizing field was up to now neglected in theoretical studies while they might play a role , at least in some cases . the mechanism of the switching and domain - wall motion in ultrathin films is an important question that has been studied in detail experimentally @xcite but that has not been addressed yet at the first - principles level , although the first - steps on multi - scale computations based on molecular dynamics and coarse - grained monte carlo simulations have been recently taken.@xcite recent studies reported interesting perspectives for ferroelectric tunnel junctions @xcite but no first - principles quantitative estimate of the tunneling current and of the electroresistance has been reported yet . finally and without being exhaustive , the case of a ferroelectric layer between magnetic electrodes was proposed as a mechanism to achieve ferroelectric control of magnetism @xcite but is still widely unexplored . ferroelectric superlattices constitute a promising alternative avenue that offers practical solutions to bypass some of the drawbacks of epitaxial ultrathin films ( huge depolarizing fields , high leakage currents , strain relaxation ) , while preserving perfect crystal ordering and allowing to monitor the ferroelectric properties . up to now , fine tuning of the polarization and phase transition temperature has , for instance , been illustrated playing with the superlattice period and composition but the most exciting perspectives probably rely on the potentiality of such systems to generate totally new and unexpected phenomena . also , superlattices might offer particularly attractive opportunities in the emergent field of magneto - electric multiferroics.@xcite    the perspectives are numerous and first - principles simulations will certainly continue to play an active role in the field of nanoscale ferroelectrics in the future . in some cases , this will mandatory require new theoretical developments such as , for instance , the identification of alternative and more accurate functionals or of new efficient approaches to compute complex properties . in order cases , the computer power will constitute the main limitation . in all cases , pursuing the constructive dialog initiated during the recent years between theorists and experimentalists will certainly appear as a major motivation .","summary":"going further we also highlight promising new avenues and future challenges within this exciting field or researches .    to appear in `` _ journal of computational and theoretical nanoscience _ ''","abstract":"in this review , we propose a summary of the most recent advances in the first - principles study of ferroelectric oxide epitaxial thin films and multilayers . we discuss in detail the key roles of mechanical and electrical boundary conditions , providing to the reader the basic background for a simple and intuitive understanding of the evolution of the ferroelectric properties in many nanostructures . going further we also highlight promising new avenues and future challenges within this exciting field or researches .    to appear in `` _ journal of computational and theoretical nanoscience _ ''"}
{"article_id":"1007.0438","section_id":"i","document":"observational evidence ( e.g. spergel et al .  2007 ; komatsu et al . 2009 ) favours the hierarchical growth of structures in a universe dominated by cold dark matter ( cdm ) and dark energy ( @xmath0 ) , the so called universe . within this paradigm dark matter collapses first into small haloes which accrete matter and merge to form progressively larger haloes over time . galaxies are thought to form out of gas which cools and collapses to the centres of these dark matter haloes ( e.g. white & rees 1978 ) . in this picture the properties of galaxies are expected to be strongly related to the properties of the dark matter haloes in which they are embedded ( e.g. mo , mao & white 1998 , dutton et al . 2007 ) . it has been shown by several studies that the structural properties of dark matter ( dm ) haloes are dependent on halo mass : for example higher mass haloes are less concentrated ( navarro , frank & white 1997 , hereafter nfw ; eke et al .  2001 ; bullock et al . 2001a ; kuhlen et al . 2005 ; macci et al .  2007 ; neto et al .  2007 ; gao et al . 2008 ; duffy et al .  2008 ; macci , dutton , & van den bosch 2008 ( hereafter m08 ) ; klypin et al . 2010 ) , and are more prolate ( jing & suto 2002 ; allgood et al .  2006 ; gottlber & yepes 2007 ; bett et al .  2007 ; macci et al . 2007 ; m08 ) on average . the situation is less clear for the spin parameter , at @xmath5 there seems to be no mass dependence ( macci et al .  2007 ; m08 ) or at least a very weak one ( bett et al . 2007 ) , while for increasing values of the redshift a possible mild correlation between spin and mass seems to arise ( knebe & power 2008 ) .    in m08 the properties of dm haloes were studied in universes whose parameters were fixed by the one , three and five - year release of the wmap mission ( wmap5 ; komatsu et al . in that study the attention has been focused on the structural parameters of virialized haloes and their correlations at the present epoch , @xmath5 . in this work we extend this previous analysis to higher redshifts and study how the scaling relations of dm haloes change with time .    as in m08 we use a large suite of n - body simulations in a wmap5 cosmology with different box sizes to cover the entire halo mass range relevant for galaxy formation : from @xmath6 ( haloes that host dwarf galaxies ) to @xmath7 ( massive clusters ) . we use these simulations to investigate the evolution of concentrations , spin parameter and shapes of dark matter haloes through cosmic time . similar studies have been already conducted in the past , mainly using lower numerical resolution and/or a smaller mass range ( but with few recent exceptions ) . navarro , frank & white ( 1997 ) proposed that the characteristic density of dark matter haloes was directly proportional to the density of the universe at time of formation , making possible to connect today properties of the dark matter density profile to the halo formation history and to the evolution of the expanding universe . this idea was then expanded by wechsler et al . ( 2002 ) , who found a clear connection between the mass growth of dark matter haloes and the definition of the formation time ; connecting directly the growth history of dark matter haloes to the evolution of their concentration parameter .    in a series of papers , zhao et al . ( 2003a , 2003b , 2009 ) have re - addressed the problem of the evolution of dark matter halo density profile and the mass accretion history . zhao s main result was the finding of a correlation between @xmath8 and the characteristic mass of dark matter haloes , @xmath9 , defined as the mass inside @xmath8 . thanks to this correlation they were able to model the time evolution of the concentration parameter in a cosmology - free fashion . a comparison of the different approaches to predict dark matter halo concentrations was performed by neto et al . they made a detailed comparison of the wechsler et al . ( 2002 ) and zhao et al . ( 2003 ) models for the time evolution of dark matter halo masses and their resulting predictions for halo concentration . neto et al .  ( 2007 ) found that although these models could match the average concentration reasonably well , they performed very poorly in many cases , because their models for halo mass evolution were not able to satisfactorily reproduce `` real '' mass growth histories from n - body simulations . however , the evolution of dark matter halo properties does not reduce to the concentration parameter only ; halo shape and spin parameter are also important quantities that could influence the properties of the hosted galaxy . allgood et al . ( 2006 ) studied the mass , radius , redshift and cosmology dependence ( via variations of @xmath10 ) of the shape of dark matter haloes ; while the environment dependence of the shape has been addressed in hahn et al . ( 2007a , b ) . the distribution of the spin parameter of dark matter haloes has been studied in several works ( e.g. bullock et al . 2001b ; macci et al .  2007 ; bett et al . 2007 ; m08 ; knebe & power 2008 ; davis & natarajan 2009 ; antonuccio - delogu et al .  2010 ) as well as the correlation between halo angular momentum and large scale structure ( e.g. bailin & steinmetz 2005 , bett et al .  2010 ) . one of the conclusions was that the correlation between spin and mass ( almost absent at @xmath5 ) seems to increase with increasing redshift . such a behavior could have important influences in the modeling of properties of galaxies at high redshift . although it has been shown that the inclusion of baryonic physics may affect the properties of the dark matter distribution ( e.g. gnedin et al . 2004 , kazantzidis et al . 2004 , libeskind et al . 2010 , knebe et al . 2010 , bett et al . 2010 ) , it also known that the strength of this effect strongly depends on the implemented baryonic physics ( duffy et al . the aim of this work is to extend the findings of m08 to higher redshift and to provide a comprehensive study of the evolution and correlation of the properties of dm haloes from @xmath4 to the present day . such a study is a basic ingredient to understand the complex problem of galaxy formation and evolution . our paper is organized as follows . in section [ sec : sims ] we describe the set of simulations we used , present definitions and describe the numerical procedures . in section [ c - mrelation ] we present our results for the mass and redshift dependence of the concentration parameter , present a novel and physically motivated approach to understand the time evolution of the concentration parameter following arguments based on the spherical collapse model . next we discuss our results for the mass and redshift dependence of the shape ( section [ sec : shape ] ) and spin parameter ( section [ sec : spin ] ) . finally in section [ sec : summ ] we summarize our findings and discuss on our results and their influence on the modeling of galaxy properties .","summary":"we study the mass and redshift dependence of the concentration , shape and spin parameter in n - body simulations spanning masses from  to  and redshifts from 0 to 2 . [ firstpage ]    galaxies : haloes  cosmology : theory , dark matter , gravitation  methods : numerical , n - body simulation","abstract":"we present a detailed study of the redshift evolution of dark matter halo structural parameters in acdm cosmology . we study the mass and redshift dependence of the concentration , shape and spin parameter in n - body simulations spanning masses from  to  and redshifts from 0 to 2 . we present a series of fitting formulae that accurately describe the time evolution of the concentration  mass ( ) relation since . using arguments based on the spherical collapse model we study the behaviour of the scale length of the density profile during the assembly history of haloes , obtaining physical insights on the origin of the observed time evolution of the  relation . we also investigate the evolution with redshift of dark matter halo shape and its dependence on mass . within the studied redshift range the relation between halo shape and mass can be well fitted by a redshift dependent power law . finally we show that although for the spin parameter is practically mass independent , at increasing redshift it shows a increasing correlation with mass .    [ firstpage ]    galaxies : haloes  cosmology : theory , dark matter , gravitation  methods : numerical , n - body simulation"}
{"article_id":"0810.1918","section_id":"i","document":"since the smoothed - particle hydrodynamics method was proposed by @xcite  and @xcite thirty years ago it has become a powerful and very successful method , which is routinely used worldwide to model systems with complicated geometries . in particular the combination of the sph method with hierarchical algorithms , addressed to efficiently organize data and calculate gravity , have led to a robust and reliable schemes able to handle complex geometries in three dimensions . in spite of these achievements little effort has been put in the development of axisymmetric applications of the method . however , a large body of interesting applications has to do with systems which have axisymmetrical geometry such as accretion discs , rotating stars or explosive phenomena ( i.e. novae or supernovae events ) provided the ignition takes place in a point - like region at the symmetry axis . the interaction between the gas ejected during a supernova explosion and the circumstellar matter has been extensively simulated using cylindric coordinates either with eulerian @xcite or sph @xcite codes . in inertial confinement fusion ( icf ) studies the collapse of the deuterium capsule induced by laser ablation can be also approximated using two - dimensional hydrodynamics . axisymmetrical hydrocodes are also useful to conduct resolution studies of three - dimensional codes just by imposing an initial configuration with the adequate symmetry . in these cases a comparison between the results obtained using the 3d - hydrocode and the equivalent , although usually better resolved , 2d simulation could help in numerical convergence studies . several formulations of different complexity have been proposed to handle with the axisymmetric version of sph . while the first algorithms were in general very crude , i.e. @xcite and references therein , neglecting the so called hoop - stress terms , there were also more consistent sph approximations , @xcite . recently more complete formulations were given by @xcite and by @xcite . in particular the scheme devised by omang et al . includes not only the hoop - stress terms but also a consistent treatment of the singularity line defined by the symmetry axis . the algorithm proposed by these authors relies in the use of interpolative kernels especially adapted to the cylindrical geometry . although the resulting scheme is robust , being able to successfully pass several test cases , it has the numerical inconvenient that an elliptical integral has to be solved numerically at each integration step for each particle .    in this paper we propose a new formulation of the axisymmetric sph technique which preserves many of the virtues stated by @xcite and @xcite , being also able to handle the singularity axis in an efficient way . in our scheme there is no necessity to modify the interpolating kernel ( we use the cubic spline polynomial ) . instead , taking advantage of the symmetry properties across the z - axis , we found several analytical correction factors to the physical magnitudes . these correction factors only affect particles moving at a distance from the z - axis lesser than @xmath0 , being @xmath1  the smoothing - length parameter . for the remaining particles the sph equations are identical to those given in @xcite . in addition , we also give expressions for the artificial viscosity and a new heat conduction algorithm , which takes into account the hoop - stress contribution . finally , we propose an original method to handle gravity within the sph paradigm which is consistent with the gridless nature of that particle method . the text is organized as follows : the basic fluid equations written in axisymmetric coordinates , and corrected from axis effects when necessary , are provided in section 2 . in section 3 we add useful physics to these equations consisting of an artificial viscosity term to handle shock waves ( section 3.1 ) , an expression for thermal conduction ( section 3.2 ) and an algorithm addressed to calculate self - gravity within the axisymmetric hypothesis ( section 3.3 ) . section 4 is devoted to describe and discuss five test cases aimed at validating the proposed scheme . finally the main conclusions of our work as well as some comments about the limitations of the developed scheme and prospects for the future are presented in section 5 .","summary":"[ firstpage ]    methods : numerical","abstract":"the axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics ( sph ) formalism is presented and checked using idealized scenarios taken from astrophysics ( free fall collapse , implosion and further pulsation of a sun - like star ) , gas dynamics ( wall heating problem , collision of two streams of gas ) and inertial confinement fusion ( icf , -ablative implosion of a small capsule- ) . new material concerning the standard sph formalism is given . that includes the numerical handling of those mass points which move close to the singularity axis , more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self - gravity in the simulations . the algorithm developed to compute gravity does not rely in any sort of grid , leading to a numerical scheme totally compatible with the lagrangian nature of the sph equations .    [ firstpage ]    methods : numerical"}
{"article_id":"0912.1722","section_id":"i","document":"due to the accelerated expansion of the universe , scalar field dark matter models emerged to account for the astronomic observations ( see  @xcite for a review ) . the models describe dark matter as a scalar . these models are special issues of more general theories known as scalar - tensor theories . in contrast with pure gravity , four - dimensional scalar - tensor gravity admits a variety of _ static _ , spherically symmetric , neutral or charged configurations including schwarzschild black holes ( bh ) , phantom bhs , naked singularities ( ns ) , particle - like ( p - l ) solutions and wormholes  @xcite . we consider the four - dimensional action of general relativity coupled to a self - gravitating real scalar field with positive kinetic energy ( einstein - scalar gravity ) @xmath0\\,,\\ ] ] where @xmath1 is the scalar curvature and @xmath2 is a potential for @xmath3 . the field equations derived from   are  @xcite @xmath4 ( where @xmath5 ) , with @xmath6 being the conserved energy - momentum tensor of @xmath3 @xmath7    for static , spherically symmetric configurations , the metric can be put in the form @xmath8 we fix the behavior of @xmath9 at spatial infinity such that @xmath10 as @xmath11 ( this is no loss of generality ) . with the ansatz  , the first equation in   reduces to eq   and the second group of equations in   lead to eqs   to  @xcite @xmath12 only three equations of this set are independent ; when the last three equations , to , are satisfied the first one is automatically satisfied . theorem 1 of ref . @xcite and its generalization to @xmath13-dimension  @xcite rules out wormhole , horn and flux tube type solutions to eqs   to . a consequence of that , the range of @xmath14 is from @xmath15 at the center to @xmath16 ; correspondingly , the range of @xmath17 is from @xmath18 at the center of configuration ( @xmath19 ) to @xmath16 . since @xmath20 ( real scalar field ) , leads to @xmath21 . hence , the function @xmath9 is concave down on its range . [ fig1 ] shows a generic typical behavior of @xmath9 where @xmath22 is the location of the center . in this paper @xmath22 is treated as a(n arbitrary ) scaling constant ( which can be set to 1 ) to which we compare the masses of the solutions and the whole theory is scale invariant is the same as the rescaling @xmath23 , @xmath24 , @xmath25 , @xmath26 , @xmath27 . ] . @xmath22 is also a measure of the strength of the field . we also make it such that the value of @xmath17 at @xmath15 is precisely @xmath22 ; this is no loss of generality as justified in appendix a.        for the case of four - dimensional field equations   to  , bronnikov  @xcite established some restrictive results , which have been latter generalized to @xmath28-dimensional field equations  @xcite . we are concerned with the following conclusions  @xcite .    * all horizons are simple . * all possible global structures for @xmath29 and for @xmath30 are the same ; * possible non - singular solutions have either minkowski / ads or de sitter structures . p - l asymptotically flat solutions with mass @xmath31 and @xmath32 having both signs are not excluded ; however , if @xmath33 no such p - l solutions ( @xmath31 ) exist . * for all functions @xmath34 , eqs   to   do not admit static , spherically symmetric regular bh and wormhole solutions with any asymptotic . * for @xmath33 , eqs   to   do not admit any hairy bh solutions ( no scalar hair theorems  @xcite ) .    an asymptotically flat bh solution to eqs   to is characterized by the presence of event horizons . since all horizons are simple , there is a change in the sign of @xmath35 at each event horizon . thus for a bh , @xmath35 has both signs in the domain @xmath36 . for an asymptotically flat p - l or ns solution there are no event horizons , thus @xmath35 has a constant sign for @xmath37 and because @xmath38 at spatial infinity so it is for @xmath37 . only for p - l solutions , the functions @xmath35 , @xmath34 & @xmath39 are finite everywhere for @xmath37 . some static , spherically symmetric , asymptotically flat solutions to eqs   to   have been derived in  @xcite , some of which represent different configurations of _ singular _ bhs . in ref  @xcite , bronnikov and shikin constructed bh , ns and p - l solutions . for the latter solution , their function @xmath40 ( eq ( b.3 ) of ref  @xcite ) does not approach 1 at spatial infinity ( @xmath41 ) ; rather , it approaches the limit @xmath42 , where @xmath22 is their parametric constant . thus , their  p - l \" solution is asymptotically flat only in the limit @xmath43 , corresponding to the trivial case @xmath44 with zero mass and constant functions @xmath45 : this is minkowski space time . recently , bronnikov and chernakova  @xcite constructed a two - parameter asymptotically flat bh characterized by its negative potential @xmath32 and where @xmath46 diverge near the center and converge as @xmath47 , while @xmath40 is finite everywhere . very recently , nikonov _ et al _  @xcite have obtained a two - parameter bhs and nss as well as a one - parameter p - l solutions . for the latter , all the three functions @xmath48 are finite everywhere , @xmath32 has both signs and @xmath3 is an incomplete elliptic integral of the first kind . most of the solutions constructed previously  @xcite were derived using the inverse problem method . the method consists in choosing a suitable function @xmath9 then solving eqs   to   for @xmath49 ( eq   is automatically satisfied ) . there are physically many interesting exact solutions to eqs   to   depending on the particular form of @xmath9 . the behavior of the solutions at spatial infinity is somehow defined by the boundary condition requiring that the solutions be asymptotically flat @xmath50 where @xmath51 is the schwarzschild mass . at the center there is no specific boundary condition , this is why there is a _ variety _ of possible asymptotically flat solutions , however , grouped into three categories : different ( singular ) bh solutions , ns and p - l solutions . to be more specific , the bh set ( @xmath40 having both signs ) include solutions where @xmath32 is finite everywhere ( this paper ) as well as solutions with divergent @xmath32  @xcite ; the same applies to the ns set where @xmath52 ( this paper ) . the solutions discussed in  @xcite and those discussed in this paper have different boundary conditions at the center . it is an interesting issue to investigate the behavior of the generic solutions near the center to determine the criteria by which the solutions emerge . the solutions discussed in  @xcite have been derived by choosing a special function has been chosen such that @xmath53 , where @xmath54 is their parametric constant . ] @xmath9 , however , they lacked a systematic treatment and many questions remained unanswered . for instance , we do not know a ) whether it is possible to obtain a bh ( resp . ns ) where both @xmath32 & @xmath3 are finite everywhere , b ) what conditions are required for obtaining , say , a bh or a p - l solution , c ) under which conditions the potential @xmath32 has both signs , etc .    in section  [ sec2 ] , we derive new integral formulas for @xmath49 and proof five corollaries and a theorem on selection criteria for obtaining predefined static , spherically symmetric , asymptotically flat solutions to eqs   to . first we deal with the most generic case then focus on a constrained case with minimum conditions . in section  [ sec3 ] , the behaviors of @xmath49 near the center and at spatial infinity are discussed , instances of solutions of particular interest are provided and two energy conditions are analyzed leading to two further corollaries . in section  [ sec4 ] , we derive further solutions by the inverse problem method . two appendices have been added for completeness .","summary":"we make a systematic investigation of the generic properties of static , spherically symmetric , asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self - gravitating real scalar field . seven corollaries and a theorem on selection criteria for two- and one - parametric solutions are proven and conditions for obtaining particle - like solution , black holes or naked singularities are derived . a series of exact solutions in closed forms describing different black holes , naked singularities and particle - like solutions are provided .    * keywords . * einstein - scalar gravity ; black holes ; naked singularities ; particle - like solutions ; exact solutions    ( 1,0)431","abstract":"we make a systematic investigation of the generic properties of static , spherically symmetric , asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self - gravitating real scalar field . seven corollaries and a theorem on selection criteria for two- and one - parametric solutions are proven and conditions for obtaining particle - like solution , black holes or naked singularities are derived . a series of exact solutions in closed forms describing different black holes , naked singularities and particle - like solutions are provided .    * keywords . * einstein - scalar gravity ; black holes ; naked singularities ; particle - like solutions ; exact solutions    ( 1,0)431"}
{"article_id":"0808.0180","section_id":"i","document":"for a given weight function @xmath2 supported on a set @xmath3 , a cubature formula of degree @xmath4 is a finite sum , @xmath5 , that provides an approximation to the integral and preserves polynomials of degree up to @xmath4 ; that is , @xmath6 where @xmath7 denotes the space of polynomials of total degree at most @xmath8 in @xmath9 variables . the points @xmath10 are called _ nodes _ and the numbers @xmath11 are called _ weights _ of the cubature . our primary interests are gaussian type cubature , which has minimal or nearer minimal number of nodes . for @xmath12 , it is well known that gaussian quadrature of degree @xmath4 needs merely @xmath13 nodes and these nodes are precisely the zeros of the orthogonal polynomial of degree @xmath8 with respect to @xmath2 . the situation for @xmath14 , however , is much more complicated and not well understood in general . as in the case of @xmath12 , it is known that a cubature of degree @xmath4 needs at least @xmath15 number of nodes , but few formulas are known to attain this lower bound ( see , for example , @xcite ) . in fact , for the centrally symmetric weight function ( symmetric with respect to the origin ) , it is known that the number of nodes , @xmath16 , of a cubature of degree @xmath4 in two dimension satisfies the lower bound @xmath17 known as mller s lower bound @xcite . it is also known that the nodes of a cubature that attains the lower bound , if it exists , are necessarily the common zeros of @xmath18 orthogonal polynomials of degree @xmath8 with respect to @xmath2 . similar statements on the nodes hold for cubature formulas that have number of nodes slightly above mller s lower bound , which we shall call cubature of _ gaussian type_. these definitions also hold in @xmath9-dimension , where the lower bound for the number of nodes for the centrally symmetric weight function is given in @xcite . there are , however , only a few examples of such formulas that are explicitly constructed and fewer still can be useful for practical computation . the best known example is @xmath19^d$ ] with the weight function @xmath20 and only when @xmath21 . in this case , several families of gaussian type cubature are explicitly known , they were constructed ( @xcite ) by studying the common zeros of corresponding orthogonal polynomials , which are product chebyshev polynomials of the first kind and the second kind , respectively . furthermore , interpolation polynomials bases on the nodes of these cubature formulas turn out to possess several desirable features ( @xcite , and also @xcite ) . on the other hand , studying common zeros of orthogonal polynomials of several variables is in general notoriously difficult . in the case of , the product chebyshev polynomials have the simplest structure among all orthogonal polynomials , which permits us to study their common zeros and construct cubature formulas in the case @xmath22 , but not yet for the case @xmath23 or higher . the purpose of the present paper is to provide a completely different method for constructing cubature formulas with respect to @xmath24 and @xmath25 . it uses the discrete fourier analysis associated with lattice tiling , developed recently in @xcite . this method has been used in @xcite to establish cubature for _ trigonometric functions _ on the regular hexagon and triangle in @xmath26 , a topic that has been studied in @xcite , and on the rhombic dodecahedron and tetrahedron of @xmath27 in @xcite . the cubature on the hexagon can be transformed , by symmetry , to a cubature on the equilateral triangle that generates the hexagon by reflection , which can in turn be further transformed , by a nontrivial change of variables , to gaussian cubature formula for algebraic polynomials on the domain bounded by steiner s hypercycloid . the theory developed in @xcite uses two lattices , one determines the domain of integral and the points that defined the discrete inner product , the other determines the space of exponentials or trigonometric functions that are integrated exactly by the cubature . in @xcite the two lattices are taken to be the same . in this paper we shall choose one as @xmath28 itself , so that the integral domain is fixed as the cube , while we choose the other one differently . in @xmath21 , we choose the second lattice so that its spectral set is a rhombus , which allows us to establish cubature formulas for trigonometric functions that are equivalent to gaussian type cubature formulas for @xmath24 and @xmath25 . in the case of @xmath29 , we choose the rhombic dodecahedron as a tiling set and obtain a cubature of degree @xmath4 that uses @xmath30 nodes , worse than the expected lower bound of @xmath31 but far better than the product gaussian cubature of @xmath32 nodes . this cubature with @xmath30 nodes has appeared recently and tested numerically in @xcite . we will further study the lagrange interpolation based on its nodes , for which the first task is to identify the subspace that the interpolation polynomials belongs . we will not only identify the interpolation space , but also give the compact formulas for the fundamental interpolation polynomials . one immediate question arising from this study is if there exist cubature formulas of degree @xmath4 with @xmath33 nodes on the cube . although examples of cubature formulas of degree @xmath4 with @xmath34 nodes are known to exist for special non - centrally symmetric regions ( @xcite ) , we are not aware of any examples for symmetric domains that use @xmath35 nodes . from our approach of tiling and discrete fourier analysis , it appears that the rhombic dodecahedron gives the smallest number of nodes among all other fundamental domains that tile @xmath27 by translation . giving the fact that this approach yields the cubature formulas with optimal order for the number of nodes , it is tempting to make the conjecture that a cubature formula of degree @xmath4 on @xmath0 ^ 3 $ ] needs at least @xmath30 nodes . the paper is organized as follows . in the following section we recall the result on discrete fourier analysis and lattice tiling in @xcite . cubature and interpolation for @xmath21 are developed in section 3 and those for @xmath23 are discussed in section 4 , both the latter two sections are divided into several subsections .","summary":"several cubature formulas on the cubic domains are derived using the discrete fourier analysis associated with lattice tiling , as developed in . the main results consist of a new derivation of the gaussian type cubature for the product chebyshev weight functions and associated interpolation polynomials on ^ 2 $ ] , as well as new results on ^ 3 $ ] . in particular , compact formulas for the fundamental interpolation polynomials are derived , based on nodes of a cubature formula on ^ 3 $ ] .","abstract":"several cubature formulas on the cubic domains are derived using the discrete fourier analysis associated with lattice tiling , as developed in . the main results consist of a new derivation of the gaussian type cubature for the product chebyshev weight functions and associated interpolation polynomials on ^ 2 $ ] , as well as new results on ^ 3 $ ] . in particular , compact formulas for the fundamental interpolation polynomials are derived , based on nodes of a cubature formula on ^ 3 $ ] ."}
{"article_id":"1106.0170","section_id":"i","document":"mode - selective chemistry , that is the control of specific conformational changes or chemical reactions by directing energy into specific vibrational modes of a molecule , has been a major goal and challenge of modern chemical physics @xcite . a variety of different routes to achieve mode - selective chemistry have been considered . for example , ultrafast excitation of molecules by laser pulses provided a route for directing energy transiently into specific mode - excitation or bond - cleavage in the presence of intramolecular vibrational energy redistribution ( ivr ) processes @xcite . nevertheless , on long time scales the statistical distribution of energy usually prevails and the control of specific conformational changes or chemical reactions by directing energy into specific vibrational modes still represents a challenge @xcite .    in recent years , much interest has been devoted to the study of molecular systems out of equilibrium , in particular single - molecule junctions @xcite . these junctions consist of a single molecule that is clamped between two metal or semi - conductor electrodes . if these electrodes are set to different electrochemical potentials by applying an external bias voltage , electrons tunnel from one lead to the other trough the molecule . the geometrical structure of the molecular bridge , due to its small size and mass , is very sensitive to charge fluctuations induced by these tunneling processes . the tunneling electrons thus strongly interact with the vibrational degrees of freedom of the junction @xcite . the distribution of vibrational energy on the molecular bridge , which results from these interactions , is highly correlated with the applied bias voltage and often deviates from a boltzmann distribution @xcite . in a single - molecule junction , it is thus possible to control a `` non - statistical '' non - equilibrium distribution of vibrational energy by an external potential bias . this offers an alternative route to mode - selective excitation ( or mode - selective chemistry ) . moreover , in the steady - state transport regime of a molecular junction , this could be achieved even without the cumbersome preparation of a specific initial - state .    employing generic model systems , we have recently shown @xcite that in a single - molecule junction the excitation of vibrational modes can be , indeed , selectively controlled by the external bias voltage . considering molecules with an asymmetric orbital structure and vibronic coupling to specific normal modes , it was demonstrated that , by adjusting the external bias voltage , such a system can be driven into different non - equilibrium states with different levels of excitation for specific nuclear modes . particularly , the excitation of a high frequency mode can be tuned much higher than that of a low frequency mode , thus overcoming the statistical distribution of vibrational energy that favors the excitation of low frequency modes . in this article , we extend our previous studies @xcite , where the principle of mode - selective vibrational excitation ( msve ) in a single - molecule junction was demonstrated for the first time . to this end , we outline in detail how the excitation of a single vibrational mode can be controlled by an external bias voltage . this bias - controlled excitation is then generalized to more than one vibrational mode , reviewing the basic msve phenomenon and emphasizing the role of intra - molecular interactions . in particular , we demonstrate msve in the presence of electronically mediated mode - mode coupling @xcite , which results from coupling of the vibrational modes to the same electronic state . these interactions induce energy transfer between the vibrational modes and tend to distribute current - induced vibrational excitation between the different modes . similarly , electronic correlations , _ e.g. _  due to coulomb repulsion , may influence msve by reorganizing the electronic population between specific electronic states at the molecule , which , to some extent and in different ways , is related to the phenomenon of msve . extending our previous work , we investigate complementary models for asymmetric molecular junctions exhibiting msve . these models are related , for example , to experiments on single - molecule junctions performed with a scanning tunneling microscope ( stm ) @xcite .    to describe this nonequilibrium transport problem , we employ two complementary approaches . the first one is a master equation approach ( me ) that is based on the time - evolution of the reduced density matrix of the molecular bridge @xcite . the respective equation of motion is evaluated strictly to second - order in the molecule - lead coupling , for which all resonant transport processes are included . within such a framework , no approximations with respect to the interactions on the molecular bridge need to be invoked , in particular not with respect to electron - electron interactions or electronic - vibrational coupling . however , higher - order processes @xcite like co - tunneling processes or the broadening of molecular levels due to the molecule - lead coupling are missing in this description . note that master equation approaches that take into account such higher - order effects have already been put forward @xcite . in the present work , however , we selected a nonequilibrium green s function approach ( negf ) @xcite to account for the higher - order effects . especially for the description of multiple vibrational modes @xcite , the negf methodology is typically more efficient . we employ a nonequilibrium green s function approach , which was originally proposed by galperin _ _ @xcite and recently extended to account for multiple vibrational and multiple electronic degrees of freedom of the molecular bridge @xcite . other theoretical approaches used to describe electron transport through a single - molecule junction are based _ e.g. _  on scattering theory @xcite , path integrals @xcite , multiconfigurational wave - function methods @xcite , flux - correlation approaches @xcite or exact diagonalization @xcite . the paper is organized as follows . the hamiltonian that we use to describe electron transport through a single - molecule junction is outlined in sec . [ modham ] . the me and negf methodologies that we employ to calculate steady - state observables of a biased single - molecule junction are briefly described in secs . [ meapproach ] and [ negfapproach ] , respectively . the basic physical mechanisms for vibrational heating and cooling in an asymmetric molecular junction , which lead to msve , are reviewed and analyzed for a single - level conductor in sec . [ vse ] . thereby , the role of electron - hole pair creation processes , which constitutes an important cooling mechanism in a molecular junction @xcite , is discussed in detail . moreover , the comparison of results obtained from our negf and me schemes enables us to distinguish resonant and non - resonant contributions . in sec . [ msve ] , we discuss msve in two model systems , representing generic asymmetric molecular junctions : a single - molecule junction with an intrinsically asymmetric molecular bridge ( model a ) @xcite , and a junction , where the bridging molecule is asymmetrically coupled to the leads ( model b ) . the latter scenario is typical for stm experiments . we demonstrate that the magnitude and the polarity of the external bias voltage can be used to direct vibrational energy into specific vibrational modes , even in the presence of intra - molecular interactions that tend to suppress the effect . thus , we predict that in the steady - state transport regime of a molecular junction , a bias - controlled `` non - statistical '' distribution of vibrational energy can be realized , where modes with higher frequency ( stronger bonds ) can be much higher excited than modes with a lower frequency ( weaker bonds ) .","summary":"we show that individual vibrational modes in single - molecule junctions with asymmetric molecule - lead coupling can be selectively excited by applying an external bias voltage . thereby , a non - statistical distribution of vibrational energy can be generated , that is , a mode with a high frequency can be stronger excited than a mode with a lower frequency . this is of particular interest in the context of mode - selective chemistry , where one aims to break specific ( not necessarily the weakest ) chemical bond in a molecule .","abstract":"we show that individual vibrational modes in single - molecule junctions with asymmetric molecule - lead coupling can be selectively excited by applying an external bias voltage . thereby , a non - statistical distribution of vibrational energy can be generated , that is , a mode with a high frequency can be stronger excited than a mode with a lower frequency . this is of particular interest in the context of mode - selective chemistry , where one aims to break specific ( not necessarily the weakest ) chemical bond in a molecule . such mode - selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments . to this end , we employ two complementary theoretical approaches , a nonequilibrium green s function approach and a master equation approach . the comparison of both methods reveals good agreement in describing resonant electron transport through a single - molecule contact , but also highlights the role of non - resonant transport processes , in particular co - tunneling and off - resonant electron - hole pair creation processes ."}
{"article_id":"1106.0170","section_id":"r","document":"in this section , we employ the me and the negf methodology , outlined in secs .  [ meapproach ] and [ negfapproach ] , respectively , to analyze transport characteristics of asymmetric single - molecule junctions . in particular , we consider a single vibrational mode coupled to a single electronic state in sec . [ vse ] , and demonstrate that an external bias voltage can be used to control its level of excitation . in sec . [ msve ] , we extend these studies to two vibrational modes and show that their level of excitation , despite their different frequencies , can be selectively controlled by switching the polarity of the applied bias voltage . to demonstrate the generality of the phenomenon and to corroborate our findings , we consider a variety of parameter regimes , including the effect of intra - molecular interactions . we first consider a model with a single vibrational mode coupled to a single electronic state in sec . [ vse ] and study how the excitation of the vibrational mode can be controlled by an external bias voltage @xmath128 . to this end , we consider a vibrational mode with frequency @xmath129 that is coupled to a single electronic state with coupling strength @xmath130 . the electronic state is located @xmath131ev above the fermi - level , and is asymmetrically coupled to the left , @xmath132 , and to the right lead , @xmath133 , respectively . the specific model parameters are detailed in table [ tablei ] . these parameters ( including those given in tab .  [ tableii ] ) reflect typical values for molecular junctions , as they are determined for example in ab - initio calculations @xcite or experiments @xcite . @xmath134 & @xmath135 & @xmath136 & @xmath137 & @xmath138 & @xmath139 & @xmath46 & @xmath140 & @xmath141 & @xmath142 + figs . [ fig1a ] and [ vse2 ] & 0.6 & 0.1 & 0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15 & 0.09 & 0 + fig . [ varye0 ] & 0  1 & 0.1 & 0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15 & 0.09 & 0 + fig . [ varyratio ] & 0.6 & 0.1 & 0.01  0.1 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15 & 0.09 & 0 + fig . [ fig.7 ] & 0.6 & 0.1 & 0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15 & 0.09 & 0  0.04 +    [ tablei ]    current - voltage characteristics for this model molecular junction and the respective population of the electronic state are shown in fig . [ fig1a ] . thereby , the solid black lines represent results obtained with the reduced density matrix approach , while the dashed black lines show results , for which we employed the nonequilibrium green s function approach . the results of both approaches agree very well . minor deviations between the approaches occur due to the broadening of the molecular levels , which is not included in the me scheme . for positive bias voltages , the current and the population of the electronic state display a single step . this step indicates the onset of transport at @xmath143 ( @xmath144 denotes the polaron - shifted energy of state 1 ( cf . [ negfapproach ] ) ) , where electrons from the left lead can resonantly tunnel onto the molecular bridge . notice that the molecular energy level is located well above the fermi - level of the junction , that is by several units of the vibrational frequency : @xmath145 . therefore , at the onset of transport by electron tunneling from the left electrode , several inelastic channels corresponding to processes described in figs . [ basmech]a , [ basmech]c and [ basmech]d open up simultaneously . as the bias increases further , additional heating channels become available , involving tunneling of high energy electrons from the strongly coupled ( left ) electrode onto the molecule ( see fig .  [ basmech]b ) . however , these additional channels do not significantly increase the current , since the bottleneck for transport in this asymmetric junction is tunneling processes from the molecular bridge to the weakly coupled ( right ) electrode that are already active . accordingly , the electronic state is populated ( from the left ) much faster than it is depopulated by tunneling processes to the right , and is therefore almost fully occupied for @xmath146 . for negative bias voltages , however , both the current and the electronic population exhibit a number of pronounced steps at @xmath147 ( @xmath148 ) . again , different inelastic transport channels open up simultaneously at the onset of the current . however , in this case , as the bias decreases further , @xmath149 , additional heating channels open up one by one at the bottleneck for transport , that is additional tunneling processes with respect to the right lead . since these processes are inactive for higher negative bias voltages , @xmath150 , one observes significant steps in the current - voltage as well as in the respective population characteristics . notice that in this bias direction the electronic state is depopulated ( to the left ) much faster than it is populated ( from the right ) , so that it is almost unoccupied for @xmath151 . the relative step heights that occur in these characteristics qualitatively reflect the transition probabilities @xmath152 for a transition from the vibrational ground- to its @xmath153th excited state . for a quantitative analysis of the step heights , however , the nonequilibrium state of the vibrational mode , which is typically highly excited , needs to be considered ( cf . [ vse2 ] ) . as a result of electronic - vibrational coupling and the asymmetry in the coupling to the leads , the current - voltage characteristics thus exhibits a pronounced asymmetry with respect to the polarity of the applied bias voltage @xmath128 , which is also referred to as vibrational rectification . this has been theoretically analyzed @xcite and experimentally verified @xcite before .    [ cols=\"^,^,^,^ \" , ]     in contrast to these electronic observables , the corresponding vibrational excitation number , @xmath154 , increases in a series of distinct steps for both polarities of the bias voltage ( see fig . [ vse2 ] ) . this finding can not be solely understood in terms of electron transport processes . although vibrational excitation is a result of inelastic electron transport processes ( cf . [ basmech]a - d ) , another class of processes , which does not contribute to the current , needs to be considered . resonant electron - hole pair creation processes @xcite , such as those depicted by figs . [ el - h - pair - creation]a and [ el - h - pair - creation]b , are effectively cooling the vibrational mode and diminish the current - induced vibrational excitation . since these processes involve two sequential tunneling events , they occur with the same probability as respective transport processes . due to the asymmetry in the molecule - lead coupling , electron - hole pair creation processes with respect to the left lead are the most important ones . they are typically more effective the less vibrational quanta are involved . for this particular model system , cooling by electron - hole pair creation is therefore more pronounced for positive bias voltages , @xmath155 , where _ e.g. _  an electron - hole pair in the left lead can be produced by absorption of just a single quantum of vibrational energy . for negative bias voltages , @xmath149 , the creation of an electron - hole pair in the left lead requires the absorption of more than ten vibrational quanta . as a result , vibrational excitation is much smaller for positive bias voltages than for negative ones . increasing the bias voltage , these pair creation processes are blocked one by one , as the energy gap between the molecular level and the electrode chemical potential increases . the steps in the vibrational excitation characteristics thus become larger with increasing bias voltage due to less efficient cooling by electron - hole pair creation processes @xcite . this blocking of pair creation processes appears for both polarities of the bias voltage . c +    apart from the broadening of steps , the me and the negf approach give almost the same vibrational excitation characteristics . however , negf can be expected to give slightly larger values for the vibrational excitation , because inelastic co - tunneling processes @xcite , which are not included in the me scheme , additionally contribute to the level of excitation for the vibrational mode . this is particularly important in the off - resonant transport regime , _ i.e. _  for @xmath156 , where negf gives a small vibrational excitation while me does not . significant deviations between both approaches occur only for large bias voltages . especially for large positive bias voltages , _ e.g. _  at @xmath157v , the vibrational excitation obtained from negf is significantly smaller than the one obtained by the me scheme . we attribute this behavior to the contribution of cooling by off - resonant electron - hole pair creation processes , which are missing in the me approach ( an example of an off - resonant pair creation process is depicted in fig . [ el - h - pair - creation]c ) . these processes become the dominant cooling mechanism at large bias voltages , where resonant electron - hole pair creation processes are suppressed , as they require increasingly higher vibrational energy . in contrast , off - resonant pair creation processes can occur by the absorption of just a single quantum of vibrational energy for all bias voltages . the me approach thus gives a somewhat larger vibrational excitation than the negf method for bias voltages , where resonant electron - hole pair creation processes are strongly suppressed . the importance of cooling by electron - hole pair creation processes can be corroborated by studying the behavior of the vibrational excitation characteristics with respect to the energy of the electronic state , which for a given bias voltage influences the efficiency of resonant electron - hole pair creation processes . [ varye0]a shows results for the vibrational excitation as a function of the energy @xmath158 at a fixed bias voltage . thereby , the blue lines refer to a fixed bias voltage of @xmath159v , and the red lines to @xmath160v . as before , solid ( dashed ) lines refer to calculations performed with the me ( negf ) scheme . if the energy of the electronic state is closer to the fermi - level of the system , @xmath161 , resonant electron - hole pair creation processes are more strongly suppressed , as they require the absorption of an increasing number of vibrational quanta . the less efficient cooling by resonant electron - hole pair creation leads to the general observed trend of an increasing vibrational excitation with a decreasing energy of the electronic state ( for example from @xmath162ev to @xmath163ev ) . for @xmath164ev , the negf scheme gives a significantly smaller vibrational excitation than the me method . here , cooling by off - resonant electron - hole pair creation processes ( missing in the me treatment ) results in a significantly lower level of vibrational excitation . notice that for an asymmetric junction , the value of @xmath165 for which the vibrational excitation obtains its maximal value differs from zero and depends on the bias polarity . considering , _ e.g. _  the negative bias voltage ( blue lines ) , a maximum of vibrational excitation is obtained at @xmath166ev ( @xmath167ev ) . for this bias , shifting the electronic level to lower values enhances cooling at the left electrode and suppresses cooling at the right electrode . due to the asymmetry in the molecule - lead coupling , pair creation processes with respect to the left lead are more important than with respect to the right lead . a minimum of cooling efficiency by electron - hole pair creation processes , which corresponds to a maximum in vibrational excitation , is thus reached for positive values of @xmath165 . similarly , for positive bias , a maximum in vibrational excitation appears for negative values of @xmath165 . [ varye0]b represents the ratio @xmath168 . it shows that the asymmetry in the vibrational excitation characteristics , as well as in the current - voltage characteristics and the electronic population ( data not shown ) , disappears , once the electronic level is located close to the fermi - level of the system . this demonstrates that for an electronic state close to the fermi - level , which can be controlled for example by a gate electrode @xcite , the efficiency of both current - induced heating and cooling by electron - hole pair creation processes is the same for both polarities of the bias voltage @xmath128 .    at this point , it is interesting to study the extent of vibrational excitation for different ratios of the molecule - lead couplings @xmath169 . in fig . [ varyratio ] , we show the level of excitation of the vibrational mode as a function of the ratio @xmath169 , where @xmath132ev is fixed . again , red and blue lines refer to calculations performed at a fixed bias voltage of @xmath170v , respectively . trivially , for a symmetric junction with @xmath171 , we obtain the same level of vibrational excitation for both polarities of the bias voltage . decreasing the coupling to the right lead , the asymmetry in vibrational excitation increases almost linearly . interestingly , for negative bias voltages , the vibrational excitation obtained by the negf scheme ( dashed blue line ) and by the me method ( solid blue line ) approach one another upon decreasing @xmath135 . this points to the fact that off - resonant electron - hole pair creation processes with respect to the right lead become strongly suppressed . for even smaller coupling strengths to the right lead , @xmath172ev , the turnover in the dashed blue line ( negf scheme ) indicates that in the limit @xmath173 current - induced vibrational excitation vanishes , as does the corresponding current . the solid blue line ( me scheme ) exhibits the same turn - over but for even smaller coupling strengths to the right lead . on the other hand , for @xmath160v , the dashed and solid red lines remain well separated upon decreasing the coupling to the right lead , as the ratio between resonant and off - resonant pair creation processes with respect to the left lead remains constant . so far , we have discussed cooling mechanisms for the vibrational mode , which are solely induced by electronic - vibrational coupling . other vibrational energy relaxation processes , which can be of relevance in molecular junctions , include intramolecular vibrational energy redistribution processes ( ivr ) or energy transfer to the environment ( _ e.g. _  phononic excitation of the electrodes ) @xcite . such relaxation mechanisms are commonly described by coupling of the primary vibrational mode(s ) to a thermal heat bath . [ fig.7 ] shows the level of vibrational excitation as a function of the mode - bath coupling strength @xmath142 for a fixed bias voltage ( blue lines correspond to @xmath159v , and red lines to @xmath174v ) . naturally , the molecular junction responds to an increased coupling to a `` cold '' thermal bath by decreased levels of current - induced vibrational excitation . however , as can be seen by inspection of eqs . ( [ formulavibex ] ) , vibrational excitation is not only a result of inelastic transport processes , but also stems from the population of the electronic states , that is the formation of a polaronic state @xcite . such polaron - formation leads to a finite vibrational excitation even in the limit of strong mode - bath coupling @xmath142 . since the electronic level is almost fully populated for positive , but almost unoccupied for negative bias voltages , one observes a higher vibrational excitation for positive bias voltages than for negative bias voltages , if the mode - bath coupling strength @xmath142 exceeds a value of @xmath175ev . we finally conclude that in an asymmetric molecular junction the level of vibrational excitation can be controlled by the magnitude and the polarity of the applied bias voltage . it is noted that a gate voltage , which allows to align the energy of electronic states , @xmath176 , with respect to the fermi - level , may facilitate a control mechanism for the ratio between the different levels of vibrational excitation at different bias polarities .      in sec . [ vse ] we have outlined how the level of excitation of a single vibrational mode can be controlled by an external bias voltage @xmath128 . in this section , we extend this concept to selective excitation of specific vibrational modes in a junction with multiple vibrational degrees of freedom . in particular , we show that modes with higher frequencies can be stronger excited than low - frequency modes , which corresponds to a `` non - statistical '' distribution of vibrational energy . a minimal model for two vibrational modes ( model a ) , which demonstrates such mode - selective vibrational excitation , was recently introduced @xcite . it involves two electronic states , where each state is coupled to one of the vibrational modes and asymmetrically to the leads . thereby , the asymmetry in the coupling to the leads reflects an inherent asymmetry of the contacted molecule . in this section , we review and extend our earlier study of model a , taking into account intra - molecular correlations , in particular off - diagonal electronic - vibrational coupling , @xmath177 , and electron - electron interactions , @xmath178 . moreover , we consider a different generic realization of an asymmetric molecular junction exhibiting msve , model b. model b also comprises two vibrational modes and two electronic states , asymmetrically coupled to leads , but in contrast to model a , the asymmetry in the molecule - lead coupling is not a result of an intrinsic asymmetry of the molecule , but rather stems from an asymmetry in the electrodes . this corresponds for example to an stm setup , where the molecule bridging the gap between the two electrodes is typically much stronger coupled to the substrate than to the stm tip . these two scenarios , where msve can be controlled by an external bias voltage , are schematically depicted in fig . [ fig.8 ] . respective model parameters are detailed in table [ tableii ] . note that an asymmetric molecule - lead as well as electronic - vibrational coupling is necessary to observe msve in both model systems ( cf . the discussion of fig . [ varyratio ] ) . @xmath179 & @xmath180 & @xmath136 & @xmath137 & @xmath138 & @xmath181 & @xmath46 & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 + fig . [ fig.9 ] & 0.65,0.575 & 0.1,0.03 & 0.03,0.1 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0 & 0 + fig . [ fig.9c ] & 0.65,0.575 & 0.1,0.03 & 0.03,0.1 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0 & 0 + fig . [ fig.10 ] & 0.65,-0.5 & 0.1,0.1 & 0.03,0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0 & 0 + fig . [ fig.10c ] & 0.65,-0.5 & 0.1,0.1 & 0.03,0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0 & 0 + fig . [ fig.11 ] & 0.65,0.575 & 0.1,0.03 & 0.03,0.1 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12 & 0  1 & 0 & 0 + fig . [ fig.12 ] & 0.65,-0.5 & 0.1,0.1 & 0.03,0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12 & 0  1 & 0 & 0 + fig . [ fig.15 ] & 0.65,0.575 & 0.1,0.03 & 0.03,0.1 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0  1.5 & 0 + fig . [ fig.16 ] & 0.65,-0.5 & 0.1,0.1 & 0.03,0.03 & 1 & 2 & 0.01 & 1 & 0.001 & 0.15,0.2 & 0.09,0.12&0 & 0  1.5 & 0 +    [ tableii ]      first , we discuss results , where we do not account for a coupling between the vibrational modes and a thermal bath ( @xmath187 ) , nor for off - diagonal electronic - vibrational coupling ( @xmath188 ) or electron - electron interactions ( @xmath189 ) . current - voltage characteristics and the corresponding population of the electronic states are shown in figs . [ fig.9 ] and [ fig.10 ] for model a and b , respectively . the corresponding levels of vibrational excitation are depicted in figs . [ fig.9c ] and [ fig.10c ] . in both models , the excitation of the two normal modes is calculated with respect to the neutral molecule , in which the two electronic states ( lumo and lumo+1 ) are unoccupied . notice , however , that while in model a these states become occupied only for non - zero bias , in model b the molecule ( lumo ) is charged ( and therefore to some extent vibrationally excited ) already at zero bias . since @xmath190 and @xmath189 , the two subsystems , the one comprising state 1 and mode 1 , and the other consisting of state 2 and mode 2 , are interrelated only by the coupling of the two electronic states to the leads . this coupling , however , does not induce strong correlations between the two subsystems , because the electronic states are non - degenerate , i.e. , @xmath191 . the transport characteristics of model a and b can therefore , in principle , be understood by the arguments given in sec . [ vse ] for a single electronic state and a single vibrational mode . in particular , the agreement of the results obtained with negf and me , which we already found in sec . [ vse ] , is maintained .    while for both models the current - voltage characteristics is almost anti - symmetric with respect to the applied bias voltage @xmath128 , the electronic population and average levels of vibrational excitation exhibit strong asymmetric behavior . in particular , for negative bias voltages mode 1 shows a much higher level of vibrational excitation than mode 2 . for positive bias voltages , however , the distribution of vibrational energy is reversed and mode 2 is higher excited than mode 1 , despite the fact that @xmath192 .    these results , where no intra - molecular interactions are considered , are in line with the interpretation and the analysis for cooling of vibrational modes by electron - hole pair creation processes ( cf . [ vse ] ) . in particular , it is sufficient to consider the asymmetry in the coupling of each electronic state to the two leads , and the energy gap between each electronic state and the chemical potential of the two electrodes in order to assess which of the two vibrations is more effectively excited . in a realistic model of a molecular junction , however , correlations need to be taken into account . to this end , we analyze msve in the next three sections in terms of off - diagonal electronic - vibrational coupling , @xmath193 , electron - electron interactions , @xmath194 , and in the presence of efficient cooling by coupling to a cold nuclear bath , @xmath195 and @xmath196 . as shown above , the msve phenomenon depends predominantly on the efficiency of cooling by electron - hole pair creation processes . this efficiency can be selectively controlled by the external bias voltage due to the asymmetry not only in the molecule - lead coupling , but also in the electronic - vibrational coupling . the latter is most pronounced when each mode is coupled exclusively to a different electronic state , _ i.e. _ , @xmath197 . in figs . [ fig.11 ] and [ fig.12 ] , for model a and b , respectively , the vibrational excitation of the two modes is shown for increasing off - diagonal electronic - vibrational coupling : @xmath198 and @xmath199 , where @xmath200 describes the absence of off - diagonal vibronic coupling , while for @xmath201 off - diagonal coupling is as strong as the diagonal one . thereby , we use a fixed bias voltage @xmath174v for figs . [ fig.11]a and [ fig.12]a , and @xmath159v for figs . [ fig.11]b and [ fig.12]b . the results demonstrate that off - diagonal electronic - vibrational coupling tends to decrease msve for these model molecular junctions , as might have been anticipated . msve , however , remains significant for a broad range of coupling strengths @xmath184 . a more detailed analysis rationalizes the trends in each case .    in model a , at positive bias ( fig . [ fig.11]a ) and for @xmath200 , cooling by electron - hole pair creation is more effective via the state that is coupled more strongly to the left electrode ( state 1 ) . therefore , the mode coupled to this state , that is mode 1 , is more effectively cooled . as @xmath184 increases , mode 2 becomes coupled to state 1 , and cooling by electron - hole pair creation becomes effective also for this mode . while the level of excitation of mode 1 is thus almost the same for all values of @xmath184 , the one of mode 2 decreases . similar arguments hold for negative bias voltages ( fig . [ fig.11]b ) , where electron - hole pair creation via state 2 at the right electrode is the dominant cooling mechanism . + notice that off - diagonal coupling also involves a change in the nuclear reorganization energy of each electronic state . this is particularly pronounced for transport and pair creation processes involving the di - anionic states ( or a doubly occupied molecular bridge , cf . [ fig.17 ] ) , which reorganization energies also involve vibrationally induced electron - electron interactions ( @xmath202ev for @xmath201 , see sec .  [ negfapproach ] ) . since state 1 ( 2 ) is almost fully occupied for @xmath160v ( @xmath159v ) , processes involving state 2 ( 1 ) are dominated by the di - anionic resonance at @xmath203 . increasing @xmath184 shifts this resonance to significantly lower energies . this shift manifests itself in the kink observed in the vibrational excitation of mode 2 ( 1 ) at @xmath204 for @xmath160v ( at @xmath205 for @xmath159v ) , indicating the suppression of electron - hole pair creation processes ( cf . [ fig.17]a ) as the respective resonance is shifted further away from the chemical potential in the left ( right ) electrode . note that such kinks are less pronounced for larger values of @xmath184 , where cooling by electron - hole pair creation processes occurs for each mode via both electronic states such that the closure of one of these cooling channels is less significant . similar trends are observed for model b ( cf . [ fig.12 ] ) . for negative bias and @xmath200 , mode 2 is more effectively cooled due to the strong coupling between state 2 and the left electrode . increasing @xmath184 , mode 1 becomes coupled to that state as well , leading to a suppression of vibrational excitation also for this mode . notice that di - anionic resonances are less important in this case as the two states are almost unoccupied . therefore , kinks associated with the reorganization energy of the electronic levels are also less pronounced . for positive bias , however , the two electronic states are almost fully occupied , and therefore , transport and pair creation processes do occur predominantly by the di - anionic resonances . since these resonances are shifted to lower energies with increasing @xmath184 , state 1 is effectively located further away from the chemical potential in the left electrode and state 2 closer to the one in the right electrode . this results in less ( more ) efficient cooling by electron - hole pair creation processes , and respectively , in an increased ( decreased ) level of vibrational excitation . the latter trends bring the excitation levels of the two modes to similar values already for @xmath206 , which suppresses msve for this model . we note however , that the coulomb - like attraction term ( @xmath207 ) , which dominates the suppression of msve , is typically compensated by repulsive electron - electron interactions , which , however , are not accounted for in the present model .    . the position of the two electronic states with respect to the chemical potentials in the left and the right lead , @xmath208 , and the positions of the di - anionic resonances , @xmath209 , determine the efficiency of heating and cooling processes.,title=\"fig : \" ] . the position of the two electronic states with respect to the chemical potentials in the left and the right lead , @xmath208 , and the positions of the di - anionic resonances , @xmath209 , determine the efficiency of heating and cooling processes.,title=\"fig : \" ] . the position of the two electronic states with respect to the chemical potentials in the left and the right lead , @xmath208 , and the positions of the di - anionic resonances , @xmath209 , determine the efficiency of heating and cooling processes.,title=\"fig : \" ]      a comparison of the electronic populations , shown in figs . [ fig.9]b and [ fig.10]b , and the associated levels of vibrational excitation , given in figs . [ fig.9c ] and [ fig.10c ] , shows that these quantities are strongly correlated . electron - electron interactions , @xmath178 , can strongly influence the electronic population of the different states @xcite and thus the degree of msve in an asymmetric molecular junction . we study the effect of such inter - state correlations on msve in figs . [ fig.15 ] and [ fig.16 ] , where the levels of excitation for the two vibrational modes in model a and b are plotted as functions of the electron - electron interaction strength @xmath210 , using fixed bias voltages @xmath211v .    in model a ( fig . [ fig.15 ] ) , the dependence of the two vibrational mode - excitations on @xmath212 is nearly reversed when the bias is reversed , demonstrating msve for most values of @xmath212 . the particular levels of vibrational excitation and the direction of msve reflect the detailed asymmetry of the molecular junction . for example , for @xmath160v the excitation of mode 1 is nearly independent on @xmath212 , while the one of mode 2 shows a strong non - monotonic dependence . since mode 1 is coupled to state 1 , and because state 2 is almost unoccupied in this regime , mode 1 is efficiently cooled by electron - hole pair creation processes with respect to the left electrode , regardless of the electron - electron interaction strength @xmath212 . in contrast , mode 2 is coupled to state 2 that is only weakly coupled to the left lead , and therefore , not efficiently cooled by electron - hole pair creation processes for @xmath213 . however , as @xmath212 increases , electron tunneling with respect to state 2 involves an increasingly larger charging energy , @xmath214 , since state 1 is almost fully occupied . this brings the electronic energy in this transport channel first closer to and then further away from the chemical potential in the left electrode . cooling of mode 2 by electron - hole pair creation processes ( coulomb - assisted electron - hole pair creation processes as depicted in figs . [ fig.17]b and [ fig.17]c ) is thus first enhanced and then suppressed as @xmath212 increases , resulting in the observed non - monotonic level of vibrational excitation . notice that the pronounced cooling due to coulomb - assisted electron - hole pair creation processes , in the intermediate regime of electron - electron interaction strengths , @xmath212 , reverses the direction of msve with respect to the @xmath213 case ( cf . [ fig.15 ] ) .    in model b ( fig . [ fig.16 ] ) the asymmetry in the coupling of the molecular bridge to the electrodes leads to very different dependencies of the vibrational mode - excitations on @xmath212 for different polarities of the applied bias voltage . the resulting dependence of msve on @xmath212 is non - trivial , ranging from enhancement to suppression of the effect with respect to @xmath213 . at negative bias voltages the two electronic states remain nearly unoccupied , so that the effect of electron - electron interactions is negligible . the lower excitation level of mode 2 at this polarity of the bias voltage reflects more efficient cooling by electron - hole pair creation via state 2 at the left electrode ( fig . [ fig.16 ] ) , which is maintained for different values of @xmath212 . for positive bias voltages , the two electronic states are almost fully occupied . cooling of mode 1 and 2 is thus dominated by electron - hole pair creation at the left and the right leads , respectively , according to the proximity of the corresponding energy levels , @xmath215 and @xmath214 , to the respective chemical potentials . as @xmath212 increases , electron - hole pair creation at the left electrode is enhanced , while pair creation with respect to the right lead is suppressed . this leads first to an enhancement of msve with respect to @xmath213 . at @xmath216ev , however , the electronic energy @xmath215 crosses the chemical potential in the left lead , and state 1 becomes discharged . at this point , cooling of mode 1 is at its maximal efficiency . simultaneously , since state 1 is no longer populated ( @xmath217 drops from @xmath218 to @xmath219 ) , processes involving state 2 occur predominantly via the anionic channel at @xmath220 , such that cooling of mode 2 by electron - hole pair creation processes with respect to the right electrode becomes as efficient as for @xmath213 . accordingly , the level of excitation for mode 2 returns to its original value . increasing @xmath212 even further cooling of mode 1 ( via the di - anionic channel , @xmath215 ) becomes less efficient , and the level of excitation for mode 1 increases again . as @xmath214 is closer to the chemical potential in the left lead , the cooling efficiency of mode 2 by electron - hole pair creation processes with respect to the left lead increases . the overall effect leads to a suppression of msve for @xmath221ev in the given range of electron - electron interactions strengths @xmath212 . note , however , that for yet larger values of the electron - electron interaction strength , @xmath222ev , msve is regained and becomes approximately as pronounced as for @xmath213 . in this regime , transport and pair creation processes are dominated by the anionic resonances ( at @xmath223 ) so that the asymmetry in the cooling efficiency of the two modes ( at least for the present model ) is the same as for @xmath213 .      in the discussion of fig . [ fig.7 ] in sec . [ vse ] , we have already seen that the level of excitation of a single vibrational mode consists of two contributions : current - induced local heating due to inelastic electron transport processes ( as shown in figs . [ basmech]a - d ) , and polaron - formation @xcite , which can be quantified by the difference @xmath224 strong vibrational relaxation results in a strong suppression of current - induced vibrational excitation , especially if the time - scale for vibrational relaxation is much shorter than the time - scale between two consecutive transport events . the contribution due to polaron formation , however , stems from the steady - state population of the electronic levels in a molecular junction . hence , for model a , msve occurs in the presence of strong vibrational relaxation @xcite , since the population of the electronic levels can be selectively controlled by the external bias voltage @xmath128 ( cf . [ fig.9]b ) . in model b , however , both states are either fully populated or empty such that strong vibrational relaxation is likely to hinder msve for this model system .","summary":"the comparison of both methods reveals good agreement in describing resonant electron transport through a single - molecule contact , but also highlights the role of non - resonant transport processes , in particular co - tunneling and off - resonant electron - hole pair creation processes .","abstract":"we show that individual vibrational modes in single - molecule junctions with asymmetric molecule - lead coupling can be selectively excited by applying an external bias voltage . thereby , a non - statistical distribution of vibrational energy can be generated , that is , a mode with a high frequency can be stronger excited than a mode with a lower frequency . this is of particular interest in the context of mode - selective chemistry , where one aims to break specific ( not necessarily the weakest ) chemical bond in a molecule . such mode - selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments . to this end , we employ two complementary theoretical approaches , a nonequilibrium green s function approach and a master equation approach . the comparison of both methods reveals good agreement in describing resonant electron transport through a single - molecule contact , but also highlights the role of non - resonant transport processes , in particular co - tunneling and off - resonant electron - hole pair creation processes ."}
{"article_id":"1106.0170","section_id":"c","document":"in this work we have studied and analyzed transport characteristics of single - molecule junctions , focusing on the excitation of specific molecular vibrational modes . in particular , we have shown that the level of excitation of specific modes can be controlled by the polarity and the magnitude of an external bias voltage . thereby , high - frequency modes ( typically associated with strong chemical bonds ) can be higher excited than low - frequency modes , which translates to a `` non - statistical '' distribution of energy among the vibrational modes . we refer to this phenomenon as mode - selective vibrational excitation .      * _ the importance of cooling by electron - hole pair creation _ + our analysis shows that cooling of the vibrational modes in a molecular junction by electron - hole pair creation processes is crucial to understand the extent of the msve phenomenon . in particular , since the efficiency of these processes is sensitive to the position of the chemical potentials in the leads , the levels of vibrational excitation in the molecule can be controlled by an external bias voltage . considering a molecule with multiple vibrational modes and typical asymmetries in the vibronic as well as molecule - lead couplings , the level of excitation of specific vibrational modes can thus be tuned by the polarity and the magnitude of the external bias voltage . * _ the role of asymmetry and intra - molecular interactions _ + our studies suggest that msve is a rather general phenomenon and is likely to be observed experimentally . the required asymmetry in the electronic interaction between different molecular states and the leads may be due to an inherent asymmetric molecular structure ( model a ) or stem from an inherent difference between the two electrodes , as _ e.g. _  in stm experiments ( model b ) . intra - molecular interactions , _ e.g. _  due to off diagonal electronic - vibrational coupling or electron - electron repulsion tend to redistribute the excitation energy between the different modes , and thus work against msve . however , having analyzed a broad range of parameters , we found the msve phenomenon to prevail even in the presence of such interactions . * _ the importance of off - resonant processes : comparing me to negf calculations . _ + our numerical studies of generic models of molecular junctions were based on two complementary theoretical methods : a nonequilibrium green s function approach @xcite and a master equation approach @xcite . both approaches are based on a second - order expansion in the coupling of the molecular bridge to the leads . while the negf method also accounts for higher - order effects , the me approach describes only resonant electron tunneling processes . however , intra - molecular interactions , either due to electronic - vibrational coupling or electron - electron interactions , can be described by the me method without invoking further approximations , while these interactions are described by our negf approach approximately in terms of a non - perturbative scheme . although the results obtained by both methodologies agree in most cases reasonably well , further insights into the relevant mechanisms can be gained when the results exhibit differences . thus , for example , the importance of off - resonant electron - hole pair creation processes for local cooling @xcite of vibrational modes in the high - bias regime could be revealed . we end by noting that this work considered only generic models to study the basic mechanisms and prerequisites of bias - controlled msve . the identification of specific molecules that exhibit msve requires transport studies based on first - principles electronic structure calculations @xcite . this will be the subject of future work . another interesting extension concerns the external control mechanism for msve . in the present work , we have considered an external bias voltage as the means to control msve . a gate electrode @xcite may provide another tool for addressing a molecular junction with an electric field , and thus , may also be used to control vibrational excitation . finally , in the context of mode - selective chemistry , studies of msve in single - molecule junctions may pave the way to control chemical processes in molecules adsorbed on surfaces . for example , an additional electrode that provides an external potential bias may induce catalytic reactions in a selective manner . we gratefully acknowledge fruitful discussions with o.  godsi , d.  brisker klaiman , m.  butzin , p.  brana - coto and o.  rubio - pons . this research was supported by the german - israeli foundation for scientific development ( gif ) . rv acknowledges support from the gutwirth foundation . the leibniz rechenzentrum munich ( lrz ) and the regionales rechenzentrum erlangen ( rrze ) were providing the computer resources for our studies . the work at the friedrich - alexander universitt erlangen - nrnberg was carried out in the framework of the cluster of excellence `` engineering of advanced materials '' .","summary":"such mode - selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments . to this end , we employ two complementary theoretical approaches , a nonequilibrium green s function approach and a master equation approach .","abstract":"we show that individual vibrational modes in single - molecule junctions with asymmetric molecule - lead coupling can be selectively excited by applying an external bias voltage . thereby , a non - statistical distribution of vibrational energy can be generated , that is , a mode with a high frequency can be stronger excited than a mode with a lower frequency . this is of particular interest in the context of mode - selective chemistry , where one aims to break specific ( not necessarily the weakest ) chemical bond in a molecule . such mode - selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments . to this end , we employ two complementary theoretical approaches , a nonequilibrium green s function approach and a master equation approach . the comparison of both methods reveals good agreement in describing resonant electron transport through a single - molecule contact , but also highlights the role of non - resonant transport processes , in particular co - tunneling and off - resonant electron - hole pair creation processes ."}
{"article_id":"1609.02134","section_id":"i","document":"observational evidence has emerged over the past few decades indicating that carbon is ubiquitous in the early universe . the class of carbon - enhanced metal - poor ( cemp ; @xmath3$]@xmath11 , e.g. , * ? ? ? * ; * ? ? ? * ) stars are found with increasing fractions at lower metallicities , and account for at least 80% of all ultra metal - poor ( ump ; [ fe / h]$ ] = @xmath12 , where @xmath13 is the number density of atoms of elements @xmath14 and @xmath15 in the star ( @xmath16 ) and the sun ( @xmath17 ) , respectively . ] @xmath18 ) stars observed to date @xcite . in particular , the so - called cemp - no stars ( which exhibit sub - solar abundances of neutron - capture elements ; e.g. , @xmath5 $ ] @xmath19 0.0 ) are believed to be direct descendants from the very first stellar generations formed after the big bang @xcite . in addition , the discovery of high - redshift carbon - enhanced damped ly@xmath20 systems @xcite , which present qualitatively similar light - element ( from c to si ) abundance patterns as the cemp - no stars , provides additional evidence that carbon is an important contributor to the earliest chemical evolution . one of the main open questions is whether the presence of carbon is required for the formation of low - mass second - generation stars @xcite . this idea can be tested with low - mass long - lived ump stars that are thought to have formed from an ism polluted by the nucleosynthesis products of massive metal - free population iii ( pop iii ) stars . these massive stars could have formed as early as several hundred million years after the big bang , at redshift @xmath21 @xcite . the recently discovered quasar ulas  j1120@xmath40641 at redshift @xmath22 @xcite , with an overall metal abundance ( defined as elements heavier then helium ) of @xmath23$]@xmath24 , could be an example of a viable site for the formation of the first stars . the lack of heavy metals may prevent the formation of low - mass stars ( due to inefficient cooling ; * ? ? ? * ) , supporting the suggestion that the early - universe initial mass function was strongly biased toward high - mass stars . in the picture that has developed , it is these high - mass stars that would quickly evolve and enrich the primordial ism with elements heavier than helium , including carbon @xcite .    even though the relevance of cemp - no stars as probes of the first stellar generations in the universe is well - established , the exact conditions that led to their formation remain an active area of inquiry . there have been a number of advances in the theoretical description of the likely stellar progenitors of cemp - no stars over the last decade ( see * ? ? * for a recent review on the subject ) . the suggested scenarios include the `` spinstar '' model ( rapidly - rotating , near zero - metallicity , massive stars ; * ? ? ? * ; * ? ? ? * ) , the `` faint sne '' that undergo mixing and fallback @xcite , and the metal - free massive stars from @xcite .    in the spinstar model , it is assumed that the chemical composition of the observed ump stars is a combination of the evolution of the massive star itself mixed with some amount of interstellar material @xcite . it follows that the source of heavy metals in the ump stars could arise from a different set of progenitors . for the faint sne and metal - free massive stars , the initial chemical abundances of the progenitor mimic the primordial big bang nucleosynthesis composition : 76% hydrogen , about 24% helium , and a trace amount of lithium . in both cases , the observed chemical elements in ump stars were formed during the progenitor stellar evolution , either by internal burning and/or explosive events , and their abundance is the result of mixing between the sne ejecta with surrounding primordial gas . these two models differ in terms of the treatment of the mixing and fallback of processed materials in the progenitor , which varies with mass and explosion energy ( see * ? ? ? * for details ) . the @xcite models compute explosion energy and fallback self - consistently based on a hydrodynamic model , considering that the sn explosion is spherical . all of the aforementioned models are able to reproduce a subset of ( but not all ) of the observed elemental - abundance patterns of ump stars reasonably well . nevertheless , the question of whether one or more classes of progenitors were present ( and their relative frequencies ) in the primordial universe is still under discussion . in paper i of this series , @xcite present evidence based on the morphology of the relationship between the absolute abundance of carbon , @xmath7(c ) @xmath25(c ) , and [ fe / h ] , coupled with clear differences in the absolute abundances of the light elements na and mg among cemp - no stars , that at least two classes of progenitors are likely to be required . it appears that one class ( spinstars ) dominates at the very lowest metallicities , [ fe / h ] @xmath26 , whereas the other ( faint sne ) dominates over the range @xmath27 [ fe / h ] @xmath28 . in the metallicity range @xmath29 [ fe / h ] @xmath30 , there are examples of stars that are associated with either .    for the above reasons , we suggest that the very best stars to place constraints on the nature of the cemp - no progenitors are the ump stars with metallicities between @xmath31 and @xmath32 . unfortunately , such stars are still exceedingly rare @xcite . even though their numbers have increased considerably over the last decade ( 21 stars according to * ? ? ? * ) , many more are needed , in order to fully understand the nature of their stellar progenitors and the associated nucleosynthesis processes .    in this paper , we report on a high - resolution spectroscopic abundance analysis , a relatively bright ( @xmath33 ) cemp - no ( @xmath1 $ ]  @xmath34 , @xmath3 $ ]  =  @xmath41.74 , and @xmath5 $ ]  =  @xmath35 ) star , which was first identified as the metal - poor candidate cs  30324 - 0063 in the hk survey @xcite , and later re - identified in the hamburg / eso survey ( he s ; * ? ? ? * ) and the radial velocity experiment ( rave ; * ? ? ? was also studied by @xcite , focusing on long - term radial - velocity monitoring of cemp - no stars . we use the newly derived abundance pattern of , along with literature data for 11 other ump and hyper metal - poor ( hmp ; [ fe / h ] @xmath36 ) stars , to assess evidence in support of the conclusion in paper  i that cemp - no stars require more than one class of stellar progenitors . this paper is outlined as follows : section  [ secobs ] describes the medium - resolution spectroscopic target selection and high - resolution follow - up observations , followed by the determinations of the stellar parameters and chemical abundances in section  [ secatm ] . section  [ disc ] details our analysis of ump and hmp stars from the literature with a grid of supernova yields , and evaluates the impact of these data on current hypotheses for chemical evolution in the early universe . our conclusions are provided in section  [ final ] .","summary":"we report on the first high - resolution spectroscopic analysis of , a bright ( ) , ultra metal - poor ( $ ]  = .1 ) , carbon - enhanced ( $ ]  = .7 ) star selected from the hamburg / eso survey . this star exhibits low abundances of neutron - capture elements ( $ ]  =  ) , and an absolute carbon abundance(c ) = 6.1 ; based on either criterion ,  is sub - classified as a cemp - no star . we show that the light - element abundance pattern of  is consistent with predicted yields from a massive ( m  =  ) , primordial composition , supernova ( sn ) progenitor .","abstract":"we report on the first high - resolution spectroscopic analysis of , a bright ( ) , ultra metal - poor ( $ ]  = .1 ) , carbon - enhanced ( $ ]  = .7 ) star selected from the hamburg / eso survey . this star exhibits low abundances of neutron - capture elements ( $ ]  =  ) , and an absolute carbon abundance(c ) = 6.1 ; based on either criterion ,  is sub - classified as a cemp - no star . we show that the light - element abundance pattern of  is consistent with predicted yields from a massive ( m  =  ) , primordial composition , supernova ( sn ) progenitor . we also compare the abundance patterns of other ultra metal - poor stars from the literature with available measures of c , n , na , mg , and fe abundances with an extensive grid of sn models ( covering the mass range ) , in order to probe the nature of their likely stellar progenitors . our results suggest that at least two classes of progenitors are required at $ ]  , as the abundance patterns for more than half of the sample studied in this work ( 7 out of 12 stars ) can not be easily reproduced by the predicted yields ."}
{"article_id":"1609.02134","section_id":"c","document":"we have presented the first high - resolution spectroscopic study of the ultra metal - poor , cemp - no star . this star adds to the small number of stars with @xmath1 $ ]  @xmath88 identified to date , and presents the same behavior as most ( more than 80% ) of ump stars : @xmath3$]@xmath128 and @xmath5$]@xmath129 . we have attempted to characterize the progenitor stellar population of ump stars by comparing the yields from a grid of metal - free , massive - star models with the observed elemental abundances for  and 11 other ump stars from the literature for which at least abundances of c , n , na , mg , al , and fe have been reported . based on our residual analysis , we find that 42% ( 5 of 12 ) of the sample stars have elemental - abundance patterns that are well - reproduced by the sne models of @xcite . we conclude that this class of sne explosions and their associated nucleosynthesis can not alone account for the observed abundance patterns of the entire set of ump stars we have considered . in particular , pop iii , massive metal - free star models can not reproduce abundance patterns of stars with @xmath70 @xmath130 , @xmath103   @xmath131 , and @xmath105   @xmath132 . carbon and sodium could potentially be used as tracers of the stellar progenitor , in addition to the metallicity . this could be evidence of different progenitor signatures , such as fast - rotating massive pop iii stars from @xcite , or the faint sne from @xcite . if we assume that the models used in this work are a viable candidate for the stellar progenitors of ump stars , there must exist _ at least _ one additional class of progenitor operating at @xmath1$]@xmath10 , or a single process , yet to be identified , that could account for the abundances of all ump stars . we should also acknowledge the possibility that more than one progenitor could contribute to the observed abundance patterns of the high - residual stars presented in this work . recent evidence presented by @xcite suggests that the carbon abundance may be key to differentiate between different stellar progenitors of ump stars . the classifications based on absolute carbon abundances , @xmath7(c ) , are further confirmed when looking at the sodium and magnesium abundances . the analysis presented in this paper supports this hypothesis , and suggests that the progenitor population(s ) for ump stars may be even more rich and complex than previously thought . we emphasize that abundances for additional ump stars , in particular those in the metallicity regime @xmath133 [ fe / h ] @xmath88 , are needed to better constrain the nature of the possible stellar progenitors . nitrogen abundances are an important constraint to the theoretical models , and currently more than half of the observed ump stars have only limits for this element reported . we thank chris sneden , who kindly provided part of the linelists used for the spectral synthesis , nozomu tominaga , for clarifying specific characteristics of the faint sne models , richard stancliffe , for clarifications on the stellar evolution models used for the cn corrections , and the anonymous referee , who made valuable suggestions that helped improve the paper . v.m.p . , t.c.b . , and j.y .  acknowledge partial support for this work from the national science foundation under grant no . phy-1430152 ( jina center for the evolution of the elements ) . a.f . and a.c . are supported by nsf career grant ast-1255160 . a.h .  was supported by a future fellowship of the australian research council ( ft120100363 ) . this research has made use of nasa s astrophysics data system bibliographic services ; the arxiv pre - print server operated by cornell university ; the simbad database hosted by the strasbourg astronomical data center ; the iraf software packages distributed by the national optical astronomy observatories , which are operated by aura , under cooperative agreement with the nsf ; the saga database ( stellar abundances for galactic archeology ; * ? ? ? * ) ; the ` r - project ` software package @xcite ; the ` gnuplot ` command - line plotting program @xcite ; and the online q&a platform ` stackoverflow ` ( http://stackoverflow.com/ ) . lrrrrr c ch & 4246.000 & & & syn & 5.83 + c ch & 4313.000 & & & syn & 5.73 + n cn & 3883.000 & & & syn & 6.13 + na i & 5889.950 & 0.00 & 0.108 & 97.06 & 2.77 + na i & 5895.924 & 0.00 & @xmath20.194 & 83.35 & 2.79 + mg i & 3829.355 & 2.71 & @xmath20.208 & syn & 4.60 + mg i & 3832.304 & 2.71 & 0.270 & syn & 4.60 + mg i & 3838.292 & 2.72 & 0.490 & syn & 4.60 + mg i & 4571.096 & 0.00 & @xmath25.688 & syn & 4.90 + mg i & 4702.990 & 4.33 & @xmath20.380 & syn & 4.90 + mg i & 5172.684 & 2.71 & @xmath20.450 & syn & 4.25 + mg i & 5183.604 & 2.72 & @xmath20.239 & syn & 4.25 + mg i & 5528.405 & 4.34 & @xmath20.498 & syn & 4.85 + al i & 3961.520 & 0.01 & @xmath20.340 & syn & 2.05 + si i & 4102.936 & 1.91 & @xmath23.140 & syn & 4.36 + ca i & 4454.780 & 1.90 & 0.260 & syn & 2.64 + ca i & 5588.760 & 2.52 & 0.210 & 4.87 & 2.71 + ca i & 6122.220 & 1.89 & @xmath20.315 & 8.78 & 2.75 + ca i & 6162.170 & 1.90 & @xmath20.089 & 11.92 & 2.68 + sc ii & 4246.820 & 0.32 & 0.240 & 57.45 & @xmath20.75 + sc ii & 4400.389 & 0.61 & @xmath20.540 & 13.70 & @xmath20.69 + sc ii & 4415.544 & 0.59 & @xmath20.670 & 10.63 & @xmath20.72 + ti i & 3989.760 & 0.02 & @xmath20.062 & 10.92 & 1.14 + ti i & 4533.249 & 0.85 & 0.532 & 6.36 & 1.19 + ti i & 4981.730 & 0.84 & 0.560 & 7.55 & 1.17 + ti i & 4991.070 & 0.84 & 0.436 & 6.31 & 1.20 + ti ii & 3759.291 & 0.61 & 0.280 & 85.34 & 1.10 + ti ii & 3761.320 & 0.57 & 0.180 & 84.26 & 1.12 + ti ii & 4012.396 & 0.57 & @xmath21.750 & 26.82 & 1.30 + ti ii & 4417.714 & 1.17 & @xmath21.190 & 23.80 & 1.31 + ti ii & 4443.801 & 1.08 & @xmath20.720 & 39.21 & 1.07 + ti ii & 4450.482 & 1.08 & @xmath21.520 & 17.08 & 1.34 + ti ii & 4468.517 & 1.13 & @xmath20.600 & 42.03 & 1.07 + ti ii & 4501.270 & 1.12 & @xmath20.770 & 37.73 & 1.13 + ti ii & 4533.960 & 1.24 & @xmath20.530 & 42.09 & 1.12 + ti ii & 4563.770 & 1.22 & @xmath20.960 & 29.43 & 1.25 + ti ii & 4571.971 & 1.57 & @xmath20.320 & 38.54 & 1.23 + cr i & 4254.332 & 0.00 & @xmath20.114 & 57.03 & 1.50 + cr i & 4274.800 & 0.00 & @xmath20.220 & 52.38 & 1.48 + cr i & 4289.720 & 0.00 & @xmath20.370 & 49.12 & 1.56 + cr i & 5206.040 & 0.94 & 0.020 & 19.37 & 1.48 + cr i & 5208.419 & 0.94 & 0.160 & 26.73 & 1.52 + mn i & 4041.380 & 2.11 & @xmath20.350 & syn & 1.43 + mn i & 4754.021 & 2.28 & @xmath20.647 & syn & 1.43 + mn i & 4783.424 & 2.30 & @xmath20.736 & syn & 1.43 + mn i & 4823.514 & 2.32 & @xmath20.466 & syn & 1.43 + fe i & 3727.619 & 0.96 & @xmath20.609 & 70.55 & 3.28 + fe i & 3743.362 & 0.99 & @xmath20.790 & 65.97 & 3.32 + fe i & 3753.611 & 2.18 & @xmath20.890 & 16.00 & 3.41 + fe i & 3758.233 & 0.96 & @xmath20.005 & 97.02 & 3.50 + fe i & 3763.789 & 0.99 & @xmath20.221 & 80.31 & 3.23 + fe i & 3765.539 & 3.24 & 0.482 & 13.97 & 3.20 + fe i & 3767.192 & 1.01 & @xmath20.390 & 78.19 & 3.35 + fe i & 3786.677 & 1.01 & @xmath22.185 & 15.44 & 3.30 + fe i & 3820.425 & 0.86 & 0.157 & 105.31 & 3.33 + fe i & 3824.444 & 0.00 & @xmath21.360 & 82.76 & 3.28 + fe i & 3886.282 & 0.05 & @xmath21.080 & 96.13 & 3.48 + fe i & 3887.048 & 0.91 & @xmath21.140 & 57.68 & 3.22 + fe i & 3899.707 & 0.09 & @xmath21.515 & 80.32 & 3.39 + fe i & 3902.946 & 1.56 & @xmath20.442 & 57.99 & 3.30 + fe i & 3917.181 & 0.99 & @xmath22.155 & 25.67 & 3.51 + fe i & 3920.258 & 0.12 & @xmath21.734 & 72.13 & 3.33 + fe i & 3922.912 & 0.05 & @xmath21.626 & 83.66 & 3.57 + fe i & 3940.878 & 0.96 & @xmath22.600 & 9.80 & 3.39 + fe i & 3949.953 & 2.18 & @xmath21.251 & 9.97 & 3.49 + fe i & 3977.741 & 2.20 & @xmath21.120 & 14.87 & 3.58 + fe i & 4005.242 & 1.56 & @xmath20.583 & 57.44 & 3.38 + fe i & 4045.812 & 1.49 & 0.284 & 91.47 & 3.49 + fe i & 4063.594 & 1.56 & 0.062 & 80.91 & 3.45 + fe i & 4071.738 & 1.61 & @xmath20.008 & 71.90 & 3.28 + fe i & 4132.058 & 1.61 & @xmath20.675 & 56.36 & 3.47 + fe i & 4143.414 & 3.05 & @xmath20.200 & 8.23 & 3.32 + fe i & 4143.868 & 1.56 & @xmath20.511 & 64.30 & 3.46 + fe i & 4147.669 & 1.48 & @xmath22.071 & 12.23 & 3.55 + fe i & 4181.755 & 2.83 & @xmath20.371 & 14.24 & 3.51 + fe i & 4187.039 & 2.45 & @xmath20.514 & 20.15 & 3.40 + fe i & 4187.795 & 2.42 & @xmath20.510 & 25.89 & 3.51 + fe i & 4191.430 & 2.47 & @xmath20.666 & 13.35 & 3.35 + fe i & 4202.029 & 1.49 & @xmath20.689 & 60.77 & 3.43 + fe i & 4216.184 & 0.00 & @xmath23.357 & 31.11 & 3.60 + fe i & 4227.427 & 3.33 & 0.266 & 11.13 & 3.31 + fe i & 4233.603 & 2.48 & @xmath20.579 & 18.59 & 3.44 + fe i & 4250.787 & 1.56 & @xmath20.713 & 65.76 & 3.67 + fe i & 4260.474 & 2.40 & 0.077 & 42.71 & 3.27 + fe i & 4337.046 & 1.56 & @xmath21.695 & 20.27 & 3.51 + fe i & 4375.930 & 0.00 & @xmath23.005 & 36.62 & 3.33 + fe i & 4383.545 & 1.48 & 0.200 & 93.96 & 3.46 + fe i & 4404.750 & 1.56 & @xmath20.147 & 84.25 & 3.60 + fe i & 4415.122 & 1.61 & @xmath20.621 & 62.06 & 3.48 + fe i & 4427.310 & 0.05 & @xmath22.924 & 50.84 & 3.61 + fe i & 4447.717 & 2.22 & @xmath21.339 & 10.82 & 3.58 + fe i & 4459.118 & 2.18 & @xmath21.279 & 14.36 & 3.62 + fe i & 4461.653 & 0.09 & @xmath23.194 & 31.59 & 3.50 + fe i & 4494.563 & 2.20 & @xmath21.143 & 14.62 & 3.51 + fe i & 4528.614 & 2.18 & @xmath20.822 & 23.98 & 3.44 + fe i & 4531.148 & 1.48 & @xmath22.101 & 14.00 & 3.59 + fe i & 4602.941 & 1.49 & @xmath22.208 & 13.52 & 3.68 + fe i & 4871.318 & 2.87 & @xmath20.362 & 13.81 & 3.44 + fe i & 4872.137 & 2.88 & @xmath20.567 & 8.68 & 3.43 + fe i & 4890.755 & 2.88 & @xmath20.394 & 11.25 & 3.37 + fe i & 4891.492 & 2.85 & @xmath20.111 & 19.51 & 3.35 + fe i & 4918.994 & 2.85 & @xmath20.342 & 13.04 & 3.36 + fe i & 4920.503 & 2.83 & 0.068 & 24.34 & 3.28 + fe i & 5012.068 & 0.86 & @xmath22.642 & 22.92 & 3.60 + fe i & 5041.756 & 1.49 & @xmath22.200 & 9.41 & 3.44 + fe i & 5051.634 & 0.92 & @xmath22.764 & 16.69 & 3.61 + fe i & 5083.339 & 0.96 & @xmath22.842 & 12.69 & 3.59 + fe i & 5142.929 & 0.96 & @xmath23.080 & 9.26 & 3.67 + fe i & 5171.596 & 1.49 & @xmath21.721 & 24.59 & 3.46 + fe i & 5194.942 & 1.56 & @xmath22.021 & 14.64 & 3.55 + fe i & 5216.274 & 1.61 & @xmath22.082 & 10.02 & 3.48 + fe i & 5232.940 & 2.94 & @xmath20.057 & 17.98 & 3.33 + fe i & 5269.537 & 0.86 & @xmath21.333 & 80.63 & 3.60 + fe i & 5328.039 & 0.92 & @xmath21.466 & 74.91 & 3.64 + fe i & 5328.531 & 1.56 & @xmath21.850 & 21.81 & 3.59 + fe i & 5371.489 & 0.96 & @xmath21.644 & 65.45 & 3.61 + fe i & 5397.128 & 0.92 & @xmath21.982 & 44.81 & 3.44 + fe i & 5405.775 & 0.99 & @xmath21.852 & 45.96 & 3.42 + fe i & 5429.696 & 0.96 & @xmath21.881 & 45.71 & 3.40 + fe i & 5434.524 & 1.01 & @xmath22.126 & 37.72 & 3.56 + fe i & 5446.917 & 0.99 & @xmath21.910 & 45.31 & 3.46 + fe i & 5455.609 & 1.01 & @xmath22.090 & 38.32 & 3.53 + fe i & 5615.644 & 3.33 & 0.050 & 10.91 & 3.39 + fe ii & 4583.840 & 2.81 & @xmath21.930 & 15.01 & 3.63 + fe ii & 4923.930 & 2.89 & @xmath21.320 & 25.42 & 3.38 + fe ii & 5018.450 & 2.89 & @xmath21.220 & 28.24 & 3.34 + co i & 3845.468 & 0.92 & 0.010 & 33.28 & 1.33 + co i & 3995.306 & 0.92 & @xmath20.220 & 21.90 & 1.24 + co i & 4118.767 & 1.05 & @xmath20.490 & 12.50 & 1.33 + co i & 4121.318 & 0.92 & @xmath20.320 & 21.33 & 1.29 + ni i & 3500.850 & 0.17 & @xmath21.294 & 38.99 & 1.92 + ni i & 3519.770 & 0.28 & @xmath21.422 & 32.90 & 2.00 + ni i & 3566.370 & 0.42 & @xmath20.251 & 61.60 & 1.90 + ni i & 3597.710 & 0.21 & @xmath21.115 & 44.05 & 1.88 + ni i & 3783.520 & 0.42 & @xmath21.420 & 32.18 & 2.01 + ni i & 3807.140 & 0.42 & @xmath21.220 & 36.58 & 1.91 + ni i & 3858.301 & 0.42 & @xmath20.951 & 51.19 & 1.99 + sr ii & 4077.714 & 0.00 & 0.150 & syn & @xmath21.93 + sr ii & 4215.524 & 0.00 & @xmath20.180 & syn & @xmath21.88 + ba ii & 4554.033 & 0.00 & 0.163 & syn & @xmath22.97 + ba ii & 4934.086 & 0.00 & @xmath20.160 & syn & @xmath22.97 + eu ii & 4129.720 & 0.00 & 0.220 & syn & @xmath653.28 + pb i & 4057.810 & 1.32 & @xmath20.170 & syn & @xmath650.25 +","summary":"we also compare the abundance patterns of other ultra metal - poor stars from the literature with available measures of c , n , na , mg , and fe abundances with an extensive grid of sn models ( covering the mass range ) , in order to probe the nature of their likely stellar progenitors . our results suggest that at least two classes of progenitors are required at $ ]  , as the abundance patterns for more than half of the sample studied in this work ( 7 out of 12 stars ) can not be easily reproduced by the predicted yields .","abstract":"we report on the first high - resolution spectroscopic analysis of , a bright ( ) , ultra metal - poor ( $ ]  = .1 ) , carbon - enhanced ( $ ]  = .7 ) star selected from the hamburg / eso survey . this star exhibits low abundances of neutron - capture elements ( $ ]  =  ) , and an absolute carbon abundance(c ) = 6.1 ; based on either criterion ,  is sub - classified as a cemp - no star . we show that the light - element abundance pattern of  is consistent with predicted yields from a massive ( m  =  ) , primordial composition , supernova ( sn ) progenitor . we also compare the abundance patterns of other ultra metal - poor stars from the literature with available measures of c , n , na , mg , and fe abundances with an extensive grid of sn models ( covering the mass range ) , in order to probe the nature of their likely stellar progenitors . our results suggest that at least two classes of progenitors are required at $ ]  , as the abundance patterns for more than half of the sample studied in this work ( 7 out of 12 stars ) can not be easily reproduced by the predicted yields ."}
{"article_id":"0902.3493","section_id":"i","document":"redshifted observations of the 21-cm spin - flip transition of neutral hydrogen ( ) trace the cool component of the gas in distant galaxies . since the surface brightness has a @xmath4 dependence , the detection of the 21-cm in emission is very difficult at redshifts of @xmath0 , and so the neutral gas in distant active galactic nuclei ( agn ) is usually studied in absorption . furthermore , since most published searches survey of @xcite . ] have been at redshifts of @xmath5 , there are generally no observations of the lyman-  transition , which is redshifted into the optical bands at @xmath6 . therefore , to date 21-cm absorption has been the most common probe of the neutral gas in the galaxies host to agn , being detected in approximately 40% of @xmath7 cases ( see @xcite ) .    in order to explain the detection rate , many studies invoke unified schemes of active galactic nuclei , which attempt to unify the many classes of luminous extragalactic object , a key element of which is the presence of a torus of highly obscuring circumnuclear material : in these schemes , the appearance of the object is dependent upon the orientation of this material along our line - of - sight to the nucleus @xcite , with the popular consensus being that only type-2 objects present a dense column of intervening gas , which can absorb in 21-cm ( see @xcite , figure 2 of @xcite ) . other observational examples of this include :    1 .   from a survey for 21-cm absorption in 23 radio galaxies , @xcite find that of the five detections , four occur in sources which could be considered type-2 objects , whereas there is only one detected case for a type-1 object . 2 .   from a study of 49 gigahertz peaked spectrum ( gps ) and compact steep spectrum ( css ) sources , @xcite find that 21-cm absorption is more likely to arise in objects classified as galaxies , rather than in quasars . since the former are generally considered to be type-2 objects , while latter are type-1 objects , this is consistent with the orientation of the central obscuration playing a major rle in producing strong 21-cm absorption along our sight - line . also , from a study of 27 gpss and csss , @xcite find that 21-cm absorption is twice as likely to be detected in the galaxies than in the quasars of the sample , again suggesting that the absorption occurs in the dense sub - parsec torus . 4 .   from a sample of 23 galaxies and 9 quasars , @xcite find that 15 of the galaxies exhibit 21-cm absorption , compared to just a single case for the quasars . like @xcite , this is consistent with unified schemes , where galaxies are host to edge - on obscurations , whereas quasars have their tori oriented more face - on . however , the situation may be more complex than this with evidence that 21-cm absorption may also be due to in - falling gas or outflows ( e.g. @xcite ) , and if these are directed along the radio jet axis , we would expect outflows of neutral gas to render absorption detectable towards type-1 sources . whether due to an outflow or the presence of an intervening circumnuclear obscuration , these scenarios are consistent with unified schemes of agn , playing a major rle in whether  21-cm absorption is detected .    therefore , from these possibilities in addition to absorption by the large reservoir of neutral gas in the galactic disk , we may expect a high 21-cm detection rate in distant radio galaxies and quasars . however , from a recent survey of the host galaxies of @xmath8 quasars , @xcite found no evidence of absorption in any of the ten sources searched . upon an analysis of the spectral types of the targets , as well as those of all the other @xmath0 published searches , they found the non - detections all to be type-1 objects , as are many of the lower redshift non - detections ( see fig . [ lum - z ] ) . superficially , this suggests that the orientation of the circumnuclear obscuration may be key in the detection of 21-cm absorption , although there may also be other effects at play , the evidence for which we discuss in this paper .","summary":", we further explore the implications that this has for the currently popular consensus that it is the orientation of the circumnuclear obscuring torus , invoked by unified schemes of agn , which determines whether absorption is present along our sight - line . the fact that at , both type-1 and type-2 objects exhibit a 50% probability of detection , suggests that this is not the case and that the bias against detection of  absorption in type-1 objects is due purely to the inclusion of the  sources . similarly , the ultra - violet luminosities can also explain why the presence of 21-cm absorption shows a preference for radio galaxies over quasars and the higher detection rate in compact sources , such as css or gps sources , may also be biased by the inclusion of high - luminosity sources . additionally , the high uv fluxes could be sufficiently exciting / ionising the  above 21-cm detection thresholds , although the extent to which this is related to the neutral gas deficit in ellipticals is currently unclear .   ","abstract":"in a recent study of active galactic nuclei ( agn ) , we found that 21-cm absorption has never been detected in objects in which the ultra - violet luminosity exceeds . in this paper , we further explore the implications that this has for the currently popular consensus that it is the orientation of the circumnuclear obscuring torus , invoked by unified schemes of agn , which determines whether absorption is present along our sight - line . the fact that at , both type-1 and type-2 objects exhibit a 50% probability of detection , suggests that this is not the case and that the bias against detection of  absorption in type-1 objects is due purely to the inclusion of the  sources . similarly , the ultra - violet luminosities can also explain why the presence of 21-cm absorption shows a preference for radio galaxies over quasars and the higher detection rate in compact sources , such as css or gps sources , may also be biased by the inclusion of high - luminosity sources . being comprised of all 21-cm searched sources at , this is a necessarily heterogeneous sample , the constituents of which have been observed by various instruments . by this same token , however , the dependence on the uv luminosity may be an all encompassing effect , superseding the unified schemes model , although there is the possibility that the exclusive 21-cm non - detections at high uv luminosities could be caused by a bias towards gas - poor ellipticals . additionally , the high uv fluxes could be sufficiently exciting / ionising the  above 21-cm detection thresholds , although the extent to which this is related to the neutral gas deficit in ellipticals is currently unclear .    examining the moderate uv luminosity ( ) sample further , from the profile widths and offsets from the systemic velocities , we find no discernible differences between the two agn types . this may suggest that the bulk of the absorption generally occurs in the galactic disk , which must therefore be randomly orientated with respect to the circumnuclear torus . furthermore , we see no difference in the reddening between the two agn types , indicating , like the 21-cm absorption , that the orientation of the torus has little bearing on this . we also find a correlation between 21-cm line strength and the optical - near - infrared colour , which suggests that the reddening is caused by dust located in the large - scale ,  absorbing disk which intervenes the sight - line to the agn ."}
{"article_id":"0902.3493","section_id":"c","document":"in a previous paper @xcite we found that the ultra - violet luminosity plays more of a rle than the agn type in the detection of 21-cm absorption in @xmath0 radio galaxies _ and _ quasars . specifically , to date , 21-cm absorption has never been detected in a host galaxy when @xmath140 . although these high uv luminosities occur exclusively in type-1 objects , for the moderately uv luminous ( @xmath112 ) sample there is a 50% probability of detection in _ either _ agn type , with any apparent bias against type-1 objects being caused by the 17 high uv luminosity objects . expanding upon these results , in this paper we show :    1 .   that the bias against 21-cm absorption in quasars , compared to radio galaxies , also appears to be due to uv luminosity effects : for the radio galaxies , the 21-cm detections and non - detections both arise in objects with a mean @xmath196 , whereas the 21-cm detected quasars have @xmath197 , with the non - detected quasars having @xmath198 . although there is this decrease in the 21-cm detection rate with increasing @xmath73 , it is possible that the exclusive 21-cm non - detections at @xmath140  are due to the fact that highly luminous sources are believed to trace the ( neutral ) gas - poor elliptical galaxies . however only two of the 17 @xmath140  sources are _ known _ to be located in ellipticals ( although all of them could be ) , whereas all are known to have high ultra - violet luminosities . therefore it is not clear whether the lack of 21-cm absorption is due to a low abundance of neutral galaxy in the host or excitation effects caused by the high luminosities , or indeed how these two scenarios may be related . the exclusion of the @xmath140 sources , the skew towards the detection of 21-cm absorption in compact objects ( cso / css / gps / hfp ) becomes much less significant . again , this indicates a bias introduced by the high uv luminosity sample and perhaps suggests that it is more meaningful to discuss the 21-cm absorption incidence in terms of the rest frame ultra - violet luminosities rather than by agn type or radio sed classifications . regarding the @xmath112  sources , in addition to both agn types having a 50% detection rate , there is no evidence for the expected larger degree of reddening in the type-2 objects , which would be caused by the presence of a dusty obscuration . we do find , however , that the optical  near - infrared colour appears to be correlated with the 21-cm absorption line strength over the _ these points would therefore appear to contradict the notion that the 21-cm optical depth in the hosts of high redshift galaxies and quasars is determined by the orientation of the central obscuring torus . although , like the literature , we find a higher incidence of 21-cm absorption in galaxies than in quasars , unlike the literature , we believe this to be a consequence of their lower ultra - violet luminosities , rather than their agn classification  is not likely to be coincidental . they do , however , seem to be quite distinct from their lower uv luminosity counterparts , which exhibit the same 21-cm detection rate as the type-2 objects . ] . furthermore , the fact that the reddening is also independent of agn type , suggests that this is also unrelated to the torus and the correlation between the reddening and the absorption line strength suggests that the bulk  and dust share a similar ( non - nuclear ) distribution . this could explain why only a fraction of  absorbing agn are detection in -maser emission @xcite : -masers are believed to arise close to the black hole in the central obscuration @xcite and thus trace type-2 objects . therefore , if  absorption also arose in the torus , one would expect a high detection rate of -masers in agn detected in  absorption . however , @xcite find  and  common to only 8 out of 19 objects searched and this 42% rate is very close to the overall  detection rate in agn ( see @xcite ) . this therefore suggests that the lines - of - sight through the masing disk and the  absorbing clouds are randomly oriented with respect to one another .    in the moderate uv luminous sample , not dominated by elliptical hosts , we therefore argue that the absorption may be occuring in the main galactic disk which must be randomly oriented with respect to the torus . in attempting to verify this :    1 . we find no real difference in the full - width half maxima of the 21-cm absorption profiles between the two agn types . this may suggest that these are subject to geometric effects ( covering factors and radio source sizes ) and thus can not give the full kinematical picture . although , again , absorption due to a randomly oriented disk could account for this . we also find no discernible difference in the offset of the centroid of the absorption and the systemic velocity of the host between the two agn types . although through a sample nearly double in size , we can confirm the findings of @xcite , that on average the offsets are blue - shifted . that is , there _ may be _ evidence for outflowing gas , although , again , we see no distinction between the two agn types . if the galactic disk were aligned with the obscuring torus , the 50% detection rate for _ both _ agn types suggests that absorption must occur in both galactic disks _ and _ outflows : the outflowing gas is expected to be directed along the radio jets ( e.g. @xcite ) , which are coincident with the axis of the torus , thus giving rise to the absorption in the type-1 objects . the fact that we can not discriminate between the disk and outflow absorption would suggest rapid , wide outflows of cold neutral gas , perhaps enveloping the wide ionisation cones observed in low redshift agn ( see table 1.2 of @xcite)@xmath199 . a 90  wide outflow of cool neutral gas expanding at @xmath200 , in which the molecular gas mass rivals that in the disk ( @xmath201 ) , is known of in the circinus galaxy @xcite , the proximate type-2 seyfert ( see also @xcite for further examples ) . however , it would therefore remain a mystery as to why only 50% of each agn type ( of @xmath112 ) are detected in 21-cm absorption , although the bulk absorption occuring in the galactic disk , which is randomly oriented with respect to the obscuring torus , could account for this . + this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . this research has also made use of nasa s astrophysics data system bibliographic service and asurv rev 1.2 @xcite , which implements the methods presented in @xcite . , e.  m. , oosterloo , t. , & morganti , r. 2002 , in astronomical society of the pacific conference series , vol . 273 , the dynamics , structure & history of galaxies : a workshop in honour of professor ken freeman , ed . g.  s.  da costa & h.  jerjen , 215                                                , a. , king , e. , morganti , r. , dallacasa , d. , tadhunter , c. , fanti , c. , reynolds , j. , jauncey , d. , preston , r. , mcculloch , p. , tingay , s. , edwards , p. , costa , m. , jones , d. , lovell , j. , clay , r. , meier , d. , murphy , d. , gough , r. , ferris , r. , white , g. , & jones , p. 2002 , a&a , 392 , 841                vermeulen , r.  c. , pihlstrm , y.  m. , tschager , w. , de  vries , w.  h. , conway , j.  e. , barthel , p.  d. , baum , s.  a. , braun , r. , bremer , m.  n. , miley , g.  k. , odea , c.  p. , roettgering , h. j.  a. , schilizzi , r.  t. , snellen , i. a.  g. , & taylor , g.  b. 2003 , a&a , 404 , 861","summary":"in a recent study of active galactic nuclei ( agn ) , we found that 21-cm absorption has never been detected in objects in which the ultra - violet luminosity exceeds . in this paper this may suggest that the bulk of the absorption generally occurs in the galactic disk , which must therefore be randomly orientated with respect to the circumnuclear torus .","abstract":"in a recent study of active galactic nuclei ( agn ) , we found that 21-cm absorption has never been detected in objects in which the ultra - violet luminosity exceeds . in this paper , we further explore the implications that this has for the currently popular consensus that it is the orientation of the circumnuclear obscuring torus , invoked by unified schemes of agn , which determines whether absorption is present along our sight - line . the fact that at , both type-1 and type-2 objects exhibit a 50% probability of detection , suggests that this is not the case and that the bias against detection of  absorption in type-1 objects is due purely to the inclusion of the  sources . similarly , the ultra - violet luminosities can also explain why the presence of 21-cm absorption shows a preference for radio galaxies over quasars and the higher detection rate in compact sources , such as css or gps sources , may also be biased by the inclusion of high - luminosity sources . being comprised of all 21-cm searched sources at , this is a necessarily heterogeneous sample , the constituents of which have been observed by various instruments . by this same token , however , the dependence on the uv luminosity may be an all encompassing effect , superseding the unified schemes model , although there is the possibility that the exclusive 21-cm non - detections at high uv luminosities could be caused by a bias towards gas - poor ellipticals . additionally , the high uv fluxes could be sufficiently exciting / ionising the  above 21-cm detection thresholds , although the extent to which this is related to the neutral gas deficit in ellipticals is currently unclear .    examining the moderate uv luminosity ( ) sample further , from the profile widths and offsets from the systemic velocities , we find no discernible differences between the two agn types . this may suggest that the bulk of the absorption generally occurs in the galactic disk , which must therefore be randomly orientated with respect to the circumnuclear torus . furthermore , we see no difference in the reddening between the two agn types , indicating , like the 21-cm absorption , that the orientation of the torus has little bearing on this . we also find a correlation between 21-cm line strength and the optical - near - infrared colour , which suggests that the reddening is caused by dust located in the large - scale ,  absorbing disk which intervenes the sight - line to the agn ."}
{"article_id":"1004.0127","section_id":"i","document":"among a large variety of random walk and primordial noise models / choices , a distinguished role is played by heavy - tailed symmetric lvy - stable distributions , commonly thought to be an exclusive support for so - called lvy flights . that view is founded on the concept of independent and identically - distributed random variables of the jump - type and a broad class of infinitely divisible distributions , that are admitted by generalizing the familiar central limit theorem , as encoded in the lvy - khintchine formula . stable densities generically have no second moments . the response of lvy noise to external potentials is most often quantified by means of the langevin equation with an additive lvy ( stable ) driver . the affiliated distribution functions ( pdfs ) obey so - called fractional fokker - planck equations where , in order to handle heavy - tailed pdfs , the ( brownian case ) second spatial derivative is replaced by the fractional one of order @xmath3 , c.f . @xcite-@xcite and references therein . under confining conditions , the second moments of resultant pdfs may exist and then the temporal behavior of the variance may be employed to quantify ( on suitable time scales ) sub- , or super - diffusive features of the underlying jump - type dynamics .    in our previous papers @xcite we have noticed that in addition to standard langevin equation based methods , an alternative modeling approach is worth investigation . it is based on the concept of the lvy - schrdinger semigroup - driven dynamics , @xcite . contrary to the familiar ( in the context of the brownian motion ) mapping of the fokker - planck equation into the hamiltonian dynamical system , the non - gaussian case makes a distinction between these two dynamical patterns of behavior . they are inequivalent . our departure point was , and still remains , the `` stochastic targeting '' ( also named `` reverse engineering '' ) strategy , @xcite : given an invariant pdf @xmath4 , design a stochastic jump - type process for which that preselected density is a unique _ asymptotic _ target . in case of langevin - driven processes , the basic reconstruction goal amounts to deducing the drift function of the process .    in refs . @xcite , given the very same @xmath4 , we have addressed the existence issue of a semigroup - driven dynamics ( e.g. the fractional version of the generalized diffusion equation ) , which relies on the existence of a semigroup potential @xmath5 . since @xmath4 is presumed to be shared with the langevin - driven lvy process , we know that it has a non - gibbsian functional form , @xcite . therefore standard thermalization and ( ultimate ) thermal equilibrium concepts are invalid in the lvy context .    in ref . @xcite we have relaxed the common pdf constraint and addressed a fully fledged reconstruction problem for the semigroup dynamics : given an invariant pdf , identify the semigroup - driven lvy process for which the prescribed pdf @xmath6 may stand for a unique asymptotic one . since , to this end , there is no need to invoke the langevin connection , the ensuing non - gibbsian obstacle does not appear anymore . indeed , under new premises , asymptotic pdfs in the gibbs form are admissible and a class of jump - type processes , non - trivially responding to environmental inhomogeneities , becomes largely extended to pdfs that are definitely related to gibbsian thermal equilibria , @xcite . the last observation suggests a possibility of a major recasting of the original `` reverse engineering '' problem of ref . @xcite which was designed to handle jump - type processes only . namely , while before we have set common invariant pdfs for various jump - type processes , presently we shall consider invariant pdfs that are shared by , seemingly disparate , jump - type ( discontinuous ) and diffusion - type ( continuous ) processes . invariant pdfs that show up a power - law behavior ( being e.g. of the inverse polynomial form ) are here allowed and thus an issue of a proper thermalization framework ( gibbsian equilibria ) , that encompasses heavy - tailed distributions , reappears again .    an issue disregarded in the past @xcite is that generic lvy pdfs ( like e.g. the familiar cauchy distribution ) , plainly against casual views , may be embedded in suitable `` exponential families '' of pdfs @xcite . a careful exploitation of standard ( shannon ) entropy extremum principles , @xcite , allows to single out a concrete lvy pdf as a specific exponential family member , at a uniquely defined inverse temperature value . anticipating further discussion , let us point out that our major observations are quite general and refer to a broad class of pdfs that are associated with symmetric stable noises and their perturbed ( confining regime ) versions . it is only an analytical and numerical tractability reason , that makes us mostly to refer to the cauchy driver in the present paper . we note that in the heavy - tailed asymptotic regime of diffusion - type processes , the process remains continuous and there is not ( albeit appealing ) `` switch '' to any jumping scenario . for all times we deal with a diffusion proceeding in conservative force fields , whose pdf asymptotic features ultimately appear to mimic those normally attributed to jump - type processes .    in a slightly careless manner one may think of a transition `` from a diffusive motion to the lvy flight behavior '' . the corresponding transient phenomena ( that have been literally interpreted as a transition from a diffusive to jump - type motion ) were experimentally recorded in the past @xcite . the diffusion vs jump scenario interpretation issue has appeared as well in the semiclassical description of so - called optical lattices , see e.g. @xcite-@xcite . apart from an obvious possibility to regard the lvy driver ( and thus to invoke the corresponding non - gaussian probability distribution ) as the major random displacement mechanism , it is perhaps less obvious that the wiener driver actually may give rise to heavy - tailed pdfs as well . then we encounter the dynamically generated intermediate and/or transitional regimes , where the number of the pdf moments asymptotically drops down to a finite number or none at all .    to elucidate these points , here we employ as a toy model ( albeit directly related to the previously mentioned optical lattice issue ) a one - parameter family of cauchy power pdfs , @xcite : @xmath7 as a reference exponential family of pdfs ( see e.g. @xcite ) that comprises the classic cauchy distribution as its member . this familiy is an exponential one due to a trivial transformatin into the gibbs - loking function with a logarthmic exponent . ( actually , for each `` canonical '' lvy pdf an analogous exponential family embedding can be accomplished . ) the above cauchy family arises naturally via the _ standard maximum entropy principle . namely , one seeks an extremum of the ( dimensionless ) shannon entropy @xmath8 of a continuous probability distribution @xmath9 under the constraint that the expectation value @xmath10 takes an a priori prescribed value , @xcite . _    if we regard a logarithmic function @xmath11 as an external force potential , with @xmath12 being interpreted as the forward drift in the langevin equation , then we end up with a familiar fokker - planck equation ( wiener driver in action ) . a functional form of the force term is identical to that of the physically motivated `` cooling force '' in optical lattice discussions @xcite . with that restoring force , we are capable of generating all members of the above cauchy family as target pdfs in the large time asymptotic of diffusion - type processes . this linear fokker - planck equation option has appeared in the literature before , @xcite , also in the attempt to interpret the cauchy family as a family of tsallis distribution functions @xcite . all members of the cauchy family can be achieved as asymptotic targets for jump - type processes . both the lvy - langevin and lvy semigroup driven dynamics may be employed to this end . in turn , the same `` targeting '' is valid if we resort to diffusion - type processes . an important intrinsic property of the cauchy family has to do with a number of moments of those pdfs . for a while , let us consider a parameter @xmath13 in eq . to assume integer values only : @xmath14 . then one immediately observes that the cauchy hierarchy of pdfs , c.f . [ fig : jed ] , involves a monotonically growing number ( as parameter @xmath15 grows from @xmath16 to infinity ) of moments of the probability distribution , beginning from none at all for @xmath16 . the growing number of moments in existence amounts to an improvement of the pdf localization and entails increasing strength of confinement of cauchy jumps ( e.g. flights ) , c.f . also @xcite , if the cauchy driver is assumed to be in action .    . ]    an appealing feature of the cauchy family is that , even if looking exceptional in many respects , it has received an ample literature coverage not only in the semiclassical analysis of optical lattices @xcite-@xcite . in below , we shall elaborate a bit on another physically important context of tsallis entropies and related ( via entropy maximum principles ) tsallis pdfs . indeed , cauchy family pdfs were discussed in search for a statistical and thermal ( equilibrium ) foundation for tsallis entropies and associated with them probability distributions . that includes asymptotic properties of various fokker - planck equations , nonlinear being included , as a dynamical justification for them , see e.g. refs . @xcite-@xcite . from a thermal equilibrium point of view , in reference to heavy - tailed pdfs , our approach appears to provide an alternative proposal to that originally formulated in refs . @xcite and @xcite . subsequently we shall discuss in some detail various random motion scenarios that may generate the above cauchy family of pdfs in their large time asymptotics . after identifying the involved cauchy semigroup dynamics , we shall demonstrate that diffusion - type processes as well generate heavy - tailed ( cauchy , to be specific ) pdfs , in affinity with the case of jump - type processes described by fractional fokker - planck equations . somewhat surprisingly , it turns out that the conventional diffusive dynamics may be regarded as an alternative ( to the fractional one ) dynamical model of random behavior that produces non - gaussian pdfs . this includes heavy tailed ones , that are casually thought to arise exclusively in relation to `` free '' ( we stress the role of independent , identically distributed random displacements ) jump - type random motions . in fact , we demonstrate the validity of the diffusive relaxation scenario from an initial @xmath17 or a gaussian function to virtually _ any _ member of cauchy power pdf hierarchy . in the diffusive dynamics , the resultant pdfs appear to have the gibbs - boltzmann form ( as should be for the exponential family of pdfs ) . all those observations readily extend to a broad variety of non - gaussian pdfs that have been invented in connection with the concept of confined lvy flights . our discussion uncovers an interplay between lvy and diffusion - type processes that has been left basically ignored in the current `` stochastic modeling '' literature . we point out that , in principle , one may even not be able to discriminate between these two classes ( continuous vs discontinuous ) of random processes , if in the vicinity of respective ( common for both ) equilibrium states . such observation may be particularly useful to avoid erroneous interpretation , in cases when an experimentally founded data analysis indicates a transient dynamics with a ( possibly unusual ) crossover behavior , like e.g. that reported in ref . @xcite .    in the present paper langevin noises ( lvy and wiener driver alike ) are considered as additive . for a completeness of exposition , we point out that there are reports in the literature that langevin equations with the multiplicative ( wiener ) noise do give rise to heavy - tailed distributions , see e.g. ref .","summary":"our main focus is on their transient regimes and specifically the crossover features , when initially infinite number of the pdf moments drops down to a few or none at all .","abstract":"we investigate temporal behavior of probability density functions ( pdfs ) of paradigmatic jump - type and continuous processes that , under confining regimes , share common heavy - tailed asymptotic ( target ) pdfs . namely , we have shown that under suitable confinement conditions , the ordinary fokker - planck equation may generate non - gaussian heavy - tailed pdfs ( like e.g. cauchy or more general lvy stable distribution ) in its long time asymptotics . for diffusion - type processes , our main focus is on their transient regimes and specifically the crossover features , when initially infinite number of the pdf moments drops down to a few or none at all . the time - dependence of the variance ( if in existence ) , with , in principle may be interpreted as a signature of sub- , normal or super - diffusive behavior under confining conditions ; the exponent is generically well defined in substantial periods of time . however , there is no indication of any universal time rate hierarchy , due to a proper choice of the driver and/or external potential ."}
{"article_id":"1004.0127","section_id":"c","document":"the main message of the present paper is that , under suitable confinement conditions , the ordinary fokker - planck equation may generate a non - gaussian heavy - tailed pdf ( like e.g. cauchy or more general lvy stable distribution ) as its long time asymptotics . that implies a continuous interpolation between an initial highly localized pdf ( like dirac @xmath250 - function ) having all moments and the terminal heavy - tailed pdf , with only few ( or none at all ) moments in existence . since it is the fractional generalization of fpe which is customarily invoked to generate the same heavy - tailed pdfs , albeit with a very different choice of drift functions , we have uncovered an unexpected link between non - gaussian jump - type processes ( inherent in the fractional fpe derivation ) and ordinary diffusion processes that are based on the gaussian ( wiener driver ) paradigm .    in the present paper we have paid attention not only to random processes that have found their place in the literature , all stemming from different forms of langevin modeling ( here , only additive noise has been considered ) , but also to alternative jump - type scenarios based on the concept of the semigroup - driven dynamics , @xcite . this pattern of dynamical behavior has not been satisfactorily explored within the area of anomalous random transport .    to make our findings transparent , we have undertaken a direct numerical verification of them , by invoking two kinds of modeling . the first one amounts to solving numerically both ordinary ( with the laplace operator ) and fractional fpe s with the drift functions selected to generate , the same for both , non - gaussian ( specifically cauchy family ) pdfs . the second one presumes that one has the above drift functions at disposal . then , we undertake a direct numerical modeling of random trajectories ( sample paths ) of the underlying stochastic process , both brownian and of the jump - type . these trajectories have next been used to generate the associated pdfs which turn out to coincide with those obtained from numerical solution of both ordinary and fractional fpe s . we note that a traditional interpretation of random data relies on the existence of at least two lower moments of involved probability distributions . therefore , the case of lvy flights could have been placed within this interpretational paradigm only under confining conditions . in such case , in view of the existence of second moments , one may address their time - dependence in transitional regimes , when the process is yet far from its equilibrium pdf . the above numerical solutions of the fpe and of its fractional analog permit us to investigate the time dependence of different moments ( see fig . 8) of the corresponding pdfs . at this point we have passed to an approximation of the variance @xmath285 by the power law @xmath286 , with the hope that its validity would shed some light on the problem of assigning terms like `` subdiffusion '' or `` superdiffusion '' to anomalous transport processes . namely , the time evolution of variances is often considered as a signature of subdiffusive , normal or superdiffusive behavior , typically considered with no bounds on the duration time of the process ( unless set be experiment ) . taken literally , all such motions would belong to the sweeping category , where the variance grows indefinitely .    in this connection , our analysis shows that ( i ) near initial @xmath287 the exponent @xmath104 depends strongly on time , ( ii ) deeply in the asymptotic @xmath228 regime @xmath104 can be equated to @xmath288 , ( iii ) in a transitional regime ( i.e. for pdfs lying somewhere between initial and terminal ones ) the exponent @xmath104 happens to take almost constant _ positive values ( observe e.g. almost straight lines in time dependence of variances in the middle parts of the corresponding plots in fig . _    we have focused on possible signatures of ( ab)normal relaxation patterns , expecting that in a transitional regime we might possibly identify an undoubtful subdiffusive or superdiffusive dynamics . our answer is negative . we have confirmed that widely used terms `` sub- '' and/or `` superdiffusion '' are rather vague and become meaningless for confined stochastic processes , likewise in the presence of lvy and wiener drivers . the pertinent exponent value is not indicative for the stochastic process in question , to justify its naming ( sub- , normal , super- ) , because it depends strongly on the location ( position ) of the initial pdf relative to the drift potential profile , and on its curvature . it appears that the above `` anomaly '' in the description of random motions appears to have much deeper foundations . one can alternatively use incompatible microscopic mechanisms to model an engineered asymptotic approach to the same a priori prescribed non - gaussian target pdf .    if those pdfs are an outcome of a statistical analysis of experimental data , clearly a distinction between diffusive and jumping patterns of dynamical behavior appears not to be that sharp as commonly expected . on the other hand , a possible discrimination tool , e.g. the single - particle / molecule experiments in the nano- or mesoscopic domain should be set under scrutiny , since microscopic features of motion may not be verifiable at current levels of precision / resolution in collecting the data . the specific stochastic model that would seemingly fit to the data , might possibly be not more than a lucky guess , to be invalidated in a more thorough analysis . another message worth spelling is that apparently divorced dynamical mechanisms ( langevin - cauchy , cauchy semigroup and diffusion - type process ) may share common asymptotic pdfs . contrary to the wide - spread belief , heavy - tailed probability distributions , casually associated with jump - type processes , may as well have gaussian ( e.g. diffusive ) origins . that is possible if drift functions refer to properly functioning potentials , which we attribute to a cumulative effect of inhomogeneities of the environment ) . their role would be to _ attenuate the casually considered counterbalancing of the wiener driver , `` normally '' necessary to eliminate heavy tails of the resultant pdf . _    99 i. eliazar and j. klafter , j. stat . phys . * 111 * , 739 , ( 2003 ) . s. jespersen , r. metzler and h. c. fogedby , phys . rev . * e 59 * , 2736 , ( 1999 ) v. v. janovsky et al . , physica * a 282 * , 13 , ( 2000 ) h. risken , _ the fokker - 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verlag , berlin , 1992 k. sobczyk , _ stochastic differential equations _ , kluwer , dordrecht , 1991 w. horsthemke and r. lefever , _ noise - induced transitions _ , springer - verlag , berlin , 1984 n. g. van kampen , _ stochastic processes in physics and chemistry _ , nort - holland , amsterdam , 1987 d. brockmann and i. sokolov , chem . phys . * 284 * , 409 , ( 2002 )","summary":"we investigate temporal behavior of probability density functions ( pdfs ) of paradigmatic jump - type and continuous processes that , under confining regimes , share common heavy - tailed asymptotic ( target ) pdfs . namely , we have shown that under suitable confinement conditions , the ordinary fokker - planck equation may generate non - gaussian heavy - tailed pdfs ( like e.g. cauchy or more general lvy stable distribution ) in its long time asymptotics . for diffusion - type processes , the time - dependence of the variance ( if in existence ) , with , in principle may be interpreted as a signature of sub- , normal or super - diffusive behavior under confining conditions ; the exponent is generically well defined in substantial periods of time . however , there is no indication of any universal time rate hierarchy , due to a proper choice of the driver and/or external potential .","abstract":"we investigate temporal behavior of probability density functions ( pdfs ) of paradigmatic jump - type and continuous processes that , under confining regimes , share common heavy - tailed asymptotic ( target ) pdfs . namely , we have shown that under suitable confinement conditions , the ordinary fokker - planck equation may generate non - gaussian heavy - tailed pdfs ( like e.g. cauchy or more general lvy stable distribution ) in its long time asymptotics . for diffusion - type processes , our main focus is on their transient regimes and specifically the crossover features , when initially infinite number of the pdf moments drops down to a few or none at all . the time - dependence of the variance ( if in existence ) , with , in principle may be interpreted as a signature of sub- , normal or super - diffusive behavior under confining conditions ; the exponent is generically well defined in substantial periods of time . however , there is no indication of any universal time rate hierarchy , due to a proper choice of the driver and/or external potential ."}
{"article_id":"nucl-th0512063","section_id":"c","document":"[ sec : conclusion ]    in this work we examined elastic compton scattering from the deuteron . diagrams without an intermediate two - nucleon state have been calculated up to next - to - leading order in the small scale expansion , an effective field theory with nucleons , pions and the @xmath1 resonance as explicit degrees of freedom . those diagrams including the propagation of the two - nucleon system between the two photon vertices have been calculated using greens - function methods . therefore , and because of the fact that we use deuteron wave functions that have been derived from state - of - the - art @xmath0-potentials , we refer to this approach as the `` greens - function hybrid approach '' . for the photon coupling we make use of siegert s theorem  @xcite , which is well - known to guarantee the exact static limit , see e.g.  @xcite .    in section  [ sec : comparison ] , we show that we have achieved a consistent description of elastic deuteron compton scattering which is valid from 0  mev up to @xmath55  mev . the advantage of our calculation with respect to refs . @xcite is that we obtain a good description of the data published below 60  mev . this improvement is of course connected to the correct static limit , which had not been obtained in those publications . therefore , other calculations reaching this limit and thus being manifestly gauge invariant are also able to describe the low - energy data well , see e.g.  @xcite . however , we achieve good agreement also with high - energy data , measured around 94.2  mev  @xcite . in this energy regime the work of ref .  @xcite fails and the `` pion - less '' effective field theory used in @xcite is inapplicable . the authors of @xcite have also problems to describe the data in the backward direction without introducing surprisingly large isovector polarizabilities . it was already shown in  @xcite that the main difference between their approach and ours is in the energy dependence of the resonant compton multipoles , which is well captured in our calculation due to the inclusion of explicit @xmath33-resonance degrees of freedom , whereas the authors of ref . @xcite include the polarizabilities only via the leading and subleading terms of a taylor expansion in the photon energy . there are a number of ways to check the theoretical uncertainties of our calculation . as demonstrated in section  [ sec : wavefunctiondep ] and fig . [ fig : wavefunctiondep ] , the error induced by dependence on the deuteron wave function is tiny and may well be set to zero , while it is sizeable in the extractions of refs . @xcite . in section  [ sec : potentialdep ] and fig . [ fig : lochipt ] , we compared the cross - sections derived using either the av18-potential , or the much cruder one - pion exchange potential , regulated to reproduce the deuteron binding energy and @xmath56-scattering length . this may for the time being serve as lo potential of @xmath30eft . we find that the magnetic polarizability using this potential is less than @xmath57 larger than using av18 , and the electric polarizability decreases by practically the same amount . as it is safe to assume that av18 is a better representative of a fully self - consistent @xmath30eft potential at the level of our calculation ( next - to - leading order ) than one - pion exchange , we classify uncertainties induced by the potential as negligible . a third way to estimate the errors from the theory side is to compare to our previous calculation  @xcite . with the single - nucleon sector treated identically to the approach presented here , its only difference is that the interaction kernel is expanded perturbatively . as argued in section  [ sec : comparison ] , this approximation is justified in the rgime @xmath58 . there , both results should thus coincide up to higher - order corrections stemming from the different treatment of the two - nucleon sector . figure  [ fig:2parameterfit3 ] and in particular the extracted polarizabilities in table  [ tab : fits ] show that both approaches agree well within the statistical error , and do not deviate by more than @xmath59 . finally , higher - order corrections to the energy - dependence of the polarizabilities themselves were in sse estimated by nave dimensional analysis to be less than @xmath60  @xcite . all these interdependent estimates suggest a theory uncertainty of our extraction of @xmath61 as appropriate . this is comparable with the statistical error . having achieved a good description of all elastic deuteron compton - scattering data enabled us therefore to perform a global fit of the isoscalar polarizabilities to all existing data points , published in @xcite . our 2-parameter - fit results are ( see table  [ tab : fits ] ) @xmath62 we note that the numbers of eq . ( [ eq : globalfitconclusion ] ) are very close to the fit results ( [ eq : expphghp ] ) for the proton polarizabilities , determined in  @xcite within the sse framework . this leaves little space for large isovector polarizabilities . furthermore they agree extraordinarily well with the isoscalar baldin - sum - rule value , eq . ( [ eq : baldin ] ) . therefore , in order to reduce the statistical error , we repeated our fits including this constraint : @xmath63 combining eqs . ( [ eq : globalfitconclusion ] ) or  ( [ eq : globalfitbaldinconclusion ] ) , respectively , with the proton numbers of eq . ( [ eq : expphghp ] ) , we obtained the neutron polarizabilities @xmath64 for the 2-parameter fit and @xmath65 for the 1-parameter fit including the baldin constraint . in both fits the fact that our deuteron compton - scattering calculation is applicable in the whole energy range from 0  mev to 100  mev enables us to include all data into our fit of the isoscalar polarizabilities . from these results we deduce that the neutron is paramagnetic and that proton and neutron behave rather similarly when exposed to external electromagnetic fields . in both points our deuteron compton calculation agrees with refs . @xcite and with the chiral perturbation theory prediction that contributions to the isovector polarizabilities only start beyond leading - one - loop order . this also justifies again that the two iso - scalar short - distance contributions to the electric and magnetic scalar polarizabilities in sec . [ sec : nonresonant ] are the smallest set which needs to be promoted by one order as in refs . @xcite to describe the data , given present uncertainties . our results for @xmath66 and @xmath41 are in excellent agreement with those from a comprehensive , experimental analysis of all quasi - free data  @xcite . that analysis did , however , not include elastic deuteron compton scattering due to the alleged discrepancy between theory and elastic @xmath2 experiments . this discrepancy has now been resolved , both in  @xcite and in the greens - function hybrid approach presented in this work . finally , we strongly advocate enlarging the data base for elastic compton scattering on the deuteron . if further experiments , as planned or running at tunl / hi@xmath67s  @xcite , at the s - dalinac  @xcite and at maxlab  @xcite , provide additional quality data below the pion threshold , the increased statistics would reduce the statistical error in our fit of the isoscalar polarizabilities . recall that the statistical errors of the two - parameter fit are larger than our theoretical uncertainty , and that the combined statistical and baldin - sum - rule error of the one - parameter fit is comparable to it . these errors are increased by the systematic experimental uncertainties which may be estimated more comfortably if more experiments using different methods were available . on the theory side , a wider effort is under way to describe elastic compton scattering on the proton , deuteron and @xmath68he from the thomson limit to well into the @xmath33-resonance region in one model - independent , unified framework . we focus at present on improving the accuracy by a full next - to - next - to - leading order calculation with nucleons , pions and the @xmath1 as dynamical , effective degrees of freedom  @xcite . clearly , reduced error bars in coherent compton scattering from the deuteron would enable us to quantify by how much proton and neutron polarizabilities differ .","summary":"we examine elastic compton scattering from the deuteron for photon energies ranging from zero to 100  mev , using state - of - the - art deuteron wave functions and-potentials . nucleon - nucleon rescattering between emission and absorption of the two photons is treated by green s functions in order to ensure gauge invariance and the correct thomson limit . with this greens - function hybrid approach , we fulfill the low - energy theorem of deuteron compton scattering and there is no significant dependence on the deuteron wave function used . concerning the nucleon structure , we use chiral effective field theory with explicit degrees of freedom within the small scale expansion up to leading - one - loop order . agreement with available data is good at all energies . + _ center for nuclear studies , department of physics , the  george  washington  university ,  washington dc 20052 , usa _    1.0 cm    [ cols= \" > , < \" , ]     even with this rather crude approximation of the neutron - proton interaction , we obtain results close to those of the av18-potential , cf . fig .  [ fig : lochipt ] . obviously , the one - pion - exchange potential , adequately regulated for , together with a reasonable parameterization of the hard core gives an approximation of the potential which is well sufficient for the process under consideration . we conclude that we are mainly sensitive to the long - range part of the potential . nevertheless , there are small deviations ( of the order of ) visible in fig .  these deviations increase with increasing photon energy and scattering angle . however , the correct thomson limit is reached with any combination of wave - function and two - nucleon rescattering potential , as shown by arenhvel  and recalled in sec .  one can therefore not simply determine if the seed of discrepancies is a difference between lo potential and phase shifts at low energies , and/or if the different curves arise from the well - explored poor lo - description of the , and partial waves at energies for some cutoffs , see e.g.  . the situation is complicated by the fact that rescattering contributions are small at high energies , see sec .  the error induced by neglecting them is comparable to that from using the cruder lo potential in fig .  [ fig : thomson2].,title=\"fig : \" ] -potentials : the av18-potential  ( solid ) and the lo chiral potential  ( dashed ) . for both curves the chiral wave function  has been used . [ fig : thomson2].,title=\"fig : \" ]    having proven that our calculation is rather insensitive to the choice of the deuteron wave function and the-potential , we turn now to fits of the isoscalar nucleon polarizabilities ( or equivalently the short - distance contributions and ) to all existing elastic data .","abstract":"we examine elastic compton scattering from the deuteron for photon energies ranging from zero to 100  mev , using state - of - the - art deuteron wave functions and-potentials . nucleon - nucleon rescattering between emission and absorption of the two photons is treated by green s functions in order to ensure gauge invariance and the correct thomson limit . with this greens - function hybrid approach , we fulfill the low - energy theorem of deuteron compton scattering and there is no significant dependence on the deuteron wave function used . concerning the nucleon structure , we use chiral effective field theory with explicit degrees of freedom within the small scale expansion up to leading - one - loop order . agreement with available data is good at all energies . our 2-parameter fit to all elastic data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar baldin sum rule . taking this value as additional input , we find and and conclude by comparison to the proton numbers that neutron and proton polarizabilities are the same within rather small errors .    nucl - th/0512063 ; tum - t39 - 05 - 18 ; fau - tp3 - 05/9 + revised version 3rd august 2010 .    * robert p. hildebrandt * , * harald w. griehammer * + and * thomas r.  hemmert * _ institut fr theoretische physik ( t39 ) , physik - department , + technische universitt mnchen , d-85747 garching , germany _ + _ institut fr theoretische physik iii , naturwissenschaftliche fakultt i , universitt  erlangen - nrnberg , d-91058 erlangen , germany _ + _ center for nuclear studies , department of physics , the  george  washington  university ,  washington dc 20052 , usa _    1.0 cm    [ cols= \" > , < \" , ]     even with this rather crude approximation of the neutron - proton interaction , we obtain results close to those of the av18-potential , cf . fig .  [ fig : lochipt ] . obviously , the one - pion - exchange potential , adequately regulated for , together with a reasonable parameterization of the hard core gives an approximation of the potential which is well sufficient for the process under consideration . we conclude that we are mainly sensitive to the long - range part of the potential . nevertheless , there are small deviations ( of the order of ) visible in fig .  [ fig : lochipt ] , which justify the application of a more sophisticated potential . these deviations increase with increasing photon energy and scattering angle . however , the correct thomson limit is reached with any combination of wave - function and two - nucleon rescattering potential , as shown by arenhvel  and recalled in sec .  [ sec : thomson ] . therefore , deviations coming from using different wave - functions or potentials must necessarily increase with increasing energy . one can therefore not simply determine if the seed of discrepancies is a difference between lo potential and phase shifts at low energies , and/or if the different curves arise from the well - explored poor lo - description of the , and partial waves at energies for some cutoffs , see e.g.  . the situation is complicated by the fact that rescattering contributions are small at high energies , see sec .  [ sec : comparison ] . the error induced by neglecting them is comparable to that from using the cruder lo potential in fig .  [ fig : lochipt ] but has a different angular dependence .    -potentials : the av18-potential  ( solid ) and the lo chiral potential  ( dashed ) . for both curves the chiral wave function  has been used . lower panels : corresponding error plots , calculated in analogy to fig .  [ fig : thomson2].,title=\"fig : \" ] -potentials : the av18-potential  ( solid ) and the lo chiral potential  ( dashed ) . for both curves the chiral wave function  has been used . lower panels : corresponding error plots , calculated in analogy to fig .  [ fig : thomson2].,title=\"fig : \" ] -potentials : the av18-potential  ( solid ) and the lo chiral potential  ( dashed ) . for both curves the chiral wave function  has been used . lower panels : corresponding error plots , calculated in analogy to fig .  [ fig : thomson2].,title=\"fig : \" ] -potentials : the av18-potential  ( solid ) and the lo chiral potential  ( dashed ) . for both curves the chiral wave function   has been used . lower panels : corresponding error plots , calculated in analogy to fig .  [ fig : thomson2].,title=\"fig : \" ]    having proven that our calculation is rather insensitive to the choice of the deuteron wave function and the-potential , we turn now to fits of the isoscalar nucleon polarizabilities ( or equivalently the short - distance contributions and ) to all existing elastic data ."}
{"article_id":"0809.3534","section_id":"i","document":"this is a largely expository paper about the an li  ruan version of relative gromov  witten invariants ; cf . these have been used for a long time to help solve enumerative problems ( cf . parker  @xcite for example ) but have only recently been much used in other areas of symplectic geometry . for example , they are an essential ingredient in hu  li  ruan s work in  @xcite on the symplectic birational invariance of the uniruled property as well as in later papers @xcite on related topics . they are still rather little understood by symplectic geometers , even in the genus zero case .     1 describes the moduli spaces of stable maps that enter into their definition . these involve curves on several levels as in many sft moduli spaces . ( of course , relative gromov  witten invariants can be considered as a special case of sft ; cf . * example  2.2 ) . ) we do not attempt to do any analysis , but rather to explain the structure of these moduli spaces through examples .  2 and  3 describe the decomposition formula and give several examples of its use .    here are our main results . * we show in remark  [ rmk : g0 ] that when the normal bundle of the divisor @xmath0 is suitably positive one can calculate genus zero gromov  witten invariants without involving higher level curves . ( this result is greatly strengthened by zinger in @xcite . ) however , in genus one this need not be the case ; cf . example [ ex : rel2 ] . * 2 . * our second set of results concern the contributions to the relative invariants from curves in or near @xmath0 . more formally , these are the relative invariants of the pair @xmath3 , where @xmath4 is the projectivization of a complex line bundle @xmath5 and @xmath6 is the copy of @xmath0 at infinity \" with normal bundle @xmath7 . we denote by @xmath8 the copy of @xmath0 along the zero section ( with normal bundle @xmath9 ) . understanding the relative invariants of @xmath3 is a crucial ingredient of the proofs of many results , such as the blow up formulas in @xcite . as a first step , one needs to know that certain invariants vanish . lemma  [ le : reld ] gives a version of this result for relative invariants in class @xmath10 under the condition that @xmath11 and the homological constraints are pulled back from @xmath0 . the argument is elementary , based on a dimension count . this argument fails when @xmath12 , but there were no explicit examples showing that the result may also not hold in this case . example [ ex : reld ] gives such an example in the genus zero case . our first application of the decomposition formula is to give conditions under which the absolute and relative genus zero invariants agree for classes @xmath1 such that @xmath2 : see proposition [ prop : g0 ] . its statement is slightly stronger than other similar results in the literature ( cf . @xcite ) because we do not make the usual positivity assumptions on the normal bundle of @xmath0 . however the argument is still based on a dimension count . finally we give examples where the absolute and relative invariants differ for classes @xmath1 such that @xmath2 . it is easy to find such examples in genus @xmath13 ; see example [ ex : g1 ] . the genus zero example is trickier and is given in proposition  [ prop:=0 ] . the reason why such examples exist is that in calculating the relative invariants one uses almost complex structures @xmath14 and perturbing @xmath15-forms @xmath16 that respect the divisor @xmath0 . if @xmath0 is nonnegative `` then a generic pair @xmath17 of this form should satisfy the regularity conditions for stable maps to @xmath18 as as well as those for maps to @xmath19 . ( this statement is made precise in zinger @xcite . ) however , if @xmath0 is sufficiently negative '' then this is not so , and there may be contributions to the relative invariant that are perturbed away in the absolute invariant . * acknowledgements * i wish to thank the many people who have helped me understand relative invariants , in particular t .- j . li , yongbin ruan , rahul pandharipande , and aleksey zinger .","summary":"we give explicit examples where these invariants differ even though it seems at first that they should agree , for example when counting genus zero curves in a class such that .","abstract":"this note compares the usual ( absolute ) gromov - witten invariants of a symplectic manifold with the invariants that count the curves relative to a ( symplectic ) divisor . we give explicit examples where these invariants differ even though it seems at first that they should agree , for example when counting genus zero curves in a class such that . the main tool is the decomposition formula in the form developed by a. li  ruan ."}
{"article_id":"physics0309124","section_id":"i","document":"the concept of reaction mechanism plays a major role in chemistry and represents a synthesis of our understanding of the way in which different topological changes in the bonding structure of a reactant or product are correlated as the reaction proceeds . recent advances in ultrafast lasers@xcite , x - ray@xcite and other spectroscopies as well as in computational chemistry@xcite have made possible the study of most gas - phase and some condensed - phase reactions in molecular detail . however , most experimental investigations of complex reaction mechanisms taking place in liquid environments are still inferred from isotope and solvent ( medium ) effects on the reaction rate@xcite . consequently , the interpretation of the experimental results as well as the reaction mechanisms inferred are more controversial than those of gas - phase reactions . computer studies can be useful as a complement to experimental data in cases where experiments alone can not provide a definitive picture of the mechanism of the chemical process . it is therefore desirable to develop systematic computational approaches to carefully examine the relation between isotope effects and reaction mechanism in condensed phase systems . however , computational calculations of kinetic isotope effects in condensed - phase reactions can become expensive due to a number of difficulties . some of the practical challenges involving the calculation of kinetic isotope effects and reaction rates in solution are associated with the fact that accurate descriptions of transformations in which chemical bonds are broken and formed require time - consuming _ ab initio _ electronic structure methods . computer time limitations become particularly relevant when investigating `` rare events '' such as chemical reactions , especially when the reactions are accompanied by substantial differences in the structure of the solvent . to further complicate matters , quantum effects such as zero - point vibrations and tunneling effects are important in some chemical processes , such as proton transfer reactions . another technical problem in the simulations of reactive systems is that the statistical resolution of calculations of the reaction rate depends on how many statistically independent configurations are obtained during the simulation : simulations in which a large number of successive configurations have similar configurations of the reactive core or of the solvent molecules suffer from large uncertainties in the calculated reaction rates , precluding any definitive interpretation of the reaction mechanism . it is therefore critical to develop methods which sample statistically independent configurations along the reaction path rapidly and correctly . in the case where the reaction path can be characterized by means of a small number of reaction coordinates , accurate , statistically well - resolved calculations of reaction rates can be performed by developing improved methods for computing reaction free energy profiles along these reaction coordinates . a number of techniques for computing free energy profiles along reaction coordinates have been proposed in the literature , including umbrella sampling@xcite , thermodynamic integration in conjunction with the blue - moon ensemble method@xcite , projection methods@xcite , variable transformation approaches@xcite and guiding potentials@xcite . the use of molecular mechanics - based guiding potentials was proposed simultaneously and independently by iftimie et al.@xcite and vondele et al.@xcite and implemented in a monte carlo and a molecular dynamics framework , respectively . the basic idea of the method consists of using a `` fast '' _ molecular mechanics _ potential to guide a computationally intensive _ ab initio _ simulation . the monte carlo version of the `` guiding '' approach in reference [ was called the molecular mechanics based importance function method ( mmbif ) . it was demonstrated that the utilization of a reasonably accurate molecular mechanics potential as an importance function decreases the correlation of an _ ab initio _ monte carlo calculation by two orders of magnitude . the method was illustrated on a gas - phase formic acid - water system in which the activated processes involved breaking and forming hydrogen bonds@xcite , and was successfully applied to calculate the kinetic isotope effects in a model gas - phase intramolecular proton transfer reaction@xcite . one of the major challenges in _ ab initio _ simulations of reactions in condensed phase environments is to thoroughly sample configurations of the system when changes in the solvent occur on long time scales . for instance , in molecular dynamics simulations of proton transfer reactions in which the collective behavior of the solvent can strongly influence the dynamics of the reaction , the sampling efficiency can be limited by long solvent dielectric relaxation time . in essence , an independent configuration of the system requires that the equations of motion be propagated for a time which is longer than the dielectric relaxation time . even simple organic solvents such as tetrahydrofuran , the relevant solvent in this study , have dielectric relaxation times on the order of @xmath0 ps@xcite , so that independent solvent configurations are only obtained after several thousand elementary propagation steps . more structured solvents such as water , with a dielectric relaxation time of roughly @xmath1 ps@xcite , require even longer propagation for proper sampling of solvent configurations . the long time scale of structural rearrangements in solvents pose a serious challenge to _ ab initio _ calculations even when the solvent is modeled using molecular mechanics since each propagation step in the dynamics involves a time - consuming _ ab initio _ calculation . ideally , successive configurations in a simulation involve drastically different solvent and solute configurations . this is only possible using an artificial dynamics to generate the sequence of configurations . one way to generate relatively uncorrelated successive configurations is to apply importance sampling ideas .    in this paper , the molecular mechanics - based importance sampling method is adapted to calculate reaction rates of chemical processes in condensed phases where collective motions of the environment can influence the quantitative features of the chemical process and , in some cases , play a critical role in determining the mechanism of a reaction . the monte carlo procedure involves separating the task of sampling the configurations of the condensed phase system into two parts . the first part involves an efficient scheme of updating the solvent configuration while the second focuses on the relatively slow _ ab initio _ calculation of the reactive core . this approach allows extensive sampling of the molecular mechanical solvent without a significant increase in the overall computational work over a gas phase _ ab initio _ simulation . the method is applied to study the double proton transfer reaction in an acetic acid - methanol complex solvated by tetrahydrofuran .","summary":"the method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran .","abstract":"in this article , we propose an efficient method for sampling the relevant state space in condensed phase reactions . in the present method , the reaction is described by solving the electronic schrdinger equation for the solute atoms in the presence of explicit solvent molecules . the sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long . the method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran . it is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas - phase calculations .    * h *  * s * * u * *p *    * h *  * s * * u * *p *"}
{"article_id":"physics0309124","section_id":"m","document":"the computational study of proton - transfer reactions can be used to understand the conditions for the validity of a well - known conjecture proposed in the physical organic chemistry literature , stating that the breakdown of the rule of geometric mean for kinetic isotope effects , which is a relation@xcite involving ratios of kinetic isotope effects corresponding to different isotopic substitutions at the primary and secondary atoms , is a signature of tunneling for both primary and secondary atoms@xcite . the consequences of applying the rule of geometric mean to interpret experimentally determined isotope effects are of far - reaching importance : the inferred relationship between the rule of geometric mean and reaction mechanism forms the basis for the proposal that _ multiple _ _ intramolecular _ proton transfer reactions are likely to proceed via a two - step mechanism , in contrast to _ multiple intermolecular _ proton transfers which are believed to proceed via a synchronous pathway@xcite . the same relationship is at the heart of the recent suggestion that tunneling effects have played an important role in the design of the active sites of some proteins@xcite . some of the most striking consequences of the rule of geometric mean@xcite appear when studying multiple proton transfer reactions in condensed phases . the study of reactions involving the exchange of a pair of protons between two molecules may provide insight into the dynamics of certain types of enzymatic reactions in which several functional groups in the active center are properly aligned so that concerted catalysis can occur . this type of catalysis mechanism is called _ bifunctional catalysis _ and is the principal mechanism responsible for the several orders of magnitude increase in the reaction rate in several important biochemical transformations @xcite . the double proton transfer reaction between acetic acid and methanol is one of the simplest examples of reactions involving an intermolecular exchange of protons between two molecules and therefore is a good candidate for computationally investigating general aspects of bifunctional catalysis . the chemical processes occurring in a solution of acetic acid - methanol in tetrahydrofuran ( thf ) have been studied experimentally by gerritzen and limbach@xcite . the majority species in the system consist of complexes formed from either a single molecule of acetic acid or a single molecule of methanol hydrogen - bonded with a single molecule of solvent . the minority species in the system consist of linear and cyclic clusters of acetic acid hydrogen - bonded with methanol and solvated by tetrahydrofuran . the double - proton transfer reaction takes place along the hydrogen bonds of the cyclic clusters . when the concentrations of acetic acid and methanol are reduced , the only cyclic cluster formed within which double - proton transfer is experimentally observed is formed from one molecule of acetic acid and a single molecule of methanol@xcite ( see fig . 1 ) .    in this work , we will focus only on the intermolecular double proton transfer which takes place in the cyclic cluster formed from one molecule of methanol and a single molecule of acetic acid in a solution of tetrahydrofuran ( thf ) . the quantum nuclear effects due to the small mass of the hydrogen atoms will be neglected here , and we will concentrate only on the sampling issues . once the sampling method is tested for classical atoms , the method will be developed in a later article to include nuclear quantum effects via centroid transition state theory using sampling ideas similar to those used in our previous studies of malonaldehyde@xcite . since it is impractical to treat large systems quantum mechanically , one is inevitably faced with the decision of how to combine _ ab initio _ electronic structure methods with more empirical approaches . one alternative to full _ ab initio _ calculations consists of using a mixed quantum - mechanical / molecular - mechanical ( qm / mm ) description of the system . however , in general it is problematic to clearly define the physics of the interface region between the quantum and molecular mechanical subsystems . in the best of circumstances , the separation can be made without `` cutting '' a covalent bond . for reactive processes in which the reaction occurs in a small solute which can be simulated in isolation using _ ab initio _ methods , the logical separation between the quantum and molecular mechanical regions is at the solute - solvent level . that is , the energies of the solute in which the reaction is occurring are calculated using electronic structure methods for the solute in the presence of the solvent , while the solvent energies are described by molecular mechanical potentials . even after this separation has been defined , one is faced with another technical issue of how an infinite condensed phase system can be represented in a practical fashion . one common approach utilized in simulations of condensed phase systems is to simulate explicitly a system consisting of a solute surrounded by a small number of solvent molecules periodically replicated in an infinite fashion . unfortunately , such a periodic replication of the system introduces artifacts . one such artifact is the existence of spurious long - ranged correlations due to the periodicity of the system . in principle , such correlations could have a large impact on the reactive process . the use of periodic boundary conditions also introduces complexity in the electronic structure calculation itself when localized basis sets are used . an alternative approach is to use toroidal boundary conditions in which part of the solvent is explicitly represented while the influence of the solvent from regions far from the solute is implicitly incorporated .    in the present study we have utilized a quantum mechanics / molecular mechanics / implicit solvent ( qm / mm / continuum ) approach , in which the bond breaking and forming processes taking place in the solute are described by including all solute electron - electron , electron - nuclei and nuclei - nuclei interactions in an electronic hamiltonian . the interactions between the solvent molecules which form the first few solvation shells ( in practice , @xmath2 thf molecules ) are described using a molecular mechanics potential . the electrostatic interactions between the solute and the solvent molecules in the first few solvation shells are incorporated into this approach by solving the _ ab initio _ electronic structure equations for the solute in the presence of the electric field generated by the molecular mechanics solvent charges . the total energy of the system also includes the lennard - jones interaction energy between solute and the solvent molecules in the first solvation shells , and the reaction field energy which accounts for the long - range electrostatic interactions between solute and solvent molecules ( see fig . the simulations were performed using the toroidal boundary conditions approach@xcite , in which a cutoff distance is used that sets the boundaries of the region within which intermolecular interactions are explicitly counted . therefore , the only quantum electron - electron , electron - nuclei and nuclei - nuclei interactions which were explicitly counted in the present treatment were those which correspond to atoms separated by less than the cutoff distance , here chosen to be @xmath3 angstroms . the effects of the neglected interactions in the toroidal boundary conditions approach have been approximately accounted for by adding reaction field corrections@xcite to the electronic energy@xcite :    @xmath4    where the sum is over all molecules i inside the primitive cell , @xmath5 is the dielectric constant of the solvent , @xmath6 is the radius of the spherical surface , @xmath7 is the dipole moment of molecule @xmath8 , and @xmath9 is the total dipole moment inside the spherical surface surrounding the molecule @xmath8 . the correct energetics in hydrogen - bonded systems and in systems undergoing proton transfer reactions is difficult to describe even with _ ab initio _ methods . in particular , dft studies of weak hydrogen - bonding systems have proved to be particularly difficult and only limited success has been achieved in predicting the geometries and energies for reactant and transition state configurations on the potential energy surface using most exchange - correlation functionals @xcite . care should therefore be exercised when choosing a particular _ ab initio _ method to calculate proton transfer reaction rates . the non - local exchange - correlation schemes developed by proynov , vela and salahub @xcite have shown particular promise for the description of hydrogen - bonded systems . sirois et al . @xcite have demonstrated that their kinetic - energy dependent exchange functionals ( blap and plap ) performed better than all gga options ( bp86 , pp86 , pw91 ) , blyp , or other hybrid methods ( b3lyp , b3pw91 ) on systems involving intra - molecular hydrogen bonds . the predictions for equilibrium and transition state geometries as well as the energetics was in agreement with high - quality post - hartree - fock calculations [ ccsd(t ) and g2]@xcite . specifically , for the gas - phase cyclic cluster of acetic acid and methanol in fig . 1 , the activation energy using the plap exchange correlation functional was found to be approximately @xmath10 kcal / mol , in excellent agreement with the qcisd value of @xmath11 kcal / mol@xcite .    for the simulations described in the present work , the energies of different configurations were carried out using a modified version of the lcgto - dft program demon - ks3.4 @xcite using the plap exchange - correlation functional . the dft electronic structure calculations were carried out as in reference [ ] , where the application of dft electronic structure methods to hydrogen - bonding systems is discussed in detail . a double-@xmath12 plus polarization ( dzvp ) orbital basis set was used for all atoms and the convergence level for the scf ( self - consistent field ) energy using the auxiliary fitting basis sets @xcite was @xmath13 kcal / mol .      in order to implement the qm / mm / continuum approach to compute reaction rates for the double proton transfer reaction in the acetic acid - methanol cluster solvated by tetrahydrofuran , a sufficiently accurate molecular mechanics description of the interaction between the solvent molecules is needed@xcite . in this work , the opls all atom ( opls - aa ) force field of jorgensen et al.@xcite with a modified electrostatic interaction term has been used to describe the interactions between thf solvent molecules . the modifications to the electrostatics were designed to improve the gas - phase distribution of the partial charges in a thf molecule as well as to improve the description of polarization effects in condensed phases . since the local electrostatic environment as well as long ranged polarization effects can influence the proton transfer process , it is important to properly account for the permanent and induced charges in the solvent . to describe all such electrostatic phenomena , all solvent molecules have been assigned permanent and induced charges . it can be demonstrated@xcite using second - order perturbation theory that the electrostatic interaction energy between two polarizable molecules @xmath14 and @xmath15 , each of which carries a set of atomic permanent and induced charges , @xmath16 and @xmath17 , with @xmath18 corresponding to the charges on molecule @xmath19 , and @xmath20 and @xmath21 , where @xmath22 are the site charges on molecule @xmath23 , respectively , can be written to a good approximation as :    @xmath24    where @xmath25 is the distance between sites @xmath26 and @xmath27 on molecules @xmath19 and @xmath23 . in principle , the induced charge appearing on a given solvent molecule is dependent on its local environment . one simple way of incorporating solvent polarization effects is to assign each solvent molecule the same average induced charge in a `` mean - field '' fashion . more sophisticated methods of including polarization effects either assign site polarizabilities or use fluctuating charges distributed at specific locations on each solvent molecule@xcite . such methods when combined with _ ab initio _ electronic structure methods either necessitate an iterative solution of the electronic structure and fluctuating charge distributions or involve dynamical methods in an extended lagrangian system@xcite . unfortunately , each of these approaches has shortcomings which make them impractical to implement in conjunction with importance sampling monte - carlo methods .    in principle , the iterative minimization of the kohn - sham and fluctuating charge functionals can be implemented within a monte - carlo sampling approach at the cost of additional computational effort . however , provided the solvent is not very polarizable , the variation of the induced charges on the solvent molecules from their mean due to the presence of the solute is expected to be small . for this reason , we have utilized fixed induced charges for all solvent molecules . this corresponds to computing ground state energies for the reactive core @xmath28 based on a kohn - sham functional@xcite @xmath29 $ ] which depends on the ground state electron distribution @xmath30 of the solute in the presence of the fixed permanent and induced external solvent charges . note that this functional includes the electrostatic energy of interaction between the quantum solute and the charges on the molecular - mechanical solvent molecules .    in general , one complication must be considered when discussing electrostatic interactions in mixed qm / mm systems that arises from the fact that the quantum mechanical electron density can become over - polarized by the molecular mechanical point charges due to the absence of considerations of the fermi repulsion between quantum and molecular mechanical charges@xcite . such effects are particularly severe when using delocalized basis sets to represent the quantum subsystem , but are less significant when gaussian or other local basis sets are utilized . in the present work , the full coulomb interaction potential has been used to describe electrostatic interaction terms between the solute and the solvent charges without any screening modifications at short distances since all dft calculations for the quantum subsystem use localized basis sets .    in our study of the acetic acid - methanol system in a thf solution , the permanent charges have been assigned the value @xmath31 , whereas the induced charges are set to a mean - field value of @xmath32 for all indices @xmath8 and @xmath33 , where @xmath34 are the standard charges in the opls force field . it can be verified that the electrostatic interaction energy calculated using eq . ( [ totalinteractionenergypermanentplusinducedtext ] ) with this set of permanent and average induced charges is precisely the electrostatic energy calculated using the standard set of fixed opls charges . on the other hand , by assigning a mean induced charge to each solvent molecule , the computed values for the gas - phase dipole moment and condensed phase dielectric constant are in better agreement with the corresponding experimental values ( see table 1 ) . it should be emphasized that a less satisfactory means of describing electrostatic interactions between the solute and the solvent would consist of calculating the electrostatic interactions between the gas phase electron distribution with the solvent charges . in such a scenario , the ground state electron distribution for the solute interacts with the solvent via a coulomb interaction of the form @xmath35 where @xmath36 is the gas - phase electron distribution and @xmath37 is defined to be the distance between the ith charge @xmath38 in the solvent and the point @xmath39 . this approximation corresponds to calculating the solute energy in the condensed phase by a zeroth order approximation for the electronic distribution of the solute , that is , @xmath40 \\approx   f\\left [ \\rho _ { 0}(\\mathbf{x})\\right ] + v.\\ ] ] such a description neglects the fact that the ground state solute electron distribution is influenced by the presence of the solvent charges . the influence of the solvent charges on the ground state energy can be accounted for by incorporating a polarization energy of the solute by the solvent . although such a crude level of description of the electrostatic interactions may be incomplete , it is useful in developing importance sampling monte - carlo schemes based on guiding potentials , such as the molecular mechanics based importance function method ( mmbif ) described in the next section . the mmbif method@xcite consists of utilizing an auxiliary markov chain with a known asymptotic molecular mechanical distribution to propose trial configurations for an _ ab initio _ based monte carlo simulation . in the method , each trial configuration is obtained as the last state in a classical markov chain generated from the current configuration in the _ ab initio _ simulation using various updating schemes . the proposed configurations are then accepted or rejected in the _ ab initio _ chain according to the usual metropolis - hastings algorithm@xcite . if the previous and new trial configurations in the _ ab initio _ mc chain are denoted by @xmath41 and @xmath42 respectively , the proposed state is accepted with the probability @xmath43 , where @xmath44 is defined to be @xmath45 where @xmath46 and @xmath47 are the potential energies of configuration @xmath48 calculated by _ ab initio _ methods ( here density functional theory , abbreviated dft ) and the classical potential , respectively , and @xmath49 is boltzmann s constant . it is straightforward to show that this acceptance criterion guarantees that the _ ab initio _ markov chain has the correct limiting boltzmann distribution@xcite , regardless of the number of classical updates used to generate the proposed configuration . the efficiency of the mmbif approach relies on constructing a molecular mechanics potential for the entire system which approximates the true interactions of the system at a qualitative level . at first glance , the construction of a molecular mechanics potential for a condensed phase system appears a daunting task given that the electron distribution of the solute changes considerably during the reactive process and is influenced in a complicated fashion by its local environment . however , it is relatively straightforward to construct a molecular mechanics potential based on simple approximate forms of the interaction potentials , such as that in eq . ( [ interactionsolutesolventcorrect ] ) . for such forms of the potential , the construction of the potential is reduced to modeling the reaction in gas phase and calculating effective charges on the gas - phase solute which mimic the correct electron distribution . the approximate form for the potential can be corrected for using importance sampling methods . for example , a monte - carlo chain of states generated using an approximate expression for the energy can be manipulated by re - weighting the configurations appearing in the chain by an appropriate factor@xcite . the efficiency of this approach is highly dependent on the quality of the approximation for the true energy of the system . one might anticipate that the crude of level of description of the electrostatic interactions in eq . ( [ interactionsolutesolventcorrect ] ) which neglects any polarization effects of the solute by the solvent molecules would introduce large statistical uncertainties at the re - weighting step . however , the polarization of the solute by the solvent can be approximated by adjusting the charge of the solvent molecules in the expression for the interaction between the solute and the solvent . as will be discussed , the effective charge on the solvent molecules can be designed to approximate solute polarization effects and thereby improve the statistical resolution of the re - weighting procedure . the task of constructing a molecular mechanics potential for the gas - phase proton transfer reaction is facilitated by using bond evolution theory considerations . following these lines , the molecular mechanics description of the acetic acid - methanol complex in the absence of the solvent was created as suggested in reference [ . the total molecular mechanics energy was decomposed into two components . the first component of the total energy was written as a sum of harmonic potentials representing the variation of the potential with bond length , bond angle or bond dihedral displacements from their minimum energy values at a fixed value of the control parameter @xmath50 , defined by @xmath51 where the numbering of the atoms is that from fig . the second component of the total energy was written as a sum of four morse potentials depending on the four @xmath52 bond lengths , plus two effective potentials depending on two parameters , @xmath53 and @xmath54 defined as @xmath55 these effective potentials account for the flow of electronic charge during the reaction , as well as for the fermi repulsion between the oxygen atoms @xmath56 and @xmath57 , and between @xmath58 and @xmath57 . this second component of the total energy was implemented using the same functional forms as in reference [ . as in the case of the malonaldehyde study , no potential which depends explicitly on the angles @xmath59 or @xmath60 was utilized , although some dependence on the angle @xmath61 was explicitly introduced using a functional form which interpolates between a harmonic potential for transition state values of the parameter @xmath50 , and zero for values of @xmath50 characteristic for the reactant or product configurations . the complete details for the construction of the guiding potential for the solute can be found in reference [ . the simplest practical means of incorporating the electrostatic interactions between the solute and the solvent molecules in the molecular mechanics potential is to fit partial charges to atomic sites in the solute to reproduce the gas - phase electronic distribution . however , since the electron distribution of the solute varies appreciably with the configuration of the solute , the guiding potential must incorporate solute charges which vary as the reaction proceeds . in their bond evolution theory analysis of the tautomerization of malonaldehyde , krokidis et al.@xcite found that the total charge in the basins of attraction of the proton and oxygen atoms varies approximately linearly with a control parameter similar to the parameter @xmath50 . therefore , it can reasonably be assumed that most of the variation of the charges on atomic sites in the solute can be explained by a linear variation with @xmath50 . an alternative approach to incorporate the solute - solvent interactions can be constructed using simulated tempering methods@xcite . the advantage of this procedure is that it does not rely on any approximation for the variation of the fitted charges on the solute during the reaction . the method essentially consists of using an extended state space to gradually turn on electrostatic interactions between the solute and the solvent . this approach is represented schematically in figure 4 .    in the simulated tempering method , a markov chain is constructed whose states ( @xmath62 ) are defined on the space formed by the direct product between a finite set of `` electrostatic '' indices , @xmath63 and the entire solvent plus the solute configurational space . in vector notation , the states @xmath64 will be denoted @xmath65 , where @xmath66 and @xmath67 represent the solute and solvent degrees of freedom , respectively . this markov chain , whose generic state is denoted ( @xmath62 ) , is constructed to produce states asymptotically distributed according to the probability density    @xmath68    where @xmath69 are constants which will be referred to as the weights for the unnormalized probability densities @xmath70 defined by    @xmath71    where @xmath72 . the potentials @xmath73 contain five components : the _ ab initio _ potential @xmath74 calculated for the gas - phase solute configuration , the molecular mechanics potential @xmath75 describing the interaction between the explicit solvent atoms , the lennard - jones potential @xmath76 describing the dispersive and short - ranged interactions between solute and solvent atoms , the coulomb electrostatic interaction @xmath77 between some charges on the solute atoms and the permanent and induced charges on the solvent atoms , and the reaction field energies @xmath78 describing the long - range solute - solvent electrostatic interactions :    @xmath79    the coulomb solute - solvent electrostatic interaction potential between charges @xmath80 on the solute and @xmath81 on the solvent , given by @xmath82 where @xmath83 and @xmath84 are the number of charge sites on the solute and solvent molecules , respectively , and @xmath85 is a scaling factor henceforth called the charge fraction . note that this interaction potential depends on the choice of charges assigned to the solvent and solute molecules . in our calculations , the charges on the solute were fitted using the kollman - singh procedure@xcite from the gas - phase electron distribution of the solute . the use of charges fitted from the gas - phase calculation of the electron distribution does not account for the polarization of the solute by the solvent . to partially compensate for the neglect of this effect , the total charge on the solvent molecules used in eq . ( [ electrosolutesolvent ] ) is set to the sum of the permanent and induced charges on the solvent , @xmath86 . this is in contrast to the calculation of the electrostatic interaction between solvent molecules in which the effective charges are set to @xmath87 . this approximation is consistent with first - order perturbation theory in which the polarization energy of the solute by the solvent is approximated by the polarization energy of the solvent by the solute@xcite . note that the only difference between the potentials @xmath88 for different electrostatic indices @xmath8 consists of the form of the electrostatic interaction energy @xmath77 between the solute and the explicit solvent atoms . the energy @xmath89 is chosen to be zero in this work implying that @xmath90 , which amounts to turning off solute charges . for this system all electrostatic interactions between the solvent and the solute are scaled to zero although the solvent and solute still interact through lennard - jones potentials . by design , the last electrostatic index is set to unity , @xmath91 so that the energy @xmath92 corresponds to calculating the electrostatic interaction between the solvent and solute atoms using the fitted configuration - dependent solute charges obtained _ via _ the kollman - singh method . the additional dimension of the solute plus solvent state space represented by the electrostatic index @xmath93 ensures that the solvent configuration adapts smoothly to the solute via a stepwise process in which the charges of the solute atoms gradually interact with the other charges in the system . it should be noted that an equivalent result can be achieved by using a parallel tempering scheme in which the label @xmath93 corresponds to a stepwise decrease of a `` sampling temperature '' associated with the solute - solvent electrostatic interaction .    in our implementation of the importance sampling , a markov chain of extended state space configurations was generated by two types of transitions . in transitions of the first type the electrostatic index @xmath8 was kept fixed while the configuration of the system * @xmath94 * was updated using a transition matrix which leaves @xmath95 invariant . the way in which the configurations were updated for fixed electrostatic index was dependent on the electrostatic scaling factor . when the scaling factor was zero both the configuration of the solute and the solvent were updated simultaneously using the mmbif approach . the background molecular mechanics simulations used to guide the updates were run so as to produce effectively independent but energetically reasonable configurations of the entire system . the simultaneous update of both solute and solvent configuration is possible in the absence of electrostatic interactions between the solute and solvent since the fitted charges are not used in the molecular mechanics auxiliary chain . however , after the calculation of the _ ab initio _ dft energy in the acceptance - rejection step of the mmbif method , the fitted charges for the given solute configuration can be calculated . when the electrostatic scaling factor is nonzero and solute - solvent electrostatic interactions occur , the solvent was allowed to adjust to the charge distribution on the solute by updating the solvent configuration while maintaining the configuration of the core reactive region unchanged . transitions of the second type move the system through the auxiliary parameter space by applying a transition matrix that changes the electrostatic index while leaving the configuration of the solute and solvent unchanged . in this study , the method for updating the electrostatic index @xmath8 consisted of using a metropolis algorithm , with a proposal distribution in which the proposed indices @xmath96 and @xmath97 are equally probable . the proposed change of electrostatic index is rejected if @xmath98 is outside the valid range @xmath93 , otherwise it is accepted with probability    @xmath99 = \\min \\left [ 1,\\frac{w_{i_{\\textrm{new}}}}{\\textrm{w}_{i_{\\textrm{old } } } } \\exp \\left ( -\\beta \\left ( e_{i_{\\textrm{new}}}-e_{i_{\\textrm{old}}}\\right ) \\right ) \\right ] .\\ ] ]    the marginal distribution of @xmath8 with respect to the equilibrium distribution is given by    @xmath100    where the configuration partition function @xmath101 is defined as    @xmath102    if the distributions @xmath103 are all to play a useful role in sampling , the weights @xmath69 should be chosen such that a roughly uniform distribution over @xmath8 is obtained . since the @xmath101 are initially unknown , suitable values for the weights are found through a trial and error process using preliminary runs . to do this , an iterative procedure can be used in which the markov chain is simulated using the current values for @xmath69 , and the frequencies @xmath104 with which each distribution is visited are recorded .    next , new and improved weights @xmath105 are calculated as @xmath106 for electrostatic index @xmath8 . if some of the frequencies @xmath104 are zero , various elaborations of the estimation procedure can be used and some of them are summarized in reference [ . the number @xmath107 of values of the electrostatic scaling parameter @xmath85 used and the actual values of @xmath69 , @xmath93 are chosen by minimizing the average computer time necessary for a new solute configuration to appear with an electrostatic scaling parameter @xmath91 . a good starting estimate for the numbers @xmath69 and @xmath107 can be obtained by optimizing the weights and the number of intermediate chains using only the molecular mechanics guiding potential with a reasonable set of atomic charges on the solute atoms .","summary":"the reaction is described by solving the electronic schrdinger equation for the solute atoms in the presence of explicit solvent molecules .","abstract":"in this article , we propose an efficient method for sampling the relevant state space in condensed phase reactions . in the present method , the reaction is described by solving the electronic schrdinger equation for the solute atoms in the presence of explicit solvent molecules . the sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long . the method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran . it is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas - phase calculations .    * h *  * s * * u * *p *    * h *  * s * * u * *p *"}
{"article_id":"physics0309124","section_id":"r","document":"to explore the issue of how importance sampling methods can be effectively utilized in simulations of reactions in condensed phases , two different implementations of the mmbif sampling method were analyzed . in the first implementation , the dependence of the solute charges on the reactive state of the system was taken to vary linearly with the control parameter @xmath108 defined in eq . ( [ a_b_1andb_2definitions ] ) . for this simulation , the electrostatic interactions between the interpolated charges on the solute and the charges in the solvent were taken to be coulombic . in the second simulation , the simulated tempering method described above was applied to the solvated acetic acid - methanol cluster . both simulations generate chains of states asymptotically distributed according to a boltzmann distribution based on eq . ( [ interactionsolutesolventcorrect ] ) in which the solute - solvent electrostatic interactions are modeled by calculating the coulomb interaction between the gas phase electron distribution with the charges in the solvent . in both simulations , the desired distribution for the chain of states based on the universal kohn - sham functional @xmath109 $ ] can be recovered at the end of the simulation by re - weighting each of the @xmath110 total configurations by a configuration dependent factor @xmath111 where @xmath112 - \\left ( f[\\rho_0 ( x_i)]+v \\right ) = f[\\rho_s(x_i)]-e^{s}(r_{i}^{s } ) - e^{ss}(r_{i}^{s},r_{i}^{s})\\ ] ] is the difference in the polarization energy of the solute by the solvent estimated by calculating the energy of the ground state electron distribution in the presence of the solvent charges and the energy of a gas - phase electron distribution interacting with the optimized solvent charges .    in all simulations , the calculations for the solvated cluster ( shown in fig . 3 ) have been carried out by treating all nuclei as classical point particles . the calculations were conducted in the isobaric - isothermal ensemble at @xmath113 atm and @xmath114 k. in order to improve the sampling along the reaction coordinate , an umbrella potential@xcite was constructed for the guiding potential using a self - adaptive scheme . simulations biased by the converged umbrella potential yielded a uniform sampling of the important regions of the reaction coordinate even though the activation barriers for the proton transfer reaction was on the order of @xmath115 @xmath116 . two thirds of the _ ab initio _ markov chain transition steps in the simulation using the linearly - interpolated charges on the core were generated using the mmbif method . the same fraction of base transitions were generated using the mmbif updates when the electrostatic index is zero in the simulated tempering simulation ( see fig . the rest of the _ ab initio _ markov chain transitions were performed utilizing metropolis single - variable updates using the _ ab initio _ dft energy . as demonstrated in a previous study [ , the role of the metropolis dft updates is to prevent the guiding molecular mechanics markov chain of states from spending a large number of successive steps in those regions of the configuration space where the molecular mechanics density of states in the solute configuration space substantially underestimates the corresponding _ ab initio _ dft density of states .    in the previous studies of the formic acid - water@xcite and of the malonaldehyde@xcite systems it was demonstrated that a useful strategy for optimizing the mmbif method was to separate the variables to be updated in a classical mc step into several groups , with strongly correlated variables grouped together . in the case of the double proton transfer in the cyclic cluster formed by acetic acid and methanol , the vibrations of the two methyl groups should be relatively uncoupled from the motions of the other atoms in the cluster . applying this separation of which variables are updated in the mmbif method , the percent of rejections of proposed configurations obtained with the mmbif method was about @xmath117 . the percent of rejections of the transitions which employed single - variable metropolis updates using the _ ab initio _ potential was @xmath118 . it is important to compare the computational effort of performing liquid - phase versus gas - phase simulations of chemical reactions within the mmbif approach . the potentials of mean force obtained using the reaction coordinate    @xmath119    describing the double proton - transfer in the acetic acid - methanol system in tetrahydrofuran obtained in the first simulation and in a gas - phase simulation are represented in fig . although equal cpu times were spent in computing the two potentials of mean force depicted in fig . 5 , the statistical uncertainties for the activation energy calculated for the double proton reaction rate in the solvated system is approximately @xmath120 times larger than the error bar for the activation energy calculated from the gas - phase simulation . this decrease in the statistical resolution of the computations in the solvated system with respect to the gas - phase system is due to a larger integrated correlation time of the overall markov chain as well as to the fact that @xmath121 of the cpu time in the simulation of the solvated system is dedicated to calculating the molecular mechanics interactions between the _ solvent _ molecules . although a single _ ab initio _ calculation is roughly @xmath0 orders of magnitude slower than a single update of the configuration of the molecular mechanical solvent , the long dielectric relaxation of the solvent required that many updates be carried out on the solvent before an independent solvent configuration was generated . this translated into an approximately equal amount of cpu time for the molecular mechanical and quantum mechanical components of the simulation . the approximation of the variation of the charges fitted using the kollman - singh procedure with the solute configuration by a linear variation with the parameter @xmath50 in equation ( [ a_b_1andb_2definitions ] ) proved quite accurate . the standard deviation of the differences between the electrostatic interaction energies calculated using these fitted charges obtained via the kollman - singh procedure and the same energies calculated using solute charges which vary linearly with the parameter @xmath50 defined in equation ( [ a_b_1andb_2definitions ] ) is @xmath122 kcal / mol . this small deviation should be contrasted with the value of @xmath123 kcal / mol representing the standard deviation of the values of the electrostatic interaction energy between the solute and solvent molecules ( see fig . the distribution of the values of the polarization energy difference @xmath124 defined in eq . ( [ deltaepol ] ) relevant for the final re - weighting of data points is plotted in fig . as expected , the values of @xmath124 are distributed over a small range of energy values of approximately @xmath125 kcal / mol . in fact , calculation of the activation energy in the double proton reaction rate in tetrahydrofuran without re - weighting yields an activation energy which differs from the activation energy in fig . 5 only by a statistically irrelevant value of @xmath126 kcal / mol . it should be emphasized that the small values of @xmath124 in fig . 7 are in part a consequence of approximating the polarization energy of the solute by the solvent by the polarization energy of the solvent by the solute . we estimated that if the solvent charges used in eq . ( 11 ) were set to @xmath127 , the standard deviation for @xmath124 would have been approximately @xmath128 kcal / mol .    the potentials of mean force for the double proton transfer reaction in tetrahydrofuran calculated using the linearly - interpolated charge approach and using the simulated tempering method are identical within error bars . however , if the error bars for the activation energy in the linearly - interpolated charge method is @xmath125 kcal / mol , they are roughly four times larger in the simulation using the parallel tempering algorithm for comparable cpu times . the optimal number of electrostatic indices in the simulated tempering approach was found to be @xmath129 . in the optimized setting for the simulated tempering method in which equal amounts of time were spent at all values of the electrostatic index , the gibbs free energy differences @xmath130 computed for consecutive values of the index were found to be approximately @xmath131 kcal / mol . the gibbs free energy @xmath132 of the electrostatic interaction between the solute and solvent charges have been estimated using equation([partition ] ) and are plotted in fig . 8 as a function of the fraction of solute charge @xmath85 being turned on . several comments are worth making about the results in fig . first , the partition functions @xmath133 for the umbrella potential - biased ensemble from which the free energies were computed correspond to a particular value of the electrostatic fraction parameter @xmath85 . it should also be noted that although a difference in free energy between adjacent values of the electrostatic index of the order of @xmath116 seems to suggest a low probability of rejecting swaps between consecutive values of the index , the actual rejection rate was found to be significantly higher . the relatively large rejection rate is due to the fact that differences in free energy reflect the _ average _ energetic _ and _ entropic differences between thermodynamic states with different @xmath134 , whereas the acceptance probability in equation ( [ acceptancecriterion ] ) involves only the difference in the energies of the actual configurations to be swapped . in particular , it was observed that the enthalpic @xmath135 and entropic @xmath136 contributions to the gibbs free energy @xmath132 vary in opposite directions as the fraction of the solute charge @xmath137 increases from zero to one . these variations of enthalpic and entropic terms with the charge fraction can be visualized by comparing the results plotted in fig . 8 and fig . 9 . from the two figures it appears that @xmath135 increases and @xmath136 decreases with @xmath137 . the opposite directions in which enthalpic and entropic terms vary with @xmath137 is reflected in the mobility of the state @xmath138 of the simulated tempering algorithm in the @xmath27 ( or @xmath137 ) subspace . turning our attention to equation ( [ acceptancecriterion ] ) , note that an increase of @xmath136 with @xmath137 suggests that for a large fraction of configurations ( i,*r * ) transitions in which @xmath27 is _ increased _ are accepted only if the ratio @xmath139 is approximately unity , @xmath140 . such is the case for an important number of transitions from electrostatic index @xmath141 to electrostatic index @xmath142 , for example , for which an increase in @xmath137 is accompanied only by a small decrease and occasionally even an increase in energy . on the other hand , for a @xmath137 near unity , a decrease of @xmath135 with @xmath137 suggests that a large fraction of transitions in which @xmath27 is _ decreased _ are rejected unless @xmath143 . such is the case in a large number of transitions which are attempted from the final index @xmath144 to @xmath145 for example , which are accompanied by a significant increase in energy . the choice of the weights @xmath146 suggested in equation ( [ choicew ] ) represents a good compromise in the sense that transitions which increase and which decrease @xmath27 have an equal probability of being accepted on average . nevertheless , this analysis points to the fact that if one uses the simulated tempering approach for the study of chemical reactions in solution , one should try to avoid turning on the charges of the reactive core all the way from zero to their final values . as enthalpic and entropic terms will always vary in opposite directions during the charging process , the sampling could become quite inefficient , especially when studying reactions in which there is a difference in the net charge between reactants and transition states , and not just in their dipole moments as in the present case . however , this conclusion does not mean that the mmbif approach used in the simulation with linearly interpolated charges will always be more efficient than the simulated tempering method . the efficiency of the mmbif approach relies heavily on the appropriateness of the postulated variation of the charges in a reactive system with the reaction coordinate . in the present study , the approximation of the variation of the fitted kollman - singh charges with the solute configuration by a linear variation with the parameter @xmath50 in equation ( [ a_b_1andb_2definitions ] ) proved quite accurate . however , such a simple relation could break down , especially when studying reactions with a net transfer of charge . in this case , we suggest using an approach which combines the benefits of both methods illustrated in the present study : the use of a simulated tempering approach in which the solute charge is gradually modified from a linear variation with the reaction coordinate to their actual values obtained via the kollman - singh approach .","summary":"in this article , we propose an efficient method for sampling the relevant state space in condensed phase reactions . in the present method , the sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long .","abstract":"in this article , we propose an efficient method for sampling the relevant state space in condensed phase reactions . in the present method , the reaction is described by solving the electronic schrdinger equation for the solute atoms in the presence of explicit solvent molecules . the sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long . the method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran . it is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas - phase calculations .    * h *  * s * * u * *p *    * h *  * s * * u * *p *"}
{"article_id":"physics0309124","section_id":"c","document":"in this article , two important issues on the applicability of the molecular mechanics based importance sampling method to the study of reactive events in condensed phase environments have been addressed . one major concern in developing a successful implementation of the mmbif approach is the ease of development of a sufficiently accurate molecular mechanics potential to guide the sampling . although a fully automated approach to generating guiding potentials for general reactions is still not available , it is encouraging to note that the use of the same principles of bond - evolution theory@xcite as in our earlier study of the malonaldehyde system@xcite were adequate for designing a molecular mechanics potential for the acetic acid - methanol system . this success is particularly impressive in light of the fact that the malonaldehyde and acetic acid - methanol systems differ substantially not only in their barrier heights ( by a factor of @xmath0 ) , but also in the qualitative nature of the chemical event ( one proton versus two protons transferred ) . it suggests that bond - evolution theory guidelines are likely to be practical in developing molecular mechanics potentials for other proton transfer reactions , and for possibly other types of chemical events . the study of the double proton transfer reaction between acetic acid and methanol in tetrahydrofuran also demonstrates that the mmbif method can be applied in reaction rate calculations of chemical transformations in solvents of medium polarity . in particular , an increase in the cpu time of factors of @xmath0 and @xmath147 with respect to gas - phase calculations were obtained using two different sampling methods . hence , we conclude that it should be possible in many instances to compute solvent mediated reaction rates with statistical accuracies comparable to those obtained in gas - phase calculations , even though the complexity of the calculation is increased enormously by the presence of the solvent .    it should be emphasized that the contribution of the solvent to the total activation energy in the present study is only on the order of a few factors of @xmath116 at room temperature . as a result , the actual mechanism of the proton transfer event is virtually unchanged from the process in gas phase . this simplification allowed the separation of the reactive _ ab initio _ core and the solvent degrees of freedom into effectively disjoint sets which were updated in isolation in the parallel tempering implementation of the sampling . in many cases , the structure of the solvent plays a more substantial role in the reactive process . under such circumstances , care must be taken to devise methods in which the reactive core and the solvent structure are updated in a more correlated fashion . for example , for a reaction in a solvent with a larger dielectric constant , the simulated tempering approach can be implemented by incorporating simultaneous mmbif updates of the solute and solvent degrees of freedom at each electrostatic index . it is informative to compare and contrast the advantages and disadvantages of using the mmbif method versus using present day molecular dynamics based methods for calculating reaction rates in solution using a hybrid qm / mm approach . the practical use of the simple molecular dynamics methods for sampling configurations of a system containing a reactive core which is described using _ ab initio _ electronic structure methods and the solvent molecules which are described using a molecular mechanics potential is limited by the fact that calculating the time - evolution of the system necessitates the computation of the time - consuming _ ab initio _ forces acting on the core atoms . these time - consuming calculations must be performed in traditional molecular dynamics calculations even when only the solvent degrees of freedom change significantly . several methods have been proposed for circumventing the inefficiency of the traditional qm / mm molecular dynamics calculations which are based on an `` artificial '' separation of time scales associated with the solute and solvent atoms@xcite . the central idea of these methods is to use a large mass in conjunction with a high temperature thermostat for the solute atoms , whereas the solvent atoms have usual masses and are in contact with a room temperature thermostat@xcite . the large mass of the core atoms is chosen in such a way that the solvent degrees of freedom relax on a time scale which is much smaller than the time scale of the massive core atoms . multiple - time scale arguments can be utilized to demonstrate that the integration of hamilton s equations describing the evolution of the solute plus solvent system can be performed by computing the forces acting on the solvent degrees of freedom significantly more often than the _ ab initio _ forces acting on the solute without altering the asymptotic boltzmann distribution of the configurations of the system . in addition , the decoupling between the solute and solvent time scales enables the use of a large temperature thermostat coupled to the solute atoms without introducing an irreversible heat flow , thereby ensuring that the average kinetic energy of the core atoms is comparable with the magnitude of the reaction barrier which separates reactant and product configurations on the potential energy surface . therefore , a relatively small number of _ ab initio _ calculations must be performed before a reactive event occurs . both the mmbif and the modified molecular dynamics approach succinctly described above have a number of advantages and shortcomings when studying chemical reactions in solution which are essentially driven by fluctuations in the structure of the _ solute _ using a qm / mm approach . the main disadvantage of the mmbif method consists of the fact that a reasonable molecular mechanics description of the reactive event in the _ gas - phase _ solute is required , and this molecular mechanics potential must usually be created from scratch . nevertheless , once such molecular mechanics potential has been constructed , the cpu time necessary for calculating reaction rates in solution is essentially independent of the characteristics of the solvent such as its dielectric relaxation time . in contrast , the molecular dynamics approach does not necessitate prior information with respect to the potential energy surface of the cluster , although if such information exists , it can be used to improve the efficiency of the sampling@xcite . however , the average time needed to observe a reaction event increases as the square root of the effective mass of the reactive degree of freedom . on the other hand , given the requirement of the separation of time scales between the solvent and solute degrees of freedom , the characteristic time scale of the solute atom motion and therefore the lower bound for the value of the mass needed for the core atoms is _ determined _ by the duration of the solvent dielectric relaxation time . therefore , it appears that the efficiency of the above mentioned molecular dynamics scheme decreases with the increase in the solvent dielectric relaxation time . the methodology proposed in the present work can be combined with the ideas presented in reference [ to include nuclear quantum effects via centroid transition state theory with a supplementary increase in the cpu time by a factor of @xmath148 times the number of path - integral beads . such a combination of procedures provides a rigorous and practical platform for calculation of kinetic isotope effects . an important goal for future work is to clarify the mechanistic origin of the relation between the breakdown of the rule of geometric mean in multiple proton transfer reactions and tunneling effects . 10 g. r. fleming and p. g. wolynes , physics today * 43 * , 36 ( 1990 ) . d. zhong and a. h. zewail , j. phys . chem . a , * 102 * , 4031 ( 1998 ) . b. perman , v. srajer , z. ren , t. teng , c. pradervand , t. ursby , d. bourgeois , f. schotte , m. wulff , r. kort , k. hellingwerf and k. moffat , science * 279 * , 1946 ( 1998 ) . p. j. rossky and j. d. simon , nature * 370 * , 263 ( 1994 ) . d. c. clary , science * 279 * , 1879 ( 1998 ) . a. kohen , r. cannio , s. bartolucci and j. p. klinman , nature * 399 * , 496 ( 1999 ) ; b. j. bahnson , t. d. colby , j. k. chin , b. m. goldstein and j. p. klinman , proc . 94 * , 12797 ( 1997 ) ; y. cha , c. j. murray and j. p. klinman , science * 243 * , 1325 ( 1989 ) . m. page and a. williams , _ organic and bio - 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proton transfer reaction studied here takes place along the hydrogen bonds of the cyclic cluster formed from one molecule of acetic acid and one molecule of methanol . figure 2 : a pictorial view of the qm / mm / continuum solvent method and of the reaction field approach . the `` reactive core '' region contains a quantum representation ( i.e : nuclei + electrons ) of the atoms which are involved in the actual covalent bond - breaking and bond - forming events . the `` explicit solvent '' region contains an atomic representation of the first few shells of solvent molecules . the effects of the solvent molecules which are far from the reaction center are included in an implicit manner in the qm / mm / continuum approach using the reaction field method . in our implementation , the reaction field method consists of calculating an effective electrostatic interaction between the dipole moments of the molecules inside the first two regions ( see equation [ [ reactionfieldenergy ] ] ) . figure 4 : a schematic representation of the simulated tempering method which uses the mmbif approach to generate configurations of the system in a simulation where solute polarizability is neglected . the values of the electrostatic scaling parameter @xmath85 for electrostatic indices @xmath153 are gradually increased from zero to one . figure 5 : the calculated potentials of mean force for the double - proton transfer reaction in the acetic acid - methanol cluster in gas - phase and in a solution of tetrahydrofuran using the reaction coordinate @xmath154 defined in equation ( [ reactioncoordinatemalonaldehyde2 ] ) . note that the difference between the activation energies is approximately @xmath155 kcal / mol . this difference is larger than the width of the @xmath156 confidence intervals for the activation energies , which have been estimated to be @xmath157 kcal / mol for the gas - phase and @xmath158 kcal / mol for the liquid - phase simulations ( inset ) . figure 6 : the values of the electrostatic interaction energy between the solute and solvent molecules obtained for @xmath159 in the simulated tempering method in which the solute charges are the gas - phase kollman - singh charges . note that the values of the solute - solvent electrostatic interaction energies are scattered over an energy range of approximately @xmath160 kcal / mol . in contrast , the differences in the electrostatic interaction energies calculated using the kollman - singh charges and the same energies calculated using solute charges which vary linearly with the parameter @xmath161 defined in equation ( [ a_b_1andb_2definitions ] ) are scattered over an interval of only @xmath162 kcal / mol ( data not shown ) . figure 7 : the values of the polarization energy difference @xmath163 defined in equation ( [ deltaepol ] ) . note that the distribution of values is centered roughly at @xmath164 kcal / mol and has a small standard deviation of @xmath158 kcal / mol . figure 8 : the free electrostatic interaction energy between an acetic acid - methanol complex and molecules of tetrahydrofuran solvent as a function of the charge state of the complex . @xmath165 and @xmath159 correspond to fully uncharged and charged solute . the stars and diamonds represent the estimated values of the free energy obtained from the preliminary and from the optimized simulated tempering runs , respectively . the continous line represents a spline interpolation between the computed values . figure 9 : the normalized probability density of the solvent - solute electrostatic interaction energy on for electrostatic indices @xmath142 ( solid curve ) , @xmath166 ( long dashed curve ) and @xmath167 ( dashed curve ) . note that the enthalpies , calculated as the average solute - solvent electrostatic interaction energies , are approximately @xmath168 , @xmath169 and @xmath170 kcal / mol . comparing these results with the corresponding free energies in fig . 8 one obtains the corresponding entropies as being @xmath171 , @xmath172 and @xmath173 kcal / mol . the variations in the mechanical work @xmath174 with the number of chain are negligible . .[oplsaaexperimentalmodoplsaa]the values of the gas - phase dipole moment @xmath175 expressed in debyes , and of the static dielectric constant @xmath176 , obtained by considering the opls - aa charges as permanent charges , obtained from our modified version of the opls - aa force field ( see text ) which accounts approximately for electronic polarization effects , and from experimental data from reference [ . [ cols=\"^,^,^,^\",options=\"header \" , ]","summary":"it is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas - phase calculations .    * h *  * s * * u * *p *    * h *  * s * * u * *p *","abstract":"in this article , we propose an efficient method for sampling the relevant state space in condensed phase reactions . in the present method , the reaction is described by solving the electronic schrdinger equation for the solute atoms in the presence of explicit solvent molecules . the sampling algorithm uses a molecular mechanics guiding potential in combination with simulated tempering ideas and allows thorough exploration of the solvent state space in the context of an ab initio calculation even when the dielectric relaxation time of the solvent is long . the method is applied to the study of the double proton transfer reaction that takes place between a molecule of acetic acid and a molecule of methanol in tetrahydrofuran . it is demonstrated that calculations of rates of chemical transformations occurring in solvents of medium polarity can be performed with an increase in the cpu time of factors ranging from 4 to 15 with respect to gas - phase calculations .    * h *  * s * * u * *p *    * h *  * s * * u * *p *"}
{"article_id":"hep-ph0405192","section_id":"i","document":"the measurements of the branching ratios at cleo , aleph and belle @xcite give the combined result @xmath5 which agrees with the next - to - leading order ( nlo ) standard model ( sm ) prediction @xcite @xmath6 good agreement between the experiment and the theoretical prediction of the sm implies that the new physics scale should lie well above the electroweak ( ew ) scale . the systematic analysis of new physics corrections to @xmath4 up to two - loop order can help us understanding where the new physics scale sets in , and the distribution of new physical particle masses around this scale . in principle , the two - loop corrections can be large when some additional parameters are involved at this perturbation order beside the parameters appearing in one loop results . in other words , including the two - loop contributions one can obtain a more exact constraint on the new physics parameter space from the present experimental results .    beside the cabibbo - kobayashi - maskawa ( ckm ) mechanism , the soft breaking terms provide a new source of @xmath3 and flavor violation in the mssm . those @xmath3 violating phases can affect the important observables in the mixing of higgs bosons @xcite , the lepton and neutron s electric dipole moments ( edms ) @xcite , lepton polarization asymmetries in the semi - leptonic decays @xcite , the production of @xmath7-wave charmonium and bottomonium @xcite , and @xmath3 violation in rare @xmath8-decays and in @xmath9 mixing @xcite . at present , the strictest constraints on those @xmath3 violation phases originate from the lepton and neutron s edms . nevertheless , if we invoke a cancellation mechanism among different supersymmetric contributions @xcite , or choose the sfermions of the first generation heavy enough @xcite , the loop inducing lepton and neutron s edms bound the argument of the @xmath10 parameter to be @xmath11 , leaving no constraints on the other explicitly @xmath3 violating phases . the supersymmetry models at large @xmath1 are implied by grand unified theories , where the unification of up- and down - type quark yukawa couplings is made @xcite . from the technical viewpoint , the dominant contributions to the relevant effective lagrangian are the terms proportional to @xmath12 in a large @xmath1 scenario . this will simplify our two - loop analysis drastically since we just keep those terms enhanced by @xmath1 .    assuming no additional sources of flavor violation other than the ckm matrix elements , the authors of @xcite present an exact analysis of the two - loop gluino corrections to the rare decay @xmath0 in which quark flavor change is mediated by the charged higgs in @xmath3 conserving mssm at large @xmath1 . they also compare their exact result with that originating from the heavy mass expansion ( hme ) approximation @xcite . although the hme result approximates the exact two - loop analysis adequately when the supersymmetry energy scale is high enough , their analysis implies that the difference between the hme approximation and exact calculation is obvious in some parameter space of the mssm . however , they do not consider the case in which quark flavor change is mediated by the charginos ( the super partners of the charged higgs and @xmath13 bosons ) . in fact , we can not provide any strong reason to ignore the contribution from the diagrams in which quark flavor change is induced by the charginos , even within large @xmath1 scenarios . in this work , we present a complete analysis on the two - loop gluino corrections to the rare transitions @xmath0 by including the contributions of those diagrams where quark flavor change is mediated by charginos in the framework of @xmath3 violating mssm at large @xmath1 . furthermore , we also simplify our expressions to concise forms through loop momentum invariant and the wtis that are required by the @xmath14 gauge invariance . the paper is organized as follows . in sec . [ dia ] , we give all the diagrams needed to evaluate the @xmath15 contributions to the wilson coefficients @xmath16 and @xmath17 entering the branching ratio @xmath18 . the corresponding wilson coefficients at the matching ew scale @xmath19 are also presented there . we apply the effective lagrangian to the rare decay @xmath4 in sec . [ cp ] . by the numerical method , we show the two - loop corrections on the @xmath3 asymmetry for the process . our conclusion is given in sec . [ con ] , and some long formulae are collected in appendices .","summary":"we investigate two - loop gluino corrections to the effective lagrangian for in the minimal supersymmetric extension of the standard model ( mssm ) at large , including the contributions in which quark flavor change is mediated by charginos . using the translation invariant of loop momenta and the ward - takahashi identities ( wtis ) that are required by the gauge invariance , we simplify our expressions to concise forms . as an example , we discuss two - loop gluino corrections to the asymmetry of inclusive decay in violating mssm .","abstract":"we investigate two - loop gluino corrections to the effective lagrangian for in the minimal supersymmetric extension of the standard model ( mssm ) at large , including the contributions in which quark flavor change is mediated by charginos . using the translation invariant of loop momenta and the ward - takahashi identities ( wtis ) that are required by the gauge invariance , we simplify our expressions to concise forms . as an example , we discuss two - loop gluino corrections to the asymmetry of inclusive decay in violating mssm ."}
{"article_id":"1609.08593","section_id":"i","document":"the concept of graded nilpotent pairs has been discussed in @xcite basically as a lie - theoretic generalization of ginzburg s principal nilpotent pairs @xcite . such graded nilpotent pair is given as an element @xmath0 of the nilpotent commuting variety of a fixed bi - graded vector space @xmath1 , such that both nilpotent operators are compatible with the bi - grading in a natural commuting way : @xmath2 respects the bigrading in horizontal direction and @xmath3 respects the bigrading vertically . + a standard generalization of this setup is given by multi - graded nilpotent pairs @xmath4 of a @xmath5-graded vector space @xmath1 ; the notion of a @xmath5-graded vector space is a well - known and basic concept , and such multi - graded , or @xmath5-graded , nilpotent tuple respects the grading in all @xmath5 directions in a natural manner : each @xmath6 respects the grading in exactly one direction , such that the whole situation commutes . this generalized setup determines the situation upon which we mainly focus our interest in this article . + the non - zero components of the multi - grading of @xmath1 induce a @xmath5-dimensional ( generalized ) young diagram @xmath7 in a natural way and every corresponding @xmath5-graded nilpotent tuple is called @xmath7-shaped , thus . + our main results gives a complete and explicit answer to a standard lie - theoretic question : are there only finitely many @xmath7-shaped multi - graded nilpotent pairs up to base change by a levi respecting the grading ? the methods of proof are mainly taken from representation theory of finite - dimensional algebras . for each generalized young diagram , we define a so - called multi - staircase algebra @xmath8 which generalizes the concept of staircase algebras as in @xcite . the above posed question is then answered by discussing the representation types of all multi - staircase algebras which leads to our classification theorem . let @xmath7 be a generalized proper @xmath5-dimensional young diagram . the multi - staircase algebra @xmath8 is    1 .   of finite representation type if and only if @xmath7 is listed as a ( generalized ) young diagram in theorem [ thm : stair_rep_type ] ( a ) or theorem [ thm : tri_stair_rep_type ] ( a ) , 2 . tame concealed if and only if @xmath7 is listed as a young diagram in theorem [ thm : stair_rep_type ] ( b ) , theorem [ thm : tri_stair_rep_type ] ( b ) or theorem [ thm : high_stair_rep_type ] ( b ) . tame non - concealed if and only if @xmath7 is listed as a young diagram in theorem [ thm : stair_rep_type ] ( c ) , theorem [ thm : tri_stair_rep_type ] ( c ) or theorem [ thm : high_stair_rep_type ] ( c ) .    otherwise , and in particular if @xmath9 , the algebra @xmath8 is of wild representation type .    by theorem [ thm : crit_multi_grad_pairs ] , this classification provides our main theorem about @xmath7-shaped multi - graded nilpotent tuples as a direct consequence . let @xmath7 be a generalized @xmath5-dimensional partition . the number of @xmath7-graded nilpotent pairs ( up to levi - base change ) is finite if and only if the algebra @xmath8 is of finite representation type . these cases are those of classification theorem ( a ) . in particular , whenever @xmath10 , there are infinitely many such pairs ( see corollary [ cor : high_grad_inf_tuples ] ) . results are extended by considering certain minimal nullroots of particular tame concealed multi - staircase algebras which yield information about multi - graded nilpotent tuples of fixed vector spaces @xmath1 . + * acknowledgments : * the author would like to thank markus reineke for interesting discussions on the subject and edward richmond for his support with drawing generalized young diagrams in latex .","summary":"our methods make use of a translation to the class of so - called multi - staircase algebras   and we classify their representation types .","abstract":"we discuss multi - graded nilpotent tuples of multi - graded vector spaces which are a generalization of graded nilpotent pairs . the multi - grading yields a natural notion of a shape of such tuple and our main interest is to answer the question is the number of multi - graded nilpotent tuples of a fixed shape , up to base change in the homogeneous components , finite ?   our methods make use of a translation to the class of so - called multi - staircase algebras   and we classify their representation types ."}
{"article_id":"1609.08593","section_id":"i","document":"we sketch some theoretical background now which we will refer to later when studying our main questions . let @xmath11 be an algebraically closed field and let @xmath12 be the general linear group for a fixed integer @xmath13 regarded as an affine variety . the concepts of this subsection can be found in @xcite . a _ finite quiver _ @xmath14 is a directed graph @xmath15 , given by a finite set of _ vertices _ @xmath16 , a finite set of _ arrows _ @xmath17 and two maps @xmath18 defining the source @xmath19 and the target @xmath20 of an arrow @xmath21 . a _ path _ is a sequence of arrows @xmath22 , such that @xmath23 for all @xmath24 . + we define the _ path algebra _ @xmath25 as the @xmath26-vector space with a basis consisting of all paths in @xmath14 , formally included is a path @xmath27 of length zero for each @xmath28 starting and ending in @xmath29 . the multiplication is defined by concatenation of paths , if possible , and equals @xmath30 , otherwise . + let us define the _ arrow ideal _ @xmath31 of @xmath25 as the ( two - sided ) ideal which is generated ( as an ideal ) by all arrows in @xmath14 . in particular , the arrow ideal of @xmath14 equals the radical of @xmath25 if @xmath14 does not contain oriented cycles . an arbitrary ideal @xmath32 is called _ admissible _ if there exists an integer @xmath33 , such that @xmath34 . given such admissible ideal @xmath35 , we denote by @xmath36 the set of paths in @xmath35 starting in @xmath29 and ending in @xmath37 . + given such admissible ideal @xmath35 , the path algebra of @xmath14 , _ bound by _ @xmath35 is defined as @xmath38 ; it is a basic and finite - dimensional @xmath26-algebra @xcite ; the elements of @xmath35 are the so - called _ relations _ of @xmath39 . then @xmath39 is called _ triangular _ , if @xmath14 does not contain an oriented cycle . let us fix such triangular algebra @xmath40 in the following . + let @xmath41 be the abelian @xmath26-linear category of all finite - dimensional @xmath39-representations which is equivalent to the category of _ @xmath26-representations _ of @xmath14 , which are _ bound by @xmath35 _ , defined as follows : the objects are given by tuples @xmath42 , where the @xmath43 are @xmath26-vector spaces , and the @xmath44 are @xmath26-linear maps . for each path @xmath45 in @xmath14 as above , we denote @xmath46 and ask a representation @xmath47 to fulfill @xmath48 whenever @xmath49 . morphism of representations _ @xmath50 and consists of a tuple of @xmath26-linear maps @xmath51 , such that @xmath52 for every arrow @xmath53 in @xmath17 . + the _ dimension vector _ of an @xmath39-representation @xmath47 is defined by @xmath54 ; in more detail @xmath55 for @xmath28 . let us fix such a dimension vector @xmath56 and denote by @xmath57 the full subcategory of @xmath41 which consists of all representations of dimension vector @xmath58 . + by defining the affine space @xmath59 , it is clear that its points @xmath60 naturally correspond to representations @xmath61 with @xmath62 for @xmath28 . via this correspondence , the set of such representations bound by @xmath35 corresponds to a closed subvariety @xmath63 . + the algebraic group @xmath64 acts on @xmath65 and on @xmath66 via base change , furthermore the @xmath67-orbits @xmath68 of this action are in bijection to the isomorphism classes of representations @xmath47 in @xmath57 . + due to krull , remak and schmidt , every finite - dimensional @xmath39-representation decomposes into a direct sum of _ indecomposables _ ( which by definition do not decompose further ) . for certain classes of finite - dimensional algebras , a convenient tool for the classification of these indecomposable representations is the _ auslander - reiten quiver _ @xmath69 of @xmath70 . its vertices @xmath71 $ ] are given by the isomorphism classes of indecomposable representations of @xmath70 ; the arrows between two such vertices @xmath71 $ ] and @xmath72 $ ] are parametrized by a basis of the space of so - called _ irreducible maps _ @xmath73 . one standard technique to calculate @xmath74 is the _ knitting process _ ( see , for example , ( * ? ? ? * iv.4 ) ) . + let @xmath75 be an algebra of a quiver with only commutativity and zero relations . we say that an algebra @xmath76 is a _ convex subcategory _ of @xmath39 , if @xmath77 is a pathclosed _ subquiver _ of @xmath14 ( that is , for every two vertices @xmath78 and @xmath79 in @xmath77 , every path of @xmath14 from @xmath78 to @xmath79 is a path in @xmath77 , as well ) and @xmath80 . + an indecomposable projective @xmath81 has a so - called _ separated _ radical , if for arbitrary two non - isomorphic direct summands of its radical , their supports are contained in different components of the subquiver @xmath14 obtained by deleting all starting points of paths ending in @xmath29 . we say that @xmath39 _ fulfills the separation condition _ , if every projective indecomposable has a separated radical . if this condition is fulfilled , @xmath39 admits a preprojective component , see @xcite . + in general , the definition of an algebra to be _ strongly simply connected _ algebra is quite involved . in case of a triangular algebra @xmath39 , there is an equivalent description , though : @xmath39 is _ strongly simply connected _ if and only if every convex subcategory of @xmath39 satisfies the separation condition @xcite . + the algebra @xmath39 is called of _ finite representation type _ , if there are only finitely many isomorphism classes of indecomposable representations . if it is not of finite representation type , the algebra is of _ infinite representation type_. these infinite types split up into exactly two disjoint cases by drozd s dichotomy statement @xcite :    * @xmath39 has _ tame representation type _ ( or _ is tame _ ) if for every integer @xmath82 there is an integer @xmath83 and there are finitely generated @xmath84$]-@xmath39-bimodules @xmath85 which are free over @xmath84 $ ] , such that for all but finitely many isomorphism classes of indecomposable right @xmath39-modules @xmath47 of dimension @xmath82 , there are elements @xmath86 and @xmath87 , such that @xmath88/(x-\\lambda)\\otimes_{k[x]}m_i$ ] . * or @xmath39 has _ wild representation type _ ( or _ is wild _ ) if there is a finitely generated @xmath89-@xmath39-bimodule @xmath47 which is free over @xmath89 and sends non - isomorphic finite - dimensional indecomposable @xmath89-modules via the functor @xmath90 to non - isomorphic indecomposable @xmath39-modules . the notion of a tame algebra @xmath39 yields that there are at most one - parameter families of pairwise non - isomorphic indecomposable @xmath39-modules ; in the wild case there are parameter families of arbitrary many parameters . + for a triangular algebra @xmath75 , the _ tits form _ @xmath91 is the integral quadratic form defined by @xmath92 here @xmath93 equals the number of elements in @xmath94 whenever @xmath95 is a minimal set of generators of @xmath35 , such that @xmath96 . the quadratic form @xmath97 is called _ weakly positive _ , if @xmath98 for every @xmath99 ; and _ ( weakly ) non - negative _ , if @xmath100 for every @xmath101 ( or @xmath99 , respectively ) . if @xmath97 is weakly non - negative , we define its _ radical _ by @xmath102 and call its elements _ nullroots_. + the definiteness of the tits form is closely related to the representation type of @xmath39 , and many results are , for example , summarized by de la pea and skowroski in @xcite . the following criterion for finite representation type is due to bongartz @xcite . [ thm : crit_finite ] let @xmath75 be a triangular algebra , which admits a preprojective component . then @xmath39 is representation - finite if and only if the tits form @xmath97 is weakly positive . furthermore , if the equivalent conditions hold true , then the dimension vector function @xmath103 induces a bijection between the set of isomorphism classes of indecomposable @xmath39-modules and the set of positive roots of @xmath97 . assume that @xmath74 has a preprojective component . the algebra @xmath39 is called _ critical _ if @xmath97 is not weakly positive , but every proper restriction of @xmath97 is weakly positive . the term `` critical '' is actually intuitive , since the conditions of theorem [ thm : crit_finite ] are equivalent to @xmath39 not having a convex subcategories which is critical . the critical algebras are ( mostly ) the minimal tame ones , that is , the tame concealed algebras which are listed in the famous bongartz - happel - vossieck list ( bhv - list ) @xcite . + the algebra @xmath39 is called _ hypercritical _ if @xmath97 is not weakly non - negative while every proper restriction of @xmath97 is weakly non - negative . the hypercritical algebras have been classified @xcite . for strongly simply connected algebras , they turn out to be the minimal wild algebras as the following classification of tame types due to of brstle , de la pea and skowroski yields @xcite . [ thm : crit_tame ] let @xmath39 be strongly simply connnected of infinite representation type . then the following are equivalent :    1 . @xmath39 is tame ; 2 . @xmath97 is weakly non - negative ; 3 . @xmath39 does not contain a full convex subcategory which is hypercritical .    by dichotomy , theorem [ thm : crit_tame ] yields a sufficient criterion for wildness . [ cor : crit_wild ] let @xmath39 be strongly simply connnected . whenever there exists @xmath104 , such that @xmath105 , then @xmath39 is of wild representation type . let @xmath106 be an integer , then a partition of @xmath107 is a decreasing tuple @xmath108 , such that @xmath109 ; let @xmath110 denote the set of partitions of @xmath107 and by @xmath111 denote the set of all partitions of integers . for easier notation , we merge similar entries of partitions by potencies , for example @xmath112 . corresponding to @xmath113 there is a young diagram ; we fill its boxes with tuples @xmath114 as sketched in the example and identify partitions and young diagrams :    [ ex : partition ] let @xmath115 and @xmath116 . then the young diagram is    & & & _ ( 2,3 ) & _ ( 1,3 ) + & & _ ( 3,2 ) & _ ( 2,2 ) & _ ( 1,2 ) + _ ( 5,1)&_(4,1 ) & _ ( 3,1)&_(2,1 ) & _ ( 1,1 ) +    thus , we can identify each partition , or each young diagram , with a subset of @xmath117 . furthermore , a subset @xmath118 defines a partition if and only if the condition `` if @xmath119 , then @xmath120 whenever @xmath121 and @xmath122 '' is fulfilled . this in particular yields @xmath123    this setup can be generalized to @xmath5 dimensions as follows : let @xmath124 we call an element of @xmath125 a @xmath5-dimensional young diagram ; and in particular a generalized young diagram . + another special case of generalized young diagrams is of particulat interest : namely , @xmath126-dimensional young diagrams . these are subdivided into two kinds , flat ones and non - flat ones . + let @xmath7 be a @xmath126-dimensional young diagram , then @xmath7 is called flat , if one of the following conditions is fulfilled :    * @xmath127 * @xmath128 * @xmath129    graphically speaking , this means that it can be properly embedded into the plane . in particular , every flat @xmath126-dimensional young diagram is given by two decreasing partitions @xmath130 and @xmath131 , such that @xmath132 . we denote @xmath133 . if @xmath7 is not flat , it is called non - flat . [ ex:3_yd ] the @xmath126-dimensional young diagram    in 4,2,1 , 3,0,0 , 3,0,0    in    is flat and its tuple of partitions is given by @xmath134 , that is , @xmath135 and @xmath136 . we can embed it into the plane by    & & 4 & & + 3 & 3 & & & + & & & 2 & + & & & & 1 +    the following @xmath126-dimensional young diagram is non - flat . in 4,2,2 , 2,2,1 , 2,2,1 ,    in      let @xmath137 be an @xmath107-dimensional multi - graded @xmath26-vector space ; we formally set @xmath138 for @xmath139 and denote @xmath140 . let @xmath1 be called _ @xmath5-graded _ in general , _ bi - graded _ for @xmath141 and _ tri - graded _ for @xmath142 . + we denote by @xmath143 the _ nilpotent cone _ of nilpotent operators on @xmath1 . the _ @xmath5-fold nilpotent commuting variety _ of @xmath1 is defined by @xmath144=0~\\mathrm{for~all}~i , j\\},\\ ] ] its elements are called _ commuting nilpotent tuples_. + such tuple is called _ graded nilpotent tuple _ or _ @xmath5-graded nilpotent tuple _ of @xmath1 , if @xmath6 restrict to each @xmath145 on the @xmath29-th component via @xmath146 we define the _ shape _ of @xmath1 by @xmath147 the shape of a @xmath5-graded vector space is a @xmath5-dimensional young diagram by definition and the special case of bi - graded nilpotent pairs coincides with the notion of graded nilpotent pairs for which the shape @xmath113 of @xmath1 is given by an ordinary young diagram @xmath148 @xcite . + let @xmath7 be the shape of @xmath1 , then every graded nilpotent tuple of @xmath1 is called a _ @xmath7-graded nilpotent pair_.    [ ex : multi_grad ] let @xmath149 be a tri - graded @xmath26-vector space , such that @xmath150 , @xmath151 , @xmath152 and @xmath153 , otherwise . let @xmath154 be a graded nilpotent pair on @xmath1 . then we can illustrate the latter by    \\(m ) [ matrix of math nodes , row sep=1.81em , column sep=1.8em , text height=0.9ex , text depth=0.1ex ] & v_2,1,1 & v_2,2,1 + v_2,1,2 & v_1,1,1 & v_1,2,1 + v_1,1,2 & v_1,2,2 & + ; ( m-1 - 3 ) edge ( m-1 - 2 ) ( m-1 - 2 ) edge ( m-2 - 2 ) ( m-2 - 1 ) edge ( m-1 - 2 ) ( m-1 - 3 ) edge ( m-2 - 3 ) ( m-2 - 3 ) edge ( m-2 - 2 ) ( m-2 - 1 ) edge ( m-3 - 1 ) ( m-3 - 1 ) edge ( m-2 - 2 ) ( m-3 - 2 ) edge ( m-2 - 3 ) ( m-3 - 2 ) edge ( m-3 - 1 ) ( m-2 - 1 ) edge[-,dotted ] ( m-2 - 2 ) ( m-1 - 3 ) edge[-,dotted ] ( m-2 - 2 ) ( m-3 - 2 ) edge[-,dotted ] ( m-2 - 2 ) ;    the shape of @xmath1 is given by the generalized young diagram    in 2,2 , 2,1    in","summary":"we discuss multi - graded nilpotent tuples of multi - graded vector spaces which are a generalization of graded nilpotent pairs . the multi - grading yields","abstract":"we discuss multi - graded nilpotent tuples of multi - graded vector spaces which are a generalization of graded nilpotent pairs . the multi - grading yields a natural notion of a shape of such tuple and our main interest is to answer the question is the number of multi - graded nilpotent tuples of a fixed shape , up to base change in the homogeneous components , finite ?   our methods make use of a translation to the class of so - called multi - staircase algebras   and we classify their representation types ."}